Repository: ElementsProject/simplicity Branch: master Commit: c6ab4dd8f178 Files: 307 Total size: 47.3 MB Directory structure: gitextract__1j3kvgc/ ├── .github/ │ └── workflows/ │ └── ci.yml ├── .gitignore ├── C/ │ ├── Makefile │ ├── bitcoin/ │ │ ├── bitcoinJets.c │ │ ├── bitcoinJets.h │ │ ├── decodeBitcoinJets.inc │ │ ├── env.c │ │ ├── ops.c │ │ ├── ops.h │ │ ├── primitive.c │ │ ├── primitive.h │ │ ├── primitiveEnumJet.inc │ │ ├── primitiveEnumTy.inc │ │ ├── primitiveInitTy.inc │ │ ├── primitiveJetNode.inc │ │ ├── txEnv.c │ │ └── txEnv.h │ ├── bitstream.c │ ├── bitstream.h │ ├── bitstring.h │ ├── bounded.h │ ├── ctx8Pruned.c │ ├── ctx8Pruned.h │ ├── ctx8Unpruned.c │ ├── ctx8Unpruned.h │ ├── dag.c │ ├── dag.h │ ├── decodeCoreJets.inc │ ├── deserialize.c │ ├── deserialize.h │ ├── elements/ │ │ ├── checkSigHashAllTx1.c │ │ ├── checkSigHashAllTx1.h │ │ ├── cmr.c │ │ ├── decodeElementsJets.inc │ │ ├── elementsJets.c │ │ ├── elementsJets.h │ │ ├── env.c │ │ ├── exec.c │ │ ├── ops.c │ │ ├── ops.h │ │ ├── primitive.c │ │ ├── primitive.h │ │ ├── primitiveEnumJet.inc │ │ ├── primitiveEnumTy.inc │ │ ├── primitiveInitTy.inc │ │ ├── primitiveJetNode.inc │ │ ├── txEnv.c │ │ └── txEnv.h │ ├── elements-sources.mk │ ├── eval.c │ ├── eval.h │ ├── frame.c │ ├── frame.h │ ├── hashBlock.c │ ├── hashBlock.h │ ├── include/ │ │ └── simplicity/ │ │ ├── bitcoin/ │ │ │ └── env.h │ │ ├── elements/ │ │ │ ├── cmr.h │ │ │ ├── env.h │ │ │ └── exec.h │ │ └── errorCodes.h │ ├── jets-secp256k1.c │ ├── jets.c │ ├── jets.h │ ├── limitations.h │ ├── precomputed.h │ ├── regression4.c │ ├── regression4.h │ ├── rsort.c │ ├── rsort.h │ ├── schnorr0.c │ ├── schnorr0.h │ ├── schnorr6.c │ ├── schnorr6.h │ ├── secp256k1/ │ │ ├── README.md │ │ ├── assumptions.h │ │ ├── eckey.h │ │ ├── eckey_impl.h │ │ ├── ecmult.h │ │ ├── ecmult_impl.h │ │ ├── extrakeys.h │ │ ├── extrakeys_impl.h │ │ ├── field.h │ │ ├── field_5x52.h │ │ ├── field_5x52_asm_impl.h │ │ ├── field_5x52_impl.h │ │ ├── field_5x52_int128_impl.h │ │ ├── field_impl.h │ │ ├── generator.h │ │ ├── generator_impl.h │ │ ├── group.h │ │ ├── group_impl.h │ │ ├── int128.h │ │ ├── int128_impl.h │ │ ├── int128_native.h │ │ ├── int128_native_impl.h │ │ ├── int128_struct.h │ │ ├── int128_struct_impl.h │ │ ├── modinv64.h │ │ ├── modinv64_impl.h │ │ ├── precomputed_ecmult.h │ │ ├── scalar.h │ │ ├── scalar_4x64.h │ │ ├── scalar_4x64_impl.h │ │ ├── scalar_impl.h │ │ ├── schnorrsig.h │ │ ├── schnorrsig_impl.h │ │ ├── secp256k1.h │ │ ├── secp256k1_impl.h │ │ └── util.h │ ├── sha256.c │ ├── sha256.h │ ├── sha256_x86.inc │ ├── simplicity_alloc.h │ ├── simplicity_assert.h │ ├── taptweak.h │ ├── test.c │ ├── type.c │ ├── type.h │ ├── typeInference.c │ ├── typeInference.h │ ├── typeSkipTest.c │ ├── typeSkipTest.h │ └── uword.h ├── Coq/ │ ├── C/ │ │ ├── divstep.v │ │ ├── extraMath.v │ │ ├── jets_secp256k1.v │ │ ├── modinv.v │ │ ├── progressC.v │ │ └── secp256k1/ │ │ ├── spec_int128.v │ │ ├── spec_modinv64.v │ │ ├── verif_int128_impl.v │ │ └── verif_modinv64_impl.v │ ├── Simplicity/ │ │ ├── Alg.v │ │ ├── Bit.v │ │ ├── BitMachine.v │ │ ├── Core.v │ │ ├── Delegation.v │ │ ├── Digest.v │ │ ├── MerkleRoot.v │ │ ├── Primitive/ │ │ │ └── Bitcoin.v │ │ ├── Primitive.v │ │ ├── SHA256.v │ │ ├── StaticAnalysis.v │ │ ├── Translate.v │ │ ├── Ty.v │ │ ├── Util/ │ │ │ ├── Arith.v │ │ │ ├── List.v │ │ │ ├── Monad/ │ │ │ │ └── Reader.v │ │ │ ├── Monad.v │ │ │ ├── Option.v │ │ │ ├── PackedClass.v │ │ │ └── Thrist.v │ │ └── Word.v │ └── _CoqProject ├── Haskell/ │ ├── Bitcoin/ │ │ └── Simplicity/ │ │ └── Bitcoin/ │ │ ├── DataTypes.hs │ │ └── Primitive.hs │ ├── Core/ │ │ └── Simplicity/ │ │ ├── BitMachine/ │ │ │ ├── Authentic.hs │ │ │ ├── StaticAnalysis/ │ │ │ │ ├── Cost.hs │ │ │ │ └── TCO.hs │ │ │ ├── StaticAnalysis.hs │ │ │ ├── Translate/ │ │ │ │ └── TCO.hs │ │ │ ├── Translate.hs │ │ │ └── Ty.hs │ │ ├── BitMachine.hs │ │ ├── Bitcoin.hs │ │ ├── CoreJets.hs │ │ ├── Delegator/ │ │ │ └── Impl.hs │ │ ├── Delegator.hs │ │ ├── Digest/ │ │ │ └── Pure/ │ │ │ └── SHA.hs │ │ ├── Digest.hs │ │ ├── FFI/ │ │ │ ├── Frame.hs │ │ │ └── Jets.hs │ │ ├── Functor.hs │ │ ├── LibSecp256k1/ │ │ │ ├── Schnorr.hs │ │ │ └── Spec.hs │ │ ├── MerkleRoot/ │ │ │ └── Impl.hs │ │ ├── MerkleRoot.hs │ │ ├── Programs/ │ │ │ ├── Arith.hs │ │ │ ├── Bit.hs │ │ │ ├── Bitcoin/ │ │ │ │ └── Lib.hs │ │ │ ├── Bitcoin.hs │ │ │ ├── CheckSig/ │ │ │ │ └── Lib.hs │ │ │ ├── CheckSig.hs │ │ │ ├── Elements/ │ │ │ │ └── Lib.hs │ │ │ ├── Elements.hs │ │ │ ├── Generic.hs │ │ │ ├── LibSecp256k1/ │ │ │ │ └── Lib.hs │ │ │ ├── LibSecp256k1.hs │ │ │ ├── Loop.hs │ │ │ ├── Sha256/ │ │ │ │ └── Lib.hs │ │ │ ├── Sha256.hs │ │ │ ├── TimeLock.hs │ │ │ └── Word.hs │ │ ├── Serialization.hs │ │ ├── Tags.hs │ │ ├── Tensor.hs │ │ ├── Term/ │ │ │ └── Core.hs │ │ ├── Tree.hs │ │ ├── Ty/ │ │ │ ├── Bit.hs │ │ │ ├── LibSecp256k1.hs │ │ │ ├── Sha256.hs │ │ │ └── Word.hs │ │ ├── Ty.hs │ │ ├── Weight.hs │ │ └── Word.hs │ ├── Elements/ │ │ └── Simplicity/ │ │ └── Elements/ │ │ ├── DataTypes.hs │ │ └── Primitive.hs │ ├── Indef/ │ │ └── Simplicity/ │ │ ├── Dag.hs │ │ ├── Inference.hs │ │ ├── JetType.hs │ │ ├── Primitive.hsig │ │ ├── Semantics.hs │ │ ├── Serialization/ │ │ │ ├── BitString.hs │ │ │ └── ByteString.hs │ │ ├── StaticAnalysis/ │ │ │ └── Cost.hs │ │ └── Term.hs │ ├── Simplicity/ │ │ ├── Bitcoin/ │ │ │ ├── Benchmarks.hs │ │ │ ├── FFI/ │ │ │ │ ├── Env.hs │ │ │ │ └── Jets.hs │ │ │ ├── Jets.hs │ │ │ └── Programs/ │ │ │ ├── SigHash/ │ │ │ │ └── Lib.hs │ │ │ ├── SigHash.hs │ │ │ ├── TimeLock.hs │ │ │ ├── Transaction/ │ │ │ │ └── Lib.hs │ │ │ └── Transaction.hs │ │ └── Elements/ │ │ ├── Benchmarks.hs │ │ ├── FFI/ │ │ │ ├── Env.hs │ │ │ └── Jets.hs │ │ ├── Jets.hs │ │ └── Programs/ │ │ ├── Issuance/ │ │ │ └── Lib.hs │ │ ├── Issuance.hs │ │ ├── SigHash/ │ │ │ └── Lib.hs │ │ ├── SigHash.hs │ │ ├── TimeLock.hs │ │ ├── Transaction/ │ │ │ └── Lib.hs │ │ └── Transaction.hs │ ├── Tests/ │ │ ├── Simplicity/ │ │ │ ├── Arbitrary.hs │ │ │ ├── Bip0340.hs │ │ │ ├── BitMachine/ │ │ │ │ ├── StaticAnalysis/ │ │ │ │ │ └── Tests.hs │ │ │ │ └── Tests.hs │ │ │ ├── Bitcoin/ │ │ │ │ ├── Arbitrary.hs │ │ │ │ ├── FFI/ │ │ │ │ │ ├── Primitive.hs │ │ │ │ │ └── Tests.hs │ │ │ │ ├── Serialization/ │ │ │ │ │ └── Tests.hs │ │ │ │ ├── TestEval.hs │ │ │ │ └── Tests.hs │ │ │ ├── Elements/ │ │ │ │ ├── Arbitrary.hs │ │ │ │ ├── FFI/ │ │ │ │ │ ├── Primitive.hs │ │ │ │ │ └── Tests.hs │ │ │ │ ├── Regression.hs │ │ │ │ ├── Serialization/ │ │ │ │ │ └── Tests.hs │ │ │ │ ├── TestEval.hs │ │ │ │ └── Tests.hs │ │ │ ├── FFI/ │ │ │ │ ├── Bitstream.hs │ │ │ │ ├── Dag.hs │ │ │ │ └── Tests.hs │ │ │ ├── Programs/ │ │ │ │ ├── Example.hs │ │ │ │ └── Tests.hs │ │ │ ├── Serialization/ │ │ │ │ └── Tests.hs │ │ │ ├── TestCoreEval.hs │ │ │ └── Ty/ │ │ │ ├── Arbitrary.hs │ │ │ └── Tests.hs │ │ └── Tests.hs │ └── cbits/ │ ├── bitcoin/ │ │ ├── env.c │ │ └── jets.c │ ├── bitstream.c │ ├── coreJets.c │ ├── dag.c │ ├── elements/ │ │ ├── env.c │ │ └── jets.c │ ├── frame.c │ └── wrappers.h ├── Haskell-Examples/ │ └── TestnetTransaction.hs ├── Haskell-Generate/ │ ├── GenDecodeJet.hs │ ├── GenPrecomputed.hs │ ├── GenPrimitive.hs │ ├── GenRustJets.hs │ ├── GenTests.hs │ └── NameWrangler.hs ├── LICENSE ├── README.md ├── Setup.hs ├── Simplicity-Primitive.html ├── Simplicity-TR.tm ├── Simplicity.C.nix ├── Simplicity.Coq.nix ├── Simplicity.Haskell.nix ├── Simplicity.bib ├── Simplicity.cabal ├── alectryon/ │ ├── alectryon.css │ ├── alectryon.js │ ├── divstep.v.html │ ├── pygments.css │ ├── spec_int128.v.html │ ├── spec_modinv64.v.html │ ├── verif_int128_impl.v.html │ └── verif_modinv64_impl.v.html ├── compcert-opensource.nix ├── compcert-opensource.patch ├── default.nix ├── inheritance.Coq.dot ├── manual-index.html ├── safegcd-bounds.nix ├── shell.nix ├── spelling.ignore.txt ├── unification.patch └── vst.nix ================================================ FILE CONTENTS ================================================ ================================================ FILE: .github/workflows/ci.yml ================================================ name: CI on: [push, pull_request] jobs: codespell: runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - uses: codespell-project/actions-codespell@v2 with: ignore_words_file: spelling.ignore.txt skip: alectryon build: strategy: fail-fast: false matrix: project: ["c", "haskell"] # coq takes a very long time and times out at 6 hours... os: ["ubuntu-latest", macos-latest] channel: ["nixos-25.05", "nixpkgs-unstable"] runs-on: ${{ matrix.os }} permissions: id-token: write contents: read steps: - uses: actions/checkout@v4 - uses: DeterminateSystems/nix-installer-action@v17 - name: Update channel ${{matrix.channel}} run: | nix-channel --add https://nixos.org/channels/${{matrix.channel}} nixpkgs nix-channel --update - run: nix-build -A ${{matrix.project}} ================================================ FILE: .gitignore ================================================ # Tech report Simplicity-TR.pdf *.eps # Haskell /Haskell/*.pdf dist-newstyle cabal.project.local # Nix result result-doc # Coq /Coq/*Makefile* /Coq/.Makefile.d /Coq/.nia.cache .lia.cache *.vok *.vos *.glob *.aux *.vo *.crashcoqide alectryon-doc # C /C/test *.o *.out *.a # Coverage *.gcda *.gcno *.gcov *.info # Gen /*.rs /*.c /*.h /*.inc ================================================ FILE: C/Makefile ================================================ CORE_OBJS := bitstream.o dag.o deserialize.o eval.o frame.o jets.o jets-secp256k1.o rsort.o sha256.o type.o typeInference.o BITCOIN_OBJS := bitcoin/env.o bitcoin/ops.o bitcoin/bitcoinJets.o bitcoin/primitive.o bitcoin/txEnv.o ELEMENTS_OBJS := elements/env.o elements/exec.o elements/ops.o elements/elementsJets.o elements/primitive.o elements/cmr.o elements/txEnv.o TEST_OBJS := test.o ctx8Pruned.o ctx8Unpruned.o hashBlock.o regression4.o schnorr0.o schnorr6.o typeSkipTest.o elements/checkSigHashAllTx1.o # From https://fastcompression.blogspot.com/2019/01/compiler-warnings.html CWARN := -Werror -Wall -Wextra -Wcast-qual -Wcast-align -Wstrict-aliasing -Wpointer-arith -Winit-self -Wshadow -Wswitch-enum -Wstrict-prototypes -Wmissing-prototypes -Wredundant-decls -Wfloat-equal -Wundef -Wconversion ifneq ($(doCheck), 1) CPPFLAGS := $(CPPFLAGS) -DPRODUCTION endif CFLAGS := $(CFLAGS) -I include # libsecp256k1 is full of conversion warnings, so we compile jets-secp256k1.c separately. jets-secp256k1.o: jets-secp256k1.c $(CC) -c $(CFLAGS) $(CWARN) -Wno-conversion $(CPPFLAGS) -o $@ $< elements/elementsJets.o: elements/elementsJets.c $(CC) -c $(CFLAGS) $(CWARN) -Wno-switch-enum -Wswitch $(CPPFLAGS) -o $@ $< sha256.o: sha256.c $(CC) -c $(CFLAGS) $(X86_SHANI_CXXFLAGS) $(CWARN) -Wno-cast-align -Wno-sign-conversion $(CPPFLAGS) -o $@ $< %.o: %.c $(CC) -c $(CFLAGS) $(CWARN) $(CPPFLAGS) -o $@ $< libBitcoinSimplicity.a: $(CORE_OBJS) $(BITCOIN_OBJS) ar rcs $@ $^ libElementsSimplicity.a: $(CORE_OBJS) $(ELEMENTS_OBJS) ar rcs $@ $^ test: $(TEST_OBJS) libElementsSimplicity.a $(CC) $^ -o $@ $(LDFLAGS) install: libBitcoinSimplicity.a libElementsSimplicity.a mkdir -p $(out)/lib cp $^ $(out)/lib/ cp -R include $(out)/include check: test ./test clean: -rm -f test libElementsSimplicity.a $(TEST_OBJS) $(OBJS) .PHONY: install check clean ================================================ FILE: C/bitcoin/bitcoinJets.c ================================================ #include "bitcoinJets.h" #include "ops.h" #include "txEnv.h" #include "../taptweak.h" #include "../simplicity_assert.h" /* Read a 256-bit hash value from the 'src' frame, advancing the cursor 256 cells. * * Precondition: '*src' is a valid read frame for 256 more cells; * NULL != h; */ static void readHash(sha256_midstate* h, frameItem *src) { read32s(h->s, 8, src); } /* Write a 256-bit hash value to the 'dst' frame, advancing the cursor 256 cells. * * Precondition: '*dst' is a valid write frame for 256 more cells; * NULL != h; */ static void writeHash(frameItem* dst, const sha256_midstate* h) { write32s(dst, h->s, 8); } /* Write an outpoint value to the 'dst' frame, advancing the cursor 288 cells. * * Precondition: '*dst' is a valid write frame for 288 more cells; * NULL != op; */ static void prevOutpoint(frameItem* dst, const outpoint* op) { writeHash(dst, &op->txid); simplicity_write32(dst, op->ix); } static uint_fast32_t lockHeight(const bitcoinTransaction* tx) { return !tx->isFinal && tx->lockTime < 500000000U ? tx->lockTime : 0; } static uint_fast32_t lockTime(const bitcoinTransaction* tx) { return !tx->isFinal && 500000000U <= tx->lockTime ? tx->lockTime : 0; } static uint_fast16_t lockDistance(const bitcoinTransaction* tx, uint_fast32_t ix) { simplicity_assert(ix < tx->numInputs); if (2 <= tx->version && tx->input[ix].sequence < 0x80000000 && !(tx->input[ix].sequence & ((uint_fast32_t)1 << 22))) { return tx->input[ix].sequence & 0xffff; } else { return 0; } } static uint_fast16_t lockDuration(const bitcoinTransaction* tx, uint_fast32_t ix) { simplicity_assert(ix < tx->numInputs); if (2 <= tx->version && tx->input[ix].sequence < 0x80000000 && !!(tx->input[ix].sequence & ((uint_fast32_t)1 << 22))) { return tx->input[ix].sequence & 0xffff; } else { return 0; } } /* version : ONE |- TWO^32 */ bool simplicity_bitcoin_version(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->version); return true; } /* lock_time : ONE |- TWO^32 */ bool simplicity_bitcoin_lock_time(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->lockTime); return true; } /* input_prev_outpoint : TWO^32 |- S (TWO^256 * TWO^32) */ bool simplicity_bitcoin_input_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { prevOutpoint(dst, &env->tx->input[i].prevOutpoint); } else { skipBits(dst, 288); } return true; } /* input_value : TWO^32 |- S TWO^64 */ bool simplicity_bitcoin_input_value(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { simplicity_write64(dst, env->tx->input[i].txo.value); } else { skipBits(dst, 64); } return true; } /* input_script_hash : TWO^32 |- S TWO^256 */ bool simplicity_bitcoin_input_script_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { writeHash(dst, &env->tx->input[i].txo.scriptPubKey); } else { skipBits(dst, 256); } return true; } /* input_sequence : TWO^32 |- S TWO^32 */ bool simplicity_bitcoin_input_sequence(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { simplicity_write32(dst, env->tx->input[i].sequence); } else { skipBits(dst, 32); } return true; } /* input_annex_hash : TWO^32 |- S (S (TWO^256)) */ bool simplicity_bitcoin_input_annex_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { if (writeBit(dst, env->tx->input[i].hasAnnex)) { writeHash(dst, &env->tx->input[i].annexHash); } else { skipBits(dst, 256); } } else { skipBits(dst, 257); } return true; } /* input_script_sig_hash : TWO^32 |- (S (TWO^256) */ bool simplicity_bitcoin_input_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { writeHash(dst, &env->tx->input[i].scriptSigHash); } else { skipBits(dst, 256); } return true; } /* output_value : TWO^32 |- S (TWO^64) */ bool simplicity_bitcoin_output_value(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { simplicity_write64(dst, env->tx->output[i].value); } else { skipBits(dst, 64); } return true; } /* output_script_hash : TWO^32 |- S TWO^256 */ bool simplicity_bitcoin_output_script_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { writeHash(dst, &env->tx->output[i].scriptPubKey); } else { skipBits(dst, 256); } return true; } /* fee : ONE |- TWO^64 */ bool simplicity_bitcoin_fee(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write64(dst, env->tx->totalInputValue - env->tx->totalOutputValue); return true; } /* total_input_value : ONE |- TWO^64 */ bool simplicity_bitcoin_total_input_value(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write64(dst, env->tx->totalInputValue); return true; } /* total_output_value : ONE |- TWO^64 */ bool simplicity_bitcoin_total_output_value(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write64(dst, env->tx->totalOutputValue); return true; } /* script_cmr : ONE |- TWO^256 */ bool simplicity_bitcoin_script_cmr(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; write32s(dst, env->taproot->scriptCMR.s, 8); return true; } /* transaction_id : ONE |- TWO^256 */ bool simplicity_bitcoin_transaction_id(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; write32s(dst, env->tx->txid.s, 8); return true; } /* current_index : ONE |- TWO^32 */ bool simplicity_bitcoin_current_index(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->ix); return true; } /* current_prev_outpoint : ONE |- TWO^256 * TWO^32 */ bool simplicity_bitcoin_current_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; prevOutpoint(dst, &env->tx->input[env->ix].prevOutpoint); return true; } /* current_value : ONE |- (TWO^64) */ bool simplicity_bitcoin_current_value(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; simplicity_write64(dst, env->tx->input[env->ix].txo.value); return true; } /* current_script_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_current_script_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; writeHash(dst, &env->tx->input[env->ix].txo.scriptPubKey); return true; } /* current_sequence : ONE |- TWO^32 */ bool simplicity_bitcoin_current_sequence(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; simplicity_write32(dst, env->tx->input[env->ix].sequence); return true; } /* current_script_sig_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_current_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; writeHash(dst, &env->tx->input[env->ix].scriptSigHash); return true; } /* current_annex_hash : ONE |- S (TWO^256) */ bool simplicity_bitcoin_current_annex_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; if (writeBit(dst, env->tx->input[env->ix].hasAnnex)) { writeHash(dst, &env->tx->input[env->ix].annexHash); } else { skipBits(dst, 256); } return true; } /* tapleaf_version : ONE |- TWO^8 */ bool simplicity_bitcoin_tapleaf_version(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write8(dst, env->taproot->leafVersion); return true; } /* tappath : TWO^8 |- S (TWO^256) */ bool simplicity_bitcoin_tappath(frameItem* dst, frameItem src, const txEnv* env) { uint_fast8_t i = simplicity_read8(&src); if (writeBit(dst, i < env->taproot->pathLen)) { writeHash(dst, &env->taproot->path[i]); } else { skipBits(dst, 256); } return true; } /* internal_key : ONE |- TWO^256 */ bool simplicity_bitcoin_internal_key(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->internalKey); return true; } /* num_inputs : ONE |- TWO^32 */ bool simplicity_bitcoin_num_inputs(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->numInputs); return true; } /* num_outputs : ONE |- TWO^32 */ bool simplicity_bitcoin_num_outputs(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->numOutputs); return true; } /* tx_is_final : ONE |- TWO */ bool simplicity_bitcoin_tx_is_final(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeBit(dst, env->tx->isFinal); return true; } /* tx_lock_height : ONE |- TWO^32 */ bool simplicity_bitcoin_tx_lock_height(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, lockHeight(env->tx)); return true; } /* tx_lock_time : ONE |- TWO^32 */ bool simplicity_bitcoin_tx_lock_time(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, lockTime(env->tx)); return true; } /* tx_lock_distance : ONE |- TWO^16 */ bool simplicity_bitcoin_tx_lock_distance(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; simplicity_write16(dst, lockDistance(env->tx, env->ix)); return true; } /* tx_lock_duration : ONE |- TWO^16 */ bool simplicity_bitcoin_tx_lock_duration(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; simplicity_write16(dst, lockDuration(env->tx, env->ix)); return true; } /* check_lock_height : TWO^32 |- ONE */ bool simplicity_bitcoin_check_lock_height(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; uint_fast32_t x = simplicity_read32(&src); return x <= lockHeight(env->tx); } /* check_lock_time : TWO^32 |- ONE */ bool simplicity_bitcoin_check_lock_time(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; uint_fast32_t x = simplicity_read32(&src); return x <= lockTime(env->tx); } /* check_lock_distance : TWO^16 |- ONE */ bool simplicity_bitcoin_check_lock_distance(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; if (env->tx->numInputs <= env->ix) return false; uint_fast16_t x = simplicity_read16(&src); return x <= lockDistance(env->tx, env->ix); } /* check_lock_duration : TWO^16 |- ONE */ bool simplicity_bitcoin_check_lock_duration(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; if (env->tx->numInputs <= env->ix) return false; uint_fast16_t x = simplicity_read16(&src); return x <= lockDuration(env->tx, env->ix); } /* build_tapleaf_simplicity : TWO^256 |- TWO^256 */ bool simplicity_bitcoin_build_tapleaf_simplicity(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate cmr; readHash(&cmr, &src); sha256_midstate result = simplicity_bitcoin_make_tapleaf(0xbe, &cmr); writeHash(dst, &result); return true; } /* build_tapbranch : TWO^256 * TWO^256 |- TWO^256 */ bool simplicity_bitcoin_build_tapbranch(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate a, b; readHash(&a, &src); readHash(&b, &src); sha256_midstate result = simplicity_bitcoin_make_tapbranch(&a, &b); writeHash(dst, &result); return true; } /* build_taptweak : PUBKEY * TWO^256 |- PUBKEY */ bool simplicity_bitcoin_build_taptweak(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. static unsigned char taptweak[] = "TapTweak"; return simplicity_generic_taptweak(dst, &src, taptweak, sizeof(taptweak)-1); } /* outpoint_hash : CTX8 * TWO^256 * TWO^32 |- CTX8 */ bool simplicity_bitcoin_outpoint_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate midstate; unsigned char buf[36]; sha256_context ctx = {.output = midstate.s}; /* Read a SHA-256 context. */ if (!simplicity_read_sha256_context(&ctx, &src)) return false; /* Read an outpoint (hash and index). */ read8s(buf, 36, &src); sha256_uchars(&ctx, buf, 36); return simplicity_write_sha256_context(dst, &ctx); } /* annex_hash : CTX8 * S TWO^256 |- CTX8 */ bool simplicity_bitcoin_annex_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate midstate; unsigned char buf[32]; sha256_context ctx = {.output = midstate.s}; /* Read a SHA-256 context. */ if (!simplicity_read_sha256_context(&ctx, &src)) return false; /* Read an optional hash. (257 bits) */ if (readBit(&src)) { /* Read a hash. (256 bits) */ read8s(buf, 32, &src); sha256_uchar(&ctx, 0x01); sha256_uchars(&ctx, buf, 32); } else { /* No hash. */ sha256_uchar(&ctx, 0x00); } return simplicity_write_sha256_context(dst, &ctx); } /* output_amounts_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_output_values_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputValuesHash); return true; } /* output_scripts_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_output_scripts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputScriptsHash); return true; } /* outputs_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_outputs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputsHash); return true; } /* output_hash : TWO^32 |- S TWO^256 */ bool simplicity_bitcoin_output_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { const sigOutput* output = &env->tx->output[i]; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); sha256_u64be(&ctx, output->value); sha256_hash(&ctx, &output->scriptPubKey); sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* input_outpoints_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_outpoints_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputOutpointsHash); return true; } /* input_values_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_values_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputValuesHash); return true; } /* input_scripts_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_scripts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputScriptsHash); return true; } /* input_utxos_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_utxos_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputUTXOsHash); return true; } /* input_utxo_hash : TWO^32 |- S TWO^256 */ bool simplicity_bitcoin_input_utxo_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigOutput* txo = &env->tx->input[i].txo; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); sha256_u64be(&ctx, txo->value); sha256_hash(&ctx, &txo->scriptPubKey); sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* input_sequences_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_sequences_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputSequencesHash); return true; } /* input_annexes_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_annexes_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputAnnexesHash); return true; } /* input_script_sigs_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_input_script_sigs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputScriptSigsHash); return true; } /* inputs_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_inputs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputsHash); return true; } /* input_hash : TWO^32 |- S TWO^256 */ bool simplicity_bitcoin_input_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigInput* input = &env->tx->input[i]; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); sha256_hash(&ctx, &input->prevOutpoint.txid); sha256_u32be(&ctx, input->prevOutpoint.ix); sha256_u32be(&ctx, input->sequence); if (input->hasAnnex) { sha256_uchar(&ctx, 1); sha256_hash(&ctx, &input->annexHash); } else { sha256_uchar(&ctx, 0); } sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* tx_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_tx_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->txHash); return true; } /* tapleaf_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_tapleaf_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->tapLeafHash); return true; } /* tappath_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_tappath_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->tappathHash); return true; } /* tap_env_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_tap_env_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->tapEnvHash); return true; } /* sig_all_hash : ONE |- TWO^256 */ bool simplicity_bitcoin_sig_all_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->sigAllHash); return true; } ================================================ FILE: C/bitcoin/bitcoinJets.h ================================================ /* This module defines primitives and jets that are specific to the Bitcoin application for Simplicity. */ #ifndef SIMPLICITY_BITCOIN_BITCOINJETS_H #define SIMPLICITY_BITCOIN_BITCOINJETS_H #include "../jets.h" /* Jets for the Bitcoin application of Simplicity. */ bool simplicity_bitcoin_version(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_lock_time(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_value(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_script_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_sequence(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_annex_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_output_value(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_output_script_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_fee(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_total_input_value(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_total_output_value(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_script_cmr(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_transaction_id(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_index(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_value(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_script_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_sequence(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_annex_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_current_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tapleaf_version(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tappath(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_internal_key(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_num_inputs(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_num_outputs(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tx_is_final(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tx_lock_height(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tx_lock_time(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tx_lock_distance(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tx_lock_duration(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_check_lock_height(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_check_lock_time(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_check_lock_distance(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_check_lock_duration(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_build_tapleaf_simplicity(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_build_tapbranch(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_build_taptweak(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_outpoint_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_annex_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_output_values_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_output_scripts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_outputs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_output_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_outpoints_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_values_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_scripts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_utxos_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_utxo_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_sequences_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_annexes_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_script_sigs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_inputs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_input_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tx_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tapleaf_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tappath_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_tap_env_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bitcoin_sig_all_hash(frameItem* dst, frameItem src, const txEnv* env); #endif ================================================ FILE: C/bitcoin/decodeBitcoinJets.inc ================================================ /* This file has been automatically generated. */ { int32_t code; code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SIG_ALL_HASH; return SIMPLICITY_NO_ERROR; case 2: *result = TX_HASH; return SIMPLICITY_NO_ERROR; case 3: *result = TAP_ENV_HASH; return SIMPLICITY_NO_ERROR; case 4: *result = OUTPUTS_HASH; return SIMPLICITY_NO_ERROR; case 5: *result = INPUTS_HASH; return SIMPLICITY_NO_ERROR; case 6: *result = INPUT_UTXOS_HASH; return SIMPLICITY_NO_ERROR; case 7: *result = OUTPUT_HASH; return SIMPLICITY_NO_ERROR; case 8: *result = OUTPUT_VALUES_HASH; return SIMPLICITY_NO_ERROR; case 9: *result = OUTPUT_SCRIPTS_HASH; return SIMPLICITY_NO_ERROR; case 10: *result = INPUT_HASH; return SIMPLICITY_NO_ERROR; case 11: *result = INPUT_OUTPOINTS_HASH; return SIMPLICITY_NO_ERROR; case 12: *result = INPUT_SEQUENCES_HASH; return SIMPLICITY_NO_ERROR; case 13: *result = INPUT_ANNEXES_HASH; return SIMPLICITY_NO_ERROR; case 14: *result = INPUT_SCRIPT_SIGS_HASH; return SIMPLICITY_NO_ERROR; case 15: *result = INPUT_UTXO_HASH; return SIMPLICITY_NO_ERROR; case 16: *result = INPUT_VALUES_HASH; return SIMPLICITY_NO_ERROR; case 17: *result = INPUT_SCRIPTS_HASH; return SIMPLICITY_NO_ERROR; case 18: *result = TAPLEAF_HASH; return SIMPLICITY_NO_ERROR; case 19: *result = TAPPATH_HASH; return SIMPLICITY_NO_ERROR; case 20: *result = OUTPOINT_HASH; return SIMPLICITY_NO_ERROR; case 21: *result = ANNEX_HASH; return SIMPLICITY_NO_ERROR; case 22: *result = BUILD_TAPLEAF_SIMPLICITY; return SIMPLICITY_NO_ERROR; case 23: *result = BUILD_TAPBRANCH; return SIMPLICITY_NO_ERROR; case 24: *result = BUILD_TAPTWEAK; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = CHECK_LOCK_HEIGHT; return SIMPLICITY_NO_ERROR; case 2: *result = CHECK_LOCK_TIME; return SIMPLICITY_NO_ERROR; case 3: *result = CHECK_LOCK_DISTANCE; return SIMPLICITY_NO_ERROR; case 4: *result = CHECK_LOCK_DURATION; return SIMPLICITY_NO_ERROR; case 5: *result = TX_LOCK_HEIGHT; return SIMPLICITY_NO_ERROR; case 6: *result = TX_LOCK_TIME; return SIMPLICITY_NO_ERROR; case 7: *result = TX_LOCK_DISTANCE; return SIMPLICITY_NO_ERROR; case 8: *result = TX_LOCK_DURATION; return SIMPLICITY_NO_ERROR; case 9: *result = TX_IS_FINAL; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SCRIPT_CMR; return SIMPLICITY_NO_ERROR; case 2: *result = INTERNAL_KEY; return SIMPLICITY_NO_ERROR; case 3: *result = CURRENT_INDEX; return SIMPLICITY_NO_ERROR; case 4: *result = NUM_INPUTS; return SIMPLICITY_NO_ERROR; case 5: *result = NUM_OUTPUTS; return SIMPLICITY_NO_ERROR; case 6: *result = LOCK_TIME; return SIMPLICITY_NO_ERROR; case 7: *result = FEE; return SIMPLICITY_NO_ERROR; case 8: *result = OUTPUT_VALUE; return SIMPLICITY_NO_ERROR; case 9: *result = OUTPUT_SCRIPT_HASH; return SIMPLICITY_NO_ERROR; case 10: *result = TOTAL_OUTPUT_VALUE; return SIMPLICITY_NO_ERROR; case 11: *result = CURRENT_PREV_OUTPOINT; return SIMPLICITY_NO_ERROR; case 12: *result = CURRENT_VALUE; return SIMPLICITY_NO_ERROR; case 13: *result = CURRENT_SCRIPT_HASH; return SIMPLICITY_NO_ERROR; case 14: *result = CURRENT_SEQUENCE; return SIMPLICITY_NO_ERROR; case 15: *result = CURRENT_ANNEX_HASH; return SIMPLICITY_NO_ERROR; case 16: *result = CURRENT_SCRIPT_SIG_HASH; return SIMPLICITY_NO_ERROR; case 17: *result = INPUT_PREV_OUTPOINT; return SIMPLICITY_NO_ERROR; case 18: *result = INPUT_VALUE; return SIMPLICITY_NO_ERROR; case 19: *result = INPUT_SCRIPT_HASH; return SIMPLICITY_NO_ERROR; case 20: *result = INPUT_SEQUENCE; return SIMPLICITY_NO_ERROR; case 21: *result = INPUT_ANNEX_HASH; return SIMPLICITY_NO_ERROR; case 22: *result = INPUT_SCRIPT_SIG_HASH; return SIMPLICITY_NO_ERROR; case 23: *result = TOTAL_INPUT_VALUE; return SIMPLICITY_NO_ERROR; case 24: *result = TAPLEAF_VERSION; return SIMPLICITY_NO_ERROR; case 25: *result = TAPPATH; return SIMPLICITY_NO_ERROR; case 26: *result = VERSION; return SIMPLICITY_NO_ERROR; case 27: *result = TRANSACTION_ID; return SIMPLICITY_NO_ERROR; } break; } } ================================================ FILE: C/bitcoin/env.c ================================================ #include #include #include #include #include "txEnv.h" #include "ops.h" #include "../sha256.h" #include "../simplicity_assert.h" #include "../simplicity_alloc.h" #define PADDING(alignType, allocated) ((alignof(alignType) - (allocated) % alignof(alignType)) % alignof(alignType)) /* Compute the SHA-256 hash of a scriptPubKey and write it into 'result'. * * Precondition: NULL != result; * NULL != scriptPubKey; */ static void hashBuffer(sha256_midstate* result, const rawBitcoinBuffer* buffer) { sha256_context ctx = sha256_init(result->s); sha256_uchars(&ctx, buffer->buf, buffer->len); sha256_finalize(&ctx); } /* Initialize a 'sigOutput' from a 'rawOutput', copying or hashing the data as needed. * * Precondition: NULL != result; * NULL != output; */ static void copyOutput(sigOutput* result, const rawBitcoinOutput* output) { hashBuffer(&result->scriptPubKey, &output->scriptPubKey); result->value = output->value; } /* Initialize a 'sigInput' from a 'rawBitcoinInput', copying or hashing the data as needed. * * Precondition: NULL != result; * NULL != input; */ static void copyInput(sigInput* result, const rawBitcoinInput* input) { *result = (sigInput){ .prevOutpoint = { .ix = input->prevIx } , .sequence = input->sequence , .hasAnnex = !!input->annex }; if (input->annex) hashBuffer(&result->annexHash, input->annex); sha256_toMidstate(result->prevOutpoint.txid.s, input->prevTxid); copyOutput(&result->txo, &input->txo); hashBuffer(&result->scriptSigHash, &input->scriptSig); } /* Allocate and initialize a 'bitcoinTransaction' from a 'rawBitcoinTransaction', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: NULL != rawTx */ extern bitcoinTransaction* simplicity_bitcoin_mallocTransaction(const rawBitcoinTransaction* rawTx) { if (!rawTx) return NULL; size_t allocationSize = sizeof(bitcoinTransaction); const size_t pad1 = PADDING(sigInput, allocationSize); if (SIZE_MAX - allocationSize < pad1) return NULL; allocationSize += pad1; /* Multiply by (size_t)1 to disable type-limits warning. */ if (SIZE_MAX / sizeof(sigInput) < (size_t)1 * rawTx->numInputs) return NULL; if (SIZE_MAX - allocationSize < rawTx->numInputs * sizeof(sigInput)) return NULL; allocationSize += rawTx->numInputs * sizeof(sigInput); const size_t pad2 = PADDING(sigOutput, allocationSize); if (SIZE_MAX - allocationSize < pad2) return NULL; allocationSize += pad2; /* Multiply by (size_t)1 to disable type-limits warning. */ if (SIZE_MAX / sizeof(sigOutput) < (size_t)1 * rawTx->numOutputs) return NULL; if (SIZE_MAX - allocationSize < rawTx->numOutputs * sizeof(sigOutput)) return NULL; allocationSize += rawTx->numOutputs * sizeof(sigOutput); char *allocation = simplicity_malloc(allocationSize); if (!allocation) return NULL; /* Casting through void* to avoid warning about pointer alignment. * Our padding is done carefully to ensure alignment. */ bitcoinTransaction* const tx = (bitcoinTransaction*)(void*)allocation; allocation += sizeof(bitcoinTransaction) + pad1; sigInput* const input = (sigInput*)(void*)allocation; allocation += rawTx->numInputs * sizeof(sigInput) + pad2; sigOutput* const output = (sigOutput*)(void*)allocation; *tx = (bitcoinTransaction){ .input = input , .output = output , .numInputs = rawTx->numInputs , .numOutputs = rawTx->numOutputs , .version = rawTx->version , .lockTime = rawTx->lockTime , .isFinal = true }; sha256_toMidstate(tx->txid.s, rawTx->txid); { sha256_context ctx_inputOutpointsHash = sha256_init(tx->inputOutpointsHash.s); sha256_context ctx_inputValuesHash = sha256_init(tx->inputValuesHash.s); sha256_context ctx_inputScriptsHash = sha256_init(tx->inputScriptsHash.s); sha256_context ctx_inputUTXOsHash = sha256_init(tx->inputUTXOsHash.s); sha256_context ctx_inputSequencesHash = sha256_init(tx->inputSequencesHash.s); sha256_context ctx_inputAnnexesHash = sha256_init(tx->inputAnnexesHash.s); sha256_context ctx_inputScriptSigsHash = sha256_init(tx->inputScriptSigsHash.s); sha256_context ctx_inputsHash = sha256_init(tx->inputsHash.s); for (uint_fast32_t i = 0; i < tx->numInputs; ++i) { copyInput(&input[i], &rawTx->input[i]); tx->totalInputValue += input[i].txo.value; if (input[i].sequence < 0xffffffff) { tx->isFinal = false; } sha256_hash(&ctx_inputOutpointsHash, &input[i].prevOutpoint.txid); sha256_u32be(&ctx_inputOutpointsHash, input[i].prevOutpoint.ix); sha256_u64be(&ctx_inputValuesHash, input[i].txo.value); sha256_hash(&ctx_inputScriptsHash, &input[i].txo.scriptPubKey); sha256_u32be(&ctx_inputSequencesHash, input[i].sequence); if (input[i].hasAnnex) { sha256_uchar(&ctx_inputAnnexesHash, 1); sha256_hash(&ctx_inputAnnexesHash, &input[i].annexHash); } else { sha256_uchar(&ctx_inputAnnexesHash, 0); } sha256_hash(&ctx_inputScriptSigsHash, &input[i].scriptSigHash); } sha256_finalize(&ctx_inputOutpointsHash); sha256_finalize(&ctx_inputValuesHash); sha256_finalize(&ctx_inputScriptsHash); sha256_finalize(&ctx_inputSequencesHash); sha256_finalize(&ctx_inputAnnexesHash); sha256_finalize(&ctx_inputScriptSigsHash); sha256_hash(&ctx_inputUTXOsHash, &tx->inputValuesHash); sha256_hash(&ctx_inputUTXOsHash, &tx->inputScriptsHash); sha256_finalize(&ctx_inputUTXOsHash); sha256_hash(&ctx_inputsHash, &tx->inputOutpointsHash); sha256_hash(&ctx_inputsHash, &tx->inputSequencesHash); sha256_hash(&ctx_inputsHash, &tx->inputAnnexesHash); sha256_finalize(&ctx_inputsHash); } { sha256_context ctx_outputValuesHash = sha256_init(tx->outputValuesHash.s); sha256_context ctx_outputScriptsHash = sha256_init(tx->outputScriptsHash.s); sha256_context ctx_outputsHash = sha256_init(tx->outputsHash.s); for (uint_fast32_t i = 0; i < tx->numOutputs; ++i) { copyOutput(&output[i], &rawTx->output[i]); tx->totalOutputValue += output[i].value; sha256_u64be(&ctx_outputValuesHash, output[i].value); sha256_hash(&ctx_outputScriptsHash, &output[i].scriptPubKey); } sha256_finalize(&ctx_outputValuesHash); sha256_finalize(&ctx_outputScriptsHash); sha256_hash(&ctx_outputsHash, &tx->outputValuesHash); sha256_hash(&ctx_outputsHash, &tx->outputScriptsHash); sha256_finalize(&ctx_outputsHash); } { sha256_context ctx_txHash = sha256_init(tx->txHash.s); sha256_u32be(&ctx_txHash, tx->version); sha256_u32be(&ctx_txHash, tx->lockTime); sha256_hash(&ctx_txHash, &tx->inputsHash); sha256_hash(&ctx_txHash, &tx->outputsHash); sha256_hash(&ctx_txHash, &tx->inputUTXOsHash); sha256_finalize(&ctx_txHash); } return tx; } /* Free a pointer to 'bitcoinTransaction'. */ extern void simplicity_bitcoin_freeTransaction(bitcoinTransaction* tx) { simplicity_free(tx); } /* Allocate and initialize a 'bitcoinTapEnv' from a 'rawBitcoinTapEnv', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: *rawEnv is well-formed (i.e. rawEnv->pathLen <= 128.) */ extern bitcoinTapEnv* simplicity_bitcoin_mallocTapEnv(const rawBitcoinTapEnv* rawEnv) { if (!rawEnv) return NULL; if (128 < rawEnv->pathLen) return NULL; size_t allocationSize = sizeof(bitcoinTapEnv); const size_t numMidstate = rawEnv->pathLen; const size_t pad1 = PADDING(sha256_midstate, allocationSize); if (numMidstate) { if (SIZE_MAX - allocationSize < pad1) return NULL; allocationSize += pad1; if (SIZE_MAX / sizeof(sha256_midstate) < numMidstate) return NULL; if (SIZE_MAX - allocationSize < numMidstate * sizeof(sha256_midstate)) return NULL; allocationSize += numMidstate * sizeof(sha256_midstate); } char *allocation = simplicity_malloc(allocationSize); if (!allocation) return NULL; /* Casting through void* to avoid warning about pointer alignment. * Our padding is done carefully to ensure alignment. */ bitcoinTapEnv* const env = (bitcoinTapEnv*)(void*)allocation; sha256_midstate* path = NULL; sha256_midstate internalKey; sha256_toMidstate(internalKey.s, &rawEnv->controlBlock[1]); if (numMidstate) { allocation += sizeof(bitcoinTapEnv) + pad1; if (rawEnv->pathLen) { path = (sha256_midstate*)(void*)allocation; } } *env = (bitcoinTapEnv){ .leafVersion = rawEnv->controlBlock[0] & 0xfe , .internalKey = internalKey , .path = path , .pathLen = rawEnv->pathLen }; sha256_toMidstate(env->scriptCMR.s, rawEnv->scriptCMR); { sha256_context ctx = sha256_init(env->tappathHash.s); for (int i = 0; i < env->pathLen; ++i) { sha256_toMidstate(path[i].s, &rawEnv->controlBlock[33+32*i]); sha256_hash(&ctx, &path[i]); } sha256_finalize(&ctx); } env->tapLeafHash = simplicity_bitcoin_make_tapleaf(env->leafVersion, &env->scriptCMR); { sha256_context ctx = sha256_init(env->tapEnvHash.s); sha256_hash(&ctx, &env->tapLeafHash); sha256_hash(&ctx, &env->tappathHash); sha256_hash(&ctx, &env->internalKey); sha256_finalize(&ctx); } return env; } /* Free a pointer to 'bitcoinTapEnv'. */ extern void simplicity_bitcoin_freeTapEnv(bitcoinTapEnv* env) { simplicity_free(env); } ================================================ FILE: C/bitcoin/ops.c ================================================ #include "ops.h" /* Compute Bitcoins's tapleaf hash from a tapleaf version and a 256-bit script value. * A reimplementation of ComputeTapleafHash from Bitcoin's 'interpreter.cpp'. * Only 256-bit script values are supported as that is the size used for Simplicity CMRs. * * Precondition: NULL != cmr; */ sha256_midstate simplicity_bitcoin_make_tapleaf(unsigned char version, const sha256_midstate* cmr) { sha256_midstate result; sha256_midstate tapleafTag; { static unsigned char tagName[] = "TapLeaf"; sha256_context ctx = sha256_init(tapleafTag.s); sha256_uchars(&ctx, tagName, sizeof(tagName) - 1); sha256_finalize(&ctx); } sha256_context ctx = sha256_init(result.s); sha256_hash(&ctx, &tapleafTag); sha256_hash(&ctx, &tapleafTag); sha256_uchar(&ctx, version); sha256_uchar(&ctx, 32); sha256_hash(&ctx, cmr); sha256_finalize(&ctx); return result; } /* Compute Bitcoins's tapbrach hash from two branches. * * Precondition: NULL != a; * NULL != b; */ sha256_midstate simplicity_bitcoin_make_tapbranch(const sha256_midstate* a, const sha256_midstate* b) { sha256_midstate result; sha256_midstate tapbranchTag; { static unsigned char tagName[] = "TapBranch"; sha256_context ctx = sha256_init(tapbranchTag.s); sha256_uchars(&ctx, tagName, sizeof(tagName) - 1); sha256_finalize(&ctx); } sha256_context ctx = sha256_init(result.s); sha256_hash(&ctx, &tapbranchTag); sha256_hash(&ctx, &tapbranchTag); if (sha256_cmp_be(a, b) < 0) { sha256_hash(&ctx, a); sha256_hash(&ctx, b); } else { sha256_hash(&ctx, b); sha256_hash(&ctx, a); } sha256_finalize(&ctx); return result; } ================================================ FILE: C/bitcoin/ops.h ================================================ /* This module defines operations used in the construction the environment ('txEnv') and some jets. */ #ifndef SIMPLICITY_BITCOIN_OPS_H #define SIMPLICITY_BITCOIN_OPS_H #include "../sha256.h" /* Compute Bitcoin's tapleaf hash from a tapleaf version and a 256-bit script value. * A reimplementation of ComputeTapleafHash from Bitcoin's 'interpreter.cpp'. * Only 256-bit script values are supported as that is the size used for Simplicity CMRs. * * Precondition: NULL != cmr; */ sha256_midstate simplicity_bitcoin_make_tapleaf(unsigned char version, const sha256_midstate* cmr); /* Compute an Bitcoin's tapbrach hash from two branches. * * Precondition: NULL != a; * NULL != b; */ sha256_midstate simplicity_bitcoin_make_tapbranch(const sha256_midstate* a, const sha256_midstate* b); #endif ================================================ FILE: C/bitcoin/primitive.c ================================================ /* This module implements the 'primitive.h' interface for the Bitcoin application of Simplicity. */ #include "primitive.h" #include "bitcoinJets.h" #include "../limitations.h" #include "../simplicity_alloc.h" #include "../simplicity_assert.h" /* An enumeration of all the types we need to construct to specify the input and output types of all jets created by 'decodeJet'. */ enum TypeNamesForJets { #include "primitiveEnumTy.inc" NumberOfTypeNames }; /* Allocate a fresh set of unification variables bound to at least all the types necessary * for all the jets that can be created by 'decodeJet', and also the type 'TWO^256', * and also allocate space for 'extra_var_len' many unification variables. * Return the number of non-trivial bindings created. * * However, if malloc fails, then return 0. * * Precondition: NULL != bound_var; * NULL != word256_ix; * NULL != extra_var_start; * extra_var_len <= 6*DAG_LEN_MAX; * * Postcondition: Either '*bound_var == NULL' and the function returns 0 * or 'unification_var (*bound_var)[*extra_var_start + extra_var_len]' is an array of unification variables * such that for any 'jet : A |- B' there is some 'i < *extra_var_start' and 'j < *extra_var_start' such that * '(*bound_var)[i]' is bound to 'A' and '(*bound_var)[j]' is bound to 'B' * and, '*word256_ix < *extra_var_start' and '(*bound_var)[*word256_ix]' is bound the type 'TWO^256' */ size_t simplicity_bitcoin_mallocBoundVars(unification_var** bound_var, size_t* word256_ix, size_t* extra_var_start, size_t extra_var_len) { static_assert(1 <= NumberOfTypeNames, "Missing TypeNamesForJets."); static_assert(NumberOfTypeNames <= NUMBER_OF_TYPENAMES_MAX, "Too many TypeNamesForJets."); static_assert(DAG_LEN_MAX <= (SIZE_MAX - NumberOfTypeNames) / 6, "NumberOfTypeNames + 6*DAG_LEN_MAX doesn't fit in size_t"); static_assert(NumberOfTypeNames + 6*DAG_LEN_MAX <= SIZE_MAX/sizeof(unification_var) , "bound_var array too large"); static_assert(NumberOfTypeNames + 6*DAG_LEN_MAX - 1 <= UINT32_MAX, "bound_var array index doesn't fit in uint32_t"); simplicity_assert(extra_var_len <= 6*DAG_LEN_MAX); *bound_var = simplicity_malloc((NumberOfTypeNames + extra_var_len) * sizeof(unification_var)); if (!(*bound_var)) return 0; #include "primitiveInitTy.inc" *word256_ix = ty_w256; *extra_var_start = NumberOfTypeNames; /* 'ty_u' is a trivial binding, so we made 'NumberOfTypeNames - 1' non-trivial bindings. */ return NumberOfTypeNames - 1; }; /* An enumeration of the names of Bitcoin specific jets and primitives. */ typedef enum jetName { #include "primitiveEnumJet.inc" NUMBER_OF_JET_NAMES } jetName; /* Decode an Bitcoin specific jet name from 'stream' into 'result'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'result' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != result * NULL != stream */ static simplicity_err decodePrimitive(jetName* result, bitstream* stream) { int32_t bit = read1Bit(stream); if (bit < 0) return (simplicity_err)bit; if (!bit) { /* Core jets */ #include "../decodeCoreJets.inc" return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; } else { /* Bitcoin jets */ #include "decodeBitcoinJets.inc" return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; } } /* Return a copy of the Simplicity node corresponding to the given Bitcoin specific jet 'name'. */ static dag_node jetNode(jetName name) { static const dag_node jet_node[] = { #include "primitiveJetNode.inc" }; return jet_node[name]; } /* Decode a Bitcoin specific jet from 'stream' into 'node'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERR' if successful. * * Precondition: NULL != node * NULL != stream */ simplicity_err simplicity_bitcoin_decodeJet(dag_node* node, bitstream* stream) { jetName name; simplicity_err error = decodePrimitive(&name, stream); if (!IS_OK(error)) return error; *node = jetNode(name); return SIMPLICITY_NO_ERROR; } ================================================ FILE: C/bitcoin/primitive.h ================================================ /* Implements the primitive.h interface for the Bitcoin Simplicity application. */ #ifndef SIMPLICITY_BITCOIN_PRIMITIVE_H #define SIMPLICITY_BITCOIN_PRIMITIVE_H #include "../bitstream.h" #include "../typeInference.h" /* Allocate a fresh set of unification variables bound to at least all the types necessary * for all the jets that can be created by 'decodeJet', and also the type 'TWO^256', * and also allocate space for 'extra_var_len' many unification variables. * Return the number of non-trivial bindings created. * * However, if malloc fails, then return 0. * * Precondition: NULL != bound_var; * NULL != word256_ix; * NULL != extra_var_start; * extra_var_len <= 6*DAG_LEN_MAX; * * Postcondition: Either '*bound_var == NULL' and the function returns 0 * or 'unification_var (*bound_var)[*extra_var_start + extra_var_len]' is an array of unification variables * such that for any 'jet : A |- B' there is some 'i < *extra_var_start' and 'j < *extra_var_start' such that * '(*bound_var)[i]' is bound to 'A' and '(*bound_var)[j]' is bound to 'B' * and, '*word256_ix < *extra_var_start' and '(*bound_var)[*word256_ix]' is bound the type 'TWO^256' */ size_t simplicity_bitcoin_mallocBoundVars(unification_var** bound_var, size_t* word256_ix, size_t* extra_var_start, size_t extra_var_len); /* Decode a Bitcoin specific jet from 'stream' into 'node'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != node * NULL != stream */ simplicity_err simplicity_bitcoin_decodeJet(dag_node* node, bitstream* stream); #endif ================================================ FILE: C/bitcoin/primitiveEnumJet.inc ================================================ /* This file has been automatically generated. */ ADD_16, ADD_32, ADD_64, ADD_8, ALL_16, ALL_32, ALL_64, ALL_8, AND_1, AND_16, AND_32, AND_64, AND_8, ANNEX_HASH, BIP_0340_VERIFY, BUILD_TAPBRANCH, BUILD_TAPLEAF_SIMPLICITY, BUILD_TAPTWEAK, CH_1, CH_16, CH_32, CH_64, CH_8, CHECK_LOCK_DISTANCE, CHECK_LOCK_DURATION, CHECK_LOCK_HEIGHT, CHECK_LOCK_TIME, CHECK_SIG_VERIFY, COMPLEMENT_1, COMPLEMENT_16, COMPLEMENT_32, COMPLEMENT_64, COMPLEMENT_8, CURRENT_ANNEX_HASH, CURRENT_INDEX, CURRENT_PREV_OUTPOINT, CURRENT_SCRIPT_HASH, CURRENT_SCRIPT_SIG_HASH, CURRENT_SEQUENCE, CURRENT_VALUE, DECOMPRESS, DECREMENT_16, DECREMENT_32, DECREMENT_64, DECREMENT_8, DIV_MOD_128_64, DIV_MOD_16, DIV_MOD_32, DIV_MOD_64, DIV_MOD_8, DIVIDE_16, DIVIDE_32, DIVIDE_64, DIVIDE_8, DIVIDES_16, DIVIDES_32, DIVIDES_64, DIVIDES_8, EQ_1, EQ_16, EQ_256, EQ_32, EQ_64, EQ_8, FE_ADD, FE_INVERT, FE_IS_ODD, FE_IS_ZERO, FE_MULTIPLY, FE_MULTIPLY_BETA, FE_NEGATE, FE_NORMALIZE, FE_SQUARE, FE_SQUARE_ROOT, FEE, FULL_ADD_16, FULL_ADD_32, FULL_ADD_64, FULL_ADD_8, FULL_DECREMENT_16, FULL_DECREMENT_32, FULL_DECREMENT_64, FULL_DECREMENT_8, FULL_INCREMENT_16, FULL_INCREMENT_32, FULL_INCREMENT_64, FULL_INCREMENT_8, FULL_LEFT_SHIFT_16_1, FULL_LEFT_SHIFT_16_2, FULL_LEFT_SHIFT_16_4, FULL_LEFT_SHIFT_16_8, FULL_LEFT_SHIFT_32_1, FULL_LEFT_SHIFT_32_16, FULL_LEFT_SHIFT_32_2, FULL_LEFT_SHIFT_32_4, FULL_LEFT_SHIFT_32_8, FULL_LEFT_SHIFT_64_1, FULL_LEFT_SHIFT_64_16, FULL_LEFT_SHIFT_64_2, FULL_LEFT_SHIFT_64_32, FULL_LEFT_SHIFT_64_4, FULL_LEFT_SHIFT_64_8, FULL_LEFT_SHIFT_8_1, FULL_LEFT_SHIFT_8_2, FULL_LEFT_SHIFT_8_4, FULL_MULTIPLY_16, FULL_MULTIPLY_32, FULL_MULTIPLY_64, FULL_MULTIPLY_8, FULL_RIGHT_SHIFT_16_1, FULL_RIGHT_SHIFT_16_2, FULL_RIGHT_SHIFT_16_4, FULL_RIGHT_SHIFT_16_8, FULL_RIGHT_SHIFT_32_1, FULL_RIGHT_SHIFT_32_16, FULL_RIGHT_SHIFT_32_2, FULL_RIGHT_SHIFT_32_4, FULL_RIGHT_SHIFT_32_8, FULL_RIGHT_SHIFT_64_1, FULL_RIGHT_SHIFT_64_16, FULL_RIGHT_SHIFT_64_2, FULL_RIGHT_SHIFT_64_32, FULL_RIGHT_SHIFT_64_4, FULL_RIGHT_SHIFT_64_8, FULL_RIGHT_SHIFT_8_1, FULL_RIGHT_SHIFT_8_2, FULL_RIGHT_SHIFT_8_4, FULL_SUBTRACT_16, FULL_SUBTRACT_32, FULL_SUBTRACT_64, FULL_SUBTRACT_8, GE_IS_ON_CURVE, GE_NEGATE, GEJ_ADD, GEJ_DOUBLE, GEJ_EQUIV, GEJ_GE_ADD, GEJ_GE_ADD_EX, GEJ_GE_EQUIV, GEJ_INFINITY, GEJ_IS_INFINITY, GEJ_IS_ON_CURVE, GEJ_NEGATE, GEJ_NORMALIZE, GEJ_RESCALE, GEJ_X_EQUIV, GEJ_Y_IS_ODD, GENERATE, HASH_TO_CURVE, HIGH_1, HIGH_16, HIGH_32, HIGH_64, HIGH_8, INCREMENT_16, INCREMENT_32, INCREMENT_64, INCREMENT_8, INPUT_ANNEX_HASH, INPUT_ANNEXES_HASH, INPUT_HASH, INPUT_OUTPOINTS_HASH, INPUT_PREV_OUTPOINT, INPUT_SCRIPT_HASH, INPUT_SCRIPT_SIG_HASH, INPUT_SCRIPT_SIGS_HASH, INPUT_SCRIPTS_HASH, INPUT_SEQUENCE, INPUT_SEQUENCES_HASH, INPUT_UTXO_HASH, INPUT_UTXOS_HASH, INPUT_VALUE, INPUT_VALUES_HASH, INPUTS_HASH, INTERNAL_KEY, IS_ONE_16, IS_ONE_32, IS_ONE_64, IS_ONE_8, IS_ZERO_16, IS_ZERO_32, IS_ZERO_64, IS_ZERO_8, LE_16, LE_32, LE_64, LE_8, LEFT_EXTEND_16_32, LEFT_EXTEND_16_64, LEFT_EXTEND_1_16, LEFT_EXTEND_1_32, LEFT_EXTEND_1_64, LEFT_EXTEND_1_8, LEFT_EXTEND_32_64, LEFT_EXTEND_8_16, LEFT_EXTEND_8_32, LEFT_EXTEND_8_64, LEFT_PAD_HIGH_16_32, LEFT_PAD_HIGH_16_64, LEFT_PAD_HIGH_1_16, LEFT_PAD_HIGH_1_32, LEFT_PAD_HIGH_1_64, LEFT_PAD_HIGH_1_8, LEFT_PAD_HIGH_32_64, LEFT_PAD_HIGH_8_16, LEFT_PAD_HIGH_8_32, LEFT_PAD_HIGH_8_64, LEFT_PAD_LOW_16_32, LEFT_PAD_LOW_16_64, LEFT_PAD_LOW_1_16, LEFT_PAD_LOW_1_32, LEFT_PAD_LOW_1_64, LEFT_PAD_LOW_1_8, LEFT_PAD_LOW_32_64, LEFT_PAD_LOW_8_16, LEFT_PAD_LOW_8_32, LEFT_PAD_LOW_8_64, LEFT_ROTATE_16, LEFT_ROTATE_32, LEFT_ROTATE_64, LEFT_ROTATE_8, LEFT_SHIFT_16, LEFT_SHIFT_32, LEFT_SHIFT_64, LEFT_SHIFT_8, LEFT_SHIFT_WITH_16, LEFT_SHIFT_WITH_32, LEFT_SHIFT_WITH_64, LEFT_SHIFT_WITH_8, LEFTMOST_16_1, LEFTMOST_16_2, LEFTMOST_16_4, LEFTMOST_16_8, LEFTMOST_32_1, LEFTMOST_32_16, LEFTMOST_32_2, LEFTMOST_32_4, LEFTMOST_32_8, LEFTMOST_64_1, LEFTMOST_64_16, LEFTMOST_64_2, LEFTMOST_64_32, LEFTMOST_64_4, LEFTMOST_64_8, LEFTMOST_8_1, LEFTMOST_8_2, LEFTMOST_8_4, LINEAR_COMBINATION_1, LINEAR_VERIFY_1, LOCK_TIME, LOW_1, LOW_16, LOW_32, LOW_64, LOW_8, LT_16, LT_32, LT_64, LT_8, MAJ_1, MAJ_16, MAJ_32, MAJ_64, MAJ_8, MAX_16, MAX_32, MAX_64, MAX_8, MEDIAN_16, MEDIAN_32, MEDIAN_64, MEDIAN_8, MIN_16, MIN_32, MIN_64, MIN_8, MODULO_16, MODULO_32, MODULO_64, MODULO_8, MULTIPLY_16, MULTIPLY_32, MULTIPLY_64, MULTIPLY_8, NEGATE_16, NEGATE_32, NEGATE_64, NEGATE_8, NUM_INPUTS, NUM_OUTPUTS, ONE_16, ONE_32, ONE_64, ONE_8, OR_1, OR_16, OR_32, OR_64, OR_8, OUTPOINT_HASH, OUTPUT_HASH, OUTPUT_SCRIPT_HASH, OUTPUT_SCRIPTS_HASH, OUTPUT_VALUE, OUTPUT_VALUES_HASH, OUTPUTS_HASH, PARSE_LOCK, PARSE_SEQUENCE, POINT_VERIFY_1, RIGHT_EXTEND_16_32, RIGHT_EXTEND_16_64, RIGHT_EXTEND_32_64, RIGHT_EXTEND_8_16, RIGHT_EXTEND_8_32, RIGHT_EXTEND_8_64, RIGHT_PAD_HIGH_16_32, RIGHT_PAD_HIGH_16_64, RIGHT_PAD_HIGH_1_16, RIGHT_PAD_HIGH_1_32, RIGHT_PAD_HIGH_1_64, RIGHT_PAD_HIGH_1_8, RIGHT_PAD_HIGH_32_64, RIGHT_PAD_HIGH_8_16, RIGHT_PAD_HIGH_8_32, RIGHT_PAD_HIGH_8_64, RIGHT_PAD_LOW_16_32, RIGHT_PAD_LOW_16_64, RIGHT_PAD_LOW_1_16, RIGHT_PAD_LOW_1_32, RIGHT_PAD_LOW_1_64, RIGHT_PAD_LOW_1_8, RIGHT_PAD_LOW_32_64, RIGHT_PAD_LOW_8_16, RIGHT_PAD_LOW_8_32, RIGHT_PAD_LOW_8_64, RIGHT_ROTATE_16, RIGHT_ROTATE_32, RIGHT_ROTATE_64, RIGHT_ROTATE_8, RIGHT_SHIFT_16, RIGHT_SHIFT_32, RIGHT_SHIFT_64, RIGHT_SHIFT_8, RIGHT_SHIFT_WITH_16, RIGHT_SHIFT_WITH_32, RIGHT_SHIFT_WITH_64, RIGHT_SHIFT_WITH_8, RIGHTMOST_16_1, RIGHTMOST_16_2, RIGHTMOST_16_4, RIGHTMOST_16_8, RIGHTMOST_32_1, RIGHTMOST_32_16, RIGHTMOST_32_2, RIGHTMOST_32_4, RIGHTMOST_32_8, RIGHTMOST_64_1, RIGHTMOST_64_16, RIGHTMOST_64_2, RIGHTMOST_64_32, RIGHTMOST_64_4, RIGHTMOST_64_8, RIGHTMOST_8_1, RIGHTMOST_8_2, RIGHTMOST_8_4, SCALAR_ADD, SCALAR_INVERT, SCALAR_IS_ZERO, SCALAR_MULTIPLY, SCALAR_MULTIPLY_LAMBDA, SCALAR_NEGATE, SCALAR_NORMALIZE, SCALAR_SQUARE, SCALE, SCRIPT_CMR, SHA_256_BLOCK, SHA_256_CTX_8_ADD_1, SHA_256_CTX_8_ADD_128, SHA_256_CTX_8_ADD_16, SHA_256_CTX_8_ADD_2, SHA_256_CTX_8_ADD_256, SHA_256_CTX_8_ADD_32, SHA_256_CTX_8_ADD_4, SHA_256_CTX_8_ADD_512, SHA_256_CTX_8_ADD_64, SHA_256_CTX_8_ADD_8, SHA_256_CTX_8_ADD_BUFFER_511, SHA_256_CTX_8_FINALIZE, SHA_256_CTX_8_INIT, SHA_256_IV, SIG_ALL_HASH, SOME_1, SOME_16, SOME_32, SOME_64, SOME_8, SUBTRACT_16, SUBTRACT_32, SUBTRACT_64, SUBTRACT_8, SWU, TAP_ENV_HASH, TAPDATA_INIT, TAPLEAF_HASH, TAPLEAF_VERSION, TAPPATH, TAPPATH_HASH, TOTAL_INPUT_VALUE, TOTAL_OUTPUT_VALUE, TRANSACTION_ID, TX_HASH, TX_IS_FINAL, TX_LOCK_DISTANCE, TX_LOCK_DURATION, TX_LOCK_HEIGHT, TX_LOCK_TIME, VERIFY, VERSION, XOR_1, XOR_16, XOR_32, XOR_64, XOR_8, XOR_XOR_1, XOR_XOR_16, XOR_XOR_32, XOR_XOR_64, XOR_XOR_8, ================================================ FILE: C/bitcoin/primitiveEnumTy.inc ================================================ /* This file has been automatically generated. */ ty_u = 0, ty_b = 1, ty_w2 = 2, ty_w4 = 3, ty_w8 = 4, ty_w16 = 5, ty_w32 = 6, ty_w64 = 7, ty_w128 = 8, ty_w256 = 9, ty_w512 = 10, ty_w1Ki = 11, ty_w2Ki = 12, ty_w4Ki = 13, ty_w8Ki = 14, ty_w16Ki = 15, ty_w32Ki = 16, ty_w64Ki = 17, ty_w128Ki = 18, ty_w256Ki = 19, ty_w512Ki = 20, ty_w1Mi = 21, ty_w2Mi = 22, ty_w4Mi = 23, ty_w8Mi = 24, ty_w16Mi = 25, ty_w32Mi = 26, ty_w64Mi = 27, ty_w128Mi = 28, ty_w256Mi = 29, ty_w512Mi = 30, ty_w1Gi = 31, ty_w2Gi = 32, ty_mw8, ty_mw16, ty_mw32, ty_mw64, ty_mw128, ty_mw256, ty_mw512, ty_mw1Ki, ty_mw2Ki, ty_mmw256, ty_msw16w16, ty_mpw256w32, ty_sw16w16, ty_sw32w32, ty_pbw2, ty_pbw8, ty_pbw16, ty_pbw32, ty_pbw64, ty_pbw128, ty_pbw256, ty_pbpw4w8, ty_pbpw4w16, ty_pbpw8w32, ty_pbpw8w64, ty_pw2w8, ty_pw2w16, ty_pw2w32, ty_pw2w64, ty_pw4w8, ty_pw4w16, ty_pw4w32, ty_pw4w64, ty_pw8b, ty_pw8w2, ty_pw8w4, ty_pw8w16, ty_pw8w32, ty_pw8w64, ty_pw16b, ty_pw16w2, ty_pw16w4, ty_pw16w8, ty_pw16w32, ty_pw16w64, ty_pw32b, ty_pw32w2, ty_pw32w4, ty_pw32w8, ty_pw32w16, ty_pw32w64, ty_pw64b, ty_pw64w2, ty_pw64w4, ty_pw64w8, ty_pw64w16, ty_pw64w32, ty_pw64w128, ty_pw64w256, ty_pw128w64, ty_pw256w32, ty_pw256w512, ty_pw256pbw256, ty_pw256pw512w256, ty_pw512w256, ty_pmw16mw8, ty_pmw32pmw16mw8, ty_pmw64pmw32pmw16mw8, ty_pmw128pmw64pmw32pmw16mw8, ty_pmw256pmw128pmw64pmw32pmw16mw8, ty_pmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_pmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_ppw256w512w256, ty_ppw256w512w512, ty_ppw256pbw256w256, ty_ppw256pw512w256w256, ty_ppw512w256w256, ty_ppw512w256w512, ty_ppw512w256pw512w256, ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256, ty_pppw256w512w256w512, ty_pppw256pbw256w256pbw256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w8, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w16, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w32, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w64, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w128, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w512, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w1Ki, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w2Ki, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w4Ki, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mw256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pw256w32, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8, ================================================ FILE: C/bitcoin/primitiveInitTy.inc ================================================ /* This file has been automatically generated. */ (*bound_var)[ty_u] = (unification_var){ .isBound = true, .bound = { .kind = ONE }}; (*bound_var)[ty_b] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_u] } }}; (*bound_var)[ty_w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_w128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_w1Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_w2Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w1Ki], &(*bound_var)[ty_w1Ki] } }}; (*bound_var)[ty_w4Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2Ki], &(*bound_var)[ty_w2Ki] } }}; (*bound_var)[ty_w8Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4Ki], &(*bound_var)[ty_w4Ki] } }}; (*bound_var)[ty_w16Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8Ki], &(*bound_var)[ty_w8Ki] } }}; (*bound_var)[ty_w32Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16Ki], &(*bound_var)[ty_w16Ki] } }}; (*bound_var)[ty_w64Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32Ki], &(*bound_var)[ty_w32Ki] } }}; (*bound_var)[ty_w128Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64Ki], &(*bound_var)[ty_w64Ki] } }}; (*bound_var)[ty_w256Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128Ki], &(*bound_var)[ty_w128Ki] } }}; (*bound_var)[ty_w512Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256Ki], &(*bound_var)[ty_w256Ki] } }}; (*bound_var)[ty_w1Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512Ki], &(*bound_var)[ty_w512Ki] } }}; (*bound_var)[ty_w2Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w1Mi], &(*bound_var)[ty_w1Mi] } }}; (*bound_var)[ty_w4Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2Mi], &(*bound_var)[ty_w2Mi] } }}; (*bound_var)[ty_w8Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4Mi], &(*bound_var)[ty_w4Mi] } }}; (*bound_var)[ty_w16Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8Mi], &(*bound_var)[ty_w8Mi] } }}; (*bound_var)[ty_w32Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16Mi], &(*bound_var)[ty_w16Mi] } }}; (*bound_var)[ty_w64Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32Mi], &(*bound_var)[ty_w32Mi] } }}; (*bound_var)[ty_w128Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64Mi], &(*bound_var)[ty_w64Mi] } }}; (*bound_var)[ty_w256Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128Mi], &(*bound_var)[ty_w128Mi] } }}; (*bound_var)[ty_w512Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256Mi], &(*bound_var)[ty_w256Mi] } }}; (*bound_var)[ty_w1Gi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512Mi], &(*bound_var)[ty_w512Mi] } }}; (*bound_var)[ty_w2Gi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w1Gi], &(*bound_var)[ty_w1Gi] } }}; (*bound_var)[ty_mw8] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_mw16] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_mw32] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_mw64] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_mw128] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_mw256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_mw512] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_mw1Ki] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w1Ki] } }}; (*bound_var)[ty_mw2Ki] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w2Ki] } }}; (*bound_var)[ty_mmw256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_mw256] } }}; (*bound_var)[ty_msw16w16] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_sw16w16] } }}; (*bound_var)[ty_mpw256w32] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_pw256w32] } }}; (*bound_var)[ty_sw16w16] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_sw32w32] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pbw2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pbw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pbw16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pbw32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pbw64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pbw128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_pbw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pbpw4w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw4w8] } }}; (*bound_var)[ty_pbpw4w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw4w16] } }}; (*bound_var)[ty_pbpw8w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw8w32] } }}; (*bound_var)[ty_pbpw8w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw8w64] } }}; (*bound_var)[ty_pw2w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw2w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw2w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw2w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw4w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw4w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw4w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw4w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw8b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw8w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw8w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw8w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw8w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw8w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw16b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw16w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw16w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw16w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw16w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw16w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw32b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw32w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw32w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw32w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw32w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw32w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw64b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw64w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw64w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw64w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw64w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw64w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw64w128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_pw64w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pw128w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_pw256pbw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_pbw256] } }}; (*bound_var)[ty_pw256pw512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_pw512w256] } }}; (*bound_var)[ty_pw512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw16], &(*bound_var)[ty_mw8] } }}; (*bound_var)[ty_pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw32], &(*bound_var)[ty_pmw16mw8] } }}; (*bound_var)[ty_pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw64], &(*bound_var)[ty_pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw128], &(*bound_var)[ty_pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw256], &(*bound_var)[ty_pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw512], &(*bound_var)[ty_pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw1Ki], &(*bound_var)[ty_pmw512pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw2Ki], &(*bound_var)[ty_pmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_ppw256w512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256w512], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw256w512w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256w512], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_ppw256pbw256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256pbw256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw256pw512w256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256pw512w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw512w256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw512w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw512w256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw512w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_ppw512w256pw512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw512w256], &(*bound_var)[ty_pw512w256] } }}; (*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pmw256pmw128pmw64pmw32pmw16mw8], &(*bound_var)[ty_pw64w256] } }}; (*bound_var)[ty_pppw256w512w256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppw256w512w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_pppw256pbw256w256pbw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppw256pbw256w256], &(*bound_var)[ty_pbw256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w1Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w1Ki] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w2Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w2Ki] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w4Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w4Ki] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_mw256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pw256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_pw256w32] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] } }}; ================================================ FILE: C/bitcoin/primitiveJetNode.inc ================================================ /* This file has been automatically generated. */ [ADD_16] = { .tag = JET , .jet = simplicity_add_16 , .cmr = {{0x49425a86u, 0xe20a676du, 0x8b87e3c1u, 0xa9b8ea6eu, 0xc75d859cu, 0x12c51bcbu, 0x7fa9f969u, 0x12c349cfu}} , .sourceIx = ty_w32 , .targetIx = ty_pbw16 , .cost = 80 /* milli weight units */ } ,[ADD_32] = { .tag = JET , .jet = simplicity_add_32 , .cmr = {{0x4668cd55u, 0xe8d15919u, 0x53327014u, 0xec64c8e7u, 0xd52b86b5u, 0x3e11c014u, 0x57eaf2c3u, 0xd3cebf9fu}} , .sourceIx = ty_w64 , .targetIx = ty_pbw32 , .cost = 92 /* milli weight units */ } ,[ADD_64] = { .tag = JET , .jet = simplicity_add_64 , .cmr = {{0xbe2b7519u, 0x303a67eeu, 0xa6b48295u, 0x0eda8343u, 0x5e1de855u, 0x9c394a23u, 0x6222ff5bu, 0xf089d346u}} , .sourceIx = ty_w128 , .targetIx = ty_pbw64 , .cost = 105 /* milli weight units */ } ,[ADD_8] = { .tag = JET , .jet = simplicity_add_8 , .cmr = {{0xdfa179adu, 0xf4550b28u, 0x4873bf30u, 0x123e0d4eu, 0x54069b08u, 0x5834ce56u, 0x5815ef7eu, 0x45784acbu}} , .sourceIx = ty_w16 , .targetIx = ty_pbw8 , .cost = 97 /* milli weight units */ } ,[ALL_16] = { .tag = JET , .jet = simplicity_all_16 , .cmr = {{0x24f482a5u, 0x13d33362u, 0x015d28dfu, 0x4bb6c3eeu, 0x08ab8afbu, 0xbd25571fu, 0x0ea89d8cu, 0xaba31404u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 60 /* milli weight units */ } ,[ALL_32] = { .tag = JET , .jet = simplicity_all_32 , .cmr = {{0xa716522du, 0x0f3787c8u, 0xb4d50764u, 0x7f1f807bu, 0x67f320d6u, 0xeb67b84bu, 0x609cec1du, 0x2f12218au}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 62 /* milli weight units */ } ,[ALL_64] = { .tag = JET , .jet = simplicity_all_64 , .cmr = {{0x7aeefe2eu, 0xce24bab3u, 0x7c6e5430u, 0xeed419fcu, 0xd5f03791u, 0x2d1770cbu, 0x7d6520dcu, 0xe525291au}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 63 /* milli weight units */ } ,[ALL_8] = { .tag = JET , .jet = simplicity_all_8 , .cmr = {{0x4637f40eu, 0x5f4726b0u, 0x0570765au, 0xc794e29eu, 0xd1bb2655u, 0xffc412b2u, 0xdc41258eu, 0x41aac624u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 50 /* milli weight units */ } ,[AND_1] = { .tag = JET , .jet = simplicity_and_1 , .cmr = {{0x10684d0du, 0xd72cb0a8u, 0x26a86383u, 0x4e011f50u, 0xfa0d558bu, 0xa77d6b9fu, 0x49a1ac22u, 0x902a6ad0u}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 77 /* milli weight units */ } ,[AND_16] = { .tag = JET , .jet = simplicity_and_16 , .cmr = {{0x373c730fu, 0xad3e8847u, 0x991aa417u, 0xd9f080eeu, 0x1cb88a7fu, 0x7206f3fau, 0x840b1950u, 0x7761fb23u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 83 /* milli weight units */ } ,[AND_32] = { .tag = JET , .jet = simplicity_and_32 , .cmr = {{0x13b02c4cu, 0x60ae6ea4u, 0x91161649u, 0xacf9a47au, 0x7025af84u, 0x7d5f581eu, 0x6f1cccfbu, 0x21d3001du}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 77 /* milli weight units */ } ,[AND_64] = { .tag = JET , .jet = simplicity_and_64 , .cmr = {{0x92185535u, 0xd4505407u, 0xdea3c8a6u, 0x0826ede6u, 0x4a8fbb3du, 0xb486d56fu, 0x642d217cu, 0x29cbd795u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 78 /* milli weight units */ } ,[AND_8] = { .tag = JET , .jet = simplicity_and_8 , .cmr = {{0x269a1b44u, 0x6266f8f4u, 0xa4a38fa7u, 0xe7e39182u, 0xf1521436u, 0x142badedu, 0xf3aa63fbu, 0x2f172d2fu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 98 /* milli weight units */ } ,[ANNEX_HASH] = { .tag = JET , .jet = simplicity_bitcoin_annex_hash , .cmr = {{0x51fa1913u, 0xa6297348u, 0x4a700af3u, 0xff932694u, 0xd3890ae0u, 0xad87a455u, 0xdaf4906fu, 0x224a48d5u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mw256 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1491 /* milli weight units */ } ,[BIP_0340_VERIFY] = { .tag = JET , .jet = simplicity_bip_0340_verify , .cmr = {{0x491565feu, 0x23a7bdc1u, 0x842be749u, 0x509337f9u, 0x6890d5b3u, 0x58b36520u, 0x90da5566u, 0x54e29549u}} , .sourceIx = ty_w1Ki , .targetIx = ty_u , .cost = 49421 /* milli weight units */ } ,[BUILD_TAPBRANCH] = { .tag = JET , .jet = simplicity_bitcoin_build_tapbranch , .cmr = {{0xef8e9291u, 0x9b2608eau, 0x6b5bcdd3u, 0x9c5178e5u, 0x46249553u, 0x914b0f8du, 0x33735d28u, 0x86e1a5e8u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 2554 /* milli weight units */ } ,[BUILD_TAPLEAF_SIMPLICITY] = { .tag = JET , .jet = simplicity_bitcoin_build_tapleaf_simplicity , .cmr = {{0x22411909u, 0x984147deu, 0x8f5a0428u, 0x358b4716u, 0xdb087664u, 0xa7285608u, 0x52b0e616u, 0xebc62d30u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 1927 /* milli weight units */ } ,[BUILD_TAPTWEAK] = { .tag = JET , .jet = simplicity_bitcoin_build_taptweak , .cmr = {{0xf192db17u, 0x06608defu, 0x165dbddau, 0x72a38c88u, 0x82cb36c6u, 0xda47070du, 0x8a5f5896u, 0xfbda8434u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 77780 /* milli weight units */ } ,[CH_1] = { .tag = JET , .jet = simplicity_ch_1 , .cmr = {{0x73b2a981u, 0xd721986fu, 0x8cded697u, 0xe06305d4u, 0x5854102du, 0xff20c0e5u, 0xb98ae176u, 0x232ff25bu}} , .sourceIx = ty_pbw2 , .targetIx = ty_b , .cost = 50 /* milli weight units */ } ,[CH_16] = { .tag = JET , .jet = simplicity_ch_16 , .cmr = {{0x78de465eu, 0x61d9a50fu, 0x78252ff4u, 0xab23c9e6u, 0x3ae68c76u, 0x9d366612u, 0x71207dc6u, 0x93f469b4u}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 83 /* milli weight units */ } ,[CH_32] = { .tag = JET , .jet = simplicity_ch_32 , .cmr = {{0xed93bef1u, 0xf66e3a75u, 0xe6120602u, 0xecee6740u, 0x653e7bd4u, 0x6e07eb77u, 0x144ef1bbu, 0x2c9de53du}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 69 /* milli weight units */ } ,[CH_64] = { .tag = JET , .jet = simplicity_ch_64 , .cmr = {{0xced0079bu, 0x0bd1cc00u, 0x209a7cbcu, 0x23f13dfdu, 0x202808f0u, 0xf5257d8au, 0x50ac543eu, 0x64ee3a05u}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 78 /* milli weight units */ } ,[CH_8] = { .tag = JET , .jet = simplicity_ch_8 , .cmr = {{0xc707ca72u, 0x3e24f6b2u, 0x5bf394a9u, 0x9a4d75e8u, 0x1379b467u, 0x8438ac78u, 0x9dee188eu, 0xdcce75fau}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 86 /* milli weight units */ } ,[CHECK_LOCK_DISTANCE] = { .tag = JET , .jet = simplicity_bitcoin_check_lock_distance , .cmr = {{0x38fdf7ddu, 0x28538670u, 0xfb34c1bfu, 0xe72f17e2u, 0xca5784f8u, 0x7fed88eau, 0xb584792bu, 0x3974bd18u}} , .sourceIx = ty_w16 , .targetIx = ty_u , .cost = 84 /* milli weight units */ } ,[CHECK_LOCK_DURATION] = { .tag = JET , .jet = simplicity_bitcoin_check_lock_duration , .cmr = {{0x77503832u, 0x6eae25c7u, 0x209b2443u, 0x06eaa9f9u, 0x204c7eceu, 0x2dd63b45u, 0x2e10017fu, 0xa4ea53cfu}} , .sourceIx = ty_w16 , .targetIx = ty_u , .cost = 78 /* milli weight units */ } ,[CHECK_LOCK_HEIGHT] = { .tag = JET , .jet = simplicity_bitcoin_check_lock_height , .cmr = {{0xb90f151fu, 0x45b4eb37u, 0x210621f9u, 0x700a36c8u, 0xc504bee0u, 0x67771163u, 0xa8b83a77u, 0x18e6686au}} , .sourceIx = ty_w32 , .targetIx = ty_u , .cost = 108 /* milli weight units */ } ,[CHECK_LOCK_TIME] = { .tag = JET , .jet = simplicity_bitcoin_check_lock_time , .cmr = {{0xa451ebb2u, 0x25d6b133u, 0xa5e63539u, 0x7800d487u, 0xb3968b0du, 0xe55c96ebu, 0x82f290ecu, 0xff9c2590u}} , .sourceIx = ty_w32 , .targetIx = ty_u , .cost = 123 /* milli weight units */ } ,[CHECK_SIG_VERIFY] = { .tag = JET , .jet = simplicity_check_sig_verify , .cmr = {{0xb5801554u, 0x6d285266u, 0x5dd21bf1u, 0x12662670u, 0x20fa5e27u, 0x5001dd46u, 0x18fa4156u, 0x25952e68u}} , .sourceIx = ty_ppw256w512w512 , .targetIx = ty_u , .cost = 50000 /* milli weight units */ } ,[COMPLEMENT_1] = { .tag = JET , .jet = simplicity_complement_1 , .cmr = {{0x1bcfae13u, 0xd5d237a0u, 0xbb9b1d75u, 0x32047462u, 0xb27690deu, 0x5cac0e20u, 0x19298964u, 0x57934060u}} , .sourceIx = ty_b , .targetIx = ty_b , .cost = 51 /* milli weight units */ } ,[COMPLEMENT_16] = { .tag = JET , .jet = simplicity_complement_16 , .cmr = {{0x81ad4d2cu, 0x3d16bf34u, 0x0af3886du, 0x355cc5bdu, 0x1d5967e1u, 0x6ace924fu, 0x19ecf7d4u, 0x86d6c7e9u}} , .sourceIx = ty_w16 , .targetIx = ty_w16 , .cost = 86 /* milli weight units */ } ,[COMPLEMENT_32] = { .tag = JET , .jet = simplicity_complement_32 , .cmr = {{0x13742c18u, 0x04a96e6cu, 0x039528bfu, 0xd03b8cf2u, 0xb462526bu, 0xb181a3d8u, 0xb432f99au, 0xc4f5a7efu}} , .sourceIx = ty_w32 , .targetIx = ty_w32 , .cost = 58 /* milli weight units */ } ,[COMPLEMENT_64] = { .tag = JET , .jet = simplicity_complement_64 , .cmr = {{0x65b7bd09u, 0x3639c56du, 0xa285cefau, 0x2d046464u, 0x5e14dd13u, 0x642f3495u, 0x7d4737bdu, 0x52fac588u}} , .sourceIx = ty_w64 , .targetIx = ty_w64 , .cost = 64 /* milli weight units */ } ,[COMPLEMENT_8] = { .tag = JET , .jet = simplicity_complement_8 , .cmr = {{0x954b70dcu, 0xec539e6bu, 0x67dffec5u, 0x3cf24a66u, 0x9939608bu, 0x223f5f8bu, 0x6d129daau, 0x48ca1cf0u}} , .sourceIx = ty_w8 , .targetIx = ty_w8 , .cost = 62 /* milli weight units */ } ,[CURRENT_ANNEX_HASH] = { .tag = JET , .jet = simplicity_bitcoin_current_annex_hash , .cmr = {{0xced9022eu, 0xdc69241fu, 0xe70749a7u, 0xf5d489c3u, 0x135ee8c9u, 0x6fe64c44u, 0x64401f98u, 0x51d7a17du}} , .sourceIx = ty_u , .targetIx = ty_mw256 , .cost = 74 /* milli weight units */ } ,[CURRENT_INDEX] = { .tag = JET , .jet = simplicity_bitcoin_current_index , .cmr = {{0x0e8c964cu, 0x2f2b3490u, 0x362f3bbcu, 0x7483dea3u, 0x7fda810bu, 0x69314ff6u, 0x64fea0e3u, 0x2708ec8fu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 66 /* milli weight units */ } ,[CURRENT_PREV_OUTPOINT] = { .tag = JET , .jet = simplicity_bitcoin_current_prev_outpoint , .cmr = {{0x6443391bu, 0x34408684u, 0x6d5a17a6u, 0x2e3e0628u, 0x2ad6962cu, 0x4dfced2fu, 0x6a83d0dfu, 0xbf6a5c54u}} , .sourceIx = ty_u , .targetIx = ty_pw256w32 , .cost = 130 /* milli weight units */ } ,[CURRENT_SCRIPT_HASH] = { .tag = JET , .jet = simplicity_bitcoin_current_script_hash , .cmr = {{0x23498dd6u, 0x645ed138u, 0xb344937cu, 0xf654aaffu, 0xa627f85au, 0x47caa689u, 0x54f13f4cu, 0x6a4dc772u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 127 /* milli weight units */ } ,[CURRENT_SCRIPT_SIG_HASH] = { .tag = JET , .jet = simplicity_bitcoin_current_script_sig_hash , .cmr = {{0x34a3c55du, 0x147374d8u, 0xf3a1761bu, 0xbab28696u, 0x8455404cu, 0x2ca03f69u, 0x393f6339u, 0xd0f58b59u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 126 /* milli weight units */ } ,[CURRENT_SEQUENCE] = { .tag = JET , .jet = simplicity_bitcoin_current_sequence , .cmr = {{0xc49f76acu, 0x79f8f15cu, 0x409ba815u, 0xc16edcb8u, 0xd11e9a07u, 0x565c8e09u, 0xb63e7fdfu, 0x3103009fu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 66 /* milli weight units */ } ,[CURRENT_VALUE] = { .tag = JET , .jet = simplicity_bitcoin_current_value , .cmr = {{0x91b96e82u, 0x9e3b4972u, 0xb0cb091au, 0x0a904ba4u, 0x11338abfu, 0xc08da786u, 0xd5a84f04u, 0x9b5ba3b8u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 85 /* milli weight units */ } ,[DECOMPRESS] = { .tag = JET , .jet = simplicity_decompress , .cmr = {{0x890056dfu, 0x828a766eu, 0xe9f65607u, 0x221e8946u, 0xfa77c256u, 0xbb96e231u, 0xe194d300u, 0x8cf356f6u}} , .sourceIx = ty_pbw256 , .targetIx = ty_mw512 , .cost = 10495 /* milli weight units */ } ,[DECREMENT_16] = { .tag = JET , .jet = simplicity_decrement_16 , .cmr = {{0x35fda38bu, 0x672c3831u, 0xd8ca11a4u, 0xf3a95962u, 0x22529eb1u, 0xc15f8c70u, 0x5013977du, 0x7dfb5d8bu}} , .sourceIx = ty_w16 , .targetIx = ty_pbw16 , .cost = 58 /* milli weight units */ } ,[DECREMENT_32] = { .tag = JET , .jet = simplicity_decrement_32 , .cmr = {{0x3b2b1939u, 0x552284f6u, 0x14694ba1u, 0x8dce70ceu, 0xe476ff42u, 0xdcd089e1u, 0xa3c0a42bu, 0xebd108f6u}} , .sourceIx = ty_w32 , .targetIx = ty_pbw32 , .cost = 57 /* milli weight units */ } ,[DECREMENT_64] = { .tag = JET , .jet = simplicity_decrement_64 , .cmr = {{0x7ef7bdd3u, 0x5db685aeu, 0x99055337u, 0x35a2c7a7u, 0xccbc1708u, 0xae636f93u, 0x1b5ce026u, 0xe5a17fedu}} , .sourceIx = ty_w64 , .targetIx = ty_pbw64 , .cost = 79 /* milli weight units */ } ,[DECREMENT_8] = { .tag = JET , .jet = simplicity_decrement_8 , .cmr = {{0xe364f2e5u, 0xc08ae011u, 0x8ebe993eu, 0x8b3c958cu, 0x2bcc6062u, 0xa33baab9u, 0x28c04b3eu, 0xc932f51bu}} , .sourceIx = ty_w8 , .targetIx = ty_pbw8 , .cost = 77 /* milli weight units */ } ,[DIV_MOD_128_64] = { .tag = JET , .jet = simplicity_div_mod_128_64 , .cmr = {{0x9a9443a2u, 0xb541e29fu, 0x272ffd56u, 0x7d1bf742u, 0xd68ccbe9u, 0x538a8729u, 0x1b0ca638u, 0x1563ac2cu}} , .sourceIx = ty_pw128w64 , .targetIx = ty_w128 , .cost = 169 /* milli weight units */ } ,[DIV_MOD_16] = { .tag = JET , .jet = simplicity_div_mod_16 , .cmr = {{0x39bcb5c0u, 0x1dc1805cu, 0x4919895cu, 0xb59e8f3bu, 0x41446717u, 0xf7ff48fdu, 0xc937dd03u, 0x8024a08au}} , .sourceIx = ty_w32 , .targetIx = ty_w32 , .cost = 92 /* milli weight units */ } ,[DIV_MOD_32] = { .tag = JET , .jet = simplicity_div_mod_32 , .cmr = {{0xfb1202f4u, 0xe8663a87u, 0xf568992au, 0x185024c7u, 0x0b4f079fu, 0xbe953001u, 0x0f6db284u, 0x218af6cdu}} , .sourceIx = ty_w64 , .targetIx = ty_w64 , .cost = 90 /* milli weight units */ } ,[DIV_MOD_64] = { .tag = JET , .jet = simplicity_div_mod_64 , .cmr = {{0x6764df5eu, 0x2aa03032u, 0x6ee544c6u, 0xe53ff38eu, 0xf0b28517u, 0x915eec65u, 0xc72ea57au, 0x129828ebu}} , .sourceIx = ty_w128 , .targetIx = ty_w128 , .cost = 82 /* milli weight units */ } ,[DIV_MOD_8] = { .tag = JET , .jet = simplicity_div_mod_8 , .cmr = {{0xd300244eu, 0x480dd974u, 0x1213e4cbu, 0x0eba836du, 0x3059e778u, 0xb8122f78u, 0x90032673u, 0x739c6a2cu}} , .sourceIx = ty_w16 , .targetIx = ty_w16 , .cost = 91 /* milli weight units */ } ,[DIVIDE_16] = { .tag = JET , .jet = simplicity_divide_16 , .cmr = {{0x52abfef1u, 0x79754c90u, 0xf9a4260fu, 0x323a8ca4u, 0x95159290u, 0x2b8ecbd6u, 0x4ba42656u, 0xfac05968u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 85 /* milli weight units */ } ,[DIVIDE_32] = { .tag = JET , .jet = simplicity_divide_32 , .cmr = {{0x4a8ae535u, 0x44e147edu, 0x02250423u, 0x7934cc25u, 0x4479bcf9u, 0x3de1e197u, 0x4ddab3bbu, 0x516e606cu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 82 /* milli weight units */ } ,[DIVIDE_64] = { .tag = JET , .jet = simplicity_divide_64 , .cmr = {{0xd7025d05u, 0xadfae66bu, 0x4710d0ffu, 0x1e87e828u, 0x15573e9cu, 0xb631b4c7u, 0xd13d2f1bu, 0xe4dd26d2u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 81 /* milli weight units */ } ,[DIVIDE_8] = { .tag = JET , .jet = simplicity_divide_8 , .cmr = {{0x40cd1dacu, 0xea24669bu, 0x6a589b61u, 0x475474afu, 0x31d14f8du, 0x46877084u, 0x52d3df37u, 0x30253126u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 85 /* milli weight units */ } ,[DIVIDES_16] = { .tag = JET , .jet = simplicity_divides_16 , .cmr = {{0x10bb1818u, 0x0eab5badu, 0xdc165d03u, 0x37c4ada0u, 0x88e157b1u, 0xaa678334u, 0x2a4520a3u, 0x24dd9d2bu}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 84 /* milli weight units */ } ,[DIVIDES_32] = { .tag = JET , .jet = simplicity_divides_32 , .cmr = {{0xf5e8e78cu, 0x82769a48u, 0xc9103e44u, 0xddb47f84u, 0x1d7693b0u, 0x419e5e7du, 0xa4e68b78u, 0xb237a572u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 80 /* milli weight units */ } ,[DIVIDES_64] = { .tag = JET , .jet = simplicity_divides_64 , .cmr = {{0x9ebd55fau, 0xe418885eu, 0xea04c3cdu, 0xfff531b7u, 0xd714d059u, 0x4fa7da87u, 0xeb6555d3u, 0x6b953db2u}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 67 /* milli weight units */ } ,[DIVIDES_8] = { .tag = JET , .jet = simplicity_divides_8 , .cmr = {{0xa236bc3eu, 0x5cf4d256u, 0x408ba38cu, 0x1eaee736u, 0x9a9c402fu, 0x74bcd1c8u, 0x02f9094fu, 0xbf36803du}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 73 /* milli weight units */ } ,[EQ_1] = { .tag = JET , .jet = simplicity_eq_1 , .cmr = {{0x6549f986u, 0x203a6497u, 0x356e432bu, 0x2aa160d6u, 0xee870b11u, 0x190865bdu, 0x36a47cb0u, 0x470433a5u}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 63 /* milli weight units */ } ,[EQ_16] = { .tag = JET , .jet = simplicity_eq_16 , .cmr = {{0x0c5402b0u, 0xadc8fc65u, 0x701bb75bu, 0x3254c835u, 0xf8fec130u, 0x81cd35e1u, 0x328f2bd7u, 0xdbd23fa6u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 68 /* milli weight units */ } ,[EQ_256] = { .tag = JET , .jet = simplicity_eq_256 , .cmr = {{0x260e1d13u, 0x6dd744fcu, 0xb0507a2du, 0x277027a7u, 0x724354ebu, 0x176b2fbfu, 0x31c6c7d7u, 0xfb3ecd6fu}} , .sourceIx = ty_w512 , .targetIx = ty_b , .cost = 188 /* milli weight units */ } ,[EQ_32] = { .tag = JET , .jet = simplicity_eq_32 , .cmr = {{0xf5d6edc8u, 0xb6164e12u, 0x5bbbef08u, 0xc9e08a1eu, 0x6fd492f5u, 0xbdca6fdcu, 0x8b5f5a6fu, 0x05c5ab96u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 74 /* milli weight units */ } ,[EQ_64] = { .tag = JET , .jet = simplicity_eq_64 , .cmr = {{0x1f93acb8u, 0x092fa06du, 0xeaf3c387u, 0xf54a18ffu, 0xeaa69a47u, 0xa6f5caf4u, 0xae497e5cu, 0xc2b36c43u}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 82 /* milli weight units */ } ,[EQ_8] = { .tag = JET , .jet = simplicity_eq_8 , .cmr = {{0xd752fa7fu, 0x51473014u, 0xebb69e1eu, 0x1d2c86d5u, 0x1148b6bau, 0xa02137a4u, 0x8f62d57eu, 0xaf8df1cdu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 76 /* milli weight units */ } ,[FE_ADD] = { .tag = JET , .jet = simplicity_fe_add , .cmr = {{0xa6c90e02u, 0xfde4ee6eu, 0xef666737u, 0x492e14afu, 0xc8762504u, 0x974af5d5u, 0x472bb943u, 0x3ad2d294u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 777 /* milli weight units */ } ,[FE_INVERT] = { .tag = JET , .jet = simplicity_fe_invert , .cmr = {{0x7c4abaceu, 0x33c72b3bu, 0xe1fd0ee3u, 0x9fc6cb3eu, 0xe5c8f11eu, 0xf21998c0u, 0x602b5215u, 0xaa2a75c2u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 3237 /* milli weight units */ } ,[FE_IS_ODD] = { .tag = JET , .jet = simplicity_fe_is_odd , .cmr = {{0x30f5171fu, 0x58f1089du, 0x5dcfb6e6u, 0x683f5adeu, 0x984c0799u, 0x763ca738u, 0x3f75df1cu, 0xa0813efeu}} , .sourceIx = ty_w256 , .targetIx = ty_b , .cost = 313 /* milli weight units */ } ,[FE_IS_ZERO] = { .tag = JET , .jet = simplicity_fe_is_zero , .cmr = {{0xb0b74d86u, 0x51ff557cu, 0xa96044ddu, 0x97281338u, 0xa8f7d3acu, 0xb3847d03u, 0xacbf3d32u, 0xd96fae55u}} , .sourceIx = ty_w256 , .targetIx = ty_b , .cost = 277 /* milli weight units */ } ,[FE_MULTIPLY] = { .tag = JET , .jet = simplicity_fe_multiply , .cmr = {{0x506b9319u, 0xc17a14a9u, 0x469d4627u, 0x61a3303au, 0xb47ddb3au, 0x3079fba3u, 0x4073aa55u, 0x4216a388u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 813 /* milli weight units */ } ,[FE_MULTIPLY_BETA] = { .tag = JET , .jet = simplicity_fe_multiply_beta , .cmr = {{0x6e180eeau, 0xbe8422b7u, 0x9968e711u, 0xdd00a4b6u, 0x578bb275u, 0xbef47fe5u, 0xff968f14u, 0x72d76f2au}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 607 /* milli weight units */ } ,[FE_NEGATE] = { .tag = JET , .jet = simplicity_fe_negate , .cmr = {{0xd437ea00u, 0x339880b3u, 0x83d85fb2u, 0xaeaf201bu, 0xbe8ffc83u, 0x705062f9u, 0xc968590du, 0x5db337f6u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 541 /* milli weight units */ } ,[FE_NORMALIZE] = { .tag = JET , .jet = simplicity_fe_normalize , .cmr = {{0xec0c3dd9u, 0xc5286364u, 0x78bec0e1u, 0x60e50ad9u, 0xbf452c5bu, 0x6f84e940u, 0xe16584ebu, 0x085ace38u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 656 /* milli weight units */ } ,[FE_SQUARE] = { .tag = JET , .jet = simplicity_fe_square , .cmr = {{0xb904772du, 0x74a185b8u, 0x28eb1547u, 0x28d249c5u, 0x084711e9u, 0xa1832b89u, 0xcaf2af59u, 0xf960e118u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 570 /* milli weight units */ } ,[FE_SQUARE_ROOT] = { .tag = JET , .jet = simplicity_fe_square_root , .cmr = {{0x16fb9aceu, 0xbe8b5b87u, 0xf2ea7db6u, 0xaa3a2af8u, 0x8ca2b58fu, 0x02cdc87eu, 0x7ce6be0cu, 0x1ffce014u}} , .sourceIx = ty_w256 , .targetIx = ty_mw256 , .cost = 10162 /* milli weight units */ } ,[FEE] = { .tag = JET , .jet = simplicity_bitcoin_fee , .cmr = {{0xfb9ca939u, 0x81673d1du, 0x23aed24du, 0x612c1f5du, 0xc7cd49f8u, 0x6d348e67u, 0xa15bc4a7u, 0x130ae185u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 65 /* milli weight units */ } ,[FULL_ADD_16] = { .tag = JET , .jet = simplicity_full_add_16 , .cmr = {{0xc503b078u, 0xdde399c6u, 0x3ac4a232u, 0xbd2a329bu, 0x04308c75u, 0xeaec53a2u, 0xf889b8dfu, 0x0d033472u}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw16 , .cost = 106 /* milli weight units */ } ,[FULL_ADD_32] = { .tag = JET , .jet = simplicity_full_add_32 , .cmr = {{0xa7afd040u, 0xfcb0b2f2u, 0x7190781au, 0xe53a6ccau, 0x00e9fe59u, 0x531115c2u, 0x58ccb69du, 0x3be5a213u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw32 , .cost = 96 /* milli weight units */ } ,[FULL_ADD_64] = { .tag = JET , .jet = simplicity_full_add_64 , .cmr = {{0x80a3ef6cu, 0xdb84ae7cu, 0x8dbcf3a1u, 0x842484c0u, 0x98df6f19u, 0x427a5a4au, 0xdfe76cd5u, 0xff2836cau}} , .sourceIx = ty_pbw128 , .targetIx = ty_pbw64 , .cost = 93 /* milli weight units */ } ,[FULL_ADD_8] = { .tag = JET , .jet = simplicity_full_add_8 , .cmr = {{0x4b9076b8u, 0xc1ad56c9u, 0xdb6bb3bau, 0xf5938954u, 0x46ce61c7u, 0x4f797eb8u, 0xb230d205u, 0x421c9617u}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw8 , .cost = 131 /* milli weight units */ } ,[FULL_DECREMENT_16] = { .tag = JET , .jet = simplicity_full_decrement_16 , .cmr = {{0xfba3c978u, 0x6ea307f6u, 0xd85434fdu, 0xa2562482u, 0x43a00bacu, 0x9a5353b6u, 0x1ed39c60u, 0x55b693b0u}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw16 , .cost = 60 /* milli weight units */ } ,[FULL_DECREMENT_32] = { .tag = JET , .jet = simplicity_full_decrement_32 , .cmr = {{0x623d21d0u, 0x467922c0u, 0x01c56568u, 0x61d0ddb8u, 0x60c0c9a8u, 0x6bd4cfdcu, 0x37a14c14u, 0x06e3446eu}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw32 , .cost = 71 /* milli weight units */ } ,[FULL_DECREMENT_64] = { .tag = JET , .jet = simplicity_full_decrement_64 , .cmr = {{0x148b3ee1u, 0xf749ea0bu, 0xfba763beu, 0xe999a296u, 0x77456eaeu, 0x9ef53ad8u, 0x78f8b614u, 0x94f08f00u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw64 , .cost = 71 /* milli weight units */ } ,[FULL_DECREMENT_8] = { .tag = JET , .jet = simplicity_full_decrement_8 , .cmr = {{0xb41afe97u, 0x4eaa1182u, 0xac461052u, 0x1e282781u, 0x318ce295u, 0xa3f23f0bu, 0x876ae269u, 0x673fb1dfu}} , .sourceIx = ty_pbw8 , .targetIx = ty_pbw8 , .cost = 68 /* milli weight units */ } ,[FULL_INCREMENT_16] = { .tag = JET , .jet = simplicity_full_increment_16 , .cmr = {{0xa68eccdbu, 0x9ead2926u, 0xc3e45b4bu, 0xae431cc4u, 0x66d58b8fu, 0xacc95a1bu, 0x4844b912u, 0xdf5676dfu}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw16 , .cost = 70 /* milli weight units */ } ,[FULL_INCREMENT_32] = { .tag = JET , .jet = simplicity_full_increment_32 , .cmr = {{0xd0eb0e94u, 0xa5c25713u, 0xeb944cadu, 0x4d701c6au, 0x968809bcu, 0x1af903fdu, 0xb11e6fadu, 0x0bb31b10u}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw32 , .cost = 57 /* milli weight units */ } ,[FULL_INCREMENT_64] = { .tag = JET , .jet = simplicity_full_increment_64 , .cmr = {{0xc003d2e9u, 0xb0a510c2u, 0xdd783e7du, 0x64eb87b3u, 0x3855d329u, 0x90dfc286u, 0x266e478du, 0xa4e74791u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw64 , .cost = 68 /* milli weight units */ } ,[FULL_INCREMENT_8] = { .tag = JET , .jet = simplicity_full_increment_8 , .cmr = {{0x0bea2429u, 0x18f2dd17u, 0x64777811u, 0xe4442863u, 0x935225b0u, 0xf8b239c2u, 0x3752f9d8u, 0x5392a139u}} , .sourceIx = ty_pbw8 , .targetIx = ty_pbw8 , .cost = 73 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_1] = { .tag = JET , .jet = simplicity_full_left_shift_16_1 , .cmr = {{0xb366a816u, 0x922fc455u, 0x010fe88au, 0x5f6a5cf2u, 0xcea917e1u, 0x2bd140aeu, 0x6d43b641u, 0xe57f42b3u}} , .sourceIx = ty_pw16b , .targetIx = ty_pbw16 , .cost = 76 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_2] = { .tag = JET , .jet = simplicity_full_left_shift_16_2 , .cmr = {{0x27960d0du, 0xf2fbbc38u, 0x993d86fbu, 0x8f0cd2c3u, 0x434edb11u, 0x048213c1u, 0x411893cau, 0x9933b2eeu}} , .sourceIx = ty_pw16w2 , .targetIx = ty_pw2w16 , .cost = 59 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_4] = { .tag = JET , .jet = simplicity_full_left_shift_16_4 , .cmr = {{0x655137beu, 0xc5c0368fu, 0x29bc992cu, 0x88421a15u, 0x98564039u, 0x7b617fc4u, 0x8d33210fu, 0xc0053ad1u}} , .sourceIx = ty_pw16w4 , .targetIx = ty_pw4w16 , .cost = 68 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_8] = { .tag = JET , .jet = simplicity_full_left_shift_16_8 , .cmr = {{0x168f576au, 0xa56ea47eu, 0x070646e7u, 0x8896beb2u, 0x498b1ae6u, 0xb1ff9c78u, 0x6270e955u, 0x65841929u}} , .sourceIx = ty_pw16w8 , .targetIx = ty_pw8w16 , .cost = 68 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_1] = { .tag = JET , .jet = simplicity_full_left_shift_32_1 , .cmr = {{0xd7cd5224u, 0x49118e81u, 0x00a7662fu, 0x4df039f8u, 0xcaebf433u, 0xeb039edcu, 0x42e88237u, 0x92ccea8au}} , .sourceIx = ty_pw32b , .targetIx = ty_pbw32 , .cost = 58 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_16] = { .tag = JET , .jet = simplicity_full_left_shift_32_16 , .cmr = {{0x8bd80d4du, 0x2f8b2246u, 0xc12315c4u, 0x2841b4e4u, 0x0a71ae76u, 0x966a0895u, 0x4d666b86u, 0x32867437u}} , .sourceIx = ty_pw32w16 , .targetIx = ty_pw16w32 , .cost = 52 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_2] = { .tag = JET , .jet = simplicity_full_left_shift_32_2 , .cmr = {{0x13063d62u, 0x93832931u, 0x1fb7dabbu, 0x15c3fe58u, 0xc2887683u, 0x0097ecc6u, 0xbfdd480bu, 0xe1988146u}} , .sourceIx = ty_pw32w2 , .targetIx = ty_pw2w32 , .cost = 73 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_4] = { .tag = JET , .jet = simplicity_full_left_shift_32_4 , .cmr = {{0x25a1b5ddu, 0xe5db284eu, 0x8a882126u, 0x7c265301u, 0x14bbe671u, 0xcfafb44au, 0x60d75027u, 0x67db782eu}} , .sourceIx = ty_pw32w4 , .targetIx = ty_pw4w32 , .cost = 59 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_8] = { .tag = JET , .jet = simplicity_full_left_shift_32_8 , .cmr = {{0xce5470afu, 0xbfadbfbau, 0x68f9b2d5u, 0xb0645a44u, 0x08be6f85u, 0xa69c7f09u, 0xd0964553u, 0x68048764u}} , .sourceIx = ty_pw32w8 , .targetIx = ty_pw8w32 , .cost = 60 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_1] = { .tag = JET , .jet = simplicity_full_left_shift_64_1 , .cmr = {{0x051f3605u, 0x86c379acu, 0x2ce399cbu, 0xeb687e77u, 0x53b15d73u, 0x03dd316cu, 0xbd123012u, 0x087cc66fu}} , .sourceIx = ty_pw64b , .targetIx = ty_pbw64 , .cost = 74 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_16] = { .tag = JET , .jet = simplicity_full_left_shift_64_16 , .cmr = {{0xb248be4du, 0xfcb88c5du, 0x89b1ca61u, 0x86a041e9u, 0x02b4c8a6u, 0x2bb16e09u, 0xfe15616eu, 0x0e3abd6du}} , .sourceIx = ty_pw64w16 , .targetIx = ty_pw16w64 , .cost = 69 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_2] = { .tag = JET , .jet = simplicity_full_left_shift_64_2 , .cmr = {{0x34bb5162u, 0x6b1d6b89u, 0x7abc155du, 0x034fe066u, 0x3a0ec0fdu, 0x8f640e5fu, 0xe1bf3cb7u, 0x670a2925u}} , .sourceIx = ty_pw64w2 , .targetIx = ty_pw2w64 , .cost = 70 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_32] = { .tag = JET , .jet = simplicity_full_left_shift_64_32 , .cmr = {{0x9dac8cd7u, 0xfd8b4888u, 0x9e55c5aau, 0x12fe97b7u, 0x29febc04u, 0x1a9fff44u, 0xc4d9b6f1u, 0xe07eb442u}} , .sourceIx = ty_pw64w32 , .targetIx = ty_pw32w64 , .cost = 73 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_4] = { .tag = JET , .jet = simplicity_full_left_shift_64_4 , .cmr = {{0x94b73dadu, 0xc3eeeb2eu, 0xe4a4d444u, 0xdd0f72acu, 0x306201f2u, 0xffcf714bu, 0x8ebe7982u, 0x744c0c7eu}} , .sourceIx = ty_pw64w4 , .targetIx = ty_pw4w64 , .cost = 66 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_8] = { .tag = JET , .jet = simplicity_full_left_shift_64_8 , .cmr = {{0x0ef71475u, 0x7ecf11cau, 0x3c73ce25u, 0xef24ee72u, 0x95dd4171u, 0xcc16287fu, 0xe6971bd6u, 0x7b478b46u}} , .sourceIx = ty_pw64w8 , .targetIx = ty_pw8w64 , .cost = 68 /* milli weight units */ } ,[FULL_LEFT_SHIFT_8_1] = { .tag = JET , .jet = simplicity_full_left_shift_8_1 , .cmr = {{0x9bfa48b7u, 0xad510091u, 0xba608544u, 0x62d859efu, 0xd1a2aa18u, 0x731b5f0cu, 0x9e2ba4d8u, 0x9d3aa843u}} , .sourceIx = ty_pw8b , .targetIx = ty_pbw8 , .cost = 60 /* milli weight units */ } ,[FULL_LEFT_SHIFT_8_2] = { .tag = JET , .jet = simplicity_full_left_shift_8_2 , .cmr = {{0x797c2087u, 0x01b2a4e1u, 0x049e83d6u, 0x95f554b9u, 0x84f5db28u, 0x21525558u, 0x7c373421u, 0x51b7241du}} , .sourceIx = ty_pw8w2 , .targetIx = ty_pw2w8 , .cost = 64 /* milli weight units */ } ,[FULL_LEFT_SHIFT_8_4] = { .tag = JET , .jet = simplicity_full_left_shift_8_4 , .cmr = {{0x37bdac91u, 0x538f2219u, 0xcb89df0eu, 0xf9f197cdu, 0x68031f27u, 0x67e894f0u, 0x01c26fffu, 0x5eeb58cdu}} , .sourceIx = ty_pw8w4 , .targetIx = ty_pw4w8 , .cost = 72 /* milli weight units */ } ,[FULL_MULTIPLY_16] = { .tag = JET , .jet = simplicity_full_multiply_16 , .cmr = {{0x09baff92u, 0x1e9f14d1u, 0x208d1dd8u, 0x264cf1f3u, 0xb854c9afu, 0x21f778b2u, 0xb55a8a42u, 0x6dfe8928u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 99 /* milli weight units */ } ,[FULL_MULTIPLY_32] = { .tag = JET , .jet = simplicity_full_multiply_32 , .cmr = {{0x10c4b8c4u, 0xc0acd973u, 0x90f85cb3u, 0xf5ffe36au, 0x292037c1u, 0x90eebab3u, 0xe98934feu, 0x93b2ed90u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 87 /* milli weight units */ } ,[FULL_MULTIPLY_64] = { .tag = JET , .jet = simplicity_full_multiply_64 , .cmr = {{0x2db19dbau, 0x90ef867bu, 0x5a3e914bu, 0x89fda2dau, 0x637ca80cu, 0x4267e198u, 0x1837ee3cu, 0x6fe3daf5u}} , .sourceIx = ty_w256 , .targetIx = ty_w128 , .cost = 103 /* milli weight units */ } ,[FULL_MULTIPLY_8] = { .tag = JET , .jet = simplicity_full_multiply_8 , .cmr = {{0x7f46ee72u, 0x84f39e73u, 0x4275a250u, 0x9a0b737eu, 0xd939115fu, 0x0219a574u, 0xd469cd30u, 0xb819efe3u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 95 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_1] = { .tag = JET , .jet = simplicity_full_right_shift_16_1 , .cmr = {{0x7ebe0c66u, 0xc3c7dc16u, 0xa5469e91u, 0x79098417u, 0xac5f20a3u, 0x9cc41ac3u, 0x82fb1dbdu, 0x98e8e30fu}} , .sourceIx = ty_pbw16 , .targetIx = ty_pw16b , .cost = 55 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_2] = { .tag = JET , .jet = simplicity_full_right_shift_16_2 , .cmr = {{0x8db0c216u, 0x19c62d63u, 0xd4c27bfcu, 0xf647d709u, 0xce37bed0u, 0x5718e93eu, 0x4515e29eu, 0xf3730cf4u}} , .sourceIx = ty_pw2w16 , .targetIx = ty_pw16w2 , .cost = 60 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_4] = { .tag = JET , .jet = simplicity_full_right_shift_16_4 , .cmr = {{0x5c74b132u, 0x06317917u, 0xe070e5fcu, 0x1c82f4c5u, 0xc2fbe9f3u, 0x1b812946u, 0xba230d8cu, 0x94d40616u}} , .sourceIx = ty_pw4w16 , .targetIx = ty_pw16w4 , .cost = 64 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_8] = { .tag = JET , .jet = simplicity_full_right_shift_16_8 , .cmr = {{0x1105818au, 0xc948d7bbu, 0x634707e6u, 0x9dbf1f67u, 0x9058a13du, 0x35fac2a6u, 0x4df97262u, 0xf242b63bu}} , .sourceIx = ty_pw8w16 , .targetIx = ty_pw16w8 , .cost = 55 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_1] = { .tag = JET , .jet = simplicity_full_right_shift_32_1 , .cmr = {{0x9b42c8f3u, 0x3bc5750eu, 0x2a83aadbu, 0xf29cc7fcu, 0xb950fe5au, 0x40aa0ec5u, 0x2452e533u, 0xf825a115u}} , .sourceIx = ty_pbw32 , .targetIx = ty_pw32b , .cost = 49 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_16] = { .tag = JET , .jet = simplicity_full_right_shift_32_16 , .cmr = {{0x0ae5659cu, 0x2fa75794u, 0x78ebd57cu, 0x4c98aee7u, 0x77015645u, 0xb2843181u, 0x64fcbd30u, 0x65fc873cu}} , .sourceIx = ty_pw16w32 , .targetIx = ty_pw32w16 , .cost = 48 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_2] = { .tag = JET , .jet = simplicity_full_right_shift_32_2 , .cmr = {{0x57fb1c03u, 0xc2eb17f6u, 0x23478734u, 0xfd6937f9u, 0xe3ef027cu, 0x1560038fu, 0xa6066905u, 0x1789e368u}} , .sourceIx = ty_pw2w32 , .targetIx = ty_pw32w2 , .cost = 66 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_4] = { .tag = JET , .jet = simplicity_full_right_shift_32_4 , .cmr = {{0x8582cdfau, 0x74ef466bu, 0x8127b197u, 0x88134593u, 0x998e4969u, 0x00b38f0fu, 0x3d375818u, 0xd673451eu}} , .sourceIx = ty_pw4w32 , .targetIx = ty_pw32w4 , .cost = 49 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_8] = { .tag = JET , .jet = simplicity_full_right_shift_32_8 , .cmr = {{0xd905932eu, 0xbfca2a38u, 0x619d807eu, 0x28ff2e0du, 0x3be08a26u, 0x0676d257u, 0xefa040c3u, 0x05aadc33u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_pw32w8 , .cost = 66 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_1] = { .tag = JET , .jet = simplicity_full_right_shift_64_1 , .cmr = {{0x3c15209bu, 0x99d2845eu, 0x225e14e1u, 0xe9e5e6a4u, 0x878bc8ceu, 0xa3f9f36bu, 0x8b535ac6u, 0x83e29d00u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pw64b , .cost = 60 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_16] = { .tag = JET , .jet = simplicity_full_right_shift_64_16 , .cmr = {{0x0285257bu, 0x090d8da1u, 0x28ef64a8u, 0x0c8d16fdu, 0xc3bf5ce5u, 0x0fcd56feu, 0xc5f90255u, 0xd9c8df47u}} , .sourceIx = ty_pw16w64 , .targetIx = ty_pw64w16 , .cost = 73 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_2] = { .tag = JET , .jet = simplicity_full_right_shift_64_2 , .cmr = {{0x7ec2dd65u, 0xc9e013e3u, 0xe4ce90fbu, 0xeb3fb1c7u, 0x8ccc5d2au, 0x7d26d8afu, 0x77f99de8u, 0x4cf72973u}} , .sourceIx = ty_pw2w64 , .targetIx = ty_pw64w2 , .cost = 76 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_32] = { .tag = JET , .jet = simplicity_full_right_shift_64_32 , .cmr = {{0x356f7dd4u, 0x6ba33f84u, 0xb06672fdu, 0xe9a2972eu, 0x80f3ea96u, 0x5ae8bc0bu, 0xff67aa2fu, 0x69f10b56u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_pw64w32 , .cost = 73 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_4] = { .tag = JET , .jet = simplicity_full_right_shift_64_4 , .cmr = {{0x05464a33u, 0x35afbb09u, 0xd046828au, 0x922c4da0u, 0xeceeb109u, 0x77e46801u, 0xc93cdd66u, 0x8f22ee63u}} , .sourceIx = ty_pw4w64 , .targetIx = ty_pw64w4 , .cost = 56 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_8] = { .tag = JET , .jet = simplicity_full_right_shift_64_8 , .cmr = {{0x70172e1au, 0x6948bf40u, 0x120e68fbu, 0x8b4b23bcu, 0x355a1200u, 0x2ccc1db6u, 0x47c89b12u, 0xd10ec506u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_pw64w8 , .cost = 68 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_8_1] = { .tag = JET , .jet = simplicity_full_right_shift_8_1 , .cmr = {{0x5669dbfcu, 0xc633ec0bu, 0xdf59e22fu, 0x03ed4b64u, 0x192095f5u, 0xdf20ffc1u, 0x2dd90d7cu, 0xda11374fu}} , .sourceIx = ty_pbw8 , .targetIx = ty_pw8b , .cost = 59 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_8_2] = { .tag = JET , .jet = simplicity_full_right_shift_8_2 , .cmr = {{0x1f944361u, 0x09df52b3u, 0x45fa3a89u, 0xac2a49edu, 0xc9d285f2u, 0x1f45ed11u, 0xd775f7f7u, 0xf39d3e8fu}} , .sourceIx = ty_pw2w8 , .targetIx = ty_pw8w2 , .cost = 49 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_8_4] = { .tag = JET , .jet = simplicity_full_right_shift_8_4 , .cmr = {{0x714698a2u, 0x7684b5bau, 0xa6b6480eu, 0xe3b257cbu, 0xb7cdab74u, 0x72f371a6u, 0x270618c0u, 0xab12908bu}} , .sourceIx = ty_pw4w8 , .targetIx = ty_pw8w4 , .cost = 51 /* milli weight units */ } ,[FULL_SUBTRACT_16] = { .tag = JET , .jet = simplicity_full_subtract_16 , .cmr = {{0x40096152u, 0xb54e7425u, 0x4555a65du, 0xccc629dfu, 0x57b979c8u, 0x47005450u, 0x36fe190au, 0x6af3d38au}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw16 , .cost = 99 /* milli weight units */ } ,[FULL_SUBTRACT_32] = { .tag = JET , .jet = simplicity_full_subtract_32 , .cmr = {{0xe7930d64u, 0x35a9680bu, 0xefb49db7u, 0xd87c2f50u, 0xafd46d98u, 0x880ded50u, 0xe5055fa3u, 0x09e1afcau}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw32 , .cost = 92 /* milli weight units */ } ,[FULL_SUBTRACT_64] = { .tag = JET , .jet = simplicity_full_subtract_64 , .cmr = {{0xff281df8u, 0xc42a3159u, 0xd9ffa925u, 0x16ca893eu, 0x23b0eb93u, 0x8b4cb0b3u, 0xf134468eu, 0x9f4ebc46u}} , .sourceIx = ty_pbw128 , .targetIx = ty_pbw64 , .cost = 109 /* milli weight units */ } ,[FULL_SUBTRACT_8] = { .tag = JET , .jet = simplicity_full_subtract_8 , .cmr = {{0x7e3dcfe4u, 0x56ae3c5cu, 0x87debf04u, 0x7189c274u, 0x82a4ff4eu, 0x8cfd1f17u, 0x30c87d2bu, 0x7bff73bau}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw8 , .cost = 106 /* milli weight units */ } ,[GE_IS_ON_CURVE] = { .tag = JET , .jet = simplicity_ge_is_on_curve , .cmr = {{0x7d448719u, 0xf5f9572bu, 0xf5402e12u, 0xd193aff6u, 0x77482d66u, 0xff3dcf27u, 0x48f25c6bu, 0x7377028cu}} , .sourceIx = ty_w512 , .targetIx = ty_b , .cost = 688 /* milli weight units */ } ,[GE_NEGATE] = { .tag = JET , .jet = simplicity_ge_negate , .cmr = {{0x3d2c8de4u, 0xc7015fd3u, 0x132695fdu, 0x66dfcf0fu, 0x1778c791u, 0x85268e9fu, 0xae7789dau, 0x538eca59u}} , .sourceIx = ty_w512 , .targetIx = ty_w512 , .cost = 1071 /* milli weight units */ } ,[GEJ_ADD] = { .tag = JET , .jet = simplicity_gej_add , .cmr = {{0x45ba7f3du, 0x1e1e6d34u, 0x9fcf8698u, 0x7b0e7f7au, 0xce662e82u, 0x201d3502u, 0x60454e2fu, 0xfeecb54du}} , .sourceIx = ty_ppw512w256pw512w256 , .targetIx = ty_pw512w256 , .cost = 3000 /* milli weight units */ } ,[GEJ_DOUBLE] = { .tag = JET , .jet = simplicity_gej_double , .cmr = {{0x23e978f3u, 0x4154119bu, 0xdefc5d13u, 0xfcfd0a34u, 0xa75e3726u, 0xd6cb2581u, 0x3370ad7du, 0x9de5e133u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_pw512w256 , .cost = 1862 /* milli weight units */ } ,[GEJ_EQUIV] = { .tag = JET , .jet = simplicity_gej_equiv , .cmr = {{0xb94b2aacu, 0x73a67f44u, 0x95859913u, 0x4de23017u, 0x9e9d6bb6u, 0x47fd0611u, 0x158aaba7u, 0x0b73e400u}} , .sourceIx = ty_ppw512w256pw512w256 , .targetIx = ty_b , .cost = 2376 /* milli weight units */ } ,[GEJ_GE_ADD] = { .tag = JET , .jet = simplicity_gej_ge_add , .cmr = {{0xf1160b6fu, 0x5ee2c582u, 0xe49566e6u, 0xc386b380u, 0x94abc1a7u, 0x182d33a1u, 0x501fa2aau, 0xf00af3eau}} , .sourceIx = ty_ppw512w256w512 , .targetIx = ty_pw512w256 , .cost = 2609 /* milli weight units */ } ,[GEJ_GE_ADD_EX] = { .tag = JET , .jet = simplicity_gej_ge_add_ex , .cmr = {{0xc3d7347fu, 0xfe2d9c83u, 0x9aac567eu, 0x2998e016u, 0xaf394e2au, 0x1929314bu, 0x52e31eedu, 0x678e30bfu}} , .sourceIx = ty_ppw512w256w512 , .targetIx = ty_pw256pw512w256 , .cost = 2860 /* milli weight units */ } ,[GEJ_GE_EQUIV] = { .tag = JET , .jet = simplicity_gej_ge_equiv , .cmr = {{0x27c29969u, 0x139f8d57u, 0xedc9895cu, 0x30403df0u, 0x15c50ce7u, 0x21c381fbu, 0x197c0c04u, 0x03f1db0cu}} , .sourceIx = ty_ppw512w256w512 , .targetIx = ty_b , .cost = 1823 /* milli weight units */ } ,[GEJ_INFINITY] = { .tag = JET , .jet = simplicity_gej_infinity , .cmr = {{0xaafb9380u, 0xd61a7f14u, 0x7846806bu, 0x2cc374fbu, 0xe82dd1aeu, 0xd485b98au, 0x0f164b3au, 0x54c2c0b0u}} , .sourceIx = ty_u , .targetIx = ty_pw512w256 , .cost = 765 /* milli weight units */ } ,[GEJ_IS_INFINITY] = { .tag = JET , .jet = simplicity_gej_is_infinity , .cmr = {{0xdb495fd1u, 0x3142e9b3u, 0x3763fc6du, 0x48d2fb0eu, 0x71b0d9d9u, 0x9bd726f4u, 0x7ad13fc5u, 0x560670a2u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_b , .cost = 701 /* milli weight units */ } ,[GEJ_IS_ON_CURVE] = { .tag = JET , .jet = simplicity_gej_is_on_curve , .cmr = {{0xbf4ca13fu, 0xf212e34bu, 0xf17d90c1u, 0x2e453d08u, 0xac7daa4au, 0x47d57e85u, 0xb43f2d43u, 0x66d43ddau}} , .sourceIx = ty_pw512w256 , .targetIx = ty_b , .cost = 1039 /* milli weight units */ } ,[GEJ_NEGATE] = { .tag = JET , .jet = simplicity_gej_negate , .cmr = {{0x01bd1a35u, 0x1fb8164cu, 0x813d916du, 0x07774999u, 0x6b7db118u, 0xd31586cau, 0x9d75e756u, 0x3518f454u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_pw512w256 , .cost = 1549 /* milli weight units */ } ,[GEJ_NORMALIZE] = { .tag = JET , .jet = simplicity_gej_normalize , .cmr = {{0xec597d17u, 0xe2efb6d2u, 0xa002d50eu, 0x677527d3u, 0xd4a2907au, 0x119d68f1u, 0x2284b9a1u, 0xb0d2303au}} , .sourceIx = ty_pw512w256 , .targetIx = ty_mw512 , .cost = 4184 /* milli weight units */ } ,[GEJ_RESCALE] = { .tag = JET , .jet = simplicity_gej_rescale , .cmr = {{0x2977d953u, 0xef7a1156u, 0xcec6db2du, 0xc2925412u, 0x75cbc82fu, 0xb829fd67u, 0x1b972e89u, 0xebed0c24u}} , .sourceIx = ty_ppw512w256w256 , .targetIx = ty_pw512w256 , .cost = 2011 /* milli weight units */ } ,[GEJ_X_EQUIV] = { .tag = JET , .jet = simplicity_gej_x_equiv , .cmr = {{0xf9f189fcu, 0x00b61f72u, 0xf10baaa2u, 0x1bcd88e5u, 0xd22e0aa9u, 0xb7509ae1u, 0x62a183a4u, 0xb664a4afu}} , .sourceIx = ty_pw256pw512w256 , .targetIx = ty_b , .cost = 1103 /* milli weight units */ } ,[GEJ_Y_IS_ODD] = { .tag = JET , .jet = simplicity_gej_y_is_odd , .cmr = {{0x9eb6e453u, 0x5fb69bf6u, 0x09916599u, 0xf1345ad7u, 0x735da3f3u, 0x948d0686u, 0x908e44f4u, 0x5b2ff60cu}} , .sourceIx = ty_pw512w256 , .targetIx = ty_b , .cost = 3702 /* milli weight units */ } ,[GENERATE] = { .tag = JET , .jet = simplicity_generate , .cmr = {{0x148885acu, 0x73813113u, 0xc523e809u, 0xbea47ffdu, 0x8b1daf37u, 0x8d9dd54bu, 0xf966ccb8u, 0x83b1a984u}} , .sourceIx = ty_w256 , .targetIx = ty_pw512w256 , .cost = 49851 /* milli weight units */ } ,[HASH_TO_CURVE] = { .tag = JET , .jet = simplicity_hash_to_curve , .cmr = {{0xef4f548bu, 0x3c6c7517u, 0x5f2ce2d1u, 0x993b2d19u, 0x9beb16c0u, 0xa140175cu, 0x48a1277eu, 0xfc43a99bu}} , .sourceIx = ty_w256 , .targetIx = ty_w512 , .cost = 69844 /* milli weight units */ } ,[HIGH_1] = { .tag = JET , .jet = simplicity_high_1 , .cmr = {{0xb109cf1cu, 0xce35f7e9u, 0xb649671au, 0x9b45dbc2u, 0x4099a713u, 0xaeb9a89cu, 0xc4cf6ef6u, 0xed8b308bu}} , .sourceIx = ty_u , .targetIx = ty_b , .cost = 42 /* milli weight units */ } ,[HIGH_16] = { .tag = JET , .jet = simplicity_high_16 , .cmr = {{0x035dadd9u, 0xd7bf7433u, 0x6445e71du, 0xdc4d8202u, 0x24ff7e38u, 0xe0b8d52bu, 0xec9729b5u, 0x72b531f9u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 50 /* milli weight units */ } ,[HIGH_32] = { .tag = JET , .jet = simplicity_high_32 , .cmr = {{0xc5f1df0du, 0x64a2737au, 0x631b3aaeu, 0x8f260e8bu, 0x8dc1957bu, 0xd092911bu, 0x91d2078au, 0xd21e418au}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 64 /* milli weight units */ } ,[HIGH_64] = { .tag = JET , .jet = simplicity_high_64 , .cmr = {{0xa312633eu, 0x0a2305e6u, 0x9b3f341du, 0x91d683ddu, 0x94196a2fu, 0x9005c9b1u, 0x872a2c15u, 0xad46cf17u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 52 /* milli weight units */ } ,[HIGH_8] = { .tag = JET , .jet = simplicity_high_8 , .cmr = {{0xcbd78d50u, 0xaf779985u, 0x5adc4903u, 0xdbbefc13u, 0x45d51484u, 0xf03d3c75u, 0x5caaa5cau, 0xa97d4a14u}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 59 /* milli weight units */ } ,[INCREMENT_16] = { .tag = JET , .jet = simplicity_increment_16 , .cmr = {{0x86774949u, 0x39b27b86u, 0xcb5a8c7fu, 0x8172ad55u, 0x509531c9u, 0xb0e11e99u, 0x757e296cu, 0xc3c7c192u}} , .sourceIx = ty_w16 , .targetIx = ty_pbw16 , .cost = 56 /* milli weight units */ } ,[INCREMENT_32] = { .tag = JET , .jet = simplicity_increment_32 , .cmr = {{0x6bdbab7cu, 0xfc16c503u, 0x363c2f07u, 0x7e02c335u, 0xda406175u, 0xd192fbefu, 0x50c07fc2u, 0x79b3f40cu}} , .sourceIx = ty_w32 , .targetIx = ty_pbw32 , .cost = 73 /* milli weight units */ } ,[INCREMENT_64] = { .tag = JET , .jet = simplicity_increment_64 , .cmr = {{0x20e75e71u, 0x7cb76d46u, 0x95564f7cu, 0x20221b7au, 0x01431387u, 0x38f151aau, 0x195eb170u, 0xec13c049u}} , .sourceIx = ty_w64 , .targetIx = ty_pbw64 , .cost = 64 /* milli weight units */ } ,[INCREMENT_8] = { .tag = JET , .jet = simplicity_increment_8 , .cmr = {{0x5f4e056eu, 0xf4ed8d68u, 0xbf911fc5u, 0xcb69037eu, 0xbf6c9221u, 0x7343a890u, 0x5d38c432u, 0xc183233cu}} , .sourceIx = ty_w8 , .targetIx = ty_pbw8 , .cost = 69 /* milli weight units */ } ,[INPUT_ANNEX_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_annex_hash , .cmr = {{0x945b147eu, 0x5f0edb83u, 0x2d62348cu, 0xaeeac224u, 0x56eee944u, 0x65376dbfu, 0x596b9d62u, 0x985b01b6u}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 77 /* milli weight units */ } ,[INPUT_ANNEXES_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_annexes_hash , .cmr = {{0x89b60270u, 0x44141f20u, 0x65b6f236u, 0xcfcc13b9u, 0x68485e00u, 0x746b7859u, 0x286903c6u, 0x8c7f880du}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 124 /* milli weight units */ } ,[INPUT_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_hash , .cmr = {{0x3ad22231u, 0xd6b9dff6u, 0xa0b4dbcfu, 0xf044e11cu, 0x082e0468u, 0x4e73ce95u, 0xc205e0c4u, 0x496e5ecau}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 832 /* milli weight units */ } ,[INPUT_OUTPOINTS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_outpoints_hash , .cmr = {{0x1759c6f4u, 0x70b9aba6u, 0x2a31791eu, 0xa01056e3u, 0x608bdf22u, 0xf5dd43bfu, 0x7db00ea5u, 0x823f7cceu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 126 /* milli weight units */ } ,[INPUT_PREV_OUTPOINT] = { .tag = JET , .jet = simplicity_bitcoin_input_prev_outpoint , .cmr = {{0x5d171242u, 0x09ee0521u, 0x24e55238u, 0xe0b6a6feu, 0x85a48688u, 0xc1e15e61u, 0x81de94f7u, 0x8db04018u}} , .sourceIx = ty_w32 , .targetIx = ty_mpw256w32 , .cost = 140 /* milli weight units */ } ,[INPUT_SCRIPT_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_script_hash , .cmr = {{0x0562412fu, 0x021da481u, 0x9b019c8cu, 0xd887d530u, 0x492b9f94u, 0x2c4ebf21u, 0xae39ed32u, 0x330d7cfeu}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 143 /* milli weight units */ } ,[INPUT_SCRIPT_SIG_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_script_sig_hash , .cmr = {{0x1c7efb37u, 0xcbc4b996u, 0xd9b8c617u, 0x08e66573u, 0xce87c1f0u, 0xaa0522d0u, 0x65ba9025u, 0x056e3f80u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 137 /* milli weight units */ } ,[INPUT_SCRIPT_SIGS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_script_sigs_hash , .cmr = {{0xe729c5f5u, 0x8a938908u, 0x1a5ca845u, 0xf76cb980u, 0xf08599ceu, 0xb3c7d7eau, 0xe1145b53u, 0xa60ae3d5u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 127 /* milli weight units */ } ,[INPUT_SCRIPTS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_scripts_hash , .cmr = {{0xf177671du, 0x60960e46u, 0x3a9a8f7eu, 0x1f5213aau, 0xba9122d2u, 0xdb75fe91u, 0xf8f1cf91u, 0xbe001907u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 129 /* milli weight units */ } ,[INPUT_SEQUENCE] = { .tag = JET , .jet = simplicity_bitcoin_input_sequence , .cmr = {{0x5dd17fe1u, 0x550f48f7u, 0xbaed4d06u, 0x8008d4a1u, 0xff98cbebu, 0xe2541c5du, 0xc77ac53au, 0xd83fa779u}} , .sourceIx = ty_w32 , .targetIx = ty_mw32 , .cost = 78 /* milli weight units */ } ,[INPUT_SEQUENCES_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_sequences_hash , .cmr = {{0x55973d64u, 0x43457472u, 0x81377364u, 0xbad2a80bu, 0x758f4566u, 0x60c18de5u, 0xc01a3882u, 0x071d50e8u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 125 /* milli weight units */ } ,[INPUT_UTXO_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_utxo_hash , .cmr = {{0x931e4e95u, 0xe0a64760u, 0x276e91b5u, 0xdc746780u, 0xd0697d0au, 0xf5aaf5bbu, 0xc81dbeb3u, 0x98596abbu}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 824 /* milli weight units */ } ,[INPUT_UTXOS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_utxos_hash , .cmr = {{0xd6f90cd1u, 0x04e1a5c6u, 0x1a4b5000u, 0xad9aba8du, 0x43004bf9u, 0x43df325fu, 0xa636d1a2u, 0x2beca0cbu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 122 /* milli weight units */ } ,[INPUT_VALUE] = { .tag = JET , .jet = simplicity_bitcoin_input_value , .cmr = {{0x7d3c3f95u, 0x5b2cf0d0u, 0xd1280a1bu, 0xb1204692u, 0x92d1329cu, 0x83a9c2ffu, 0x7e7e1eb3u, 0xf69783a3u}} , .sourceIx = ty_w32 , .targetIx = ty_mw64 , .cost = 81 /* milli weight units */ } ,[INPUT_VALUES_HASH] = { .tag = JET , .jet = simplicity_bitcoin_input_values_hash , .cmr = {{0x29839eadu, 0x0eb03fe4u, 0x6542e36du, 0x71e9e6afu, 0xdf969301u, 0x533d74eeu, 0x099b1266u, 0xa250552cu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 126 /* milli weight units */ } ,[INPUTS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_inputs_hash , .cmr = {{0xabbfe1c7u, 0xd115c419u, 0x1f504839u, 0xf98c3f20u, 0x422b84e7u, 0xfa14da14u, 0x02896c4du, 0x98bfa8d8u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 122 /* milli weight units */ } ,[INTERNAL_KEY] = { .tag = JET , .jet = simplicity_bitcoin_internal_key , .cmr = {{0x37483699u, 0x2810022fu, 0x88e0145bu, 0xcad77f4au, 0x8491fa80u, 0x83cb51c3u, 0x01fcf7a1u, 0x3478c2ccu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 124 /* milli weight units */ } ,[IS_ONE_16] = { .tag = JET , .jet = simplicity_is_one_16 , .cmr = {{0x1bd3a253u, 0xdb243fcau, 0x45533799u, 0xfe914838u, 0xc38e3806u, 0xb12bd7e8u, 0x5ca71207u, 0xa88462b0u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 64 /* milli weight units */ } ,[IS_ONE_32] = { .tag = JET , .jet = simplicity_is_one_32 , .cmr = {{0x78b1bae0u, 0x99ec9c59u, 0xcbf41262u, 0x51c1e967u, 0x41b350d5u, 0x63bd74d5u, 0x4418ba78u, 0xebea25bfu}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 64 /* milli weight units */ } ,[IS_ONE_64] = { .tag = JET , .jet = simplicity_is_one_64 , .cmr = {{0x817b95a5u, 0x395efbecu, 0xbb8515a5u, 0x5b3ffe1au, 0x4d7bac6eu, 0x23dbca54u, 0xad606666u, 0x2f202b93u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 66 /* milli weight units */ } ,[IS_ONE_8] = { .tag = JET , .jet = simplicity_is_one_8 , .cmr = {{0xf6925491u, 0xd34b3774u, 0x2cb08decu, 0x193ee512u, 0x5f933cadu, 0xcc232aedu, 0xeedb572du, 0x1260ffd5u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 47 /* milli weight units */ } ,[IS_ZERO_16] = { .tag = JET , .jet = simplicity_is_zero_16 , .cmr = {{0x1ba7213bu, 0x588be092u, 0xb446599cu, 0x2a60ff54u, 0x67136a79u, 0x7599610bu, 0xd7a5f178u, 0x04e32a2cu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 52 /* milli weight units */ } ,[IS_ZERO_32] = { .tag = JET , .jet = simplicity_is_zero_32 , .cmr = {{0x5ebf1466u, 0x93f0e2d2u, 0xf9361b47u, 0x6dba3485u, 0x8b832d66u, 0xfacf713bu, 0xfb32c3bbu, 0x8db9eebfu}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 58 /* milli weight units */ } ,[IS_ZERO_64] = { .tag = JET , .jet = simplicity_is_zero_64 , .cmr = {{0x19ab9ac0u, 0xcf426682u, 0x19ba6cb8u, 0x97e487feu, 0x3680937fu, 0xffa8d203u, 0x511db75du, 0xbb10c7e5u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 68 /* milli weight units */ } ,[IS_ZERO_8] = { .tag = JET , .jet = simplicity_is_zero_8 , .cmr = {{0x8eff6208u, 0x4407e9afu, 0xd540f318u, 0xf66bcf31u, 0xdf1d42a5u, 0xc161cae3u, 0x5a294818u, 0x0ca2aa2eu}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 59 /* milli weight units */ } ,[LE_16] = { .tag = JET , .jet = simplicity_le_16 , .cmr = {{0x016705a7u, 0xd7dce1afu, 0xc63eab84u, 0x203f5f42u, 0xd6b6bbadu, 0x75cee38cu, 0xec5a515bu, 0x5997489fu}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 83 /* milli weight units */ } ,[LE_32] = { .tag = JET , .jet = simplicity_le_32 , .cmr = {{0x5351fc5du, 0xebe5b298u, 0xad7057e4u, 0xa5a76a3bu, 0x9c658acdu, 0xe7d1bb52u, 0xe5889ca1u, 0xe38f5efbu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 99 /* milli weight units */ } ,[LE_64] = { .tag = JET , .jet = simplicity_le_64 , .cmr = {{0xae2de1e0u, 0xcf730d1du, 0xcc96d7ccu, 0xfe71168au, 0x240deaf8u, 0x04615a7bu, 0xa920dc16u, 0xfd6ea45fu}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 79 /* milli weight units */ } ,[LE_8] = { .tag = JET , .jet = simplicity_le_8 , .cmr = {{0xaf29f616u, 0x8ebdc09eu, 0xfbe0e639u, 0xcb750b12u, 0x05788f90u, 0x21d666efu, 0xcefe13f1u, 0x2f9671f0u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 93 /* milli weight units */ } ,[LEFT_EXTEND_16_32] = { .tag = JET , .jet = simplicity_left_extend_16_32 , .cmr = {{0x289997fbu, 0xa1fae7ecu, 0x1c4531c5u, 0x0bbf8671u, 0xb897139bu, 0xdd3aad97u, 0xa3763957u, 0x4a047c80u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 72 /* milli weight units */ } ,[LEFT_EXTEND_16_64] = { .tag = JET , .jet = simplicity_left_extend_16_64 , .cmr = {{0x5dff21f6u, 0xe6124775u, 0xc578eaf4u, 0x855c0b01u, 0x64f7879bu, 0x1760f902u, 0x7cb50f7bu, 0x5acb4918u}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 69 /* milli weight units */ } ,[LEFT_EXTEND_1_16] = { .tag = JET , .jet = simplicity_left_extend_1_16 , .cmr = {{0x8c87d756u, 0xd14bd3d9u, 0xa7869081u, 0x2912b894u, 0x29c0171au, 0x41103a58u, 0xc6e9f225u, 0x141a0222u}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 50 /* milli weight units */ } ,[LEFT_EXTEND_1_32] = { .tag = JET , .jet = simplicity_left_extend_1_32 , .cmr = {{0xc8f154d4u, 0x6d2e7895u, 0xda1b33c2u, 0xb315e6d4u, 0xd4851ddeu, 0xe28aef8bu, 0x70709061u, 0x6bc7eea0u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 48 /* milli weight units */ } ,[LEFT_EXTEND_1_64] = { .tag = JET , .jet = simplicity_left_extend_1_64 , .cmr = {{0xa3404df6u, 0x8cc92075u, 0x4c6e1847u, 0x207db384u, 0x5d11c749u, 0x09d07ca8u, 0x2ad1f1ccu, 0x67bf3a9bu}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 49 /* milli weight units */ } ,[LEFT_EXTEND_1_8] = { .tag = JET , .jet = simplicity_left_extend_1_8 , .cmr = {{0x3bca3397u, 0xb83c27f3u, 0x6316f8b8u, 0xb303350au, 0xfe8ba007u, 0x8f77f1d4u, 0x2a9b7892u, 0xb2a4dbeeu}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 46 /* milli weight units */ } ,[LEFT_EXTEND_32_64] = { .tag = JET , .jet = simplicity_left_extend_32_64 , .cmr = {{0x42cbeb01u, 0xfe7a3a6du, 0xd3311db3u, 0x365f91e5u, 0xc118c7e4u, 0x1f03aae7u, 0xb283de6bu, 0xb9053e6bu}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 69 /* milli weight units */ } ,[LEFT_EXTEND_8_16] = { .tag = JET , .jet = simplicity_left_extend_8_16 , .cmr = {{0x9a57c96au, 0xf5714896u, 0xb724de45u, 0xeb9fe97du, 0x73697de6u, 0x2e8dad78u, 0x71eb58f5u, 0x81a011bbu}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 58 /* milli weight units */ } ,[LEFT_EXTEND_8_32] = { .tag = JET , .jet = simplicity_left_extend_8_32 , .cmr = {{0xd624bd40u, 0x40763cb1u, 0x3ccad498u, 0xf53d38c1u, 0x12f19295u, 0x6826dafeu, 0xc9ac9165u, 0x792b347au}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 86 /* milli weight units */ } ,[LEFT_EXTEND_8_64] = { .tag = JET , .jet = simplicity_left_extend_8_64 , .cmr = {{0x9dc4a205u, 0x4d5d2634u, 0x2ac590b6u, 0x67f1b01du, 0xf54fd0cdu, 0xaa405ef8u, 0xcbb76fd8u, 0xf9b00ee5u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 98 /* milli weight units */ } ,[LEFT_PAD_HIGH_16_32] = { .tag = JET , .jet = simplicity_left_pad_high_16_32 , .cmr = {{0x0545c4b5u, 0x8f004a21u, 0xe7f129a4u, 0xc0518997u, 0x1714caa2u, 0xd91d1dfdu, 0x5fad3e63u, 0x24499428u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 71 /* milli weight units */ } ,[LEFT_PAD_HIGH_16_64] = { .tag = JET , .jet = simplicity_left_pad_high_16_64 , .cmr = {{0x1c61d03du, 0x493bbd05u, 0x822259d1u, 0x730a8d7au, 0x5f55b0bau, 0x2a9391a6u, 0xc8881eb4u, 0x7504affdu}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 82 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_16] = { .tag = JET , .jet = simplicity_left_pad_high_1_16 , .cmr = {{0x56fdf54fu, 0x1fcd1982u, 0x5e7c3b79u, 0x0615c1d3u, 0xfe82886cu, 0x747bc487u, 0x5987f505u, 0x16945fb3u}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 106 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_32] = { .tag = JET , .jet = simplicity_left_pad_high_1_32 , .cmr = {{0xdb33059au, 0xbe2d432du, 0x67f42b1eu, 0x942756dcu, 0xa6cde637u, 0x85e5bd43u, 0x0dc8f4aeu, 0xfc31b8dfu}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 220 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_64] = { .tag = JET , .jet = simplicity_left_pad_high_1_64 , .cmr = {{0x1d669c1fu, 0xa5fd3ef6u, 0x6eb4aef6u, 0x186e3ec1u, 0x36ee7584u, 0x10df3edeu, 0xbb31bf26u, 0xd4562051u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 302 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_8] = { .tag = JET , .jet = simplicity_left_pad_high_1_8 , .cmr = {{0x9a1bad3du, 0x8ab90030u, 0x3da202f0u, 0xf449f0b7u, 0xe6795c2au, 0x7c121718u, 0x800ac40cu, 0x87d82729u}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 73 /* milli weight units */ } ,[LEFT_PAD_HIGH_32_64] = { .tag = JET , .jet = simplicity_left_pad_high_32_64 , .cmr = {{0x3920cc4bu, 0x33baf7efu, 0xa5caf9e7u, 0x80014467u, 0x06f6e4e8u, 0x26567405u, 0x7eed8717u, 0x78089e94u}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 69 /* milli weight units */ } ,[LEFT_PAD_HIGH_8_16] = { .tag = JET , .jet = simplicity_left_pad_high_8_16 , .cmr = {{0x752e29f2u, 0xfe2becc3u, 0xf66290feu, 0x44e1aeb3u, 0x784180ddu, 0x905e1962u, 0x4e195f21u, 0x6c07c57cu}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 65 /* milli weight units */ } ,[LEFT_PAD_HIGH_8_32] = { .tag = JET , .jet = simplicity_left_pad_high_8_32 , .cmr = {{0xbee88f1cu, 0x8c30634cu, 0x6e95caccu, 0x0e9add49u, 0x413221fdu, 0xabbd8d4cu, 0x0accf1cau, 0xe2d2a778u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 105 /* milli weight units */ } ,[LEFT_PAD_HIGH_8_64] = { .tag = JET , .jet = simplicity_left_pad_high_8_64 , .cmr = {{0x392387f6u, 0xdc04bfc5u, 0x4dd4a281u, 0x19c81d15u, 0xd7a5809bu, 0xbf62fcc2u, 0x7dc55cf8u, 0x2e9e5ee6u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 113 /* milli weight units */ } ,[LEFT_PAD_LOW_16_32] = { .tag = JET , .jet = simplicity_left_pad_low_16_32 , .cmr = {{0x4ffd6cb3u, 0x40230582u, 0x1dd89970u, 0xd722d1c1u, 0x3f1ff773u, 0x9fd5f34bu, 0xa16c7365u, 0x3b044718u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 65 /* milli weight units */ } ,[LEFT_PAD_LOW_16_64] = { .tag = JET , .jet = simplicity_left_pad_low_16_64 , .cmr = {{0xbe3eb85cu, 0x5f199153u, 0xfb1c4613u, 0x5c04facfu, 0xdbc6f1b7u, 0x8c2bb7aeu, 0x75f155bcu, 0x3ea08a8bu}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 68 /* milli weight units */ } ,[LEFT_PAD_LOW_1_16] = { .tag = JET , .jet = simplicity_left_pad_low_1_16 , .cmr = {{0xddd0153eu, 0xf312f28du, 0x642cd94cu, 0xb36f3297u, 0x75b00da8u, 0x8fccc4ceu, 0xa1bae89bu, 0xad13be6bu}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 59 /* milli weight units */ } ,[LEFT_PAD_LOW_1_32] = { .tag = JET , .jet = simplicity_left_pad_low_1_32 , .cmr = {{0xbc9d3114u, 0x35467bc0u, 0x8b1008e5u, 0x47aa7a07u, 0xe83b1514u, 0x6861a9e9u, 0xb5413be3u, 0x1b82b6b5u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 47 /* milli weight units */ } ,[LEFT_PAD_LOW_1_64] = { .tag = JET , .jet = simplicity_left_pad_low_1_64 , .cmr = {{0x8bc62f93u, 0x60894e48u, 0xa4732c95u, 0x769c8faau, 0xe9568f9du, 0xe8e8a200u, 0x836bd4e5u, 0x0b02cd84u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 46 /* milli weight units */ } ,[LEFT_PAD_LOW_1_8] = { .tag = JET , .jet = simplicity_left_pad_low_1_8 , .cmr = {{0xf66cd7a4u, 0x2b320f97u, 0xc19f2d54u, 0x16cde087u, 0x253a2791u, 0x2965d55bu, 0x65712ad8u, 0x09b83cfdu}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 48 /* milli weight units */ } ,[LEFT_PAD_LOW_32_64] = { .tag = JET , .jet = simplicity_left_pad_low_32_64 , .cmr = {{0xa33a07b9u, 0xbcf945f6u, 0x4f072b8bu, 0x9c914839u, 0xa585bfa9u, 0xf3425b14u, 0x7754ab55u, 0xa8ba6c0fu}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 62 /* milli weight units */ } ,[LEFT_PAD_LOW_8_16] = { .tag = JET , .jet = simplicity_left_pad_low_8_16 , .cmr = {{0x2a516a79u, 0x3f97c45fu, 0xeaebb1ccu, 0x961a156du, 0x80354928u, 0x79789d6eu, 0xdc9b57e7u, 0x2f11e5b5u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 56 /* milli weight units */ } ,[LEFT_PAD_LOW_8_32] = { .tag = JET , .jet = simplicity_left_pad_low_8_32 , .cmr = {{0x1aa2e4d0u, 0x4bd69055u, 0x123dd6aau, 0xfe27f5f7u, 0xf47c3b30u, 0x90c3a827u, 0x2973fe2fu, 0x75165a5du}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 75 /* milli weight units */ } ,[LEFT_PAD_LOW_8_64] = { .tag = JET , .jet = simplicity_left_pad_low_8_64 , .cmr = {{0xb652e0aeu, 0xdd0f4f66u, 0xf6a1cd4bu, 0xebf875ffu, 0x7bbb2dd9u, 0x9b065b2du, 0xb5b5b590u, 0x5361614du}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 116 /* milli weight units */ } ,[LEFT_ROTATE_16] = { .tag = JET , .jet = simplicity_left_rotate_16 , .cmr = {{0x8a12ff6au, 0x4bf23715u, 0xdd3b766bu, 0x9967c715u, 0x8bf3ed74u, 0xb3dce730u, 0xaffcf466u, 0x16478ecbu}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 88 /* milli weight units */ } ,[LEFT_ROTATE_32] = { .tag = JET , .jet = simplicity_left_rotate_32 , .cmr = {{0x2fcb5217u, 0x2fd49c36u, 0x217deae0u, 0xc2371432u, 0x1f69f5f1u, 0x3f6e94b2u, 0xbdfe4b74u, 0x88697fd5u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 62 /* milli weight units */ } ,[LEFT_ROTATE_64] = { .tag = JET , .jet = simplicity_left_rotate_64 , .cmr = {{0x72ccd6c4u, 0xe5fdf68au, 0xd33b6d58u, 0xfb372be4u, 0xf1b80eefu, 0x701f9db7u, 0xe5ed859bu, 0x96b36209u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 68 /* milli weight units */ } ,[LEFT_ROTATE_8] = { .tag = JET , .jet = simplicity_left_rotate_8 , .cmr = {{0x1aaec9f3u, 0xb75d89f8u, 0x2a649845u, 0x8c4483cbu, 0x9a784489u, 0x05f3bb39u, 0xfc083f14u, 0xddccdc9bu}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 66 /* milli weight units */ } ,[LEFT_SHIFT_16] = { .tag = JET , .jet = simplicity_left_shift_16 , .cmr = {{0x37ac6387u, 0x21ab097au, 0x9602ba4du, 0xc92e19b5u, 0xa185b232u, 0x9f1aa600u, 0xcb9c1561u, 0x5a0081f8u}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 109 /* milli weight units */ } ,[LEFT_SHIFT_32] = { .tag = JET , .jet = simplicity_left_shift_32 , .cmr = {{0x8e3c473bu, 0x2867f154u, 0x73b3632du, 0xbfdd9977u, 0x5551ef5fu, 0x9dba475eu, 0x9cf09075u, 0x8070f0bfu}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 79 /* milli weight units */ } ,[LEFT_SHIFT_64] = { .tag = JET , .jet = simplicity_left_shift_64 , .cmr = {{0x5049f404u, 0xd173299au, 0x3aee04cbu, 0xc2462cb3u, 0x4c8069c1u, 0xb6db7fedu, 0x0e388ff6u, 0xd467a086u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 70 /* milli weight units */ } ,[LEFT_SHIFT_8] = { .tag = JET , .jet = simplicity_left_shift_8 , .cmr = {{0x832f636eu, 0x63446cefu, 0xba8df3a4u, 0x6efbb361u, 0x59c18854u, 0x567768adu, 0xc9b8db8au, 0x07492a58u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 72 /* milli weight units */ } ,[LEFT_SHIFT_WITH_16] = { .tag = JET , .jet = simplicity_left_shift_with_16 , .cmr = {{0xe64762b1u, 0xc5e6144au, 0x7181eaafu, 0x4dd9d9b3u, 0xaa43aad9u, 0x55158198u, 0xee2090ebu, 0xd9e4bb0du}} , .sourceIx = ty_pbpw4w16 , .targetIx = ty_w16 , .cost = 72 /* milli weight units */ } ,[LEFT_SHIFT_WITH_32] = { .tag = JET , .jet = simplicity_left_shift_with_32 , .cmr = {{0x6476ba89u, 0x95f83b5eu, 0xe1ebc22cu, 0xb416f558u, 0x157f2e57u, 0x699a5cafu, 0x84291ff3u, 0xfc1483c1u}} , .sourceIx = ty_pbpw8w32 , .targetIx = ty_w32 , .cost = 87 /* milli weight units */ } ,[LEFT_SHIFT_WITH_64] = { .tag = JET , .jet = simplicity_left_shift_with_64 , .cmr = {{0x06b8fe67u, 0xcfc58632u, 0x2397af02u, 0x4fde2911u, 0xf7ae87a0u, 0x6abc6c59u, 0x30934097u, 0x15691c19u}} , .sourceIx = ty_pbpw8w64 , .targetIx = ty_w64 , .cost = 97 /* milli weight units */ } ,[LEFT_SHIFT_WITH_8] = { .tag = JET , .jet = simplicity_left_shift_with_8 , .cmr = {{0xb1ac9c68u, 0x2358c45bu, 0xabf40695u, 0x56fe6e37u, 0x5b4554deu, 0x9e10c591u, 0xc1483984u, 0x47ac180eu}} , .sourceIx = ty_pbpw4w8 , .targetIx = ty_w8 , .cost = 104 /* milli weight units */ } ,[LEFTMOST_16_1] = { .tag = JET , .jet = simplicity_leftmost_16_1 , .cmr = {{0x5bff4cb5u, 0x587605d5u, 0xfd059d77u, 0x33490d7du, 0xd22d278bu, 0x599e06d3u, 0xb5db6d79u, 0xf3c923bdu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 68 /* milli weight units */ } ,[LEFTMOST_16_2] = { .tag = JET , .jet = simplicity_leftmost_16_2 , .cmr = {{0x536db486u, 0xb12227e5u, 0xb09d6febu, 0xd2776b1au, 0xbbc67499u, 0x96aa783eu, 0xd7e53744u, 0x6bbf151bu}} , .sourceIx = ty_w16 , .targetIx = ty_w2 , .cost = 58 /* milli weight units */ } ,[LEFTMOST_16_4] = { .tag = JET , .jet = simplicity_leftmost_16_4 , .cmr = {{0xf2321367u, 0x496d1a77u, 0xeea05e95u, 0xe3b807d3u, 0xba5f0513u, 0x6ce0912au, 0xe717c83au, 0x0261b2e1u}} , .sourceIx = ty_w16 , .targetIx = ty_w4 , .cost = 51 /* milli weight units */ } ,[LEFTMOST_16_8] = { .tag = JET , .jet = simplicity_leftmost_16_8 , .cmr = {{0x24148ef3u, 0x0ad43ebeu, 0xc5637283u, 0x22c3ce11u, 0x79aed7a7u, 0x8216d799u, 0x888bf18bu, 0x39570671u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 62 /* milli weight units */ } ,[LEFTMOST_32_1] = { .tag = JET , .jet = simplicity_leftmost_32_1 , .cmr = {{0xb92e15ecu, 0x5da07ee8u, 0xed397cb9u, 0xf60a4c5du, 0xa8386293u, 0x1a907359u, 0xd27caeb6u, 0x0e60ef8au}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 53 /* milli weight units */ } ,[LEFTMOST_32_16] = { .tag = JET , .jet = simplicity_leftmost_32_16 , .cmr = {{0xadb027b2u, 0x06567358u, 0x5326c01cu, 0x3be2faebu, 0x386349e2u, 0x9009b657u, 0x6ee53a85u, 0x5512cc67u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 63 /* milli weight units */ } ,[LEFTMOST_32_2] = { .tag = JET , .jet = simplicity_leftmost_32_2 , .cmr = {{0xb75b31c5u, 0x59123d3du, 0x63359859u, 0x32b8b1b2u, 0x664ee597u, 0xafb15fd1u, 0xa499d007u, 0xcff2755cu}} , .sourceIx = ty_w32 , .targetIx = ty_w2 , .cost = 62 /* milli weight units */ } ,[LEFTMOST_32_4] = { .tag = JET , .jet = simplicity_leftmost_32_4 , .cmr = {{0xcb757e47u, 0x1e9d9a40u, 0x771dd1cfu, 0x3c1bf5d2u, 0x3c17ed68u, 0xcdbdb22du, 0xada17a73u, 0xa7b407b2u}} , .sourceIx = ty_w32 , .targetIx = ty_w4 , .cost = 61 /* milli weight units */ } ,[LEFTMOST_32_8] = { .tag = JET , .jet = simplicity_leftmost_32_8 , .cmr = {{0xbfc534b4u, 0x9e06006eu, 0x19f3b68eu, 0x0a02391cu, 0x149f9a34u, 0xf43ee36bu, 0x9f1d79a7u, 0x9c9a9e4du}} , .sourceIx = ty_w32 , .targetIx = ty_w8 , .cost = 60 /* milli weight units */ } ,[LEFTMOST_64_1] = { .tag = JET , .jet = simplicity_leftmost_64_1 , .cmr = {{0x1b1d4e92u, 0x384b8b15u, 0x9ba0d806u, 0x558b5494u, 0xe3614eedu, 0xe03c946cu, 0xeaf141f3u, 0x6f01c79bu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 65 /* milli weight units */ } ,[LEFTMOST_64_16] = { .tag = JET , .jet = simplicity_leftmost_64_16 , .cmr = {{0x0debdc1au, 0xa0433034u, 0x42e18fe0u, 0x3d8a99d2u, 0xbe6bb8a8u, 0x691aba19u, 0x566259e3u, 0x6760f7f9u}} , .sourceIx = ty_w64 , .targetIx = ty_w16 , .cost = 62 /* milli weight units */ } ,[LEFTMOST_64_2] = { .tag = JET , .jet = simplicity_leftmost_64_2 , .cmr = {{0x839ecfa3u, 0x18705c25u, 0x3d0c52ffu, 0x27b90464u, 0x923d8c0eu, 0x55a82c0du, 0x16240239u, 0x7f365378u}} , .sourceIx = ty_w64 , .targetIx = ty_w2 , .cost = 61 /* milli weight units */ } ,[LEFTMOST_64_32] = { .tag = JET , .jet = simplicity_leftmost_64_32 , .cmr = {{0x929197a9u, 0x642861a7u, 0x7bd66258u, 0x051197beu, 0x86ff08e6u, 0x28e30f7eu, 0xfcbd2c4du, 0xfecf9bddu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 77 /* milli weight units */ } ,[LEFTMOST_64_4] = { .tag = JET , .jet = simplicity_leftmost_64_4 , .cmr = {{0x02bd1645u, 0xd575f04bu, 0x3cbbaa6du, 0x8ca986efu, 0x1c8cd0ffu, 0xe1658903u, 0x939db764u, 0x562a2647u}} , .sourceIx = ty_w64 , .targetIx = ty_w4 , .cost = 80 /* milli weight units */ } ,[LEFTMOST_64_8] = { .tag = JET , .jet = simplicity_leftmost_64_8 , .cmr = {{0x3558b31bu, 0x3b6e8f9au, 0x288fdc72u, 0xf24602beu, 0x05581910u, 0x71a54a99u, 0xfa03a025u, 0x34f88005u}} , .sourceIx = ty_w64 , .targetIx = ty_w8 , .cost = 54 /* milli weight units */ } ,[LEFTMOST_8_1] = { .tag = JET , .jet = simplicity_leftmost_8_1 , .cmr = {{0x2865efd4u, 0x2983cbe3u, 0xf816373au, 0xb8a882f1u, 0x8317194du, 0xc1aba38du, 0xa0304b8cu, 0x144b1da4u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 54 /* milli weight units */ } ,[LEFTMOST_8_2] = { .tag = JET , .jet = simplicity_leftmost_8_2 , .cmr = {{0x51964cb0u, 0x7405a8d2u, 0x3d218774u, 0x1a9ed304u, 0xbcb469d9u, 0xac9f5d92u, 0x55825cfdu, 0xa3da07c0u}} , .sourceIx = ty_w8 , .targetIx = ty_w2 , .cost = 71 /* milli weight units */ } ,[LEFTMOST_8_4] = { .tag = JET , .jet = simplicity_leftmost_8_4 , .cmr = {{0x883c94f8u, 0xa26cdab7u, 0xbc5cd631u, 0xe52255a8u, 0x5ef6e070u, 0x766457f6u, 0x321e2ccbu, 0x119d9b2bu}} , .sourceIx = ty_w8 , .targetIx = ty_w4 , .cost = 65 /* milli weight units */ } ,[LINEAR_COMBINATION_1] = { .tag = JET , .jet = simplicity_linear_combination_1 , .cmr = {{0x3410a9eeu, 0x333df8c8u, 0xa01c1411u, 0x5b544327u, 0xe324e287u, 0xaa1107e0u, 0x1955bd20u, 0x506ea987u}} , .sourceIx = ty_ppw256pw512w256w256 , .targetIx = ty_pw512w256 , .cost = 85743 /* milli weight units */ } ,[LINEAR_VERIFY_1] = { .tag = JET , .jet = simplicity_linear_verify_1 , .cmr = {{0xdc66d331u, 0xc17f3fddu, 0xa3994698u, 0x1b39b357u, 0xd0555c35u, 0x62ecae02u, 0xaa2dad16u, 0x3e6c9a2eu}} , .sourceIx = ty_pppw256w512w256w512 , .targetIx = ty_u , .cost = 43579 /* milli weight units */ } ,[LOCK_TIME] = { .tag = JET , .jet = simplicity_bitcoin_lock_time , .cmr = {{0x9ae0acc3u, 0x7bc20447u, 0x79b07c3du, 0x4602a5fdu, 0xe8bc33f8u, 0x79f66b73u, 0x9b10f01au, 0xeb1154ecu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 66 /* milli weight units */ } ,[LOW_1] = { .tag = JET , .jet = simplicity_low_1 , .cmr = {{0xfe6214f9u, 0x67156dcdu, 0xe6dd49fdu, 0xc55efb86u, 0x5069feabu, 0xfff0fe93u, 0x1dba8531u, 0x34eed130u}} , .sourceIx = ty_u , .targetIx = ty_b , .cost = 40 /* milli weight units */ } ,[LOW_16] = { .tag = JET , .jet = simplicity_low_16 , .cmr = {{0x7493cf69u, 0x8a4882e5u, 0xc3579d06u, 0x518e7ecau, 0x2b8428f6u, 0x2e2b5138u, 0x02abe622u, 0x170c20feu}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 60 /* milli weight units */ } ,[LOW_32] = { .tag = JET , .jet = simplicity_low_32 , .cmr = {{0x362d66a4u, 0xf0aeb965u, 0x84a56757u, 0x8271b1f7u, 0xbbfcc2deu, 0x0dcf9579u, 0x6b6f7a82u, 0x6b2a8af7u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 52 /* milli weight units */ } ,[LOW_64] = { .tag = JET , .jet = simplicity_low_64 , .cmr = {{0x973323bcu, 0x2b92e428u, 0x04d2e4f5u, 0x8b86f65bu, 0x56f91deeu, 0xb4810eabu, 0x8a1deda9u, 0x697a0872u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 50 /* milli weight units */ } ,[LOW_8] = { .tag = JET , .jet = simplicity_low_8 , .cmr = {{0xcd1a8558u, 0xef99a322u, 0x60217a76u, 0x49ff5140u, 0xda69da70u, 0x0672690bu, 0x27917b07u, 0xd7c14c67u}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 45 /* milli weight units */ } ,[LT_16] = { .tag = JET , .jet = simplicity_lt_16 , .cmr = {{0x04aca87eu, 0x3e17f805u, 0xa21cf291u, 0x7aee9957u, 0xb950b2dbu, 0x5d7ae5c8u, 0x26d4ac2eu, 0xc97b5a52u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 83 /* milli weight units */ } ,[LT_32] = { .tag = JET , .jet = simplicity_lt_32 , .cmr = {{0x23a0a5c1u, 0x97747e3au, 0x9579e90eu, 0x0f22f84au, 0x29bfb5f0u, 0x7b84b59bu, 0x26688a0cu, 0xd59dfebdu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 89 /* milli weight units */ } ,[LT_64] = { .tag = JET , .jet = simplicity_lt_64 , .cmr = {{0xd299901cu, 0x7b5b3a59u, 0xffc8dd09u, 0x545a3238u, 0x24b779a9u, 0x9b2d1a2fu, 0x87452d9eu, 0x4befaf30u}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 71 /* milli weight units */ } ,[LT_8] = { .tag = JET , .jet = simplicity_lt_8 , .cmr = {{0xdd94413bu, 0x529c298cu, 0x1696e9fbu, 0x08e66767u, 0xb3f8337au, 0xc02e44b0u, 0x68e94014u, 0xf7c41f2au}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 86 /* milli weight units */ } ,[MAJ_1] = { .tag = JET , .jet = simplicity_maj_1 , .cmr = {{0x0e6fb40fu, 0xe31a3a52u, 0x6b44cf0bu, 0x7c7936c7u, 0x77cbba89u, 0x65a72552u, 0x32a7cf53u, 0xa922885au}} , .sourceIx = ty_pbw2 , .targetIx = ty_b , .cost = 54 /* milli weight units */ } ,[MAJ_16] = { .tag = JET , .jet = simplicity_maj_16 , .cmr = {{0x38669ce5u, 0xe1e17147u, 0x5400731bu, 0xeeb60bcau, 0xfad66604u, 0xc9394016u, 0x0cd71288u, 0x35559342u}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 85 /* milli weight units */ } ,[MAJ_32] = { .tag = JET , .jet = simplicity_maj_32 , .cmr = {{0x5554349bu, 0x584f5c38u, 0x72c7f4f2u, 0x57829e2au, 0xe822d823u, 0x424ceb95u, 0x98f08318u, 0x586a8807u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 73 /* milli weight units */ } ,[MAJ_64] = { .tag = JET , .jet = simplicity_maj_64 , .cmr = {{0x734903bau, 0xefb71d5eu, 0xa41648ffu, 0x43eee698u, 0x94e063b3u, 0x88ea422fu, 0x96aede19u, 0x3ceab839u}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 79 /* milli weight units */ } ,[MAJ_8] = { .tag = JET , .jet = simplicity_maj_8 , .cmr = {{0xba47a399u, 0xdc9435e1u, 0x8e080a4eu, 0x18af7c65u, 0x7fd39f7cu, 0xe7d6052eu, 0x46902311u, 0xb078d585u}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 64 /* milli weight units */ } ,[MAX_16] = { .tag = JET , .jet = simplicity_max_16 , .cmr = {{0xaa552374u, 0x6cabfaf5u, 0x668e9e07u, 0x37e56b06u, 0x062251d7u, 0xe80ab9b9u, 0x106d8f17u, 0x2dc84dd6u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 80 /* milli weight units */ } ,[MAX_32] = { .tag = JET , .jet = simplicity_max_32 , .cmr = {{0x6922965du, 0x144345c9u, 0x13ecb30bu, 0x5ed47e88u, 0xdae35c12u, 0x21f26aa9u, 0x2dd5a5f6u, 0x15dbdb53u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 70 /* milli weight units */ } ,[MAX_64] = { .tag = JET , .jet = simplicity_max_64 , .cmr = {{0x8a9be907u, 0xb6a4c30au, 0xbcc0f22du, 0x013074c2u, 0xd56bb081u, 0xf2621857u, 0xd538cc97u, 0x131e4409u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 75 /* milli weight units */ } ,[MAX_8] = { .tag = JET , .jet = simplicity_max_8 , .cmr = {{0xb4bf9323u, 0x4022e860u, 0xfe76c0b5u, 0x360e8b36u, 0xff81ee67u, 0x05b593acu, 0xdf655ac6u, 0xe6d7aebau}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 79 /* milli weight units */ } ,[MEDIAN_16] = { .tag = JET , .jet = simplicity_median_16 , .cmr = {{0x17e2e87fu, 0x0760f4fbu, 0x3c9fd0beu, 0xd000d739u, 0x73ab60f5u, 0xe6c2c1fau, 0xb17f9b23u, 0xee6aca48u}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 80 /* milli weight units */ } ,[MEDIAN_32] = { .tag = JET , .jet = simplicity_median_32 , .cmr = {{0x1160ae8eu, 0xa8d30f9au, 0x2233c48eu, 0x731240f8u, 0x4493b828u, 0xb55793e2u, 0xf4042a19u, 0x82ac26a5u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 77 /* milli weight units */ } ,[MEDIAN_64] = { .tag = JET , .jet = simplicity_median_64 , .cmr = {{0xc8737364u, 0x9e7e4050u, 0xbb73337eu, 0x08eb5de4u, 0x5228ab86u, 0xad4e1f41u, 0x91e5202au, 0xa6afa0c5u}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 89 /* milli weight units */ } ,[MEDIAN_8] = { .tag = JET , .jet = simplicity_median_8 , .cmr = {{0xc3b4e089u, 0x8a21bde9u, 0x4daed37au, 0x20adf90cu, 0x8be5691au, 0x03b6a1e5u, 0x56385d42u, 0xeb19022bu}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 77 /* milli weight units */ } ,[MIN_16] = { .tag = JET , .jet = simplicity_min_16 , .cmr = {{0x5fd0051eu, 0xdb3719a6u, 0x45b272a0u, 0x2108efbbu, 0x3d9bc0f6u, 0x0621bf5au, 0x5babe116u, 0xd555d578u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 83 /* milli weight units */ } ,[MIN_32] = { .tag = JET , .jet = simplicity_min_32 , .cmr = {{0xd80782a2u, 0xb5d86ab6u, 0xb9c9c3fbu, 0x778a3473u, 0xf600b185u, 0xfe1925eeu, 0x9fc2e877u, 0x7ed26601u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 96 /* milli weight units */ } ,[MIN_64] = { .tag = JET , .jet = simplicity_min_64 , .cmr = {{0xc5c09d50u, 0x1338e9a5u, 0x12cf8976u, 0xca4b32b9u, 0x2480bef6u, 0xaeb29d36u, 0xd590d35bu, 0xf9f9ece1u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 82 /* milli weight units */ } ,[MIN_8] = { .tag = JET , .jet = simplicity_min_8 , .cmr = {{0x81d21e12u, 0x81423881u, 0x802c0e0cu, 0x7d22bd34u, 0xd26bd12au, 0x4c4f1b70u, 0x68e7e183u, 0x820848e9u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 78 /* milli weight units */ } ,[MODULO_16] = { .tag = JET , .jet = simplicity_modulo_16 , .cmr = {{0xb6b87cfau, 0xb67e5519u, 0xf1c998dau, 0x479437bbu, 0x79e674f7u, 0x15e9a2e5u, 0x38eec5ecu, 0x18e18ea5u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 85 /* milli weight units */ } ,[MODULO_32] = { .tag = JET , .jet = simplicity_modulo_32 , .cmr = {{0x8d486e83u, 0x1654f38au, 0x32da35ebu, 0x7bb655a6u, 0xed694dbfu, 0xa058957du, 0x9f5cbfccu, 0x5792c65bu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 81 /* milli weight units */ } ,[MODULO_64] = { .tag = JET , .jet = simplicity_modulo_64 , .cmr = {{0x14df20d9u, 0x3dfdefe2u, 0x559bac50u, 0xed38193bu, 0xd78bd63fu, 0x929d86fbu, 0x4f29a7c5u, 0xaf3242adu}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 71 /* milli weight units */ } ,[MODULO_8] = { .tag = JET , .jet = simplicity_modulo_8 , .cmr = {{0x2c758a7cu, 0x0f59e800u, 0xe94f3dc5u, 0xa001bf8eu, 0xd9435f75u, 0xa2d96930u, 0xc57eaab0u, 0xcd80af5cu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 85 /* milli weight units */ } ,[MULTIPLY_16] = { .tag = JET , .jet = simplicity_multiply_16 , .cmr = {{0x75bd41f2u, 0xd2b339f0u, 0x69bfdfd8u, 0x02d61e6cu, 0xa8e3bad6u, 0xfb6d95b6u, 0x72095b93u, 0x345f047fu}} , .sourceIx = ty_w32 , .targetIx = ty_w32 , .cost = 79 /* milli weight units */ } ,[MULTIPLY_32] = { .tag = JET , .jet = simplicity_multiply_32 , .cmr = {{0x84cbe6ceu, 0x87037992u, 0x13877c1bu, 0xd505c764u, 0x34336900u, 0x2e502c43u, 0xd97f3d57u, 0x772d6c87u}} , .sourceIx = ty_w64 , .targetIx = ty_w64 , .cost = 78 /* milli weight units */ } ,[MULTIPLY_64] = { .tag = JET , .jet = simplicity_multiply_64 , .cmr = {{0x92987b80u, 0x1b92f679u, 0xeb961368u, 0x8444a178u, 0x8750a850u, 0x6e03a921u, 0x8c21ecc7u, 0x2082dc6au}} , .sourceIx = ty_w128 , .targetIx = ty_w128 , .cost = 72 /* milli weight units */ } ,[MULTIPLY_8] = { .tag = JET , .jet = simplicity_multiply_8 , .cmr = {{0x764cab71u, 0xdb9459a7u, 0x696d944au, 0x50095b1au, 0xebdfd928u, 0x4bdb7496u, 0xa7b30241u, 0xccba3eceu}} , .sourceIx = ty_w16 , .targetIx = ty_w16 , .cost = 79 /* milli weight units */ } ,[NEGATE_16] = { .tag = JET , .jet = simplicity_negate_16 , .cmr = {{0xe760ee40u, 0x29c34f89u, 0x7406ffdeu, 0xa5558486u, 0x62e89c98u, 0x3e6070bdu, 0x0272ad0fu, 0xa342efa3u}} , .sourceIx = ty_w16 , .targetIx = ty_pbw16 , .cost = 69 /* milli weight units */ } ,[NEGATE_32] = { .tag = JET , .jet = simplicity_negate_32 , .cmr = {{0x8495b740u, 0x09ad07c9u, 0x302a25aeu, 0x56c3e973u, 0x3f00c2bau, 0xa410eac4u, 0xa58e75dbu, 0x83af1d22u}} , .sourceIx = ty_w32 , .targetIx = ty_pbw32 , .cost = 56 /* milli weight units */ } ,[NEGATE_64] = { .tag = JET , .jet = simplicity_negate_64 , .cmr = {{0x34e89fafu, 0x345afd5eu, 0x7b290014u, 0x52fc5fc2u, 0xe3783af7u, 0xf2101643u, 0xbd76706au, 0x6fc3f36au}} , .sourceIx = ty_w64 , .targetIx = ty_pbw64 , .cost = 56 /* milli weight units */ } ,[NEGATE_8] = { .tag = JET , .jet = simplicity_negate_8 , .cmr = {{0xe81be0b1u, 0x5c671ab8u, 0xdf1f4869u, 0xc57f1111u, 0x18cb6683u, 0x54975c63u, 0x66ecb2b8u, 0xbb7c15cfu}} , .sourceIx = ty_w8 , .targetIx = ty_pbw8 , .cost = 69 /* milli weight units */ } ,[NUM_INPUTS] = { .tag = JET , .jet = simplicity_bitcoin_num_inputs , .cmr = {{0x5c5ac4ffu, 0x6da56cb3u, 0x72b23266u, 0x6e8334b9u, 0xe2cfb0dcu, 0xb418f161u, 0xbff149e8u, 0x4ec92c3eu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 74 /* milli weight units */ } ,[NUM_OUTPUTS] = { .tag = JET , .jet = simplicity_bitcoin_num_outputs , .cmr = {{0x98a1cca7u, 0x05dfcfafu, 0xd3a69e9au, 0xdc05ba47u, 0xe1fefa6au, 0x29f34286u, 0x2048e496u, 0x8648c3d7u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 68 /* milli weight units */ } ,[ONE_16] = { .tag = JET , .jet = simplicity_one_16 , .cmr = {{0x2e5e3d95u, 0xe4531688u, 0x8e4f3709u, 0xef832b9fu, 0xd9e15f30u, 0x719bf55fu, 0xc2e0e09au, 0x3657d882u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 45 /* milli weight units */ } ,[ONE_32] = { .tag = JET , .jet = simplicity_one_32 , .cmr = {{0x06426b85u, 0x3c1bcb33u, 0x8aedbe1fu, 0x89a6d9b7u, 0xa3da038cu, 0xd00a4471u, 0x18369349u, 0x669e2976u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 45 /* milli weight units */ } ,[ONE_64] = { .tag = JET , .jet = simplicity_one_64 , .cmr = {{0xab1d2cd9u, 0x9678da3cu, 0x128d39adu, 0x9fe6ffa9u, 0x55c16e5eu, 0xf2c25bb4u, 0x31831559u, 0x6951f427u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 45 /* milli weight units */ } ,[ONE_8] = { .tag = JET , .jet = simplicity_one_8 , .cmr = {{0x3cc5f523u, 0xd6a6355du, 0xc924ee0au, 0xc1f5fe2cu, 0x521275e3u, 0xaa9f21d3u, 0x1b082db2u, 0xac230d9du}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 46 /* milli weight units */ } ,[OR_1] = { .tag = JET , .jet = simplicity_or_1 , .cmr = {{0xc4659643u, 0x69fca209u, 0x7f83530cu, 0x87bcbc90u, 0xc306579du, 0x9f3bfeddu, 0xf4a172a4u, 0xea0b58ecu}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 56 /* milli weight units */ } ,[OR_16] = { .tag = JET , .jet = simplicity_or_16 , .cmr = {{0x5a985e04u, 0x3b85273bu, 0x90f90e20u, 0xf82b7532u, 0x3351cf2au, 0x4e62a7f9u, 0xcb2f0596u, 0x402e9e28u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 78 /* milli weight units */ } ,[OR_32] = { .tag = JET , .jet = simplicity_or_32 , .cmr = {{0x3552383au, 0x57ffb48du, 0x63a0337au, 0xf0dd6efau, 0xb6b46c5du, 0xe1720e42u, 0x0bdd1c82u, 0x276bc9a9u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 80 /* milli weight units */ } ,[OR_64] = { .tag = JET , .jet = simplicity_or_64 , .cmr = {{0x51a173dau, 0xdca01ac6u, 0xf62e75d5u, 0xcd3522f0u, 0x9fde62b1u, 0x1513e068u, 0x422852a4u, 0x9167b606u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 71 /* milli weight units */ } ,[OR_8] = { .tag = JET , .jet = simplicity_or_8 , .cmr = {{0x79efbdcbu, 0x537bebcbu, 0x188d1116u, 0xb78a109bu, 0xffbc2a6cu, 0xe3d1f870u, 0x154a7956u, 0x091b342fu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 81 /* milli weight units */ } ,[OUTPOINT_HASH] = { .tag = JET , .jet = simplicity_bitcoin_outpoint_hash , .cmr = {{0x3a1ae90eu, 0x167fb40du, 0x6e13b451u, 0xad67410du, 0x8dd991c8u, 0x7d6a4a59u, 0xcc76c63fu, 0x3b9e5e56u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pw256w32 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1788 /* milli weight units */ } ,[OUTPUT_HASH] = { .tag = JET , .jet = simplicity_bitcoin_output_hash , .cmr = {{0x91211fc6u, 0x011a6493u, 0x00c6bee9u, 0x4fdd48a9u, 0x7fa2a9b6u, 0xf284be01u, 0x5d462d17u, 0xde664ac3u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 822 /* milli weight units */ } ,[OUTPUT_SCRIPT_HASH] = { .tag = JET , .jet = simplicity_bitcoin_output_script_hash , .cmr = {{0xbdfdb231u, 0xf4f1a62cu, 0x9d7b0393u, 0x1e7f19a4u, 0x546af234u, 0x754cbf70u, 0x059fdd42u, 0xbbbc4126u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 135 /* milli weight units */ } ,[OUTPUT_SCRIPTS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_output_scripts_hash , .cmr = {{0xff20bc43u, 0x65e71707u, 0x571c6e17u, 0x38e1ed32u, 0x6f7c351du, 0xe13022aeu, 0xa3d6406bu, 0x8aee8e3bu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 123 /* milli weight units */ } ,[OUTPUT_VALUE] = { .tag = JET , .jet = simplicity_bitcoin_output_value , .cmr = {{0x933643b6u, 0xc5a6220au, 0xbbca6f35u, 0x09feff6du, 0x13efa6c9u, 0xfae95924u, 0x575364f2u, 0xb164d2bcu}} , .sourceIx = ty_w32 , .targetIx = ty_mw64 , .cost = 82 /* milli weight units */ } ,[OUTPUT_VALUES_HASH] = { .tag = JET , .jet = simplicity_bitcoin_output_values_hash , .cmr = {{0x22899379u, 0x0057066fu, 0x2016971du, 0xf55e6f67u, 0xd252efb6u, 0xdaabd0fcu, 0x566a8d21u, 0x56efbbfcu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 119 /* milli weight units */ } ,[OUTPUTS_HASH] = { .tag = JET , .jet = simplicity_bitcoin_outputs_hash , .cmr = {{0xf2eb6d0fu, 0x018e6f15u, 0xe35baa82u, 0xe57e14feu, 0x343796f2u, 0x196826beu, 0xd7c78755u, 0x98d6641du}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 117 /* milli weight units */ } ,[PARSE_LOCK] = { .tag = JET , .jet = simplicity_parse_lock , .cmr = {{0x3db84535u, 0xfa3d90efu, 0x0b581e22u, 0xb61d2127u, 0x844b2116u, 0xe84f814au, 0x5cbac52du, 0xf515f2d2u}} , .sourceIx = ty_w32 , .targetIx = ty_sw32w32 , .cost = 82 /* milli weight units */ } ,[PARSE_SEQUENCE] = { .tag = JET , .jet = simplicity_parse_sequence , .cmr = {{0x38b2533fu, 0x5fede869u, 0xbaa17069u, 0x83df4c89u, 0xd62d5f90u, 0x800b47eau, 0xb2111331u, 0x1a5aaec9u}} , .sourceIx = ty_w32 , .targetIx = ty_msw16w16 , .cost = 93 /* milli weight units */ } ,[POINT_VERIFY_1] = { .tag = JET , .jet = simplicity_point_verify_1 , .cmr = {{0xbe2a9890u, 0xf1d5b615u, 0x147f8241u, 0xe0609b5cu, 0xac01ece0u, 0xa3f92368u, 0x67b2bfdeu, 0xa1b8044eu}} , .sourceIx = ty_pppw256pbw256w256pbw256 , .targetIx = ty_u , .cost = 41394 /* milli weight units */ } ,[RIGHT_EXTEND_16_32] = { .tag = JET , .jet = simplicity_right_extend_16_32 , .cmr = {{0xdbf18d87u, 0xa7892139u, 0xa388e9a9u, 0x83c48992u, 0xac35a845u, 0x56ee0defu, 0xc1dadf0cu, 0x5f471a26u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 73 /* milli weight units */ } ,[RIGHT_EXTEND_16_64] = { .tag = JET , .jet = simplicity_right_extend_16_64 , .cmr = {{0xd011acc7u, 0x94e3c478u, 0x9accd0d5u, 0xfe4997d3u, 0x34d91f08u, 0x31a1eb35u, 0x04b4cb2du, 0xdf4797afu}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 70 /* milli weight units */ } ,[RIGHT_EXTEND_32_64] = { .tag = JET , .jet = simplicity_right_extend_32_64 , .cmr = {{0xa5aa5db1u, 0xe535e723u, 0x2ad36dafu, 0xba6d5a20u, 0x0d54eb85u, 0x3b75dc70u, 0xa594ed64u, 0xaa6bd9abu}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 62 /* milli weight units */ } ,[RIGHT_EXTEND_8_16] = { .tag = JET , .jet = simplicity_right_extend_8_16 , .cmr = {{0x8106d58au, 0x8066ee6eu, 0x15e55ca5u, 0x2cb7afd8u, 0xe3277587u, 0xbfd7dec0u, 0xbe37d406u, 0x742a3931u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 63 /* milli weight units */ } ,[RIGHT_EXTEND_8_32] = { .tag = JET , .jet = simplicity_right_extend_8_32 , .cmr = {{0xdfa4bafau, 0x432a5338u, 0xd374deb6u, 0xb724b7f6u, 0xeae55861u, 0xfe731d43u, 0x048aa304u, 0xd1f7f9a2u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 69 /* milli weight units */ } ,[RIGHT_EXTEND_8_64] = { .tag = JET , .jet = simplicity_right_extend_8_64 , .cmr = {{0x620a3703u, 0x8b6fa127u, 0x495f0b46u, 0x496f6435u, 0xdd2dad7eu, 0xf0c0fd2cu, 0xd65f54dcu, 0x185e997bu}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 141 /* milli weight units */ } ,[RIGHT_PAD_HIGH_16_32] = { .tag = JET , .jet = simplicity_right_pad_high_16_32 , .cmr = {{0x2b6abc38u, 0x321a7c54u, 0x2fb16974u, 0x621ced80u, 0x880db519u, 0xbb486093u, 0x426e8ce1u, 0x8e0169b1u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 66 /* milli weight units */ } ,[RIGHT_PAD_HIGH_16_64] = { .tag = JET , .jet = simplicity_right_pad_high_16_64 , .cmr = {{0xad90d8ffu, 0xa57450b3u, 0xb5e90962u, 0x25349ed8u, 0xf072e101u, 0x7293f392u, 0xef854e03u, 0x19abc934u}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 81 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_16] = { .tag = JET , .jet = simplicity_right_pad_high_1_16 , .cmr = {{0x288158b1u, 0xc910877bu, 0x7eea3dfcu, 0xf2b2b788u, 0x922808b6u, 0xd6fa75f8u, 0x96771904u, 0x8b141249u}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 114 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_32] = { .tag = JET , .jet = simplicity_right_pad_high_1_32 , .cmr = {{0xee2ad77fu, 0x668d3d6au, 0x2e68506eu, 0x4904cf50u, 0xa08460e1u, 0xd2b86a81u, 0xe14e41f8u, 0xda4cddf2u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 220 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_64] = { .tag = JET , .jet = simplicity_right_pad_high_1_64 , .cmr = {{0x3d6a7fe6u, 0x9a11642au, 0xced6842bu, 0x89aa1bb8u, 0x413e3990u, 0x63cc1678u, 0x6af7c033u, 0xdad58b95u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 313 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_8] = { .tag = JET , .jet = simplicity_right_pad_high_1_8 , .cmr = {{0x2844bdfdu, 0x6aba29dfu, 0x03f93aa6u, 0xaeb21c06u, 0x4028db05u, 0xff77d8d9u, 0x1cfdcdefu, 0xb190c5bdu}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 73 /* milli weight units */ } ,[RIGHT_PAD_HIGH_32_64] = { .tag = JET , .jet = simplicity_right_pad_high_32_64 , .cmr = {{0xb432e532u, 0x1ae1714cu, 0xe19529d8u, 0x5f24ff89u, 0x87910ebcu, 0xf015f87fu, 0x15bbed55u, 0xf0a0e892u}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 62 /* milli weight units */ } ,[RIGHT_PAD_HIGH_8_16] = { .tag = JET , .jet = simplicity_right_pad_high_8_16 , .cmr = {{0x6f2d96c9u, 0x5413ca9au, 0xa8cc550fu, 0x2573e166u, 0x9956d607u, 0x692cf1cau, 0x6dc76d2fu, 0x2b4a3ac8u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 75 /* milli weight units */ } ,[RIGHT_PAD_HIGH_8_32] = { .tag = JET , .jet = simplicity_right_pad_high_8_32 , .cmr = {{0xdf2c7f92u, 0x9900a449u, 0x01e6ff65u, 0x276a951au, 0xeb95df25u, 0x0b139714u, 0xd4195404u, 0xd77898edu}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 81 /* milli weight units */ } ,[RIGHT_PAD_HIGH_8_64] = { .tag = JET , .jet = simplicity_right_pad_high_8_64 , .cmr = {{0x79c01da3u, 0xe60b9c69u, 0x35ce3e15u, 0x98b17840u, 0xaf82dcb0u, 0xddc63aefu, 0x4a06e7f9u, 0xca5d2741u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 118 /* milli weight units */ } ,[RIGHT_PAD_LOW_16_32] = { .tag = JET , .jet = simplicity_right_pad_low_16_32 , .cmr = {{0x6f201027u, 0xcc759802u, 0x30a07085u, 0x9c3e3802u, 0x36a1cb10u, 0xe61a01aau, 0x1f6d231du, 0x15142f25u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 62 /* milli weight units */ } ,[RIGHT_PAD_LOW_16_64] = { .tag = JET , .jet = simplicity_right_pad_low_16_64 , .cmr = {{0xb86e1f0bu, 0xfec65598u, 0xd0a3d1ecu, 0x960305b9u, 0x6745673eu, 0x1b16bf32u, 0x7a716805u, 0x83d71d90u}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 98 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_16] = { .tag = JET , .jet = simplicity_right_pad_low_1_16 , .cmr = {{0x052a6499u, 0xc93ee6bcu, 0x1ae657f8u, 0x5fd4d4feu, 0x677abceeu, 0x540d1340u, 0x33542e9au, 0xb60a63ddu}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 60 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_32] = { .tag = JET , .jet = simplicity_right_pad_low_1_32 , .cmr = {{0x5b70d428u, 0x960e95ccu, 0x40d51846u, 0xf53a4d0au, 0x35c9015du, 0x1500b6bcu, 0x849b7283u, 0x5e2bd440u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 47 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_64] = { .tag = JET , .jet = simplicity_right_pad_low_1_64 , .cmr = {{0x44efeb87u, 0xca2ad7fdu, 0x4b73f163u, 0x07c7f059u, 0x02656f35u, 0x090fb0a4u, 0x326c6489u, 0x88ae1d39u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 57 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_8] = { .tag = JET , .jet = simplicity_right_pad_low_1_8 , .cmr = {{0x9340398bu, 0xcc8ea83eu, 0xc840be72u, 0x9dbb8b81u, 0x207824eeu, 0x875d1582u, 0x59d6dad2u, 0x0a83930cu}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 48 /* milli weight units */ } ,[RIGHT_PAD_LOW_32_64] = { .tag = JET , .jet = simplicity_right_pad_low_32_64 , .cmr = {{0x693e2810u, 0x1e04fda4u, 0x3b97e611u, 0xf0fe9800u, 0x0e14302eu, 0x5dcd6ed6u, 0x5eee42e3u, 0x4014242fu}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 74 /* milli weight units */ } ,[RIGHT_PAD_LOW_8_16] = { .tag = JET , .jet = simplicity_right_pad_low_8_16 , .cmr = {{0x096b25c3u, 0xc8415f04u, 0xd8832743u, 0xeb2f8456u, 0xd5f0a644u, 0x913d3ec5u, 0x9d34f455u, 0x2501fa20u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 62 /* milli weight units */ } ,[RIGHT_PAD_LOW_8_32] = { .tag = JET , .jet = simplicity_right_pad_low_8_32 , .cmr = {{0xfc7f5722u, 0xa62aa220u, 0x18cc81cdu, 0x00a9326cu, 0x7fe9c63au, 0xbce2bda4u, 0xc0e66a3fu, 0x47c67c53u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 69 /* milli weight units */ } ,[RIGHT_PAD_LOW_8_64] = { .tag = JET , .jet = simplicity_right_pad_low_8_64 , .cmr = {{0xa5bb7d5eu, 0xfca0e48du, 0x9d80c502u, 0x7115b485u, 0x781051e0u, 0xef46e4d6u, 0x08317a1cu, 0x4261bc46u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 98 /* milli weight units */ } ,[RIGHT_ROTATE_16] = { .tag = JET , .jet = simplicity_right_rotate_16 , .cmr = {{0x482ea7e1u, 0x214501d9u, 0x3c9ad16fu, 0xa8b97bf5u, 0xb384fc2bu, 0x54789b8cu, 0xd9e784ccu, 0xd0eb9d57u}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 67 /* milli weight units */ } ,[RIGHT_ROTATE_32] = { .tag = JET , .jet = simplicity_right_rotate_32 , .cmr = {{0x0941b6eeu, 0xea9af819u, 0x5b028afcu, 0x0bd2a534u, 0x218bf90du, 0x1a0e373du, 0x74741854u, 0x0b726d73u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 77 /* milli weight units */ } ,[RIGHT_ROTATE_64] = { .tag = JET , .jet = simplicity_right_rotate_64 , .cmr = {{0x444dbbc3u, 0xdd2a11a5u, 0xc7b0439fu, 0xdba99ac7u, 0x4a11b8eeu, 0xb2db301eu, 0x243ea891u, 0x22907152u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 64 /* milli weight units */ } ,[RIGHT_ROTATE_8] = { .tag = JET , .jet = simplicity_right_rotate_8 , .cmr = {{0x7265a30cu, 0x2e836e65u, 0x544aba91u, 0x1b64d18fu, 0xa69b1765u, 0x45856c77u, 0xc4f0d76fu, 0xc3f58351u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 72 /* milli weight units */ } ,[RIGHT_SHIFT_16] = { .tag = JET , .jet = simplicity_right_shift_16 , .cmr = {{0xcd57a3d3u, 0xab2d92d4u, 0xf0865504u, 0x3a8b8bb6u, 0x738981fau, 0xe6da0134u, 0xb4dedaceu, 0x5f008860u}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 60 /* milli weight units */ } ,[RIGHT_SHIFT_32] = { .tag = JET , .jet = simplicity_right_shift_32 , .cmr = {{0xd6b326b1u, 0xa32357a3u, 0x32807d3fu, 0xa1b156c2u, 0x8b1622f7u, 0x38def126u, 0x81467f34u, 0x9bd3494bu}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 69 /* milli weight units */ } ,[RIGHT_SHIFT_64] = { .tag = JET , .jet = simplicity_right_shift_64 , .cmr = {{0xb2095f2du, 0x47335d5fu, 0x98c85434u, 0xa2faf5b0u, 0xf75cf899u, 0x012a34bbu, 0xcd0a14cbu, 0xedb61107u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 68 /* milli weight units */ } ,[RIGHT_SHIFT_8] = { .tag = JET , .jet = simplicity_right_shift_8 , .cmr = {{0x4b2b1aa2u, 0xef732173u, 0x170d621au, 0x38deb261u, 0xe473c07cu, 0x558b055au, 0x25a86e4eu, 0x321afc04u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 63 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_16] = { .tag = JET , .jet = simplicity_right_shift_with_16 , .cmr = {{0x14b77685u, 0x47b3d3f4u, 0x7ee5c2b8u, 0x0d9bdae2u, 0xaec1f9c6u, 0x594ed312u, 0x7b12645au, 0xdcf59754u}} , .sourceIx = ty_pbpw4w16 , .targetIx = ty_w16 , .cost = 83 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_32] = { .tag = JET , .jet = simplicity_right_shift_with_32 , .cmr = {{0x327b6e98u, 0xa6fd340cu, 0x60cf83aau, 0x64993311u, 0x4cb8d84fu, 0x590e0121u, 0x3a261001u, 0x2b4607eau}} , .sourceIx = ty_pbpw8w32 , .targetIx = ty_w32 , .cost = 78 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_64] = { .tag = JET , .jet = simplicity_right_shift_with_64 , .cmr = {{0x062fa74au, 0xf3476e59u, 0x387be08eu, 0x6949a005u, 0x43bc84a2u, 0xb689ea39u, 0xad6eed7fu, 0x756785d4u}} , .sourceIx = ty_pbpw8w64 , .targetIx = ty_w64 , .cost = 72 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_8] = { .tag = JET , .jet = simplicity_right_shift_with_8 , .cmr = {{0x141be47eu, 0x967b2fd7u, 0xc7126c5au, 0xdf2dfe47u, 0x315bbc10u, 0x53bbe605u, 0xb38898dbu, 0xed49f227u}} , .sourceIx = ty_pbpw4w8 , .targetIx = ty_w8 , .cost = 71 /* milli weight units */ } ,[RIGHTMOST_16_1] = { .tag = JET , .jet = simplicity_rightmost_16_1 , .cmr = {{0x3f3c4346u, 0x87174226u, 0x5e87f001u, 0xb46de7d1u, 0x98751b34u, 0xfaa18018u, 0xde60c846u, 0x8d9b98a4u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 70 /* milli weight units */ } ,[RIGHTMOST_16_2] = { .tag = JET , .jet = simplicity_rightmost_16_2 , .cmr = {{0xc18b9fddu, 0x340a267au, 0xc16d4f39u, 0xee754356u, 0x52aaca52u, 0x5650b51au, 0x45879804u, 0x8e627d51u}} , .sourceIx = ty_w16 , .targetIx = ty_w2 , .cost = 65 /* milli weight units */ } ,[RIGHTMOST_16_4] = { .tag = JET , .jet = simplicity_rightmost_16_4 , .cmr = {{0xc6c53fa7u, 0x1e230cf0u, 0x585158f4u, 0x70588bacu, 0x5c518f84u, 0xf9fc2386u, 0x52f175fbu, 0x6ea18c11u}} , .sourceIx = ty_w16 , .targetIx = ty_w4 , .cost = 72 /* milli weight units */ } ,[RIGHTMOST_16_8] = { .tag = JET , .jet = simplicity_rightmost_16_8 , .cmr = {{0xee769c1cu, 0xc8a3fdd1u, 0x838fc9f0u, 0x490ce703u, 0x93fd91bau, 0x3cbd4abdu, 0x08649fb9u, 0xc44311bdu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 69 /* milli weight units */ } ,[RIGHTMOST_32_1] = { .tag = JET , .jet = simplicity_rightmost_32_1 , .cmr = {{0x1c442369u, 0xfb81f611u, 0xd328010bu, 0x864bccb7u, 0xf35ed477u, 0xdfa38555u, 0x74c13564u, 0xcdbdb860u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 70 /* milli weight units */ } ,[RIGHTMOST_32_16] = { .tag = JET , .jet = simplicity_rightmost_32_16 , .cmr = {{0xadd2c339u, 0x0d9af7c2u, 0x4a159a37u, 0xd69d4484u, 0xd2c24a2cu, 0xb5b0eb2du, 0x3c493d98u, 0x12acfd74u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 56 /* milli weight units */ } ,[RIGHTMOST_32_2] = { .tag = JET , .jet = simplicity_rightmost_32_2 , .cmr = {{0x00b8815au, 0xd7423dd5u, 0x8cb98be8u, 0x2cad2667u, 0x5c3bf54au, 0x0bedbadeu, 0x3464b4feu, 0x5a4e8ce6u}} , .sourceIx = ty_w32 , .targetIx = ty_w2 , .cost = 74 /* milli weight units */ } ,[RIGHTMOST_32_4] = { .tag = JET , .jet = simplicity_rightmost_32_4 , .cmr = {{0x84fa5a54u, 0xf7729f9du, 0x68994beau, 0xb93ae79bu, 0x8c4a10d5u, 0xb7ae9727u, 0xaa1716e5u, 0x7d033b74u}} , .sourceIx = ty_w32 , .targetIx = ty_w4 , .cost = 57 /* milli weight units */ } ,[RIGHTMOST_32_8] = { .tag = JET , .jet = simplicity_rightmost_32_8 , .cmr = {{0x7d3805d3u, 0xc78c4eeau, 0x91e3d35eu, 0xfdd47eedu, 0xd421af84u, 0xd2191032u, 0x9332a0b5u, 0x487fab63u}} , .sourceIx = ty_w32 , .targetIx = ty_w8 , .cost = 55 /* milli weight units */ } ,[RIGHTMOST_64_1] = { .tag = JET , .jet = simplicity_rightmost_64_1 , .cmr = {{0xd3b164c5u, 0xdc66cc7eu, 0xf9234fedu, 0xe4dc7f0du, 0xa5cd71c1u, 0xc1d4cad6u, 0x0fb4ec57u, 0x3e2b8a75u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 61 /* milli weight units */ } ,[RIGHTMOST_64_16] = { .tag = JET , .jet = simplicity_rightmost_64_16 , .cmr = {{0xeae43478u, 0xf9f2f452u, 0xefac15eeu, 0xe60f8b52u, 0x53d80a2du, 0x32129b4eu, 0x5ba38300u, 0xad9852fdu}} , .sourceIx = ty_w64 , .targetIx = ty_w16 , .cost = 63 /* milli weight units */ } ,[RIGHTMOST_64_2] = { .tag = JET , .jet = simplicity_rightmost_64_2 , .cmr = {{0x9cd4a98bu, 0xbdb8a335u, 0x85c00f47u, 0xd6adab7au, 0xf54286fbu, 0x8ae60f72u, 0x3011fb84u, 0xc0ee78f9u}} , .sourceIx = ty_w64 , .targetIx = ty_w2 , .cost = 65 /* milli weight units */ } ,[RIGHTMOST_64_32] = { .tag = JET , .jet = simplicity_rightmost_64_32 , .cmr = {{0x7f2420aeu, 0x5b0f5a3fu, 0x6f2e60b6u, 0x1f8a415cu, 0x088b94b2u, 0x1c1a62a3u, 0xfdaac749u, 0xdbdf4c71u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 64 /* milli weight units */ } ,[RIGHTMOST_64_4] = { .tag = JET , .jet = simplicity_rightmost_64_4 , .cmr = {{0xe265552au, 0x24fbcdecu, 0x0583d718u, 0x3e48ebc2u, 0xff6d3165u, 0x57bac591u, 0x5c03cb23u, 0x35d23295u}} , .sourceIx = ty_w64 , .targetIx = ty_w4 , .cost = 57 /* milli weight units */ } ,[RIGHTMOST_64_8] = { .tag = JET , .jet = simplicity_rightmost_64_8 , .cmr = {{0x98cd95f9u, 0x5d46641bu, 0x049e77bfu, 0x90eea598u, 0xadf29ee5u, 0x00e65072u, 0x87548bb1u, 0xcdaf784du}} , .sourceIx = ty_w64 , .targetIx = ty_w8 , .cost = 49 /* milli weight units */ } ,[RIGHTMOST_8_1] = { .tag = JET , .jet = simplicity_rightmost_8_1 , .cmr = {{0x0876fcd4u, 0x698591f3u, 0x31910157u, 0x4ce153fcu, 0xdfe94f58u, 0x1aac5e75u, 0xf3cd7446u, 0xdf56f3c7u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 65 /* milli weight units */ } ,[RIGHTMOST_8_2] = { .tag = JET , .jet = simplicity_rightmost_8_2 , .cmr = {{0xb9f7b290u, 0xafe7f189u, 0xe32aebf2u, 0xcc4ddca9u, 0x6bb00764u, 0xc7be2887u, 0xdce054d0u, 0x9e38c353u}} , .sourceIx = ty_w8 , .targetIx = ty_w2 , .cost = 63 /* milli weight units */ } ,[RIGHTMOST_8_4] = { .tag = JET , .jet = simplicity_rightmost_8_4 , .cmr = {{0xf28e9af5u, 0xaf4c9ccau, 0x4b43cc6au, 0xdf9d9d8du, 0x169c87c5u, 0x559f9f3cu, 0xcac8f235u, 0x2b629f18u}} , .sourceIx = ty_w8 , .targetIx = ty_w4 , .cost = 56 /* milli weight units */ } ,[SCALAR_ADD] = { .tag = JET , .jet = simplicity_scalar_add , .cmr = {{0x11ddbebau, 0xebf42180u, 0xa0b7eddfu, 0xfdc48ec7u, 0x511330fbu, 0x3315fa65u, 0xd58aff66u, 0xb9caf2d4u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 778 /* milli weight units */ } ,[SCALAR_INVERT] = { .tag = JET , .jet = simplicity_scalar_invert , .cmr = {{0xa6392725u, 0xbb2dadbbu, 0x1e76df2du, 0xec57df55u, 0xc3fcc577u, 0x3b62218au, 0xec55a75eu, 0x14f3d60du}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 3178 /* milli weight units */ } ,[SCALAR_IS_ZERO] = { .tag = JET , .jet = simplicity_scalar_is_zero , .cmr = {{0xf75eda06u, 0xce6af09fu, 0xae37db4eu, 0x6225e6a8u, 0xac86a236u, 0x37627d62u, 0x6409190fu, 0xf3b39d90u}} , .sourceIx = ty_w256 , .targetIx = ty_b , .cost = 271 /* milli weight units */ } ,[SCALAR_MULTIPLY] = { .tag = JET , .jet = simplicity_scalar_multiply , .cmr = {{0x4a61672au, 0xcec48877u, 0x56de1db6u, 0x0421a12bu, 0x901a858au, 0x6ee6352eu, 0x559d4ce5u, 0x973352beu}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 793 /* milli weight units */ } ,[SCALAR_MULTIPLY_LAMBDA] = { .tag = JET , .jet = simplicity_scalar_multiply_lambda , .cmr = {{0x49ea9c3fu, 0xb1d8ff52u, 0xd2db0346u, 0x9fdfe850u, 0x503fddebu, 0x45e16d26u, 0xe8928addu, 0x25870e91u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 567 /* milli weight units */ } ,[SCALAR_NEGATE] = { .tag = JET , .jet = simplicity_scalar_negate , .cmr = {{0x1dbf8b49u, 0x1ec66580u, 0x3f633330u, 0xd3ffb0e7u, 0x81e67c18u, 0x01ac9d49u, 0xbbf43589u, 0xabf782bfu}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 516 /* milli weight units */ } ,[SCALAR_NORMALIZE] = { .tag = JET , .jet = simplicity_scalar_normalize , .cmr = {{0x4633180eu, 0xa02c4df7u, 0x819d3d54u, 0xa401734fu, 0x965b31acu, 0xc784054eu, 0xbfb73168u, 0x16b029ecu}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 500 /* milli weight units */ } ,[SCALAR_SQUARE] = { .tag = JET , .jet = simplicity_scalar_square , .cmr = {{0x8a279e6fu, 0x613aa9e9u, 0x34f2f2a3u, 0x43c0d329u, 0x1c3670e2u, 0x97ddae20u, 0x529e8250u, 0x69efea0eu}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 571 /* milli weight units */ } ,[SCALE] = { .tag = JET , .jet = simplicity_scale , .cmr = {{0x126e2212u, 0x5bac80b9u, 0x9b7b7343u, 0xb4e5e586u, 0x60821610u, 0x5d4de6f7u, 0x94add34eu, 0x23b195cau}} , .sourceIx = ty_pw256pw512w256 , .targetIx = ty_pw512w256 , .cost = 73548 /* milli weight units */ } ,[SCRIPT_CMR] = { .tag = JET , .jet = simplicity_bitcoin_script_cmr , .cmr = {{0xa8a4a622u, 0x10b5e495u, 0x0e253424u, 0x7c7411d1u, 0xc8ff2286u, 0x5b5456bbu, 0xb21638e9u, 0x14f5e528u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 122 /* milli weight units */ } ,[SHA_256_BLOCK] = { .tag = JET , .jet = simplicity_sha_256_block , .cmr = {{0x4535f3e1u, 0xab9f1b75u, 0x7a069137u, 0xe1d5b1cau, 0xad8e31f7u, 0x8dc5fbd0u, 0x734649f9u, 0x40a7fc96u}} , .sourceIx = ty_pw256w512 , .targetIx = ty_w256 , .cost = 765 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_1] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_1 , .cmr = {{0x9a4711b8u, 0xc5690e58u, 0x7e5f79e6u, 0x8d6eca04u, 0x7458aa63u, 0xb8bc9ee5u, 0x68086a4au, 0x1b56d834u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w8 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 664 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_128] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_128 , .cmr = {{0x1cb1db8au, 0x055b3197u, 0xacf0f08cu, 0xe9c635adu, 0xd695b60fu, 0x234b18e0u, 0xb323c937u, 0xb0385aeau}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w1Ki , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1778 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_16] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_16 , .cmr = {{0xe0845475u, 0xebb90140u, 0xfa4e01afu, 0x8a943599u, 0x1ad87af9u, 0x8c08aeceu, 0x110e99cbu, 0xcecdee79u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w128 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 781 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_2] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_2 , .cmr = {{0x7d69138fu, 0x1c942beeu, 0x2fdf600cu, 0xe44b36ffu, 0x97839dc2u, 0xbbdafbd5u, 0xfab4dfbcu, 0x3c976f29u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w16 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 674 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_256] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_256 , .cmr = {{0x4f5c29d5u, 0x3686c060u, 0x62b38324u, 0xf8aff17eu, 0xc556a295u, 0xff098b10u, 0xe705dd22u, 0xe13bc3c9u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w2Ki , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 2894 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_32] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_32 , .cmr = {{0xd57b67b1u, 0x74e78e38u, 0xf9bca8e0u, 0x7add61c7u, 0x53e2c156u, 0xd8e9832au, 0xa6620455u, 0x00f51a80u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w256 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 928 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_4] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_4 , .cmr = {{0x95da3299u, 0x3f5c7d00u, 0x83064cdfu, 0xf1bec3b9u, 0x36c63833u, 0x7adec547u, 0x487af232u, 0xd69fdf65u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w32 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 656 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_512] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_512 , .cmr = {{0x4acb163au, 0xa48f09d5u, 0xf26d2b2au, 0xb188a6c6u, 0xb6c4aedfu, 0x23c91900u, 0x1c02ee15u, 0xb337a96eu}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w4Ki , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 5161 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_64] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_64 , .cmr = {{0x52e53ec5u, 0x770f9be4u, 0x069aeefcu, 0xb21322b1u, 0x3ab6e394u, 0x1fdc2c85u, 0xf4b41be6u, 0x7d38ea7eu}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w512 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1220 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_8] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_8 , .cmr = {{0xc26b28afu, 0xe5e866d8u, 0x4616814du, 0x1a13fb86u, 0x30b9e84eu, 0x5d781556u, 0xc6d8236eu, 0xfb45dff9u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w64 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 694 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_BUFFER_511] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_buffer_511 , .cmr = {{0xad699046u, 0x48a8238du, 0x00d85163u, 0xfce81963u, 0xa0047ab5u, 0x82be97a4u, 0x14006559u, 0x79cfdd28u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 5137 /* milli weight units */ } ,[SHA_256_CTX_8_FINALIZE] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_finalize , .cmr = {{0x8e45bdc3u, 0x87d4edfau, 0x733525f3u, 0xab19e42bu, 0x58ecb1b5u, 0xf6dccf94u, 0xedbf5995u, 0x8ae3e116u}} , .sourceIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .targetIx = ty_w256 , .cost = 833 /* milli weight units */ } ,[SHA_256_CTX_8_INIT] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_init , .cmr = {{0x635f6405u, 0x848685c0u, 0x11febd41u, 0xfaac874bu, 0xbbf5b24du, 0x5fb12fedu, 0xbcb6cbffu, 0x95a0f366u}} , .sourceIx = ty_u , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 123 /* milli weight units */ } ,[SHA_256_IV] = { .tag = JET , .jet = simplicity_sha_256_iv , .cmr = {{0x12e45937u, 0x51c9463bu, 0x562503c1u, 0x40d78b3bu, 0x757a1f4fu, 0x16321d28u, 0x62d32543u, 0x8538971bu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 92 /* milli weight units */ } ,[SIG_ALL_HASH] = { .tag = JET , .jet = simplicity_bitcoin_sig_all_hash , .cmr = {{0x0978b9e5u, 0x0b9e8e09u, 0x8b27f2b8u, 0xb59de54fu, 0x62ba7c13u, 0x33df3bedu, 0x221e2662u, 0x6805bc55u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 120 /* milli weight units */ } ,[SOME_1] = { .tag = JET , .jet = simplicity_some_1 , .cmr = {{0x15ca4e4bu, 0x82c2f91bu, 0x9a792992u, 0xcdc1b292u, 0xab86a2d2u, 0x939c9a64u, 0xb50be60bu, 0xda6ab4cau}} , .sourceIx = ty_b , .targetIx = ty_b , .cost = 60 /* milli weight units */ } ,[SOME_16] = { .tag = JET , .jet = simplicity_some_16 , .cmr = {{0xa9dfbbeau, 0xb59df72au, 0x45fc3fc7u, 0xac581ec8u, 0xda713f2fu, 0x8103f787u, 0xaa1cee4eu, 0x0ba64866u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 52 /* milli weight units */ } ,[SOME_32] = { .tag = JET , .jet = simplicity_some_32 , .cmr = {{0x4633a397u, 0x742ef482u, 0xbe2fa3fbu, 0x6410ec79u, 0xc3738365u, 0x69fbbcb1u, 0xf948ec32u, 0x487378b7u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 49 /* milli weight units */ } ,[SOME_64] = { .tag = JET , .jet = simplicity_some_64 , .cmr = {{0x1dc245acu, 0x6f5b422bu, 0xd1886ef5u, 0x144c4dc7u, 0x2c967315u, 0x5966076cu, 0xd839681du, 0x9ec7f8f5u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 62 /* milli weight units */ } ,[SOME_8] = { .tag = JET , .jet = simplicity_some_8 , .cmr = {{0x33afb9c6u, 0x454e590eu, 0xc13ed75eu, 0x1b7d9c3au, 0x3de6752bu, 0xcc7c1d4cu, 0xb363fa51u, 0x828bcb74u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 57 /* milli weight units */ } ,[SUBTRACT_16] = { .tag = JET , .jet = simplicity_subtract_16 , .cmr = {{0x4e06ec31u, 0x376222e2u, 0x5e27d015u, 0x9dc1c071u, 0x4a44ca6au, 0xacf9505cu, 0xaad280e9u, 0x73fb5cabu}} , .sourceIx = ty_w32 , .targetIx = ty_pbw16 , .cost = 93 /* milli weight units */ } ,[SUBTRACT_32] = { .tag = JET , .jet = simplicity_subtract_32 , .cmr = {{0xb9c0f36eu, 0x7522a8d9u, 0x49050d51u, 0x6a05ce20u, 0x3a1f9a9eu, 0x372fd263u, 0xde38b0e9u, 0x03134198u}} , .sourceIx = ty_w64 , .targetIx = ty_pbw32 , .cost = 87 /* milli weight units */ } ,[SUBTRACT_64] = { .tag = JET , .jet = simplicity_subtract_64 , .cmr = {{0x1cdb5c74u, 0xadd102f5u, 0x0f938ed8u, 0x86f496e5u, 0xbab2755cu, 0x3c484e88u, 0x87903d2fu, 0x6a57f3aau}} , .sourceIx = ty_w128 , .targetIx = ty_pbw64 , .cost = 125 /* milli weight units */ } ,[SUBTRACT_8] = { .tag = JET , .jet = simplicity_subtract_8 , .cmr = {{0x4f2117a0u, 0xe81059ffu, 0x0cd64d84u, 0x886542e5u, 0x75ea8d6eu, 0xc03108fdu, 0x0b508b39u, 0x208cd0efu}} , .sourceIx = ty_w16 , .targetIx = ty_pbw8 , .cost = 96 /* milli weight units */ } ,[SWU] = { .tag = JET , .jet = simplicity_swu , .cmr = {{0x00f51f4fu, 0x4bece790u, 0x03ecad48u, 0x1a125af7u, 0x176e4de9u, 0x8c339242u, 0x5cb91466u, 0x26c13b3bu}} , .sourceIx = ty_w256 , .targetIx = ty_w512 , .cost = 32780 /* milli weight units */ } ,[TAP_ENV_HASH] = { .tag = JET , .jet = simplicity_bitcoin_tap_env_hash , .cmr = {{0x19d9944cu, 0x4d457c70u, 0xbabc45ccu, 0xcbd573b3u, 0x9a51d0c9u, 0x9115b412u, 0x783b4900u, 0x82fd0e58u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 120 /* milli weight units */ } ,[TAPDATA_INIT] = { .tag = JET , .jet = simplicity_tapdata_init , .cmr = {{0xa4d022efu, 0x5cf467bcu, 0xa0325e46u, 0x3fcace7cu, 0xbdd64ff8u, 0xf71c5c7fu, 0x63e60784u, 0xaa0ac486u}} , .sourceIx = ty_u , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1233 /* milli weight units */ } ,[TAPLEAF_HASH] = { .tag = JET , .jet = simplicity_bitcoin_tapleaf_hash , .cmr = {{0x0c0716feu, 0x5d978ea8u, 0xe0c75adcu, 0x8210d660u, 0x062e3da0u, 0x6f1a6661u, 0x317927d3u, 0xb84b5073u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 116 /* milli weight units */ } ,[TAPLEAF_VERSION] = { .tag = JET , .jet = simplicity_bitcoin_tapleaf_version , .cmr = {{0xe2ecb1cbu, 0x0ed4ed93u, 0x483545fdu, 0x8a62f8aau, 0x10175349u, 0xffcc5ad3u, 0xde7f3484u, 0xea1f103fu}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 66 /* milli weight units */ } ,[TAPPATH] = { .tag = JET , .jet = simplicity_bitcoin_tappath , .cmr = {{0x99e8211eu, 0x8c1be6d9u, 0xca98d3d4u, 0x3d914256u, 0x7e06a840u, 0x22393303u, 0xfab0b57du, 0x394074e8u}} , .sourceIx = ty_w8 , .targetIx = ty_mw256 , .cost = 76 /* milli weight units */ } ,[TAPPATH_HASH] = { .tag = JET , .jet = simplicity_bitcoin_tappath_hash , .cmr = {{0x0211546du, 0x0778e787u, 0x141ece65u, 0xdf6cd1dbu, 0x31388fc1u, 0x421968c8u, 0xcfd8d759u, 0x26db47b3u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 123 /* milli weight units */ } ,[TOTAL_INPUT_VALUE] = { .tag = JET , .jet = simplicity_bitcoin_total_input_value , .cmr = {{0x81287a15u, 0x89ddc217u, 0x9926b706u, 0x5e9b2677u, 0xb7fb099bu, 0x95f947a7u, 0xdd590cddu, 0x4ccf4a56u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 69 /* milli weight units */ } ,[TOTAL_OUTPUT_VALUE] = { .tag = JET , .jet = simplicity_bitcoin_total_output_value , .cmr = {{0xba032f3eu, 0x62f8fcb0u, 0x4b0429a2u, 0x53b5ec57u, 0xe4c87ae2u, 0xe951e145u, 0xd7650e7fu, 0x0c63e555u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 71 /* milli weight units */ } ,[TRANSACTION_ID] = { .tag = JET , .jet = simplicity_bitcoin_transaction_id , .cmr = {{0x5c49ea98u, 0x6b328be2u, 0xa4e0b315u, 0xb6b3fef2u, 0x3c1f6856u, 0xbbc3b056u, 0xc99cf59fu, 0xbd546e65u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 122 /* milli weight units */ } ,[TX_HASH] = { .tag = JET , .jet = simplicity_bitcoin_tx_hash , .cmr = {{0x54e53c99u, 0x93abd55du, 0x1f8523d2u, 0xbb217b32u, 0xe6fe861fu, 0x84c986b7u, 0xee8bdc68u, 0x8106874au}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 119 /* milli weight units */ } ,[TX_IS_FINAL] = { .tag = JET , .jet = simplicity_bitcoin_tx_is_final , .cmr = {{0x7b0e4f4cu, 0xa8e5af61u, 0xa1d3454eu, 0x11ef9ab6u, 0x88706121u, 0x1c0090ebu, 0xa9553da2u, 0xe45d8473u}} , .sourceIx = ty_u , .targetIx = ty_b , .cost = 62 /* milli weight units */ } ,[TX_LOCK_DISTANCE] = { .tag = JET , .jet = simplicity_bitcoin_tx_lock_distance , .cmr = {{0xb6fbaac2u, 0x10a306beu, 0x8b58d0d7u, 0xb1563f62u, 0x2336d2aeu, 0xb56c393du, 0x276445a9u, 0xa22cc4a7u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 72 /* milli weight units */ } ,[TX_LOCK_DURATION] = { .tag = JET , .jet = simplicity_bitcoin_tx_lock_duration , .cmr = {{0x53572818u, 0xe7e5b98fu, 0x968c9da7u, 0xdf5090d9u, 0x826f9bcfu, 0x84b63639u, 0x5eea321bu, 0x6909ece9u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 66 /* milli weight units */ } ,[TX_LOCK_HEIGHT] = { .tag = JET , .jet = simplicity_bitcoin_tx_lock_height , .cmr = {{0x449f61dfu, 0x1a7bad8du, 0x9e0a9667u, 0x14227e57u, 0x1007f93cu, 0x517b805du, 0x616510e8u, 0xff62172bu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 72 /* milli weight units */ } ,[TX_LOCK_TIME] = { .tag = JET , .jet = simplicity_bitcoin_tx_lock_time , .cmr = {{0x31df363fu, 0x17b2cfc9u, 0x7a1f9372u, 0xc14a3258u, 0x64d7cb13u, 0xaa8d5215u, 0xfb253d33u, 0x10917762u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 72 /* milli weight units */ } ,[VERIFY] = { .tag = JET , .jet = simplicity_verify , .cmr = {{0xcdca2a05u, 0xe52cefa5u, 0x9dc7a5b0u, 0xdae22098u, 0xfb896e39u, 0x13bfdd44u, 0x6b594e1fu, 0x9250783eu}} , .sourceIx = ty_b , .targetIx = ty_u , .cost = 44 /* milli weight units */ } ,[VERSION] = { .tag = JET , .jet = simplicity_bitcoin_version , .cmr = {{0x83735864u, 0x00b6790bu, 0x46ab0410u, 0x523cf01eu, 0xb74d10fau, 0xf48a3accu, 0x86c4c51du, 0x06a52c49u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 78 /* milli weight units */ } ,[XOR_1] = { .tag = JET , .jet = simplicity_xor_1 , .cmr = {{0x8c4e4e6eu, 0xbf4630b2u, 0x9b5a57eau, 0x79f0c9afu, 0x6bff54c4u, 0xd2d769bfu, 0x51594774u, 0xa52b99c9u}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 60 /* milli weight units */ } ,[XOR_16] = { .tag = JET , .jet = simplicity_xor_16 , .cmr = {{0xd9f0af3fu, 0xe3fd247cu, 0x1df34a25u, 0x2713b2e9u, 0x33a945a5u, 0x6719487fu, 0x8ed7f563u, 0xea861ab5u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 73 /* milli weight units */ } ,[XOR_32] = { .tag = JET , .jet = simplicity_xor_32 , .cmr = {{0xd5ae2712u, 0xedeaf676u, 0x520fa3bau, 0x0f40bf4au, 0x1657437eu, 0xffbd9986u, 0xd06ae81bu, 0x29a4f98cu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 77 /* milli weight units */ } ,[XOR_64] = { .tag = JET , .jet = simplicity_xor_64 , .cmr = {{0xc4df1ccfu, 0x333edebdu, 0xd40dea9au, 0x0e6cbb83u, 0x0631e83au, 0x94bb779fu, 0xe6007bc6u, 0xcb53a544u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 68 /* milli weight units */ } ,[XOR_8] = { .tag = JET , .jet = simplicity_xor_8 , .cmr = {{0x4ab14a81u, 0x4a39528au, 0x80fdb430u, 0x589ba450u, 0x104b9c72u, 0x09aa2fe2u, 0x85cd60c0u, 0x9043114au}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 80 /* milli weight units */ } ,[XOR_XOR_1] = { .tag = JET , .jet = simplicity_xor_xor_1 , .cmr = {{0x18b9446au, 0x4166a3feu, 0xe2bcb254u, 0x5bb90118u, 0xdcf0e8f8u, 0x86a1076du, 0x4c386006u, 0x0cde1a51u}} , .sourceIx = ty_pbw2 , .targetIx = ty_b , .cost = 50 /* milli weight units */ } ,[XOR_XOR_16] = { .tag = JET , .jet = simplicity_xor_xor_16 , .cmr = {{0x946cde87u, 0x2e30e650u, 0x9daff405u, 0xf0e0fefeu, 0x275547b4u, 0x0eb20384u, 0xafe9a863u, 0x60fc80efu}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 82 /* milli weight units */ } ,[XOR_XOR_32] = { .tag = JET , .jet = simplicity_xor_xor_32 , .cmr = {{0x6527df67u, 0xa50d148du, 0xb4fc8feeu, 0xc7845564u, 0x99a8c7f0u, 0xfa7d28e6u, 0x278e997fu, 0x4959be39u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 82 /* milli weight units */ } ,[XOR_XOR_64] = { .tag = JET , .jet = simplicity_xor_xor_64 , .cmr = {{0xf162f9e6u, 0x5663a69au, 0xc5f92a5eu, 0xb52c0332u, 0x392edd1eu, 0xd1ba355eu, 0x6f19406eu, 0xabe3f6edu}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 80 /* milli weight units */ } ,[XOR_XOR_8] = { .tag = JET , .jet = simplicity_xor_xor_8 , .cmr = {{0xe06d694cu, 0x5b407ddau, 0xd7aa1f88u, 0x0716bcb7u, 0x0acdba75u, 0x85ca4009u, 0x9a0a0a61u, 0xf3ad2db5u}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 86 /* milli weight units */ } ================================================ FILE: C/bitcoin/txEnv.c ================================================ #include "txEnv.h" /* Construct a txEnv structure from its components. * This function will precompute any cached values. * * Precondition: NULL != tx * NULL != taproot * ix < tx->numInputs */ txEnv simplicity_bitcoin_build_txEnv(const bitcoinTransaction* tx, const bitcoinTapEnv* taproot, uint_fast32_t ix) { txEnv result = { .tx = tx , .taproot = taproot , .ix = ix }; sha256_context ctx = sha256_init(result.sigAllHash.s); sha256_hash(&ctx, &tx->txHash); sha256_hash(&ctx, &taproot->tapEnvHash); sha256_u32be(&ctx, ix); sha256_finalize(&ctx); return result; } ================================================ FILE: C/bitcoin/txEnv.h ================================================ /* This module defines the environment ('txEnv') for Simplicity evaluation for Bitcoin. * It includes the transaction data and input index of the input whose Simplicity program is being executed. * It also includes the commitment Merkle root of the program being executed. */ #ifndef SIMPLICITY_BITCOIN_TXENV_H #define SIMPLICITY_BITCOIN_TXENV_H #include #include "../sha256.h" /* An Bitcoin 'outpoint' consists of a transaction id and output index within that transaction. */ typedef struct outpoint { sha256_midstate txid; uint_fast32_t ix; } outpoint; /* A structure representing data from one output from a Bitcoin transaction. * 'scriptPubKey' is the SHA-256 hash of the outputs scriptPubKey. */ typedef struct sigOutput { uint_fast64_t value; sha256_midstate scriptPubKey; } sigOutput; /* A structure representing data from one input from a Bitcoin transaction along with the utxo data of the output being redeemed. * When 'hasAnnex' then 'annexHash' is a cache of the hash of the input's segwit annex. */ typedef struct sigInput { sha256_midstate annexHash; sha256_midstate scriptSigHash; outpoint prevOutpoint; sigOutput txo; uint_fast32_t sequence; bool hasAnnex; } sigInput; /* A structure representing data from a Bitcoin transaction (along with the utxo data of the outputs being redeemed). * Includes a variety of cached hash values that are used in signature hash jets. */ typedef struct bitcoinTransaction { const sigInput* input; const sigOutput* output; sha256_midstate outputValuesHash; sha256_midstate outputScriptsHash; sha256_midstate outputsHash; sha256_midstate inputOutpointsHash; sha256_midstate inputValuesHash; sha256_midstate inputScriptsHash; sha256_midstate inputUTXOsHash; sha256_midstate inputSequencesHash; sha256_midstate inputAnnexesHash; sha256_midstate inputScriptSigsHash; sha256_midstate inputsHash; sha256_midstate txHash; sha256_midstate txid; uint_fast64_t totalInputValue; uint_fast64_t totalOutputValue; uint_fast32_t numInputs; uint_fast32_t numOutputs; uint_fast32_t version; uint_fast32_t lockTime; bool isFinal; } bitcoinTransaction; /* A structure representing taproot spending data from a Bitcoin transaction. * * Invariant: pathLen <= 128 * sha256_midstate path[pathLen]; */ typedef struct bitcoinTapEnv { const sha256_midstate *path; sha256_midstate tapLeafHash; sha256_midstate tappathHash; sha256_midstate tapEnvHash; sha256_midstate internalKey; sha256_midstate scriptCMR; unsigned char pathLen; unsigned char leafVersion; } bitcoinTapEnv; /* The 'txEnv' structure used by the Bitcoin application of Simplicity. * * It includes * + the transaction data, which may be shared when Simplicity expressions are used for multiple inputs in the same transaction), * + the input index under consideration, */ typedef struct txEnv { const bitcoinTransaction* tx; const bitcoinTapEnv* taproot; sha256_midstate sigAllHash; uint_fast32_t ix; } txEnv; /* Construct a txEnv structure from its components. * This function will precompute any cached values. * * Precondition: NULL != tx * NULL != taproot * ix < tx->numInputs */ txEnv simplicity_bitcoin_build_txEnv(const bitcoinTransaction* tx, const bitcoinTapEnv* taproot, uint_fast32_t ix); #endif ================================================ FILE: C/bitstream.c ================================================ #include "bitstream.h" #include #include "simplicity_assert.h" /* Closes a bitstream by consuming all remaining bits. * Returns 'SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES' if CHAR_BIT or more bits remain in the stream. * Otherwise, returns 'SIMPLICITY_ERR_BITSTREAM_ILLEGAL_PADDING' if any remaining bits are non-zero. * Otherwise returns 'SIMPLICITY_NO_ERROR'. * * Precondition: NULL != stream */ simplicity_err simplicity_closeBitstream(bitstream* stream) { if (1 < stream->len) return SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES; /* If there is more than one byte remaining. */ if (1 == stream->len) { if (0 == stream->offset) return SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES; /* If there is one byte remaining */ if (0 != (*stream->arr & (UCHAR_MAX >> stream->offset))) { /* If any of the unconsumed bits are non-zero */ return SIMPLICITY_ERR_BITSTREAM_ILLEGAL_PADDING; } } /* Otherwise there are either 0 bits remaining or there are between 1 and CHAR_BITS-1 bits remaining and they are all zero. */ *stream = (bitstream){0}; return SIMPLICITY_NO_ERROR; } /* Fetches up to 31 bits from 'stream' as the 'n' least significant bits of return value. * The 'n' bits are set from the MSB to the LSB. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if not enough bits are available. * * Precondition: 0 <= n < 32 * NULL != stream */ int32_t simplicity_readNBits(int n, bitstream* stream) { simplicity_assert(0 <= n && n < 32); uint32_t result = 0; while (CHAR_BIT <= stream->offset + n) { if (!stream->len) return SIMPLICITY_ERR_BITSTREAM_EOF; n -= CHAR_BIT - stream->offset; result |= (uint32_t)(*stream->arr & (UCHAR_MAX >> stream->offset)) << n; stream->arr++; stream->len--; stream->offset = 0; } /* stream->offset + n < CHAR_BIT */ if (n) { if (!stream->len) return SIMPLICITY_ERR_BITSTREAM_EOF; stream->offset += (unsigned char)n; result |= (*stream->arr >> (CHAR_BIT - stream->offset)) & ((UCHAR_MAX >> (CHAR_BIT - n))); } return (int32_t)result; } /* Decode an encoded bitstring up to length 1. * If successful returns the length of the bitstring and 'result' contains the decoded bits. * The decoded bitstring is stored in the LSBs of 'result', with the LSB being the last bit decoded. * Any remaining bits in 'result' are reset to 0. * If the decoded bitstring would be too long 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned ('result' may be modified). * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned ('result' may be modified). * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned ('result' may be modified). * * Precondition: NULL != result * NULL != stream */ static int32_t decodeUpto1Bit(int32_t* result, bitstream* stream) { *result = read1Bit(stream); if (*result <= 0) return *result; *result = read1Bit(stream); if (*result < 0) return *result; if (0 != *result) return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; *result = read1Bit(stream); if (*result < 0) return *result; return 1; } /* Decode an encoded number between 1 and 3 inclusive. * When successful returns the decoded result. * If the decoded value would be too large, 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned. * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned. * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned. * * Precondition: NULL != stream */ static int32_t decodeUpto3(bitstream* stream) { int32_t result; int32_t len = decodeUpto1Bit(&result, stream); if (len < 0) return len; result |= 1 << len; return result; } /* Decode an encoded bitstring up to length 3. * If successful returns the length of the bitstring and 'result' contains the decoded bits. * The decoded bitstring is stored in the LSBs of 'result', with the LSB being the last bit decoded. * Any remaining bits in 'result' are reset to 0. * If the decoded bitstring would be too long 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned ('result' may be modified). * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned ('result' may be modified). * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned ('result' may be modified). * * Precondition: NULL != result * NULL != stream */ static int32_t decodeUpto3Bits(int32_t* result, bitstream* stream) { int32_t bit = read1Bit(stream); if (bit < 0) return bit; *result = 0; if (0 == bit) { return 0; } else { int32_t n = decodeUpto3(stream); if (0 <= n) { *result = simplicity_readNBits(n, stream); if (*result < 0) return *result; } return n; } } /* Decode an encoded number between 1 and 15 inclusive. * When successful returns the decoded result. * If the decoded value would be too large, 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned. * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned. * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned. * * Precondition: NULL != stream */ static int32_t decodeUpto15(bitstream* stream) { int32_t result; int32_t len = decodeUpto3Bits(&result, stream); if (len < 0) return len; result |= 1 << len; return result; } /* Decode an encoded bitstring up to length 15. * If successful returns the length of the bitstring and 'result' contains the decoded bits. * The decoded bitstring is stored in the LSBs of 'result', with the LSB being the last bit decoded. * Any remaining bits in 'result' are reset to 0. * If the decoded bitstring would be too long 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned ('result' may be modified). * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned ('result' may be modified). * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned ('result' may be modified). * * Precondition: NULL != result * NULL != stream */ static int32_t decodeUpto15Bits(int32_t* result, bitstream* stream) { int32_t bit = read1Bit(stream); if (bit < 0) return bit; *result = 0; if (0 == bit) { return 0; } else { int32_t n = decodeUpto15(stream); if (0 <= n) { *result = simplicity_readNBits(n, stream); if (*result < 0) return *result; } return n; } } /* Decode an encoded number between 1 and 65535 inclusive. * When successful returns the decoded result. * If the decoded value would be too large, 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned. * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned. * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned. * * Precondition: NULL != stream */ static int32_t decodeUpto65535(bitstream* stream) { int32_t result; int32_t len = decodeUpto15Bits(&result, stream); if (len < 0) return len; result |= 1 << len; return result; } /* Decode an encoded number between 1 and 2^31 - 1 inclusive. * When successful returns the decoded result. * If the decoded value would be too large, 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned. * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned. * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned. * * Precondition: NULL != stream */ int32_t simplicity_decodeUptoMaxInt(bitstream* stream) { int32_t bit = read1Bit(stream); if (bit < 0) return bit; if (0 == bit) { return 1; } else { int32_t n = decodeUpto65535(stream); if (n < 0) return n; if (30 < n) return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; { int32_t result = simplicity_readNBits(n, stream); if (result < 0) return result; return ((1 << n) | result); } } } /* Fills a 'bitstring' containing 'n' bits from 'stream'. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if not enough bits are available. * If successful, '*result' is set to a bitstring with 'n' bits read from 'stream' and 'SIMPLICITY_NO_ERROR' is returned. * * If an error is returned '*result' might be modified. * * Precondition: NULL != result * n <= 2^31 * NULL != stream */ simplicity_err simplicity_readBitstring(bitstring* result, size_t n, bitstream* stream) { static_assert(0x80000000u + 2*(CHAR_BIT - 1) <= SIZE_MAX, "size_t needs to be at least 32-bits"); simplicity_assert(n <= 0x80000000u); size_t total_offset = n + stream->offset; /* |= stream->len * CHAR_BIT < total_offset iff stream->len < (total_offset + (CHAR_BIT - 1)) / CHAR_BIT */ if (stream->len < (total_offset + (CHAR_BIT - 1)) / CHAR_BIT) return SIMPLICITY_ERR_BITSTREAM_EOF; /* total_offset <= stream->len * CHAR_BIT */ *result = (bitstring) { .arr = stream->arr , .offset = stream->offset , .len = n }; { size_t delta = total_offset / CHAR_BIT; stream->arr += delta; stream->len -= delta; stream->offset = total_offset % CHAR_BIT; /* Note that if 0 == stream->len then 0 == stream->offset. */ } return SIMPLICITY_NO_ERROR; } ================================================ FILE: C/bitstream.h ================================================ /* This module provides functions for initializing and reading from a stream of bits from a 'FILE'. */ #ifndef SIMPLICITY_BITSTREAM_H #define SIMPLICITY_BITSTREAM_H #include #include #include #include #include "bitstring.h" /* :TODO: consider adding an 'invalid' state that can be set when parsing has failed and should not be resumed. */ /* Datatype representing a bit stream. * Bits are streamed from MSB to LSB. * * Invariant: unsigned char arr[len] * 0 <= offset < CHAR_BIT * 0 == len implies 0 == offset */ typedef struct bitstream { const unsigned char *arr; /* Underlying byte array */ size_t len; /* Length of arr (in bytes) */ unsigned char offset; /* Number of bits parsed from the beginning of arr */ } bitstream; /* Initialize a bit stream, 'stream', from a given byte array. * Precondition: unsigned char arr[len]; */ static inline bitstream initializeBitstream(const unsigned char* arr, size_t len) { return (bitstream){ .arr = arr, .len = len }; } /* Closes a bitstream by consuming all remaining bits. * Returns 'SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES' if CHAR_BIT or more bits remain in the stream. * Otherwise, returns 'SIMPLICITY_ERR_BITSTREAM_ILLEGAL_PADDING' if any remaining bits are non-zero. * Otherwise returns 'SIMPLICITY_NO_ERROR'. * * Precondition: NULL != stream */ simplicity_err simplicity_closeBitstream(bitstream* stream); /* Fetches up to 31 bits from 'stream' as the 'n' least significant bits of return value. * The 'n' bits are set from the MSB to the LSB. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if not enough bits are available. * * Precondition: 0 <= n < 32 * NULL != stream */ int32_t simplicity_readNBits(int n, bitstream* stream); /* Returns one bit from 'stream', 0 or 1. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if no bits are available. * * Precondition: NULL != stream */ static inline int32_t read1Bit(bitstream* stream) { return simplicity_readNBits(1, stream); } /* Decode an encoded number between 1 and 2^31 - 1 inclusive. * When successful returns the decoded result. * If the decoded value would be too large, 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' is returned. * If more bits are needed than available in the 'stream', 'SIMPLICITY_ERR_BITSTRING_EOF' is returned. * If an I/O error occurs when reading from the 'stream', 'SIMPLICITY_ERR_BISTRING_ERROR' is returned. * * Precondition: NULL != stream */ int32_t simplicity_decodeUptoMaxInt(bitstream* stream); /* Fills a 'bitstring' containing 'n' bits from 'stream'. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if not enough bits are available. * If successful, '*result' is set to a bitstring with 'n' bits read from 'stream' and 'SIMPLICITY_NO_ERROR' is returned. * * If an error is returned '*result' might be modified. * * Precondition: NULL != result * n <= 2^31 * NULL != stream */ simplicity_err simplicity_readBitstring(bitstring* result, size_t n, bitstream* stream); #endif ================================================ FILE: C/bitstring.h ================================================ /* This modules defines a structure representing bit strings. */ #ifndef SIMPLICITY_BITSTRING_H #define SIMPLICITY_BITSTRING_H #include #include #include #include #include "simplicity_assert.h" /* Represents a bitstring of length 'len' bits using an array of unsigned char. * The bit at index 'n', where 0 <= 'n' < 'len', is located at bit '1 << (CHAR_BIT - 1 - (offset + n) % CHAR_BIT)' of * array element 'arr[(offset + n) / CHAR_BIT]'. * Other bits in the array may be any value. * * Invariant: len <= 2^31 * offset + length <= SIZE_MAX * 0 < len implies unsigned char arr[(offset + len - 1) / CHAR_BIT + 1]; */ typedef struct bitstring { const unsigned char* arr; size_t len; size_t offset; } bitstring; /* Return the nth bit from a bitstring. * * Precondition: NULL != s * n < s->len; */ static inline bool getBit(const bitstring *s, size_t n) { size_t total_offset = s->offset + n; simplicity_assert(n < s->len); return 1 & (s->arr[total_offset / CHAR_BIT] >> (CHAR_BIT - 1 - (total_offset % CHAR_BIT))); } /* Return 8 bits from a bitstring staring from the nth bit. * * Precondition: NULL != s * n + 8 <= s->len; */ static inline uint_fast8_t getByte(const bitstring *s, size_t n) { simplicity_assert(8 <= s->len); simplicity_assert(n <= s->len - 8); size_t total_offset = s->offset + n; if (total_offset % CHAR_BIT <= CHAR_BIT - 8) { return (uint_fast8_t)(0xff & (s->arr[total_offset / CHAR_BIT] >> (CHAR_BIT - 8 - (total_offset % CHAR_BIT)))); } else { /* CHAR_BIT < total_offset % CHAR_BIT + 8 */ return (uint_fast8_t)(0xff & (((1U * s->arr[total_offset / CHAR_BIT]) << (total_offset % CHAR_BIT - (CHAR_BIT - 8))) | (s->arr[total_offset / CHAR_BIT + 1] >> (CHAR_BIT - (total_offset % CHAR_BIT - (CHAR_BIT - 8)))))); } } #endif ================================================ FILE: C/bounded.h ================================================ #ifndef SIMPLICITY_BOUNDED_H #define SIMPLICITY_BOUNDED_H #include #include typedef uint_least32_t ubounded; #define UBOUNDED_MAX UINT32_MAX static inline ubounded bounded_max(ubounded x, ubounded y) { return x <= y ? y : x; } /* Returns min(x + y, UBOUNDED_MAX) */ static inline ubounded bounded_add(ubounded x, ubounded y) { return UBOUNDED_MAX < x ? UBOUNDED_MAX : UBOUNDED_MAX - x < y ? UBOUNDED_MAX : x + y; } /* *x = min(*x + 1, UBOUNDED_MAX) */ static inline void bounded_inc(ubounded* x) { if (*x < UBOUNDED_MAX) (*x)++; } /* 'pad(false, a, b)' computes the PADL(a, b) function. * 'pad( true, a, b)' computes the PADR(a, b) function. */ static inline ubounded pad(bool right, ubounded a, ubounded b) { return bounded_max(a, b) - (right ? b : a); } enum { overhead = 100 }; /* milli weight units */ #endif ================================================ FILE: C/ctx8Pruned.c ================================================ #include "ctx8Pruned.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&& * (ctx8Init &&& scribe (toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn vector16 >>> ctx8Finalize) >>> * eq >>> verify */ const unsigned char ctx8Pruned[] = { 0xeb, 0x11, 0xe9, 0x20, 0x40, 0x82, 0xe0, 0x2c, 0x02, 0x98, 0x8a, 0x05, 0x88, 0x58, 0xe2, 0x2c, 0x42, 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0x30, 0xf0, 0x50, 0x2c, 0x47, 0xcc, 0x3c, 0x54, 0x05, 0x03, 0xab, 0x09, 0xea, 0x8c, 0x01, 0x00, 0xe3, 0xf0 }; const size_t sizeof_ctx8Pruned = sizeof(ctx8Pruned); const unsigned char ctx8Pruned_witness[] = ""; const size_t sizeof_ctx8Pruned_witness = 0; /* The commitment Merkle root of the above ctx8Pruned Simplicity expression. */ const uint32_t ctx8Pruned_cmr[] = { 0x7f11746fu, 0xb68fdaedu, 0x3cadda80u, 0xc7cd0245u, 0xa341b927u, 0xe98e60f8u, 0x745dc441u, 0xe11ce1a3u }; /* The identity hash of the root of the above ctx8Pruned Simplicity expression. */ const uint32_t ctx8Pruned_ihr[] = { 0x8e8742acu, 0x27f42d29u, 0xd87f5229u, 0x02bc0ae2u, 0xbcfc1298u, 0x1641a2ddu, 0x77091830u, 0xb79bf12du }; /* The annotated Merkle root of the above ctx8Pruned Simplicity expression. */ const uint32_t ctx8Pruned_amr[] = { 0x6ee37b0cu, 0x66d30684u, 0x7f3c8290u, 0xbbd9e65fu, 0x30576a3au, 0x904cae07u, 0x932c3790u, 0x92a8310du }; /* The cost of the above ctx8Pruned Simplicity expression in milli weight units. */ const ubounded ctx8Pruned_cost = 274149781; ================================================ FILE: C/ctx8Pruned.h ================================================ #ifndef SIMPLICITY_CTX8PRUNED_H #define SIMPLICITY_CTX8PRUNED_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&& * (ctx8Init &&& scribe (toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn vector16 >>> ctx8Finalize) >>> * eq >>> verify */ extern const unsigned char ctx8Pruned[]; extern const size_t sizeof_ctx8Pruned; extern const unsigned char ctx8Pruned_witness[]; extern const size_t sizeof_ctx8Pruned_witness; /* The commitment Merkle root of the above ctx8Pruned Simplicity expression. */ extern const uint32_t ctx8Pruned_cmr[]; /* The identity hash of the root of the above ctx8Pruned Simplicity expression. */ extern const uint32_t ctx8Pruned_ihr[]; /* The annotated Merkle root of the above ctx8Pruned Simplicity expression. */ extern const uint32_t ctx8Pruned_amr[]; /* The cost of the above ctx8Pruned Simplicity expression in milli weight units. */ extern const ubounded ctx8Pruned_cost; #endif ================================================ FILE: C/ctx8Unpruned.c ================================================ #include "ctx8Unpruned.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&& * (ctx8Init &&& scribe (toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn vector16 >>> ctx8Finalize) >>> * eq >>> verify */ const unsigned char ctx8Unpruned[] = { 0xeb, 0x1a, 0x49, 0x20, 0x40, 0x82, 0xe0, 0x2c, 0x02, 0x98, 0x8a, 0x05, 0x88, 0x58, 0xe2, 0x2c, 0x42, 0x9a, 0x45, 0x02, 0xc4, 0x2d, 0x3a, 0x45, 0xb7, 0x21, 0x40, 0xb7, 0xec, 0x17, 0x00, 0xd8, 0x28, 0x16, 0x01, 0x68, 0x0b, 0x80, 0x70, 0x11, 0x70, 0x00, 0xb7, 0x69, 0x14, 0x0b, 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0xc2, 0x75, 0x58, 0x49, 0x20, 0xe3, 0xe4, 0x18, 0x06, 0x40, 0x75, 0x5b, 0x61, 0x3a, 0xad, 0x64, 0x90, 0x71, 0xf2, 0x0c, 0x03, 0x20, 0x3a, 0xaf, 0x00, 0x9d, 0x57, 0x59, 0x39, 0xef, 0x38, 0xf8, 0x86, 0x01, 0x88, 0x1d, 0x58, 0x20, 0x4e, 0xab, 0xfc, 0x9c, 0xd2, 0x9c, 0x7c, 0x43, 0x00, 0xc4, 0x0e, 0xac, 0x54, 0x27, 0x56, 0x22, 0x4e, 0x9d, 0x69, 0xc7, 0xc4, 0x30, 0x0c, 0x40, 0xea, 0xc9, 0xc2, 0x75, 0x64, 0x47, 0xea, 0x8d, 0xcf, 0x80, 0x60, 0x18, 0x01, 0xc6, 0xc1, 0x74, 0xf4, 0x7a, 0x79, 0x62, 0x83, 0xf4, 0x2a, 0x1f, 0x10, 0xc0, 0x30, 0x03, 0x8f, 0xc7, 0xea, 0xe4, 0x0c, 0x3c, 0x14, 0x0b, 0x11, 0x39, 0xe5, 0x38, 0xfa, 0x43, 0x00, 0xc4, 0x0e, 0xab, 0xc3, 0xa0, 0xf4, 0x10, 0x0e, 0x47, 0x00 }; const size_t sizeof_ctx8Unpruned = sizeof(ctx8Unpruned); const unsigned char ctx8Unpruned_witness[] = ""; const size_t sizeof_ctx8Unpruned_witness = 0; /* The commitment Merkle root of the above ctx8Unpruned Simplicity expression. */ const uint32_t ctx8Unpruned_cmr[] = { 0x7f11746fu, 0xb68fdaedu, 0x3cadda80u, 0xc7cd0245u, 0xa341b927u, 0xe98e60f8u, 0x745dc441u, 0xe11ce1a3u }; /* The identity hash of the root of the above ctx8Unpruned Simplicity expression. */ const uint32_t ctx8Unpruned_ihr[] = { 0x8e8742acu, 0x27f42d29u, 0xd87f5229u, 0x02bc0ae2u, 0xbcfc1298u, 0x1641a2ddu, 0x77091830u, 0xb79bf12du }; /* The annotated Merkle root of the above ctx8Unpruned Simplicity expression. */ const uint32_t ctx8Unpruned_amr[] = { 0x3e7c69acu, 0xf73edce8u, 0x386c121eu, 0xc3b4d11bu, 0x14923861u, 0xe97ae926u, 0xcccd9f1fu, 0x85a076d5u }; /* The cost of the above ctx8Unpruned Simplicity expression in milli weight units. */ const ubounded ctx8Unpruned_cost = UBOUNDED_MAX; ================================================ FILE: C/ctx8Unpruned.h ================================================ #ifndef SIMPLICITY_CTX8UNPRUNED_H #define SIMPLICITY_CTX8UNPRUNED_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&& * (ctx8Init &&& scribe (toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn vector16 >>> ctx8Finalize) >>> * eq >>> verify */ extern const unsigned char ctx8Unpruned[]; extern const size_t sizeof_ctx8Unpruned; extern const unsigned char ctx8Unpruned_witness[]; extern const size_t sizeof_ctx8Unpruned_witness; /* The commitment Merkle root of the above ctx8Unpruned Simplicity expression. */ extern const uint32_t ctx8Unpruned_cmr[]; /* The identity hash of the root of the above ctx8Unpruned Simplicity expression. */ extern const uint32_t ctx8Unpruned_ihr[]; /* The annotated Merkle root of the above ctx8Unpruned Simplicity expression. */ extern const uint32_t ctx8Unpruned_amr[]; /* The cost of the above ctx8Unpruned Simplicity expression in milli weight units. */ extern const ubounded ctx8Unpruned_cost; #endif ================================================ FILE: C/dag.c ================================================ #include "dag.h" #include #include "bounded.h" #include "precomputed.h" #include "rsort.h" #include "sha256.h" #include "simplicity_alloc.h" #include "uword.h" /* Given a tag for a node, return the SHA-256 hash of its associated CMR tag. * This is the "initial value" for computing the commitment Merkle root for that expression. * * Precondition: 'tag' \notin {HIDDEN, JET, WORD} */ static sha256_midstate cmrIV(tag_t tag) { switch (tag) { case COMP: return cmr_compIV; case ASSERTL: case ASSERTR: case CASE: return cmr_caseIV; case PAIR: return cmr_pairIV; case DISCONNECT: return cmr_disconnectIV; case INJL: return cmr_injlIV; case INJR: return cmr_injrIV; case TAKE: return cmr_takeIV; case DROP: return cmr_dropIV; case IDEN: return cmr_idenIV; case UNIT: return cmr_unitIV; case WITNESS: return cmr_witnessIV; /* Precondition violated. */ case WORD: case HIDDEN: case JET: break; } SIMPLICITY_UNREACHABLE; } /* Given a tag for a node, return the SHA-256 hash of its associated IMR tag. * This is the "initial value" for computing the commitment Merkle root for that expression. * * Precondition: 'tag' \notin {HIDDEN, JET, WORD} */ static sha256_midstate imrIV(tag_t tag) { return DISCONNECT == tag ? imr_disconnectIV : WITNESS == tag ? imr_witnessIV : cmrIV(tag); } /* Given a tag for a node, return the SHA-256 hash of its associated AMR tag. * This is the "initial value" for computing the annotated Merkle root for that expression. * * Precondition: 'tag' \notin {HIDDEN, JET, WORD} */ static sha256_midstate amrIV(tag_t tag) { switch (tag) { case COMP: return amr_compIV; case ASSERTL: return amr_assertlIV; case ASSERTR: return amr_assertrIV; case CASE: return amr_caseIV; case PAIR: return amr_pairIV; case DISCONNECT: return amr_disconnectIV; case INJL: return amr_injlIV; case INJR: return amr_injrIV; case TAKE: return amr_takeIV; case DROP: return amr_dropIV; case IDEN: return amr_idenIV; case UNIT: return amr_unitIV; case WITNESS: return amr_witnessIV; /* Precondition violated. */ case HIDDEN: case JET: case WORD: break; } SIMPLICITY_UNREACHABLE; } /* Given the identity hash of a jet specification, return the CMR for a jet that implements that specification. * * Precondition: uint32_t ih[8] */ static sha256_midstate mkJetCMR(uint32_t *ih, uint_fast64_t weight) { sha256_midstate result = jetIV; uint32_t block[16] = {0}; block[6] = (uint32_t)(weight >> 32); block[7] = (uint32_t)weight; memcpy(&block[8], ih, sizeof(uint32_t[8])); simplicity_sha256_compression(result.s, block); return result; } /* Compute the CMR of a jet of scribe(v) : ONE |- TWO^(2^n) that outputs a given bitstring. * * Precondition: 2^n == value->len */ sha256_midstate simplicity_computeWordCMR(const bitstring* value, size_t n) { /* 'stack' is an array of 30 hashes consisting of 8 'uint32_t's each. */ uint32_t stack[8*30] = {0}; uint32_t *stack_ptr = stack; sha256_midstate ih = identityIV; simplicity_assert(n < 32); simplicity_assert((size_t)1 << n == value->len); /* Pass 1: Compute the CMR for the expression that writes 'value'. * This expression consists of deeply nested PAIRs of expressions that write one bit each. */ /* stack[0..7] (8 bytes) is kept as all zeros for later. * We start the stack_ptr at the second item. */ if (n < 3) { stack_ptr += 8; size_t i; switch(n) { case 0: i = getBit(value, 0); break; case 1: i = 2 + ((1U * getBit(value, 0) << 1) | getBit(value, 1)); break; case 2: i = 6 + ((1U * getBit(value, 0) << 3) | (1U * getBit(value, 1) << 2) | (1U * getBit(value, 2) << 1) | getBit(value, 3)); break; } memcpy(stack_ptr, &word_cmr[i], sizeof(uint32_t[8])); } else { for (size_t i = 0; i < value->len >> 3; ++i) { /* stack_ptr == stack + 8* */ stack_ptr += 8; memcpy(stack_ptr, &word_cmr[22 + getByte(value, 8*i)], sizeof(uint32_t[8])); /* This inner for loop runs in amortized constant time. */ for (size_t j = i; j & 1; j = j >> 1) { sha256_midstate pair = cmrIV(PAIR); stack_ptr -= 8; simplicity_sha256_compression(pair.s, stack_ptr); memcpy(stack_ptr, pair.s, sizeof(uint32_t[8])); } } } /* value->len is a power of 2.*/ simplicity_assert(stack_ptr == stack + 8); /* Pass 2: Compute the identity hash for the expression by adding the type roots of ONE and TWO^(2^n) to the CMR. */ simplicity_sha256_compression(ih.s, stack); memcpy(&stack[0], word_type_root[0].s, sizeof(uint32_t[8])); memcpy(&stack[8], word_type_root[n+1].s, sizeof(uint32_t[8])); simplicity_sha256_compression(ih.s, stack); /* Pass 3: Compute the jet's CMR from the specificion's identity hash. */ return mkJetCMR(ih.s, ((uint_fast64_t)1 << n)); } /* Given a well-formed dag[i + 1], such that for all 'j', 0 <= 'j' < 'i', * 'dag[j].cmr' is the CMR of the subexpression denoted by the slice * * (dag_nodes[j + 1])dag, * * then we set the value of 'dag[i].cmr' to be the CMR of the subexpression denoted by 'dag'. * * Precondition: dag_node dag[i + 1] and 'dag' is well-formed. * dag[i].'tag' \notin {HIDDEN, JET, WORD} */ void simplicity_computeCommitmentMerkleRoot(dag_node* dag, const uint_fast32_t i) { uint32_t block[16] = {0}; size_t j = 8; simplicity_assert(HIDDEN != dag[i].tag); simplicity_assert(JET != dag[i].tag); simplicity_assert(WORD != dag[i].tag); dag[i].cmr = cmrIV(dag[i].tag); /* Hash the child sub-expression's CMRs (if there are any children). */ switch (dag[i].tag) { case COMP: case ASSERTL: case ASSERTR: case CASE: case PAIR: memcpy(block + j, dag[dag[i].child[1]].cmr.s, sizeof(uint32_t[8])); j = 0; /*@fallthrough@*/ case DISCONNECT: /* Only the first child is used in the CMR. */ case INJL: case INJR: case TAKE: case DROP: memcpy(block + j, dag[dag[i].child[0]].cmr.s, sizeof(uint32_t[8])); simplicity_sha256_compression(dag[i].cmr.s, block); case IDEN: case UNIT: case WITNESS: case HIDDEN: case JET: case WORD: break; } } /* Computes the identity hash roots of every subexpression in a well-typed 'dag' with witnesses. * 'ihr[i]' is set to the identity hash of the root of the subexpression 'dag[i]'. * When 'HIDDEN == dag[i].tag', then 'ihr[i]' is instead set to a hidden root hash for that hidden node. * * Precondition: sha256_midstate ihr[len]; * dag_node dag[len] and 'dag' is well-typed with 'type_dag' and contains witnesses. */ static void computeIdentityHashRoots(sha256_midstate* ihr, const dag_node* dag, const type* type_dag, const uint_fast32_t len) { /* Pass 1 */ for (size_t i = 0; i < len; ++i) { uint32_t block[16] = {0}; size_t j = 8; /* For jets, the first pass identity Merkle root is the same as their commitment Merkle root. */ ihr[i] = HIDDEN == dag[i].tag ? dag[i].cmr : JET == dag[i].tag ? dag[i].cmr : WORD == dag[i].tag ? dag[i].cmr : imrIV(dag[i].tag); switch (dag[i].tag) { case WITNESS: simplicity_sha256_bitstring(block, &dag[i].compactValue); memcpy(block + 8, type_dag[WITNESS_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(ihr[i].s, block); break; case COMP: case ASSERTL: case ASSERTR: case CASE: case PAIR: case DISCONNECT: memcpy(block + j, ihr[dag[i].child[1]].s, sizeof(uint32_t[8])); j = 0; /*@fallthrough@*/ case INJL: case INJR: case TAKE: case DROP: memcpy(block + j, ihr[dag[i].child[0]].s, sizeof(uint32_t[8])); simplicity_sha256_compression(ihr[i].s, block); case IDEN: case UNIT: case HIDDEN: case JET: case WORD: break; } } /* Pass 2 */ for (size_t i = 0; i < len; ++i) { uint32_t block[16] = {0}; if (HIDDEN == dag[i].tag) { memcpy(block + 8, ihr[i].s, sizeof(uint32_t[8])); ihr[i] = hiddenIV; simplicity_sha256_compression(ihr[i].s, block); } else { memcpy(block + 8, ihr[i].s, sizeof(uint32_t[8])); ihr[i] = identityIV; simplicity_sha256_compression(ihr[i].s, block); memcpy(block, type_dag[dag[i].sourceType].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[dag[i].targetType].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(ihr[i].s, block); } } } /* Given a well-typed dag representing a Simplicity expression, compute the annotated Merkle roots of all subexpressions. * For all 'i', 0 <= 'i' < 'len', 'analysis[i].annotatedMerkleRoot' will be the AMR of the subexpression denoted by the slice * * (dag_nodes[i + 1])dag. * * The AMR of the overall expression will be 'analysis[len - 1].annotatedMerkleRoot'. * * Precondition: analyses analysis[len]; * dag_node dag[len] and 'dag' has witness data and is well-typed with 'type_dag'. * Postconditon: analyses analysis[len] contains the annotated Merkle roots of each subexpressions of 'dag'. */ void simplicity_computeAnnotatedMerkleRoot(analyses* analysis, const dag_node* dag, const type* type_dag, const uint_fast32_t len) { for (uint_fast32_t i = 0; i < len; ++i) { uint32_t block[16] = {0}; /* For jets, their annotated Merkle root is the same as their commitment Merkle root. */ analysis[i].annotatedMerkleRoot = HIDDEN == dag[i].tag ? dag[i].cmr : JET == dag[i].tag ? dag[i].cmr : WORD == dag[i].tag ? dag[i].cmr : amrIV(dag[i].tag); switch (dag[i].tag) { case ASSERTL: case ASSERTR: case CASE: memcpy(block, type_dag[CASE_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[CASE_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[CASE_C(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[CASE_D(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, analysis[dag[i].child[0]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, analysis[dag[i].child[1]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case DISCONNECT: memcpy(block, type_dag[DISCONNECT_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[DISCONNECT_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[DISCONNECT_C(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[DISCONNECT_D(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, analysis[dag[i].child[0]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, analysis[dag[i].child[1]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case COMP: memcpy(block + 8, type_dag[COMP_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[COMP_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[COMP_C(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, analysis[dag[i].child[0]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, analysis[dag[i].child[1]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case PAIR: memcpy(block + 8, type_dag[PAIR_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[PAIR_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[PAIR_C(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, analysis[dag[i].child[0]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, analysis[dag[i].child[1]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case INJL: case INJR: memcpy(block, type_dag[INJ_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[INJ_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[INJ_C(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, analysis[dag[i].child[0]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case TAKE: case DROP: memcpy(block, type_dag[PROJ_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[PROJ_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[PROJ_C(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, analysis[dag[i].child[0]].annotatedMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case IDEN: memcpy(block + 8, type_dag[IDEN_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case UNIT: memcpy(block + 8, type_dag[UNIT_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case WITNESS: memcpy(block + 8, type_dag[WITNESS_A(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); memcpy(block, type_dag[WITNESS_B(dag, type_dag, i)].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_bitstring(block + 8, &dag[i].compactValue); simplicity_sha256_compression(analysis[i].annotatedMerkleRoot.s, block); break; case HIDDEN: case JET: case WORD: break; } } } /* Verifies that the 'dag' is in canonical order, meaning that nodes under the left branches have lower indices than nodes under * right branches, with the exception that nodes under right branches may (cross-)reference identical nodes that already occur under * left branches. * * Returns 'SIMPLICITY_NO_ERROR' if the 'dag' is in canonical order, and returns 'SIMPLICITY_ERR_DATA_OUT_OF_ORDER' if it is not. * * May modify dag[i].aux values and invalidate dag[i].sourceType and dag[i].targetType. * This function should only be used prior to calling 'mallocTypeInference'. * * Precondition: dag_node dag[len] and 'dag' is well-formed. */ simplicity_err simplicity_verifyCanonicalOrder(dag_node* dag, const uint_fast32_t len) { uint_fast32_t bottom = 0; uint_fast32_t top = len-1; /* Underflow is checked below. */ if (!len) { simplicity_assert(false); /* A well-formed dag has non-zero length */ return SIMPLICITY_NO_ERROR; /* However, an empty dag is technically in canonical order */ } /* We use dag[i].aux as a "stack" to manage the traversal of the DAG. */ dag[top].aux = len; /* We will set top to 'len' to indicate we are finished. */ /* Each time any particular 'top' value is revisited in this loop, bottom has increased to be strictly larger than the last 'child' value examined. Therefore we will make further progress in the loop the next time around. By this reasoning any given 'top' value will be visited no more than numChildren(dag[top].tag) + 1 <= 3 times. Thus this loop iterates at most O('len') times. */ while (top < len) { /* We determine canonical order by iterating through the dag in canonical (pre-)order, incrementing 'bottom' each time we encounter a node that is (correctly) placed at the 'bottom' index. We take advantage of the precondition that the dag is well-formed to know in advance that any children of a node have index strictly less than the node itself. */ /* Check first child. */ uint_fast32_t child = dag[top].child[0]; switch (dag[top].tag) { case ASSERTL: case ASSERTR: case CASE: case DISCONNECT: case COMP: case PAIR: case INJL: case INJR: case TAKE: case DROP: if (bottom < child) { dag[child].aux = top; top = child; continue; } if (bottom == child) bottom++; case IDEN: case UNIT: case WITNESS: case HIDDEN: case JET: case WORD: break; } /* Check second child. */ child = dag[top].child[1]; switch (dag[top].tag) { case ASSERTL: case ASSERTR: case CASE: case DISCONNECT: case COMP: case PAIR: if (bottom < child) { dag[child].aux = top; top = child; continue; } if (bottom == child) bottom++; case INJL: case INJR: case TAKE: case DROP: case IDEN: case UNIT: case WITNESS: case HIDDEN: case JET: case WORD: break; } /* Check current node. */ if (bottom < top) return SIMPLICITY_ERR_DATA_OUT_OF_ORDER; if (bottom == top) bottom++; /* top < bottom */ top = dag[top].aux; /* Return. */ } simplicity_assert(bottom == top && top == len); return SIMPLICITY_NO_ERROR; } /* This function fills in the 'WITNESS' nodes of a 'dag' with the data from 'witness'. * For each 'WITNESS' : A |- B expression in 'dag', the bits from the 'witness' bitstring are decoded in turn * to construct a compact representation of a witness value of type B. * If there are not enough bits, then 'SIMPLICITY_ERR_WITNESS_EOF' is returned. * If a witness node would end up with more than CELLS_MAX bits, then 'SIMPLICITY_ERR_EXEC_MEMORY' is returned. * Otherwise, returns 'SIMPLICITY_NO_ERROR'. * * Precondition: dag_node dag[len] and 'dag' without witness data and is well-typed with 'type_dag'; * witness is a valid bitstream; * * Postcondition: dag_node dag[len] and 'dag' has witness data and is well-typed with 'type_dag' * when the result is 'SIMPLICITY_NO_ERROR'; */ simplicity_err simplicity_fillWitnessData(dag_node* dag, type* type_dag, const uint_fast32_t len, bitstream *witness) { static_assert(CELLS_MAX <= 0x80000000, "CELLS_MAX is too large."); for (uint_fast32_t i = 0; i < len; ++i) { if (WITNESS == dag[i].tag) { if (CELLS_MAX < type_dag[WITNESS_B(dag, type_dag, i)].bitSize) return SIMPLICITY_ERR_EXEC_MEMORY; if (witness->len <= 0) { /* There is no data in the witness. */ dag[i].compactValue = (bitstring){0}; /* This is fine as long as the witness type is trivial */ if (type_dag[WITNESS_B(dag, type_dag, i)].bitSize) return SIMPLICITY_ERR_WITNESS_EOF; } else { dag[i].compactValue = (bitstring) { .arr = witness->arr , .offset = witness->offset , .len = 0 /* The value of .len will computed within the while loop. */ }; /* Traverse the witness type to parse the witness's compact representation as a bit string. */ size_t cur = typeSkip(WITNESS_B(dag, type_dag, i), type_dag); bool calling = true; setTypeBack(cur, type_dag, 0); while (cur) { if (SUM == type_dag[cur].kind) { /* Parse one bit and traverse the left type or the right type depending on the value of the bit parsed. */ simplicity_assert(calling); int32_t bit = read1Bit(witness); if (bit < 0) return SIMPLICITY_ERR_WITNESS_EOF; dag[i].compactValue.len++; size_t next = typeSkip(type_dag[cur].typeArg[bit], type_dag); if (next) { setTypeBack(next, type_dag, type_dag[cur].back); cur = next; } else { cur = type_dag[cur].back; calling = false; } } else { simplicity_assert(PRODUCT == type_dag[cur].kind); size_t next; if (calling) { next = typeSkip(type_dag[cur].typeArg[0], type_dag); /* Note: Because we are using 'typeSkip' we have an invarant on 'cur' such that whenever type_dag[cur].kind == PRODUCT, then it is a product of two non-trival types. This implies that 'next' cannot actually be 0. */ if (next) { /* Traverse the first element of the product type, if it has any data. */ setTypeBack(next, type_dag, cur); cur = next; continue; } } next = typeSkip(type_dag[cur].typeArg[1], type_dag); /* Note: Because we are using 'typeSkip' we have an invarant on 'cur' such that whenever type_dag[cur].kind == PRODUCT, then it is a product of two non-trival types. This implies that 'next' cannot actually be 0. */ if (next) { /* Traverse the second element of the product type, if it has any data. */ setTypeBack(next, type_dag, type_dag[cur].back); cur = next; calling = true; } else { cur = type_dag[cur].back; calling = false; } } } /* Note: Above we use 'typeSkip' to skip over long chains of products against trivial types * This avoids a potential DOS vulnerability where a DAG of deeply nested products of unit types with sharing is traversed, * taking exponential time. * While traversing still could take exponential time in terms of the size of the type's dag, * at least one bit of witness data is required per PRODUCT type encountered. * This ought to limit the total number of times through the above loop to no more that 3 * dag[i].witness.len. */ } } } return SIMPLICITY_NO_ERROR; } /* Verifies that identity hash of every subexpression in a well-typed 'dag' with witnesses are all unique, * including that each hidden root hash for every 'HIDDEN' node is unique. * * if 'ihr' is not NULL, then '*ihr' is set to the identity hash of the root of the 'dag'. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * If all the identity hahes (and hidden roots) are all unique, returns 'SIMPLICITY_NO_ERROR'. * Otherwise returns 'SIMPLICITY_ERR_UNSHARED_SUBEXPRESSION'. * * Precondition: dag_node dag[len] and 'dag' is well-typed with 'type_dag' and contains witnesses. */ simplicity_err simplicity_verifyNoDuplicateIdentityHashes(sha256_midstate* ihr, const dag_node* dag, const type* type_dag, const uint_fast32_t dag_len) { simplicity_assert(0 < dag_len); simplicity_assert(dag_len <= DAG_LEN_MAX); sha256_midstate* ih_buf = simplicity_malloc((size_t)dag_len * sizeof(sha256_midstate)); if (!ih_buf) return SIMPLICITY_ERR_MALLOC; computeIdentityHashRoots(ih_buf, dag, type_dag, dag_len); if (ihr) *ihr = ih_buf[dag_len-1]; int result = simplicity_hasDuplicates(ih_buf, dag_len); simplicity_free(ih_buf); switch (result) { case -1: return SIMPLICITY_ERR_MALLOC; case 0: return SIMPLICITY_NO_ERROR; default: return SIMPLICITY_ERR_UNSHARED_SUBEXPRESSION; } } ================================================ FILE: C/dag.h ================================================ /* This module defines the structure for Simplicity DAGs, and functions for some analysis of that structure, * such as computing Merkle Roots. */ #ifndef SIMPLICITY_DAG_H #define SIMPLICITY_DAG_H #include #include #include #include "bitstream.h" #include "bitstring.h" #include "bounded.h" #include "jets.h" #include "simplicity_assert.h" #include "type.h" /* An enumeration of the various kinds of Simplicity nodes. */ typedef enum tag_t { COMP , CASE , ASSERTL , ASSERTR , PAIR , DISCONNECT , INJL , INJR , TAKE , DROP , IDEN , UNIT , HIDDEN , WITNESS , JET , WORD } tag_t; /* This structure is use to count the different kinds of combinators in a Simplicity DAG. */ typedef struct combinator_counters { size_t comp_cnt, case_cnt, pair_cnt, disconnect_cnt, injl_cnt, injr_cnt, take_cnt, drop_cnt; } combinator_counters; /* Given a tag for an expression, add it to the 'census'. */ static inline void enumerator(combinator_counters* census, tag_t tag) { if (!census) return; switch (tag) { case COMP: census->comp_cnt++; return; case ASSERTL: case ASSERTR: /* Assertions are counted as CASE combinators. */ case CASE: census->case_cnt++; return; case PAIR: census->pair_cnt++; return; case DISCONNECT: census->disconnect_cnt++; return; case INJL: census->injl_cnt++; return; case INJR: census->injr_cnt++; return; case TAKE: census->take_cnt++; return; case DROP: census->drop_cnt++; return; /* These tags are not accounted for in the census. */ case IDEN: case UNIT: case HIDDEN: case WITNESS: case JET: case WORD: return; } } /* Returns the number of children that a Simplicity combinator of the 'tag' kind has. */ static inline size_t numChildren(tag_t tag) { switch (tag) { case COMP: case ASSERTL: case ASSERTR: case CASE: case PAIR: case DISCONNECT: return 2; case INJL: case INJR: case TAKE: case DROP: return 1; case IDEN: case UNIT: case HIDDEN: case WITNESS: case JET: case WORD: return 0; } } /* Compute the CMR of a jet of scribe(v) : ONE |- TWO^(2^n) that outputs a given bitstring. * * Precondition: 2^n == value->len */ sha256_midstate simplicity_computeWordCMR(const bitstring* value, size_t n); /* A node the the DAG of a Simplicity expression. * It consists of a 'tag' indicating the kind of expression the node represents. * The contents of a node depend on the kind of the expressions. * The node may have references to children, when it is a combinator kind of expression. * * Invariant: 'NULL != jet' when 'tag == JET'; * bitstring compactValue is active when tag == WITNESS and the node has witness data; * bitstring compactValue is also active and has a length that is a power of 2 when tag == WORD; * size_t sourceIx is active when tag == JET; * unbounded cost is active when tag == JET; * size_t child[numChildren(tag)] when tag \notin {HIDDEN, WITNESS, JET, WORD}; */ typedef struct dag_node { jet_ptr jet; sha256_midstate cmr; union { uint_fast32_t aux; /* Used as scratch space for verifyCanonicalOrder. */ struct { size_t sourceType, targetType; }; }; union { struct { size_t sourceIx; }; struct { uint_fast32_t child[2]; }; bitstring compactValue; }; size_t targetIx; /* cost is normalized so that the 'CheckSigVerify' jet has 50 000 milli weight units. */ ubounded cost; /* in milli weight units */ tag_t tag; } dag_node; /* Inline functions for accessing the type annotations of combinators */ static inline size_t IDEN_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(IDEN == dag[i].tag); return dag[i].sourceType; } static inline size_t UNIT_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(UNIT == dag[i].tag); return dag[i].sourceType; } static inline size_t COMP_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(COMP == dag[i].tag); return dag[i].sourceType; } static inline size_t COMP_B(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(COMP == dag[i].tag); return dag[dag[i].child[1]].sourceType; } static inline size_t COMP_C(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(COMP == dag[i].tag); return dag[i].targetType; } static inline size_t CASE_A(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(CASE == dag[i].tag || ASSERTL == dag[i].tag || ASSERTR == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].sourceType].kind); simplicity_debug_assert(SUM == type_dag[type_dag[dag[i].sourceType].typeArg[0]].kind); return type_dag[type_dag[dag[i].sourceType].typeArg[0]].typeArg[0]; } static inline size_t CASE_B(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(CASE == dag[i].tag || ASSERTL == dag[i].tag || ASSERTR == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].sourceType].kind); simplicity_debug_assert(SUM == type_dag[type_dag[dag[i].sourceType].typeArg[0]].kind); return type_dag[type_dag[dag[i].sourceType].typeArg[0]].typeArg[1]; } static inline size_t CASE_C(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(CASE == dag[i].tag || ASSERTL == dag[i].tag || ASSERTR == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].sourceType].kind); return type_dag[dag[i].sourceType].typeArg[1]; } static inline size_t CASE_D(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(CASE == dag[i].tag || ASSERTL == dag[i].tag || ASSERTR == dag[i].tag); return dag[i].targetType; } static inline size_t PAIR_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(PAIR == dag[i].tag); return dag[i].sourceType; } static inline size_t PAIR_B(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(PAIR == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].targetType].kind); return type_dag[dag[i].targetType].typeArg[0]; } static inline size_t PAIR_C(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(PAIR == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].targetType].kind); return type_dag[dag[i].targetType].typeArg[1]; } static inline size_t DISCONNECT_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(DISCONNECT == dag[i].tag); return dag[i].sourceType; } static inline size_t DISCONNECT_B(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(DISCONNECT == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].targetType].kind); return type_dag[dag[i].targetType].typeArg[0]; } static inline size_t DISCONNECT_C(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(DISCONNECT == dag[i].tag); return dag[dag[i].child[1]].sourceType; } static inline size_t DISCONNECT_D(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(DISCONNECT == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].targetType].kind); return type_dag[dag[i].targetType].typeArg[1]; } static inline size_t DISCONNECT_W256A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(DISCONNECT == dag[i].tag); return dag[dag[i].child[0]].sourceType; } static inline size_t DISCONNECT_BC(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(DISCONNECT == dag[i].tag); return dag[dag[i].child[0]].targetType; } static inline size_t INJ_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(INJL == dag[i].tag || INJR == dag[i].tag); return dag[i].sourceType; } static inline size_t INJ_B(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(INJL == dag[i].tag || INJR == dag[i].tag); simplicity_debug_assert(SUM == type_dag[dag[i].targetType].kind); return type_dag[dag[i].targetType].typeArg[0]; } static inline size_t INJ_C(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(INJL == dag[i].tag || INJR == dag[i].tag); simplicity_debug_assert(SUM == type_dag[dag[i].targetType].kind); return type_dag[dag[i].targetType].typeArg[1]; } static inline size_t PROJ_A(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(TAKE == dag[i].tag || DROP == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].sourceType].kind); return type_dag[dag[i].sourceType].typeArg[0]; } static inline size_t PROJ_B(const dag_node* dag, const type* type_dag, size_t i) { simplicity_debug_assert(TAKE == dag[i].tag || DROP == dag[i].tag); simplicity_debug_assert(PRODUCT == type_dag[dag[i].sourceType].kind); return type_dag[dag[i].sourceType].typeArg[1]; } static inline size_t PROJ_C(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(TAKE == dag[i].tag || DROP == dag[i].tag); return dag[i].targetType; } static inline size_t WITNESS_A(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(WITNESS == dag[i].tag); return dag[i].sourceType; } static inline size_t WITNESS_B(const dag_node* dag, const type* type_dag, size_t i) { (void)type_dag; simplicity_debug_assert(WITNESS == dag[i].tag); return dag[i].targetType; } /* A well-formed Simplicity DAG is an array of 'dag_node's, * * dag_node dag[len], * * such that * * 1 <= len <= DAG_LEN_MAX * * and for all 'i', 0 <= 'i' < 'len' and for all 'j', 0 <= 'j' < 'numChildren(dag[i].tag)', * * dag[i].child[j] < i * * and for all 'i', 0 <= 'i' < 'len', * * if dag[dag[i].child[0]].tag == HIDDEN then dag[i].tag == ASSERTR * * and * * if dag[dag[i].child[1]].tag == HIDDEN then dag[i].tag == ASSERTL * * Note that a well-formed Simplicity DAG is not necessarily a well-typed Simplicity DAG. */ /* A structure of static analyses for a particular node of a Simplicity DAG. * 'annotatedMerkleRoot' is the a Merkle root to includes the type annotations of all subexpressions. */ typedef struct analyses { sha256_midstate annotatedMerkleRoot; } analyses; /* Given a well-formed dag[i + 1], such that for all 'j', 0 <= 'j' < 'i', * 'dag[j].cmr' is the CMR of the subexpression denoted by the slice * * (dag_nodes[j + 1])dag, * * then we set the value of 'dag[i].cmr' to be the CMR of the subexpression denoted by 'dag'. * * Precondition: dag_node dag[i + 1] and 'dag' is well-formed. * dag[i].'tag' \notin {HIDDEN, JET, WORD} */ void simplicity_computeCommitmentMerkleRoot(dag_node* dag, uint_fast32_t i); /* Given a well-typed dag representing a Simplicity expression, compute the annotated Merkle roots of all subexpressions. * For all 'i', 0 <= 'i' < 'len', 'analysis[i].annotatedMerkleRoot' will be the AMR of the subexpression denoted by the slice * * (dag_nodes[i + 1])dag. * * The AMR of the overall expression will be 'analysis[len - 1].annotatedMerkleRoot'. * * Precondition: analyses analysis[len]; * dag_node dag[len] and 'dag' has witness data and is well-typed with 'type_dag'. * Postconditon: analyses analysis[len] contains the annotated Merkle roots of each subexpressions of 'dag'. */ void simplicity_computeAnnotatedMerkleRoot(analyses* analysis, const dag_node* dag, const type* type_dag, uint_fast32_t len); /* Verifies that the 'dag' is in canonical order, meaning that nodes under the left branches have lower indices than nodes under * right branches, with the exception that nodes under right branches may (cross-)reference identical nodes that already occur under * left branches. * * Returns 'SIMPLICITY_NO_ERROR' if the 'dag' is in canonical order, and returns 'SIMPLICITY_ERR_DATA_OUT_OF_ORDER' if it is not. * * May modify dag[i].aux values and invalidate dag[i].sourceType and dag[i].targetType. * This function should only be used prior to calling 'mallocTypeInference'. * * Precondition: dag_node dag[len] and 'dag' is well-formed. */ simplicity_err simplicity_verifyCanonicalOrder(dag_node* dag, const uint_fast32_t len); /* This function fills in the 'WITNESS' nodes of a 'dag' with the data from 'witness'. * For each 'WITNESS' : A |- B expression in 'dag', the bits from the 'witness' bitstring are decoded in turn * to construct a compact representation of a witness value of type B. * If there are not enough bits, then 'SIMPLICITY_ERR_WITNESS_EOF' is returned. * If a witness node would end up with more than CELLS_MAX bits, then 'SIMPLICITY_ERR_EXEC_MEMORY' is returned. * Otherwise, returns 'SIMPLICITY_NO_ERROR'. * * Precondition: dag_node dag[len] and 'dag' without witness data and is well-typed with 'type_dag'; * witness is a valid bitstream; * * Postcondition: dag_node dag[len] and 'dag' has witness data and is well-typed with 'type_dag' * when the result is 'SIMPLICITY_NO_ERROR'; */ simplicity_err simplicity_fillWitnessData(dag_node* dag, type* type_dag, const uint_fast32_t len, bitstream *witness); /* Verifies that identity hash of every subexpression in a well-typed 'dag' with witnesses are all unique, * including that each hidden root hash for every 'HIDDEN' node is unique. * * if 'ihr' is not NULL, then '*ihr' is set to the identity hash of the root of the 'dag'. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * If all the identity hahes (and hidden roots) are all unique, returns 'SIMPLICITY_NO_ERROR'. * Otherwise returns 'SIMPLICITY_ERR_UNSHARED_SUBEXPRESSION'. * * Precondition: dag_node dag[len] and 'dag' is well-typed with 'type_dag' and contains witnesses. */ simplicity_err simplicity_verifyNoDuplicateIdentityHashes(sha256_midstate* ihr, const dag_node* dag, const type* type_dag, const uint_fast32_t dag_len); #endif ================================================ FILE: C/decodeCoreJets.inc ================================================ /* This file has been automatically generated. */ { int32_t code; code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = VERIFY; return SIMPLICITY_NO_ERROR; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LOW_1; return SIMPLICITY_NO_ERROR; case 3: *result = LOW_8; return SIMPLICITY_NO_ERROR; case 4: *result = LOW_16; return SIMPLICITY_NO_ERROR; case 5: *result = LOW_32; return SIMPLICITY_NO_ERROR; case 6: *result = LOW_64; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = HIGH_1; return SIMPLICITY_NO_ERROR; case 3: *result = HIGH_8; return SIMPLICITY_NO_ERROR; case 4: *result = HIGH_16; return SIMPLICITY_NO_ERROR; case 5: *result = HIGH_32; return SIMPLICITY_NO_ERROR; case 6: *result = HIGH_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = COMPLEMENT_1; return SIMPLICITY_NO_ERROR; case 3: *result = COMPLEMENT_8; return SIMPLICITY_NO_ERROR; case 4: *result = COMPLEMENT_16; return SIMPLICITY_NO_ERROR; case 5: *result = COMPLEMENT_32; return SIMPLICITY_NO_ERROR; case 6: *result = COMPLEMENT_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = AND_1; return SIMPLICITY_NO_ERROR; case 3: *result = AND_8; return SIMPLICITY_NO_ERROR; case 4: *result = AND_16; return SIMPLICITY_NO_ERROR; case 5: *result = AND_32; return SIMPLICITY_NO_ERROR; case 6: *result = AND_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = OR_1; return SIMPLICITY_NO_ERROR; case 3: *result = OR_8; return SIMPLICITY_NO_ERROR; case 4: *result = OR_16; return SIMPLICITY_NO_ERROR; case 5: *result = OR_32; return SIMPLICITY_NO_ERROR; case 6: *result = OR_64; return SIMPLICITY_NO_ERROR; } break; case 7: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = XOR_1; return SIMPLICITY_NO_ERROR; case 3: *result = XOR_8; return SIMPLICITY_NO_ERROR; case 4: *result = XOR_16; return SIMPLICITY_NO_ERROR; case 5: *result = XOR_32; return SIMPLICITY_NO_ERROR; case 6: *result = XOR_64; return SIMPLICITY_NO_ERROR; } break; case 8: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = MAJ_1; return SIMPLICITY_NO_ERROR; case 3: *result = MAJ_8; return SIMPLICITY_NO_ERROR; case 4: *result = MAJ_16; return SIMPLICITY_NO_ERROR; case 5: *result = MAJ_32; return SIMPLICITY_NO_ERROR; case 6: *result = MAJ_64; return SIMPLICITY_NO_ERROR; } break; case 9: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = XOR_XOR_1; return SIMPLICITY_NO_ERROR; case 3: *result = XOR_XOR_8; return SIMPLICITY_NO_ERROR; case 4: *result = XOR_XOR_16; return SIMPLICITY_NO_ERROR; case 5: *result = XOR_XOR_32; return SIMPLICITY_NO_ERROR; case 6: *result = XOR_XOR_64; return SIMPLICITY_NO_ERROR; } break; case 10: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = CH_1; return SIMPLICITY_NO_ERROR; case 3: *result = CH_8; return SIMPLICITY_NO_ERROR; case 4: *result = CH_16; return SIMPLICITY_NO_ERROR; case 5: *result = CH_32; return SIMPLICITY_NO_ERROR; case 6: *result = CH_64; return SIMPLICITY_NO_ERROR; } break; case 11: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SOME_1; return SIMPLICITY_NO_ERROR; case 3: *result = SOME_8; return SIMPLICITY_NO_ERROR; case 4: *result = SOME_16; return SIMPLICITY_NO_ERROR; case 5: *result = SOME_32; return SIMPLICITY_NO_ERROR; case 6: *result = SOME_64; return SIMPLICITY_NO_ERROR; } break; case 12: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = ALL_8; return SIMPLICITY_NO_ERROR; case 4: *result = ALL_16; return SIMPLICITY_NO_ERROR; case 5: *result = ALL_32; return SIMPLICITY_NO_ERROR; case 6: *result = ALL_64; return SIMPLICITY_NO_ERROR; } break; case 13: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = EQ_1; return SIMPLICITY_NO_ERROR; case 3: *result = EQ_8; return SIMPLICITY_NO_ERROR; case 4: *result = EQ_16; return SIMPLICITY_NO_ERROR; case 5: *result = EQ_32; return SIMPLICITY_NO_ERROR; case 6: *result = EQ_64; return SIMPLICITY_NO_ERROR; case 8: *result = EQ_256; return SIMPLICITY_NO_ERROR; } break; case 14: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_LEFT_SHIFT_8_1; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_LEFT_SHIFT_16_1; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_LEFT_SHIFT_32_1; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_LEFT_SHIFT_64_1; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 2: *result = FULL_LEFT_SHIFT_8_2; return SIMPLICITY_NO_ERROR; case 3: *result = FULL_LEFT_SHIFT_16_2; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_LEFT_SHIFT_32_2; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_LEFT_SHIFT_64_2; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_LEFT_SHIFT_8_4; return SIMPLICITY_NO_ERROR; case 2: *result = FULL_LEFT_SHIFT_16_4; return SIMPLICITY_NO_ERROR; case 3: *result = FULL_LEFT_SHIFT_32_4; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_LEFT_SHIFT_64_4; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_LEFT_SHIFT_16_8; return SIMPLICITY_NO_ERROR; case 2: *result = FULL_LEFT_SHIFT_32_8; return SIMPLICITY_NO_ERROR; case 3: *result = FULL_LEFT_SHIFT_64_8; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_LEFT_SHIFT_32_16; return SIMPLICITY_NO_ERROR; case 2: *result = FULL_LEFT_SHIFT_64_16; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_LEFT_SHIFT_64_32; return SIMPLICITY_NO_ERROR; } break; } break; case 15: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_RIGHT_SHIFT_8_1; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_RIGHT_SHIFT_16_1; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_RIGHT_SHIFT_32_1; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_RIGHT_SHIFT_64_1; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 2: *result = FULL_RIGHT_SHIFT_8_2; return SIMPLICITY_NO_ERROR; case 3: *result = FULL_RIGHT_SHIFT_16_2; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_RIGHT_SHIFT_32_2; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_RIGHT_SHIFT_64_2; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_RIGHT_SHIFT_8_4; return SIMPLICITY_NO_ERROR; case 2: *result = FULL_RIGHT_SHIFT_16_4; return SIMPLICITY_NO_ERROR; case 3: *result = FULL_RIGHT_SHIFT_32_4; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_RIGHT_SHIFT_64_4; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_RIGHT_SHIFT_16_8; return SIMPLICITY_NO_ERROR; case 2: *result = FULL_RIGHT_SHIFT_32_8; return SIMPLICITY_NO_ERROR; case 3: *result = FULL_RIGHT_SHIFT_64_8; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_RIGHT_SHIFT_32_16; return SIMPLICITY_NO_ERROR; case 2: *result = FULL_RIGHT_SHIFT_64_16; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = FULL_RIGHT_SHIFT_64_32; return SIMPLICITY_NO_ERROR; } break; } break; case 16: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFTMOST_8_1; return SIMPLICITY_NO_ERROR; case 4: *result = LEFTMOST_16_1; return SIMPLICITY_NO_ERROR; case 5: *result = LEFTMOST_32_1; return SIMPLICITY_NO_ERROR; case 6: *result = LEFTMOST_64_1; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 2: *result = LEFTMOST_8_2; return SIMPLICITY_NO_ERROR; case 3: *result = LEFTMOST_16_2; return SIMPLICITY_NO_ERROR; case 4: *result = LEFTMOST_32_2; return SIMPLICITY_NO_ERROR; case 5: *result = LEFTMOST_64_2; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFTMOST_8_4; return SIMPLICITY_NO_ERROR; case 2: *result = LEFTMOST_16_4; return SIMPLICITY_NO_ERROR; case 3: *result = LEFTMOST_32_4; return SIMPLICITY_NO_ERROR; case 4: *result = LEFTMOST_64_4; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFTMOST_16_8; return SIMPLICITY_NO_ERROR; case 2: *result = LEFTMOST_32_8; return SIMPLICITY_NO_ERROR; case 3: *result = LEFTMOST_64_8; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFTMOST_32_16; return SIMPLICITY_NO_ERROR; case 2: *result = LEFTMOST_64_16; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFTMOST_64_32; return SIMPLICITY_NO_ERROR; } break; } break; case 17: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = RIGHTMOST_8_1; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHTMOST_16_1; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHTMOST_32_1; return SIMPLICITY_NO_ERROR; case 6: *result = RIGHTMOST_64_1; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 2: *result = RIGHTMOST_8_2; return SIMPLICITY_NO_ERROR; case 3: *result = RIGHTMOST_16_2; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHTMOST_32_2; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHTMOST_64_2; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHTMOST_8_4; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHTMOST_16_4; return SIMPLICITY_NO_ERROR; case 3: *result = RIGHTMOST_32_4; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHTMOST_64_4; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHTMOST_16_8; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHTMOST_32_8; return SIMPLICITY_NO_ERROR; case 3: *result = RIGHTMOST_64_8; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHTMOST_32_16; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHTMOST_64_16; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHTMOST_64_32; return SIMPLICITY_NO_ERROR; } break; } break; case 18: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFT_PAD_LOW_1_8; return SIMPLICITY_NO_ERROR; case 4: *result = LEFT_PAD_LOW_1_16; return SIMPLICITY_NO_ERROR; case 5: *result = LEFT_PAD_LOW_1_32; return SIMPLICITY_NO_ERROR; case 6: *result = LEFT_PAD_LOW_1_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_PAD_LOW_8_16; return SIMPLICITY_NO_ERROR; case 2: *result = LEFT_PAD_LOW_8_32; return SIMPLICITY_NO_ERROR; case 3: *result = LEFT_PAD_LOW_8_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_PAD_LOW_16_32; return SIMPLICITY_NO_ERROR; case 2: *result = LEFT_PAD_LOW_16_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_PAD_LOW_32_64; return SIMPLICITY_NO_ERROR; } break; } break; case 19: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFT_PAD_HIGH_1_8; return SIMPLICITY_NO_ERROR; case 4: *result = LEFT_PAD_HIGH_1_16; return SIMPLICITY_NO_ERROR; case 5: *result = LEFT_PAD_HIGH_1_32; return SIMPLICITY_NO_ERROR; case 6: *result = LEFT_PAD_HIGH_1_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_PAD_HIGH_8_16; return SIMPLICITY_NO_ERROR; case 2: *result = LEFT_PAD_HIGH_8_32; return SIMPLICITY_NO_ERROR; case 3: *result = LEFT_PAD_HIGH_8_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_PAD_HIGH_16_32; return SIMPLICITY_NO_ERROR; case 2: *result = LEFT_PAD_HIGH_16_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_PAD_HIGH_32_64; return SIMPLICITY_NO_ERROR; } break; } break; case 20: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFT_EXTEND_1_8; return SIMPLICITY_NO_ERROR; case 4: *result = LEFT_EXTEND_1_16; return SIMPLICITY_NO_ERROR; case 5: *result = LEFT_EXTEND_1_32; return SIMPLICITY_NO_ERROR; case 6: *result = LEFT_EXTEND_1_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_EXTEND_8_16; return SIMPLICITY_NO_ERROR; case 2: *result = LEFT_EXTEND_8_32; return SIMPLICITY_NO_ERROR; case 3: *result = LEFT_EXTEND_8_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_EXTEND_16_32; return SIMPLICITY_NO_ERROR; case 2: *result = LEFT_EXTEND_16_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LEFT_EXTEND_32_64; return SIMPLICITY_NO_ERROR; } break; } break; case 21: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = RIGHT_PAD_LOW_1_8; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHT_PAD_LOW_1_16; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHT_PAD_LOW_1_32; return SIMPLICITY_NO_ERROR; case 6: *result = RIGHT_PAD_LOW_1_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_PAD_LOW_8_16; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHT_PAD_LOW_8_32; return SIMPLICITY_NO_ERROR; case 3: *result = RIGHT_PAD_LOW_8_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_PAD_LOW_16_32; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHT_PAD_LOW_16_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_PAD_LOW_32_64; return SIMPLICITY_NO_ERROR; } break; } break; case 22: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = RIGHT_PAD_HIGH_1_8; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHT_PAD_HIGH_1_16; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHT_PAD_HIGH_1_32; return SIMPLICITY_NO_ERROR; case 6: *result = RIGHT_PAD_HIGH_1_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_PAD_HIGH_8_16; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHT_PAD_HIGH_8_32; return SIMPLICITY_NO_ERROR; case 3: *result = RIGHT_PAD_HIGH_8_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_PAD_HIGH_16_32; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHT_PAD_HIGH_16_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_PAD_HIGH_32_64; return SIMPLICITY_NO_ERROR; } break; } break; case 23: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_EXTEND_8_16; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHT_EXTEND_8_32; return SIMPLICITY_NO_ERROR; case 3: *result = RIGHT_EXTEND_8_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_EXTEND_16_32; return SIMPLICITY_NO_ERROR; case 2: *result = RIGHT_EXTEND_16_64; return SIMPLICITY_NO_ERROR; } break; case 6: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = RIGHT_EXTEND_32_64; return SIMPLICITY_NO_ERROR; } break; } break; case 24: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFT_SHIFT_WITH_8; return SIMPLICITY_NO_ERROR; case 4: *result = LEFT_SHIFT_WITH_16; return SIMPLICITY_NO_ERROR; case 5: *result = LEFT_SHIFT_WITH_32; return SIMPLICITY_NO_ERROR; case 6: *result = LEFT_SHIFT_WITH_64; return SIMPLICITY_NO_ERROR; } break; case 25: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = RIGHT_SHIFT_WITH_8; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHT_SHIFT_WITH_16; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHT_SHIFT_WITH_32; return SIMPLICITY_NO_ERROR; case 6: *result = RIGHT_SHIFT_WITH_64; return SIMPLICITY_NO_ERROR; } break; case 26: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFT_SHIFT_8; return SIMPLICITY_NO_ERROR; case 4: *result = LEFT_SHIFT_16; return SIMPLICITY_NO_ERROR; case 5: *result = LEFT_SHIFT_32; return SIMPLICITY_NO_ERROR; case 6: *result = LEFT_SHIFT_64; return SIMPLICITY_NO_ERROR; } break; case 27: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = RIGHT_SHIFT_8; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHT_SHIFT_16; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHT_SHIFT_32; return SIMPLICITY_NO_ERROR; case 6: *result = RIGHT_SHIFT_64; return SIMPLICITY_NO_ERROR; } break; case 28: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LEFT_ROTATE_8; return SIMPLICITY_NO_ERROR; case 4: *result = LEFT_ROTATE_16; return SIMPLICITY_NO_ERROR; case 5: *result = LEFT_ROTATE_32; return SIMPLICITY_NO_ERROR; case 6: *result = LEFT_ROTATE_64; return SIMPLICITY_NO_ERROR; } break; case 29: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = RIGHT_ROTATE_8; return SIMPLICITY_NO_ERROR; case 4: *result = RIGHT_ROTATE_16; return SIMPLICITY_NO_ERROR; case 5: *result = RIGHT_ROTATE_32; return SIMPLICITY_NO_ERROR; case 6: *result = RIGHT_ROTATE_64; return SIMPLICITY_NO_ERROR; } break; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = ONE_8; return SIMPLICITY_NO_ERROR; case 4: *result = ONE_16; return SIMPLICITY_NO_ERROR; case 5: *result = ONE_32; return SIMPLICITY_NO_ERROR; case 6: *result = ONE_64; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_ADD_8; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_ADD_16; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_ADD_32; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_ADD_64; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = ADD_8; return SIMPLICITY_NO_ERROR; case 4: *result = ADD_16; return SIMPLICITY_NO_ERROR; case 5: *result = ADD_32; return SIMPLICITY_NO_ERROR; case 6: *result = ADD_64; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_INCREMENT_8; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_INCREMENT_16; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_INCREMENT_32; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_INCREMENT_64; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = INCREMENT_8; return SIMPLICITY_NO_ERROR; case 4: *result = INCREMENT_16; return SIMPLICITY_NO_ERROR; case 5: *result = INCREMENT_32; return SIMPLICITY_NO_ERROR; case 6: *result = INCREMENT_64; return SIMPLICITY_NO_ERROR; } break; case 7: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_SUBTRACT_8; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_SUBTRACT_16; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_SUBTRACT_32; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_SUBTRACT_64; return SIMPLICITY_NO_ERROR; } break; case 8: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = SUBTRACT_8; return SIMPLICITY_NO_ERROR; case 4: *result = SUBTRACT_16; return SIMPLICITY_NO_ERROR; case 5: *result = SUBTRACT_32; return SIMPLICITY_NO_ERROR; case 6: *result = SUBTRACT_64; return SIMPLICITY_NO_ERROR; } break; case 9: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = NEGATE_8; return SIMPLICITY_NO_ERROR; case 4: *result = NEGATE_16; return SIMPLICITY_NO_ERROR; case 5: *result = NEGATE_32; return SIMPLICITY_NO_ERROR; case 6: *result = NEGATE_64; return SIMPLICITY_NO_ERROR; } break; case 10: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_DECREMENT_8; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_DECREMENT_16; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_DECREMENT_32; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_DECREMENT_64; return SIMPLICITY_NO_ERROR; } break; case 11: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = DECREMENT_8; return SIMPLICITY_NO_ERROR; case 4: *result = DECREMENT_16; return SIMPLICITY_NO_ERROR; case 5: *result = DECREMENT_32; return SIMPLICITY_NO_ERROR; case 6: *result = DECREMENT_64; return SIMPLICITY_NO_ERROR; } break; case 12: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = FULL_MULTIPLY_8; return SIMPLICITY_NO_ERROR; case 4: *result = FULL_MULTIPLY_16; return SIMPLICITY_NO_ERROR; case 5: *result = FULL_MULTIPLY_32; return SIMPLICITY_NO_ERROR; case 6: *result = FULL_MULTIPLY_64; return SIMPLICITY_NO_ERROR; } break; case 13: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = MULTIPLY_8; return SIMPLICITY_NO_ERROR; case 4: *result = MULTIPLY_16; return SIMPLICITY_NO_ERROR; case 5: *result = MULTIPLY_32; return SIMPLICITY_NO_ERROR; case 6: *result = MULTIPLY_64; return SIMPLICITY_NO_ERROR; } break; case 14: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = IS_ZERO_8; return SIMPLICITY_NO_ERROR; case 4: *result = IS_ZERO_16; return SIMPLICITY_NO_ERROR; case 5: *result = IS_ZERO_32; return SIMPLICITY_NO_ERROR; case 6: *result = IS_ZERO_64; return SIMPLICITY_NO_ERROR; } break; case 15: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = IS_ONE_8; return SIMPLICITY_NO_ERROR; case 4: *result = IS_ONE_16; return SIMPLICITY_NO_ERROR; case 5: *result = IS_ONE_32; return SIMPLICITY_NO_ERROR; case 6: *result = IS_ONE_64; return SIMPLICITY_NO_ERROR; } break; case 16: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LE_8; return SIMPLICITY_NO_ERROR; case 4: *result = LE_16; return SIMPLICITY_NO_ERROR; case 5: *result = LE_32; return SIMPLICITY_NO_ERROR; case 6: *result = LE_64; return SIMPLICITY_NO_ERROR; } break; case 17: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = LT_8; return SIMPLICITY_NO_ERROR; case 4: *result = LT_16; return SIMPLICITY_NO_ERROR; case 5: *result = LT_32; return SIMPLICITY_NO_ERROR; case 6: *result = LT_64; return SIMPLICITY_NO_ERROR; } break; case 18: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = MIN_8; return SIMPLICITY_NO_ERROR; case 4: *result = MIN_16; return SIMPLICITY_NO_ERROR; case 5: *result = MIN_32; return SIMPLICITY_NO_ERROR; case 6: *result = MIN_64; return SIMPLICITY_NO_ERROR; } break; case 19: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = MAX_8; return SIMPLICITY_NO_ERROR; case 4: *result = MAX_16; return SIMPLICITY_NO_ERROR; case 5: *result = MAX_32; return SIMPLICITY_NO_ERROR; case 6: *result = MAX_64; return SIMPLICITY_NO_ERROR; } break; case 20: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = MEDIAN_8; return SIMPLICITY_NO_ERROR; case 4: *result = MEDIAN_16; return SIMPLICITY_NO_ERROR; case 5: *result = MEDIAN_32; return SIMPLICITY_NO_ERROR; case 6: *result = MEDIAN_64; return SIMPLICITY_NO_ERROR; } break; case 21: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 6: *result = DIV_MOD_128_64; return SIMPLICITY_NO_ERROR; } break; case 22: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = DIV_MOD_8; return SIMPLICITY_NO_ERROR; case 4: *result = DIV_MOD_16; return SIMPLICITY_NO_ERROR; case 5: *result = DIV_MOD_32; return SIMPLICITY_NO_ERROR; case 6: *result = DIV_MOD_64; return SIMPLICITY_NO_ERROR; } break; case 23: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = DIVIDE_8; return SIMPLICITY_NO_ERROR; case 4: *result = DIVIDE_16; return SIMPLICITY_NO_ERROR; case 5: *result = DIVIDE_32; return SIMPLICITY_NO_ERROR; case 6: *result = DIVIDE_64; return SIMPLICITY_NO_ERROR; } break; case 24: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = MODULO_8; return SIMPLICITY_NO_ERROR; case 4: *result = MODULO_16; return SIMPLICITY_NO_ERROR; case 5: *result = MODULO_32; return SIMPLICITY_NO_ERROR; case 6: *result = MODULO_64; return SIMPLICITY_NO_ERROR; } break; case 25: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 3: *result = DIVIDES_8; return SIMPLICITY_NO_ERROR; case 4: *result = DIVIDES_16; return SIMPLICITY_NO_ERROR; case 5: *result = DIVIDES_32; return SIMPLICITY_NO_ERROR; case 6: *result = DIVIDES_64; return SIMPLICITY_NO_ERROR; } break; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SHA_256_BLOCK; return SIMPLICITY_NO_ERROR; case 2: *result = SHA_256_IV; return SIMPLICITY_NO_ERROR; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SHA_256_CTX_8_ADD_1; return SIMPLICITY_NO_ERROR; case 2: *result = SHA_256_CTX_8_ADD_2; return SIMPLICITY_NO_ERROR; case 3: *result = SHA_256_CTX_8_ADD_4; return SIMPLICITY_NO_ERROR; case 4: *result = SHA_256_CTX_8_ADD_8; return SIMPLICITY_NO_ERROR; case 5: *result = SHA_256_CTX_8_ADD_16; return SIMPLICITY_NO_ERROR; case 6: *result = SHA_256_CTX_8_ADD_32; return SIMPLICITY_NO_ERROR; case 7: *result = SHA_256_CTX_8_ADD_64; return SIMPLICITY_NO_ERROR; case 8: *result = SHA_256_CTX_8_ADD_128; return SIMPLICITY_NO_ERROR; case 9: *result = SHA_256_CTX_8_ADD_256; return SIMPLICITY_NO_ERROR; case 10: *result = SHA_256_CTX_8_ADD_512; return SIMPLICITY_NO_ERROR; } break; case 4: *result = SHA_256_CTX_8_ADD_BUFFER_511; return SIMPLICITY_NO_ERROR; case 5: *result = SHA_256_CTX_8_FINALIZE; return SIMPLICITY_NO_ERROR; case 6: *result = SHA_256_CTX_8_INIT; return SIMPLICITY_NO_ERROR; } break; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = POINT_VERIFY_1; return SIMPLICITY_NO_ERROR; } break; case 2: *result = DECOMPRESS; return SIMPLICITY_NO_ERROR; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LINEAR_VERIFY_1; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = LINEAR_COMBINATION_1; return SIMPLICITY_NO_ERROR; } break; case 5: *result = SCALE; return SIMPLICITY_NO_ERROR; case 6: *result = GENERATE; return SIMPLICITY_NO_ERROR; case 7: *result = GEJ_INFINITY; return SIMPLICITY_NO_ERROR; case 8: *result = GEJ_NORMALIZE; return SIMPLICITY_NO_ERROR; case 9: *result = GEJ_NEGATE; return SIMPLICITY_NO_ERROR; case 10: *result = GE_NEGATE; return SIMPLICITY_NO_ERROR; case 11: *result = GEJ_DOUBLE; return SIMPLICITY_NO_ERROR; case 12: *result = GEJ_ADD; return SIMPLICITY_NO_ERROR; case 13: *result = GEJ_GE_ADD_EX; return SIMPLICITY_NO_ERROR; case 14: *result = GEJ_GE_ADD; return SIMPLICITY_NO_ERROR; case 15: *result = GEJ_RESCALE; return SIMPLICITY_NO_ERROR; case 16: *result = GEJ_IS_INFINITY; return SIMPLICITY_NO_ERROR; case 17: *result = GEJ_EQUIV; return SIMPLICITY_NO_ERROR; case 18: *result = GEJ_GE_EQUIV; return SIMPLICITY_NO_ERROR; case 19: *result = GEJ_X_EQUIV; return SIMPLICITY_NO_ERROR; case 20: *result = GEJ_Y_IS_ODD; return SIMPLICITY_NO_ERROR; case 21: *result = GEJ_IS_ON_CURVE; return SIMPLICITY_NO_ERROR; case 22: *result = GE_IS_ON_CURVE; return SIMPLICITY_NO_ERROR; case 23: *result = SCALAR_NORMALIZE; return SIMPLICITY_NO_ERROR; case 24: *result = SCALAR_NEGATE; return SIMPLICITY_NO_ERROR; case 25: *result = SCALAR_ADD; return SIMPLICITY_NO_ERROR; case 26: *result = SCALAR_SQUARE; return SIMPLICITY_NO_ERROR; case 27: *result = SCALAR_MULTIPLY; return SIMPLICITY_NO_ERROR; case 28: *result = SCALAR_MULTIPLY_LAMBDA; return SIMPLICITY_NO_ERROR; case 29: *result = SCALAR_INVERT; return SIMPLICITY_NO_ERROR; case 30: *result = SCALAR_IS_ZERO; return SIMPLICITY_NO_ERROR; case 35: *result = FE_NORMALIZE; return SIMPLICITY_NO_ERROR; case 36: *result = FE_NEGATE; return SIMPLICITY_NO_ERROR; case 37: *result = FE_ADD; return SIMPLICITY_NO_ERROR; case 38: *result = FE_SQUARE; return SIMPLICITY_NO_ERROR; case 39: *result = FE_MULTIPLY; return SIMPLICITY_NO_ERROR; case 40: *result = FE_MULTIPLY_BETA; return SIMPLICITY_NO_ERROR; case 41: *result = FE_INVERT; return SIMPLICITY_NO_ERROR; case 42: *result = FE_SQUARE_ROOT; return SIMPLICITY_NO_ERROR; case 43: *result = FE_IS_ZERO; return SIMPLICITY_NO_ERROR; case 44: *result = FE_IS_ODD; return SIMPLICITY_NO_ERROR; case 46: *result = HASH_TO_CURVE; return SIMPLICITY_NO_ERROR; case 47: *result = SWU; return SIMPLICITY_NO_ERROR; } break; case 5: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = CHECK_SIG_VERIFY; return SIMPLICITY_NO_ERROR; case 2: *result = BIP_0340_VERIFY; return SIMPLICITY_NO_ERROR; } break; case 7: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = PARSE_LOCK; return SIMPLICITY_NO_ERROR; case 2: *result = PARSE_SEQUENCE; return SIMPLICITY_NO_ERROR; case 3: *result = TAPDATA_INIT; return SIMPLICITY_NO_ERROR; } break; } } ================================================ FILE: C/deserialize.c ================================================ #include "deserialize.h" #include #include "limitations.h" #include "simplicity_alloc.h" #include "simplicity_assert.h" /* Fetches 'len' 'uint32_t's from 'stream' into 'result'. * The bits in each 'uint32_t' are set from the MSB to the LSB and the 'uint32_t's of 'result' are set from 0 up to 'len'. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if not enough bits are available ('result' may be modified). * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: uint32_t result[len]; * NULL != stream */ static simplicity_err getWord32Array(uint32_t* result, const size_t len, bitstream* stream) { for (size_t i = 0; i < len; ++i) { /* Due to error codes, readNBits cannot fetch 32 bits at once. Instead we fetch two groups of 16 bits. */ int32_t bits16 = simplicity_readNBits(16, stream); if (bits16 < 0) return (simplicity_err)bits16; result[i] = (uint32_t)bits16 << 16; bits16 = simplicity_readNBits(16, stream); if (bits16 < 0) return (simplicity_err)bits16; result[i] |= (uint32_t)bits16; } return SIMPLICITY_NO_ERROR; } /* Fetches a 256-bit hash value from 'stream' into 'result'. * Returns 'SIMPLICITY_ERR_BITSTREAM_EOF' if not enough bits are available ('result' may be modified). * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != result * NULL != stream */ static simplicity_err getHash(sha256_midstate* result, bitstream* stream) { return getWord32Array(result->s, 8, stream); } /* Decode a single node of a Simplicity dag from 'stream' into 'dag'['i']. * Returns 'SIMPLICITY_ERR_FAIL_CODE' if the encoding of a fail expression is encountered * (all fail subexpressions ought to have been pruned prior to serialization). * Returns 'SIMPLICITY_ERR_RESERVED_CODE' if a reserved codeword is encountered. * Returns 'SIMPLICITY_ERR_HIDDEN' if the decoded node has a HIDDEN child in a position where it is not allowed. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the node's child isn't a reference to one of the preceding nodes. * or some encoding for a non-existent jet is encountered * or the size of a WORD encoding is greater than 2^31 bits. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: dag_node dag[i + 1]; * i < 2^31 - 1 * NULL != stream */ static simplicity_err decodeNode(dag_node* dag, simplicity_callback_decodeJet decodeJet, uint_fast32_t i, bitstream* stream) { int32_t bit = read1Bit(stream); if (bit < 0) return (simplicity_err)bit; dag[i] = (dag_node){0}; if (bit) { bit = read1Bit(stream); if (bit < 0) return (simplicity_err)bit; if (bit) { return decodeJet(&dag[i], stream); } else { /* Decode WORD. */ int32_t depth = simplicity_decodeUptoMaxInt(stream); if (depth < 0) return (simplicity_err)depth; if (32 < depth) return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; { simplicity_err error = simplicity_readBitstring(&dag[i].compactValue, (size_t)1 << (depth - 1), stream); if (!IS_OK(error)) return error; } dag[i].tag = WORD; dag[i].targetIx = (size_t)depth; dag[i].cmr = simplicity_computeWordCMR(&dag[i].compactValue, (size_t)(depth - 1)); } } else { int32_t code = simplicity_readNBits(2, stream); if (code < 0) return (simplicity_err)code; int32_t subcode = simplicity_readNBits(code < 3 ? 2 : 1, stream); if (subcode < 0) return (simplicity_err)subcode; for (int32_t j = 0; j < 2 - code; ++j) { int32_t ix = simplicity_decodeUptoMaxInt(stream); if (ix < 0) return (simplicity_err)ix; if (i < (uint_fast32_t)ix) return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; dag[i].child[j] = i - (uint_fast32_t)ix; } switch (code) { case 0: switch (subcode) { case 0: dag[i].tag = COMP; break; case 1: dag[i].tag = (HIDDEN == dag[dag[i].child[0]].tag) ? ASSERTR : (HIDDEN == dag[dag[i].child[1]].tag) ? ASSERTL : CASE; break; case 2: dag[i].tag = PAIR; break; case 3: dag[i].tag = DISCONNECT; break; } break; case 1: switch (subcode) { case 0: dag[i].tag = INJL; break; case 1: dag[i].tag = INJR; break; case 2: dag[i].tag = TAKE; break; case 3: dag[i].tag = DROP; break; } break; case 2: switch (subcode) { case 0: dag[i].tag = IDEN; break; case 1: dag[i].tag = UNIT; break; case 2: return SIMPLICITY_ERR_FAIL_CODE; case 3: return SIMPLICITY_ERR_RESERVED_CODE; } break; case 3: switch (subcode) { case 0: dag[i].tag = HIDDEN; return getHash(&(dag[i].cmr), stream); case 1: dag[i].tag = WITNESS; break; } break; } /* Verify that there are no illegal HIDDEN children. */ for (int32_t j = 0; j < 2 - code; ++j) { if (HIDDEN == dag[dag[i].child[j]].tag && dag[i].tag != (j ? ASSERTL : ASSERTR)) return SIMPLICITY_ERR_HIDDEN; } simplicity_computeCommitmentMerkleRoot(dag, i); } return SIMPLICITY_NO_ERROR; } /* Decode a Simplicity DAG consisting of 'len' nodes from 'stream' into 'dag'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if some node's child isn't a reference to one of the preceding nodes. * Returns 'SIMPLICITY_ERR_FAIL_CODE' if the encoding of a fail expression is encountered * (all fail subexpressions ought to have been pruned prior to deserialization). * Returns 'SIMPLICITY_ERR_RESERVED_CODE' if a reserved codeword is encountered. * Returns 'SIMPLICITY_ERR_HIDDEN' if the decoded node has a HIDDEN child in a position where it is not allowed. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: dag_node dag[len]; * len < 2^31 * NULL != stream */ static simplicity_err decodeDag(dag_node* dag, simplicity_callback_decodeJet decodeJet, const uint_fast32_t len, combinator_counters* census, bitstream* stream) { for (uint_fast32_t i = 0; i < len; ++i) { simplicity_err error = decodeNode(dag, decodeJet, i, stream); if (!IS_OK(error)) return error; enumerator(census, dag[i].tag); } return SIMPLICITY_NO_ERROR; } /* Decode a length-prefixed Simplicity DAG from 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' the length prefix's value is too large. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if some node's child isn't a reference to one of the preceding nodes. * Returns 'SIMPLICITY_ERR_FAIL_CODE' if the encoding of a fail expression is encountered * (all fail subexpressions ought to have been pruned prior to deserialization). * Returns 'SIMPLICITY_ERR_RESERVED_CODE' if a reserved codeword is encountered. * Returns 'SIMPLICITY_ERR_HIDDEN' if the decoded node has a HIDDEN child in a position where it is not allowed. * Returns 'SIMPLICITY_ERR_HIDDEN_ROOT' if the root of the DAG is a HIDDEN node. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_ORDER' if nodes are not serialized in the canonical order. * Returns 'SIMPLICITY_ERR_MALLOC' if malloc fails. * In the above error cases, '*dag' is set to NULL. * If successful, returns a positive value equal to the length of an allocated array of (*dag). * * Precondition: NULL != dag * NULL != stream * * Postcondition: if the return value of the function is positive * then (dag_node (*dag)[return_value] and '*dag' is a well-formed dag without witness data); * '*census' contains a tally of the different tags that occur in 'dag' when the return value * of the function is positive and when NULL != census; * NULL == *dag when the return value is negative. */ int_fast32_t simplicity_decodeMallocDag(dag_node** dag, simplicity_callback_decodeJet decodeJet, combinator_counters* census, bitstream* stream) { *dag = NULL; int32_t dagLen = simplicity_decodeUptoMaxInt(stream); if (dagLen <= 0) return dagLen; static_assert(DAG_LEN_MAX <= (uint32_t)INT32_MAX, "DAG_LEN_MAX exceeds supported parsing range."); if (DAG_LEN_MAX < (uint32_t)dagLen) return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; static_assert(DAG_LEN_MAX <= SIZE_MAX / sizeof(dag_node), "dag array too large."); static_assert(1 <= DAG_LEN_MAX, "DAG_LEN_MAX is zero."); static_assert(DAG_LEN_MAX - 1 <= UINT32_MAX, "dag array index does not fit in uint32_t."); *dag = simplicity_malloc((size_t)dagLen * sizeof(dag_node)); if (!*dag) return SIMPLICITY_ERR_MALLOC; if (census) *census = (combinator_counters){0}; simplicity_err error = decodeDag(*dag, decodeJet, (uint_fast32_t)dagLen, census, stream); if (IS_OK(error)) { error = HIDDEN == (*dag)[dagLen - 1].tag ? SIMPLICITY_ERR_HIDDEN_ROOT : simplicity_verifyCanonicalOrder(*dag, (uint_fast32_t)(dagLen)); } if (IS_OK(error)) { return dagLen; } else { simplicity_free(*dag); *dag = NULL; return (int_fast32_t)error; } } ================================================ FILE: C/deserialize.h ================================================ /* This module provides functions for deserializing Simplicity's bit-wise prefix coding. */ #ifndef SIMPLICITY_DESERIALIZE_H #define SIMPLICITY_DESERIALIZE_H #include #include "bitstream.h" #include "dag.h" /* Decode an application specific jet from 'stream' into 'node'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != node * NULL != stream */ typedef simplicity_err (*simplicity_callback_decodeJet)(dag_node* node, bitstream* stream); /* Decode a length-prefixed Simplicity DAG from 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' the length prefix's value is too large. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if some node's child isn't a reference to one of the preceding nodes. * Returns 'SIMPLICITY_ERR_FAIL_CODE' if the encoding of a fail expression is encountered * (all fail subexpressions ought to have been pruned prior to deserialization). * Returns 'SIMPLICITY_ERR_RESERVED_CODE' if a reserved codeword is encountered. * Returns 'SIMPLICITY_ERR_HIDDEN' if the decoded node has a HIDDEN child in a position where it is not allowed. * Returns 'SIMPLICITY_ERR_HIDDEN_ROOT' if the root of the DAG is a HIDDEN node. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * Returns 'SIMPLICITY_ERR_MALLOC' if malloc fails. * In the above error cases, '*dag' is set to NULL. * If successful, returns a positive value equal to the length of an allocated array of (*dag). * * Precondition: NULL != dag * NULL != stream * * Postcondition: if the return value of the function is positive * then (dag_node (*dag)[return_value] and '*dag' is a well-formed dag without witness data); * '*census' contains a tally of the different tags that occur in 'dag' when the return value * of the function is positive and when NULL != census; * NULL == *dag when the return value is negative. */ int_fast32_t simplicity_decodeMallocDag(dag_node** dag, simplicity_callback_decodeJet decodeJet, combinator_counters* census, bitstream* stream); #endif ================================================ FILE: C/elements/checkSigHashAllTx1.c ================================================ #include "checkSigHashAllTx1.h" /* A length-prefixed encoding of the following Simplicity program: * Simplicity.Programs.CheckSig.Lib.checkSigVerify' Simplicity.Elements.Programs.SigHash.Lib.sigAllHash * (Simplicity.LibSecp256k1.Spec.PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63) * (Simplicity.LibSecp256k1.Spec.Sig 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 * 0xcb176adea9659b35a79d44c78b940b363d0d6b6356b9ac8bb1dd1fbe9ba36986) * with jets. */ const unsigned char elementsCheckSigHashAllTx1[] = { 0xd3, 0x69, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x3b, 0x78, 0xce, 0x56, 0x3f, 0x89, 0xa0, 0xed, 0x94, 0x14, 0xf5, 0xaa, 0x28, 0xad, 0x0d, 0x96, 0xd6, 0x79, 0x5f, 0x9c, 0x63, 0x47, 0x07, 0x02, 0xc0, 0xe2, 0x8d, 0x88, 0x10 }; const size_t sizeof_elementsCheckSigHashAllTx1 = sizeof(elementsCheckSigHashAllTx1); const unsigned char elementsCheckSigHashAllTx1_witness[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x3b, 0x78, 0xce, 0x56, 0x3f, 0x89, 0xa0, 0xed, 0x94, 0x14, 0xf5, 0xaa, 0x28, 0xad, 0x0d, 0x96, 0xd6, 0x79, 0x5f, 0x9c, 0x63, 0xcb, 0x17, 0x6a, 0xde, 0xa9, 0x65, 0x9b, 0x35, 0xa7, 0x9d, 0x44, 0xc7, 0x8b, 0x94, 0x0b, 0x36, 0x3d, 0x0d, 0x6b, 0x63, 0x56, 0xb9, 0xac, 0x8b, 0xb1, 0xdd, 0x1f, 0xbe, 0x9b, 0xa3, 0x69, 0x86 }; const size_t sizeof_elementsCheckSigHashAllTx1_witness = sizeof(elementsCheckSigHashAllTx1_witness); /* The commitment Merkle root of the above elementsCheckSigHashAllTx1 Simplicity expression. */ const uint32_t elementsCheckSigHashAllTx1_cmr[] = { 0xf3cd4537u, 0xd7ebb201u, 0x73220319u, 0x5b30b549u, 0xb8dc0c2cu, 0x6257b3a0u, 0xd53bedb0u, 0x8ea02874u }; /* The identity hash of the root of the above elementsCheckSigHashAllTx1 Simplicity expression. */ const uint32_t elementsCheckSigHashAllTx1_ihr[] = { 0xd3a5130du, 0xf6abce06u, 0x51eb717au, 0x6dd04222u, 0xb7517651u, 0x9117ec5cu, 0x07bb9edbu, 0xac335e1bu }; /* The annotated Merkle root of the above elementsCheckSigHashAllTx1 Simplicity expression. */ const uint32_t elementsCheckSigHashAllTx1_amr[] = { 0xb1a514f7u, 0x85458faeu, 0x8e900fefu, 0x45e97fa6u, 0xaa8276deu, 0x181f0a9du, 0x448a10adu, 0x6c38034du }; /* The cost of the above elementsCheckSigHashAllTx1 Simplicity expression in milli weight units. */ const ubounded elementsCheckSigHashAllTx1_cost = 54361; ================================================ FILE: C/elements/checkSigHashAllTx1.h ================================================ #ifndef SIMPLICITY_ELEMENTS_CHECKSIGHASHALLTX1_H #define SIMPLICITY_ELEMENTS_CHECKSIGHASHALLTX1_H #include #include #include "../bounded.h" /* A length-prefixed encoding of the following Simplicity program: * Simplicity.Programs.CheckSig.Lib.checkSigVerify' Simplicity.Elements.Programs.SigHash.Lib.sigAllHash * (Simplicity.LibSecp256k1.Spec.PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63) * (Simplicity.LibSecp256k1.Spec.Sig 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 * 0xcb176adea9659b35a79d44c78b940b363d0d6b6356b9ac8bb1dd1fbe9ba36986) * with jets. */ extern const unsigned char elementsCheckSigHashAllTx1[]; extern const size_t sizeof_elementsCheckSigHashAllTx1; extern const unsigned char elementsCheckSigHashAllTx1_witness[]; extern const size_t sizeof_elementsCheckSigHashAllTx1_witness; /* The commitment Merkle root of the above elementsCheckSigHashAllTx1 Simplicity expression. */ extern const uint32_t elementsCheckSigHashAllTx1_cmr[]; /* The identity hash of the root of the above elementsCheckSigHashAllTx1 Simplicity expression. */ extern const uint32_t elementsCheckSigHashAllTx1_ihr[]; /* The annotated Merkle root of the above elementsCheckSigHashAllTx1 Simplicity expression. */ extern const uint32_t elementsCheckSigHashAllTx1_amr[]; /* The cost of the above elementsCheckSigHashAllTx1 Simplicity expression in milli weight units. */ extern const ubounded elementsCheckSigHashAllTx1_cost; #endif ================================================ FILE: C/elements/cmr.c ================================================ #include #include "../deserialize.h" #include "../limitations.h" #include "../simplicity_alloc.h" #include "../simplicity_assert.h" #include "primitive.h" /* Deserialize a Simplicity 'program' and compute its CMR. * * Caution: no typechecking is performed, only a well-formedness check. * * If at any time malloc fails then '*error' is set to 'SIMPLICITY_ERR_MALLOC' and 'false' is returned, * Otherwise, 'true' is returned indicating that the result was successfully computed and returned in the '*error' value. * * If the operation completes successfully then '*error' is set to 'SIMPLICITY_NO_ERROR', and the 'cmr' array is filled in with the program's computed CMR. * * Precondition: NULL != error; * unsigned char cmr[32] * unsigned char program[program_len] */ bool simplicity_elements_computeCmr( simplicity_err* error, unsigned char* cmr , const unsigned char* program, size_t program_len) { simplicity_assert(NULL != error); simplicity_assert(NULL != cmr); simplicity_assert(NULL != program || 0 == program_len); bitstream stream = initializeBitstream(program, program_len); dag_node* dag = NULL; int_fast32_t dag_len = simplicity_decodeMallocDag(&dag, simplicity_elements_decodeJet, NULL, &stream); if (dag_len <= 0) { simplicity_assert(dag_len < 0); *error = (simplicity_err)dag_len; } else { simplicity_assert(NULL != dag); simplicity_assert((uint_fast32_t)dag_len <= DAG_LEN_MAX); *error = simplicity_closeBitstream(&stream); sha256_fromMidstate(cmr, dag[dag_len-1].cmr.s); } simplicity_free(dag); return IS_PERMANENT(*error); } ================================================ FILE: C/elements/decodeElementsJets.inc ================================================ /* This file has been automatically generated. */ { int32_t code; code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SIG_ALL_HASH; return SIMPLICITY_NO_ERROR; case 2: *result = TX_HASH; return SIMPLICITY_NO_ERROR; case 3: *result = TAP_ENV_HASH; return SIMPLICITY_NO_ERROR; case 4: *result = OUTPUTS_HASH; return SIMPLICITY_NO_ERROR; case 5: *result = INPUTS_HASH; return SIMPLICITY_NO_ERROR; case 6: *result = ISSUANCES_HASH; return SIMPLICITY_NO_ERROR; case 7: *result = INPUT_UTXOS_HASH; return SIMPLICITY_NO_ERROR; case 8: *result = OUTPUT_HASH; return SIMPLICITY_NO_ERROR; case 9: *result = OUTPUT_AMOUNTS_HASH; return SIMPLICITY_NO_ERROR; case 10: *result = OUTPUT_SCRIPTS_HASH; return SIMPLICITY_NO_ERROR; case 11: *result = OUTPUT_NONCES_HASH; return SIMPLICITY_NO_ERROR; case 12: *result = OUTPUT_RANGE_PROOFS_HASH; return SIMPLICITY_NO_ERROR; case 13: *result = OUTPUT_SURJECTION_PROOFS_HASH; return SIMPLICITY_NO_ERROR; case 14: *result = INPUT_HASH; return SIMPLICITY_NO_ERROR; case 15: *result = INPUT_OUTPOINTS_HASH; return SIMPLICITY_NO_ERROR; case 16: *result = INPUT_SEQUENCES_HASH; return SIMPLICITY_NO_ERROR; case 17: *result = INPUT_ANNEXES_HASH; return SIMPLICITY_NO_ERROR; case 18: *result = INPUT_SCRIPT_SIGS_HASH; return SIMPLICITY_NO_ERROR; case 19: *result = ISSUANCE_HASH; return SIMPLICITY_NO_ERROR; case 20: *result = ISSUANCE_ASSET_AMOUNTS_HASH; return SIMPLICITY_NO_ERROR; case 21: *result = ISSUANCE_TOKEN_AMOUNTS_HASH; return SIMPLICITY_NO_ERROR; case 22: *result = ISSUANCE_RANGE_PROOFS_HASH; return SIMPLICITY_NO_ERROR; case 23: *result = ISSUANCE_BLINDING_ENTROPY_HASH; return SIMPLICITY_NO_ERROR; case 24: *result = INPUT_UTXO_HASH; return SIMPLICITY_NO_ERROR; case 25: *result = INPUT_AMOUNTS_HASH; return SIMPLICITY_NO_ERROR; case 26: *result = INPUT_SCRIPTS_HASH; return SIMPLICITY_NO_ERROR; case 27: *result = TAPLEAF_HASH; return SIMPLICITY_NO_ERROR; case 28: *result = TAPPATH_HASH; return SIMPLICITY_NO_ERROR; case 29: *result = OUTPOINT_HASH; return SIMPLICITY_NO_ERROR; case 30: *result = ASSET_AMOUNT_HASH; return SIMPLICITY_NO_ERROR; case 31: *result = NONCE_HASH; return SIMPLICITY_NO_ERROR; case 32: *result = ANNEX_HASH; return SIMPLICITY_NO_ERROR; case 33: *result = BUILD_TAPLEAF_SIMPLICITY; return SIMPLICITY_NO_ERROR; case 34: *result = BUILD_TAPBRANCH; return SIMPLICITY_NO_ERROR; case 35: *result = BUILD_TAPTWEAK; return SIMPLICITY_NO_ERROR; } break; case 2: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = CHECK_LOCK_HEIGHT; return SIMPLICITY_NO_ERROR; case 2: *result = CHECK_LOCK_TIME; return SIMPLICITY_NO_ERROR; case 3: *result = BROKEN_DO_NOT_USE_CHECK_LOCK_DISTANCE; return SIMPLICITY_NO_ERROR; case 4: *result = BROKEN_DO_NOT_USE_CHECK_LOCK_DURATION; return SIMPLICITY_NO_ERROR; case 5: *result = TX_LOCK_HEIGHT; return SIMPLICITY_NO_ERROR; case 6: *result = TX_LOCK_TIME; return SIMPLICITY_NO_ERROR; case 7: *result = BROKEN_DO_NOT_USE_TX_LOCK_DISTANCE; return SIMPLICITY_NO_ERROR; case 8: *result = BROKEN_DO_NOT_USE_TX_LOCK_DURATION; return SIMPLICITY_NO_ERROR; case 9: *result = TX_IS_FINAL; return SIMPLICITY_NO_ERROR; } break; case 3: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = ISSUANCE; return SIMPLICITY_NO_ERROR; case 2: *result = ISSUANCE_ASSET; return SIMPLICITY_NO_ERROR; case 3: *result = ISSUANCE_TOKEN; return SIMPLICITY_NO_ERROR; case 4: *result = ISSUANCE_ENTROPY; return SIMPLICITY_NO_ERROR; case 5: *result = CALCULATE_ISSUANCE_ENTROPY; return SIMPLICITY_NO_ERROR; case 6: *result = CALCULATE_ASSET; return SIMPLICITY_NO_ERROR; case 7: *result = CALCULATE_EXPLICIT_TOKEN; return SIMPLICITY_NO_ERROR; case 8: *result = CALCULATE_CONFIDENTIAL_TOKEN; return SIMPLICITY_NO_ERROR; case 9: *result = LBTC_ASSET; return SIMPLICITY_NO_ERROR; } break; case 4: code = simplicity_decodeUptoMaxInt(stream); if (code < 0) return (simplicity_err)code; switch (code) { case 1: *result = SCRIPT_CMR; return SIMPLICITY_NO_ERROR; case 2: *result = INTERNAL_KEY; return SIMPLICITY_NO_ERROR; case 3: *result = CURRENT_INDEX; return SIMPLICITY_NO_ERROR; case 4: *result = NUM_INPUTS; return SIMPLICITY_NO_ERROR; case 5: *result = NUM_OUTPUTS; return SIMPLICITY_NO_ERROR; case 6: *result = LOCK_TIME; return SIMPLICITY_NO_ERROR; case 7: *result = OUTPUT_ASSET; return SIMPLICITY_NO_ERROR; case 8: *result = OUTPUT_AMOUNT; return SIMPLICITY_NO_ERROR; case 9: *result = OUTPUT_NONCE; return SIMPLICITY_NO_ERROR; case 10: *result = OUTPUT_SCRIPT_HASH; return SIMPLICITY_NO_ERROR; case 11: *result = OUTPUT_NULL_DATUM; return SIMPLICITY_NO_ERROR; case 12: *result = OUTPUT_IS_FEE; return SIMPLICITY_NO_ERROR; case 13: *result = OUTPUT_SURJECTION_PROOF; return SIMPLICITY_NO_ERROR; case 14: *result = OUTPUT_RANGE_PROOF; return SIMPLICITY_NO_ERROR; case 15: *result = TOTAL_FEE; return SIMPLICITY_NO_ERROR; case 16: *result = CURRENT_PEGIN; return SIMPLICITY_NO_ERROR; case 17: *result = CURRENT_PREV_OUTPOINT; return SIMPLICITY_NO_ERROR; case 18: *result = CURRENT_ASSET; return SIMPLICITY_NO_ERROR; case 19: *result = CURRENT_AMOUNT; return SIMPLICITY_NO_ERROR; case 20: *result = CURRENT_SCRIPT_HASH; return SIMPLICITY_NO_ERROR; case 21: *result = CURRENT_SEQUENCE; return SIMPLICITY_NO_ERROR; case 22: *result = CURRENT_ANNEX_HASH; return SIMPLICITY_NO_ERROR; case 23: *result = CURRENT_SCRIPT_SIG_HASH; return SIMPLICITY_NO_ERROR; case 24: *result = CURRENT_REISSUANCE_BLINDING; return SIMPLICITY_NO_ERROR; case 25: *result = CURRENT_NEW_ISSUANCE_CONTRACT; return SIMPLICITY_NO_ERROR; case 26: *result = CURRENT_REISSUANCE_ENTROPY; return SIMPLICITY_NO_ERROR; case 27: *result = CURRENT_ISSUANCE_ASSET_AMOUNT; return SIMPLICITY_NO_ERROR; case 28: *result = CURRENT_ISSUANCE_TOKEN_AMOUNT; return SIMPLICITY_NO_ERROR; case 29: *result = CURRENT_ISSUANCE_ASSET_PROOF; return SIMPLICITY_NO_ERROR; case 30: *result = CURRENT_ISSUANCE_TOKEN_PROOF; return SIMPLICITY_NO_ERROR; case 31: *result = INPUT_PEGIN; return SIMPLICITY_NO_ERROR; case 32: *result = INPUT_PREV_OUTPOINT; return SIMPLICITY_NO_ERROR; case 33: *result = INPUT_ASSET; return SIMPLICITY_NO_ERROR; case 34: *result = INPUT_AMOUNT; return SIMPLICITY_NO_ERROR; case 35: *result = INPUT_SCRIPT_HASH; return SIMPLICITY_NO_ERROR; case 36: *result = INPUT_SEQUENCE; return SIMPLICITY_NO_ERROR; case 37: *result = INPUT_ANNEX_HASH; return SIMPLICITY_NO_ERROR; case 38: *result = INPUT_SCRIPT_SIG_HASH; return SIMPLICITY_NO_ERROR; case 39: *result = REISSUANCE_BLINDING; return SIMPLICITY_NO_ERROR; case 40: *result = NEW_ISSUANCE_CONTRACT; return SIMPLICITY_NO_ERROR; case 41: *result = REISSUANCE_ENTROPY; return SIMPLICITY_NO_ERROR; case 42: *result = ISSUANCE_ASSET_AMOUNT; return SIMPLICITY_NO_ERROR; case 43: *result = ISSUANCE_TOKEN_AMOUNT; return SIMPLICITY_NO_ERROR; case 44: *result = ISSUANCE_ASSET_PROOF; return SIMPLICITY_NO_ERROR; case 45: *result = ISSUANCE_TOKEN_PROOF; return SIMPLICITY_NO_ERROR; case 46: *result = TAPLEAF_VERSION; return SIMPLICITY_NO_ERROR; case 47: *result = TAPPATH; return SIMPLICITY_NO_ERROR; case 48: *result = VERSION; return SIMPLICITY_NO_ERROR; case 49: *result = GENESIS_BLOCK_HASH; return SIMPLICITY_NO_ERROR; case 50: *result = TRANSACTION_ID; return SIMPLICITY_NO_ERROR; } break; } } ================================================ FILE: C/elements/elementsJets.c ================================================ #include "elementsJets.h" #include "ops.h" #include "txEnv.h" #include "../taptweak.h" #include "../simplicity_assert.h" /* Read a 256-bit hash value from the 'src' frame, advancing the cursor 256 cells. * * Precondition: '*src' is a valid read frame for 256 more cells; * NULL != h; */ static void readHash(sha256_midstate* h, frameItem *src) { read32s(h->s, 8, src); } /* Write a 256-bit hash value to the 'dst' frame, advancing the cursor 256 cells. * * Precondition: '*dst' is a valid write frame for 256 more cells; * NULL != h; */ static void writeHash(frameItem* dst, const sha256_midstate* h) { write32s(dst, h->s, 8); } /* Write an outpoint value to the 'dst' frame, advancing the cursor 288 cells. * * Precondition: '*dst' is a valid write frame for 288 more cells; * NULL != op; */ static void prevOutpoint(frameItem* dst, const outpoint* op) { writeHash(dst, &op->txid); simplicity_write32(dst, op->ix); } /* Write an confidential asset to the 'dst' frame, advancing the cursor 258 cells. * * Precondition: '*dst' is a valid write frame for 258 more cells; * NULL != asset; */ static void asset(frameItem* dst, const confidential* asset) { if (writeBit(dst, EXPLICIT == asset->prefix)) { skipBits(dst, 1); } else { writeBit(dst, ODD_Y == asset->prefix); } writeHash(dst, &asset->data); } /* Write an confidential amount to the 'dst' frame, advancing the cursor 258 cells. * * Precondition: '*dst' is a valid write frame for 258 more cells; * NULL != amt; */ static void amt(frameItem* dst, const confAmount* amt) { if (writeBit(dst, EXPLICIT == amt->prefix)) { skipBits(dst, 1 + 256 - 64); simplicity_write64(dst, amt->explicit); } else { writeBit(dst, ODD_Y == amt->prefix); writeHash(dst, &amt->confidential); } } /* Write an optional confidential nonce to the 'dst' frame, advancing the cursor 259 cells. * * Precondition: '*dst' is a valid write frame for 259 more cells; * NULL != nonce; */ static void nonce(frameItem* dst, const confidential* nonce) { if (writeBit(dst, NONE != nonce->prefix)) { if (writeBit(dst, EXPLICIT == nonce->prefix)) { skipBits(dst, 1); } else { writeBit(dst, ODD_Y == nonce->prefix); } writeHash(dst, &nonce->data); } else { skipBits(dst, 1+1+256); } } /* Write an optional 'blindingNonce' from an 'assetIssuance' to the 'dst' frame, advancing the cursor 257 cells. * * Precondition: '*dst' is a valid write frame for 257 more cells; * NULL != issuance; */ static void reissuanceBlinding(frameItem* dst, const assetIssuance* issuance) { if (writeBit(dst, REISSUANCE == issuance->type)) { writeHash(dst, &issuance->blindingNonce); } else { skipBits(dst, 256); } } /* Write an optional 'contractHash' from an 'assetIssuance' to the 'dst' frame, advancing the cursor 257 cells. * * Precondition: '*dst' is a valid write frame for 257 more cells; * NULL != issuance; */ static void newIssuanceContract(frameItem* dst, const assetIssuance* issuance) { if (writeBit(dst, NEW_ISSUANCE == issuance->type)) { writeHash(dst, &issuance->contractHash); } else { skipBits(dst, 256); } } /* Write an optional 'entropy' from an 'assetIssuance' to the 'dst' frame, advancing the cursor 257 cells. * * Precondition: '*dst' is a valid write frame for 257 more cells; * NULL != issuance; */ static void reissuanceEntropy(frameItem* dst, const assetIssuance* issuance) { if (writeBit(dst, REISSUANCE == issuance->type)) { writeHash(dst, &issuance->entropy); } else { skipBits(dst, 256); } } /* Write an optional confidential asset amount from an 'assetIssuance' to the 'dst' frame, advancing the cursor 259 cells. * * Precondition: '*dst' is a valid write frame for 259 more cells; * NULL != issuance; */ static void issuanceAssetAmt(frameItem* dst, const assetIssuance* issuance) { if (writeBit(dst, NO_ISSUANCE != issuance->type)) { amt(dst, &issuance->assetAmt); } else { skipBits(dst, 258); } } /* Write an optional confidential token amount from an 'assetIssuance' to the 'dst' frame, advancing the cursor. * * Precondition: '*dst' is a valid write frame for 259 more cells; * NULL != issuance; */ static void issuanceTokenAmt(frameItem* dst, const assetIssuance* issuance) { if (writeBit(dst, NO_ISSUANCE != issuance->type)) { amt(dst, NEW_ISSUANCE == issuance->type ? &issuance->tokenAmt : &(confAmount){ .prefix = EXPLICIT, .explicit = 0}); } else { skipBits(dst, 258); } } static uint_fast32_t lockHeight(const elementsTransaction* tx) { return !tx->isFinal && tx->lockTime < 500000000U ? tx->lockTime : 0; } static uint_fast32_t lockTime(const elementsTransaction* tx) { return !tx->isFinal && 500000000U <= tx->lockTime ? tx->lockTime : 0; } static uint_fast16_t obsolete_lockDistance(const elementsTransaction* tx) { return 2 <= tx->version ? tx->obsolete_lockDistance : 0; } static uint_fast16_t obsolete_lockDuration(const elementsTransaction* tx) { return 2 <= tx->version ? tx->obsolete_lockDuration : 0; } static bool isFee(const sigOutput* output) { /* As specified in https://github.com/ElementsProject/elements/blob/de942511a67c3a3fcbdf002a8ee7e9ba49679b78/src/primitives/transaction.h#L304-L307. */ return output->emptyScript && EXPLICIT == output->asset.prefix && EXPLICIT == output->amt.prefix; } /* Lookup the assetFee from a sorted array of feeOutputs by the given assetid, returning 0 if no entry is found. * * Precondition: NULL != assetid; * feeOutputs is uniquely sorted by it asset.data.s field, which is to say * for all 0 <= i < j < len, * 0 < memcmp(feeOutputs[j]->asset.data.s, feeOutputs[i]->asset.data.s, sizeof(feeOutputs[i]->asset.data.s)); */ static uint_fast64_t lookup_fee(const sha256_midstate* assetid, const sigOutput* const * feeOutputs, uint_fast32_t len) { /* This loop runs in O(log(len)) time. */ while(len) { int cmp = memcmp(assetid->s, feeOutputs[len/2]->asset.data.s, sizeof(assetid->s)); if (0 == cmp) return feeOutputs[len/2]->assetFee; if (0 < cmp) { feeOutputs += len/2 + 1; len -= len/2 + 1; } else { len /= 2; } } return 0; } /* version : ONE |- TWO^32 */ bool simplicity_version(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->version); return true; } /* lock_time : ONE |- TWO^32 */ bool simplicity_lock_time(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->lockTime); return true; } /* input_pegin : TWO^32 |- S (S TWO^256) */ bool simplicity_input_pegin(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { if (writeBit(dst, env->tx->input[i].isPegin)) { writeHash(dst, &env->tx->input[i].pegin); } else { skipBits(dst, 256); } } else { skipBits(dst, 257); } return true; } /* input_prev_outpoint : TWO^32 |- S (TWO^256 * TWO^32) */ bool simplicity_input_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { prevOutpoint(dst, &env->tx->input[i].prevOutpoint); } else { skipBits(dst, 288); } return true; } /* input_asset : TWO^32 |- S (Conf TWO^256) */ bool simplicity_input_asset(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { asset(dst, &env->tx->input[i].txo.asset); } else { skipBits(dst, 258); } return true; } /* input_amount : TWO^32 |- S (Conf TWO^256, Conf TWO^64) */ bool simplicity_input_amount(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { asset(dst, &env->tx->input[i].txo.asset); amt(dst, &env->tx->input[i].txo.amt); } else { skipBits(dst, 516); } return true; } /* input_script_hash : TWO^32 |- S TWO^256 */ bool simplicity_input_script_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { writeHash(dst, &env->tx->input[i].txo.scriptPubKey); } else { skipBits(dst, 256); } return true; } /* input_sequence : TWO^32 |- S TWO^32 */ bool simplicity_input_sequence(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { simplicity_write32(dst, env->tx->input[i].sequence); } else { skipBits(dst, 32); } return true; } /* reissuance_blinding : TWO^32 |- S (S TWO^256) */ bool simplicity_reissuance_blinding(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { reissuanceBlinding(dst, &env->tx->input[i].issuance); } else { skipBits(dst, 257); } return true; } /* new_issuance_contract : TWO^32 |- S (S TWO^256) */ bool simplicity_new_issuance_contract(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { newIssuanceContract(dst, &env->tx->input[i].issuance); } else { skipBits(dst, 257); } return true; } /* reissuance_entropy : TWO^32 |- S (S TWO^256) */ bool simplicity_reissuance_entropy(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { reissuanceEntropy(dst, &env->tx->input[i].issuance); } else { skipBits(dst, 257); } return true; } /* issuance_asset_amount : TWO^32 |- S (S (Conf TWO^64)) */ bool simplicity_issuance_asset_amount(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { issuanceAssetAmt(dst, &env->tx->input[i].issuance); } else { skipBits(dst, 259); } return true; } /* issuance_token_amount : TWO^32 |- S (S (Conf TWO^64)) */ bool simplicity_issuance_token_amount(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { issuanceTokenAmt(dst, &env->tx->input[i].issuance); } else { skipBits(dst, 259); } return true; } /* issuance_asset_proof : TWO^32 |- S TWO^256 */ bool simplicity_issuance_asset_proof(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { writeHash(dst, &env->tx->input[i].issuance.assetRangeProofHash); } else { skipBits(dst, 256); } return true; } /* issuance_token_proof : TWO^32 |- S TWO^256 */ bool simplicity_issuance_token_proof(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { writeHash(dst, &env->tx->input[i].issuance.tokenRangeProofHash); } else { skipBits(dst, 256); } return true; } /* input_annex_hash : TWO^32 |- S (S (TWO^256)) */ bool simplicity_input_annex_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { if (writeBit(dst, env->tx->input[i].hasAnnex)) { writeHash(dst, &env->tx->input[i].annexHash); } else { skipBits(dst, 256); } } else { skipBits(dst, 257); } return true; } /* input_script_sig_hash : TWO^32 |- (S (TWO^256) */ bool simplicity_input_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { writeHash(dst, &env->tx->input[i].scriptSigHash); } else { skipBits(dst, 256); } return true; } /* output_asset : TWO^32 |- S (Conf TWO^256) */ bool simplicity_output_asset(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { asset(dst, &env->tx->output[i].asset); } else { skipBits(dst, 258); } return true; } /* output_amount : TWO^32 |- S (Conf TWO^256, Conf TWO^64) */ bool simplicity_output_amount(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { asset(dst, &env->tx->output[i].asset); amt(dst, &env->tx->output[i].amt); } else { skipBits(dst, 516); } return true; } /* output_nonce : TWO^32 |- S (S (Conf TWO^256)) */ bool simplicity_output_nonce(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { nonce(dst, &env->tx->output[i].nonce); } else { skipBits(dst, 259); } return true; } /* output_script_hash : TWO^32 |- S TWO^256 */ bool simplicity_output_script_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { writeHash(dst, &env->tx->output[i].scriptPubKey); } else { skipBits(dst, 256); } return true; } /* output_null_datum : TWO^32 * TWO^32 |- S (S (TWO^2 * TWO^256 + (TWO + TWO^4))) */ bool simplicity_output_null_datum(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs && env->tx->output[i].isNullData)) { uint_fast32_t j = simplicity_read32(&src); if (writeBit(dst, j < env->tx->output[i].pnd.len)) { if (writeBit(dst, OP_PUSHDATA4 < env->tx->output[i].pnd.op[j].code)) { skipBits(dst, 2 + 256 - 5); if (writeBit(dst, OP_1 <= env->tx->output[i].pnd.op[j].code)) { switch (env->tx->output[i].pnd.op[j].code) { case OP_1 : writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 0); break; case OP_2 : writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 1); break; case OP_3 : writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 0); break; case OP_4 : writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 1); break; case OP_5 : writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 0); break; case OP_6 : writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 1); break; case OP_7 : writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 0); break; case OP_8 : writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 1); break; case OP_9 : writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 0); break; case OP_10: writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 0); writeBit(dst, 1); break; case OP_11: writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 0); break; case OP_12: writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 1); writeBit(dst, 1); break; case OP_13: writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 0); break; case OP_14: writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 0); writeBit(dst, 1); break; case OP_15: writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 0); break; case OP_16: writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 1); writeBit(dst, 1); break; default: SIMPLICITY_UNREACHABLE; } } else { simplicity_debug_assert(OP_RESERVED == env->tx->output[i].pnd.op[j].code || OP_1NEGATE == env->tx->output[i].pnd.op[j].code); skipBits(dst, 3); writeBit(dst, OP_RESERVED == env->tx->output[i].pnd.op[j].code); } } else { switch (env->tx->output[i].pnd.op[j].code) { case OP_IMMEDIATE: writeBit(dst, 0); writeBit(dst, 0); break; case OP_PUSHDATA: writeBit(dst, 0); writeBit(dst, 1); break; case OP_PUSHDATA2: writeBit(dst, 1); writeBit(dst, 0); break; case OP_PUSHDATA4: writeBit(dst, 1); writeBit(dst, 1); break; default: SIMPLICITY_UNREACHABLE; } writeHash(dst, &env->tx->output[i].pnd.op[j].dataHash); } } else { skipBits(dst, 1 + 2 + 256); } } else { skipBits(dst, 1 + 1 + 2 + 256); } return true; } /* output_is_fee : TWO^32 |- S TWO */ bool simplicity_output_is_fee(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { writeBit(dst, isFee(&env->tx->output[i])); } else { skipBits(dst, 1); } return true; } /* output_surjection_proof : TWO^32 |- S TWO^256 */ bool simplicity_output_surjection_proof(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { writeHash(dst, &env->tx->output[i].surjectionProofHash); } else { skipBits(dst, 256); } return true; } /* output_range_proof : TWO^32 |- S TWO^256 */ bool simplicity_output_range_proof(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { writeHash(dst, &env->tx->output[i].rangeProofHash); } else { skipBits(dst, 256); } return true; } /* total_fee : TWO^256 |- TWO^64 */ bool simplicity_total_fee(frameItem* dst, frameItem src, const txEnv* env) { sha256_midstate assetid; readHash(&assetid, &src); simplicity_write64(dst, lookup_fee(&assetid, env->tx->feeOutputs, env->tx->numFees)); return true; } /* genesis_block_hash : ONE |- TWO^256 */ bool simplicity_genesis_block_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; write32s(dst, env->genesisHash.s, 8); return true; } /* script_cmr : ONE |- TWO^256 */ bool simplicity_script_cmr(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; write32s(dst, env->taproot->scriptCMR.s, 8); return true; } /* transaction_id : ONE |- TWO^256 */ bool simplicity_transaction_id(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; write32s(dst, env->tx->txid.s, 8); return true; } /* current_index : ONE |- TWO^32 */ bool simplicity_current_index(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->ix); return true; } /* current_pegin : ONE |- S TWO^256 */ bool simplicity_current_pegin(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; if (writeBit(dst, env->tx->input[env->ix].isPegin)) { writeHash(dst, &env->tx->input[env->ix].pegin); } else { skipBits(dst, 256); } return true; } /* current_prev_outpoint : ONE |- TWO^256 * TWO^32 */ bool simplicity_current_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; prevOutpoint(dst, &env->tx->input[env->ix].prevOutpoint); return true; } /* current_asset : ONE |- Conf TWO^256 */ bool simplicity_current_asset(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; asset(dst, &env->tx->input[env->ix].txo.asset); return true; } /* current_amount : ONE |- (Conf TWO^256, Conf TWO^64) */ bool simplicity_current_amount(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; asset(dst, &env->tx->input[env->ix].txo.asset); amt(dst, &env->tx->input[env->ix].txo.amt); return true; } /* current_script_hash : ONE |- TWO^256 */ bool simplicity_current_script_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; writeHash(dst, &env->tx->input[env->ix].txo.scriptPubKey); return true; } /* current_sequence : ONE |- TWO^32 */ bool simplicity_current_sequence(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; simplicity_write32(dst, env->tx->input[env->ix].sequence); return true; } /* current_reissuance_blinding : ONE |- S (Conf TWO^256) */ bool simplicity_current_reissuance_blinding(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; reissuanceBlinding(dst, &env->tx->input[env->ix].issuance); return true; } /* current_new_issuance_contract : ONE |- S (Conf TWO^256) */ bool simplicity_current_new_issuance_contract(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; newIssuanceContract(dst, &env->tx->input[env->ix].issuance); return true; } /* current_reissuance_entropy : ONE |- S (Conf TWO^256) */ bool simplicity_current_reissuance_entropy(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; reissuanceEntropy(dst, &env->tx->input[env->ix].issuance); return true; } /* current_issuance_asset_amount : ONE |- S (Conf TWO^64) */ bool simplicity_current_issuance_asset_amount(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; issuanceAssetAmt(dst, &env->tx->input[env->ix].issuance); return true; } /* current_issuance_token_amount : ONE |- S (Conf TWO^64) */ bool simplicity_current_issuance_token_amount(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; issuanceTokenAmt(dst, &env->tx->input[env->ix].issuance); return true; } /* current_issuance_asset_proof : ONE |- TWO^256 */ bool simplicity_current_issuance_asset_proof(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; writeHash(dst, &env->tx->input[env->ix].issuance.assetRangeProofHash); return true; } /* current_issuance_token_proof : ONE |- TWO^256 */ bool simplicity_current_issuance_token_proof(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; writeHash(dst, &env->tx->input[env->ix].issuance.tokenRangeProofHash); return true; } /* current_script_sig_hash : ONE |- TWO^256 */ bool simplicity_current_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; writeHash(dst, &env->tx->input[env->ix].scriptSigHash); return true; } /* current_annex_hash : ONE |- S (TWO^256) */ bool simplicity_current_annex_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; if (env->tx->numInputs <= env->ix) return false; if (writeBit(dst, env->tx->input[env->ix].hasAnnex)) { writeHash(dst, &env->tx->input[env->ix].annexHash); } else { skipBits(dst, 256); } return true; } /* tapleaf_version : ONE |- TWO^8 */ bool simplicity_tapleaf_version(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write8(dst, env->taproot->leafVersion); return true; } /* tappath : TWO^8 |- S (TWO^256) */ bool simplicity_tappath(frameItem* dst, frameItem src, const txEnv* env) { uint_fast8_t i = simplicity_read8(&src); if (writeBit(dst, i < env->taproot->pathLen)) { writeHash(dst, &env->taproot->path[i]); } else { skipBits(dst, 256); } return true; } /* internal_key : ONE |- TWO^256 */ bool simplicity_internal_key(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->internalKey); return true; } /* num_inputs : ONE |- TWO^32 */ bool simplicity_num_inputs(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->numInputs); return true; } /* num_outputs : ONE |- TWO^32 */ bool simplicity_num_outputs(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, env->tx->numOutputs); return true; } /* tx_is_final : ONE |- TWO */ bool simplicity_tx_is_final(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeBit(dst, env->tx->isFinal); return true; } /* tx_lock_height : ONE |- TWO^32 */ bool simplicity_tx_lock_height(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, lockHeight(env->tx)); return true; } /* tx_lock_time : ONE |- TWO^32 */ bool simplicity_tx_lock_time(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write32(dst, lockTime(env->tx)); return true; } /* tx_lock_distance : ONE |- TWO^16 */ bool simplicity_broken_do_not_use_tx_lock_distance(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write16(dst, obsolete_lockDistance(env->tx)); return true; } /* tx_lock_duration : ONE |- TWO^16 */ bool simplicity_broken_do_not_use_tx_lock_duration(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; simplicity_write16(dst, obsolete_lockDuration(env->tx)); return true; } /* check_lock_height : TWO^32 |- ONE */ bool simplicity_check_lock_height(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; uint_fast32_t x = simplicity_read32(&src); return x <= lockHeight(env->tx); } /* check_lock_time : TWO^32 |- ONE */ bool simplicity_check_lock_time(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; uint_fast32_t x = simplicity_read32(&src); return x <= lockTime(env->tx); } /* check_lock_distance : TWO^16 |- ONE */ bool simplicity_broken_do_not_use_check_lock_distance(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; uint_fast16_t x = simplicity_read16(&src); return x <= obsolete_lockDistance(env->tx); } /* check_lock_duration : TWO^16 |- ONE */ bool simplicity_broken_do_not_use_check_lock_duration(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; uint_fast16_t x = simplicity_read16(&src); return x <= obsolete_lockDuration(env->tx); } /* calculate_issuance_entropy : TWO^256 * TWO^32 * TWO^256 |- TWO^256 */ bool simplicity_calculate_issuance_entropy(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. outpoint op; sha256_midstate contract; sha256_midstate result; read32s(op.txid.s, 8, &src); op.ix = simplicity_read32(&src); read32s(contract.s, 8, &src); result = simplicity_generateIssuanceEntropy(&op, &contract); writeHash(dst, &result); return true; } /* calculate_asset : TWO^256 |- TWO^256 */ bool simplicity_calculate_asset(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate entropy; sha256_midstate result; read32s(entropy.s, 8, &src); result = simplicity_calculateAsset(&entropy); writeHash(dst, &result); return true; } /* calculate_explicit_token : TWO^256 |- TWO^256 */ bool simplicity_calculate_explicit_token(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate entropy; sha256_midstate result; read32s(entropy.s, 8, &src); result = simplicity_calculateToken(&entropy, EXPLICIT); writeHash(dst, &result); return true; } /* calculate_confidential_token : TWO^256 |- TWO^256 */ bool simplicity_calculate_confidential_token(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate entropy; sha256_midstate result; read32s(entropy.s, 8, &src); result = simplicity_calculateToken(&entropy, EVEN_Y /* ODD_Y would also work. */); writeHash(dst, &result); return true; } /* lbtc_asset : ONE |- TWO^256 */ bool simplicity_lbtc_asset(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused. (void) env; // env is unused. const sha256_midstate lbtc_assetid = {{ 0x6d521c38u, 0xec1ea157u, 0x34ae22b7u, 0xc4606441u, 0x2829c0d0u, 0x579f0a71u, 0x3d1c04edu, 0xe979026fu }}; writeHash(dst, &lbtc_assetid); return true; } /* build_tapleaf_simplicity : TWO^256 |- TWO^256 */ bool simplicity_build_tapleaf_simplicity(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate cmr; readHash(&cmr, &src); sha256_midstate result = simplicity_make_tapleaf(0xbe, &cmr); writeHash(dst, &result); return true; } /* build_tapbranch : TWO^256 * TWO^256 |- TWO^256 */ bool simplicity_build_tapbranch(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate a, b; readHash(&a, &src); readHash(&b, &src); sha256_midstate result = simplicity_make_tapbranch(&a, &b); writeHash(dst, &result); return true; } /* build_taptweak : PUBKEY * TWO^256 |- PUBKEY */ bool simplicity_build_taptweak(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. static unsigned char taptweak[] = "TapTweak/elements"; return simplicity_generic_taptweak(dst, &src, taptweak, sizeof(taptweak)-1); } /* outpoint_hash : CTX8 * S TWO^256 * TWO^256 * TWO^32 |- CTX8 */ bool simplicity_outpoint_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate midstate; unsigned char buf[36]; sha256_context ctx = {.output = midstate.s}; /* Read a SHA-256 context. */ if (!simplicity_read_sha256_context(&ctx, &src)) return false; /* Read an optional pegin parent chain hash. */ if (readBit(&src)) { /* Read a pegin parent chain hash. */ read8s(buf, 32, &src); sha256_uchar(&ctx, 0x01); sha256_uchars(&ctx, buf, 32); } else { /* No pegin. */ sha256_uchar(&ctx, 0x00); forwardBits(&src, 256); } /* Read an outpoint (hash and index). */ read8s(buf, 36, &src); sha256_uchars(&ctx, buf, 36); return simplicity_write_sha256_context(dst, &ctx); } /* asset_amount_hash : CTX8 * Conf TWO^256 * Conf TWO^64 |- CTX8 */ bool simplicity_asset_amount_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate midstate; unsigned char buf[32]; sha256_context ctx = {.output = midstate.s}; /* Read a SHA-256 context. */ if (!simplicity_read_sha256_context(&ctx, &src)) return false; /* Read an asset id prefix. (2 bits) */ if (readBit(&src)) { /* Read an explicit asset id prefix. (1 bit) */ forwardBits(&src, 1); sha256_uchar(&ctx, 0x01); } else { /* Read an confidential asset id prefix. (1 bit) */ if (readBit(&src)) { sha256_uchar(&ctx, 0x0b); } else { sha256_uchar(&ctx, 0x0a); } } /* Read an asset id body (both confidential and explicit asset bodies are the same size). (256 bits) */ read8s(buf, 32, &src); sha256_uchars(&ctx, buf, 32); /* Read an amount. (258 bits) */ if (readBit(&src)) { /* Read an explicit amount. (257 bits) */ sha256_uchar(&ctx, 0x01); forwardBits(&src, 257-64); read8s(buf, 8, &src); sha256_uchars(&ctx, buf, 8); } else { /* Read an confidential amount. (257 bits) */ if (readBit(&src)) { sha256_uchar(&ctx, 0x09); } else { sha256_uchar(&ctx, 0x08); } read8s(buf, 32, &src); sha256_uchars(&ctx, buf, 32); } return simplicity_write_sha256_context(dst, &ctx); } /* nonce_hash : CTX8 * S (Conf TWO^256) |- CTX8 */ bool simplicity_nonce_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate midstate; unsigned char buf[32]; sha256_context ctx = {.output = midstate.s}; /* Read a SHA-256 context. */ if (!simplicity_read_sha256_context(&ctx, &src)) return false; /* Read an optional nonce. (259 bits) */ if (readBit(&src)) { /* Read a nonce prefix. (2 bits) */ if (readBit(&src)) { /* Read an explicit none prefix. (1 bit) */ forwardBits(&src, 1); sha256_uchar(&ctx, 0x01); } else { /* Read a confidential none prefix. (1 bit) */ if (readBit(&src)) { sha256_uchar(&ctx, 0x03); } else { sha256_uchar(&ctx, 0x02); } } /* Read a nonce id body (both confidential and explicit nonce bodies are the same size). (256 bits) */ read8s(buf, 32, &src); sha256_uchars(&ctx, buf, 32); } else { sha256_uchar(&ctx, 0x00); } return simplicity_write_sha256_context(dst, &ctx); } /* annex_hash : CTX8 * S TWO^256 |- CTX8 */ bool simplicity_annex_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused. sha256_midstate midstate; unsigned char buf[32]; sha256_context ctx = {.output = midstate.s}; /* Read a SHA-256 context. */ if (!simplicity_read_sha256_context(&ctx, &src)) return false; /* Read an optional hash. (257 bits) */ if (readBit(&src)) { /* Read a hash. (256 bits) */ read8s(buf, 32, &src); sha256_uchar(&ctx, 0x01); sha256_uchars(&ctx, buf, 32); } else { /* No hash. */ sha256_uchar(&ctx, 0x00); } return simplicity_write_sha256_context(dst, &ctx); } /* issuance : TWO^256 |- S (S TWO) */ bool simplicity_issuance(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigInput* input = &env->tx->input[i]; if (writeBit(dst, NO_ISSUANCE != input->issuance.type)) { writeBit(dst, REISSUANCE == input->issuance.type); } else { skipBits(dst, 1); } } else { skipBits(dst, 2); } return true; } /* issuance_entropy : TWO^256 |- S (S TWO^256) */ bool simplicity_issuance_entropy(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigInput* input = &env->tx->input[i]; if (writeBit(dst, NO_ISSUANCE != input->issuance.type)) { writeHash(dst, &input->issuance.entropy); } else { skipBits(dst, 256); } } else { skipBits(dst, 257); } return true; } /* issuance_asset : TWO^256 |- S (S TWO^256) */ bool simplicity_issuance_asset(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigInput* input = &env->tx->input[i]; if (writeBit(dst, NO_ISSUANCE != input->issuance.type)) { writeHash(dst, &input->issuance.assetId); } else { skipBits(dst, 256); } } else { skipBits(dst, 257); } return true; } /* issuance_token : TWO^256 |- S (S TWO^256) */ bool simplicity_issuance_token(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigInput* input = &env->tx->input[i]; if (writeBit(dst, NO_ISSUANCE != input->issuance.type)) { writeHash(dst, &input->issuance.tokenId); } else { skipBits(dst, 256); } } else { skipBits(dst, 257); } return true; } /* output_amounts_hash : ONE |- TWO^256 */ bool simplicity_output_amounts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputAssetAmountsHash); return true; } /* output_nonces_hash : ONE |- TWO^256 */ bool simplicity_output_nonces_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputNoncesHash); return true; } /* output_scripts_hash : ONE |- TWO^256 */ bool simplicity_output_scripts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputScriptsHash); return true; } /* output_range_proofs_hash : ONE |- TWO^256 */ bool simplicity_output_range_proofs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputRangeProofsHash); return true; } /* output_surjection_proofs_hash : ONE |- TWO^256 */ bool simplicity_output_surjection_proofs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputSurjectionProofsHash); return true; } /* outputs_hash : ONE |- TWO^256 */ bool simplicity_outputs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->outputsHash); return true; } /* output_hash : TWO^32 |- S TWO^256 */ bool simplicity_output_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numOutputs)) { const sigOutput* output = &env->tx->output[i]; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); simplicity_sha256_confAsset(&ctx, &output->asset); simplicity_sha256_confAmt(&ctx, &output->amt); simplicity_sha256_confNonce(&ctx, &output->nonce); sha256_hash(&ctx, &output->scriptPubKey); sha256_hash(&ctx, &output->rangeProofHash); sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* input_outpoints_hash : ONE |- TWO^256 */ bool simplicity_input_outpoints_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputOutpointsHash); return true; } /* input_amounts_hash : ONE |- TWO^256 */ bool simplicity_input_amounts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputAssetAmountsHash); return true; } /* input_scripts_hash : ONE |- TWO^256 */ bool simplicity_input_scripts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputScriptsHash); return true; } /* input_utxos_hash : ONE |- TWO^256 */ bool simplicity_input_utxos_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputUTXOsHash); return true; } /* input_utxo_hash : TWO^32 |- S TWO^256 */ bool simplicity_input_utxo_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const utxo* txo = &env->tx->input[i].txo; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); simplicity_sha256_confAsset(&ctx, &txo->asset); simplicity_sha256_confAmt(&ctx, &txo->amt); sha256_hash(&ctx, &txo->scriptPubKey); sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* input_sequences_hash : ONE |- TWO^256 */ bool simplicity_input_sequences_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputSequencesHash); return true; } /* input_annexes_hash : ONE |- TWO^256 */ bool simplicity_input_annexes_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputAnnexesHash); return true; } /* input_script_sigs_hash : ONE |- TWO^256 */ bool simplicity_input_script_sigs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputScriptSigsHash); return true; } /* inputs_hash : ONE |- TWO^256 */ bool simplicity_inputs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->inputsHash); return true; } /* input_hash : TWO^32 |- S TWO^256 */ bool simplicity_input_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const sigInput* input = &env->tx->input[i]; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); if (input->isPegin) { sha256_uchar(&ctx, 1); sha256_hash(&ctx, &input->pegin); } else { sha256_uchar(&ctx, 0); } sha256_hash(&ctx, &input->prevOutpoint.txid); sha256_u32be(&ctx, input->prevOutpoint.ix); sha256_u32be(&ctx, input->sequence); if (input->hasAnnex) { sha256_uchar(&ctx, 1); sha256_hash(&ctx, &input->annexHash); } else { sha256_uchar(&ctx, 0); } sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* issuance_asset_amounts_hash : ONE |- TWO^256 */ bool simplicity_issuance_asset_amounts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->issuanceAssetAmountsHash); return true; } /* issuance_token_amounts_hash : ONE |- TWO^256 */ bool simplicity_issuance_token_amounts_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->issuanceTokenAmountsHash); return true; } /* issuance_range_proofs_hash : ONE |- TWO^256 */ bool simplicity_issuance_range_proofs_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->issuanceRangeProofsHash); return true; } /* issuance_blinding_entropy_hash : ONE |- TWO^256 */ bool simplicity_issuance_blinding_entropy_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->issuanceBlindingEntropyHash); return true; } /* issuances_hash : ONE |- TWO^256 */ bool simplicity_issuances_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->issuancesHash); return true; } /* issuance_hash : TWO^32 |- S TWO^256 */ bool simplicity_issuance_hash(frameItem* dst, frameItem src, const txEnv* env) { uint_fast32_t i = simplicity_read32(&src); if (writeBit(dst, i < env->tx->numInputs)) { const assetIssuance* issuance = &env->tx->input[i].issuance; sha256_midstate midstate; sha256_context ctx = sha256_init(midstate.s); if (NO_ISSUANCE == issuance->type) { sha256_uchar(&ctx, 0); sha256_uchar(&ctx, 0); sha256_uchar(&ctx, 0); sha256_uchar(&ctx, 0); sha256_hash(&ctx, &issuance->assetRangeProofHash); sha256_hash(&ctx, &issuance->tokenRangeProofHash); sha256_uchar(&ctx, 0); } else { simplicity_sha256_confAsset(&ctx, &(confidential){ .prefix = EXPLICIT, .data = issuance->assetId}); simplicity_sha256_confAmt(&ctx, &issuance->assetAmt); simplicity_sha256_confAsset(&ctx, &(confidential){ .prefix = EXPLICIT, .data = issuance->tokenId}); simplicity_sha256_confAmt(&ctx, NEW_ISSUANCE == issuance->type ? &issuance->tokenAmt : &(confAmount){ .prefix = EXPLICIT, .explicit = 0}); sha256_hash(&ctx, &issuance->assetRangeProofHash); sha256_hash(&ctx, &issuance->tokenRangeProofHash); sha256_uchar(&ctx, 1); if (NEW_ISSUANCE == issuance->type) { sha256_uchars(&ctx, (unsigned char[32]){0}, 32); sha256_hash(&ctx, &issuance->contractHash); } else { sha256_hash(&ctx, &issuance->blindingNonce); sha256_hash(&ctx, &issuance->entropy); } } sha256_finalize(&ctx); writeHash(dst, &midstate); } else { skipBits(dst, 256); } return true; } /* tx_hash : ONE |- TWO^256 */ bool simplicity_tx_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->tx->txHash); return true; } /* tapleaf_hash : ONE |- TWO^256 */ bool simplicity_tapleaf_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->tapLeafHash); return true; } /* tappath_hash : ONE |- TWO^256 */ bool simplicity_tappath_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->tappathHash); return true; } /* tap_env_hash : ONE |- TWO^256 */ bool simplicity_tap_env_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->taproot->tapEnvHash); return true; } /* sig_all_hash : ONE |- TWO^256 */ bool simplicity_sig_all_hash(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; writeHash(dst, &env->sigAllHash); return true; } ================================================ FILE: C/elements/elementsJets.h ================================================ /* This module defines primitives and jets that are specific to the Elements application for Simplicity. */ #ifndef SIMPLICITY_ELEMENTS_ELEMENTSJETS_H #define SIMPLICITY_ELEMENTS_ELEMENTSJETS_H #include "../jets.h" /* Jets for the Elements application of Simplicity. */ bool simplicity_version(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_lock_time(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_pegin(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_asset(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_script_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_sequence(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_annex_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_reissuance_blinding(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_new_issuance_contract(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_reissuance_entropy(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_asset_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_token_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_asset_proof(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_token_proof(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_asset(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_nonce(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_script_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_null_datum(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_is_fee(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_surjection_proof(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_range_proof(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_total_fee(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_genesis_block_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_script_cmr(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_transaction_id(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_index(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_pegin(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_prev_outpoint(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_asset(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_script_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_sequence(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_reissuance_blinding(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_new_issuance_contract(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_reissuance_entropy(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_issuance_asset_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_issuance_token_amount(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_issuance_asset_proof(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_issuance_token_proof(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_annex_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_current_script_sig_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tapleaf_version(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tappath(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_internal_key(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_num_inputs(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_num_outputs(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tx_is_final(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tx_lock_height(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tx_lock_time(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_broken_do_not_use_tx_lock_distance(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_broken_do_not_use_tx_lock_duration(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_check_lock_height(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_check_lock_time(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_broken_do_not_use_check_lock_distance(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_broken_do_not_use_check_lock_duration(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_calculate_issuance_entropy(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_calculate_asset(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_calculate_explicit_token(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_calculate_confidential_token(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_lbtc_asset(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_build_tapleaf_simplicity(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_build_tapbranch(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_build_taptweak(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_outpoint_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_asset_amount_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_nonce_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_annex_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_entropy(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_asset(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_token(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_amounts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_nonces_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_scripts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_range_proofs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_surjection_proofs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_outputs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_output_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_outpoints_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_amounts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_scripts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_utxos_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_utxo_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_sequences_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_annexes_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_script_sigs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_inputs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_input_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_asset_amounts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_token_amounts_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_range_proofs_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_blinding_entropy_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuances_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_issuance_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tx_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tapleaf_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tappath_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tap_env_hash(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sig_all_hash(frameItem* dst, frameItem src, const txEnv* env); #endif ================================================ FILE: C/elements/env.c ================================================ #include #include #include #include #include "txEnv.h" #include "ops.h" #include "../rsort.h" #include "../sha256.h" #include "../simplicity_assert.h" #include "../simplicity_alloc.h" #define PADDING(alignType, allocated) ((alignof(alignType) - (allocated) % alignof(alignType)) % alignof(alignType)) /* Compute the SHA-256 hash of a scriptPubKey and write it into 'result'. * * Precondition: NULL != result; * NULL != scriptPubKey; */ static void hashBuffer(sha256_midstate* result, const rawElementsBuffer* buffer) { sha256_context ctx = sha256_init(result->s); sha256_uchars(&ctx, buffer->buf, buffer->len); sha256_finalize(&ctx); } /* Initialize a 'confidential' asset or 'confidential' nonce from an unsigned char array from a 'rawElementsTransaction'. * * Precondition: NULL != conf; * unsigned char rawConf[33] or rawConf == NULL; */ static void copyRawConfidential(confidential* conf, const unsigned char* rawConf) { if (rawConf) { *conf = (confidential){ .prefix = 0x01 == rawConf[0] ? EXPLICIT : 0x01 == (0x01 & rawConf[0]) ? ODD_Y : EVEN_Y }; sha256_toMidstate(conf->data.s, &rawConf[1]); } else { *conf = (confidential){0}; } } /* Initialize a 'confAmount' from an unsigned char array from a 'rawElementsTransaction'. * * Precondition: NULL != amt; * unsigned char rawAmt[rawAmt[0] == 0x01 ? 9 : 33] or rawAmt == NULL */ static void copyRawAmt(confAmount* amt, const unsigned char* rawAmt) { if (rawAmt) { if (0x01 == rawAmt[0]) { amt->prefix = EXPLICIT; amt->explicit = ReadBE64(&rawAmt[1]); } else { amt->prefix = 0x01 == (0x01 & rawAmt[0]) ? ODD_Y : EVEN_Y; sha256_toMidstate(amt->confidential.s, &rawAmt[1]); } } else { amt->prefix = EXPLICIT; amt->explicit = 0; } } /* Initialize a 'sigInput' from a 'rawElementsInput', copying or hashing the data as needed. * * Precondition: NULL != result; * NULL != input; */ static void copyInput(sigInput* result, const rawElementsInput* input) { *result = (sigInput){ .prevOutpoint = { .ix = input->prevIx } , .sequence = input->sequence , .isPegin = !!input->pegin , .hasAnnex = !!input->annex }; if (input->annex) hashBuffer(&result->annexHash, input->annex); if (input->pegin) sha256_toMidstate(result->pegin.s, input->pegin); sha256_toMidstate(result->prevOutpoint.txid.s, input->prevTxid); hashBuffer(&result->txo.scriptPubKey, &input->txo.scriptPubKey); copyRawConfidential(&result->txo.asset, input->txo.asset); copyRawAmt(&result->txo.amt, input->txo.value); hashBuffer(&result->scriptSigHash, &input->scriptSig); hashBuffer(&result->issuance.assetRangeProofHash, &(rawElementsBuffer){0}); hashBuffer(&result->issuance.tokenRangeProofHash, &(rawElementsBuffer){0}); if (input->issuance.amount || input->issuance.inflationKeys) { sha256_toMidstate(result->issuance.blindingNonce.s, input->issuance.blindingNonce); copyRawAmt(&result->issuance.assetAmt, input->issuance.amount); if (is_confidential(result->issuance.assetAmt.prefix)) hashBuffer(&result->issuance.assetRangeProofHash, &input->issuance.amountRangePrf); if (0 == result->issuance.blindingNonce.s[0] && 0 == result->issuance.blindingNonce.s[1] && 0 == result->issuance.blindingNonce.s[2] && 0 == result->issuance.blindingNonce.s[3] && 0 == result->issuance.blindingNonce.s[4] && 0 == result->issuance.blindingNonce.s[5] && 0 == result->issuance.blindingNonce.s[6] && 0 == result->issuance.blindingNonce.s[7]) { sha256_toMidstate(result->issuance.contractHash.s, input->issuance.assetEntropy); result->issuance.entropy = simplicity_generateIssuanceEntropy(&result->prevOutpoint, &result->issuance.contractHash); copyRawAmt(&result->issuance.tokenAmt, input->issuance.inflationKeys); if (is_confidential(result->issuance.tokenAmt.prefix)) hashBuffer(&result->issuance.tokenRangeProofHash, &input->issuance.inflationKeysRangePrf); result->issuance.type = NEW_ISSUANCE; } else { sha256_toMidstate(result->issuance.entropy.s, input->issuance.assetEntropy); result->issuance.type = REISSUANCE; } result->issuance.assetId = simplicity_calculateAsset(&result->issuance.entropy); result->issuance.tokenId = simplicity_calculateToken(&result->issuance.entropy, result->issuance.assetAmt.prefix); } } /* As specified in https://github.com/ElementsProject/elements/blob/de942511a67c3a3fcbdf002a8ee7e9ba49679b78/src/primitives/transaction.h#L304-L307. */ static bool isFee(const rawElementsOutput* output) { return 0 == output->scriptPubKey.len && /* Empty scriptPubKey */ NULL != output->asset && 0x01 == output->asset[0] && /* Explicit asset */ NULL != output->value && 0x01 == output->value[0]; /* Explicit amount */ } static uint_fast32_t countFeeOutputs(const rawElementsTransaction* rawTx) { uint_fast32_t result = 0; for (uint_fast32_t i = 0; i < rawTx->numOutputs; ++i) { result += isFee(&rawTx->output[i]); } return result; } /* If the 'scriptPubKey' is a TX_NULL_DATA, return a count of the number of "push only" operations (this excludes the OP_RETURN). * Otherwise return 0. * * Note: that a TX_NULL_DATA could have zero "push only" operations, * in which case 0 is returned even though it is a TX_NULL_DATA scriptPubKey. * * Precondition: NULL != scriptPubKey */ static uint_fast32_t countNullDataCodes(const rawElementsBuffer* scriptPubKey) { if (0 == scriptPubKey->len || 0x6a != scriptPubKey->buf[0] ) return 0; uint_fast32_t result = 0; for (uint_fast32_t i = 1; i < scriptPubKey->len;) { uint_fast32_t skip = 0; unsigned char code = scriptPubKey->buf[i++]; if (0x60 < code) return 0; if (code < 0x4c) { skip = code; } else if (code < 0x4f) { if (scriptPubKey->len == i) return 0; skip = scriptPubKey->buf[i++]; if (0x4d <= code) { if (scriptPubKey->len == i) return 0; skip += (uint_fast32_t)(scriptPubKey->buf[i++]) << 8; if (0x4e <= code) { if (scriptPubKey->len == i) return 0; skip += (uint_fast32_t)(scriptPubKey->buf[i++]) << 16; if (scriptPubKey->len == i) return 0; skip += (uint_fast32_t)(scriptPubKey->buf[i++]) << 24; } } } if (scriptPubKey->len - i < skip) return 0; i += skip; result++; } return result; } /* Return a count of the total number of "push only" operations in all output scriptPubKey's that are TX_NULL_DATA. * * Precondition: NULL != rawTx */ static uint_fast64_t countTotalNullDataCodes(const rawElementsTransaction* rawTx) { uint_fast64_t result = 0; for (uint_fast32_t i = 0; i < rawTx->numOutputs; ++i) { result += countNullDataCodes(&rawTx->output[i].scriptPubKey); } return result; } /* Determine if 'scriptPubKey' is a TX_NULL_DATA script, and fill 'result' with (digests of) the push data opcodes. * If 'scriptPubKey' isn't a TX_NULL_DATA, then 'result->op' is set to NULL. * Otherwise '*result' is set to '(parsedNullData){ .op = *allocation, .len = countNullDataCodes(scriptPubKey) }. * and then the 'opcode result->op[result->len]' array is filled in with (digests of) the pus data opcode. * and '*allocation' is incremented by 'result->len' * and '*allocationLen' is decremented by 'result->len'. * Values in the '*allocation' array may be modified. * * Note: even if '*allocationLen == 0' we require that '*allocation != NULL' as a precondition * in order for 'result' to distinguish between non-NULL_TX_DATA and empty NULL_TX_data * * Precondition: NULL != result; * NULL != *allocation; * opcode (*allocation)[*allocationLen]; * NULL != scriptPubKey; * countNullDataCodes(scriptPubKey) <= *allocationLen */ static void parseNullData(parsedNullData* result, opcode** allocation, size_t* allocationLen, const rawElementsBuffer* scriptPubKey) { *result = (parsedNullData){ .op = *allocation }; if (0 == scriptPubKey->len || 0x6a != scriptPubKey->buf[0] ) { result->op = NULL; return; } for (uint_fast32_t i = 1; i < scriptPubKey->len; ++result->len) { unsigned char code = scriptPubKey->buf[i++]; if (*allocationLen <= result->len || 0x60 < code) { result->op = NULL; return; } if (0x4f <= code) { (*allocation)[result->len].code = OP_1NEGATE + (code - 0x4f); } else { uint_fast32_t skip = 0; if (code < 0x4c) { skip = code; (*allocation)[result->len].code = OP_IMMEDIATE; } else { if (scriptPubKey->len == i) { result->op = NULL; return; } skip = scriptPubKey->buf[i++]; if (code < 0x4d) { (*allocation)[result->len].code = OP_PUSHDATA; } else { if (scriptPubKey->len == i) { result->op = NULL; return; } skip += (uint_fast32_t)(scriptPubKey->buf[i++]) << 8; if (code < 0x4e) { (*allocation)[result->len].code = OP_PUSHDATA2; } else { if (scriptPubKey->len == i) { result->op = NULL; return; } skip += (uint_fast32_t)(scriptPubKey->buf[i++]) << 16; if (scriptPubKey->len == i) { result->op = NULL; return; } skip += (uint_fast32_t)(scriptPubKey->buf[i++]) << 24; (*allocation)[result->len].code = OP_PUSHDATA4; } } } if (scriptPubKey->len - i < skip) { result->op = NULL; return; } { sha256_context ctx = sha256_init((*allocation)[result->len].dataHash.s); sha256_uchars(&ctx, &scriptPubKey->buf[i], skip); sha256_finalize(&ctx); } i += skip; } } *allocation += result->len; /* C requires '*allocation != NULL', even when 'result->len == 0'. */ *allocationLen -= result->len; } /* Initialize a 'sigOutput' from a 'rawElementsOutput', copying or hashing the data as needed. * * '*allocation' is incremented by 'countNullDataCodes(&output->scriptPubKey)' * '*allocationLen' is decremented by 'countNullDataCodes(&output->scriptPubKey)'. * Values in the '*allocation' array may be modified. * * Precondition: NULL != result; * NULL != *allocation; * opcode (*allocation)[*allocationLen]; * NULL != output; * countNullDataCodes(&output->scriptPubKey) <= *allocationLen */ static void copyOutput(sigOutput* result, opcode** allocation, size_t* allocationLen, const rawElementsOutput* output) { hashBuffer(&result->scriptPubKey, &output->scriptPubKey); result->emptyScript = 0 == output->scriptPubKey.len; copyRawConfidential(&result->asset, output->asset); copyRawAmt(&result->amt, output->value); copyRawConfidential(&result->nonce, output->nonce); parseNullData(&result->pnd, allocation, allocationLen, &output->scriptPubKey); result->isNullData = NULL != result->pnd.op; hashBuffer(&result->surjectionProofHash, is_confidential(result->asset.prefix) ? &output->surjectionProof : &(rawElementsBuffer){0}); hashBuffer(&result->rangeProofHash, is_confidential(result->amt.prefix) ? &output->rangeProof : &(rawElementsBuffer){0}); result->assetFee = 0; } /* Tally a sorted list of feeOutputs * * Given a sorted array of feeOutput pointers, tally all the (explicit) amounts of the entries with the same asset id, * which are all necessarily next to each other, into the assetFee field of the first entry of the bunch. * * Discard all entries other than the first one of each bunch. * Return 'ret_value', the number of remaining entries in the array after these discards. * * Note: the array is not re-allocated, so there will be "junk" values in the array past the end of 'ret_value'. * * Precondition: feeOutputs is sorted by it asset.data.s field, which is to say * for all 0 <= i <= j < numFees, * 0 <= memcmp(feeOutputs[j]->asset.data.s, feeOutputs[i]->asset.data.s, sizeof(feeOutputs[i]->asset.data.s)); * for all 0 <= i < numFees, * feeOutputs[i]->assetFee = 0 and * feeOutputs[i]->amt.explicit is the active union member. * Postcondition: feeOutputs is uniquely sorted by it asset.data.s field, which is to say * for all 0 <= i < j < ret_value, * 0 < memcmp(feeOutputs[j]->asset.data.s, feeOutputs[i]->asset.data.s, sizeof(feeOutputs[i]->asset.data.s)); * for all ret_value <= i < numFees, * feeOutputs[i] remains allocated. */ static uint_fast32_t sumFees(sigOutput** feeOutputs, uint_fast32_t numFees) { uint_fast32_t result = 0; if (numFees < 1) return result; for(uint_fast32_t i = 0; i < numFees; ++i) { int cmp = memcmp(feeOutputs[i]->asset.data.s, feeOutputs[result]->asset.data.s, sizeof(feeOutputs[i]->asset.data.s)); simplicity_assert(0 <= cmp); if (0 < cmp) { result++; feeOutputs[result] = feeOutputs[i]; } static_assert(0 == offsetof(sigOutput, asset.data), "asset ID is not first field of sigOutput."); /* In Elements consensus rules, the total about of fees is not allowed to exceed MoneyRange: * https://github.com/ElementsProject/elements/blob/de942511a67c3a3fcbdf002a8ee7e9ba49679b78/src/confidential_validation.cpp#L36-L38 * * In case of invalid transaction environments, we end up taking the result modulo the size of uint_fast64_t, * which in turn is compatible with our jet specification which returns the tally modulo 2^64. */ feeOutputs[result]->assetFee += feeOutputs[i]->amt.explicit; } return result + 1; } /* Allocate and initialize a 'elementsTransaction' from a 'rawElementsTransaction', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: NULL != rawTx */ extern elementsTransaction* simplicity_elements_mallocTransaction(const rawElementsTransaction* rawTx) { if (!rawTx) return NULL; size_t allocationSize = sizeof(elementsTransaction); const size_t pad1 = PADDING(sigInput, allocationSize); if (SIZE_MAX - allocationSize < pad1) return NULL; allocationSize += pad1; /* Multiply by (size_t)1 to disable type-limits warning. */ if (SIZE_MAX / sizeof(sigInput) < (size_t)1 * rawTx->numInputs) return NULL; if (SIZE_MAX - allocationSize < rawTx->numInputs * sizeof(sigInput)) return NULL; allocationSize += rawTx->numInputs * sizeof(sigInput); const size_t pad2 = PADDING(sigOutput, allocationSize); if (SIZE_MAX - allocationSize < pad2) return NULL; allocationSize += pad2; /* Multiply by (size_t)1 to disable type-limits warning. */ if (SIZE_MAX / sizeof(sigOutput) < (size_t)1 * rawTx->numOutputs) return NULL; if (SIZE_MAX - allocationSize < rawTx->numOutputs * sizeof(sigOutput)) return NULL; allocationSize += rawTx->numOutputs * sizeof(sigOutput); const size_t pad3 = PADDING(sigOutput*, allocationSize); if (SIZE_MAX - allocationSize < pad3) return NULL; allocationSize += pad3; const uint_fast32_t numFees = countFeeOutputs(rawTx); /* Multiply by (size_t)1 to disable type-limits warning. */ if (SIZE_MAX / sizeof(sigOutput*) < (size_t)1 * numFees) return NULL; if (SIZE_MAX - allocationSize < numFees * sizeof(sigOutput*)) return NULL; allocationSize += numFees * sizeof(sigOutput*); const size_t pad4 = PADDING(opcode, allocationSize); if (SIZE_MAX - allocationSize < pad4) return NULL; allocationSize += pad4; const uint_fast64_t totalNullDataCodes = countTotalNullDataCodes(rawTx); /* Multiply by (size_t)1 to disable type-limits warning. */ if (SIZE_MAX / sizeof(opcode) < (size_t)1 * totalNullDataCodes) return NULL; if (SIZE_MAX - allocationSize < totalNullDataCodes * sizeof(opcode)) return NULL; allocationSize += (size_t)totalNullDataCodes * sizeof(opcode); char *allocation = simplicity_malloc(allocationSize); if (!allocation) return NULL; /* Casting through void* to avoid warning about pointer alignment. * Our padding is done carefully to ensure alignment. */ elementsTransaction* const tx = (elementsTransaction*)(void*)allocation; allocation += sizeof(elementsTransaction) + pad1; sigInput* const input = (sigInput*)(void*)allocation; allocation += rawTx->numInputs * sizeof(sigInput) + pad2; sigOutput* const output = (sigOutput*)(void*)allocation; allocation += rawTx->numOutputs * sizeof(sigOutput) + pad3; sigOutput** const feeOutputs = (sigOutput**)(void*)allocation; allocation += numFees * sizeof(sigOutput*) + pad4; opcode* ops = (opcode*)(void*)allocation; size_t opsLen = (size_t)totalNullDataCodes; /* In C++ an assignment from (sigOutput**) to (const sigOutput * const *) is allowed, but C forgoes the complicated specification of C++. Therefore we must make an explicit cast of feeOutputs in C. See for details. */ *tx = (elementsTransaction){ .input = input , .output = output , .feeOutputs = (sigOutput const * const *)feeOutputs , .numInputs = rawTx->numInputs , .numOutputs = rawTx->numOutputs , .version = rawTx->version , .lockTime = rawTx->lockTime , .isFinal = true }; sha256_toMidstate(tx->txid.s, rawTx->txid); { sha256_context ctx_inputOutpointsHash = sha256_init(tx->inputOutpointsHash.s); sha256_context ctx_inputAssetAmountsHash = sha256_init(tx->inputAssetAmountsHash.s); sha256_context ctx_inputScriptsHash = sha256_init(tx->inputScriptsHash.s); sha256_context ctx_inputUTXOsHash = sha256_init(tx->inputUTXOsHash.s); sha256_context ctx_inputSequencesHash = sha256_init(tx->inputSequencesHash.s); sha256_context ctx_inputAnnexesHash = sha256_init(tx->inputAnnexesHash.s); sha256_context ctx_inputScriptSigsHash = sha256_init(tx->inputScriptSigsHash.s); sha256_context ctx_inputsHash = sha256_init(tx->inputsHash.s); sha256_context ctx_issuanceAssetAmountsHash = sha256_init(tx->issuanceAssetAmountsHash.s); sha256_context ctx_issuanceTokenAmountsHash = sha256_init(tx->issuanceTokenAmountsHash.s); sha256_context ctx_issuanceRangeProofsHash = sha256_init(tx->issuanceRangeProofsHash.s); sha256_context ctx_issuanceBlindingEntropyHash = sha256_init(tx->issuanceBlindingEntropyHash.s); sha256_context ctx_issuancesHash = sha256_init(tx->issuancesHash.s); for (uint_fast32_t i = 0; i < tx->numInputs; ++i) { copyInput(&input[i], &rawTx->input[i]); if (input[i].sequence < 0xffffffff) { tx->isFinal = false; } if (input[i].sequence < 0x80000000) { const uint_fast16_t maskedSequence = input[i].sequence & 0xffff; if (input[i].sequence & ((uint_fast32_t)1 << 22)) { if (tx->obsolete_lockDuration < maskedSequence) tx->obsolete_lockDuration = maskedSequence; } else { if (tx->obsolete_lockDistance < maskedSequence) tx->obsolete_lockDistance = maskedSequence; } } if (input[i].isPegin) { sha256_uchar(&ctx_inputOutpointsHash, 1); sha256_hash(&ctx_inputOutpointsHash, &input[i].pegin); } else { sha256_uchar(&ctx_inputOutpointsHash, 0); } sha256_hash(&ctx_inputOutpointsHash, &input[i].prevOutpoint.txid); sha256_u32be(&ctx_inputOutpointsHash, input[i].prevOutpoint.ix); simplicity_sha256_confAsset(&ctx_inputAssetAmountsHash, &input[i].txo.asset); simplicity_sha256_confAmt(&ctx_inputAssetAmountsHash, &input[i].txo.amt); sha256_hash(&ctx_inputScriptsHash, &input[i].txo.scriptPubKey); sha256_u32be(&ctx_inputSequencesHash, input[i].sequence); if (input[i].hasAnnex) { sha256_uchar(&ctx_inputAnnexesHash, 1); sha256_hash(&ctx_inputAnnexesHash, &input[i].annexHash); } else { sha256_uchar(&ctx_inputAnnexesHash, 0); } sha256_hash(&ctx_inputScriptSigsHash, &input[i].scriptSigHash); if (NO_ISSUANCE == input[i].issuance.type) { sha256_uchar(&ctx_issuanceAssetAmountsHash, 0); sha256_uchar(&ctx_issuanceAssetAmountsHash, 0); sha256_uchar(&ctx_issuanceTokenAmountsHash, 0); sha256_uchar(&ctx_issuanceTokenAmountsHash, 0); sha256_uchar(&ctx_issuanceBlindingEntropyHash, 0); } else { simplicity_sha256_confAsset(&ctx_issuanceAssetAmountsHash, &(confidential){ .prefix = EXPLICIT, .data = input[i].issuance.assetId}); simplicity_sha256_confAsset(&ctx_issuanceTokenAmountsHash, &(confidential){ .prefix = EXPLICIT, .data = input[i].issuance.tokenId}); simplicity_sha256_confAmt(&ctx_issuanceAssetAmountsHash, &input[i].issuance.assetAmt); simplicity_sha256_confAmt(&ctx_issuanceTokenAmountsHash, NEW_ISSUANCE == input[i].issuance.type ? &input[i].issuance.tokenAmt : &(confAmount){ .prefix = EXPLICIT, .explicit = 0}); sha256_uchar(&ctx_issuanceBlindingEntropyHash, 1); if (NEW_ISSUANCE == input[i].issuance.type) { sha256_uchars(&ctx_issuanceBlindingEntropyHash, (unsigned char[32]){0}, 32); sha256_hash(&ctx_issuanceBlindingEntropyHash, &input[i].issuance.contractHash); } else { sha256_hash(&ctx_issuanceBlindingEntropyHash, &input[i].issuance.blindingNonce); sha256_hash(&ctx_issuanceBlindingEntropyHash, &input[i].issuance.entropy); } } sha256_hash(&ctx_issuanceRangeProofsHash, &input[i].issuance.assetRangeProofHash); sha256_hash(&ctx_issuanceRangeProofsHash, &input[i].issuance.tokenRangeProofHash); } sha256_finalize(&ctx_inputOutpointsHash); sha256_finalize(&ctx_inputAssetAmountsHash); sha256_finalize(&ctx_inputScriptsHash); sha256_finalize(&ctx_inputSequencesHash); sha256_finalize(&ctx_inputAnnexesHash); sha256_finalize(&ctx_inputScriptSigsHash); sha256_hash(&ctx_inputUTXOsHash, &tx->inputAssetAmountsHash); sha256_hash(&ctx_inputUTXOsHash, &tx->inputScriptsHash); sha256_finalize(&ctx_inputUTXOsHash); sha256_hash(&ctx_inputsHash, &tx->inputOutpointsHash); sha256_hash(&ctx_inputsHash, &tx->inputSequencesHash); sha256_hash(&ctx_inputsHash, &tx->inputAnnexesHash); sha256_finalize(&ctx_inputsHash); sha256_finalize(&ctx_issuanceAssetAmountsHash); sha256_finalize(&ctx_issuanceTokenAmountsHash); sha256_finalize(&ctx_issuanceRangeProofsHash); sha256_finalize(&ctx_issuanceBlindingEntropyHash); sha256_hash(&ctx_issuancesHash, &tx->issuanceAssetAmountsHash); sha256_hash(&ctx_issuancesHash, &tx->issuanceTokenAmountsHash); sha256_hash(&ctx_issuancesHash, &tx->issuanceRangeProofsHash); sha256_hash(&ctx_issuancesHash, &tx->issuanceBlindingEntropyHash); sha256_finalize(&ctx_issuancesHash); } { sha256_context ctx_outputAssetAmountsHash = sha256_init(tx->outputAssetAmountsHash.s); sha256_context ctx_outputNoncesHash = sha256_init(tx->outputNoncesHash.s); sha256_context ctx_outputScriptsHash = sha256_init(tx->outputScriptsHash.s); sha256_context ctx_outputRangeProofsHash = sha256_init(tx->outputRangeProofsHash.s); sha256_context ctx_outputSurjectionProofsHash = sha256_init(tx->outputSurjectionProofsHash.s); sha256_context ctx_outputsHash = sha256_init(tx->outputsHash.s); uint_fast32_t ix_fee = 0; /* perm is a temporary array the same length (numFees) and size as feeOutputs. * perm is used to initialize feeOutputs and is not used afterward. * This makes it safe for perm to use the same memory allocation as feeOutputs. */ static_assert(sizeof(const sha256_midstate*) == sizeof(sigOutput*), "Pointers (to structures) ought to have the same size."); static_assert(alignof(const sha256_midstate*) == alignof(sigOutput*), "Pointers (to structures) ought to have the same alignment."); const sha256_midstate** const perm = (const sha256_midstate**)(void*)feeOutputs; for (uint_fast32_t i = 0; i < tx->numOutputs; ++i) { copyOutput(&output[i], &ops, &opsLen, &rawTx->output[i]); if (isFee(&rawTx->output[i])) { simplicity_assert(ix_fee < numFees); perm[ix_fee] = &output[i].asset.data; ++ix_fee; } simplicity_sha256_confAsset(&ctx_outputAssetAmountsHash, &output[i].asset); simplicity_sha256_confAmt(&ctx_outputAssetAmountsHash, &output[i].amt); simplicity_sha256_confNonce(&ctx_outputNoncesHash, &output[i].nonce); sha256_hash(&ctx_outputScriptsHash, &output[i].scriptPubKey); sha256_hash(&ctx_outputRangeProofsHash, &output[i].rangeProofHash); sha256_hash(&ctx_outputSurjectionProofsHash, &output[i].surjectionProofHash); } simplicity_assert(numFees == ix_fee); if (!simplicity_rsort(perm, numFees)) { simplicity_free(tx); return NULL; } /* Initialize the feeOutputs array from the perm array. * Because the perm array entries are the same size as the feeOutputs array entries, it is safe to initialize one by one. * * In practical C implementations, the feeOutputs array entries are initialized to the same value as the perm array entries. * In practical C implementations, this is a no-op, and generally compilers are able to see this fact and eliminate this loop. * * We keep the loop in the code just to be pedantic. */ for (size_t i = 0; i < numFees; ++i) { static_assert(0 == offsetof(sigOutput, asset.data), "asset ID is not first field of sigOutput."); /* The uintptr_t cast is to suppress warning about both casting away const and a change in pointer alignment. * Each pointer in perm is pointing the the first field of some (non-const) sigOutput*, so this cast is safe. */ feeOutputs[i] = (sigOutput*)(uintptr_t)(perm[i]); } tx->numFees = sumFees(feeOutputs, numFees); sha256_finalize(&ctx_outputAssetAmountsHash); sha256_finalize(&ctx_outputNoncesHash); sha256_finalize(&ctx_outputScriptsHash); sha256_finalize(&ctx_outputRangeProofsHash); sha256_finalize(&ctx_outputSurjectionProofsHash); sha256_hash(&ctx_outputsHash, &tx->outputAssetAmountsHash); sha256_hash(&ctx_outputsHash, &tx->outputNoncesHash); sha256_hash(&ctx_outputsHash, &tx->outputScriptsHash); sha256_hash(&ctx_outputsHash, &tx->outputRangeProofsHash); sha256_finalize(&ctx_outputsHash); } { sha256_context ctx_txHash = sha256_init(tx->txHash.s); sha256_u32be(&ctx_txHash, tx->version); sha256_u32be(&ctx_txHash, tx->lockTime); sha256_hash(&ctx_txHash, &tx->inputsHash); sha256_hash(&ctx_txHash, &tx->outputsHash); sha256_hash(&ctx_txHash, &tx->issuancesHash); sha256_hash(&ctx_txHash, &tx->outputSurjectionProofsHash); sha256_hash(&ctx_txHash, &tx->inputUTXOsHash); sha256_finalize(&ctx_txHash); } return tx; } /* Free a pointer to 'elementsTransaction'. */ extern void simplicity_elements_freeTransaction(elementsTransaction* tx) { simplicity_free(tx); } /* Allocate and initialize a 'elementsTapEnv' from a 'rawElementsTapEnv', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: *rawEnv is well-formed (i.e. rawEnv->pathLen <= 128.) */ extern elementsTapEnv* simplicity_elements_mallocTapEnv(const rawElementsTapEnv* rawEnv) { if (!rawEnv) return NULL; if (128 < rawEnv->pathLen) return NULL; size_t allocationSize = sizeof(elementsTapEnv); const size_t numMidstate = rawEnv->pathLen; const size_t pad1 = PADDING(sha256_midstate, allocationSize); if (numMidstate) { if (SIZE_MAX - allocationSize < pad1) return NULL; allocationSize += pad1; if (SIZE_MAX / sizeof(sha256_midstate) < numMidstate) return NULL; if (SIZE_MAX - allocationSize < numMidstate * sizeof(sha256_midstate)) return NULL; allocationSize += numMidstate * sizeof(sha256_midstate); } char *allocation = simplicity_malloc(allocationSize); if (!allocation) return NULL; /* Casting through void* to avoid warning about pointer alignment. * Our padding is done carefully to ensure alignment. */ elementsTapEnv* const env = (elementsTapEnv*)(void*)allocation; sha256_midstate* path = NULL; sha256_midstate internalKey; sha256_toMidstate(internalKey.s, &rawEnv->controlBlock[1]); if (numMidstate) { allocation += sizeof(elementsTapEnv) + pad1; if (rawEnv->pathLen) { path = (sha256_midstate*)(void*)allocation; } } *env = (elementsTapEnv){ .leafVersion = rawEnv->controlBlock[0] & 0xfe , .internalKey = internalKey , .path = path , .pathLen = rawEnv->pathLen }; sha256_toMidstate(env->scriptCMR.s, rawEnv->scriptCMR); { sha256_context ctx = sha256_init(env->tappathHash.s); for (int i = 0; i < env->pathLen; ++i) { sha256_toMidstate(path[i].s, &rawEnv->controlBlock[33+32*i]); sha256_hash(&ctx, &path[i]); } sha256_finalize(&ctx); } env->tapLeafHash = simplicity_make_tapleaf(env->leafVersion, &env->scriptCMR); { sha256_context ctx = sha256_init(env->tapEnvHash.s); sha256_hash(&ctx, &env->tapLeafHash); sha256_hash(&ctx, &env->tappathHash); sha256_hash(&ctx, &env->internalKey); sha256_finalize(&ctx); } return env; } /* Free a pointer to 'elementsTapEnv'. */ extern void simplicity_elements_freeTapEnv(elementsTapEnv* env) { simplicity_free(env); } ================================================ FILE: C/elements/exec.c ================================================ #include #include #include #include "primitive.h" #include "txEnv.h" #include "../deserialize.h" #include "../eval.h" #include "../limitations.h" #include "../simplicity_alloc.h" #include "../simplicity_assert.h" #include "../typeInference.h" /* Deserialize a Simplicity 'program' with its 'witness' data and execute it in the environment of the 'ix'th input of 'tx' with `taproot`. * * If at any time malloc fails then '*error' is set to 'SIMPLICITY_ERR_MALLOC' and 'false' is returned, * meaning we were unable to determine the result of the simplicity program. * Otherwise, 'true' is returned indicating that the result was successfully computed and returned in the '*error' value. * * If deserialization, analysis, or execution fails, then '*error' is set to some simplicity_err. * In particular, if the cost analysis exceeds the budget, or exceeds BUDGET_MAX, then '*error' is set to 'SIMPLICITY_ERR_EXEC_BUDGET'. * On the other hand, if the cost analysis is less than or equal to minCost, then '*error' is set to 'SIMPLICITY_ERR_OVERWEIGHT'. * * Note that minCost and budget parameters are in WU, while the cost analysis will be performed in milliWU. * Thus the minCost and budget specify a half open interval (minCost, budget] of acceptable cost values in milliWU. * Setting minCost to 0 effectively disables the minCost check as every Simplicity program has a non-zero cost analysis. * * If 'amr != NULL' and the annotated Merkle root of the decoded expression doesn't match 'amr' then '*error' is set to 'SIMPLICITY_ERR_AMR'. * * Otherwise '*error' is set to 'SIMPLICITY_NO_ERROR'. * * If 'ihr != NULL' and '*error' is set to 'SIMPLICITY_NO_ERROR', then the identity hash of the root of the decoded expression is written to 'ihr'. * Otherwise if 'ihr != NULL' and '*error' is not set to 'SIMPLCITY_NO_ERROR', then 'ihr' may or may not be written to. * * Precondition: NULL != error; * NULL != ihr implies unsigned char ihr[32] * NULL != tx; * NULL != taproot; * unsigned char genesisBlockHash[32] * 0 <= minCost <= budget; * NULL != amr implies unsigned char amr[32] * unsigned char program[program_len] * unsigned char witness[witness_len] */ extern bool simplicity_elements_execSimplicity( simplicity_err* error, unsigned char* ihr , const elementsTransaction* tx, uint_fast32_t ix, const elementsTapEnv* taproot , const unsigned char* genesisBlockHash , int64_t minCost, int64_t budget , const unsigned char* amr , const unsigned char* program, size_t program_len , const unsigned char* witness, size_t witness_len) { simplicity_assert(NULL != error); simplicity_assert(NULL != tx); simplicity_assert(NULL != taproot); simplicity_assert(NULL != genesisBlockHash); simplicity_assert(0 <= minCost); simplicity_assert(minCost <= budget); simplicity_assert(NULL != program || 0 == program_len); simplicity_assert(NULL != witness || 0 == witness_len); combinator_counters census; dag_node* dag = NULL; int_fast32_t dag_len; sha256_midstate amr_hash, genesis_hash; if (amr) sha256_toMidstate(amr_hash.s, amr); sha256_toMidstate(genesis_hash.s, genesisBlockHash); { bitstream stream = initializeBitstream(program, program_len); dag_len = simplicity_decodeMallocDag(&dag, simplicity_elements_decodeJet, &census, &stream); if (dag_len <= 0) { simplicity_assert(dag_len < 0); *error = (simplicity_err)dag_len; return IS_PERMANENT(*error); } simplicity_assert(NULL != dag); simplicity_assert((uint_fast32_t)dag_len <= DAG_LEN_MAX); *error = simplicity_closeBitstream(&stream); } if (IS_OK(*error)) { if (0 != memcmp(taproot->scriptCMR.s, dag[dag_len-1].cmr.s, sizeof(uint32_t[8]))) { *error = SIMPLICITY_ERR_CMR; } } if (IS_OK(*error)) { type* type_dag = NULL; *error = simplicity_mallocTypeInference(&type_dag, simplicity_elements_mallocBoundVars, dag, (uint_fast32_t)dag_len, &census); if (IS_OK(*error)) { simplicity_assert(NULL != type_dag); if (0 != dag[dag_len-1].sourceType || 0 != dag[dag_len-1].targetType) { *error = SIMPLICITY_ERR_TYPE_INFERENCE_NOT_PROGRAM; } } if (IS_OK(*error)) { bitstream witness_stream = initializeBitstream(witness, witness_len); *error = simplicity_fillWitnessData(dag, type_dag, (uint_fast32_t)dag_len, &witness_stream); if (IS_OK(*error)) { *error = simplicity_closeBitstream(&witness_stream); if (SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES == *error) *error = SIMPLICITY_ERR_WITNESS_TRAILING_BYTES; if (SIMPLICITY_ERR_BITSTREAM_ILLEGAL_PADDING == *error) *error = SIMPLICITY_ERR_WITNESS_ILLEGAL_PADDING; } } if (IS_OK(*error)) { sha256_midstate ihr_buf; *error = simplicity_verifyNoDuplicateIdentityHashes(&ihr_buf, dag, type_dag, (uint_fast32_t)dag_len); if (IS_OK(*error) && ihr) sha256_fromMidstate(ihr, ihr_buf.s); } if (IS_OK(*error) && amr) { static_assert(DAG_LEN_MAX <= SIZE_MAX / sizeof(analyses), "analysis array too large."); static_assert(1 <= DAG_LEN_MAX, "DAG_LEN_MAX is zero."); static_assert(DAG_LEN_MAX - 1 <= UINT32_MAX, "analysis array index does nto fit in uint32_t."); analyses *analysis = simplicity_malloc((size_t)dag_len * sizeof(analyses)); if (analysis) { simplicity_computeAnnotatedMerkleRoot(analysis, dag, type_dag, (uint_fast32_t)dag_len); if (0 != memcmp(amr_hash.s, analysis[dag_len-1].annotatedMerkleRoot.s, sizeof(uint32_t[8]))) { *error = SIMPLICITY_ERR_AMR; } } else { /* malloc failed which counts as a transient error. */ *error = SIMPLICITY_ERR_MALLOC; } simplicity_free(analysis); } if (IS_OK(*error)) { txEnv env = simplicity_elements_build_txEnv(tx, taproot, &genesis_hash, ix); static_assert(BUDGET_MAX <= UBOUNDED_MAX, "BUDGET_MAX doesn't fit in ubounded."); *error = evalTCOProgram( dag, type_dag, (size_t)dag_len , minCost <= BUDGET_MAX ? (ubounded)minCost : BUDGET_MAX , &(ubounded){budget <= BUDGET_MAX ? (ubounded)budget : BUDGET_MAX} , &env); } simplicity_free(type_dag); } simplicity_free(dag); return IS_PERMANENT(*error); } ================================================ FILE: C/elements/ops.c ================================================ #include "ops.h" /* Add an 'confidential' value to be consumed by an ongoing SHA-256 evaluation. * If the 'confidential' value is blinded, then the 'evenPrefix' used if the y coordinate is even, * and the 'oddPrefix' is used if the y coordinate is odd. * If the 'confidential' value is explicit, then '0x01' is used as the prefix. * If the 'confidential' value is "NULL" then only '0x00' added. * * Precondition: NULL != ctx; * NULL != conf; */ void simplicity_sha256_confidential(unsigned char evenPrefix, unsigned char oddPrefix, sha256_context* ctx, const confidential* conf) { switch (conf->prefix) { case NONE: sha256_uchar(ctx, 0x00); return; case EXPLICIT: sha256_uchar(ctx, 0x01); break; case EVEN_Y: sha256_uchar(ctx, evenPrefix); break; case ODD_Y: sha256_uchar(ctx, oddPrefix); break; } sha256_hash(ctx, &conf->data); } /* Add an 'confidential' asset to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != asset; */ void simplicity_sha256_confAsset(sha256_context* ctx, const confidential* asset) { simplicity_sha256_confidential(0x0a, 0x0b, ctx, asset); } /* Add an 'confidential' nonce to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != nonce; */ void simplicity_sha256_confNonce(sha256_context* ctx, const confidential* nonce) { simplicity_sha256_confidential(0x02, 0x03, ctx, nonce); } /* Add an 'confidential' amount to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != amt; */ void simplicity_sha256_confAmt(sha256_context* ctx, const confAmount* amt) { switch (amt->prefix) { case NONE: SIMPLICITY_UNREACHABLE; case EXPLICIT: sha256_uchar(ctx, 0x01); sha256_u64be(ctx, amt->explicit); return; case EVEN_Y: case ODD_Y: sha256_uchar(ctx, EVEN_Y == amt->prefix ? 0x08 : 0x09); sha256_hash(ctx, &amt->confidential); return; } } /* Compute an Element's entropy value from a prevoutpoint and a contract hash. * A reimplementation of GenerateAssetEntropy from Element's 'issuance.cpp'. * * Precondition: NULL != op; * NULL != contract; */ sha256_midstate simplicity_generateIssuanceEntropy(const outpoint* op, const sha256_midstate* contract) { uint32_t block[16]; unsigned char buf[32]; sha256_midstate result; /* First hash the outpoint data. */ { sha256_context ctx = sha256_init(result.s); sha256_fromMidstate(buf, op->txid.s); sha256_uchars(&ctx, buf, 32); sha256_u32le(&ctx, op->ix); sha256_finalize(&ctx); } /* Fill in the first half of the block with the double hashed outpoint data. */ { sha256_context ctx = sha256_init(&block[0]); sha256_fromMidstate(buf, result.s); sha256_uchars(&ctx, buf, 32); sha256_finalize(&ctx); } memcpy(&block[8], contract->s, sizeof(contract->s)); sha256_iv(result.s); simplicity_sha256_compression(result.s, block); return result; } /* Compute an Element's issuance Asset ID value from an entropy value. * A reimplementation of CalculateAsset from Element's 'issuance.cpp'. * * Precondition: NULL != entropy; */ sha256_midstate simplicity_calculateAsset(const sha256_midstate* entropy) { uint32_t block[16] = {0}; sha256_midstate result; memcpy(&block[0], entropy->s, sizeof(entropy->s)); sha256_iv(result.s); simplicity_sha256_compression(result.s, block); return result; } /* Compute an Element's issuance Token ID value from an entropy value and an amount prefix. * A reimplementation of CalculateReissuanceToken from Element's 'issuance.cpp'. * * Precondition: NULL != entropy; */ sha256_midstate simplicity_calculateToken(const sha256_midstate* entropy, confPrefix prefix) { uint32_t block[16] = {0}; sha256_midstate result; memcpy(&block[0], entropy->s, sizeof(entropy->s)); block[8] = is_confidential(prefix) ? 0x02000000 : 0x01000000; sha256_iv(result.s); simplicity_sha256_compression(result.s, block); return result; } /* Compute an Element's tapleaf hash from a tapleaf version and a 256-bit script value. * A reimplementation of ComputeTapleafHash from Element's 'interpreter.cpp'. * Only 256-bit script values are supported as that is the size used for Simplicity CMRs. * * Precondition: NULL != cmr; */ sha256_midstate simplicity_make_tapleaf(unsigned char version, const sha256_midstate* cmr) { sha256_midstate result; sha256_midstate tapleafTag; { static unsigned char tagName[] = "TapLeaf/elements"; sha256_context ctx = sha256_init(tapleafTag.s); sha256_uchars(&ctx, tagName, sizeof(tagName) - 1); sha256_finalize(&ctx); } sha256_context ctx = sha256_init(result.s); sha256_hash(&ctx, &tapleafTag); sha256_hash(&ctx, &tapleafTag); sha256_uchar(&ctx, version); sha256_uchar(&ctx, 32); sha256_hash(&ctx, cmr); sha256_finalize(&ctx); return result; } /* Compute an Element's tapbrach hash from two branches. * * Precondition: NULL != a; * NULL != b; */ sha256_midstate simplicity_make_tapbranch(const sha256_midstate* a, const sha256_midstate* b) { sha256_midstate result; sha256_midstate tapbranchTag; { static unsigned char tagName[] = "TapBranch/elements"; sha256_context ctx = sha256_init(tapbranchTag.s); sha256_uchars(&ctx, tagName, sizeof(tagName) - 1); sha256_finalize(&ctx); } sha256_context ctx = sha256_init(result.s); sha256_hash(&ctx, &tapbranchTag); sha256_hash(&ctx, &tapbranchTag); if (sha256_cmp_be(a, b) < 0) { sha256_hash(&ctx, a); sha256_hash(&ctx, b); } else { sha256_hash(&ctx, b); sha256_hash(&ctx, a); } sha256_finalize(&ctx); return result; } ================================================ FILE: C/elements/ops.h ================================================ /* This module defines operations used in the construction the environment ('txEnv') and some jets. */ #ifndef SIMPLICITY_ELEMENTS_OPS_H #define SIMPLICITY_ELEMENTS_OPS_H #include "../sha256.h" #include "txEnv.h" /* Add an 'confidential' value to be consumed by an ongoing SHA-256 evaluation. * If the 'confidential' value is blinded, then the 'evenPrefix' used if the y coordinate is even, * and the 'oddPrefix' is used if the y coordinate is odd. * If the 'confidential' value is explicit, then '0x01' is used as the prefix. * If the 'confidential' value is "NULL" then only '0x00' added. * * Precondition: NULL != ctx; * NULL != conf; */ void simplicity_sha256_confidential(unsigned char evenPrefix, unsigned char oddPrefix, sha256_context* ctx, const confidential* conf); /* Add an 'confidential' asset to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != asset; */ void simplicity_sha256_confAsset(sha256_context* ctx, const confidential* asset); /* Add an 'confidential' nonce to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != nonce; */ void simplicity_sha256_confNonce(sha256_context* ctx, const confidential* nonce); /* Add an 'confidential' amount to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != amt; */ void simplicity_sha256_confAmt(sha256_context* ctx, const confAmount* amt); /* Compute an Element's entropy value from a prevoutpoint and a contract hash. * A reimplementation of GenerateAssetEntropy from Element's 'issuance.cpp'. * * Precondition: NULL != op; * NULL != contract; */ sha256_midstate simplicity_generateIssuanceEntropy(const outpoint* op, const sha256_midstate* contract); /* Compute an Element's issuance Asset ID value from an entropy value. * A reimplementation of CalculateAsset from Element's 'issuance.cpp'. * * Precondition: NULL != entropy; */ sha256_midstate simplicity_calculateAsset(const sha256_midstate* entropy); /* Compute an Element's issuance Token ID value from an entropy value and an amount prefix. * A reimplementation of CalculateReissuanceToken from Element's 'issuance.cpp'. * * Precondition: NULL != entropy; */ sha256_midstate simplicity_calculateToken(const sha256_midstate* entropy, confPrefix prefix); /* Compute an Element's tapleaf hash from a tapleaf version and a 256-bit script value. * A reimplementation of ComputeTapleafHash from Element's 'interpreter.cpp'. * Only 256-bit script values are supported as that is the size used for Simplicity CMRs. * * Precondition: NULL != cmr; */ sha256_midstate simplicity_make_tapleaf(unsigned char version, const sha256_midstate* cmr); /* Compute an Element's tapbrach hash from two branches. * * Precondition: NULL != a; * NULL != b; */ sha256_midstate simplicity_make_tapbranch(const sha256_midstate* a, const sha256_midstate* b); #endif ================================================ FILE: C/elements/primitive.c ================================================ #include "primitive.h" #include "elementsJets.h" #include "../limitations.h" #include "../simplicity_alloc.h" #include "../simplicity_assert.h" /* An enumeration of all the types we need to construct to specify the input and output types of all jets created by 'decodeJet'. */ enum TypeNamesForJets { #include "primitiveEnumTy.inc" NumberOfTypeNames }; /* Allocate a fresh set of unification variables bound to at least all the types necessary * for all the jets that can be created by 'decodeJet', and also the type 'TWO^256', * and also allocate space for 'extra_var_len' many unification variables. * Return the number of non-trivial bindings created. * * However, if malloc fails, then return 0. * * Precondition: NULL != bound_var; * NULL != word256_ix; * NULL != extra_var_start; * extra_var_len <= 6*DAG_LEN_MAX; * * Postcondition: Either '*bound_var == NULL' and the function returns 0 * or 'unification_var (*bound_var)[*extra_var_start + extra_var_len]' is an array of unification variables * such that for any 'jet : A |- B' there is some 'i < *extra_var_start' and 'j < *extra_var_start' such that * '(*bound_var)[i]' is bound to 'A' and '(*bound_var)[j]' is bound to 'B' * and, '*word256_ix < *extra_var_start' and '(*bound_var)[*word256_ix]' is bound the type 'TWO^256' */ size_t simplicity_elements_mallocBoundVars(unification_var** bound_var, size_t* word256_ix, size_t* extra_var_start, size_t extra_var_len) { static_assert(1 <= NumberOfTypeNames, "Missing TypeNamesForJets."); static_assert(NumberOfTypeNames <= NUMBER_OF_TYPENAMES_MAX, "Too many TypeNamesForJets."); static_assert(DAG_LEN_MAX <= (SIZE_MAX - NumberOfTypeNames) / 6, "NumberOfTypeNames + 6*DAG_LEN_MAX doesn't fit in size_t"); static_assert(NumberOfTypeNames + 6*DAG_LEN_MAX <= SIZE_MAX/sizeof(unification_var) , "bound_var array too large"); static_assert(NumberOfTypeNames + 6*DAG_LEN_MAX - 1 <= UINT32_MAX, "bound_var array index doesn't fit in uint32_t"); simplicity_assert(extra_var_len <= 6*DAG_LEN_MAX); *bound_var = simplicity_malloc((NumberOfTypeNames + extra_var_len) * sizeof(unification_var)); if (!(*bound_var)) return 0; #include "primitiveInitTy.inc" *word256_ix = ty_w256; *extra_var_start = NumberOfTypeNames; /* 'ty_u' is a trivial binding, so we made 'NumberOfTypeNames - 1' non-trivial bindings. */ return NumberOfTypeNames - 1; }; /* An enumeration of the names of Elements specific jets and primitives. */ typedef enum jetName { #include "primitiveEnumJet.inc" NUMBER_OF_JET_NAMES } jetName; /* Decode an Elements specific jet name from 'stream' into 'result'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'result' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != result * NULL != stream */ static simplicity_err decodePrimitive(jetName* result, bitstream* stream) { int32_t bit = read1Bit(stream); if (bit < 0) return (simplicity_err)bit; if (!bit) { /* Core jets */ #include "../decodeCoreJets.inc" return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; } else { /* Elements jets */ #include "decodeElementsJets.inc" return SIMPLICITY_ERR_DATA_OUT_OF_RANGE; } } /* Return a copy of the Simplicity node corresponding to the given Elements specific jet 'name'. */ static dag_node jetNode(jetName name) { static const dag_node jet_node[] = { #include "primitiveJetNode.inc" }; return jet_node[name]; } /* Decode an Elements specific jet from 'stream' into 'node'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != node * NULL != stream */ simplicity_err simplicity_elements_decodeJet(dag_node* node, bitstream* stream) { jetName name; simplicity_err error = decodePrimitive(&name, stream); if (!IS_OK(error)) return error; *node = jetNode(name); return SIMPLICITY_NO_ERROR; } ================================================ FILE: C/elements/primitive.h ================================================ /* Implements the required callbacks for the Elements Simplicity application. */ #ifndef SIMPLICITY_ELEMENTS_PRIMITIVE_H #define SIMPLICITY_ELEMENTS_PRIMITIVE_H #include "../bitstream.h" #include "../typeInference.h" /* Allocate a fresh set of unification variables bound to at least all the types necessary * for all the jets that can be created by 'decodeJet', and also the type 'TWO^256', * and also allocate space for 'extra_var_len' many unification variables. * Return the number of non-trivial bindings created. * * However, if malloc fails, then return 0. * * Precondition: NULL != bound_var; * NULL != word256_ix; * NULL != extra_var_start; * extra_var_len <= 6*DAG_LEN_MAX; * * Postcondition: Either '*bound_var == NULL' and the function returns 0 * or 'unification_var (*bound_var)[*extra_var_start + extra_var_len]' is an array of unification variables * such that for any 'jet : A |- B' there is some 'i < *extra_var_start' and 'j < *extra_var_start' such that * '(*bound_var)[i]' is bound to 'A' and '(*bound_var)[j]' is bound to 'B' * and, '*word256_ix < *extra_var_start' and '(*bound_var)[*word256_ix]' is bound the type 'TWO^256' */ size_t simplicity_elements_mallocBoundVars(unification_var** bound_var, size_t* word256_ix, size_t* extra_var_start, size_t extra_var_len); /* Decode an Elements specific jet from 'stream' into 'node'. * All jets begin with a bit prefix of '1' which needs to have already been consumed from the 'stream'. * Returns 'SIMPLICITY_ERR_DATA_OUT_OF_RANGE' if the stream's prefix doesn't match any valid code for a jet. * Returns 'SIMPLICITY_ERR_BITSTRING_EOF' if not enough bits are available in the 'stream'. * In the above error cases, 'dag' may be modified. * Returns 'SIMPLICITY_NO_ERROR' if successful. * * Precondition: NULL != node * NULL != stream */ simplicity_err simplicity_elements_decodeJet(dag_node* node, bitstream* stream); #endif ================================================ FILE: C/elements/primitiveEnumJet.inc ================================================ /* This file has been automatically generated. */ ADD_16, ADD_32, ADD_64, ADD_8, ALL_16, ALL_32, ALL_64, ALL_8, AND_1, AND_16, AND_32, AND_64, AND_8, ANNEX_HASH, ASSET_AMOUNT_HASH, BIP_0340_VERIFY, BROKEN_DO_NOT_USE_CHECK_LOCK_DISTANCE, BROKEN_DO_NOT_USE_CHECK_LOCK_DURATION, BROKEN_DO_NOT_USE_TX_LOCK_DISTANCE, BROKEN_DO_NOT_USE_TX_LOCK_DURATION, BUILD_TAPBRANCH, BUILD_TAPLEAF_SIMPLICITY, BUILD_TAPTWEAK, CALCULATE_ASSET, CALCULATE_CONFIDENTIAL_TOKEN, CALCULATE_EXPLICIT_TOKEN, CALCULATE_ISSUANCE_ENTROPY, CH_1, CH_16, CH_32, CH_64, CH_8, CHECK_LOCK_HEIGHT, CHECK_LOCK_TIME, CHECK_SIG_VERIFY, COMPLEMENT_1, COMPLEMENT_16, COMPLEMENT_32, COMPLEMENT_64, COMPLEMENT_8, CURRENT_AMOUNT, CURRENT_ANNEX_HASH, CURRENT_ASSET, CURRENT_INDEX, CURRENT_ISSUANCE_ASSET_AMOUNT, CURRENT_ISSUANCE_ASSET_PROOF, CURRENT_ISSUANCE_TOKEN_AMOUNT, CURRENT_ISSUANCE_TOKEN_PROOF, CURRENT_NEW_ISSUANCE_CONTRACT, CURRENT_PEGIN, CURRENT_PREV_OUTPOINT, CURRENT_REISSUANCE_BLINDING, CURRENT_REISSUANCE_ENTROPY, CURRENT_SCRIPT_HASH, CURRENT_SCRIPT_SIG_HASH, CURRENT_SEQUENCE, DECOMPRESS, DECREMENT_16, DECREMENT_32, DECREMENT_64, DECREMENT_8, DIV_MOD_128_64, DIV_MOD_16, DIV_MOD_32, DIV_MOD_64, DIV_MOD_8, DIVIDE_16, DIVIDE_32, DIVIDE_64, DIVIDE_8, DIVIDES_16, DIVIDES_32, DIVIDES_64, DIVIDES_8, EQ_1, EQ_16, EQ_256, EQ_32, EQ_64, EQ_8, FE_ADD, FE_INVERT, FE_IS_ODD, FE_IS_ZERO, FE_MULTIPLY, FE_MULTIPLY_BETA, FE_NEGATE, FE_NORMALIZE, FE_SQUARE, FE_SQUARE_ROOT, FULL_ADD_16, FULL_ADD_32, FULL_ADD_64, FULL_ADD_8, FULL_DECREMENT_16, FULL_DECREMENT_32, FULL_DECREMENT_64, FULL_DECREMENT_8, FULL_INCREMENT_16, FULL_INCREMENT_32, FULL_INCREMENT_64, FULL_INCREMENT_8, FULL_LEFT_SHIFT_16_1, FULL_LEFT_SHIFT_16_2, FULL_LEFT_SHIFT_16_4, FULL_LEFT_SHIFT_16_8, FULL_LEFT_SHIFT_32_1, FULL_LEFT_SHIFT_32_16, FULL_LEFT_SHIFT_32_2, FULL_LEFT_SHIFT_32_4, FULL_LEFT_SHIFT_32_8, FULL_LEFT_SHIFT_64_1, FULL_LEFT_SHIFT_64_16, FULL_LEFT_SHIFT_64_2, FULL_LEFT_SHIFT_64_32, FULL_LEFT_SHIFT_64_4, FULL_LEFT_SHIFT_64_8, FULL_LEFT_SHIFT_8_1, FULL_LEFT_SHIFT_8_2, FULL_LEFT_SHIFT_8_4, FULL_MULTIPLY_16, FULL_MULTIPLY_32, FULL_MULTIPLY_64, FULL_MULTIPLY_8, FULL_RIGHT_SHIFT_16_1, FULL_RIGHT_SHIFT_16_2, FULL_RIGHT_SHIFT_16_4, FULL_RIGHT_SHIFT_16_8, FULL_RIGHT_SHIFT_32_1, FULL_RIGHT_SHIFT_32_16, FULL_RIGHT_SHIFT_32_2, FULL_RIGHT_SHIFT_32_4, FULL_RIGHT_SHIFT_32_8, FULL_RIGHT_SHIFT_64_1, FULL_RIGHT_SHIFT_64_16, FULL_RIGHT_SHIFT_64_2, FULL_RIGHT_SHIFT_64_32, FULL_RIGHT_SHIFT_64_4, FULL_RIGHT_SHIFT_64_8, FULL_RIGHT_SHIFT_8_1, FULL_RIGHT_SHIFT_8_2, FULL_RIGHT_SHIFT_8_4, FULL_SUBTRACT_16, FULL_SUBTRACT_32, FULL_SUBTRACT_64, FULL_SUBTRACT_8, GE_IS_ON_CURVE, GE_NEGATE, GEJ_ADD, GEJ_DOUBLE, GEJ_EQUIV, GEJ_GE_ADD, GEJ_GE_ADD_EX, GEJ_GE_EQUIV, GEJ_INFINITY, GEJ_IS_INFINITY, GEJ_IS_ON_CURVE, GEJ_NEGATE, GEJ_NORMALIZE, GEJ_RESCALE, GEJ_X_EQUIV, GEJ_Y_IS_ODD, GENERATE, GENESIS_BLOCK_HASH, HASH_TO_CURVE, HIGH_1, HIGH_16, HIGH_32, HIGH_64, HIGH_8, INCREMENT_16, INCREMENT_32, INCREMENT_64, INCREMENT_8, INPUT_AMOUNT, INPUT_AMOUNTS_HASH, INPUT_ANNEX_HASH, INPUT_ANNEXES_HASH, INPUT_ASSET, INPUT_HASH, INPUT_OUTPOINTS_HASH, INPUT_PEGIN, INPUT_PREV_OUTPOINT, INPUT_SCRIPT_HASH, INPUT_SCRIPT_SIG_HASH, INPUT_SCRIPT_SIGS_HASH, INPUT_SCRIPTS_HASH, INPUT_SEQUENCE, INPUT_SEQUENCES_HASH, INPUT_UTXO_HASH, INPUT_UTXOS_HASH, INPUTS_HASH, INTERNAL_KEY, IS_ONE_16, IS_ONE_32, IS_ONE_64, IS_ONE_8, IS_ZERO_16, IS_ZERO_32, IS_ZERO_64, IS_ZERO_8, ISSUANCE, ISSUANCE_ASSET, ISSUANCE_ASSET_AMOUNT, ISSUANCE_ASSET_AMOUNTS_HASH, ISSUANCE_ASSET_PROOF, ISSUANCE_BLINDING_ENTROPY_HASH, ISSUANCE_ENTROPY, ISSUANCE_HASH, ISSUANCE_RANGE_PROOFS_HASH, ISSUANCE_TOKEN, ISSUANCE_TOKEN_AMOUNT, ISSUANCE_TOKEN_AMOUNTS_HASH, ISSUANCE_TOKEN_PROOF, ISSUANCES_HASH, LBTC_ASSET, LE_16, LE_32, LE_64, LE_8, LEFT_EXTEND_16_32, LEFT_EXTEND_16_64, LEFT_EXTEND_1_16, LEFT_EXTEND_1_32, LEFT_EXTEND_1_64, LEFT_EXTEND_1_8, LEFT_EXTEND_32_64, LEFT_EXTEND_8_16, LEFT_EXTEND_8_32, LEFT_EXTEND_8_64, LEFT_PAD_HIGH_16_32, LEFT_PAD_HIGH_16_64, LEFT_PAD_HIGH_1_16, LEFT_PAD_HIGH_1_32, LEFT_PAD_HIGH_1_64, LEFT_PAD_HIGH_1_8, LEFT_PAD_HIGH_32_64, LEFT_PAD_HIGH_8_16, LEFT_PAD_HIGH_8_32, LEFT_PAD_HIGH_8_64, LEFT_PAD_LOW_16_32, LEFT_PAD_LOW_16_64, LEFT_PAD_LOW_1_16, LEFT_PAD_LOW_1_32, LEFT_PAD_LOW_1_64, LEFT_PAD_LOW_1_8, LEFT_PAD_LOW_32_64, LEFT_PAD_LOW_8_16, LEFT_PAD_LOW_8_32, LEFT_PAD_LOW_8_64, LEFT_ROTATE_16, LEFT_ROTATE_32, LEFT_ROTATE_64, LEFT_ROTATE_8, LEFT_SHIFT_16, LEFT_SHIFT_32, LEFT_SHIFT_64, LEFT_SHIFT_8, LEFT_SHIFT_WITH_16, LEFT_SHIFT_WITH_32, LEFT_SHIFT_WITH_64, LEFT_SHIFT_WITH_8, LEFTMOST_16_1, LEFTMOST_16_2, LEFTMOST_16_4, LEFTMOST_16_8, LEFTMOST_32_1, LEFTMOST_32_16, LEFTMOST_32_2, LEFTMOST_32_4, LEFTMOST_32_8, LEFTMOST_64_1, LEFTMOST_64_16, LEFTMOST_64_2, LEFTMOST_64_32, LEFTMOST_64_4, LEFTMOST_64_8, LEFTMOST_8_1, LEFTMOST_8_2, LEFTMOST_8_4, LINEAR_COMBINATION_1, LINEAR_VERIFY_1, LOCK_TIME, LOW_1, LOW_16, LOW_32, LOW_64, LOW_8, LT_16, LT_32, LT_64, LT_8, MAJ_1, MAJ_16, MAJ_32, MAJ_64, MAJ_8, MAX_16, MAX_32, MAX_64, MAX_8, MEDIAN_16, MEDIAN_32, MEDIAN_64, MEDIAN_8, MIN_16, MIN_32, MIN_64, MIN_8, MODULO_16, MODULO_32, MODULO_64, MODULO_8, MULTIPLY_16, MULTIPLY_32, MULTIPLY_64, MULTIPLY_8, NEGATE_16, NEGATE_32, NEGATE_64, NEGATE_8, NEW_ISSUANCE_CONTRACT, NONCE_HASH, NUM_INPUTS, NUM_OUTPUTS, ONE_16, ONE_32, ONE_64, ONE_8, OR_1, OR_16, OR_32, OR_64, OR_8, OUTPOINT_HASH, OUTPUT_AMOUNT, OUTPUT_AMOUNTS_HASH, OUTPUT_ASSET, OUTPUT_HASH, OUTPUT_IS_FEE, OUTPUT_NONCE, OUTPUT_NONCES_HASH, OUTPUT_NULL_DATUM, OUTPUT_RANGE_PROOF, OUTPUT_RANGE_PROOFS_HASH, OUTPUT_SCRIPT_HASH, OUTPUT_SCRIPTS_HASH, OUTPUT_SURJECTION_PROOF, OUTPUT_SURJECTION_PROOFS_HASH, OUTPUTS_HASH, PARSE_LOCK, PARSE_SEQUENCE, POINT_VERIFY_1, REISSUANCE_BLINDING, REISSUANCE_ENTROPY, RIGHT_EXTEND_16_32, RIGHT_EXTEND_16_64, RIGHT_EXTEND_32_64, RIGHT_EXTEND_8_16, RIGHT_EXTEND_8_32, RIGHT_EXTEND_8_64, RIGHT_PAD_HIGH_16_32, RIGHT_PAD_HIGH_16_64, RIGHT_PAD_HIGH_1_16, RIGHT_PAD_HIGH_1_32, RIGHT_PAD_HIGH_1_64, RIGHT_PAD_HIGH_1_8, RIGHT_PAD_HIGH_32_64, RIGHT_PAD_HIGH_8_16, RIGHT_PAD_HIGH_8_32, RIGHT_PAD_HIGH_8_64, RIGHT_PAD_LOW_16_32, RIGHT_PAD_LOW_16_64, RIGHT_PAD_LOW_1_16, RIGHT_PAD_LOW_1_32, RIGHT_PAD_LOW_1_64, RIGHT_PAD_LOW_1_8, RIGHT_PAD_LOW_32_64, RIGHT_PAD_LOW_8_16, RIGHT_PAD_LOW_8_32, RIGHT_PAD_LOW_8_64, RIGHT_ROTATE_16, RIGHT_ROTATE_32, RIGHT_ROTATE_64, RIGHT_ROTATE_8, RIGHT_SHIFT_16, RIGHT_SHIFT_32, RIGHT_SHIFT_64, RIGHT_SHIFT_8, RIGHT_SHIFT_WITH_16, RIGHT_SHIFT_WITH_32, RIGHT_SHIFT_WITH_64, RIGHT_SHIFT_WITH_8, RIGHTMOST_16_1, RIGHTMOST_16_2, RIGHTMOST_16_4, RIGHTMOST_16_8, RIGHTMOST_32_1, RIGHTMOST_32_16, RIGHTMOST_32_2, RIGHTMOST_32_4, RIGHTMOST_32_8, RIGHTMOST_64_1, RIGHTMOST_64_16, RIGHTMOST_64_2, RIGHTMOST_64_32, RIGHTMOST_64_4, RIGHTMOST_64_8, RIGHTMOST_8_1, RIGHTMOST_8_2, RIGHTMOST_8_4, SCALAR_ADD, SCALAR_INVERT, SCALAR_IS_ZERO, SCALAR_MULTIPLY, SCALAR_MULTIPLY_LAMBDA, SCALAR_NEGATE, SCALAR_NORMALIZE, SCALAR_SQUARE, SCALE, SCRIPT_CMR, SHA_256_BLOCK, SHA_256_CTX_8_ADD_1, SHA_256_CTX_8_ADD_128, SHA_256_CTX_8_ADD_16, SHA_256_CTX_8_ADD_2, SHA_256_CTX_8_ADD_256, SHA_256_CTX_8_ADD_32, SHA_256_CTX_8_ADD_4, SHA_256_CTX_8_ADD_512, SHA_256_CTX_8_ADD_64, SHA_256_CTX_8_ADD_8, SHA_256_CTX_8_ADD_BUFFER_511, SHA_256_CTX_8_FINALIZE, SHA_256_CTX_8_INIT, SHA_256_IV, SIG_ALL_HASH, SOME_1, SOME_16, SOME_32, SOME_64, SOME_8, SUBTRACT_16, SUBTRACT_32, SUBTRACT_64, SUBTRACT_8, SWU, TAP_ENV_HASH, TAPDATA_INIT, TAPLEAF_HASH, TAPLEAF_VERSION, TAPPATH, TAPPATH_HASH, TOTAL_FEE, TRANSACTION_ID, TX_HASH, TX_IS_FINAL, TX_LOCK_HEIGHT, TX_LOCK_TIME, VERIFY, VERSION, XOR_1, XOR_16, XOR_32, XOR_64, XOR_8, XOR_XOR_1, XOR_XOR_16, XOR_XOR_32, XOR_XOR_64, XOR_XOR_8, ================================================ FILE: C/elements/primitiveEnumTy.inc ================================================ /* This file has been automatically generated. */ ty_u = 0, ty_b = 1, ty_w2 = 2, ty_w4 = 3, ty_w8 = 4, ty_w16 = 5, ty_w32 = 6, ty_w64 = 7, ty_w128 = 8, ty_w256 = 9, ty_w512 = 10, ty_w1Ki = 11, ty_w2Ki = 12, ty_w4Ki = 13, ty_w8Ki = 14, ty_w16Ki = 15, ty_w32Ki = 16, ty_w64Ki = 17, ty_w128Ki = 18, ty_w256Ki = 19, ty_w512Ki = 20, ty_w1Mi = 21, ty_w2Mi = 22, ty_w4Mi = 23, ty_w8Mi = 24, ty_w16Mi = 25, ty_w32Mi = 26, ty_w64Mi = 27, ty_w128Mi = 28, ty_w256Mi = 29, ty_w512Mi = 30, ty_w1Gi = 31, ty_w2Gi = 32, ty_mb, ty_mw8, ty_mw16, ty_mw32, ty_mw64, ty_mw128, ty_mw256, ty_mw512, ty_mw1Ki, ty_mw2Ki, ty_mmb, ty_mmw256, ty_mmspbw256w64, ty_mmspbw256w256, ty_mmspw2w256sbw4, ty_msw16w16, ty_mspbw256w64, ty_mspbw256w256, ty_mspw2w256sbw4, ty_mpw256w32, ty_mpspbw256w256spbw256w64, ty_sbw4, ty_sw16w16, ty_sw32w32, ty_spbw256w64, ty_spbw256w256, ty_spw2w256sbw4, ty_pbw2, ty_pbw8, ty_pbw16, ty_pbw32, ty_pbw64, ty_pbw128, ty_pbw256, ty_pbpw4w8, ty_pbpw4w16, ty_pbpw8w32, ty_pbpw8w64, ty_pw2w8, ty_pw2w16, ty_pw2w32, ty_pw2w64, ty_pw2w256, ty_pw4w8, ty_pw4w16, ty_pw4w32, ty_pw4w64, ty_pw8b, ty_pw8w2, ty_pw8w4, ty_pw8w16, ty_pw8w32, ty_pw8w64, ty_pw16b, ty_pw16w2, ty_pw16w4, ty_pw16w8, ty_pw16w32, ty_pw16w64, ty_pw32b, ty_pw32w2, ty_pw32w4, ty_pw32w8, ty_pw32w16, ty_pw32w64, ty_pw64b, ty_pw64w2, ty_pw64w4, ty_pw64w8, ty_pw64w16, ty_pw64w32, ty_pw64w128, ty_pw64w256, ty_pw128w64, ty_pw256w32, ty_pw256w512, ty_pw256pbw256, ty_pw256pw512w256, ty_pw512w256, ty_pmw16mw8, ty_pmw32pmw16mw8, ty_pmw64pmw32pmw16mw8, ty_pmw128pmw64pmw32pmw16mw8, ty_pmw256pw256w32, ty_pmw256pmw128pmw64pmw32pmw16mw8, ty_pmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_pmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_pspbw256w256spbw256w64, ty_ppw256w32w256, ty_ppw256w512w256, ty_ppw256w512w512, ty_ppw256pbw256w256, ty_ppw256pw512w256w256, ty_ppw512w256w256, ty_ppw512w256w512, ty_ppw512w256pw512w256, ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256, ty_pppw256w512w256w512, ty_pppw256pbw256w256pbw256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w8, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w16, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w32, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w64, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w128, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w512, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w1Ki, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w2Ki, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w4Ki, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mw256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mspbw256w256, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw256pw256w32, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8, ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pspbw256w256spbw256w64, ================================================ FILE: C/elements/primitiveInitTy.inc ================================================ /* This file has been automatically generated. */ (*bound_var)[ty_u] = (unification_var){ .isBound = true, .bound = { .kind = ONE }}; (*bound_var)[ty_b] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_u] } }}; (*bound_var)[ty_w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_w128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_w1Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_w2Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w1Ki], &(*bound_var)[ty_w1Ki] } }}; (*bound_var)[ty_w4Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2Ki], &(*bound_var)[ty_w2Ki] } }}; (*bound_var)[ty_w8Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4Ki], &(*bound_var)[ty_w4Ki] } }}; (*bound_var)[ty_w16Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8Ki], &(*bound_var)[ty_w8Ki] } }}; (*bound_var)[ty_w32Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16Ki], &(*bound_var)[ty_w16Ki] } }}; (*bound_var)[ty_w64Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32Ki], &(*bound_var)[ty_w32Ki] } }}; (*bound_var)[ty_w128Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64Ki], &(*bound_var)[ty_w64Ki] } }}; (*bound_var)[ty_w256Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128Ki], &(*bound_var)[ty_w128Ki] } }}; (*bound_var)[ty_w512Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256Ki], &(*bound_var)[ty_w256Ki] } }}; (*bound_var)[ty_w1Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512Ki], &(*bound_var)[ty_w512Ki] } }}; (*bound_var)[ty_w2Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w1Mi], &(*bound_var)[ty_w1Mi] } }}; (*bound_var)[ty_w4Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2Mi], &(*bound_var)[ty_w2Mi] } }}; (*bound_var)[ty_w8Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4Mi], &(*bound_var)[ty_w4Mi] } }}; (*bound_var)[ty_w16Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8Mi], &(*bound_var)[ty_w8Mi] } }}; (*bound_var)[ty_w32Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16Mi], &(*bound_var)[ty_w16Mi] } }}; (*bound_var)[ty_w64Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32Mi], &(*bound_var)[ty_w32Mi] } }}; (*bound_var)[ty_w128Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64Mi], &(*bound_var)[ty_w64Mi] } }}; (*bound_var)[ty_w256Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128Mi], &(*bound_var)[ty_w128Mi] } }}; (*bound_var)[ty_w512Mi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256Mi], &(*bound_var)[ty_w256Mi] } }}; (*bound_var)[ty_w1Gi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512Mi], &(*bound_var)[ty_w512Mi] } }}; (*bound_var)[ty_w2Gi] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w1Gi], &(*bound_var)[ty_w1Gi] } }}; (*bound_var)[ty_mb] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_mw8] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_mw16] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_mw32] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_mw64] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_mw128] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_mw256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_mw512] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_mw1Ki] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w1Ki] } }}; (*bound_var)[ty_mw2Ki] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_w2Ki] } }}; (*bound_var)[ty_mmb] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_mb] } }}; (*bound_var)[ty_mmw256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_mw256] } }}; (*bound_var)[ty_mmspbw256w64] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_mspbw256w64] } }}; (*bound_var)[ty_mmspbw256w256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_mspbw256w256] } }}; (*bound_var)[ty_mmspw2w256sbw4] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_mspw2w256sbw4] } }}; (*bound_var)[ty_msw16w16] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_sw16w16] } }}; (*bound_var)[ty_mspbw256w64] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_spbw256w64] } }}; (*bound_var)[ty_mspbw256w256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_spbw256w256] } }}; (*bound_var)[ty_mspw2w256sbw4] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_spw2w256sbw4] } }}; (*bound_var)[ty_mpw256w32] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_pw256w32] } }}; (*bound_var)[ty_mpspbw256w256spbw256w64] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_u], &(*bound_var)[ty_pspbw256w256spbw256w64] } }}; (*bound_var)[ty_sbw4] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_sw16w16] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_sw32w32] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_spbw256w64] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_pbw256], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_spbw256w256] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_pbw256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_spw2w256sbw4] = (unification_var){ .isBound = true, .bound = { .kind = SUM, .arg = { &(*bound_var)[ty_pw2w256], &(*bound_var)[ty_sbw4] } }}; (*bound_var)[ty_pbw2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pbw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pbw16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pbw32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pbw64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pbw128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_pbw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pbpw4w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw4w8] } }}; (*bound_var)[ty_pbpw4w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw4w16] } }}; (*bound_var)[ty_pbpw8w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw8w32] } }}; (*bound_var)[ty_pbpw8w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_b], &(*bound_var)[ty_pw8w64] } }}; (*bound_var)[ty_pw2w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw2w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw2w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw2w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw2w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w2], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pw4w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw4w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw4w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw4w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w4], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw8b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw8w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw8w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw8w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw8w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw8w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w8], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw16b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw16w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw16w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw16w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw16w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw16w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w16], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw32b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw32w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw32w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw32w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw32w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw32w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w32], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw64b] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_b] } }}; (*bound_var)[ty_pw64w2] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w2] } }}; (*bound_var)[ty_pw64w4] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w4] } }}; (*bound_var)[ty_pw64w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pw64w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pw64w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw64w128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_pw64w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w64], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pw128w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w128], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pw256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pw256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_pw256pbw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_pbw256] } }}; (*bound_var)[ty_pw256pw512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w256], &(*bound_var)[ty_pw512w256] } }}; (*bound_var)[ty_pw512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_w512], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw16], &(*bound_var)[ty_mw8] } }}; (*bound_var)[ty_pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw32], &(*bound_var)[ty_pmw16mw8] } }}; (*bound_var)[ty_pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw64], &(*bound_var)[ty_pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw128], &(*bound_var)[ty_pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw256pw256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw256], &(*bound_var)[ty_pw256w32] } }}; (*bound_var)[ty_pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw256], &(*bound_var)[ty_pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw512], &(*bound_var)[ty_pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw1Ki], &(*bound_var)[ty_pmw512pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_mw2Ki], &(*bound_var)[ty_pmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pspbw256w256spbw256w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_spbw256w256], &(*bound_var)[ty_spbw256w64] } }}; (*bound_var)[ty_ppw256w32w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256w32], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw256w512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256w512], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw256w512w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256w512], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_ppw256pbw256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256pbw256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw256pw512w256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw256pw512w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw512w256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw512w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_ppw512w256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw512w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_ppw512w256pw512w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pw512w256], &(*bound_var)[ty_pw512w256] } }}; (*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_pmw256pmw128pmw64pmw32pmw16mw8], &(*bound_var)[ty_pw64w256] } }}; (*bound_var)[ty_pppw256w512w256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppw256w512w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_pppw256pbw256w256pbw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppw256pbw256w256], &(*bound_var)[ty_pbw256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w8] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w16] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w16] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w32] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w64] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w128] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w128] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w512] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w512] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w1Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w1Ki] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w2Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w2Ki] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w4Ki] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_w4Ki] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mw256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_mw256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mspbw256w256] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_mspbw256w256] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw256pw256w32] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_pmw256pw256w32] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8] } }}; (*bound_var)[ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pspbw256w256spbw256w64] = (unification_var){ .isBound = true, .bound = { .kind = PRODUCT, .arg = { &(*bound_var)[ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256], &(*bound_var)[ty_pspbw256w256spbw256w64] } }}; ================================================ FILE: C/elements/primitiveJetNode.inc ================================================ /* This file has been automatically generated. */ [ADD_16] = { .tag = JET , .jet = simplicity_add_16 , .cmr = {{0x26ae0994u, 0xce8b771au, 0xf7ad2851u, 0xb83b49a5u, 0x95053658u, 0x9f67bd85u, 0x59470460u, 0x29751c0du}} , .sourceIx = ty_w32 , .targetIx = ty_pbw16 , .cost = 108 /* milli weight units */ } ,[ADD_32] = { .tag = JET , .jet = simplicity_add_32 , .cmr = {{0x3d767446u, 0x6ed69e1du, 0xbedcd480u, 0x57a9e628u, 0x8c222532u, 0xfbc50480u, 0x49928cfbu, 0x77f829d9u}} , .sourceIx = ty_w64 , .targetIx = ty_pbw32 , .cost = 117 /* milli weight units */ } ,[ADD_64] = { .tag = JET , .jet = simplicity_add_64 , .cmr = {{0x9b56e61eu, 0xefe2805cu, 0xa87396bdu, 0xfb03f5e1u, 0xb1385f7au, 0xc4bff768u, 0x4026a07cu, 0xf97fb6f6u}} , .sourceIx = ty_w128 , .targetIx = ty_pbw64 , .cost = 109 /* milli weight units */ } ,[ADD_8] = { .tag = JET , .jet = simplicity_add_8 , .cmr = {{0xd7328c09u, 0x14ee999eu, 0xfa0a6cb2u, 0x6eb40912u, 0xc215c062u, 0xe58a981au, 0xe6b2e4a8u, 0x0474a1dau}} , .sourceIx = ty_w16 , .targetIx = ty_pbw8 , .cost = 112 /* milli weight units */ } ,[ALL_16] = { .tag = JET , .jet = simplicity_all_16 , .cmr = {{0x16f0c930u, 0x7eb8f4c1u, 0xfdd1bafau, 0xef287924u, 0x2958498eu, 0x8f5b2e0du, 0x29f06553u, 0xdc06a0bdu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 62 /* milli weight units */ } ,[ALL_32] = { .tag = JET , .jet = simplicity_all_32 , .cmr = {{0x0eb8b40du, 0x29021747u, 0xeec451d4u, 0xe663586au, 0x436c2db0u, 0x932675dau, 0xf2166123u, 0xbfe452a6u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 65 /* milli weight units */ } ,[ALL_64] = { .tag = JET , .jet = simplicity_all_64 , .cmr = {{0xa65c82d5u, 0x3d382ee2u, 0x9aa88b77u, 0x18a97fbbu, 0xce6475ecu, 0x32c4b4cdu, 0x6908fde4u, 0x5d81b624u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 79 /* milli weight units */ } ,[ALL_8] = { .tag = JET , .jet = simplicity_all_8 , .cmr = {{0x1d3ec7fbu, 0x6a07847cu, 0x92b8a998u, 0xe1f6b478u, 0x319d050au, 0x387642f4u, 0x032d2f7du, 0x2e027fcdu}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 76 /* milli weight units */ } ,[AND_1] = { .tag = JET , .jet = simplicity_and_1 , .cmr = {{0xb773cefau, 0x418957feu, 0xa7dfb49cu, 0x6c43b3dbu, 0xfa35fa3du, 0x80de8cfdu, 0x4d70c08du, 0x945f5fbau}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 79 /* milli weight units */ } ,[AND_16] = { .tag = JET , .jet = simplicity_and_16 , .cmr = {{0x57dd730bu, 0x1c8ddff1u, 0x3cae2769u, 0x562be0abu, 0xc6ca3bc8u, 0x02da0abbu, 0xb7fc138cu, 0xa463da59u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 88 /* milli weight units */ } ,[AND_32] = { .tag = JET , .jet = simplicity_and_32 , .cmr = {{0x753e332du, 0xdfa096f0u, 0x8399ffaau, 0x7ec4da40u, 0x35bcbaa1u, 0x42e6e38du, 0x4cb607ceu, 0x1f0b051du}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 94 /* milli weight units */ } ,[AND_64] = { .tag = JET , .jet = simplicity_and_64 , .cmr = {{0xf1ad5e6cu, 0x63ee5c89u, 0x0b0f2e71u, 0x1561b905u, 0x316487acu, 0x4044dd23u, 0x0cf6a736u, 0xf81bd4f3u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 93 /* milli weight units */ } ,[AND_8] = { .tag = JET , .jet = simplicity_and_8 , .cmr = {{0xac828b72u, 0x4c5f5340u, 0xb51e76e7u, 0xb6e8b23au, 0xeab7533fu, 0xd8c091aeu, 0x2a515530u, 0xae7ab200u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 91 /* milli weight units */ } ,[ANNEX_HASH] = { .tag = JET , .jet = simplicity_annex_hash , .cmr = {{0xeba1b7fbu, 0x2ea8d57au, 0xf3b6273eu, 0x5182fb99u, 0xdb1708b2u, 0xd0afb9c6u, 0xad0358ccu, 0x3f647dc8u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mw256 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 241 /* milli weight units */ } ,[ASSET_AMOUNT_HASH] = { .tag = JET , .jet = simplicity_asset_amount_hash , .cmr = {{0xa864d1f1u, 0xf83950b6u, 0x3196fe88u, 0xbaec2e42u, 0x28953230u, 0xbe45c88cu, 0x4e0b9917u, 0x8b338f07u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pspbw256w256spbw256w64 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 308 /* milli weight units */ } ,[BIP_0340_VERIFY] = { .tag = JET , .jet = simplicity_bip_0340_verify , .cmr = {{0xc9c45a8au, 0xec865914u, 0x3bfe2af6u, 0xead48d4eu, 0x0542453au, 0xcae84b9bu, 0xbb97656bu, 0x670bdfddu}} , .sourceIx = ty_w1Ki , .targetIx = ty_u , .cost = 49087 /* milli weight units */ } ,[BROKEN_DO_NOT_USE_CHECK_LOCK_DISTANCE] = { .tag = JET , .jet = simplicity_broken_do_not_use_check_lock_distance , .cmr = {{0x7f78c7a7u, 0x7a25ada2u, 0x23267d23u, 0x9a5922f7u, 0x64b8ac0cu, 0x2fcef68eu, 0xb93c0d92u, 0xda4af515u}} , .sourceIx = ty_w16 , .targetIx = ty_u , .cost = 105 /* milli weight units */ } ,[BROKEN_DO_NOT_USE_CHECK_LOCK_DURATION] = { .tag = JET , .jet = simplicity_broken_do_not_use_check_lock_duration , .cmr = {{0x73dac8e2u, 0x5d87eaf3u, 0x82c2a772u, 0x06ad38b9u, 0x384361e7u, 0xd0dc87c0u, 0xfa7af7eau, 0x524597b7u}} , .sourceIx = ty_w16 , .targetIx = ty_u , .cost = 102 /* milli weight units */ } ,[BROKEN_DO_NOT_USE_TX_LOCK_DISTANCE] = { .tag = JET , .jet = simplicity_broken_do_not_use_tx_lock_distance , .cmr = {{0x4c7773b8u, 0x18cb7ee5u, 0xf54f925au, 0xad015677u, 0xa043a72fu, 0x316a187cu, 0xc28c696cu, 0xfcb90807u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 91 /* milli weight units */ } ,[BROKEN_DO_NOT_USE_TX_LOCK_DURATION] = { .tag = JET , .jet = simplicity_broken_do_not_use_tx_lock_duration , .cmr = {{0xcc9c64c8u, 0xb6eb4bf0u, 0x9694af5au, 0x35d957a4u, 0x05e66c1bu, 0x35224ed6u, 0x75878918u, 0x452440b2u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 84 /* milli weight units */ } ,[BUILD_TAPBRANCH] = { .tag = JET , .jet = simplicity_build_tapbranch , .cmr = {{0xcbecf9bcu, 0xe172c50fu, 0x585951dfu, 0xf0e0523du, 0xb109e570u, 0x25ec37deu, 0x2c3a74d4u, 0xa673f225u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 2563 /* milli weight units */ } ,[BUILD_TAPLEAF_SIMPLICITY] = { .tag = JET , .jet = simplicity_build_tapleaf_simplicity , .cmr = {{0x736e9fceu, 0xfb5b873eu, 0x09f2681eu, 0x74e49f5au, 0x1056f90au, 0xf52ab3ecu, 0x5b197727u, 0xd39834beu}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 1843 /* milli weight units */ } ,[BUILD_TAPTWEAK] = { .tag = JET , .jet = simplicity_build_taptweak , .cmr = {{0x38741f80u, 0xa2bf10f8u, 0xf8723077u, 0xc6741cbeu, 0xae2dcac8u, 0x57901b81u, 0x3725806fu, 0x21898ee3u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 92813 /* milli weight units */ } ,[CALCULATE_ASSET] = { .tag = JET , .jet = simplicity_calculate_asset , .cmr = {{0x676f988eu, 0x547251e7u, 0xa09eede1u, 0x920a9c5du, 0x35e75759u, 0xe6d8d49bu, 0x580ceb3eu, 0x146bcf7eu}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 807 /* milli weight units */ } ,[CALCULATE_CONFIDENTIAL_TOKEN] = { .tag = JET , .jet = simplicity_calculate_confidential_token , .cmr = {{0x8e402905u, 0x60743398u, 0x40c0e700u, 0x9b66f382u, 0xbb98d7ddu, 0xe719dd2cu, 0x9f2fd3acu, 0xd9325ac6u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 707 /* milli weight units */ } ,[CALCULATE_EXPLICIT_TOKEN] = { .tag = JET , .jet = simplicity_calculate_explicit_token , .cmr = {{0x87522802u, 0x0b456c99u, 0x8aad3ac5u, 0xc4836f71u, 0x9445dcbeu, 0x6bd274e8u, 0xca145d82u, 0x797e1b92u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 771 /* milli weight units */ } ,[CALCULATE_ISSUANCE_ENTROPY] = { .tag = JET , .jet = simplicity_calculate_issuance_entropy , .cmr = {{0xa6e7c434u, 0xaee5a733u, 0x0c1fc246u, 0xf71dcf05u, 0x1ce54bdeu, 0xe7b8e639u, 0x57be18c2u, 0xd751c653u}} , .sourceIx = ty_ppw256w32w256 , .targetIx = ty_w256 , .cost = 2095 /* milli weight units */ } ,[CH_1] = { .tag = JET , .jet = simplicity_ch_1 , .cmr = {{0xb841b857u, 0xa4aa50eau, 0xca27a26fu, 0x7442fcbfu, 0xe954677au, 0xe6d455f6u, 0x05654989u, 0xe35aeb13u}} , .sourceIx = ty_pbw2 , .targetIx = ty_b , .cost = 78 /* milli weight units */ } ,[CH_16] = { .tag = JET , .jet = simplicity_ch_16 , .cmr = {{0x9cff11a0u, 0x9b6041e5u, 0xf2639ae4u, 0xc065a18fu, 0xc675db2fu, 0xbd985408u, 0xe28f027au, 0x99110e11u}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 94 /* milli weight units */ } ,[CH_32] = { .tag = JET , .jet = simplicity_ch_32 , .cmr = {{0x071cef80u, 0x39c79f71u, 0x31cd6a5fu, 0xe493dc26u, 0x8f9db58fu, 0x7b20a855u, 0x55e297bdu, 0xd216cf40u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 91 /* milli weight units */ } ,[CH_64] = { .tag = JET , .jet = simplicity_ch_64 , .cmr = {{0xd555d219u, 0x63b0192fu, 0xc97214b6u, 0x3dc1c3afu, 0x758b2911u, 0x58f0e1a3u, 0xbcfdea67u, 0x9c666da6u}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 91 /* milli weight units */ } ,[CH_8] = { .tag = JET , .jet = simplicity_ch_8 , .cmr = {{0x353f63b0u, 0xf8cb54f5u, 0xae6575afu, 0x8ca2242cu, 0xeee9f27au, 0x84186eb8u, 0x0e620d5eu, 0x2e8548ecu}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 77 /* milli weight units */ } ,[CHECK_LOCK_HEIGHT] = { .tag = JET , .jet = simplicity_check_lock_height , .cmr = {{0x9e7898d0u, 0x37627134u, 0xd2bd70c7u, 0xfca9cba4u, 0x5eaf267du, 0x4d09ad50u, 0xa9ef717au, 0x8f2749dbu}} , .sourceIx = ty_w32 , .targetIx = ty_u , .cost = 77 /* milli weight units */ } ,[CHECK_LOCK_TIME] = { .tag = JET , .jet = simplicity_check_lock_time , .cmr = {{0x68673d12u, 0xe2732faau, 0x1d39e213u, 0x6b1406afu, 0xa098a84cu, 0x96e8d605u, 0x02a2dd61u, 0xc59570bbu}} , .sourceIx = ty_w32 , .targetIx = ty_u , .cost = 93 /* milli weight units */ } ,[CHECK_SIG_VERIFY] = { .tag = JET , .jet = simplicity_check_sig_verify , .cmr = {{0xb5801554u, 0x6d285266u, 0x5dd21bf1u, 0x12662670u, 0x20fa5e27u, 0x5001dd46u, 0x18fa4156u, 0x25952e68u}} , .sourceIx = ty_ppw256w512w512 , .targetIx = ty_u , .cost = 50000 /* milli weight units */ } ,[COMPLEMENT_1] = { .tag = JET , .jet = simplicity_complement_1 , .cmr = {{0xed74eeb8u, 0x3a00c713u, 0xcc14f33eu, 0xfe553383u, 0xcd0411ccu, 0x3020fd89u, 0x27931667u, 0x5d910e66u}} , .sourceIx = ty_b , .targetIx = ty_b , .cost = 79 /* milli weight units */ } ,[COMPLEMENT_16] = { .tag = JET , .jet = simplicity_complement_16 , .cmr = {{0x61fdd904u, 0xa4aeb7ebu, 0x7684af61u, 0x8e25aae9u, 0x07cd1db0u, 0xf62d9703u, 0xc5b854e1u, 0x663cac9fu}} , .sourceIx = ty_w16 , .targetIx = ty_w16 , .cost = 75 /* milli weight units */ } ,[COMPLEMENT_32] = { .tag = JET , .jet = simplicity_complement_32 , .cmr = {{0xfeb02cc3u, 0x6e195b46u, 0x2ae504a9u, 0x12dadfe6u, 0x6ad47f23u, 0xa0cb3baeu, 0xa21d31aau, 0xa0ce101du}} , .sourceIx = ty_w32 , .targetIx = ty_w32 , .cost = 93 /* milli weight units */ } ,[COMPLEMENT_64] = { .tag = JET , .jet = simplicity_complement_64 , .cmr = {{0x45072d5au, 0xa0e5c37cu, 0x9e521dccu, 0x92e8f39au, 0x5f75e7d9u, 0x28670acau, 0xb79cd8c8u, 0xb5b59e1au}} , .sourceIx = ty_w64 , .targetIx = ty_w64 , .cost = 88 /* milli weight units */ } ,[COMPLEMENT_8] = { .tag = JET , .jet = simplicity_complement_8 , .cmr = {{0x6916b28fu, 0xb574d9c9u, 0x08a3f33fu, 0x74bf06f7u, 0xed937254u, 0x247f9efcu, 0x2603d717u, 0x1dd497beu}} , .sourceIx = ty_w8 , .targetIx = ty_w8 , .cost = 80 /* milli weight units */ } ,[CURRENT_AMOUNT] = { .tag = JET , .jet = simplicity_current_amount , .cmr = {{0x9e7bc96du, 0x06c1f4a4u, 0xd2bd4333u, 0xd55643cbu, 0xa6863d3au, 0x338e31dcu, 0x0d179558u, 0x4156ea69u}} , .sourceIx = ty_u , .targetIx = ty_pspbw256w256spbw256w64 , .cost = 225 /* milli weight units */ } ,[CURRENT_ANNEX_HASH] = { .tag = JET , .jet = simplicity_current_annex_hash , .cmr = {{0x5f68bdafu, 0xd417febbu, 0x10dee16bu, 0x1d47c21fu, 0xa97efc91u, 0x9157c7f7u, 0xbc54a61du, 0xc4f9f7d6u}} , .sourceIx = ty_u , .targetIx = ty_mw256 , .cost = 79 /* milli weight units */ } ,[CURRENT_ASSET] = { .tag = JET , .jet = simplicity_current_asset , .cmr = {{0x03c84459u, 0xa5ecdfdbu, 0x46e3d38eu, 0xcb79ff22u, 0x243fdcf7u, 0x0d80da1bu, 0xa45699e7u, 0x008eecfeu}} , .sourceIx = ty_u , .targetIx = ty_spbw256w256 , .cost = 171 /* milli weight units */ } ,[CURRENT_INDEX] = { .tag = JET , .jet = simplicity_current_index , .cmr = {{0x15e1051fu, 0xf23f851cu, 0x19131f0du, 0xe6edc488u, 0x2376a257u, 0x90dbd910u, 0x2824aa22u, 0xa889ae84u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 88 /* milli weight units */ } ,[CURRENT_ISSUANCE_ASSET_AMOUNT] = { .tag = JET , .jet = simplicity_current_issuance_asset_amount , .cmr = {{0xdc410ec6u, 0x9946f08bu, 0x9c4a40cfu, 0x38819cbbu, 0x014e98fcu, 0xe0a9b196u, 0x51455747u, 0x7fe1c2a7u}} , .sourceIx = ty_u , .targetIx = ty_mspbw256w64 , .cost = 165 /* milli weight units */ } ,[CURRENT_ISSUANCE_ASSET_PROOF] = { .tag = JET , .jet = simplicity_current_issuance_asset_proof , .cmr = {{0xe5c1c6f7u, 0xea029614u, 0x8e76f8b1u, 0x79d41519u, 0x8273dcc8u, 0xe1fd891fu, 0x83ef2bdfu, 0xb0692936u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 140 /* milli weight units */ } ,[CURRENT_ISSUANCE_TOKEN_AMOUNT] = { .tag = JET , .jet = simplicity_current_issuance_token_amount , .cmr = {{0xe3ea9c61u, 0x70955f27u, 0xb01b120cu, 0xd63a3608u, 0x50cc700fu, 0x4725193bu, 0xdff88e01u, 0xdfb04eadu}} , .sourceIx = ty_u , .targetIx = ty_mspbw256w64 , .cost = 188 /* milli weight units */ } ,[CURRENT_ISSUANCE_TOKEN_PROOF] = { .tag = JET , .jet = simplicity_current_issuance_token_proof , .cmr = {{0x92e7d9ddu, 0xbf756e3eu, 0x622a44d4u, 0xd00e8423u, 0x6bcce42fu, 0x16f3200eu, 0x8b89c03cu, 0x441e458au}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 144 /* milli weight units */ } ,[CURRENT_NEW_ISSUANCE_CONTRACT] = { .tag = JET , .jet = simplicity_current_new_issuance_contract , .cmr = {{0x23781567u, 0x5e9e9cf4u, 0xd8548560u, 0xc761e3bau, 0x7f64dcf2u, 0x5c99521bu, 0xe9d857e4u, 0xea41d868u}} , .sourceIx = ty_u , .targetIx = ty_mw256 , .cost = 145 /* milli weight units */ } ,[CURRENT_PEGIN] = { .tag = JET , .jet = simplicity_current_pegin , .cmr = {{0x369ad5f6u, 0xd760481cu, 0xb353a9bau, 0xcf900ff1u, 0x62b76040u, 0xc07ad0a8u, 0x3e52fcceu, 0xf1295790u}} , .sourceIx = ty_u , .targetIx = ty_mw256 , .cost = 147 /* milli weight units */ } ,[CURRENT_PREV_OUTPOINT] = { .tag = JET , .jet = simplicity_current_prev_outpoint , .cmr = {{0xa1ec909cu, 0x81e508e8u, 0x6e1361bau, 0x82e5fb47u, 0xa2c76bffu, 0xba7321a6u, 0xfc13cb12u, 0xaf7f697cu}} , .sourceIx = ty_u , .targetIx = ty_pw256w32 , .cost = 156 /* milli weight units */ } ,[CURRENT_REISSUANCE_BLINDING] = { .tag = JET , .jet = simplicity_current_reissuance_blinding , .cmr = {{0xb71550c8u, 0xf62e7aacu, 0xff13e8d3u, 0xc0ae054eu, 0xf036409du, 0x76c06579u, 0xc026ad68u, 0xa1b561f8u}} , .sourceIx = ty_u , .targetIx = ty_mw256 , .cost = 94 /* milli weight units */ } ,[CURRENT_REISSUANCE_ENTROPY] = { .tag = JET , .jet = simplicity_current_reissuance_entropy , .cmr = {{0x8b271532u, 0x7a0ac6b0u, 0xd18a2e51u, 0xfbda46c4u, 0xb118ee06u, 0x37d114aeu, 0x3e58a23bu, 0x45d67ff8u}} , .sourceIx = ty_u , .targetIx = ty_mw256 , .cost = 85 /* milli weight units */ } ,[CURRENT_SCRIPT_HASH] = { .tag = JET , .jet = simplicity_current_script_hash , .cmr = {{0xbfaf8584u, 0x43cec833u, 0x7e37839du, 0xc4113502u, 0x7184580cu, 0x892157ceu, 0x730418c0u, 0x8d5ed838u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 134 /* milli weight units */ } ,[CURRENT_SCRIPT_SIG_HASH] = { .tag = JET , .jet = simplicity_current_script_sig_hash , .cmr = {{0x8baa9df8u, 0x54fe33eeu, 0xea66195cu, 0x97ce18edu, 0x701e107eu, 0xea7e02fbu, 0x2603b2c1u, 0x21575066u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 139 /* milli weight units */ } ,[CURRENT_SEQUENCE] = { .tag = JET , .jet = simplicity_current_sequence , .cmr = {{0x0f4224f9u, 0xaa8644f5u, 0xc0f7910fu, 0x1739041au, 0xec8e7af7u, 0x7b5f38cfu, 0xdca0fdf4u, 0x8267a6c3u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 89 /* milli weight units */ } ,[DECOMPRESS] = { .tag = JET , .jet = simplicity_decompress , .cmr = {{0x13973317u, 0xd587418eu, 0xf3063631u, 0xa6edb0acu, 0xfa1cbe49u, 0x83d7574bu, 0x1b305f96u, 0x61c048cbu}} , .sourceIx = ty_pbw256 , .targetIx = ty_mw512 , .cost = 10861 /* milli weight units */ } ,[DECREMENT_16] = { .tag = JET , .jet = simplicity_decrement_16 , .cmr = {{0xe34db118u, 0x79272b32u, 0x7a3bd034u, 0xc0f61ef6u, 0x0a2be96fu, 0xdfe0b2d5u, 0x7ffe39ceu, 0x714c78fbu}} , .sourceIx = ty_w16 , .targetIx = ty_pbw16 , .cost = 85 /* milli weight units */ } ,[DECREMENT_32] = { .tag = JET , .jet = simplicity_decrement_32 , .cmr = {{0x019ead5au, 0x7305606du, 0xc950fb55u, 0x476d09c1u, 0x7d66f570u, 0xdab510b9u, 0x0d2a27e2u, 0x266599cfu}} , .sourceIx = ty_w32 , .targetIx = ty_pbw32 , .cost = 91 /* milli weight units */ } ,[DECREMENT_64] = { .tag = JET , .jet = simplicity_decrement_64 , .cmr = {{0x34752cf4u, 0xe1d0a431u, 0xf017a68bu, 0xebfab741u, 0xbbc88affu, 0xb57cc0b3u, 0x025ccfddu, 0x67622f35u}} , .sourceIx = ty_w64 , .targetIx = ty_pbw64 , .cost = 89 /* milli weight units */ } ,[DECREMENT_8] = { .tag = JET , .jet = simplicity_decrement_8 , .cmr = {{0x2892ceb3u, 0xb6ec5325u, 0xd0c1b9f5u, 0x20425e4bu, 0x05c2e1f4u, 0x37e0b3f5u, 0x81f41b9du, 0x0f7dff4du}} , .sourceIx = ty_w8 , .targetIx = ty_pbw8 , .cost = 79 /* milli weight units */ } ,[DIV_MOD_128_64] = { .tag = JET , .jet = simplicity_div_mod_128_64 , .cmr = {{0x2296b70fu, 0x600e8a21u, 0x4ad070b2u, 0x194a677du, 0x3051bc1cu, 0x49018397u, 0x5f2a1d3eu, 0x0cade378u}} , .sourceIx = ty_pw128w64 , .targetIx = ty_w128 , .cost = 208 /* milli weight units */ } ,[DIV_MOD_16] = { .tag = JET , .jet = simplicity_div_mod_16 , .cmr = {{0x648fab86u, 0x4374846au, 0xbf4f9d9du, 0xefe27561u, 0x4d33f482u, 0x9c36a47eu, 0xcb53d7bfu, 0xb605485fu}} , .sourceIx = ty_w32 , .targetIx = ty_w32 , .cost = 118 /* milli weight units */ } ,[DIV_MOD_32] = { .tag = JET , .jet = simplicity_div_mod_32 , .cmr = {{0xbd3d4d55u, 0x2d7b347bu, 0xd8a44e3eu, 0xe224c846u, 0xbe230ff6u, 0xe2044ddbu, 0x97f48e27u, 0xd20c4225u}} , .sourceIx = ty_w64 , .targetIx = ty_w64 , .cost = 115 /* milli weight units */ } ,[DIV_MOD_64] = { .tag = JET , .jet = simplicity_div_mod_64 , .cmr = {{0xfa6bad6au, 0x95e2aba4u, 0x305bfe91u, 0xcc47acc3u, 0xd99b92e6u, 0x75e69d3bu, 0x37bb0913u, 0x3d390d0fu}} , .sourceIx = ty_w128 , .targetIx = ty_w128 , .cost = 86 /* milli weight units */ } ,[DIV_MOD_8] = { .tag = JET , .jet = simplicity_div_mod_8 , .cmr = {{0x48cd501bu, 0xb2aa2acau, 0xe014fe20u, 0x8bb9941du, 0x07a9bffeu, 0x1ad6cd3du, 0x36fc6b08u, 0x60f6eba7u}} , .sourceIx = ty_w16 , .targetIx = ty_w16 , .cost = 128 /* milli weight units */ } ,[DIVIDE_16] = { .tag = JET , .jet = simplicity_divide_16 , .cmr = {{0x470b01a5u, 0x7c4f9d8fu, 0x997fcde0u, 0x06191611u, 0xdda4c98bu, 0xa2a5f1dau, 0x134ae4c2u, 0x2d52e920u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 98 /* milli weight units */ } ,[DIVIDE_32] = { .tag = JET , .jet = simplicity_divide_32 , .cmr = {{0xab03acd8u, 0x93610c3cu, 0x6582e7f7u, 0xfbe5e756u, 0x2574a7b2u, 0x6646f1c2u, 0xfdc6e76eu, 0x445a77a1u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 100 /* milli weight units */ } ,[DIVIDE_64] = { .tag = JET , .jet = simplicity_divide_64 , .cmr = {{0xebfc56fbu, 0xb8a47e73u, 0xffabb7eau, 0x228ac784u, 0x37be820eu, 0xddfa4781u, 0x4ccebd26u, 0x1bd8cfffu}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 101 /* milli weight units */ } ,[DIVIDE_8] = { .tag = JET , .jet = simplicity_divide_8 , .cmr = {{0x2ccfbc7cu, 0x02bf4d53u, 0x0493bb22u, 0x867a951du, 0x8ae91312u, 0x66875972u, 0x84e9bbb3u, 0xe1e7e349u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 108 /* milli weight units */ } ,[DIVIDES_16] = { .tag = JET , .jet = simplicity_divides_16 , .cmr = {{0x5fc3ac38u, 0x4d5f4540u, 0x4156971au, 0x768d93bcu, 0x064bc17cu, 0x15a37c27u, 0x019ddeefu, 0x17046dd4u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 93 /* milli weight units */ } ,[DIVIDES_32] = { .tag = JET , .jet = simplicity_divides_32 , .cmr = {{0xcc45b405u, 0x246438f7u, 0x65740b4fu, 0xb0a34dc8u, 0x1b347801u, 0x98863b0fu, 0xb186446au, 0xdfbb09deu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 87 /* milli weight units */ } ,[DIVIDES_64] = { .tag = JET , .jet = simplicity_divides_64 , .cmr = {{0xdc473bfdu, 0xec30ab98u, 0xd48cd088u, 0x84ef4fffu, 0xef3d4b16u, 0xad5c3711u, 0x2a2035b9u, 0x9bb77458u}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 91 /* milli weight units */ } ,[DIVIDES_8] = { .tag = JET , .jet = simplicity_divides_8 , .cmr = {{0x0b5502acu, 0x4f21f230u, 0xa09ccfafu, 0xfaac77a7u, 0xc41b2bf3u, 0x0b146848u, 0x1e4dfb98u, 0xb6187a0du}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 98 /* milli weight units */ } ,[EQ_1] = { .tag = JET , .jet = simplicity_eq_1 , .cmr = {{0x607f6b8fu, 0x5d25b80eu, 0x05a2bf79u, 0xd62e8707u, 0x99522cc3u, 0xe39ce962u, 0x57455293u, 0xf9b2b2edu}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 74 /* milli weight units */ } ,[EQ_16] = { .tag = JET , .jet = simplicity_eq_16 , .cmr = {{0xc996e42bu, 0x979abc53u, 0x0cc27163u, 0x6671e920u, 0x54876a1eu, 0xcaed1433u, 0xfd619a25u, 0xfe6d03adu}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 84 /* milli weight units */ } ,[EQ_256] = { .tag = JET , .jet = simplicity_eq_256 , .cmr = {{0x778d1506u, 0xc735d277u, 0x6b950facu, 0xefc159b6u, 0x78dec038u, 0x28cf0273u, 0xeeea64a9u, 0xda98c12cu}} , .sourceIx = ty_w512 , .targetIx = ty_b , .cost = 225 /* milli weight units */ } ,[EQ_32] = { .tag = JET , .jet = simplicity_eq_32 , .cmr = {{0x66d38903u, 0xe73b1a13u, 0x20c68a4au, 0x3970d71fu, 0x94ba9e2bu, 0x15168399u, 0x43fb15e4u, 0x4ebf57fbu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 88 /* milli weight units */ } ,[EQ_64] = { .tag = JET , .jet = simplicity_eq_64 , .cmr = {{0xd6a666b4u, 0xe0f9f575u, 0x508dbf3bu, 0x31ceea68u, 0x393c7db2u, 0xe98bc592u, 0xfdd26faeu, 0x837a0b87u}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 100 /* milli weight units */ } ,[EQ_8] = { .tag = JET , .jet = simplicity_eq_8 , .cmr = {{0x99787ba2u, 0x672dd0ebu, 0x4d7d2ea9u, 0x9449de8fu, 0x798e7cb1u, 0x81a5e166u, 0xe1a53f98u, 0x02b62064u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 95 /* milli weight units */ } ,[FE_ADD] = { .tag = JET , .jet = simplicity_fe_add , .cmr = {{0xb0593e18u, 0x7ee7333cu, 0x47a05467u, 0xdf66d582u, 0x0a6f5befu, 0x914a4b76u, 0xe5d16331u, 0x4b5ef20eu}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 755 /* milli weight units */ } ,[FE_INVERT] = { .tag = JET , .jet = simplicity_fe_invert , .cmr = {{0x343e9c90u, 0xf1285060u, 0x56b548d2u, 0xed5e223cu, 0x81f5b06au, 0x1ed86b7cu, 0xd9354057u, 0xaa595102u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 3175 /* milli weight units */ } ,[FE_IS_ODD] = { .tag = JET , .jet = simplicity_fe_is_odd , .cmr = {{0xdcf0375du, 0x20818a99u, 0xf723f812u, 0x3cbd051au, 0x3878a428u, 0x24b3740fu, 0x6821a5fau, 0x123f14c7u}} , .sourceIx = ty_w256 , .targetIx = ty_b , .cost = 290 /* milli weight units */ } ,[FE_IS_ZERO] = { .tag = JET , .jet = simplicity_fe_is_zero , .cmr = {{0x28ff4169u, 0x9a881aafu, 0xb7a976c0u, 0xc576353fu, 0x7fe54463u, 0xb6aa754cu, 0xf2c6329au, 0xf2650e3bu}} , .sourceIx = ty_w256 , .targetIx = ty_b , .cost = 268 /* milli weight units */ } ,[FE_MULTIPLY] = { .tag = JET , .jet = simplicity_fe_multiply , .cmr = {{0x5669929bu, 0x5f31fa3du, 0x02c5839du, 0xd06354cdu, 0x171635f3u, 0xa0727f32u, 0x2abfc994u, 0xba6290deu}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 808 /* milli weight units */ } ,[FE_MULTIPLY_BETA] = { .tag = JET , .jet = simplicity_fe_multiply_beta , .cmr = {{0x7a781345u, 0x0d82e935u, 0x690f433eu, 0x65df707au, 0x4dd17534u, 0xa00ddd40u, 0xdd85e3e3u, 0xf78402c3u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 579 /* milli weight units */ } ,[FE_NEGATE] = { .tag = JET , .jet = simplicity_fe_negate , .cmr = {{0x3b0d7b5cu, 0x2e6c3aebu, 0x5e00085bu, 0x9d30585au, 0xff054e32u, 0x5a998361u, 0x113bfd23u, 0x28c008f6u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 531 /* milli weight units */ } ,[FE_NORMALIZE] = { .tag = JET , .jet = simplicity_fe_normalize , .cmr = {{0xc51beffau, 0x215e9cdeu, 0x8e933bb9u, 0x4680bae0u, 0x12c4daabu, 0x3d04b6cbu, 0xf0733fd7u, 0x35733538u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 521 /* milli weight units */ } ,[FE_SQUARE] = { .tag = JET , .jet = simplicity_fe_square , .cmr = {{0x5a6e7b2eu, 0xac73f4e4u, 0x4dfa28fbu, 0x86bb117bu, 0x65606f28u, 0x74d565c9u, 0x799c63e0u, 0xfe692b1au}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 556 /* milli weight units */ } ,[FE_SQUARE_ROOT] = { .tag = JET , .jet = simplicity_fe_square_root , .cmr = {{0xe00142eau, 0x03094a30u, 0x4ac82bc1u, 0xe2d2dc71u, 0xfb064ed0u, 0x82856735u, 0xb14ff2c7u, 0xfaf036f0u}} , .sourceIx = ty_w256 , .targetIx = ty_mw256 , .cost = 10275 /* milli weight units */ } ,[FULL_ADD_16] = { .tag = JET , .jet = simplicity_full_add_16 , .cmr = {{0xfc9e5df8u, 0x3bfdb902u, 0x8c87d139u, 0xf8583903u, 0xcb2a0704u, 0x2a73e534u, 0x81deb52fu, 0xf1f1f884u}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw16 , .cost = 121 /* milli weight units */ } ,[FULL_ADD_32] = { .tag = JET , .jet = simplicity_full_add_32 , .cmr = {{0xa7d98d50u, 0xd045cb90u, 0x6b195e65u, 0x11879495u, 0xc8510959u, 0x49a9c01eu, 0x6039a84bu, 0x2a5ec909u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw32 , .cost = 119 /* milli weight units */ } ,[FULL_ADD_64] = { .tag = JET , .jet = simplicity_full_add_64 , .cmr = {{0x7aecc8c9u, 0x053bb2fbu, 0x170c1c97u, 0x2fd40025u, 0x64e152a0u, 0x6d9f4580u, 0x75e38c7au, 0x0698a7f4u}} , .sourceIx = ty_pbw128 , .targetIx = ty_pbw64 , .cost = 121 /* milli weight units */ } ,[FULL_ADD_8] = { .tag = JET , .jet = simplicity_full_add_8 , .cmr = {{0xed3ba5b7u, 0x9ea45b18u, 0x7a2d43e8u, 0xed802de1u, 0xed442659u, 0x6cbe32e7u, 0x57c85119u, 0x15ffa5cfu}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw8 , .cost = 127 /* milli weight units */ } ,[FULL_DECREMENT_16] = { .tag = JET , .jet = simplicity_full_decrement_16 , .cmr = {{0xd4c2eddau, 0x872c0550u, 0x6f792cf5u, 0x46a89d4du, 0x7cffcb1eu, 0x17f5da61u, 0x03100e7eu, 0x73a7737du}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw16 , .cost = 92 /* milli weight units */ } ,[FULL_DECREMENT_32] = { .tag = JET , .jet = simplicity_full_decrement_32 , .cmr = {{0x7cc2304du, 0x17431210u, 0x2e9b7363u, 0x45c77f77u, 0x1d1f6a9cu, 0x9e1d1cd8u, 0xdb8cb461u, 0x3980c8c2u}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw32 , .cost = 107 /* milli weight units */ } ,[FULL_DECREMENT_64] = { .tag = JET , .jet = simplicity_full_decrement_64 , .cmr = {{0x15c16345u, 0x4bcd7544u, 0x30da5579u, 0xbbcaad26u, 0xe57e95c7u, 0x72224b7bu, 0x83c705f7u, 0xdeb64aa6u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw64 , .cost = 81 /* milli weight units */ } ,[FULL_DECREMENT_8] = { .tag = JET , .jet = simplicity_full_decrement_8 , .cmr = {{0x7c5e94a9u, 0x98028182u, 0x1737b1ceu, 0x73bfda4cu, 0x79ef649bu, 0x3d05cc1cu, 0x00c4a8b6u, 0x4b949bbeu}} , .sourceIx = ty_pbw8 , .targetIx = ty_pbw8 , .cost = 91 /* milli weight units */ } ,[FULL_INCREMENT_16] = { .tag = JET , .jet = simplicity_full_increment_16 , .cmr = {{0x81380adau, 0xa3a547f1u, 0xbc4bbb64u, 0x6bda9d9fu, 0xb7bd4dc1u, 0xb3a9f3ddu, 0x220b56a4u, 0x7c2798fbu}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw16 , .cost = 89 /* milli weight units */ } ,[FULL_INCREMENT_32] = { .tag = JET , .jet = simplicity_full_increment_32 , .cmr = {{0xa760a844u, 0x9a2ab5deu, 0xdb4ee51bu, 0xf5c25a8fu, 0x06af0666u, 0xdf7fc419u, 0xb498b909u, 0x76d698cbu}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw32 , .cost = 104 /* milli weight units */ } ,[FULL_INCREMENT_64] = { .tag = JET , .jet = simplicity_full_increment_64 , .cmr = {{0xc6af30ddu, 0x286d6e21u, 0xc38860edu, 0x1e2f212au, 0x21b2fd1eu, 0xdeadb5e0u, 0xfce2e3fdu, 0x75b7f3c2u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw64 , .cost = 99 /* milli weight units */ } ,[FULL_INCREMENT_8] = { .tag = JET , .jet = simplicity_full_increment_8 , .cmr = {{0xd304ea28u, 0xa95d496du, 0x14b4f2fbu, 0x5c860372u, 0xecf247beu, 0xfde3ea3bu, 0x2ad67bceu, 0x99039dbcu}} , .sourceIx = ty_pbw8 , .targetIx = ty_pbw8 , .cost = 72 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_1] = { .tag = JET , .jet = simplicity_full_left_shift_16_1 , .cmr = {{0x14dcc346u, 0x6fa828a3u, 0xf0740451u, 0xb8037d7au, 0xd603eadcu, 0x80aaeadcu, 0x664434acu, 0x2ad7fd9cu}} , .sourceIx = ty_pw16b , .targetIx = ty_pbw16 , .cost = 83 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_2] = { .tag = JET , .jet = simplicity_full_left_shift_16_2 , .cmr = {{0xafb7e928u, 0xb052c228u, 0x7921662cu, 0xd8ab122fu, 0xe074efd2u, 0x51a5c9cfu, 0xbcaa369du, 0x06337392u}} , .sourceIx = ty_pw16w2 , .targetIx = ty_pw2w16 , .cost = 83 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_4] = { .tag = JET , .jet = simplicity_full_left_shift_16_4 , .cmr = {{0x166f348cu, 0x59e26f89u, 0xa83a991fu, 0x67e5dbf7u, 0x10cfae3du, 0x6d969382u, 0x82bb44c1u, 0xafa7109bu}} , .sourceIx = ty_pw16w4 , .targetIx = ty_pw4w16 , .cost = 89 /* milli weight units */ } ,[FULL_LEFT_SHIFT_16_8] = { .tag = JET , .jet = simplicity_full_left_shift_16_8 , .cmr = {{0xc0cd015du, 0xe8ac4fccu, 0xd8db89f4u, 0xe5142fdeu, 0x279755b5u, 0x42a24f57u, 0xa2a3c7c1u, 0xf50d1db5u}} , .sourceIx = ty_pw16w8 , .targetIx = ty_pw8w16 , .cost = 65 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_1] = { .tag = JET , .jet = simplicity_full_left_shift_32_1 , .cmr = {{0xce33b5d0u, 0xc58d2d0bu, 0x9b5a9944u, 0xd3dabda0u, 0x23cd4464u, 0x7be67cf4u, 0x082830bbu, 0x205f8fbbu}} , .sourceIx = ty_pw32b , .targetIx = ty_pbw32 , .cost = 84 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_16] = { .tag = JET , .jet = simplicity_full_left_shift_32_16 , .cmr = {{0x1cb36e6fu, 0x99308515u, 0xd4b71190u, 0x9c574b21u, 0x24c1ff42u, 0x2d8d7d94u, 0x82e25d87u, 0x88b3b957u}} , .sourceIx = ty_pw32w16 , .targetIx = ty_pw16w32 , .cost = 81 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_2] = { .tag = JET , .jet = simplicity_full_left_shift_32_2 , .cmr = {{0x3faea9b5u, 0x73fc069du, 0x8f430facu, 0xa897b687u, 0x1ea09573u, 0xc715094bu, 0x1f1be081u, 0x8488a716u}} , .sourceIx = ty_pw32w2 , .targetIx = ty_pw2w32 , .cost = 67 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_4] = { .tag = JET , .jet = simplicity_full_left_shift_32_4 , .cmr = {{0xcdbb0d23u, 0x31059011u, 0x3c934fe6u, 0x6004d2a1u, 0x1da9cbf8u, 0x873d00deu, 0xe7f02296u, 0xff0a2f12u}} , .sourceIx = ty_pw32w4 , .targetIx = ty_pw4w32 , .cost = 84 /* milli weight units */ } ,[FULL_LEFT_SHIFT_32_8] = { .tag = JET , .jet = simplicity_full_left_shift_32_8 , .cmr = {{0xccd924e1u, 0xa6184942u, 0x0ff62ed8u, 0xb245a3aau, 0x18c98c41u, 0xf9c5a3c0u, 0xb885863cu, 0x449b7d14u}} , .sourceIx = ty_pw32w8 , .targetIx = ty_pw8w32 , .cost = 91 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_1] = { .tag = JET , .jet = simplicity_full_left_shift_64_1 , .cmr = {{0xd463ccdcu, 0x7fd14e5eu, 0x894162b2u, 0xae714128u, 0xa10dc920u, 0x00b54c84u, 0x3b649ccbu, 0x775626e5u}} , .sourceIx = ty_pw64b , .targetIx = ty_pbw64 , .cost = 99 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_16] = { .tag = JET , .jet = simplicity_full_left_shift_64_16 , .cmr = {{0x882dce21u, 0x2a0e61f8u, 0xf94cb5e3u, 0x2e00a528u, 0x7cf64f20u, 0xc21fca84u, 0xf1e3df7fu, 0x4a6291cdu}} , .sourceIx = ty_pw64w16 , .targetIx = ty_pw16w64 , .cost = 90 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_2] = { .tag = JET , .jet = simplicity_full_left_shift_64_2 , .cmr = {{0x48c89b19u, 0x1a51b6abu, 0x034c80eau, 0xff348238u, 0xd93fb31cu, 0x1e92e7f2u, 0xae49317eu, 0x0e33f82du}} , .sourceIx = ty_pw64w2 , .targetIx = ty_pw2w64 , .cost = 94 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_32] = { .tag = JET , .jet = simplicity_full_left_shift_64_32 , .cmr = {{0x39759073u, 0x33e12730u, 0x6255b7f8u, 0x8939e285u, 0x7f42ae1bu, 0xf0c66240u, 0xa8224c8du, 0xa38bb1beu}} , .sourceIx = ty_pw64w32 , .targetIx = ty_pw32w64 , .cost = 86 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_4] = { .tag = JET , .jet = simplicity_full_left_shift_64_4 , .cmr = {{0x293132ebu, 0x15ddf417u, 0x74b0005au, 0x3b5c5095u, 0x9fa8982bu, 0x759e8328u, 0x27c74fa8u, 0x2850666cu}} , .sourceIx = ty_pw64w4 , .targetIx = ty_pw4w64 , .cost = 94 /* milli weight units */ } ,[FULL_LEFT_SHIFT_64_8] = { .tag = JET , .jet = simplicity_full_left_shift_64_8 , .cmr = {{0xe6abded8u, 0xbe585eb0u, 0xb6d46e0cu, 0x5eb28a74u, 0x5f4e5c56u, 0xfd6521f8u, 0xf396cb21u, 0xa758f74cu}} , .sourceIx = ty_pw64w8 , .targetIx = ty_pw8w64 , .cost = 86 /* milli weight units */ } ,[FULL_LEFT_SHIFT_8_1] = { .tag = JET , .jet = simplicity_full_left_shift_8_1 , .cmr = {{0x733fed08u, 0x47a2ffacu, 0x9aabf50au, 0x2feb5059u, 0x8984f16du, 0x8b732468u, 0xb3d315c0u, 0x1ea4299bu}} , .sourceIx = ty_pw8b , .targetIx = ty_pbw8 , .cost = 96 /* milli weight units */ } ,[FULL_LEFT_SHIFT_8_2] = { .tag = JET , .jet = simplicity_full_left_shift_8_2 , .cmr = {{0xb4474d0bu, 0xa1cf4fa2u, 0xd64cd4feu, 0x67bdc92cu, 0xb89efa70u, 0xcb99af77u, 0x91bf7ef6u, 0xe909d2c7u}} , .sourceIx = ty_pw8w2 , .targetIx = ty_pw2w8 , .cost = 96 /* milli weight units */ } ,[FULL_LEFT_SHIFT_8_4] = { .tag = JET , .jet = simplicity_full_left_shift_8_4 , .cmr = {{0x8eb522b9u, 0x970474adu, 0xbb7ab0deu, 0x37c4e7a0u, 0x56a1cb21u, 0x2e4103e4u, 0xa8cbbbb6u, 0x3d975606u}} , .sourceIx = ty_pw8w4 , .targetIx = ty_pw4w8 , .cost = 85 /* milli weight units */ } ,[FULL_MULTIPLY_16] = { .tag = JET , .jet = simplicity_full_multiply_16 , .cmr = {{0x88470cbfu, 0x9b4dec37u, 0xea05d7b6u, 0x30f2f112u, 0x547567d3u, 0x4f33d96eu, 0x5f611bd9u, 0xda97abb5u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 112 /* milli weight units */ } ,[FULL_MULTIPLY_32] = { .tag = JET , .jet = simplicity_full_multiply_32 , .cmr = {{0x28040600u, 0xa66e1a0cu, 0x52258520u, 0x488b94c8u, 0x20c6cf86u, 0xca27ae39u, 0x034dddcau, 0xb904d1d5u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 96 /* milli weight units */ } ,[FULL_MULTIPLY_64] = { .tag = JET , .jet = simplicity_full_multiply_64 , .cmr = {{0x53014f35u, 0xa8df2091u, 0xaf3ef9b8u, 0xd16b38b9u, 0xbc9661bfu, 0xdbc95733u, 0x3fba2a94u, 0x8c1e8c25u}} , .sourceIx = ty_w256 , .targetIx = ty_w128 , .cost = 127 /* milli weight units */ } ,[FULL_MULTIPLY_8] = { .tag = JET , .jet = simplicity_full_multiply_8 , .cmr = {{0xd3d24554u, 0xc466dd60u, 0x37545247u, 0x36a71eb2u, 0x35def9b5u, 0x06965e32u, 0xd56826e1u, 0x9fbad6c1u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 109 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_1] = { .tag = JET , .jet = simplicity_full_right_shift_16_1 , .cmr = {{0xb379e296u, 0xe9a98fb3u, 0xb5662b8bu, 0xa04e3cc1u, 0xa43c7442u, 0x9e931233u, 0xfdd7fc8fu, 0xe6b7a2e0u}} , .sourceIx = ty_pbw16 , .targetIx = ty_pw16b , .cost = 80 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_2] = { .tag = JET , .jet = simplicity_full_right_shift_16_2 , .cmr = {{0xaeb8c608u, 0x06a47920u, 0x7758e390u, 0x83b4a9a7u, 0xa14da4eeu, 0x9bc1097fu, 0xc5cb4b75u, 0x540d7578u}} , .sourceIx = ty_pw2w16 , .targetIx = ty_pw16w2 , .cost = 79 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_4] = { .tag = JET , .jet = simplicity_full_right_shift_16_4 , .cmr = {{0x60b7f084u, 0x75cc0cceu, 0x64dca12du, 0x9f6a919cu, 0x30618110u, 0xeda14065u, 0x929c004eu, 0x7fc1b0fbu}} , .sourceIx = ty_pw4w16 , .targetIx = ty_pw16w4 , .cost = 88 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_16_8] = { .tag = JET , .jet = simplicity_full_right_shift_16_8 , .cmr = {{0xf79dba3eu, 0x0af3d6a5u, 0x59a9e9dfu, 0xfea710afu, 0x623fe6e6u, 0x644b8979u, 0x95d71b8au, 0x4167ddb0u}} , .sourceIx = ty_pw8w16 , .targetIx = ty_pw16w8 , .cost = 57 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_1] = { .tag = JET , .jet = simplicity_full_right_shift_32_1 , .cmr = {{0xad0d5c75u, 0xea684371u, 0x91770d7fu, 0xdf804bbcu, 0x9d573d5fu, 0x10199823u, 0xd809c9c4u, 0x6cd275adu}} , .sourceIx = ty_pbw32 , .targetIx = ty_pw32b , .cost = 74 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_16] = { .tag = JET , .jet = simplicity_full_right_shift_32_16 , .cmr = {{0x455299fdu, 0x6f42ab49u, 0xdbb709e6u, 0x5a3b5366u, 0x250bdc54u, 0x5d6229e8u, 0xe236056du, 0xdd1977fdu}} , .sourceIx = ty_pw16w32 , .targetIx = ty_pw32w16 , .cost = 64 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_2] = { .tag = JET , .jet = simplicity_full_right_shift_32_2 , .cmr = {{0x44384b15u, 0x06d443d2u, 0xf8a2882bu, 0x4563d793u, 0x1a7ebce6u, 0x4acf0d02u, 0xee59ec69u, 0xd3065239u}} , .sourceIx = ty_pw2w32 , .targetIx = ty_pw32w2 , .cost = 63 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_4] = { .tag = JET , .jet = simplicity_full_right_shift_32_4 , .cmr = {{0x2e9a8ab5u, 0xa1817bd0u, 0xb8a46626u, 0x994917a0u, 0xde1a745eu, 0x99520ce6u, 0xebcc67d4u, 0x636551b7u}} , .sourceIx = ty_pw4w32 , .targetIx = ty_pw32w4 , .cost = 71 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_32_8] = { .tag = JET , .jet = simplicity_full_right_shift_32_8 , .cmr = {{0xaf47d4f9u, 0x6e7d8026u, 0xd44e6ecau, 0x1b807f73u, 0x344ce2eau, 0xf700b2c8u, 0x2b4bb002u, 0x61a86f94u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_pw32w8 , .cost = 84 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_1] = { .tag = JET , .jet = simplicity_full_right_shift_64_1 , .cmr = {{0x03afb547u, 0xc30913f1u, 0x6f3e370du, 0x7f9ca029u, 0x0b615b42u, 0x85051bb9u, 0x3c3c1a9bu, 0x72ee8de4u}} , .sourceIx = ty_pbw64 , .targetIx = ty_pw64b , .cost = 99 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_16] = { .tag = JET , .jet = simplicity_full_right_shift_64_16 , .cmr = {{0x1fb056fcu, 0xb690cee3u, 0xcff72c7du, 0xecda806du, 0x2146c492u, 0xae731a6bu, 0x94b8bb4fu, 0x1599b0ccu}} , .sourceIx = ty_pw16w64 , .targetIx = ty_pw64w16 , .cost = 86 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_2] = { .tag = JET , .jet = simplicity_full_right_shift_64_2 , .cmr = {{0x0673bff2u, 0x1e375e5du, 0xbcaf3804u, 0x664825ddu, 0x674844d2u, 0xfdb784a4u, 0xfefbc925u, 0xcf6b27adu}} , .sourceIx = ty_pw2w64 , .targetIx = ty_pw64w2 , .cost = 86 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_32] = { .tag = JET , .jet = simplicity_full_right_shift_64_32 , .cmr = {{0x356f7dd4u, 0x6ba33f84u, 0xb06672fdu, 0xe9a2972eu, 0x80f3ea96u, 0x5ae8bc0bu, 0xff67aa2fu, 0x69f10b56u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_pw64w32 , .cost = 73 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_4] = { .tag = JET , .jet = simplicity_full_right_shift_64_4 , .cmr = {{0x4c25f601u, 0x1fd3d1acu, 0x18e11eb4u, 0x3061fad6u, 0x9f3ce39fu, 0x7a99cedeu, 0x50cc85bfu, 0x88bfba82u}} , .sourceIx = ty_pw4w64 , .targetIx = ty_pw64w4 , .cost = 93 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_64_8] = { .tag = JET , .jet = simplicity_full_right_shift_64_8 , .cmr = {{0xa51df944u, 0x8602fa81u, 0x001aa1b5u, 0xb13be88du, 0x4b2f4d0fu, 0x60740801u, 0xcef99100u, 0x2fe37d6du}} , .sourceIx = ty_pw8w64 , .targetIx = ty_pw64w8 , .cost = 99 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_8_1] = { .tag = JET , .jet = simplicity_full_right_shift_8_1 , .cmr = {{0xd9d4b16du, 0x37e4eb5cu, 0xc5150426u, 0xe3e86cf6u, 0x0abbdfa1u, 0xd0ecb415u, 0x82965e80u, 0x00cbd291u}} , .sourceIx = ty_pbw8 , .targetIx = ty_pw8b , .cost = 88 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_8_2] = { .tag = JET , .jet = simplicity_full_right_shift_8_2 , .cmr = {{0x079aa166u, 0x17198ad5u, 0xdf2c98a6u, 0x3af76c1bu, 0x3e120fd2u, 0x106b225fu, 0x63fd06acu, 0x571d04a4u}} , .sourceIx = ty_pw2w8 , .targetIx = ty_pw8w2 , .cost = 86 /* milli weight units */ } ,[FULL_RIGHT_SHIFT_8_4] = { .tag = JET , .jet = simplicity_full_right_shift_8_4 , .cmr = {{0x9d9d3f63u, 0x8a846386u, 0xa21e715fu, 0x39461686u, 0x4a2ef798u, 0x4a88cd95u, 0x50556629u, 0x7be7e06cu}} , .sourceIx = ty_pw4w8 , .targetIx = ty_pw8w4 , .cost = 89 /* milli weight units */ } ,[FULL_SUBTRACT_16] = { .tag = JET , .jet = simplicity_full_subtract_16 , .cmr = {{0x1fc88e23u, 0x29f4aaf1u, 0x2b30513fu, 0x7a21cf5du, 0x8de24b60u, 0x0a19a217u, 0x41281b4du, 0x61aac633u}} , .sourceIx = ty_pbw32 , .targetIx = ty_pbw16 , .cost = 121 /* milli weight units */ } ,[FULL_SUBTRACT_32] = { .tag = JET , .jet = simplicity_full_subtract_32 , .cmr = {{0x782705fbu, 0x42e36a7eu, 0xf831200cu, 0x617738d3u, 0x1e13b1d0u, 0xe7ceed69u, 0x3f133388u, 0x35b30acbu}} , .sourceIx = ty_pbw64 , .targetIx = ty_pbw32 , .cost = 116 /* milli weight units */ } ,[FULL_SUBTRACT_64] = { .tag = JET , .jet = simplicity_full_subtract_64 , .cmr = {{0xb2856a91u, 0x80231beeu, 0x3cb89230u, 0xf75c292au, 0xf3e75239u, 0xdbeb3965u, 0x48441e6bu, 0x5a27e813u}} , .sourceIx = ty_pbw128 , .targetIx = ty_pbw64 , .cost = 98 /* milli weight units */ } ,[FULL_SUBTRACT_8] = { .tag = JET , .jet = simplicity_full_subtract_8 , .cmr = {{0x6885e141u, 0xae234c1eu, 0x2a7e4f23u, 0x52989390u, 0x36969c95u, 0x0f2cefd4u, 0x59b498acu, 0x3dd89220u}} , .sourceIx = ty_pbw16 , .targetIx = ty_pbw8 , .cost = 126 /* milli weight units */ } ,[GE_IS_ON_CURVE] = { .tag = JET , .jet = simplicity_ge_is_on_curve , .cmr = {{0x69f0e7a0u, 0xc5fff870u, 0x84ed6925u, 0xf8db762eu, 0x419e057bu, 0x96834dceu, 0x9699b0b0u, 0x09423059u}} , .sourceIx = ty_w512 , .targetIx = ty_b , .cost = 642 /* milli weight units */ } ,[GE_NEGATE] = { .tag = JET , .jet = simplicity_ge_negate , .cmr = {{0x1ed0ced8u, 0xdd2558e3u, 0x485f6fc3u, 0x2d69a240u, 0x5ecaee31u, 0x2dc4dc65u, 0xe0fd3477u, 0x73f5983du}} , .sourceIx = ty_w512 , .targetIx = ty_w512 , .cost = 945 /* milli weight units */ } ,[GEJ_ADD] = { .tag = JET , .jet = simplicity_gej_add , .cmr = {{0x5a1c3103u, 0x49e8ff5cu, 0x5a61ac3eu, 0x10123f74u, 0xe87faba1u, 0x4c78bc83u, 0xf9e34136u, 0x87ecf28bu}} , .sourceIx = ty_ppw512w256pw512w256 , .targetIx = ty_pw512w256 , .cost = 2897 /* milli weight units */ } ,[GEJ_DOUBLE] = { .tag = JET , .jet = simplicity_gej_double , .cmr = {{0x1edd0582u, 0xe2fcad99u, 0xb12d506du, 0x29b50a63u, 0x017f6769u, 0x28be5113u, 0x69006e07u, 0xcb80d982u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_pw512w256 , .cost = 1764 /* milli weight units */ } ,[GEJ_EQUIV] = { .tag = JET , .jet = simplicity_gej_equiv , .cmr = {{0x02747105u, 0x9487a12cu, 0xa207f094u, 0x0594d6cdu, 0x87fc930au, 0x8b5b3143u, 0x4a16a2d6u, 0x7f1d8dd4u}} , .sourceIx = ty_ppw512w256pw512w256 , .targetIx = ty_b , .cost = 2220 /* milli weight units */ } ,[GEJ_GE_ADD] = { .tag = JET , .jet = simplicity_gej_ge_add , .cmr = {{0x1ea710d5u, 0x6eafee32u, 0x5d2607ddu, 0xb45ff017u, 0x0adec2e0u, 0xee9bcc68u, 0xe4b93e1du, 0xe6ad3568u}} , .sourceIx = ty_ppw512w256w512 , .targetIx = ty_pw512w256 , .cost = 2477 /* milli weight units */ } ,[GEJ_GE_ADD_EX] = { .tag = JET , .jet = simplicity_gej_ge_add_ex , .cmr = {{0x78f0871bu, 0x8173abdeu, 0x71871126u, 0x3b3ac1d9u, 0x22337ed5u, 0xed138d29u, 0x4962d65cu, 0xe559bd92u}} , .sourceIx = ty_ppw512w256w512 , .targetIx = ty_pw256pw512w256 , .cost = 2719 /* milli weight units */ } ,[GEJ_GE_EQUIV] = { .tag = JET , .jet = simplicity_gej_ge_equiv , .cmr = {{0xba899a00u, 0x6216d1c9u, 0x3bd5ecbeu, 0x0080d907u, 0x8a500a72u, 0x9bbd396au, 0x004af51du, 0x4ff7d93au}} , .sourceIx = ty_ppw512w256w512 , .targetIx = ty_b , .cost = 1765 /* milli weight units */ } ,[GEJ_INFINITY] = { .tag = JET , .jet = simplicity_gej_infinity , .cmr = {{0x88a952dbu, 0x3816e942u, 0x59a67537u, 0xfa8fca1au, 0x35a907a8u, 0x6f51ede4u, 0x51fd32ecu, 0x253d9c62u}} , .sourceIx = ty_u , .targetIx = ty_pw512w256 , .cost = 716 /* milli weight units */ } ,[GEJ_IS_INFINITY] = { .tag = JET , .jet = simplicity_gej_is_infinity , .cmr = {{0x2980a735u, 0x414e4321u, 0xafeffefau, 0x8837edb0u, 0xa3309a33u, 0x7d59b7bdu, 0xea921c13u, 0x056b0428u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_b , .cost = 666 /* milli weight units */ } ,[GEJ_IS_ON_CURVE] = { .tag = JET , .jet = simplicity_gej_is_on_curve , .cmr = {{0x0187e1e5u, 0xef7634a5u, 0xf016124du, 0x4feb5a93u, 0xdde6aa78u, 0x176cda48u, 0xb165a9aau, 0x8e0449f2u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_b , .cost = 1016 /* milli weight units */ } ,[GEJ_NEGATE] = { .tag = JET , .jet = simplicity_gej_negate , .cmr = {{0xb32c74cau, 0xb2c7500bu, 0x73f8ec05u, 0x60fe23fcu, 0x4c21aa66u, 0x596d7f2au, 0xcf496788u, 0x6b76d856u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_pw512w256 , .cost = 1381 /* milli weight units */ } ,[GEJ_NORMALIZE] = { .tag = JET , .jet = simplicity_gej_normalize , .cmr = {{0x5de0976au, 0xe7f38b36u, 0xf0022814u, 0x966db2bau, 0xed5c4767u, 0x14944d74u, 0x1a8979c4u, 0xbcf8be25u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_mw512 , .cost = 4099 /* milli weight units */ } ,[GEJ_RESCALE] = { .tag = JET , .jet = simplicity_gej_rescale , .cmr = {{0xdcfc72a7u, 0x68d5be77u, 0x0f8db278u, 0xaeafd18eu, 0x27704c64u, 0xf8b40fa6u, 0xfe54ca94u, 0x727a076eu}} , .sourceIx = ty_ppw512w256w256 , .targetIx = ty_pw512w256 , .cost = 1908 /* milli weight units */ } ,[GEJ_X_EQUIV] = { .tag = JET , .jet = simplicity_gej_x_equiv , .cmr = {{0x52cc2147u, 0x09c0d9fcu, 0xa9db1d09u, 0xcc807c75u, 0xcf5a6313u, 0xca540a77u, 0x2d4ea992u, 0x1f37e624u}} , .sourceIx = ty_pw256pw512w256 , .targetIx = ty_b , .cost = 1047 /* milli weight units */ } ,[GEJ_Y_IS_ODD] = { .tag = JET , .jet = simplicity_gej_y_is_odd , .cmr = {{0xfe0106afu, 0xb9d9e24fu, 0xd4dbe545u, 0x11fe272fu, 0x4dcb307au, 0x0ea56d59u, 0x1ceb93abu, 0x4bf88745u}} , .sourceIx = ty_pw512w256 , .targetIx = ty_b , .cost = 3651 /* milli weight units */ } ,[GENERATE] = { .tag = JET , .jet = simplicity_generate , .cmr = {{0xdf44e17du, 0x2a559dd0u, 0xa7034954u, 0xab333777u, 0x78b151f1u, 0xcd1e4f9fu, 0xd31b361du, 0x34a8d973u}} , .sourceIx = ty_w256 , .targetIx = ty_pw512w256 , .cost = 50071 /* milli weight units */ } ,[GENESIS_BLOCK_HASH] = { .tag = JET , .jet = simplicity_genesis_block_hash , .cmr = {{0x0060b60du, 0x02b13360u, 0x72846acfu, 0xf44dd0f4u, 0x346c74a3u, 0x5e7b5642u, 0x3f9519c4u, 0x42d15dafu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 148 /* milli weight units */ } ,[HASH_TO_CURVE] = { .tag = JET , .jet = simplicity_hash_to_curve , .cmr = {{0x76f7ca1du, 0xb944ee31u, 0x5ed362feu, 0xe0673c58u, 0x94f8853bu, 0x44607090u, 0x1b857901u, 0xf9499d9bu}} , .sourceIx = ty_w256 , .targetIx = ty_w512 , .cost = 68094 /* milli weight units */ } ,[HIGH_1] = { .tag = JET , .jet = simplicity_high_1 , .cmr = {{0xc32d877eu, 0x670d6c03u, 0x7cb33533u, 0x289e19a7u, 0x24c368aau, 0x7551daa6u, 0xd2dacccdu, 0x8c95f4d0u}} , .sourceIx = ty_u , .targetIx = ty_b , .cost = 57 /* milli weight units */ } ,[HIGH_16] = { .tag = JET , .jet = simplicity_high_16 , .cmr = {{0x4164ab6eu, 0x2ff8eef6u, 0x3c06c080u, 0xf1dec697u, 0x0b4c5c31u, 0xc02305abu, 0xccd8ed2cu, 0x5e1c45ceu}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 66 /* milli weight units */ } ,[HIGH_32] = { .tag = JET , .jet = simplicity_high_32 , .cmr = {{0xd3a7ce9cu, 0xd5d5fb67u, 0x9a98ef57u, 0xb8632277u, 0x0cb66fb6u, 0xf0616e16u, 0x34cfa84cu, 0x8f6809c6u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 58 /* milli weight units */ } ,[HIGH_64] = { .tag = JET , .jet = simplicity_high_64 , .cmr = {{0x4af91fafu, 0x8e39f4dau, 0x7c28a879u, 0x6594a922u, 0x8213d732u, 0x3eea2ca6u, 0x30752ce4u, 0xc57f16e1u}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 68 /* milli weight units */ } ,[HIGH_8] = { .tag = JET , .jet = simplicity_high_8 , .cmr = {{0xcbd78d50u, 0xaf779985u, 0x5adc4903u, 0xdbbefc13u, 0x45d51484u, 0xf03d3c75u, 0x5caaa5cau, 0xa97d4a14u}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 59 /* milli weight units */ } ,[INCREMENT_16] = { .tag = JET , .jet = simplicity_increment_16 , .cmr = {{0xdf274888u, 0xce4cebddu, 0x5708b38du, 0xc3dbb19cu, 0xc2f0364bu, 0x2463e99cu, 0xf5aab4f8u, 0xa23ea58au}} , .sourceIx = ty_w16 , .targetIx = ty_pbw16 , .cost = 69 /* milli weight units */ } ,[INCREMENT_32] = { .tag = JET , .jet = simplicity_increment_32 , .cmr = {{0x54f757aeu, 0xa76bc7a3u, 0x9fc43d19u, 0xb8dd563au, 0x6807df02u, 0x77a56fcbu, 0x501089ceu, 0x7d06774cu}} , .sourceIx = ty_w32 , .targetIx = ty_pbw32 , .cost = 92 /* milli weight units */ } ,[INCREMENT_64] = { .tag = JET , .jet = simplicity_increment_64 , .cmr = {{0x79ed5f77u, 0x99fb09dau, 0x510429a2u, 0x0128bed0u, 0x91d85876u, 0x47071285u, 0xcdec3a0cu, 0x95709e5bu}} , .sourceIx = ty_w64 , .targetIx = ty_pbw64 , .cost = 87 /* milli weight units */ } ,[INCREMENT_8] = { .tag = JET , .jet = simplicity_increment_8 , .cmr = {{0x0c717e84u, 0xdf67823fu, 0x5741b3d5u, 0x5dbeb472u, 0x9c2bd62fu, 0x5d1def3cu, 0xabccdd6cu, 0xb8dcb56cu}} , .sourceIx = ty_w8 , .targetIx = ty_pbw8 , .cost = 85 /* milli weight units */ } ,[INPUT_AMOUNT] = { .tag = JET , .jet = simplicity_input_amount , .cmr = {{0xdd65ac32u, 0xc87d996bu, 0x407200feu, 0xefc479a9u, 0x119c1f28u, 0xcaa488b0u, 0xaac3acf5u, 0x9378d6bau}} , .sourceIx = ty_w32 , .targetIx = ty_mpspbw256w256spbw256w64 , .cost = 285 /* milli weight units */ } ,[INPUT_AMOUNTS_HASH] = { .tag = JET , .jet = simplicity_input_amounts_hash , .cmr = {{0x2b4df47eu, 0x758ffe88u, 0xe9cd5d39u, 0x6df3d7f9u, 0xec2fbd5au, 0x5395a6d8u, 0xc1ab7044u, 0x00c64f70u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 140 /* milli weight units */ } ,[INPUT_ANNEX_HASH] = { .tag = JET , .jet = simplicity_input_annex_hash , .cmr = {{0x0fd9e4c6u, 0x316b3728u, 0x6e885443u, 0x0e7d7418u, 0x21dc8954u, 0x4a3a59f0u, 0x3dfa40e5u, 0x32b8107fu}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 90 /* milli weight units */ } ,[INPUT_ANNEXES_HASH] = { .tag = JET , .jet = simplicity_input_annexes_hash , .cmr = {{0xded1522eu, 0xfa5a2b37u, 0x6173e440u, 0xde227ad0u, 0xc92be2edu, 0xce7c23b5u, 0x1480e50au, 0x77fc564bu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 155 /* milli weight units */ } ,[INPUT_ASSET] = { .tag = JET , .jet = simplicity_input_asset , .cmr = {{0x872b3653u, 0xd65ae7f9u, 0x166cbf70u, 0xd4fd3140u, 0x4798884du, 0x611b647fu, 0xb9f4a307u, 0xc48011b8u}} , .sourceIx = ty_w32 , .targetIx = ty_mspbw256w256 , .cost = 162 /* milli weight units */ } ,[INPUT_HASH] = { .tag = JET , .jet = simplicity_input_hash , .cmr = {{0x3309bb46u, 0xb3158d23u, 0x124f8cedu, 0xaaa1ed3bu, 0x09a8aefeu, 0x81212e11u, 0x335523b6u, 0xb207c544u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 965 /* milli weight units */ } ,[INPUT_OUTPOINTS_HASH] = { .tag = JET , .jet = simplicity_input_outpoints_hash , .cmr = {{0x140a2baeu, 0xad083baau, 0xc806128au, 0xb649e52bu, 0xbd3c6456u, 0x700cbcfcu, 0x6dbb2959u, 0x173a4df2u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 142 /* milli weight units */ } ,[INPUT_PEGIN] = { .tag = JET , .jet = simplicity_input_pegin , .cmr = {{0xdb376f4au, 0xe84ec051u, 0xa494d766u, 0x8039727bu, 0x53353be5u, 0xae045be7u, 0x6c4b04dau, 0xbd5bbfbbu}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 151 /* milli weight units */ } ,[INPUT_PREV_OUTPOINT] = { .tag = JET , .jet = simplicity_input_prev_outpoint , .cmr = {{0x91f4d6ecu, 0x484f60cau, 0xe9297858u, 0xcac47dadu, 0x50db07dcu, 0x1f937ac6u, 0x144c9cb4u, 0xa9ef79d2u}} , .sourceIx = ty_w32 , .targetIx = ty_mpw256w32 , .cost = 160 /* milli weight units */ } ,[INPUT_SCRIPT_HASH] = { .tag = JET , .jet = simplicity_input_script_hash , .cmr = {{0xc316df21u, 0x778e6241u, 0x05ca5990u, 0x4b9208e2u, 0xd423228bu, 0x3eb1cf68u, 0xb8eca47bu, 0xbc7b2ff3u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 147 /* milli weight units */ } ,[INPUT_SCRIPT_SIG_HASH] = { .tag = JET , .jet = simplicity_input_script_sig_hash , .cmr = {{0x941f2b4fu, 0x3b7f2097u, 0xd6ea00e9u, 0x7c1e2ba0u, 0x1cb26487u, 0xc5d2f472u, 0x3738b37cu, 0x732c05c4u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 153 /* milli weight units */ } ,[INPUT_SCRIPT_SIGS_HASH] = { .tag = JET , .jet = simplicity_input_script_sigs_hash , .cmr = {{0x6c748142u, 0x0124b664u, 0x5d32ff9bu, 0x454a1c92u, 0xc6718641u, 0x0e23cf60u, 0x9915df90u, 0x72120fc6u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 138 /* milli weight units */ } ,[INPUT_SCRIPTS_HASH] = { .tag = JET , .jet = simplicity_input_scripts_hash , .cmr = {{0xdc13519eu, 0x753e5875u, 0x3c709885u, 0x41ad8a0bu, 0xb5888d08u, 0x46e35e4du, 0x4273f656u, 0x85322ae9u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 137 /* milli weight units */ } ,[INPUT_SEQUENCE] = { .tag = JET , .jet = simplicity_input_sequence , .cmr = {{0x3c6e4a3cu, 0x21ced524u, 0x736c545cu, 0x20e4e2deu, 0xf7678f08u, 0x4cd12bcdu, 0x6506a520u, 0x0b5c1738u}} , .sourceIx = ty_w32 , .targetIx = ty_mw32 , .cost = 99 /* milli weight units */ } ,[INPUT_SEQUENCES_HASH] = { .tag = JET , .jet = simplicity_input_sequences_hash , .cmr = {{0xc888c873u, 0x302b92b0u, 0x0f206852u, 0xc9eaef00u, 0x0b40109au, 0x53dd686au, 0x53f11db5u, 0x074d9937u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 142 /* milli weight units */ } ,[INPUT_UTXO_HASH] = { .tag = JET , .jet = simplicity_input_utxo_hash , .cmr = {{0x8503d052u, 0x6ba95a8fu, 0xba8ca135u, 0x1c7991c2u, 0xa386b72fu, 0xa81431eau, 0xdbab62ccu, 0x1f5dc518u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 1996 /* milli weight units */ } ,[INPUT_UTXOS_HASH] = { .tag = JET , .jet = simplicity_input_utxos_hash , .cmr = {{0x9c48ab31u, 0xc050ed06u, 0x5aed5168u, 0x66c16c1bu, 0x96c195eau, 0x8e18b024u, 0xbfc0b817u, 0x5849f04eu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 140 /* milli weight units */ } ,[INPUTS_HASH] = { .tag = JET , .jet = simplicity_inputs_hash , .cmr = {{0x523cd71cu, 0x5789882fu, 0x8375a5a5u, 0x4560def8u, 0x463d1c51u, 0xe56b7e11u, 0x2693e77bu, 0x844f4740u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 154 /* milli weight units */ } ,[INTERNAL_KEY] = { .tag = JET , .jet = simplicity_internal_key , .cmr = {{0x9b742e47u, 0x1b0e591au, 0x972b0d44u, 0x21f9c965u, 0x9397f5dau, 0xba2c14dau, 0xc62c4a33u, 0x9cc3e7ecu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 152 /* milli weight units */ } ,[IS_ONE_16] = { .tag = JET , .jet = simplicity_is_one_16 , .cmr = {{0x8435879cu, 0xcb864419u, 0x8dcb9a0cu, 0xd73546d7u, 0x01fdd5a4u, 0xc44323f5u, 0x63971599u, 0xc37d16fbu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 82 /* milli weight units */ } ,[IS_ONE_32] = { .tag = JET , .jet = simplicity_is_one_32 , .cmr = {{0xddfbd9f0u, 0xa2e67c07u, 0xdedb89e8u, 0x96b6c4f7u, 0xd45c5147u, 0xeed0614eu, 0x4ce7d087u, 0x69aff82du}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 65 /* milli weight units */ } ,[IS_ONE_64] = { .tag = JET , .jet = simplicity_is_one_64 , .cmr = {{0x35c52554u, 0x8e48eea0u, 0xf77b3bf9u, 0x7ab67a1fu, 0xfe8fb094u, 0xede3325eu, 0x4064b165u, 0x9c6d0765u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 83 /* milli weight units */ } ,[IS_ONE_8] = { .tag = JET , .jet = simplicity_is_one_8 , .cmr = {{0x0aba9e57u, 0x6e64d280u, 0x4c8ac468u, 0x2bbba539u, 0x0ebc31a6u, 0xe3e2650fu, 0x9219235du, 0xf4a6ecbbu}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 91 /* milli weight units */ } ,[IS_ZERO_16] = { .tag = JET , .jet = simplicity_is_zero_16 , .cmr = {{0xa25abd9cu, 0xd2a4070cu, 0x742ef8deu, 0xb0682922u, 0x46032b96u, 0xa517223bu, 0x128cfc12u, 0xd215c5bau}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 75 /* milli weight units */ } ,[IS_ZERO_32] = { .tag = JET , .jet = simplicity_is_zero_32 , .cmr = {{0x612a480cu, 0xed6a79dau, 0x6119546eu, 0x056b8df9u, 0xfa95d112u, 0x4b96d601u, 0xe1d3ea91u, 0x8cc56069u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 85 /* milli weight units */ } ,[IS_ZERO_64] = { .tag = JET , .jet = simplicity_is_zero_64 , .cmr = {{0x18e8e177u, 0x6ba080ccu, 0xd3e1d60cu, 0xb7534145u, 0x36bf70dfu, 0x185f72c9u, 0xe070796fu, 0x4c63cc71u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 80 /* milli weight units */ } ,[IS_ZERO_8] = { .tag = JET , .jet = simplicity_is_zero_8 , .cmr = {{0xb4baa509u, 0x38108426u, 0x740d82cfu, 0x1211e0edu, 0x126de3b7u, 0x6b8d259cu, 0x50ad4b8fu, 0xcab10ab6u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 77 /* milli weight units */ } ,[ISSUANCE] = { .tag = JET , .jet = simplicity_issuance , .cmr = {{0x5c646312u, 0xc169c680u, 0x27979e1bu, 0xc326c5dcu, 0x95e5c516u, 0x8d00d98eu, 0x9d504a7cu, 0xde21d768u}} , .sourceIx = ty_w32 , .targetIx = ty_mmb , .cost = 91 /* milli weight units */ } ,[ISSUANCE_ASSET] = { .tag = JET , .jet = simplicity_issuance_asset , .cmr = {{0x690bf918u, 0xe1527756u, 0xcfbbf51cu, 0x83136214u, 0x3756d52du, 0x04e1294fu, 0x1264950cu, 0x6267e5c9u}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 151 /* milli weight units */ } ,[ISSUANCE_ASSET_AMOUNT] = { .tag = JET , .jet = simplicity_issuance_asset_amount , .cmr = {{0x83605146u, 0xff26a49cu, 0xa16f1c4au, 0x6e0ce0b7u, 0xc214df12u, 0xc377f522u, 0x523deb6du, 0x5d0ee44du}} , .sourceIx = ty_w32 , .targetIx = ty_mmspbw256w64 , .cost = 162 /* milli weight units */ } ,[ISSUANCE_ASSET_AMOUNTS_HASH] = { .tag = JET , .jet = simplicity_issuance_asset_amounts_hash , .cmr = {{0x70f11c3bu, 0x3b5d1657u, 0xd3b7c7eeu, 0xec850c30u, 0xa32ea96au, 0xa36426fau, 0x30ebf549u, 0x9851a880u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 139 /* milli weight units */ } ,[ISSUANCE_ASSET_PROOF] = { .tag = JET , .jet = simplicity_issuance_asset_proof , .cmr = {{0x0b061f9fu, 0x670c05dcu, 0x39f43831u, 0x3c1379d9u, 0xbf63f44fu, 0x9876b956u, 0x693b41b7u, 0xf94c6c9du}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 150 /* milli weight units */ } ,[ISSUANCE_BLINDING_ENTROPY_HASH] = { .tag = JET , .jet = simplicity_issuance_blinding_entropy_hash , .cmr = {{0xbfb6a934u, 0x44e2a0b3u, 0xfb7c13d1u, 0x589a787bu, 0x66e84b69u, 0xb6274ceau, 0x20ad9999u, 0xeb8ca67cu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 129 /* milli weight units */ } ,[ISSUANCE_ENTROPY] = { .tag = JET , .jet = simplicity_issuance_entropy , .cmr = {{0x6ddf99f2u, 0x8c70198du, 0x65417a83u, 0x6074f1b9u, 0xb610f21fu, 0x5119fd55u, 0x0f60b6f8u, 0xe995bbf3u}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 153 /* milli weight units */ } ,[ISSUANCE_HASH] = { .tag = JET , .jet = simplicity_issuance_hash , .cmr = {{0x6e9f8ae8u, 0xc45bfb7eu, 0x4e0cf2d0u, 0x0f66832bu, 0x479de758u, 0x2cdbc851u, 0xd0b3230fu, 0xdfbbb78du}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 3738 /* milli weight units */ } ,[ISSUANCE_RANGE_PROOFS_HASH] = { .tag = JET , .jet = simplicity_issuance_range_proofs_hash , .cmr = {{0x7e97f519u, 0x534831c7u, 0x7acf73a2u, 0x0fd53cb3u, 0x1d1d156cu, 0x9acbbf87u, 0x3d1492d6u, 0x0d1367d8u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 129 /* milli weight units */ } ,[ISSUANCE_TOKEN] = { .tag = JET , .jet = simplicity_issuance_token , .cmr = {{0xbc2cb7e9u, 0x64b2a2aeu, 0xd79b75c5u, 0xf4408fe8u, 0x4a6dc9b9u, 0xe8cd2c69u, 0x4d57c5f9u, 0xb61205b9u}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 149 /* milli weight units */ } ,[ISSUANCE_TOKEN_AMOUNT] = { .tag = JET , .jet = simplicity_issuance_token_amount , .cmr = {{0x7e106464u, 0xa13b6764u, 0xce74d3feu, 0x6ba1cbd5u, 0xf4aeb86bu, 0xbbdf5888u, 0xddf9901du, 0xd8b619aau}} , .sourceIx = ty_w32 , .targetIx = ty_mmspbw256w64 , .cost = 196 /* milli weight units */ } ,[ISSUANCE_TOKEN_AMOUNTS_HASH] = { .tag = JET , .jet = simplicity_issuance_token_amounts_hash , .cmr = {{0x94b5a459u, 0x5b674dbfu, 0xc49c4e8eu, 0xa1a9abc9u, 0x3ed2f770u, 0x7c4212a3u, 0x2b5b86acu, 0x1318c9deu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 138 /* milli weight units */ } ,[ISSUANCE_TOKEN_PROOF] = { .tag = JET , .jet = simplicity_issuance_token_proof , .cmr = {{0x46ed5275u, 0xf55ab341u, 0xf57c3519u, 0xffedf4e3u, 0x7f3f59c9u, 0x7ce9b8e1u, 0x7fffae16u, 0xc6cc1c0eu}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 150 /* milli weight units */ } ,[ISSUANCES_HASH] = { .tag = JET , .jet = simplicity_issuances_hash , .cmr = {{0x58659f3fu, 0x7e0130c4u, 0xfc916f49u, 0xbc32eaa0u, 0x883acb90u, 0x22fcad5eu, 0x7805839au, 0x99e50cf9u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 141 /* milli weight units */ } ,[LBTC_ASSET] = { .tag = JET , .jet = simplicity_lbtc_asset , .cmr = {{0x2af7f73au, 0xe3fbbfa2u, 0xd23a8774u, 0xe6e3ca09u, 0x3254da2fu, 0xd2a9f397u, 0xa6ae0a30u, 0xbb48f0d7u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 145 /* milli weight units */ } ,[LE_16] = { .tag = JET , .jet = simplicity_le_16 , .cmr = {{0x63da727cu, 0xcb4c6a9du, 0x4e000964u, 0xe763bff9u, 0x34eaafd0u, 0x44287e12u, 0x68d07ecdu, 0xfde207e1u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 112 /* milli weight units */ } ,[LE_32] = { .tag = JET , .jet = simplicity_le_32 , .cmr = {{0xdee29a91u, 0x656d7ae7u, 0x3df4956fu, 0xd8a2c6b6u, 0x27aab51cu, 0x1129f9feu, 0x7f6ed3e3u, 0x4792c762u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 93 /* milli weight units */ } ,[LE_64] = { .tag = JET , .jet = simplicity_le_64 , .cmr = {{0x01c55df7u, 0xd4465966u, 0x659ddfc9u, 0x4b36d033u, 0x242c2ec5u, 0x93cee121u, 0x22440775u, 0x66ed015fu}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 93 /* milli weight units */ } ,[LE_8] = { .tag = JET , .jet = simplicity_le_8 , .cmr = {{0x0fb72d9fu, 0x8ee2370au, 0xba55663au, 0x4899162eu, 0x40ca5514u, 0x713efb25u, 0xe4a89e2au, 0x104b34dbu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 109 /* milli weight units */ } ,[LEFT_EXTEND_16_32] = { .tag = JET , .jet = simplicity_left_extend_16_32 , .cmr = {{0xdcf42b65u, 0x42f6d41cu, 0xb7b50e7cu, 0x772f3c7fu, 0x6e432232u, 0xf2ba2079u, 0xb386a05du, 0x7b466addu}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 86 /* milli weight units */ } ,[LEFT_EXTEND_16_64] = { .tag = JET , .jet = simplicity_left_extend_16_64 , .cmr = {{0x2eee48a9u, 0x2237947cu, 0x1a517df9u, 0x95f44f1du, 0xfef20ddbu, 0x4e9b530bu, 0x22d18a0au, 0x7fd628aau}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 89 /* milli weight units */ } ,[LEFT_EXTEND_1_16] = { .tag = JET , .jet = simplicity_left_extend_1_16 , .cmr = {{0x9a48a477u, 0x8e7c3c28u, 0x5ab65329u, 0xd1ccc499u, 0x9d2d194eu, 0x005bd794u, 0x6949533du, 0x8cba806cu}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 67 /* milli weight units */ } ,[LEFT_EXTEND_1_32] = { .tag = JET , .jet = simplicity_left_extend_1_32 , .cmr = {{0xdab6a533u, 0xcbcbe836u, 0x2cf1d5a1u, 0x6ea37cbcu, 0x7edc7fc8u, 0xa9428571u, 0xe171ec6eu, 0xe44d0800u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 60 /* milli weight units */ } ,[LEFT_EXTEND_1_64] = { .tag = JET , .jet = simplicity_left_extend_1_64 , .cmr = {{0x110e5c1eu, 0xf0b469a7u, 0x638570dau, 0x944d232eu, 0x0f28c461u, 0x51a22535u, 0x7de3e904u, 0x57a88ea2u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 76 /* milli weight units */ } ,[LEFT_EXTEND_1_8] = { .tag = JET , .jet = simplicity_left_extend_1_8 , .cmr = {{0x5a831ca9u, 0x9621517au, 0x2b354e5cu, 0xac38bc3au, 0x30c4001fu, 0x20d25d77u, 0x97addcacu, 0x5da86106u}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 65 /* milli weight units */ } ,[LEFT_EXTEND_32_64] = { .tag = JET , .jet = simplicity_left_extend_32_64 , .cmr = {{0x84fcc69bu, 0xa1db50dbu, 0xd5363cf2u, 0x77795760u, 0x1de2568au, 0xdf07af41u, 0x61debb1eu, 0x5e37310au}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 63 /* milli weight units */ } ,[LEFT_EXTEND_8_16] = { .tag = JET , .jet = simplicity_left_extend_8_16 , .cmr = {{0xfea1f25au, 0x82fdf6f8u, 0x669cc40fu, 0xbb8e54a9u, 0x2658bfabu, 0x94eb082fu, 0x717ba265u, 0xb5d844b4u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 88 /* milli weight units */ } ,[LEFT_EXTEND_8_32] = { .tag = JET , .jet = simplicity_left_extend_8_32 , .cmr = {{0x09d703cau, 0x46f75d05u, 0x1a93d0e8u, 0xa2af0501u, 0xa38e8486u, 0x83ef109cu, 0x1fb4b5beu, 0x20e6315du}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 90 /* milli weight units */ } ,[LEFT_EXTEND_8_64] = { .tag = JET , .jet = simplicity_left_extend_8_64 , .cmr = {{0xd3dafcbdu, 0xab69a2bbu, 0x320f8d23u, 0x0cefd09cu, 0x27a154c5u, 0x1e7e5cd5u, 0x334eafedu, 0x19e20df4u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 107 /* milli weight units */ } ,[LEFT_PAD_HIGH_16_32] = { .tag = JET , .jet = simplicity_left_pad_high_16_32 , .cmr = {{0x888c7e0au, 0xb0031475u, 0xc514f9b3u, 0x7c81f45au, 0x47314984u, 0xe5027508u, 0xddc5eb8du, 0x8d10beb9u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 91 /* milli weight units */ } ,[LEFT_PAD_HIGH_16_64] = { .tag = JET , .jet = simplicity_left_pad_high_16_64 , .cmr = {{0x526b3505u, 0x450136d6u, 0x81a50b4bu, 0xde4fa612u, 0xda9d69bdu, 0x08170ea3u, 0x2d0a2651u, 0x115072ebu}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 110 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_16] = { .tag = JET , .jet = simplicity_left_pad_high_1_16 , .cmr = {{0x93aed6f6u, 0x8750774bu, 0x2dbf8314u, 0xcadebe5au, 0x415243fbu, 0xdf7c2eeau, 0x8b223df3u, 0x261e3bdbu}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 141 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_32] = { .tag = JET , .jet = simplicity_left_pad_high_1_32 , .cmr = {{0x008298f8u, 0x2fb6cf37u, 0xe9dc703eu, 0xa4f94956u, 0x5c2965a7u, 0xc7f4fa22u, 0xf5545642u, 0x3408a3abu}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 263 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_64] = { .tag = JET , .jet = simplicity_left_pad_high_1_64 , .cmr = {{0x2b454ebdu, 0x791ec7dau, 0xcedcb86cu, 0x69d02679u, 0x4a5dc372u, 0x5261e7dcu, 0x1650cc88u, 0x8117fc4fu}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 422 /* milli weight units */ } ,[LEFT_PAD_HIGH_1_8] = { .tag = JET , .jet = simplicity_left_pad_high_1_8 , .cmr = {{0x6c277c4cu, 0xd053dd35u, 0x02dbe0bbu, 0xc14eb0b3u, 0x6a201abeu, 0xf3b174b0u, 0xebfe0520u, 0x18b67e67u}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 99 /* milli weight units */ } ,[LEFT_PAD_HIGH_32_64] = { .tag = JET , .jet = simplicity_left_pad_high_32_64 , .cmr = {{0x5d41221cu, 0xf6158297u, 0xb06c1957u, 0x112c0d12u, 0xf3eb917au, 0x2f509a53u, 0x9d5c9b79u, 0x10219b65u}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 93 /* milli weight units */ } ,[LEFT_PAD_HIGH_8_16] = { .tag = JET , .jet = simplicity_left_pad_high_8_16 , .cmr = {{0x2178dc76u, 0xc04c79d9u, 0x1815d38cu, 0x967f3421u, 0x3ffcc6c5u, 0xf243c956u, 0x2973f090u, 0xca5caefau}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 88 /* milli weight units */ } ,[LEFT_PAD_HIGH_8_32] = { .tag = JET , .jet = simplicity_left_pad_high_8_32 , .cmr = {{0xa4e86b53u, 0xe5d00fafu, 0x0b3e9d53u, 0x202af773u, 0x8dcb8887u, 0xa18dfee5u, 0xbe34c497u, 0x698ca6b7u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 103 /* milli weight units */ } ,[LEFT_PAD_HIGH_8_64] = { .tag = JET , .jet = simplicity_left_pad_high_8_64 , .cmr = {{0xc843a72cu, 0x41170f40u, 0x3433c436u, 0xa39b05cfu, 0x193c27d8u, 0xbe3530f9u, 0xb94e42d7u, 0x63003d54u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 136 /* milli weight units */ } ,[LEFT_PAD_LOW_16_32] = { .tag = JET , .jet = simplicity_left_pad_low_16_32 , .cmr = {{0x21537f7du, 0x8f97f220u, 0x3cccb035u, 0xef1d4628u, 0x9ee8aa50u, 0xf0236077u, 0xd0d0b210u, 0x700440a1u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 69 /* milli weight units */ } ,[LEFT_PAD_LOW_16_64] = { .tag = JET , .jet = simplicity_left_pad_low_16_64 , .cmr = {{0x6b2ea963u, 0x0c5dde03u, 0x7aab2bf7u, 0x33219b99u, 0xc7edc2ecu, 0xedb9a03au, 0xdfd16943u, 0x0b08bb9cu}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 106 /* milli weight units */ } ,[LEFT_PAD_LOW_1_16] = { .tag = JET , .jet = simplicity_left_pad_low_1_16 , .cmr = {{0x4aa40520u, 0xfaed72e6u, 0xe9be3be6u, 0x930f1e32u, 0xb0b182c4u, 0x327ada94u, 0xa71f006du, 0x149015f9u}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 65 /* milli weight units */ } ,[LEFT_PAD_LOW_1_32] = { .tag = JET , .jet = simplicity_left_pad_low_1_32 , .cmr = {{0xcfb4753bu, 0xb9ba3621u, 0xba093782u, 0x5fade643u, 0x098e385eu, 0xd68efb16u, 0xff58ecf3u, 0x65d7e5e2u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 63 /* milli weight units */ } ,[LEFT_PAD_LOW_1_64] = { .tag = JET , .jet = simplicity_left_pad_low_1_64 , .cmr = {{0xe6f1c09bu, 0x5fe126d0u, 0xea86e7bfu, 0xc0b28e84u, 0x9f8f7efdu, 0x31064ea4u, 0xfd1cca07u, 0x1b45db93u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 61 /* milli weight units */ } ,[LEFT_PAD_LOW_1_8] = { .tag = JET , .jet = simplicity_left_pad_low_1_8 , .cmr = {{0xdc5a47f8u, 0xd77765c9u, 0x94cbe86au, 0xae44a9c5u, 0xff2ebc38u, 0x10d79cd8u, 0x3bd2c409u, 0x8c762bf5u}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 56 /* milli weight units */ } ,[LEFT_PAD_LOW_32_64] = { .tag = JET , .jet = simplicity_left_pad_low_32_64 , .cmr = {{0x2d88e4d0u, 0x1e0108c0u, 0xd6880f3cu, 0xe8482bb0u, 0x951f2b3fu, 0xc5df4b1au, 0xdb184a1bu, 0xfd1f6465u}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 91 /* milli weight units */ } ,[LEFT_PAD_LOW_8_16] = { .tag = JET , .jet = simplicity_left_pad_low_8_16 , .cmr = {{0xac1a4c97u, 0x83e4dbedu, 0x2700eb29u, 0x52e3062au, 0x5a72712fu, 0x82159861u, 0xb08e67efu, 0x4a71f5f2u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 66 /* milli weight units */ } ,[LEFT_PAD_LOW_8_32] = { .tag = JET , .jet = simplicity_left_pad_low_8_32 , .cmr = {{0x3da5f1a8u, 0xc97819aeu, 0x7e10b936u, 0x4ff84996u, 0xd0d73e69u, 0x8a49da69u, 0x1f69a273u, 0x254201cdu}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 61 /* milli weight units */ } ,[LEFT_PAD_LOW_8_64] = { .tag = JET , .jet = simplicity_left_pad_low_8_64 , .cmr = {{0x25bc18d4u, 0x9f934072u, 0x277d3f61u, 0x3bf16c11u, 0x8df197bcu, 0x92872d2au, 0xffe417adu, 0xeaaf1a85u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 112 /* milli weight units */ } ,[LEFT_ROTATE_16] = { .tag = JET , .jet = simplicity_left_rotate_16 , .cmr = {{0x88c12337u, 0xcd754f83u, 0x80986d86u, 0xfe3a89e2u, 0x62746653u, 0xe1badd9cu, 0xc9b47645u, 0xfe57195au}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 77 /* milli weight units */ } ,[LEFT_ROTATE_32] = { .tag = JET , .jet = simplicity_left_rotate_32 , .cmr = {{0x39816ccdu, 0x9e9cf119u, 0x1f065d2eu, 0xb7a7fb83u, 0x828d91ecu, 0x7d9977a1u, 0xfc70be9bu, 0x31a468b9u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 106 /* milli weight units */ } ,[LEFT_ROTATE_64] = { .tag = JET , .jet = simplicity_left_rotate_64 , .cmr = {{0x8b2355c3u, 0x1e3b614bu, 0xd4b41c3eu, 0xcf277424u, 0xd026766bu, 0x37bc6c10u, 0x5621f4f6u, 0xa16f9bdfu}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 98 /* milli weight units */ } ,[LEFT_ROTATE_8] = { .tag = JET , .jet = simplicity_left_rotate_8 , .cmr = {{0x9e966e88u, 0x0c6b0c48u, 0x3c90beeeu, 0xd7c5737cu, 0xa5f3facfu, 0x85aab3d5u, 0x31ad34bdu, 0x7b1a9b68u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 88 /* milli weight units */ } ,[LEFT_SHIFT_16] = { .tag = JET , .jet = simplicity_left_shift_16 , .cmr = {{0xb0536018u, 0x4d0602b5u, 0x81405e32u, 0x960b31c0u, 0x5219358du, 0xe89efdf4u, 0x9464723du, 0xd625617au}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 72 /* milli weight units */ } ,[LEFT_SHIFT_32] = { .tag = JET , .jet = simplicity_left_shift_32 , .cmr = {{0x34bf54f5u, 0x94c26210u, 0x07f8c78bu, 0x30fad396u, 0x72009bb3u, 0x66aace1eu, 0x5e41ee4du, 0x9cc541a8u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 78 /* milli weight units */ } ,[LEFT_SHIFT_64] = { .tag = JET , .jet = simplicity_left_shift_64 , .cmr = {{0x5de953f0u, 0x4deaed90u, 0x47567647u, 0xa1eb7abeu, 0x665feccbu, 0xe7ed10cbu, 0x7dbe6912u, 0x73c094b0u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 82 /* milli weight units */ } ,[LEFT_SHIFT_8] = { .tag = JET , .jet = simplicity_left_shift_8 , .cmr = {{0xab9d3e9au, 0xc39038adu, 0x88b103f0u, 0x72254c0eu, 0xc6e27475u, 0xe275c245u, 0xe88cce0du, 0x072e6446u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 91 /* milli weight units */ } ,[LEFT_SHIFT_WITH_16] = { .tag = JET , .jet = simplicity_left_shift_with_16 , .cmr = {{0xe2910788u, 0x5550450eu, 0xb727d0cfu, 0x14e104aeu, 0x12f83a24u, 0xe2e2aca3u, 0xcce433deu, 0x2f35d7b3u}} , .sourceIx = ty_pbpw4w16 , .targetIx = ty_w16 , .cost = 83 /* milli weight units */ } ,[LEFT_SHIFT_WITH_32] = { .tag = JET , .jet = simplicity_left_shift_with_32 , .cmr = {{0xf39250c4u, 0x5a1310ccu, 0x638c788du, 0xeec5c365u, 0xb4d176d1u, 0x0efbf4c6u, 0x01cf5eebu, 0xe0a573e9u}} , .sourceIx = ty_pbpw8w32 , .targetIx = ty_w32 , .cost = 95 /* milli weight units */ } ,[LEFT_SHIFT_WITH_64] = { .tag = JET , .jet = simplicity_left_shift_with_64 , .cmr = {{0xad8794cfu, 0xaef2b7f7u, 0x74fa68d3u, 0x09bbc98du, 0xfee58c40u, 0x400b2eb5u, 0x78a212f4u, 0x38bd07abu}} , .sourceIx = ty_pbpw8w64 , .targetIx = ty_w64 , .cost = 103 /* milli weight units */ } ,[LEFT_SHIFT_WITH_8] = { .tag = JET , .jet = simplicity_left_shift_with_8 , .cmr = {{0xdd9cc1ceu, 0xa7490948u, 0x1ff58f87u, 0x6ff66e0fu, 0x5d52bf89u, 0xb0258fa9u, 0x5b320002u, 0xc32a7915u}} , .sourceIx = ty_pbpw4w8 , .targetIx = ty_w8 , .cost = 107 /* milli weight units */ } ,[LEFTMOST_16_1] = { .tag = JET , .jet = simplicity_leftmost_16_1 , .cmr = {{0xde6a4c98u, 0x337e680du, 0x6e6ee2bfu, 0x36d3a081u, 0x7d2a9a98u, 0x325f87e5u, 0xeceb8a6fu, 0x1168f5cau}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 93 /* milli weight units */ } ,[LEFTMOST_16_2] = { .tag = JET , .jet = simplicity_leftmost_16_2 , .cmr = {{0x005809b8u, 0x051a2a50u, 0x2833b22cu, 0x2c17981eu, 0xaf9dd1d3u, 0xdbc8f8c8u, 0x94516c1du, 0x5f31146cu}} , .sourceIx = ty_w16 , .targetIx = ty_w2 , .cost = 90 /* milli weight units */ } ,[LEFTMOST_16_4] = { .tag = JET , .jet = simplicity_leftmost_16_4 , .cmr = {{0x9c50ee22u, 0x84d857c4u, 0x7c054447u, 0x1354105eu, 0x98dfe027u, 0x54d2e42du, 0xe11d3234u, 0xed10b642u}} , .sourceIx = ty_w16 , .targetIx = ty_w4 , .cost = 75 /* milli weight units */ } ,[LEFTMOST_16_8] = { .tag = JET , .jet = simplicity_leftmost_16_8 , .cmr = {{0x5a1a7291u, 0x4e149c22u, 0xb464c8f6u, 0xa3d9cf41u, 0xb07192beu, 0xf0d8a1ccu, 0x7cbe5704u, 0xa9e8ea70u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 71 /* milli weight units */ } ,[LEFTMOST_32_1] = { .tag = JET , .jet = simplicity_leftmost_32_1 , .cmr = {{0x5fb8e634u, 0x2ab74ee2u, 0xc9225b87u, 0x2fa0c912u, 0x046a69dbu, 0xb719bcd6u, 0xc8d79b76u, 0x60c4ebcau}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 77 /* milli weight units */ } ,[LEFTMOST_32_16] = { .tag = JET , .jet = simplicity_leftmost_32_16 , .cmr = {{0x54ae50b4u, 0x6b5b2e68u, 0xf536c01cu, 0x39617b0cu, 0xee42e1c4u, 0x9a2cd1d2u, 0x6af8ea87u, 0x15ac4d11u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 102 /* milli weight units */ } ,[LEFTMOST_32_2] = { .tag = JET , .jet = simplicity_leftmost_32_2 , .cmr = {{0x12306855u, 0x4595427eu, 0x3c1de243u, 0xbab66f33u, 0x48368aaau, 0x44617d6au, 0x02479fb7u, 0x04bcfd1eu}} , .sourceIx = ty_w32 , .targetIx = ty_w2 , .cost = 66 /* milli weight units */ } ,[LEFTMOST_32_4] = { .tag = JET , .jet = simplicity_leftmost_32_4 , .cmr = {{0x55a87b66u, 0xc339e363u, 0xe03d4daau, 0xc62290ebu, 0xa93c1a3au, 0x7382cbf6u, 0x1f20b34au, 0x505124adu}} , .sourceIx = ty_w32 , .targetIx = ty_w4 , .cost = 52 /* milli weight units */ } ,[LEFTMOST_32_8] = { .tag = JET , .jet = simplicity_leftmost_32_8 , .cmr = {{0x9f345beeu, 0x0b162d42u, 0xa035718fu, 0x8ca1adc8u, 0xac2f710du, 0xc40052a8u, 0x2566e6d8u, 0x07bef8b8u}} , .sourceIx = ty_w32 , .targetIx = ty_w8 , .cost = 103 /* milli weight units */ } ,[LEFTMOST_64_1] = { .tag = JET , .jet = simplicity_leftmost_64_1 , .cmr = {{0xb924d33bu, 0x5efefc8eu, 0x20420819u, 0x25917cffu, 0x239b31c8u, 0xbdbdf4acu, 0xae6bb8d9u, 0xcd217b4fu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 78 /* milli weight units */ } ,[LEFTMOST_64_16] = { .tag = JET , .jet = simplicity_leftmost_64_16 , .cmr = {{0x12aa85e0u, 0x5c1e9622u, 0x279c4c2du, 0xdcf897c9u, 0x5ddcc011u, 0x3997283bu, 0x6b3e0949u, 0xbc8113cbu}} , .sourceIx = ty_w64 , .targetIx = ty_w16 , .cost = 88 /* milli weight units */ } ,[LEFTMOST_64_2] = { .tag = JET , .jet = simplicity_leftmost_64_2 , .cmr = {{0xbcec97f4u, 0x3ba55cd4u, 0x0d85a1e7u, 0x6cbade7bu, 0x0b1e9f13u, 0x9747793du, 0xcb3480beu, 0xe1f751cau}} , .sourceIx = ty_w64 , .targetIx = ty_w2 , .cost = 71 /* milli weight units */ } ,[LEFTMOST_64_32] = { .tag = JET , .jet = simplicity_leftmost_64_32 , .cmr = {{0x9c896939u, 0x86e55733u, 0xab962a30u, 0x0b057950u, 0x3d83de8au, 0xc19b179bu, 0x417e1ca2u, 0x5385b38fu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 90 /* milli weight units */ } ,[LEFTMOST_64_4] = { .tag = JET , .jet = simplicity_leftmost_64_4 , .cmr = {{0xd2d64520u, 0x92d6566fu, 0x89a1f64eu, 0x736596f9u, 0x000e5e6fu, 0x63e40017u, 0xd0cb80f3u, 0xf7adfd18u}} , .sourceIx = ty_w64 , .targetIx = ty_w4 , .cost = 79 /* milli weight units */ } ,[LEFTMOST_64_8] = { .tag = JET , .jet = simplicity_leftmost_64_8 , .cmr = {{0xf77b62bbu, 0x01b90511u, 0xb6d06ebfu, 0x2e36c065u, 0x65acb5aau, 0xd1efc77cu, 0x36a10a26u, 0x1de921dau}} , .sourceIx = ty_w64 , .targetIx = ty_w8 , .cost = 86 /* milli weight units */ } ,[LEFTMOST_8_1] = { .tag = JET , .jet = simplicity_leftmost_8_1 , .cmr = {{0x5a730b58u, 0xe3abcb2fu, 0x4de22159u, 0x80302310u, 0x2cd66421u, 0x911920cau, 0x21a2a05cu, 0x9b211ce8u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 90 /* milli weight units */ } ,[LEFTMOST_8_2] = { .tag = JET , .jet = simplicity_leftmost_8_2 , .cmr = {{0x25790856u, 0x103dce6cu, 0x7bbb3dd7u, 0x18b16910u, 0x9cae8537u, 0x99d12456u, 0xc85d8349u, 0xec18dc53u}} , .sourceIx = ty_w8 , .targetIx = ty_w2 , .cost = 90 /* milli weight units */ } ,[LEFTMOST_8_4] = { .tag = JET , .jet = simplicity_leftmost_8_4 , .cmr = {{0x73d9f018u, 0x157a1478u, 0x4ee70b21u, 0x9ceb4042u, 0xfa621d0eu, 0xe6d545a0u, 0xfdbab944u, 0x4346e331u}} , .sourceIx = ty_w8 , .targetIx = ty_w4 , .cost = 87 /* milli weight units */ } ,[LINEAR_COMBINATION_1] = { .tag = JET , .jet = simplicity_linear_combination_1 , .cmr = {{0x6d9f4a87u, 0x0fbf740cu, 0x220efff3u, 0x07b5ed91u, 0xa58c5e51u, 0xa8adfc3bu, 0x159030f5u, 0x12d39941u}} , .sourceIx = ty_ppw256pw512w256w256 , .targetIx = ty_pw512w256 , .cost = 84674 /* milli weight units */ } ,[LINEAR_VERIFY_1] = { .tag = JET , .jet = simplicity_linear_verify_1 , .cmr = {{0x278313d7u, 0xce4ad589u, 0x11de24eeu, 0x540d19ecu, 0xebb62f4au, 0xb4a71e2au, 0xadd4512bu, 0x2e4bc2e2u}} , .sourceIx = ty_pppw256w512w256w512 , .targetIx = ty_u , .cost = 43364 /* milli weight units */ } ,[LOCK_TIME] = { .tag = JET , .jet = simplicity_lock_time , .cmr = {{0xa16897c5u, 0xdb4927c6u, 0xcb07b165u, 0xbd2cc38bu, 0x36a60268u, 0x6c74a190u, 0x34aa3787u, 0xac582a0bu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 85 /* milli weight units */ } ,[LOW_1] = { .tag = JET , .jet = simplicity_low_1 , .cmr = {{0xf27b69bbu, 0x091609f5u, 0x9e003305u, 0x0d01a5bcu, 0x77ff07d9u, 0x42707a79u, 0xcf5ee410u, 0xa998a043u}} , .sourceIx = ty_u , .targetIx = ty_b , .cost = 38 /* milli weight units */ } ,[LOW_16] = { .tag = JET , .jet = simplicity_low_16 , .cmr = {{0x977cbd1eu, 0x7ffc05e7u, 0x16d9c1b4u, 0x9f7d517fu, 0x853dbf3eu, 0x98a4c748u, 0x046eacf4u, 0x17f89c2fu}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 69 /* milli weight units */ } ,[LOW_32] = { .tag = JET , .jet = simplicity_low_32 , .cmr = {{0xbe416982u, 0x8f076778u, 0xb60d5456u, 0xf7886ed7u, 0xf30b101du, 0x6ccbd9eau, 0x0c4db142u, 0xeac66b12u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 62 /* milli weight units */ } ,[LOW_64] = { .tag = JET , .jet = simplicity_low_64 , .cmr = {{0x019a66bfu, 0xba175168u, 0x8be71389u, 0xed7bf371u, 0xb3014dfbu, 0x329562acu, 0x3b3e9dfeu, 0x9206a5bcu}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 47 /* milli weight units */ } ,[LOW_8] = { .tag = JET , .jet = simplicity_low_8 , .cmr = {{0x217b5643u, 0x956b4833u, 0xaa5622f0u, 0x0f0688bau, 0x860d4adbu, 0xf940cbdcu, 0xd2b59f26u, 0xd61593b1u}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 47 /* milli weight units */ } ,[LT_16] = { .tag = JET , .jet = simplicity_lt_16 , .cmr = {{0x56a20d55u, 0xedb44388u, 0x180544c3u, 0xed404145u, 0xa3b66fd2u, 0xc4113842u, 0xf64eaeafu, 0xbad4bb06u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 123 /* milli weight units */ } ,[LT_32] = { .tag = JET , .jet = simplicity_lt_32 , .cmr = {{0xcab0dc5bu, 0x0ecbf6d2u, 0x4816fc20u, 0x10fc3119u, 0x3663c306u, 0x968d9ceeu, 0x3b004c0bu, 0xc184b478u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 107 /* milli weight units */ } ,[LT_64] = { .tag = JET , .jet = simplicity_lt_64 , .cmr = {{0x47d67e52u, 0xb27ba78eu, 0xdd075aa2u, 0x70ded007u, 0xa7a9a684u, 0x99344f28u, 0x62f50690u, 0x49a0cefeu}} , .sourceIx = ty_w128 , .targetIx = ty_b , .cost = 76 /* milli weight units */ } ,[LT_8] = { .tag = JET , .jet = simplicity_lt_8 , .cmr = {{0x73d00446u, 0x55c0df45u, 0xc271a171u, 0x3ff9b9a4u, 0x3dde56e6u, 0x74d1754eu, 0x76edb16fu, 0x949c4fabu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 107 /* milli weight units */ } ,[MAJ_1] = { .tag = JET , .jet = simplicity_maj_1 , .cmr = {{0xcb2d986du, 0x7f00107au, 0x3c25f6b2u, 0xf14891d0u, 0x2e20ae16u, 0xf0a1252cu, 0x92d9b58au, 0xe73388aau}} , .sourceIx = ty_pbw2 , .targetIx = ty_b , .cost = 62 /* milli weight units */ } ,[MAJ_16] = { .tag = JET , .jet = simplicity_maj_16 , .cmr = {{0x0af6d0c1u, 0x71fe33a2u, 0x159bf988u, 0x00f0412cu, 0x2597e997u, 0x84d074fdu, 0xfa33d7fdu, 0xe597ddfdu}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 80 /* milli weight units */ } ,[MAJ_32] = { .tag = JET , .jet = simplicity_maj_32 , .cmr = {{0x3060838du, 0x48456f33u, 0x92d5d69bu, 0x5eec0892u, 0x76cd58bbu, 0x67a12c64u, 0x2ec73aebu, 0x9adacbddu}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 96 /* milli weight units */ } ,[MAJ_64] = { .tag = JET , .jet = simplicity_maj_64 , .cmr = {{0x8ebcc174u, 0x57ea2b14u, 0x231b0e90u, 0x1ea7b1d4u, 0x7b9b7898u, 0x6372a441u, 0x6fe73f67u, 0x63feb24bu}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 93 /* milli weight units */ } ,[MAJ_8] = { .tag = JET , .jet = simplicity_maj_8 , .cmr = {{0x8930d1d0u, 0x991b0a58u, 0x1d0b1d85u, 0xad72147du, 0x6649a359u, 0x93283fc9u, 0x7214431fu, 0x0b6a7aa8u}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 94 /* milli weight units */ } ,[MAX_16] = { .tag = JET , .jet = simplicity_max_16 , .cmr = {{0xe0114717u, 0x691ac1a7u, 0x39288fc6u, 0xffa1c650u, 0x7c43e6f1u, 0xd4c18770u, 0xffa166aeu, 0x839dd533u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 114 /* milli weight units */ } ,[MAX_32] = { .tag = JET , .jet = simplicity_max_32 , .cmr = {{0x1d723cb3u, 0x89942219u, 0xec103485u, 0x317fa5d8u, 0x7ee15c24u, 0xb2080f50u, 0x46650d80u, 0x308b189du}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 92 /* milli weight units */ } ,[MAX_64] = { .tag = JET , .jet = simplicity_max_64 , .cmr = {{0x0073ac3cu, 0x6ea939dcu, 0xc7eee4eau, 0x63dcfd75u, 0x2037355bu, 0x484f6e70u, 0x16b300e2u, 0xd28c07c3u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 104 /* milli weight units */ } ,[MAX_8] = { .tag = JET , .jet = simplicity_max_8 , .cmr = {{0x6bc10370u, 0xf3e7a7b9u, 0x2acb1423u, 0xbbdf0b3du, 0x7e3cd0d2u, 0xdbc705a3u, 0x4d8dc99cu, 0x910422fbu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 96 /* milli weight units */ } ,[MEDIAN_16] = { .tag = JET , .jet = simplicity_median_16 , .cmr = {{0x2414e3c4u, 0x39659d8au, 0xa9d087e1u, 0xade77266u, 0x673d1c8bu, 0xd4e7501bu, 0x22ac46a3u, 0xff39975du}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 123 /* milli weight units */ } ,[MEDIAN_32] = { .tag = JET , .jet = simplicity_median_32 , .cmr = {{0x0792356bu, 0x610b57d0u, 0xec199e98u, 0x535ea9bcu, 0xcce843a5u, 0xdf5dd240u, 0x8c414886u, 0xdfd6bd1eu}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 101 /* milli weight units */ } ,[MEDIAN_64] = { .tag = JET , .jet = simplicity_median_64 , .cmr = {{0x0766d89bu, 0x430ffdf0u, 0x38691b18u, 0x439cd6fcu, 0x4929172eu, 0xa884fdafu, 0x166936b3u, 0x8b15fd0cu}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 109 /* milli weight units */ } ,[MEDIAN_8] = { .tag = JET , .jet = simplicity_median_8 , .cmr = {{0xa4a0b631u, 0x0ff0ed4au, 0x4c3e03ebu, 0xc7a91306u, 0xef660424u, 0xbc95a0d3u, 0xf2fdb71fu, 0xb6afd8b7u}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 122 /* milli weight units */ } ,[MIN_16] = { .tag = JET , .jet = simplicity_min_16 , .cmr = {{0xf158f40au, 0x860993b4u, 0x107fb271u, 0xfb4c8f95u, 0x5ba4542au, 0xd1821cd2u, 0xf13c880cu, 0xa4bee2e2u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 97 /* milli weight units */ } ,[MIN_32] = { .tag = JET , .jet = simplicity_min_32 , .cmr = {{0xe5e413dcu, 0x5de5e22du, 0x66f32d8du, 0xbf50053eu, 0xd278e175u, 0xc0d4b344u, 0xebd461beu, 0xb108e55eu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 113 /* milli weight units */ } ,[MIN_64] = { .tag = JET , .jet = simplicity_min_64 , .cmr = {{0x43d82f6cu, 0x6128aa01u, 0xa997bb17u, 0xe5e7f501u, 0xe7be7db9u, 0x589e566du, 0xe97a32eau, 0xe7e7b339u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 102 /* milli weight units */ } ,[MIN_8] = { .tag = JET , .jet = simplicity_min_8 , .cmr = {{0x6b012ca3u, 0x185dc005u, 0xe8942cfbu, 0xc9f238dcu, 0xedaf0c00u, 0x43526447u, 0xe3ec31ceu, 0xfa6e4064u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 99 /* milli weight units */ } ,[MODULO_16] = { .tag = JET , .jet = simplicity_modulo_16 , .cmr = {{0x62c179acu, 0x84c5750bu, 0x425f9a1bu, 0x8f81edaau, 0x7f5cf22cu, 0x19d86b0du, 0xcf96dea6u, 0xbad99b3bu}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 103 /* milli weight units */ } ,[MODULO_32] = { .tag = JET , .jet = simplicity_modulo_32 , .cmr = {{0xa1f01c10u, 0x6fc36a76u, 0x4e99b233u, 0x98e21e7cu, 0x267f889fu, 0xccebd148u, 0x7d3de1ccu, 0x67c32bd9u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 102 /* milli weight units */ } ,[MODULO_64] = { .tag = JET , .jet = simplicity_modulo_64 , .cmr = {{0x50c82fd0u, 0x3109c98bu, 0x7237e916u, 0x74041964u, 0x381e6c2eu, 0xbbe25bf3u, 0xe0d37a9fu, 0x060f1502u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 85 /* milli weight units */ } ,[MODULO_8] = { .tag = JET , .jet = simplicity_modulo_8 , .cmr = {{0x5c63c77au, 0x1608e2f6u, 0xa3748c11u, 0x0fbb9a1cu, 0x569fb4d5u, 0x40f3dd2eu, 0x4f80e90du, 0xd5ea9982u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 102 /* milli weight units */ } ,[MULTIPLY_16] = { .tag = JET , .jet = simplicity_multiply_16 , .cmr = {{0x46e62abfu, 0x8e30a774u, 0x6de0e929u, 0xf7beeddbu, 0xde8b269bu, 0xab08f76eu, 0x9547108bu, 0x1c360174u}} , .sourceIx = ty_w32 , .targetIx = ty_w32 , .cost = 90 /* milli weight units */ } ,[MULTIPLY_32] = { .tag = JET , .jet = simplicity_multiply_32 , .cmr = {{0x2decdc5bu, 0x0c6ff63du, 0x11f53852u, 0xe0deed11u, 0x4481355bu, 0xb6c6ce15u, 0x46ae9f81u, 0x5bee7750u}} , .sourceIx = ty_w64 , .targetIx = ty_w64 , .cost = 90 /* milli weight units */ } ,[MULTIPLY_64] = { .tag = JET , .jet = simplicity_multiply_64 , .cmr = {{0xbfa8626du, 0xbf10001du, 0xe390d997u, 0xf2ee7b19u, 0x0c24a78cu, 0xfecb91f5u, 0xd7c10c3fu, 0x9ddbb1e6u}} , .sourceIx = ty_w128 , .targetIx = ty_w128 , .cost = 85 /* milli weight units */ } ,[MULTIPLY_8] = { .tag = JET , .jet = simplicity_multiply_8 , .cmr = {{0x29da1337u, 0x4f7cb308u, 0x405fe230u, 0xf899485cu, 0x500e6e95u, 0x20c15e8au, 0x76e53a92u, 0xe7ac64d6u}} , .sourceIx = ty_w16 , .targetIx = ty_w16 , .cost = 93 /* milli weight units */ } ,[NEGATE_16] = { .tag = JET , .jet = simplicity_negate_16 , .cmr = {{0xf642173bu, 0x85ef2196u, 0x9d8d9048u, 0x807e3d4fu, 0xacf3f5f9u, 0xe59aa5cfu, 0x0c60f874u, 0x22ed7c8fu}} , .sourceIx = ty_w16 , .targetIx = ty_pbw16 , .cost = 70 /* milli weight units */ } ,[NEGATE_32] = { .tag = JET , .jet = simplicity_negate_32 , .cmr = {{0x549b65ceu, 0x97c6b334u, 0xb8ae9456u, 0x960e365bu, 0xb284d76du, 0x4005e921u, 0xf489bc36u, 0x26171b06u}} , .sourceIx = ty_w32 , .targetIx = ty_pbw32 , .cost = 85 /* milli weight units */ } ,[NEGATE_64] = { .tag = JET , .jet = simplicity_negate_64 , .cmr = {{0x35acca27u, 0xce658579u, 0xef1c55adu, 0x1abea005u, 0x0d9366d1u, 0x2209ad13u, 0x052549c3u, 0x436491d0u}} , .sourceIx = ty_w64 , .targetIx = ty_pbw64 , .cost = 94 /* milli weight units */ } ,[NEGATE_8] = { .tag = JET , .jet = simplicity_negate_8 , .cmr = {{0xd871c542u, 0x473f4dd9u, 0x02d31fe3u, 0xfc9ac0f3u, 0x319e42e8u, 0x0cae2181u, 0xffc85e6cu, 0x60fb0988u}} , .sourceIx = ty_w8 , .targetIx = ty_pbw8 , .cost = 91 /* milli weight units */ } ,[NEW_ISSUANCE_CONTRACT] = { .tag = JET , .jet = simplicity_new_issuance_contract , .cmr = {{0xdb64808cu, 0x3ff44880u, 0xd72bc295u, 0xd9ac0643u, 0xe51404deu, 0x5398ad9eu, 0x931bd3d2u, 0xadbca6c4u}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 157 /* milli weight units */ } ,[NONCE_HASH] = { .tag = JET , .jet = simplicity_nonce_hash , .cmr = {{0xfb1e0344u, 0xdcdaf9dbu, 0x91b987e8u, 0xf9661067u, 0x9f05deb2u, 0x06b40105u, 0x7502a484u, 0xaa87f8bfu}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256mspbw256w256 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 317 /* milli weight units */ } ,[NUM_INPUTS] = { .tag = JET , .jet = simplicity_num_inputs , .cmr = {{0xb2288ebau, 0xadcbcfceu, 0x1c631964u, 0xc86b127du, 0x6f91dc65u, 0x7c59a7fbu, 0x453e9111u, 0xd87481f5u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 86 /* milli weight units */ } ,[NUM_OUTPUTS] = { .tag = JET , .jet = simplicity_num_outputs , .cmr = {{0x267d4165u, 0x4493903eu, 0x0257751au, 0xe6d42d9cu, 0xe1bb9224u, 0x6d0ef767u, 0xc337b0c3u, 0x2b1972fdu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 79 /* milli weight units */ } ,[ONE_16] = { .tag = JET , .jet = simplicity_one_16 , .cmr = {{0x3f9f8dd1u, 0x4c46ee02u, 0x47155792u, 0x9ac2bb6cu, 0x1aca0052u, 0x1d8afaf0u, 0xdcd9f2cau, 0x7f31e604u}} , .sourceIx = ty_u , .targetIx = ty_w16 , .cost = 60 /* milli weight units */ } ,[ONE_32] = { .tag = JET , .jet = simplicity_one_32 , .cmr = {{0x478dc39du, 0xc3995e2eu, 0xdb7ec674u, 0x656cae79u, 0x8f52e572u, 0x926174a6u, 0x68cc97bcu, 0xa448d1ccu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 59 /* milli weight units */ } ,[ONE_64] = { .tag = JET , .jet = simplicity_one_64 , .cmr = {{0xa392cefcu, 0x0da53c65u, 0xaee612f5u, 0xc6816ca8u, 0x92fc156du, 0x43714876u, 0xb3a00568u, 0xe1ba3ebau}} , .sourceIx = ty_u , .targetIx = ty_w64 , .cost = 59 /* milli weight units */ } ,[ONE_8] = { .tag = JET , .jet = simplicity_one_8 , .cmr = {{0xff594e22u, 0xbfd75813u, 0xc056e0a2u, 0x34ed12fau, 0x8287d1d5u, 0x316f2390u, 0x2bf079dbu, 0xcc4f4ea8u}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 62 /* milli weight units */ } ,[OR_1] = { .tag = JET , .jet = simplicity_or_1 , .cmr = {{0x9bf59174u, 0x410a809du, 0x3da2b58cu, 0x7e0d05c5u, 0x5cec38bdu, 0xaa5fcac3u, 0x82a31177u, 0x0ee0eb38u}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 77 /* milli weight units */ } ,[OR_16] = { .tag = JET , .jet = simplicity_or_16 , .cmr = {{0xdd9a3193u, 0xd619d959u, 0xfa0b6d8bu, 0x47af7854u, 0xf7e0467bu, 0xa35901ceu, 0x43d800fcu, 0xaf730ff9u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 94 /* milli weight units */ } ,[OR_32] = { .tag = JET , .jet = simplicity_or_32 , .cmr = {{0x9a019f07u, 0xdf4996b3u, 0x3e647f4du, 0xe7e56c1du, 0x8f03269cu, 0xbfa3c758u, 0x2cfe808eu, 0x909870b7u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 105 /* milli weight units */ } ,[OR_64] = { .tag = JET , .jet = simplicity_or_64 , .cmr = {{0xc24f3580u, 0x05f80377u, 0x2b1c3e43u, 0x9cf1b709u, 0xbd9f4d42u, 0x52759130u, 0x3a36f6b1u, 0xc3cf29ccu}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 99 /* milli weight units */ } ,[OR_8] = { .tag = JET , .jet = simplicity_or_8 , .cmr = {{0x84b53689u, 0xf21d4e69u, 0x7d0fe898u, 0x8ce736abu, 0x72c9c86fu, 0x847589dau, 0xa9ae6a78u, 0x4630e620u}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 93 /* milli weight units */ } ,[OUTPOINT_HASH] = { .tag = JET , .jet = simplicity_outpoint_hash , .cmr = {{0x8d2a5aa0u, 0x6e98c41bu, 0x30fd0703u, 0xe5e54c86u, 0xb42bee33u, 0xbc89cb60u, 0x93cdb094u, 0x05a72d9du}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw256pw256w32 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 319 /* milli weight units */ } ,[OUTPUT_AMOUNT] = { .tag = JET , .jet = simplicity_output_amount , .cmr = {{0x55e41399u, 0x2169408eu, 0x338e11a8u, 0xd7be602bu, 0x3ec9511eu, 0x7eb691dfu, 0x32d9797au, 0x6395a1a1u}} , .sourceIx = ty_w32 , .targetIx = ty_mpspbw256w256spbw256w64 , .cost = 298 /* milli weight units */ } ,[OUTPUT_AMOUNTS_HASH] = { .tag = JET , .jet = simplicity_output_amounts_hash , .cmr = {{0x40236963u, 0xe10ef8adu, 0x9cb6e0a7u, 0xc79ac866u, 0x0d2fc1a5u, 0x7feff885u, 0x15a78527u, 0x91b186cbu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 140 /* milli weight units */ } ,[OUTPUT_ASSET] = { .tag = JET , .jet = simplicity_output_asset , .cmr = {{0x575a49bau, 0xb21ffee8u, 0xe5bd00edu, 0xce324061u, 0x04a05ddeu, 0xf5fc31a1u, 0xa645b129u, 0x548c8f3eu}} , .sourceIx = ty_w32 , .targetIx = ty_mspbw256w256 , .cost = 170 /* milli weight units */ } ,[OUTPUT_HASH] = { .tag = JET , .jet = simplicity_output_hash , .cmr = {{0x7cb17f8fu, 0xc7a1ae4eu, 0xfce30a14u, 0x54e52f85u, 0x85213cd0u, 0xf367a127u, 0xac27bb97u, 0x66ea9eeeu}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 2849 /* milli weight units */ } ,[OUTPUT_IS_FEE] = { .tag = JET , .jet = simplicity_output_is_fee , .cmr = {{0x9fbbe8aeu, 0xbdedd577u, 0xae466280u, 0xa99b67b7u, 0x343287efu, 0x34069253u, 0x4a009803u, 0x15e51772u}} , .sourceIx = ty_w32 , .targetIx = ty_mb , .cost = 92 /* milli weight units */ } ,[OUTPUT_NONCE] = { .tag = JET , .jet = simplicity_output_nonce , .cmr = {{0x7175fd99u, 0xa2baa1c3u, 0xafaaf7fau, 0xbdaa67c2u, 0xc827483bu, 0xc8a0b976u, 0x50cb7942u, 0xea295a18u}} , .sourceIx = ty_w32 , .targetIx = ty_mmspbw256w256 , .cost = 196 /* milli weight units */ } ,[OUTPUT_NONCES_HASH] = { .tag = JET , .jet = simplicity_output_nonces_hash , .cmr = {{0x50f18766u, 0xde9828dbu, 0x0a8c41d7u, 0xbeb840f7u, 0x7bc6e121u, 0xff123d54u, 0x96f1ea0du, 0x6a78b83au}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 151 /* milli weight units */ } ,[OUTPUT_NULL_DATUM] = { .tag = JET , .jet = simplicity_output_null_datum , .cmr = {{0x38a5a7e8u, 0x61b3b36cu, 0xce683a77u, 0x2db0c862u, 0x8b7fd3b4u, 0xcf8e7bceu, 0x70758fa6u, 0xf6f147bfu}} , .sourceIx = ty_w64 , .targetIx = ty_mmspw2w256sbw4 , .cost = 87 /* milli weight units */ } ,[OUTPUT_RANGE_PROOF] = { .tag = JET , .jet = simplicity_output_range_proof , .cmr = {{0x6ff9ef3du, 0xac504310u, 0xdfbc6056u, 0x1d2addebu, 0x44932f77u, 0x7e7f13adu, 0xf0774eb6u, 0xb14df966u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 154 /* milli weight units */ } ,[OUTPUT_RANGE_PROOFS_HASH] = { .tag = JET , .jet = simplicity_output_range_proofs_hash , .cmr = {{0x0d7d8ac9u, 0x7af9539au, 0xbba64d81u, 0x04d17e97u, 0x0854677cu, 0x27461d25u, 0xdf21a7f6u, 0xb662081eu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 136 /* milli weight units */ } ,[OUTPUT_SCRIPT_HASH] = { .tag = JET , .jet = simplicity_output_script_hash , .cmr = {{0x2f513926u, 0x6f143a33u, 0xe1668e59u, 0x4f43e8d1u, 0x394407e3u, 0xa9b8b802u, 0xb39a5e1eu, 0xdc54e851u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 151 /* milli weight units */ } ,[OUTPUT_SCRIPTS_HASH] = { .tag = JET , .jet = simplicity_output_scripts_hash , .cmr = {{0x21333ac9u, 0x58a4ebfdu, 0x5eab7956u, 0xdb73ed03u, 0x269426afu, 0x8d7d2498u, 0xde57eef6u, 0x8704fb0au}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 142 /* milli weight units */ } ,[OUTPUT_SURJECTION_PROOF] = { .tag = JET , .jet = simplicity_output_surjection_proof , .cmr = {{0x09166008u, 0x1d52c33fu, 0x17a956bdu, 0xdac62aa2u, 0xd2ed928fu, 0x8cffef4cu, 0xf8dbb697u, 0xb153aa65u}} , .sourceIx = ty_w32 , .targetIx = ty_mw256 , .cost = 151 /* milli weight units */ } ,[OUTPUT_SURJECTION_PROOFS_HASH] = { .tag = JET , .jet = simplicity_output_surjection_proofs_hash , .cmr = {{0x3630b520u, 0x8302641bu, 0xf19c4bf5u, 0xca047ac3u, 0xeb7af54du, 0x5d3f5bf8u, 0xf1d41312u, 0x499d6384u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 138 /* milli weight units */ } ,[OUTPUTS_HASH] = { .tag = JET , .jet = simplicity_outputs_hash , .cmr = {{0x95b3511au, 0xea00d043u, 0xa4e028b2u, 0x5a171c74u, 0x2ec2ff7au, 0xd3a7df2fu, 0x1f6edad0u, 0x8bad2b69u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 135 /* milli weight units */ } ,[PARSE_LOCK] = { .tag = JET , .jet = simplicity_parse_lock , .cmr = {{0x3d3836fdu, 0x3085c1fbu, 0xac6cd5fau, 0x0dbf4a3fu, 0xb2554593u, 0x17a266d6u, 0xd6f7382bu, 0xb05f07adu}} , .sourceIx = ty_w32 , .targetIx = ty_sw32w32 , .cost = 97 /* milli weight units */ } ,[PARSE_SEQUENCE] = { .tag = JET , .jet = simplicity_parse_sequence , .cmr = {{0x74f35c01u, 0x9ef514b7u, 0x0ab008bfu, 0x2a126de7u, 0xe00f6e3cu, 0xcd285d51u, 0xdbd3ac71u, 0xbea9c88du}} , .sourceIx = ty_w32 , .targetIx = ty_msw16w16 , .cost = 116 /* milli weight units */ } ,[POINT_VERIFY_1] = { .tag = JET , .jet = simplicity_point_verify_1 , .cmr = {{0x90a3d669u, 0xb00da795u, 0xefb2bed8u, 0xc370c9e3u, 0xea0f19c4u, 0x1c7cf23eu, 0x492e3317u, 0x1a47f5ffu}} , .sourceIx = ty_pppw256pbw256w256pbw256 , .targetIx = ty_u , .cost = 41494 /* milli weight units */ } ,[REISSUANCE_BLINDING] = { .tag = JET , .jet = simplicity_reissuance_blinding , .cmr = {{0xeb6e581eu, 0x20ba0babu, 0xe904c8dau, 0x71a81f7cu, 0x88b9cf4fu, 0x42d78b54u, 0x0c1b398cu, 0x3f105cccu}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 91 /* milli weight units */ } ,[REISSUANCE_ENTROPY] = { .tag = JET , .jet = simplicity_reissuance_entropy , .cmr = {{0xd1d22c49u, 0x7f129c6du, 0x6fdbe491u, 0x364a3513u, 0xbcd66e15u, 0x618cbbe2u, 0xe50739bdu, 0x834db7f8u}} , .sourceIx = ty_w32 , .targetIx = ty_mmw256 , .cost = 93 /* milli weight units */ } ,[RIGHT_EXTEND_16_32] = { .tag = JET , .jet = simplicity_right_extend_16_32 , .cmr = {{0x780716d3u, 0xe8291a51u, 0xe45ada50u, 0x558efe41u, 0x1c475c08u, 0x5eec5a28u, 0xad9791c3u, 0x12fee2bcu}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 74 /* milli weight units */ } ,[RIGHT_EXTEND_16_64] = { .tag = JET , .jet = simplicity_right_extend_16_64 , .cmr = {{0xc770497eu, 0x452308ebu, 0xf52e51b0u, 0x585e9151u, 0xe0ffc350u, 0x86ab772du, 0x7241532au, 0x1be15e07u}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 82 /* milli weight units */ } ,[RIGHT_EXTEND_32_64] = { .tag = JET , .jet = simplicity_right_extend_32_64 , .cmr = {{0x42b43adcu, 0x74b5266cu, 0x91d73df4u, 0x91dcae59u, 0x738804ebu, 0x440b23dau, 0x32753048u, 0x7486b7e8u}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 94 /* milli weight units */ } ,[RIGHT_EXTEND_8_16] = { .tag = JET , .jet = simplicity_right_extend_8_16 , .cmr = {{0xbcb2683au, 0x8cb8b8c2u, 0x35faa896u, 0xa9c069e1u, 0xb55bb055u, 0x8e739e70u, 0xe2891421u, 0x1e3275c8u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 76 /* milli weight units */ } ,[RIGHT_EXTEND_8_32] = { .tag = JET , .jet = simplicity_right_extend_8_32 , .cmr = {{0x6ddb5548u, 0xfd583cd2u, 0xd3586e6bu, 0x8bf99524u, 0x6b61934fu, 0x49764467u, 0x77dd5740u, 0xb319e462u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 106 /* milli weight units */ } ,[RIGHT_EXTEND_8_64] = { .tag = JET , .jet = simplicity_right_extend_8_64 , .cmr = {{0xda4f9c21u, 0x45512682u, 0x0758a2e4u, 0xb53fceb4u, 0x523e6e7au, 0x2923a1a1u, 0x61fc3789u, 0x2ac8da2au}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 124 /* milli weight units */ } ,[RIGHT_PAD_HIGH_16_32] = { .tag = JET , .jet = simplicity_right_pad_high_16_32 , .cmr = {{0x3e4e5e9eu, 0x71e137a2u, 0x686343e0u, 0x5ac56316u, 0xacfc5899u, 0x1cb38db1u, 0xb3234413u, 0xf730a142u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 70 /* milli weight units */ } ,[RIGHT_PAD_HIGH_16_64] = { .tag = JET , .jet = simplicity_right_pad_high_16_64 , .cmr = {{0xde09df9du, 0x43ddad2du, 0x69120498u, 0x6cf0819du, 0x6b8045bcu, 0xa414d80au, 0xf2162892u, 0xa9257eadu}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 88 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_16] = { .tag = JET , .jet = simplicity_right_pad_high_1_16 , .cmr = {{0xff1297d8u, 0x78e26e19u, 0x59bcc7e8u, 0xaef97ac0u, 0xb65adc39u, 0x923ec650u, 0x5e50f983u, 0x05733b6cu}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 143 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_32] = { .tag = JET , .jet = simplicity_right_pad_high_1_32 , .cmr = {{0x283f8afbu, 0x41382d2bu, 0xe18f8a77u, 0xc314ba17u, 0x76cb80c8u, 0xec36ca12u, 0xaa67b32bu, 0xb64ed843u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 223 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_64] = { .tag = JET , .jet = simplicity_right_pad_high_1_64 , .cmr = {{0xa3423528u, 0x60a3350du, 0x79c3e9fcu, 0x7a4ab378u, 0x9b8b0297u, 0x856fd169u, 0xca4d7de2u, 0x5f7d7cc4u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 476 /* milli weight units */ } ,[RIGHT_PAD_HIGH_1_8] = { .tag = JET , .jet = simplicity_right_pad_high_1_8 , .cmr = {{0x7103c0feu, 0x00f522a2u, 0x216c4a6bu, 0xe5f7e0ebu, 0x4d703ca7u, 0x8f9c598fu, 0x6b3dfde4u, 0x37d80c84u}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 107 /* milli weight units */ } ,[RIGHT_PAD_HIGH_32_64] = { .tag = JET , .jet = simplicity_right_pad_high_32_64 , .cmr = {{0x5dc9107du, 0x4534958cu, 0xe4422767u, 0x563a031au, 0x380f60d3u, 0x837148abu, 0x3c8cc9c4u, 0xc7d996a2u}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 94 /* milli weight units */ } ,[RIGHT_PAD_HIGH_8_16] = { .tag = JET , .jet = simplicity_right_pad_high_8_16 , .cmr = {{0xc0e2fd46u, 0xf7883b12u, 0x85a6f1a1u, 0xdb96d93cu, 0x2548040fu, 0xcd3f5c23u, 0xfbb20b5eu, 0x83037c96u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 89 /* milli weight units */ } ,[RIGHT_PAD_HIGH_8_32] = { .tag = JET , .jet = simplicity_right_pad_high_8_32 , .cmr = {{0x291e6277u, 0x08520c2cu, 0xa6aece32u, 0xa877b778u, 0x49c4a7a2u, 0x13cb89e1u, 0xbda7c5c5u, 0xfe755f73u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 110 /* milli weight units */ } ,[RIGHT_PAD_HIGH_8_64] = { .tag = JET , .jet = simplicity_right_pad_high_8_64 , .cmr = {{0x6b6fa237u, 0x2ed25e4au, 0x34d4ae17u, 0x2342adbbu, 0x259be898u, 0x7600db19u, 0x2ecb8da4u, 0x34b9d88fu}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 107 /* milli weight units */ } ,[RIGHT_PAD_LOW_16_32] = { .tag = JET , .jet = simplicity_right_pad_low_16_32 , .cmr = {{0x7731d560u, 0xd37592d1u, 0xa31f7362u, 0x967ab2e4u, 0x7592aca6u, 0xe92ab858u, 0x823792dau, 0xe5d2db52u}} , .sourceIx = ty_w16 , .targetIx = ty_w32 , .cost = 71 /* milli weight units */ } ,[RIGHT_PAD_LOW_16_64] = { .tag = JET , .jet = simplicity_right_pad_low_16_64 , .cmr = {{0x0fe1c0dbu, 0x9d4a2d63u, 0xe2ba4a33u, 0x117aadbau, 0x64514a2bu, 0x87a7a4e7u, 0x93faacfeu, 0x6b363447u}} , .sourceIx = ty_w16 , .targetIx = ty_w64 , .cost = 96 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_16] = { .tag = JET , .jet = simplicity_right_pad_low_1_16 , .cmr = {{0x7914c8f2u, 0x2247c2c3u, 0x4b9c84e9u, 0x2d1444aeu, 0xc2e17a0eu, 0xf586bab2u, 0x788ee6efu, 0x68840d98u}} , .sourceIx = ty_b , .targetIx = ty_w16 , .cost = 81 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_32] = { .tag = JET , .jet = simplicity_right_pad_low_1_32 , .cmr = {{0x31b6ce26u, 0xe559f76cu, 0xf366f480u, 0x6985ecc2u, 0x99550f15u, 0xd4c3a672u, 0x9e29d70eu, 0x39895652u}} , .sourceIx = ty_b , .targetIx = ty_w32 , .cost = 75 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_64] = { .tag = JET , .jet = simplicity_right_pad_low_1_64 , .cmr = {{0xc5524ae6u, 0x548acd63u, 0x082d9489u, 0x3e18f9edu, 0xbb9231e7u, 0x6bb4e11bu, 0xbff6a7bdu, 0x16f4b029u}} , .sourceIx = ty_b , .targetIx = ty_w64 , .cost = 73 /* milli weight units */ } ,[RIGHT_PAD_LOW_1_8] = { .tag = JET , .jet = simplicity_right_pad_low_1_8 , .cmr = {{0x59d72270u, 0xef0e8f77u, 0x0c8d11f3u, 0x1773f9b6u, 0xe90a4aecu, 0xeb5bfb3du, 0xfe968c4eu, 0x9dac5fe8u}} , .sourceIx = ty_b , .targetIx = ty_w8 , .cost = 68 /* milli weight units */ } ,[RIGHT_PAD_LOW_32_64] = { .tag = JET , .jet = simplicity_right_pad_low_32_64 , .cmr = {{0xd4227d06u, 0x6f18b911u, 0xd6f5d9bfu, 0xb9d9f46eu, 0x9aeadbbeu, 0xfa34d474u, 0x432a1e78u, 0x9e4886ffu}} , .sourceIx = ty_w32 , .targetIx = ty_w64 , .cost = 80 /* milli weight units */ } ,[RIGHT_PAD_LOW_8_16] = { .tag = JET , .jet = simplicity_right_pad_low_8_16 , .cmr = {{0xaba47a53u, 0x6e1227e1u, 0x22baacf1u, 0x9cfd2823u, 0xb9b78d79u, 0xcc06d34cu, 0x348b14a1u, 0xa15abd64u}} , .sourceIx = ty_w8 , .targetIx = ty_w16 , .cost = 75 /* milli weight units */ } ,[RIGHT_PAD_LOW_8_32] = { .tag = JET , .jet = simplicity_right_pad_low_8_32 , .cmr = {{0x8f80a6c2u, 0x74716b67u, 0x22041134u, 0xea1c68aau, 0xbf021329u, 0x8f4e18f8u, 0xf492dc53u, 0x808a3174u}} , .sourceIx = ty_w8 , .targetIx = ty_w32 , .cost = 77 /* milli weight units */ } ,[RIGHT_PAD_LOW_8_64] = { .tag = JET , .jet = simplicity_right_pad_low_8_64 , .cmr = {{0xd69c85e7u, 0xb2d7e949u, 0x436cb129u, 0x5e4aa705u, 0x57d75e7cu, 0xbdec02ccu, 0xa85fbfb1u, 0x3308b210u}} , .sourceIx = ty_w8 , .targetIx = ty_w64 , .cost = 82 /* milli weight units */ } ,[RIGHT_ROTATE_16] = { .tag = JET , .jet = simplicity_right_rotate_16 , .cmr = {{0xe5107082u, 0x47f91b4fu, 0x0a8a22a4u, 0x46b8137du, 0x0d42bee7u, 0x4c8c1eddu, 0x6d446edbu, 0x2013b598u}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 99 /* milli weight units */ } ,[RIGHT_ROTATE_32] = { .tag = JET , .jet = simplicity_right_rotate_32 , .cmr = {{0x98915731u, 0x412922dbu, 0xc516a737u, 0x3afc4de6u, 0x4809f83bu, 0x264bcfcau, 0x6ae74883u, 0xdbe104d6u}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 92 /* milli weight units */ } ,[RIGHT_ROTATE_64] = { .tag = JET , .jet = simplicity_right_rotate_64 , .cmr = {{0x9e2fb98au, 0xdf102933u, 0x9dbe45a2u, 0x2a54a390u, 0xca0986edu, 0xcea32eacu, 0xb82ebcc8u, 0x94a2711au}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 93 /* milli weight units */ } ,[RIGHT_ROTATE_8] = { .tag = JET , .jet = simplicity_right_rotate_8 , .cmr = {{0x00c7c26du, 0x95a50b5au, 0xf9349ffeu, 0x47e1d43fu, 0x3d761f17u, 0xa7453c98u, 0x4791e87du, 0xc6a311c8u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 75 /* milli weight units */ } ,[RIGHT_SHIFT_16] = { .tag = JET , .jet = simplicity_right_shift_16 , .cmr = {{0x8b5e0febu, 0x958130f0u, 0x50833215u, 0x9e54c2dfu, 0x98af8352u, 0x1acab308u, 0x4fd4f7c3u, 0xa2ccea77u}} , .sourceIx = ty_pw4w16 , .targetIx = ty_w16 , .cost = 84 /* milli weight units */ } ,[RIGHT_SHIFT_32] = { .tag = JET , .jet = simplicity_right_shift_32 , .cmr = {{0x4b1f2580u, 0xe0850d38u, 0xe2a11573u, 0x38052f1cu, 0x379f9d81u, 0x57f62d33u, 0x890af24fu, 0xd9a7f73eu}} , .sourceIx = ty_pw8w32 , .targetIx = ty_w32 , .cost = 88 /* milli weight units */ } ,[RIGHT_SHIFT_64] = { .tag = JET , .jet = simplicity_right_shift_64 , .cmr = {{0x91a297d7u, 0xb58a393bu, 0xf5902594u, 0x7747c86du, 0xd487659cu, 0xc56fb5a6u, 0xf6439955u, 0x129a9563u}} , .sourceIx = ty_pw8w64 , .targetIx = ty_w64 , .cost = 91 /* milli weight units */ } ,[RIGHT_SHIFT_8] = { .tag = JET , .jet = simplicity_right_shift_8 , .cmr = {{0xa4c3546fu, 0xf27e56d6u, 0x4e918ab2u, 0xfa6d00fcu, 0x2704585bu, 0x25bde004u, 0x9d6d8f48u, 0xd8cf1cd0u}} , .sourceIx = ty_pw4w8 , .targetIx = ty_w8 , .cost = 88 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_16] = { .tag = JET , .jet = simplicity_right_shift_with_16 , .cmr = {{0xfd977030u, 0xe3a25a32u, 0xe775b8d5u, 0xe87174a7u, 0xa9e8731eu, 0xc36cf132u, 0x6420ad91u, 0x502e6e98u}} , .sourceIx = ty_pbpw4w16 , .targetIx = ty_w16 , .cost = 105 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_32] = { .tag = JET , .jet = simplicity_right_shift_with_32 , .cmr = {{0x2829ba02u, 0x1f54077au, 0xffb66ac6u, 0xb6dfd3feu, 0xf38bc414u, 0x91845a41u, 0xce9dd370u, 0x586c2d04u}} , .sourceIx = ty_pbpw8w32 , .targetIx = ty_w32 , .cost = 92 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_64] = { .tag = JET , .jet = simplicity_right_shift_with_64 , .cmr = {{0x006fa3c5u, 0x45797547u, 0x86fc64dcu, 0x32e19a22u, 0x5cc152c9u, 0x4deeb3c6u, 0xab2967ddu, 0xbfc64653u}} , .sourceIx = ty_pbpw8w64 , .targetIx = ty_w64 , .cost = 97 /* milli weight units */ } ,[RIGHT_SHIFT_WITH_8] = { .tag = JET , .jet = simplicity_right_shift_with_8 , .cmr = {{0xfcb5be65u, 0x07f0ca44u, 0xbe2be1ccu, 0x3c3cfe39u, 0x94404b80u, 0x83bd7602u, 0xb2102cb1u, 0xfcfa2c61u}} , .sourceIx = ty_pbpw4w8 , .targetIx = ty_w8 , .cost = 103 /* milli weight units */ } ,[RIGHTMOST_16_1] = { .tag = JET , .jet = simplicity_rightmost_16_1 , .cmr = {{0x3f3c4346u, 0x87174226u, 0x5e87f001u, 0xb46de7d1u, 0x98751b34u, 0xfaa18018u, 0xde60c846u, 0x8d9b98a4u}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 70 /* milli weight units */ } ,[RIGHTMOST_16_2] = { .tag = JET , .jet = simplicity_rightmost_16_2 , .cmr = {{0x78f17147u, 0x6a3b0ed1u, 0xe3a5455au, 0x5fbbcc90u, 0x1981b323u, 0x0fea1264u, 0x204dacd0u, 0x81f94080u}} , .sourceIx = ty_w16 , .targetIx = ty_w2 , .cost = 82 /* milli weight units */ } ,[RIGHTMOST_16_4] = { .tag = JET , .jet = simplicity_rightmost_16_4 , .cmr = {{0x75a1dfb6u, 0xae2c066bu, 0x2d0e2093u, 0x048adbc5u, 0x0d465065u, 0x6fb2d357u, 0x8b57d9deu, 0x4c61c8b5u}} , .sourceIx = ty_w16 , .targetIx = ty_w4 , .cost = 76 /* milli weight units */ } ,[RIGHTMOST_16_8] = { .tag = JET , .jet = simplicity_rightmost_16_8 , .cmr = {{0xee769c1cu, 0xc8a3fdd1u, 0x838fc9f0u, 0x490ce703u, 0x93fd91bau, 0x3cbd4abdu, 0x08649fb9u, 0xc44311bdu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 69 /* milli weight units */ } ,[RIGHTMOST_32_1] = { .tag = JET , .jet = simplicity_rightmost_32_1 , .cmr = {{0xcb0db569u, 0xa36186a2u, 0x5605a9d2u, 0xe4e10a20u, 0xc111d50cu, 0x34f17246u, 0x520bc454u, 0xd8682836u}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 90 /* milli weight units */ } ,[RIGHTMOST_32_16] = { .tag = JET , .jet = simplicity_rightmost_32_16 , .cmr = {{0x06faa3beu, 0x678cd6fdu, 0xd7f3112eu, 0xbf2c4862u, 0x7afa7875u, 0xf7068d26u, 0xa9cc045bu, 0x2c8f11bcu}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 64 /* milli weight units */ } ,[RIGHTMOST_32_2] = { .tag = JET , .jet = simplicity_rightmost_32_2 , .cmr = {{0x00b8815au, 0xd7423dd5u, 0x8cb98be8u, 0x2cad2667u, 0x5c3bf54au, 0x0bedbadeu, 0x3464b4feu, 0x5a4e8ce6u}} , .sourceIx = ty_w32 , .targetIx = ty_w2 , .cost = 74 /* milli weight units */ } ,[RIGHTMOST_32_4] = { .tag = JET , .jet = simplicity_rightmost_32_4 , .cmr = {{0x3dfa7a20u, 0x198e42d6u, 0xa7948c8eu, 0xd8e0d47eu, 0xc7c0007bu, 0x3d6866cau, 0x15e3da04u, 0x5b8563c7u}} , .sourceIx = ty_w32 , .targetIx = ty_w4 , .cost = 92 /* milli weight units */ } ,[RIGHTMOST_32_8] = { .tag = JET , .jet = simplicity_rightmost_32_8 , .cmr = {{0x17b58d6eu, 0x304b1c7eu, 0x5dbf0c4du, 0xf6fcc803u, 0xc008944cu, 0x7995555bu, 0x94e1289bu, 0x2549be99u}} , .sourceIx = ty_w32 , .targetIx = ty_w8 , .cost = 78 /* milli weight units */ } ,[RIGHTMOST_64_1] = { .tag = JET , .jet = simplicity_rightmost_64_1 , .cmr = {{0x5e8fb49fu, 0xace03448u, 0x1dc65361u, 0x8e2a8b65u, 0xeaf0993fu, 0x28844cc9u, 0xb130caccu, 0xe45e82deu}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 77 /* milli weight units */ } ,[RIGHTMOST_64_16] = { .tag = JET , .jet = simplicity_rightmost_64_16 , .cmr = {{0xc64ca996u, 0x5536f237u, 0xbc4d166eu, 0x4aeca56eu, 0xac2662e6u, 0x3accb98bu, 0x6e542560u, 0xf9e538dau}} , .sourceIx = ty_w64 , .targetIx = ty_w16 , .cost = 86 /* milli weight units */ } ,[RIGHTMOST_64_2] = { .tag = JET , .jet = simplicity_rightmost_64_2 , .cmr = {{0x83d2da6fu, 0x3420d779u, 0xbcb8f60du, 0x0b696eedu, 0x74c31db0u, 0x8addbebdu, 0x1235a5dfu, 0x8f59c42fu}} , .sourceIx = ty_w64 , .targetIx = ty_w2 , .cost = 74 /* milli weight units */ } ,[RIGHTMOST_64_32] = { .tag = JET , .jet = simplicity_rightmost_64_32 , .cmr = {{0x7d2dff6eu, 0x3dd504bbu, 0x0e5703a0u, 0x33586d27u, 0xd96644c0u, 0x48ab34a4u, 0x5bf53512u, 0x9d501167u}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 76 /* milli weight units */ } ,[RIGHTMOST_64_4] = { .tag = JET , .jet = simplicity_rightmost_64_4 , .cmr = {{0x841bbd65u, 0x2742ddd3u, 0xadeae43cu, 0xfed6329fu, 0x2fd62e6fu, 0xecd0fd58u, 0xe3c3fb8bu, 0x5a0e4dd5u}} , .sourceIx = ty_w64 , .targetIx = ty_w4 , .cost = 70 /* milli weight units */ } ,[RIGHTMOST_64_8] = { .tag = JET , .jet = simplicity_rightmost_64_8 , .cmr = {{0xa0a61c76u, 0x58a18623u, 0xbf1d011au, 0x9792d518u, 0xfbd02414u, 0x2a904400u, 0xecdeea92u, 0x457a0a81u}} , .sourceIx = ty_w64 , .targetIx = ty_w8 , .cost = 69 /* milli weight units */ } ,[RIGHTMOST_8_1] = { .tag = JET , .jet = simplicity_rightmost_8_1 , .cmr = {{0x999b686eu, 0x60b3d1ecu, 0xd6c6d77fu, 0xbca82cb2u, 0xabbd4182u, 0xc8211267u, 0x475fa0c1u, 0x901d89f9u}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 79 /* milli weight units */ } ,[RIGHTMOST_8_2] = { .tag = JET , .jet = simplicity_rightmost_8_2 , .cmr = {{0x5307ffbfu, 0x516cd0eeu, 0xf3ff4387u, 0xb9052c14u, 0x4a4dfa23u, 0x29237c6bu, 0x274992b2u, 0xc8047b60u}} , .sourceIx = ty_w8 , .targetIx = ty_w2 , .cost = 98 /* milli weight units */ } ,[RIGHTMOST_8_4] = { .tag = JET , .jet = simplicity_rightmost_8_4 , .cmr = {{0x7f52e645u, 0xbbbbd792u, 0x69c43ef0u, 0x2db982f8u, 0xc63633c1u, 0x79e40691u, 0x73933604u, 0xcc635bcau}} , .sourceIx = ty_w8 , .targetIx = ty_w4 , .cost = 98 /* milli weight units */ } ,[SCALAR_ADD] = { .tag = JET , .jet = simplicity_scalar_add , .cmr = {{0x34baa40bu, 0x2e0aa8cbu, 0x7e97c73eu, 0x3ed3b365u, 0xa15b7c3fu, 0x7661fb19u, 0x715ec605u, 0xc1149d11u}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 739 /* milli weight units */ } ,[SCALAR_INVERT] = { .tag = JET , .jet = simplicity_scalar_invert , .cmr = {{0x6231bdabu, 0x73ca34eau, 0x7e837daau, 0xd692ede5u, 0xbabfae09u, 0xb5756d2au, 0xb36c5a36u, 0x475a6589u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 3193 /* milli weight units */ } ,[SCALAR_IS_ZERO] = { .tag = JET , .jet = simplicity_scalar_is_zero , .cmr = {{0xf75eda06u, 0xce6af09fu, 0xae37db4eu, 0x6225e6a8u, 0xac86a236u, 0x37627d62u, 0x6409190fu, 0xf3b39d90u}} , .sourceIx = ty_w256 , .targetIx = ty_b , .cost = 271 /* milli weight units */ } ,[SCALAR_MULTIPLY] = { .tag = JET , .jet = simplicity_scalar_multiply , .cmr = {{0xb2bcc390u, 0xd637b9e0u, 0x3fbfc42fu, 0xff71d22eu, 0x7200f693u, 0x29cef716u, 0x9e68a8c7u, 0x1a7f0a4bu}} , .sourceIx = ty_w512 , .targetIx = ty_w256 , .cost = 774 /* milli weight units */ } ,[SCALAR_MULTIPLY_LAMBDA] = { .tag = JET , .jet = simplicity_scalar_multiply_lambda , .cmr = {{0x89d5855cu, 0x5f85c003u, 0x5d27b0c0u, 0x9e20330bu, 0x001c684bu, 0x5986abceu, 0xd8360cd3u, 0x9b08c4e1u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 557 /* milli weight units */ } ,[SCALAR_NEGATE] = { .tag = JET , .jet = simplicity_scalar_negate , .cmr = {{0x0705acdfu, 0xb8664000u, 0x0e3d3badu, 0x509a14a7u, 0x8c171f61u, 0xedc08423u, 0xb042b947u, 0x48439cf8u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 490 /* milli weight units */ } ,[SCALAR_NORMALIZE] = { .tag = JET , .jet = simplicity_scalar_normalize , .cmr = {{0xa061e19du, 0x75c325a2u, 0x6d565aadu, 0x7e3f9ae2u, 0x6b222f25u, 0xe802174fu, 0x6bacd511u, 0x277aeaa5u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 472 /* milli weight units */ } ,[SCALAR_SQUARE] = { .tag = JET , .jet = simplicity_scalar_square , .cmr = {{0x49f734a2u, 0x659ca0abu, 0x7c9e67fcu, 0xfc3c0d72u, 0xaf0f917cu, 0x9edcb992u, 0x9d177a0fu, 0x0de89d59u}} , .sourceIx = ty_w256 , .targetIx = ty_w256 , .cost = 575 /* milli weight units */ } ,[SCALE] = { .tag = JET , .jet = simplicity_scale , .cmr = {{0xc04543dcu, 0x85ef1137u, 0x4a930f4au, 0x948eb735u, 0xa6500a1au, 0x7158d573u, 0x123f0721u, 0x7175f318u}} , .sourceIx = ty_pw256pw512w256 , .targetIx = ty_pw512w256 , .cost = 72675 /* milli weight units */ } ,[SCRIPT_CMR] = { .tag = JET , .jet = simplicity_script_cmr , .cmr = {{0xec15f59cu, 0x524d9414u, 0x69811954u, 0x654f6358u, 0x30ecd7deu, 0x517662b2u, 0x5ca4e8d0u, 0x5c2cce89u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 136 /* milli weight units */ } ,[SHA_256_BLOCK] = { .tag = JET , .jet = simplicity_sha_256_block , .cmr = {{0x0c97a008u, 0xade87bb1u, 0xe0ac06b7u, 0xd0313023u, 0x362858efu, 0x90ec14ecu, 0x9cb95f0du, 0xa964e008u}} , .sourceIx = ty_pw256w512 , .targetIx = ty_w256 , .cost = 771 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_1] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_1 , .cmr = {{0x37066c67u, 0xad95249du, 0x4ba6e181u, 0x44ca0a41u, 0x5d9c832au, 0xa6b60628u, 0xe97c967eu, 0xb1793383u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w8 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 642 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_128] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_128 , .cmr = {{0x2dcf484cu, 0x257f6794u, 0x0ca375bau, 0x98e83ce0u, 0xe2a71e16u, 0xda5051d1u, 0xbb19fb5fu, 0x346f154fu}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w1Ki , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1779 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_16] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_16 , .cmr = {{0x82992520u, 0x40cb39e3u, 0x26a248d5u, 0xc788f951u, 0x6d15a2ffu, 0x4145bb64u, 0xad6577aeu, 0x1a3ef727u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w128 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 747 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_2] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_2 , .cmr = {{0x8bae3e7eu, 0x1ed4dcbau, 0x6e645aa1u, 0x4341bbaeu, 0x0dbb3ae2u, 0x1bb63dc0u, 0x30ca0e44u, 0x7a857ec2u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w16 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 661 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_256] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_256 , .cmr = {{0x44b717e1u, 0x970999b6u, 0x6b693d8cu, 0x9d1d3b06u, 0x05c2b7a6u, 0x213e6ba5u, 0x6c69af8du, 0x7fae1686u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w2Ki , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 2912 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_32] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_32 , .cmr = {{0x39239a43u, 0xa84bac6fu, 0x2969bfa9u, 0x5bfe6a04u, 0xfcba8092u, 0x895939f1u, 0x2a1ce0e2u, 0x6321ec10u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w256 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 896 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_4] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_4 , .cmr = {{0xd7d74561u, 0x4b37a7e0u, 0x7dce22f6u, 0x4e7b1edfu, 0xe23beda8u, 0x51f1e76fu, 0x1a6b028fu, 0xcc5e9fc0u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w32 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 645 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_512] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_512 , .cmr = {{0xbe368032u, 0xd86ebcf2u, 0x13ca45bau, 0x6ecab54cu, 0xb1f2661du, 0x403da059u, 0x06300bc5u, 0x1137aab5u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w4Ki , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 5299 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_64] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_64 , .cmr = {{0xfdc434ceu, 0x83dbdce0u, 0x782aa36du, 0x418def7fu, 0x99af8293u, 0xafb29e83u, 0x9fe4948fu, 0x6234f77fu}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w512 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1187 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_8] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_8 , .cmr = {{0x9c988330u, 0x799a680bu, 0xfe73d7cau, 0xa3689fe4u, 0xe483da4eu, 0xe6d81858u, 0x7927c7f4u, 0x3392def7u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256w64 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 674 /* milli weight units */ } ,[SHA_256_CTX_8_ADD_BUFFER_511] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_add_buffer_511 , .cmr = {{0xc027e106u, 0x2996ae94u, 0xac3971a2u, 0xc4fae549u, 0x97ebf09bu, 0x9f7da575u, 0x639be617u, 0x167f02e3u}} , .sourceIx = ty_pppmw256pmw128pmw64pmw32pmw16mw8pw64w256pmw2Kipmw1Kipmw512pmw256pmw128pmw64pmw32pmw16mw8 , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 5060 /* milli weight units */ } ,[SHA_256_CTX_8_FINALIZE] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_finalize , .cmr = {{0xcbba1f1du, 0x8a97ab4du, 0x1fa9686eu, 0x7aeef066u, 0xfb5bf290u, 0x716eae10u, 0xe70b6199u, 0x96c59594u}} , .sourceIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .targetIx = ty_w256 , .cost = 835 /* milli weight units */ } ,[SHA_256_CTX_8_INIT] = { .tag = JET , .jet = simplicity_sha_256_ctx_8_init , .cmr = {{0xa53c7679u, 0xe3ae0347u, 0xd4d79126u, 0xa7c7e49au, 0xc0dec90cu, 0xdf935799u, 0xcddb58dau, 0x8f4496e4u}} , .sourceIx = ty_u , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 118 /* milli weight units */ } ,[SHA_256_IV] = { .tag = JET , .jet = simplicity_sha_256_iv , .cmr = {{0x7389f002u, 0x5305dce8u, 0x28d4a1feu, 0x83743046u, 0xa367c923u, 0xf18abf36u, 0x5e391e5bu, 0x04af1a47u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 93 /* milli weight units */ } ,[SIG_ALL_HASH] = { .tag = JET , .jet = simplicity_sig_all_hash , .cmr = {{0x6ac53d3fu, 0x93b8caf3u, 0xea8534aeu, 0x612abd32u, 0x325d2b0fu, 0xec17de36u, 0xaf0f71aau, 0x978f7cdeu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 133 /* milli weight units */ } ,[SOME_1] = { .tag = JET , .jet = simplicity_some_1 , .cmr = {{0xfbdad6b0u, 0x22a0c78fu, 0xf35604aau, 0xfacd27ccu, 0x10f51ee0u, 0x698c41f1u, 0xada90397u, 0x618d526fu}} , .sourceIx = ty_b , .targetIx = ty_b , .cost = 70 /* milli weight units */ } ,[SOME_16] = { .tag = JET , .jet = simplicity_some_16 , .cmr = {{0x7e2ccdbfu, 0xc24dd8d8u, 0xa904b017u, 0xdd4f57e7u, 0xc8749634u, 0x8aca7d04u, 0x58c9d16bu, 0x68bcda1cu}} , .sourceIx = ty_w16 , .targetIx = ty_b , .cost = 63 /* milli weight units */ } ,[SOME_32] = { .tag = JET , .jet = simplicity_some_32 , .cmr = {{0x4536aeb1u, 0x21c4273fu, 0xfc2a48feu, 0xd9eed031u, 0x2ebd972du, 0xec5681f4u, 0x7ead0f62u, 0xd954452au}} , .sourceIx = ty_w32 , .targetIx = ty_b , .cost = 64 /* milli weight units */ } ,[SOME_64] = { .tag = JET , .jet = simplicity_some_64 , .cmr = {{0x7f0bbd9du, 0x6631c130u, 0x9f901c2fu, 0x0d7a0d28u, 0x4a34416cu, 0xf750db1fu, 0xe2b9f3d6u, 0xed709409u}} , .sourceIx = ty_w64 , .targetIx = ty_b , .cost = 93 /* milli weight units */ } ,[SOME_8] = { .tag = JET , .jet = simplicity_some_8 , .cmr = {{0x2d8c8f71u, 0xee5e7582u, 0xf0ed65f5u, 0x26c02605u, 0xdcb93c0bu, 0xddb9433au, 0xff3f25c2u, 0x28acda8au}} , .sourceIx = ty_w8 , .targetIx = ty_b , .cost = 75 /* milli weight units */ } ,[SUBTRACT_16] = { .tag = JET , .jet = simplicity_subtract_16 , .cmr = {{0x569e6c6bu, 0x39e7d812u, 0x659b67aau, 0xc08ad150u, 0x99eead79u, 0x8fd1d42du, 0xa17ee3f0u, 0xd4d4492au}} , .sourceIx = ty_w32 , .targetIx = ty_pbw16 , .cost = 113 /* milli weight units */ } ,[SUBTRACT_32] = { .tag = JET , .jet = simplicity_subtract_32 , .cmr = {{0x19d35e0au, 0xf1e16514u, 0xa6dfc29au, 0x91418713u, 0x3964c480u, 0xf660e7ebu, 0x924ee16du, 0xbaa249cbu}} , .sourceIx = ty_w64 , .targetIx = ty_pbw32 , .cost = 118 /* milli weight units */ } ,[SUBTRACT_64] = { .tag = JET , .jet = simplicity_subtract_64 , .cmr = {{0x523e1186u, 0x28bf3ac1u, 0xa6be5a72u, 0xbdb1141bu, 0x89e0e001u, 0xe402addau, 0x82587900u, 0x03f88ad8u}} , .sourceIx = ty_w128 , .targetIx = ty_pbw64 , .cost = 115 /* milli weight units */ } ,[SUBTRACT_8] = { .tag = JET , .jet = simplicity_subtract_8 , .cmr = {{0x40950b86u, 0xf6f1f993u, 0x55dee11fu, 0x77daf279u, 0xa0cb6c6du, 0x156ae44bu, 0x7d5d2571u, 0x64b267c5u}} , .sourceIx = ty_w16 , .targetIx = ty_pbw8 , .cost = 109 /* milli weight units */ } ,[SWU] = { .tag = JET , .jet = simplicity_swu , .cmr = {{0xabf70be0u, 0x0b30f577u, 0xf987cb50u, 0x488996bau, 0x3596dbf9u, 0xc1e844a8u, 0xb1b8b710u, 0x853b65ebu}} , .sourceIx = ty_w256 , .targetIx = ty_w512 , .cost = 32120 /* milli weight units */ } ,[TAP_ENV_HASH] = { .tag = JET , .jet = simplicity_tap_env_hash , .cmr = {{0x72270771u, 0x93ec1741u, 0x8ebf7877u, 0xafdc7097u, 0xbd5eed57u, 0xe826df66u, 0x05c64869u, 0x1d003403u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 162 /* milli weight units */ } ,[TAPDATA_INIT] = { .tag = JET , .jet = simplicity_tapdata_init , .cmr = {{0x6c67e5c1u, 0x0735305eu, 0xe7deb59au, 0x6c6ac2efu, 0xfcab4ff7u, 0xbb479ea7u, 0x0081606eu, 0x60484ca7u}} , .sourceIx = ty_u , .targetIx = ty_ppmw256pmw128pmw64pmw32pmw16mw8pw64w256 , .cost = 1178 /* milli weight units */ } ,[TAPLEAF_HASH] = { .tag = JET , .jet = simplicity_tapleaf_hash , .cmr = {{0xd45a661fu, 0xc9100e2eu, 0xa9df789cu, 0xa2346da8u, 0x42717ef6u, 0xa8c82418u, 0x4f2da8c7u, 0xfb016203u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 136 /* milli weight units */ } ,[TAPLEAF_VERSION] = { .tag = JET , .jet = simplicity_tapleaf_version , .cmr = {{0xddb0edd6u, 0xce1e0798u, 0x3d1a6226u, 0xf00b1251u, 0x89af13bdu, 0x5cd06812u, 0x3ad43f48u, 0x201b006fu}} , .sourceIx = ty_u , .targetIx = ty_w8 , .cost = 105 /* milli weight units */ } ,[TAPPATH] = { .tag = JET , .jet = simplicity_tappath , .cmr = {{0x42c0c1f2u, 0xef0e28aeu, 0x7defa15eu, 0x84a06f35u, 0xfbf6fc89u, 0x7b29f683u, 0xfe1a24e3u, 0x0dc58bafu}} , .sourceIx = ty_w8 , .targetIx = ty_mw256 , .cost = 83 /* milli weight units */ } ,[TAPPATH_HASH] = { .tag = JET , .jet = simplicity_tappath_hash , .cmr = {{0x9da906e3u, 0xec086065u, 0xbe144136u, 0xb51620b6u, 0x6ddf4d71u, 0x3857354eu, 0xba3b97c7u, 0x7585f443u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 143 /* milli weight units */ } ,[TOTAL_FEE] = { .tag = JET , .jet = simplicity_total_fee , .cmr = {{0x4eba3f22u, 0xbac0a465u, 0xe4d08a9au, 0xc40518efu, 0x972c2e86u, 0x12090a51u, 0xe3203fcbu, 0xd2f4edbeu}} , .sourceIx = ty_w256 , .targetIx = ty_w64 , .cost = 230 /* milli weight units */ } ,[TRANSACTION_ID] = { .tag = JET , .jet = simplicity_transaction_id , .cmr = {{0x08b8eb3cu, 0x2d2d9584u, 0x58e163e9u, 0x4334950cu, 0x0bb914a0u, 0xb9d214fcu, 0x5e9de8f7u, 0x0a17a0d4u}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 139 /* milli weight units */ } ,[TX_HASH] = { .tag = JET , .jet = simplicity_tx_hash , .cmr = {{0xc36102aeu, 0xda8bcf62u, 0xa85e714bu, 0x18e4c50cu, 0xd417ffbfu, 0x86d73734u, 0xe02cbfcbu, 0x5313fccfu}} , .sourceIx = ty_u , .targetIx = ty_w256 , .cost = 143 /* milli weight units */ } ,[TX_IS_FINAL] = { .tag = JET , .jet = simplicity_tx_is_final , .cmr = {{0x8b314572u, 0x2470a07du, 0xe90a28bau, 0x89f3f886u, 0x42610096u, 0x54ce866cu, 0xd8eaf76cu, 0x5d8626ebu}} , .sourceIx = ty_u , .targetIx = ty_b , .cost = 71 /* milli weight units */ } ,[TX_LOCK_HEIGHT] = { .tag = JET , .jet = simplicity_tx_lock_height , .cmr = {{0xc20257f8u, 0xe76ecd0au, 0xe7ad634fu, 0x5dfa68aeu, 0x9a5eded0u, 0xe2eebe4eu, 0xe52cb47au, 0xcfb0264cu}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 80 /* milli weight units */ } ,[TX_LOCK_TIME] = { .tag = JET , .jet = simplicity_tx_lock_time , .cmr = {{0x3ee19005u, 0x42d01efdu, 0x4e9a01d4u, 0xefb1f9ddu, 0x992ced35u, 0xb7a752f8u, 0x3da59338u, 0x1538dea4u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 80 /* milli weight units */ } ,[VERIFY] = { .tag = JET , .jet = simplicity_verify , .cmr = {{0x343e6dc1u, 0x6b3f52e8u, 0x3e3b4cccu, 0x99b8c6f9u, 0x6a074fe3u, 0x99327af3u, 0x64bc285eu, 0x299745a2u}} , .sourceIx = ty_b , .targetIx = ty_u , .cost = 57 /* milli weight units */ } ,[VERSION] = { .tag = JET , .jet = simplicity_version , .cmr = {{0x087fc95cu, 0x41003348u, 0x759fd840u, 0x372c6f91u, 0x2d9be4e6u, 0x1eee3c6au, 0x7a40dc13u, 0xc9c1bc70u}} , .sourceIx = ty_u , .targetIx = ty_w32 , .cost = 93 /* milli weight units */ } ,[XOR_1] = { .tag = JET , .jet = simplicity_xor_1 , .cmr = {{0x9dc9fe42u, 0xf7eb3464u, 0x9f1c72d2u, 0xe5dd167du, 0xb21be532u, 0x1372d5cau, 0x7f6a184fu, 0x93e05ee3u}} , .sourceIx = ty_w2 , .targetIx = ty_b , .cost = 67 /* milli weight units */ } ,[XOR_16] = { .tag = JET , .jet = simplicity_xor_16 , .cmr = {{0x1fcaf40bu, 0xdedd72e7u, 0x97b09fe7u, 0x8753b0abu, 0x27872c0bu, 0xd12b0349u, 0x55fbfac2u, 0x3812ef26u}} , .sourceIx = ty_w32 , .targetIx = ty_w16 , .cost = 83 /* milli weight units */ } ,[XOR_32] = { .tag = JET , .jet = simplicity_xor_32 , .cmr = {{0x1d49fc94u, 0xf22b5d31u, 0xb7f9efb5u, 0x378e5f8au, 0x42626aedu, 0x4e927993u, 0x48d6b788u, 0xdfe86b1cu}} , .sourceIx = ty_w64 , .targetIx = ty_w32 , .cost = 92 /* milli weight units */ } ,[XOR_64] = { .tag = JET , .jet = simplicity_xor_64 , .cmr = {{0x7a3f3f55u, 0x20478365u, 0x3344311du, 0x1dc509d3u, 0x5b6639c0u, 0xd8b967a2u, 0x07806cd8u, 0x7d31d6e6u}} , .sourceIx = ty_w128 , .targetIx = ty_w64 , .cost = 95 /* milli weight units */ } ,[XOR_8] = { .tag = JET , .jet = simplicity_xor_8 , .cmr = {{0xd8335f48u, 0x90c1d8edu, 0x766c7135u, 0x902e01a0u, 0x094e3a98u, 0x16f70c84u, 0x7cc3d7c0u, 0x00406efeu}} , .sourceIx = ty_w16 , .targetIx = ty_w8 , .cost = 85 /* milli weight units */ } ,[XOR_XOR_1] = { .tag = JET , .jet = simplicity_xor_xor_1 , .cmr = {{0x1e107b05u, 0xff941d31u, 0xd7578b43u, 0x7328ba52u, 0xf3ff20a0u, 0x68c0d2bdu, 0xef087680u, 0x93cc7c63u}} , .sourceIx = ty_pbw2 , .targetIx = ty_b , .cost = 72 /* milli weight units */ } ,[XOR_XOR_16] = { .tag = JET , .jet = simplicity_xor_xor_16 , .cmr = {{0xb776989du, 0xa5095c4bu, 0xe94b1aefu, 0x759466e1u, 0x1f639c19u, 0x39471fa1u, 0x8e36e7e4u, 0x90c38961u}} , .sourceIx = ty_pw16w32 , .targetIx = ty_w16 , .cost = 79 /* milli weight units */ } ,[XOR_XOR_32] = { .tag = JET , .jet = simplicity_xor_xor_32 , .cmr = {{0xd168fac1u, 0xac7fc483u, 0x57be1b65u, 0x3375ec5eu, 0x3f05823au, 0xae6ac985u, 0xe9403eeau, 0xb12bb9f8u}} , .sourceIx = ty_pw32w64 , .targetIx = ty_w32 , .cost = 96 /* milli weight units */ } ,[XOR_XOR_64] = { .tag = JET , .jet = simplicity_xor_xor_64 , .cmr = {{0x361c5793u, 0x0ef97d49u, 0xcbc679fau, 0xef1e3bcfu, 0xfb787995u, 0xb961e553u, 0x7d2b1eebu, 0xc9c9a6e8u}} , .sourceIx = ty_pw64w128 , .targetIx = ty_w64 , .cost = 93 /* milli weight units */ } ,[XOR_XOR_8] = { .tag = JET , .jet = simplicity_xor_xor_8 , .cmr = {{0xc2da6e9cu, 0xa64d8a73u, 0xc1772667u, 0xb3d7a093u, 0x8bcb8a6cu, 0x43fd0473u, 0xeec71b77u, 0x494aad94u}} , .sourceIx = ty_pw8w16 , .targetIx = ty_w8 , .cost = 98 /* milli weight units */ } ================================================ FILE: C/elements/txEnv.c ================================================ #include "txEnv.h" /* Construct a txEnv structure from its components. * This function will precompute any cached values. * * Precondition: NULL != tx * NULL != taproot * NULL != genesisHash * ix < tx->numInputs */ txEnv simplicity_elements_build_txEnv(const elementsTransaction* tx, const elementsTapEnv* taproot, const sha256_midstate* genesisHash, uint_fast32_t ix) { txEnv result = { .tx = tx , .taproot = taproot , .genesisHash = *genesisHash , .ix = ix }; sha256_context ctx = sha256_init(result.sigAllHash.s); sha256_hash(&ctx, genesisHash); sha256_hash(&ctx, genesisHash); sha256_hash(&ctx, &tx->txHash); sha256_hash(&ctx, &taproot->tapEnvHash); sha256_u32be(&ctx, ix); sha256_finalize(&ctx); return result; } ================================================ FILE: C/elements/txEnv.h ================================================ /* This module defines the environment ('txEnv') for Simplicity evaluation for Elements. * It includes the transaction data and input index of the input whose Simplicity program is being executed. * It also includes the commitment Merkle root of the program being executed. */ #ifndef SIMPLICITY_ELEMENTS_TXENV_H #define SIMPLICITY_ELEMENTS_TXENV_H #include #include "../sha256.h" /* An Elements 'outpoint' consists of a transaction id and output index within that transaction. * The transaction id can be a either a transaction within the chain, or the transaction id from another chain in case of a peg-in. */ typedef struct outpoint { sha256_midstate txid; uint_fast32_t ix; } outpoint; /* In Elements, many fields can optionally be blinded and encoded as a point on the secp256k1 curve. * This prefix determines the parity of the y-coordinate of that point point, or indicates the value is explicit. * Sometimes values are entirely optional, in which case 'NONE' is a possibility. */ typedef enum confPrefix { NONE = 0, EXPLICIT = 1, EVEN_Y = 2, ODD_Y = 3 } confPrefix; /* Returns true when the prefix indicates the associated value is a confidential value. */ static inline bool is_confidential(confPrefix prefix) { return EVEN_Y == prefix || ODD_Y == prefix; } /* A confidential (256-bit) hash. * When 'prefix' is either 'EVEN_Y' or 'ODD_Y' then 'data' contains the x-coordinate of the point on the secp256k1 curve * representing the blinded value. * When 'prefix' is 'EXPLICIT' then 'data' is the unblinded 256-bit hash. * When 'prefix' is 'NONE' the value is "NULL" and the 'data' field is unused. */ typedef struct confidential { sha256_midstate data; confPrefix prefix; } confidential; /* A confidential 64-bit value. * When 'prefix' is either 'EVEN_Y' or 'ODD_Y' then 'confidential' contains the x-coordinate of the point on the secp256k1 curve * representing the blinded value. * When 'prefix' is 'EXPLICIT' then 'explicit' is the unblinded 256-bit hash. * invariant: 'prefix' != 'NONE' */ typedef struct confAmount { union { sha256_midstate confidential; uint_fast64_t explicit; }; confPrefix prefix; } confAmount; /* In Elements, a null-data scriptPubKey consists of an OP_RETURN followed by data only pushes (i.e. only opcodes less than OP_16). * This is an enumeration of all such data only push operation names. * OP_IMMEDIATE represents OP_0 and all the one-byte prefixes of data pushes up to 75 bytes. */ typedef enum opcodeType { OP_IMMEDIATE, OP_PUSHDATA, OP_PUSHDATA2, OP_PUSHDATA4, OP_1NEGATE, OP_RESERVED, OP_1, OP_2, OP_3, OP_4, OP_5, OP_6, OP_7, OP_8, OP_9, OP_10, OP_11, OP_12, OP_13, OP_14, OP_15, OP_16 } opcodeType; /* In Elements, a null-data scriptPubKey consists of an OP_RETURN followed by data only pushes (i.e. only opcodes less than OP_16). * This is a structure represents a digest of all such operations. * 'code' represents the operation name. * If 'code' \in {OP_IMMEDIATE, OP_PUSHDATA, OP_PUSHDATA2, OP_PUSHDATA4} then 'dataHash' represents the SHA-256 hash of data pushed * by the push operation. */ typedef struct opcode { sha256_midstate dataHash; opcodeType code; } opcode; /* In Elements, a null-data scriptPubKey consists of an OP_RETURN followed by data only pushes (i.e. only opcodes less than OP_16). * This is an structure for an array of digets of null-data scriptPubKeys. * 'op' is an array of the (digests of) each data push. * Note that 'len' is 0 for a null-data scriptPubKey consisting of only an OP_RETURN. * * Invariant: opcode op[len] (or op == NULL and len == 0) */ typedef struct parsedNullData { const opcode* op; uint_fast32_t len; } parsedNullData; /* A structure representing data from one output from an Elements transaction. * 'surjectionProofHash' is the SHA-256 hash of the output's surjection proof. * 'rangeProofHash' is the SHA-256 hash of the output's range proof. * 'scriptPubKey' is the SHA-256 hash of the outputs scriptPubKey. * 'isNullData' is true if the output has a null-data scriptPubKey. */ typedef struct sigOutput { confidential asset; sha256_midstate surjectionProofHash; sha256_midstate rangeProofHash; confAmount amt; confidential nonce; sha256_midstate scriptPubKey; uint_fast64_t assetFee; parsedNullData pnd; bool isNullData; bool emptyScript; } sigOutput; /* The data held by an Elements unspent transaction output database. * This 'scriptPubKey' of the unspent transaction output, which in our application is digested as a SHA-256 hash. * This also includes the asset and amount of the output, each of which may or may not be blinded. */ typedef struct utxo { sha256_midstate scriptPubKey; confidential asset; confAmount amt; } utxo; /* In Elements, a transaction input can optionally issue a new asset or reissue an existing asset. * This enumerates those possibilities. */ typedef enum issuanceType { NO_ISSUANCE = 0, NEW_ISSUANCE, REISSUANCE } issuanceType; /* In Elements, a transaction input can optionally issue a new asset or reissue an existing asset. * This structure contains data about such an issuance. * 'assetRangeProofHash' is the SHA-256 hash of the asset amount's range proof. * 'tokenRangeProofHash' is the SHA-256 hash of the token amount's range proof. * * Invariant: If 'type == NEW_ISSUANCE' then 'contractHash' and 'tokenAmt' are active; * If 'type == REISSUANCE' then 'blindingNonce' is active; */ typedef struct assetIssuance { union { struct { sha256_midstate contractHash; confAmount tokenAmt; }; struct { sha256_midstate blindingNonce; }; }; sha256_midstate entropy; sha256_midstate assetRangeProofHash; sha256_midstate tokenRangeProofHash; sha256_midstate assetId; /* Cached asset ID calculation. */ sha256_midstate tokenId; /* Cached token ID calculation. */ confAmount assetAmt; issuanceType type; } assetIssuance; /* A structure representing data from one input from an Elements transaction along with the utxo data of the output being redeemed. * When 'hasAnnex' then 'annexHash' is a cache of the hash of the input's segwit annex. * When 'isPegin' then the 'prevOutpoint' represents an outpoint of another chain * and 'pegin' contains the hash of the parent chain's genesis block. */ typedef struct sigInput { sha256_midstate annexHash; sha256_midstate pegin; sha256_midstate scriptSigHash; outpoint prevOutpoint; utxo txo; uint_fast32_t sequence; assetIssuance issuance; bool hasAnnex; bool isPegin; } sigInput; /* A structure representing data from an Elements transaction (along with the utxo data of the outputs being redeemed). * Includes a variety of cached hash values that are used in signature hash jets. */ typedef struct elementsTransaction { const sigInput* input; const sigOutput* output; const sigOutput* const * feeOutputs; sha256_midstate outputAssetAmountsHash; sha256_midstate outputNoncesHash; sha256_midstate outputScriptsHash; sha256_midstate outputRangeProofsHash; sha256_midstate outputSurjectionProofsHash; sha256_midstate outputsHash; sha256_midstate inputOutpointsHash; sha256_midstate inputAssetAmountsHash; sha256_midstate inputScriptsHash; sha256_midstate inputUTXOsHash; sha256_midstate inputSequencesHash; sha256_midstate inputAnnexesHash; sha256_midstate inputScriptSigsHash; sha256_midstate inputsHash; sha256_midstate issuanceAssetAmountsHash; sha256_midstate issuanceTokenAmountsHash; sha256_midstate issuanceRangeProofsHash; sha256_midstate issuanceBlindingEntropyHash; sha256_midstate issuancesHash; sha256_midstate txHash; sha256_midstate txid; uint_fast32_t numInputs; uint_fast32_t numOutputs; uint_fast32_t numFees; uint_fast32_t version; uint_fast32_t lockTime; /* These two fields are used to implement broken jets and only remain here for consensus purposes. */ uint_fast16_t obsolete_lockDistance; uint_fast16_t obsolete_lockDuration; bool isFinal; } elementsTransaction; /* A structure representing taproot spending data from an Elements transaction. * * Invariant: pathLen <= 128 * sha256_midstate path[pathLen]; */ typedef struct elementsTapEnv { const sha256_midstate *path; sha256_midstate tapLeafHash; sha256_midstate tappathHash; sha256_midstate tapEnvHash; sha256_midstate internalKey; sha256_midstate scriptCMR; unsigned char pathLen; unsigned char leafVersion; } elementsTapEnv; /* The 'txEnv' structure used by the Elements application of Simplicity. * * It includes * + the transaction data, which may be shared when Simplicity expressions are used for multiple inputs in the same transaction), * + the input index under consideration, * + the hash of the genesis block for the chain, */ typedef struct txEnv { const elementsTransaction* tx; const elementsTapEnv* taproot; sha256_midstate genesisHash; sha256_midstate sigAllHash; uint_fast32_t ix; } txEnv; /* Construct a txEnv structure from its components. * This function will precompute any cached values. * * Precondition: NULL != tx * NULL != taproot * NULL != genesisHash * ix < tx->numInputs */ txEnv simplicity_elements_build_txEnv(const elementsTransaction* tx, const elementsTapEnv* taproot, const sha256_midstate* genesisHash, uint_fast32_t ix); #endif ================================================ FILE: C/elements-sources.mk ================================================ # - All Variables ending in _HEADERS or _SOURCES confuse automake, so the # _INT postfix is applied. # - The %reldir% is the relative path from the Makefile.am. ELEMENTS_SIMPLICITY_INCLUDE_DIR_INT = %reldir%/include ELEMENTS_SIMPLICITY_DIST_HEADERS_INT = ELEMENTS_SIMPLICITY_DIST_HEADERS_INT += %reldir%/include/simplicity/errorCodes.h ELEMENTS_SIMPLICITY_DIST_HEADERS_INT += %reldir%/include/simplicity/elements/cmr.h ELEMENTS_SIMPLICITY_DIST_HEADERS_INT += %reldir%/include/simplicity/elements/env.h ELEMENTS_SIMPLICITY_DIST_HEADERS_INT += %reldir%/include/simplicity/elements/exec.h ELEMENTS_SIMPLICITY_LIB_SOURCES_INT = ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/bitstream.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/dag.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/deserialize.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/eval.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/frame.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/jets-secp256k1.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/jets.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/rsort.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/sha256.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/type.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/typeInference.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/cmr.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/env.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/exec.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/elementsJets.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/ops.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/primitive.c ELEMENTS_SIMPLICITY_LIB_SOURCES_INT += %reldir%/elements/txEnv.c ELEMENTS_SIMPLICITY_LIB_HEADERS_INT = ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/bitstream.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/bitstring.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/bounded.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/dag.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/decodeCoreJets.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/deserialize.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/eval.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/frame.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/jets.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/limitations.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/precomputed.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/rsort.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/sha256.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/sha256_x86.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/simplicity_alloc.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/simplicity_assert.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/taptweak.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/type.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/typeInference.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/uword.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/assumptions.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/eckey.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/eckey_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/ecmult.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/ecmult_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/extrakeys.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/extrakeys_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/field.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/field_5x52.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/field_5x52_asm_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/field_5x52_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/field_5x52_int128_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/field_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/generator.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/generator_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/group.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/group_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/int128.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/int128_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/int128_native.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/int128_native_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/int128_struct.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/int128_struct_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/modinv64.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/modinv64_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/precomputed_ecmult.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/scalar.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/scalar_4x64.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/scalar_4x64_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/scalar_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/schnorrsig.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/schnorrsig_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/secp256k1.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/secp256k1_impl.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/secp256k1/util.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/decodeElementsJets.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/elementsJets.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/ops.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/primitive.h ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/primitiveEnumJet.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/primitiveEnumTy.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/primitiveInitTy.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/primitiveJetNode.inc ELEMENTS_SIMPLICITY_LIB_HEADERS_INT += %reldir%/elements/txEnv.h ================================================ FILE: C/eval.c ================================================ #include "eval.h" #include #include "bounded.h" #include "limitations.h" #include "simplicity_alloc.h" #include "simplicity_assert.h" /* We choose an unusual representation for frames of the Bit Machine. * * An 'n'-bit frame is stored in the array of 'UWORD's of length 'l' where 'l' is the least value such that 'n <= l * UWORD_BIT'. * Thus there may be extra "padding" bits in the array when 'n < l * UWORD_BIT'. * * We choose to store the frames bits in a sequence with the first bits in the last element of the array and * the last bits in the first element of the array. * Within a 'UWORD' array element, the bits of the frame are stored with the first bits in the most significant positions * and the last bits in the least significant positions. * We choose to put padding bits entirely within the most significant bits of the last element of the array. * * Thus the last bit of the frame will always be the least significant bit of the first element of the array. * When there are no padding bits, the first bit of the frame will be the most significant bit of the last element of the array. * When there are padding bits, the first bit of the frame will occur at the most significant non-padding bit. * * More precisely, bit 'm' of an 'n'-bit frame (with '0 <= m < n') is the bit at position '1 << ((n-m-1) % UWORD_BIT)' * of the element of the array at index '(n-m-1 / UWORD_BIT)'. * * 0-bit frames are allowed, in which case the array will have length 0. * * Rationale: * * The Bit Machine's standard library of jets operates using a "big endian" representation of integers * from the Bit Machine's perspective. * It is often the case that we encounter types that are sums of various integers sizes. * For example, the Bitcoin primitive 'outputValue : TWO^32 |- ONE + TWO^64' has a target type * that is the sum of 64-bit integer (with a 0-bit integer). * * When a frame is generated from a type such as 'ONE + TWO^64' our representation places the tag for this type * by itself as the least significant bit of the last element of the frame's array (as long as 'UWORD_BIT' divides 64). * When this frame contains a value of the right-hand type, 'TWO^64', this value entirely fits perfectly within * the within the first elements of the array (again, as long as 'UWORD_BIT' divides 64). * Furthermore, if 'UWORD_BIT == 8', then this representation place this value of type 'TWO^64' * into the machine's memory in little endian byte order. * * All of the above means that when jets need to marshal values from the Bit Machine's representation * to the architecture's representation, it will often be the case that the data is already byte-aligned and * in the correct order for little endian processors. * When a jet marshals a architecture-sized word, and 'UWORD' is the architecture's native integer size, then * it will often be the case that the data is word-aligned (for both big and little endian processors). * Only the case when 'UWORD_BIT == 8' and architecture's processor is big-endian will the compiler need to emit * byte-swapping instructions. * * Nevertheless, our implementation is independent of architecture and will function correctly on all architectures * for any value of UWORD_BIT. * * Note: while we do attempt make the fast path for marshaling values for jets common, when assigning discounts to jets * it is important to only consider the worst case, slow path, behaviour, as good byte or bit alignment is not guaranteed in * presence of oddly shaped pairs of values. */ /* The main memory used by the Bit Machine during execution is contained in a single allocation of an array of 'UWORD's * named 'cells'. * The read and write frames used by the Bit Machine during execution are slices of this single array allocation. * We represent the read frame and write frame stacks within 'cells' using a [gap buffer](https://en.wikipedia.org/wiki/Gap_buffer). * The frames of the read frame stack are assigned to the beginning of the cell array * with the active read frame occurring as the last of these frames. * The frames of the write frame stack are assigned to the end of the cell array * with the active write frame occurring as the first of these frames. * This leaves a (possibly empty) gap of unused UWORDs between the '.edge' of the active read frame * and the '.edge' of the active write frame. * This gap will shrink / grow / move during the execution of the Bit Machine. * Thus whether a particular UWORD from 'cells' belongs to some read frame or write frame will vary during the execution. * Static analysis determines a safe size that is acceptable for the 'cells' array. */ /* To keep track of the individual frames of the read frame and write frame stacks we another single allocation of * an array of 'frameItem's called 'frames'. * This 'frames' array is another instance of a [gap buffer](https://en.wikipedia.org/wiki/Gap_buffer). * The read frames are tracked by 'frameItem's occurring at the beginning of the 'frames' array * with the active read frame tracked the last of these 'frameItem's. * The write frames are tracked by 'frameItem's occurring at the end of the 'frames' array * with the active write frame tracked the first of these 'frameItem's. * This leaves a (possibly empty) gap of unused 'frameItem's between the item that tracks active read frame * and the item that tracks the active write frame. * This gap will shrink / grow / move during the execution of the Bit Machine. * Thus whether a particular 'frameItem' from 'frames' tracks a read frame or write frame will vary during the execution. * The 'frameItem' that tracks the active read frame is located at 'state.activeReadFrame'. * The 'frameItem' that tracks the active write frame is located at 'state.activeWriteFrame'. * There is always an active read frame and an active write frame, though these frames are initially of size 0 * when evaluating Simplicity programs. * Static analysis determines a safe size that is acceptable for the 'frames' array. */ /* When a 'frameItem' tracks a read frame, its '.edge' field points to the UWORD from 'cell' that is * one-past-the-end of the 'cells' slice that makes up that frame. * The '.offset' value indirectly tracks the position of the read frame's cursor. * A cursor at the beginning of a read frame is denoted by an '.offset' value equal to that frame's padding. * When the frame has no padding, a cursor at the beginning of a read frame is denoted by an '.offset' of 0. * For each subsequent cursor position within the read frame, the '.offset' increments by one. * When the cursor is at (one-cell past) the end of the read frame, the '.offset' value will be equal to the total number of bits * allocated for the frame (including padding bits), which is necessarily some multiple of (UWORD_BIT). * We say "a read frame is valid for /n/ more cells" when '.edge - ROUND_UWORD(.offset + n)' points to a * 'UWORD[ROUND_UWORD(.offset + n)]' array of initialized values. * We say "a read frame is valid" if it is valid for 0 more cells. * * When a 'frameItem' tracks a write frame, its '.edge' field points the UWORD from 'cell' that is * the first element of the 'cells' slice that makes up that frame. * The '.offset' value indirectly tracks the position of the write frame's cursor. * A cursor at the beginning of a read frame is denoted by an '.offset' value equal to * that frame's number of bits (excluding padding). * For each subsequent cursor position within the write frame, the '.offset' decrements by one. * When the cursor is at (one-cell past) the end of the write frame, the '.offset' value will be equal to 0. * We say "a write frame is valid for /n/ more cells" when '.edge' points to an 'UWORD[ROUND_UWORD(.offset)]' array of * initialized values and 'n <= .offset'. * We say "a write frame is valid" if it is valid for 0 more cells. * * Notice that the interpretation of the fields of a 'frameItem' depends on whether the 'frameItem' is tracking a read frame or * a write frame. */ /* Given a read frame, advance its cursor by 'n' cells. * * Precondition: NULL != frame. */ static void forward(frameItem* frame, size_t n) { frame->offset += n; } /* Given a read frame, move its cursor backwards by 'n' cells. * * Precondition: n <= frame->offset */ static void backward(frameItem* frame, size_t n) { simplicity_debug_assert(n <= frame->offset); frame->offset -= n; } /* Given a write frame, advance its cursor by 'n' cells. * * Precondition: n <= frame->offset */ static void skip(frameItem* frame, size_t n) { simplicity_debug_assert(n <= frame->offset); frame->offset -= n; } /* Given a compact bit representation of a value 'v : B', write the value 'v' to a write frame, skipping cells as needed * and advance its cursor. * Cells in front of the '*dst's cursor's final position may be overwritten. * * :TODO: Consider writing an optimized version of this function for word type 'TWO^(2^n)' which is a very common case and * doesn't need any skipping of cells. * * Precondition: '*dst' is a valid write frame for 'bitSize(B)' more cells; * 'compactValue' is a compact bitstring representation of a value 'v : B'; * 'type_dag[typeIx]' is a type dag for the type B. */ static void writeValue(frameItem* dst, const bitstring* compactValue, size_t typeIx, type* type_dag) { size_t cur = typeSkip(typeIx, type_dag); size_t offset = 0; bool calling = true; setTypeBack(cur, type_dag, 0); while (cur) { if (SUM == type_dag[cur].kind) { simplicity_debug_assert(calling); /* Write one bit to the write frame and then skip over any padding bits. */ bool bit = getBit(compactValue, offset); offset++; writeBit(dst, bit); skip(dst, pad(bit, type_dag[type_dag[cur].typeArg[0]].bitSize, type_dag[type_dag[cur].typeArg[1]].bitSize)); size_t next = typeSkip(type_dag[cur].typeArg[bit], type_dag); if (next) { setTypeBack(next, type_dag, type_dag[cur].back); cur = next; } else { cur = type_dag[cur].back; calling = false; } } else { simplicity_debug_assert(PRODUCT == type_dag[cur].kind); size_t next; if (calling) { next = typeSkip(type_dag[cur].typeArg[0], type_dag); /* Note: Because we are using 'typeSkip' we have an invarant on 'cur' such that whenever type_dag[cur].kind == PRODUCT, then it is a product of two non-trival types. This implies that 'next' cannot actually be 0. */ if (next) { /* Traverse the first element of the product type, if it has any data. */ setTypeBack(next, type_dag, cur); cur = next; continue; } } next = typeSkip(type_dag[cur].typeArg[1], type_dag); /* Note: Because we are using 'typeSkip' we have an invarant on 'cur' such that whenever type_dag[cur].kind == PRODUCT, then it is a product of two non-trival types. This implies that 'next' cannot actually be 0. */ if (next) { /* Traverse the second element of the product type, if it has any data. */ setTypeBack(next, type_dag, type_dag[cur].back); cur = next; calling = true; } else { cur = type_dag[cur].back; calling = false; } } } /* Note: Above we use 'typeSkip' to skip over long chains of products against trivial types * This avoids a potential DOS vulnerability where a DAG of deeply nested products of unit types with sharing is traversed, * taking exponential time. * While traversing still could take exponential time in terms of the size of the type's dag, * at least one bit of witness data is required per PRODUCT type encountered. * This ought to limit the total number of times through the above loop to no more that 3 * compactValue->len. */ } /* Our representation of the Bit Machine state consists of a gap buffer of 'frameItem's. * The gap buffer is allocated at 'frame' * The read frames of the gap buffer extends from the beginning of the buffer to '.activeReadFrame'. * The write frames extend from the end of the buffer down to '.activeWriteFrame'. */ typedef struct evalState { frameItem* activeReadFrame; frameItem* activeWriteFrame; } evalState; /* 'call' is an item is used to track the "call stack" of the Bit Machine during evaluation. * Each call stack frame remembers where to return to after the call and a set of flags to hold various bits of state. */ typedef struct call { size_t return_to; flags_type flags; } call; #define FLAG_TCO 0x01 // Whether TCO is on (1) or off (0). #define FLAG_LAST_CASE 0x02 // For case combinators, last branch executed was right (1) or left (0). #define FLAG_EXEC 0x10 // Whether this combinator has ever been executed (1) or not (0). #define FLAG_CASE_LEFT 0x20 // For case combinators, whether the left branch has ever been executed (1) or not (0). #define FLAG_CASE_RIGHT 0x40 // For case combinators, whether the right branch has ever been executed (1) or not (0). static inline bool get_tco_flag(const call *stack) { return FLAG_TCO == (stack->flags & FLAG_TCO); } static inline void set_tco_flag(call *stack, bool flag) { if (flag) { stack->flags |= FLAG_TCO; } else { stack->flags &= (flags_type)(~FLAG_TCO); } } static inline bool get_case_last_flag(const call *stack) { return FLAG_LAST_CASE == (stack->flags & FLAG_LAST_CASE); } static inline void set_case_last_flag(call *stack, bool flag) { if (flag) { stack->flags |= FLAG_LAST_CASE; } else { stack->flags &= (flags_type)(~FLAG_LAST_CASE); } } /* Starting from the Bit Machine 'state', * run the machine with the TCO (off) program generated by the well-typed Simplicity expression 'dag[len]' of type 'A |- B'. * If some jet execution fails, returns 'SIMPLICITY_ERR_EXEC_JET'. * If some 'assertr' or 'assertl' combinator fails, returns 'SIMPLICITY_ERR_EXEC_ASSERT'. * Otherwise returns 'SIMPLICITY_NO_ERROR'. * * The 'state' of the Bit Machine is whatever the state is after the last successfully executed Bit Machine instruction. * * ** No heap allocations are allowed in 'runTCO' or any of its subroutines. ** * * Precondition: The gap between 'state.activeReadFrame' and 'state.activeWriteFrame' is sufficient for execution of 'dag' * and the values are initialized; * The gap between 'activeReadFrame(state)->edge' and 'activeWriteFrame(state)->edge' * is sufficient for execution of 'dag'; * '*activeReadFrame(state)' is a valid read frame for 'bitSize(A)' more cells. * '*activeWriteFrame(state)' is a valid write frame for 'bitSize(B)' more cells. * call stack[len]; * for all i < len, stack[i].flags = 0; * dag_node dag[len] and 'dag' is well-typed with 'type_dag'; * if 'dag[len]' represents a Simplicity expression with primitives then 'NULL != env'; */ static simplicity_err runTCO(evalState state, call* stack, const dag_node* dag, type* type_dag, size_t len, const txEnv* env) { /* The program counter, 'pc', is the current combinator being interpreted. */ size_t pc = len - 1; /* 'stack' represents the interpreter's call stack. * However, the stack is not directly represented as an array. * Instead, the bottom of the call stack is located at 'stack[len - 1]' and the top of the call stack is located at 'stack[pc]'. * The intermediate call stack items are somewhere between 'pc' and 'len - 1'. * The each call stack item references the one below it through the 'stack[i].return_to' values. * The bottom of the stack's '.return_to' value is set to 'len' which is an out-of-bounds index. * * During CALLs, a new 'stack[i]' value is created where 'i' is index of the combinator being called, * and 'stack[i].return_to' is set to the current 'pc' value. * During TAIL_CALLs, 'stack[i].return_to' is instead set to the 'stack[pc].return_to' value. * During RETURNs, the 'pc' is set to the 'stack[pc].return_to' value. * TAIL_CALLs allows for faster returns within the interpreter (unrelated to Simplicity's TCO), * skipping over intermediate combinators. */ stack[pc].return_to = len; set_tco_flag(&stack[pc], false); /* 'calling' lets us know if we are entering a CALL or returning from a CALL. */ bool calling = true; /* :TODO: Use static analysis to limit the number of iterations through this loop. */ while(pc < len) { stack[pc].flags |= FLAG_EXEC; tag_t tag = dag[pc].tag; simplicity_debug_assert(state.activeReadFrame < state.activeWriteFrame); simplicity_debug_assert(state.activeReadFrame->edge <= state.activeWriteFrame->edge); if (dag[pc].jet) { if(!dag[pc].jet(state.activeWriteFrame, *state.activeReadFrame, env)) return SIMPLICITY_ERR_EXEC_JET; /* Like IDEN and WITNESS, we want to "fallthrough" to the UNIT case. */ tag = UNIT; } switch (tag) { case COMP: if (calling) { /* NEW_FRAME(BITSIZE(B)) */ *(state.activeWriteFrame - 1) = initWriteFrame(type_dag[COMP_B(dag, type_dag, pc)].bitSize, state.activeWriteFrame->edge); state.activeWriteFrame--; /* CALL(dag[pc].child[0], SAME_TCO) */ stack[dag[pc].child[0]].return_to = pc; set_tco_flag(&stack[dag[pc].child[0]], get_tco_flag(&stack[pc])); pc = dag[pc].child[0]; } else { /* MOVE_FRAME */ simplicity_debug_assert(0 == state.activeWriteFrame->offset); memmove( state.activeReadFrame->edge, state.activeWriteFrame->edge , (size_t)((state.activeWriteFrame + 1)->edge - state.activeWriteFrame->edge) * sizeof(UWORD) ); *(state.activeReadFrame + 1) = initReadFrame(type_dag[COMP_B(dag, type_dag, pc)].bitSize, state.activeReadFrame->edge); state.activeWriteFrame++; state.activeReadFrame++; /* TAIL_CALL(dag[pc].child[1], true) */ calling = true; stack[dag[pc].child[1]].return_to = stack[pc].return_to; set_tco_flag(&stack[dag[pc].child[1]], true); pc = dag[pc].child[1]; } break; case ASSERTL: case ASSERTR: case CASE: if (calling) { bool bit = peekBit(state.activeReadFrame); if (bit) { stack[pc].flags |= FLAG_CASE_RIGHT; } else { stack[pc].flags |= FLAG_CASE_LEFT; } /* FWD(1 + PADL(A,B) when bit = 0; FWD(1 + PADR(A,B) when bit = 1 */ forward(state.activeReadFrame, 1 + pad( bit , type_dag[CASE_A(dag, type_dag, pc)].bitSize , type_dag[CASE_B(dag, type_dag, pc)].bitSize)); /* CONDITIONAL_TAIL_CALL(dag[pc].child[bit]); */ stack[dag[pc].child[bit]].return_to = get_tco_flag(&stack[pc]) ? stack[pc].return_to : pc; set_tco_flag(&stack[dag[pc].child[bit]], get_tco_flag(&stack[pc])); /* Remember the bit we peeked at for the case when we return. */ set_case_last_flag(&stack[pc], bit); pc = dag[pc].child[bit]; } else { /* BWD(1 + PADL(A,B) when bit = 0; BWD(1 + PADR(A,B) when bit = 1 */ backward(state.activeReadFrame, 1 + pad( get_case_last_flag(&stack[pc]) , type_dag[CASE_A(dag, type_dag, pc)].bitSize , type_dag[CASE_B(dag, type_dag, pc)].bitSize)); /* RETURN; */ pc = stack[pc].return_to; } break; case PAIR: if (calling) { /* CALL(dag[pc].child[0], false); */ stack[dag[pc].child[0]].return_to = pc; set_tco_flag(&stack[dag[pc].child[0]], false); pc = dag[pc].child[0]; } else { /* TAIL_CALL(dag[pc].child[1], SAME_TCO); */ calling = true; stack[dag[pc].child[1]].return_to = stack[pc].return_to; set_tco_flag(&stack[dag[pc].child[1]], get_tco_flag(&stack[pc])); pc = dag[pc].child[1]; } break; case DISCONNECT: if (calling) { /* NEW_FRAME(BITSIZE(WORD256 * A)) */ *(state.activeWriteFrame - 1) = initWriteFrame(type_dag[DISCONNECT_W256A(dag, type_dag, pc)].bitSize, state.activeWriteFrame->edge); state.activeWriteFrame--; /* WRITE_HASH(dag[dag[pc].child[1]].cmr) */ write32s(state.activeWriteFrame, dag[dag[pc].child[1]].cmr.s, 8); /* COPY(BITSIZE(A)) */ simplicity_copyBits(state.activeWriteFrame, state.activeReadFrame, type_dag[DISCONNECT_A(dag, type_dag, pc)].bitSize); if (get_tco_flag(&stack[pc])) { /* DROP_FRAME */ state.activeReadFrame--; } /* MOVE_FRAME */ simplicity_debug_assert(0 == state.activeWriteFrame->offset); memmove( state.activeReadFrame->edge, state.activeWriteFrame->edge , (size_t)((state.activeWriteFrame + 1)->edge - state.activeWriteFrame->edge) * sizeof(UWORD) ); *(state.activeReadFrame + 1) = initReadFrame(type_dag[DISCONNECT_W256A(dag, type_dag, pc)].bitSize, state.activeReadFrame->edge); state.activeWriteFrame++; state.activeReadFrame++; /* NEW_FRAME(BITSIZE(B * C)) */ *(state.activeWriteFrame - 1) = initWriteFrame(type_dag[DISCONNECT_BC(dag, type_dag, pc)].bitSize, state.activeWriteFrame->edge); state.activeWriteFrame--; /* CALL(dag[pc].child[0], true) */ stack[dag[pc].child[0]].return_to = pc; set_tco_flag(&stack[dag[pc].child[0]], true); pc = dag[pc].child[0]; } else { /* MOVE_FRAME */ simplicity_debug_assert(0 == state.activeWriteFrame->offset); memmove( state.activeReadFrame->edge, state.activeWriteFrame->edge , (size_t)((state.activeWriteFrame + 1)->edge - state.activeWriteFrame->edge) * sizeof(UWORD) ); *(state.activeReadFrame + 1) = initReadFrame(type_dag[DISCONNECT_BC(dag, type_dag, pc)].bitSize, state.activeReadFrame->edge); state.activeWriteFrame++; state.activeReadFrame++; /* COPY(BITSIZE(B)) */ simplicity_copyBits(state.activeWriteFrame, state.activeReadFrame, type_dag[DISCONNECT_B(dag, type_dag, pc)].bitSize); /* FWD(BITSIZE(B)) */ forward(state.activeReadFrame, type_dag[DISCONNECT_B(dag, type_dag, pc)].bitSize); /* TAIL_CALL(dag[pc].child[1], true) */ calling = true; stack[dag[pc].child[1]].return_to = stack[pc].return_to; set_tco_flag(&stack[dag[pc].child[1]], true); pc = dag[pc].child[1]; } break; case INJL: case INJR: /* WRITE(0) when INJL; WRITE(1) when INJR */ writeBit(state.activeWriteFrame, INJR == dag[pc].tag); /* SKIP(PADL(A,B)) when INJL; SKIP(PADR(A,B)) when INJR */ skip(state.activeWriteFrame, pad( INJR == dag[pc].tag , type_dag[INJ_B(dag, type_dag, pc)].bitSize , type_dag[INJ_C(dag, type_dag, pc)].bitSize)); /*@fallthrough@*/ case TAKE: simplicity_debug_assert(calling); /* TAIL_CALL(dag[pc].child[0], SAME_TCO); */ stack[dag[pc].child[0]].return_to = stack[pc].return_to; set_tco_flag(&stack[dag[pc].child[0]], get_tco_flag(&stack[pc])); pc = dag[pc].child[0]; break; case DROP: if (calling) { /* FWD(BITSIZE(A)) */ forward(state.activeReadFrame, type_dag[PROJ_A(dag, type_dag, pc)].bitSize); /* CONDITIONAL_TAIL_CALL(dag[pc].child[0]); */ stack[dag[pc].child[0]].return_to = get_tco_flag(&stack[pc]) ? stack[pc].return_to : pc; set_tco_flag(&stack[dag[pc].child[0]], get_tco_flag(&stack[pc])); pc = dag[pc].child[0]; } else { /* BWD(BITSIZE(A)) */ backward(state.activeReadFrame, type_dag[PROJ_A(dag, type_dag, pc)].bitSize); /* RETURN; */ pc = stack[pc].return_to; } break; case IDEN: case WORD: case WITNESS: if (IDEN == tag) { /* COPY(BITSIZE(A)) */ simplicity_copyBits(state.activeWriteFrame, state.activeReadFrame, type_dag[IDEN_A(dag, type_dag, pc)].bitSize); } else { writeValue(state.activeWriteFrame, &dag[pc].compactValue, dag[pc].targetType, type_dag); } /*@fallthrough@*/ case UNIT: simplicity_debug_assert(calling); if (get_tco_flag(&stack[pc])) { /* DROP_FRAME */ state.activeReadFrame--; } /* RETURN; */ calling = false; pc = stack[pc].return_to; break; case HIDDEN: return SIMPLICITY_ERR_EXEC_ASSERT; /* We have failed an 'ASSERTL' or 'ASSERTR' combinator. */ case JET: /* Jets (and primitives) should already have been processed by dag[i].jet already */ SIMPLICITY_UNREACHABLE; } } simplicity_assert(pc == len); return SIMPLICITY_NO_ERROR; } /* Inspects the stack contents after a successful runTCO execution to verify anti-DOS properties: * 1. If 'checks' includes 'CHECK_EXEC', then check that all non-HIDDEN dag nodes were executed at least once. * 2. If 'checks' includes 'CHECK_CASE', then check that both branches of every CASE node were executed. * * If these are violated, it means that the dag had unpruned nodes. * * Returns 'SIMPLICITY_ERR_ANTIDOS' if any of the anti-DOS checks fail. * Otherwise returns 'SIMPLICITY_NO_ERR'. * * Precondition: call stack[len]; * dag_node dag[len]; */ static simplicity_err antiDos(flags_type checks, const call* stack, const dag_node* dag, size_t len) { static_assert(CHECK_EXEC == FLAG_EXEC, "CHECK_EXEC does not match FLAG_EXEC"); static_assert(CHECK_CASE == (FLAG_CASE_LEFT | FLAG_CASE_RIGHT), "CHECK_CASE does not match FLAG_CASE"); simplicity_assert(CHECK_CASE == (checks & CHECK_CASE) || 0 == (checks & CHECK_CASE)); if (!checks) return SIMPLICITY_NO_ERROR; for(size_t i = 0; i < len; ++i) { /* All non-HIDDEN nodes must be executed at least once. */ /* Both branches of every case combinator must be executed at least once. */ flags_type test_flags = (HIDDEN != dag[i].tag ? CHECK_EXEC : 0) | (CASE == dag[i].tag ? CHECK_CASE : 0); /* Only enable requested checks */ test_flags &= checks; if (test_flags != (test_flags & stack[i].flags)) { return SIMPLICITY_ERR_ANTIDOS; } } return SIMPLICITY_NO_ERROR; } /* This structure is used by the static analysis that computes bounds on the working memory that suffices for * the Simplicity interpreter, and the CPU cost bounds in milliWU */ typedef struct boundsAnalysis { ubounded extraCellsBound[2]; ubounded extraUWORDBound[2]; ubounded extraFrameBound[2]; /* extraFrameBound[0] is for TCO off and extraFrameBound[1] is for TCO on */ ubounded cost; /* milliWU */ } boundsAnalysis; /* :TODO: Document extraFrameBound in the Tech Report (and implement it in Haskell) */ /* Given a well-typed dag representing a Simplicity expression, compute the memory and CPU requirements for evaluation. * * If 'malloc' fails, then returns SIMPLICITY_ERR_MALLOC. * When maxCells < UBOUNDED_MAX, if the bounds on the number of cells needed for evaluation of 'dag' on an idealized Bit Machine exceeds maxCells, * then return SIMPLICITY_ERR_EXEC_MEMORY. * When maxCost < UBOUNDED_MAX, if the bounds on the dag's CPU cost exceeds 'maxCost', then return SIMPLICITY_ERR_EXEC_BUDGET. * If the bounds on the dag's CPU cost is less than or equal to 'minCost', then return SIMPLICITY_ERR_OVERWEIGHT. * Otherwise returns SIMPLICITY_NO_ERR. * * Precondition: NULL != cellsBound * NULL != UWORDBound * NULL != frameBound * NULL != costBound * dag_node dag[len] and 'dag' is well-typed with 'type_dag'. * Postcondition: if the result is 'SIMPLICITY_NO_ERR' * then if maxCost < UBOUNDED_MAX then '*costBound' bounds the dag's CPU cost measured in milli weight units * and if maxCells < UBOUNDED_MAX then '*cellsBound' bounds the number of cells needed for evaluation of 'dag' on an idealized Bit Machine * and if maxCells < UBOUNDED_MAX then '*UWORDBound' bounds the number of UWORDs needed for the frames during evaluation of 'dag' * and if maxCells < UBOUNDED_MAX then '*frameBound' bounds the number of stack frames needed during execution of 'dag'. */ simplicity_err simplicity_analyseBounds( ubounded *cellsBound, ubounded *UWORDBound, ubounded *frameBound, ubounded *costBound , ubounded maxCells, ubounded minCost, ubounded maxCost, const dag_node* dag, const type* type_dag, const size_t len) { static_assert(DAG_LEN_MAX <= SIZE_MAX / sizeof(boundsAnalysis), "bound array too large."); static_assert(1 <= DAG_LEN_MAX, "DAG_LEN_MAX is zero."); static_assert(DAG_LEN_MAX - 1 <= UINT32_MAX, "bound array index does not fit in uint32_t."); simplicity_assert(1 <= len); simplicity_assert(len <= DAG_LEN_MAX); boundsAnalysis* bound = simplicity_malloc(len * sizeof(boundsAnalysis)); if (!bound) return SIMPLICITY_ERR_MALLOC; /* Sum up the total costs. * The computations for extraCells and cost are clipped at UBOUNDED_MAX, * so a result of UBOUNDED_MAX means "UBOUNDED_MAX or larger". * * The extraUWORD computation may produce unsigned overflow. * However the extraUWORD true value is less than the true value of extraCells. * As long as extraCells is strictly less than UBOUNDED_MAX, extraUWORD will be too. * * The extraFrame computation is bounded by DAG_LEN, and cannot overflow. */ for (size_t i = 0; i < len; ++i) { switch (dag[i].tag) { case ASSERTL: case ASSERTR: case CASE: bound[i].extraCellsBound[0] = bounded_max( bound[dag[i].child[0]].extraCellsBound[0] , bound[dag[i].child[1]].extraCellsBound[0] ); bound[i].extraCellsBound[1] = bounded_max( bound[dag[i].child[0]].extraCellsBound[1] , bound[dag[i].child[1]].extraCellsBound[1] ); bound[i].extraUWORDBound[0] = bounded_max( bound[dag[i].child[0]].extraUWORDBound[0] , bound[dag[i].child[1]].extraUWORDBound[0] ); bound[i].extraUWORDBound[1] = bounded_max( bound[dag[i].child[0]].extraUWORDBound[1] , bound[dag[i].child[1]].extraUWORDBound[1] ); bound[i].extraFrameBound[0] = bounded_max( bound[dag[i].child[0]].extraFrameBound[0] , bound[dag[i].child[1]].extraFrameBound[0] ); bound[i].extraFrameBound[1] = bounded_max( bound[dag[i].child[0]].extraFrameBound[1] , bound[dag[i].child[1]].extraFrameBound[1] ); bound[i].cost = bounded_add(overhead, bounded_max( bound[dag[i].child[0]].cost , bound[dag[i].child[1]].cost )); break; case DISCONNECT: bound[i].extraCellsBound[1] = type_dag[DISCONNECT_W256A(dag, type_dag, i)].bitSize; bound[i].extraCellsBound[0] = bounded_max( bounded_add( type_dag[DISCONNECT_BC(dag, type_dag, i)].bitSize , bounded_max( bounded_add(bound[i].extraCellsBound[1], bound[dag[i].child[0]].extraCellsBound[1]) , bounded_max(bound[dag[i].child[0]].extraCellsBound[0], bound[dag[i].child[1]].extraCellsBound[1]))), bound[dag[i].child[1]].extraCellsBound[0]); bound[i].extraUWORDBound[1] = (ubounded)ROUND_UWORD(type_dag[DISCONNECT_W256A(dag, type_dag, i)].bitSize); bound[i].extraUWORDBound[0] = bounded_max( (ubounded)ROUND_UWORD(type_dag[DISCONNECT_BC(dag, type_dag, i)].bitSize) + bounded_max( bound[i].extraUWORDBound[1] + bound[dag[i].child[0]].extraUWORDBound[1] , bounded_max(bound[dag[i].child[0]].extraUWORDBound[0], bound[dag[i].child[1]].extraUWORDBound[1])), bound[dag[i].child[1]].extraUWORDBound[0]); bound[i].extraFrameBound[1] = bounded_max( bound[dag[i].child[0]].extraFrameBound[1] + 1 , bound[dag[i].child[1]].extraFrameBound[1]); bound[i].extraFrameBound[0] = bound[i].extraFrameBound[1] + 1; bound[i].cost = bounded_add(overhead , bounded_add(type_dag[DISCONNECT_W256A(dag, type_dag, i)].bitSize , bounded_add(type_dag[DISCONNECT_W256A(dag, type_dag, i)].bitSize /* counted twice because the frame is both filled in and moved. */ , bounded_add(type_dag[DISCONNECT_BC(dag, type_dag, i)].bitSize , bounded_add(type_dag[DISCONNECT_B(dag, type_dag, i)].bitSize , bounded_add(bound[dag[i].child[0]].cost, bound[dag[i].child[1]].cost)))))); break; case COMP: bound[i].extraCellsBound[0] = bounded_max( bounded_add( type_dag[COMP_B(dag, type_dag, i)].bitSize , bounded_max( bound[dag[i].child[0]].extraCellsBound[0] , bound[dag[i].child[1]].extraCellsBound[1] )) , bound[dag[i].child[1]].extraCellsBound[0] ); bound[i].extraCellsBound[1] = bounded_add( type_dag[COMP_B(dag, type_dag, i)].bitSize , bound[dag[i].child[0]].extraCellsBound[1] ); bound[i].extraUWORDBound[0] = bounded_max( (ubounded)ROUND_UWORD(type_dag[COMP_B(dag, type_dag, i)].bitSize) + bounded_max( bound[dag[i].child[0]].extraUWORDBound[0] , bound[dag[i].child[1]].extraUWORDBound[1] ) , bound[dag[i].child[1]].extraUWORDBound[0] ); bound[i].extraUWORDBound[1] = (ubounded)ROUND_UWORD(type_dag[COMP_B(dag, type_dag, i)].bitSize) + bound[dag[i].child[0]].extraUWORDBound[1]; bound[i].extraFrameBound[0] = bounded_max( bound[dag[i].child[0]].extraFrameBound[0] , bound[dag[i].child[1]].extraFrameBound[1] ) + 1; bound[i].extraFrameBound[1] = bounded_max( bound[dag[i].child[0]].extraFrameBound[1] + 1 , bound[dag[i].child[1]].extraFrameBound[1] ); bound[i].cost = bounded_add(overhead , bounded_add(type_dag[COMP_B(dag, type_dag, i)].bitSize , bounded_add(bound[dag[i].child[0]].cost, bound[dag[i].child[1]].cost))); break; case PAIR: bound[i].extraCellsBound[0] = bound[dag[i].child[1]].extraCellsBound[0]; bound[i].extraCellsBound[1] = bounded_max( bound[dag[i].child[0]].extraCellsBound[0] , bounded_max( bound[dag[i].child[0]].extraCellsBound[1] , bound[dag[i].child[1]].extraCellsBound[1] )); bound[i].extraUWORDBound[0] = bound[dag[i].child[1]].extraUWORDBound[0]; bound[i].extraUWORDBound[1] = bounded_max( bound[dag[i].child[0]].extraUWORDBound[0] , bounded_max( bound[dag[i].child[0]].extraUWORDBound[1] , bound[dag[i].child[1]].extraUWORDBound[1] )); bound[i].extraFrameBound[0] = bounded_max( bound[dag[i].child[0]].extraFrameBound[0] , bound[dag[i].child[1]].extraFrameBound[0] ); bound[i].extraFrameBound[1] = bounded_max( bound[dag[i].child[0]].extraFrameBound[0] , bound[dag[i].child[1]].extraFrameBound[1] ); bound[i].cost = bounded_add(overhead, bounded_add( bound[dag[i].child[0]].cost , bound[dag[i].child[1]].cost )); break; case INJL: case INJR: case TAKE: case DROP: bound[i].extraCellsBound[0] = bound[dag[i].child[0]].extraCellsBound[0]; bound[i].extraCellsBound[1] = bound[dag[i].child[0]].extraCellsBound[1]; bound[i].extraUWORDBound[0] = bound[dag[i].child[0]].extraUWORDBound[0]; bound[i].extraUWORDBound[1] = bound[dag[i].child[0]].extraUWORDBound[1]; bound[i].extraFrameBound[0] = bound[dag[i].child[0]].extraFrameBound[0]; bound[i].extraFrameBound[1] = bound[dag[i].child[0]].extraFrameBound[1]; bound[i].cost = bounded_add(overhead, bound[dag[i].child[0]].cost); break; case IDEN: case UNIT: case HIDDEN: case WITNESS: case JET: case WORD: bound[i].extraCellsBound[0] = bound[i].extraCellsBound[1] = 0; bound[i].extraUWORDBound[0] = bound[i].extraUWORDBound[1] = 0; bound[i].extraFrameBound[0] = bound[i].extraFrameBound[1] = 0; bound[i].cost = IDEN == dag[i].tag ? bounded_add(overhead, type_dag[IDEN_A(dag, type_dag, i)].bitSize) : WITNESS == dag[i].tag || WORD == dag[i].tag ? bounded_add(overhead, type_dag[dag[i].targetType].bitSize) : JET == dag[i].tag ? bounded_add(overhead, dag[i].cost) : HIDDEN == dag[i].tag ? 0 : overhead; } } { const ubounded inputSize = type_dag[dag[len-1].sourceType].bitSize; const ubounded outputSize = type_dag[dag[len-1].targetType].bitSize; *cellsBound = bounded_add( bounded_add(inputSize, outputSize) , bounded_max(bound[len-1].extraCellsBound[0], bound[len-1].extraCellsBound[1]) ); *UWORDBound = (ubounded)ROUND_UWORD(inputSize) + (ubounded)ROUND_UWORD(outputSize) + bounded_max(bound[len-1].extraUWORDBound[0], bound[len-1].extraUWORDBound[1]); *frameBound = bound[len-1].extraFrameBound[0] + 2; /* add the initial input and output frames to the count. */ *costBound = bound[len-1].cost; } simplicity_free(bound); /* Note that the cellsBound and costBound computations have been clipped at UBOUNDED_MAX. * Therefore setting maxCells or maxCost to UBOUNDED_MAX will disable the corresponding error check. */ return (maxCells < *cellsBound) ? SIMPLICITY_ERR_EXEC_MEMORY : (maxCost < *costBound) ? SIMPLICITY_ERR_EXEC_BUDGET : (*costBound <= minCost) ? SIMPLICITY_ERR_OVERWEIGHT : SIMPLICITY_NO_ERROR; } /* Run the Bit Machine on the well-typed Simplicity expression 'dag[len]' of type A |- B. * If bitSize(A) > 0, initialize the active read frame's data with 'input[ROUND_UWORD(bitSize(A))]'. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * When a budget is given, if static analysis results determines the bound on cpu requirements exceed the allowed budget, returns 'SIMPLICITY_ERR_EXEC_BUDGET'. * If static analysis results determines the bound on cpu requirements is less than or equal to the minCost, returns 'SIMPLICITY_ERR_OVERWEIGHT'. * If static analysis results determines the bound on memory allocation requirements exceed the allowed limits, returns 'SIMPLICITY_ERR_EXEC_MEMORY'. * If during execution some jet execution fails, returns 'SIMPLICITY_ERR_EXEC_JET'. * If during execution some 'assertr' or 'assertl' combinator fails, returns 'SIMPLICITY_ERR_EXEC_ASESRT'. * * Note that minCost and budget parameters are in WU, while the cost analysis will be performed in milliWU. * Thus the minCost and budget specify a half open interval (minCost, budget] of acceptable cost values in milliWU. * Setting minCost to 0 effectively disables the minCost check as every Simplicity program has a non-zero cost analysis. * * If none of the above conditions fail and bitSize(B) > 0, then a copy the final active write frame's data is written to 'output[roundWord(bitSize(B))]'. * * If 'anti_dos_checks' includes the 'CHECK_EXEC' flag, and not every non-HIDDEN dag node is executed, returns 'SIMPLICITY_ERR_ANTIDOS' * If 'anti_dos_checks' includes the 'CHECK_CASE' flag, and not every case node has both branches executed, returns 'SIMPLICITY_ERR_ANTIDOS' * * Otherwise 'SIMPLICITY_NO_ERROR' is returned. * * Precondition: dag_node dag[len] and 'dag' is well-typed with 'type_dag' for an expression of type A |- B; * bitSize(A) == 0 or UWORD input[ROUND_UWORD(bitSize(A))]; * bitSize(B) == 0 or UWORD output[ROUND_UWORD(bitSize(B))]; * if NULL != budget then *budget <= BUDGET_MAX * if NULL != budget then minCost <= *budget * minCost <= BUDGET_MAX * if 'dag[len]' represents a Simplicity expression with primitives then 'NULL != env'; */ simplicity_err simplicity_evalTCOExpression( flags_type anti_dos_checks, UWORD* output, const UWORD* input , const dag_node* dag, type* type_dag, size_t len, ubounded minCost, const ubounded* budget, const txEnv* env ) { simplicity_assert(1 <= len); simplicity_assert(len <= DAG_LEN_MAX); if (budget) { simplicity_assert(*budget <= BUDGET_MAX); simplicity_assert(minCost <= *budget); } simplicity_assert(minCost <= BUDGET_MAX); static_assert(1 <= UBOUNDED_MAX, "UBOUNDED_MAX is zero."); static_assert(BUDGET_MAX <= (UBOUNDED_MAX - 1) / 1000, "BUDGET_MAX is too large."); static_assert(CELLS_MAX < UBOUNDED_MAX, "CELLS_MAX is too large."); ubounded cellsBound, UWORDBound, frameBound, costBound; simplicity_err result = simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, CELLS_MAX, minCost*1000, budget ? *budget*1000 : UBOUNDED_MAX, dag, type_dag, len); if (!IS_OK(result)) return result; /* frameBound is at most 2*len. */ static_assert(DAG_LEN_MAX <= UBOUNDED_MAX / 2, "2*DAG_LEN_MAX does not fit in size_t."); simplicity_assert(frameBound <= 2*len); /* UWORDBound * UWORD_BIT, the number of bits actually allocacted, is at most the cellBound count plus (worse case) padding bits in each frame. */ static_assert(1 <= UWORD_BIT, "UWORD_BIT is zero."); static_assert(2*DAG_LEN_MAX <= (SIZE_MAX - CELLS_MAX) / (UWORD_BIT - 1), "cellsBound + frameBound*(UWORD_BIT - 1) doesn't fit in size_t."); simplicity_assert(UWORDBound <= (cellsBound + frameBound*(UWORD_BIT - 1)) / UWORD_BIT); /* UWORDBound, is also at most the cellsBound, with an entire UWORD per cell (the rest of the UWORD being padding). */ simplicity_assert(UWORDBound <= cellsBound); /* We use calloc for 'cells' because the frame data must be initialized before we can perform bitwise operations. */ static_assert(CELLS_MAX - 1 <= UINT32_MAX, "cells array index does not fit in uint32_t."); UWORD* cells = simplicity_calloc(UWORDBound ? UWORDBound : 1, sizeof(UWORD)); static_assert(2*DAG_LEN_MAX <= SIZE_MAX / sizeof(frameItem), "frames array does not fit in size_t."); static_assert(1 <= DAG_LEN_MAX, "DAG_LEN_MAX is zero."); static_assert(2*DAG_LEN_MAX - 1 <= UINT32_MAX, "frames array index does not fit in uint32_t."); frameItem* frames = simplicity_malloc(frameBound * sizeof(frameItem)); call* stack = simplicity_calloc(len, sizeof(call)); result = cells && frames && stack ? SIMPLICITY_NO_ERROR : SIMPLICITY_ERR_MALLOC; if (IS_OK(result)) { const ubounded inputSize = type_dag[dag[len-1].sourceType].bitSize; const ubounded outputSize = type_dag[dag[len-1].targetType].bitSize; simplicity_assert(NULL != input || 0 == inputSize); if (inputSize) memcpy(cells, input, ROUND_UWORD(inputSize) * sizeof(UWORD)); evalState state = { .activeReadFrame = frames , .activeWriteFrame = frames + (frameBound - 1) }; *(state.activeReadFrame) = initReadFrame(inputSize, cells); *(state.activeWriteFrame) = initWriteFrame(outputSize, cells + UWORDBound); result = runTCO(state, stack, dag, type_dag, len, env); if (IS_OK(result)) { simplicity_assert(NULL != output || 0 == outputSize); if (outputSize) memcpy(output, state.activeWriteFrame->edge, ROUND_UWORD(outputSize) * sizeof(UWORD)); result = antiDos(anti_dos_checks, stack, dag, len); } } simplicity_free(stack); simplicity_free(frames); simplicity_free(cells); return result; } ================================================ FILE: C/eval.h ================================================ /* This module provides functions for evaluating Simplicity programs and expressions. */ #ifndef SIMPLICITY_EVAL_H #define SIMPLICITY_EVAL_H #include "bounded.h" #include "dag.h" typedef unsigned char flags_type; #define CHECK_NONE 0 #define CHECK_EXEC 0x10 #define CHECK_CASE 0x60 #define CHECK_ALL ((flags_type)(-1)) /* Given a well-typed dag representing a Simplicity expression, compute the memory and CPU requirements for evaluation. * * If 'malloc' fails, then returns SIMPLICITY_ERR_MALLOC. * When maxCells < UBOUNDED_MAX, if the bounds on the number of cells needed for evaluation of 'dag' on an idealized Bit Machine exceeds maxCells, * then return SIMPLICITY_ERR_EXEC_MEMORY. * When maxCost < UBOUNDED_MAX, if the bounds on the dag's CPU cost exceeds 'maxCost', then return SIMPLICITY_ERR_EXEC_BUDGET. * If the bounds on the dag's CPU cost is less than or equal to 'minCost', then return SIMPLICITY_ERR_OVERWEIGHT. * Otherwise returns SIMPLICITY_NO_ERR. * * Precondition: NULL != cellsBound * NULL != UWORDBound * NULL != frameBound * NULL != costBound * dag_node dag[len] and 'dag' is well-typed with 'type_dag'. * Postcondition: if the result is 'SIMPLICITY_NO_ERR' * then if maxCost < UBOUNDED_MAX then '*costBound' bounds the dag's CPU cost measured in milli weight units * and if maxCells < UBOUNDED_MAX then '*cellsBound' bounds the number of cells needed for evaluation of 'dag' on an idealized Bit Machine * and if maxCells < UBOUNDED_MAX then '*UWORDBound' bounds the number of UWORDs needed for the frames during evaluation of 'dag' * and if maxCells < UBOUNDED_MAX then '*frameBound' bounds the number of stack frames needed during execution of 'dag'. */ simplicity_err simplicity_analyseBounds( ubounded *cellsBound, ubounded *UWORDBound, ubounded *frameBound, ubounded *costBound , ubounded maxCells, ubounded minCost, ubounded maxCost, const dag_node* dag, const type* type_dag, const size_t len); /* Run the Bit Machine on the well-typed Simplicity expression 'dag[len]' of type A |- B. * If bitSize(A) > 0, initialize the active read frame's data with 'input[ROUND_UWORD(bitSize(A))]'. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * When a budget is given, if static analysis results determines the bound on cpu requirements exceed the allowed budget, returns 'SIMPLICITY_ERR_EXEC_BUDGET'. * If static analysis results determines the bound on cpu requirements is less than or equal to the minCost, returns 'SIMPLICITY_ERR_OVERWEIGHT'. * If static analysis results determines the bound on memory allocation requirements exceed the allowed limits, returns 'SIMPLICITY_ERR_EXEC_MEMORY'. * If during execution some jet execution fails, returns 'SIMPLICITY_ERR_EXEC_JET'. * If during execution some 'assertr' or 'assertl' combinator fails, returns 'SIMPLICITY_ERR_EXEC_ASESRT'. * * Note that minCost and budget parameters are in WU, while the cost analysis will be performed in milliWU. * Thus the minCost and budget specify a half open interval (minCost, budget] of acceptable cost values in milliWU. * Setting minCost to 0 effectively disables the minCost check as every Simplicity program has a non-zero cost analysis. * * If none of the above conditions fail and bitSize(B) > 0, then a copy the final active write frame's data is written to 'output[roundWord(bitSize(B))]'. * * If 'anti_dos_checks' includes the 'CHECK_EXEC' flag, and not every non-HIDDEN dag node is executed, returns 'SIMPLICITY_ERR_ANTIDOS' * If 'anti_dos_checks' includes the 'CHECK_CASE' flag, and not every case node has both branches executed, returns 'SIMPLICITY_ERR_ANTIDOS' * * Otherwise 'SIMPLICITY_NO_ERROR' is returned. * * Precondition: dag_node dag[len] and 'dag' is well-typed with 'type_dag' for an expression of type A |- B; * bitSize(A) == 0 or UWORD input[ROUND_UWORD(bitSize(A))]; * bitSize(B) == 0 or UWORD output[ROUND_UWORD(bitSize(B))]; * if NULL != budget then *budget <= BUDGET_MAX * if NULL != budget then minCost <= *budget * minCost <= BUDGET_MAX * if 'dag[len]' represents a Simplicity expression with primitives then 'NULL != env'; */ simplicity_err simplicity_evalTCOExpression( flags_type anti_dos_checks, UWORD* output, const UWORD* input , const dag_node* dag, type* type_dag, size_t len, ubounded minCost, const ubounded* budget, const txEnv* env ); /* Run the Bit Machine on the well-typed Simplicity program 'dag[len]'. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * When a budget is given, if static analysis results determines the bound on cpu requirements exceed the allowed budget, returns 'SIMPLICITY_ERR_EXEC_BUDGET'. * If static analysis results determines the bound on cpu requirements is less than or equal to the minCost, returns 'SIMPLICITY_ERR_OVERWEIGHT'. * If static analysis results determines the bound on memory allocation requirements exceed the allowed limits, returns 'SIMPLICITY_ERR_EXEC_MEMORY'. * If during execution some jet execution fails, returns 'SIMPLICITY_ERR_EXEC_JET'. * If during execution some 'assertr' or 'assertl' combinator fails, returns 'SIMPLICITY_ERR_EXEC_ASESRT'. * * Note that minCost and budget parameters are in WU, while the cost analysis will be performed in milliWU. * Thus the minCost and budget specify a half open interval (minCost, budget] of acceptable cost values in milliWU. * Setting minCost to 0 effectively disables the minCost check as every Simplicity program has a non-zero cost analysis. * * If not every non-HIDDEN dag node is executed, returns 'SIMPLICITY_ERR_ANTIDOS' * If not every case node has both branches executed, returns 'SIMPLICITY_ERR_ANTIDOS' * * Otherwise 'SIMPLICITY_NO_ERROR' is returned. * * Precondition: dag_node dag[len] and 'dag' is well-typed with 'type_dag' for an expression of type ONE |- ONE; * if NULL != budget then *budget <= BUDGET_MAX * if NULL != budget then minCost <= *budget * minCost <= BUDGET_MAX * if 'dag[len]' represents a Simplicity expression with primitives then 'NULL != env'; */ static inline simplicity_err evalTCOProgram(const dag_node* dag, type* type_dag, size_t len, ubounded minCost, const ubounded* budget, const txEnv* env) { return simplicity_evalTCOExpression(CHECK_ALL, NULL, NULL, dag, type_dag, len, minCost, budget, env); } #endif ================================================ FILE: C/frame.c ================================================ #include "frame.h" #define READ_(bits,size) \ /* Given a read frame, return the value of the bits cells after the cursor and advance the frame's cursor by bits##. \ * The cell values are returned with the first cell in the MSB of the result and the last cell in the LSB of the result. \ * \ * Precondition: '*frame' is a valid read frame for bits more cells. \ */ \ uint_fast##size##_t simplicity_read##bits(frameItem* frame) { \ static_assert(bits <= size, "Return type too small to hold the requested number of bits."); \ uint_fast##size##_t result = 0; \ /* Pointers to the UWORD of the read frame that contains the frame's cursor (or is immediately after the cursor). */ \ UWORD* frame_ptr = frame->edge - 1 - frame->offset / UWORD_BIT; \ /* The specific bit within the above UWORD that is immediately in front of the cursor. \ * That bit is specifically '1 << (frame_shift - 1)'. \ */ \ size_t frame_shift = UWORD_BIT - (frame->offset % UWORD_BIT); \ size_t n = bits; \ if (frame_shift < n) { \ /* We may only want part of the LSBs from the read frame's current UWORD. \ * Copy that data to 'x', and move the frame_ptr to the frame's next UWORD. \ */ \ result |= (uint_fast##size##_t)((uint_fast##size##_t)LSBkeep(*frame_ptr, frame_shift) << (n - frame_shift)); \ frame->offset += frame_shift; \ n -= frame_shift; \ frame_shift = UWORD_BIT; \ frame_ptr--; \ while (UWORD_BIT < n) { \ /* Copy the entire read frame's current UWORD to 'x', and move the frame_ptr to the frame's next UWORD. */ \ result |= (uint_fast##size##_t)((uint_fast##size##_t)(*frame_ptr) << (n - UWORD_BIT)); \ frame->offset += UWORD_BIT; \ n -= UWORD_BIT; \ frame_ptr--; \ } \ } \ /* We may only want part of the bits from the middle of the read frame's current UWORD. \ * Copy that data to fill the remainder of 'x'. \ */ \ result |= (uint_fast##size##_t)(LSBkeep((UWORD)(*frame_ptr >> (frame_shift - n)), n)); \ frame->offset += n; \ return result; \ } READ_(4,8) READ_(8,8) READ_(16,16) READ_(32,32) READ_(64,64) #define WRITE_(bits) \ /* Given a write frame, set the value of the bits cells after the cursor and advance the frame's cursor by bits##. \ * The first cell is set to the value of the MSB of 'x' and the last cell is set to the LSB of 'x'. \ * Cells in front of the cursor's final position may be overwritten. \ * \ * Precondition: '*frame' is a valid write frame for bits more cells. \ */ \ void simplicity_write##bits(frameItem* frame, uint_fast##bits##_t x) { \ /* Pointers to the UWORD of the write frame that contains the frame's cursor (or is immediately after the cursor). */ \ UWORD* frame_ptr = frame->edge + (frame->offset - 1) / UWORD_BIT; \ /* The specific bit within the above UWORD that is immediately in front of the cursor. \ * That bit is specifically '1 << (frame_shift - 1)'. \ */ \ size_t frame_shift = (frame->offset - 1) % UWORD_BIT + 1; \ size_t n = bits; \ if (frame_shift < n) { \ /* The write frame's current UWORD may be partially filled. \ * Fill the rest of it with data from 'x', and move the frame_ptr to the frame's next UWORD. \ */ \ *frame_ptr = LSBclear(*frame_ptr, frame_shift) | LSBkeep((UWORD)(x >> (n - frame_shift)), frame_shift); \ frame->offset -= frame_shift; \ n -= frame_shift; \ frame_shift = UWORD_BIT; \ frame_ptr--; \ while (UWORD_BIT < n) { \ /* Fill the write frame's entire current UWORD with data from 'x', and move the frame_ptr to the frame's next UWORD. */ \ *frame_ptr = (UWORD)(x >> (n - UWORD_BIT)); \ frame->offset -= UWORD_BIT; \ n -= UWORD_BIT; \ frame_ptr--; \ } \ } \ /* The current write frame's UWORD may be partially filled. \ * Fill the UWORD with the last of the data from 'x', which may or may not be enough to fill the rest of the UWORD. \ */ \ *frame_ptr = (UWORD)(LSBclear(*frame_ptr, frame_shift) | (LSBkeep((UWORD)x, n) << (frame_shift - n))); \ frame->offset -= n; \ } WRITE_(8) WRITE_(16) WRITE_(32) WRITE_(64) /* Read bytes from a Simplicity buffer of type (TWO^8)^<2^(n+1) into 'buf'. * Set 'len' to the number of bytes read from the buffer. * Advance the 'src' frame to the end of the buffer type. * * The notation X^<2 is notation for the type (S X) * The notation X^<(2*n) is notation for the type S (X^n) * X^output; * '*src' is a valid read frame for 838 more cells; */ bool simplicity_read_sha256_context(sha256_context* ctx, frameItem* src) { size_t len; uint_fast64_t compressionCount; simplicity_read_buffer8(ctx->block, &len, src, 5); compressionCount = simplicity_read64(src); ctx->counter = ((compressionCount*1U) << 6) + len; read32s(ctx->output, 8, src); ctx->overflow = (sha256_max_counter >> 6) <= compressionCount; return !ctx->overflow; } /* Write data to a Simplicity CTX8 type (TWO^8)^<2^64 * TWO^64 * TWO^256 from a sha256_context value. * Advance the 'dst' frame to the end of the CTX8 type. * Returns false if the ctx had overflowed. * * The notation X^<2 is notation for the type (S X) * The notation X^<(2*n) is notation for the type S (X^n) * X^output; * ctx->counter < 2^61; */ bool simplicity_write_sha256_context(frameItem* dst, const sha256_context* ctx) { simplicity_write_buffer8(dst, ctx->block, ctx->counter % 64, 5); simplicity_write64(dst, ctx->counter >> 6); write32s(dst, ctx->output, 8); return !ctx->overflow; } /* Given a write frame and a read frame, copy 'n' cells from after the read frame's cursor to after the write frame's cursor, * Cells in within the write frame beyond 'n' cells after the write frame's cursor may also be overwritten. * * Precondition: '*dst' is a valid write frame for 'n' more cells; * '*src' is a valid read frame for 'n' more cells; * '0 < n'; */ static void copyBitsHelper(const frameItem* dst, const frameItem *src, size_t n) { /* Pointers to the UWORDs of the read and write frame that contain the frame's cursor. */ UWORD* src_ptr = src->edge - 1 - src->offset / UWORD_BIT; UWORD* dst_ptr = dst->edge + (dst->offset - 1) / UWORD_BIT; /* The specific bit within those UWORDs that is immediately in front of their respective cursors. * That bit is specifically '1 << (src_shift - 1)' for the read frame, * and '1 << (dst_shift - 1)' for the write frame, unless 'dst_shift == 0', in which case it is '1 << (UWORD_BIT - 1)'. */ size_t src_shift = UWORD_BIT - (src->offset % UWORD_BIT); size_t dst_shift = dst->offset % UWORD_BIT; if (dst_shift) { /* The write frame's current UWORD is partially filled. * Fill the rest of it without overwriting the existing data. */ *dst_ptr = LSBclear(*dst_ptr, dst_shift); if (src_shift < dst_shift) { /* The read frame's current UWORD doesn't have enough data to entirely fill the rest of the write frame's current UWORD. * Fill as much as we can and move src_ptr to the read frame's next UWORD. */ *dst_ptr |= (UWORD)(LSBkeep(*src_ptr, src_shift) << (dst_shift - src_shift)); if (n <= src_shift) return; n -= src_shift; dst_shift -= src_shift; src_ptr--; src_shift = UWORD_BIT; } /* Fill the rest of the write frame's current UWORD and move dst_ptr to the write frame's next UWORD. */ *dst_ptr |= LSBkeep((UWORD)(*src_ptr >> (src_shift - dst_shift)), dst_shift); if (n <= dst_shift) return; n -= dst_shift; src_shift -= dst_shift; dst_ptr--; } /* The next cell in the write frame to be filled begins at the boundary of a UWORD. */ /* :TODO: Use static analysis to limit the total amount of copied memory. */ if (0 == src_shift % UWORD_BIT) { /* The next cell in the read frame to be filled also begins at the boundary of a UWORD. * We can use 'memcpy' to copy data in bulk. */ size_t m = ROUND_UWORD(n); /* If we went through the previous 'if (dst_shift)' block then 'src_shift == 0' and we need to decrement src_ptr. * If we did not go through the previous 'if (dst_shift)' block then 'src_shift == UWORD_BIT' * and we do not need to decrement src_ptr. * We have folded this conditional decrement into the equation applied to 'src_ptr' below. */ memcpy(dst_ptr - (m - 1), src_ptr - (m - src_shift / UWORD_BIT), m * sizeof(UWORD)); } else { while(1) { /* Fill the write frame's UWORD by copying the LSBs of the read frame's current UWORD * to the MSBs of the write frame's current UWORD, * and copy the MSBs of the read frame's next UWORD to the LSBs of the write frame's current UWORD. * Then move both the src_ptr and dst_ptr to their next UWORDs. */ *dst_ptr = (UWORD)(LSBkeep(*src_ptr, src_shift) << (UWORD_BIT - src_shift)); if (n <= src_shift) return; *dst_ptr |= (UWORD)(*(src_ptr - 1) >> src_shift); if (n <= UWORD_BIT) return; n -= UWORD_BIT; dst_ptr--; src_ptr--; } } } /* Given a write frame and a read frame, copy 'n' cells from after the read frame's cursor to after the write frame's cursor, * and then advance the write frame's cursor by 'n'. * Cells in front of the '*dst's cursor's final position may be overwritten. * * Precondition: '*dst' is a valid write frame for 'n' more cells; * '*src' is a valid read frame for 'n' more cells; */ void simplicity_copyBits(frameItem* dst, const frameItem* src, size_t n) { if (0 == n) return; copyBitsHelper(dst, src, n); dst->offset -= n; } ================================================ FILE: C/frame.h ================================================ /* This module provides functions writing initial data to and reading results from the frame used during evaluation * of Simplicity expressions. * These helper functions are also used for marshaling data to and from jets. */ #ifndef SIMPLICITY_FRAME_H #define SIMPLICITY_FRAME_H #include #include "sha256.h" #include "simplicity_assert.h" #include "uword.h" /* A Bit Machine frame contains an '.edge' pointer to a slice of an array of UWORDs to hold the frame's cells. * The '.offset' is used to represent the cursors position. * For a read frame, the '.edge' points to one-past-the-end of the slice of the UWORDs array for the frame's cells, * and the '.offset' value is equal to the frame's cursor position plus the amount of padding used in the frame. * For a write frame, the '.edge' points to the beginning of the slice of the UWORDs array for the frame's cells, * and the '.offset' value is equal to the total number of cells minus the frame's cursor position. */ typedef struct frameItem { UWORD* edge; size_t offset; } frameItem; /* Initialize a new read frame. * 'n' is the number of cells for the read frame. * 'from' is a pointer to the beginning of the new slice for the array of UWORDS to hold the frame's cells. * * Precondition: UWORD from[ROUND_UWORD(n)]; */ static inline frameItem initReadFrame(size_t n, UWORD* from) { const size_t len = ROUND_UWORD(n); /* '(1U * len) * UWORD_BIT - n' equals the number of padding bits in a frame of size 'n'. * Note that even if (len * UWORD_BIT) overflows, * (1) We have ensured an unsigned computation by multiplying by 1U so the behaviour is well-defined. * (2) after subtracting 'n' we are left with a value in the range 0 .. UWORD-BIT - 1. */ return (frameItem){ .edge = from + len, .offset = (1U * len) * UWORD_BIT - n }; } /* Initialize a new write frame. * 'n' is the number of cells for the write frame. * 'from' is a pointer to the one-past-the-end of the new slice for the array of UWORDS to hold the frame's cells. * * Precondition: UWORD (from - ROUND_UWORD(n))[ROUND_UWORD(n)]; */ static inline frameItem initWriteFrame(size_t n, UWORD* from) { return (frameItem){ .edge = from - ROUND_UWORD(n), .offset = n }; } /* Given a read frame, return the value of the cell at the cursor. * * Precondition: '*frame' is a valid read frame for 1 more cell. */ static inline bool peekBit(const frameItem* frame) { return 1 & (*(frame->edge - 1 - frame->offset / UWORD_BIT) >> (UWORD_BIT - (frame->offset % UWORD_BIT) - 1)); } /* Given a read frame, return the value of the cell at the cursor and advance the cursor by one cell. * * Precondition: '*frame' is a valid read frame for 1 more cell. */ static inline bool readBit(frameItem* frame) { bool result = peekBit(frame); frame->offset++; return result; } /* Given a write frame, set its cursor's cell to 'bit' and advance the cursor by one cell. * Cells in front of the cursor's final position may be overwritten. * * The function returns the same value as bit. This facilitates using 'writeBit' within an 'if' statement * * if (writeBit(frame, bit)) { ... } else { ... } * * so that one can both decide conditions based on a Boolean value while at the same time writing to the frame the choice made. * * Precondition: '*frame' is a valid write frame for 1 more cell. */ static inline bool writeBit(frameItem* frame, bool bit) { simplicity_debug_assert(0 < frame->offset); frame->offset--; UWORD* dst_ptr = frame->edge + frame->offset / UWORD_BIT; if (bit) { *dst_ptr |= (UWORD)((UWORD)1 << (frame->offset % UWORD_BIT)); } else { *dst_ptr = LSBclear(*dst_ptr, frame->offset % UWORD_BIT + 1); } return bit; } /* Given a read frame, advance the cursor by 'n' cells. * * Precondition: '*frame' is a valid read frame for 'n' more cells. */ static inline void forwardBits(frameItem* frame, size_t n) { frame->offset += n; } /* Given a write frame, advance the cursor by 'n' cells. * * Precondition: '*frame' is a valid write frame for 'n' more cells. */ static inline void skipBits(frameItem* frame, size_t n) { simplicity_debug_assert(n <= frame->offset); frame->offset -= n; } /* Given a read frame, the 'readN' function returns the value of the 'N' cells after the cursor and * advances the frame's cursor by 'N'. * The cell values are returned with the first cell in the MSB of the result and the last cell in the LSB of the result. * * Precondition: '*frame' is a valid read frame for 'N' more cells. */ uint_fast8_t simplicity_read4(frameItem* frame); uint_fast8_t simplicity_read8(frameItem* frame); uint_fast16_t simplicity_read16(frameItem* frame); uint_fast32_t simplicity_read32(frameItem* frame); uint_fast64_t simplicity_read64(frameItem* frame); /* Given a write frame, the 'writeN' function sets the value of the 'N' cells after the cursor and * advances the frame's cursor by 'N'. * The first cell is set to the value of the MSB of 'x' and the last cell is set to the LSB of 'x'. * Cells in front of the cursor's final position may be overwritten. * * Precondition: '*frame' is a valid write frame for 'N' more cells. */ void simplicity_write8(frameItem* frame, uint_fast8_t x); void simplicity_write16(frameItem* frame, uint_fast16_t x); void simplicity_write32(frameItem* frame, uint_fast32_t x); void simplicity_write64(frameItem* frame, uint_fast64_t x); static inline void read8s(unsigned char* x, size_t n, frameItem* frame) { for(; n; --n) *(x++) = (unsigned char)simplicity_read8(frame); } static inline void write8s(frameItem* frame, const unsigned char* x, size_t n) { for(; n; --n) simplicity_write8(frame, *(x++)); } static inline void read32s(uint32_t* x, size_t n, frameItem* frame) { for(; n; --n) *(x++) = (uint32_t)simplicity_read32(frame); } static inline void write32s(frameItem* frame, const uint32_t* x, size_t n) { for(; n; --n) simplicity_write32(frame, *(x++)); } /* Read bytes from a Simplicity buffer of type (TWO^8)^<2^(n+1) into 'buf'. * Set 'len' to the number of bytes read from the buffer. * Advance the 'src' frame to the end of the buffer type. * * The notation X^<2 is notation for the type (S X) * The notation X^<(2*n) is notation for the type S (X^n) * X^output; * '*src' is a valid read frame for 838 more cells; */ bool simplicity_read_sha256_context(sha256_context* ctx, frameItem* src); /* Write data to a Simplicity CTX8 type (TWO^8)^<2^64 * TWO^64 * TWO^256 from a sha256_context value. * Advance the 'dst' frame to the end of the CTX8 type. * Returns false if the ctx had overflowed. * * The notation X^<2 is notation for the type (S X) * The notation X^<(2*n) is notation for the type S (X^n) * X^output; * ctx->counter < 2^61; */ bool simplicity_write_sha256_context(frameItem* dst, const sha256_context* ctx); /* Given a write frame and a read frame, copy 'n' cells from after the read frame's cursor to after the write frame's cursor, * and then advance the write frame's cursor by 'n'. * Cells in front of the '*dst's cursor's final position may be overwritten. * * Precondition: '*dst' is a valid write frame for 'n' more cells; * '*src' is a valid read frame for 'n' more cells; */ void simplicity_copyBits(frameItem* dst, const frameItem* src, size_t n); #endif ================================================ FILE: C/hashBlock.c ================================================ #include "hashBlock.h" /* A length-prefixed encoding of the following Simplicity program: * hashBlock */ const unsigned char hashBlock[] = { 0xea, 0x70, 0x50, 0x62, 0x48, 0x2c, 0x14, 0x0a, 0xd1, 0x40, 0xb0, 0xc4, 0x54, 0x2a, 0x15, 0xc4, 0x58, 0x60, 0x28, 0x16, 0x01, 0x6b, 0xd6, 0x20, 0x5a, 0x02, 0xd5, 0xb4, 0x4d, 0x02, 0xa1, 0x66, 0x40, 0xa1, 0x24, 0x16, 0x0a, 0x05, 0x20, 0xa0, 0x58, 0xe2, 0x26, 0x02, 0xa1, 0x5c, 0x44, 0xc4, 0x54, 0x2d, 0x39, 0x08, 0x16, 0xcd, 0xa2, 0x6c, 0x13, 0x48, 0xb0, 0x0b, 0x32, 0x0c, 0x34, 0x30, 0xc3, 0x0e, 0x38, 0x59, 0x92, 0x42, 0x05, 0x08, 0x30, 0xc3, 0xc1, 0x41, 0xc8, 0x30, 0xfa, 0x0c, 0x3c, 0x14, 0x1c, 0x2c, 0x88, 0x30, 0xc3, 0xc1, 0x41, 0xc6, 0xdc, 0x7c, 0xcc, 0x3c, 0x14, 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0x9d, 0xe0, 0x39, 0xe6, 0x03, 0x9e, 0xd0, 0x39, 0xf2, 0x03, 0x9f, 0xa0, 0x3a, 0x00, 0x80, 0xe8, 0x0a, 0x03, 0xa0, 0x44, 0x0e, 0x81, 0x90, 0x3a, 0x08, 0x80, 0xe8, 0x2a, 0x03, 0xa0, 0xc4, 0x0e, 0x83, 0x90, 0x3a, 0x10, 0x00, 0xe8, 0x48, 0x03, 0xa1, 0x40, 0x0e, 0x85, 0x70, 0x3a, 0x17, 0x40, 0xe8, 0x66, 0x03, 0xa1, 0xbc, 0x0e, 0x87, 0x70, 0x3a, 0x20, 0x00, 0xe8, 0x89, 0x03, 0xa2, 0x44, 0x0e, 0x89, 0xa0, 0x3a, 0x28, 0xc0, 0xe8, 0xad, 0x03, 0xa2, 0xd4, 0x0e, 0x8c, 0x00, 0x3a, 0x32, 0xc0, 0xe8, 0xd9, 0x03, 0xa9, 0x83, 0x0b, 0xa9, 0x9a, 0x0b, 0xa9, 0x6c, 0xe9, 0x20, 0x01, 0xd4, 0x5e, 0x1b, 0xa4, 0xa6, 0x7e, 0x92, 0xa0, 0xa0, 0x0e, 0xa3, 0x00, 0x58, 0x8d, 0xd2, 0xe7, 0x30, 0xf0, 0x50, 0x07, 0x51, 0x8c, 0x6e, 0x96, 0x31, 0xfa, 0x58, 0xe2, 0x80, 0x3a, 0x8c, 0xa1, 0x62, 0x16, 0xb1, 0xba, 0x59, 0x67, 0xe9, 0x66, 0x0a, 0x00, 0xea, 0x34, 0x0d, 0xd2, 0x61, 0x3f, 0x49, 0x88, 0x50, 0x07, 0x51, 0xa8, 0x2c, 0x46, 0xe9, 0x20, 0x1f, 0xa4, 0x82, 0x28, 0x03, 0xa8, 0xd9, 0x17, 0x49, 0x83, 0xa4, 0xb2, 0x07, 0x51, 0xb6, 0x2a, 0x16, 0x80, 0xb8, 0x10, 0x1c, 0x4a }; const size_t sizeof_hashBlock = sizeof(hashBlock); const unsigned char hashBlock_witness[] = ""; const size_t sizeof_hashBlock_witness = 0; /* The commitment Merkle root of the above hashBlock Simplicity expression. */ const uint32_t hashBlock_cmr[] = { 0xa07dd7d8u, 0x22aed1adu, 0x40576a7au, 0x69fa1082u, 0x52d3dd89u, 0x539b1e4eu, 0x1f567851u, 0x9abf54e5u }; /* The identity hash of the root of the above hashBlock Simplicity expression. */ const uint32_t hashBlock_ihr[] = { 0x609cc145u, 0x9375db72u, 0x8f2172c9u, 0x62807e31u, 0x61df4cceu, 0xd6592d2cu, 0x4e594a77u, 0x79ab3175u }; /* The annotated Merkle root of the above hashBlock Simplicity expression. */ const uint32_t hashBlock_amr[] = { 0xc0b19e09u, 0x2443349au, 0x09b8b92fu, 0x369c1cd1u, 0x66d58d87u, 0x3e9d10cbu, 0x8d8ec427u, 0x707874fcu }; /* The cost of the above hashBlock Simplicity expression in milli weight units. */ const ubounded hashBlock_cost = 258978952; ================================================ FILE: C/hashBlock.h ================================================ #ifndef SIMPLICITY_HASHBLOCK_H #define SIMPLICITY_HASHBLOCK_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * hashBlock */ extern const unsigned char hashBlock[]; extern const size_t sizeof_hashBlock; extern const unsigned char hashBlock_witness[]; extern const size_t sizeof_hashBlock_witness; /* The commitment Merkle root of the above hashBlock Simplicity expression. */ extern const uint32_t hashBlock_cmr[]; /* The identity hash of the root of the above hashBlock Simplicity expression. */ extern const uint32_t hashBlock_ihr[]; /* The annotated Merkle root of the above hashBlock Simplicity expression. */ extern const uint32_t hashBlock_amr[]; /* The cost of the above hashBlock Simplicity expression in milli weight units. */ extern const ubounded hashBlock_cost; #endif ================================================ FILE: C/include/simplicity/bitcoin/env.h ================================================ #ifndef SIMPLICITY_BITCOIN_ENV_H #define SIMPLICITY_BITCOIN_ENV_H #include #include /* This section builds the 'rawBitcoinTransaction' structure which is the transaction data needed to build a Bitcoin 'txEnv' environment * for evaluating Simplicity expressions within. * The 'rawBitcoinTransaction' is copied into an opaque 'bitcoinTransaction' structure that can be reused within evaluating Simplicity on multiple * inputs within the same transaction. */ /* A type for an unparsed buffer * * Invariant: if 0 < len then unsigned char buf[len] */ typedef struct rawBitcoinBuffer { const unsigned char* buf; uint32_t len; } rawBitcoinBuffer; /* A structure representing data for one output from a Bitcoin transaction. */ typedef struct rawBitcoinOutput { uint64_t value; rawBitcoinBuffer scriptPubKey; } rawBitcoinOutput; /* A structure representing data for one input from a Bitcoin transaction, including its taproot annex, * plus the TXO data of the output being redeemed. * * Invariant: unsigned char prevTxid[32]; */ typedef struct rawInput { const rawBitcoinBuffer* annex; const unsigned char* prevTxid; rawBitcoinOutput txo; rawBitcoinBuffer scriptSig; uint32_t prevIx; uint32_t sequence; } rawBitcoinInput; /* A structure representing data for a Bitcoin transaction, including the TXO data of each output being redeemed. * * Invariant: unsigned char txid[32]; * rawBitcoinInput input[numInputs]; * rawBitcoinOutput output[numOutputs]; */ typedef struct rawBitcoinTransaction { const unsigned char* txid; /* While in theory we could recompute the txid ourselves, it is easier and safer for it to be provided. */ const rawBitcoinInput* input; const rawBitcoinOutput* output; uint32_t numInputs; uint32_t numOutputs; uint32_t version; uint32_t lockTime; } rawBitcoinTransaction; /* A forward declaration for the structure containing a copy (and digest) of the rawTransaction data */ typedef struct bitcoinTransaction bitcoinTransaction; /* Allocate and initialize a 'bitcoinTransaction' from a 'rawBitcoinTransaction', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: NULL != rawTx */ extern bitcoinTransaction* simplicity_bitcoin_mallocTransaction(const rawBitcoinTransaction* rawTx); /* Free a pointer to 'bitcoinTransaction'. */ extern void simplicity_bitcoin_freeTransaction(bitcoinTransaction* tx); /* A structure representing taproot spending data for a Bitcoin transaction. * * Invariant: pathLen <= 128; * unsigned char controlBlock[33+pathLen*32]; * unsigned char scriptCMR[32]; */ typedef struct rawBitcoinTapEnv { const unsigned char* controlBlock; const unsigned char* scriptCMR; unsigned char pathLen; } rawBitcoinTapEnv; /* A forward declaration for the structure containing a copy (and digest) of the rawBitcoinTapEnv data */ typedef struct bitcoinTapEnv bitcoinTapEnv; /* Allocate and initialize a 'bitcoinTapEnv' from a 'rawBitcoinTapEnv', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: *rawEnv is well-formed (i.e. rawEnv->pathLen <= 128.) */ extern bitcoinTapEnv* simplicity_bitcoin_mallocTapEnv(const rawBitcoinTapEnv* rawEnv); /* Free a pointer to 'bitcoinTapEnv'. */ extern void simplicity_bitcoin_freeTapEnv(bitcoinTapEnv* env); #endif ================================================ FILE: C/include/simplicity/elements/cmr.h ================================================ #ifndef SIMPLICITY_ELEMENTS_CMR_H #define SIMPLICITY_ELEMENTS_CMR_H #include #include #include /* Deserialize a Simplicity 'program' and compute its CMR. * * Caution: no typechecking is performed, only a well-formedness check. * * If at any time malloc fails then '*error' is set to 'SIMPLICITY_ERR_MALLOC' and 'false' is returned, * Otherwise, 'true' is returned indicating that the result was successfully computed and returned in the '*error' value. * * If the operation completes successfully then '*error' is set to 'SIMPLICITY_NO_ERROR', and the 'cmr' array is filled in with the program's computed CMR. * * Precondition: NULL != error; * unsigned char cmr[32] * unsigned char program[program_len] */ extern bool simplicity_elements_computeCmr( simplicity_err* error, unsigned char* cmr , const unsigned char* program, size_t program_len); #endif ================================================ FILE: C/include/simplicity/elements/env.h ================================================ #ifndef SIMPLICITY_ELEMENTS_ENV_H #define SIMPLICITY_ELEMENTS_ENV_H #include #include /* This section builds the 'rawElementsTransaction' structure which is the transaction data needed to build an Elements 'txEnv' environment * for evaluating Simplicity expressions within. * The 'rawElementsTransaction' is copied into an opaque 'elementsTransaction' structure that can be reused within evaluating Simplicity on multiple * inputs within the same transaction. */ /* A type for an unparsed buffer * * Invariant: if 0 < len then unsigned char buf[len] */ typedef struct rawElementsBuffer { const unsigned char* buf; uint32_t len; } rawElementsBuffer; /* A structure representing data for one output from an Elements transaction. * * Invariant: unsigned char asset[33] or asset == NULL; * unsigned char value[value[0] == 1 ? 9 : 33] or value == NULL; * unsigned char nonce[33] or nonce == NULL; */ typedef struct rawElementsOutput { const unsigned char* asset; const unsigned char* value; const unsigned char* nonce; rawElementsBuffer scriptPubKey; rawElementsBuffer surjectionProof; rawElementsBuffer rangeProof; } rawElementsOutput; /* A structure representing data for one input from an Elements transaction, including its taproot annex, * plus the TXO data of the output being redeemed. * * Invariant: unsigned char prevTxid[32]; * unsigned char pegin[32] or pegin == NULL; * unsigned char issuance.blindingNonce[32] or (issuance.amount == NULL and issuance.inflationKeys == NULL); * unsigned char issuance.assetEntropy[32] or (issuance.amount == NULL and issuance.inflationKeys == NULL); * unsigned char issuance.amount[issuance.amount[0] == 1 ? 9 : 33] or issuance.amount == NULL; * unsigned char issuance.inflationKeys[issuance.inflaitonKeys[0] == 1 ? 9 : 33] or issuance.inflationKeys == NULL; * unsigned char txo.asset[33] or txo.asset == NULL; * unsigned char txo.value[txo.value[0] == 1 ? 9 : 33] or txo.value == NULL; */ typedef struct rawElementsInput { const rawElementsBuffer* annex; const unsigned char* prevTxid; const unsigned char* pegin; struct { const unsigned char* blindingNonce; const unsigned char* assetEntropy; const unsigned char* amount; const unsigned char* inflationKeys; rawElementsBuffer amountRangePrf; rawElementsBuffer inflationKeysRangePrf; } issuance; struct { const unsigned char* asset; const unsigned char* value; rawElementsBuffer scriptPubKey; } txo; rawElementsBuffer scriptSig; uint32_t prevIx; uint32_t sequence; } rawElementsInput; /* A structure representing data for an Elements transaction, including the TXO data of each output being redeemed. * * Invariant: unsigned char txid[32]; * rawElementsInput input[numInputs]; * rawElementsOutput output[numOutputs]; */ typedef struct rawElementsTransaction { const unsigned char* txid; /* While in theory we could recompute the txid ourselves, it is easier and safer for it to be provided. */ const rawElementsInput* input; const rawElementsOutput* output; uint32_t numInputs; uint32_t numOutputs; uint32_t version; uint32_t lockTime; } rawElementsTransaction; /* A forward declaration for the structure containing a copy (and digest) of the rawElementsTransaction data */ typedef struct elementsTransaction elementsTransaction; /* Allocate and initialize a 'elementsTransaction' from a 'rawElementsTransaction', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: NULL != rawTx */ extern elementsTransaction* simplicity_elements_mallocTransaction(const rawElementsTransaction* rawTx); /* Free a pointer to 'elementsTransaction'. */ extern void simplicity_elements_freeTransaction(elementsTransaction* tx); /* A structure representing taproot spending data for an Elements transaction. * * Invariant: pathLen <= 128; * unsigned char controlBlock[33+pathLen*32]; * unsigned char scriptCMR[32]; */ typedef struct rawElementsTapEnv { const unsigned char* controlBlock; const unsigned char* scriptCMR; unsigned char pathLen; } rawElementsTapEnv; /* A forward declaration for the structure containing a copy (and digest) of the rawElementsTapEnv data */ typedef struct elementsTapEnv elementsTapEnv; /* Allocate and initialize a 'elementsTapEnv' from a 'rawElementsTapEnv', copying or hashing the data as needed. * Returns NULL if malloc fails (or if malloc cannot be called because we require an allocation larger than SIZE_MAX). * * Precondition: *rawEnv is well-formed (i.e. rawEnv->pathLen <= 128.) */ extern elementsTapEnv* simplicity_elements_mallocTapEnv(const rawElementsTapEnv* rawEnv); /* Free a pointer to 'elementsTapEnv'. */ extern void simplicity_elements_freeTapEnv(elementsTapEnv* env); #endif ================================================ FILE: C/include/simplicity/elements/exec.h ================================================ #ifndef SIMPLICITY_ELEMENTS_EXEC_H #define SIMPLICITY_ELEMENTS_EXEC_H #include #include #include #include #include /* Deserialize a Simplicity 'program' with its 'witness' data and execute it in the environment of the 'ix'th input of 'tx' with `taproot`. * * If at any time malloc fails then '*error' is set to 'SIMPLICITY_ERR_MALLOC' and 'false' is returned, * meaning we were unable to determine the result of the simplicity program. * Otherwise, 'true' is returned indicating that the result was successfully computed and returned in the '*error' value. * * If deserialization, analysis, or execution fails, then '*error' is set to some simplicity_err. * In particular, if the cost analysis exceeds the budget, or exceeds BUDGET_MAX, then '*error' is set to 'SIMPLICITY_ERR_EXEC_BUDGET'. * On the other hand, if the cost analysis is less than or equal to minCost, then '*error' is set to 'SIMPLICITY_ERR_OVERWEIGHT'. * * Note that minCost and budget parameters are in WU, while the cost analysis will be performed in milliWU. * Thus the minCost and budget specify a half open interval (minCost, budget] of acceptable cost values in milliWU. * Setting minCost to 0 effectively disables the minCost check as every Simplicity program has a non-zero cost analysis. * * If 'amr != NULL' and the annotated Merkle root of the decoded expression doesn't match 'amr' then '*error' is set to 'SIMPLICITY_ERR_AMR'. * * Otherwise '*error' is set to 'SIMPLICITY_NO_ERROR'. * * If 'ihr != NULL' and '*error' is set to 'SIMPLICITY_NO_ERROR', then the identity hash of the root of the decoded expression is written to 'ihr'. * Otherwise if 'ihr != NULL' and '*error' is not set to 'SIMPLCITY_NO_ERROR', then 'ihr' may or may not be written to. * * Precondition: NULL != error; * NULL != ihr implies unsigned char ihr[32] * NULL != tx; * NULL != taproot; * unsigned char genesisBlockHash[32] * 0 <= minCost <= budget; * NULL != amr implies unsigned char amr[32] * unsigned char program[program_len] * unsigned char witness[witness_len] */ extern bool simplicity_elements_execSimplicity( simplicity_err* error, unsigned char* ihr , const elementsTransaction* tx, uint_fast32_t ix, const elementsTapEnv* taproot , const unsigned char* genesisBlockHash , int64_t minCost, int64_t budget , const unsigned char* amr , const unsigned char* program, size_t program_len , const unsigned char* witness, size_t witness_len); #endif ================================================ FILE: C/include/simplicity/errorCodes.h ================================================ /* This module defines some constants used for error codes when processing Simplicity. * Errors can either indicate a transient or a permanent failure. */ #ifndef SIMPLICITY_ERRORCODES_H #define SIMPLICITY_ERRORCODES_H #include /* By convention, odd error codes are transient failures (i.e. out of memory) * while even error codes are permanent failures (i.e. unexpected end of file or parsing error, etc.) */ typedef enum { SIMPLICITY_NO_ERROR = 0, SIMPLICITY_ERR_MALLOC = -1, SIMPLICITY_ERR_NOT_YET_IMPLEMENTED = -3, SIMPLICITY_ERR_DATA_OUT_OF_RANGE = -2, SIMPLICITY_ERR_DATA_OUT_OF_ORDER = -4, SIMPLICITY_ERR_FAIL_CODE = -6, SIMPLICITY_ERR_RESERVED_CODE = -8, SIMPLICITY_ERR_HIDDEN = -10, SIMPLICITY_ERR_BITSTREAM_EOF = -12, SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES = -14, SIMPLICITY_ERR_BITSTREAM_ILLEGAL_PADDING = -16, SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION = -18, SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK = -20, SIMPLICITY_ERR_TYPE_INFERENCE_NOT_PROGRAM = -22, SIMPLICITY_ERR_WITNESS_EOF = -24, SIMPLICITY_ERR_WITNESS_TRAILING_BYTES = -26, SIMPLICITY_ERR_WITNESS_ILLEGAL_PADDING = -28, SIMPLICITY_ERR_UNSHARED_SUBEXPRESSION = -30, SIMPLICITY_ERR_CMR = -32, SIMPLICITY_ERR_EXEC_BUDGET = -34, SIMPLICITY_ERR_EXEC_MEMORY = -36, SIMPLICITY_ERR_EXEC_JET = -38, SIMPLICITY_ERR_EXEC_ASSERT = -40, SIMPLICITY_ERR_ANTIDOS = -42, SIMPLICITY_ERR_HIDDEN_ROOT = -44, SIMPLICITY_ERR_AMR = -46, SIMPLICITY_ERR_OVERWEIGHT = -48, } simplicity_err; /* Check if failure is permanent (or success which is always permanent). */ static inline bool IS_PERMANENT(simplicity_err err) { return !(err & 1); } /* Check if no failure. */ static inline bool IS_OK(simplicity_err err) { return SIMPLICITY_NO_ERROR == err; } static inline const char * SIMPLICITY_ERR_MSG(simplicity_err err) { switch (err) { case SIMPLICITY_NO_ERROR: return "No error"; case SIMPLICITY_ERR_MALLOC: return "Memory allocation failed"; case SIMPLICITY_ERR_NOT_YET_IMPLEMENTED: return "Incomplete implementation (this should not occur)"; case SIMPLICITY_ERR_DATA_OUT_OF_RANGE: return "Value out of range"; case SIMPLICITY_ERR_DATA_OUT_OF_ORDER: return "Non-canonical order"; case SIMPLICITY_ERR_FAIL_CODE: return "Program has FAIL node"; case SIMPLICITY_ERR_RESERVED_CODE: return "Program has reserved codeword"; case SIMPLICITY_ERR_HIDDEN: return "Program has node with a HIDDEN child in a position where it is not allowed"; case SIMPLICITY_ERR_BITSTREAM_EOF: return "Unexpected end of bitstream"; case SIMPLICITY_ERR_BITSTREAM_TRAILING_BYTES: return "Trailing bytes after final byte of program"; case SIMPLICITY_ERR_BITSTREAM_ILLEGAL_PADDING: return "Illegal padding in final byte of program"; case SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION: return "Unification failure"; case SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK: return "Occurs check failure"; case SIMPLICITY_ERR_TYPE_INFERENCE_NOT_PROGRAM: return "Expression not unit to unit"; case SIMPLICITY_ERR_WITNESS_EOF: return "Unexpected end of witness block"; case SIMPLICITY_ERR_WITNESS_TRAILING_BYTES: return "Trailing bytes after final byte of witness"; case SIMPLICITY_ERR_WITNESS_ILLEGAL_PADDING: return "Illegal padding in final byte of witness"; case SIMPLICITY_ERR_UNSHARED_SUBEXPRESSION: return "Subexpression not properly shared"; case SIMPLICITY_ERR_CMR: return "Program's CMR does not match"; case SIMPLICITY_ERR_EXEC_BUDGET: return "Program's execution cost could exceed budget"; case SIMPLICITY_ERR_EXEC_MEMORY: return "Program's memory cost could exceed limit"; case SIMPLICITY_ERR_EXEC_JET: return "Assertion failed inside jet"; case SIMPLICITY_ERR_EXEC_ASSERT: return "Assertion failed"; case SIMPLICITY_ERR_ANTIDOS: return "Anti-DOS check failed"; case SIMPLICITY_ERR_HIDDEN_ROOT: return "Program's root is HIDDEN"; case SIMPLICITY_ERR_AMR: return "Program's AMR does not match"; case SIMPLICITY_ERR_OVERWEIGHT: return "Program's budget is too large"; default: return "Unknown error code"; } } #endif ================================================ FILE: C/jets-secp256k1.c ================================================ #include "jets.h" #include "taptweak.h" #include "precomputed.h" #include "sha256.h" #include "secp256k1/secp256k1_impl.h" /* Tests to see if a secp256k1 jacobian point is on curve. * * This function doesn't occur in the libsecp256k1 library, so we implement it here. * We test if the point satisfies the jacobian equation y^2 = x^3 + 7*z^6. * * Warning, the degenerate point (0, 0, 0) is accepted by this definition even though arguably it isn't on curve. * However libsecp256k1 sets the point to (0, 0, 0) when the infinity flag is set See 'secp256k1_gej_set_infinity', * and we end up using it as a canonical representative of infinity. */ static bool simplicity_gej_is_valid_var(const secp256k1_gej *a) { secp256k1_fe x3, y2, z6; secp256k1_fe_sqr(&y2, &a->y); secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x); secp256k1_fe_sqr(&z6, &a->z); secp256k1_fe_mul(&z6, &z6, &a->z); secp256k1_fe_sqr(&z6, &z6); secp256k1_fe_mul_int(&z6, 7); secp256k1_fe_add(&x3, &z6); return secp256k1_fe_equal_var(&y2, &x3); } /* Read a secp256k1 field element value from the 'src' frame, advancing the cursor 256 cells. * * Precondition: '*src' is a valid read frame for 256 more cells; * NULL != r; */ static inline void read_fe(secp256k1_fe* r, frameItem* src) { unsigned char buf[32]; read8s(buf, 32, src); if (!secp256k1_fe_set_b32(r, buf)) secp256k1_fe_normalize_var(r); } /* Write a secp256k1 field element value to the 'dst' frame, advancing the cursor 256 cells. * The field value 'r' is normalized as a side-effect. * * Precondition: '*dst' is a valid write frame for 256 more cells; * NULL != r; */ static inline void write_fe(frameItem* dst, secp256k1_fe* r) { unsigned char buf[32]; secp256k1_fe_normalize_var(r); secp256k1_fe_get_b32(buf, r); write8s(dst, buf, 32); } /* Skip 256 cells, the size of a secp256k1 field element value, in the 'dst' frame. * * Precondition: '*dst' is a valid write frame for 256 more cells; */ static inline void skip_fe(frameItem* dst) { skipBits(dst, 256); } /* Read a (non-infinity) secp256k1 affine group element value from the 'src' frame, advancing the cursor 512 cells. * * Precondition: '*src' is a valid read frame for 512 more cells; * NULL != r; */ static inline void read_ge(secp256k1_ge* r, frameItem* src) { read_fe(&r->x, src); read_fe(&r->y, src); r->infinity = 0; } /* Write a secp256k1 affine group element value to the 'dst' frame, advancing the cursor 512 cells. * * Precondition: '*dst' is a valid write frame for 512 more cells; * NULL != r; */ static inline void write_ge(frameItem* dst, secp256k1_ge* r) { write_fe(dst, &r->x); write_fe(dst, &r->y); } /* Skip 512 cells, the size of a secp256k1 affine group element value, in the 'dst' frame. * * Precondition: '*dst' is a valid write frame for 512 more cells; */ static inline void skip_ge(frameItem* dst) { skip_fe(dst); skip_fe(dst); } /* Read a secp256k1 jacobian group element value from the 'src' frame, advancing the cursor 768 cells. * * Precondition: '*src' is a valid read frame for 768 more cells; * NULL != r; */ static inline void read_gej(secp256k1_gej* r, frameItem* src) { read_fe(&r->x, src); read_fe(&r->y, src); read_fe(&r->z, src); r->infinity = secp256k1_fe_is_zero(&r->z); } /* Write a secp256k1 jacobian group element value to the 'dst' frame, advancing the cursor 768 cells. * If 'r->infinity' then an fe_zero value to all coordinates in the 'dst' frame. * The components of 'r' may be normalized as a side-effect. * * Precondition: '*dst' is a valid write frame for 768 more cells; * NULL != r; */ static inline void write_gej(frameItem* dst, secp256k1_gej* r) { write_fe(dst, &r->x); write_fe(dst, &r->y); write_fe(dst, &r->z); } /* Read a secp256k1 scalar element value from the 'src' frame, advancing the cursor 256 cells. * * Precondition: '*src' is a valid read frame for 256 more cells; * NULL != r; */ static inline void read_scalar(secp256k1_scalar* r, frameItem* src) { unsigned char buf[32]; read8s(buf, 32, src); secp256k1_scalar_set_b32(r, buf, NULL); } /* Write a secp256k1 scalar element value to the 'dst' frame, advancing the cursor 256 cells. * * Precondition: '*dst' is a valid write frame for 256 more cells; * NULL != r; */ static inline void write_scalar(frameItem* dst, const secp256k1_scalar* r) { unsigned char buf[32]; secp256k1_scalar_get_b32(buf, r); write8s(dst, buf, 32); } bool simplicity_fe_normalize(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); write_fe(dst, &a); return true; } bool simplicity_fe_negate(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); secp256k1_fe_negate(&a, &a, 1); write_fe(dst, &a); return true; } bool simplicity_fe_add(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a, b; read_fe(&a, &src); read_fe(&b, &src); secp256k1_fe_add(&a, &b); write_fe(dst, &a); return true; } bool simplicity_fe_square(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); secp256k1_fe_sqr(&a, &a); write_fe(dst, &a); return true; } bool simplicity_fe_multiply(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a, b; read_fe(&a, &src); read_fe(&b, &src); secp256k1_fe_mul(&a, &a, &b); write_fe(dst, &a); return true; } bool simplicity_fe_multiply_beta(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); secp256k1_fe_mul(&a, &a, &secp256k1_const_beta); write_fe(dst, &a); return true; } bool simplicity_fe_invert(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); secp256k1_fe_inv_var(&a, &a); write_fe(dst, &a); return true; } bool simplicity_fe_square_root(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe r, a; read_fe(&a, &src); int result = secp256k1_fe_sqrt_var(&r, &a); if (writeBit(dst, result)) { write_fe(dst, &r); } else { skip_fe(dst); } return true; } bool simplicity_fe_is_zero(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); writeBit(dst, secp256k1_fe_is_zero(&a)); return true; } bool simplicity_fe_is_odd(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe a; read_fe(&a, &src); writeBit(dst, secp256k1_fe_is_odd(&a)); return true; } bool simplicity_scalar_normalize(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a; read_scalar(&a, &src); write_scalar(dst, &a); return true; } bool simplicity_scalar_negate(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a; read_scalar(&a, &src); secp256k1_scalar_negate(&a, &a); write_scalar(dst, &a); return true; } bool simplicity_scalar_add(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a, b; read_scalar(&a, &src); read_scalar(&b, &src); secp256k1_scalar_add(&a, &a, &b); write_scalar(dst, &a); return true; } bool simplicity_scalar_square(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a; read_scalar(&a, &src); secp256k1_scalar_mul(&a, &a, &a); write_scalar(dst, &a); return true; } bool simplicity_scalar_multiply(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a, b; read_scalar(&a, &src); read_scalar(&b, &src); secp256k1_scalar_mul(&a, &a, &b); write_scalar(dst, &a); return true; } bool simplicity_scalar_multiply_lambda(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a; read_scalar(&a, &src); secp256k1_scalar_mul(&a, &a, &secp256k1_const_lambda); write_scalar(dst, &a); return true; } bool simplicity_scalar_invert(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a; read_scalar(&a, &src); secp256k1_scalar_inverse_var(&a, &a); write_scalar(dst, &a); return true; } bool simplicity_scalar_is_zero(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_scalar a; read_scalar(&a, &src); writeBit(dst, secp256k1_scalar_is_zero(&a)); return true; } bool simplicity_gej_infinity(frameItem* dst, frameItem src, const txEnv* env) { (void) src; // src is unused; (void) env; // env is unused; secp256k1_gej a; secp256k1_gej_set_infinity(&a); write_gej(dst, &a); return true; } bool simplicity_gej_rescale(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; secp256k1_fe c; read_gej(&a, &src); read_fe(&c, &src); secp256k1_gej_rescale(&a, &c); write_gej(dst, &a); return true; } bool simplicity_gej_normalize(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; secp256k1_ge r; read_gej(&a, &src); if (writeBit(dst, !secp256k1_gej_is_infinity(&a))) { secp256k1_ge_set_gej_var(&r, &a); write_ge(dst, &r); } else { skip_ge(dst); } return true; } bool simplicity_gej_negate(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; read_gej(&a, &src); secp256k1_gej_neg(&a, &a); write_gej(dst, &a); return true; } bool simplicity_ge_negate(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_ge a; read_ge(&a, &src); secp256k1_ge_neg(&a, &a); write_ge(dst, &a); return true; } bool simplicity_gej_double(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; read_gej(&a, &src); secp256k1_gej_double_var(&a, &a, NULL); write_gej(dst, &a); return true; } bool simplicity_gej_add(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a, b; read_gej(&a, &src); read_gej(&b, &src); secp256k1_gej_add_var(&a, &a, &b, NULL); write_gej(dst, &a); return true; } bool simplicity_gej_ge_add_ex(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; secp256k1_ge b; secp256k1_fe rzr; secp256k1_fe_clear(&rzr); read_gej(&a, &src); read_ge(&b, &src); secp256k1_gej_add_ge_var(&a, &a, &b, &rzr); write_fe(dst, &rzr); write_gej(dst, &a); return true; } bool simplicity_gej_ge_add(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; secp256k1_ge b; read_gej(&a, &src); read_ge(&b, &src); secp256k1_gej_add_ge_var(&a, &a, &b, NULL); write_gej(dst, &a); return true; } bool simplicity_gej_is_infinity(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; read_gej(&a, &src); writeBit(dst, secp256k1_gej_is_infinity(&a)); return true; } bool simplicity_gej_equiv(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a, b; read_gej(&a, &src); read_gej(&b, &src); writeBit(dst, secp256k1_gej_eq_var(&a, &b)); return true; } bool simplicity_gej_ge_equiv(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; secp256k1_ge b; read_gej(&a, &src); read_ge(&b, &src); writeBit(dst, secp256k1_gej_eq_ge_var(&a, &b)); return true; } bool simplicity_gej_x_equiv(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe x; secp256k1_gej a; read_fe(&x, &src); read_gej(&a, &src); writeBit(dst, (!secp256k1_gej_is_infinity(&a)) && secp256k1_gej_eq_x_var(&x, &a)); return true; } bool simplicity_gej_y_is_odd(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; secp256k1_ge b; read_gej(&a, &src); if (secp256k1_gej_is_infinity(&a)) { writeBit(dst, false); } else { secp256k1_ge_set_gej_var(&b, &a); secp256k1_fe_normalize_var(&b.y); writeBit(dst, secp256k1_fe_is_odd(&b.y)); } return true; } bool simplicity_gej_is_on_curve(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej a; read_gej(&a, &src); writeBit(dst, simplicity_gej_is_valid_var(&a)); return true; } bool simplicity_ge_is_on_curve(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_ge a; read_ge(&a, &src); writeBit(dst, secp256k1_ge_is_valid_var(&a)); return true; } bool simplicity_off_curve_scale(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej r, a; secp256k1_scalar na; static const secp256k1_scalar ng = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); read_scalar(&na, &src); read_gej(&a, &src); secp256k1_ecmult(&r, &a, &na, &ng); write_gej(dst, &r); return true; } bool simplicity_scale(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej r, a; secp256k1_scalar na; static const secp256k1_scalar ng = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); read_scalar(&na, &src); read_gej(&a, &src); if (simplicity_gej_is_valid_var(&a)) { secp256k1_ecmult(&r, &a, &na, &ng); write_gej(dst, &r); return true; } else { return false; } } bool simplicity_generate(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej r; static const secp256k1_gej a = SECP256K1_GEJ_CONST_INFINITY; static const secp256k1_scalar na = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); secp256k1_scalar ng; read_scalar(&ng, &src); secp256k1_ecmult(&r, &a, &na, &ng); write_gej(dst, &r); return true; } bool simplicity_off_curve_linear_combination_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej r, a; secp256k1_scalar na, ng; read_scalar(&na, &src); read_gej(&a, &src); read_scalar(&ng, &src); secp256k1_ecmult(&r, &a, &na, &ng); write_gej(dst, &r); return true; } bool simplicity_linear_combination_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_gej r, a; secp256k1_scalar na, ng; read_scalar(&na, &src); read_gej(&a, &src); read_scalar(&ng, &src); if (simplicity_gej_is_valid_var(&a)) { secp256k1_ecmult(&r, &a, &na, &ng); write_gej(dst, &r); return true; } else { return false; } } bool simplicity_linear_verify_1(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; (void) env; // env is unused; secp256k1_ge a, b; secp256k1_scalar na, ng; read_scalar(&na, &src); read_ge(&a, &src); read_scalar(&ng, &src); read_ge(&b, &src); if (secp256k1_ge_is_valid_var(&a) && secp256k1_ge_is_valid_var(&b)) { secp256k1_gej r, a0; secp256k1_gej_set_ge(&a0, &a); secp256k1_ge_neg(&b, &b); secp256k1_ecmult(&r, &a0, &na, &ng); secp256k1_gej_add_ge_var(&r, &r, &b, NULL); return secp256k1_gej_is_infinity(&r); } else { return false; } } bool simplicity_decompress(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe x; secp256k1_ge r; bool y = readBit(&src); read_fe(&x, &src); if (writeBit(dst, secp256k1_ge_set_xo_var(&r, &x, y))) { write_ge(dst, &r); } else { skip_ge(dst); } return true; } bool simplicity_point_verify_1(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; (void) env; // env is unused; bool ay, by; secp256k1_fe ax, bx; secp256k1_ge a, b; secp256k1_scalar na, ng; read_scalar(&na, &src); ay = readBit(&src); read_fe(&ax, &src); read_scalar(&ng, &src); by = readBit(&src); read_fe(&bx, &src); if (secp256k1_ge_set_xo_var(&a, &ax, ay) && secp256k1_ge_set_xo_var(&b, &bx, by)) { secp256k1_gej r, a0; secp256k1_gej_set_ge(&a0, &a); secp256k1_ge_neg(&b, &b); secp256k1_ecmult(&r, &a0, &na, &ng); secp256k1_gej_add_ge_var(&r, &r, &b, NULL); return secp256k1_gej_is_infinity(&r); } else { return false; } } bool simplicity_bip_0340_verify(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; (void) env; // env is unused; unsigned char buf[32]; secp256k1_xonly_pubkey pubkey; unsigned char msg[32]; unsigned char sig[64]; read8s(buf, 32, &src); if (!secp256k1_xonly_pubkey_parse(&pubkey, buf)) return false; read8s(msg, 32, &src); read8s(sig, 64, &src); return secp256k1_schnorrsig_verify(sig, msg, sizeof(msg), &pubkey); } /* check_sig_verify : TWO^256*TWO^512*TWO^512 |- ONE */ bool simplicity_check_sig_verify(frameItem* dst, frameItem src, const txEnv* env) { (void) dst; // dst is unused; (void) env; // env is unused; unsigned char buf[32]; secp256k1_xonly_pubkey pubkey; unsigned char msg[64]; unsigned char sig[64]; read8s(buf, 32, &src); if (!secp256k1_xonly_pubkey_parse(&pubkey, buf)) return false; { sha256_midstate output; sha256_context ctx = sha256_tagged_init(output.s, &signatureIV); read8s(msg, 64, &src); sha256_uchars(&ctx, msg, 64); sha256_finalize(&ctx); sha256_fromMidstate(buf, output.s); } read8s(sig, 64, &src); return secp256k1_schnorrsig_verify(sig, buf, sizeof(buf), &pubkey); } /* swu : FE |- GE */ bool simplicity_swu(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; secp256k1_fe t; secp256k1_ge ge; read_fe(&t, &src); shallue_van_de_woestijne(&ge, &t); write_ge(dst, &ge); return true; } /* hash_to_curve : TWO^256 |- GE */ bool simplicity_hash_to_curve(frameItem* dst, frameItem src, const txEnv* env) { (void) env; // env is unused; unsigned char key[32]; secp256k1_generator gen; secp256k1_ge ge; read8s(key, 32, &src); if(!secp256k1_generator_generate(&gen, key)) return false; secp256k1_generator_load(&ge, &gen); write_ge(dst, &ge); return true; } /* THIS IS NOT A JET. It doesn't have the type signature of a jet * This is a generic taptweak jet implementation parameterized by the tag used in the hash. * It is designed to be specialized to implement slightly different taptweak operations for Bitcoin and Elements. * * PUBKEY * TWO^256 |- PUBKEY * * Precondition: unsigned char[tagLen] tag */ bool simplicity_generic_taptweak(frameItem* dst, frameItem *src, const unsigned char *tagName, size_t tagLen) { unsigned char buf[32]; secp256k1_xonly_pubkey input_pubkey, output_pubkey; secp256k1_pubkey pubkey; sha256_midstate taptweakTag, input_hash, output_hash; { sha256_context ctx = sha256_init(taptweakTag.s); sha256_uchars(&ctx, tagName, tagLen); sha256_finalize(&ctx); } sha256_context ctx = sha256_init(output_hash.s); sha256_hash(&ctx, &taptweakTag); sha256_hash(&ctx, &taptweakTag); read8s(buf, 32, src); sha256_uchars(&ctx, buf, 32); if (!secp256k1_xonly_pubkey_parse(&input_pubkey, buf)) return false; read32s(input_hash.s, 8, src); sha256_hash(&ctx, &input_hash); sha256_finalize(&ctx); sha256_fromMidstate(buf, output_hash.s); if (!secp256k1_xonly_pubkey_tweak_add(&pubkey, &input_pubkey, buf)) return false; if (!secp256k1_xonly_pubkey_from_pubkey(&output_pubkey, NULL, &pubkey)) return false; if (!secp256k1_xonly_pubkey_serialize(buf,&output_pubkey)) return false; write8s(dst, buf, 32); return true; } ================================================ FILE: C/jets.c ================================================ #include "jets.h" #include "secp256k1/secp256k1.h" #include "secp256k1/util.h" #ifdef SECP256K1_WIDEMUL_INT128 # include "secp256k1/int128.h" # include "secp256k1/int128_impl.h" #else # include "secp256k1/int128_struct.h" # include "secp256k1/int128_struct_impl.h" #endif static void write128(frameItem* frame, const secp256k1_uint128* x) { simplicity_write64(frame, secp256k1_u128_hi_u64(x)); simplicity_write64(frame, secp256k1_u128_to_u64(x)); } /* verify : TWO |- ONE */ bool simplicity_verify(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ (void) dst; /* dst is unused. */ return readBit(&src); } /* low_1 : ONE |- TWO */ bool simplicity_low_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ (void) src; /* src is unused. */ writeBit(dst, 0); return true; } #define LOW_(bits) \ /* low_n : ONE |- TWO^n */ \ bool simplicity_low_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ (void) src; /* src is unused. */ \ simplicity_write##bits(dst, 0); \ return true; \ } LOW_(8) LOW_(16) LOW_(32) LOW_(64) /* high_1 : ONE |- TWO */ bool simplicity_high_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ (void) src; /* src is unused. */ writeBit(dst, 1); return true; } #define HIGH_(bits) \ /* high_n : ONE |- TWO^n */ \ bool simplicity_high_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ (void) src; /* src is unused. */ \ simplicity_write##bits(dst, UINT##bits##_MAX); \ return true; \ } HIGH_(8) HIGH_(16) HIGH_(32) HIGH_(64) /* complement_1 : TWO |- TWO */ bool simplicity_complement_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); writeBit(dst, !x); return true; } #define COMPLEMENT_(bits) \ /* complement_n : TWO^n |- TWO^n */ \ bool simplicity_complement_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ simplicity_write##bits(dst, ~(1U*x)); \ return true; \ } COMPLEMENT_(8) COMPLEMENT_(16) COMPLEMENT_(32) COMPLEMENT_(64) /* and_1 : TWO * TWO |- TWO */ bool simplicity_and_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); writeBit(dst, x && y); return true; } #define AND_(bits) \ /* and_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_and_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x & y); \ return true; \ } AND_(8) AND_(16) AND_(32) AND_(64) /* or_1 : TWO * TWO |- TWO */ bool simplicity_or_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); writeBit(dst, x || y); return true; } #define OR_(bits) \ /* or_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_or_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x | y); \ return true; \ } OR_(8) OR_(16) OR_(32) OR_(64) /* xor_1 : TWO * TWO |- TWO */ bool simplicity_xor_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); writeBit(dst, x ^ y); return true; } #define XOR_(bits) \ /* xor_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_xor_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x ^ y); \ return true; \ } XOR_(8) XOR_(16) XOR_(32) XOR_(64) /* maj_1 : TWO * TWO * TWO |- TWO */ bool simplicity_maj_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); bool z = readBit(&src); writeBit(dst, (x && y) || (y && z) || (z && x)); return true; } #define MAJ_(bits) \ /* maj_n : TWO^n * TWO^n * TWO^n |- TWO^n */ \ bool simplicity_maj_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ uint_fast##bits##_t z = simplicity_read##bits(&src); \ simplicity_write##bits(dst, (x&y) | (y&z) | (z&x)); \ return true; \ } MAJ_(8) MAJ_(16) MAJ_(32) MAJ_(64) /* xor_xor_1 : TWO * TWO * TWO |- TWO */ bool simplicity_xor_xor_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); bool z = readBit(&src); writeBit(dst, x ^ y ^ z); return true; } #define XOR_XOR_(bits) \ /* xor_xor_n : TWO^n * TWO^n * TWO^n |- TWO^n */ \ bool simplicity_xor_xor_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ uint_fast##bits##_t z = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x ^ y ^ z); \ return true; \ } XOR_XOR_(8) XOR_XOR_(16) XOR_XOR_(32) XOR_XOR_(64) /* ch_1 : TWO * TWO * TWO |- TWO */ bool simplicity_ch_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); bool z = readBit(&src); writeBit(dst, x ? y : z); return true; } #define CH_(bits) \ /* ch_n : TWO^n * TWO^n * TWO^n |- TWO^n */ \ bool simplicity_ch_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ uint_fast##bits##_t z = simplicity_read##bits(&src); \ simplicity_write##bits(dst, ((x&y) | ((~(1U*x))&z))); \ return true; \ } CH_(8) CH_(16) CH_(32) CH_(64) /* some_1 : TWO |- TWO */ bool simplicity_some_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); writeBit(dst, x); return true; } #define SOME_(bits) \ /* some_n : TWO^n |- TWO */ \ bool simplicity_some_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, x != 0); \ return true; \ } SOME_(8) SOME_(16) SOME_(32) SOME_(64) #define ALL_(bits) \ /* all_n : TWO^n |- TWO */ \ bool simplicity_all_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, x == UINT##bits##_MAX); \ return true; \ } ALL_(8) ALL_(16) ALL_(32) ALL_(64) /* eq_1 : TWO * TWO |- TWO */ bool simplicity_eq_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ bool x = readBit(&src); bool y = readBit(&src); writeBit(dst, x == y); return true; } #define EQ_(bits) \ /* eq_n : TWO^n * TWO^n |- TWO */ \ bool simplicity_eq_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, x == y); \ return true; \ } EQ_(8) EQ_(16) EQ_(32) EQ_(64) /* eq_256 : TWO^256 * TWO^256 |- TWO */ bool simplicity_eq_256(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint32_t arr[16]; read32s(arr, 16, &src); for (int i = 0; i < 8; ++i) { if (arr[i] != arr[i+8]) { writeBit(dst, false); return true; } } writeBit(dst, true); return true; } #define FULL_LEFT_SHIFT_(bitsN, bitsM) \ /* full_left_shift_n_m : TWO^n * TWO^m |- TWO^m * TWO^n */ \ bool simplicity_full_left_shift_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 <= (bitsM) && (bitsM) <= (bitsN) && (bitsN) <= 64, "Bad arguments for bitsN or bitsM"); \ simplicity_copyBits(dst, &src, (bitsN) + (bitsM)); \ return true; \ } FULL_LEFT_SHIFT_(8,1) FULL_LEFT_SHIFT_(8,2) FULL_LEFT_SHIFT_(8,4) FULL_LEFT_SHIFT_(16,1) FULL_LEFT_SHIFT_(16,2) FULL_LEFT_SHIFT_(16,4) FULL_LEFT_SHIFT_(16,8) FULL_LEFT_SHIFT_(32,1) FULL_LEFT_SHIFT_(32,2) FULL_LEFT_SHIFT_(32,4) FULL_LEFT_SHIFT_(32,8) FULL_LEFT_SHIFT_(32,16) FULL_LEFT_SHIFT_(64,1) FULL_LEFT_SHIFT_(64,2) FULL_LEFT_SHIFT_(64,4) FULL_LEFT_SHIFT_(64,8) FULL_LEFT_SHIFT_(64,16) FULL_LEFT_SHIFT_(64,32) #define FULL_RIGHT_SHIFT_(bitsN, bitsM) \ /* full_right_shift_n_m : TWO^m * TWO^n |- TWO^n * TWO^m */ \ bool simplicity_full_right_shift_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 <= (bitsM) && (bitsM) <= (bitsN) && (bitsN) <= 64, "Bad arguments for bitsN or bitsM"); \ simplicity_copyBits(dst, &src, (bitsN) + (bitsM)); \ return true; \ } FULL_RIGHT_SHIFT_(8,1) FULL_RIGHT_SHIFT_(8,2) FULL_RIGHT_SHIFT_(8,4) FULL_RIGHT_SHIFT_(16,1) FULL_RIGHT_SHIFT_(16,2) FULL_RIGHT_SHIFT_(16,4) FULL_RIGHT_SHIFT_(16,8) FULL_RIGHT_SHIFT_(32,1) FULL_RIGHT_SHIFT_(32,2) FULL_RIGHT_SHIFT_(32,4) FULL_RIGHT_SHIFT_(32,8) FULL_RIGHT_SHIFT_(32,16) FULL_RIGHT_SHIFT_(64,1) FULL_RIGHT_SHIFT_(64,2) FULL_RIGHT_SHIFT_(64,4) FULL_RIGHT_SHIFT_(64,8) FULL_RIGHT_SHIFT_(64,16) FULL_RIGHT_SHIFT_(64,32) #define LEFTMOST_(bitsN, bitsM) \ /* leftmost_n_m : TWO^n |- TWO^m */ \ bool simplicity_leftmost_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 <= (bitsM) && (bitsM) <= (bitsN) && (bitsN) <= 64, "Bad arguments for bitsN or bitsM"); \ simplicity_copyBits(dst, &src, (bitsM)); \ return true; \ } LEFTMOST_(8,1) LEFTMOST_(8,2) LEFTMOST_(8,4) LEFTMOST_(16,1) LEFTMOST_(16,2) LEFTMOST_(16,4) LEFTMOST_(16,8) LEFTMOST_(32,1) LEFTMOST_(32,2) LEFTMOST_(32,4) LEFTMOST_(32,8) LEFTMOST_(32,16) LEFTMOST_(64,1) LEFTMOST_(64,2) LEFTMOST_(64,4) LEFTMOST_(64,8) LEFTMOST_(64,16) LEFTMOST_(64,32) #define RIGHTMOST_(bitsN, bitsM) \ /* rightmost_n_m : TWO^n |- TWO^m */ \ bool simplicity_rightmost_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 <= (bitsM) && (bitsM) <= (bitsN) && (bitsN) <= 64, "Bad arguments for bitsN or bitsM"); \ forwardBits(&src, (bitsN) - (bitsM)); \ simplicity_copyBits(dst, &src, (bitsM)); \ return true; \ } RIGHTMOST_(8,1) RIGHTMOST_(8,2) RIGHTMOST_(8,4) RIGHTMOST_(16,1) RIGHTMOST_(16,2) RIGHTMOST_(16,4) RIGHTMOST_(16,8) RIGHTMOST_(32,1) RIGHTMOST_(32,2) RIGHTMOST_(32,4) RIGHTMOST_(32,8) RIGHTMOST_(32,16) RIGHTMOST_(64,1) RIGHTMOST_(64,2) RIGHTMOST_(64,4) RIGHTMOST_(64,8) RIGHTMOST_(64,16) RIGHTMOST_(64,32) #define LEFT_PAD_LOW_1_(bitsM) \ /* left_pad_low_1_m : TWO |- TWO^m */ \ bool simplicity_left_pad_low_1_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool bit = readBit(&src); \ simplicity_write##bitsM(dst, bit); \ return true; \ } LEFT_PAD_LOW_1_(8) LEFT_PAD_LOW_1_(16) LEFT_PAD_LOW_1_(32) LEFT_PAD_LOW_1_(64) #define LEFT_PAD_LOW_(bitsN, bitsM) \ /* left_pad_low_n_m : TWO^n |- TWO^m */ \ bool simplicity_left_pad_low_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsN) && (bitsN) <= 64, "bitsN is out of range"); \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ static_assert(0 == (bitsM) % (bitsN), "bitsM is not a multiple of bitsN"); \ for(int i = 0; i < (bitsM)/(bitsN) - 1; ++i) { simplicity_write##bitsN(dst, 0); } \ simplicity_copyBits(dst, &src, (bitsN)); \ return true; \ } LEFT_PAD_LOW_(8,16) LEFT_PAD_LOW_(8,32) LEFT_PAD_LOW_(8,64) LEFT_PAD_LOW_(16,32) LEFT_PAD_LOW_(16,64) LEFT_PAD_LOW_(32,64) #define LEFT_PAD_HIGH_1_(bitsM) \ /* left_pad_high_1_m : TWO |- TWO^m */ \ bool simplicity_left_pad_high_1_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ for(int i = 0; i < (bitsM) - 1; ++i) { writeBit(dst, true); } \ simplicity_copyBits(dst, &src, 1); \ return true; \ } LEFT_PAD_HIGH_1_(8) LEFT_PAD_HIGH_1_(16) LEFT_PAD_HIGH_1_(32) LEFT_PAD_HIGH_1_(64) #define LEFT_PAD_HIGH_(bitsN, bitsM) \ /* left_pad_high_n_m : TWO^n |- TWO^m */ \ bool simplicity_left_pad_high_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsN) && (bitsN) <= 64, "bitsN is out of range"); \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ static_assert(0 == (bitsM) % (bitsN), "bitsM is not a multiple of bitsN"); \ for(int i = 0; i < (bitsM)/(bitsN) - 1; ++i) { simplicity_write##bitsN(dst, UINT##bitsN##_MAX); } \ simplicity_copyBits(dst, &src, (bitsN)); \ return true; \ } LEFT_PAD_HIGH_(8,16) LEFT_PAD_HIGH_(8,32) LEFT_PAD_HIGH_(8,64) LEFT_PAD_HIGH_(16,32) LEFT_PAD_HIGH_(16,64) LEFT_PAD_HIGH_(32,64) #define LEFT_EXTEND_1_(bitsM) \ /* left_extend_1_m : TWO |- TWO^m */ \ bool simplicity_left_extend_1_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool bit = readBit(&src); \ simplicity_write##bitsM(dst, bit ? UINT##bitsM##_MAX : 0); \ return true; \ } LEFT_EXTEND_1_(8) LEFT_EXTEND_1_(16) LEFT_EXTEND_1_(32) LEFT_EXTEND_1_(64) #define LEFT_EXTEND_(bitsN, bitsM) \ /* left_extend_n_m : TWO^n |- TWO^m */ \ bool simplicity_left_extend_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsN) && (bitsN) <= 64, "bitsN is out of range"); \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ static_assert(0 == (bitsM) % (bitsN), "bitsM is not a multiple of bitsN"); \ uint_fast##bitsN##_t input = simplicity_read##bitsN(&src); \ bool msb = input >> ((bitsN) - 1); \ for(int i = 0; i < (bitsM)/(bitsN) - 1; ++i) { simplicity_write##bitsN(dst, msb ? UINT##bitsN##_MAX : 0); } \ simplicity_write##bitsN(dst, input); \ return true; \ } LEFT_EXTEND_(8,16) LEFT_EXTEND_(8,32) LEFT_EXTEND_(8,64) LEFT_EXTEND_(16,32) LEFT_EXTEND_(16,64) LEFT_EXTEND_(32,64) #define RIGHT_PAD_LOW_1_(bitsM) \ /* right_pad_low_1_m : TWO |- TWO^m */ \ bool simplicity_right_pad_low_1_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ bool bit = readBit(&src); \ simplicity_write##bitsM(dst, (uint_fast##bitsM##_t)((uint_fast##bitsM##_t)bit << ((bitsM) - 1))); \ return true; \ } RIGHT_PAD_LOW_1_(8) RIGHT_PAD_LOW_1_(16) RIGHT_PAD_LOW_1_(32) RIGHT_PAD_LOW_1_(64) #define RIGHT_PAD_LOW_(bitsN, bitsM) \ /* right_pad_low_n_m : TWO^n |- TWO^m */ \ bool simplicity_right_pad_low_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsN) && (bitsN) <= 64, "bitsN is out of range"); \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ static_assert(0 == (bitsM) % (bitsN), "bitsM is not a multiple of bitsN"); \ simplicity_copyBits(dst, &src, (bitsN)); \ for(int i = 0; i < (bitsM)/(bitsN) - 1; ++i) { simplicity_write##bitsN(dst, 0); } \ return true; \ } RIGHT_PAD_LOW_(8,16) RIGHT_PAD_LOW_(8,32) RIGHT_PAD_LOW_(8,64) RIGHT_PAD_LOW_(16,32) RIGHT_PAD_LOW_(16,64) RIGHT_PAD_LOW_(32,64) #define RIGHT_PAD_HIGH_1_(bitsM) \ /* right_pad_high_1_m : TWO |- TWO^m */ \ bool simplicity_right_pad_high_1_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ simplicity_copyBits(dst, &src, 1); \ for(int i = 0; i < (bitsM) - 1; ++i) { writeBit(dst, true); } \ return true; \ } RIGHT_PAD_HIGH_1_(8) RIGHT_PAD_HIGH_1_(16) RIGHT_PAD_HIGH_1_(32) RIGHT_PAD_HIGH_1_(64) #define RIGHT_PAD_HIGH_(bitsN, bitsM) \ /* right_pad_high_n_m : TWO^n |- TWO^m */ \ bool simplicity_right_pad_high_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsN) && (bitsN) <= 64, "bitsN is out of range"); \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ static_assert(0 == (bitsM) % (bitsN), "bitsM is not a multiple of bitsN"); \ simplicity_copyBits(dst, &src, (bitsN)); \ for(int i = 0; i < (bitsM)/(bitsN) - 1; ++i) { simplicity_write##bitsN(dst, UINT##bitsN##_MAX); } \ return true; \ } RIGHT_PAD_HIGH_(8,16) RIGHT_PAD_HIGH_(8,32) RIGHT_PAD_HIGH_(8,64) RIGHT_PAD_HIGH_(16,32) RIGHT_PAD_HIGH_(16,64) RIGHT_PAD_HIGH_(32,64) #define RIGHT_EXTEND_(bitsN, bitsM) \ /* right_extend_n_m : TWO^n |- TWO^m */ \ bool simplicity_right_extend_##bitsN##_##bitsM(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ static_assert(0 < (bitsN) && (bitsN) <= 64, "bitsN is out of range"); \ static_assert(0 < (bitsM) && (bitsM) <= 64, "bitsM is out of range"); \ static_assert(0 == (bitsM) % (bitsN), "bitsM is not a multiple of bitsN"); \ uint_fast##bitsN##_t input = simplicity_read##bitsN(&src); \ bool lsb = input & 1; \ simplicity_write##bitsN(dst, input); \ for(int i = 0; i < (bitsM)/(bitsN) - 1; ++i) { simplicity_write##bitsN(dst, lsb ? UINT##bitsN##_MAX : 0); } \ return true; \ } RIGHT_EXTEND_(8,16) RIGHT_EXTEND_(8,32) RIGHT_EXTEND_(8,64) RIGHT_EXTEND_(16,32) RIGHT_EXTEND_(16,64) RIGHT_EXTEND_(32,64) #define LEFT_SHIFT_(log, bits) \ static inline void left_shift_helper_##bits(bool with, frameItem* dst, frameItem *src) { \ static_assert(log <= 8, "Only log parameter up to 8 is supported."); \ uint_fast8_t amt = simplicity_read##log(src); \ uint_fast##bits##_t output = simplicity_read##bits(src); \ if (with) output = UINT##bits##_MAX ^ output; \ if (amt < bits) { \ output = (uint_fast##bits##_t)((1U * output) << amt); \ } else { \ output = 0; \ } \ if (with) output = UINT##bits##_MAX ^ output; \ simplicity_write##bits(dst, output); \ } \ \ /* left_shift_with_n : TWO * TWO^l * TWO^n |- TWO^n */ \ bool simplicity_left_shift_with_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool with = readBit(&src); \ left_shift_helper_##bits(with, dst, &src); \ return true; \ } \ \ /* left_shift_n : TWO^l * TWO^n |- TWO^n */ \ bool simplicity_left_shift_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ left_shift_helper_##bits(0, dst, &src); \ return true; \ } LEFT_SHIFT_(4,8) LEFT_SHIFT_(4,16) LEFT_SHIFT_(8,32) LEFT_SHIFT_(8,64) #define RIGHT_SHIFT_(log, bits) \ static inline void right_shift_helper_##bits(bool with, frameItem* dst, frameItem *src) { \ static_assert(log <= 8, "Only log parameter up to 8 is supported."); \ uint_fast8_t amt = simplicity_read##log(src); \ uint_fast##bits##_t output = simplicity_read##bits(src); \ if (with) output = UINT##bits##_MAX ^ output; \ if (amt < bits) { \ output = (uint_fast##bits##_t)(output >> amt); \ } else { \ output = 0; \ } \ if (with) output = UINT##bits##_MAX ^ output; \ simplicity_write##bits(dst, output); \ } \ \ /* right_shift_with_n : TWO * TWO^l * TWO^n |- TWO^n */ \ bool simplicity_right_shift_with_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool with = readBit(&src); \ right_shift_helper_##bits(with, dst, &src); \ return true; \ } \ \ /* right_shift_n : TWO^l * TWO^n |- TWO^n */ \ bool simplicity_right_shift_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ right_shift_helper_##bits(0, dst, &src); \ return true; \ } RIGHT_SHIFT_(4,8) RIGHT_SHIFT_(4,16) RIGHT_SHIFT_(8,32) RIGHT_SHIFT_(8,64) #define ROTATE_(log, bits) \ /* Precondition: 0 <= amt < bits */ \ static inline uint_fast##bits##_t rotate_##bits(uint_fast##bits##_t value, uint_fast8_t amt) { \ if (amt) { \ return (uint_fast##bits##_t)((1U * value << amt) | value >> (bits - amt)); \ } else { \ return value; \ } \ } \ \ /* left_rotate_n : TWO^l * TWO^n |- TWO^n */ \ bool simplicity_left_rotate_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast8_t amt = simplicity_read##log(&src) % bits; \ uint_fast##bits##_t input = simplicity_read##bits(&src); \ simplicity_write##bits(dst, rotate_##bits(input, amt)); \ return true; \ } \ \ /* right_rotate_n : TWO^l * TWO^n |- TWO^n */ \ bool simplicity_right_rotate_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ static_assert(bits <= UINT8_MAX, "'bits' is too large."); \ (void) env; /* env is unused. */ \ uint_fast8_t amt = simplicity_read##log(&src) % bits; \ uint_fast##bits##_t input = simplicity_read##bits(&src); \ simplicity_write##bits(dst, rotate_##bits(input, (uint_fast8_t)((bits - amt) % bits))); \ return true; \ } ROTATE_(4,8) ROTATE_(4,16) ROTATE_(8,32) ROTATE_(8,64) #define ONE_(bits) \ /* one_n : ONE |- TWO^n */ \ bool simplicity_one_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ (void) src; /* src is unused. */ \ simplicity_write##bits(dst, 1); \ return true; \ } ONE_(8) ONE_(16) ONE_(32) ONE_(64) #define ADD_(bits) \ /* add_n : TWO^n * TWO^n |- TWO * TWO^n */ \ bool simplicity_add_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, 1U * UINT##bits##_MAX - y < x); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x + y)); \ return true; \ } ADD_(8) ADD_(16) ADD_(32) ADD_(64) #define FULL_ADD_(bits) \ /* full_add_n : TWO * TWO^n * TWO^n |- TWO * TWO^n */ \ bool simplicity_full_add_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool z = readBit(&src); \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, 1U * UINT##bits##_MAX - y < x || 1U * UINT##bits##_MAX - z < 1U * x + y); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x + y + z)); \ return true; \ } FULL_ADD_(8) FULL_ADD_(16) FULL_ADD_(32) FULL_ADD_(64) #define FULL_INCREMENT_(bits) \ /* full_increment_n : TWO * TWO^n |- TWO * TWO^n */ \ bool simplicity_full_increment_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool z = readBit(&src); \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, 1U * UINT##bits##_MAX - z < x); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x + z)); \ return true; \ } FULL_INCREMENT_(8) FULL_INCREMENT_(16) FULL_INCREMENT_(32) FULL_INCREMENT_(64) #define INCREMENT_(bits) \ /* increment_n : TWO^n |- TWO * TWO^n */ \ bool simplicity_increment_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, 1U * UINT##bits##_MAX - 1 < x); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x + 1)); \ return true; \ } INCREMENT_(8) INCREMENT_(16) INCREMENT_(32) INCREMENT_(64) #define SUBTRACT_(bits) \ /* subtract_n : TWO^n * TWO^n |- TWO * TWO^n */ \ bool simplicity_subtract_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, x < y); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x - y)); \ return true; \ } SUBTRACT_(8) SUBTRACT_(16) SUBTRACT_(32) SUBTRACT_(64) #define NEGATE_(bits) \ /* negate_n : TWO^n |- TWO * TWO^n */ \ bool simplicity_negate_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, x != 0); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(- (1U * x))); \ return true; \ } NEGATE_(8) NEGATE_(16) NEGATE_(32) NEGATE_(64) #define FULL_DECREMENT_(bits) \ /* full_decrement_n : TWO * TWO^n |- TWO * TWO^n */ \ bool simplicity_full_decrement_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool z = readBit(&src); \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, 1U * x < 1U * z); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x - z)); \ return true; \ } FULL_DECREMENT_(8) FULL_DECREMENT_(16) FULL_DECREMENT_(32) FULL_DECREMENT_(64) #define DECREMENT_(bits) \ /* decrement_n : TWO^n |- TWO * TWO^n */ \ bool simplicity_decrement_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, x < 1); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x - 1)); \ return true; \ } DECREMENT_(8) DECREMENT_(16) DECREMENT_(32) DECREMENT_(64) #define FULL_SUBTRACT_(bits) \ /* full_subtract_n : TWO * TWO^n * TWO^n |- TWO * TWO^n */ \ bool simplicity_full_subtract_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ bool z = readBit(&src); \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, 1U * x < 1U * y || 1U * x - y < 1U * z); \ simplicity_write##bits(dst, (uint_fast##bits##_t)(1U * x - y - z)); \ return true; \ } FULL_SUBTRACT_(8) FULL_SUBTRACT_(16) FULL_SUBTRACT_(32) FULL_SUBTRACT_(64) #define MULTIPLY_(bits,bitsx2) \ bool simplicity_multiply_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bitsx2##_t x = simplicity_read##bits(&src); \ uint_fast##bitsx2##_t y = simplicity_read##bits(&src); \ simplicity_write##bitsx2(dst, x * y); \ return true; \ } MULTIPLY_(8, 16) MULTIPLY_(16, 32) MULTIPLY_(32, 64) bool simplicity_multiply_64(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint_fast64_t x = simplicity_read64(&src); uint_fast64_t y = simplicity_read64(&src); secp256k1_uint128 r; secp256k1_u128_mul(&r, x, y); write128(dst, &r); return true; } #define FULL_MULTIPLY_(bits,bitsx2) \ bool simplicity_full_multiply_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bitsx2##_t x = simplicity_read##bits(&src); \ uint_fast##bitsx2##_t y = simplicity_read##bits(&src); \ uint_fast##bitsx2##_t z = simplicity_read##bits(&src); \ uint_fast##bitsx2##_t w = simplicity_read##bits(&src); \ simplicity_write##bitsx2(dst, x * y + z + w); \ return true; \ } FULL_MULTIPLY_(8, 16) FULL_MULTIPLY_(16, 32) FULL_MULTIPLY_(32, 64) bool simplicity_full_multiply_64(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint_fast64_t x = simplicity_read64(&src); uint_fast64_t y = simplicity_read64(&src); uint_fast64_t z = simplicity_read64(&src); uint_fast64_t w = simplicity_read64(&src); secp256k1_uint128 r; secp256k1_u128_mul(&r, x, y); secp256k1_u128_accum_u64(&r, z); secp256k1_u128_accum_u64(&r, w); write128(dst, &r); return true; } #define IS_ZERO_(bits) \ /* is_zero_n : TWO^n |- TWO */ \ bool simplicity_is_zero_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, x == 0); \ return true; \ } IS_ZERO_(8) IS_ZERO_(16) IS_ZERO_(32) IS_ZERO_(64) #define IS_ONE_(bits) \ /* is_one_n : TWO^n |- TWO */ \ bool simplicity_is_one_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ writeBit(dst, x == 1); \ return true; \ } IS_ONE_(8) IS_ONE_(16) IS_ONE_(32) IS_ONE_(64) #define LE_(bits) \ /* le_n : TWO^n * TWO^n |- TWO */ \ bool simplicity_le_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, x <= y); \ return true; \ } LE_(8) LE_(16) LE_(32) LE_(64) #define LT_(bits) \ /* lt_n : TWO^n * TWO^n |- TWO */ \ bool simplicity_lt_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, x < y); \ return true; \ } LT_(8) LT_(16) LT_(32) LT_(64) #define MIN_(bits) \ /* min_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_min_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x < y ? x : y); \ return true; \ } MIN_(8) MIN_(16) MIN_(32) MIN_(64) #define MAX_(bits) \ /* max_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_max_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x < y ? y : x); \ return true; \ } MAX_(8) MAX_(16) MAX_(32) MAX_(64) #define MEDIAN_(bits) \ /* median_n : TWO^n * TWO^n * TWO^n |- TWO^n */ \ bool simplicity_median_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ uint_fast##bits##_t z = simplicity_read##bits(&src); \ simplicity_write##bits(dst, x < y \ ? (y < z ? y : (z < x ? x : z)) \ : (x < z ? x : (z < y ? y : z))); \ return true; \ } MEDIAN_(8) MEDIAN_(16) MEDIAN_(32) MEDIAN_(64) #define DIV_MOD_(bits) \ /* div_mod_n : TWO^n * TWO^n |- TWO^n * TWO^n */ \ bool simplicity_div_mod_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, 0 == y ? 0 : x / y); \ simplicity_write##bits(dst, 0 == y ? x : x % y); \ return true; \ } DIV_MOD_(8) DIV_MOD_(16) DIV_MOD_(32) DIV_MOD_(64) #define DIVIDE_(bits) \ /* divide_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_divide_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, 0 == y ? 0 : x / y); \ return true; \ } DIVIDE_(8) DIVIDE_(16) DIVIDE_(32) DIVIDE_(64) #define MODULO_(bits) \ /* modulo_n : TWO^n * TWO^n |- TWO^n */ \ bool simplicity_modulo_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ simplicity_write##bits(dst, 0 == y ? x : x % y); \ return true; \ } MODULO_(8) MODULO_(16) MODULO_(32) MODULO_(64) #define DIVIDES_(bits) \ /* divides_n : TWO^n * TWO^n |- TWO */ \ bool simplicity_divides_##bits(frameItem* dst, frameItem src, const txEnv* env) { \ (void) env; /* env is unused. */ \ uint_fast##bits##_t x = simplicity_read##bits(&src); \ uint_fast##bits##_t y = simplicity_read##bits(&src); \ writeBit(dst, 0 == (0 == x ? y : y % x)); \ return true; \ } DIVIDES_(8) DIVIDES_(16) DIVIDES_(32) DIVIDES_(64) /* Implements the 3n/2n division algorithm for n=32 bits. * For more details see "Fast Recursive Division" by Christoph Burnikel and Joachim Ziegler, MPI-I-98-1-022, Oct. 1998. * * Given a 96 bit (unsigned) value A and a 64 bit value B, set *q and *r to the quotient and remainder of A divided by B. * * ah is passed the high 64 bits of A, and al is passed the low 32 bits of A. * We say that A = [ah;al] where [ah;al] denotes ah * 2^32 + al. * * The value of B is passed in as b. * * This algorithm requires certain preconditons: * 1. A < [B;0] * 2. 2^63 <= B. * * Preconditon 1 ensures that the quotient fits in 32-bits. * * We define the quotient Q and remainder R by the equation: * A == Q * B + R where 0 <= R < B. * * The algorithm works by estimating the value of Q by * estQ = (A >> 32) / (B >> 32). * * Preconditon 2 ensures that this estimate is close to the true value of Q. In fact Q <= estQ <= Q + 2 (see proof below) * * There is a corresponding estR value satisfying the equation estR = A - estQ * B. * This estR is one of {R, R - B, R - 2B}. * Therefore if estR is non-negative, then estR is equal to the true R value, and hence estQ is equal to the true Q value. * * If estR is negative we decrement our estimated value of Q and repeatedly try again until the computed remainder is non-negative. * * Lemma 1: Q <= estQ. * A - estQ * B == [ah;al] - estQ * [bh;bl] * == [ah - estQ * bh; al - estQ * bl] * == [ah % bh; al] - estQ * bl * <= [ah % bh; al] * < [(ah % bh) + 1; 0] * <= [bh; 0] * <= B * Therefore A - (estQ + 1)*B < 0, and hence Q == A/B < estQ + 1. * * Lemma 2: estQ < [1;2] (== 2^32 + 2). * First note that ah - [bh;0] < [1;0] because * ah < B (by precondition 1) * < [bh+1;0] * == [bh;0] + [1;0] * * ah - [1;2]*bh == ah - [bh;2*bh] * < [1;0] - [0;2*bh] * <= 0 (by precondition 2.) * Therefore estQ == ah / bh < [1;2]. * * Lemma 3: estQ - 2 <= Q. * A - (estQ - 2)*B == 2*B + estR * == 2*B + [ah % bh; al] - estQ * bl * >= 2*B - estQ * bl * == 2*[bh;bl] - estQ * bl * == [2*bh;0] + 2*bl - estQ * bl * == [2*bh;0] - (estQ - 2) * bl * > [2*bh;0] - [1;0] * bl (by lemma 2.) * == [2*bh - bl;0] * >= 0 (by precondition 2.) * Therefore Q = A/B >= estQ - 2. */ static void div_mod_96_64(uint_fast32_t *q, uint_fast64_t *r, uint_fast64_t ah, uint_fast32_t al, uint_fast64_t b) { simplicity_debug_assert(ah < b); simplicity_debug_assert(0x8000000000000000u <= b); uint_fast64_t bh = b >> 32; uint_fast64_t bl = b & 0xffffffffu; /* B == b == [bh;bl] */ uint_fast64_t estQ = ah / bh; /* Precondition 1 guarantees Q is 32-bits, if estQ is greater than UINT32_MAX, then reduce our initial estimated quotient to UINT32_MAX. */ *q = estQ <= UINT32_MAX ? (uint_fast32_t)estQ : UINT32_MAX; /* *q * bh <= estQ * bh <= ah */ uint_fast64_t rh = ah - 1u * *q * bh; uint_fast64_t d = 1u * *q * bl; /* Test if our estimated remainder, A - *q * B is negative. * A - *q * B == [ah;al] - *q * [bh;bl] * == [ah - *q * bh;al - *q * bl] * == [rh;al] - d * * This value is negative when [rh;al] < d. * Note that d is 64 bit and thus if rh is greater than UINT32_MAX, then this value cannot be negative. */ /* This loop is executed at most twice. */ while (rh <= UINT32_MAX && 0x100000000u*rh + al < d) { /* Our estimated remainder, A - *q * B is negative. */ /* 0 < d == *q * bl and hence 0 < *q, so this decrement does not underflow. */ (*q)--; rh += bh; /* rh == ah - *q * bh */ d -= bl; /* d == *q * bl */; } /* *q is the correct quotient. */ /* Compute the remainder. * The computation below is performed modulo 2^64. * However since we know the remainder lies within [0,b) which is within [0,2^64), * the computation must end up with the correct result even if overflow/underflow occurs. */ *r = 0x100000000u*rh + al - d; } /* div_mod_128_64 : TWO^128 * TWO^64 |- TWO^64 * TWO^64 */ bool simplicity_div_mod_128_64(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint_fast32_t qh, ql; uint_fast64_t r; uint_fast64_t ah = simplicity_read64(&src); uint_fast32_t am = simplicity_read32(&src); uint_fast32_t al = simplicity_read32(&src); uint_fast64_t b = simplicity_read64(&src); /* div2n1n is only defined when 2^(n-1) <= b and when the quotient q < 2^n. */ if (0x8000000000000000 <= b && ah < b) { /* We compute the division and remainder of A = [[ah;am];al] by B = b by long division with 32-bit "digits" * * 1. Q * ______ * BB) AAAA * XXX * --- * RR * * First divide the high 3 "digit"s (96-bits) of A by the two "digit"s (64-bits) of B, * returning the first "digit" (high 32-bits) of the quotient, and an intermediate remainder consisiting of 2 "digit"s (64-bits). */ div_mod_96_64(&qh, &r, ah, am, b); simplicity_debug_assert(r < b); /* 2. QQ * ______ * BB) AAA| * XXX| * ---| * RRA * XXX * --- * RR * * Then append the last "digit" of A to the intermediate remainder and divide that value (96_bits) by the two "digit"s (64-bits) of B, * returning the second "digit" (low 32-bits) of the quotient, and the final remainder consisiting of 2 "digit"s (64-bits). */ div_mod_96_64(&ql, &r, r, al, b); simplicity_write32(dst, qh); simplicity_write32(dst, ql); simplicity_write64(dst, r); } else { /* Set all the bits in the output when the input is out of bounds. */ simplicity_write64(dst, (uint64_t)(-1)); simplicity_write64(dst, (uint64_t)(-1)); } return true; } /* sha_256_iv : ONE |- TWO^256 */ bool simplicity_sha_256_iv(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ (void) src; /* env is unused. */ uint32_t iv[8]; sha256_iv(iv); write32s(dst, iv, 8); return true; } /* sha_256_block : TWO^256 * TWO^512 |- TWO^256 */ bool simplicity_sha_256_block(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint32_t h[8]; uint32_t block[16]; read32s(h, 8, &src); read32s(block, 16, &src); simplicity_sha256_compression(h, block); write32s(dst, h, 8); return true; } /* sha_256_ctx_8_init : ONE |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_init(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ (void) src; /* env is unused. */ uint32_t iv[8]; sha256_context ctx = sha256_init(iv); return simplicity_write_sha256_context(dst, &ctx); } /* sha_256_ctx_8_add_n : CTX8 * (TWO^8)^n |- CTX8 * where * n is a power of 2 less than or equal to 512 * and * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ static bool sha_256_ctx_8_add_n(frameItem* dst, frameItem *src, size_t n) { simplicity_debug_assert(0 < n && n <= 512 && (n & (n - 1)) == 0); sha256_midstate midstate; unsigned char buf[512]; sha256_context ctx = {.output = midstate.s}; if (!simplicity_read_sha256_context(&ctx, src)) return false; read8s(buf, n, src); sha256_uchars(&ctx, buf, n); return simplicity_write_sha256_context(dst, &ctx); } /* sha_256_ctx_8_add_1 : CTX8 * TWO^8 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_1(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 1); } /* sha_256_ctx_8_add_2 : CTX8 * (TWO^8)^2 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_2(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 2); } /* sha_256_ctx_8_add_4 : CTX8 * (TWO^8)^4 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_4(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 4); } /* sha_256_ctx_8_add_8 : CTX8 * (TWO^8)^8 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_8(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 8); } /* sha_256_ctx_8_add_16 : CTX8 * (TWO^8)^16 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_16(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 16); } /* sha_256_ctx_8_add_32 : CTX8 * (TWO^8)^32 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_32(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 32); } /* sha_256_ctx_8_add_64 : CTX8 * (TWO^8)^64 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_64(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 64); } /* sha_256_ctx_8_add_128 : CTX8 * (TWO^8)^128 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_128(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 128); } /* sha_256_ctx_8_add_256 : CTX8 * (TWO^8)^256 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_256(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 256); } /* sha_256_ctx_8_add_512 : CTX8 * (TWO^8)^512 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_512(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ return sha_256_ctx_8_add_n(dst, &src, 512); } /* sha_256_ctx_8_add_buffer_511 : CTX8 * (TWO^8)^<512 |- CTX8 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_add_buffer_511(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ sha256_midstate midstate; unsigned char buf[511]; size_t buf_len; sha256_context ctx = {.output = midstate.s}; if (!simplicity_read_sha256_context(&ctx, &src)) return false; simplicity_read_buffer8(buf, &buf_len, &src, 8); sha256_uchars(&ctx, buf, buf_len); return simplicity_write_sha256_context(dst, &ctx); } /* sha_256_ctx_8_finalize : CTX8 |- TWO^256 * where * CTX8 = (TWO^8)^<64 * TWO^64 * TWO^256 */ bool simplicity_sha_256_ctx_8_finalize(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ sha256_midstate midstate; sha256_context ctx = {.output = midstate.s}; if (!simplicity_read_sha256_context(&ctx, &src)) return false; sha256_finalize(&ctx); write32s(dst, midstate.s, 8); return true; } /* parse_sequence : TWO^32 |- TWO^32 + TWO^32 */ bool simplicity_parse_lock(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint_fast32_t nLockTime = simplicity_read32(&src); writeBit(dst, 500000000U <= nLockTime); simplicity_write32(dst, nLockTime); return true; } /* parse_sequence : TWO^32 |- S (TWO^16 + TWO^16) */ bool simplicity_parse_sequence(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ uint_fast32_t nSequence = simplicity_read32(&src); if (writeBit(dst, nSequence < ((uint_fast32_t)1 << 31))) { writeBit(dst, nSequence & ((uint_fast32_t)1 << 22)); simplicity_write16(dst, nSequence & 0xffff); } else { skipBits(dst, 17); } return true; } /* simplicity_tapdata_init : ONE |- CTX8 */ bool simplicity_tapdata_init(frameItem* dst, frameItem src, const txEnv* env) { (void) env; /* env is unused. */ (void) src; /* env is unused. */ sha256_midstate tapleafTag; { static const unsigned char tagName[] = "TapData"; sha256_context ctx = sha256_init(tapleafTag.s); sha256_uchars(&ctx, tagName, sizeof(tagName) - 1); sha256_finalize(&ctx); } uint32_t iv[8]; sha256_context ctx = sha256_init(iv); sha256_hash(&ctx, &tapleafTag); sha256_hash(&ctx, &tapleafTag); return simplicity_write_sha256_context(dst, &ctx); } ================================================ FILE: C/jets.h ================================================ /* This module defines jets that simulate various Simplicity expressions. * Their specifications are given by the specific Simplicity expressions they are simulating. */ #ifndef SIMPLICITY_JETS_H #define SIMPLICITY_JETS_H #include "frame.h" /* Forward declaration of the structure holding the environment in which a Simplicity expression is evaluated within. */ typedef struct txEnv txEnv; /* A jet simulates the execution of some Simplicity expression (without witnesses or delegation) of A |- B. * It reads data from a read frame 'src', and writes its output to a write frame 'dst'. * If successful then 'true' is returned. * If the expression being simulated would fail an 'ASSERTL' or 'ASSERTR' combinator, then 'false' is returned. * Cells in front of 'dst's cursor's final position may be overwritten. * * Precondition: 'src' is a valid read frame for 'bitSize(A)' more cells; * '*dst' is a valid write frame for 'bitSize(B)' more cells; * if the jet simulates a Simplicity expression with primitives then 'NULL != env'; */ typedef bool (*jet_ptr)(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_verify(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_low_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_low_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_low_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_low_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_low_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_high_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_high_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_high_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_high_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_high_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_complement_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_complement_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_complement_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_complement_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_complement_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_and_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_and_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_and_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_and_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_and_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_or_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_or_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_or_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_or_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_or_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_maj_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_maj_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_maj_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_maj_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_maj_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_xor_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_xor_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_xor_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_xor_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_xor_xor_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ch_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ch_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ch_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ch_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ch_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_some_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_some_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_some_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_some_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_some_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_all_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_all_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_all_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_all_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_one_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_one_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_one_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_one_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_eq_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_eq_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_eq_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_eq_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_eq_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_eq_256(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_8_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_8_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_8_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_16_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_16_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_16_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_16_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_32_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_32_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_32_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_32_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_32_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_64_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_64_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_64_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_64_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_64_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_left_shift_64_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_8_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_8_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_8_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_16_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_16_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_16_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_16_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_32_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_32_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_32_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_32_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_32_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_64_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_64_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_64_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_64_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_64_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_right_shift_64_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_8_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_8_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_8_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_16_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_16_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_16_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_16_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_32_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_32_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_32_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_32_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_32_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_64_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_64_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_64_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_64_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_64_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_leftmost_64_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_8_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_8_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_8_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_16_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_16_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_16_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_16_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_32_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_32_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_32_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_32_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_32_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_64_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_64_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_64_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_64_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_64_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_rightmost_64_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_1_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_1_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_8_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_1_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_8_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_16_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_1_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_8_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_16_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_low_32_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_1_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_1_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_8_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_1_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_8_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_16_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_1_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_8_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_16_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_pad_high_32_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_1_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_1_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_8_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_1_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_8_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_16_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_1_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_8_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_16_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_extend_32_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_1_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_1_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_8_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_1_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_8_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_16_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_1_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_8_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_16_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_low_32_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_1_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_1_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_8_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_1_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_8_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_16_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_1_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_8_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_16_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_pad_high_32_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_extend_8_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_extend_8_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_extend_16_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_extend_8_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_extend_16_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_extend_32_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_with_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_with_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_with_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_with_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_shift_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_with_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_with_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_with_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_with_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_shift_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_rotate_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_rotate_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_rotate_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_left_rotate_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_rotate_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_rotate_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_rotate_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_right_rotate_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_add_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_add_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_add_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_add_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_add_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_add_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_add_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_add_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_increment_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_increment_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_increment_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_increment_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_increment_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_increment_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_increment_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_increment_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_subtract_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_subtract_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_subtract_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_subtract_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_negate_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_negate_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_negate_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_negate_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_decrement_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_decrement_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_decrement_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_decrement_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_decrement_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_decrement_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_decrement_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_decrement_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_subtract_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_subtract_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_subtract_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_subtract_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_multiply_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_multiply_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_multiply_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_multiply_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_multiply_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_multiply_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_multiply_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_full_multiply_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_zero_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_zero_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_zero_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_zero_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_one_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_one_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_one_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_is_one_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_le_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_le_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_le_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_le_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_lt_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_lt_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_lt_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_lt_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_min_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_min_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_min_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_min_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_max_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_max_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_max_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_max_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_median_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_median_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_median_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_median_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_div_mod_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_div_mod_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_div_mod_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_div_mod_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divide_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divide_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divide_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divide_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_modulo_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_modulo_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_modulo_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_modulo_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divides_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divides_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divides_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_divides_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_div_mod_128_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_iv(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_block(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_init(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_2(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_4(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_8(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_16(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_32(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_64(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_128(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_256(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_512(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_add_buffer_511(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_sha_256_ctx_8_finalize(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_normalize(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_negate(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_add(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_square(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_multiply(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_multiply_beta(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_invert(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_square_root(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_is_zero(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_fe_is_odd(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_normalize(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_negate(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_add(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_square(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_multiply(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_multiply_lambda(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_invert(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scalar_is_zero(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_infinity(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_rescale(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_normalize(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_negate(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ge_negate(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_double(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_add(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_ge_add_ex(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_ge_add(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_is_infinity(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_equiv(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_ge_equiv(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_x_equiv(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_y_is_odd(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_gej_is_on_curve(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_ge_is_on_curve(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_off_curve_scale(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_scale(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_generate(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_off_curve_linear_combination_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_linear_combination_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_linear_verify_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_decompress(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_point_verify_1(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_swu(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_hash_to_curve(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_check_sig_verify(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_bip_0340_verify(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_parse_lock(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_parse_sequence(frameItem* dst, frameItem src, const txEnv* env); bool simplicity_tapdata_init(frameItem* dst, frameItem src, const txEnv* env); #endif ================================================ FILE: C/limitations.h ================================================ #ifndef SIMPLICITY_LIMITATIONS_H #define SIMPLICITY_LIMITATIONS_H #include #define DAG_LEN_MAX 8000000U #define NUMBER_OF_TYPENAMES_MAX 0x1000U #define CELLS_MAX 0x500000U /* 5120 Kibibits ought to be enough for anyone. */ #define BUDGET_MAX 4000050U _Static_assert(DAG_LEN_MAX <= SIZE_MAX , "DAG_LEN_MAX doesn't fit in size_t."); _Static_assert(NUMBER_OF_TYPENAMES_MAX <= SIZE_MAX, "NUMBER_OF_TYPENAMES_MAX doesn't fit in size_t."); _Static_assert(CELLS_MAX <= SIZE_MAX, "CELLS_MAX doesn't fit in size_t."); _Static_assert(BUDGET_MAX <= UINT32_MAX, "BUDGET_MAX doesn't fit in uint32_t."); #endif ================================================ FILE: C/precomputed.h ================================================ /* This file has been automatically generated by GenPecomputed.hs */ #ifndef SIMPLICITY_PRECOMPUTED_H #define SIMPLICITY_PRECOMPUTED_H #include "sha256.h" /* Initial values for Simplicity's standard tagged message digest. */ static const sha256_midstate signatureIV = {{0xedebc74bu, 0x774c1bb2u, 0xcb6be27eu, 0x38d63c82u, 0x6f0c6ee6u, 0x02399eb6u, 0x483bde91u, 0x270a1b9bu}}; /* Initial values for all the 'typeName's. */ static const sha256_midstate unitIV = {{0x50b38cd7u, 0x6475ff89u, 0x29288bfcu, 0xd0d9df0eu, 0x4a241c0au, 0x5708572au, 0xd264192au, 0x4fe67beeu}}; static const sha256_midstate sumIV = {{0x920cfd83u, 0xcf96bb32u, 0x7317360fu, 0x6d3ad760u, 0x1eef0a16u, 0xdd53146cu, 0x2e5de35fu, 0x51ef8da4u}}; static const sha256_midstate prodIV = {{0xae992a3eu, 0xe0713bf6u, 0x195d3bacu, 0x1af505a7u, 0x29c14d47u, 0x9558f0d6u, 0x299630f7u, 0xfa972ef8u}}; /* Initial values for all the tags for 'CMR's, 'AMR's and 'IMR's. */ static const sha256_midstate cmr_compIV = {{0x57ec23a2u, 0xa4778e01u, 0x58a6217au, 0xea3ef742u, 0x8ba09092u, 0x73b973fau, 0x1432a927u, 0x843e927au}}; static const sha256_midstate cmr_caseIV = {{0x295e2a6du, 0xc8c5ce59u, 0xe4edcfe9u, 0xb4d8f764u, 0x133aa551u, 0x4bd3ee8bu, 0x4b75ec8fu, 0x4deb08beu}}; static const sha256_midstate cmr_pairIV = {{0x7d5e6dacu, 0x15b1428au, 0x0d260c94u, 0x29dbe889u, 0x6593f31fu, 0x708627eeu, 0x75b27eeeu, 0xfdd05005u}}; static const sha256_midstate cmr_disconnectIV = {{0x35338b5bu, 0x81740c6du, 0x67dc1ea3u, 0xc831e4c0u, 0xafd86409u, 0xbc04d0ddu, 0x4324b7d9u, 0xd583f4ebu}}; static const sha256_midstate cmr_injlIV = {{0x54e91d18u, 0xd8f81f6du, 0x2986bb58u, 0x479a54ebu, 0x630e9523u, 0xb69ee853u, 0x2980d055u, 0x58194f15u}}; static const sha256_midstate cmr_injrIV = {{0xd70ffdceu, 0x97777b4du, 0xfe31fd9fu, 0xf5d017a6u, 0x305d7ec6u, 0x0df3b1bfu, 0x6d25e816u, 0x33ded4bfu}}; static const sha256_midstate cmr_takeIV = {{0x505fc081u, 0xb5ba2acdu, 0x095067c3u, 0xdfb8ea12u, 0x6fa15d55u, 0xcb211e6au, 0xed34e8d1u, 0xe37af0fau}}; static const sha256_midstate cmr_dropIV = {{0x8a308d38u, 0xa113a260u, 0xb4c7145au, 0xbdc5224du, 0xeb701379u, 0x590e0c8cu, 0x38860babu, 0x1271a8a8u}}; static const sha256_midstate cmr_idenIV = {{0x541a1a69u, 0xbd4bcbdau, 0x7f34310eu, 0x3078f726u, 0x443122fbu, 0xcc1cb536u, 0x0c7864ecu, 0x0d323ac0u}}; static const sha256_midstate cmr_unitIV = {{0xc40a1026u, 0x3f7436b4u, 0x160acbefu, 0x1c36fba4u, 0xbe4d95dfu, 0x181a968au, 0xfeab5eacu, 0x247adff7u}}; static const sha256_midstate cmr_witnessIV = {{0xa0fc8debu, 0xd6796917u, 0xc86b77adu, 0xed82e6c6u, 0x1649889au, 0xe8f2ed65u, 0xb57b41aau, 0x9d90e375u}}; static const sha256_midstate amr_assertlIV = {{0xd5ddd741u, 0xd727e220u, 0x3556b0f8u, 0xba4f7fd0u, 0xb48f8dbfu, 0x7a858487u, 0x9baba8d6u, 0xecaa43efu}}; static const sha256_midstate amr_assertrIV = {{0xc5fecd9cu, 0xadc16a7au, 0x08cf215au, 0xe75840f6u, 0xd205e7aau, 0x27f6fff2u, 0x6bfa1e6bu, 0x3a0f76fau}}; static const sha256_midstate amr_compIV = {{0x737fd053u, 0x08d60500u, 0x3bde8eb2u, 0x0a3b9397u, 0xc1daaae5u, 0x43d8a4e4u, 0xfeef4838u, 0x76859384u}}; static const sha256_midstate amr_caseIV = {{0x595814f9u, 0xe0c889b4u, 0x847aba1du, 0x51e14e04u, 0x8f95344bu, 0x2a432091u, 0xf81bd3b8u, 0x36ec3504u}}; static const sha256_midstate amr_pairIV = {{0x7996b3bfu, 0xa6033673u, 0x2515a124u, 0x3f6b3c23u, 0x6bff0eb0u, 0x662f8addu, 0x54af0c98u, 0xd1fddda7u}}; static const sha256_midstate amr_disconnectIV = {{0x27ebbcaau, 0x5a537c25u, 0xd8bb4340u, 0x37bb2fffu, 0x6b881535u, 0x435e6d60u, 0xa5f85cd0u, 0xf05a6147u}}; static const sha256_midstate amr_injlIV = {{0xbacb6356u, 0x6980dcacu, 0x45591f5au, 0xef0d91d4u, 0x9ea4c1e0u, 0x072b1ce3u, 0xdd207521u, 0xc9ead808u}}; static const sha256_midstate amr_injrIV = {{0x7b116ebcu, 0x3f909eefu, 0x13879871u, 0x99844b91u, 0xbcc7402cu, 0x2430c485u, 0x2975d48fu, 0x490c547au}}; static const sha256_midstate amr_takeIV = {{0x4175a134u, 0xe6b4d15bu, 0xb48ac582u, 0xd9bc83a2u, 0x9484c7ecu, 0x27004dffu, 0x94aae4cbu, 0x5d876fb6u}}; static const sha256_midstate amr_dropIV = {{0x3b3293abu, 0xbcc9b9dbu, 0xe1bd70a3u, 0x315f38ffu, 0x2605fb30u, 0xe31f3ceeu, 0x7b251a88u, 0x31c15689u}}; static const sha256_midstate amr_idenIV = {{0x451f688cu, 0x41509968u, 0x3a8d36a7u, 0x09ba4249u, 0xe6def71bu, 0x3529b4c1u, 0xf2e4d563u, 0x855491afu}}; static const sha256_midstate amr_unitIV = {{0xdbfee784u, 0x3b591e8fu, 0x7ce485dcu, 0xb5d66bccu, 0x23984810u, 0xbd6be52au, 0xa76eaf2bu, 0x25cb4423u}}; static const sha256_midstate amr_witnessIV = {{0x6bc620cbu, 0x52f90c63u, 0x0ef8c80du, 0x5f690db4u, 0xe9930ad0u, 0xfa707136u, 0x5b5c93e0u, 0x391bd796u}}; static const sha256_midstate imr_disconnectIV = {{0x4eb7995fu, 0xb5dde5d0u, 0x85f47085u, 0xcd953d16u, 0x845411edu, 0xc689e27au, 0xf9c3dea2u, 0xfb1225d5u}}; static const sha256_midstate imr_witnessIV = {{0xcb37ff70u, 0x01c62d94u, 0x424f987fu, 0x3023b35eu, 0x30d21723u, 0x96276f89u, 0xd09f07aau, 0x67b62196u}}; static const sha256_midstate identityIV = {{0x0c5bc1ceu, 0xc8f14185u, 0x0e333e28u, 0xea01c05au, 0xc642eb30u, 0xb49e692cu, 0x56b122bbu, 0x6949c5cdu}}; static const sha256_midstate hiddenIV = {{0x104d6d85u, 0x2466c4b4u, 0x18aee81au, 0x256f3432u, 0x00bead20u, 0x2c95ccd6u, 0x8c1ef894u, 0x956a16d9u}}; static const sha256_midstate jetIV = {{0x9532ee28u, 0xcdca69deu, 0xc8a0a218u, 0xb79be362u, 0xf740ceafu, 0x647f15b3u, 0x8aed9168u, 0x163f921bu}}; /* This array contains the cmr of all canonical expressions of type X |- TWO through X |- TWO^8 that output distinct values. * word_cmr[0..1] contain the cmrs for scribe(0) .. scribe(1) : X | - TWO * word_cmr[2..5] contain the cmrs for scribe(0) .. scribe(3) : X | - TWO^2 * word_cmr[6..21] contain the cmrs for scribe(0) .. scribe(15) : X | - TWO^4 * word_cmr[22..277] contain the cmrs for scribe(0) .. scribe(255) : X | - TWO^8 */ static const sha256_midstate word_cmr[] = { {{0x8881aff5u, 0x160cc0c9u, 0xf8ecead8u, 0xb401fa97u, 0xeef5fc60u, 0x752e98d2u, 0x47561a4du, 0xa6ce965eu}} , {{0xa0438b72u, 0x3648727bu, 0x3f2d185fu, 0xcd9569e0u, 0x22a4478eu, 0xb25fdfa5u, 0x38eac59du, 0x817c311cu}} , {{0xd7fe8db3u, 0x4cbe07fbu, 0xbbbe2dfbu, 0x5f93f678u, 0x35f28251u, 0xc5699d69u, 0x7e5329b1u, 0x098e557du}} , {{0xc8acfd1eu, 0xc3362653u, 0xd5116e84u, 0x1ed1c856u, 0x56a1b140u, 0x4b27285cu, 0xd5583292u, 0x869dbea0u}} , {{0xc05e06a0u, 0x597a5ca6u, 0x380337fau, 0x9ee62e6cu, 0x756b80b9u, 0x8e26ec2eu, 0x4cd8854du, 0x53a53ce1u}} , {{0xcadff522u, 0xee374c32u, 0x9fa84480u, 0x7ac2d8e7u, 0x4034c5efu, 0x19a40043u, 0x149fcc1du, 0x5e14c2cbu}} , {{0x93e415c1u, 0x81757105u, 0x3d8603feu, 0x85585840u, 0xe43c6af1u, 0x699fbc63u, 0x74018768u, 0x7793713fu}} , {{0xa50f9ad3u, 0x2f7b9900u, 0x4c1d1354u, 0x1cb3202bu, 0x20edcbbau, 0xdf50d062u, 0xf0b4a4edu, 0x0b741549u}} , {{0x7a1223a2u, 0x8ac472d8u, 0xc64f003fu, 0x88d8a2d1u, 0x81045f4cu, 0x32b95bd4u, 0x9f1df21fu, 0x371d5ab0u}} , {{0x04f7548fu, 0xb4659eb8u, 0xce4e38dau, 0x517cb5a9u, 0x19e9bb82u, 0x8abb2fa2u, 0xeb5f5d0bu, 0x7a09aa0bu}} , {{0xc4a49fc4u, 0xceadccc2u, 0x34b9d2eau, 0xabdba05fu, 0xee8627b5u, 0xa93898fau, 0x1b7b5b54u, 0x36dcdf25u}} , {{0x60e08b90u, 0x8aac6e49u, 0x242aeaadu, 0x15883170u, 0x4da76a92u, 0xc31971d4u, 0xb8783db7u, 0x77bd9cd9u}} , {{0x7b9d9624u, 0xa92159e0u, 0xc0240863u, 0x041f3049u, 0x130f6965u, 0xa7f8e3b7u, 0x8037469bu, 0xf9b0a971u}} , {{0xd0018e78u, 0x8cec5176u, 0x93687f27u, 0x42c86d09u, 0xf7c7749fu, 0xb15da620u, 0x0871fbbau, 0x88945e73u}} , {{0xece5ca22u, 0xe2b1a94bu, 0xd10a64aeu, 0x731a3223u, 0xf42e5bbeu, 0x5feb55cbu, 0x453b5484u, 0xdb5837a0u}} , {{0x7090ebfbu, 0xa23c088cu, 0xd4b3050au, 0xfa96246eu, 0xbeda85c0u, 0x700e3ae5u, 0x3b321f29u, 0x647097f0u}} , {{0x0513c250u, 0xb0b5f8d8u, 0x3de6b1ecu, 0xfed51b4cu, 0xe57682a9u, 0x5a78c03du, 0x06de85d6u, 0x34213f8bu}} , {{0x534b3c8bu, 0xe145a334u, 0x7725f932u, 0x141fcc04u, 0x04f0aa53u, 0x42ee18efu, 0xa5fc9a4bu, 0xc65a22c7u}} , {{0xe64a6c69u, 0xb1abc702u, 0xa217faa9u, 0x967f6059u, 0xe884565fu, 0xdcf472ffu, 0xea8f5f4fu, 0x9aa642d8u}} , {{0xd5dd3331u, 0xf2ff9417u, 0x607ab989u, 0x91218d15u, 0xbb09575cu, 0x02ecb7dfu, 0x1bfc1445u, 0x146e2a90u}} , {{0xb93d3419u, 0x19ae147du, 0x305b477au, 0x4b5a1728u, 0x2f935014u, 0x1c3808ffu, 0xc8df5633u, 0x64f6f456u}} , {{0x3a95256eu, 0x380d2cb8u, 0x2c38d940u, 0x3f358478u, 0x6fef84a5u, 0x08dd1ddau, 0x3eded3bcu, 0x93e198bbu}} , {{0x7af386bau, 0x2dba1bcbu, 0x4cddb26fu, 0xfd493045u, 0x8f02c364u, 0xd7df7cbfu, 0xa351055eu, 0x045a5624u}} , {{0xdc8b76c8u, 0x65959c63u, 0x1049ec2au, 0x3f6061aeu, 0x2789a890u, 0x5a8657e8u, 0x05c06ac3u, 0xfaf3f20au}} , {{0xa74f73d3u, 0x71924a85u, 0x342d08a6u, 0x0882d544u, 0x3ab1cac3u, 0xdebe1f85u, 0xcd8d2b8au, 0x70ffa2b4u}} , {{0x7c2151ecu, 0x89df8159u, 0x0d4a67b3u, 0x08fae25bu, 0x502d0fc2u, 0xf3e960d4u, 0xf42cc7bfu, 0xaf33c46bu}} , {{0x085a83d4u, 0x649cbf51u, 0x0aaa3885u, 0x230c0150u, 0x2d0a2e71u, 0xe2b2a153u, 0x054c8b95u, 0x67941422u}} , {{0xddfee6aau, 0x30ccfbb8u, 0x24c56798u, 0x52bbad8eu, 0xe543bf78u, 0x8c962badu, 0x38a4a141u, 0x5cfe3a76u}} , {{0x2f348af8u, 0xb030cad1u, 0x7ae72777u, 0x83b829a0u, 0xc2d19f52u, 0x9a77dfc8u, 0xc2baf39fu, 0x2fae450cu}} , {{0x2d570cf0u, 0x76e8d4e2u, 0x7543a45du, 0x1f5bee5au, 0x81be4535u, 0xf23930bbu, 0x987a68dcu, 0xb60f1f86u}} , {{0x576c5225u, 0x997d8223u, 0x3019bcc9u, 0xe5d3c8dfu, 0xaf078862u, 0xd3b7ea3eu, 0x16dc7330u, 0xe16a2cbfu}} , {{0xce8ca19au, 0x8407af50u, 0x6f3edbc4u, 0xd3ee91a5u, 0xc968e144u, 0xc41e28b2u, 0x7ecf0745u, 0xdefa07c5u}} , {{0xda82e2beu, 0x43bd8bbcu, 0x1cafb331u, 0xf3750d68u, 0x5f97e5adu, 0x2d7000a0u, 0xc7037536u, 0x8a510714u}} , {{0x7395c56cu, 0x670c8f34u, 0x03683dbdu, 0x862ca100u, 0x164e8b9du, 0xb2027299u, 0xe17a1645u, 0xa0801ab8u}} , {{0xef0bf612u, 0x951a8e36u, 0x43819010u, 0x2706aa8bu, 0x1892a3a3u, 0x6db218b9u, 0x340a69a4u, 0xa55862a3u}} , {{0xf06564ccu, 0x99b9724du, 0x3efd8362u, 0xdfd36b4bu, 0x390b6124u, 0xfdadfe00u, 0x9c894204u, 0x617f0078u}} , {{0x1b33142eu, 0x08b15183u, 0xbf91fc20u, 0xaf3e9b6au, 0xa5836c51u, 0xbb4d77b9u, 0x996a5261u, 0x6f769a25u}} , {{0x3a838808u, 0x7015d689u, 0x0dd6717au, 0x8610b2cfu, 0xda3c40cfu, 0xf0137c21u, 0x6169ce21u, 0x3e0ffdc5u}} , {{0xff46be6bu, 0x5d9754e6u, 0x09038295u, 0xbf0a3802u, 0xf365e046u, 0x54f92221u, 0x2a530f8au, 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0x03b0f67fu, 0x8dec7c4eu, 0xbea69a77u, 0x5c118944u, 0x928178eau, 0xaad0e2e0u, 0x2228a989u}} , {{0xbcd86730u, 0xfb320141u, 0xd6d0bb5cu, 0x3c262042u, 0xe50cd398u, 0x3d934e15u, 0xfaac21d4u, 0xd3910232u}} , {{0x5fbdde64u, 0x60ca1aa2u, 0xb6c01000u, 0xde6ef674u, 0xa192fb3bu, 0x1862a85fu, 0x08285c29u, 0x0d2acef6u}} , {{0x5b613c33u, 0xeab49406u, 0x6a1aff5au, 0x71743c9bu, 0x0f49d921u, 0xb3a447c0u, 0x2be157dcu, 0xcb9d8ec1u}} , {{0x97073c08u, 0xd57e8a2fu, 0x5397126fu, 0x17074a29u, 0x353528b5u, 0x65ad3b97u, 0x642784a9u, 0x6c734426u}} , {{0xd2291db2u, 0xd501e9fbu, 0x4d6cefe1u, 0x8faa9bfcu, 0x78e3eb0au, 0x1b910da3u, 0xabb03144u, 0x2b772712u}} , {{0x5babcd3au, 0xc364f6e7u, 0x1052de02u, 0x3f870903u, 0x7677d682u, 0x3884cae5u, 0x4d970746u, 0x8e9c8ca5u}} , {{0xbbaa82a5u, 0xc665e47eu, 0x5659b399u, 0x741f89bdu, 0xe6526ac2u, 0x0b3db8feu, 0x52aa30cau, 0x2f698dadu}} , {{0x3c292246u, 0x623a5860u, 0x642cfb41u, 0xf41f56d5u, 0x9e19b345u, 0x6befa319u, 0xb73797adu, 0x15538874u}} , {{0xc3be2380u, 0xbb222cc0u, 0xe2a9965cu, 0x22da2a89u, 0x4e2cefc8u, 0x32e714feu, 0x860f3495u, 0xf04b5b99u}} , {{0x996c3463u, 0x3e0e5f63u, 0x970730b7u, 0xc13a8a0au, 0xe65ac408u, 0x4882ab16u, 0x3b68e5ecu, 0xce616620u}} , {{0x0d39ca65u, 0x451af6a7u, 0x4dc33900u, 0x4615bf50u, 0x92c783e0u, 0xf7be031bu, 0x13a69127u, 0x5796e260u}} , {{0x45a63234u, 0xc81f6235u, 0x13ab2474u, 0x070682d7u, 0xf1a52234u, 0x6c080863u, 0x63a61fddu, 0xf8fcc539u}} , {{0x7da0701eu, 0xbfdbb918u, 0x52219ed9u, 0x261d6f65u, 0x454a13e4u, 0x537ac788u, 0xaa9abfd3u, 0x4f42b60bu}} , {{0x8855a91cu, 0x921f8fe2u, 0x630b5368u, 0x139a14d2u, 0xea0bc7d6u, 0xcf93e506u, 0xa3846410u, 0xd0a7468eu}} , {{0x83ad6566u, 0x1de347c2u, 0x92266fcbu, 0x78bf6ad4u, 0xad27f915u, 0xbe50c53au, 0x119c5d28u, 0xa42cff20u}} , {{0x851a3c3cu, 0xf89f7be6u, 0xd7c59fdfu, 0xa9052fd8u, 0x31670667u, 0x6155b367u, 0xbb7a0f7au, 0x4d854288u}} , {{0x59621ebcu, 0x5a011db1u, 0x5e2ab89bu, 0xfaf6b4f9u, 0x828568a8u, 0xaf32ae94u, 0xff151df2u, 0xd417ba5eu}} , {{0x5d3eefedu, 0x83c56c91u, 0xca413d0bu, 0x98dd1669u, 0xf9099fe5u, 0xee266e4au, 0x65f8c3d7u, 0xf8155d37u}} , {{0xb419a583u, 0xd6dfe1abu, 0x72b7349au, 0xdb66489fu, 0x0a43caa7u, 0xceb259e4u, 0x4343cac5u, 0xb84cfe69u}} , {{0x9d9d77ddu, 0x8717759cu, 0x959499b8u, 0x18b70b1eu, 0xa55bf8f4u, 0xa18941b8u, 0x7b82c31fu, 0xf2cf21dau}} , {{0xafbad0d0u, 0xa3895ac7u, 0x469903e3u, 0x5449558du, 0x8842a578u, 0x68755aaau, 0x88702018u, 0x26fda7b7u}} , {{0x815a828cu, 0x2d0cd41du, 0xa1ed61f2u, 0x2914df98u, 0x72e8d28bu, 0x98a0dee9u, 0x493706e7u, 0xb2700c78u}} , {{0x53ff110fu, 0x1e8ac892u, 0xd3cbba91u, 0x987434cdu, 0x61f34407u, 0xee742f9fu, 0xb97cdd80u, 0x0dcfd719u}} , {{0x8cce2a93u, 0xf1cd10acu, 0x004cf1bfu, 0x2bb67328u, 0xd455f4a2u, 0xcf85d7f1u, 0xaedcb905u, 0xa2cfb840u}} , {{0x675dc32bu, 0xe9c55317u, 0xeb4da59eu, 0xb5833bc2u, 0x5bd8468eu, 0xf84bd69au, 0x312d160fu, 0x6c541b09u}} , {{0xd02036a5u, 0xad7498e7u, 0xd2562389u, 0x1311da79u, 0x8c2790edu, 0xe75660f7u, 0xd9c25a42u, 0xcd81de59u}} , {{0xa71a6371u, 0xacae3841u, 0x3aa6a748u, 0x4f143459u, 0xc7e3fc57u, 0x2164b2f0u, 0xbf0aad80u, 0x80ac3c46u}} , {{0x0d8a20ebu, 0x4f02c90au, 0xae14abb1u, 0xfca46237u, 0xe02ce550u, 0x7b5f8f92u, 0xe4ffb942u, 0xf8ec1910u}} , {{0x3a4d5afdu, 0xfc7e1438u, 0x92e105e2u, 0xc4724671u, 0xc076ea27u, 0xfee68c89u, 0x1e4607edu, 0x4801fa30u}} , {{0x07fb0b10u, 0xe7dbb106u, 0x64e26a2fu, 0xd25ecb2du, 0xdfb17f78u, 0x01f1807au, 0xfa17d9f1u, 0xbef0cbbau}} , {{0x6798e89cu, 0xbc3c9eebu, 0x33843251u, 0x901fd826u, 0x34ab8ea8u, 0xe0a10a58u, 0x8991998eu, 0x4bb781b5u}} , {{0x559cea96u, 0x57cbceb5u, 0xa9ed0ebau, 0x4eefadacu, 0xec12e596u, 0xa4f25834u, 0x1a929036u, 0xbe058561u}} , {{0x125e31f8u, 0x2eb6bd56u, 0xfbbcf45bu, 0xb9c7370fu, 0xd29d066cu, 0x27e11154u, 0xf5b5a2b0u, 0x909faae0u}} , {{0xa738e749u, 0x3be6cde5u, 0x38fecc05u, 0x99419484u, 0x5369123cu, 0x73e2aab0u, 0x6a81eec8u, 0xfffea92du}} , {{0x32e1b335u, 0x6ab69305u, 0x08520477u, 0xffca0098u, 0x62fd2e63u, 0xcf706d45u, 0x96c5e2d1u, 0xb83140cfu}} , {{0xd0c746b7u, 0xb4e3af74u, 0xfb1557ccu, 0x40a60b38u, 0x112934c2u, 0xa8c0b0a0u, 0x2efc3194u, 0x45cda8f7u}} , {{0x27997665u, 0x67db5937u, 0xcb66d8ebu, 0xbe2e4e07u, 0x393077d3u, 0x1f128668u, 0x4a68bcc1u, 0xce8e0041u}} , {{0x19d64885u, 0x1c9f40aau, 0xf0a1cfe9u, 0x9d14a634u, 0x5956b543u, 0x982b6c13u, 0x8499d6e6u, 0x7bed2782u}} , {{0x10272b2fu, 0x79b00972u, 0x35263c59u, 0x10f00216u, 0x7d0735bau, 0x652f3a98u, 0x7f45773au, 0x225ce8e6u}} , {{0xf6ff5664u, 0xc0f7783du, 0x2fe858bcu, 0x4e5203bau, 0x1263c2edu, 0x06c81bb2u, 0xc2dbb7a4u, 0xd02cd35du}} , {{0xe4829d2bu, 0xf98b3486u, 0x43a2eee7u, 0x8b5c2218u, 0xe180e73bu, 0x183ccca3u, 0xad96a88eu, 0x6ba8af4au}} , {{0x3675668au, 0x3991f960u, 0xbbd4e887u, 0x10de87cfu, 0x544b554eu, 0x4a9895d0u, 0x4fe5e6c5u, 0x3527b39fu}} , {{0x709c2eb2u, 0xfb759d30u, 0x12cdced6u, 0x8d33b266u, 0x86c1fbddu, 0xc6c3ddffu, 0x80429129u, 0x6d014bc5u}} , {{0xccb5dedau, 0xe6888c9fu, 0xf5c63104u, 0x6891c3f1u, 0xa93f432eu, 0xb715dd7au, 0xe55a7a3cu, 0x67304423u}} , {{0x00790e93u, 0xa9532f30u, 0x46de3e2au, 0x38b79242u, 0x7258614eu, 0x11f40dc2u, 0x0fdf33a8u, 0xb5d82625u}} , {{0x5a8fd5edu, 0x42ea2ed6u, 0x388da92au, 0x2e574f66u, 0x3672eec8u, 0x453e50a5u, 0xde631cdau, 0xbf253394u}} , {{0x75543666u, 0xa82c1c19u, 0xd914a943u, 0x0639a3c9u, 0xedd12fb3u, 0xd4bc83aeu, 0x00bf9b09u, 0x6ea321f6u}} , {{0xe10eb310u, 0x0fa7be69u, 0x08cfeb8cu, 0x797fbe5au, 0x4b12f9d1u, 0xed857a7fu, 0x17adc968u, 0x84f723e2u}} , {{0x4bc32595u, 0x0fb88e2au, 0x92860fa8u, 0x71238772u, 0x24fede8cu, 0x8231982bu, 0xd28156a1u, 0x657134e6u}} , {{0xd39514b6u, 0xe75ed246u, 0xe0a572cdu, 0x1ca95222u, 0x2a7ce8c0u, 0x79cccc9du, 0x4842b1dbu, 0xc995a67au}} , {{0x19640f96u, 0x448114ecu, 0xdc30139du, 0xcbdff79bu, 0x264a933cu, 0xc8c5a32fu, 0x9745de2du, 0xbdc10085u}} , {{0xbea2163du, 0xd4861003u, 0x5da78be1u, 0xa7545006u, 0x981f2b5au, 0x91f2d1cdu, 0xade23398u, 0xde59cef5u}} , {{0xfad705d3u, 0x86889cb6u, 0x60d0bc19u, 0x0dbd1c2cu, 0x582badfeu, 0x7565647du, 0x79d38681u, 0xccd9b9adu}} , {{0xdfec881fu, 0x681227abu, 0xd922d952u, 0xa27c6fb8u, 0x2f6b3adeu, 0x1ec605aau, 0x5d3347a1u, 0x7e036865u}} , {{0x4a225c47u, 0x38987e6eu, 0x23876ea9u, 0x03dcb053u, 0x1a50f3b9u, 0xd00c0272u, 0x5797c032u, 0xda753132u}} , {{0xca0d5c3cu, 0x68e28ce8u, 0x8edd2a1bu, 0x9113bdb8u, 0xc64ce2f6u, 0x2420127cu, 0xc60b0fabu, 0x59632173u}} , {{0xc8ed088bu, 0xb317143du, 0x4ecdb573u, 0x04fde044u, 0xa5db2ef6u, 0x112ecd16u, 0xbe002ec9u, 0xa368ce39u}} , {{0xaf57849fu, 0xd42e8638u, 0xf990ac40u, 0xbf0b852eu, 0xf6e99bf1u, 0x307df888u, 0xf555eca0u, 0x47c46112u}} , {{0x2af14e2cu, 0x9be86b3cu, 0xae1a2d7bu, 0x914deda1u, 0xc3aa0319u, 0x45d3f7feu, 0x983426fbu, 0xcc90ed6bu}} , {{0x64b0f02fu, 0xab280716u, 0x803b2b44u, 0xefda680bu, 0x12b94f13u, 0xe8ac1f23u, 0xb775dae8u, 0xf0e7c3abu}} , {{0x9c1989d9u, 0x7fc6ad53u, 0xd5807b12u, 0x6d9f22ebu, 0x8120c767u, 0x0c107b58u, 0x0088b630u, 0x5b1aff80u}} , {{0xe1571617u, 0x46970d7cu, 0x4645e23bu, 0x903a537eu, 0xac56c358u, 0x63a81e08u, 0xfe420b78u, 0x1b12a8feu}} , {{0x0ee369a9u, 0x97c8fb63u, 0x6b4762b5u, 0x4624bc82u, 0x932cde16u, 0xfb3fcdbdu, 0x19fe3c41u, 0x2ad6ed6bu}} , {{0x83c36c89u, 0xdd96b088u, 0xb010995fu, 0x50d1f4aau, 0x25f2240du, 0x3ff7e691u, 0xe0c96800u, 0x493d34d9u}} , {{0xeadedcaeu, 0x45ec7f03u, 0x47420869u, 0xe4073311u, 0x2fe75d42u, 0x14e64af7u, 0x7e5706feu, 0xb44fbb07u}} , {{0xe19c92b2u, 0x3abc447eu, 0x89ba0cdau, 0xdd020377u, 0x522f42d2u, 0xa03cfee5u, 0xc5ccf7b6u, 0x2def4e34u}} , {{0xc524fcbcu, 0x1fca61a8u, 0x788aedc0u, 0x151c7988u, 0xc9aef898u, 0xa7933be4u, 0x305490f1u, 0xf6b36a48u}} , {{0x9ae6cd99u, 0x0e7dba7cu, 0x58377496u, 0xac228a91u, 0x23de5910u, 0x24189780u, 0x9b6c6d6cu, 0xc0cf3dd3u}} , {{0x109a6c47u, 0xa79efb78u, 0x7c678ce0u, 0x76c5727du, 0xc408fecfu, 0x95858794u, 0x4e885c8au, 0x7f050e06u}} , {{0x92bb2826u, 0xb52ab062u, 0x5e04cbcfu, 0xab35462au, 0xf7fbb1c8u, 0x2cb2c8e0u, 0x4a537755u, 0xfe9e57b3u}} , {{0x6c2c48b8u, 0x52ac9e1fu, 0x13226c66u, 0x80099d96u, 0xd7e29b9au, 0x3abe558eu, 0xdbd659c1u, 0xd9b72c35u}} , {{0x2fbae8e1u, 0x66edb0deu, 0x34f72e99u, 0xd748bb85u, 0xe8d30e01u, 0x28aa3d64u, 0xd9c420a6u, 0xcd1a82e2u}} , {{0x93bed54eu, 0xc80f5a0bu, 0x4a94d31au, 0x2cedd559u, 0x865fecb1u, 0x8e5a6485u, 0x78891723u, 0x2e205115u}} , {{0xcb4c3a4cu, 0x805bb36fu, 0xe35b1793u, 0x64c756bdu, 0x5275b49au, 0x82f1bfecu, 0x77784f53u, 0xc0bf962cu}} }; /* word_type_root[0] contains the type root of the ONE type. * word_type_root[1] contains the type root of the TWO type. * word_type_root[2] contains the type root of the TWO^2 type. * word_type_root[3] contains the type root of the TWO^4 type. * ... * word_type_root[32] contains the type root of the TWO^(2^31) type. */ static const sha256_midstate word_type_root[] = { {{0x50b38cd7u, 0x6475ff89u, 0x29288bfcu, 0xd0d9df0eu, 0x4a241c0au, 0x5708572au, 0xd264192au, 0x4fe67beeu}} , {{0x885a22deu, 0x3edb3f40u, 0xdb0609c2u, 0x4023303fu, 0xec6787beu, 0x4d4921e4u, 0x5ee9d983u, 0xacb5d89du}} , {{0x5522ba1cu, 0x92894df2u, 0x5723cfebu, 0x5af259f4u, 0xc55a5cfcu, 0x8200d59bu, 0xad096499u, 0x7f9b2b04u}} , {{0xfa28ba9fu, 0x0f07b4fau, 0xe4dd8623u, 0x614112ffu, 0x3bafabe2u, 0x9c415d2eu, 0x0c1ed3c4u, 0x135128e0u}} , {{0xd343e4d5u, 0xfaa4cea4u, 0x4bb711efu, 0x4b1b96b7u, 0xe0fb26cfu, 0xa85a9604u, 0x39ba8458u, 0xc0b6c5c3u}} , {{0x628c361fu, 0x09cb2e5bu, 0xaad9c6b7u, 0x26a9fa95u, 0xd1da6779u, 0x7ee24ccfu, 0x01410c97u, 0x93399500u}} , {{0xb1a9f968u, 0x7833dc44u, 0xbc8f17d3u, 0xcbc255b7u, 0xaa499a78u, 0xfec85cc9u, 0x8a0c335cu, 0x86ed26e9u}} , {{0xfd75bcd8u, 0xcb55a5e4u, 0x24e09288u, 0xac8eb429u, 0x42534ec1u, 0x099b72beu, 0xce0ea2c5u, 0x479bf3e7u}} , {{0xe394d2a0u, 0x516d738du, 0x6e0459b9u, 0x1bb0dd47u, 0x1d0daa77u, 0x9671a531u, 0x3b62140eu, 0xc70a226eu}} , {{0xe4c4728du, 0x876749beu, 0xbe4d6297u, 0xdfadd42cu, 0xe2684450u, 0x0d96c5e9u, 0x14615750u, 0x8eb9098fu}} , {{0x1ae545b7u, 0xc3fd85feu, 0x816c70eau, 0x4c78b741u, 0x9d8be3c1u, 0xfb3f7223u, 0xfa7d8d50u, 0x3675518fu}} , {{0x6a9c7240u, 0xe5d71d5au, 0x8330b3b3u, 0xb6650bc3u, 0x666c3fefu, 0x2e803ed8u, 0x64f12fcdu, 0x8feac1cau}} , {{0x0a2a587au, 0xebc96b0eu, 0x3e260138u, 0x2eb32a9fu, 0x1e29c850u, 0x1cbdd80eu, 0x8705c0e7u, 0xd3f5b34fu}} , {{0xb3edb6fdu, 0x838ec405u, 0x7b768c86u, 0xb0e8a96du, 0x1ce3f169u, 0x54314dcdu, 0x3dbf7285u, 0xeba563a9u}} , {{0xd0474c0cu, 0x1e2c09d9u, 0xc5f05098u, 0x9357ce71u, 0xab5d904eu, 0x8e2e8287u, 0x4286c0c2u, 0x12de3e71u}} , {{0x379246dcu, 0x866d370du, 0xbfc9704fu, 0xbc57cd7au, 0x6eb5ede7u, 0x97a00c4au, 0x72b3b4a5u, 0xd9f09fe1u}} , {{0x8a59e83fu, 0x43e2a1f9u, 0x07d3a296u, 0x6753336au, 0x1da20d23u, 0xfe636328u, 0x58f94ec0u, 0x7d1913d2u}} , {{0x0f519568u, 0x9f556d00u, 0xbe92fc2du, 0xc57bcbb1u, 0x25620ffcu, 0x00963c09u, 0x14b19615u, 0x1a77841cu}} , {{0x6d2a4799u, 0xa16eb678u, 0x4e4966b8u, 0x1da627d3u, 0x5aa708fdu, 0x9725d604u, 0x777b143eu, 0x28d4acf0u}} , {{0x2a075c50u, 0xca10e500u, 0x927786cau, 0x86a52bb7u, 0xe52ddb16u, 0x42e37745u, 0xfb441491u, 0x39b32d67u}} , {{0xf567c81bu, 0x825dc900u, 0xe0bc0c59u, 0xcea6aa1fu, 0x1f34283fu, 0xcbeeff73u, 0x2db8e217u, 0x576c2255u}} , {{0x0aee1039u, 0xd3c8af91u, 0x41bcb9fdu, 0xf3f8241eu, 0xf9fd4b85u, 0x853a79bau, 0xbcfb2ab4u, 0xdb8ef38cu}} , {{0x30aae9b8u, 0xf2c6faf0u, 0x7a62072fu, 0x55b29698u, 0x5dd73bc1u, 0x0442c802u, 0x7932fff4u, 0x1f2a2d72u}} , {{0xbc146cb5u, 0xae67e00au, 0x6d8e3fd0u, 0x56fb7a72u, 0x820484c6u, 0x1acf17feu, 0xccf130cbu, 0xa622d27fu}} , {{0xa867bacfu, 0xf8d1c25cu, 0x9e824f1bu, 0x63a49c17u, 0x679bba8au, 0xd87699a0u, 0xcdf77defu, 0x0a1b7511u}} , {{0xc128dc7eu, 0x8d794a7au, 0x48081495u, 0xa6eb2b2du, 0x3cb66bc0u, 0xe033273bu, 0xf9ddbc98u, 0x6c226892u}} , {{0x199ffde4u, 0x7d2791a3u, 0x58f23ae5u, 0x082516c6u, 0x5e57f55au, 0xe66ddf44u, 0x65baab4bu, 0xfa3c3a5fu}} , {{0x4038095du, 0xbb32e27eu, 0x6e316652u, 0x7bcedda8u, 0x4e8b21f6u, 0xd42f7e56u, 0xeaff2185u, 0x6ad204a2u}} , {{0xc3a0a6f8u, 0x7e6c3f02u, 0xbf98051cu, 0xe45d6d69u, 0x55382478u, 0xf10fa06au, 0xdd5130e5u, 0x9917f8c7u}} , {{0x7c25bf44u, 0x7a45ba13u, 0x23e8db8bu, 0x817887a8u, 0x858bee25u, 0x6e5ca352u, 0x8e79cfbcu, 0x2d419ce3u}} , {{0x75a77a6cu, 0x7b6de91du, 0x23c1004du, 0x8eb0b35du, 0x9cdf6fa1u, 0xdfc7cabdu, 0x046692f1u, 0xa2431417u}} , {{0x9fc24ab6u, 0x9970f866u, 0x6d7b1e52u, 0x5a3a8e79u, 0x439976e7u, 0x792bfe1au, 0x1b0d0d84u, 0xff038434u}} , {{0x64251ab9u, 0x7077170eu, 0x19911576u, 0x5e9343e7u, 0x1b590e41u, 0x7888f2a8u, 0x364311d8u, 0x6540edfau}} }; #endif ================================================ FILE: C/regression4.c ================================================ #include "regression4.h" /* A length-prefixed encoding of the following Simplicity program: * uWitness OneV : f 15 ++ [uComp (3*2^16) 1] * where * f 0 = [uIden, uTake 1, uIden, uDrop 1, uComp 3 1] * f n = rec ++ rec ++ [uComp (3*2^n) 1] * where * rec = f (n-1) */ const unsigned char regression4[] = { 0xf0, 0x18, 0x00, 0x0b, 0xa0, 0xc4, 0x1c, 0x0a, 0x41, 0x88, 0x38, 0x14, 0x0c, 0x88, 0x31, 0x07, 0x02, 0x90, 0x62, 0x0e, 0x05, 0x03, 0x20, 0x36, 0x10, 0x62, 0x0e, 0x05, 0x20, 0xc4, 0x1c, 0x0a, 0x06, 0x44, 0x18, 0x83, 0x81, 0x48, 0x31, 0x07, 0x02, 0x81, 0x90, 0x1b, 0x00, 0xe1, 0x04, 0x18, 0x83, 0x81, 0x48, 0x31, 0x07, 0x02, 0x81, 0x91, 0x06, 0x20, 0xe0, 0x52, 0x0c, 0x41, 0xc0, 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0x28, 0x00, 0xe7, 0x00, 0x0e, 0x88, 0x00, 0x3a, 0x60, 0x00, 0x75, 0x40, 0x00, 0x75, 0xc0, 0x00, 0x3b, 0x20, 0x00, 0x0e, 0xd8, 0x00, 0x01, 0xdd, 0x00, 0x00, 0x1d, 0xf0, 0x00, 0x00, 0xf0, 0x08, 0x00, 0x00, 0x3c, 0x06, 0x00, 0x00 }; const size_t sizeof_regression4 = sizeof(regression4); ================================================ FILE: C/regression4.h ================================================ #ifndef SIMPLICITY_REGRESSION4_H #define SIMPLICITY_REGRESSION4_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * uWitness OneV : f 15 ++ [uComp (3*2^16) 1] * where * f 0 = [uIden, uTake 1, uIden, uDrop 1, uComp 3 1] * f n = rec ++ rec ++ [uComp (3*2^n) 1] * where * rec = f (n-1) */ extern const unsigned char regression4[]; extern const size_t sizeof_regression4; #endif ================================================ FILE: C/rsort.c ================================================ #include "rsort.h" #include #include "simplicity_assert.h" #include "simplicity_alloc.h" static_assert(UCHAR_MAX < SIZE_MAX, "UCHAR_MAX >= SIZE_MAX"); #define CHAR_COUNT ((size_t)1 << CHAR_BIT) /* Return the 'i'th char of the object representation of the midstate pointed to by a. * * In C, values are represented as 'unsigned char [sizeof(v)]' array. However the exact * specification of how this representation works is implementation defined. * * For the 'uint32_t' values of 'sha256_midstate', the object representation of these values will differ * between big endian and little endian architectures. * * Precondition: NULL != a * i < sizeof(a->s); */ static unsigned char readIndex(const sha256_midstate* a, unsigned int i) { return ((const unsigned char*)(a->s))[i]; } /* Given an array of midstate pointers, * count the frequencies of the values of the 'j'th character of each midstate's internal representation. * Returns 'true' if the 'j'th character of every entry is the same, otherwise returns 'false'. * * The time complexity of 'freq' is O('len'). * * Precondition: uint32_t result[CHAR_COUNT]; * for all 0 <= i < len, NULL != a[i]; * j < sizeof((*a)->s) */ static bool freq(uint32_t* result, const sha256_midstate * const * a, uint_fast32_t len, unsigned int j) { memset(result, 0, CHAR_COUNT * sizeof(uint32_t)); if (0 == len) return true; for (size_t i = 0; i < len - 1; ++i) { result[readIndex(a[i],j)]++; } /* Check the final iteration to see if the frequency is equal to 'len'. */ return len == ++result[readIndex(a[len-1],j)]; } /* Given an array of bucket sizes, and an initial value 'bucketEdge[0]', * add subsequent bucket edges of the given bucket sizes. * * Precondition: uint32_t bucketEdge[CHAR_COUNT]; * const uint32_t sizes[CHAR_COUNT]; */ static void cumulative(uint32_t* restrict bucketEdge, const uint32_t* restrict sizes) { uint32_t accumulator = bucketEdge[0] + sizes[0]; for (unsigned int i = 1; i < CHAR_COUNT; ++i) { bucketEdge[i] = accumulator; accumulator += sizes[i]; } } /* Exchange two pointers. * (a == b is acceptable.) * * Precondition: NULL != a; * NULL != b; */ static void swap(const sha256_midstate** a, const sha256_midstate** b) { const sha256_midstate* tmp = *a; *a = *b; *b = tmp; } /* Sort the subarray a[begin:end) by their ix-th character, * where begin = bucketEdge[0] and end = bucketEdge[UMAX_CHAR] + bucketSize[UMAX_CHAR]. * * We expect that the ix-length prefix of every entry in a[being:end) to be identical * so that the result is that the a[begin:end) subarray ends up sorted by their first 'ix + 1' characters. * * Precondition: For all begin <= i < end, NULL != a[i]; * for all i < CHAR_COUNT, bucketSize[i] is the number of of entries in the subentries in a[begin:end) whose ix-th character is 'i'. * for all i < UMAX_CHAR, bucketEdge[i] + bucketSize[i] = bucketEdge[i+1]; * ix < sizeof((*a)->s); * Postcondition: The contents of bucketSize is not preserved! */ static void sort_buckets(const sha256_midstate** a, uint32_t* restrict bucketSize, const uint32_t* restrict bucketEdge, unsigned int ix) { /* The implementation works by finding the first non-empty bucket and then swapping the first element of that bucket into its position at the far end of the bucket where it belongs. After moving the element into that position the size of the target bucket is decreased by one, and thus the next element that will be swapped into that bucket will be placed behind it. This process continues until the first element of the first non-empty bucket gets swapped with itself and its own bucket is decremented from size 1 to size 0. At that point we search again for the next non-empty bucket and repeat this process until there are no more non-empty buckets. */ for (unsigned int i = 0; i < CHAR_COUNT; ++i) { size_t start = bucketEdge[i]; while (bucketSize[i]) { /* Each time through this while loop some bucketSize is decremented. Therefore this body is executed 'sum(i < CHAR_COUNT, bucketSize[i]) = end - begin' many times. */ size_t bucket = readIndex(a[start], ix); simplicity_assert(bucketSize[bucket]); bucketSize[bucket]--; swap(a + start, a + bucketEdge[bucket] + bucketSize[bucket]); } } } /* Attempts to (partially) sort an array of pointers to 'sha256_midstate's in place in memcmp order. * If NULL == hasDuplicates then sorting is always run to completion. * Otherwise, if NULL != hasDuplicates and if duplicate entries are found, the sorting is aborted and * *hasDuplicates is set to one of pointers of a duplicate entry. * If NULL != hasDuplicates and no duplicate entries are found, then *hasDuplicates is set to NULL. * * The time complexity of rsort is O('len'). * * Precondition: For all 0 <= i < len, NULL != a[i]; * uint32_t stack[(CHAR_COUNT - 1)*(sizeof(*a)->s) + 1]; */ static void rsort_ex(const sha256_midstate** a, uint_fast32_t len, const sha256_midstate** hasDuplicates, uint32_t* stack) { unsigned int depth = 0; size_t bucketCount[sizeof((*a)->s) + 1]; size_t totalBucketCount = 1; static_assert(sizeof((*a)->s) <= UINT_MAX, "UINT_MAX too small to hold depth."); stack[0]=0; bucketCount[depth] = 1; /* This implementation contains a 'stack' of 'totalBucketCount' many subarrays (called buckets) that have been partially sorted up to various prefix length. The buckets are disjoint and cover the entire array from 0 up to len. As sorting proceeds, the end of the array will be sorted first. We will decrease len as we go as we find out that items at the end of the array are in their proper, sorted position. The 'i'th bucket is the subarray a[stack[i]:stack[i+1]), except for the last bucket which is the subarray a[stack[totalBucketCount-1]:len). The depth to which various buckets are sorted increases the further down the stack you go. The 'bucketCount' stores how many buckets are sorted to various depths. * for all i <= depth, the subarray a[sum(j < i, bucketCount[i]):end) have their first i characters sorted. * for all i <= depth, the (sum(j < i, bucketCount[i]))th and later buckets have all the first i characters of their entries identical. So all buckets are sorted up to a prefix length of 0 many characters. Then, if 1 <= depth, all bucket except for the first bucketCount[0]-many buckets are sorted by their 1 character prefix And then, if 2 <= depth, all bucket except for the first (bucketCount[0] + bucket[1])-many buckets are sorted by their 2 character prefix And so on. It is always the case that 'totalBucketCount = sum(i <= depth, bucketCount[i])', and thus the last bucket in the stack is located at stack[totalBucketCount-1]. 'totalBucketCount' and 'bucketCount' items are always increased and decreased in tandum. The loop is initialized with a 'totalBucketCount' of 1 and this one bucket contains the whole array a[0:len). 'depth' is initialized to 0, and all the entries are trivialy sorted by the first 0-many characters. As we go through the loop, the last bucket is "popped" off the stack and processed, which can go one of two ways. If the last bucket is size 2 or greater, we proceed to sort it by its 'depth' character and partition the bucket into 256 sub-buckets which are then pushed onto the stack (notice this causes a net increase of the stack size by 255 items, because one was popped off). If ever the depth is beyond the size of the data being sorted, we can immediately halt as we have found 2 or more item that are identical. Note: there is an added optimization where by if there is only one non-empty bucket found when attempting to sort, i.e. it happens that every bucket item already has identical 'depth' characters, we skip the subdivision and move onto the next depth immediately. (This is equivalent to pushing the one non-empty bucket onto the stack and immediately popping it back off.) If the last bucket is of size 0 or 1, it must be already be sorted. Since this bucket is at the end of the array we decrease 'len'. */ while(totalBucketCount) { /* Find the correct "depth" of the last bucket. */ while(0 == bucketCount[depth]) { simplicity_assert(depth); depth--; } /* "pop" last bucket off the stack. */ bucketCount[depth]--; totalBucketCount--; if (2 <= len - stack[totalBucketCount]) { uint32_t bucketSize[CHAR_COUNT]; uint32_t* bucketEdge = stack + totalBucketCount; uint32_t begin = bucketEdge[0]; /* Set bucketSize[i] to the count of the number of items in the array whose 'depth' character is 'i'. The time complexity of 'freq' is O('len - begin'). WARNING: the 'freq' function modifies the contents of 'bucketSize' but is only executed when depth < sizeof((*a)->s). */ while (depth < sizeof((*a)->s) && freq(bucketSize, a + begin, len - begin, depth)) { /* Optimize the case where there is only one bucket. i.e. when the 'depth' character of the interval [begin, len) are all identical. */ depth++; bucketCount[depth] = 0; }; if (depth < sizeof((*a)->s)) { /* Using bucketSize, compute all then next set of bucket edges based on where items will end up when they are sorted by their 'depth' character. */ cumulative(bucketEdge, bucketSize); simplicity_assert(len == bucketEdge[UCHAR_MAX] + bucketSize[UCHAR_MAX]); /* Sort this bucket by their depth character, placing them into their proper buckets based on their bucketEdges. */ sort_buckets(a, bucketSize, bucketEdge, depth); depth++; bucketCount[depth] = CHAR_COUNT; totalBucketCount += CHAR_COUNT; continue; } if (hasDuplicates) { /* Early return if we are searching for duplicates and have found a bucket of size 2 or more whose "prefix" agree up to then entire length of the hash value, and hence are all identical. */ *hasDuplicates = a[begin]; return; } } /* len - stack[totalBucketCount] < 2 || sizeof((*a)->s) == depth */ /* When the last bucket size is 0 or 1, or when the depth exceeds sizeof((*a)->s), there is no sorting to do within the bucket. It is already sorted, and since it is at the end we can decrease len. */ len = stack[totalBucketCount]; } simplicity_assert(0 == len); if (hasDuplicates) *hasDuplicates = NULL; } /* Sorts an array of pointers to 'sha256_midstate's in place in memcmp order. * If malloc fails, returns false. * Otherwise, returns true. * * The time complexity of rsort is O('len'). * * We are sorting in memcmp order, which is the lexicographical order of the object representation, i.e. the order that one * gets when casting 'sha256_midstate' to a 'unsigned char[]'. This representation is implementation defined, and will differ * on big endian and little endian architectures. * * It is critical that the details of this order remain unobservable from the consensus rules. * * Precondition: For all 0 <= i < len, NULL != a[i]; */ bool simplicity_rsort(const sha256_midstate** a, uint_fast32_t len) { uint32_t *stack = simplicity_malloc(((CHAR_COUNT - 1)*(sizeof((*a)->s)) + 1) * sizeof(uint32_t)); if (!stack) return false; rsort_ex(a, len, NULL, stack); simplicity_free(stack); return true; } /* Searches for duplicates in an array of 'sha256_midstate's. * If malloc fails, returns -1. * If no duplicates are found, returns 0. * If duplicates are found, returns a positive value. * * Precondition: const sha256_midstate a[len]; * len <= DAG_LEN_MAX; */ int simplicity_hasDuplicates(const sha256_midstate* a, uint_fast32_t len) { if (len < 2) return 0; static_assert(sizeof(a->s) * CHAR_BIT == 256, "sha256_midstate.s has unnamed padding."); static_assert(DAG_LEN_MAX <= UINT32_MAX, "DAG_LEN_MAX does not fit in uint32_t."); static_assert(DAG_LEN_MAX <= SIZE_MAX / sizeof(const sha256_midstate*), "perm array too large."); simplicity_assert((size_t)len <= SIZE_MAX / sizeof(const sha256_midstate*)); const sha256_midstate **perm = simplicity_malloc(len * sizeof(const sha256_midstate*)); uint32_t *stack = simplicity_malloc(((CHAR_COUNT - 1)*(sizeof((*perm)->s)) + 1) * sizeof(uint32_t)); int result = perm && stack ? 0 : -1; if (0 <= result) { for (uint_fast32_t i = 0; i < len; ++i) { perm[i] = a + i; } const sha256_midstate *duplicate; rsort_ex(perm, len, &duplicate, stack); result = NULL != duplicate; } simplicity_free(perm); simplicity_free(stack); return result; } ================================================ FILE: C/rsort.h ================================================ #ifndef SIMPLICITY_RSORT_H #define SIMPLICITY_RSORT_H #include #include #include #include "limitations.h" #include "sha256.h" /* Sorts an array of pointers to 'sha256_midstate's in place in memcmp order. * If malloc fails, returns false. * Otherwise, returns true. * * The time complexity of rsort is O('len'). * * We are sorting in memcmp order, which is the lexicographical order of the object representation, i.e. the order that one * gets when casting 'sha256_midstate' to a 'unsigned char[]'. This representation is implementation defined, and will differ * on big endian and little endian architectures. * * It is critical that the details of this order remain unobservable from the consensus rules. * * Precondition: For all 0 <= i < len, NULL != a[i]; */ bool simplicity_rsort(const sha256_midstate** a, uint_fast32_t len); /* Searches for duplicates in an array of 'sha256_midstate's. * If malloc fails, returns -1. * If no duplicates are found, returns 0. * If duplicates are found, returns a positive value. * * Precondition: const sha256_midstate a[len]; * len <= DAG_LEN_MAX; */ int simplicity_hasDuplicates(const sha256_midstate* a, uint_fast32_t len); #endif ================================================ FILE: C/schnorr0.c ================================================ #include "schnorr0.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9) &&& * zero word256) &&& * witness (toWord512 0xE907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0) >>> * Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify * with jets. */ const unsigned char schnorr0[] = { 0xc6, 0xd5, 0xf2, 0x61, 0x14, 0x03, 0x24, 0xb1, 0x86, 0x20, 0x92, 0x68, 0x9f, 0x0b, 0xf1, 0x3a, 0xa4, 0x53, 0x6a, 0x63, 0x90, 0x8b, 0x06, 0xdf, 0x33, 0x61, 0x0c, 0x03, 0xe2, 0x27, 0x79, 0xc0, 0x6d, 0xf2, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe2, 0x8d, 0x8c, 0x04, 0x00 }; const size_t sizeof_schnorr0 = sizeof(schnorr0); const unsigned char schnorr0_witness[] = { 0xe9, 0x07, 0x83, 0x1f, 0x80, 0x84, 0x8d, 0x10, 0x69, 0xa5, 0x37, 0x1b, 0x40, 0x24, 0x10, 0x36, 0x4b, 0xdf, 0x1c, 0x5f, 0x83, 0x07, 0xb0, 0x08, 0x4c, 0x55, 0xf1, 0xce, 0x2d, 0xca, 0x82, 0x15, 0x25, 0xf6, 0x6a, 0x4a, 0x85, 0xea, 0x8b, 0x71, 0xe4, 0x82, 0xa7, 0x4f, 0x38, 0x2d, 0x2c, 0xe5, 0xeb, 0xee, 0xe8, 0xfd, 0xb2, 0x17, 0x2f, 0x47, 0x7d, 0xf4, 0x90, 0x0d, 0x31, 0x05, 0x36, 0xc0 }; const size_t sizeof_schnorr0_witness = sizeof(schnorr0_witness); /* The commitment Merkle root of the above schnorr0 Simplicity expression. */ const uint32_t schnorr0_cmr[] = { 0x8a9e9767u, 0x6b24be77u, 0x97d9ee0bu, 0xf32dd76bu, 0xcd78028eu, 0x973025f7u, 0x85eae8dcu, 0x91c8a0dau }; /* The identity hash of the root of the above schnorr0 Simplicity expression. */ const uint32_t schnorr0_ihr[] = { 0xad7c38b1u, 0x6b912964u, 0x6dc89b52u, 0xcff144deu, 0x94a80e38u, 0x3c4983b5u, 0x3de65e35u, 0x75abcf38u }; /* The annotated Merkle root of the above schnorr0 Simplicity expression. */ const uint32_t schnorr0_amr[] = { 0xec97c877u, 0x4cb6bfb3u, 0x81fdbbccu, 0x8d964380u, 0xfb3a3b45u, 0x77932262u, 0x4490d623u, 0x1ae777a4u }; /* The cost of the above schnorr0 Simplicity expression in milli weight units. */ const ubounded schnorr0_cost = 51635; ================================================ FILE: C/schnorr0.h ================================================ #ifndef SIMPLICITY_SCHNORR0_H #define SIMPLICITY_SCHNORR0_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9) &&& * zero word256) &&& * witness (toWord512 0xE907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0) >>> * Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify * with jets. */ extern const unsigned char schnorr0[]; extern const size_t sizeof_schnorr0; extern const unsigned char schnorr0_witness[]; extern const size_t sizeof_schnorr0_witness; /* The commitment Merkle root of the above schnorr0 Simplicity expression. */ extern const uint32_t schnorr0_cmr[]; /* The identity hash of the root of the above schnorr0 Simplicity expression. */ extern const uint32_t schnorr0_ihr[]; /* The annotated Merkle root of the above schnorr0 Simplicity expression. */ extern const uint32_t schnorr0_amr[]; /* The cost of the above schnorr0 Simplicity expression in milli weight units. */ extern const ubounded schnorr0_cost; #endif ================================================ FILE: C/schnorr6.c ================================================ #include "schnorr6.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659) &&& * scribe (toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)) &&& * witness (toWord512 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2) >>> * Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify * with jets. */ const unsigned char schnorr6[] = { 0xc6, 0xd5, 0xbf, 0xe3, 0xae, 0xfe, 0x54, 0xce, 0x38, 0xbe, 0x6c, 0x30, 0x6e, 0x4d, 0xb6, 0x46, 0x83, 0x7c, 0xb1, 0xfd, 0x5c, 0x3b, 0x45, 0xbd, 0x9d, 0xb0, 0x86, 0x48, 0x1e, 0xf6, 0xa0, 0x57, 0x4c, 0xb2, 0xbc, 0x5a, 0xb1, 0xb1, 0x67, 0x79, 0xbe, 0x35, 0x75, 0xbd, 0x8f, 0x05, 0x20, 0xa9, 0xf2, 0x1b, 0xb5, 0x30, 0x0b, 0x55, 0x6a, 0xd8, 0xee, 0x66, 0x60, 0x49, 0x73, 0xa1, 0x4a, 0x11, 0x6e, 0xb8, 0xe2, 0x8d, 0x8c, 0x04, 0x00 }; const size_t sizeof_schnorr6 = sizeof(schnorr6); const unsigned char schnorr6_witness[] = { 0xff, 0xf9, 0x7b, 0xd5, 0x75, 0x5e, 0xee, 0xa4, 0x20, 0x45, 0x3a, 0x14, 0x35, 0x52, 0x35, 0xd3, 0x82, 0xf6, 0x47, 0x2f, 0x85, 0x68, 0xa1, 0x8b, 0x2f, 0x05, 0x7a, 0x14, 0x60, 0x29, 0x75, 0x56, 0x3c, 0xc2, 0x79, 0x44, 0x64, 0x0a, 0xc6, 0x07, 0xcd, 0x10, 0x7a, 0xe1, 0x09, 0x23, 0xd9, 0xef, 0x7a, 0x73, 0xc6, 0x43, 0xe1, 0x66, 0xbe, 0x5e, 0xbe, 0xaf, 0xa3, 0x4b, 0x1a, 0xc5, 0x53, 0xe2 }; const size_t sizeof_schnorr6_witness = sizeof(schnorr6_witness); /* The commitment Merkle root of the above schnorr6 Simplicity expression. */ const uint32_t schnorr6_cmr[] = { 0x83b6b5bcu, 0xc9bdc956u, 0xaf326376u, 0xf201aa7au, 0x2e65bb9eu, 0xedca6a06u, 0x65976452u, 0x5203cf68u }; /* The identity hash of the root of the above schnorr6 Simplicity expression. */ const uint32_t schnorr6_ihr[] = { 0x53acece2u, 0xa5e61e36u, 0xd6c57f92u, 0x4cff9c45u, 0x0a283badu, 0x853aab59u, 0xebdf384du, 0x26264fefu }; /* The annotated Merkle root of the above schnorr6 Simplicity expression. */ const uint32_t schnorr6_amr[] = { 0x76440feau, 0x109aaf4cu, 0xd2e62eeeu, 0xd46f168cu, 0xf848b90eu, 0x9f11cb54u, 0x445b7d45u, 0x5e20a18eu }; /* The cost of the above schnorr6 Simplicity expression in milli weight units. */ const ubounded schnorr6_cost = 51635; ================================================ FILE: C/schnorr6.h ================================================ #ifndef SIMPLICITY_SCHNORR6_H #define SIMPLICITY_SCHNORR6_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * (scribe (toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659) &&& * scribe (toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)) &&& * witness (toWord512 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2) >>> * Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify * with jets. */ extern const unsigned char schnorr6[]; extern const size_t sizeof_schnorr6; extern const unsigned char schnorr6_witness[]; extern const size_t sizeof_schnorr6_witness; /* The commitment Merkle root of the above schnorr6 Simplicity expression. */ extern const uint32_t schnorr6_cmr[]; /* The identity hash of the root of the above schnorr6 Simplicity expression. */ extern const uint32_t schnorr6_ihr[]; /* The annotated Merkle root of the above schnorr6 Simplicity expression. */ extern const uint32_t schnorr6_amr[]; /* The cost of the above schnorr6 Simplicity expression in milli weight units. */ extern const ubounded schnorr6_cost; #endif ================================================ FILE: C/secp256k1/README.md ================================================ This directory contains a modified copy of the libsecp256k1 at `bdf39000b9c6a0818e7149ccb500873d079e6e85` from . In general, the files in this directory should be compared with the corresponding files in the `src` directory from libsecp256k1. There are some exceptions however: * `precompute_ecmult.h` should be compared with `src/precompute_ecmult.c` * `secp256k1.h` should be compared with `include/secp256k1.h`. * `secp256k1_impl.h` should be compared with `src/secp256k1.c`. * `extrakeys.h` should be compared with `include/secp256k1_extrakeys.h`. * `extrakeys_impl.h` should be compared with `src/modules/extrakeys/main_impl.h`. * `schnorrsig.h` should be compared with `include/secp256k1_schnorrsig.h`. * `schnorrsig_impl.h` should be compared with `src/modules/schnorrsig/main_impl.h`. * `generator.h` should be compared with `include/secp256k1_generator.h` from . * `generator_impl.h` should be compared with `src/modules/generator/main_impl.h` from ; however see `shallue_van_de_woestijne` below. Our use of libsecp256k1 for various jets requires access to the internal functions that are not exposed by their API, so we cannot use libsecp256k1's normal interface. Furthermore, because Simplicity has no abstract data types, the specific details of the representation of field and group elements computed by jetted functions ends up being consensus critical. Therefore, even if libsecp256k1's interface exposed the functionality we needed, we still wouldn't be able perform libsecp256k1 version upgrades because different versions of libsecp256k1 do not guarantee that their functions won't change the representation of computed field and group elements. Even libsecp256k1's configuration options, including `ECMULT_WINDOW_SIZE`, all can affect the representation of the computed group elements. Therefore we need to fix these options to specific values. Simplicity computations are on public data and therefore we do not jet functions that manipulate private or secret data. In particular, we only need to jet variable-time algorithms when there is a choice of variable-time or constant-time algorithms. In incorporating the libsecp256k1 library into the Simplicity library, there is a tension between making minimal changes to the library versus removing configuration options and other code that, if they were activated, could cause consensus incompatible changes in functionality. Because we will not be able to easily migrate to newer versions of libsecp256k1 anyways, we have taken a heavy-handed approach to trimming unused configuration options, dead code, functions specific to working with secret data, etc. In some cases we have made minor code changes: * `secp256k1_fe_sqrt` has been modified to call `secp256k1_fe_equal_var` (as `secp256k1_fe_equal` has been removed). The function has been renamed to `secp256k1_fe_sqrt_var` and similar for other indirect callers. * The implementation of `secp256k1_gej_eq_ge_var` is taken from . * The use of secp256k1's `hash.h` for Schnorr signatures has been replaced with calls to Simplicity's internal `sha256.h` implementation. This removes the duplication of functionality ~~and replaces the non-portable use of the `WORDS_BIGENDIAN` flag in `hash_impl.h` with our portable implementation~~. * `checked_malloc` and `checked_realloc` have been removed along with any functions that called them. * `ARG_CHECK` doesn't call the callback. * Callbacks have been removed. * `secp256k1_context` has been removed. * `shallue_van_de_woestijne`'s implementation is taken from https://github.com/BlockstreamResearch/secp256k1-zkp/blob/03aecafe4c45f51736ce05b339d2e8bcc2e5da55/src/modules/generator/main_impl.h>, which fixes . Additionally, some changes have been made to ensure that the `infinity` flag of `secp256k1_gej` always corresponds to whether or not the z-coordinate is zero or not. Adjustments have been made in the following functions: * `secp256k1_gej_set_ge` * `secp256k1_gej_double_var` * `secp256k1_gej_add_zinv_var` Also, our jets are designed to operate on off-curve points. However, the ecmult algorithms in libsecp256k1 are not designed to handle extremely low order, off-curve points[^1]. We have patched `secp256k1_gej_add_ge_var` to ensure `rzr` is set even when `a` is infinity. Lastly, all active uses of normalize are replaced with the variable-time implementation. [^1]: More specifically, the when a point has a very low and odd order, the `ai` values in the `secp256k1_ecmult_odd_multiples_table` can reach infinity, violating libsecp256k1's assumption that `secp256k1_gej_add_ge_var`'s `a` parameter is never infinity. The value we set to the `rzr` in this case does not matter since it ends up only being multiplied with zero in `secp256k1_ge_table_set_globalz`. It just needs to be set to some value to avoid reading uninitialized memory. ================================================ FILE: C/secp256k1/assumptions.h ================================================ /*********************************************************************** * Copyright (c) 2020 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_ASSUMPTIONS_H #define SECP256K1_ASSUMPTIONS_H #include #include "util.h" #if defined(SECP256K1_INT128_NATIVE) #include "int128_native.h" #endif /* This library, like most software, relies on a number of compiler implementation defined (but not undefined) behaviours. Although the behaviours we require are essentially universal we test them specifically here to reduce the odds of experiencing an unwelcome surprise. */ struct secp256k1_assumption_checker { /* This uses a trick to implement a static assertion in C89: a type with an array of negative size is not allowed. */ int dummy_array[( /* Bytes are 8 bits. */ (CHAR_BIT == 8) && /* No integer promotion for uint32_t. This ensures that we can multiply uintXX_t values where XX >= 32 without signed overflow, which would be undefined behaviour. */ (UINT_MAX <= UINT32_MAX) && /* Conversions from unsigned to signed outside of the bounds of the signed type are implementation-defined. Verify that they function as reinterpreting the lower bits of the input in two's complement notation. Do this for conversions: - from uint(N)_t to int(N)_t with negative result - from uint(2N)_t to int(N)_t with negative result - from int(2N)_t to int(N)_t with negative result - from int(2N)_t to int(N)_t with positive result */ /* To int8_t. */ ((int8_t)(uint8_t)0xAB == (int8_t)-(int8_t)0x55) && ((int8_t)(uint16_t)0xABCD == (int8_t)-(int8_t)0x33) && ((int8_t)(int16_t)(uint16_t)0xCDEF == (int8_t)(uint8_t)0xEF) && ((int8_t)(int16_t)(uint16_t)0x9234 == (int8_t)(uint8_t)0x34) && /* To int16_t. */ ((int16_t)(uint16_t)0xBCDE == (int16_t)-(int16_t)0x4322) && ((int16_t)(uint32_t)0xA1B2C3D4 == (int16_t)-(int16_t)0x3C2C) && ((int16_t)(int32_t)(uint32_t)0xC1D2E3F4 == (int16_t)(uint16_t)0xE3F4) && ((int16_t)(int32_t)(uint32_t)0x92345678 == (int16_t)(uint16_t)0x5678) && /* To int32_t. */ ((int32_t)(uint32_t)0xB2C3D4E5 == (int32_t)-(int32_t)0x4D3C2B1B) && ((int32_t)(uint64_t)0xA123B456C789D012ULL == (int32_t)-(int32_t)0x38762FEE) && ((int32_t)(int64_t)(uint64_t)0xC1D2E3F4A5B6C7D8ULL == (int32_t)(uint32_t)0xA5B6C7D8) && ((int32_t)(int64_t)(uint64_t)0xABCDEF0123456789ULL == (int32_t)(uint32_t)0x23456789) && /* To int64_t. */ ((int64_t)(uint64_t)0xB123C456D789E012ULL == (int64_t)-(int64_t)0x4EDC3BA928761FEEULL) && #if defined(SECP256K1_INT128_NATIVE) ((int64_t)(((uint128_t)0xA1234567B8901234ULL << 64) + 0xC5678901D2345678ULL) == (int64_t)-(int64_t)0x3A9876FE2DCBA988ULL) && (((int64_t)(int128_t)(((uint128_t)0xB1C2D3E4F5A6B7C8ULL << 64) + 0xD9E0F1A2B3C4D5E6ULL)) == (int64_t)(uint64_t)0xD9E0F1A2B3C4D5E6ULL) && (((int64_t)(int128_t)(((uint128_t)0xABCDEF0123456789ULL << 64) + 0x0123456789ABCDEFULL)) == (int64_t)(uint64_t)0x0123456789ABCDEFULL) && /* To int128_t. */ ((int128_t)(((uint128_t)0xB1234567C8901234ULL << 64) + 0xD5678901E2345678ULL) == (int128_t)(-(int128_t)0x8E1648B3F50E80DCULL * 0x8E1648B3F50E80DDULL + 0x5EA688D5482F9464ULL)) && #endif /* Right shift on negative signed values is implementation defined. Verify that it acts as a right shift in two's complement with sign extension (i.e duplicating the top bit into newly added bits). */ ((((int8_t)0xE8) >> 2) == (int8_t)(uint8_t)0xFA) && ((((int16_t)0xE9AC) >> 4) == (int16_t)(uint16_t)0xFE9A) && ((((int32_t)0x937C918A) >> 9) == (int32_t)(uint32_t)0xFFC9BE48) && ((((int64_t)0xA8B72231DF9CF4B9ULL) >> 19) == (int64_t)(uint64_t)0xFFFFF516E4463BF3ULL) && #if defined(SECP256K1_INT128_NATIVE) ((((int128_t)(((uint128_t)0xCD833A65684A0DBCULL << 64) + 0xB349312F71EA7637ULL)) >> 39) == (int128_t)(((uint128_t)0xFFFFFFFFFF9B0674ULL << 64) + 0xCAD0941B79669262ULL)) && #endif 1) * 2 - 1]; }; #endif /* SECP256K1_ASSUMPTIONS_H */ ================================================ FILE: C/secp256k1/eckey.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_ECKEY_H #define SECP256K1_ECKEY_H #include #include "group.h" #include "scalar.h" #if 0 #include "ecmult.h" #include "ecmult_gen.h" static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size); static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed); static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak); #endif static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak); #if 0 static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak); static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak); #endif #endif /* SECP256K1_ECKEY_H */ ================================================ FILE: C/secp256k1/eckey_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_ECKEY_IMPL_H #define SECP256K1_ECKEY_IMPL_H #include "eckey.h" #include "scalar.h" #include "field.h" #include "group.h" #if 0 #include "ecmult_gen.h" static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) { if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) { secp256k1_fe x; return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD); } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { secp256k1_fe x, y; if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) { return 0; } secp256k1_ge_set_xy(elem, &x, &y); if ((pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD) && secp256k1_fe_is_odd(&y) != (pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { return 0; } return secp256k1_ge_is_valid_var(elem); } else { return 0; } } static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) { if (secp256k1_ge_is_infinity(elem)) { return 0; } secp256k1_fe_normalize_var(&elem->x); secp256k1_fe_normalize_var(&elem->y); secp256k1_fe_get_b32(&pub[1], &elem->x); if (compressed) { *size = 33; pub[0] = secp256k1_fe_is_odd(&elem->y) ? SECP256K1_TAG_PUBKEY_ODD : SECP256K1_TAG_PUBKEY_EVEN; } else { *size = 65; pub[0] = SECP256K1_TAG_PUBKEY_UNCOMPRESSED; secp256k1_fe_get_b32(&pub[33], &elem->y); } return 1; } static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) { secp256k1_scalar_add(key, key, tweak); return !secp256k1_scalar_is_zero(key); } #endif static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak) { secp256k1_gej pt; secp256k1_scalar one; secp256k1_gej_set_ge(&pt, key); secp256k1_scalar_set_int(&one, 1); secp256k1_ecmult(&pt, &pt, &one, tweak); if (secp256k1_gej_is_infinity(&pt)) { return 0; } secp256k1_ge_set_gej_var(key, &pt); return 1; } #if 0 static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) { int ret; ret = !secp256k1_scalar_is_zero(tweak); secp256k1_scalar_mul(key, key, tweak); return ret; } static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak) { secp256k1_scalar zero; secp256k1_gej pt; if (secp256k1_scalar_is_zero(tweak)) { return 0; } secp256k1_scalar_set_int(&zero, 0); secp256k1_gej_set_ge(&pt, key); secp256k1_ecmult(&pt, &pt, tweak, &zero); secp256k1_ge_set_gej(key, &pt); return 1; } #endif #endif /* SECP256K1_ECKEY_IMPL_H */ ================================================ FILE: C/secp256k1/ecmult.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_ECMULT_H #define SECP256K1_ECMULT_H #include "group.h" #include "scalar.h" #define ECMULT_WINDOW_SIZE 15 /** The number of entries a table with precomputed multiples needs to have. */ #define ECMULT_TABLE_SIZE(w) (1L << ((w)-2)) /** Double multiply: R = na*A + ng*G */ static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng); #if 0 typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data); /** * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai. * Chooses the right algorithm for a given number of points and scratch space * size. Resets and overwrites the given scratch space. If the points do not * fit in the scratch space the algorithm is repeatedly run with batches of * points. If no scratch space is given then a simple algorithm is used that * simply multiplies the points with the corresponding scalars and adds them up. * Returns: 1 on success (including when inp_g_sc is NULL and n is 0) * 0 if there is not enough scratch space for a single point or * callback returns 0 */ static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n); #endif #endif /* SECP256K1_ECMULT_H */ ================================================ FILE: C/secp256k1/ecmult_impl.h ================================================ /****************************************************************************** * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php. * ******************************************************************************/ #ifndef SECP256K1_ECMULT_IMPL_H #define SECP256K1_ECMULT_IMPL_H #include #include #include "util.h" #include "group.h" #include "scalar.h" #include "ecmult.h" #include "precomputed_ecmult.h" #if defined(EXHAUSTIVE_TEST_ORDER) /* We need to lower these values for exhaustive tests because * the tables cannot have infinities in them (this breaks the * affine-isomorphism stuff which tracks z-ratios) */ # if EXHAUSTIVE_TEST_ORDER > 128 # define WINDOW_A 5 # elif EXHAUSTIVE_TEST_ORDER > 8 # define WINDOW_A 4 # else # define WINDOW_A 2 # endif #else /* optimal for 128-bit and 256-bit exponents. */ # define WINDOW_A 5 /** Larger values for ECMULT_WINDOW_SIZE result in possibly better * performance at the cost of an exponentially larger precomputed * table. The exact table size is * (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage) bytes, * where sizeof(secp256k1_ge_storage) is typically 64 bytes but can * be larger due to platform-specific padding and alignment. * Two tables of this size are used (due to the endomorphism * optimization). */ #endif #define WNAF_BITS 128 #define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w)) #define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w) /* The number of objects allocated on the scratch space for ecmult_multi algorithms */ #define PIPPENGER_SCRATCH_OBJECTS 6 #define STRAUSS_SCRATCH_OBJECTS 5 #define PIPPENGER_MAX_BUCKET_WINDOW 12 /* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */ #define ECMULT_PIPPENGER_THRESHOLD 88 #define ECMULT_MAX_POINTS_PER_BATCH 5000000 /** Fill a table 'pre_a' with precomputed odd multiples of a. * pre_a will contain [1*a,3*a,...,(2*n-1)*a], so it needs space for n group elements. * zr needs space for n field elements. * * Although pre_a is an array of _ge rather than _gej, it actually represents elements * in Jacobian coordinates with their z coordinates omitted. The omitted z-coordinates * can be recovered using z and zr. Using the notation z(b) to represent the omitted * z coordinate of b: * - z(pre_a[n-1]) = 'z' * - z(pre_a[i-1]) = z(pre_a[i]) / zr[i] for n > i > 0 * * Lastly the zr[0] value, which isn't used above, is set so that: * - a.z = z(pre_a[0]) / zr[0] */ static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_ge *pre_a, secp256k1_fe *zr, secp256k1_fe *z, const secp256k1_gej *a) { secp256k1_gej d, ai; secp256k1_ge d_ge; int i; VERIFY_CHECK(!a->infinity); secp256k1_gej_double_var(&d, a, NULL); /* * Perform the additions using an isomorphic curve Y^2 = X^3 + 7*C^6 where C := d.z. * The isomorphism, phi, maps a secp256k1 point (x, y) to the point (x*C^2, y*C^3) on the other curve. * In Jacobian coordinates phi maps (x, y, z) to (x*C^2, y*C^3, z) or, equivalently to (x, y, z/C). * * phi(x, y, z) = (x*C^2, y*C^3, z) = (x, y, z/C) * d_ge := phi(d) = (d.x, d.y, 1) * ai := phi(a) = (a.x*C^2, a.y*C^3, a.z) * * The group addition functions work correctly on these isomorphic curves. * In particular phi(d) is easy to represent in affine coordinates under this isomorphism. * This lets us use the faster secp256k1_gej_add_ge_var group addition function that we wouldn't be able to use otherwise. */ secp256k1_ge_set_xy(&d_ge, &d.x, &d.y); secp256k1_ge_set_gej_zinv(&pre_a[0], a, &d.z); secp256k1_gej_set_ge(&ai, &pre_a[0]); ai.z = a->z; /* pre_a[0] is the point (a.x*C^2, a.y*C^3, a.z*C) which is equivalent to a. * Set zr[0] to C, which is the ratio between the omitted z(pre_a[0]) value and a.z. */ zr[0] = d.z; for (i = 1; i < n; i++) { secp256k1_gej_add_ge_var(&ai, &ai, &d_ge, &zr[i]); secp256k1_ge_set_xy(&pre_a[i], &ai.x, &ai.y); } /* Multiply the last z-coordinate by C to undo the isomorphism. * Since the z-coordinates of the pre_a values are implied by the zr array of z-coordinate ratios, * undoing the isomorphism here undoes the isomorphism for all pre_a values. */ secp256k1_fe_mul(z, &ai.z, &d.z); } #define SECP256K1_ECMULT_TABLE_VERIFY(n,w) \ VERIFY_CHECK(((n) & 1) == 1); \ VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge(secp256k1_ge *r, const secp256k1_ge *pre, int n, int w) { SECP256K1_ECMULT_TABLE_VERIFY(n,w) if (n > 0) { *r = pre[(n-1)/2]; } else { *r = pre[(-n-1)/2]; secp256k1_fe_negate(&(r->y), &(r->y), 1); } } SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_lambda(secp256k1_ge *r, const secp256k1_ge *pre, const secp256k1_fe *x, int n, int w) { SECP256K1_ECMULT_TABLE_VERIFY(n,w) if (n > 0) { secp256k1_ge_set_xy(r, &x[(n-1)/2], &pre[(n-1)/2].y); } else { secp256k1_ge_set_xy(r, &x[(-n-1)/2], &pre[(-n-1)/2].y); secp256k1_fe_negate(&(r->y), &(r->y), 1); } } SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_storage(secp256k1_ge *r, const secp256k1_ge_storage *pre, int n, int w) { SECP256K1_ECMULT_TABLE_VERIFY(n,w) if (n > 0) { secp256k1_ge_from_storage(r, &pre[(n-1)/2]); } else { secp256k1_ge_from_storage(r, &pre[(-n-1)/2]); secp256k1_fe_negate(&(r->y), &(r->y), 1); } } /** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits), * with the following guarantees: * - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1) * - two non-zero entries in wnaf are separated by at least w-1 zeroes. * - the number of set values in wnaf is returned. This number is at most 256, and at most one more * than the number of bits in the (absolute value) of the input. */ static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) { secp256k1_scalar s; int last_set_bit = -1; int bit = 0; int sign = 1; int carry = 0; VERIFY_CHECK(wnaf != NULL); VERIFY_CHECK(0 <= len && len <= 256); VERIFY_CHECK(a != NULL); VERIFY_CHECK(2 <= w && w <= 31); memset(wnaf, 0, len * sizeof(wnaf[0])); s = *a; if (secp256k1_scalar_get_bits(&s, 255, 1)) { secp256k1_scalar_negate(&s, &s); sign = -1; } while (bit < len) { int now; int word; if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) { bit++; continue; } now = w; if (now > len - bit) { now = len - bit; } word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry; carry = (word >> (w-1)) & 1; word -= carry << w; wnaf[bit] = sign * word; last_set_bit = bit; bit += now; } #ifdef VERIFY { int verify_bit = bit; VERIFY_CHECK(carry == 0); while (verify_bit < 256) { VERIFY_CHECK(secp256k1_scalar_get_bits(&s, verify_bit, 1) == 0); verify_bit++; } } #endif return last_set_bit + 1; } struct secp256k1_strauss_point_state { int wnaf_na_1[129]; int wnaf_na_lam[129]; int bits_na_1; int bits_na_lam; }; struct secp256k1_strauss_state { /* aux is used to hold z-ratios, and then used to hold pre_a[i].x * BETA values. */ secp256k1_fe* aux; secp256k1_ge* pre_a; struct secp256k1_strauss_point_state* ps; }; static void secp256k1_ecmult_strauss_wnaf(const struct secp256k1_strauss_state *state, secp256k1_gej *r, size_t num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { secp256k1_ge tmpa; secp256k1_fe Z; /* Split G factors. */ secp256k1_scalar ng_1, ng_128; int wnaf_ng_1[129]; int bits_ng_1 = 0; int wnaf_ng_128[129]; int bits_ng_128 = 0; int i; int bits = 0; size_t np; size_t no = 0; secp256k1_fe_set_int(&Z, 1); for (np = 0; np < num; ++np) { secp256k1_gej tmp; secp256k1_scalar na_1, na_lam; if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) { continue; } /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */ secp256k1_scalar_split_lambda(&na_1, &na_lam, &na[np]); /* build wnaf representation for na_1 and na_lam. */ state->ps[no].bits_na_1 = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1, 129, &na_1, WINDOW_A); state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 129, &na_lam, WINDOW_A); VERIFY_CHECK(state->ps[no].bits_na_1 <= 129); VERIFY_CHECK(state->ps[no].bits_na_lam <= 129); if (state->ps[no].bits_na_1 > bits) { bits = state->ps[no].bits_na_1; } if (state->ps[no].bits_na_lam > bits) { bits = state->ps[no].bits_na_lam; } /* Calculate odd multiples of a. * All multiples are brought to the same Z 'denominator', which is stored * in Z. Due to secp256k1' isomorphism we can do all operations pretending * that the Z coordinate was 1, use affine addition formulae, and correct * the Z coordinate of the result once at the end. * The exception is the precomputed G table points, which are actually * affine. Compared to the base used for other points, they have a Z ratio * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same * isomorphism to efficiently add with a known Z inverse. */ tmp = a[np]; if (no) { #ifdef VERIFY secp256k1_fe_normalize_var(&Z); #endif secp256k1_gej_rescale(&tmp, &Z); } secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->pre_a + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &Z, &tmp); if (no) secp256k1_fe_mul(state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &(a[np].z)); ++no; } /* Bring them to the same Z denominator. */ secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, state->aux); for (np = 0; np < no; ++np) { for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { secp256k1_fe_mul(&state->aux[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i].x, &secp256k1_const_beta); } } if (ng) { /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */ secp256k1_scalar_split_128(&ng_1, &ng_128, ng); /* Build wnaf representation for ng_1 and ng_128 */ bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G); bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G); if (bits_ng_1 > bits) { bits = bits_ng_1; } if (bits_ng_128 > bits) { bits = bits_ng_128; } } secp256k1_gej_set_infinity(r); for (i = bits - 1; i >= 0; i--) { int n; secp256k1_gej_double_var(r, r, NULL); for (np = 0; np < no; ++np) { if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) { secp256k1_ecmult_table_get_ge(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); } if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) { secp256k1_ecmult_table_get_ge_lambda(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); } } if (i < bits_ng_1 && (n = wnaf_ng_1[i])) { secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g, n, WINDOW_G); secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); } if (i < bits_ng_128 && (n = wnaf_ng_128[i])) { secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g_128, n, WINDOW_G); secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); } } if (!r->infinity) { secp256k1_fe_mul(&r->z, &r->z, &Z); } } static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { secp256k1_fe aux[ECMULT_TABLE_SIZE(WINDOW_A)]; secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; struct secp256k1_strauss_point_state ps[1]; struct secp256k1_strauss_state state; state.aux = aux; state.pre_a = pre_a; state.ps = ps; secp256k1_ecmult_strauss_wnaf(&state, r, 1, a, na, ng); } #if 0 static size_t secp256k1_strauss_scratch_size(size_t n_points) { static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); return n_points*point_size; } static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) { secp256k1_gej* points; secp256k1_scalar* scalars; struct secp256k1_strauss_state state; size_t i; const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); secp256k1_gej_set_infinity(r); if (inp_g_sc == NULL && n_points == 0) { return 1; } /* We allocate STRAUSS_SCRATCH_OBJECTS objects on the scratch space. If these * allocations change, make sure to update the STRAUSS_SCRATCH_OBJECTS * constant and strauss_scratch_size accordingly. */ points = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_gej)); scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar)); state.aux = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe)); state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state)); if (points == NULL || scalars == NULL || state.aux == NULL || state.pre_a == NULL || state.ps == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } for (i = 0; i < n_points; i++) { secp256k1_ge point; if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } secp256k1_gej_set_ge(&points[i], &point); } secp256k1_ecmult_strauss_wnaf(&state, r, n_points, points, scalars, inp_g_sc); secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 1; } /* Wrapper for secp256k1_ecmult_multi_func interface */ static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { return secp256k1_ecmult_strauss_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0); } static size_t secp256k1_strauss_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) { return secp256k1_scratch_max_allocation(error_callback, scratch, STRAUSS_SCRATCH_OBJECTS) / secp256k1_strauss_scratch_size(1); } /** Convert a number to WNAF notation. * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. * It has the following guarantees: * - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w) * - the number of words set is always WNAF_SIZE(w) * - the returned skew is 0 or 1 */ static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) { int skew = 0; int pos; int max_pos; int last_w; const secp256k1_scalar *work = s; if (secp256k1_scalar_is_zero(s)) { for (pos = 0; pos < WNAF_SIZE(w); pos++) { wnaf[pos] = 0; } return 0; } if (secp256k1_scalar_is_even(s)) { skew = 1; } wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew; /* Compute last window size. Relevant when window size doesn't divide the * number of bits in the scalar */ last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w; /* Store the position of the first nonzero word in max_pos to allow * skipping leading zeros when calculating the wnaf. */ for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) { int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w); if(val != 0) { break; } wnaf[pos] = 0; } max_pos = pos; pos = 1; while (pos <= max_pos) { int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w); if ((val & 1) == 0) { wnaf[pos - 1] -= (1 << w); wnaf[pos] = (val + 1); } else { wnaf[pos] = val; } /* Set a coefficient to zero if it is 1 or -1 and the proceeding digit * is strictly negative or strictly positive respectively. Only change * coefficients at previous positions because above code assumes that * wnaf[pos - 1] is odd. */ if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) { if (wnaf[pos - 1] == 1) { wnaf[pos - 2] += 1 << w; } else { wnaf[pos - 2] -= 1 << w; } wnaf[pos - 1] = 0; } ++pos; } return skew; } struct secp256k1_pippenger_point_state { int skew_na; size_t input_pos; }; struct secp256k1_pippenger_state { int *wnaf_na; struct secp256k1_pippenger_point_state* ps; }; /* * pippenger_wnaf computes the result of a multi-point multiplication as * follows: The scalars are brought into wnaf with n_wnaf elements each. Then * for every i < n_wnaf, first each point is added to a "bucket" corresponding * to the point's wnaf[i]. Second, the buckets are added together such that * r += 1*bucket[0] + 3*bucket[1] + 5*bucket[2] + ... */ static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_window, struct secp256k1_pippenger_state *state, secp256k1_gej *r, const secp256k1_scalar *sc, const secp256k1_ge *pt, size_t num) { size_t n_wnaf = WNAF_SIZE(bucket_window+1); size_t np; size_t no = 0; int i; int j; for (np = 0; np < num; ++np) { if (secp256k1_scalar_is_zero(&sc[np]) || secp256k1_ge_is_infinity(&pt[np])) { continue; } state->ps[no].input_pos = np; state->ps[no].skew_na = secp256k1_wnaf_fixed(&state->wnaf_na[no*n_wnaf], &sc[np], bucket_window+1); no++; } secp256k1_gej_set_infinity(r); if (no == 0) { return 1; } for (i = n_wnaf - 1; i >= 0; i--) { secp256k1_gej running_sum; for(j = 0; j < ECMULT_TABLE_SIZE(bucket_window+2); j++) { secp256k1_gej_set_infinity(&buckets[j]); } for (np = 0; np < no; ++np) { int n = state->wnaf_na[np*n_wnaf + i]; struct secp256k1_pippenger_point_state point_state = state->ps[np]; secp256k1_ge tmp; int idx; if (i == 0) { /* correct for wnaf skew */ int skew = point_state.skew_na; if (skew) { secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]); secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL); } } if (n > 0) { idx = (n - 1)/2; secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &pt[point_state.input_pos], NULL); } else if (n < 0) { idx = -(n + 1)/2; secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]); secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &tmp, NULL); } } for(j = 0; j < bucket_window; j++) { secp256k1_gej_double_var(r, r, NULL); } secp256k1_gej_set_infinity(&running_sum); /* Accumulate the sum: bucket[0] + 3*bucket[1] + 5*bucket[2] + 7*bucket[3] + ... * = bucket[0] + bucket[1] + bucket[2] + bucket[3] + ... * + 2 * (bucket[1] + 2*bucket[2] + 3*bucket[3] + ...) * using an intermediate running sum: * running_sum = bucket[0] + bucket[1] + bucket[2] + ... * * The doubling is done implicitly by deferring the final window doubling (of 'r'). */ for(j = ECMULT_TABLE_SIZE(bucket_window+2) - 1; j > 0; j--) { secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[j], NULL); secp256k1_gej_add_var(r, r, &running_sum, NULL); } secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[0], NULL); secp256k1_gej_double_var(r, r, NULL); secp256k1_gej_add_var(r, r, &running_sum, NULL); } return 1; } /** * Returns optimal bucket_window (number of bits of a scalar represented by a * set of buckets) for a given number of points. */ static int secp256k1_pippenger_bucket_window(size_t n) { if (n <= 1) { return 1; } else if (n <= 4) { return 2; } else if (n <= 20) { return 3; } else if (n <= 57) { return 4; } else if (n <= 136) { return 5; } else if (n <= 235) { return 6; } else if (n <= 1260) { return 7; } else if (n <= 4420) { return 9; } else if (n <= 7880) { return 10; } else if (n <= 16050) { return 11; } else { return PIPPENGER_MAX_BUCKET_WINDOW; } } /** * Returns the maximum optimal number of points for a bucket_window. */ static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) { switch(bucket_window) { case 1: return 1; case 2: return 4; case 3: return 20; case 4: return 57; case 5: return 136; case 6: return 235; case 7: return 1260; case 8: return 1260; case 9: return 4420; case 10: return 7880; case 11: return 16050; case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX; } return 0; } SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) { secp256k1_scalar tmp = *s1; secp256k1_scalar_split_lambda(s1, s2, &tmp); secp256k1_ge_mul_lambda(p2, p1); if (secp256k1_scalar_is_high(s1)) { secp256k1_scalar_negate(s1, s1); secp256k1_ge_neg(p1, p1); } if (secp256k1_scalar_is_high(s2)) { secp256k1_scalar_negate(s2, s2); secp256k1_ge_neg(p2, p2); } } /** * Returns the scratch size required for a given number of points (excluding * base point G) without considering alignment. */ static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) { size_t entries = 2*n_points + 2; size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int); return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size; } static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) { const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); /* Use 2(n+1) with the endomorphism, when calculating batch * sizes. The reason for +1 is that we add the G scalar to the list of * other scalars. */ size_t entries = 2*n_points + 2; secp256k1_ge *points; secp256k1_scalar *scalars; secp256k1_gej *buckets; struct secp256k1_pippenger_state *state_space; size_t idx = 0; size_t point_idx = 0; int i, j; int bucket_window; secp256k1_gej_set_infinity(r); if (inp_g_sc == NULL && n_points == 0) { return 1; } bucket_window = secp256k1_pippenger_bucket_window(n_points); /* We allocate PIPPENGER_SCRATCH_OBJECTS objects on the scratch space. If * these allocations change, make sure to update the * PIPPENGER_SCRATCH_OBJECTS constant and pippenger_scratch_size * accordingly. */ points = (secp256k1_ge *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*points)); scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*scalars)); state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(error_callback, scratch, sizeof(*state_space)); if (points == NULL || scalars == NULL || state_space == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps)); state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int)); buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, (1<ps == NULL || state_space->wnaf_na == NULL || buckets == NULL) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } if (inp_g_sc != NULL) { scalars[0] = *inp_g_sc; points[0] = secp256k1_ge_const_g; idx++; secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]); idx++; } while (point_idx < n_points) { if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) { secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); return 0; } idx++; secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]); idx++; point_idx++; } secp256k1_ecmult_pippenger_wnaf(buckets, bucket_window, state_space, r, scalars, points, idx); /* Clear data */ for(i = 0; (size_t)i < idx; i++) { secp256k1_scalar_clear(&scalars[i]); state_space->ps[i].skew_na = 0; for(j = 0; j < WNAF_SIZE(bucket_window+1); j++) { state_space->wnaf_na[i * WNAF_SIZE(bucket_window+1) + j] = 0; } } for(i = 0; i < 1< max_alloc) { break; } space_for_points = max_alloc - space_overhead; n_points = space_for_points/entry_size; n_points = n_points > max_points ? max_points : n_points; if (n_points > res) { res = n_points; } if (n_points < max_points) { /* A larger bucket_window may support even more points. But if we * would choose that then the caller couldn't safely use any number * smaller than what this function returns */ break; } } return res; } /* Computes ecmult_multi by simply multiplying and adding each point. Does not * require a scratch space */ static int secp256k1_ecmult_multi_simple_var(secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) { size_t point_idx; secp256k1_scalar szero; secp256k1_gej tmpj; secp256k1_scalar_set_int(&szero, 0); secp256k1_gej_set_infinity(r); secp256k1_gej_set_infinity(&tmpj); /* r = inp_g_sc*G */ secp256k1_ecmult(r, &tmpj, &szero, inp_g_sc); for (point_idx = 0; point_idx < n_points; point_idx++) { secp256k1_ge point; secp256k1_gej pointj; secp256k1_scalar scalar; if (!cb(&scalar, &point, point_idx, cbdata)) { return 0; } /* r += scalar*point */ secp256k1_gej_set_ge(&pointj, &point); secp256k1_ecmult(&tmpj, &pointj, &scalar, NULL); secp256k1_gej_add_var(r, r, &tmpj, NULL); } return 1; } /* Compute the number of batches and the batch size given the maximum batch size and the * total number of points */ static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n_batch_points, size_t max_n_batch_points, size_t n) { if (max_n_batch_points == 0) { return 0; } if (max_n_batch_points > ECMULT_MAX_POINTS_PER_BATCH) { max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; } if (n == 0) { *n_batches = 0; *n_batch_points = 0; return 1; } /* Compute ceil(n/max_n_batch_points) and ceil(n/n_batches) */ *n_batches = 1 + (n - 1) / max_n_batch_points; *n_batch_points = 1 + (n - 1) / *n_batches; return 1; } typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t); static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { size_t i; int (*f)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t); size_t n_batches; size_t n_batch_points; secp256k1_gej_set_infinity(r); if (inp_g_sc == NULL && n == 0) { return 1; } else if (n == 0) { secp256k1_scalar szero; secp256k1_scalar_set_int(&szero, 0); secp256k1_ecmult(r, r, &szero, inp_g_sc); return 1; } if (scratch == NULL) { return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n); } /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than * a threshold use Pippenger's algorithm. Otherwise use Strauss' algorithm. * As a first step check if there's enough space for Pippenger's algo (which requires less space * than Strauss' algo) and if not, use the simple algorithm. */ if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(error_callback, scratch), n)) { return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n); } if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) { f = secp256k1_ecmult_pippenger_batch; } else { if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(error_callback, scratch), n)) { return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n); } f = secp256k1_ecmult_strauss_batch; } for(i = 0; i < n_batches; i++) { size_t nbp = n < n_batch_points ? n : n_batch_points; size_t offset = n_batch_points*i; secp256k1_gej tmp; if (!f(error_callback, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) { return 0; } secp256k1_gej_add_var(r, r, &tmp, NULL); n -= nbp; } return 1; } #endif #endif /* SECP256K1_ECMULT_IMPL_H */ ================================================ FILE: C/secp256k1/extrakeys.h ================================================ #ifndef SECP256K1_EXTRAKEYS_H #define SECP256K1_EXTRAKEYS_H #include "secp256k1.h" /** Opaque data structure that holds a parsed and valid "x-only" public key. * An x-only pubkey encodes a point whose Y coordinate is even. It is * serialized using only its X coordinate (32 bytes). See BIP-340 for more * information about x-only pubkeys. * * The exact representation of data inside is implementation defined and not * guaranteed to be portable between different platforms or versions. It is * however guaranteed to be 64 bytes in size, and can be safely copied/moved. * If you need to convert to a format suitable for storage, transmission, use * use secp256k1_xonly_pubkey_serialize and secp256k1_xonly_pubkey_parse. To * compare keys, use secp256k1_xonly_pubkey_cmp. */ typedef struct { unsigned char data[64]; } secp256k1_xonly_pubkey; /** Parse a 32-byte sequence into a xonly_pubkey object. * * Returns: 1 if the public key was fully valid. * 0 if the public key could not be parsed or is invalid. * * Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a * parsed version of input. If not, it's set to an invalid value. * In: input32: pointer to a serialized xonly_pubkey. */ static SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_parse( secp256k1_xonly_pubkey* pubkey, const unsigned char *input32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); /** Serialize an xonly_pubkey object into a 32-byte sequence. * * Returns: 1 always. * * Out: output32: a pointer to a 32-byte array to place the serialized key in. * In: pubkey: a pointer to a secp256k1_xonly_pubkey containing an initialized public key. */ static int secp256k1_xonly_pubkey_serialize( unsigned char *output32, const secp256k1_xonly_pubkey* pubkey ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); /** Converts a secp256k1_pubkey into a secp256k1_xonly_pubkey. * * Returns: 1 always. * * Out: xonly_pubkey: pointer to an x-only public key object for placing the converted public key. * pk_parity: Ignored if NULL. Otherwise, pointer to an integer that * will be set to 1 if the point encoded by xonly_pubkey is * the negation of the pubkey and set to 0 otherwise. * In: pubkey: pointer to a public key that is converted. */ static SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_from_pubkey( secp256k1_xonly_pubkey *xonly_pubkey, int *pk_parity, const secp256k1_pubkey *pubkey ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3); /** Tweak an x-only public key by adding the generator multiplied with tweak32 * to it. * * Note that the resulting point can not in general be represented by an x-only * pubkey because it may have an odd Y coordinate. Instead, the output_pubkey * is a normal secp256k1_pubkey. * * Returns: 0 if the arguments are invalid or the resulting public key would be * invalid (only when the tweak is the negation of the corresponding * secret key). 1 otherwise. * * Out: output_pubkey: pointer to a public key to store the result. Will be set * to an invalid value if this function returns 0. * In: internal_pubkey: pointer to an x-only pubkey to apply the tweak to. * tweak32: pointer to a 32-byte tweak. If the tweak is invalid * according to secp256k1_ec_seckey_verify, this function * returns 0. For uniformly random 32-byte arrays the * chance of being invalid is negligible (around 1 in 2^128). */ static SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add( secp256k1_pubkey *output_pubkey, const secp256k1_xonly_pubkey *internal_pubkey, const unsigned char *tweak32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); #endif /* SECP256K1_EXTRAKEYS_H */ ================================================ FILE: C/secp256k1/extrakeys_impl.h ================================================ /*********************************************************************** * Copyright (c) 2020 Jonas Nick * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_EXTRAKEYS_IMPL #define SECP256K1_EXTRAKEYS_IMPL #include "secp256k1.h" #include "extrakeys.h" static SECP256K1_INLINE int secp256k1_xonly_pubkey_load(secp256k1_ge *ge, const secp256k1_xonly_pubkey *pubkey) { return secp256k1_pubkey_load(ge, (const secp256k1_pubkey *) pubkey); } static SECP256K1_INLINE void secp256k1_xonly_pubkey_save(secp256k1_xonly_pubkey *pubkey, secp256k1_ge *ge) { secp256k1_pubkey_save((secp256k1_pubkey *) pubkey, ge); } static int secp256k1_xonly_pubkey_parse(secp256k1_xonly_pubkey *pubkey, const unsigned char *input32) { secp256k1_ge pk; secp256k1_fe x; ARG_CHECK(pubkey != NULL); memset(pubkey, 0, sizeof(*pubkey)); ARG_CHECK(input32 != NULL); if (!secp256k1_fe_set_b32(&x, input32)) { return 0; } if (!secp256k1_ge_set_xo_var(&pk, &x, 0)) { return 0; } if (!secp256k1_ge_is_in_correct_subgroup(&pk)) { return 0; } secp256k1_xonly_pubkey_save(pubkey, &pk); return 1; } static int secp256k1_xonly_pubkey_serialize(unsigned char *output32, const secp256k1_xonly_pubkey *pubkey) { secp256k1_ge pk; ARG_CHECK(output32 != NULL); memset(output32, 0, 32); ARG_CHECK(pubkey != NULL); if (!secp256k1_xonly_pubkey_load(&pk, pubkey)) { return 0; } secp256k1_fe_get_b32(output32, &pk.x); return 1; } /** Keeps a group element as is if it has an even Y and otherwise negates it. * y_parity is set to 0 in the former case and to 1 in the latter case. * Requires that the coordinates of r are normalized. */ static int secp256k1_extrakeys_ge_even_y(secp256k1_ge *r) { int y_parity = 0; VERIFY_CHECK(!secp256k1_ge_is_infinity(r)); if (secp256k1_fe_is_odd(&r->y)) { secp256k1_fe_negate(&r->y, &r->y, 1); y_parity = 1; } return y_parity; } static int secp256k1_xonly_pubkey_from_pubkey(secp256k1_xonly_pubkey *xonly_pubkey, int *pk_parity, const secp256k1_pubkey *pubkey) { secp256k1_ge pk; int tmp; ARG_CHECK(xonly_pubkey != NULL); ARG_CHECK(pubkey != NULL); if (!secp256k1_pubkey_load(&pk, pubkey)) { return 0; } tmp = secp256k1_extrakeys_ge_even_y(&pk); if (pk_parity != NULL) { *pk_parity = tmp; } secp256k1_xonly_pubkey_save(xonly_pubkey, &pk); return 1; } static int secp256k1_xonly_pubkey_tweak_add(secp256k1_pubkey *output_pubkey, const secp256k1_xonly_pubkey *internal_pubkey, const unsigned char *tweak32) { secp256k1_ge pk; ARG_CHECK(output_pubkey != NULL); memset(output_pubkey, 0, sizeof(*output_pubkey)); ARG_CHECK(internal_pubkey != NULL); ARG_CHECK(tweak32 != NULL); if (!secp256k1_xonly_pubkey_load(&pk, internal_pubkey) || !secp256k1_ec_pubkey_tweak_add_helper(&pk, tweak32)) { return 0; } secp256k1_pubkey_save(output_pubkey, &pk); return 1; } #endif ================================================ FILE: C/secp256k1/field.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_FIELD_H #define SECP256K1_FIELD_H /** Field element module. * * Field elements can be represented in several ways, but code accessing * it (and implementations) need to take certain properties into account: * - Each field element can be normalized or not. * - Each field element has a magnitude, which represents how far away * its representation is away from normalization. Normalized elements * always have a magnitude of 0 or 1, but a magnitude of 1 doesn't * imply normality. */ #include "util.h" #if defined(SECP256K1_WIDEMUL_INT128) #include "field_5x52.h" #else #error "Please select wide multiplication implementation" #endif static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST( 0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul, 0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul ); #if 0 /** Normalize a field element. This brings the field element to a canonical representation, reduces * its magnitude to 1, and reduces it modulo field size `p`. */ static void secp256k1_fe_normalize(secp256k1_fe *r); #endif /** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */ static void secp256k1_fe_normalize_weak(secp256k1_fe *r); /** Normalize a field element, without constant-time guarantee. */ static void secp256k1_fe_normalize_var(secp256k1_fe *r); #if 0 /** Verify whether a field element represents zero i.e. would normalize to a zero value. */ static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r); #endif /** Verify whether a field element represents zero i.e. would normalize to a zero value, * without constant-time guarantee. */ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r); /** Set a field element equal to a small (not greater than 0x7FFF), non-negative integer. * Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise. */ static void secp256k1_fe_set_int(secp256k1_fe *r, int a); /** Sets a field element equal to zero, initializing all fields. */ static void secp256k1_fe_clear(secp256k1_fe *a); /** Verify whether a field element is zero. Requires the input to be normalized. */ static int secp256k1_fe_is_zero(const secp256k1_fe *a); /** Check the "oddness" of a field element. Requires the input to be normalized. */ static int secp256k1_fe_is_odd(const secp256k1_fe *a); #if 0 /** Compare two field elements. Requires magnitude-1 inputs. */ static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b); #endif /** Same as secp256k1_fe_equal, but may be variable time. */ static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b); #if 0 /** Compare two field elements. Requires both inputs to be normalized */ static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b); #endif /** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */ static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a); /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a); /** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input * as an argument. The magnitude of the output is one higher. */ static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m); /** Adds a small integer (up to 0x7FFF) to r. The resulting magnitude increases by one. */ static void secp256k1_fe_add_int(secp256k1_fe *r, int a); /** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that * small integer. */ static void secp256k1_fe_mul_int(secp256k1_fe *r, int a); /** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */ static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a); /** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8. * The output magnitude is 1 (but not guaranteed to be normalized). */ static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b); /** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8. * The output magnitude is 1 (but not guaranteed to be normalized). */ static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a); /** If a has a square root, it is computed in r and 1 is returned. If a does not * have a square root, the root of its negation is computed and 0 is returned. * The input's magnitude can be at most 8. The output magnitude is 1 (but not * guaranteed to be normalized). The result in r will always be a square * itself. * No constant-time guarantee. */ static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a); #if 0 /** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be * at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */ static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a); #endif /** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a); /** Convert a field element to the storage type. */ static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a); /** Convert a field element back from the storage type. */ static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a); #if 0 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag); #endif /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag); /** Halves the value of a field element modulo the field prime. Constant-time. * For an input magnitude 'm', the output magnitude is set to 'floor(m/2) + 1'. * The output is not guaranteed to be normalized, regardless of the input. */ static void secp256k1_fe_half(secp256k1_fe *r); #if 0 /** Sets each limb of 'r' to its upper bound at magnitude 'm'. The output will also have its * magnitude set to 'm' and is normalized if (and only if) 'm' is zero. */ static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m); /** Determine whether a is a square (modulo p). */ static int secp256k1_fe_is_square_var(const secp256k1_fe *a); #endif #endif /* SECP256K1_FIELD_H */ ================================================ FILE: C/secp256k1/field_5x52.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_FIELD_REPR_H #define SECP256K1_FIELD_REPR_H #include typedef struct { /* X = sum(i=0..4, n[i]*2^(i*52)) mod p * where p = 2^256 - 0x1000003D1 */ uint64_t n[5]; #ifdef VERIFY int magnitude; int normalized; #endif } secp256k1_fe; /* Unpacks a constant into a overlapping multi-limbed FE element. */ #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \ (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \ ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \ ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \ ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \ ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \ } #ifdef VERIFY #define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1} #else #define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))} #endif typedef struct { uint64_t n[4]; } secp256k1_fe_storage; #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \ (d0) | (((uint64_t)(d1)) << 32), \ (d2) | (((uint64_t)(d3)) << 32), \ (d4) | (((uint64_t)(d5)) << 32), \ (d6) | (((uint64_t)(d7)) << 32) \ }} #define SECP256K1_FE_STORAGE_CONST_GET(d) \ (uint32_t)(d.n[3] >> 32), (uint32_t)d.n[3], \ (uint32_t)(d.n[2] >> 32), (uint32_t)d.n[2], \ (uint32_t)(d.n[1] >> 32), (uint32_t)d.n[1], \ (uint32_t)(d.n[0] >> 32), (uint32_t)d.n[0] #endif /* SECP256K1_FIELD_REPR_H */ ================================================ FILE: C/secp256k1/field_5x52_asm_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ /** * Changelog: * - March 2013, Diederik Huys: original version * - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm * - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly */ #ifndef SECP256K1_FIELD_INNER5X52_IMPL_H #define SECP256K1_FIELD_INNER5X52_IMPL_H SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { /** * Registers: rdx:rax = multiplication accumulator * r9:r8 = c * r15:rcx = d * r10-r14 = a0-a4 * rbx = b * rdi = r * rsi = a / t? */ uint64_t tmp1, tmp2, tmp3; __asm__ __volatile__( "movq 0(%%rsi),%%r10\n" "movq 8(%%rsi),%%r11\n" "movq 16(%%rsi),%%r12\n" "movq 24(%%rsi),%%r13\n" "movq 32(%%rsi),%%r14\n" /* d += a3 * b0 */ "movq 0(%%rbx),%%rax\n" "mulq %%r13\n" "movq %%rax,%%rcx\n" "movq %%rdx,%%r15\n" /* d += a2 * b1 */ "movq 8(%%rbx),%%rax\n" "mulq %%r12\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a1 * b2 */ "movq 16(%%rbx),%%rax\n" "mulq %%r11\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d = a0 * b3 */ "movq 24(%%rbx),%%rax\n" "mulq %%r10\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* c = a4 * b4 */ "movq 32(%%rbx),%%rax\n" "mulq %%r14\n" "movq %%rax,%%r8\n" "movq %%rdx,%%r9\n" /* d += (c & M) * R */ "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* c >>= 52 (%%r8 only) */ "shrdq $52,%%r9,%%r8\n" /* t3 (tmp1) = d & M */ "movq %%rcx,%%rsi\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rsi\n" "movq %%rsi,%q1\n" /* d >>= 52 */ "shrdq $52,%%r15,%%rcx\n" "xorq %%r15,%%r15\n" /* d += a4 * b0 */ "movq 0(%%rbx),%%rax\n" "mulq %%r14\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a3 * b1 */ "movq 8(%%rbx),%%rax\n" "mulq %%r13\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a2 * b2 */ "movq 16(%%rbx),%%rax\n" "mulq %%r12\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a1 * b3 */ "movq 24(%%rbx),%%rax\n" "mulq %%r11\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a0 * b4 */ "movq 32(%%rbx),%%rax\n" "mulq %%r10\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += c * R */ "movq %%r8,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* t4 = d & M (%%rsi) */ "movq %%rcx,%%rsi\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rsi\n" /* d >>= 52 */ "shrdq $52,%%r15,%%rcx\n" "xorq %%r15,%%r15\n" /* tx = t4 >> 48 (tmp3) */ "movq %%rsi,%%rax\n" "shrq $48,%%rax\n" "movq %%rax,%q3\n" /* t4 &= (M >> 4) (tmp2) */ "movq $0xffffffffffff,%%rax\n" "andq %%rax,%%rsi\n" "movq %%rsi,%q2\n" /* c = a0 * b0 */ "movq 0(%%rbx),%%rax\n" "mulq %%r10\n" "movq %%rax,%%r8\n" "movq %%rdx,%%r9\n" /* d += a4 * b1 */ "movq 8(%%rbx),%%rax\n" "mulq %%r14\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a3 * b2 */ "movq 16(%%rbx),%%rax\n" "mulq %%r13\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a2 * b3 */ "movq 24(%%rbx),%%rax\n" "mulq %%r12\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a1 * b4 */ "movq 32(%%rbx),%%rax\n" "mulq %%r11\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* u0 = d & M (%%rsi) */ "movq %%rcx,%%rsi\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rsi\n" /* d >>= 52 */ "shrdq $52,%%r15,%%rcx\n" "xorq %%r15,%%r15\n" /* u0 = (u0 << 4) | tx (%%rsi) */ "shlq $4,%%rsi\n" "movq %q3,%%rax\n" "orq %%rax,%%rsi\n" /* c += u0 * (R >> 4) */ "movq $0x1000003d1,%%rax\n" "mulq %%rsi\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* r[0] = c & M */ "movq %%r8,%%rax\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq %%rax,0(%%rdi)\n" /* c >>= 52 */ "shrdq $52,%%r9,%%r8\n" "xorq %%r9,%%r9\n" /* c += a1 * b0 */ "movq 0(%%rbx),%%rax\n" "mulq %%r11\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* c += a0 * b1 */ "movq 8(%%rbx),%%rax\n" "mulq %%r10\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d += a4 * b2 */ "movq 16(%%rbx),%%rax\n" "mulq %%r14\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a3 * b3 */ "movq 24(%%rbx),%%rax\n" "mulq %%r13\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a2 * b4 */ "movq 32(%%rbx),%%rax\n" "mulq %%r12\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* c += (d & M) * R */ "movq %%rcx,%%rax\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d >>= 52 */ "shrdq $52,%%r15,%%rcx\n" "xorq %%r15,%%r15\n" /* r[1] = c & M */ "movq %%r8,%%rax\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq %%rax,8(%%rdi)\n" /* c >>= 52 */ "shrdq $52,%%r9,%%r8\n" "xorq %%r9,%%r9\n" /* c += a2 * b0 */ "movq 0(%%rbx),%%rax\n" "mulq %%r12\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* c += a1 * b1 */ "movq 8(%%rbx),%%rax\n" "mulq %%r11\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* c += a0 * b2 (last use of %%r10 = a0) */ "movq 16(%%rbx),%%rax\n" "mulq %%r10\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */ "movq %q2,%%rsi\n" "movq %q1,%%r10\n" /* d += a4 * b3 */ "movq 24(%%rbx),%%rax\n" "mulq %%r14\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* d += a3 * b4 */ "movq 32(%%rbx),%%rax\n" "mulq %%r13\n" "addq %%rax,%%rcx\n" "adcq %%rdx,%%r15\n" /* c += (d & M) * R */ "movq %%rcx,%%rax\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d >>= 52 (%%rcx only) */ "shrdq $52,%%r15,%%rcx\n" /* r[2] = c & M */ "movq %%r8,%%rax\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq %%rax,16(%%rdi)\n" /* c >>= 52 */ "shrdq $52,%%r9,%%r8\n" "xorq %%r9,%%r9\n" /* c += t3 */ "addq %%r10,%%r8\n" /* c += d * R */ "movq %%rcx,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* r[3] = c & M */ "movq %%r8,%%rax\n" "movq $0xfffffffffffff,%%rdx\n" "andq %%rdx,%%rax\n" "movq %%rax,24(%%rdi)\n" /* c >>= 52 (%%r8 only) */ "shrdq $52,%%r9,%%r8\n" /* c += t4 (%%r8 only) */ "addq %%rsi,%%r8\n" /* r[4] = c */ "movq %%r8,32(%%rdi)\n" : "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3) : "b"(b), "D"(r) : "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory" ); } SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { /** * Registers: rdx:rax = multiplication accumulator * r9:r8 = c * rcx:rbx = d * r10-r14 = a0-a4 * r15 = M (0xfffffffffffff) * rdi = r * rsi = a / t? */ uint64_t tmp1, tmp2, tmp3; __asm__ __volatile__( "movq 0(%%rsi),%%r10\n" "movq 8(%%rsi),%%r11\n" "movq 16(%%rsi),%%r12\n" "movq 24(%%rsi),%%r13\n" "movq 32(%%rsi),%%r14\n" "movq $0xfffffffffffff,%%r15\n" /* d = (a0*2) * a3 */ "leaq (%%r10,%%r10,1),%%rax\n" "mulq %%r13\n" "movq %%rax,%%rbx\n" "movq %%rdx,%%rcx\n" /* d += (a1*2) * a2 */ "leaq (%%r11,%%r11,1),%%rax\n" "mulq %%r12\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* c = a4 * a4 */ "movq %%r14,%%rax\n" "mulq %%r14\n" "movq %%rax,%%r8\n" "movq %%rdx,%%r9\n" /* d += (c & M) * R */ "andq %%r15,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* c >>= 52 (%%r8 only) */ "shrdq $52,%%r9,%%r8\n" /* t3 (tmp1) = d & M */ "movq %%rbx,%%rsi\n" "andq %%r15,%%rsi\n" "movq %%rsi,%q1\n" /* d >>= 52 */ "shrdq $52,%%rcx,%%rbx\n" "xorq %%rcx,%%rcx\n" /* a4 *= 2 */ "addq %%r14,%%r14\n" /* d += a0 * a4 */ "movq %%r10,%%rax\n" "mulq %%r14\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* d+= (a1*2) * a3 */ "leaq (%%r11,%%r11,1),%%rax\n" "mulq %%r13\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* d += a2 * a2 */ "movq %%r12,%%rax\n" "mulq %%r12\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* d += c * R */ "movq %%r8,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* t4 = d & M (%%rsi) */ "movq %%rbx,%%rsi\n" "andq %%r15,%%rsi\n" /* d >>= 52 */ "shrdq $52,%%rcx,%%rbx\n" "xorq %%rcx,%%rcx\n" /* tx = t4 >> 48 (tmp3) */ "movq %%rsi,%%rax\n" "shrq $48,%%rax\n" "movq %%rax,%q3\n" /* t4 &= (M >> 4) (tmp2) */ "movq $0xffffffffffff,%%rax\n" "andq %%rax,%%rsi\n" "movq %%rsi,%q2\n" /* c = a0 * a0 */ "movq %%r10,%%rax\n" "mulq %%r10\n" "movq %%rax,%%r8\n" "movq %%rdx,%%r9\n" /* d += a1 * a4 */ "movq %%r11,%%rax\n" "mulq %%r14\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* d += (a2*2) * a3 */ "leaq (%%r12,%%r12,1),%%rax\n" "mulq %%r13\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* u0 = d & M (%%rsi) */ "movq %%rbx,%%rsi\n" "andq %%r15,%%rsi\n" /* d >>= 52 */ "shrdq $52,%%rcx,%%rbx\n" "xorq %%rcx,%%rcx\n" /* u0 = (u0 << 4) | tx (%%rsi) */ "shlq $4,%%rsi\n" "movq %q3,%%rax\n" "orq %%rax,%%rsi\n" /* c += u0 * (R >> 4) */ "movq $0x1000003d1,%%rax\n" "mulq %%rsi\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* r[0] = c & M */ "movq %%r8,%%rax\n" "andq %%r15,%%rax\n" "movq %%rax,0(%%rdi)\n" /* c >>= 52 */ "shrdq $52,%%r9,%%r8\n" "xorq %%r9,%%r9\n" /* a0 *= 2 */ "addq %%r10,%%r10\n" /* c += a0 * a1 */ "movq %%r10,%%rax\n" "mulq %%r11\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d += a2 * a4 */ "movq %%r12,%%rax\n" "mulq %%r14\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* d += a3 * a3 */ "movq %%r13,%%rax\n" "mulq %%r13\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* c += (d & M) * R */ "movq %%rbx,%%rax\n" "andq %%r15,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d >>= 52 */ "shrdq $52,%%rcx,%%rbx\n" "xorq %%rcx,%%rcx\n" /* r[1] = c & M */ "movq %%r8,%%rax\n" "andq %%r15,%%rax\n" "movq %%rax,8(%%rdi)\n" /* c >>= 52 */ "shrdq $52,%%r9,%%r8\n" "xorq %%r9,%%r9\n" /* c += a0 * a2 (last use of %%r10) */ "movq %%r10,%%rax\n" "mulq %%r12\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */ "movq %q2,%%rsi\n" "movq %q1,%%r10\n" /* c += a1 * a1 */ "movq %%r11,%%rax\n" "mulq %%r11\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d += a3 * a4 */ "movq %%r13,%%rax\n" "mulq %%r14\n" "addq %%rax,%%rbx\n" "adcq %%rdx,%%rcx\n" /* c += (d & M) * R */ "movq %%rbx,%%rax\n" "andq %%r15,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* d >>= 52 (%%rbx only) */ "shrdq $52,%%rcx,%%rbx\n" /* r[2] = c & M */ "movq %%r8,%%rax\n" "andq %%r15,%%rax\n" "movq %%rax,16(%%rdi)\n" /* c >>= 52 */ "shrdq $52,%%r9,%%r8\n" "xorq %%r9,%%r9\n" /* c += t3 */ "addq %%r10,%%r8\n" /* c += d * R */ "movq %%rbx,%%rax\n" "movq $0x1000003d10,%%rdx\n" "mulq %%rdx\n" "addq %%rax,%%r8\n" "adcq %%rdx,%%r9\n" /* r[3] = c & M */ "movq %%r8,%%rax\n" "andq %%r15,%%rax\n" "movq %%rax,24(%%rdi)\n" /* c >>= 52 (%%r8 only) */ "shrdq $52,%%r9,%%r8\n" /* c += t4 (%%r8 only) */ "addq %%rsi,%%r8\n" /* r[4] = c */ "movq %%r8,32(%%rdi)\n" : "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3) : "D"(r) : "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory" ); } #endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ ================================================ FILE: C/secp256k1/field_5x52_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_FIELD_REPR_IMPL_H #define SECP256K1_FIELD_REPR_IMPL_H #include "util.h" #include "field.h" #include "modinv64_impl.h" #if defined(USE_ASM_X86_64) #include "field_5x52_asm_impl.h" #else #include "field_5x52_int128_impl.h" #endif /** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, * represented as 5 uint64_t's in base 2^52, least significant first. Note that the limbs are allowed to * contain >52 bits each. * * Each field element has a 'magnitude' associated with it. Internally, a magnitude M means: * - 2*M*(2^48-1) is the max (inclusive) of the most significant limb * - 2*M*(2^52-1) is the max (inclusive) of the remaining limbs * * Operations have different rules for propagating magnitude to their outputs. If an operation takes a * magnitude M as a parameter, that means the magnitude of input field elements can be at most M (inclusive). * * Each field element also has a 'normalized' flag. A field element is normalized if its magnitude is either * 0 or 1, and its value is already reduced modulo the order of the field. */ #ifdef VERIFY static void secp256k1_fe_verify(const secp256k1_fe *a) { const uint64_t *d = a->n; int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m); r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m); r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m); r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m); r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m); r &= (a->magnitude >= 0); r &= (a->magnitude <= 2048); if (a->normalized) { r &= (a->magnitude <= 1); if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) { r &= (d[0] < 0xFFFFEFFFFFC2FULL); } } VERIFY_CHECK(r == 1); } #endif #if 0 static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) { VERIFY_CHECK(m >= 0); VERIFY_CHECK(m <= 2048); r->n[0] = 0xFFFFFFFFFFFFFULL * 2 * m; r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * m; r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * m; r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * m; r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * m; #ifdef VERIFY r->magnitude = m; r->normalized = (m == 0); secp256k1_fe_verify(r); #endif } static void secp256k1_fe_normalize(secp256k1_fe *r) { uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; /* Reduce t4 at the start so there will be at most a single carry from the first pass */ uint64_t m; uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; /* The first pass ensures the magnitude is 1, ... */ t0 += x * 0x1000003D1ULL; t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ VERIFY_CHECK(t4 >> 49 == 0); /* At most a single final reduction is needed; check if the value is >= the field characteristic */ x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) & (t0 >= 0xFFFFEFFFFFC2FULL)); /* Apply the final reduction (for constant-time behaviour, we do it always) */ t0 += x * 0x1000003D1ULL; t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ VERIFY_CHECK(t4 >> 48 == x); /* Mask off the possible multiple of 2^256 from the final reduction */ t4 &= 0x0FFFFFFFFFFFFULL; r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; #ifdef VERIFY r->magnitude = 1; r->normalized = 1; secp256k1_fe_verify(r); #endif } #endif static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; /* Reduce t4 at the start so there will be at most a single carry from the first pass */ uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; /* The first pass ensures the magnitude is 1, ... */ t0 += x * 0x1000003D1ULL; t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ VERIFY_CHECK(t4 >> 49 == 0); r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; #ifdef VERIFY r->magnitude = 1; secp256k1_fe_verify(r); #endif } static void secp256k1_fe_normalize_var(secp256k1_fe *r) { uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; /* Reduce t4 at the start so there will be at most a single carry from the first pass */ uint64_t m; uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; /* The first pass ensures the magnitude is 1, ... */ t0 += x * 0x1000003D1ULL; t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ VERIFY_CHECK(t4 >> 49 == 0); /* At most a single final reduction is needed; check if the value is >= the field characteristic */ x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) & (t0 >= 0xFFFFEFFFFFC2FULL)); if (x) { t0 += 0x1000003D1ULL; t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ VERIFY_CHECK(t4 >> 48 == x); /* Mask off the possible multiple of 2^256 from the final reduction */ t4 &= 0x0FFFFFFFFFFFFULL; } r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; #ifdef VERIFY r->magnitude = 1; r->normalized = 1; secp256k1_fe_verify(r); #endif } #if 0 static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) { uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ uint64_t z0, z1; /* Reduce t4 at the start so there will be at most a single carry from the first pass */ uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; /* The first pass ensures the magnitude is 1, ... */ t0 += x * 0x1000003D1ULL; t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL; t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ VERIFY_CHECK(t4 >> 49 == 0); return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); } #endif static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) { uint64_t t0, t1, t2, t3, t4; uint64_t z0, z1; uint64_t x; t0 = r->n[0]; t4 = r->n[4]; /* Reduce t4 at the start so there will be at most a single carry from the first pass */ x = t4 >> 48; /* The first pass ensures the magnitude is 1, ... */ t0 += x * 0x1000003D1ULL; /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ z0 = t0 & 0xFFFFFFFFFFFFFULL; z1 = z0 ^ 0x1000003D0ULL; /* Fast return path should catch the majority of cases */ if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) { return 0; } t1 = r->n[1]; t2 = r->n[2]; t3 = r->n[3]; t4 &= 0x0FFFFFFFFFFFFULL; t1 += (t0 >> 52); t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ VERIFY_CHECK(t4 >> 49 == 0); return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); } SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { VERIFY_CHECK(0 <= a && a <= 0x7FFF); r->n[0] = a; r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; #ifdef VERIFY r->magnitude = (a != 0); r->normalized = 1; secp256k1_fe_verify(r); #endif } SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { const uint64_t *t = a->n; #ifdef VERIFY VERIFY_CHECK(a->normalized); secp256k1_fe_verify(a); #endif return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0; } SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { #ifdef VERIFY VERIFY_CHECK(a->normalized); secp256k1_fe_verify(a); #endif return a->n[0] & 1; } SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { int i; #ifdef VERIFY a->magnitude = 0; a->normalized = 1; #endif for (i=0; i<5; i++) { a->n[i] = 0; } } #if 0 static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { int i; #ifdef VERIFY VERIFY_CHECK(a->normalized); VERIFY_CHECK(b->normalized); secp256k1_fe_verify(a); secp256k1_fe_verify(b); #endif for (i = 4; i >= 0; i--) { if (a->n[i] > b->n[i]) { return 1; } if (a->n[i] < b->n[i]) { return -1; } } return 0; } #endif static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { int ret; r->n[0] = (uint64_t)a[31] | ((uint64_t)a[30] << 8) | ((uint64_t)a[29] << 16) | ((uint64_t)a[28] << 24) | ((uint64_t)a[27] << 32) | ((uint64_t)a[26] << 40) | ((uint64_t)(a[25] & 0xF) << 48); r->n[1] = (uint64_t)((a[25] >> 4) & 0xF) | ((uint64_t)a[24] << 4) | ((uint64_t)a[23] << 12) | ((uint64_t)a[22] << 20) | ((uint64_t)a[21] << 28) | ((uint64_t)a[20] << 36) | ((uint64_t)a[19] << 44); r->n[2] = (uint64_t)a[18] | ((uint64_t)a[17] << 8) | ((uint64_t)a[16] << 16) | ((uint64_t)a[15] << 24) | ((uint64_t)a[14] << 32) | ((uint64_t)a[13] << 40) | ((uint64_t)(a[12] & 0xF) << 48); r->n[3] = (uint64_t)((a[12] >> 4) & 0xF) | ((uint64_t)a[11] << 4) | ((uint64_t)a[10] << 12) | ((uint64_t)a[9] << 20) | ((uint64_t)a[8] << 28) | ((uint64_t)a[7] << 36) | ((uint64_t)a[6] << 44); r->n[4] = (uint64_t)a[5] | ((uint64_t)a[4] << 8) | ((uint64_t)a[3] << 16) | ((uint64_t)a[2] << 24) | ((uint64_t)a[1] << 32) | ((uint64_t)a[0] << 40); ret = !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL)); #ifdef VERIFY r->magnitude = 1; if (ret) { r->normalized = 1; secp256k1_fe_verify(r); } else { r->normalized = 0; } #endif return ret; } /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { #ifdef VERIFY VERIFY_CHECK(a->normalized); secp256k1_fe_verify(a); #endif r[0] = (a->n[4] >> 40) & 0xFF; r[1] = (a->n[4] >> 32) & 0xFF; r[2] = (a->n[4] >> 24) & 0xFF; r[3] = (a->n[4] >> 16) & 0xFF; r[4] = (a->n[4] >> 8) & 0xFF; r[5] = a->n[4] & 0xFF; r[6] = (a->n[3] >> 44) & 0xFF; r[7] = (a->n[3] >> 36) & 0xFF; r[8] = (a->n[3] >> 28) & 0xFF; r[9] = (a->n[3] >> 20) & 0xFF; r[10] = (a->n[3] >> 12) & 0xFF; r[11] = (a->n[3] >> 4) & 0xFF; r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4); r[13] = (a->n[2] >> 40) & 0xFF; r[14] = (a->n[2] >> 32) & 0xFF; r[15] = (a->n[2] >> 24) & 0xFF; r[16] = (a->n[2] >> 16) & 0xFF; r[17] = (a->n[2] >> 8) & 0xFF; r[18] = a->n[2] & 0xFF; r[19] = (a->n[1] >> 44) & 0xFF; r[20] = (a->n[1] >> 36) & 0xFF; r[21] = (a->n[1] >> 28) & 0xFF; r[22] = (a->n[1] >> 20) & 0xFF; r[23] = (a->n[1] >> 12) & 0xFF; r[24] = (a->n[1] >> 4) & 0xFF; r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4); r[26] = (a->n[0] >> 40) & 0xFF; r[27] = (a->n[0] >> 32) & 0xFF; r[28] = (a->n[0] >> 24) & 0xFF; r[29] = (a->n[0] >> 16) & 0xFF; r[30] = (a->n[0] >> 8) & 0xFF; r[31] = a->n[0] & 0xFF; } SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { #ifdef VERIFY VERIFY_CHECK(a->magnitude <= m); secp256k1_fe_verify(a); VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m); VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m); VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m); #endif r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0]; r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1]; r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2]; r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3]; r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4]; #ifdef VERIFY r->magnitude = m + 1; r->normalized = 0; secp256k1_fe_verify(r); #endif } SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { r->n[0] *= a; r->n[1] *= a; r->n[2] *= a; r->n[3] *= a; r->n[4] *= a; #ifdef VERIFY r->magnitude *= a; r->normalized = 0; secp256k1_fe_verify(r); #endif } SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) { #ifdef VERIFY secp256k1_fe_verify(r); VERIFY_CHECK(a >= 0); VERIFY_CHECK(a <= 0x7FFF); #endif r->n[0] += a; #ifdef VERIFY r->magnitude += 1; r->normalized = 0; secp256k1_fe_verify(r); #endif } SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { #ifdef VERIFY secp256k1_fe_verify(a); #endif r->n[0] += a->n[0]; r->n[1] += a->n[1]; r->n[2] += a->n[2]; r->n[3] += a->n[3]; r->n[4] += a->n[4]; #ifdef VERIFY r->magnitude += a->magnitude; r->normalized = 0; secp256k1_fe_verify(r); #endif } static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { #ifdef VERIFY VERIFY_CHECK(a->magnitude <= 8); VERIFY_CHECK(b->magnitude <= 8); secp256k1_fe_verify(a); secp256k1_fe_verify(b); VERIFY_CHECK(r != b); VERIFY_CHECK(a != b); #endif secp256k1_fe_mul_inner(r->n, a->n, b->n); #ifdef VERIFY r->magnitude = 1; r->normalized = 0; secp256k1_fe_verify(r); #endif } static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { #ifdef VERIFY VERIFY_CHECK(a->magnitude <= 8); secp256k1_fe_verify(a); #endif secp256k1_fe_sqr_inner(r->n, a->n); #ifdef VERIFY r->magnitude = 1; r->normalized = 0; secp256k1_fe_verify(r); #endif } static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { uint64_t mask0, mask1; #if 0 SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n)); #endif mask0 = flag + ~((uint64_t)0); mask1 = ~mask0; r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); #ifdef VERIFY if (flag) { r->magnitude = a->magnitude; r->normalized = a->normalized; } #endif } static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) { uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; uint64_t one = (uint64_t)1; uint64_t mask = -(t0 & one) >> 12; #ifdef VERIFY secp256k1_fe_verify(r); VERIFY_CHECK(r->magnitude < 32); #endif /* Bounds analysis (over the rationals). * * Let m = r->magnitude * C = 0xFFFFFFFFFFFFFULL * 2 * D = 0x0FFFFFFFFFFFFULL * 2 * * Initial bounds: t0..t3 <= C * m * t4 <= D * m */ t0 += 0xFFFFEFFFFFC2FULL & mask; t1 += mask; t2 += mask; t3 += mask; t4 += mask >> 4; VERIFY_CHECK((t0 & one) == 0); /* t0..t3: added <= C/2 * t4: added <= D/2 * * Current bounds: t0..t3 <= C * (m + 1/2) * t4 <= D * (m + 1/2) */ r->n[0] = (t0 >> 1) + ((t1 & one) << 51); r->n[1] = (t1 >> 1) + ((t2 & one) << 51); r->n[2] = (t2 >> 1) + ((t3 & one) << 51); r->n[3] = (t3 >> 1) + ((t4 & one) << 51); r->n[4] = (t4 >> 1); /* t0..t3: shifted right and added <= C/4 + 1/2 * t4: shifted right * * Current bounds: t0..t3 <= C * (m/2 + 1/2) * t4 <= D * (m/2 + 1/4) */ #ifdef VERIFY /* Therefore the output magnitude (M) has to be set such that: * t0..t3: C * M >= C * (m/2 + 1/2) * t4: D * M >= D * (m/2 + 1/4) * * It suffices for all limbs that, for any input magnitude m: * M >= m/2 + 1/2 * * and since we want the smallest such integer value for M: * M == floor(m/2) + 1 */ r->magnitude = (r->magnitude >> 1) + 1; r->normalized = 0; secp256k1_fe_verify(r); #endif } #if 0 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { uint64_t mask0, mask1; SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n)); mask0 = flag + ~((uint64_t)0); mask1 = ~mask0; r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); } #endif static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { #ifdef VERIFY VERIFY_CHECK(a->normalized); #endif r->n[0] = a->n[0] | a->n[1] << 52; r->n[1] = a->n[1] >> 12 | a->n[2] << 40; r->n[2] = a->n[2] >> 24 | a->n[3] << 28; r->n[3] = a->n[3] >> 36 | a->n[4] << 16; } static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL; r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL); r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL); r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL); r->n[4] = a->n[3] >> 16; #ifdef VERIFY r->magnitude = 1; r->normalized = 1; secp256k1_fe_verify(r); #endif } static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64_signed62 *a) { const uint64_t M52 = UINT64_MAX >> 12; const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4]; /* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and * have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4). */ VERIFY_CHECK(a0 >> 62 == 0); VERIFY_CHECK(a1 >> 62 == 0); VERIFY_CHECK(a2 >> 62 == 0); VERIFY_CHECK(a3 >> 62 == 0); VERIFY_CHECK(a4 >> 8 == 0); r->n[0] = a0 & M52; r->n[1] = (a0 >> 52 | a1 << 10) & M52; r->n[2] = (a1 >> 42 | a2 << 20) & M52; r->n[3] = (a2 >> 32 | a3 << 30) & M52; r->n[4] = (a3 >> 22 | a4 << 40); #ifdef VERIFY r->magnitude = 1; r->normalized = 1; secp256k1_fe_verify(r); #endif } static void secp256k1_fe_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_fe *a) { const uint64_t M62 = UINT64_MAX >> 2; const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4]; #ifdef VERIFY VERIFY_CHECK(a->normalized); #endif r->v[0] = (a0 | a1 << 52) & M62; r->v[1] = (a1 >> 10 | a2 << 42) & M62; r->v[2] = (a2 >> 20 | a3 << 32) & M62; r->v[3] = (a3 >> 30 | a4 << 22) & M62; r->v[4] = a4 >> 40; } static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_fe = { {{-0x1000003D1LL, 0, 0, 0, 256}}, 0x27C7F6E22DDACACFLL }; #if 0 static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) { secp256k1_fe tmp; secp256k1_modinv64_signed62 s; tmp = *x; secp256k1_fe_normalize(&tmp); secp256k1_fe_to_signed62(&s, &tmp); secp256k1_modinv64(&s, &secp256k1_const_modinfo_fe); secp256k1_fe_from_signed62(r, &s); #ifdef VERIFY VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); #endif } #endif static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) { secp256k1_fe tmp; secp256k1_modinv64_signed62 s; tmp = *x; secp256k1_fe_normalize_var(&tmp); secp256k1_fe_to_signed62(&s, &tmp); secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_fe); secp256k1_fe_from_signed62(r, &s); #ifdef VERIFY VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); #endif } #if 0 static int secp256k1_fe_is_square_var(const secp256k1_fe *x) { secp256k1_fe tmp; secp256k1_modinv64_signed62 s; int jac, ret; tmp = *x; secp256k1_fe_normalize_var(&tmp); /* secp256k1_jacobi64_maybe_var cannot deal with input 0. */ if (secp256k1_fe_is_zero(&tmp)) return 1; secp256k1_fe_to_signed62(&s, &tmp); jac = secp256k1_jacobi64_maybe_var(&s, &secp256k1_const_modinfo_fe); if (jac == 0) { /* secp256k1_jacobi64_maybe_var failed to compute the Jacobi symbol. Fall back * to computing a square root. This should be extremely rare with random * input (except in VERIFY mode, where a lower iteration count is used). */ secp256k1_fe dummy; ret = secp256k1_fe_sqrt_var(&dummy, &tmp); } else { #ifdef VERIFY secp256k1_fe dummy; VERIFY_CHECK(jac == 2*secp256k1_fe_sqrt_var(&dummy, &tmp) - 1); #endif ret = jac >= 0; } return ret; } #endif #endif /* SECP256K1_FIELD_REPR_IMPL_H */ ================================================ FILE: C/secp256k1/field_5x52_int128_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_FIELD_INNER5X52_IMPL_H #define SECP256K1_FIELD_INNER5X52_IMPL_H #include #include "int128.h" #ifdef VERIFY #define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) #define VERIFY_BITS_128(x, n) VERIFY_CHECK(secp256k1_u128_check_bits((x), (n))) #else #define VERIFY_BITS(x, n) do { } while(0) #define VERIFY_BITS_128(x, n) do { } while(0) #endif SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { secp256k1_uint128 c, d; uint64_t t3, t4, tx, u0; uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; VERIFY_BITS(a[0], 56); VERIFY_BITS(a[1], 56); VERIFY_BITS(a[2], 56); VERIFY_BITS(a[3], 56); VERIFY_BITS(a[4], 52); VERIFY_BITS(b[0], 56); VERIFY_BITS(b[1], 56); VERIFY_BITS(b[2], 56); VERIFY_BITS(b[3], 56); VERIFY_BITS(b[4], 52); VERIFY_CHECK(r != b); VERIFY_CHECK(a != b); /* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. * for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x). * for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4) * Note that [x 0 0 0 0 0] = [x*R]. */ secp256k1_u128_mul(&d, a0, b[3]); secp256k1_u128_accum_mul(&d, a1, b[2]); secp256k1_u128_accum_mul(&d, a2, b[1]); secp256k1_u128_accum_mul(&d, a3, b[0]); VERIFY_BITS_128(&d, 114); /* [d 0 0 0] = [p3 0 0 0] */ secp256k1_u128_mul(&c, a4, b[4]); VERIFY_BITS_128(&c, 112); /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64); VERIFY_BITS_128(&d, 115); VERIFY_BITS_128(&c, 48); /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); VERIFY_BITS(t3, 52); VERIFY_BITS_128(&d, 63); /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ secp256k1_u128_accum_mul(&d, a0, b[4]); secp256k1_u128_accum_mul(&d, a1, b[3]); secp256k1_u128_accum_mul(&d, a2, b[2]); secp256k1_u128_accum_mul(&d, a3, b[1]); secp256k1_u128_accum_mul(&d, a4, b[0]); VERIFY_BITS_128(&d, 115); /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c)); VERIFY_BITS_128(&d, 116); /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); VERIFY_BITS(t4, 52); VERIFY_BITS_128(&d, 64); /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ tx = (t4 >> 48); t4 &= (M >> 4); VERIFY_BITS(tx, 4); VERIFY_BITS(t4, 48); /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ secp256k1_u128_mul(&c, a0, b[0]); VERIFY_BITS_128(&c, 112); /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ secp256k1_u128_accum_mul(&d, a1, b[4]); secp256k1_u128_accum_mul(&d, a2, b[3]); secp256k1_u128_accum_mul(&d, a3, b[2]); secp256k1_u128_accum_mul(&d, a4, b[1]); VERIFY_BITS_128(&d, 115); /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); VERIFY_BITS(u0, 52); VERIFY_BITS_128(&d, 63); /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ u0 = (u0 << 4) | tx; VERIFY_BITS(u0, 56); /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ secp256k1_u128_accum_mul(&c, u0, R >> 4); VERIFY_BITS_128(&c, 115); /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[0], 52); VERIFY_BITS_128(&c, 61); /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ secp256k1_u128_accum_mul(&c, a0, b[1]); secp256k1_u128_accum_mul(&c, a1, b[0]); VERIFY_BITS_128(&c, 114); /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ secp256k1_u128_accum_mul(&d, a2, b[4]); secp256k1_u128_accum_mul(&d, a3, b[3]); secp256k1_u128_accum_mul(&d, a4, b[2]); VERIFY_BITS_128(&d, 114); /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52); VERIFY_BITS_128(&c, 115); VERIFY_BITS_128(&d, 62); /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[1], 52); VERIFY_BITS_128(&c, 63); /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ secp256k1_u128_accum_mul(&c, a0, b[2]); secp256k1_u128_accum_mul(&c, a1, b[1]); secp256k1_u128_accum_mul(&c, a2, b[0]); VERIFY_BITS_128(&c, 114); /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ secp256k1_u128_accum_mul(&d, a3, b[4]); secp256k1_u128_accum_mul(&d, a4, b[3]); VERIFY_BITS_128(&d, 114); /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64); VERIFY_BITS_128(&c, 115); VERIFY_BITS_128(&d, 50); /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[2], 52); VERIFY_BITS_128(&c, 63); /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d)); secp256k1_u128_accum_u64(&c, t3); VERIFY_BITS_128(&c, 100); /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[3], 52); VERIFY_BITS_128(&c, 48); /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ r[4] = secp256k1_u128_to_u64(&c) + t4; VERIFY_BITS(r[4], 49); /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ } SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { secp256k1_uint128 c, d; uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; int64_t t3, t4, tx, u0; const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; VERIFY_BITS(a[0], 56); VERIFY_BITS(a[1], 56); VERIFY_BITS(a[2], 56); VERIFY_BITS(a[3], 56); VERIFY_BITS(a[4], 52); /** [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. * px is a shorthand for sum(a[i]*a[x-i], i=0..x). * Note that [x 0 0 0 0 0] = [x*R]. */ secp256k1_u128_mul(&d, a0*2, a3); secp256k1_u128_accum_mul(&d, a1*2, a2); VERIFY_BITS_128(&d, 114); /* [d 0 0 0] = [p3 0 0 0] */ secp256k1_u128_mul(&c, a4, a4); VERIFY_BITS_128(&c, 112); /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64); VERIFY_BITS_128(&d, 115); VERIFY_BITS_128(&c, 48); /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); VERIFY_BITS(t3, 52); VERIFY_BITS_128(&d, 63); /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ a4 *= 2; secp256k1_u128_accum_mul(&d, a0, a4); secp256k1_u128_accum_mul(&d, a1*2, a3); secp256k1_u128_accum_mul(&d, a2, a2); VERIFY_BITS_128(&d, 115); /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c)); VERIFY_BITS_128(&d, 116); /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); VERIFY_BITS(t4, 52); VERIFY_BITS_128(&d, 64); /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ tx = (t4 >> 48); t4 &= (M >> 4); VERIFY_BITS(tx, 4); VERIFY_BITS(t4, 48); /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ secp256k1_u128_mul(&c, a0, a0); VERIFY_BITS_128(&c, 112); /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ secp256k1_u128_accum_mul(&d, a1, a4); secp256k1_u128_accum_mul(&d, a2*2, a3); VERIFY_BITS_128(&d, 114); /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52); VERIFY_BITS(u0, 52); VERIFY_BITS_128(&d, 62); /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ u0 = (u0 << 4) | tx; VERIFY_BITS(u0, 56); /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ secp256k1_u128_accum_mul(&c, u0, R >> 4); VERIFY_BITS_128(&c, 113); /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[0], 52); VERIFY_BITS_128(&c, 61); /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ a0 *= 2; secp256k1_u128_accum_mul(&c, a0, a1); VERIFY_BITS_128(&c, 114); /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ secp256k1_u128_accum_mul(&d, a2, a4); secp256k1_u128_accum_mul(&d, a3, a3); VERIFY_BITS_128(&d, 114); /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52); VERIFY_BITS_128(&c, 115); VERIFY_BITS_128(&d, 62); /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[1], 52); VERIFY_BITS_128(&c, 63); /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ secp256k1_u128_accum_mul(&c, a0, a2); secp256k1_u128_accum_mul(&c, a1, a1); VERIFY_BITS_128(&c, 114); /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ secp256k1_u128_accum_mul(&d, a3, a4); VERIFY_BITS_128(&d, 114); /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64); VERIFY_BITS_128(&c, 115); VERIFY_BITS_128(&d, 50); /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[2], 52); VERIFY_BITS_128(&c, 63); /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d)); secp256k1_u128_accum_u64(&c, t3); VERIFY_BITS_128(&c, 100); /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52); VERIFY_BITS(r[3], 52); VERIFY_BITS_128(&c, 48); /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ r[4] = secp256k1_u128_to_u64(&c) + t4; VERIFY_BITS(r[4], 49); /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ } #endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ ================================================ FILE: C/secp256k1/field_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_FIELD_IMPL_H #define SECP256K1_FIELD_IMPL_H #include "util.h" #if defined(SECP256K1_WIDEMUL_INT128) #include "field_5x52_impl.h" #else #error "Please select wide multiplication implementation" #endif #if 0 SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { secp256k1_fe na; secp256k1_fe_negate(&na, a, 1); secp256k1_fe_add(&na, b); return secp256k1_fe_normalizes_to_zero(&na); } #endif SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) { secp256k1_fe na; secp256k1_fe_negate(&na, a, 1); secp256k1_fe_add(&na, b); return secp256k1_fe_normalizes_to_zero_var(&na); } static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) { /** Given that p is congruent to 3 mod 4, we can compute the square root of * a mod p as the (p+1)/4'th power of a. * * As (p+1)/4 is an even number, it will have the same result for a and for * (-a). Only one of these two numbers actually has a square root however, * so we test at the end by squaring and comparing to the input. * Also because (p+1)/4 is an even number, the computed square root is * itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)). */ secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; int j; VERIFY_CHECK(r != a); /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in * { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: * 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] */ secp256k1_fe_sqr(&x2, a); secp256k1_fe_mul(&x2, &x2, a); secp256k1_fe_sqr(&x3, &x2); secp256k1_fe_mul(&x3, &x3, a); x6 = x3; for (j=0; j<3; j++) { secp256k1_fe_sqr(&x6, &x6); } secp256k1_fe_mul(&x6, &x6, &x3); x9 = x6; for (j=0; j<3; j++) { secp256k1_fe_sqr(&x9, &x9); } secp256k1_fe_mul(&x9, &x9, &x3); x11 = x9; for (j=0; j<2; j++) { secp256k1_fe_sqr(&x11, &x11); } secp256k1_fe_mul(&x11, &x11, &x2); x22 = x11; for (j=0; j<11; j++) { secp256k1_fe_sqr(&x22, &x22); } secp256k1_fe_mul(&x22, &x22, &x11); x44 = x22; for (j=0; j<22; j++) { secp256k1_fe_sqr(&x44, &x44); } secp256k1_fe_mul(&x44, &x44, &x22); x88 = x44; for (j=0; j<44; j++) { secp256k1_fe_sqr(&x88, &x88); } secp256k1_fe_mul(&x88, &x88, &x44); x176 = x88; for (j=0; j<88; j++) { secp256k1_fe_sqr(&x176, &x176); } secp256k1_fe_mul(&x176, &x176, &x88); x220 = x176; for (j=0; j<44; j++) { secp256k1_fe_sqr(&x220, &x220); } secp256k1_fe_mul(&x220, &x220, &x44); x223 = x220; for (j=0; j<3; j++) { secp256k1_fe_sqr(&x223, &x223); } secp256k1_fe_mul(&x223, &x223, &x3); /* The final result is then assembled using a sliding window over the blocks. */ t1 = x223; for (j=0; j<23; j++) { secp256k1_fe_sqr(&t1, &t1); } secp256k1_fe_mul(&t1, &t1, &x22); for (j=0; j<6; j++) { secp256k1_fe_sqr(&t1, &t1); } secp256k1_fe_mul(&t1, &t1, &x2); secp256k1_fe_sqr(&t1, &t1); secp256k1_fe_sqr(r, &t1); /* Check that a square root was actually calculated */ secp256k1_fe_sqr(&t1, r); return secp256k1_fe_equal_var(&t1, a); } #endif /* SECP256K1_FIELD_IMPL_H */ ================================================ FILE: C/secp256k1/generator.h ================================================ #ifndef SECP256K1_GENERATOR_H # define SECP256K1_GENERATOR_H # include "secp256k1.h" #include /** Opaque data structure that stores a base point * * The exact representation of data inside is implementation defined and not * guaranteed to be portable between different platforms or versions. It is * however guaranteed to be 64 bytes in size, and can be safely copied/moved. * If you need to convert to a format suitable for storage, transmission, or * comparison, use secp256k1_generator_serialize and secp256k1_generator_parse. */ typedef struct { unsigned char data[64]; } secp256k1_generator; /** Generate a generator for the curve. * * Returns: 0 in the highly unlikely case the seed is not acceptable, * 1 otherwise. * Out: gen: a generator object * In: seed32: a 32-byte seed * * If successful a valid generator will be placed in gen. The produced * generators are distributed uniformly over the curve, and will not have a * known discrete logarithm with respect to any other generator produced, * or to the base generator G. */ static SECP256K1_WARN_UNUSED_RESULT int secp256k1_generator_generate( secp256k1_generator *gen, const unsigned char *seed32 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); #endif ================================================ FILE: C/secp256k1/generator_impl.h ================================================ /********************************************************************** * Copyright (c) 2016 Andrew Poelstra & Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or http://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ #ifndef SECP256K1_GENERATOR_IMPL_H #define SECP256K1_GENERATOR_IMPL_H #include "field.h" #include "group.h" #include "generator.h" #include "../sha256.h" #include "scalar.h" #if 0 #include "../generator/pedersen_impl.h" /** Alternative generator for secp256k1. * This is the sha256 of 'g' after standard encoding (without compression), * which happens to be a point on the curve. More precisely, the generator is * derived by running the following script with the sage mathematics software. import hashlib F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F) G = '0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8' H = EllipticCurve ([F (0), F (7)]).lift_x(F(int(hashlib.sha256(G.decode('hex')).hexdigest(),16))) print('%x %x' % H.xy()) */ static const secp256k1_generator secp256k1_generator_h_internal = {{ 0x50, 0x92, 0x9b, 0x74, 0xc1, 0xa0, 0x49, 0x54, 0xb7, 0x8b, 0x4b, 0x60, 0x35, 0xe9, 0x7a, 0x5e, 0x07, 0x8a, 0x5a, 0x0f, 0x28, 0xec, 0x96, 0xd5, 0x47, 0xbf, 0xee, 0x9a, 0xce, 0x80, 0x3a, 0xc0, 0x31, 0xd3, 0xc6, 0x86, 0x39, 0x73, 0x92, 0x6e, 0x04, 0x9e, 0x63, 0x7c, 0xb1, 0xb5, 0xf4, 0x0a, 0x36, 0xda, 0xc2, 0x8a, 0xf1, 0x76, 0x69, 0x68, 0xc3, 0x0c, 0x23, 0x13, 0xf3, 0xa3, 0x89, 0x04 }}; const secp256k1_generator *secp256k1_generator_h = &secp256k1_generator_h_internal; #endif static void secp256k1_generator_load(secp256k1_ge* ge, const secp256k1_generator* gen) { int succeed; succeed = secp256k1_fe_set_b32(&ge->x, &gen->data[0]); VERIFY_CHECK(succeed != 0); succeed = secp256k1_fe_set_b32(&ge->y, &gen->data[32]); VERIFY_CHECK(succeed != 0); ge->infinity = 0; (void) succeed; } static void secp256k1_generator_save(secp256k1_generator *gen, secp256k1_ge* ge) { VERIFY_CHECK(!secp256k1_ge_is_infinity(ge)); secp256k1_fe_normalize_var(&ge->x); secp256k1_fe_normalize_var(&ge->y); secp256k1_fe_get_b32(&gen->data[0], &ge->x); secp256k1_fe_get_b32(&gen->data[32], &ge->y); } #if 0 int secp256k1_generator_parse(const secp256k1_context* ctx, secp256k1_generator* gen, const unsigned char *input) { secp256k1_fe x; secp256k1_ge ge; VERIFY_CHECK(ctx != NULL); ARG_CHECK(gen != NULL); ARG_CHECK(input != NULL); if ((input[0] & 0xFE) != 10 || !secp256k1_fe_set_b32(&x, &input[1]) || !secp256k1_ge_set_xquad(&ge, &x)) { return 0; } if (input[0] & 1) { secp256k1_ge_neg(&ge, &ge); } secp256k1_generator_save(gen, &ge); return 1; } int secp256k1_generator_serialize(const secp256k1_context* ctx, unsigned char *output, const secp256k1_generator* gen) { secp256k1_ge ge; VERIFY_CHECK(ctx != NULL); ARG_CHECK(output != NULL); ARG_CHECK(gen != NULL); secp256k1_generator_load(&ge, gen); output[0] = 11 ^ secp256k1_fe_is_quad_var(&ge.y); secp256k1_fe_normalize_var(&ge.x); secp256k1_fe_get_b32(&output[1], &ge.x); return 1; } #endif static void shallue_van_de_woestijne(secp256k1_ge* ge, const secp256k1_fe* t) { /* Implements the algorithm from: * Indifferentiable Hashing to Barreto-Naehrig Curves * Pierre-Alain Fouque and Mehdi Tibouchi * Latincrypt 2012 */ /* Basic algorithm: c = sqrt(-3) d = (c - 1)/2 w = c * t / (1 + b + t^2) [with b = 7] x1 = d - t*w x2 = -(x1 + 1) x3 = 1 + 1/w^2 To avoid the 2 divisions, compute the joint denominator j = wd * x3d, where wd = 1 + b + t^2 x3d = c^2 * t^2 = -3 * t^2 so that if j != 0, then 1 / wd = 1/j * x3d 1 / x3d = 1/j * wd x1 = d - c * t^2 * x3d / j x3 = 1 + wd^3 / j If j = 0, the function outputs the point (d, f(d)). This point is equal to (x1, f(x1)) as defined above if division by 0 is defined to be 0. In below code this is not special-cased because secp256k1_fe_inv returns 0 on input 0. j = 0 happens only when t = 0 (since wd != 0 as -8 is not a square). */ static const secp256k1_fe negc = SECP256K1_FE_CONST(0xf5d2d456, 0xcaf80e20, 0xdcc88f3d, 0x586869d3, 0x39e092ea, 0x25eb132b, 0x8272d850, 0xe32a03dd); static const secp256k1_fe d = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa40); secp256k1_fe wd, x3d, jinv, tmp, x1, x2, x3, alphain, betain, gammain, y1, y2, y3; int alphaquad, betaquad; /* wd = t^2 */ secp256k1_fe_sqr(&wd, t); /* mag 1 */ /* x1 = -c * t^2 */ secp256k1_fe_mul(&x1, &negc, &wd); /* mag 1 */ /* x3d = t^2 */ x3d = wd; /* mag 1 */ /* x3d = 3 * t^2 */ secp256k1_fe_mul_int(&x3d, 3); /* mag 3 */ /* x3d = -3 * t^2 */ secp256k1_fe_negate(&x3d, &x3d, 3); /* mag 4 */ /* wd = 1 + b + t^2 */ secp256k1_fe_add_int(&wd, SECP256K1_B + 1); /* mag 2 */ /* jinv = wd * x3d */ secp256k1_fe_mul(&jinv, &wd, &x3d); /* mag 1 */ /* jinv = 1/(wd * x3d) */ secp256k1_fe_inv_var(&jinv, &jinv); /* mag 1 */ /* x1 = -c * t^2 * x3d */ secp256k1_fe_mul(&x1, &x1, &x3d); /* mag 1 */ /* x1 = -c * t^2 * x3d * 1/j */ secp256k1_fe_mul(&x1, &x1, &jinv); /* mag 1 */ /* x1 = d + -c * t^2 * x3d * 1/j */ secp256k1_fe_add(&x1, &d); /* mag 2 */ /* x2 = x1 */ x2 = x1; /* mag 2 */ /* x2 = x1 + 1 */ secp256k1_fe_add_int(&x2, 1); /* mag 3 */ /* x2 = - (x1 + 1) */ secp256k1_fe_negate(&x2, &x2, 3); /* mag 4 */ /* x3 = wd^2 */ secp256k1_fe_sqr(&x3, &wd); /* mag 1 */ /* x3 = wd^3 */ secp256k1_fe_mul(&x3, &x3, &wd); /* mag 1 */ /* x3 = wd^3 * 1/j */ secp256k1_fe_mul(&x3, &x3, &jinv); /* mag 1 */ /* x3 = 1 + (wd^3 * 1/j) */ secp256k1_fe_add_int(&x3, 1); /* mag 2 */ secp256k1_fe_sqr(&alphain, &x1); /* mag 1 */ secp256k1_fe_mul(&alphain, &alphain, &x1); /* mag 1 */ secp256k1_fe_add_int(&alphain, SECP256K1_B); /* mag 2 */ secp256k1_fe_sqr(&betain, &x2); /* mag 1 */ secp256k1_fe_mul(&betain, &betain, &x2); /* mag 1 */ secp256k1_fe_add_int(&betain, SECP256K1_B); /* mag 2 */ secp256k1_fe_sqr(&gammain, &x3); /* mag 1 */ secp256k1_fe_mul(&gammain, &gammain, &x3); /* mag 1 */ secp256k1_fe_add_int(&gammain, SECP256K1_B); /* mag 2 */ alphaquad = secp256k1_fe_sqrt_var(&y1, &alphain); betaquad = secp256k1_fe_sqrt_var(&y2, &betain); secp256k1_fe_sqrt_var(&y3, &gammain); secp256k1_fe_cmov(&x1, &x2, (!alphaquad) & betaquad); secp256k1_fe_cmov(&y1, &y2, (!alphaquad) & betaquad); secp256k1_fe_cmov(&x1, &x3, (!alphaquad) & !betaquad); secp256k1_fe_cmov(&y1, &y3, (!alphaquad) & !betaquad); secp256k1_ge_set_xy(ge, &x1, &y1); /* The linked algorithm from the paper uses the Jacobi symbol of t to * determine the Jacobi symbol of the produced y coordinate. Since the * rest of the algorithm only uses t^2, we can safely use another criterion * as long as negation of t results in negation of the y coordinate. Here * we choose to use t's oddness, as it is faster to determine. */ secp256k1_fe_negate(&tmp, &ge->y, 1); secp256k1_fe_cmov(&ge->y, &tmp, secp256k1_fe_is_odd(t)); } static int secp256k1_generator_generate_internal(secp256k1_generator* gen, const unsigned char *key32, const unsigned char *blind32) { static const unsigned char prefix1[17] = "1st generation: "; static const unsigned char prefix2[17] = "2nd generation: "; secp256k1_fe t = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 4); secp256k1_ge add; secp256k1_gej accum; int overflow; sha256_midstate sha256_buf; unsigned char b32[32]; int ret = 1; if (blind32) { static const secp256k1_gej inf = SECP256K1_GEJ_CONST_INFINITY; static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); secp256k1_scalar blind; secp256k1_scalar_set_b32(&blind, blind32, &overflow); ret = !overflow; secp256k1_ecmult(&accum, &inf, &zero, &blind); } { sha256_context sha256_ctx = sha256_init(sha256_buf.s); sha256_uchars(&sha256_ctx, prefix1, 16); sha256_uchars(&sha256_ctx, key32, 32); sha256_finalize(&sha256_ctx); sha256_fromMidstate(b32, sha256_buf.s); } ret &= secp256k1_fe_set_b32(&t, b32); shallue_van_de_woestijne(&add, &t); if (blind32) { secp256k1_gej_add_ge_var(&accum, &accum, &add, NULL); } else { secp256k1_gej_set_ge(&accum, &add); } { sha256_context sha256_ctx = sha256_init(sha256_buf.s); sha256_uchars(&sha256_ctx, prefix2, 16); sha256_uchars(&sha256_ctx, key32, 32); sha256_finalize(&sha256_ctx); sha256_fromMidstate(b32, sha256_buf.s); } ret &= secp256k1_fe_set_b32(&t, b32); shallue_van_de_woestijne(&add, &t); secp256k1_gej_add_ge_var(&accum, &accum, &add, NULL); secp256k1_ge_set_gej_var(&add, &accum); secp256k1_generator_save(gen, &add); return ret; } int secp256k1_generator_generate(secp256k1_generator* gen, const unsigned char *key32) { ARG_CHECK(gen != NULL); ARG_CHECK(key32 != NULL); return secp256k1_generator_generate_internal(gen, key32, NULL); } #if 0 int secp256k1_generator_generate_blinded(const secp256k1_context* ctx, secp256k1_generator* gen, const unsigned char *key32, const unsigned char *blind32) { VERIFY_CHECK(ctx != NULL); ARG_CHECK(gen != NULL); ARG_CHECK(key32 != NULL); ARG_CHECK(blind32 != NULL); ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); return secp256k1_generator_generate_internal(ctx, gen, key32, blind32); } static void secp256k1_pedersen_commitment_load(secp256k1_ge* ge, const secp256k1_pedersen_commitment* commit) { secp256k1_fe fe; secp256k1_fe_set_b32(&fe, &commit->data[1]); secp256k1_ge_set_xquad(ge, &fe); if (commit->data[0] & 1) { secp256k1_ge_neg(ge, ge); } } static void secp256k1_pedersen_commitment_save(secp256k1_pedersen_commitment* commit, secp256k1_ge* ge) { secp256k1_fe_normalize(&ge->x); secp256k1_fe_get_b32(&commit->data[1], &ge->x); commit->data[0] = 9 ^ secp256k1_fe_is_quad_var(&ge->y); } int secp256k1_pedersen_commitment_parse(const secp256k1_context* ctx, secp256k1_pedersen_commitment* commit, const unsigned char *input) { secp256k1_fe x; secp256k1_ge ge; VERIFY_CHECK(ctx != NULL); ARG_CHECK(commit != NULL); ARG_CHECK(input != NULL); (void) ctx; if ((input[0] & 0xFE) != 8 || !secp256k1_fe_set_b32(&x, &input[1]) || !secp256k1_ge_set_xquad(&ge, &x)) { return 0; } if (input[0] & 1) { secp256k1_ge_neg(&ge, &ge); } secp256k1_pedersen_commitment_save(commit, &ge); return 1; } int secp256k1_pedersen_commitment_serialize(const secp256k1_context* ctx, unsigned char *output, const secp256k1_pedersen_commitment* commit) { secp256k1_ge ge; VERIFY_CHECK(ctx != NULL); ARG_CHECK(output != NULL); ARG_CHECK(commit != NULL); secp256k1_pedersen_commitment_load(&ge, commit); output[0] = 9 ^ secp256k1_fe_is_quad_var(&ge.y); secp256k1_fe_normalize_var(&ge.x); secp256k1_fe_get_b32(&output[1], &ge.x); return 1; } /* Generates a pedersen commitment: *commit = blind * G + value * G2. The blinding factor is 32 bytes.*/ int secp256k1_pedersen_commit(const secp256k1_context* ctx, secp256k1_pedersen_commitment *commit, const unsigned char *blind, uint64_t value, const secp256k1_generator* gen) { secp256k1_ge genp; secp256k1_gej rj; secp256k1_ge r; secp256k1_scalar sec; int overflow; int ret = 0; VERIFY_CHECK(ctx != NULL); ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); ARG_CHECK(commit != NULL); ARG_CHECK(blind != NULL); ARG_CHECK(gen != NULL); secp256k1_generator_load(&genp, gen); secp256k1_scalar_set_b32(&sec, blind, &overflow); if (!overflow) { secp256k1_pedersen_ecmult(&ctx->ecmult_gen_ctx, &rj, &sec, value, &genp); if (!secp256k1_gej_is_infinity(&rj)) { secp256k1_ge_set_gej(&r, &rj); secp256k1_pedersen_commitment_save(commit, &r); ret = 1; } secp256k1_gej_clear(&rj); secp256k1_ge_clear(&r); } secp256k1_scalar_clear(&sec); return ret; } /** Takes a list of n pointers to 32 byte blinding values, the first negs of which are treated with positive sign and the rest * negative, then calculates an additional blinding value that adds to zero. */ int secp256k1_pedersen_blind_sum(const secp256k1_context* ctx, unsigned char *blind_out, const unsigned char * const *blinds, size_t n, size_t npositive) { secp256k1_scalar acc; secp256k1_scalar x; size_t i; int overflow; VERIFY_CHECK(ctx != NULL); ARG_CHECK(blind_out != NULL); ARG_CHECK(blinds != NULL); ARG_CHECK(npositive <= n); (void) ctx; secp256k1_scalar_set_int(&acc, 0); for (i = 0; i < n; i++) { secp256k1_scalar_set_b32(&x, blinds[i], &overflow); if (overflow) { return 0; } if (i >= npositive) { secp256k1_scalar_negate(&x, &x); } secp256k1_scalar_add(&acc, &acc, &x); } secp256k1_scalar_get_b32(blind_out, &acc); secp256k1_scalar_clear(&acc); secp256k1_scalar_clear(&x); return 1; } /* Takes two lists of commitments and sums the first set and subtracts the second and verifies that they sum to excess. */ int secp256k1_pedersen_verify_tally(const secp256k1_context* ctx, const secp256k1_pedersen_commitment * const* commits, size_t pcnt, const secp256k1_pedersen_commitment * const* ncommits, size_t ncnt) { secp256k1_gej accj; secp256k1_ge add; size_t i; VERIFY_CHECK(ctx != NULL); ARG_CHECK(!pcnt || (commits != NULL)); ARG_CHECK(!ncnt || (ncommits != NULL)); (void) ctx; secp256k1_gej_set_infinity(&accj); for (i = 0; i < ncnt; i++) { secp256k1_pedersen_commitment_load(&add, ncommits[i]); secp256k1_gej_add_ge_var(&accj, &accj, &add, NULL); } secp256k1_gej_neg(&accj, &accj); for (i = 0; i < pcnt; i++) { secp256k1_pedersen_commitment_load(&add, commits[i]); secp256k1_gej_add_ge_var(&accj, &accj, &add, NULL); } return secp256k1_gej_is_infinity(&accj); } int secp256k1_pedersen_blind_generator_blind_sum(const secp256k1_context* ctx, const uint64_t *value, const unsigned char* const* generator_blind, unsigned char* const* blinding_factor, size_t n_total, size_t n_inputs) { secp256k1_scalar sum; secp256k1_scalar tmp; size_t i; VERIFY_CHECK(ctx != NULL); ARG_CHECK(n_total == 0 || value != NULL); ARG_CHECK(n_total == 0 || generator_blind != NULL); ARG_CHECK(n_total == 0 || blinding_factor != NULL); ARG_CHECK(n_total > n_inputs); (void) ctx; if (n_total == 0) { return 1; } secp256k1_scalar_set_int(&sum, 0); secp256k1_scalar_set_int(&tmp, 0); /* Here, n_total > 0. Thus the loop runs at least once. Thus we may use a do-while loop, which checks the loop condition only at the end. The do-while loop helps GCC prove that the loop runs at least once and suppresses a -Wmaybe-uninitialized warning. */ i = 0; do { int overflow = 0; secp256k1_scalar addend; secp256k1_scalar_set_u64(&addend, value[i]); /* s = v */ secp256k1_scalar_set_b32(&tmp, generator_blind[i], &overflow); if (overflow == 1) { secp256k1_scalar_clear(&tmp); secp256k1_scalar_clear(&addend); secp256k1_scalar_clear(&sum); return 0; } secp256k1_scalar_mul(&addend, &addend, &tmp); /* s = vr */ secp256k1_scalar_set_b32(&tmp, blinding_factor[i], &overflow); if (overflow == 1) { secp256k1_scalar_clear(&tmp); secp256k1_scalar_clear(&addend); secp256k1_scalar_clear(&sum); return 0; } secp256k1_scalar_add(&addend, &addend, &tmp); /* s = vr + r' */ secp256k1_scalar_cond_negate(&addend, i < n_inputs); /* s is negated if it's an input */ secp256k1_scalar_add(&sum, &sum, &addend); /* sum += s */ secp256k1_scalar_clear(&addend); i++; } while (i < n_total); /* Right now tmp has the last pedersen blinding factor. Subtract the sum from it. */ secp256k1_scalar_negate(&sum, &sum); secp256k1_scalar_add(&tmp, &tmp, &sum); secp256k1_scalar_get_b32(blinding_factor[n_total - 1], &tmp); secp256k1_scalar_clear(&tmp); secp256k1_scalar_clear(&sum); return 1; } #endif #endif ================================================ FILE: C/secp256k1/group.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_GROUP_H #define SECP256K1_GROUP_H #include "field.h" /** A group element in affine coordinates on the secp256k1 curve, * or occasionally on an isomorphic curve of the form y^2 = x^3 + 7*t^6. * Note: For exhaustive test mode, secp256k1 is replaced by a small subgroup of a different curve. */ typedef struct { secp256k1_fe x; secp256k1_fe y; int infinity; /* whether this represents the point at infinity */ } secp256k1_ge; #define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0} #define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} /** A group element of the secp256k1 curve, in jacobian coordinates. * Note: For exhastive test mode, secp256k1 is replaced by a small subgroup of a different curve. */ typedef struct { secp256k1_fe x; /* actual X: x/z^2 */ secp256k1_fe y; /* actual Y: y/z^3 */ secp256k1_fe z; int infinity; /* whether this represents the point at infinity */ } secp256k1_gej; #define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0} #define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} typedef struct { secp256k1_fe_storage x; secp256k1_fe_storage y; } secp256k1_ge_storage; #define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))} #define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y) /** Set a group element equal to the point with given X and Y coordinates */ static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y); /** Set a group element (affine) equal to the point with the given X coordinate, and given oddness * for Y. Return value indicates whether the result is valid. */ static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd); /** Check whether a group element is the point at infinity. */ static int secp256k1_ge_is_infinity(const secp256k1_ge *a); /** Check whether a group element is valid (i.e., on the curve). */ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a); /** Set r equal to the inverse of a (i.e., mirrored around the X axis) */ static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a); #if 0 /** Set a group element equal to another which is given in jacobian coordinates. Constant time. */ static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a); #endif /** Set a group element equal to another which is given in jacobian coordinates. */ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a); #if 0 /** Set a batch of group elements equal to the inputs given in jacobian coordinates */ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len); #endif /** Bring a batch of inputs to the same global z "denominator", based on ratios between * (omitted) z coordinates of adjacent elements. * * Although the elements a[i] are _ge rather than _gej, they actually represent elements * in Jacobian coordinates with their z coordinates omitted. * * Using the notation z(b) to represent the omitted z coordinate of b, the array zr of * z coordinate ratios must satisfy zr[i] == z(a[i]) / z(a[i-1]) for 0 < 'i' < len. * The zr[0] value is unused. * * This function adjusts the coordinates of 'a' in place so that for all 'i', z(a[i]) == z(a[len-1]). * In other words, the initial value of z(a[len-1]) becomes the global z "denominator". Only the * a[i].x and a[i].y coordinates are explicitly modified; the adjustment of the omitted z coordinate is * implicit. * * The coordinates of the final element a[len-1] are not changed. */ static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr); /** Set a group element (affine) equal to the point at infinity. */ static void secp256k1_ge_set_infinity(secp256k1_ge *r); /** Set a group element (jacobian) equal to the point at infinity. */ static void secp256k1_gej_set_infinity(secp256k1_gej *r); /** Set a group element (jacobian) equal to another which is given in affine coordinates. */ static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a); /** Check two group elements (jacobian) for equality in variable time. */ static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b); /** Check two group elements (jacobian and affine) for equality in variable time. */ static int secp256k1_gej_eq_ge_var(const secp256k1_gej *a, const secp256k1_ge *b); /** Compare the X coordinate of a group element (jacobian). */ static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a); /** Set r equal to the inverse of a (i.e., mirrored around the X axis) */ static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a); /** Check whether a group element is the point at infinity. */ static int secp256k1_gej_is_infinity(const secp256k1_gej *a); /** Set r equal to the double of a. Constant time. */ static void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a); /** Set r equal to the double of a. If rzr is not-NULL this sets *rzr such that r->z == a->z * *rzr (where infinity means an implicit z = 0). */ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr); /** Set r equal to the sum of a and b. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr); #if 0 /** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b); #endif /** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time guarantee, and b is allowed to be infinity. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr); /** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv); #if 0 /** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */ static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a); /** Clear a secp256k1_gej to prevent leaking sensitive information. */ static void secp256k1_gej_clear(secp256k1_gej *r); /** Clear a secp256k1_ge to prevent leaking sensitive information. */ static void secp256k1_ge_clear(secp256k1_ge *r); #endif /** Convert a group element to the storage type. */ static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a); /** Convert a group element back from the storage type. */ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a); #if 0 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag); /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag); #endif /** Rescale a jacobian point by b which must be non-zero. Constant-time. */ static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b); /** Determine if a point (which is assumed to be on the curve) is in the correct (sub)group of the curve. * * In normal mode, the used group is secp256k1, which has cofactor=1 meaning that every point on the curve is in the * group, and this function returns always true. * * When compiling in exhaustive test mode, a slightly different curve equation is used, leading to a group with a * (very) small subgroup, and that subgroup is what is used for all cryptographic operations. In that mode, this * function checks whether a point that is on the curve is in fact also in that subgroup. */ static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge); #endif /* SECP256K1_GROUP_H */ ================================================ FILE: C/secp256k1/group_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_GROUP_IMPL_H #define SECP256K1_GROUP_IMPL_H #include "field.h" #include "group.h" /* Begin of section generated by sage/gen_exhaustive_groups.sage. */ #define SECP256K1_G_ORDER_7 SECP256K1_GE_CONST(\ 0x66625d13, 0x317ffe44, 0x63d32cff, 0x1ca02b9b,\ 0xe5c6d070, 0x50b4b05e, 0x81cc30db, 0xf5166f0a,\ 0x1e60e897, 0xa7c00c7c, 0x2df53eb6, 0x98274ff4,\ 0x64252f42, 0x8ca44e17, 0x3b25418c, 0xff4ab0cf\ ) #define SECP256K1_G_ORDER_13 SECP256K1_GE_CONST(\ 0xa2482ff8, 0x4bf34edf, 0xa51262fd, 0xe57921db,\ 0xe0dd2cb7, 0xa5914790, 0xbc71631f, 0xc09704fb,\ 0x942536cb, 0xa3e49492, 0x3a701cc3, 0xee3e443f,\ 0xdf182aa9, 0x15b8aa6a, 0x166d3b19, 0xba84b045\ ) #define SECP256K1_G_ORDER_199 SECP256K1_GE_CONST(\ 0x7fb07b5c, 0xd07c3bda, 0x553902e2, 0x7a87ea2c,\ 0x35108a7f, 0x051f41e5, 0xb76abad5, 0x1f2703ad,\ 0x0a251539, 0x5b4c4438, 0x952a634f, 0xac10dd4d,\ 0x6d6f4745, 0x98990c27, 0x3a4f3116, 0xd32ff969\ ) /** Generator for secp256k1, value 'g' defined in * "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ #define SECP256K1_G SECP256K1_GE_CONST(\ 0x79be667e, 0xf9dcbbac, 0x55a06295, 0xce870b07,\ 0x029bfcdb, 0x2dce28d9, 0x59f2815b, 0x16f81798,\ 0x483ada77, 0x26a3c465, 0x5da4fbfc, 0x0e1108a8,\ 0xfd17b448, 0xa6855419, 0x9c47d08f, 0xfb10d4b8\ ) /* These exhaustive group test orders and generators are chosen such that: * - The field size is equal to that of secp256k1, so field code is the same. * - The curve equation is of the form y^2=x^3+B for some small constant B. * - The subgroup has a generator 2*P, where P.x is as small as possible. * - The subgroup has size less than 1000 to permit exhaustive testing. * - The subgroup admits an endomorphism of the form lambda*(x,y) == (beta*x,y). */ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G; #define SECP256K1_B 7 /* End of section generated by sage/gen_exhaustive_groups.sage. */ static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, SECP256K1_B); static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) { secp256k1_fe zi2; secp256k1_fe zi3; VERIFY_CHECK(!a->infinity); secp256k1_fe_sqr(&zi2, zi); secp256k1_fe_mul(&zi3, &zi2, zi); secp256k1_fe_mul(&r->x, &a->x, &zi2); secp256k1_fe_mul(&r->y, &a->y, &zi3); r->infinity = a->infinity; } static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) { r->infinity = 0; r->x = *x; r->y = *y; } static int secp256k1_ge_is_infinity(const secp256k1_ge *a) { return a->infinity; } static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) { *r = *a; secp256k1_fe_normalize_weak(&r->y); secp256k1_fe_negate(&r->y, &r->y, 1); } #if 0 static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) { secp256k1_fe z2, z3; r->infinity = a->infinity; secp256k1_fe_inv(&a->z, &a->z); secp256k1_fe_sqr(&z2, &a->z); secp256k1_fe_mul(&z3, &a->z, &z2); secp256k1_fe_mul(&a->x, &a->x, &z2); secp256k1_fe_mul(&a->y, &a->y, &z3); secp256k1_fe_set_int(&a->z, 1); r->x = a->x; r->y = a->y; } #endif static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) { secp256k1_fe z2, z3; if (a->infinity) { secp256k1_ge_set_infinity(r); return; } secp256k1_fe_inv_var(&a->z, &a->z); secp256k1_fe_sqr(&z2, &a->z); secp256k1_fe_mul(&z3, &a->z, &z2); secp256k1_fe_mul(&a->x, &a->x, &z2); secp256k1_fe_mul(&a->y, &a->y, &z3); secp256k1_fe_set_int(&a->z, 1); secp256k1_ge_set_xy(r, &a->x, &a->y); } #if 0 static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len) { secp256k1_fe u; size_t i; size_t last_i = SIZE_MAX; for (i = 0; i < len; i++) { if (a[i].infinity) { secp256k1_ge_set_infinity(&r[i]); } else { /* Use destination's x coordinates as scratch space */ if (last_i == SIZE_MAX) { r[i].x = a[i].z; } else { secp256k1_fe_mul(&r[i].x, &r[last_i].x, &a[i].z); } last_i = i; } } if (last_i == SIZE_MAX) { return; } secp256k1_fe_inv_var(&u, &r[last_i].x); i = last_i; while (i > 0) { i--; if (!a[i].infinity) { secp256k1_fe_mul(&r[last_i].x, &r[i].x, &u); secp256k1_fe_mul(&u, &u, &a[last_i].z); last_i = i; } } VERIFY_CHECK(!a[last_i].infinity); r[last_i].x = u; for (i = 0; i < len; i++) { if (!a[i].infinity) { secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x); } } } #endif static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr) { size_t i = len - 1; secp256k1_fe zs; if (len > 0) { /* Ensure all y values are in weak normal form for fast negation of points */ secp256k1_fe_normalize_weak(&a[i].y); zs = zr[i]; /* Work our way backwards, using the z-ratios to scale the x/y values. */ while (i > 0) { secp256k1_gej tmpa; if (i != len - 1) { secp256k1_fe_mul(&zs, &zs, &zr[i]); } i--; tmpa.x = a[i].x; tmpa.y = a[i].y; tmpa.infinity = 0; secp256k1_ge_set_gej_zinv(&a[i], &tmpa, &zs); } } } static void secp256k1_gej_set_infinity(secp256k1_gej *r) { r->infinity = 1; secp256k1_fe_clear(&r->x); secp256k1_fe_clear(&r->y); secp256k1_fe_clear(&r->z); } static void secp256k1_ge_set_infinity(secp256k1_ge *r) { r->infinity = 1; secp256k1_fe_clear(&r->x); secp256k1_fe_clear(&r->y); } #if 0 static void secp256k1_gej_clear(secp256k1_gej *r) { r->infinity = 0; secp256k1_fe_clear(&r->x); secp256k1_fe_clear(&r->y); secp256k1_fe_clear(&r->z); } static void secp256k1_ge_clear(secp256k1_ge *r) { r->infinity = 0; secp256k1_fe_clear(&r->x); secp256k1_fe_clear(&r->y); } #endif static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) { secp256k1_fe x2, x3; r->x = *x; secp256k1_fe_sqr(&x2, x); secp256k1_fe_mul(&x3, x, &x2); r->infinity = 0; secp256k1_fe_add_int(&x3, SECP256K1_B); if (!secp256k1_fe_sqrt_var(&r->y, &x3)) { return 0; } secp256k1_fe_normalize_var(&r->y); if (secp256k1_fe_is_odd(&r->y) != odd) { secp256k1_fe_negate(&r->y, &r->y, 1); } return 1; } static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) { r->infinity = a->infinity; r->x = a->x; r->y = a->y; secp256k1_fe_set_int(&r->z, !r->infinity); } static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b) { secp256k1_gej tmp; secp256k1_gej_neg(&tmp, a); secp256k1_gej_add_var(&tmp, &tmp, b, NULL); return secp256k1_gej_is_infinity(&tmp); } static int secp256k1_gej_eq_ge_var(const secp256k1_gej *a, const secp256k1_ge *b) { secp256k1_gej tmp; secp256k1_gej_neg(&tmp, a); secp256k1_gej_add_ge_var(&tmp, &tmp, b, NULL); return secp256k1_gej_is_infinity(&tmp); } static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) { secp256k1_fe r, r2; VERIFY_CHECK(!a->infinity); secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x); r2 = a->x; secp256k1_fe_normalize_weak(&r2); return secp256k1_fe_equal_var(&r, &r2); } static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) { r->infinity = a->infinity; r->x = a->x; r->y = a->y; r->z = a->z; secp256k1_fe_normalize_weak(&r->y); secp256k1_fe_negate(&r->y, &r->y, 1); } static int secp256k1_gej_is_infinity(const secp256k1_gej *a) { return a->infinity; } static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) { secp256k1_fe y2, x3; if (a->infinity) { return 0; } /* y^2 = x^3 + 7 */ secp256k1_fe_sqr(&y2, &a->y); secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x); secp256k1_fe_add_int(&x3, SECP256K1_B); secp256k1_fe_normalize_weak(&x3); return secp256k1_fe_equal_var(&y2, &x3); } static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a) { /* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */ secp256k1_fe l, s, t; r->infinity = a->infinity; /* Formula used: * L = (3/2) * X1^2 * S = Y1^2 * T = -X1*S * X3 = L^2 + 2*T * Y3 = -(L*(X3 + T) + S^2) * Z3 = Y1*Z1 */ secp256k1_fe_mul(&r->z, &a->z, &a->y); /* Z3 = Y1*Z1 (1) */ secp256k1_fe_sqr(&s, &a->y); /* S = Y1^2 (1) */ secp256k1_fe_sqr(&l, &a->x); /* L = X1^2 (1) */ secp256k1_fe_mul_int(&l, 3); /* L = 3*X1^2 (3) */ secp256k1_fe_half(&l); /* L = 3/2*X1^2 (2) */ secp256k1_fe_negate(&t, &s, 1); /* T = -S (2) */ secp256k1_fe_mul(&t, &t, &a->x); /* T = -X1*S (1) */ secp256k1_fe_sqr(&r->x, &l); /* X3 = L^2 (1) */ secp256k1_fe_add(&r->x, &t); /* X3 = L^2 + T (2) */ secp256k1_fe_add(&r->x, &t); /* X3 = L^2 + 2*T (3) */ secp256k1_fe_sqr(&s, &s); /* S' = S^2 (1) */ secp256k1_fe_add(&t, &r->x); /* T' = X3 + T (4) */ secp256k1_fe_mul(&r->y, &t, &l); /* Y3 = L*(X3 + T) (1) */ secp256k1_fe_add(&r->y, &s); /* Y3 = L*(X3 + T) + S^2 (2) */ secp256k1_fe_negate(&r->y, &r->y, 2); /* Y3 = -(L*(X3 + T) + S^2) (3) */ } static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) { if (a->infinity) { secp256k1_gej_set_infinity(r); if (rzr != NULL) { secp256k1_fe_set_int(rzr, 1); } return; } if (rzr != NULL) { *rzr = a->y; secp256k1_fe_normalize_weak(rzr); } secp256k1_gej_double(r, a); /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity, * Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have * y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p. * * Having said this, if this function receives a point on a sextic twist, * it is possible for y to be 0. This happens for y^2 = x^3 + 6, * since -6 does have a cube root mod p. For this point, gej_double will not set * the infinity flag even though the point doubles to infinity, so we explicitly set it to infinity. */ r->infinity = secp256k1_fe_normalizes_to_zero_var(&r->z); } static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) { /* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */ secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t; if (a->infinity) { VERIFY_CHECK(rzr == NULL); *r = *b; return; } if (b->infinity) { if (rzr != NULL) { secp256k1_fe_set_int(rzr, 1); } *r = *a; return; } secp256k1_fe_sqr(&z22, &b->z); secp256k1_fe_sqr(&z12, &a->z); secp256k1_fe_mul(&u1, &a->x, &z22); secp256k1_fe_mul(&u2, &b->x, &z12); secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z); secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1); if (secp256k1_fe_normalizes_to_zero_var(&h)) { if (secp256k1_fe_normalizes_to_zero_var(&i)) { secp256k1_gej_double_var(r, a, rzr); } else { if (rzr != NULL) { secp256k1_fe_set_int(rzr, 0); } secp256k1_gej_set_infinity(r); } return; } r->infinity = 0; secp256k1_fe_mul(&t, &h, &b->z); if (rzr != NULL) { *rzr = t; } secp256k1_fe_mul(&r->z, &a->z, &t); secp256k1_fe_sqr(&h2, &h); secp256k1_fe_negate(&h2, &h2, 1); secp256k1_fe_mul(&h3, &h2, &h); secp256k1_fe_mul(&t, &u1, &h2); secp256k1_fe_sqr(&r->x, &i); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_add(&r->x, &t); secp256k1_fe_add(&r->x, &t); secp256k1_fe_add(&t, &r->x); secp256k1_fe_mul(&r->y, &t, &i); secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_add(&r->y, &h3); } static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) { /* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */ secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t; if (a->infinity) { VERIFY_CHECK(rzr == NULL); if (rzr != NULL) { secp256k1_fe_clear(rzr); } secp256k1_gej_set_ge(r, b); return; } if (b->infinity) { if (rzr != NULL) { secp256k1_fe_set_int(rzr, 1); } *r = *a; return; } secp256k1_fe_sqr(&z12, &a->z); u1 = a->x; secp256k1_fe_normalize_weak(&u1); secp256k1_fe_mul(&u2, &b->x, &z12); s1 = a->y; secp256k1_fe_normalize_weak(&s1); secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1); if (secp256k1_fe_normalizes_to_zero_var(&h)) { if (secp256k1_fe_normalizes_to_zero_var(&i)) { secp256k1_gej_double_var(r, a, rzr); } else { if (rzr != NULL) { secp256k1_fe_set_int(rzr, 0); } secp256k1_gej_set_infinity(r); } return; } r->infinity = 0; if (rzr != NULL) { *rzr = h; } secp256k1_fe_mul(&r->z, &a->z, &h); secp256k1_fe_sqr(&h2, &h); secp256k1_fe_negate(&h2, &h2, 1); secp256k1_fe_mul(&h3, &h2, &h); secp256k1_fe_mul(&t, &u1, &h2); secp256k1_fe_sqr(&r->x, &i); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_add(&r->x, &t); secp256k1_fe_add(&r->x, &t); secp256k1_fe_add(&t, &r->x); secp256k1_fe_mul(&r->y, &t, &i); secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_add(&r->y, &h3); } static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) { /* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */ secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t; if (a->infinity) { secp256k1_fe bzinv2, bzinv3; r->infinity = b->infinity; secp256k1_fe_sqr(&bzinv2, bzinv); secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv); secp256k1_fe_mul(&r->x, &b->x, &bzinv2); secp256k1_fe_mul(&r->y, &b->y, &bzinv3); secp256k1_fe_set_int(&r->z, !r->infinity); return; } if (b->infinity) { *r = *a; return; } /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to * secp256k1's isomorphism we can multiply the Z coordinates on both sides * by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1). * This means that (rx,ry,rz) can be calculated as * (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz. * The variable az below holds the modified Z coordinate for a, which is used * for the computation of rx and ry, but not for rz. */ secp256k1_fe_mul(&az, &a->z, bzinv); secp256k1_fe_sqr(&z12, &az); u1 = a->x; secp256k1_fe_normalize_weak(&u1); secp256k1_fe_mul(&u2, &b->x, &z12); s1 = a->y; secp256k1_fe_normalize_weak(&s1); secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az); secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1); if (secp256k1_fe_normalizes_to_zero_var(&h)) { if (secp256k1_fe_normalizes_to_zero_var(&i)) { secp256k1_gej_double_var(r, a, NULL); } else { secp256k1_gej_set_infinity(r); } return; } r->infinity = 0; secp256k1_fe_mul(&r->z, &a->z, &h); secp256k1_fe_sqr(&h2, &h); secp256k1_fe_negate(&h2, &h2, 1); secp256k1_fe_mul(&h3, &h2, &h); secp256k1_fe_mul(&t, &u1, &h2); secp256k1_fe_sqr(&r->x, &i); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_add(&r->x, &t); secp256k1_fe_add(&r->x, &t); secp256k1_fe_add(&t, &r->x); secp256k1_fe_mul(&r->y, &t, &i); secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_add(&r->y, &h3); } #if 0 static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) { /* Operations: 7 mul, 5 sqr, 24 add/cmov/half/mul_int/negate/normalize_weak/normalizes_to_zero */ secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr; secp256k1_fe m_alt, rr_alt; int degenerate; VERIFY_CHECK(!b->infinity); VERIFY_CHECK(a->infinity == 0 || a->infinity == 1); /* In: * Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks. * In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002. * we find as solution for a unified addition/doubling formula: * lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation. * x3 = lambda^2 - (x1 + x2) * 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2). * * Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives: * U1 = X1*Z2^2, U2 = X2*Z1^2 * S1 = Y1*Z2^3, S2 = Y2*Z1^3 * Z = Z1*Z2 * T = U1+U2 * M = S1+S2 * Q = -T*M^2 * R = T^2-U1*U2 * X3 = R^2+Q * Y3 = -(R*(2*X3+Q)+M^4)/2 * Z3 = M*Z * (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.) * * This formula has the benefit of being the same for both addition * of distinct points and doubling. However, it breaks down in the * case that either point is infinity, or that y1 = -y2. We handle * these cases in the following ways: * * - If b is infinity we simply bail by means of a VERIFY_CHECK. * * - If a is infinity, we detect this, and at the end of the * computation replace the result (which will be meaningless, * but we compute to be constant-time) with b.x : b.y : 1. * * - If a = -b, we have y1 = -y2, which is a degenerate case. * But here the answer is infinity, so we simply set the * infinity flag of the result, overriding the computed values * without even needing to cmov. * * - If y1 = -y2 but x1 != x2, which does occur thanks to certain * properties of our curve (specifically, 1 has nontrivial cube * roots in our field, and the curve equation has no x coefficient) * then the answer is not infinity but also not given by the above * equation. In this case, we cmov in place an alternate expression * for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these * expressions for lambda are defined, they are equal, and can be * obtained from each other by multiplication by (y1 + y2)/(y1 + y2) * then substitution of x^3 + 7 for y^2 (using the curve equation). * For all pairs of nonzero points (a, b) at least one is defined, * so this covers everything. */ secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */ u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */ secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */ s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */ secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */ secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */ t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */ m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */ secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */ secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */ secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */ secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */ /* If lambda = R/M = R/0 we have a problem (except in the "trivial" * case that Z = z1z2 = 0, and this is special-cased later on). */ degenerate = secp256k1_fe_normalizes_to_zero(&m); /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2. * This means either x1 == beta*x2 or beta*x1 == x2, where beta is * a nontrivial cube root of one. In either case, an alternate * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2), * so we set R/M equal to this. */ rr_alt = s1; secp256k1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */ secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */ secp256k1_fe_cmov(&rr_alt, &rr, !degenerate); secp256k1_fe_cmov(&m_alt, &m, !degenerate); /* Now Ralt / Malt = lambda and is guaranteed not to be Ralt / 0. * From here on out Ralt and Malt represent the numerator * and denominator of lambda; R and M represent the explicit * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */ secp256k1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */ secp256k1_fe_negate(&q, &t, 2); /* q = -T (3) */ secp256k1_fe_mul(&q, &q, &n); /* q = Q = -T*Malt^2 (1) */ /* These two lines use the observation that either M == Malt or M == 0, * so M^3 * Malt is either Malt^4 (which is computed by squaring), or * zero (which is "computed" by cmov). So the cost is one squaring * versus two multiplications. */ secp256k1_fe_sqr(&n, &n); secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */ secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */ secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Z3 = Malt*Z (1) */ secp256k1_fe_add(&t, &q); /* t = Ralt^2 + Q (2) */ r->x = t; /* r->x = X3 = Ralt^2 + Q (2) */ secp256k1_fe_mul_int(&t, 2); /* t = 2*X3 (4) */ secp256k1_fe_add(&t, &q); /* t = 2*X3 + Q (5) */ secp256k1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*X3 + Q) (1) */ secp256k1_fe_add(&t, &n); /* t = Ralt*(2*X3 + Q) + M^3*Malt (3) */ secp256k1_fe_negate(&r->y, &t, 3); /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (4) */ secp256k1_fe_half(&r->y); /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (3) */ /* In case a->infinity == 1, replace r with (b->x, b->y, 1). */ secp256k1_fe_cmov(&r->x, &b->x, a->infinity); secp256k1_fe_cmov(&r->y, &b->y, a->infinity); secp256k1_fe_cmov(&r->z, &secp256k1_fe_one, a->infinity); /* Set r->infinity if r->z is 0. * * If a->infinity is set, then r->infinity = (r->z == 0) = (1 == 0) = false, * which is correct because the function assumes that b is not infinity. * * Now assume !a->infinity. This implies Z = Z1 != 0. * * Case y1 = -y2: * In this case we could have a = -b, namely if x1 = x2. * We have degenerate = true, r->z = (x1 - x2) * Z. * Then r->infinity = ((x1 - x2)Z == 0) = (x1 == x2) = (a == -b). * * Case y1 != -y2: * In this case, we can't have a = -b. * We have degenerate = false, r->z = (y1 + y2) * Z. * Then r->infinity = ((y1 + y2)Z == 0) = (y1 == -y2) = false. */ r->infinity = secp256k1_fe_normalizes_to_zero(&r->z); } #endif static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) { /* Operations: 4 mul, 1 sqr */ secp256k1_fe zz; VERIFY_CHECK(!secp256k1_fe_is_zero(s)); secp256k1_fe_sqr(&zz, s); secp256k1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */ secp256k1_fe_mul(&r->y, &r->y, &zz); secp256k1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */ secp256k1_fe_mul(&r->z, &r->z, s); /* r->z *= s */ } static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) { secp256k1_fe x, y; VERIFY_CHECK(!a->infinity); x = a->x; secp256k1_fe_normalize_var(&x); y = a->y; secp256k1_fe_normalize_var(&y); secp256k1_fe_to_storage(&r->x, &x); secp256k1_fe_to_storage(&r->y, &y); } static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) { secp256k1_fe_from_storage(&r->x, &a->x); secp256k1_fe_from_storage(&r->y, &a->y); r->infinity = 0; } #if 0 static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) { secp256k1_fe_cmov(&r->x, &a->x, flag); secp256k1_fe_cmov(&r->y, &a->y, flag); secp256k1_fe_cmov(&r->z, &a->z, flag); r->infinity ^= (r->infinity ^ a->infinity) & flag; } static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) { secp256k1_fe_storage_cmov(&r->x, &a->x, flag); secp256k1_fe_storage_cmov(&r->y, &a->y, flag); } static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) { *r = *a; secp256k1_fe_mul(&r->x, &r->x, &secp256k1_const_beta); } #endif static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) { (void)ge; /* The real secp256k1 group has cofactor 1, so the subgroup is the entire curve. */ return 1; } #endif /* SECP256K1_GROUP_IMPL_H */ ================================================ FILE: C/secp256k1/int128.h ================================================ #ifndef SECP256K1_INT128_H #define SECP256K1_INT128_H #include "util.h" #if defined(SECP256K1_WIDEMUL_INT128) # if defined(SECP256K1_INT128_NATIVE) # include "int128_native.h" # elif defined(SECP256K1_INT128_STRUCT) # include "int128_struct.h" # else # error "Please select int128 implementation" # endif /* Construct an unsigned 128-bit value from a high and a low 64-bit value. */ static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo); /* Multiply two unsigned 64-bit values a and b and write the result to r. */ static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b); /* Multiply two unsigned 64-bit values a and b and add the result to r. * The final result is taken modulo 2^128. */ static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b); /* Add an unsigned 64-bit value a to r. * The final result is taken modulo 2^128. */ static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a); /* Unsigned (logical) right shift. * Non-constant time in n. */ static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n); /* Return the low 64-bits of a 128-bit value as an unsigned 64-bit value. */ static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a); /* Return the high 64-bits of a 128-bit value as an unsigned 64-bit value. */ static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a); /* Write an unsigned 64-bit value to r. */ static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a); /* Tests if r is strictly less than to 2^n. * n must be strictly less than 128. */ static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n); /* Construct an signed 128-bit value from a high and a low 64-bit value. */ static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo); /* Multiply two signed 64-bit values a and b and write the result to r. */ static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b); /* Multiply two signed 64-bit values a and b and add the result to r. * Overflow or underflow from the addition is undefined behaviour. */ static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b); /* Compute a*d - b*c from signed 64-bit values and write the result to r. */ static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d); /* Signed (arithmetic) right shift. * Non-constant time in b. */ static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int b); /* Return the input value modulo 2^64. */ static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a); /* Return the value as a signed 64-bit value. * Requires the input to be between INT64_MIN and INT64_MAX. */ static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a); /* Write a signed 64-bit value to r. */ static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a); /* Compare two 128-bit values for equality. */ static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b); /* Tests if r is equal to sign*2^n (sign must be 1 or -1). * n must be strictly less than 127. */ static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign); #endif #endif ================================================ FILE: C/secp256k1/int128_impl.h ================================================ #ifndef SECP256K1_INT128_IMPL_H #define SECP256K1_INT128_IMPL_H #include "util.h" #include "int128.h" #if defined(SECP256K1_WIDEMUL_INT128) # if defined(SECP256K1_INT128_NATIVE) # include "int128_native_impl.h" # elif defined(SECP256K1_INT128_STRUCT) # include "int128_struct_impl.h" # else # error "Please select int128 implementation" # endif #endif #endif ================================================ FILE: C/secp256k1/int128_native.h ================================================ #ifndef SECP256K1_INT128_NATIVE_H #define SECP256K1_INT128_NATIVE_H #include #include "util.h" #if !defined(UINT128_MAX) && defined(__SIZEOF_INT128__) SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t; SECP256K1_GNUC_EXT typedef __int128 int128_t; # define UINT128_MAX ((uint128_t)(-1)) # define INT128_MAX ((int128_t)(UINT128_MAX >> 1)) # define INT128_MIN (-INT128_MAX - 1) /* No (U)INT128_C macros because compilers providing __int128 do not support 128-bit literals. */ #endif typedef uint128_t secp256k1_uint128; typedef int128_t secp256k1_int128; #endif ================================================ FILE: C/secp256k1/int128_native_impl.h ================================================ #ifndef SECP256K1_INT128_NATIVE_IMPL_H #define SECP256K1_INT128_NATIVE_IMPL_H #include "int128.h" static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) { *r = (((uint128_t)hi) << 64) + lo; } static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { *r = (uint128_t)a * b; } static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { *r += (uint128_t)a * b; } static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) { *r += a; } static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) { VERIFY_CHECK(n < 128); *r >>= n; } static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) { return (uint64_t)(*a); } static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) { return (uint64_t)(*a >> 64); } static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) { *r = a; } static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) { VERIFY_CHECK(n < 128); return (*r >> n == 0); } static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) { *r = (secp256k1_int128)((((uint128_t)(uint64_t)hi) << 64) + lo); } static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) { *r = (int128_t)a * b; } static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) { int128_t ab = (int128_t)a * b; VERIFY_CHECK(0 <= ab ? *r <= INT128_MAX - ab : INT128_MIN - ab <= *r); *r += ab; } static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) { int128_t ad = (int128_t)a * d; int128_t bc = (int128_t)b * c; VERIFY_CHECK(0 <= bc ? INT128_MIN + bc <= ad : ad <= INT128_MAX + bc); *r = ad - bc; } static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) { VERIFY_CHECK(n < 128); *r >>= n; } static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a) { return (uint64_t)*a; } static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) { VERIFY_CHECK(INT64_MIN <= *a && *a <= INT64_MAX); return (int64_t)*a; } static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) { *r = a; } static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) { return *a == *b; } static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign) { VERIFY_CHECK(n < 127); VERIFY_CHECK(sign == 1 || sign == -1); return (*r == (int128_t)((uint128_t)sign << n)); } #endif ================================================ FILE: C/secp256k1/int128_struct.h ================================================ #ifndef SECP256K1_INT128_STRUCT_H #define SECP256K1_INT128_STRUCT_H #include #include "util.h" typedef struct secp256k1_uint128 { uint64_t lo; uint64_t hi; } secp256k1_uint128; typedef secp256k1_uint128 secp256k1_int128; #endif ================================================ FILE: C/secp256k1/int128_struct_impl.h ================================================ #ifndef SECP256K1_INT128_STRUCT_IMPL_H #define SECP256K1_INT128_STRUCT_IMPL_H #include "int128.h" #if defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) /* MSVC */ # include # if defined(_M_ARM64) || defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE) /* On ARM64 MSVC, use __(u)mulh for the upper half of 64x64 multiplications. (Define SECP256K1_MSVC_MULH_TEST_OVERRIDE to test this code path on X64, which supports both __(u)mulh and _umul128.) */ # if defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE) # pragma message(__FILE__ ": SECP256K1_MSVC_MULH_TEST_OVERRIDE is defined, forcing use of __(u)mulh.") # endif static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) { *hi = __umulh(a, b); return a * b; } static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) { *hi = __mulh(a, b); return (uint64_t)a * (uint64_t)b; } # else /* On x84_64 MSVC, use native _(u)mul128 for 64x64->128 multiplications. */ # define secp256k1_umul128 _umul128 static SECP256K1_INLINE uint64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) { return (uint64_t)_mul128(a, b, hi); } # endif #else /* On other systems, emulate 64x64->128 multiplications using 32x32->64 multiplications. */ static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) { uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b; uint64_t lh = (uint32_t)a * (b >> 32); uint64_t hl = (a >> 32) * (uint32_t)b; uint64_t hh = (a >> 32) * (b >> 32); uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl; *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32); return (mid34 << 32) + (uint32_t)ll; } static SECP256K1_INLINE uint64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) { uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b; int64_t lh = (uint32_t)a * (b >> 32); int64_t hl = (a >> 32) * (uint32_t)b; int64_t hh = (a >> 32) * (b >> 32); uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl; *hi = hh + (lh >> 32) + (hl >> 32) + (int64_t)(mid34 >> 32); return (mid34 << 32) + (uint32_t)ll; } #endif static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) { r->hi = hi; r->lo = lo; } static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { r->lo = secp256k1_umul128(a, b, &r->hi); } static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) { uint64_t lo, hi; lo = secp256k1_umul128(a, b, &hi); r->lo += lo; r->hi += hi + (r->lo < lo); } static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) { r->lo += a; r->hi += r->lo < a; } /* Unsigned (logical) right shift. * Non-constant time in n. */ static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) { VERIFY_CHECK(n < 128); if (n >= 64) { r->lo = r->hi >> (n-64); r->hi = 0; } else if (n > 0) { r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n; r->hi >>= n; } } static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) { return a->lo; } static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) { return a->hi; } static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) { r->hi = 0; r->lo = a; } static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) { VERIFY_CHECK(n < 128); return n >= 64 ? r->hi >> (n - 64) == 0 : r->hi == 0 && r->lo >> n == 0; } static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) { r->hi = (uint64_t)hi; r->lo = lo; } static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) { int64_t hi; r->lo = secp256k1_mul128(a, b, &hi); r->hi = (uint64_t)hi; } static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) { int64_t hi; uint64_t lo = secp256k1_mul128(a, b, &hi); r->lo += lo; hi += r->lo < lo; /* Verify no overflow. * If r represents a positive value (the sign bit is not set) and the value we are adding is a positive value (the sign bit is not set), * then we require that the resulting value also be positive (the sign bit is not set). * Note that (X <= Y) means (X implies Y) when X and Y are boolean values (i.e. 0 or 1). */ VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi <= 0x7fffffffffffffffu)); /* Verify no underflow. * If r represents a negative value (the sign bit is set) and the value we are adding is a negative value (the sign bit is set), * then we require that the resulting value also be negative (the sign bit is set). */ VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi > 0x7fffffffffffffffu)); r->hi += (uint64_t)hi; } static SECP256K1_INLINE void secp256k1_i128_dissip_mul(secp256k1_int128 *r, int64_t a, int64_t b) { int64_t hi; uint64_t lo = secp256k1_mul128(a, b, &hi); hi += r->lo < lo; /* Verify no overflow. * If r represents a positive value (the sign bit is not set) and the value we are subtracting is a negative value (the sign bit is set), * then we require that the resulting value also be positive (the sign bit is not set). */ VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi <= 0x7fffffffffffffffu)); /* Verify no underflow. * If r represents a negative value (the sign bit is set) and the value we are subtracting is a positive value (the sign sign bit is not set), * then we require that the resulting value also be negative (the sign bit is set). */ VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi > 0x7fffffffffffffffu)); r->hi -= (uint64_t)hi; r->lo -= lo; } static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) { secp256k1_i128_mul(r, a, d); secp256k1_i128_dissip_mul(r, b, c); } /* Signed (arithmetic) right shift. * Non-constant time in n. */ static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) { VERIFY_CHECK(n < 128); if (n >= 64) { r->lo = (uint64_t)((int64_t)(r->hi) >> (n-64)); r->hi = (uint64_t)((int64_t)(r->hi) >> 63); } else if (n > 0) { r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n; r->hi = (uint64_t)((int64_t)(r->hi) >> n); } } static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a) { return a->lo; } static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) { /* Verify that a represents a 64 bit signed value by checking that the high bits are a sign extension of the low bits. */ VERIFY_CHECK(a->hi == -(a->lo >> 63)); return (int64_t)secp256k1_i128_to_u64(a); } static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) { r->hi = (uint64_t)(a >> 63); r->lo = (uint64_t)a; } static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) { return a->hi == b->hi && a->lo == b->lo; } static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign) { VERIFY_CHECK(n < 127); VERIFY_CHECK(sign == 1 || sign == -1); return n >= 64 ? r->hi == (uint64_t)sign << (n - 64) && r->lo == 0 : r->hi == (uint64_t)((sign - 1) >> 1) && r->lo == (uint64_t)sign << n; } #endif ================================================ FILE: C/secp256k1/modinv64.h ================================================ /*********************************************************************** * Copyright (c) 2020 Peter Dettman * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ #ifndef SECP256K1_MODINV64_H #define SECP256K1_MODINV64_H #include "util.h" #ifndef SECP256K1_WIDEMUL_INT128 #error "modinv64 requires 128-bit wide multiplication support" #endif /* A signed 62-bit limb representation of integers. * * Its value is sum(v[i] * 2^(62*i), i=0..4). */ typedef struct secp256k1_modinv64_signed62 { int64_t v[5]; } secp256k1_modinv64_signed62; typedef struct secp256k1_modinv64_modinfo { /* The modulus in signed62 notation, must be odd and in [3, 2^256]. */ secp256k1_modinv64_signed62 modulus; /* modulus^{-1} mod 2^62 */ uint64_t modulus_inv62; } secp256k1_modinv64_modinfo; static inline void secp256k1_modinv64_signed62_assign(secp256k1_modinv64_signed62 *dst, const secp256k1_modinv64_signed62 *src) { #ifdef VST dst->v[0] = src->v[0]; dst->v[1] = src->v[1]; dst->v[2] = src->v[2]; dst->v[3] = src->v[3]; dst->v[4] = src->v[4]; #else *dst = *src; #endif } /* Replace x with its modular inverse mod modinfo->modulus. x must be in range [0, modulus). * If x is zero, the result will be zero as well. If not, the inverse must exist (i.e., the gcd of * x and modulus must be 1). These rules are automatically satisfied if the modulus is prime. * * On output, all of x's limbs will be in [0, 2^62). */ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); #if 0 /* Same as secp256k1_modinv64_var, but constant time in x (not in the modulus). */ static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); /* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus * cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result * cannot be computed. */ static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); #endif #endif /* SECP256K1_MODINV64_H */ ================================================ FILE: C/secp256k1/modinv64_impl.h ================================================ /*********************************************************************** * Copyright (c) 2020 Peter Dettman * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* **********************************************************************/ #ifndef SECP256K1_MODINV64_IMPL_H #define SECP256K1_MODINV64_IMPL_H #include "int128.h" #include "modinv64.h" /* This file implements modular inversion based on the paper "Fast constant-time gcd computation and * modular inversion" by Daniel J. Bernstein and Bo-Yin Yang. * * For an explanation of the algorithm, see doc/safegcd_implementation.md. This file contains an * implementation for N=62, using 62-bit signed limbs represented as int64_t. */ /* Data type for transition matrices (see section 3 of explanation). * * t = [ u v ] * [ q r ] */ typedef struct secp256k1_modinv64_trans2x2 { int64_t u, v, q, r; } secp256k1_modinv64_trans2x2; #ifdef VERIFY /* Helper function to compute the absolute value of an int64_t. * (we don't use abs/labs/llabs as it depends on the int sizes). */ static int64_t secp256k1_modinv64_abs(int64_t v) { VERIFY_CHECK(v > INT64_MIN); if (v < 0) return -v; return v; } static const secp256k1_modinv64_signed62 SECP256K1_SIGNED62_ONE = {{1}}; /* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^62). */ static void secp256k1_modinv64_mul_62(secp256k1_modinv64_signed62 *r, const secp256k1_modinv64_signed62 *a, int alen, int64_t factor) { const uint64_t M62 = UINT64_MAX >> 2; secp256k1_int128 c, d; int i; secp256k1_i128_from_i64(&c, 0); for (i = 0; i < 4; ++i) { if (i < alen) secp256k1_i128_accum_mul(&c, a->v[i], factor); r->v[i] = secp256k1_i128_to_u64(&c) & M62; secp256k1_i128_rshift(&c, 62); } if (4 < alen) secp256k1_i128_accum_mul(&c, a->v[4], factor); secp256k1_i128_from_i64(&d, secp256k1_i128_to_i64(&c)); VERIFY_CHECK(secp256k1_i128_eq_var(&c, &d)); r->v[4] = secp256k1_i128_to_i64(&c); } /* Return -1 for ab*factor. A has alen limbs; b has 5. */ static int secp256k1_modinv64_mul_cmp_62(const secp256k1_modinv64_signed62 *a, int alen, const secp256k1_modinv64_signed62 *b, int64_t factor) { int i; secp256k1_modinv64_signed62 am, bm; secp256k1_modinv64_mul_62(&am, a, alen, 1); /* Normalize all but the top limb of a. */ secp256k1_modinv64_mul_62(&bm, b, 5, factor); for (i = 0; i < 4; ++i) { /* Verify that all but the top limb of a and b are normalized. */ VERIFY_CHECK(am.v[i] >> 62 == 0); VERIFY_CHECK(bm.v[i] >> 62 == 0); } for (i = 4; i >= 0; --i) { if (am.v[i] < bm.v[i]) return -1; if (am.v[i] > bm.v[i]) return 1; } return 0; } /* Check if the determinant of t is equal to 1 << n. If abs, check if |det t| == 1 << n. */ static int secp256k1_modinv64_det_check_pow2(const secp256k1_modinv64_trans2x2 *t, unsigned int n, int abs) { secp256k1_int128 a; secp256k1_i128_det(&a, t->u, t->v, t->q, t->r); if (secp256k1_i128_check_pow2(&a, n, 1)) return 1; if (abs && secp256k1_i128_check_pow2(&a, n, -1)) return 1; return 0; } #endif /* Take as input a signed62 number in range (-2*modulus,modulus), and add a multiple of the modulus * to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the * process. The input must have limbs in range (-2^62,2^62). The output will have limbs in range * [0,2^62). */ static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int64_t sign, const secp256k1_modinv64_modinfo *modinfo) { const int64_t M62 = (int64_t)(UINT64_MAX >> 2); int64_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4]; int64_t cond_add, cond_negate; #ifdef VERIFY /* Verify that all limbs are in range (-2^62,2^62). */ int i; for (i = 0; i < 5; ++i) { VERIFY_CHECK(r->v[i] >= -M62); VERIFY_CHECK(r->v[i] <= M62); } VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, -2) > 0); /* r > -2*modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 1) < 0); /* r < modulus */ #endif /* In a first step, add the modulus if the input is negative, and then negate if requested. * This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input * limbs are in range (-2^62,2^62), this cannot overflow an int64_t. Note that the right * shifts below are signed sign-extending shifts (see assumptions.h for tests that that is * indeed the behavior of the right shift operator). */ cond_add = r4 >> 63; r0 += modinfo->modulus.v[0] & cond_add; r1 += modinfo->modulus.v[1] & cond_add; r2 += modinfo->modulus.v[2] & cond_add; r3 += modinfo->modulus.v[3] & cond_add; r4 += modinfo->modulus.v[4] & cond_add; cond_negate = sign >> 63; r0 = (r0 ^ cond_negate) - cond_negate; r1 = (r1 ^ cond_negate) - cond_negate; r2 = (r2 ^ cond_negate) - cond_negate; r3 = (r3 ^ cond_negate) - cond_negate; r4 = (r4 ^ cond_negate) - cond_negate; /* Propagate the top bits, to bring limbs back to range (-2^62,2^62). */ r1 += r0 >> 62; r0 &= M62; r2 += r1 >> 62; r1 &= M62; r3 += r2 >> 62; r2 &= M62; r4 += r3 >> 62; r3 &= M62; /* In a second step add the modulus again if the result is still negative, bringing * r to range [0,modulus). */ cond_add = r4 >> 63; r0 += modinfo->modulus.v[0] & cond_add; r1 += modinfo->modulus.v[1] & cond_add; r2 += modinfo->modulus.v[2] & cond_add; r3 += modinfo->modulus.v[3] & cond_add; r4 += modinfo->modulus.v[4] & cond_add; /* And propagate again. */ r1 += r0 >> 62; r0 &= M62; r2 += r1 >> 62; r1 &= M62; r3 += r2 >> 62; r2 &= M62; r4 += r3 >> 62; r3 &= M62; r->v[0] = r0; r->v[1] = r1; r->v[2] = r2; r->v[3] = r3; r->v[4] = r4; #ifdef VERIFY VERIFY_CHECK(r0 >> 62 == 0); VERIFY_CHECK(r1 >> 62 == 0); VERIFY_CHECK(r2 >> 62 == 0); VERIFY_CHECK(r3 >> 62 == 0); VERIFY_CHECK(r4 >> 62 == 0); VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 0) >= 0); /* r >= 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 1) < 0); /* r < modulus */ #endif } #if 0 /* Compute the transition matrix and eta for 59 divsteps (where zeta=-(delta+1/2)). * Note that the transformation matrix is scaled by 2^62 and not 2^59. * * Input: zeta: initial zeta * f0: bottom limb of initial f * g0: bottom limb of initial g * Output: t: transition matrix * Return: final zeta * * Implements the divsteps_n_matrix function from the explanation. */ static int64_t secp256k1_modinv64_divsteps_59(int64_t zeta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t) { /* u,v,q,r are the elements of the transformation matrix being built up, * starting with the identity matrix times 8 (because the caller expects * a result scaled by 2^62). Semantically they are signed integers * in range [-2^62,2^62], but here represented as unsigned mod 2^64. This * permits left shifting (which is UB for negative numbers). The range * being inside [-2^63,2^63) means that casting to signed works correctly. */ uint64_t u = 8, v = 0, q = 0, r = 8; uint64_t c1, c2, f = f0, g = g0, x, y, z; int i; for (i = 3; i < 62; ++i) { VERIFY_CHECK((f & 1) == 1); /* f must always be odd */ VERIFY_CHECK((u * f0 + v * g0) == f << i); VERIFY_CHECK((q * f0 + r * g0) == g << i); /* Compute conditional masks for (zeta < 0) and for (g & 1). */ c1 = zeta >> 63; c2 = -(g & 1); /* Compute x,y,z, conditionally negated versions of f,u,v. */ x = (f ^ c1) - c1; y = (u ^ c1) - c1; z = (v ^ c1) - c1; /* Conditionally add x,y,z to g,q,r. */ g += x & c2; q += y & c2; r += z & c2; /* In what follows, c1 is a condition mask for (zeta < 0) and (g & 1). */ c1 &= c2; /* Conditionally change zeta into -zeta-2 or zeta-1. */ zeta = (zeta ^ c1) - 1; /* Conditionally add g,q,r to f,u,v. */ f += g & c1; u += q & c1; v += r & c1; /* Shifts */ g >>= 1; u <<= 1; v <<= 1; /* Bounds on zeta that follow from the bounds on iteration count (max 10*59 divsteps). */ VERIFY_CHECK(zeta >= -591 && zeta <= 591); } /* Return data in t and return value. */ t->u = (int64_t)u; t->v = (int64_t)v; t->q = (int64_t)q; t->r = (int64_t)r; #ifdef VERIFY /* The determinant of t must be a power of two. This guarantees that multiplication with t * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which * will be divided out again). As each divstep's individual matrix has determinant 2, the * aggregate of 59 of them will have determinant 2^59. Multiplying with the initial * 8*identity (which has determinant 2^6) means the overall outputs has determinant * 2^65. */ VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 65, 0)); #endif return zeta; } #endif /* Compute the transition matrix and eta for 62 divsteps (variable time, eta=-delta). * * Input: eta: initial eta * f0: bottom limb of initial f * g0: bottom limb of initial g * Output: t: transition matrix * Return: final eta * * Implements the divsteps_n_matrix_var function from the explanation. */ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t) { /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */ uint64_t u = 1, v = 0, q = 0, r = 1; uint64_t f = f0, g = g0, m; uint32_t w; int i = 62, limit, zeros; for (;;) { /* Use a sentinel bit to count zeros only up to i. */ zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i)); /* Perform zeros divsteps at once; they all just divide g by two. */ g >>= zeros; u <<= zeros; v <<= zeros; eta -= zeros; i -= zeros; /* We're done once we've done 62 divsteps. */ if (i == 0) break; VERIFY_CHECK((f & 1) == 1); VERIFY_CHECK((g & 1) == 1); VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i)); VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i)); /* Bounds on eta that follow from the bounds on iteration count (max 12*62 divsteps). */ VERIFY_CHECK(eta >= -745 && eta <= 745); /* If eta is negative, negate it and replace f,g with g,-f. */ if (eta < 0) { uint64_t tmp; eta = -eta; tmp = f; f = g; g = -tmp; tmp = u; u = q; q = -tmp; tmp = v; v = r; r = -tmp; /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled * out (as we'd be done before that point), and no more than eta+1 can be done as its * sign will flip again once that happens. */ limit = ((int)eta + 1) > i ? i : ((int)eta + 1); VERIFY_CHECK(limit > 0 && limit <= 62); /* m is a mask for the bottom min(limit, 6) bits. */ m = (UINT64_MAX >> (64 - limit)) & 63U; /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6) * bits. */ w = (f * g * (f * f - 2)) & m; } else { /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as * eta tends to be smaller here. */ limit = ((int)eta + 1) > i ? i : ((int)eta + 1); VERIFY_CHECK(limit > 0 && limit <= 62); /* m is a mask for the bottom min(limit, 4) bits. */ m = (UINT64_MAX >> (64 - limit)) & 15U; /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4) * bits. */ w = f + (((f + 1) & 4) << 1); w = (-w * g) & m; } g += f * w; q += u * w; r += v * w; VERIFY_CHECK((g & m) == 0); } /* Return data in t and return value. */ t->u = (int64_t)u; t->v = (int64_t)v; t->q = (int64_t)q; t->r = (int64_t)r; #ifdef VERIFY /* The determinant of t must be a power of two. This guarantees that multiplication with t * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which * will be divided out again). As each divstep's individual matrix has determinant 2, the * aggregate of 62 of them will have determinant 2^62. */ VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62, 0)); #endif return eta; } #if 0 /* Compute the transition matrix and eta for 62 posdivsteps (variable time, eta=-delta), and keeps track * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^64 rather than 2^62, because * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2). * * Input: eta: initial eta * f0: bottom limb of initial f * g0: bottom limb of initial g * Output: t: transition matrix * Input/Output: (*jacp & 1) is bitflipped if and only if the Jacobi symbol of (f | g) changes sign * by applying the returned transformation matrix to it. The other bits of *jacp may * change, but are meaningless. * Return: final eta */ static int64_t secp256k1_modinv64_posdivsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t, int *jacp) { /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */ uint64_t u = 1, v = 0, q = 0, r = 1; uint64_t f = f0, g = g0, m; uint32_t w; int i = 62, limit, zeros; int jac = *jacp; for (;;) { /* Use a sentinel bit to count zeros only up to i. */ zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i)); /* Perform zeros divsteps at once; they all just divide g by two. */ g >>= zeros; u <<= zeros; v <<= zeros; eta -= zeros; i -= zeros; /* Update the bottom bit of jac: when dividing g by an odd power of 2, * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */ jac ^= (zeros & ((f >> 1) ^ (f >> 2))); /* We're done once we've done 62 posdivsteps. */ if (i == 0) break; VERIFY_CHECK((f & 1) == 1); VERIFY_CHECK((g & 1) == 1); VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i)); VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i)); /* If eta is negative, negate it and replace f,g with g,f. */ if (eta < 0) { uint64_t tmp; eta = -eta; tmp = f; f = g; g = tmp; tmp = u; u = q; q = tmp; tmp = v; v = r; r = tmp; /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign * if both f and g are 3 mod 4. */ jac ^= ((f & g) >> 1); /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled * out (as we'd be done before that point), and no more than eta+1 can be done as its * sign will flip again once that happens. */ limit = ((int)eta + 1) > i ? i : ((int)eta + 1); VERIFY_CHECK(limit > 0 && limit <= 62); /* m is a mask for the bottom min(limit, 6) bits. */ m = (UINT64_MAX >> (64 - limit)) & 63U; /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6) * bits. */ w = (f * g * (f * f - 2)) & m; } else { /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as * eta tends to be smaller here. */ limit = ((int)eta + 1) > i ? i : ((int)eta + 1); VERIFY_CHECK(limit > 0 && limit <= 62); /* m is a mask for the bottom min(limit, 4) bits. */ m = (UINT64_MAX >> (64 - limit)) & 15U; /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4) * bits. */ w = f + (((f + 1) & 4) << 1); w = (-w * g) & m; } g += f * w; q += u * w; r += v * w; VERIFY_CHECK((g & m) == 0); } /* Return data in t and return value. */ t->u = (int64_t)u; t->v = (int64_t)v; t->q = (int64_t)q; t->r = (int64_t)r; #ifdef VERIFY /* The determinant of t must be a power of two. This guarantees that multiplication with t * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which * will be divided out again). As each divstep's individual matrix has determinant 2 or -2, * the aggregate of 62 of them will have determinant 2^62 or -2^62. */ VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62, 1)); #endif *jacp = jac; return eta; } #endif /* Compute (t/2^62) * [d, e] mod modulus, where t is a transition matrix scaled by 2^62. * * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range * (-2^62,2^62). * * This implements the update_de function from the explanation. */ static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp256k1_modinv64_signed62 *e, const secp256k1_modinv64_trans2x2 *t, const secp256k1_modinv64_modinfo* modinfo) { const uint64_t M62 = UINT64_MAX >> 2; const int64_t d0 = d->v[0], d1 = d->v[1], d2 = d->v[2], d3 = d->v[3], d4 = d->v[4]; const int64_t e0 = e->v[0], e1 = e->v[1], e2 = e->v[2], e3 = e->v[3], e4 = e->v[4]; const int64_t u = t->u, v = t->v, q = t->q, r = t->r; int64_t md, me, sd, se; secp256k1_int128 cd, ce; #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0); /* d < modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, -2) > 0); /* e > -2*modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, 1) < 0); /* e < modulus */ VERIFY_CHECK(secp256k1_modinv64_abs(u) <= (((int64_t)1 << 62) - secp256k1_modinv64_abs(v))); /* |u|+|v| <= 2^62 */ VERIFY_CHECK(secp256k1_modinv64_abs(q) <= (((int64_t)1 << 62) - secp256k1_modinv64_abs(r))); /* |q|+|r| <= 2^62 */ #endif /* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */ sd = d4 >> 63; se = e4 >> 63; md = (u & sd) + (v & se); me = (q & sd) + (r & se); /* Begin computing t*[d,e]. */ secp256k1_i128_mul(&cd, u, d0); secp256k1_i128_accum_mul(&cd, v, e0); secp256k1_i128_mul(&ce, q, d0); secp256k1_i128_accum_mul(&ce, r, e0); /* Correct md,me so that t*[d,e]+modulus*[md,me] has 62 zero bottom bits. */ md -= (modinfo->modulus_inv62 * secp256k1_i128_to_u64(&cd) + md) & M62; me -= (modinfo->modulus_inv62 * secp256k1_i128_to_u64(&ce) + me) & M62; /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */ secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[0], md); secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[0], me); /* Verify that the low 62 bits of the computation are indeed zero, and then throw them away. */ VERIFY_CHECK((secp256k1_i128_to_u64(&cd) & M62) == 0); secp256k1_i128_rshift(&cd, 62); VERIFY_CHECK((secp256k1_i128_to_u64(&ce) & M62) == 0); secp256k1_i128_rshift(&ce, 62); /* Compute limb 1 of t*[d,e]+modulus*[md,me], and store it as output limb 0 (= down shift). */ secp256k1_i128_accum_mul(&cd, u, d1); secp256k1_i128_accum_mul(&cd, v, e1); secp256k1_i128_accum_mul(&ce, q, d1); secp256k1_i128_accum_mul(&ce, r, e1); if (modinfo->modulus.v[1]) { /* Optimize for the case where limb of modulus is zero. */ secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[1], md); secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[1], me); } d->v[0] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); e->v[0] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); /* Compute limb 2 of t*[d,e]+modulus*[md,me], and store it as output limb 1. */ secp256k1_i128_accum_mul(&cd, u, d2); secp256k1_i128_accum_mul(&cd, v, e2); secp256k1_i128_accum_mul(&ce, q, d2); secp256k1_i128_accum_mul(&ce, r, e2); if (modinfo->modulus.v[2]) { /* Optimize for the case where limb of modulus is zero. */ secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[2], md); secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[2], me); } d->v[1] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); e->v[1] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); /* Compute limb 3 of t*[d,e]+modulus*[md,me], and store it as output limb 2. */ secp256k1_i128_accum_mul(&cd, u, d3); secp256k1_i128_accum_mul(&cd, v, e3); secp256k1_i128_accum_mul(&ce, q, d3); secp256k1_i128_accum_mul(&ce, r, e3); if (modinfo->modulus.v[3]) { /* Optimize for the case where limb of modulus is zero. */ secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[3], md); secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[3], me); } d->v[2] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); e->v[2] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); /* Compute limb 4 of t*[d,e]+modulus*[md,me], and store it as output limb 3. */ secp256k1_i128_accum_mul(&cd, u, d4); secp256k1_i128_accum_mul(&cd, v, e4); secp256k1_i128_accum_mul(&ce, q, d4); secp256k1_i128_accum_mul(&ce, r, e4); secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[4], md); secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[4], me); d->v[3] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62); e->v[3] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62); /* What remains is limb 5 of t*[d,e]+modulus*[md,me]; store it as output limb 4. */ d->v[4] = secp256k1_i128_to_i64(&cd); e->v[4] = secp256k1_i128_to_i64(&ce); #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0); /* d < modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, -2) > 0); /* e > -2*modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, 1) < 0); /* e < modulus */ #endif } #if 0 /* Compute (t/2^62) * [f, g], where t is a transition matrix scaled by 2^62. * * This implements the update_fg function from the explanation. */ static void secp256k1_modinv64_update_fg_62(secp256k1_modinv64_signed62 *f, secp256k1_modinv64_signed62 *g, const secp256k1_modinv64_trans2x2 *t) { const uint64_t M62 = UINT64_MAX >> 2; const int64_t f0 = f->v[0], f1 = f->v[1], f2 = f->v[2], f3 = f->v[3], f4 = f->v[4]; const int64_t g0 = g->v[0], g1 = g->v[1], g2 = g->v[2], g3 = g->v[3], g4 = g->v[4]; const int64_t u = t->u, v = t->v, q = t->q, r = t->r; secp256k1_int128 cf, cg; /* Start computing t*[f,g]. */ secp256k1_i128_mul(&cf, u, f0); secp256k1_i128_accum_mul(&cf, v, g0); secp256k1_i128_mul(&cg, q, f0); secp256k1_i128_accum_mul(&cg, r, g0); /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ VERIFY_CHECK((secp256k1_i128_to_u64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62); VERIFY_CHECK((secp256k1_i128_to_u64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62); /* Compute limb 1 of t*[f,g], and store it as output limb 0 (= down shift). */ secp256k1_i128_accum_mul(&cf, u, f1); secp256k1_i128_accum_mul(&cf, v, g1); secp256k1_i128_accum_mul(&cg, q, f1); secp256k1_i128_accum_mul(&cg, r, g1); f->v[0] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); g->v[0] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); /* Compute limb 2 of t*[f,g], and store it as output limb 1. */ secp256k1_i128_accum_mul(&cf, u, f2); secp256k1_i128_accum_mul(&cf, v, g2); secp256k1_i128_accum_mul(&cg, q, f2); secp256k1_i128_accum_mul(&cg, r, g2); f->v[1] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); g->v[1] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); /* Compute limb 3 of t*[f,g], and store it as output limb 2. */ secp256k1_i128_accum_mul(&cf, u, f3); secp256k1_i128_accum_mul(&cf, v, g3); secp256k1_i128_accum_mul(&cg, q, f3); secp256k1_i128_accum_mul(&cg, r, g3); f->v[2] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); g->v[2] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); /* Compute limb 4 of t*[f,g], and store it as output limb 3. */ secp256k1_i128_accum_mul(&cf, u, f4); secp256k1_i128_accum_mul(&cf, v, g4); secp256k1_i128_accum_mul(&cg, q, f4); secp256k1_i128_accum_mul(&cg, r, g4); f->v[3] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); g->v[3] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); /* What remains is limb 5 of t*[f,g]; store it as output limb 4. */ f->v[4] = secp256k1_i128_to_i64(&cf); g->v[4] = secp256k1_i128_to_i64(&cg); } #endif /* Compute (t/2^62) * [f, g], where t is a transition matrix for 62 divsteps. * * Version that operates on a variable number of limbs in f and g. * * This implements the update_fg function from the explanation. */ static void secp256k1_modinv64_update_fg_62_var(int len, secp256k1_modinv64_signed62 *f, secp256k1_modinv64_signed62 *g, const secp256k1_modinv64_trans2x2 *t) { const uint64_t M62 = UINT64_MAX >> 2; const int64_t u = t->u, v = t->v, q = t->q, r = t->r; int64_t fi, gi; secp256k1_int128 cf, cg; int i; VERIFY_CHECK(len > 0); /* Start computing t*[f,g]. */ fi = f->v[0]; gi = g->v[0]; secp256k1_i128_mul(&cf, u, fi); secp256k1_i128_accum_mul(&cf, v, gi); secp256k1_i128_mul(&cg, q, fi); secp256k1_i128_accum_mul(&cg, r, gi); /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */ VERIFY_CHECK((secp256k1_i128_to_u64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62); VERIFY_CHECK((secp256k1_i128_to_u64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62); /* Now iteratively compute limb i=1..len of t*[f,g], and store them in output limb i-1 (shifting * down by 62 bits). */ for (i = 1; i < len; ++i) { fi = f->v[i]; gi = g->v[i]; secp256k1_i128_accum_mul(&cf, u, fi); secp256k1_i128_accum_mul(&cf, v, gi); secp256k1_i128_accum_mul(&cg, q, fi); secp256k1_i128_accum_mul(&cg, r, gi); f->v[i - 1] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62); g->v[i - 1] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62); } /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */ f->v[len - 1] = secp256k1_i128_to_i64(&cf); g->v[len - 1] = secp256k1_i128_to_i64(&cg); } #if 0 /* Compute the inverse of x modulo modinfo->modulus, and replace x with it (constant time in x). */ static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { /* Start with d=0, e=1, f=modulus, g=x, zeta=-1. */ secp256k1_modinv64_signed62 d = {{0, 0, 0, 0, 0}}; secp256k1_modinv64_signed62 e = {{1, 0, 0, 0, 0}}; secp256k1_modinv64_signed62 f = modinfo->modulus; secp256k1_modinv64_signed62 g = *x; int i; int64_t zeta = -1; /* zeta = -(delta+1/2); delta starts at 1/2. */ /* Do 10 iterations of 59 divsteps each = 590 divsteps. This suffices for 256-bit inputs. */ for (i = 0; i < 10; ++i) { /* Compute transition matrix and new zeta after 59 divsteps. */ secp256k1_modinv64_trans2x2 t; zeta = secp256k1_modinv64_divsteps_59(zeta, f.v[0], g.v[0], &t); /* Update d,e using that transition matrix. */ secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo); /* Update f,g using that transition matrix. */ #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) > 0); /* f > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) <= 0); /* f <= modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, -1) > 0); /* g > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, 1) < 0); /* g < modulus */ #endif secp256k1_modinv64_update_fg_62(&f, &g, &t); #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) > 0); /* f > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) <= 0); /* f <= modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, -1) > 0); /* g > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, 1) < 0); /* g < modulus */ #endif } /* At this point sufficient iterations have been performed that g must have reached 0 * and (if g was not originally 0) f must now equal +/- GCD of the initial f, g * values i.e. +/- 1, and d now contains +/- the modular inverse. */ #ifdef VERIFY /* g == 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &SECP256K1_SIGNED62_ONE, 0) == 0); /* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &SECP256K1_SIGNED62_ONE, -1) == 0 || secp256k1_modinv64_mul_cmp_62(&f, 5, &SECP256K1_SIGNED62_ONE, 1) == 0 || (secp256k1_modinv64_mul_cmp_62(x, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && secp256k1_modinv64_mul_cmp_62(&d, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && (secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) == 0 || secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) == 0))); #endif /* Optionally negate d, normalize to [0,modulus), and return it. */ secp256k1_modinv64_normalize_62(&d, f.v[4], modinfo); *x = d; } #endif /* Compute the inverse of x modulo modinfo->modulus, and replace x with it (variable time). */ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { /* Start with d=0, e=1, f=modulus, g=x, eta=-1. */ secp256k1_modinv64_signed62 d = {{0, 0, 0, 0, 0}}; secp256k1_modinv64_signed62 e = {{1, 0, 0, 0, 0}}; secp256k1_modinv64_signed62 f, g; secp256k1_modinv64_signed62_assign(&(f), &(modinfo->modulus)); secp256k1_modinv64_signed62_assign(&(g), &(*x)); #ifdef VERIFY int i = 0; #endif int j, len = 5; int64_t eta = -1; /* eta = -delta; delta is initially 1 */ int64_t cond, fn, gn; /* Do iterations of 62 divsteps each until g=0. */ while (1) { /* Compute transition matrix and new eta after 62 divsteps. */ secp256k1_modinv64_trans2x2 t; eta = secp256k1_modinv64_divsteps_62_var(eta, f.v[0], g.v[0], &t); /* Update d,e using that transition matrix. */ secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo); /* Update f,g using that transition matrix. */ #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ #endif secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t); /* If the bottom limb of g is zero, there is a chance that g=0. */ if (g.v[0] == 0) { cond = 0; /* Check if the other limbs are also 0. */ for (j = 1; j < len; ++j) { cond |= g.v[j]; } /* If so, we're done. */ if (cond == 0) break; } /* Determine if len>1 and limb (len-1) of both f and g is 0 or -1. */ fn = f.v[len - 1]; gn = g.v[len - 1]; cond = ((int64_t)len - 2) >> 63; cond |= fn ^ (fn >> 63); cond |= gn ^ (gn >> 63); /* If so, reduce length, propagating the sign of f and g's top limb into the one below. */ if (cond == 0) { f.v[len - 2] |= (uint64_t)fn << 62; g.v[len - 2] |= (uint64_t)gn << 62; --len; } #ifdef VERIFY VERIFY_CHECK(++i < 12); /* We should never need more than 12*62 = 744 divsteps */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ #endif } /* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of * the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */ #ifdef VERIFY /* g == 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &SECP256K1_SIGNED62_ONE, 0) == 0); /* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &SECP256K1_SIGNED62_ONE, -1) == 0 || secp256k1_modinv64_mul_cmp_62(&f, len, &SECP256K1_SIGNED62_ONE, 1) == 0 || (secp256k1_modinv64_mul_cmp_62(x, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && secp256k1_modinv64_mul_cmp_62(&d, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 && (secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) == 0 || secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) == 0))); #endif /* Optionally negate d, normalize to [0,modulus), and return it. */ secp256k1_modinv64_normalize_62(&d, f.v[len - 1], modinfo); secp256k1_modinv64_signed62_assign(&(*x), &(d)); } #if 0 /* Do up to 25 iterations of 62 posdivsteps (up to 1550 steps; more is extremely rare) each until f=1. * In VERIFY mode use a lower number of iterations (744, close to the median 756), so failure actually occurs. */ #ifdef VERIFY #define JACOBI64_ITERATIONS 12 #else #define JACOBI64_ITERATIONS 25 #endif /* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1. */ static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { /* Start with f=modulus, g=x, eta=-1. */ secp256k1_modinv64_signed62 f = modinfo->modulus; secp256k1_modinv64_signed62 g = *x; int j, len = 5; int64_t eta = -1; /* eta = -delta; delta is initially 1 */ int64_t cond, fn, gn; int jac = 0; int count; /* The input limbs must all be non-negative. */ VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0); /* If x > 0, then if the loop below converges, it converges to f=g=gcd(x,modulus). Since we * require that gcd(x,modulus)=1 and modulus>=3, x cannot be 0. Thus, we must reach f=1 (or * time out). */ VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4]) != 0); for (count = 0; count < JACOBI64_ITERATIONS; ++count) { /* Compute transition matrix and new eta after 62 posdivsteps. */ secp256k1_modinv64_trans2x2 t; eta = secp256k1_modinv64_posdivsteps_62_var(eta, f.v[0] | ((uint64_t)f.v[1] << 62), g.v[0] | ((uint64_t)g.v[1] << 62), &t, &jac); /* Update f,g using that transition matrix. */ #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ #endif secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t); /* If the bottom limb of f is 1, there is a chance that f=1. */ if (f.v[0] == 1) { cond = 0; /* Check if the other limbs are also 0. */ for (j = 1; j < len; ++j) { cond |= f.v[j]; } /* If so, we're done. When f=1, the Jacobi symbol (g | f)=1. */ if (cond == 0) return 1 - 2*(jac & 1); } /* Determine if len>1 and limb (len-1) of both f and g is 0. */ fn = f.v[len - 1]; gn = g.v[len - 1]; cond = ((int64_t)len - 2) >> 63; cond |= fn; cond |= gn; /* If so, reduce length. */ if (cond == 0) --len; #ifdef VERIFY VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ #endif } /* The loop failed to converge to f=g after 1550 iterations. Return 0, indicating unknown result. */ return 0; } #endif #endif /* SECP256K1_MODINV64_IMPL_H */ ================================================ FILE: C/secp256k1/precomputed_ecmult.h ================================================ #ifndef SECP256K1_PRECOMPUTED_ECMULT_H #define SECP256K1_PRECOMPUTED_ECMULT_H /* This file was automatically generated by precompute_ecmult. */ /* This file contains an array secp256k1_pre_g with odd multiples of the base point G and * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G. */ #include "group.h" #include "ecmult.h" #ifdef S #error macro identifier S already in use. #endif #define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) #if ECMULT_WINDOW_SIZE > 15 #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build. #endif #ifdef EXHAUSTIVE_TEST_ORDER # error Cannot compile precomputed_ecmult.c in exhaustive test mode #endif /* EXHAUSTIVE_TEST_ORDER */ #define WINDOW_G ECMULT_WINDOW_SIZE static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] #ifndef VST = { S(79be667e,f9dcbbac,55a06295,ce870b07,29bfcdb,2dce28d9,59f2815b,16f81798,483ada77,26a3c465,5da4fbfc,e1108a8,fd17b448,a6855419,9c47d08f,fb10d4b8) #if WINDOW_G > 2 ,S(f9308a01,9258c310,49344f85,f89d5229,b531c845,836f99b0,8601f113,bce036f9,388f7b0f,632de814,fe337e6,2a37f356,6500a999,34c2231b,6cb9fd75,84b8e672) #endif #if WINDOW_G > 3 ,S(2f8bde4d,1a072093,55b4a725,a5c5128,e88b84bd,dc619ab7,cba8d569,b240efe4,d8ac2226,36e5e3d6,d4dba9dd,a6c9c426,f788271b,ab0d6840,dca87d3a,a6ac62d6) ,S(5cbdf064,6e5db4ea,a398f365,f2ea7a0e,3d419b7e,330e39c,e92bdded,cac4f9bc,6aebca40,ba255960,a3178d6d,861a54db,a813d0b8,13fde7b5,a5082628,87264da) #endif #if WINDOW_G > 4 ,S(acd484e2,f0c7f653,9ad178a,9f559abd,e0979697,4c57e714,c35f110d,fc27ccbe,cc338921,b0a7d9fd,64380971,763b61e9,add888a4,375f8e0f,5cc262a,c64f9c37) ,S(774ae7f8,58a9411e,5ef4246b,70c65aac,5649980b,e5c17891,bbec1789,5da008cb,d984a032,eb6b5e19,243dd56,d7b7b365,372db1e2,dff9d6a8,301d74c9,c953c61b) ,S(f28773c2,d975288b,c7d1d205,c3748651,b075fbc6,610e58cd,deeddf8f,19405aa8,ab0902e,8d880a89,758212eb,65cdaf47,3a1a06da,521fa91f,29b5cb52,db03ed81) ,S(d7924d4f,7d43ea96,5a465ae3,95ff411,31e5946f,3c85f79e,44adbcf8,e27e080e,581e2872,a86c72a6,83842ec2,28cc6def,ea40af2b,d896d3a5,c504dc9f,f6a26b58) #endif #if WINDOW_G > 5 ,S(defdea4c,db677750,a420fee8,7eacf21,eb9898ae,79b97687,66e4faa0,4a2d4a34,4211ab06,94635168,e997b0ea,d2a93dae,ced1f4a0,4a95c0f6,cfb199f6,9e56eb77) ,S(2b4ea0a7,97a443d2,93ef5cff,444f4979,f06acfeb,d7e86d27,74756561,38385b6c,85e89bc0,37945d93,b343083b,5a1c8613,1a01f60c,50269763,b570c854,e5c09b7a) ,S(352bbf4a,4cdd1256,4f93fa33,2ce33330,1d9ad402,71f81071,81340aef,25be59d5,321eb407,5348f534,d59c1825,9dda3e1f,4a1b3b2e,71b1039c,67bd3d8b,cf81998c) ,S(2fa2104d,6b38d11b,2300105,59879124,e42ab8df,eff5ff29,dc9cdadd,4ecacc3f,2de1068,295dd865,b6456933,5bd5dd80,181d70ec,fc882648,423ba76b,532b7d67) ,S(9248279b,9b4d68d,ab21a9b0,66edda83,263c3d84,e09572e2,69ca0cd7,f5453714,73016f7b,f234aade,5d1aa71b,dea2b1ff,3fc0de2a,887912ff,e54a32ce,97cb3402) ,S(daed4f2b,e3a8bf27,8e70132f,b0beb752,2f570e14,4bf615c0,7e996d44,3dee8729,a69dce4a,7d6c98e8,d4a1aca8,7ef8d700,3f83c230,f3afa726,ab40e522,90be1c55) ,S(c44d12c7,65d812e,8acf28d7,cbb19f90,11ecd9e9,fdf281b0,e6a3b5e8,7d22e7db,2119a460,ce326cdc,76c45926,c982fdac,e106e86,1edf61c5,a039063f,e0e6482) ,S(6a245bf6,dc698504,c89a20cf,ded60853,152b6953,36c28063,b61c65cb,d269e6b4,e022cf42,c2bd4a70,8b3f5126,f16a24ad,8b33ba48,d0423b6e,fd5e6348,100d8a82) #endif #if WINDOW_G > 6 ,S(1697ffa6,fd9de627,c077e3d2,fe541084,ce13300b,bec1146,f95ae57f,d0bd6a5,b9c398f1,86806f5d,27561506,e4557433,a2cf1500,9e498ae7,adee9d63,d01b2396) ,S(605bdb01,9981718b,986d0f07,e834cb0d,9deb8360,ffb7f61d,f982345e,f27a7479,2972d2d,e4f8d206,81a78d93,ec96fe23,c26bfae8,4fb14db4,3b01e1e9,56b8c49) ,S(62d14dab,4150bf49,7402fdc4,5a215e10,dcb01c35,4959b10c,fe31c7e9,d87ff33d,80fc06bd,8cc5b010,98088a19,50eed0db,1aa1329,67ab4722,35f56424,83b25eaf) ,S(80c60ad0,40f27da,de5b4b06,c408e56b,2c50e9f5,6b9b8b42,5e555c2f,86308b6f,1c38303f,1cc5c30f,26e66bad,7fe72f70,a65eed4c,be7024eb,1aa01f56,430bd57a) ,S(7a9375ad,6167ad54,aa74c634,8cc54d34,4cc5dc94,87d84704,9d5eabb0,fa03c8fb,d0e3fa9,eca87269,9559e0d,79269046,bdc59ea1,c70ce2b,2d499ec,224dc7f7) ,S(d528ecd9,b696b54c,907a9ed0,45447a79,bb408ec3,9b68df50,4bb51f45,9bc3ffc9,eecf4125,3136e5f9,9966f218,81fd656e,bc434540,5c520dbc,63465b5,21409933) ,S(49370a4,b5f43412,ea25f514,e8ecdad0,5266115e,4a7ecb13,87231808,f8b45963,758f3f41,afd6ed42,8b3081b0,512fd62a,54c3f3af,bb5b6764,b653052a,12949c9a) ,S(77f23093,6ee88cbb,d73df930,d64702ef,881d811e,e1498e2,f1c13eb1,fc345d74,958ef42a,7886b640,a08266e,9ba1b378,96c95330,d97077cb,be8eb3c7,671c60d6) ,S(f2dac991,cc4ce4b9,ea44887e,5c7c0bce,58c80074,ab9d4dba,eb28531b,7739f530,e0dedc9b,3b2f8dad,4da1f32d,ec2531df,9eb5fbeb,598e4fd,1a117dba,703a3c37) ,S(463b3d9f,662621fb,1b4be8fb,be252012,5a216cdf,c9dae3de,bcba4850,c690d45b,5ed430d7,8c296c35,43114306,dd8622d7,c622e27c,970a1de3,1cb377b0,1af7307e) ,S(f16f8042,44e46e2a,9232d4a,ff3b5997,6b98fac1,4328a2d1,a32496b4,9998f247,cedabd9b,82203f7e,13d206fc,df4e33d9,2a6c53c2,6e5cce26,d6579962,c4e31df6) ,S(caf75427,2dc84563,b0352b7a,14311af5,5d245315,ace27c65,369e15f7,151d41d1,cb474660,ef35f5f2,a41b643f,a5e46057,5f4fa9b7,962232a5,c32f9083,18a04476) ,S(2600ca4b,282cb986,f85d0f17,9979d8b,44a09c07,cb86d7c1,24497bc8,6f082120,4119b887,53c15bd6,a693b03f,cddbb45d,5ac6be74,ab5f0ef4,4b0be947,5a7e4b40) ,S(7635ca72,d7e8432c,338ec53c,d12220bc,1c48685,e24f7dc8,c602a774,6998e435,91b6496,9489d61,3d1d5e59,f78e6d7,4ecfc061,d57048ba,d9e76f30,2c5b9c61) ,S(754e3239,f325570c,dbbf4a87,deee8a66,b7f2b334,79d468fb,c1a50743,bf56cc18,673fb86,e5bda30f,b3cd0ed3,4ea49a0,23ee33d0,197a695d,c5d9809,3c536683) ,S(e3e6bd10,71a1e96a,ff57859c,82d570f0,33080066,1d1c952f,9fe26946,91d9b9e8,59c9e0bb,a394e76f,40c0aa58,379a3cb6,a5a22839,93e90c41,67002af4,920e37f5) #endif #if WINDOW_G > 7 ,S(186b483d,56a0338,26ae73d8,8f732985,c4ccb1f3,2ba35f4b,4cc47fdc,f04aa6eb,3b952d32,c67cf77e,2e17446e,204180ab,21fb8090,895138b4,a4a797f8,6e80888b) ,S(df9d70a6,b9876ce5,44c98561,f4be4f72,5442e6d2,b737d9c9,1a832172,4ce0963f,55eb2daf,d84d6ccd,5f862b78,5dc39d4a,b1572227,20ef9da2,17b8c45c,f2ba2417) ,S(5edd5cc2,3c51e87a,497ca815,d5dce0f8,ab52554f,849ed899,5de64c5f,34ce7143,efae9c8d,bc141306,61e8cec0,30c89ad0,c13c66c0,d17a2905,cdc706ab,7399a868) ,S(290798c2,b6476830,da12fe02,287e9e77,7aa3fba1,c355b17a,722d362f,84614fba,e38da76d,cd440621,988d00bc,f79af25d,5b29c094,db2a2314,6d003afd,41943e7a) ,S(af3c423a,95d9f5b3,54754ef,a150ac39,cd29552f,e3602573,62dfdece,f4053b45,f98a3fd8,31eb2b74,9a93b0e6,f35cfb40,c8cd5aa6,67a15581,bc2feded,498fd9c6) ,S(766dbb24,d134e745,cccaa28c,99bf2749,6bb66b2,6dcf98df,8d2fed50,d884249a,744b1152,eacbe5e3,8dcc8879,80da38b8,97584a65,fa06cedd,2c924f97,cbac5996) ,S(59dbf46f,8c94759b,a21277c3,3784f416,45f7b44f,6c596a58,ce92e666,191abe3e,c534ad44,175fbc30,f4ea6ce,648309a0,42ce739a,7919798c,d85e216c,4a307f6e) ,S(f13ada95,103c4537,305e691e,74e9a4a8,dd647e71,1a95e73c,b62dc601,8cfd87b8,e13817b4,4ee14de6,63bf4bc8,8341f32,6949e21a,6a75c257,778419b,daf5733d) ,S(7754b4fa,e8aced0,6d4167a2,c59cca4c,da1869c0,6ebadfb6,48855001,5a88522c,30e93e86,4e669d82,224b967c,3020b8fa,8d1e4e35,b6cbcc5,37a48b57,841163a2) ,S(948dcadf,5990e048,aa3874d4,6abef9d7,1858f95,de8041d2,a6828c99,e2262519,e491a425,37f6e597,d5d28a32,24b1bc25,df9154ef,bd2ef1d2,cbba2cae,5347d57e) ,S(79624144,50c76c16,89c7b48f,8202ec37,fb224cf5,ac0bfa15,70328a8a,3d7c77ab,100b610e,c4ffb476,d5c1fc1,33ef6f6b,12507a05,1f04ac57,60afa5b2,9db83437) ,S(35140878,34964b54,b15b1606,44d91548,5a169772,25b8847b,b0dd0851,37ec47ca,ef0afbb2,5620544,8e1652c4,8e8127fc,6039e77c,15c2378b,7e7d15a0,de293311) ,S(d3cc30ad,6b483e4b,c79ce2c9,dd8bc549,93e947eb,8df787b4,42943d3f,7b527eaf,8b378a22,d827278d,89c5e9be,8f9508ae,3c2ad462,90358630,afb34db0,4eede0a4) ,S(1624d847,80732860,ce1c78fc,bfefe08b,2b29823d,b913f649,3975ba0f,f4847610,68651cf9,b6da903e,914448c,6cd9d4ca,896878f5,282be4c8,cc06e2a4,4078575) ,S(733ce80d,a955a8a2,6902c956,33e62a98,5192474b,5af207da,6df7b4fd,5fc61cd4,f5435a2b,d2badf7d,485a4d8b,8db9fcce,3e1ef8e0,201e4578,c54673bc,1dc5ea1d) ,S(15d94412,54945064,cf1a1c33,bbd3b49f,8966c509,2171e699,ef258dfa,b81c045c,d56eb30b,69463e72,34f5137b,73b84177,434800ba,cebfc685,fc37bbe9,efe4070d) ,S(a1d0fcf2,ec9de675,b612136e,5ce70d27,1c21417c,9d2b8aaa,ac138599,d0717940,edd77f50,bcb5a3ca,b2e90737,309667f2,641462a5,4070f3d5,19212d39,c197a629) ,S(e22fbe15,c0af8ccc,5780c073,5f84dbe9,a790bade,e8245c06,c7ca3733,1cb36980,a855bab,ad5cd60c,88b430a6,9f53a1a7,a3828915,4964799b,e43d06d7,7d31da06) ,S(311091dd,9860e8e2,ee13473,c1155f5f,69635e39,4704eaa7,40094522,46cfa9b3,66db656f,87d1f04f,ffd1f047,88c06830,871ec5a6,4feee685,bd80f0b1,286d8374) ,S(34c1fd04,d301be89,b31c0442,d3e6ac24,883928b4,5a934078,1867d423,2ec2dbdf,9414685,e97b1b59,54bd46f7,30174136,d57f1cee,b487443d,c5321857,ba73abee) ,S(f219ea5d,6b54701c,1c14de5b,557eb42a,8d13f3ab,bcd08aff,cc2a5e6b,49b8d63,4cb95957,e83d40b0,f73af454,4cccf6b1,f4b08d3c,7b27fb8,d8c2962a,400766d1) ,S(d7b8740f,74a8fbaa,b1f683db,8f45de26,543a5490,bca62708,72369124,69a0b448,fa779681,28d9c92e,e1010f33,7ad4717e,ff15db5e,d3c049b3,411e0315,eaa4593b) ,S(32d31c22,2f8f6f0e,f86f7c98,d3a3335e,ad5bcd32,abdd9428,9fe4d309,1aa824bf,5f3032f5,892156e3,9ccd3d79,15b9e1da,2e6dac9e,6f26e961,118d14b8,462e1661) ,S(7461f371,914ab326,71045a15,5d9831ea,8793d77c,d59592c4,340f86cb,c18347b5,8ec0ba23,8b96bec0,cbdddcae,aa44254,2eee1ff5,c986ea6,b39847b3,cc092ff6) ,S(ee079adb,1df18600,74356a25,aa38206a,6d716b2c,3e67453d,287698ba,d7b2b2d6,8dc2412a,afe3be5c,4c5f37e0,ecc5f9f6,a446989a,f04c4e25,ebaac479,ec1c8c1e) ,S(16ec93e4,47ec83f0,467b1830,2ee620f7,e65de331,874c9dc7,2bfd8616,ba9da6b5,5e463115,e62fb40,d0e8c2a7,ca5804a3,9d58186a,50e49713,9626778e,25b0674d) ,S(eaa5f980,c245f6f0,38978290,afa70b6b,d8855897,f98b6aa4,85b96065,d537bd99,f65f5d3e,292c2e08,19a52839,1c994624,d784869d,7e6ea67f,b1804102,4edc07dc) ,S(78c9407,544ac132,692ee191,a024399,58ae0487,7151342e,a96c4b6b,35a49f51,f3e03191,69eb9b85,d5404795,539a5e68,fa1fbd58,3c064d24,62b675f1,94a3ddb4) ,S(494f4be2,19a1a770,16dcd838,431aea00,1cdc8ae,7a6fc688,726578d9,702857a5,42242a96,9283a5f3,39ba7f07,5e36ba2a,f925ce30,d767ed6e,55f4b031,880d562c) ,S(a598a803,da6d86c,6bc7f2f5,144ea549,d28211ea,58faa70e,bf4c1e66,5c1fe9b5,204b5d6f,84822c30,7e4b4a71,40737aec,23fc63b6,5b35f86a,10026dbd,2d864e6b) ,S(c4191636,5abb2b5d,9192f5f,2dbeafec,208f020f,12570a18,4dbadc3e,58595997,4f14351,d0087efa,49d245b3,28984989,d5caf945,f34bfc0,ed16e96b,58fa9913) ,S(841d6063,a586fa47,5a724604,da03bc5b,92a2e0d2,e0a36acf,e4c73a55,14742881,73867f5,9c0659e8,1904f9a1,c7543698,e62562d6,744c169c,e7a36de0,1a8d6154) #endif #if WINDOW_G > 8 ,S(5e95bb39,9a6971d3,76026947,f89bde2f,282b3381,928be4d,ed112ac4,d70e20d5,39f23f36,6809085b,eebfc711,81313775,a99c9aed,7d8ba38b,161384c7,46012865) ,S(36e4641a,53948fd4,76c39f8a,99fd974e,5ec07564,b5315d8b,f99471bc,a0ef2f66,d2424b1b,1abe4eb8,164227b0,85c9aa94,56ea1349,3fd563e0,6fd51cf5,694c78fc) ,S(336581e,a7bfbbb2,90c191a2,f507a41c,f5643842,170e914f,aeab27c2,c579f726,ead12168,595fe1be,99252129,b6e56b33,91f7ab14,10cd1e0e,f3dcdcab,d2fda224) ,S(8ab89816,dadfd6b6,a1f2634f,cf00ec84,3781025,ed6890c4,84974270,6bd43ede,6fdcef09,f2f6d0a0,44e654ae,f624136f,503d459c,3e898458,58a47a91,29cdd24e) ,S(1e33f1a7,46c9c577,8133344d,9299fcaa,20b0938e,8acff254,4bb40284,b8c5fb94,6066025,7dd11b3a,a9c8ed61,8d24edff,2306d320,f1d03010,e33a7d20,57f3b3b6) ,S(85b7c1dc,b3cec1b7,ee7f30de,d79dd20a,ed1f4cc,18cbcfcf,a410361f,d8f08f31,3d98a9cd,d026dd43,f39048f2,5a8847f4,fcafad18,95d7a633,c6fed3c3,5e999511) ,S(29df9fbd,8d9e4650,9275f4b1,25d6d45d,7fbe9a3b,878a7af8,72a28006,61ac5f51,b4c4fe9,9c775a60,6e2d8862,179139ff,da61dc86,1c019e55,cd2876eb,2a27d84b) ,S(a0b1cae0,6b0a847a,3fea6e67,1aaf8adf,dfe58ca2,f768105c,8082b2e4,49fce252,ae434102,edde0958,ec4b19d9,17a6a28e,6b72da18,34aff0e6,50f04950,3a296cf2) ,S(4e8ceaf,b9b3e9a1,36dc7ff6,7e840295,b499dfb3,b2133e4b,a113f2e4,c0e121e5,cf217411,8c8b6d7a,4b48f6d5,34ce5c79,422c086a,63460502,b827ce62,a326683c) ,S(d24a44e0,47e19b6f,5afb81c7,ca2f6908,a507668,9a010919,f42725c2,b789a33b,6fb8d559,1b466f8f,c63db50f,1c0f1c69,13f9968,87b8244d,2cdec417,afea8fa3) ,S(ea01606a,7a6c9cdd,249fdfcf,acb99584,1edd28,abbab77b,5104e98e,8e3b35d4,322af490,8c7312b0,cfbfe369,f7a7b3cd,b7d4494b,c2823700,cfd65218,8a3ea98d) ,S(af8addbf,2b661c8a,6c632865,5eb96651,252007d8,c5ea31be,4ad196de,8ce2131f,6749e67c,29b85f5,2a034eaf,d096836b,25208186,80e26ac8,f3dfbcdb,71749700) ,S(e3ae19,74566ca0,6cc516d4,7e0fb165,a674a3da,bcfca15e,722f0e34,50f45889,2aeabe7e,45315101,16217f07,bf4d0730,de97e48,74f81f53,3420a72e,eb0bd6a4) ,S(591ee355,313d9972,1cf6993f,fed1e3e3,1993ff3,ed258802,75ea8ce,d397e246,b0ea558a,113c30be,a60fc477,5460c790,1ff0b053,d25ca2bd,eee98f1a,4be5d196) ,S(11396d55,fda54c49,f19aa973,18d8da61,fa8584e4,7b084945,77cf032,55b52984,998c74a8,cd45ac01,289d5833,a7beb474,4ff536b0,1b257be4,c5767bea,93ea57a4) ,S(3c5d2a1b,a39c5a17,90000738,c9e0c40b,8dcdfd54,68754b64,5540157,e017aa7a,b2284279,995a34e2,f9d4de73,96fc18b8,f9b8b9f,dd270f66,61f79ca4,c81bd257) ,S(cc8704b8,a60a0def,a3a99a72,99f2e9c3,fbc395af,b04ac078,425ef8a1,793cc030,bdd46039,feed1788,1d1e0862,db347f8c,f395b74f,c4bcdc4e,940b74e3,ac1f1b13) ,S(c533e4f7,ea8555aa,cd9777ac,5cad29b9,7dd4defc,cc53ee7e,a204119b,2889b197,6f0a256b,c5efdf42,9a2fb624,2f1a43a2,d9b925bb,4a4b3a26,bb8e0f45,eb596096) ,S(c14f8f2,ccb27d6f,109f6d08,d03cc96a,69ba8c34,eec07bbc,f566d48e,33da6593,c359d692,3bb398f7,fd4473e1,6fe1c284,75b740dd,98075e6,c0e86491,13dc3a38) ,S(a6cbc304,6bc6a450,bac24789,fa17115a,4c9739ed,75f8f21c,e441f72e,b90e6ef,21ae7f4,680e889b,b130619e,2c0f95a3,60ceb573,c7060313,9862afd6,17fa9b9f) ,S(347d6d9a,2c48927,ebfb86c1,359b1caf,130a3c02,67d11ce6,344b39f9,9d43cc38,60ea7f61,a353524d,1c987f6e,cec92f08,6d565ab6,87870cb1,2689ff1e,31c74448) ,S(da6545d2,181db8d9,83f7dcb3,75ef5866,d47c67b1,bf31c8cf,855ef743,7b72656a,49b96715,ab6878a7,9e78f07c,e5680c5d,6673051b,4935bd89,7fea824b,77dc208a) ,S(c40747cc,9d012cb1,a13b8148,309c6de7,ec25d694,5d657146,b9d5994b,8feb1111,5ca56075,3be2a12f,c6de6caf,2cb48956,5db93615,6b9514e1,bb5e8303,7e0fa2d4) ,S(4e42c8ec,82c99798,ccf3a610,be870e78,338c7f71,3348bd34,c8203ef4,37f3502,7571d74e,e5e0fb92,a7a8b33a,7783341,a5492144,cc54bcc4,a944736,93606437) ,S(3775ab70,89bc6af8,23aba2e1,af70b236,d251cadb,c867432,87522a1b,3b0dedea,be52d107,bcfa09d8,bcb9736a,828cfa7f,ac8db17b,f7a76a2c,42ad9614,9018cf7) ,S(cee31cbf,7e34ec37,9d94fb81,4d3d775a,d954595d,1314ba88,46959e3e,82f74e26,8fd64a14,c06b589c,26b947ae,2bcf6bfa,149ef0b,e14ed4d8,f448a01,c43b1c6d) ,S(b4f9eaea,9b69176,19f6ea6a,4eb5464e,fddb58fd,45b1ebef,cdc1a01d,8b47986,39e5c992,5b5a54b0,7433a4f1,8c61726f,8bb131c0,12ca542e,b24a8ac0,7200682a) ,S(d4263dfc,3d2df923,a0179a48,966d30ce,84e2515a,fc3dccc1,b7790779,2ebcc60e,62dfaf07,a0f78feb,30e30d62,95853ce1,89e12776,ad6cf7f,ae164e12,2a208d54) ,S(48457524,820fa65a,4f8d35eb,6930857c,32acc0,a4a2de42,2233eeda,897612c4,25a748ab,367979d9,8733c38a,1fa1c2e7,dc6cc07d,b2d60a9a,e7a76aaa,49bd0f77) ,S(dfeeef18,81101f2c,b11644f3,a2afdfc2,45e1991,9152923f,367a1767,c11cceda,ecfb7056,cf1de042,f9420bab,396793c0,c390bde7,4b4bbdff,16a83ae0,9a9a7517) ,S(6d7ef6b1,7543f837,3c573f44,e1f38983,5d89bcbc,6062ced3,6c82df83,b8fae859,cd450ec3,35438986,dfefa10c,57fea9bc,c521a095,9b2d80bb,f74b190d,ca712d10) ,S(e75605d5,9102a5a2,684500d3,b991f2e3,f3c88b93,22554703,5af25af6,6e04541f,f5c54754,a8f71ee5,40b9b487,28473e31,4f729ac5,308b0693,8360990e,2bfad125) ,S(eb98660f,4c4dfaa0,6a2be453,d5020bc9,9a0c2e60,abe38845,7dd43fef,b1ed620c,6cb9a887,6d9cb852,609af3a,dd26cd20,a0a7cd8a,9411131c,e85f4410,99223e) ,S(13e87b02,7d8514d3,5939f2e6,892b1992,21545969,41888336,dc3563e3,b8dba942,fef5a3c6,8059a6de,c5d62411,4bf1e91a,ac2b9da5,68d6abeb,2570d556,46b8adf1) ,S(ee163026,e9fd6fe0,17c38f06,a5be6fc1,25424b37,1ce2708e,7bf44916,91e5764a,1acb250f,255dd61c,43d94ccc,670d0f58,f49ae3fa,15b96623,e5430da0,ad6c62b2) ,S(b268f5ef,9ad51e4d,78de3a75,c2dc89b,1e626d43,50586799,9932e5db,33af3d80,5f310d4b,3c99b9eb,b19f77d4,1c1dee01,8cf0d34f,d4191614,3e945a,1216e423) ,S(ff07f311,8a9df035,e9fad85e,b6c7bfe4,2b02f01c,a99ceea3,bf7ffdba,93c4750d,438136d6,3e858a3,a5c440c3,8eccbadd,c1d29421,14e2eddd,4740d098,ced1f0d8) ,S(8d8b9855,c7c052a3,4146fd20,ffb658be,a4b9f69e,d825ebe,c16e8c3c,e2b526a1,cdb559ee,dc2d79f9,26baf44f,b84ea4d4,4bcf50fe,e51d7ceb,30e2e7f4,63036758) ,S(52db0b53,84dfbf05,bfa9d472,d7ae26df,e4b851ce,ca91b1eb,a5426318,da32b63,c3b997d,50ee5d4,23ebaf66,a6db9f57,b3180c90,2875679d,e924b69d,84a7b375) ,S(e62f9490,d3d51da6,395efd24,e80919cc,7d0f29c3,f3fa48c6,fff543be,cbd43352,6d89ad7b,a4876b0b,22c2ca28,c682862,f342c859,1f1daf51,70e07bfd,9ccafa7d) ,S(7f30ea24,76b399b4,957509c8,8f77d019,1afa2ff5,cb7b14fd,6d8e7d65,aaab1193,ca5ef7d4,b231c94c,3b15389a,5f6311e9,daff7bb6,7b103e98,80ef4bff,637acaec) ,S(5098ff1e,1d9f14fb,46a210fa,da6c903f,ef0fb7b4,a1dd1d9a,c60a0361,800b7a00,9731141,d81fc8f8,84d37c6,e7542006,b3ee1b40,d60dfe53,62a5b132,fd17ddc0) ,S(32b78c7d,e9ee512a,72895be6,b9cbefa6,e2f3c4cc,ce445c96,b9f2c81e,2778ad58,ee1849f5,13df71e3,2efc3896,ee28260c,73bb8054,7ae2275b,a4972377,94c8753c) ,S(e2cb74fd,dc8e9fbc,d076eef2,a7c72b0c,e37d50f0,8269dfc0,74b58155,547a4f7,d3aa2ed7,1c9dd224,7a62df06,2736eb0b,addea9e3,6122d2be,8641abcb,5cc4a4) ,S(84384475,66d4d7be,dadc2994,96ab3574,26009a35,f235cb14,1be0d99c,d10ae3a8,c4e10209,16980a4d,a5d01ac5,e6ad3307,34ef0d79,6631c4f,2390426b,2edd791f) ,S(4162d488,b8940203,9b584c6f,c6c30887,587d9c4,6f660b87,8ab65c82,c711d67e,67163e90,3236289f,776f22c2,5fb8a3af,c1732f2b,84b4e95d,bda47ae5,a0852649) ,S(3fad3fa8,4caf0f34,f0f89bfd,2dcf54fc,175d767a,ec3e5068,4f3ba4a4,bf5f683d,cd1bc7c,b6cc407b,b2f0ca64,7c718a73,cf71872,e7d0d2a5,3fa20efc,dfe61826) ,S(674f2600,a3007a00,568c1a7c,e05d0816,c1fb84bf,1370798f,1c69532f,aeb1a86b,299d21f9,413f33b3,edf43b25,7004580b,70db57da,b182259,e09eecc6,9e0d38a5) ,S(d32f4da5,4ade74ab,b81b815a,d1fb3b26,3d82d6c6,92714bcf,f87d29bd,5ee9f08f,f9429e73,8b8e53b9,68e99016,c0597077,82e14f45,35359d58,2fc41691,b3eea87) ,S(30e4e670,43538555,6e593657,135845d3,6fbb6931,f72b08cb,1ed954f1,e3ce3ff6,462f9bce,61989863,84993501,13bbc9b1,a878d35,da70740d,c695a559,eb88db7b) ,S(be206200,3c51cc30,4682904,330e4dee,7f3dcd10,b01e580b,f1971b04,d4cad297,62188bc4,9d61e542,8573d48a,74e1c655,b1c61090,905682a0,d5558ed7,2dccb9bc) ,S(93144423,ace3451e,d29e0fb9,ac2af211,cb6e84a6,1df5993,c419859f,ff5df04a,7c10dfb1,64c3425f,5c71a3f9,d7992038,f1065224,f72bb9d1,d902a6d1,3037b47c) ,S(b015f804,4f5fcbdc,f21ca26d,6c34fb81,97829205,c7b7d2a7,cb66418c,157b112c,ab8c1e08,6d04e813,744a655b,2df8d5f8,3b3cdc6f,aa3088c1,d3aea145,4e3a1d5f) ,S(d5e9e1da,649d97d8,9e486811,7a465a3a,4f8a18de,57a140d3,6b3f2af3,41a21b52,4cb04437,f391ed73,111a13cc,1d4dd0db,1693465c,2240480d,8955e859,2f27447a) ,S(d3ae4104,7dd7ca06,5dbf8ed7,7b992439,983005cd,72e16d6f,996a5316,d36966bb,bd1aeb21,ad22ebb2,2a10f030,3417c6d9,64f8cdd7,df0aca61,4b10dc14,d125ac46) ,S(463e2763,d885f958,fc66cdd2,2800f0a4,87197d0a,82e377b4,9f80af87,c897b065,bfefacdb,e5d0fd7,df3a311a,94de062b,26b80c61,fbc97508,b7999267,1ef7ca7f) ,S(7985fdfd,127c0567,c6f53ec1,bb63ec31,58e597c4,bfe747c,83cddfc9,10641917,603c12da,f3d9862e,f2b25fe1,de289aed,24ed291e,ec67087,3a5bd56,7f32ed03) ,S(74a1ad6b,5f76e39d,b2dd2494,10eac7f9,9e74c59c,b83d2d0e,d5ff1543,da7703e9,cc6157ef,18c9c63c,d6193d83,631bbea0,93e0968,942e8c33,d5737fd7,90e0db08) ,S(30682a50,703375f6,2d41666,4ba19b7f,c9bab42c,72747463,a71d0896,b22f6da3,553e04f6,b018b4fa,6c8f39e7,f311d317,6290d0e0,f19ca73f,17714d99,77a22ff8) ,S(9e2158f0,d7c0d5f2,6c3791ef,efa79597,654e7a2b,2464f52b,1ee6c134,7769ef57,712fcdd,1b9053f0,9003a348,1fa7762e,9ffd7c8e,f35a3850,9e2fbf26,29008373) ,S(176e2698,9a43c9cf,eba4029c,202538c2,8172e566,e3c4fce7,322857f3,be327d66,ed8cc9d0,4b29eb87,7d270b48,78dc43c1,9aefd31f,4eee09ee,7b47834c,1fa4b1c3) ,S(75d46efe,a3771e6e,68abb89a,13ad747e,cf189239,3dfc4f1b,7004788c,50374da8,9852390a,99507679,fd0b86fd,2b39a868,d7efc221,51346e1a,3ca47265,86a6bed8) ,S(809a20c6,7d64900f,fb698c4c,825f6d5f,2310fb04,51c86934,5b7319f6,45605721,9e994980,d9917e22,b76b0619,27fa0414,3d096ccc,54963e6a,5ebfa5f3,f8e286c1) ,S(1b38903a,43f7f114,ed4500b4,eac7083f,defece1c,f29c6352,8d563446,f972c180,4036edc9,31a60ae8,89353f77,fd53de4a,2708b26b,6f5da72a,d3394119,daf408f9) #endif #if WINDOW_G > 9 ,S(90a80db6,eb294b9e,ab0b4e8d,dfa3efe7,263458ce,2d07566d,f4e6c588,68feef23,753c8b9f,9754f18d,87f21145,d9e2936b,5ee050b2,7bbd9681,442c76e9,2fcf91e6) ,S(c2c80f84,4b705998,12d62546,f60340e,3e6f3605,4a14546e,6dc25d47,376bea9b,86ca160d,68f4d4e7,18b495b8,91d3b1b5,73b871a7,2b4cf61,23abd448,3aa79c64) ,S(9cf60674,4cf4b5f3,fdf989d3,f19fb265,2d00cfe1,d5fcd692,a323ce11,a28e7553,8147cbf7,b973fcc1,5b57b6a3,cfad6863,edd0f30e,3c45b85d,c300c513,c247759d) ,S(57488fa2,8742c6b2,5a493fd6,60d936e,a6280b0c,742005ab,ce98f585,5ad82208,31b3ca45,5073bea5,58adbe56,c27b470b,af949ae6,50213921,dc287844,f1a29574) ,S(f1133cbe,6be8bbc8,dc8df2b8,d75963c2,d40ed616,c758cdc8,4edbc5eb,4899447d,57fc2447,2225b23f,5714626d,8d67d561,10bd3a60,dd7a1687,cbbb893,f652f50f) ,S(95083e75,3301bd78,7f8989c7,9065bb81,3f3d69bf,f3e42505,f4e0417,5bbe89c0,844adb5c,e7d10de9,4617c73c,a77040e4,ee4e92e0,156b3c70,cc593fa4,94b33482) ,S(1a908355,cbb75675,5e576ed2,9c99af63,8668c7b3,63c8d973,62100443,bc5c75c6,d765466c,6e556e35,2f778722,25627d80,a7353807,4b44ff27,57ad22e,2f2454a2) ,S(c5922f74,bd343d5,aa867308,fad97f9f,8a2d1f63,c5f31db4,f04df3be,f349b648,77b1f068,7cfcdbe8,812605e5,d8b752c,da811844,236a4c43,77f53c94,6e7bd648) ,S(64e1b196,9f910297,7691a404,31b0b672,55dcf31,163897d9,96434420,e6c95dc9,c16f60c7,c11fc3c9,eb27fa26,a9035b66,9bfb77d2,1cef371d,dce94e32,9222550c) ,S(33b2e76,687744ed,6c521bad,3333dd37,c602f8a7,549e9ce7,808fb7ea,7ce08de,e1bcfe7f,c8ed8ae9,5cf6c243,7fdd94bf,d742e8ca,a6de7811,4c25112a,86988efd) ,S(20f18f4c,866d8a1c,c2a31033,17b4ac31,89fbf30f,f294a75c,951473be,45e4f294,8d6857c9,d08ef7b4,fd888336,3d37bee7,fe8529f,7173f589,43fcae81,d2d0ea0e) ,S(4d1623c9,44c9c716,a0eb4c68,5e2a8b9d,2df34653,54643bef,d1444176,d7b69a8b,ddf1b9fe,8744ad03,f996bf6b,96ec3496,2b601bd5,ed952f78,54f58388,8917be80) ,S(a901b0db,e8ab292d,280d6b36,85894785,4faad0a4,dd0da7e2,d4ad0ff5,3db079e0,3f27e7e1,834f1a61,af6f04dc,61e7ae64,716bc5e0,a6b063b3,1d0e60e,47298a9d) ,S(7e0af071,30218ffd,50bd66f4,484645b1,2f42a24f,7c80889b,3031c9a6,ebfc9a70,50bc23f3,926cd0c4,9f53fbb2,35eb1e89,d579517,f5bdc3ab,2416db78,5aaedb3f) 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,S(64778122,214e38ef,f8041796,166104e7,32f5f664,d38d7721,9b89045e,2c3b0e6c,329cf049,7e15eec7,b8eafc4a,b8a7d1c,d8b63203,8d4aef81,974cf984,4611a32d) ,S(ed4d826a,fe5762f4,79509909,9aee8664,2b475a9d,6da1017c,43d0cb9f,1af12323,8c6f81be,3fafa5ee,c8296f92,8ac7919d,c4d88c9a,59442274,d0531b7b,f7e48e78) ,S(38b42924,419aecc3,acd6f551,346fd61a,4d82ac2b,55f7afe9,7a06eb40,cd109c4a,7f42c096,2feb2f73,b2b0965a,1f359a6a,de49d768,a2ce6b07,b5acb92b,73e05583) ,S(c3cad4a8,d8bb94a7,b434cf70,183e8615,bb2a8f62,24f216e3,446ac2e9,82138911,f649be27,8cad9764,20742ce3,82dce3a1,420e372e,f1b25b27,59a8ed38,7282765e) ,S(2d408ff4,d3d236fd,54fae40d,ce3ea9ec,d9212e57,36591a9e,55588e4a,54bd6538,d596adf0,e8692a06,bc6284bf,299bef6,85e2a171,585aa132,4b9a05b5,ce815b7) ,S(ee7adf6d,247f25fb,76e90cf8,13f888eb,d67423a3,a3c6fdae,bafb7eaa,7a33c854,e077184b,4ae8f705,6c10dd9e,f541689d,143f6871,789e1801,deaefc1d,527a8fb4) ,S(2f9457c8,a9ffaca1,3d91151d,c4c5e89d,dd5d37a3,7c9a864b,7c811f3e,1144b34,eb4c9848,9093d573,a295407e,1d6fc48a,787120ce,b3d3dcfb,b40634e0,e75e221d) ,S(d3f332b8,a0f11582,1ce3478c,efe18de3,60120483,ef531c27,7b30c46e,b7fec294,ea75b9b2,5d717861,d1af1c01,9c372941,c8968b90,ef134f9f,323215e1,bb0b2155) ,S(183408d3,38b05aad,3521fcd8,6ef36dd7,5f3ddb86,66b52f7e,9a4cdf1f,8e152b91,66998520,6edf4ac6,f39be21f,20c98824,210e204c,e4499809,5de35537,1641218c) ,S(283fec5d,b1145e53,ba8f1f0f,f9cf89a7,21faffd6,c2534686,3d395609,5f40374e,70b01237,74af550e,68e68e5f,65ca6e98,8846e03,cf39af77,8511be82,bc32fefe) ,S(ce7570a,4f943cfa,413bd249,d8e7dbfc,ebc73579,770fd6da,f54a0dfb,dd52fa62,e115b14b,ef4695cf,fb85bdf9,8ba3985c,bd5e5b89,83e05390,7c36f9ce,8b75d41d) ,S(7e9c4f19,c8f4ec3f,1269f648,cd919525,df790315,74cbeb15,37794a4c,838fd470,e9d9dbfe,8cf5f5cc,a855d6cc,bd11f480,60fafa8d,ad6bd3e9,c86df5ce,b0fa5270) ,S(e2a9bbe6,d5d5bfe,a7c7f919,df2309f9,ba04f4c,722a3ec2,3bf451b4,64cb001b,e4177ce1,c3cd6ac7,78925bd6,7e72cb77,d1925b91,d06a7f16,98411a47,86393fb0) ,S(504512a4,3e17ef50,e43bf37d,42a94990,f55e641b,1558c265,e7099002,75271012,954a5fd8,57ba3acf,2d4b1f41,e8e1f2cd,1f21c4b9,6899781b,742a49d2,e61ed18b) ,S(81d1f013,a6bb325f,4b2d1d51,ba72c721,859945d8,a17b3411,cd5cbe87,285f850d,2d5d2fb1,f0c30855,3b1fe249,298b2059,259d3d49,d4d7071a,dce4bcc5,dc937193) ,S(5b66c2df,c1d28266,18a87276,7e66c33d,d90dd514,14a3b87c,a733383d,1d895022,9bd0178e,38189569,2217267b,7407e987,27fcaeda,12d8cf54,49eb5472,d554e0ff) ,S(aeb5f70e,98ec5e38,dbd2d544,bdbff8ab,99b583d9,af58c597,afaf8688,20381186,618bd6b0,d25ca70d,f08b7692,9336e421,691b0973,f2f5a05,2e7adc17,3584427b) ,S(b289eff,e841943b,84761e3c,67a9c02a,557679ca,76ad753a,707a9821,2505052e,7a981f0,c21862a8,53b4f895,dc62482c,530ed738,5e5d1e33,cfb9d0f,e879992c) ,S(abae3945,8b12199e,6b0c8360,cfd28288,3f585917,e44e1200,f81bd356,f619291c,adb23bcd,b3d069c5,e83be30b,2469b068,b2a81b7,b667e934,233b75ef,b5753f28) ,S(4a9583a6,485b5a5a,81ac224a,518eb29d,1e0f658c,8d91b013,9419c809,55fbacaa,d8003c9e,e3c842f5,ede375a8,a7768db4,803ecf11,9b7b37de,cea15631,b4e8dbca) ,S(d52f630e,dba6f7cb,65fcf465,44ab0d9e,ea236ac1,460f17ae,3a210102,10ebc169,21155748,9fa93b88,3e5bea50,da005c53,68e21a0c,41bc83d9,145c13e1,370d26d0) ,S(bdc5237,82c75858,f5c50fc0,52e4c1e9,c74a2a63,35bca9bf,8d10e120,9add6a4d,abb1d9f8,74637668,e214efba,fbf529d3,12ff023b,c1d5723e,58540436,6834f189) ,S(44770a33,8bf0aab8,3bb64e47,6eb6167a,88156d16,8f13ce86,26ee0912,e59ad087,5b5930f1,2e9c40bc,b3393a89,5c2d6457,6a3abd23,b7291b99,c965c33d,ef60a55c) ,S(b15e7b32,2e404aee,319ac203,23e36672,6503108d,8ee8e1c8,3e32d924,515e1679,5246a819,bbfb291,5f82ed56,50796f50,5ced5c25,87347d57,a873ceaf,3d997e7a) ,S(a1ed7557,5225cd0,f2c50f75,8a1c1df9,665ae108,d5e04190,27bbd9ae,ddb00f22,3c83145d,ad9f8748,7b97e746,4850ed02,d71dbd04,93281a1,3d212776,6a791ee2) ,S(e8aaf361,6a1bc60f,d9bfc43c,2c60580f,479e9ec9,c23a37a2,3cf8afb3,1d918af5,6ce693b6,4a37c672,7e141041,ab9a0d58,9ab9c303,a5ac3d3e,c89b6f27,9e79827c) ,S(5dc6f8cd,2c855e63,52a4a4ef,6187a6d6,759c043,38a3db76,c5a3aa37,54c20a3,f602c342,8593a9a8,d671d1bc,7c1d8834,fe9f5f5,2e6a7f0f,bb870146,4e6f4838) ,S(63327311,67bed8af,68a063ef,22aa489c,f6563620,461af26a,5f1a07cb,6b42f3a6,b8f7c3b2,20701320,f20ca036,761d3e56,bf94a700,9a919f1a,3ea0cb81,b74424a6) ,S(8a40d925,9a393b38,2305c201,7e8654db,ad66e50a,d798a0d3,535230f9,48080263,afb6a74d,9849454e,dd7f703a,5c6616d1,43f9cbcc,9a9a5d6f,6a7b5d1f,9d9fcaff) ,S(e7147107,27c7420a,f517fd3f,9a05b7de,a6a02c8b,cc20b17d,cdfdeaf8,2078645a,da7d67cb,c1ede9d4,fedd5dcd,c96b04f9,a3561ba0,2581b055,eaa144eb,4217daca) ,S(6131291c,d95fb878,1e42a68,553952c2,9922bce8,91c026c0,cae1f69c,9661c82d,160e1c1c,13342fd4,59d4f989,8ae632b8,42b89479,13733b89,384fc104,2d30bf01) ,S(4bc4f845,b6764692,d0a9bfa8,1788809e,fc5e2aa9,da5003bf,b782bcf1,d1ca4951,87092dcb,b9c3d254,e3b055ff,3a76ec05,64c4a7c5,7fb1783c,efdc40fc,10b751f0) ,S(45a880a2,7bbee9df,29f9bff5,c985f364,52865b5d,582a201f,698e6eca,a2be67df,fe49a6a8,b5e46bf1,ef679714,dabd590e,a831d46b,8ee94eb6,13132ba3,7855fabb) ,S(6a826a38,317c0c86,64d6847a,220145d1,877e5495,b21500d3,f21f1a0d,4af4f2a4,4521954e,fcc98263,df2f14e0,e6e6b47a,f6b83f0b,bc20722c,15445f87,e05f4513) ,S(15356506,f255f7e9,6cc8aa1b,9dce572,8bd860de,7c6cc75f,613e8a34,366a23a9,cd15abbc,d744d485,d5e401f,1f89a5df,122f37b4,e362b4ce,e3e53b1c,110bf3) ,S(f3bc12ae,f53d9f5f,6b865178,2dac2ec,cacff3a5,cca6443a,2b5e1ca0,f2b89b91,cfd4d36b,eb2e11f2,41fd0f36,7a0737ad,303e915f,f247f131,368ca509,18e00957) ,S(7e3c8c6d,fa04a536,f7a26ef1,8b387649,22320bef,58453373,6f728297,335c0fd4,72ea16b5,32a7336d,3332400b,303c0236,b6a1294d,88ce7fe9,15571284,d1f7c189) ,S(198cbfcf,a0575fc2,c161c696,d85155fe,6943ab9b,d6e17223,d8844608,ad0369d8,d5e6268b,30952422,be59fe0e,fe7ba2e7,3215994,827a46c2,f2972b26,153cf7ae) ,S(1e056e89,b68cf35a,22183c08,9089b90d,5a147caa,780b1fd6,3aeb1350,afb0e5e8,b8241453,abc44c57,ddad6ff3,86d416f4,3e258a39,c6f8837,9f80472b,943f32b9) ,S(dc7ff974,8d827e7e,a6173b2f,1a646d47,d8108144,ce7f98fb,3fac729e,72faaa21,c1fdac5a,ef4c6f0f,fcb8e1c5,c4417c71,3e3d5f07,146daa1a,aaf2e7fe,e70c4914) ,S(71b95efc,c4981e07,5354bc1,1cdfbc48,36b2eff0,bf8f8ec2,9a99da1b,2fd28e79,fd5a3197,6fad6aee,c304752c,c3ebbc51,1f3695b0,9a737fa3,af42cc6,efd684cc) ,S(43854caf,29dc2bd6,c9f3e8ff,a25bba83,f6b96121,897044ae,6876883a,de542b3a,56365176,897632f,8dde3167,7a24f558,34c5c9a5,5c1cbf36,fd8b4480,3c9c6c81) ,S(2adfe17,90e9f9c,708c9b73,d5fd084,b6eff990,fb877961,45c2ecf2,d427b222,b5ce3160,5d6dd9c6,22cae425,ccd28912,c4439820,c06950cd,4c86d9b4,53abd7ed) ,S(a123452c,2b7eaf31,15b3a534,3b3ff31a,9f70c54,ae33c620,471e3e82,27a9d6f9,933d3483,78a71f44,3788194a,afc545e7,f53e37a6,f779f96e,8fa14ccd,ede3b4eb) ,S(9b89a3c2,ca995a81,86c15217,61348737,aab166ae,7decca60,3d06e32c,cec0a6ab,2a7d3701,a8724b12,bd7c4830,224ac083,cbea83d0,543b5414,80ba8c8a,e7731232) ,S(64dd7457,e7d9d739,8e2b9a0,dc45272b,384b0433,9ed8b2ed,c9079646,11e9e9b2,ea90f8aa,e214ee16,ed608a72,36699899,4e311dc7,780ef885,b29290c3,823c470e) ,S(59227431,be607c6b,d327fd71,4eb71c87,20abba42,1c7f550a,6b35767d,6fa2176c,cb7571c4,71c5527,65bd289e,a3cf3f38,796da2b1,2c953d0b,8705125c,4861d598) ,S(53d765cd,adb26e9e,1c80ddf1,99374363,843b7d08,a7237bdc,8c5106ef,795fe2c2,7bbbb198,eb39973b,76d87f81,94d45150,a66d4f3b,128a40be,c989a405,ad7c287b) ,S(e507de9e,c16b3bf3,523a989c,f5ff6c1,452ee90,9b66ffc1,6d7b519a,57bb66af,a2f2f02a,8272de6e,3dc8b395,8959ad2,51b6d3d0,4c81952,59a501e2,8ff7892a) ,S(16f48c6,eb84fb2,81903b8c,b9f60b7a,65601d76,e2a57983,5569c983,39b4a6f2,8613bb84,8398681d,66f1e75d,5b6ef44f,d827b629,f4956a4,41d8f503,dd32b289) ,S(650471ae,774265e3,270b5132,33d12d85,bb98e38,2a3b3af9,cab6339,e1446056,838e7793,34aa6fe6,cae90a62,d359c339,187b4032,15d97cda,4e62724a,a5a50306) ,S(15dea416,fa34584f,cc90e19d,69825fae,348d1ba1,fd7ac821,559aac2a,bc21dda8,1fcabf2,1e19ce68,ee12a3d2,84bd1304,10fa5f5,d45f9c15,d4070243,a8433047) ,S(b42b2495,4f1f70ed,3db90087,8357ba46,ee9d6a07,b4f7c751,dc5cba07,b05b46e2,e15723eb,e0bdbe6,d6f28d6d,a0443c63,4851f5b4,c551bec6,9f9196a0,969ed71) ,S(8e9e4f5,c6aeac31,1dab1125,dec9b460,6ab10b7e,8e250960,a17fc57f,c0230f83,ffb0e211,c79fbb79,78bd4e53,a05a267f,f1e32c34,d6287dee,64576d31,ab959ab2) ,S(87be7323,73bd4b73,8627fb63,bd4d50bf,d6f2bb81,f804b528,29549fe9,3fe1ac2e,f6a9186f,f147b9b5,ffc844b2,ec0e255a,1ae5537d,75624288,ce8421f8,7e94e1a4) ,S(43601d61,c8363874,85e9514a,b5c8924d,d2cfd466,af34ac95,2727e1,659d60f7,8791c000,7c09c94d,b328034b,88c5bbbc,11333536,6679eb09,9a5e75b5,83bc2c2a) ,S(341b1580,f83071c5,365f0bcb,ba66af96,6902e394,2a2560ac,a0daafa3,2ab49d0d,4b985b13,c5499026,7ff564d2,d4649c6f,7e8fdbe1,ba101d94,1c034e14,64877b20) ,S(175e7cb3,ce4a3a43,7c7181e2,c79fb154,33ac1aa8,e56492eb,57627171,f14dad95,31ce61a8,7834f52e,fcf8703f,93696f42,58130155,63ca5d9c,e92d8fc2,81135b0d) ,S(5ad430cc,64e61c61,e3b3c848,2ca3ecac,89c1e495,4c80ba98,249e45c1,307165ad,bea2a060,505c13bc,317ca083,c5a8b85c,9ead5f6e,1ac23fbe,ac7cecea,9251c791) ,S(41dce0d9,6dace318,988602df,7fa84c1,80f0ce3,dd7d09f2,8aefefa6,db8b837,74962c3f,ed9a6e9c,896635ea,855323b6,8850091,f84dee33,3cdff8d0,d2827928) ,S(a5ef4498,87104dda,103c1dc2,52067643,9aed2d5e,432fe5b,a23cc142,39961bcc,1cbcf83e,a363e0d9,3e6ecc32,8653ba7a,a165c526,765b09f0,696b0d61,f122db3a) ,S(4da26ece,9ad46003,38bdf68b,852a2cbe,18225f2e,2d6d5e62,6db57235,fb3a9d45,d10b5a63,7ab546bf,cc610e2d,1c3d61f4,61b0a806,e7ba29c7,3d3de909,e9fae659) ,S(6e621e6f,53d2408e,488d8eb1,6a19a4f7,e9d95585,11e69111,29dedc69,f98f4763,7b148ef2,73e1b131,341ad477,9342c7bc,7b945a2c,b52c448e,4bb5fd50,3cea1a19) ,S(ebaf5764,5bed7469,9b57ea75,8a395a90,66bae20a,8f082ab6,da4554d5,278be83b,5847f4e0,6c653033,5e29ea94,389ee3e6,d916314a,60126028,650ab9e0,bfcfbba7) ,S(c0f88a71,711b632d,24b55dbf,52b15d2,faa38ca1,1438c17a,6a6ff635,3310182f,2cbfad4d,16c07021,86611eec,408082fb,fb2e9898,141a5248,1c59e44e,cd0676ff) ,S(5d9b6c18,84b79498,c6244fbf,262922c6,dc1cddb7,3cf70ae0,1b5287b0,5b5c6350,328e831d,2f2b162c,4abe1644,bb54cc85,18db178c,5b6ae97e,5e85110c,7d7fdf1d) ,S(d1d1360f,37ed6e69,d4f214c6,323a53b7,e57d7595,55904016,654c49f0,4e02e21c,627eea93,c6c9b53f,94559414,40a8b100,6eba68d4,6c922b6a,1521f394,6dd15e4e) ,S(efc987cb,f1023af5,58acfa18,97b1b2b2,ace29a83,65674703,e4969ccb,ee411731,195a6a65,d3790bec,71642986,3bcef432,e38242fc,9f565dbb,e159bc42,f5740c69) ,S(f3026b97,163df3bd,61b88b78,73864480,968d1d7b,83ef6b01,31090faa,18284ff0,177c3a61,682363ab,bf281615,d59f06ff,5f87644c,84d670e9,a6c56ac1,b611509b) ,S(5d34ff5f,123b5b69,92ac92c6,8c9cff46,deeecf9,68ff830b,5622090d,682c5873,2d1a0b9c,8eaba065,43204df1,48eb1618,25443efa,80f8aff3,d49b6626,c5955ac8) ,S(cbf9ba17,94a95247,c39da065,84308cc8,e0ee591d,31a9b0bb,dac67280,468447f4,549b18c3,10feaea1,225fade,934112d3,4058101d,74f00538,1b82796a,d0461736) ,S(920975ba,9e2261b,bf5982a6,b57a7344,8e7747b8,368d7a53,79acacd4,c7dcd31f,e95e0508,81af550d,9221f5a,e9541031,6367d24b,d545bdcb,434e7638,acb46dbd) ,S(815b2ae4,6fdcb55d,926cdce8,2b4f25d0,39132312,3bc180ff,33fcf132,7eeca64,62f637c6,7d886374,8f1e2e26,865118b9,99285b87,55f25512,c968b4fe,49b8c971) ,S(1bb9a6c2,8e28d4ba,30ea8639,7a4d387e,27ca8025,da231926,de3c454,f7e0b16e,a0cbc016,5e32171c,8184265e,ac7e0147,206349d5,41035a94,f56efc49,dcd7ab93) ,S(6f0153fe,dffd83ea,b099d29d,dde278f1,9c05a4ba,78eb4c3d,34d337c6,da68bc22,a532d00d,35013f85,9f4041d3,aa231f2b,9fc49967,e0e2f82,4d5051f9,e7f0c626) ,S(3454f73b,3bee77a4,d00d384,71bf555a,ed23e5e6,c6dae855,2e9cb7a9,1b20258a,92c20846,cfdf1e8f,3fe5bcaa,6bdedc3,9926833a,3f40d28f,23a8f952,d8d18dde) ,S(367807c9,a3606b4e,1b8c2616,ad528030,1dfcf686,40eddf02,fc59317c,230e9a86,1f023f2f,a2bbece7,3dba14c,124095cb,fdc4f92f,281a14,8304a412,c16ecae6) ,S(8ec4fdc3,9891f6af,1374e06f,c44b815,1b82541,75fc4909,acba5941,201af62b,2dc6cae5,cac2d887,83dca0e5,3c798f8,fe067bcf,5fc29751,13756cf7,ef4e5f1b) #endif #if WINDOW_G > 10 ,S(5cc24a6d,4c5b24f9,14542f91,e5fa937f,ffa08551,51b8b842,8729b06a,9178a263,b1da8635,81531a1f,bfb38a4e,419fa1fe,ca8d55a8,3ddbcb98,da19d5cf,fb7da472) ,S(83905926,c03905c3,a9644a6c,da810dd2,92602a50,50c52a21,9134fc4d,e3599e9f,4293260f,e8af6792,a20b115e,aa837638,9094298b,21d9de16,cf20e0c5,7a46089a) ,S(944b097e,4721e9dd,f8204ac3,d3878fa,e8fa6c14,34ae4822,481b2985,6589b6c7,5fc47565,30e9b095,f8b79643,1e745b99,1525bd4c,4764e8e,e8af4b96,9bd6ddf6) ,S(ab0b4a3f,cfb7c134,e1caaf04,a63a7331,17327a1e,5fa90301,7b5ebbf,3423b73d,e1e79263,a5bbba8a,cd78c92c,faeccd3a,b84944d3,785c0781,3763bf1a,ce96c9da) ,S(57a344b5,220f2b0e,f7bf7fbf,5a2e4e7,1aa2c3d8,7bf090bc,f803dfee,fe8b85f,f82b7d0e,8ef9620,e48c9f13,53a72a95,a9e11a3c,1678cf10,576e639b,b1a7d04e) ,S(6e053e1a,800b7c4c,51f8c4c9,5cf0f4ff,3608e396,ec46188d,a1a9263f,c8d81ac5,86389e98,e3c823c9,e1b5384f,fce428c3,62e36579,7202fdba,dc3d8c49,395e7473) ,S(62d76406,1804717f,b30d4a7c,7567b545,48a289ec,7f083f1c,59deae25,ce485cb7,f1d6314b,661d1f8d,8531d57b,9470fb53,d1509b2d,a626a0fc,4cafc941,b668be84) ,S(e5db28f2,219fb2aa,830cf108,bd2449a,5c4d0800,82d34658,9e347f31,dd29250f,c296e646,32f97dd5,ba3b7012,ead44b6f,324fcfd2,f35f8b24,8e58fe68,888bd453) ,S(4725b3e9,a3d00de4,8a53177c,9fff831f,733ec89b,c2994ab2,3fe815f1,9b32729,ac3b7747,de38c00f,145fdb74,1482bb52,324127cd,2979ee12,d4a9e689,b9f8e778) ,S(d0d3afb6,492c72e7,394ed918,7013e347,b036b65e,a76e0569,bbe9e346,41d72b3e,2dd3a45b,94aafe07,53061caa,a28560,bd952b0b,2f63f13,96f42fb7,8e02fef3) ,S(7853e735,d717c857,97b85654,a24acff3,104143ed,cf4b4b4c,7869068f,c304632c,a873d9,e70fd14a,c2777a8f,b5a02922,bae3a31a,14938e69,cb535355,de1efadd) ,S(6db26b3,7d4fdc59,13a1a01a,14c92356,ee44e2c9,7f9d72ca,7789de33,8ee904a4,14fe2225,bf2ba0cc,28c1c409,e9849c4a,d8adf792,63869b68,54a28ae9,631941fb) ,S(b52f0869,bb98af3c,b2f7f5c,669fa43e,538e400f,63a9cce6,99aa2ef8,eb2848df,24566b24,55bc454a,e7b378cc,a0e57b6a,8b821c8c,a76fb858,bb616e17,8907be5a) ,S(8614dde1,1ee6af03,eb34a9e9,970fa7c3,234152c0,1384f7e4,c1e1f93a,197b448,2a1125a2,ac996870,2ba22b5a,d230c40e,4e5c7e55,d8ba6ba1,5e54d3cc,7b72f3cc) ,S(982a37ae,625f6e5b,78e71c18,f20bdd0,8b3308eb,59d0cab2,dbc20937,938c1cfa,671fe16f,a65128,591249e2,b5070bf,2a689e2b,dd6c57dc,18e5309a,b6a40d0c) ,S(6bea9305,26b4829c,ec99742f,c9231c00,627a09af,22ca9d9b,4081a2fd,4c3e703a,aec5402a,54517b4c,1f344d14,b1943e69,d7541f10,c45bd483,2b02b059,499a6cc1) ,S(b5724781,8694487e,7cc188b3,36d116b0,54016a99,20731920,ba7bd29,96583edb,5cbbd186,1f80a4bd,3d58262d,ebc58ffd,1d278fb3,b4d7fec6,208f6286,77845cdc) ,S(de1ade62,7ba00e91,786f4f53,18ac5392,4df5a534,704edbb6,2e0e9e2d,997c5412,7ef486c5,bf23bfb,fc6dc15a,41c0673f,a9d003e6,e1d09a8e,4bffee9d,ae2021e0) 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,S(dc02c852,efc115f1,c5c08540,deceffe5,d68b82e5,99b78711,5a7a333d,e8dda172,e4e6593a,8e1ae842,ca7f4eae,d8cccaa2,8a35f8dc,cb8549ba,2367faf5,5f6c29c6) ,S(ee4769e8,223822ff,c28a5a4b,5f29fd7c,a54fc81,72175cac,1b6db5a2,91ec57c8,fca2c6bc,4076c8eb,a0978b9a,2b0158c4,33890514,28094619,38413fe6,c020385f) ,S(f3006c1d,34910c0f,d435a6de,cf088c38,2cf990cf,3124f2ab,b11d2727,d93ef066,7629f5,aa367f51,a29ebaf1,235cf267,f8016a6c,88dfcd9b,82d36904,c949eae2) ,S(7cfb203d,7bf5669,129f0a3e,325c3fd6,b1b9c804,4932f0f3,794b9357,1e7313b7,4f76b9fd,24339c38,c88c4217,387b016d,e4ae08fe,67182d39,82a45bb4,e82bc60f) ,S(cca3ce0,36e00993,9d30be8,e70455ad,efeabe71,83aeb206,a324d0eb,32312c0a,9674ae58,fe947c6d,34c63725,2058c88c,91b437dd,98da58b2,efd7e8d,1615b9e5) ,S(9fb64148,81cd5c27,82da071c,1f98d71,d9815fd2,2389d212,c66ace66,ab0d9c8,4c25454,1a513742,5f75e515,c04f1c73,d11d5047,9c76b09b,ce23c13e,d1813251) 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,S(46f3def5,9835c9ae,1a7b3b13,a920bea9,e9bc12ee,633b3edc,57251b72,3560837d,587b2e1f,2e8eb9cb,37aa6977,870214ec,818fb71c,1035eeca,91d53e68,150ce67b) ,S(8d3418fd,eb3f0968,de51f4d7,cbb60299,a50ceba4,1915d8b6,5774cfb7,7667d572,cee79910,16a28462,aa9da7c0,f67b4c7,e8b3dd38,f4b2203,9d05115a,ac661db8) ,S(98cb0f09,4510695d,78a0a672,eb67253a,30f4327b,7864fbcf,529cf212,ad6f7c10,25952dac,4e1b5035,9b47e9b5,52852d1f,300fde75,a6bd532f,9fd56af,2a0ab333) ,S(96045e4c,ca075fc,4a5383f3,f03de105,a34c7c4c,b030ceff,b58b98e1,2b39a3cf,f527b8fd,92234151,ba11f24f,7bd5dfed,6ebd03e3,a5048c6e,8f2d5231,7201bafe) ,S(f262e891,42addef8,cba26a9c,ad779761,c3f4b3e5,5990a93e,703bf56a,99cc6030,275cc764,86c86a90,f597dd6,7092ecff,5382c7b7,33939ca1,d1f3218d,6f0b594b) ,S(cd79c02,ee175336,5f9f7900,be51bb2b,ad75ef81,3c6c5634,7cc717db,156d17fe,b5ebe8ff,b30de5bd,a5326044,16abbae1,4ff9198e,b491794a,c4500031,947a985d) ,S(28b4bf22,5b1d40dd,e0122e03,e630830a,d9ba4629,cc51c9d2,80a225f9,48f858f4,24756189,98bb414d,4a534c6b,e300297b,aadf4ffc,b10e6795,4ea36e25,2cf3cac0) ,S(f018f206,7dd55df3,9c53344b,c6128a5f,cc765c36,c7b0bea0,16c8465c,c6ed2ff7,d9fc5ab2,cd619d4a,c66c1cd2,251504cc,cda34a76,86c5661a,960a00f8,e4aa7e66) ,S(496968cf,8086d02,9a5dd5c7,4f47cbda,7f661ef1,488b3942,18ed886c,424a7a13,d7d8df98,442060e0,f17a363,579c6600,360b5124,2774e2df,c8d4b787,1e1874e7) ,S(242d4c59,e9113b77,68e48574,93600da7,b984355c,a1d07949,8921016b,22efedab,470dcfd7,b0c8c2ed,63a28074,a505573b,42f50920,6b0ae577,27a8b796,7a0f42b1) ,S(b6b804cc,1a1a59d3,84c4afac,c5e5050f,466280bc,d5ab1586,1d20f4dd,1385e8c7,2f789346,2a636a9,9ba2a1d2,32829f41,39b57967,bb26d0c,898798bb,6521d439) ,S(dc30a3d0,7ecc5fdd,38b8048a,f281024b,46904b2d,2a4c51ca,d1b49b7,1d918a4e,326409b0,70550e97,58f53698,7936a54a,b701f7b6,78a7d10f,ebb511a6,c18cc917) ,S(e1fe434d,345bf330,83abb628,f4f44ac,5fb22934,977813c2,c015f2b,43d3fab8,1b251ca5,2af897ac,4c08df48,ce3d1607,d3b31b2c,2dcd7f7a,59a95b07,774c4d83) ,S(a8ed88da,e08ac5e2,afbe4a40,ee775645,82c2f513,cfd72060,bd1fd5d1,76fb8d08,f4fb60b0,74419630,fbaf5b53,717b2a6f,5cc2d98f,1d29481b,77b1f9f3,84175729) ,S(b52cf828,de1e9cd7,c95c083e,ec50d228,8e770713,a0e2543f,76fa5790,2c7c6481,635a3953,46fbbf,903dc729,d3e3b52b,43eebdc5,3748ed83,3c95eaf7,1b75790f) ,S(702079ae,f76d9bfd,ccb957a9,4aad93fc,b1297c54,d634978e,4dc78292,161d5e83,4983c08b,f2d81c52,d3b3a202,e0c6ddb9,32a43a45,c4b95f82,c8c10642,5a783b52) ,S(4638d4d1,8e9de1ce,ef4fe8cb,db4378e2,3ed3dcb9,513cc9a0,dd73ee2e,be57bbf5,561ee032,45cc3066,968853f7,51fa36be,cb50740,a5951e87,cf77ef20,cb27e110) ,S(eeb34eb7,5facadde,d561dc5e,e3d0a039,d98e4880,910439cb,ecfb22d9,3b386bfc,f2b23cff,5ebdc8c,558db8c,1c311a94,e9d8f63a,d1cf4af4,c21c2349,a6e57c4c) ,S(7f2c6e5,becf3213,c1d07df0,cfbe8e39,f70a8c64,3df7575e,5c56859e,c52c45ca,950499c0,19719dae,fda0424,8d851e52,cf9d66ee,b211d89a,77be40de,22b6c89d) ,S(6ec76722,1ec5d27c,f7e11064,d4f8b016,3cea090f,6a950f81,85623303,23e53647,9b03c757,9704e839,c8eec7d0,f063c4fd,d0aa7ba0,5ad75254,984b1703,ae69a3d6) ,S(98f6f69d,320d5eca,1f184b0,378f67cd,b44a707a,c5b2af54,99e9f8a4,524dea7e,26ef6b3d,7b037663,979333fe,56bc33a,ca54a3dd,78c9244d,79ef5426,f2b69a02) ,S(cf1ef445,58b82c76,5d77ac99,8c0170c9,2d308668,2d9ed7af,2961cf05,5b47e390,8bcc1d05,fb880ec7,8762d8f3,f5afefe8,f4345bd8,36397d23,befdf446,498511c3) ,S(10e01651,efa26f2e,f88cc5c1,594f378,9ab62b82,5a0875aa,37c280a1,8c6f07e8,2e6a15e1,1f776335,30fb2cdb,788aaa98,83105da3,7e28c0a,8fad503e,b9779df2) ,S(b94e2fe0,41ce209b,6efd77d7,44983130,af90945,120b9a58,5427966,e93eee4a,8f7abf1,103e92f5,5dcb1dde,746df10d,a86bfb8d,2776a0f0,1d07142d,c9bca443) 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,S(ae40198c,bcd54264,904b44c7,c9019553,8f3f3727,a0c9639a,764cda80,b21edd27,3a57f08,ffecccfc,cd9a0e7c,827d98a2,ffceea9a,6c39d200,5cfae623,34eeba8f) ,S(f4729787,abeac0f1,249b1d3a,c19bb025,5764a854,727b415f,73e24c88,a8a981c8,e31161a5,68d81328,c7f9783f,de146d07,b51aae15,bfe719d,ab4e9e,ae65d172) ,S(f92f02b8,34148934,f7059b61,7e84d0a6,f52d3b8c,a7d7b69,ce4c8175,7ed5884a,faed7ef8,82733020,888eb530,5c6dea4b,cacd208f,fbb66b7,6f3cf41,a8864080) ,S(a2bed8aa,e93bd682,be8cc4d,d1f84fc2,9efe4022,b2b0dec4,9ed3ce17,7cc93363,287ab9c9,62126fb7,e0340f29,9edeb89e,7bf235b3,b3f08213,d630c9df,198ada1d) ,S(5a42cfcd,3d1811d1,99b09dc8,9308134,cf6219e2,e029598e,899418f9,b7af4724,95ce721c,39929d76,b0ea83b1,80bf25c2,e301413d,60fb8717,2e0ee8f0,593f8423) ,S(1d27ab05,67e8bf19,323f1eca,44175085,2e768a6b,a1436789,40ba2b94,5b0e530f,18439939,496d29a1,58a532be,76b04932,a23e3ddd,d51a1b07,c6c33e6a,11e1afa8) ,S(592bf859,22c05bf4,4b42fcf6,e4cdf3fd,bbbf8088,b7263d31,9bc74914,6eab4326,84cbd8c3,8dccf0ef,de3946f3,ba2eac25,3aaab976,8f7f601e,7d95bc74,4c7f65) ,S(66730a70,5ae3dab8,bfc01f4a,deeadc41,d4df156,d03c4fcf,1dd9e16f,9359d5,c04c7cc4,4ea1d8b2,273b9170,19b9efb3,6e8f422c,4863f718,582f57a0,778273ee) ,S(3d002600,532420ac,9fb246d,84e48560,1ce6897b,979491ae,7c5914e,dbb7fe83,5bd73264,2f16d4e7,7bcc4855,72494523,c221fa1d,321c552a,53241dd7,94c7d98e) ,S(d42ae36,2b5dd22f,d2089d37,d22e2c2a,750395ad,710aa1c0,61ed4275,43a24487,84439e00,1571e1ea,53bcc24b,a11b6f7c,ded0a649,b2a12fc9,c2a618fe,cb39ada7) ,S(37c761ca,486fabfd,b306d,c18e9074,409e101e,5bdd1670,edef1253,aa253743,e53840e3,1110db1,89ec241a,e7b2cb89,29669da9,5c07f3d0,6277f667,b90cad12) ,S(4e672ef8,bbafbc8e,eb819f37,15ac0d6c,2afa9781,a197345b,2889ed0a,f3b0e788,9c10f0db,bb16d807,4680133f,e62e0eab,130cb0b9,51937852,4afcf4c,38814061) ,S(c1f2943b,23c07929,e9c635ae,66f62949,8e1df12,f35aba68,ed8791d6,8fd51fec,3376b6c8,93ad5ec5,991f7ef9,6a6b1105,2f2262c6,680045fd,fc4d4bfe,ea64ae75) ,S(3df2461e,739cd984,72cf10cd,f663e651,351e826d,7afdcffc,e17602ae,c0370be6,5e48fcb3,3ed9c0ec,3594eeb0,81adaaa,bd5ec5a5,7eeaf01f,c9f00d02,c692cb06) ,S(d4d3d528,f98b92d5,f4c4ecfb,ab60fd85,50f12327,5b63b3fd,5518c1f3,d62a82b7,64496d50,85435de6,991a838e,d984bc09,2554053b,54b05a2e,490d2ce,da7d5b76) ,S(ecd8399b,4aa3368f,1a7a4113,63ff03a7,ad644847,e225108,b3ee7d02,1209236b,2e1209fb,a7921c29,e351e61,73c02cb5,c629d88f,4ca51af,30f37123,75355213) ,S(d5990be5,7e6a0da9,333354a,fb344d59,416d1a70,785cdae3,8c332e09,cdf78722,b2a2cd8b,73f76f3d,1079198d,34441008,278f73c8,93979ece,eefc5911,7ba17814) ,S(7598ab65,1d8ced00,af3d5978,661d801e,b57e9089,287bd74f,85ef042a,90374b1b,589fc426,9466b1ff,b9c0cbd4,b022e9ee,7edaae87,8f4cc240,b60db60d,6c28f04f) ,S(fd071417,b12d2d31,852048b7,61c5301b,be088cfd,98ebce7d,7e0922cf,41f694e7,2d9c53f1,ee63b93,2adf679d,96b548d8,d47d8f74,58ef8b45,9664da23,be32c363) ,S(5a5b4990,e290868a,d1d571ac,8e9347f2,b1e513bf,cbc2b8d1,5e56ce01,2b72ca0e,c76852f5,7159524,541569f6,3c4c9c7d,424285e7,e83145d5,e5161998,efebf968) ,S(93deec24,3cd4f146,42f5a415,f6ea6f36,25c90081,5f3d20f5,9728c056,fde7f2bd,88f919be,b9993a16,61f78145,f54149f4,6abfa859,1907736d,d5e85f25,bf2dc7cb) ,S(9224d17b,a65ad967,969104c9,3068d439,9c9bec7e,7613a602,f5c9917e,46df82b6,346c98e3,2bc2a4e8,c7689e54,eeb1064c,1b5691fb,cf5a4710,55cefbcf,18a32f65) ,S(851acc91,24ddff9c,14cf054b,87347a71,cfc91637,6e559189,f055143,3b79c38e,d959bdf0,58d21cc3,430527e8,cc49dc56,2dd20bf1,30f0e13a,55cc69cc,1e116f35) ,S(ff6c1303,b7c111c5,87e01ef,44829510,eff0a612,931f9212,2b71075f,2cea4d96,24f09bbf,7bcf50aa,ca239be,b925505e,7e99d0ff,5a959574,5370eea1,7b4841f6) ,S(f23bd9f0,55e7bd1d,433fb51e,c8b6ecb6,fd5014f,4f4ca9d0,6a4bc636,435fdac0,9652b458,9d269ad9,68ee7012,aee47447,25ba917d,f120bda6,9d2194ee,a56d7b60) ,S(9d622c56,ea6d5d19,7b823e60,1bbd4af0,1fe070f9,391bb564,2a05527a,49f46ff7,8061bb94,d6485fe,d9fbd557,66db3dca,c648c7c4,2e025494,e6c3a91c,fd5c609e) ,S(9494efe4,cff5d5e7,6394b67c,407b9961,2915afde,56933b80,370d0adf,2f020c13,ab0c7e38,c85ee1cc,27964b2,de42372f,fd86ecb8,fd3f0a81,84f5af38,58a7e4ea) ,S(a8e4d7ba,ffbc52fc,a8cb6c,2938a01c,e028c259,97403268,dbe1600a,952e1a86,8d5b83d,dc3022c,4f79723,c6f16722,cc7eeeb9,c964496f,c9f67c29,351a0bed) ,S(83841f64,938e460f,eff191ad,4d72d7a5,203c01af,1519cdf1,f17c3bb5,e4927ac5,f5868f2,c2e87249,21373397,40415c4a,ecb1f30d,b204fe41,80e01d79,eb536800) ,S(ee8974d9,5ef03f8a,860dcba6,7b597fb2,af2a2df6,950aeacb,d623c883,20612f6,5cf10d74,3085dd7,cc695145,3f9f763d,6596abfa,eb7cf216,34ee07f8,a4f141ac) ,S(68e88d8c,23616ca3,b136e5fa,3427628d,a92dde6b,2691d857,b2d01a60,b6579606,5a9090,3766d6eb,c58c5d60,9b6a5675,e5ec7b73,86a17c41,2574d179,a0fd5450) ,S(fe34dd8a,c62ec8b6,20dbea79,44ccca40,cfe6ab5a,ce3b2e7c,50ac589a,9522345b,88cf0055,adf1e122,535611d7,bd3e00a7,30c9edd5,898d25bf,f0abb9bf,6bd6c8c0) ,S(423a7a9c,c0f81489,aaa62479,c1317368,9989366,fd18bff7,f6a5f235,8251bc1f,c926b3dd,519241d,2e776ea,16112e41,259ce896,472ce71f,de4261bd,29c678ee) ,S(7fa60bf9,7cbf54ff,e61bb840,b2e08d91,ffb0eb4,727c0e73,ed4f157,ad0b98f4,d5b1aadf,84d387b8,fddc7b26,a7f736a6,7e296fed,7978e81f,6e7b3b09,e94d733) ,S(9e53cb0e,f1eddebc,77edf8a6,6917f915,8294815d,eef898c,f1e77433,60153a66,5358daf2,60fea2a1,b9a4c6f1,b8bebe09,4983499c,fe5577a2,ed8f817f,46b41ccf) ,S(adf93641,c616c677,99b44ad5,354332c0,1404718e,8ec91e96,31e69552,3ad6f119,da3c66af,e4cfb3df,f55f6761,5c6ac42a,8dc17241,5ad38619,dfe2a13b,7e42ff9e) ,S(701e3ec,485db367,b0687ddb,2be15f4b,5b6242c4,396f6f0c,9726ecb6,474e4ca8,1098fa76,13dce1c5,29f7fea,30740377,691aa3cf,3d13cf94,6f2d8191,2d3b9e83) ,S(d8fc5ba5,d3ecaa05,9e9a7e04,2c52500a,d513645e,6149e84,aac0d910,f8ccfefc,72724b4d,eec94da,7494b4d9,83a2df06,df96ee83,e578d920,c2597089,7b4b3d8a) ,S(7bc88f9a,8279ffb7,658a186,faaa5f0c,c900cb9d,4a33b8dc,c9eea83e,ff71398e,cdcd21df,e5ed8151,1a2d8c77,e08b76f7,4939d39f,1f5581b0,aa956066,fa14a7c) ,S(8578d531,bc79e1f,6e219bc7,7f2172a3,e5fb92a5,efbf9919,f46ea11,6f5ef0e5,fcd1b2ac,39c262c6,94eef5e0,52338f9c,cac2d04d,ed17c290,768759cd,13b7d550) ,S(98bc22d7,3ea2661b,545eb5f4,37e1cc0a,d4124020,44bb9093,5cdde758,a8020a62,143c7dde,d33ba5b,c2ac8d83,cc462f94,2607bff2,a1aa32d9,f32e14c2,82232226) ,S(7fcf821e,95d2176d,d088106c,a5bf0855,9980f265,ea3c401a,aca44b0a,d5e8ee10,27c341ae,87e7afee,f8af4598,e8e27cab,c127b054,1b389cfb,266ec9d2,fe400284) ,S(898a39b9,d440ef05,f87e195b,6a334f93,67acd67a,1fc76ca8,316292ea,216a5f1,eb642fbb,fe3274e5,2fd1cae9,744fabfa,c0db80e6,2bd4f7c3,fc2ca43b,18ce52ef) ,S(3ee974a2,8918c216,a962480,1f18bf9a,87d6a627,83323e3c,bf138bf4,3f2192a4,f5b386df,ac71eb35,499d5b2a,960fd20e,fde39fc,10dd5c63,dc50b55b,cd660d9c) ,S(bdd10d2f,de76df34,9ab753ee,d06c1251,9766bbf4,2fb610a5,7ddc3f36,4047c14a,504532ed,34f97eb9,b8b27664,ab440032,2b8b47f6,9c403bbd,6bc74330,16923dec) ,S(2c179437,39784124,4ff9a4a0,eb9ff292,477a5148,c4176b23,c000a1ce,3bedd63d,a367b584,4f9b7b2b,a82fccca,b9a12a8c,2c1ca5f7,3e630173,e37e600f,f2fcfb6) ,S(282ef30e,f2d61d13,6f71e6df,6ee97ebd,a83036a3,2d3cd841,36289798,b3e71580,90b0cd33,c350ea2e,54c25264,7a3fc91f,5b4f9dc3,1f58e86f,c47825dc,e3d0f43a) ,S(a42b4d55,42acfa7c,b54ab3d5,ee0bebd,85bf6ea,db138ef7,1ea38c73,899eff23,17e38880,f10b9927,764c4997,326b0b9f,63d0e03a,fd2f0bd,b1ff3cca,1f566bb7) ,S(b23acc64,c5b00c8f,4b580d47,49589559,a06fcea5,75f3d38b,1a02251e,ff7ef00e,66bb180a,7eaa64d8,4bfe6a17,d457f5e7,73964ac,ff908729,3bc540aa,1cb6464f) ,S(942dce6,96aeb063,4681ce7a,407516e9,89df029c,ecc77023,411a628f,75885ea7,e208be8a,88be7b3f,6b6b06ce,a3aafb45,c439f0ba,d517a784,ba13f80b,707caf14) ,S(b8a6a2b9,52194ec0,8238e4db,e71eb948,23e64a94,e10ea0e1,610465ab,88392d16,f8029f31,b8e5ee3f,77a758ae,343be258,34c7bef4,c1b555c7,4cb63d51,cba5fec1) ,S(a36d3369,a1ee05f7,b1fdb083,ea614cb6,f15feac4,17a416d9,cc83fc2,868fc20,e4abd7f9,fe40f27d,5b7b7651,6a9fd714,aacd2ae0,5f0a1f10,e94327e3,76f0af52) ,S(4ea30108,3d711ae6,ffccc89b,9d6fd4d5,6f03bd68,f4508cc0,ebef5e43,88dda1d,81e9997a,8b1c5949,6554bcf,154166d3,40f9ea5f,ce55ec83,eed793d5,5ca3e513) ,S(20228716,1c1c89c7,64742e62,e427b712,fee118f,406a175e,ce2f424e,2affdc55,7837965e,cf26a7f3,428d2864,41e1d09a,91eaff0c,5ecd2c28,bc817766,67fa35b1) ,S(d3c072fc,8e4bf160,5790d429,61206123,95be9092,f166784c,f5adb7e8,6070d20c,72688262,594c75bb,bb55c0fa,af7991c8,f412e0eb,afd1c0c,f5bcab82,d8daf31a) ,S(294dac7c,e307fa7c,cf0e8f34,28a354d2,94003dbd,ca763dad,3e6df60e,530ec82,479fc222,a7bcaa62,aee807c4,ba6309e6,cfbcc783,afd49ecc,fb9b45f,cf84673d) ,S(3956ca5c,c09fe8d9,e4042a8d,67b276fe,225de609,ea24575c,7075d9ac,4e732fae,1c965fe7,a8219052,9d25ee0c,e1fd62f3,7196431d,7bd78302,e287a26a,2eeaa23e) ,S(24d2e396,da144b48,e736eb06,84940175,4f4109d6,6d87a9e6,97ee82bf,91fb3def,bb79e772,24b02fcf,dd1e3c9c,edbad212,ea875c75,1fe7c81e,76d7d0d9,a372236e) ,S(638d4042,f16e5c07,fcbf9619,dd9c2f91,18852889,3e12cd3a,b49e2b9b,99a2aa5e,d0d97842,4f0010a4,df9eb8b,8e5d8147,f618da43,74b8a4db,222e4ab2,b32b3d92) ,S(f91ad5b,a99972ba,bb323a1f,d3032e1d,94202d88,63680c5c,d7d67828,8f0d866c,60b66d45,a693175a,3a38bb4f,efb32dac,1cb558e1,b0d13571,e24a14d5,9452bdc0) ,S(3154137d,779c25f1,4ff1fb88,a6d0370b,9e6af48d,88e7fc39,c6417272,eaa69b7c,eb3bd91e,9c09178a,398e112a,9264484e,c1980c19,b1993b13,560d39fb,92295f7a) ,S(f8821e1f,dfdf9fc8,1e3acb3c,1d1d7a65,f710be2d,94a19355,721cb93,61549597,bb507868,c1e05282,51b635b9,dcf28e5a,c5770c05,c7afc2a3,f4b4c45b,7d8993ec) ,S(8409463a,521404a5,a2d8aa90,50e3ad8,ec5d6faf,870333b0,6dd4f63e,8354a655,cc99452b,85092ca5,39cc1b66,83b7ab37,1b8a6525,269a1ecf,91b857be,e1db3bd4) ,S(96802411,12d370b5,6da22eb5,35745d9e,314380e5,68229e09,f7241066,3bc471,ddac2d37,7f03c201,ffa0419d,6596d103,27d6c703,13bb492f,f495f946,285d8f38) ,S(9d1abaec,9f5715a1,5c762824,4170951e,f85e87f,68ca5393,d3f9fc3f,a23a69c8,f21ee700,50dbb61c,238c89e6,29423538,71b010e7,98867bdd,149ad28b,3f28cadf) ,S(1fb96691,8db3af46,c37234b6,a4b04371,9886d6a0,5859ba32,f72742d6,141f7ae6,8bc13ecc,207efd91,f7f4c442,6e9a425a,a17b5578,20404eca,b09d5582,d41f7379) ,S(22d9e364,b9274dab,98bcb23,e0428e8a,416d54f0,5a781281,ee221db6,9e1ec7b8,5dc23258,f93d7db5,e5799195,b74e9519,4c300a91,28f924c1,c1e4865e,2d8407d) ,S(625fa450,aed083fb,30166766,d5874131,adb168c0,247cbff8,3987297b,f873e45d,720a8104,473dc904,65585ed2,1a0244f0,fbb5a286,5b8e5117,5a21f644,8776bb7b) ,S(24acb1c1,9b6dfc25,defb01c2,e2681ae8,2deacc0f,f21ae8ff,1f82f37,a6a2147f,f729d335,210e8061,8a8abdcd,b71aabe1,93f50ada,dfaf7d52,783991dd,d3ca5d4b) ,S(d2856803,a99d30d4,f3a328e3,bbf7db3b,6c6d1896,ba5b339f,33c1302c,f75ab555,9649994d,64705b87,62c98bbf,1b41b725,2b814a89,3e780fdf,5689c9da,692d6ff) ,S(80529e65,9d196884,b15e95ef,871e5fd8,8fb5298f,3bc7831b,50a0bc98,4cb5fe0a,868b3e4f,9ae4bea8,efde50bf,c5a5b268,b74b4a8,74e86de6,e9ae476f,10b3b778) ,S(7f9199aa,3b8201ed,5d288e49,49c43277,e0bb316,953f1dde,d0674d7e,8728e183,1aba673,d0372029,546c174a,3a72268c,ee9d7e41,dd97de2f,fcbe1f9f,1a5288b9) ,S(7d32c885,8e959f6,48c4674c,dcccb191,29b4566d,644d2fb7,6d0c8966,2c29ecbc,d90e94ec,b50bfee8,c951afb8,e65c7386,875ea99e,31f553e8,66e00342,6d39698) ,S(f2b961c0,9291ecc8,576ce67e,bbd1bf01,1f1727ff,ad9eb74c,bf8819e3,2d1abfbf,ebfe5849,5a1e6a36,46c38220,8656f638,ed0aec0a,d40c0524,1707102,3126f795) ,S(d9a0c689,95283291,972d6a72,897181b2,6b4ae317,4e98a676,f75bbfbf,81be876e,d36ae886,a0acbc9a,d1564d97,4d3f0309,e9039b93,bb350d92,2b7f8c7a,c6bfa042) ,S(c7a36324,6aeb7c8c,991b2aa7,10abdf5c,fff29912,30b3a69f,be2dd481,7c7c3e0a,1298fdd7,e448d2d,79986302,6b4b2d49,2b32148,d6d1e5f8,15f5b0c0,5c9e21f) #endif #if WINDOW_G > 11 ,S(635cd7a0,5064d3bc,66535a0,4dbf563a,640d2464,c7fe0ac4,8304214f,e4985a86,e40265,913e77f6,46735cfc,af9e2f30,e8d5f047,f3281a4c,e0453e27,e9e3ae1f) ,S(5da624f,38edea25,37f5b632,695b481a,eca54bb7,2169cadc,c5b91e10,989ee5f5,d3ea6dba,a1080300,fffaeeb2,43a5256e,48c28822,37b16505,a220d771,ca721779) ,S(aa4f64a2,b19775ec,92c1f687,1fe4b6d5,ce05278c,2976c80e,fe19284f,e87d4d5e,f39f117e,95fce0fb,6976e949,9583a66c,224ea028,8396518e,293793dc,3ed4f240) ,S(9b6518ea,99ff1b42,22a93f26,62e05551,d60969ec,ebe378c1,477b5c36,427e0641,2e9f1655,8650fb3b,43aea9dd,30532ff9,bebdf7c5,1d421656,27b7487d,8f93165a) ,S(6c9b9aa2,b5972e0f,a1e01138,1ddcbeb8,6547f47f,fb101159,4b193d00,ae97b562,af09d91c,8d4c71d2,be523d0f,9d205bda,a6e78eb2,67476d3b,1624a038,6275e27d) ,S(a2a1c880,3cdc95c5,5e636541,c7112a0,cf80aec6,a37e5f71,f5366612,db467cbe,c4cf570f,3638f040,ffe5410d,50d4b175,802e2e1a,c422fc2,73eb9b2d,4e23fc09) ,S(63d3750,c961ccd6,34a5af10,48897366,13102bae,20f2c8a9,ca8437e5,ab650427,87415332,74b39a76,72de90dc,698742a1,f21125f0,71393fa0,6d670045,8e339248) ,S(8d070e66,e4428255,a53e8fb,5845d14c,bcc97dbf,19b6930e,1f5160b2,52bdd04a,4bc98c82,4f2b4f04,c9884099,f173cd22,48cdef90,ceef4bb2,497da8dd,99487ecd) ,S(f1fe56a7,2e5f008b,b5014395,cc1658f,e3f3d4df,7b361456,175bfd2b,4a91c8bd,be5ffebe,e57a7da5,d01e302a,d3688567,a19caa5f,fe8a57b2,be2c866e,f5f275f2) ,S(802c9adb,d2eb969e,9ba71a95,675bcc7,b412399d,5aecd635,7476a1fe,73554b21,42132026,f547ce69,66e6527d,370f9c0e,cc3344c9,be1047ef,b7422e13,6772bc5e) ,S(95b1b6c0,9d6ced22,f0a5cd,abc7a594,9d24cda4,f178a745,c718204b,1493db56,bc143681,53033d16,ac8ce5e9,a6cf240d,27b2331d,36cb23dd,f69009d4,b6adb01d) ,S(eaed529,1f94eae,183b2aa4,e17022f1,7b79a06e,d76b169d,2d6483a6,a6ede35d,53d5b276,91c5899c,ddac1efa,3ad6baf0,bc6e377c,99ac7f8f,9cb27fb9,5dd559b3) ,S(77c44fe5,9f6f448c,72eb485b,6ef3f7f3,906d690e,367beabe,ac7b7359,9c27d770,bcd75022,6c440f80,2ccf0360,4e3d6b38,e6629c9f,facc49d3,83322eeb,fb1102fd) ,S(e863b2e2,f00f0a46,b6752002,cd936a88,11b6279,5411944e,fadae5fb,e40a0306,b5c79ba3,6da29f17,5b9caff,631e8ead,c2ed937d,66008358,b36fe044,67243a5f) ,S(226f5bef,93df71d0,b2feedda,4ada3098,3883adb4,f3dcedec,2721e72e,eef8f191,a09204b5,2bcebc14,8a0a08fb,e8458618,f966078b,d75ccfbc,c13233ce,741707c3) ,S(aa222fb0,8c1e7c53,9f3a82b3,9c6f08de,c33beda4,aff7c46e,3a4e9036,83467184,41105cf,21cafd39,821a7c3a,a6dff931,c1653d29,906b5d4a,c5dd6431,7c1c3765) ,S(1879c2cd,26ef4ed3,dc5220bb,397b1501,f94482cc,1236da82,239754f1,e1fec96a,912d5f35,75eade14,91fb1609,21d63042,4fc68951,cb73d351,464725b7,71f0d67d) ,S(be39e4a4,e7eed88b,f4a4cfc5,970d4b7e,6df6211e,bdc2bb76,7657ecb1,ac9902e0,d8b1e4f1,13fca7b7,6306d9a2,b4cf5a49,32ae54a4,5615c899,f94cc476,7e27cb4e) ,S(1ea72fce,33378c3d,d0302836,86c3f8a8,1c2912e4,7cf44631,d3fbdc2f,752d5786,e20f4558,fe1cdd14,ccff261a,fe506b78,cb6e2b0,807fc7c9,aed0b888,3748906e) ,S(56e33dd,67bff57d,e8c638e6,f32bc396,2d0ca011,b74db242,3ac662fa,da036806,4039c0cc,165e7130,9317d4e,41de57bf,50d78ecf,3e14ee2e,fbb3b93f,c393f461) ,S(51981691,a5f1d8df,1cafb95a,738b9e3e,d036ce54,f10a7447,c470cc2,e80f37ad,9fb9047,67cf2a99,766e3c2,6e97f045,d03fabdc,471ef664,d31aa662,c5972261) ,S(ef3a5685,77a59783,6b0be7f9,5f927996,b90db9b9,bcd57f30,16ec5979,98869dbd,51cfe457,ff22749e,949782c6,ae1f4783,fabe1136,4bb524d3,72ac3d8c,1b7c5e07) ,S(efc652a1,8c3a85ba,7ee9e0b1,6e3c6433,79a66882,5304a22,523c060d,af196415,8a656c14,cef91af3,1db2498,f5987083,8fcee71c,98c09d49,737447b3,54f7b2a5) ,S(cdda1fef,f4d5ce2c,d9802198,389880f1,8adc7962,c04a95de,f07370a1,884bbf82,8bc26ffc,b0c9dc05,d799174b,4a478162,4417f9ab,8536235a,e55c9b0,49e31d6c) ,S(6f3f3985,3454aa13,134b76d7,77dedd40,d46bb6ac,dc3a3a3f,93886847,b96cf0d4,a8ba499c,4f7ca1b5,ae7e5192,ea408344,b6e32491,e5649637,e4eec5c9,2cadba81) ,S(e52d11af,91abfb83,ea842065,ed8d804f,a2a3627d,85149ee8,61cd5df,e54b13e4,59f3106d,619e5672,cb21f6ed,4e73285d,2e132a3d,e3ed069,46838e12,a9cfff97) 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,S(91313f40,3302c47f,d9f113a5,581f135c,82280927,5f658607,99550fa9,7236d0e3,f8b6ec07,5e7804bf,461daee9,1f21285b,aa9e96c2,2e0cff27,c323f627,90838a77) ,S(da248119,9d385a7,8468e86e,1b146fbd,e0be031c,3a19d0de,2f44a1d5,6c6743cb,c07c897b,5f76f6ee,f2c62511,19b37c47,5d418b6,1d2cda66,6d39ef67,40348cbf) ,S(95e36a24,b1bc2e3,fb5e6082,de9ed432,760ec3f9,6f01dbd6,2e820268,dde82220,be6990d7,3abc4a3a,8f03b209,dcb4202b,52a74a87,1e1e3d01,7665e9d1,1ce1cb63) ,S(8b05b060,3abd75b0,c57489e4,51f811e1,afe54a87,15045cdf,4888333f,3ebc6e8b,1d10f881,45db40fb,889e2ddc,e81bda7c,27f5b615,acd6179d,bb30f4fe,7f40fb39) ,S(ffabca3b,764a327a,750bbb2b,a1cb8329,d43ec0b7,dcd8f728,55a9d30c,f3020f54,93970a65,c90ba260,5b2fb393,a4e994b4,c791965c,b60a1302,cf585443,6dd0f05a) ,S(b3a85aef,ef35e4a9,8f0f05fa,9752998a,d3514868,b133e7c0,a18fb053,b866c72,30115ee1,c21e5b9e,3d6b36c,54e700e8,9ee78c7,e88a2752,38f46d1f,5b6005e2) ,S(a4f1fd5f,4c233cf2,b9c5659,f666d51,5b78fc32,ebcb52d5,d155250c,c95b7ab5,91d19f85,726a1258,444419fe,c5219c7,33754325,89d92d52,c363d61c,81faa0da) ,S(97b84b4b,7baecf13,94bf3923,2b58b5ed,9eb14637,d29b3c98,bec3e624,15bbb0a,497db4af,be8e7b3a,13493d73,ca92b4b6,5eac7f30,d86dbbf4,8b86f495,2d162435) ,S(2ceba0d9,203e3666,75e78e96,51b5b57b,a9de5f82,3cc8569a,1c274d19,946312b3,d4c2fe86,f042cfde,41f0a88a,6d77c188,b7805db6,c6ab440a,488a75c3,8ed2b437) ,S(ab8b1930,6cddaca2,8be57b78,b4836998,912391cb,c6a41e10,e91b86a2,3f2b7009,fdbbabdc,79fba1ae,9d8472a1,7a648206,7abed651,36892a03,35128650,374172cf) ,S(2763029,1ff140b1,57eac2b5,9938f26b,c149705d,aa2dacd,6bb0d305,1a15b394,c2b6b32a,38dcb9e2,f4640838,c52f5ca0,55359479,86ecd875,a91504ac,49374ee6) ,S(22d1edbd,1cc1514c,7f91d793,3e9dd124,9e703fd0,8c65ed8e,6cc79eb5,cafc78c5,7453e7ee,a53ae741,13024fca,208a3816,a93942c1,2378ff7a,5e65678,c0a85efe) ,S(70d869c0,c5729e94,270fa559,bdb3fb8,b6146527,5ecedb7c,c8e7c9bd,acffe222,4bfcad32,8ce78fb4,617baec8,48c2c3a8,f8d41474,9c131657,115dcbb8,f6ec30c5) ,S(a25b45de,da8d5782,64f60dcc,da97bd28,ed9039c0,6bb7c97d,d4a24eb8,791b1647,8fd84983,fd2ad956,32376555,4c43a664,f306f11e,2f030c7d,fe1c68d8,aa43db8f) ,S(823fcd6c,9b237c0d,5aa38336,6737066f,3e77fa14,b975a5cf,39ca8a74,3b1024b8,e691a44d,29a4f2dd,e99c2ba3,bb6d4345,d1433e4b,d1c65d72,198f16b5,4424dde0) ,S(39a5a63,8244aef6,432b1247,d394d305,ee594bd2,6ed2433a,3a96c4ce,5a158d0c,147ced39,dd8b8494,d57ff37e,a24cb108,ee4b9f43,50c556cd,32df8b27,626a8023) ,S(8f9febb5,b85bb2dc,74aaf7b,81b27796,2a18f6bb,4879f5f8,de94aa56,b3206487,48daebd6,d4175a00,e37dbde,c2b57b3d,dc7474f2,ab6a093c,32a86acb,f610c2a2) ,S(fc16fb14,2f500856,4509158a,5f6b4e35,6a08db53,36e9d3f8,4f7a03d,9143f60c,8e9326f2,7e02b73a,10f4ada5,9db85fe7,4027584e,6b32aeaf,58bcf804,dc1f7a36) 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,S(99eb23dc,e40d7159,b0a0406b,ea04b87a,2c9195c2,2afd79f3,f938018e,b8e86f16,2ef21938,a66efdec,7ff6cdda,a79fcabf,b1f17fde,9e80db37,82b47d41,64ecff66) ,S(3bf16e84,1a874418,ac7f0d0b,9abbe781,611ad0e4,7acbe904,a99ba65a,b4d37472,1d3cb9f4,e1948cb2,fc88c0f1,9277437c,7d1138b2,8aef4355,1fb35121,a3e714ad) ,S(a3ef83ff,19eb394e,b87c133,36388a86,561811ce,5449895a,f459fe4f,e7f01f3e,1955dd39,8bdcaccb,cdc7ddb4,711d08e1,9d687ccd,d335a4a1,45d13a4,8178cbab) ,S(26816f51,da9b4e81,3edc024c,223dd6b4,5a344d11,f5ade552,63ef17e,70b1af90,46278e1d,1d6b67a3,57280967,6604e897,65611b7f,bbccfd30,22007a60,294aabd6) ,S(5e1653c0,d640f148,ecbb14f6,97940b0f,1d47dcc9,48e7525a,909e8444,afdea823,9b8b81ed,e7cb8350,ecfaef22,92bdc528,8e499cc9,6feedc86,cd45cccf,4cb092c7) ,S(1bd88e45,b0d3694,56348c23,125b12b6,b7725d6f,addc08f2,47fe9dbd,e828de9e,182939e3,2d8bddda,577dae7c,a1d40164,9f6faf68,69808fe2,98dba2f,b8a95db0) ,S(4b03fe06,3adc4e40,315e754f,bebb7802,b80ab716,d4201fbd,31b12c5f,d9b73c02,a864d0a8,e2c5e519,ced537,e03f98e3,a5623c31,ea4a430e,73e8cf54,1c80fb06) ,S(e20a515,7818f33,1ed927f1,3c46f3b5,2146860f,d085e68c,5884f1e8,45d35f61,a1c12002,1a79d6c5,89e466c4,3fd48f66,a924e9a0,a3d20db0,484875e6,96bcf328) ,S(e3d11a4e,74a1e1cd,8be24d87,4885e1eb,4aaecea1,c802ba73,2db925c7,f81e37be,8f1ec01e,a1ef01f,63806787,b8831d4b,22b0a9c,7b44bc7f,73d2a3b6,861645f5) ,S(8a233215,57fe0dbe,e8e92b58,4729b163,da71fa32,f400617,d1e2a081,3e37f6e5,af5e471a,bb8c7505,aea1ed74,bd7798cb,267dbd29,61c35f5e,93889056,aecce950) ,S(3bbc0a2c,b43f4683,151070e0,7015cd6,997e8dfa,99685cbe,99f9a76d,6851d20d,9a1dfb8e,a5f14c40,b9968e88,b6083111,fd140843,96fa8278,bb0e351b,7cb4f97d) ,S(8c04d781,82d83ab,e8c59dac,9407b4b9,65380f38,39431184,811e133c,911d1deb,4d74e493,fdb22316,fcf21340,88039534,c0a3e098,7198ceab,4a65260b,4c0a3db4) 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,S(33af78ea,bfbb00c5,4d88ef81,e9661b16,e0b32c85,a1b61b95,6c6a79fd,e036aa2,713e7aaf,537a796,c4d79644,c855d0b,15331988,5ef4629,d8048c69,d3cfd3c0) ,S(c588d014,5a3f3d33,29695573,96d674c3,1326dfa4,797d63d,f9a0c720,49583bd0,b5c0cfd1,6c67cdad,ababaa8f,cfd2cd76,7f747024,8caf60d7,37531c66,ac53cdfa) ,S(96b3d5ed,b93742c6,7c48ef12,c649341b,97223f22,1f0edd5a,2f2ab523,8038d29e,db475caa,38a3a05d,3719a2e6,4ce7b4ed,bf25fe57,4b28d6aa,9961ec0c,b0e44c4e) ,S(412f4b6e,3d894ee6,fb0cb00b,14662a9c,1eea3a42,5a286782,a62da77f,5644f0c7,a84ef636,ab9bc805,bffde813,93874429,a8503e89,8c03f1d6,f139af86,f6a676fe) ,S(25f0a785,c7b43028,52f1421d,a32c418d,32fdfdc4,89c39049,3794e1fa,e4563252,efeb090d,457190b5,89c953a3,aebef406,da716af5,1dc6e334,a0226883,6004e4bc) ,S(50fd4ab7,f367faf4,acb4403a,49ea3e7f,f02fed58,4327acfd,e0bd58a4,ed741c6f,78abc1a7,3c9dcd48,6520cb52,adb1c3a,2d08abcf,a079607e,a56307c6,3d46dd5f) 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,S(e0c56d30,ef92af00,b936c2bd,951b3d51,bc439ad0,e4216e2f,d552c2d5,e8dbe588,c2bd177d,2a75c44,40dbd186,27669a0f,f35189c7,a4873e0f,6484b3b,68555fee) ,S(9bf960e5,2b7bbf52,fd839830,634baf1c,f0d6e332,4272bc15,d9999ae2,7873315b,b28719d,20e01dcc,b0016cb1,6a453739,551862f7,d9cc81c9,6662387,1d8d0405) ,S(20df196b,e60ba71a,e617a6b1,44757e0e,87fffb45,d447d9dc,d5480a0,34351198,9c722d43,c0d071b,a07d4953,9ad0abaa,f12ba358,42fee0ae,9960ce1f,26eb07d8) ,S(843c136,208b40b,9459693d,8154980,455a5f71,23b5f633,a26661d,ca9bac17,d5b5bd8d,9095fc40,d2d1820d,31dba542,d0c74f23,86770ede,c9b4df46,f2f12078) ,S(9109b4df,702c1ea0,dea4ee0c,ab46d6ef,708a3fcb,72f9dc03,e05bc722,408d11a0,75baa2c1,8be5801c,b5315195,4c2c3024,7348e9c7,913bb242,cf4ecc8b,96dc507a) ,S(f10cd1f5,c960a9bb,12adff03,c203c59d,8e51552e,3727edb2,329eef3c,5991113c,a84ac8e1,6f65daa6,16574689,8fee662c,9d2e03c6,4796151b,8f3f0bf1,5e8c465a) ,S(9f07713c,ffd3602f,ad077b69,a8a5f539,ae0d6d0,df58ba07,1eafe6ad,10e747a8,adfcc873,42b59083,cdc3d735,782f8ec1,cbb4ea3a,57970afe,58cd5e5c,8fee867b) ,S(6d1d9d0e,32905734,13b2b870,fff8978c,5ce9ec6c,b120d9f3,64063342,cd95801a,650be4a8,95d3b602,4d745f7c,23bbdce3,25a3f597,922e50ef,ba154f8c,6831018f) ,S(497185a5,6b3acc94,7a27791c,7e1fb149,5c649f99,dc767fa7,12820cc6,6cdcbd82,7d511b7c,11dae1b1,7e4078b2,fe7565a0,f33ce5bf,74181c3d,f5b6a951,fe6568c) ,S(fff738f9,848eeb9c,4ddb8bc7,52cd87c1,9a35f7be,14a470a2,c3154ff3,100a743f,106b8a55,cd913c97,76837cdc,f45c58a0,211b979a,17085df5,7bdff373,2f2c38ec) ,S(320391a4,8d3546cb,4466876a,37d60015,41899ef4,5dfc8e38,ccb9021b,981b4830,46f63030,b4559411,e742f303,25707b4b,23fa2d7d,e633800f,9c71205,6651b102) ,S(be44ce40,a925e88d,26937f7f,b7631f18,55879106,122813f9,adf16e00,5d85fe9e,1755ade7,d22e6dc6,7e6806d4,bf44b6e2,ca6948ca,9a418893,24db0266,2b6e1dc4) ,S(8d3f06b1,58ddd609,f83b0531,466fc2a3,da6aa80b,433a92dd,eeb20435,cf33ddae,2d554a99,efde513b,b8b6e5f4,dbd2e942,f1d0a641,98c3df2c,4c74705d,4b37af63) ,S(f814a79c,f258f553,255c1cb3,a054fcc0,d0c71d74,742b6627,210ea846,91596729,119fc95,be48b4b2,23c80c42,fd1f3d45,271ce8a,edeb82dc,31813f75,a32d867d) ,S(95e8fd46,1c37f1db,5da62bfb,ee2ad305,d77e57fb,ef917ec8,109e6425,e942fb60,ddc28b1e,dfdbcda1,aa5ace31,60b458b9,d3d5b1fe,306b4d09,a030302a,8e2db93) ,S(c06543fc,47e18816,bc720604,cfc20826,6f4e5cc0,f436e149,e2dab0e8,a7981e77,22070465,f3a4a7c2,1134819a,c194cc9d,28185431,17ec634e,e6634831,97021441) ,S(4983d95b,3716aefa,4a14d116,bded84e1,fd5b050,bd6001ca,a2b97086,b4d5c68e,1373426d,a2efcd14,333d47bc,ebd3befc,f5e609a6,6fac1b02,80cdae2c,7f0a279) ,S(a2bd5cc6,92e84b97,3ba2cd09,25e0850f,ad8054ed,e6b73ef6,1fdcc958,3eafe6ab,cca6e78a,f9141b1e,6159011b,99f8024d,33d8d797,9795aa4e,4f0b2767,e6a5ce2b) ,S(61c99231,a18f4e73,95076281,b367d084,b8f85226,3117ab60,bf698d4f,6b6d741a,82314b97,9e7f1d30,64861609,a08c019,af886db0,67d49929,9d340814,6e6cbfe5) ,S(4a5acfef,32c55299,3a7114fc,7913321a,d4072a2f,6c6bcdb7,3ed60bfd,6ab34304,7295a29,c06859b2,69bf9f29,64b26dbf,1323e89,4affa4da,9f61b056,9a0c03c9) ,S(e0467755,866f494c,2b36dcb6,c65ecac6,604e5013,4216ad48,7d4f5b68,bb7f4023,dead03c5,974dfa1b,f532f955,826189ad,ae945975,28ece029,d9e5a42c,30b336b3) ,S(686fdf05,c9265fdf,5b54ca74,b5b1e231,c4e8be60,20844596,40dc0d2b,bb215ea7,f4d43e1c,edf9b974,aef950e,bff3677b,c93723f2,c5901710,b6561e53,d57ea7da) ,S(12476985,f9b20c,ea62b7d7,b0d96d2f,e2bcd924,d1f15cb9,fce5ecbb,8bd21253,d3437cb3,9e904fc6,43a7b356,b4389c0b,3f1950f2,43dd7842,e32de16d,2b522004) ,S(656bdcec,9a87c9b2,e5b32291,9f657b,b5eb1e1e,d2fa724e,45388026,2ad17b1b,c7748d0c,47b6e4f7,f63f704b,3fdc08ff,cdfc830,d17c1d11,6aa3dce2,f92fa64d) ,S(5b7f710e,f721612,ca79b24,483ced12,7a3d403e,60ebc04c,3aebeb96,b483e4b5,1b5157a7,f0688aee,634196e8,de5a9eec,11db4b72,bd96b86b,698f7284,bfb08080) ,S(bfca66d0,552ba6f5,5795bf18,40f90d85,2545213d,81d2cdea,bc8d3d04,a1e6b4da,4910b0cc,290d4257,c04c4638,30cb3a10,223043a0,bddd8690,84b6dd1a,f1754e75) ,S(663fa68f,b79dcbbe,4798f8ef,2057bd14,1447c11b,cec70924,7f566032,88496f16,3ace2efa,1f3bbd23,d885598a,91d1f420,a42597a2,ab30f951,f2b27aa6,83c41786) ,S(27cce333,8a3db8f2,1fef2f86,ede68a25,7c1675ae,80cf004,6085f1de,495c4321,7156bd8c,8babe472,eb144a00,263d4fdf,7aefa69f,da2a9c29,4b16a82b,24d373ae) ,S(d49c06c4,52ec5c09,be27940e,13c575ef,b727be4b,1c0e8ce3,5aa5bc4d,64bd9560,2c653518,b298100a,72a66469,f9a03635,5d7ad789,546df3c2,f5175238,e78d18b0) ,S(6960807e,bd028026,d3cecd25,140d3bd6,3d7bf4fd,10afd129,cfa017f7,544ad08a,a785044f,28befae7,2b7cb546,5bda6bdf,6f9a6383,aa9abf4c,f7baeac0,920e7c7c) ,S(8382bf36,54b63a71,a3b75abe,ba57dbae,fc9263c5,5a54faa1,edeb5325,3df8faa1,e05eb9dc,c319cb53,4461da26,9627661e,dc9bef3d,945766dc,b6d0fcf1,849b011) ,S(803b9379,30ec876e,78c8cca9,fa932f22,b7e7059a,f605379a,cc45a3d1,4ab0bffb,7db2341c,5202d1c2,c6fec7d0,b7869471,cb90d1dd,17cd1152,b52af046,55e5790f) ,S(cb4db129,ab6ae9f,11165ff4,f73fab02,cb78fb0e,89647e08,f998ba11,d2c5292c,ccaef9a,1776384b,b5a80ad6,5bb366fe,745c2408,d754ee9e,f6154188,d7d1c9c2) ,S(fab28757,50e9f672,3838be8a,fc070fc7,8fd6af7b,84c9579a,a8152acd,ecd115a2,d59fe028,89cd562d,5397d3b8,3ae85303,764ee931,d9c6e495,6c311490,c0b3f065) ,S(dd879eba,f870ee3d,f6e3f03,60833e12,fbdf844c,d6a5b76c,19802485,6649bbc1,e7bb04c3,a99a5c11,dd7a324c,1d5696c8,b041a12a,c6a538f7,3094716c,9943c55a) ,S(7aa4afbe,29b06a1e,da9319d5,72572b13,1df68f74,1b5f8d8e,d00ccc04,80f8016e,15f79a9f,b77b8587,7f02e3c1,3202b972,423fd00d,937c0d2d,c9d94b17,53fe7130) #endif #if WINDOW_G > 12 ,S(9145f3f5,876a3265,5d7fee64,f2d6e660,c34354e9,1571d68b,a19e4cc5,8c39f890,45e0a95d,cf369fd0,5bc9ba7f,da108d6f,37650c1d,5766b6c9,98ecda28,b285d8ff) ,S(5450b752,36fb010d,1ef37afa,2077f3dc,a5a7f6c8,91a21317,13df740f,4511ac9e,a7c7ed57,62bef86d,4de1084d,3ded2d7b,13ff563a,67109ef0,8b6f0180,fe6ba175) ,S(ba6c0d72,5e48de2c,cb8256d6,7417d075,bbf2766f,d13501b8,4c32cf88,c0666a0f,cd2a9132,7137299f,50eda669,3a599032,bdecd64b,91bcc640,5ed186f3,e525e442) ,S(b94821ff,1feeebb4,6fd1006b,798fbdf5,d25a649d,aad58b05,53adb7b3,9605c921,21589ba0,79bb92a2,c7c3d950,c574afcd,f45ccfae,eec4365a,72dc58ab,f9077c05) ,S(46436446,497f7c76,b70e0d7a,5a963cc8,432f14de,93d61f81,98f8879f,da0681d,29344a4e,90c4d810,10da8aab,5ea25e5f,48c367e5,b3ec9239,8a3e608d,49c83a5f) ,S(bd8e5ac6,a2e210be,4959185b,7bcb0cf1,bd3be917,5baa0d08,2bb0b38,e4c1ae1d,6b381be4,6dcc9755,da7773a5,eec888a6,69c6f71a,7c3ec0a9,4edf08aa,2db1fa19) ,S(c27c1e1a,c428a7a5,f4c3405,58ace76d,7fb64593,b3942319,74cd18ff,99f22493,fc95d661,c12f7b3a,1cb1884c,fa9f5994,25108af3,c05e04a4,9544f919,c59cf57c) ,S(a1765561,837e4ca5,5268168e,ed90466c,44c17c01,4040fc02,9e53af22,77eb30d5,8a2dede2,b8d488bf,cd655d0b,30e6e2f7,3032c775,d0fa15ae,cfc8b66c,b6c28eb5) ,S(2bf6930d,35cacc91,87e9279f,678ba368,e9eea737,8300ef93,b03e98c1,81ddbea9,8a2d4d43,3aaa8bb0,3ffee538,38ca8e16,d0f3f930,c35d0db4,6e2fa069,e625209d) ,S(766a7725,9cc5aefd,90f005f4,d6755924,a36d085a,3a5856a,6a066a70,6877c8d7,db3fac97,4fd9e2e7,f05bfad1,5e938ef0,90b46d04,bf40bdc4,171c1e33,48049190) ,S(d25a60cd,953f21d4,5fcc333c,97329da,134196e3,9a913242,88792ff9,18461268,89bf2be8,bd04835f,dbb874e7,12352980,a07ad598,9035270f,397f24ce,790c7863) ,S(c7b28e9e,8b7125b2,6721f467,b665eafd,9bf56986,8ca180b3,60dfe429,cad95d68,ac28d58,b3a7b61a,71f947ed,8bca4768,9ec7bf34,7646a167,b37c3aa7,9e95c398) ,S(e2a5208a,c61f8c29,ada2d7a7,4cfce985,20c29160,f1f7a97,ce8b34dd,7c59bc24,de8ba14,49708a04,ccb4483b,4e90e383,a152ce27,777fce4a,880d9f5b,3dc70830) ,S(e1e8e4cd,2e8df95,d3b2b152,a540967d,6976e001,88287ca5,3e844adf,12e205b1,a5dbc6f9,cdc7547b,cb3f0091,8233723e,d34aa97,f546a491,a77d8cef,43bfc9e2) ,S(b20f0a51,4a684e55,2b228480,3f3b1c2a,3c3143b3,b895f75b,ea454bf0,9d2b6512,bc3db380,676d0d14,9c0b0c3,1941a07c,f7c95585,cd44ec31,e0edda96,e80d02c9) ,S(b71a6923,b1adbf77,94cd9d8d,407ac96f,9582cbc9,b9748949,9cfa696a,c29d3ec,75182389,9d59558f,b93113c8,d38c72d2,7b6d75ee,7679fb1c,89bfce1a,64b4f151) ,S(ca47adac,68ba38d1,8ccef76c,7565788,a82f415f,d9dda65,2004d5c6,a7d3bb3f,bd598ab,1b783382,44035385,e165fd5a,ccd8454c,3969d378,42fad050,4a8701df) ,S(5fade148,aceee9ee,9fb4eeec,edd5e4c9,4fb989c4,d99f65ee,a45f99d0,2d40e441,ba6fca3a,e82e5581,ac5104ca,c8dd2c00,15afd1cb,3943f1cb,5e61dd4c,d73831f0) ,S(767dc9d2,14fccf00,900ba01,a1cf30fa,e834c851,e633849e,8adada63,fe5f84e9,8c650911,aca30e56,2d6b97a5,2fd7cbfd,1a5bcd1,9ae197d6,9ee3215e,64404639) ,S(27f8f961,445e2a20,5daa7648,fc3c06d9,523544d7,477e686b,91d7178b,7e4f06d9,39110b27,82cd7be9,75596bce,6b79e5de,37933242,21be8172,427cdfd,82a73a60) ,S(8de0485b,343b5e4b,ada4070b,f79dde48,8a1b2889,839735bc,6a403165,3f3de668,90305767,6f43e0f7,d7d1c1a4,4c59124a,12fbba72,8302e143,1c2cfae2,ed5729d) ,S(5e43db6c,8770e8ae,8ab8d318,8e700c28,5b6af8a1,eec95fe1,b68e5cc5,952df0ff,6882628d,d85fbcfe,3a2a1091,15e59c78,9aeebb3d,37075f90,ae02a439,506c7aa6) ,S(7db2baab,4bf4300d,e7caf4e3,52df1423,6102863c,edfeb7a0,89311f42,59a4ed54,387561a2,fbbb44be,303fbbcd,685909cd,e553a84c,a3d4c0cb,d33026fe,178e8a84) ,S(96da8525,39106887,d1fdf9e8,232db3e4,cdbefdcc,abb90bbe,fc04d10d,b996c6f1,65271a31,49127341,9fb5d651,3dc33287,45948c92,b7fcc509,4023d300,9bf9edcc) ,S(84eff1cb,14eb1284,f5ba51fa,838b485e,64cd4c0f,acb97b00,81ba7848,add50613,926c9c8,a6540a8d,7b1e602b,6ce818c7,609f4511,32f284fc,7f578c52,a6febd9e) ,S(1eb96371,8e2a2a0f,f5ee6000,7bf94a00,416e6a92,25d59705,7fe19941,e2adfbbe,4870aad8,9635ddfa,dc3d4011,500639aa,d3cf0523,cff0dbb0,9c9f6a1,3005b855) ,S(2994a36a,6ea3f307,1bda8696,baf193df,c75fd4a1,f7683fd8,d454dcb8,77bdc098,e465e8ee,a7273d4c,d786bd0b,e96fd3e8,9969bf03,1b76aeb3,fc82c4c4,bf856766) ,S(25e7fb70,f3d357a2,c29b115b,5e2d97d9,d2b68fcb,b7f2fc00,237758d5,9d26c414,4959a370,a3bb895e,bf530fa0,13a86ab8,206b7330,efaca631,fed26773,f356c4f2) ,S(fc387f98,80bf6bbe,19f0481a,2d66bc5b,c3945c52,588860ea,dfd5893,347c0623,89d7b80e,83caf032,9c9d07af,734604aa,7ba33274,c1081ff,16e663eb,b49d67c4) ,S(c50af368,c25fc9fe,10220fa8,2f177720,ef5c00b4,85fa99,e2f03294,fe01e1d4,c3777b26,41983094,912b80d,9e94af7b,27d9f10f,978c931b,a4294cb6,b97579fb) ,S(a0f9d109,d524d9ba,a2e00362,941a5f20,d7015c48,554f5bea,7c97617e,10041f94,28c51c02,daa5e108,3e77ff2,c64560e1,2eae923a,3a699f1,daf3c62a,710e9ad0) ,S(41d12627,58b708,58727138,908004b3,2138bc23,cbcdfa28,5da862a3,48316de1,6277029,153bcec9,5c95f451,3d515d90,341d90a4,90eb2999,d29df4f0,7c1b9673) ,S(944c58ce,fe6cf543,d93afb77,e33adb3a,5774448c,d61d621c,fb80f856,6e99ca87,c071ec1c,9b7fc717,ca91c557,66bcb222,3294958a,b7d7b056,e7473170,284d66b5) ,S(3307ab12,e06d71ce,9c029bf1,88eebb58,9a27be59,17290635,f2babebf,be437145,889c3cb9,28cf9091,4748dd9b,f89e9809,4a6966d0,97d854c3,c6b6a949,c861d213) ,S(42baf011,1eb2224e,4ca03abd,24307b6,72b74572,2db6a8ac,dee1b7f3,45cb9ae6,bf32e128,d608dea2,4b564bec,38d22c5e,879515d2,7379cb11,25695faa,2e12ee06) ,S(856baabb,be7b4bd0,49fbe898,110d1175,166c69c0,a2bc86bf,e734c854,c402c621,24a323c9,b6d31fd3,cd424161,be229e89,1f825197,9ed4721b,943d7418,4912ac0c) ,S(38dbc18e,d998143d,874c224e,de83834d,95aeeadc,805cac1c,3216d830,d24a9cd4,273ec126,f7e85778,ea38e2ea,a90ab5c5,271c6eee,7f934a03,570891e5,167eae4a) ,S(359dc85b,ffcd2329,3166bb20,c8374af1,5e24c065,a5f48d92,c981eb81,4988dc59,de5dedf7,deef588b,90237d06,e437bdfe,c4a05703,f77b584a,e58162fa,bfbf39c6) ,S(e1068065,e2e91c88,3de2f73a,6a5f3da7,1d872a74,9d7f283b,b1ca35b7,c63666ea,810c3a52,b5df0851,87928afa,a7685035,a7e155fa,c8dd4523,c5ed1f01,73752cd9) ,S(50767f71,37e7c9a6,6e317183,cddfdfc,b564956d,cbd5f3c7,fd8506d,dbb19d83,e1c2dd5f,5e9d5fed,807d24dd,3f2e0ae2,393b6167,563db9fa,5e338664,a0d4fff8) ,S(44cecbf0,cdf88355,f1216d0d,efcea137,5e01275f,f53d8a72,5a0b5980,e6e65864,469568e,5094e9b9,ee290550,e67bc636,e8e3f022,f15c8d2e,25c3ad6,f51cd40e) ,S(1830c8ea,43cbb07e,fa2fe597,6afca2bb,87ed8a92,602e05e8,86ce3447,96aa18b3,df551328,e064aee7,67f56203,7fa31c11,3c8ce2fa,b5445d65,8bf1dd84,2f1da49d) 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,S(a3395dda,c1e760e0,fe7f7e5f,e3296bc2,99949ca2,2c034707,67c08ffc,d9576a91,4f8a879a,54036d17,16f07016,23dfcfba,3141850c,de003870,6ee940e7,452393d3) ,S(11e54d64,54aac1e0,58cef234,51f686a9,1a77300d,75330ecb,d208678b,2b8ad651,749b2960,5a8419f9,c5521dfe,f552a24d,aaa53f45,908d2679,6e08b396,c9c020f2) ,S(c8f13cdf,7b41e822,ab6d5a70,7c701d29,98f5f0da,8e4c9746,75e808fc,64327f30,489a69df,17c09c1c,dec329d6,a1f34f60,445d7aad,d609d94d,44168947,c3199404) ,S(9175e6dc,cf674838,a94c628c,3e1a9dc2,9487f394,8a25e50c,d463cf6e,92d84442,8705713f,ed377125,51e37e51,78ca7a7,c13e193b,1b83c729,8cb08186,8fde1c22) ,S(8eed492f,b6d5f0e9,ee78f6b8,953ac0a0,5df8b9ec,db17a09d,22863bf4,3620099b,23a45742,17672e98,d9cf8b94,62439ec8,82e1acfd,40db9d9,9ece889d,1e0ff1bf) ,S(cb95ce23,dbac06ef,79793f54,3105f5d7,5cde90bc,651b7756,bebfa367,d5c2dd9,9612a6ba,c023b0c0,73b5ed99,271ddeb4,57d22d74,f7ecea4f,c618be5e,164a9a48) 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,S(1c014014,9027b9a1,e3ce3c28,8f18fa87,12b25a53,49f9ac6f,97af6273,5b6628c5,672190fc,d048d3d6,b78bc34f,f160f978,87b49934,5753bd35,3a456c96,e448a4f) ,S(c2d9670a,1de5e876,5ac965cd,497e0765,8d137400,9e4ea31d,57effe5,2e8d84cc,ff818647,a6ddfbb1,3ab56b58,52956d08,b97a2e8c,f852379,cc7a7271,f13ccdf1) ,S(1a9fec47,16fd6a69,70ce094c,4141d68f,d21339e5,5396a691,e01b1e5,c996ec1d,e38eb2eb,6c8373fe,94f7639b,595de291,d29b8738,11f5d40c,24006d8b,93f8557e) ,S(b7df52ed,15e91a6d,40e9e500,6b1ab26c,53a51466,98d63bae,77856afb,1d8c464,ea60f1bf,d915fd8f,99d0706f,ff180d51,705c360d,a5fdac1,162ec530,b6e21254) ,S(2f95cca,bd092e2f,bdc86a53,40353350,918ba7f8,8488b9d1,295f9959,d7db6b5f,31456814,fe6ced86,59ea9c3d,f09bf38d,d5b0f893,8db1ea7b,5234648d,a1693ad2) ,S(763926c8,64dfe4db,6a1a432c,a37e4022,3b6ae1a3,7def3fea,883a6612,bd8a7c1c,f34d5b72,4378d10e,bb4b3e63,d80f1f98,a3e741e5,b9e4fa41,bd3f0a5,c361bd1f) ,S(2e43be7a,12916cf6,f312a513,fcb6c98b,708ce2dd,18dc4ebf,72a807c9,c8a31b0d,db919224,ce1b7e57,16e57b6c,ed514cd0,a3a9dc09,8cb59c5,971e99d0,dc24acfa) ,S(7d65e48f,1a867d28,76731984,afc6873c,2d1acdfb,13a5adf9,a56960c1,cd4a5561,9c73b955,f0957ad2,ff0e2d4b,caf795d8,bc992436,be7e69da,7b97ccbe,d983ebfc) ,S(1c6becc0,3131b772,cae166f0,4d715390,6b132c87,c5c76b7c,10b94a71,7819d725,2c3c64ff,94998533,97dd26c,dafdf608,41b84a22,cfb4906e,318c4d24,b23280ad) ,S(f5042a5d,5d118102,32ac83c7,d7edf079,aff339b0,7e9d20f8,198b2a64,13347675,19c10fbc,e644fc6d,2f238802,a045052,b2723f57,5a8bdd20,b597dffd,79a3e4c8) ,S(7c387866,c2c0353e,6e00c887,240e084f,e0ee9f0,2de12539,b4833588,bd4be300,ccc66f94,587fc58d,42fc49c6,d074800f,56f08855,6caf4ab4,c37b43,ef2b8f79) ,S(ece8ad23,d33adc2b,6ce38194,58ba2ede,104b35d1,1691f4e0,b7b206e4,eab3c140,eec976c0,7fa1d3f5,f3c245a1,2c9b728f,1c7e672f,53665e7c,5c6a408f,7c0c0a88) ,S(822b0926,a274dc38,c9eefecc,7d021774,b951cf19,3e2cbc56,a1baf58f,19d12b9d,48bcb10a,f9cac375,8314d2c4,9fcf0512,3638f008,510fe63f,1be0c2de,44118313) ,S(d26a3a03,6ef5f428,fa058d25,7ce62fe3,401dfe47,80c468a8,5cd2e77b,f85b8c3,98c39762,3a644329,7d5c6759,a308c2db,62f1bbcf,9bae4ba0,10fb1175,126a6fa7) ,S(7febb81d,8aa0cbbd,3002ab6,ca247d1d,24c8fcdf,bb1664be,b5b3c346,93019090,ee625bcb,12ca6da7,544ca6c0,2a84b9bf,966dc923,d8b23b44,6cfa4604,a6c3ec26) ,S(839e44e7,2d43b6bb,e6f63a75,cc3644ba,b7aa002a,6de2c087,33df2b0e,51d3473c,8368f635,26f41422,a563806,d775bf68,2d876d98,542b3da4,3e591e31,340fb9a9) ,S(52e947da,1c96e07c,9e2c84f3,23f2eed9,7e049b97,86d21135,ea958eac,db0d7afe,6bcfdec9,e0c70d3d,39de19a9,9fa72ba,bdbbe50e,dc44897d,9fa670e6,d473a831) ,S(72ec5426,5e4a743,1d7f6dd7,1c8e9e4c,c8b22074,cfcb00ce,db18c6b4,c67f3603,ddb9360b,7f9def94,f5ea6d71,51eed4ba,49455cf8,15bc9023,6156d4fa,786b5ee5) ,S(370a3f15,59a55689,16bf9ba,f2863d11,2ac051e9,d6a90f36,af39add3,1406c849,854cbda6,8517cee6,95ab5d3,20b1067b,ee80d993,235d1dda,ba3a0ec6,1f005840) ,S(12e57888,60d2fbdb,cb3af527,577ef6a1,41d1cf0c,f719ac6a,714f9a39,9bef5dc2,f5af7aca,5dd8126f,7dbb79ea,d5a4b475,a094969c,64adc821,ab46c5c1,86bd9ea2) ,S(b494abcd,b2fa5de,17b1abad,757bf9d2,8b7905c8,aca0a5bd,fe2ad8c3,30a2b722,c397ffd6,dad8619d,9ff8d8ae,e401a4f8,cbacf710,c6409adf,bf991d72,9294cb87) ,S(2957692d,900d0b94,b208245c,f71bdcb,118ea6e4,499dea83,1064605e,8ab9d89c,a3c55447,9284afea,37e94,fc24d50,f129342b,7ebbaa91,857d655a,40444a7b) ,S(61101879,f325e072,bca13642,dc14a5e7,1969aed3,2e49ccda,39cbf723,a1bd20eb,4e199c82,4816e4bb,d5b67269,e9d8eb0b,e5c2483e,d66757a9,c1d59847,e443b3) ,S(9eea48b2,99f3474f,8aa8c648,c2721fbe,c65f6ad4,990ab4e4,29a9c41a,ba55ab18,13954697,35ced1bc,7e857049,7f2b5a1f,b6802892,fbee0654,c1d7d89c,1f234443) ,S(dbb054d7,8ba7b707,ca475982,6a36808d,3fff42b6,31f1bc5c,c9df403b,518bd97a,396ef6c0,96343a55,dd404885,427e781f,a55a1f8,1ab95d4a,89d87975,611b923a) ,S(dba95bd5,7fdd2ef4,9dbcc0ea,35c14dc9,b2f62541,5b08e75c,d70f3caa,b61bbcf1,2af0965e,b7a17e46,18b6dba8,415159ba,b8f76ac,ae9384cc,64a90e32,d20a3d) ,S(6c312c9,7979bb0f,e72d8feb,c3c755db,bf1a132,722f6ef5,297beafb,8ad0e5be,36366388,db74739d,df78d5ea,3d8fab54,6c435961,71f78643,8be00718,8202c6ea) ,S(65eb7057,a494bc8f,549b8638,e18cd717,ad987030,aa3161e5,b9fe31b6,dc8825cd,458202a1,67f285e0,9196b4ac,f87068e2,160b7b42,2095bc92,7656694c,2fa80312) ,S(a0696917,b0e868da,ed5db7cb,d2aebd1e,c1117426,d842c0d6,b567e2b9,4effa7f6,c874d20d,a1bb4dc8,f01cb828,be8bda8b,c797ec3e,37feb0f5,ba55675c,41ecba78) ,S(4191bb82,19372a13,2dd37830,1086b64d,10874479,1d3b7879,3b27c65,782cced2,c74907c9,8ce4d218,d1ee52bf,82e130bc,49335279,2497b4a,34892fca,67dc3f2c) 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,S(8212e821,ff2f7b90,c01c8461,3d4d9df9,ce077cb2,9706a349,575b8cd1,a3d0eb52,d59c05db,2fa3e756,fda56e8f,33540639,d24bb5ed,2c8aeb5b,8f8e43ff,703185f0) ,S(ee340cc8,1d1f71d7,4b1a641e,101d15e5,24f155b7,2afb4e49,f9cd8b20,ec61220d,915d833f,25355fd7,f1efa796,4a8e8b04,86f8141e,f5811438,f0083382,ae286f37) ,S(2c535525,dd2e3d83,740b257f,bb7223e2,302b5009,7f8366b5,aa26f65,442afee1,1cd4514e,f945b668,4f38f966,2f3b5402,92d43a79,7f73f947,67272713,b61cf765) ,S(df7763cf,8b57a288,cf4a9083,a2a5f977,404b9e1d,6e814f2b,aae9ad45,fa67d94d,4f7dc336,31fdb48c,612276bd,d388ee9d,bf05295c,1a92709c,b4fc33ac,b1580ce2) ,S(3514c240,d6d0f218,11374b92,8cd6d063,8ff99b8f,4d5e4da1,8fd126a0,ecdcee60,2a0d1f4a,1a1baf80,3c98421c,7777ed1a,ac17abb2,720975ce,e530a5c6,4197fca2) ,S(3de75d9,e58bcb81,94dde551,ab541d54,237a1b58,d935f60a,b54bd3c,6ae40a27,9ada14db,be2db058,c6bad8c4,86f25037,3ec422da,fdd5bddc,455b2b8d,25d97c75) ,S(a728ce0b,1804355b,c5c144f8,1d5eb1c2,90ad3d52,f502c5dd,ae28a08a,6de0420f,4387cca8,f72b51a0,cfb4893f,a85491fd,42cce3b9,ec3344f7,ac93d001,47ddad3d) ,S(ec3c9a8a,5b844c0,947b22e0,2503a815,1d8234ab,aa94032e,16c1d874,5551c39b,7b08bcef,45f0fa93,660845ca,44edfae8,c8ac51ce,e836b043,3825e410,8ebd7fa6) ,S(b0173d56,24945acb,3bab7e6c,617532cf,e619e7cc,e9872e93,26a8ec55,a24761db,78d27b5f,3e9a0761,d0feff12,198dcb11,72a81df3,1320f10d,44591ae3,5f1b381) ,S(d9eb3bf3,cd43dc8b,977c3890,ed3a4b8f,4e04bd11,f95963a7,970d9600,40cd73f6,98196b5c,c42e808a,3f1db718,98c50048,510b9e4,c9b69c41,e7f5b2fd,63b23044) ,S(fbda51af,8a40230a,c7602606,21f92b38,29bbf1b0,1c027f10,7ca54c08,65a84e74,64833994,aa453bd5,4c8729e4,e9010fcb,8fd427ba,3bbe7c71,e812513b,fcd6ccf5) ,S(ae4b9a7,51be1966,f564661,61262faf,472b14c5,f0532cf8,8af872f,ba583f9d,8b2c248b,aa9d7e5a,6f0c6eed,9ad3ab5f,e2bd4078,da4fa281,f4b672e4,9695ee5e) ,S(58040152,6088026,1668c6a2,e462845c,f29764e0,31edf6dd,a40b6e0c,4ccf6ff5,d2f96ae6,4a83c04d,a072f9a4,e39976d8,a2e5f88f,fed070cd,5fb1a701,db329485) ,S(4c28d686,57380f81,639abbd9,fafcf47f,cf477e26,1c46a03b,57ca7326,4c7e029e,694b8a9c,4fa75e14,56a67e8,acfac16,3122a941,150da022,59fb024e,ced8a70) ,S(de205ab3,9e005587,f23b51a7,3d806f81,6984fc77,7179a6b9,465a92c,ff25c9a4,ed84325e,12efc1c2,db42cf1f,eacc12c,48f68e42,9aec9135,5af5c327,c5273d83) ,S(5ea82868,c2cb0a7,4b658dd5,721e6571,b968f589,6d22a5f1,b3ec6b69,594273f4,88d10eb0,8db264f8,13adecce,636f6c58,e1828539,1e538ad,6e2237d2,384a9499) ,S(189cf7c8,64497416,420bd98a,3e3db4e7,c3b0dd46,d7b9bc9c,37f2d036,324998ba,bb3409ce,d46dff28,36601b1c,f7dd606d,7422118d,723f7da2,4d25802,1edaa083) ,S(70a17187,38f50d43,8868026,58100245,3c3c41d7,8ee5e14d,3cf536f9,bc82789f,15c95120,e112537e,41f33870,18f09d1e,101dc445,a9f36296,2b9462d7,bc27c1d6) ,S(578ac0ff,622adb6e,8c20eed,f3011085,8e4271aa,46833865,cff46b9b,fb3a368,f711a1dd,f5f3172d,2b9b2f7d,9d50818a,6b0ceaf5,1d67e15f,1f01ca5b,bbd7f851) ,S(dc9fbc03,476aa747,d64738ba,ddce8a5b,5887f177,fa6cdaea,3e3b05e2,8d840071,c0f6752c,8087dd25,f8d94a19,d294e550,8bd26774,cf4e7ab9,515f0a4e,89eee1b4) ,S(9749acff,a348cd5f,2e84dec0,b3d73151,4bb817dc,4596d78f,e0295215,47b0294d,df667dea,35e54810,daeec20b,e0e7d203,d89856c9,94501167,23de84e0,5781a1c6) ,S(e39fbdcf,2fd2730d,c3359f21,fa815478,ae8e7a98,d6b132e8,e92d343e,32657d85,bafe9881,70a78596,76a6ae3e,364885a2,62441578,8c31c283,20a06b0b,e5b5e01c) ,S(6009014e,27f13712,c00bda4,dc913516,e04b692a,ea32b89,e0fab8bf,91402c09,34910894,f6bd1cd2,cb796f58,8ddba661,eb4006a8,6cec32e5,7086099d,42359f6b) ,S(bf04f247,d02e46d8,2fb9bec4,f76b3eef,b644c92d,43622162,d419488e,87f2f773,d646f4e8,bb3c2e4c,f19ab00,4674e354,302e125b,c1ed684d,32b1cebc,7c2172f6) ,S(9609f7ec,b122b353,85871efd,915c6d99,3e5468ab,c30e9acf,f5b4dfaa,31e5e3c3,106bc52e,b933f0b8,71578ac7,74e2ad89,ebb4d9f9,eeb95592,5d6b50dd,988f9a27) ,S(b690cc3a,e1ebe25,a07440fb,5cbdf56f,f5ae581d,4dec7366,8da2ad62,bab9abe,83cd0023,fd3a3ddb,2cda9603,2b6c1657,35e5f9f6,249a535f,b9666a97,e049dbd1) ,S(72da508c,ed507744,1aa2bc11,4a9098d8,2c947948,395bf38d,6cd00977,91d326d4,165baa93,3433ea2b,e978036,4fec922e,e5d743db,b8117e09,5eafb467,3f668457) ,S(e0fd116e,540a3009,2954322f,5125a72d,1133201b,985d1017,29b1c9b7,a9851c37,c6bc7276,48aa707e,549e899d,630d3155,a516a06b,777997ac,8509045e,e5b88a92) ,S(9d4b8bea,85d4e412,ee0d6389,e883f9db,297f01c,d0695c13,abe2b682,94c10af1,5e2280d7,3f7c0832,d9ae62fd,6a884973,5bb66ebb,e68a38d3,8a95258a,97556181) ,S(eef84395,aa4b6e04,ddc56123,cd5eb31d,69f1255,1c216d25,5057a2d4,388e08ff,45098aa4,34e14364,40d8b26c,73179c48,87797e6d,59963928,b1d6b61,d62d2376) 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,S(d4c32bf6,d8fcf5ff,be0ba34e,770c68b5,fb5db412,b1341537,7b2e9c80,3dd75461,b3c73602,e23845b3,2c44272b,4eda70b9,a1a71e51,66d13353,74153f66,4485f93d) ,S(1a08e32d,4a968e6,a44703af,6b526a32,3babe7ca,6882cd84,9fd3f769,6cc897ff,46ed98bd,b77bed4a,25c2e19b,e2b14a8d,3fdc8209,70344b39,9a6b2a8e,afad4141) ,S(8559be0e,96723f04,4b05965,da8c9777,6b40e1ee,ce49de82,e7cfdc34,354f4af7,63e24b88,854e20d1,2c3f049b,2dd0906a,ba4db6de,aba42dc0,5af03dd4,91333ef6) ,S(e0e0b223,fc7a478a,849c0ee3,f2ef2a6,edd0f08d,e8ccc8c5,5e28bdc6,5e211e8,ca38832c,3aaffac1,206d38e1,25b8847a,6609a5e,d1288d1a,511d6037,9fca60fc) ,S(a237be98,2d8ed250,75801eaa,5917582c,265c3424,5679b4e2,34539ce,68e40a19,f4cd227,976a3780,454d5de4,7026d668,dc1bfc32,9003c87c,f48982a5,5a231318) ,S(28a84882,1eb08d07,f03fe770,5a16f2bc,5edbd0d6,b4367ef2,474f9b60,1205ccf2,9067d3e9,e7d77628,ba0526b1,71d23da9,162551bd,f00fa301,eecb5fc3,f856a17c) ,S(142fe8d5,42bd6b5d,325b8fdc,3820de5b,cc83e2ee,13d59d16,f4c69adc,98c1d5e8,2973f278,32533b9,559d1421,38d7fa60,1b66d106,1bf9c453,9c8310a1,dc75b150) ,S(5b3b611c,5d20649d,19bb00a,11b4b928,8f3d5ffb,700fb6b9,9c97b012,98ad87d2,849059c8,cde0e12,cdfa7621,9ed70bb4,192ead87,5a22c58f,8ebcb58a,f2519182) ,S(248a2249,5d4905a3,f61f74c3,5f35f6f5,2edbdc63,9454cf6b,192c7ce,50beb8af,b5a6f3ff,b707c108,1cd97b24,38867a1d,61eaf73e,9b89b5c3,b1136ac7,bbfd4c83) ,S(8a474a2a,292b50e9,d4d1fa99,a229023e,31ea2093,2d3a5d2,875384d3,dbff075c,7745285c,7d5341b1,e5c39289,16cf8fd2,45b5f045,d30d5dc8,721d6b65,ef804dd9) ,S(3fa01255,7fc042ea,67cbe4ea,86637313,826d10d2,48d5bb22,8ca8d113,5015ffec,10b9d325,f59b4b8e,ecbdca5a,58c48e18,162d436c,a3228b25,e3f75f27,26a937b3) ,S(b77b5c0e,7b94f1a4,dd88f007,1af049b3,6b778d5f,c8a828c0,46ac2195,9fd65648,31246bc0,6722bbea,8c9d5722,26edd609,e2b65d2e,9df6c21a,d54cb157,faaeccc5) 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,S(493e7c16,2254a40c,54b4eca4,223a8241,d6c2abf5,f15ebbb6,3ea4814c,512b6061,56387f7b,588d9d4c,fee36b59,7ae8f21e,5fcf817b,f097ec89,7def80ba,3ceed628) ,S(672e11be,e7439165,4fe118dd,a2c5d389,8922a68e,222c9bce,902d2062,b9c51d4f,3555134a,2382a9d,b4bcfbca,45e9d62b,db6bbfa,bfce7c5f,c5102dc3,23dc36e1) ,S(8f8d0f6e,e3b86889,8de86c06,b59f8e5c,27524b2c,2959e701,38b2c3,8eda550a,e7def281,9e27abc5,9940fed6,687bcb3b,f364296c,26bf1fd4,5d417103,49212f34) ,S(da8c5783,4a11f0a5,797cf4c7,9179f30b,118f2802,1205d495,e8213fb5,78b293e3,6ecfe35c,6f663975,86bb1c3,ab5dc518,7c7a0ce1,b6338d28,a2c01df3,89c35f91) ,S(4953e0f5,3b1965ff,3efec2d6,fa99ba0c,fbce09b3,83e20ef4,2657faa1,49681955,c210c78d,9d1635b2,3e468324,7980766,3c28fa97,18d0ca39,fc09b541,975541c6) ,S(5491fdaf,48a0e1e1,be21f7fd,be910bd6,5cd3e0c8,16da38db,6c742042,3775f293,65273688,5d1c5338,a3be9b29,9b51f4f3,9c82de96,318643e,3d34ecd2,fc7ffae7) ,S(b9c4afa8,42363b9,fb583885,8f17d1b6,b0a8529,43c907f0,af3ec9b5,abc168d1,ebd3106b,1b75ebed,5d013aa1,eca7d8d5,e24d511b,6d4178e,514fe156,4b550d9a) ,S(918da36c,444847a1,b5f9826d,eab809d5,d6802e73,3abca386,24237683,92d2bd62,6e6237af,d7cc87e6,15e14113,ab38989e,889d5e6e,6166eeca,abf1ddc,8a53e218) ,S(777d2994,da1f514a,800240e,59b743cc,748eb42f,4572ac93,a2e42e37,1d3392a,6193d7,e9eb3195,2cab96f4,14e1d24f,9d92505a,9d21f864,5e6dd3a3,8a9680c6) ,S(108e6ea0,9a08c5c5,e27b8b3e,af24ef55,3988c650,34ef954c,4d17f232,5723bf3d,1a8b974b,86db6bb4,7c314ebf,f811937a,b8a0dd76,e824dbe2,88fde1bf,fc13b2eb) ,S(36d9dadb,65a54d49,1198a486,8deae1fd,3c2dcef4,4a682839,b5dac54a,456bf185,25e84356,d93b5d86,25eec306,565bef19,1edd9bf8,347dcd8d,785024b,2147bbf7) ,S(3e0ebab1,43ece776,729d8a9e,302726ce,aab89654,23292fe3,ab2e71d3,66531fa7,6e7b2608,556d6236,8948f32b,2fb04b34,8e38eae1,3d9abd5c,691383d9,958d41cd) ,S(923dc76a,f315f31a,a1de9521,a13ee9ab,ab08ab42,157f483,2babdb5c,18fa3728,7a8f17b6,7439857b,3141bfca,6d89e649,7facf685,6331003e,f6bee07c,ed3ae47) ,S(f87fff32,2dfeae3,4ce9cb81,51ce2e17,6bee02a9,37baac6d,e85c4ea0,3d6a6618,74e49037,aa726e0a,357ace25,603cdbfe,7c14a4cc,2e1e4e13,c7176121,585a03e0) ,S(1388065d,dd7f69a0,11dec106,b539f7e9,e00b5aff,7568820,e33f9c1,18881ed,acab1d8f,140661dd,422f72a5,5ab4242c,65d1a932,23fe732c,92b32317,4d13408e) ,S(e5476b1e,a99b6a08,83731542,7a3751b8,3d685b34,acc5201e,59e9b623,ac4b6941,57d5b2f1,c4dd795a,323c794c,aa8fa754,bc86dd67,3cc8577b,b418b2e9,5f3b4e21) ,S(f938ff60,f1e8ebea,4c229d89,4c98418e,90c14981,4ed7909c,3dd47cb0,15cd1f15,d7172212,1a0cc646,a0576e29,372bfbd6,37fe2c5,b6ed6821,4da50318,eebb13e1) ,S(b31bd410,7c4a5108,1795544d,5854f9bd,180b494f,a08878ad,8ad5a3bd,98a30aa3,94261097,6bd58962,5e941aff,a007eab3,d33828f0,e12b31c1,8fb6f5c0,50519e82) ,S(b3ed87ba,83210d01,1a2df141,b9a6c6d3,33abd692,55da3af7,b4447d03,f4c1cb2f,949dd379,29c757e1,a970273c,b6341e66,b90be71b,347e747a,be0914aa,4dd632b3) ,S(60e6c240,1ea790d8,4bb95e78,731bca08,89a57c0e,38b87f46,668ee16d,31221e17,f247bf35,c722098f,2a5c800a,571eaf0,36738704,4050d98c,c03bd146,ca9465c2) ,S(2ae806b0,4cc8d047,e7dd8d37,713cd71,eaf3e16a,f74c3b87,994afaf1,c3750a80,a8d978ac,b29771b5,1a87fafe,605ca0ee,6facf6a2,41aa135a,e38de4eb,b2e2e954) ,S(9af178a4,bbba2d29,e7a0bb15,51f6f3a9,d2384386,3779f439,58a424c2,29bb5c47,c1031fba,a0238857,a487ac85,72fbb3d1,4052a4ba,adcdf259,78101a21,ae79abd3) ,S(9dd6a721,e9cb27af,2e7da097,c9e8a250,fd78a531,330ecb2c,3a116d99,6008f523,e6837b7d,647309c9,4712adb1,4bc65787,fc4e975d,f4e82173,57dc9d3f,e7f36080) ,S(cf5f16be,d7a1a1e5,3b3e3f1d,e44efbb7,fcb717b6,9a28bf0f,e31a1da,a5e91c52,9549ebd5,4d87207b,c63912c9,99920cf4,b0c80a0d,8a69d4b1,4852834a,c4487497) ,S(c6794890,810954d0,782466a3,c52a0149,de577cfb,3a2001af,d45e905e,dfa64722,4a4fdf51,deb64031,bfca5fbd,5c827829,8621b625,1be69187,fcc2460d,f75ca468) ,S(a25fffcb,bee9e0ff,1659c1ea,41406aa,b03b4920,fe1a63e4,442d5241,30599713,176b9e06,5a821189,ac3fc28a,fb72a1ba,40fab791,4de987e2,1236f244,bf41486a) ,S(6079a722,fd5d923b,16acfafc,7248e329,128cab6a,cae9e5ec,dca49774,e0c5bf71,c09972de,99ca5a45,c4f6f1d9,10337efe,23f5292,bd5ecc45,df0f7aeb,d18c4bcc) ,S(188cb43d,9d4078e7,18fffc42,8b16723e,f64b950f,cab7582c,8139dcb9,2b66b403,a038fa37,ec9ea240,9a2879,9556916d,fcc8c2f3,358ab14c,140f7f1a,23af5404) ,S(e310fc40,cb575c68,f5792506,65567ec8,c445ca34,68cfd02c,d781b27e,f819bb30,31328a65,5ba312ee,5e901def,66e7b946,e0c18336,a0f1784d,df66b89e,2abe625e) ,S(dd86485d,1c8245dd,d940bdeb,1f462cc8,f15693df,246c3c8e,52b574bf,77dea4ac,cd6bb7c2,56c9a270,4c690175,ba298a09,8963a8b4,7e743b48,33fc09c6,9966ce2) ,S(1b7ed20c,f81567b8,6f7dc67c,ab69e197,dba77399,9b36097b,de85d02a,7019aef,f814e92a,d1cb4386,550d89b5,9a4bc378,df428d54,d314d531,be6fc35e,f0e3d1bb) ,S(a15587b,2d528338,ed146a03,670b3f1d,9b41cd0c,a0645897,a0f719a7,b5ded284,2aefe34b,5aba1a4e,e30d225c,c4023ee7,12fc1522,ad6b452b,fe6ea727,122e925d) ,S(57bb9f9,c99da691,98cfcf20,9a0940ce,8d19463,9e4d1054,484953e,936a5484,63d0fba8,d90226e8,2c7be5e4,1d77bf0f,700dc57b,d8d3079e,9a6a47c8,331660e4) ,S(224295b3,7fa1b4a0,d7d7f7a1,2113b21,291f84fb,8fa4b746,bab925d5,93bd262c,d60ac40,b1e4b0da,7563eb74,c222660a,46ed388e,c4517ddc,ea2962b9,38195796) ,S(2434eae6,a34ec53e,7c031b2,9e74354e,d6101ca0,f228055e,53b39a6b,5453b0e3,2ff5ed61,d57a04bb,138f3956,33a20e60,8b04f775,6476d0ed,6ce7a382,743ce23d) ,S(448de592,907c1113,bdb04c64,9fb22b05,ef2e6ab6,36d0a03b,700a5871,89885ce9,d7aacffd,6ab35068,debe6dea,25b02930,63af8b10,d4592880,3d0421cc,a879eabc) ,S(8405cf73,5aef7674,7feb92e7,1aa3ba0,defc0a1c,c1da698f,7c2a3718,6393dd76,5795d006,49cd10a0,4a661c78,3f4a8711,89c9ef2f,ba86853f,c7955258,e6c407f2) ,S(698974c1,e5c1487d,fe9349aa,371eb86,9318accd,72c66d5,581211cd,6e08efc9,37c2238c,dc8f4bf5,1f76536c,2ab9af61,bcec872a,bb84ce15,90bc1c0f,ef84509c) ,S(8a37857a,be3cabc6,7197781d,f315f78b,e6548c61,1b846d8d,ce2e5732,643fee05,29882f68,9154cd0,7e455e4d,9e3866d4,5e28e99b,21dde0b7,8b87698b,4cf674ed) ,S(a871b34f,5cdd39fe,13104c96,87a8a717,25ec8cdf,fa60846,793bce03,2397eaef,84f96417,9de103c0,9f7e2dc6,86c9213c,642312de,8de6cc5d,f3ffd7a2,c387cb28) ,S(49bcafb8,9f78a7f5,a8857905,e99e74ac,9ec66ec7,aeab8fb4,fd964ce6,8286f44a,e7db8ccb,5641ab74,a791d2ca,7bd193ea,71124a61,2716d94f,4eae407c,ed9eff6f) ,S(d5c7d92f,2f05c9e5,8f586289,dffe8499,40d9b84b,79feb686,c3f71300,f68b6df6,a68b2a5c,219ea38e,a04b272c,e1cf42bb,6fcb2b2b,fce36043,4f1802af,1d51c08e) 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,S(c411af61,547b1b38,12551e1f,4ef2b32e,fd7f33ab,7cfce378,8b5b8f93,319c0695,d2bee7d7,3d50f82a,e9266d21,2fcfbb76,294ace4e,f6222ab4,797bbf88,558cb66b) ,S(d0ff6a94,485bdda8,d0c28494,5b9dddc4,4a35f101,d0a89637,8210bdea,909ec5e7,ab3f60fd,2923a8f2,d02b7e83,d8f953c4,cb1910ff,83a92a65,e2121f22,364f620f) ,S(a0d05cc,9555ed92,2851baea,35ad6cb1,6f2744,b3fe424,98235aa7,1f08c0f1,843b1105,237158a7,bd7e67c,a20b2705,50afe2ad,318077dc,4714c7c9,d6339948) ,S(bea08445,eb295fba,5c83ef6,7d909978,7d599642,893fb9d0,568e5920,1e3f5d32,2a81a7ff,b3f7f453,d78bb2bb,41d12ed1,e26594d6,bd4f5cc7,908f322a,6cce10e3) ,S(e8ebcc4c,431be689,9eb5aea6,f6ab9700,551c3098,c5acece3,e822c7de,e6f0d5f0,ef99a461,760ae4f5,8fbd511f,59a2ae79,6d65db64,eaa0d61e,97d0a3b,31fa902e) ,S(4948606c,dd73dc44,ecf1db77,c796d8b6,806bab5,85877cd1,d9630bce,966e8fd2,3c67333f,786c8c67,841630aa,639446a8,cb8c13ed,f3db9123,bc64b925,beb95f80) ,S(4f259b32,40d9efba,4e3e40cc,a66cd494,fb5a19a6,5b5c8a16,5c18792e,9ea778c2,fdd88087,78c26999,c4a00605,49f4ea2c,b1590f7f,4748cefb,1b68eaae,4d17446d) ,S(f303a493,e14d7f52,f276e2b4,3e118eeb,1e7e918d,e7aa7f33,7e350fa4,7adfcc29,c49fa46d,befe53f,5f5bc49d,aa6ad265,453f7977,c5fe4163,cfa1bd4b,69141b57) ,S(e00c4b17,f4c0800e,c1b11859,c40a560d,58b9fdfc,29df5a41,ea4b2f53,c1df595d,62441a66,c3ec4d29,d18d0d95,7b4ccd18,a72a1003,d34832fb,8c81fb75,9763b99d) ,S(484b8486,1af6af52,a47603bd,2b754be7,ca16bef2,21581171,4cfb2301,db72ce70,36f84ff5,a0ac79a3,fe696865,2a0a6759,cf72e5c5,8c76359,d477e72c,4d32fbc7) ,S(88be58ea,d8b51f44,a1be6a8a,7cbc149b,ca07fece,11a7adab,210467b8,4cd93f14,94c10caf,7037fbc1,71cd6cd6,a0697b19,8ebbebf4,9f00c67d,4d46ebca,92687fdc) ,S(abf6ceaf,9fddd7ef,44a75e11,b10119b7,7372a3d4,7c163b77,384de944,47da781b,5cadb30c,6320c67a,e9dfe2f3,b9bb4ef5,41718392,81c4a59a,7960eccc,6795d290) ,S(e8c26522,9ef665b2,67fcf10a,17c6c3cd,4e221e0d,95663deb,74f8384e,b89d173a,9a69fbad,f9b050ef,d231965b,30d91646,bec7ba26,9fcd0934,35ae11f,ca2aeeb3) ,S(66652bd8,bf72ecb9,5e670a24,e8683155,e031f3ea,91fff58d,f60fa4ff,d9c6c23e,4844ec08,3f182b73,22c2fbb6,6f6630a6,5fa6901,52dcfb3b,4b65a3a9,30be994e) ,S(207880c2,d8421040,dc8202c4,45bf6d58,75cac841,532aaf0b,adf252dd,4c2c0964,2b1819d7,3eb24de1,ae4ef316,7c92a7b1,a562d93,80fdc54,e916d1f0,c1860cfd) ,S(46b9bde4,53d0692e,ec933485,ed0dff68,7e8f262c,7d9270cc,763fd959,2013f581,58af9be6,3ae599c0,f499b0d6,3085b7d5,394cc786,9f2fe225,6ecabd2c,a14f9bf7) ,S(5d9b2574,dbebe5d0,9756e2f,29af3aa,a2fa2555,d629a78b,82b1d679,75ea3e11,ed9f40ac,aa6ac68f,cee3dd50,7629758f,f3a64190,1658f0f0,2b87b645,ee59263) ,S(ecb5ad82,8b986425,9a76a649,1774338b,dc598fd7,77cfec52,d086c172,6e590e4f,2b78936,73c6d87e,a954b5bf,52f8212f,65d33ea7,ccc4b4e3,1d98df2,c9887886) ,S(b32b64c1,5e711b8a,1d174725,de55c,ddd62e99,fc90e96e,8f3ca532,3924ea67,af5d61d3,6dceadf2,34a7a94d,e7e4be1a,4d81b84d,e0fe16a5,403b0c24,a6ac2083) ,S(5137f71b,71582334,a6d57aa1,5cf6ab3c,8b7f6842,a800b4ab,1c308fc5,820cd364,f7ea5fec,c9b17dab,c6a248d,49757711,e4a3b38,95658381,efa652a4,4df1eab4) ,S(b9bb0e1a,390b5889,3e113a89,801c3f5c,25f94e65,63161539,e7c56297,ce9ea866,d8db3c90,3c3d35fb,ae4e14ec,e81e4e31,247f60a8,2539880e,6b66951f,8324a11) ,S(3f091967,6da40ec2,4691c21,1c42f47b,88cc1192,ec1827d3,17beb468,924fe9af,f1b44826,3e882c1f,18ae6a81,238d0724,ba4c04bd,d3fcd395,8775df5c,16bb8de9) ,S(b5fa25f1,dad4600e,8d55e7af,c70a1b2c,3767da47,d625ced8,d55ac88,d893b4fe,7575f661,f2ba296c,7ed3a190,8a49d099,83e49503,ba17a70e,1d6939b2,8ad22347) ,S(a0371ce2,dc6a025b,78db797e,90373069,e4ca06ea,6b1cc018,3d4c6f7d,680d17b0,92b5a8a8,9a5005ce,e851c521,4599b774,24f0ff74,5c4af6bc,6937c432,e859919d) ,S(5aae6e90,a49107,78863967,d7d42020,cd0a9828,da25ac8c,7b19942a,1ee2f210,ed9cc20,82a54f3f,fd7218f7,b79ec399,7e82fdc4,cd783957,5760e4f7,b7ee8fd7) ,S(54e7daec,f4a9b6f4,b100f964,850deb65,64efddb2,e6ce7b05,3fed2a28,1a0841a0,d9ada32a,54773a81,d5a857ad,8b34d96,70d46785,70943dae,cc83deca,97c9c63d) ,S(e9b29910,d8bcef46,b48d8be0,c7649b84,383ed752,391ecd7a,bdb454c8,8fbf44e8,eb268094,f669e91f,a5173965,50e4c40b,d7a26792,9a8df3de,b84c703c,261d6b69) ,S(43f95222,f254a513,1977c589,577d1d9d,3f537a1c,9fe14ef6,384e1779,da546a97,d7d3c653,43345c47,f245b305,b662a2df,eef80b3,97b3f5e1,4b0eceb5,71cb18cc) ,S(9fb45fd5,3999fb92,830bc090,216ae485,6723385c,7224b1d,cc91294b,a6c3b103,5b47081b,dbfd82d3,90d7bf7f,39a494bb,6731b506,b827213a,277f7ac9,febdf451) ,S(dd92282b,835529cd,3295919b,2eb466f5,9ca840e,20ad87f2,3cbc824b,b71dcce9,ec45f6e7,bc59d668,b1ef4a29,d1e23bcd,f3796268,3b58fb7a,d58a9e1c,5f726371) 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,S(16ea62a,d4cdc00,9d151b3,b6680b0,c68b4cbd,f144c234,71d55b7f,3bb7ebb2,8cac4a1c,53672e59,338612a8,995980c1,35f02060,2e3b9f6a,8fffce9d,e53fa629) ,S(6b9d68b5,454c6d21,678e5413,279f9a28,e1eed485,fbf512e8,49f35394,22a40970,b63f5044,98ebe37d,af9e6969,da888eb7,907f8565,4b05d472,fa4b1b27,ae365482) ,S(1fa20c8c,8f0812c,2e7dc948,afb7ec92,32c3c27d,23165d05,868dd127,b5ed3e6,c5257f4d,82133642,7df68606,2c229fea,6cd16857,280a60cf,ed84deb6,29838076) ,S(73a83c92,7daeb4de,1cf1df6b,31d8f536,af15bb38,be506263,e8e8a6a1,bf6acc86,a08acbe4,cd6c30b,82b4e24d,e8c9b891,26a21dab,e4df40ab,2fb7ad6a,82eb8adc) ,S(3a995664,924e2dee,ca278cf9,3ce265e2,85ba90ce,fd2a55a4,8e1761ee,7588bdbe,f3221adc,99eb33d3,52465d93,91caf18e,d011a1bd,3b7cf39,dd48d45c,44cbbb0e) ,S(7c65ee19,b032f5cc,1d45cd9b,9c160e86,5ca516fa,b4f88596,5e07f269,3d429c26,47c7faf9,e3df277,d31076ae,4be2224d,8cc54a5e,3743e287,ff9572a4,23704c5) ,S(c010694c,6750dbbd,bd953118,dccb8d03,2f05e6d9,65db8fb0,3dc00b22,e4d397dc,3b4914c6,dd6c5441,59dfde10,a196f132,5a5e6101,52d41be2,39583b80,6c8e730c) ,S(e255848e,d28d8b6d,6f95a12b,92136131,a33dcb2c,a723fae7,5e317cf6,62519d57,62f7d5aa,1757dad7,98207dcd,18183b24,377c9ac0,1e106fe4,d36d9264,3fcfb7b6) ,S(f31418e5,73232992,3a878dfb,f1de30d1,a9669da7,76effc45,bd1a56d0,2c236ed9,e62ab884,dce0d946,55e34c8a,630b5aef,16a1eff6,1f889552,af7234b8,ae56b84c) ,S(9adb945,b876313b,ac9c290d,47c1e6aa,1f3f3c9a,e8c67770,61512c2b,bd703181,b21fc142,b4632616,4820b82b,edddf2b2,51531d0e,df0f0f86,50f74d1e,9f0908fd) ,S(c4682b2b,9d4a63a1,855132e9,b35b390b,ca04b846,b83bf36,1726c3c5,808da322,f25a906a,7100ba32,1b659762,23e36f04,14e9075a,835ce5a2,6eeb5d03,d35f6972) ,S(ebb0fd6d,60f49c47,8167c405,597c765e,559159f3,ae04003d,a99a1066,ea80d63a,eb37d160,667ac862,1da2ffcf,28b431c8,c4202f67,706f4350,afdc868e,6aa0b0f7) ,S(78f12d20,70d8bcb4,267cbb,bff637f1,65ffb098,95f5734e,3551bcbc,9a5597a,42976ab3,36621756,1bb574d2,c87d99cb,7419a3e3,39973740,7de17090,2bbb78f8) ,S(3dffc4a,f6214b63,9839fbc2,b949621a,35ae41bb,e7679eee,5798afbe,85919f69,58174b6b,1b4021ae,22dd15a4,29d97502,a13480fe,902860e9,36fead8,57f2c456) ,S(410c9393,a4ed42ca,2115198f,4db76eb8,bd16bf0d,324528bf,55d5d745,b55a15cc,404ff4b1,df71b89b,c14c2cf9,bca25176,83c2981a,731fc3d7,59faa0a,5ed58306) ,S(6b4d5156,87d6b079,3df36632,6fe6977c,b93e6569,66797196,6c16c495,be4e3649,647a4894,bbac207f,5d2a0315,2db1760c,1a25560a,95511c81,5d6c11a5,e969f4e3) ,S(58ffad7a,e87d5986,f0bccfd8,5005d9c1,6f0d8724,6be4dfd9,4a771c5b,a5f34247,ad8b7ad8,f9ab15fa,f50d6f93,ec8629c3,b33fba6b,ee36ace5,e505cf00,f0069817) ,S(e6d3e41d,1835fade,af27738,23e883b4,adb95669,72892c72,b310eacf,a6a757fd,a136c88c,b580ece7,cef03e42,5dbdb8ef,d6395cab,b427ae61,45a0ef0,21359c15) ,S(fc47c62b,43aaa030,ac104479,21bc1026,3b561b42,a2d32a5,573ae947,d953b35,5d318d1d,65fc7806,732b5810,40a1f511,62723626,b393b29,50230600,246224f0) ,S(ceae2867,cbcb37bb,8e78da9,3553866,d0a1b8a2,933cb1ca,36bacb7c,6fdb251b,48bf2c7e,c163aa95,79417b37,343727b7,956cc629,3a188c16,d4c2d1dd,abb3dfd) ,S(abb12378,c84735b5,c23408d8,2516d887,9195fb74,c8972d78,daa8243e,1befeab0,5a0bf64b,da5a465,d9d0be91,3c8a56d9,ce901c36,67041a02,abb591b3,3f66698e) ,S(d7781e39,8330c7c9,2185302b,e116316,1a576ce9,43a4824f,274ea700,3159eeaf,6341a432,4e07c5c7,3ee7398d,d1be3d7d,261aed99,96f6f310,fbb464af,d06651a) ,S(a6918dcd,46ec2045,72d71646,d2a21df1,6f3ad133,dfd41a6d,be5b7684,7e4c760c,c0e51aba,378d498d,9a70e4b5,3521397c,1d6c7cfb,2f6634e5,1f056e7d,932fa9c) ,S(413a4ee4,fbb5de60,392b340a,65fd9706,7785e2e0,248d2770,6ef044ca,83d1a204,a0362506,c18a8f34,3bebc668,d1b08fd1,6595a674,51db27c3,43af172f,8a3dd197) ,S(e1a7bc24,de8b0920,f6c4aa08,2fbd1126,87fd8766,237311a8,9681581c,5e04001c,3e3ba9fd,d0a2873d,149aeea2,61a55c65,3a3d90b1,efa8e49b,29bab100,1a6bed16) ,S(ff9292a0,a147ccc4,b5ae077f,8a337e05,ab1dde9b,1795942d,8a9a0fc3,dd333a75,e50f027c,5f7a3463,7654b412,25ad5dfe,b555ea2b,8305c7a4,3b6f5b78,7a23a166) ,S(eae56623,437c9dd3,9dc7a36b,45c2d3,afe849c6,1980140d,900039d4,4ccb9c0c,f1b8c9e9,92847436,dcab5a9b,22fe7e78,55e62e40,372d77be,39f68974,dd32e043) ,S(7dd20cbe,3467a3df,e1eda0f3,48c39e5,7f9c6004,bcc89227,3d002cb5,54bd5282,ec4d2f23,f035d2d5,4cf4c3f8,31772a46,ee922582,8ddfd4c6,4eb6a689,7c1485d0) ,S(359811cc,5acf1291,547b8870,33bda3c3,e4e245eb,db0dbfc7,3a02da3f,12a877eb,ed2f5087,8b97a3de,6ff916f,511c3a27,7702d1be,2b683a59,bb6acd98,e908a792) ,S(fb33e89c,f2bcca4e,4ead57ea,1a24d1b,5a6c76ca,bc605a2,c031102e,49a71c24,c75e02f5,ca602705,7ab5b958,42a9272f,d7fca940,c26e980e,192861d,2f1c9f45) ,S(a1cd33e,5eed74a0,1534f836,b05a5129,b7b2970e,f293b606,9d1ebb56,e5f687aa,f90d1ab9,ccfc345,3b2b60cc,1e4380e9,bdefc37a,896a1abc,c9978d08,1ec4a6b0) ,S(461696b9,3643b7a,bfb383cf,ced8ac92,5d9f169e,1db30999,b8553504,c4213614,674f5c77,5f300fa0,c8f40a85,9aebffd3,ee91c4ce,695998d6,de0d59a,3033bc72) ,S(6c6aaa22,1b589f6b,ccc885ae,93f7e8aa,1fd5cdf2,27471727,f390d5bd,e14ab025,a77c5e03,40e1b90d,1ad64483,fb50fa76,aeb84417,88ca415c,9f8d2cbb,aa077538) ,S(c918d391,927f3310,d032c7ee,6e729e6d,792eff1a,72acc268,3874fcd7,4e61c38b,58fd746c,346048f8,eda1bed0,e5b6cb58,fce24a72,6e27f965,74243c80,780dfb5b) ,S(48679e16,1ca0a3f5,e4ac2654,213c494d,9240c3f0,33fbe2c2,142ec589,6dea5918,556f93fe,300cafe3,e93a2966,767840e3,b2a19fe7,9cf204a9,a30d1f1e,3e1d1a41) ,S(c68c05a9,e46b6440,a72d6eed,eaac085a,5e945659,ac46a584,69968a30,c6e7b858,b8b4b5dc,35d4ff80,be3d64a1,d036a117,c768746a,4d2bf2b6,1b126460,15de450d) ,S(d133ef10,6358489f,8f976dc4,b6c54699,21e3dfe3,6f326dc9,f0538757,9d444e6a,2c66abc4,db690d2c,272b0f57,afd66a6e,327ec3eb,e32b45be,cbf3c502,baf968cb) ,S(53544f59,8d759dea,b10766dc,48a7e2da,61ca0a60,a201d193,92dad05b,3df976ae,449a205e,61cb7aef,204e3f0,3a199ad7,993d711,537e17e8,79a42bfe,2869cd47) ,S(3108a074,fda5133,39e26385,14b6b7c0,9254c65d,ee374a62,2fe34acb,83b8b331,42edc90d,54263fea,8b1a473d,ac2f2244,d6fc05d1,f59e115b,5d930132,268b6243) ,S(1666c40d,52c1c04,d9e95099,aeb55861,2ee58ac0,6b22f962,154cd8ca,7cb4b23c,5065bb41,ae046638,aab55923,e0752954,abafc247,d201e84f,b6c444b1,93a82fb9) ,S(c96d07eb,d3eee6a8,f001290d,f76b2d82,ed80fa90,bbd5ead5,3a572457,ee47722e,d3d69c04,447fb7e9,a3416af1,798b749d,13ba06e4,78a432c8,d00dc2cc,7e20baf3) ,S(a9ffc39,b11b5b05,78769a9e,8ce7542c,647fa7bd,7b2c3479,fce84d91,1d81b49d,bec21248,82e928f7,e98894dc,25840712,80a64449,38e53747,375d2122,68bcbee7) 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,S(416dcdf,b3a1f0be,1a3fd6ad,52fb1c03,4e24d48c,cf34d189,e7dedea6,b65a7a4a,76909ec2,bbc93359,ac177781,2132db31,47e90a0a,3c6ca35b,ebadd113,60c204c3) ,S(b397c245,9aefc175,8ba5177,2d4b3ed3,2ed9d1c4,85d2a2b1,7318545b,93c63eb3,a106a360,30763676,ab418ffc,692043ee,22813574,e3117a7e,4471ccb6,f5e71748) ,S(75c5589b,efd61646,329dbb75,5e809b2a,c1bdb8c0,d29a3065,32ef3909,d40637df,26f3e1e5,1492105c,90ea19dd,81fce6bb,95e60295,a1fe347d,cba27adf,a3e6f631) ,S(2eeecd12,a3517432,17d5158c,439a9046,e4b0dc80,119e58b6,620e6f08,969135a5,e1deebd0,48c58ed3,1b53d753,9c4c5791,13606467,14147707,806f491d,2daaba4c) ,S(a981f091,5d39d650,66b1d52e,5addda67,8cab860a,c75ac124,aa100593,9cbe65d1,4cb09fcb,7ab60293,2d98b23c,96e5109,88d4f149,4f334e7b,66c60040,7d3ed069) ,S(1a19fae3,a7e81d02,a1260c9,a759e79e,545cd869,2666b31a,9aa4c0a0,9bd4ef62,2807d657,8af25c69,e29bf7bf,d877dc7b,79714df0,68ae0707,89c5b72a,b0937902) 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,S(cfa5df56,cc450bca,914f3a85,b370f864,e4c83600,560bfb20,93df96bc,bff6b83d,cefb9a46,bab7ffc9,1b1d96c7,48f81706,61cf56f0,264e203f,78b05f3b,8d37604b) ,S(991b6b4c,3fbb9693,f7641eed,534e7cbe,8937606a,962a83e8,b39089e4,713e404e,3ffeba6b,be556688,d3b8a0a2,f4b92b8a,98dab79,d5847c71,13bb60ee,be3f8d3e) ,S(d104c5d3,b9b0121c,58a1fa14,f226c513,2955c4e3,56938bcd,6891bb92,13c8c0d7,8c8399a,814d7cfd,32cea21,85c77738,91ddb00,a091196a,3d90d056,b0caa6e9) ,S(76192853,a45c3648,749c9a40,719424eb,415a06f7,c74b31bc,ad93194b,e355dfce,31139287,3cbb5012,d7ebc934,52613c62,b5517b37,91475ecf,84ef3745,324ad2fc) ,S(173304a8,509c1f4,c05b1de5,c51093b2,10c7f9b9,81a7d6c8,8059fb1a,e5070725,43bfbd98,c8e08394,543db2e9,c692297a,800cdc8b,398c13d5,f9e21f89,341d353e) ,S(aca057e1,d28c5514,107f5b6a,9e46fc95,9eaccaa8,b14d4c4,6b7ae515,bda104a,e17f1717,70bd76ff,18095be9,a4b72b8c,cb00e6cd,23f6d702,4dcba433,e6bf6ce8) ,S(fb202550,e0098fb1,c30a7385,900a7dc3,85b2945f,60e6eb04,b7e8489d,3476dbaa,1aaf8420,3f72c68d,bd3bc98c,77f473cf,cedda922,dfc3c996,45e4f565,ef9a0f28) ,S(e95b710c,a0227ab8,e5b66c66,c2958be3,af1aa298,422c501c,8f879bc,e11ae7ac,e645f4e1,ab5cf4b7,da909022,cedd01f8,c745a968,d9ca30a2,c5525d50,9f97cf19) ,S(6db4525c,3589bff9,605cf203,cced45ff,ab136c6c,ce77ea15,14766f3d,e844770a,e6b7f403,f5f7584b,2331d295,82c0698b,799cd7bb,3c59c903,eb5d6848,72658c81) ,S(8893aa9e,49daeae7,15fc2959,e4db9c45,1690438a,6964a2c8,fbe73133,35085eb3,70fbd83e,ae803f3b,6377a4b0,265f62c9,bd15cec5,baec8c10,d01c7094,e5987cdd) ,S(be57f6cf,ac6e8cda,871e3ece,8aa78bc9,2cd9e2c4,8f3adfd5,6e39414d,8e0207a0,78170872,99abf89c,fdcd141d,899aa7ba,8893eedd,36bb3aa1,58120f2b,ee93d5f2) ,S(77fa6d2,85a01129,c5e05ddd,8d02b5d4,a2f69bf4,5a9e7562,6718cb54,20b34925,315bb23c,13a3d218,ce886288,ec0edfeb,37a2da99,e017b97,ce04db45,326455cc) ,S(2fed7bfe,8414dc33,62c834ca,767ffb0e,61094ad,978ddd00,b2ea09b8,d1f4dc03,14e5e8f7,aa0b3d31,565e434f,11c61b,63332a60,b6c4cff2,a6de2c5,98117e01) ,S(9f4c2cd0,5a871ba1,fcb43df2,bf03ee3f,7f8af242,ce8ee6a1,1aeac89,b4d66c6,eb421f52,f2427887,8ff8a2ab,dc384e23,d0fd7df5,fc341acf,83bc5940,be922920) ,S(53c0e0b6,824a04cc,b7203ef6,e37383f0,15f0a48b,bbc1d3ce,7c8fa7ca,5dbea647,6a9b598d,9246ca1a,539729f9,be809397,13c59d5e,105a8e91,836fd3a1,4d618cf9) ,S(dbc0cc82,d7906b84,b6b7bba5,433d68eb,bb20fdbf,7b4eefd5,c0a3ad8a,ad17d714,5ebc1f86,23ff2c3a,6f81b090,4e5e6338,8aee42e2,85306e37,a4fc7676,2dcd7211) ,S(7862af32,a3c08e04,7b1a8cbb,8131d55e,ca93a478,40c52165,af20aa6d,248f5f0b,bb5f6607,6b10353c,8a367a64,587b3bf9,7e8c272e,8da92684,f1efdc33,8bfc15d8) ,S(d3571fc,800158b7,6ed2bad8,15c93b1,f8238fc9,b8753752,4e44c0ca,931049ee,162dc9e8,3e6630aa,9d0872fa,915af449,70a9e6f9,526bf15f,4d26bc74,82a44bc3) ,S(a851c894,cebbc758,642b98e5,5df3584f,b9f531da,88faea26,e908b0b7,88589d9b,74702d5c,adfac1ef,71df3898,3ae433ad,1e1af1f9,b5fae0e1,151258e3,b375b422) ,S(a92e43f4,12effaa,e0978a08,cdb2e885,2d9af1f9,1f0931e,972016ce,da58012d,d8f5a09d,5560170e,b35d7bd1,28252096,535c687b,23bc13c6,bb903b95,d02fb668) ,S(75cafe44,8b4369c8,42e658c6,4760ecda,bb29e129,d283c24c,9007fb5,f3cff6bb,ca0e12e2,43c73553,1e2affab,51d4738a,db1ea5a2,fba215f5,3c9477b1,b55dc39) ,S(ab0066,4db959ec,2f17a233,78023b5a,c48c4177,7b6e6b56,a2148453,8c41d006,8cf9e2fc,35545169,f46762fb,940758ad,e3d3387d,eb72e9b7,b5d37175,9f5d8b31) ,S(27510ef8,2e4b2134,180855bf,469d1f0,f89b9afd,573f2781,4a1bea50,9db7ecb7,20fe00e8,86b54c06,1fe07355,5be99fd3,b0a1b20c,dec68aeb,90055c34,acfb87e1) ,S(773ff5a8,d388277b,7921405c,99c9c207,f4a6c2ee,3b59ac1d,7452c8ca,4db16d3a,cf45e631,f51cc65b,afc806bd,87318e3a,f75caf,3e734284,8d7435be,f8a52f8e) ,S(2f8f2c98,e69ebfc3,b7277e35,9da1a8ef,4293fc37,2e24386f,e14cc455,1ef45746,f85d23ec,c4dcaba0,23c3e406,604aaae8,8150a6c8,feea2c36,42ccad40,9968ec06) ,S(1878acda,ab8dd0e2,a0884952,26356ce5,74575678,64da41c0,61a83de9,6277f67f,412c868d,64e092c,ade96f05,bfa48af3,ecbcc128,e6d09bb,9684565a,d5477020) ,S(8cf281a,eac4e4e2,7ec4f3cd,d1373f62,c5a17b0f,49cf69c4,cad8c4bc,4f5618c1,2f17f995,29c9ea27,cda3911e,de33029a,7dbf09db,64ffa625,cd9fd86f,29ed5973) ,S(3a597c9f,f165369e,5d90d191,3dc2aefe,a0957936,717f1ec3,9ea20698,d08939f9,8c2203b2,90c9a2de,5b464b0,988e07,a7b48c86,f5891926,da462b4e,b00a14d4) ,S(cbe3205,96f10ff,5de9c861,55290393,b9ceec90,bbac68ac,5054facb,950ca15e,446cb06a,b76aba12,c32b4855,716001cb,9bf7c72c,ade16bd0,5472b947,4fee27f4) ,S(4313c9cf,8224e70,18413b09,e6544731,1cde7100,5ee60bd5,3a8db041,56fed594,dfaf359d,d3045a8c,b181021f,9a025208,e80bbd4,abc4a331,7ab9d735,1b329a96) ,S(cead2b51,f8d8adec,2d89651b,2da5ffa5,1f5cbfab,19fb7688,2bdf0faa,bf73c60e,ab2a2480,6992f0e8,c73e7932,2bf144ae,6dd3bda7,ed2d221b,f8451ca4,56a25897) ,S(9ce75c8d,848762f,645164b8,45ee6eee,98e34dad,9f8be0e5,2d8f27ae,4a7b79a0,e0556d4f,e11ba906,6b97c04c,8b742a26,9f627559,b9163571,d0a29dbc,9aa30a05) ,S(6024489c,621de255,f92106bf,8c23847b,10214b83,1d653a9,6ba00889,326741d7,950eb24,80a90200,ec932621,6b82e5e,abf63e08,6626faa9,b1fd8e2e,104ea858) ,S(d3c746f0,108f6bcd,406c2638,c07255fd,1f55e1a3,c6845e11,546d22ed,5f08e51d,d124dbe5,d349c739,e641a776,c57ef3db,35ed4e1a,6ffc165e,25d0bcce,438dfab6) ,S(a1eb5f5c,d85dc222,f97b9e11,e08594dd,a69c69f9,bcfa4c63,52cf2717,136514b8,46ed3d35,a393e017,76247ddd,7dda3ba0,ff5e3f76,30253b68,750a7c,f8a15fff) ,S(2b24a357,fa3ac2cb,faa5f1c6,1c14147c,e4406556,b82c7639,721f7561,485a8736,d67219bd,707aad55,1a8fd7ae,d5721d45,ad192a5f,5d0b643c,18330cd,1bd73ade) ,S(9901a1ab,9dc60159,63cc9cfb,42ecb41a,ab6a623e,62e9f306,126a4f6c,fd87b2ec,8f766594,17cd7f2,fff7a3df,6cb414e7,eb5950c1,ee265730,633ccd8f,f0339317) ,S(311e8445,5890e2f1,e1d8e600,37d58c83,28a2a4e1,b21c3763,4aeb9965,8477e8da,cf593f67,6cc75762,a1b0dd00,f6703bc1,e017e927,1e61c829,a0459056,ecce030c) ,S(905f72e3,97140f6e,298ad8b8,c8faf66f,122d27e4,6fee88b3,67a8ecc7,9e83bb77,c03f155d,bde9c265,d90b94fc,1b5b253a,2d98528a,a12e19b4,698714a6,f1b65257) ,S(61df77a5,d5940001,2fcc2f02,199cbb4c,39eafd33,27dc85e,4a3f55b,a339350c,27c88b7d,de9b3f,73b0603f,2d6e40f5,f3664020,8d6dc05f,684626a2,d9049161) ,S(e1f8e199,886d4b1d,5dd6af90,6eec06c7,de36dd4,ef026129,5bc42bac,5df18c28,502c12e9,b956eaf1,2865bc4b,ae7e6348,56a98db5,4c65a5e2,9ecf8ab7,51ca45a8) ,S(ade2f5b8,3804a21c,7dfe6a7,7044cf96,9180e154,79a4aac1,9b686076,fbb8565a,d0d65e1d,7c8168c,308985d6,f5d267e5,98a9e6f6,45715eee,3751bc26,ef066aca) ,S(c55820bb,154f972,ac345dd5,c62880b8,9f7f6b85,a1755b88,ea5821de,6f268187,911b0fea,1e6ca659,263b698c,8a17488d,4dc35f5a,d817e7a2,1241e56b,cc613086) ,S(ea20966e,321020f4,53964352,b8ccc2d2,1285888c,152ddd08,9f7039c6,6c7778b5,c942f591,cdc81e52,6abdc9bd,643429c1,66f5476c,dde18d39,59e29f26,9f4fc18c) ,S(3c57552d,9c2dfe5a,67301bbd,3e1ef84a,220c908a,8e80c707,9f9f4df4,607e2bf5,d49fa0ff,bc4a6397,3e71a0a1,7265ff65,6fd34754,ed508522,b9f0200b,e71f39e3) ,S(f188ccc6,e1043ec0,59e8e133,94ada165,a3fd5c0b,cf7f071f,eb5a0951,9bd4e1c3,5f1f371f,e53e79d0,2d6fb190,8207649b,db045c41,a2fe1cf,94486053,7bfdbe4) ,S(a0145fd2,7e72232e,8055a146,aa7bfb49,447112a2,d1ca53ca,d4835e42,c11c8c6a,7bc018a0,e5e70ccc,c4bb675,f0709cb0,ceb874bf,22c7ecc5,243e49c,3de679cc) ,S(53400de8,c221153,1fb85706,b558185,c17b7bd8,b17416bd,9c93df80,f16ff48e,e1228e47,3ba565f1,e50840b6,a36ea970,2df87320,8a66a44c,89cd33da,41a6cc6f) ,S(82115d2d,9d37e3,50ce3482,1d59af85,cc8960b4,52b99904,8c6c6674,ce64b1ac,98deaa09,659a0c24,4aadab0,3b9d1881,bffc1b3d,e9226f05,e75fb9ef,b61eb048) ,S(273d8c18,53d86f1c,c49e6e9d,450dce26,8669cb7c,3083968,1fc17894,59fe7c3c,6c5531aa,8ad026c8,174c25a2,51efbadb,14974e1f,7f7f88af,2e16d101,c2ea00) ,S(616e16,a7e38191,70e33f4f,bf428fcc,41e68ccb,5b059bfe,4036751b,ba5ee319,7dbcad21,182a3efd,b99173f5,cca99374,7c7dc3c7,3e8af2ea,ba84b0e4,f506748a) ,S(6761896a,76a39812,1f773402,d033f210,dc566610,275f6774,52c37c01,60b82812,7fdd01cf,1b40939f,8091184c,8e2c8ce5,11848df1,a23607eb,e760782e,67302c9b) ,S(77f7abaa,e97605da,12535bd9,e177b6b0,bd6eb020,92345fe6,dd4a6d4f,89e508b9,fb04996c,cc7b830d,fcf5fd19,bb7c9332,dbf20fa,10d61231,889e4b65,cc7f0b9e) ,S(c12f6717,3a2e2bba,3da97378,501f9cf1,bc4b4a8a,67b0c5a4,a0d8caa3,98bce311,de930986,44d31401,510012aa,3b6cb541,97cd133,6e583853,a330319f,779a47a8) ,S(6553a2de,19c7552c,8db9d268,ddf3a034,4afe8ffa,a76bb304,ee77ef95,c18e66aa,91a72010,7c180bb7,2af4dbb7,752d374d,69f95bce,c9bbb7f5,37377060,70edb93c) ,S(f54b4be,353f4185,22e2e936,3400caa9,bba98023,e6a3d3ee,c1fc5046,b7b834e3,96be786c,bdd5f1f0,a835afde,219745ab,ab6f78b4,577d3a5,1246437c,8e96f17e) ,S(c2d317c2,a0fa6522,bbc806e,45b4dc8b,f86be37c,4b677c64,c0d5b4b4,eadbb2a,c5710969,bd68cabb,718cb16d,fc9994a7,100f078d,4a3aeaf5,8e8eb35e,d313ab6a) ,S(52a567c6,a5b8a64f,dc74b9c9,57f5d472,cc43e143,4136fcce,fe1ff313,1b89f384,332631bf,a314298a,dd45f7d6,b8192956,d7de27e9,7d835d48,5c16f7a2,9c9e8f53) ,S(f7dc086c,891a4412,88543527,831247bd,3530f0f1,99b4c5e9,8d24a207,1dba4e20,734ed712,452e59ae,b0ef5f75,10485860,da055003,ff1067e7,b82de345,b74444aa) ,S(954f9fa9,7bb6dbc0,cbed8d8c,de6f8f75,b3f2ae51,e512cd3e,90520d8b,22ec06c6,b65b43bb,8bd9660f,4bdb3017,bb4f8214,5426f614,8f04378b,f65c39db,185dd9bb) ,S(20e69b98,41416588,20b66947,f775cd96,6def2dbe,416b545e,8188db14,2604e87e,e6514659,bd12b9b,35ae45a3,d43f6023,dcce04d,87df1f51,caa67f89,28632539) ,S(5cde5b82,2dc42f04,44187fb5,33029577,71bed484,2ab39dc3,709e7c57,c72ed1c,a0f7bad8,64e405b5,94416e7,53fd6137,cea3dcbe,7625fe41,b4929299,a9a0ea9f) ,S(b586cb4c,6ba6b0dc,2aafd03f,49d4d6e8,45b20460,5de71c34,6e73b131,fb26421f,ced613e7,c26ea3b2,a31de623,506afb86,6767b469,98bb116d,2b4ac9ab,58948744) ,S(7d3f6170,35803a82,c8e13dbf,a8d601c5,4e192a54,377e4a8b,2a2a5de6,90ba6ede,138e810e,62f413c2,fb56477,80c0bcbd,77eaf84b,e78e900f,1969f4d5,2ec6cb15) ,S(e7a314be,fc4af863,e7fe6713,5304ab81,c9fa32dd,80fa9b41,d8577ec2,8f7eb925,cd978600,f0e04acf,fa99b6d0,7da970c1,13ec94ce,c50808fb,91a44f4,80f3eb1f) ,S(179c3be4,9f41902e,e21cd8e8,10f0dfc8,ba5fc0ad,9e454231,ec090263,d3c6a577,75f9f60e,fb9b9aa0,29eb03f5,a50b7e4e,64021689,a4e889dc,5b9ff0cb,4c9cf184) ,S(10a55871,464bc182,b957808e,25754fa5,8d76269,5cf8c6f,e50610b0,91e6401f,d36493b9,6d2bda2c,e305c679,f906ba9e,99a787f2,aa8cb8b3,29516a3,41b56ff4) ,S(4a903722,5e858c84,15508d45,b31ec7f6,585827a2,f3a9c99f,96af3e9a,e88e555e,da4d45a7,fb9e44d0,cc52463f,20fcde14,31c9a477,d02c464c,70c7d132,3247d145) ,S(6d109d8c,2505808f,7b4052d6,b170ec80,c68373bb,e02f2b62,1cd29773,a96acb3e,c8dea0de,511f6e40,5141088e,cb023bff,200c870b,9cb952ad,c5038b28,eadc9a57) ,S(9c219898,6d202467,c055c734,73557505,6105b3e,2874dbf2,8f7f0c39,66e1af88,8637496c,8eddff12,f9dd4146,36565e0f,efddf5cd,52d48455,ec9fb2d,8dd0914a) #endif #if WINDOW_G > 13 ,S(22ca5039,e660f60,1036dd75,2bb973b,dcd104b5,dcb8f2e7,4de8edc6,c292b03a,86fd4471,1ef6b81e,4416449a,708fa0c9,cb6731ba,c403e58e,da5e915f,646b11e8) ,S(cfc18f02,cc004640,f2116fdd,1f6ca202,2e39be25,df75e27c,80bde842,e6b6f938,d62b58df,4f79d0e5,97ba2923,f708cbe5,c09236a4,d9d01398,6451d684,6290df7d) ,S(3388bcc2,3425458e,991f46ca,6235c50a,57490556,becbaf25,9d3c14f9,9a80a087,7d4aa2f8,6f65783,1c22316,6958fbf3,6c3dca5,d4ac413b,3102e13e,a645c016) ,S(d26bd013,1b8c12de,3dd8fefc,136d9f95,44ac963d,4cbcbaa8,2ba941e,f0b46a19,66f89ea3,31b6795c,6b694872,4cab492a,d045a7d,a6780653,cb10ac25,b68d3a99) ,S(dcd3370c,db67e8f2,163960ed,fef5f66b,465a03d4,d447f5ca,1d99d29e,57d1fdb9,8b93747a,320abf87,2cf8d448,393bf732,8a9eb4bd,9b64ded9,922616a7,347084ef) ,S(74074d05,e602ad56,337105af,59c63819,21d449bb,3fe0806f,80589f3f,4f8d8e7a,1a4d4bd4,adee80ad,44fd515,a1dd5236,bf0dd8f6,c44782cf,e19b8414,b03d574d) ,S(a89cc81,f3a23ebb,6a8df438,a78092a9,97120394,d6bb4dd,732373a8,2f05c174,4b6f83dd,676df063,4e5ddc9f,db979dec,326a9ce7,5707fd77,873a9644,a3c4fda4) ,S(8f1a10ba,fa913f0e,1902ae36,b07f964a,6443c540,b60ace03,7dda380f,6616424c,1028d644,45c177c3,24416ad4,e740f31d,14e3a462,d5a0326e,86998555,5de5525f) ,S(ad8fda79,14f9a236,a7957268,ada499ad,9154a2f8,478fa6d6,f4c74048,89e27b51,9ca1d2ab,1f7da6c6,f76deffc,5c3c933,703b74f0,26063834,6174e4be,320e82ae) ,S(6c6e990a,797b2970,4408cc24,6f238e2f,2192700f,e4fb3c87,4d15e32c,fd67fbe7,1ffc1798,f355659,9fa5b32c,c040da31,39811b87,93d4d9e1,be83061a,3f91dac1) ,S(202b13ea,31ad2abd,9635351d,e09f237b,9f86f75c,a340a47c,edc1f9a3,25118969,c52fb505,a14e37f4,d5111184,ebc81873,868a4521,700004c0,fe3cc535,181bcba0) ,S(5355f0a1,25142fa,b0dc7c7c,f9855953,34053c6,12326f5f,d2284291,d7b748a5,75bbe36a,553501f6,c1c8ff9d,e60ee3ef,9cddd36a,781c518f,4b1ccf17,7e281949) ,S(b8852d78,eacbdec9,d1cf1664,4a83aec2,79a39ab1,34706235,f913aeac,c29829d7,763bab50,52b3c61f,ae42735d,2e89ec3b,8d51eed0,f729e0fa,eb431613,df183156) ,S(cab2e44b,294df78e,1c17d4d6,a09ecd0d,696d18e8,b0f188b,eecced5b,7057ae2,f351b09a,501a499a,ced49607,c55b506e,de28bfad,5b20ed5,4059a068,19ff2f43) ,S(1400b9c9,9c6d555a,2bd2355e,b54b756b,b16f9f36,b9b86658,9d46853c,57056b31,8b290816,62f41167,a0a6993b,3d4211df,5709b91f,96f24436,e569c32a,dfa077a8) ,S(52ae372e,973e9c1c,687ae7a9,a111446b,b3d31b19,5588d8a5,fbec6e6,bfd9141e,f982b40d,e6d0e42d,b9638721,a4590db4,1f87cfcc,d8ece56b,71ebfe0d,82351ccb) ,S(3d14ffbd,40824625,be241e14,850dc030,1139b708,b937f2e0,fe5f65db,61899c24,b10a64fa,477ee047,4d9cf16b,8d2213a2,799882ef,d3766872,981fc761,88a1dfb7) ,S(c6f52adf,54e0c197,a8bbc270,d4c987b,e7ab3fd1,a95fe46e,82415ecd,baa48930,7524c06f,b53873b4,9050281c,99fa44b,b9ef9193,2adeba8f,77e5afd9,3856811d) ,S(90089264,bdc47cb6,7a3c838a,4c79c1c0,5f2d1dd8,6d18f55,9fe60a3e,c944c1aa,18963846,d70b3226,6a9d582c,c430e4b6,ca140bcb,91de7064,eea0fb39,d2ee04de) ,S(e27c24ea,478b37c1,6275b2d4,ce8212a5,2db74166,96f3c6eb,c1bf7091,efda0662,27ec5279,c3a267cb,fad532bb,5031791b,bb99f4da,fc3b7b7d,8537cf09,12783de3) ,S(ca5daa12,9cf1d6eb,70025d85,7955d3bf,2549b8ee,6064092b,917eff84,c40a3eb2,682d4905,500f6f7d,33e7c7c2,7d420b4b,7c4aa5f2,77b89e9e,f6a84259,de7a9811) ,S(9069ec0f,2b2ac688,46623fb5,c89d1424,6c98ac5b,4250c170,4871699e,fc877f55,cc500ec4,eff83712,16c0617e,e2407dfe,a6c3c3a8,c8b80266,975d3a56,e71fb05e) ,S(5fe1feeb,bd5ee1b,6ba742d3,c5e8aba0,536393c,592650f,b8cb1391,c3bda16c,db11b327,1ac64ed,3425ba06,8072f76f,ea02ae6a,4375daf5,3bf942b7,9865a34b) ,S(a4a91a5,f168f883,49035b6c,f90e4e0a,6bf2602a,85e0ccb8,31866c4a,ac1b2c34,5bfeea8,fe36ed1d,18af2ff8,e2b898aa,ff7265a9,c08f4857,ce082030,7f837596) ,S(f4135f36,f0c35b52,4a870505,4eaabe4d,43f5366e,d3c7d9e3,5f06f746,fa884849,1c6707f1,b8b6c078,b4d9d0ea,43075d75,ba1a5d30,c3a9c52d,d55fc4b2,650c526b) ,S(d5a8998a,9363fbae,d2b44992,883e84b8,14a504d,92b41e0f,dcc3a9f3,94380203,96016b03,6fddc805,8bb8ae7c,6d46cd7f,2f20c5af,a62abd4b,bf9b3da,ea60e9fb) ,S(8804ca34,4b30dbd,a07fb62,210c1938,d50297e7,9910dfa8,cc38b9be,4bf3d176,5b64bee5,79927c63,7788c55f,f3871631,eb65db50,b11cac91,24caede7,57d37b0d) ,S(8691c1fc,440c21b6,bc48e78e,78bda5a5,c947c74,7d098e74,ac5dbf6,2b811021,fd8ec1c5,35f51181,556c330a,f02a7110,682f4539,f66c1c09,3d48bca,d7b1787e) ,S(445fc1f6,343be2e1,fdebfe3f,894e9293,c3ee5fab,b0ed01eb,58a40637,ef093229,857f17fe,6737f853,d04aa1b7,3eded13b,c3c087f3,48da90af,32907bdb,7d85b605) ,S(5c397fde,a657d1b0,b2e3aaf9,5b88c4d6,af1a5555,a1dcf966,7d1c5001,a76493b4,9ce74820,7b6f3c75,2d736aee,6a9fc54f,ce5cb52c,f487fd32,de79a06f,df0aff0a) ,S(9b5565cb,28d7e028,361d2bc5,bdfe1912,d9f53584,372d30c1,d7e36fa4,c7fc1b7e,7d5cfa8d,2de2a832,58a57f05,4e3f6c6d,a23af075,d98b062d,82799b11,63879eea) ,S(afbdec63,1bbf870d,3971b165,71bb195a,a5229a9f,1012bb4b,89654da3,c9194f1d,cfcba749,b9492525,f9874ad1,bbb0a267,83fe5714,1f54316a,773c2453,8f27e296) ,S(7712abcb,ca3a5347,5cbc6160,5e9e9ec7,a7cc11c6,2c4b3f4d,e01d688,acad916b,7b91c9bc,eb12555,ad2b43af,8c3bd332,b57cbbfd,1ffefead,c68f0a2,6a4b82fb) ,S(3c452346,f2935e41,2e5fe506,fdf5066b,11b43a11,66e75c9f,7a2d38b,1ca2b7e2,fd3f6de1,27f96829,3af532f8,d4811fd9,e02038a,352b6696,2c608c7f,f59cd800) ,S(bd8582f,b4dbda3f,c7da53d6,70c994b8,e04eda44,ddf0b054,7d182db0,aa48b7be,799e2769,c18268bb,8c16b282,ee7d0828,ef0dc4b7,9767033a,d6de8c63,45285c68) ,S(c41010a7,8dd9dd40,62bfb71c,1691338f,befe03ea,d99eb719,74dce6cf,b2c84112,5008c39d,e71ebc22,3b1c5dbc,f824a63c,f270f807,3143e08d,29b162da,42a2ff83) ,S(e89e807e,6cf4ba27,6586a6,a509bc8f,f786bc5d,dedb5f4a,1b6253cc,2521d311,aadecb79,7c4948de,9379fcfc,4c040029,2228f9c1,c099117a,ad6d9949,f2fea2cc) ,S(363df1b3,be2dbf90,64137919,51218c34,84091f73,866f3fdb,dca1b90f,dcb08577,aefd04e,5634e36c,49621493,f7e76f20,f9ea5b64,6309a605,7e3bdf0f,75848bae) ,S(5c8d1638,83d2824e,48121322,85cc44bb,ca8fe33a,34d5c3be,cd4a3c8b,c78ea16e,f66f91d9,c7ce66c0,89500591,49f7525a,355347df,8f31a685,872aebae,1ac0456f) ,S(10ac6676,83583ed,d837789e,ed9254da,4181dd58,be75dff4,8085e87,eacbe126,6d3eaade,23f3e7bb,7465acb,c6b25af,72e0dba0,1815ea1a,1f57ebe,bb17d22d) ,S(1e79a1ea,7bb65540,44567796,2208ea3e,974c4c0f,9b61f7da,8dba697a,8c153048,b63e3d79,20a34888,68987406,4a8008eb,e07d35be,33a055dd,394ef2a5,f0787fc4) ,S(db0d1c73,97b0a23f,508df2ab,b00ff13e,11699118,11d6476a,7bebcd09,53fa9a5b,1c9d0877,3ca74f1e,d1972431,2b5c8eef,2f85fd41,6629cdc9,d0b9e328,4900dfe8) ,S(e1fdd7b3,481ece8d,266bdc22,92e775bf,96904223,e620f622,3a03ed,cb385f27,3cfab39f,28953ff7,d6dee65,83fdc6a7,d9b31f93,e2103e6d,9e4066a,970a4c77) ,S(96797134,2b69bb8f,3d6701c9,22130c8f,9ed85fe5,bf189880,3b2df11a,a223ffd3,2d43343f,630b6f9f,7c4b6d93,cd29a3e6,632c0dc6,c095794e,5997e47,e631d31) ,S(dfb40218,6e27d494,c69d2a0f,399dd480,ec0a776d,9a99fba8,cba81417,d9c33efc,332d91dc,e9f93273,15e45bcb,79603050,9bd8501c,17820f48,61f7b12b,5d37796e) ,S(6b65c5eb,ed13dca4,51608da7,b5c1a331,171de004,7fbe35e5,189b8468,c27681ec,afd0ee8,e0aebc0b,2f246b51,f6fd4f85,3e71fc4d,f5bb9f43,e2679c8e,89a34f62) ,S(bc1c3da1,60b03965,e26396aa,5d426df3,21e5c22,fdfcd004,80a390f5,28c4b619,fd657174,65e4fea9,ad7862c,422c11b,86ad94cd,35acbbc8,76ed464,aca31640) ,S(589b1d17,96d6ca35,53f8a6a8,cbc587e1,9026406,c2c6f8e2,de613dfa,8c05913a,e655d5ec,ac254f46,e279365d,e3bba2a4,3c7b6469,da45ec87,9742cbae,503fb3e0) ,S(9e726385,6d1e6c2a,94dc2ef5,c92d94bd,6ada63cf,cea75677,6125bf98,78ae4ed5,8c238df5,1e5b38f8,b628a48e,dc7aa2b,a83bc40,43c91896,69f5341,60e304dd) ,S(12269d78,14e0f74f,ba40c551,b2080e00,4f9bd3af,255218d5,7eab5dbd,c6764263,f0f70bd,6584975c,106febcd,bbd16920,daee58c7,c22dda70,4a95f864,e385b3d6) ,S(d3212f2f,cc509014,e0c48cdd,6273effc,5c73fdbf,1676faa3,15e9173b,573088a6,39af39f1,673f51f,362618c8,49c6934c,ff59b6ea,853fafc0,9db64084,4832df82) ,S(c535f72b,9bcc0bad,44014e72,4f649623,4ef288fd,9f42adcc,dae45a20,84250052,3f79985b,6fb7631b,62814a17,f7ce829a,88447302,293000a7,4655c7ee,4a271022) ,S(4f5b7126,9b169fa5,8602bb18,60ed0df7,271e3912,ec0d7c12,1c80fad3,93399605,b60fc104,7f2a58ea,9102c6cd,b97c932a,576f63f2,6204fb5,dbe41363,cdcfd0a7) ,S(cb459b3b,244c38b1,af2c2863,e0029c14,ec70e7d,737a7851,de9c8f1b,b7d5d065,7b67b15d,3c0376c8,2f646241,1e890b3a,a888bd15,692c90ea,53a74a4f,1957fbd0) ,S(787d61c7,ebde0c5,18f121bb,7f434196,d389f563,d1a46597,ea72a1fa,4e19054e,5baf56f2,5fcf8cb8,c271cf39,6b3d150b,f42e9ebb,d72b54ba,4b93bcbe,ae72a658) ,S(c38afc2a,31d0b0c9,4b77d97c,bd639082,3373538a,602352ba,cc93b6eb,c5f6115c,b925dfca,b138fcc2,4b9a26a4,c645f8d5,875e098b,d2e58469,d842688,43ee529f) ,S(37661e3b,8e606e95,b9dc6ad5,e5b9b25f,39a5dd0b,8ab7a82a,d6ec879a,ff406d0a,ab735e5d,430d8fce,1317e07b,d6cf9441,60d8bc39,132382a4,df1b1638,a7e9b977) ,S(e5127851,b8c22b47,c3d8e934,8dc0c677,88ea5ad9,f64e6062,abd68a16,51e256ba,5847f77e,349eb7,90b4b7dc,5537ffa,5b1e7d4d,b87044b3,f947f387,270405c6) ,S(f3c7f45d,a6b8a8a1,3713e7cb,7380fe06,127a3698,520bb41,955647b9,ad7382e9,2acf9a11,eb1b9d31,f71decd0,90093677,4b469301,719d4a51,ddfe5fbd,f63e7c87) ,S(86de4047,e8d5b252,523733a1,848a990a,79125f95,3bb0e4de,ff4b2f0,84d745ba,71e6a472,dac005d,2b284cf7,d5de92d3,56921105,1a9ee007,4279a746,71bc969a) ,S(c6115c30,72259d66,d960cd96,3f3aa16a,3029d9ca,c0c5ec63,5e2875c2,f3f57504,18d690d0,b33fdd78,d797f56c,23c821a1,ced02401,3443c770,50d12850,9f7a712f) ,S(cb545099,8b43473b,91838cbd,76929b05,8bfae0f1,e2bfbc6a,c61d3674,42f53c5b,4119d74d,79e34f08,cd7684b4,f9b9df55,c00ba8ba,7bfb4ddf,de38db78,91572bbf) ,S(d0dce704,b9362bb4,fb1771e2,660a98a2,a333b73,c6d09372,5a752f28,52922d2a,f92c3b70,7947ce0d,f1f3891a,259cc2ee,124d3f54,a4c518ff,de5a3915,96e37e47) ,S(db93e238,e5aa5986,38eab857,655cc53,d4270259,e7d73a96,249a19bf,216b20a4,8d19dc8b,670e8eb6,50b4f60c,d26ef657,3ab17895,c62fc94c,815d7eb5,fbbcc7c5) ,S(c387c37f,d8cebef8,29e07e54,b0796129,4d6c6cfc,bbf11835,ba85d4ef,68c3f486,852580d9,ae7eb300,6ca0f7d7,f12d7fe7,c8e3ae0d,b6258897,994fe78e,11ddeda9) ,S(ebb58d34,f04de551,37c01b5b,192bb4b6,4d3b22dd,23ad9092,f943749c,7606c232,1b979d05,9c99f9d4,db1d3e82,905abc9b,d92ae72c,509c912b,c59488fc,ddd1ae16) ,S(7891cc66,acfda29b,765810b1,730cad13,2f13178a,fbf238d8,2525ce42,96e38e6b,22193729,20188c6c,462987ad,7ecaec3,a21ff6e7,db00adb9,72facf65,367caaf1) ,S(c0b02542,e4bc1e8d,2c2578a5,3793fd8c,acec800,c0a311f4,72c50de3,5814d081,24bdc71,f5917c0,1ae6bb5,71c09197,76b1a884,ebffd673,13698bc1,b57f8371) ,S(ea15d574,b8704507,f12fd9a3,e40ea603,c2000cf4,4eb3d4b2,f07a36b5,c426d2dd,b6596d4f,4d8ca39f,4e0faf58,ab7e3894,c5cdc16c,589a524b,6ca25a51,8a30944e) ,S(77d387df,c35a6af7,b88d5726,a249d34e,70877698,1358c672,6e51b779,cf9604de,e5daeecd,2d70a962,d2d3c235,14fa2b1d,45916506,de017249,93fcd9a4,f08b4a87) ,S(a92742cb,7d1a24fb,c1a4dc2f,9d6fefbb,1064f9d4,c3152db8,3296a9dc,9dccd7ec,665a9cf9,8cdaf0a4,ec346df6,823f3c6,66d4f163,b3e7225a,d9d18e42,31679f76) ,S(253e54f7,9f0c393d,5d34053d,37b55304,f62de9da,29e0eb6f,36cb105f,a6316a46,54e168cd,ed78ec0c,32a9417a,c5b27ef0,67c8577f,8fe0bfd7,b2ae33eb,ce7155e0) ,S(d13048e0,e9c38720,6179586f,9e38029a,55fc01c7,b33d8443,4ee45cc0,3fbf2,7c4466db,94502477,85490689,7b251c39,af257840,b9bc61e3,64075080,84743f37) ,S(e9234110,387c2122,2887d079,7bdbc9aa,a632b237,2a5632c8,8e604653,70a284a2,2b98b08c,4ca3521b,4ffb3afe,66f98ed9,839a2651,f740f63a,e80b0cfb,6f6523c4) 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,S(ee0cf184,72c453b0,c38c064,fc0d2589,d5f1afc3,3423687d,91740bdc,c3929230,d817775a,7fecd397,e954db12,fca24990,8c773c28,b36e991f,79c78264,9fff8dc8) ,S(f335f7fe,9542a587,9d48b4f,4ab1287f,ef007289,4d93bc21,23463a77,7d535d7b,336e49a3,2465d29,35389c06,d8eafb4d,7639dae9,a6b19bf7,45518502,e3350283) ,S(55bf8179,4fb37f8d,dcc200d7,b76a9040,b1326d6c,559d7f06,f0eb0e0f,c97e7739,ca33cf00,79155cc1,e902ade6,f7d703ed,3053f6a4,f49d0866,32e930a2,afe69bfc) ,S(dffccf81,6143da46,5ee2195f,abb6d943,1033b901,2fe0c623,49b7d6f6,29de29b0,9bfdf3f6,e1dc4ae7,dc29fc06,f85e1588,c04bc39d,5fded90b,bfe75b9c,74f0aff7) ,S(b9748c94,25fc6fa2,fe5c1395,b556bb12,c435bc11,2e8f577f,3c5e7d82,3539dec3,f5238bb2,b995d23b,5e96b233,6d5141ec,f76d31bc,63aa96e3,dfaca8a8,c94007a2) ,S(92c43c54,e951b157,38f29e33,5f52ad9a,2c5349e5,fa6a39a3,fb615878,ae97f7ca,7c7a6b73,dedd1bca,308924fc,6364b62a,bdc4ae79,d68a62bf,71bb0195,612b4a17) 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,S(97641f5a,a51e7ff0,f1d86183,a3fb3d60,4266c4d9,acdb9f9a,c704a05,809a8602,134ffa32,aa9fbdbe,d8d82fc9,1cfa78f,1ab169fd,459da39b,5b0d3287,ad9517dd) ,S(96a3711e,acdaf6dc,5adaa8fb,4be05c37,f59febca,1a876a5e,e23c6b55,2727292e,8fb0cfb9,681ebb7b,5e1fce0e,67ad5d81,34be9123,56100e96,b82ecd3f,a5da4392) ,S(ae64428b,8e540c6d,28d38892,6136320a,9f9f16b0,3e9d5e2a,14faadef,4f154b0a,db202e5e,b9bf73cd,b9ed5193,b0ff59e7,cc68aded,6fe6c2e4,d5b79493,fc118aeb) ,S(2c5932df,65c0c2c1,14b532cf,15b48433,e16424ff,ba87438d,42229075,6cc984fb,161ef8c4,b908a056,d395deec,38b9ff4d,1c643628,2ceb1e47,f59a2c24,c7d29130) ,S(76e21c78,6937ba69,18252d56,3ebfcbfe,2415389d,bc692071,f9c48f55,7aecca3e,de7786fe,9db47d61,e3b61d0d,49309fe9,ca634d28,8d71aa77,a3fa4efd,4533c8e6) ,S(7170dcef,ca8a138d,1d20b346,6afc6a46,99df363,fc964a36,eaa70805,b267900f,196bfd39,476f1455,98f89f7b,f870f8f8,440562e4,623fb203,3b36d5d,d8c0bb8d) ,S(98eddeb0,75bdd245,aa1fb466,ed1e89f7,61a95662,e35836f2,e6907c5b,691b6ccd,af3fb5f6,b59124b8,c9c2ddc2,108a3a2c,bdbcdc99,ab296814,731a841f,570c91be) ,S(bf42f806,59ae606f,a5e36fc5,c58379c1,8dd1c34e,fa98e67,68bf6da8,ba8e8849,d343fb70,6e4adb94,46f49578,26bae8c4,ca74a0d1,21cee98f,26be68f8,7555b8af) ,S(40c1c4a5,891e8dc6,29075c36,56249fc2,c42fd65c,8c338a0,d82df955,4662e1cd,667223d0,e68ef6c3,7195d819,2bcc12b3,f2025327,3a05703a,e5aa10e9,cc689ec3) ,S(162dd310,c8e3fe4,8384cf1b,1a0a2d6f,bfd3ef3c,5492fc92,b921133e,8f883dc1,1f2311d5,c82f02b9,f7197685,cf490e1c,3d0ebf4e,86ea0e21,a653c8e0,db5cff0) ,S(ff0f8146,89eaae3c,f3f302e5,1089ec58,5d63c4fd,5157bb3d,bdfc7e40,cc6331cb,4dc1fdb9,4eb529e3,bae54973,778d1daa,f8814cdf,5a3b0c2d,ac2b5647,551bf2e) ,S(143ae674,b011b557,2f472b22,44c6d9ab,14b3e641,54f4a033,c3ea3917,4607b78e,1528d582,faefba2,6018820c,a03dfd7,ca20298a,e199c99f,db9cb421,3601c35c) ,S(f3adce28,8fffd45f,96fa0efd,32974d98,4115a80e,cd6b86f3,5e17b017,8d9009a3,20202f00,96329bb0,69a0915e,494a586b,805580a4,eabd4ba7,2d20665b,4916a20e) ,S(d2270829,e2730d0e,2c8e6bc6,fa4c2247,4904ad22,f44fb2f8,5ad07558,c4d8cccf,d5a6b4ac,9d5bf669,5989741d,f262e412,27c66c7a,ae067a93,c6302f5e,8879a3bc) ,S(26d17eb6,7d9bf2a8,45c57a94,82bb2f3d,8347538a,65c9f567,56ecadf4,352964a6,954af3d4,7d67c345,bcfc4a52,a49aa70,b8703d1a,fcd21c6b,7f7719c1,e2068fb2) ,S(e4437f8b,e104c899,5cd1618c,e5ee7d10,36a52d99,31346476,bf68f21,e7fac74b,d6c156d5,b8256e6c,1a820dbe,3b56fc8c,f9b015bd,b81c756e,27b70db8,d995cb81) ,S(8932e04e,96db6079,662b63ed,29b5a39d,ac5bb51c,d1ec70,851474ef,a2d3c1d4,5437e77f,e030225d,53f5166,8c3551c9,fc912a0d,a3bd336e,c0587544,77e58541) ,S(fe776976,465b86c0,5b2003c7,36c8141c,933ed0e4,5c6dfd0,c7c82517,16617b26,b279dc5f,d576d506,d302b0af,359ddd50,94364d3e,255102aa,472e6d9c,c52aac39) ,S(6c60a4ff,b2a29224,5c84ecbe,1633817d,f69eb73c,a6b9f72c,b86fc91c,535b45f1,278dee6f,814bcc1c,70301a51,f9c7853,6489af2b,d23d6223,1b55cd29,2a2a0a2c) ,S(3132e58f,625f902a,98d556c5,ec9e8617,a955beb4,6e9c2a81,e121e473,9c9af04d,a5880964,a2443c5e,14db9220,446904c5,cf0a957c,945c5006,9438d869,45a9e461) ,S(b05cee36,361a9bf6,eb9003fd,c8d38587,640e180a,9de822dc,57e5012e,34903f6f,fb473886,29519a28,b745ce16,d625d85d,26fe21a2,30d798c5,305d8e82,545c9a5a) ,S(e202120f,5659e580,7a14e68d,e3aad7cc,23cd2f6c,abd86739,3a05f16,12005e83,49928b05,b66af992,d937cb4d,c05fbaf2,a70e8fac,7c081544,849d55e,fada136) ,S(57a91d89,2e5409e0,b07e68f0,450614cb,9a9bf0cd,8c5b3459,2f198633,c7a796b,47905cce,59018fa8,baa612c3,124b1192,1dbf7706,c5d8d16b,bd5c1e9f,8498e7fc) ,S(e092c40a,3ba465c2,d59e7c5,8265ddde,91c0468d,67428ee1,dd153b64,a5a7e8da,83f4e2b4,bdfc4248,2d4ab1d3,13b097f7,baa51411,134eb042,feb26f71,5bffd39b) ,S(73a3306e,7baa4fc4,a081a9c2,c335d3df,7c1ee84f,f5a46554,f78a6009,1de0ab38,1f68c8f9,2022c326,e37a7043,9552191a,3d93f684,3af0a235,bce893d,eda1f938) ,S(7c7a79f8,6e904961,73552caf,4a1401db,e99883c5,a39e493a,6a6eabbe,5f3a4434,85ceb252,e4883931,96c8ce8a,c0b596cc,a2670981,2c293554,15e17f8e,26e869bb) ,S(6a9df561,ce4ff772,b37054fa,e513657f,19f03086,eda93918,623a1c47,84a37788,bcf0274a,d9b3bf58,331ba398,a6611fed,fe719867,106eadb4,2b25b623,fdb65280) ,S(fe7bb24d,47b3adff,1c545d2d,ad2c6aff,81934cb5,bf2299ee,f3f8c53b,ff91c950,7fe65f86,9d2623c,930c27d6,f0a292cf,a881738b,4af0c5b,efde5c40,8a574e7f) ,S(26d1d2f2,7944b77c,290ba60e,17d05347,82ce2b64,ae815453,1da42907,30407d3d,ec3c5024,3106000b,d0b2372,53581384,51b768d1,d5aa206f,4d1055b4,b4f0f495) ,S(f00e51f9,38f91573,4ac563ff,8ea44de3,fb85cf4d,8f034806,e6c096d,8e73e2b8,7b7bffed,3a39a491,d3ab6a13,6fd88e0a,5854081d,21380c70,3c596771,a22c727b) ,S(73e15472,f42f8750,93abe811,a4d4bca8,8bd179d1,4e3e3b30,9e011e27,37cfc4d8,392ef4ae,58321768,1106426c,9b00b4a9,c53c826b,84bcda34,b5d0609,f85b9231) ,S(ed4667a9,aff30464,c851d86e,479df8e4,d29d2348,edaf8333,a7faf560,a9568092,77367875,6892d42d,469a9ab5,ff577e0,6d9f4fda,679882e4,3dadc7e6,3d49bb0c) ,S(d6ec16ab,10811cbd,dcc346a2,64dbfe0f,51066f2c,79034d74,af5b0ef2,541dde26,981f1cab,7ac7be22,9a91b733,6c0b89bf,4763b01e,4a1b715e,f4857e9e,4ad0527e) ,S(284ef47e,691931ac,8241d92d,2ee5b717,3f762ef2,bd1f48e6,8dca4b53,ab4c593f,ab739ee1,e6a7be47,83e1288,7ffe1b6b,b53a4d2e,3bfad3e1,c7ac5415,1bcf5e82) ,S(530f9e7,5a267d0a,fc3ba53a,c49018ef,44b490bc,835774f6,c6cc3f87,8d505c3,630c481e,44e5e9cb,cf6d7fba,8f7fded4,bee9fa70,4b88a8d3,6e2b3bc3,4e85e3f1) ,S(66a9b4fd,81d0165b,6737a4b3,8025d2da,ef9c4d20,3c49a2bc,1ba4d59c,eaa905f8,2770c44e,6a4dead9,7dd7311c,195d3051,12c86bca,257955f1,21b7b1cd,4e525e8c) 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,S(c9a6857f,db037c2e,36d5ca71,32942f34,2480cf28,a98644f5,6bc455ba,97cffc55,a69e08b9,8f678e61,6c0b8326,ced6f97d,f742d974,b68cd1c6,b798e367,8faa149f) ,S(b5d13f5,c611eb3b,c82f7db2,d89ab19f,b8fc286d,8e4699d5,3dc664d,bac4011d,27eb1650,7cdc0fdf,5b92493f,f2487d0a,ef2692d8,9c702bb6,259808b1,324b7adc) ,S(bf9ec5f3,2e0ed4ac,c001b887,18c29c6e,90218471,d7f1afad,75abb34e,da35ce44,13846488,892b4065,b79224ed,368c47a4,a1734f68,7386546b,dd837a80,467ef2d1) ,S(2c3812be,4d3b1c13,aed1f6bd,1ca6f5b8,893c5a87,ad6a8f2e,d6d92ac1,3a526e19,366b82f1,45d551e0,b7bcf877,db340bcb,1b11edad,1466baf3,24a94cef,3433aece) ,S(77bdef28,dc8ef6c8,7fcd0a13,c08a26e5,9fd17253,8d8bd3a6,f21c5c86,ca33f572,da66b0c7,bf3bd49b,ec1fec,aa580a51,6977ba8a,83f957ef,8167f69,ea3c3a1b) ,S(bc4a799d,3185877b,cd86503e,3f34c606,8693bac0,654eeb15,4effd116,8b71afe5,53fcd7f8,99a8190e,a7159c99,e261525b,f59abf6b,d331be66,4f7f7757,7255569e) ,S(301fd884,733dce05,6190e4c7,d0375078,6fccdb6f,2e13f9dc,e275c188,2efcd040,79e4f9d5,185b9f51,fd835cef,64be607c,312c910c,e25cb73,5de2c88a,51e25cb6) ,S(241b4a9b,be5e7e54,214d0bda,13719c42,133f8377,e50db2f3,87b6018a,814adb70,c66edc08,fa4fd22e,1f76bca2,7fcc00cb,a8ce2100,248b3959,3c164847,b410bdb0) ,S(be6f1639,68191289,3c5c1351,d633d51d,dcd28c16,f3294981,56ea1602,d8c79585,6f674a7e,1a65539e,a7f8a966,8f5fe5e6,1ade5da0,a543335a,5f7a71e5,fbafff21) ,S(c8b5008f,79c69e2a,7e209ef6,a2d14b9,b3f7bfba,b7fcb285,e237cb31,3dd3a283,1dc79348,6c3cf7e0,bc36dd7,46efcb36,3cea15ca,a63008f5,2d83ec0a,6bb54bb9) ,S(5014af9e,aad5ed62,4e997ec3,a796ad1e,b038edac,77cf27d4,eeda7ff4,c06c0998,e01d786f,b8faa1c5,2d44a77a,987b4b6d,91143953,34977151,1a488602,3189dd7d) ,S(6ffefde6,2c40643e,da2d4f28,4f28fcdd,b0845ec0,8d882d2b,45dadd8c,a7bb989a,8e2b183c,782d3a9e,2229e4bd,9a2becbd,ff0a5480,6a6f4471,7fb6fe5c,8411cc0e) 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,S(17c19f13,96988f62,77cb72ea,f90d37bb,86bc7a0b,e16c1c17,fcc481ff,bb78a480,cb1290d5,210164eb,621c2642,ae3e51b9,3f430e60,718f9fd9,c5ec3bb6,53c78833) ,S(7b0f06,e8746ec9,c6648b2b,bb861548,bfeee507,63c01c3f,40319beb,a2497a3c,c6949378,84297d8e,308b318f,1caa0c7b,1634b758,9d6e8c6a,2fdb778e,d6a70020) ,S(715c2b06,2414183f,9a67d8c2,8a89b754,55a80517,cb1b8134,5f56e91,12c5e8b3,f89b89c8,9a795dc7,1e2d4cca,7f84b4d5,23167f03,97787b33,9205773f,2520370b) ,S(e0d0ce00,f974fc78,76777662,efe5dbf5,57aed09,dd89a4c7,8f1f40dc,8f74d3b6,acc5be65,ed704847,94bc7f05,c4c5511f,c253befe,7cb3c0d3,e85704e2,e3e3eb56) ,S(37553289,76fbb8b7,9a5aaf75,ecd9d2a1,bdba9a87,5bad6222,e770ab1f,d26432a2,6dbbe233,1b7e064b,d80bc7d0,12b2a088,1087e7c,2c5c1d77,eb016108,c2ced92d) ,S(2e95c3ef,51ea9036,8683f6b0,8b2afb04,f46ca651,2abdc699,446ab3a0,6fe3d3ff,905ea87,b1d8dfe0,48463b94,c61dbc62,1556c66,b2b498,39cb40c3,299b554a) ,S(25310e1e,721f3245,7f35c67f,b73553f6,6467580d,b5916cf4,fe7d75a,c4ff8eb5,9c5e52f9,be42eeb5,425a359b,87dcab1d,46ecd662,c17eb041,16b5430,786b4ace) ,S(25932b1b,2b24fc2d,d7877911,7d7cb506,27a23b7d,7faf53b0,cf707f51,b7830b7b,7e8e23b4,acdb26b0,1d7969a6,ddf3a2ae,2215e206,109cf3e,4e32d91,df536765) ,S(7d232af6,251f7667,ba69ba44,397f5b8a,892e135e,b09b684e,22b16a44,73c5ed3e,a3e8f638,c8a589b5,8cfdea61,d9824f1c,131b9045,9509b92c,1cd26571,a6d8356e) ,S(4d56caa0,1b65ea87,ba3e05b0,a4495606,6afc8645,4847633,cb9e9755,c8c720f9,14c34678,36e65197,ca3f1ada,936f0348,7c1eaee1,977ae08f,50f41771,77537330) ,S(71abd165,ca6ff8bb,775c81f4,2c722ed7,2615b503,3727dc2c,122efbd9,c500a88b,79ba2467,7284f86,2fb1c46a,e11ac4b9,a5969352,64224eb9,c39ab884,492620f1) ,S(8462fccc,c3810519,cc449634,5c5d9e56,30215e74,c41179f4,2002e906,56a48965,535a966,cd7fb998,bc548a7e,29fc4640,f0eb75a7,5c3c05cb,64d09048,a7787d4b) ,S(f68eac93,fed751d0,b578b5c,665684a8,b9c2b104,6fe45ae3,286e9351,36c09826,98e0c32b,98b0a8a2,8f119ff2,fa50e54b,66f7d8d5,732a1831,7334fc45,fd48bff5) ,S(61447250,9a8d935,9c0e4014,f6ff569a,43467dc7,e4940b16,15f442b2,d9f72041,fb7177f,c7f57ee7,deea7108,dfbea888,fa58f209,2aeb2d2e,b2f33141,7ac8f807) ,S(ea69ee11,4ffa1bd2,e2259a26,e2d88cf1,c9846ac9,379a1497,fc28ecc5,4b15614f,589b81b5,1dd6d750,91014108,3dd6cf3d,63183d1b,809b62c9,b17b768c,5ce4e2de) ,S(34727b24,3404de96,641a1ce0,d7ff150b,38e6aa15,c51fab78,1464c660,4e5d5263,9198326b,cf56ca77,35b9baad,dc0069d3,1920bff2,d5bbf804,435289d4,d827d4f2) ,S(952452ae,613778dc,29e2d275,6e98b4f0,eeebf4d9,526cead9,52f8d0d9,9e217461,c08b3a28,c195fb5a,f9a50eb1,1b1411b,c17f6582,dc14b5ff,797175b,2ad486a8) ,S(fbca3f18,dc4a8bc7,7e9afeba,66610306,401b8342,bde2dbfd,2d4a156a,e78e49ff,2b829d6d,6027b2de,eda0db7b,c76b924f,4cf75573,bb9329b6,c7b7e443,f94129c9) 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,S(c35c9cd0,4afb20b4,3fd1c337,5a952ad4,8e9a806c,a64aa4b7,52fcb204,5f89d26c,b041c6aa,4a83efcb,dee79d84,19e195b2,48c765c3,f069d5a4,b7e87792,79a9c65a) ,S(9a85aa58,753868b3,f04b2af4,479141d7,11703dde,e5b6e5e8,fea8ad37,d0b82b96,465c70ab,aa16f03b,d24b8075,233ec626,4e062041,3bf485f2,551d9952,7bd75d27) ,S(3ec71bcc,e051f3e5,12d83c14,cbd23f49,b3e825a3,cfa4c61b,d12eb057,5c86fe14,f198c21d,e2daa56a,55294c5a,b033f1aa,45caba3a,9a950007,db35f05e,e9915bdc) ,S(ee1cbe22,939e1ede,9010e23,535bf33f,6b09e579,3737db45,aea48f00,b359ae63,bf604026,d4444df6,27f7d297,1dab6a91,acecb6d9,de53228d,47178017,921b90a5) ,S(ebcbf3e1,71de3a62,ef47677d,1ff4d027,5a8cd92b,bc889ee7,8dcf0c99,6746073e,878d63c7,bc9c7224,914a3f3,2dadeb9,95c6d890,a3823f98,5c3f574,9ef6ebe8) ,S(e4e92ee4,ce72ef15,b87c57d5,259520d9,b6066430,c090dae5,6e81b2fd,ab9db797,3faac465,4a03a753,559f47db,f5877452,6d21838c,9c1f8217,ebef6965,655f944c) ,S(fc1ce758,8e292b03,7b4ef743,12eb1f67,cf275fc6,7c1e3d63,5bc42dd0,deac1cc1,176b79bf,44f7d9af,7f7c791e,8cafcb7a,495bc392,c23899b4,2fe7963d,e65186d7) ,S(f1f5bfff,179e6a6c,692a86b2,1c95ef85,49482b3a,b97a491f,9e9c7056,ba94fc56,389257a8,a2cd3bc3,fb4f0620,5c2aae70,67041512,10c62093,13a2584f,8a39e143) ,S(980e7414,61c3e001,ba6bfef8,d175a141,2c7aaa2e,748c3323,ac744fd6,ab793eb9,6e37ddae,29e05e83,b3cdde28,d4286005,34cbb33a,636c4259,c7fa7625,1b31826c) ,S(f519cff7,686a5257,71986dc,7e6c1955,adb7faa6,a6f7a07f,66a257ed,a1b1c179,3e803eb0,8c765c98,7941d008,a93b8503,174ed4ed,1c31e97f,9eeb8f2,a55a807) ,S(2dd8d9ea,3851fea9,1ba9bafd,bcc5cc0,9011d939,10edceee,144e2755,ba8f8061,6147f1af,d4224689,37cd058b,4ef52618,7adfdea9,ce970dc1,365fe04d,1da52ae3) ,S(860c4262,9483537,47ac0c41,5aa00f63,2854f88c,d7d09b35,edefd780,1454a4ae,a2a7a22a,7d826d25,8e7dfc56,1eef0d85,d15378a2,80535cef,95ce6e2e,d73392f4) ,S(e76b20ec,17d82c3d,987d4ea,20535209,e0697f90,2c964b28,ae97ad0b,aed732a6,c97844b6,85f6613b,fdb7cec9,cc47f701,32bc1137,d997f8f4,ad182492,67f54bf0) ,S(26731d0d,12fba582,636862b1,62a417b7,718ec9cd,e3d047a6,50455efd,910ab88,3c10efb3,b464a61,6e2023b,b0736d6e,8d298609,47ba5714,3b1a71fc,9b542192) ,S(50cb4878,52db811a,87fe46f5,ed014db0,3fc4570e,8b2d8ea8,9865df9d,a224dcde,bb8488a8,7937ae89,88f572a0,c100e450,c69db48d,303d06f9,5d54bd83,8b39621d) ,S(fb69453b,1d67ffdb,670f9fb9,2b3fae5f,64b0c4d,cb28ba0e,7ebeeb21,ffb02a60,b0fdef36,92d881b6,3ebb1387,984120f8,d1ba17af,477364ca,41e303ee,a4fd2c39) ,S(a8f1280b,4b720226,19faec4f,ea3f784d,3f4061a,56dbbb99,38c7706d,8bb249b4,ebb3b571,ac505913,4572e501,4be7be33,a97e12b9,bc1fd9d4,484703f4,6e39b8cc) ,S(4292ce09,df305790,f17cb3be,30996016,420f83c1,bc19abb8,78b49027,6eacaa98,1b14d94c,bf2b1d1d,82cf1873,3461b76c,f32c8d5b,6746e2f9,aa2aa248,1c745d36) ,S(ac241177,f16f747f,b796750,49c83f8f,8e1a062c,9796b05b,8c5a5587,a4c9464f,dd057503,8261d044,ec84eb03,73065687,266b695c,ef5cb41d,1cba3b5d,9176cf58) ,S(692eca73,26bf2da5,7fd9d640,acf7f846,78e75c9b,86b18e7d,d7fd2545,751823d3,17d6d462,548ea78a,18557320,289d61da,14c3850,4ff03347,8f17fdd3,71c8e97f) ,S(d01b1a44,55ef5011,e4ecf946,ec02e6f5,d0e129d4,d2f59889,e823cc5b,6f10e216,84a4d89e,55e33edd,d54f38f2,1649f5fd,807879e3,388df988,34556ae6,57f91a0f) ,S(1eba61f2,96a788d8,9273a67,18f2a0cf,fb0798c2,393330f1,2f890bc7,9bfc1e9b,89f298cb,e8471046,2df0a6a6,b6c4b6af,505da2c0,9ee13266,bc47cd5d,2ddc9661) ,S(26dff8da,94603121,4649fe1f,721edcc1,a2300ca,b1a6d548,9c9b68d7,415980ea,d8264a21,55e1bbdf,c3b65862,efb9548f,3c4a0a5f,97f5b713,9d3da15c,90004e60) ,S(4e642b51,425e1822,1275f64f,283e9eb1,a3116adc,a6e25047,cee3bc0f,323fe676,f28b7d65,9125468c,4951db0a,bc35d4dd,65b9c5a0,ed27d742,47a68a23,89eafbb2) ,S(354aff5c,ee9a27db,37e7c97b,4cea476b,b4f3700c,e9c26b21,e94d2e1a,78f448a2,8d6907d1,624b79e5,6392d008,2f6a794e,99b4c4d1,6ca78dd5,97709c86,2930fcdb) ,S(5286d074,949369fe,8f69f020,c0b65f75,e76995ee,5f49b9dc,d570b956,8ffbdc3d,255ef2e5,3dd2c40c,1e462a45,27e6ee00,e0a23d3e,b16b05e2,2781de6,879703ab) ,S(b84a8346,c86e2299,9acc8ff9,1a893592,6bddeeb8,6fde121c,266d5f60,3268add7,31179a8c,79f40238,e1b80c87,81e46597,29f5c8d3,d8bea0a3,f65b403b,ef20789f) ,S(1e7bd5e6,63fc9a50,2258b9f1,14fc51c3,1b9dfc27,9022c67e,fde7872,dd12bb94,6287a9b4,555b146,7d250f11,e77ee8b5,7accefe,6d91cb6b,927611f2,c2c1b84) ,S(7ee68a21,37289ebe,7a5cfde6,be672ca6,9d28acc4,54d6b8da,9c96b2ad,37d2bc81,3ec34064,a6c3ca,f2a8aeee,9b24e023,3d7dcbe,b7acddcc,8a53db84,c570c83e) ,S(29d4b10c,f4be3bfa,a9d07fdd,da6ba7ae,f3adef75,67c3c33f,8d4d914c,f8ce570e,b6a74385,96a4f40a,40d03c25,2c7070da,2ec79e08,dbef71f2,422392ce,1058bf4c) 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,S(57a4f368,868a8a6d,572991e4,84e66481,ff14c05,c0fa0232,75251151,fe0e53d1,d6cc87c,5bc29b83,368e1786,9e964f2f,53d52ea3,aa3e5a9e,fa1fa578,123a0c6d) ,S(4f9b48f0,ae9df110,70c4c5ae,2b012cd6,4599063e,5bd32b54,43548b78,6a06db2a,d5a7a0fe,3cafc78f,66f563eb,f6fe42ae,980cd621,bf18aa15,7bdeded7,dd5ea016) ,S(e46a5308,4b11349f,44661589,38bb663d,e1910aad,35de0708,5a053b5f,6c5e7375,da46da88,9583632d,fbf923be,9f07ace2,cb8c3d2b,fa6bfc47,9e1a7d32,e1183ce9) ,S(3643d766,b94b161e,323e64de,3c925040,d62f2ad6,2b60a674,15c8b962,1c071ea,faf69af1,1f2b9e05,db29dcff,a020f6d4,80835d4f,83d35a96,7aff1b5b,9f16fa98) ,S(96769694,c026152,1bbe1b48,544e05dc,e6bea57b,7fa31478,f6ff1b1b,bf497dca,4eb5a6fd,7d0dae14,9673b033,bd97c08f,8210fd12,c759293c,40782702,b3e30b03) ,S(2e41def,2c479931,89be0ff4,b4110e28,7f80fda6,f4134ef6,5c867e66,59a24d07,26a14d7b,b8388b12,a3ba1f50,e56ffb3a,69bde3c1,17441f52,158531d,c874c313) 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,S(4f15f3f9,a67221dc,4fca1d68,429b874,c4418df8,be480591,e57d6841,e11860c9,982c0d56,1783a9c1,a16bda10,87d29061,3f1154bc,4cc62a82,b795c54,a496b7ed) ,S(21e51a20,1f226e1e,3ebd56ce,6f7258d6,4e4f9db,aa425943,9e1bf7c0,144a92ce,4c47a801,b6a5a4ad,25c1486f,ec9bd0aa,428f3167,45136359,18d47079,75aac869) ,S(fac7e42e,8865ec0c,d0b4c4f9,dff6bf8b,e0f28336,395bdf2e,d5e2a118,9c0211a0,36812d9c,8337199e,fb1fece1,1997307a,ce656fb7,3bad65c6,41e6bba2,c4dd695e) ,S(a147839e,c91bc77e,cc568671,442d29ee,57f0f42d,7b9cb469,91064549,1a26d225,f404350e,bf7267f1,86120257,fa29fc1a,fc0d064e,2f14eeda,b730770a,c85bc5a4) ,S(d1212cf9,e5086804,44883c1f,4158f3e3,44a7900f,716ade2b,df19e41c,18636b8c,720b851,7b91665,128183a0,f3235c6a,2f9c21c8,e8c6ec0,5553acb0,27fc0964) ,S(13d5f334,a7ab2578,977c125,1a07d7a,2e4852ca,8927ce7,2dd9fe90,8b948975,973869e2,d1d0abb5,1ce31db1,ae8c3816,ff998753,479fe82a,7d87b6eb,798773ca) 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,S(e217b126,acc507a1,b41e0826,b300363e,bc0a43b6,feaf3866,ecd4b8bb,cc7e11af,7eb28def,83db33d5,8b8eb733,2b27a386,921e3a5f,b0321ecd,a8d1fc6e,49e98f30) ,S(2a196fd5,82b85d5e,1772bc21,84d8aad2,b5d008ee,c795628d,20de68a9,fce1d184,994b4657,ee9ee3d4,fdf8dc8c,cad2ff1f,68526c67,89d82230,c3399f6,62201303) ,S(bc9e3bc8,3a6eca7e,8a9897c8,1118f7be,ca770cbd,7e66c2e6,1321d026,7ade4342,9d7ef7e2,d544a561,ab899291,75f35d24,e2b07661,2f84b0a3,f346542d,714f3f4b) ,S(ff2813f3,842a9f84,fea9e367,6f12f209,7e76b8ed,e691ccdf,6f6512aa,b2f198b3,206e3bd6,66d0c161,ac6de438,809f485,b8b6682a,f402bf76,18a484a2,c3fe1949) ,S(6e7599df,2d38d63e,be142321,769d7ca,34a50bbe,4e0adbaf,6c7479b8,d1af05f7,233dcf1d,4b0e4d88,4a9ed56e,b6b4946b,25614345,ecd182cd,5556faa5,e3654c8d) ,S(1edd9cd5,6c82eb28,14d844d1,a9e5c167,8397662e,b576f9f9,ba250719,33666146,a00f4a85,b2ee83e,949b5cb0,4d16820e,39d48ddc,95dd965f,e24251be,3df43f4c) ,S(2723de06,1f794cd7,76a4a090,738a81ea,818a2f73,92d7ab07,18d79fb6,407324af,35c7a9be,f9810c50,3c53429e,344ab888,38daad72,77cd0e78,3db1c1fe,c6bbf41f) ,S(4c4fb244,4cb54def,6d9659ee,b43c13c2,3874ec2b,a7c6b53a,f469ca26,ab9a213d,bbd2eafe,56447a9f,feb9ad15,349b338f,d4a1aed8,5a356472,82751e5,5b8efa3d) ,S(736359f7,347995a8,8e306977,1fb3fbcd,12847ed2,8e4e612f,25095720,667593e3,23bb37ed,4bce0512,35a215ca,6b8f9868,e303fda4,80d655f9,72c95bf9,12bd3741) ,S(15cb9594,ee936bd1,4b981394,60879bee,6f33b0f7,c0ccb293,825794d9,85f595be,aaad772a,2ec81ab6,13775e9,edb274ef,e2e133e6,5e58949a,c7f25429,fb1bb152) ,S(3b5489ab,97e5cf1e,84a90eb8,20b8772a,df574777,a61f0a9b,41e6c567,6be78fa4,145d13c8,e9674a17,ccecad63,f113d64a,d59a1eb,bbb10cf9,e7134cf6,562219be) ,S(78d1b99a,a6f9d385,b09bec7b,b59ce26b,23323e4c,3a259c56,68417597,a29dd2f5,1c8d11f8,e883b210,cf54369c,e9f6a280,a6b890ce,15b4a0ef,3cd8837b,7e16a122) ,S(385e4e8c,5ceffbbd,3a813e3f,938912e,d2fd2d18,2be81210,70cd15fb,39661e85,f4a1c414,9f5cfbc5,213ceb21,c1cc08ca,c9b168e2,58cdec70,36e2dacb,ab68069c) ,S(310f8c70,d8e46c6e,48930df3,c53e9292,a7c87230,292d6b1f,c28d9711,951aec6a,6fe319d3,c92c07b2,56715154,d5d7046f,59d92d5f,6dcedefd,b0386f5c,3417146f) ,S(764f3c30,23d1d50a,e170b80d,48d58923,c1f91a96,42210912,94066585,d7c70bbb,bd92fb1a,becdb4a0,ed941146,878c99cf,c3ee9eb8,c8f2b8e4,b547cb40,e3dca724) ,S(3d5d23ba,b357a37f,1bd3c86f,84010b8a,b37a8075,3c47b1ab,36f7ef72,a3e68126,2bbd1841,bdcf0265,838893c5,f5f9c0dd,7ccbb461,93068e0,8211595d,6b34255b) ,S(a70431ad,cdfc7b8b,febd2aff,d6759e94,6d4ddd7d,50f50dc0,87e256b8,2a7f8a1e,3ca4362b,9362b2ea,c33d77e8,befeccb8,23163921,86ff5f20,384247f5,9147f593) ,S(2a388212,2c1b2ecf,3c800432,7c5dd403,2263e9da,245dc697,bf7d63e6,300e8a7d,ac96d188,53b87bf0,3dc5f2fa,fa9b73a9,a339c0d9,a7245175,fd72c822,12f6ff78) 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,S(30486f67,23a54952,4d68c948,dbc71273,d69b4a05,5fb9e7d,a702d027,619c4a66,38ca4d4d,279ec9c0,85ea6369,5470a4b9,fd6acc6d,9a049ab6,5743ecba,c2444c76) ,S(1b83ee94,95ead1d5,80f67174,dec2a026,d6accd93,9a89d970,90f25bc8,d9e6932a,196d448,fb5e4851,e1b73d6d,a2e7d0eb,3d263034,9c2b3e0e,34584bc1,d6e20196) ,S(4ea9dc2e,edfa5a11,2fa76671,5c1579d9,328b6132,14ee64f,2e30f10c,b7517396,7414efc9,6ef83e29,5883f0b1,4019b41c,d4a192d9,d06cac9c,21e8f0f5,b06e50c2) ,S(4166c19d,bee9ad08,83b217aa,3b657436,87677792,d5cb9b31,1a097fcd,2eb033da,62c5065c,5fae6aa6,932b4d29,ab375ac6,b80e113f,d38d81f8,abc236eb,7eed541c) ,S(b17567eb,b112f54a,69c511a8,7d3d2f96,bbbc6686,af8e3f31,a2bbe0a,85a74899,f6676341,3788be54,ae3fc693,4b8936df,a6936721,c671cbb1,bdbfd72d,4c9f52c2) ,S(cd2b6515,2ab97f34,89d81fd,f3513131,a6df0685,5022102,12c2b8a9,be8095a5,cfe7952f,9ca41935,15ee40c7,2d44d023,22afff84,b8700bb4,5f492e31,e78f6a53) ,S(375603c4,9f33140a,3241a72,907ac0c7,2086c979,3aeaf74a,44732097,3618229f,7bb740f6,6322a773,e11ddb46,300975db,de08ba13,84480699,6681637b,eb85e837) ,S(102067d4,390a3dd9,6d83c176,f341dde9,7e10955d,2e001632,978f202e,efbb7432,7cf6cfd5,4d28ccc3,a7019f11,b6ba9df6,1d8b7eef,7e70722d,afa81a2f,839ba83e) ,S(47617e73,e3fbc53b,a703042c,f8b48fad,374ef42f,e8c2dd54,4fb7625c,de63081d,1fa4f423,c92a95b,b2c40f07,f43caaff,50cbae67,87c3e2a0,e4782f39,c1d439e8) ,S(2c431baf,57f75062,9f57aac0,8e28a060,46b814bd,318d74ca,82e1174e,f880f84,ddb9e7bc,68574b32,c1004108,9853f41e,62755a52,ac58badb,b8ee58c6,f209de50) ,S(91963643,8143b6e4,19b86b1f,79b708ab,3f4df44b,d774b41,338570dd,8343d599,9034ee17,7171a0d2,9fb91d68,26b87bbc,21be334,90f44049,69622a8b,76312f0d) ,S(bf28c201,af656c7b,838d42db,95683b06,2871859,2b016ddd,a4a4f7f7,c4b7754e,bbd4f04,dda510d2,a8a66c2f,46ab0681,ce6ffb5a,ac320e20,c50b6df3,a345d109) ,S(fcac7386,21825f4,4e1d531b,f598e40b,1aa4262c,a5aeb5a1,babb4f35,9518b137,3b196b7a,957bbea1,f3f2d1e4,1ba37eef,7dcca7fe,87e7c593,6ffff685,52e67b64) ,S(9cfea1df,caaee192,141f0278,e467f809,8ad89cc9,b47ed982,3029c1dd,726e9331,72d81e4e,7f30ee05,8fd0b646,95086e30,96a071c1,5b75df47,b10146b,18db211d) ,S(548d3f42,123553c7,965c7f21,f2802c30,455c5151,99b98e20,1e966f34,6a1334da,612ea25,cebb03d2,89538eeb,15b94686,8c0afb1,311278a,42694a0e,956418ae) ,S(e5be619a,ccf84c26,9b5c545,e8c4990e,ebd46756,c628de22,a6c8bdd6,74295bc0,640864a5,7d841af7,ad83aa74,fa858b91,89e246cf,9b361837,a742e2a0,71b08bf3) ,S(b560933e,3400ed4a,eea8f733,d2368c8f,a260460d,f734e209,e194e9ae,a1ac668f,5438f93d,31337853,9feab182,6cf17bbc,ac0975f4,de29a886,1b1c0c02,2c5f9da3) ,S(21dd9a97,baca3e79,77ecf7d,d74433fd,dedf2d96,8c3153c0,2c652aa2,1ccf60b1,de6e60e0,e048b0b7,b699bbd7,cda0c0c9,b851c4cd,34f4b8d9,17c07cd0,2684797e) 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,S(2239b3d2,23eace6b,8ebd287c,8b6a398c,1ca58a94,5d8b7b81,7b1133f9,cf57ef48,fda880b7,4b54a8b2,8af4b26,78e03f28,f01d70fb,3e4ebbda,94ccbd43,e2b4cd46) ,S(8b3287bc,f47e72df,7edc9178,51edb145,b88ee233,9f254f62,e86ec624,a7c7e365,54a06bc0,9f60d54e,5f900868,c0c3d37c,db6d9969,1eb605be,321f0f20,9fecabb) ,S(d9accea3,3e3cfee9,10d7e1ff,3e87539d,ace742c7,24d6d36d,d8d981ca,984f7993,6adc974a,a901e5d2,d8cf5a05,a20bd02d,62947f81,5425e690,565638a8,427dc88b) ,S(d7fc57f8,34c348bd,e6692b50,474ee038,4af245da,40b8f6b3,8df2ae5,a8b3206d,b253e4b,41fd9fea,9b28e04b,a6db0324,231edb1,1f9af406,e38d2b30,244e2d19) ,S(25808fe0,ec4a1409,36b34e16,595021e2,b815f660,7a23d505,9ad5b5c3,14d9588a,d0664ad5,b1d46ef8,8c8a1eef,bb9df1ff,a75bc16c,e8bbcec6,6f4798f7,c58e7b96) ,S(e4474780,113955d6,72152fa5,70da35a7,59e67a76,29a39ecc,3226ea13,99927914,493cc170,aa2f0486,da6834d3,3566c78e,ad4eb3d2,837ef5ea,c1adf3f9,43793bee) ,S(c5040dbe,2af9d706,76ddd900,d00f1046,44e2b985,82d46f11,47602b91,126311ad,840aab11,a2316171,cc9b6466,778a9ce5,a7cabc1b,1077586b,91a8d280,324ddb15) ,S(23391baa,316d33eb,3a7ca123,6c47d4e4,8116cd4f,93bda3a8,12a228eb,437d9f14,1d81341d,9e6d76fc,1ca69af,f6d8d119,bc97c79,c7cb8b7f,1ebb54f5,cb7efd4d) ,S(13211756,3de3ba72,2fc6682c,beb39494,8aeb8fd8,c0b95eb9,45eab34f,bc39ac38,9b772721,8a4b0823,7c961431,e26cbfb9,aa527905,41b753df,89eb9ad8,8d74f006) ,S(3b8bb898,b27a2fc7,a1cf896b,bb5cd7e1,708b943b,afee896d,2ff77a95,ba789708,d81e541c,668003e5,5a1e13e9,6a1635de,7fdcbf79,c34068c9,248100c8,9d36c1cb) ,S(e1d70a2c,9af5c4ba,c505e4f5,5c0040ff,d94f162c,815a2e21,c7ce899f,e0217b4d,b25630d6,d20e0e4b,3686d66d,e2b1e53d,eb063b99,e79c212c,2fd3cfec,97a4532e) ,S(1b1e3823,a51778fa,d38f0c56,e2b36dff,a7e681c8,30fb41b5,ff1aaa7b,d912de1c,f2e99a90,a951201d,ce725855,6bf7fd27,bebe1626,8328116c,d593ff32,2584d4c1) ,S(1e31d838,94f56191,2c134817,55e467e1,8745a91c,d903102,e48f7282,21bda7a1,11dcef88,35dae18f,3c02c6d9,7f80896e,477a7b27,41203aee,5048c94c,7cd610ce) ,S(cb9ac34,795cbc99,bf67a7ff,2bc3b497,311f687a,51b5028c,422b0301,8ab7100e,5e5f0621,c804b35c,e01e95e9,a8dc13f7,e5ff32dd,8a44f320,74e44836,3cd0db1d) ,S(afc34ac4,67dad38,a0e326fa,1a656c48,24dcb884,f00a20ce,56c73835,b4e11c1b,c8b1c404,3f6d647a,382ef031,a02c10cb,77a033ae,bfc6dde1,d7508136,28bdcb96) ,S(3a6fc160,ca85aba1,619430bc,ba14e12,3330f636,7a78273e,603f85fb,e270aa81,594a2b72,86dbb390,945a7a48,3707bc32,cb72cfc9,19c241bb,61774dba,222bc0a) ,S(a840f695,657c9c3a,3f64f56e,af18debd,bdc1e4a8,e3eaee43,46b19601,433ce7d4,8a8a7ac0,ca41e2df,461eae96,bc00131b,1a77b824,7273269d,7a41f49f,ea126fbc) ,S(c044e01,70ec6914,c39d08c3,4a293268,65cd7762,d6e0f3e5,5f69d80a,e80a39d6,7bd63082,7ae51516,25ee0b5e,c2f97b37,6dd5fd7b,9205852a,92dbf922,3a0b4657) 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,S(65499597,5be06b28,b4c339a2,b126210d,930fe920,7cc72be4,3d4ad17a,c08f38a0,bdee23bb,467fdce3,2d2cd92c,e81e3f5b,d29fe8b0,8b35abe1,c684443f,72f7900c) ,S(3791c8f6,75bb14e4,b7d4f084,483aec44,ea38eb2,9b108137,400099b0,799f0bd,2dc8f74a,da5e5eb6,f3b96ddb,cbee5ee5,8b2a3f45,c31cb16d,15a4e918,eef7bc76) ,S(d5e41065,eaf890e9,e9046936,acf6a43,59795c7a,1939d8ed,42941a8c,6ef31364,191ec4c8,a559fd4e,7abbb6b8,f2e4c32c,bd2f30cb,d06ff6d,21f156cb,f65bbcad) ,S(16ce2280,fa0b404d,28a29acb,62058b99,e504e6f2,eaaa3ae8,b77ad650,2c970dec,3d4683f4,486addb9,e54bc252,74e590c,b6eaec5e,7f96e9b8,8174b81d,56efb09b) ,S(a6b0ab30,6cdfb1f3,90e5b447,816841b7,e08f997e,d7d47016,bf3b501,c6107d07,2a62842f,b67e2794,92ed337f,d72abc9b,94e96e4,a10f658d,9cb9a4b6,a80abf7a) ,S(d7ca6d38,760b320b,21cb779c,d709f376,52b9d08a,8ff6ad90,21e00628,56033583,d6c05f72,866d59b9,6b91b6cb,b1401619,5e2d1cfa,9982db04,6d672fff,849e7bb5) 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,S(adaa9457,f60b9f3e,e0a5548c,51f945b9,78845841,51ae87fd,689b892f,8ccb19f4,834657f9,2145fefb,8df9b047,55674997,f899b951,40ce5830,2e468588,1761caa6) ,S(649296b3,9800a3b,516ef3d8,52d7fba4,597f3e35,1d303397,7495fdee,619e6ef7,44ce9c90,10215167,fdc5f078,e2edfebc,5c8b441d,d88cf853,5c78533e,d61df105) ,S(2c1d7e97,908575bf,38afe2ba,7875f1d6,9f1e9db6,b11f92ce,4bc94d3f,6006266f,9eb250bc,30abd08,bbbb4e4b,bc09cb03,8c6c8ec1,fd1a6ff5,ba23726,da2cf7f) ,S(b130ff8b,ed4ebc32,78293b10,52fa197,b44adaa7,d1bbd74f,f6d56f9,744647ec,4a0a45e9,b785c7f6,76fd0a95,66e4228,136f60b,dcc1806,212590ff,eea5eb33) ,S(4f2a5997,62ecb2d9,31ae9c74,ccd71cc,29bf684a,d68f0117,32a0cd50,cb0e6231,debf8db4,5cfc7083,fa700dde,7309edc0,fc44216,cf7bc237,377c0bf5,7ccf17de) ,S(97f9e9a1,7fbe6e25,e41419a1,8a5a24da,a178c0b,a99e30d1,cab0d2de,7a23c0b,1ab1226b,cceb480,fb4fdc8,70fb5386,6cb622bb,e71d3c0a,4ddda232,57559128) ,S(e17f3fe5,e9f5d17e,40182067,3b710940,bfd486f1,ad3ef4c,bb93b47d,9d9d8cb,f1126a52,615d3a8a,6b360b26,305124af,44ad7d62,e03ed96b,59c2903b,b5272f58) ,S(1a39f846,7d638182,900c3e94,538a0fe3,3ae66853,aac36688,7a5a8bb6,7b2fa2de,ae7c1399,5a625a4e,42b4dc01,9d7c7501,18492f3f,bb4567bf,28ddef5b,82903aa5) ,S(8a5ddc61,27f6fa44,90a93e52,f4faffb8,baa60581,5142be68,cd18692e,b42f5320,5eb62325,853dddf1,a42559eb,bd5dfcc0,328e69a5,fc787389,74c80d1a,896b0d8e) ,S(117dbfb5,74b7d6fc,d47dc17d,56f5b5da,b864906f,f08d190f,7afe1f9c,fe38c299,4acd2151,30b7144e,437bc923,302640a8,c504712f,6b903b26,bd5db8dd,5d90196b) ,S(b0c31228,431c7eb5,7310706d,950a2a60,eec84ec7,418199f3,f2985a39,8a70a537,a7de9b34,792876ff,e98c3237,260d8237,85e47c,438fe419,a1048b00,b064ff78) ,S(7c210cb9,f493275a,e17e6d5b,517606be,736cbc86,5a5897e0,8d1d1f03,f243946f,17b07523,a8bd185c,ea4a92d8,7af1f1dc,920a7fac,30faedb1,c38e3529,1759c63a) ,S(172e5167,578bed44,6397b519,2b0eca17,177b14b2,f4570aa1,38771610,6ed6e650,9c15752e,4776b805,d63de803,83c73ad3,9d3ba817,c1f88cee,1737cd85,33830ba7) ,S(161afc40,df25fda1,3637317,3dad8046,c95a6ef3,aa9c19ca,47e9ce2a,20030686,5e6fd083,c1265f76,b4b9c819,3a45e0e8,9926f160,b6257759,ab90d6f0,126089ce) ,S(b991f2a8,e18aed33,4d769cf8,b6e39144,2d194e90,ee1518d9,459d3ec3,8a16a85f,1d2ba9a6,b89f71c8,ea169d3e,923d2c1,7e6e590e,21b28e8b,1a0d0cd6,1bcab7b0) ,S(dae0689f,5a6cee77,f796f488,1fb3647c,7d623348,7d5ab502,6f1ca30d,44ca8afc,ee67b670,f730bae2,a15e6964,33be5b95,43ccc1b0,314cdfa8,c6cc8873,c39c329c) ,S(47a58ccd,75f89c15,46a17ba1,4629fb5b,d72805a4,16a12e61,aeafd8ec,8a7e4e41,c15e7fed,1bbb810e,b4be60bb,61fc1f0a,a4bc43b9,73d94767,9b954f3c,29fdd889) ,S(f7ae2fd0,2e3b6ee3,30c0697c,94ef65b6,d7582f69,5c509698,cef09b44,6b040e3c,ade9f8aa,c527139b,c54d8e6d,ddd41ac9,5eb49565,79934ea3,6a9dd8ad,d419ca03) ,S(155f9ea8,9be2ae20,8d7e9c21,4c244a58,ae61cf24,5d5f8dc8,b6c448d9,7c12989d,1204f5f3,840cd19a,fda04abe,6cbf4490,cf5ea60f,4cd17680,8c1ce9d3,65b009ff) ,S(a83cc9c3,933b5f14,fa5348a0,e0d3ee39,e35057b9,13c5a51,89a61663,1e9d74f6,40aa66d7,fad68476,1e2a9c78,e1fbe478,52b91d11,a283e1db,e30d4baf,f072a74a) ,S(ca4951cf,c07b5c23,298a20e0,fa44b554,d7acefbd,bf2a6cce,11fc3ea5,67b5f5df,186a8bd7,6700cafa,c79791a6,b28c799a,35aac545,78586050,b8012c4f,9f4afc2) ,S(cf92dde6,1bad101f,5e71f2a0,dbc2438d,d6760ba5,b84791a9,ae0ce712,9eb6787c,a7d351b7,f3e31e6b,cbcc1f05,329458e2,6c9d8a9d,1137d595,28f53e23,5c3bcbd8) ,S(b1ab0b3e,cfd8283a,3b79df9b,e83e8b37,b06154a9,6e2a687d,8f51985,129c1179,cdb7f2f3,4bab534a,41f4cd97,b812900c,99e97395,3837f058,12d5d0d6,e9506bbf) ,S(a1743329,9cd4c9e8,4fb99295,f3febad9,197296a2,98b30354,24e9524a,e1789ce,40994ef4,4cf53577,6f078088,adcfa6d7,5bee11a4,4f2f3fc4,4282f5d7,f77e1afe) ,S(241b486,4efcac7c,3c7b946a,61a55317,38b31846,607f1e0b,d0a1a2b,d9c0573b,5cce8848,eec61cd3,325f3ba8,fbca403c,2f980159,bad3997c,832f5c98,1fa0d574) ,S(81f88209,64997984,699559ad,f799ab0b,e3efd354,d258137e,d753e3e4,de91b387,8f9fedb8,5bfd7061,1b9e5caa,5f3cc8da,43bda599,afa29967,a32c71e6,aa26d15c) ,S(49d64231,bd2c2145,200793d6,4a2ec254,c22da96b,655706fe,8fbf5d49,464e5a5b,faec8eda,b0d72cad,81df8121,671c6dd9,bf986440,3f1a702b,548d4333,c751e825) ,S(74c14c32,4fad3a41,1c7e1f15,9b740980,6daea24d,9476e938,7e77db6d,66e0ae4,af795203,1fbee5cb,f031a2cb,946e6b65,3ee0165d,abdb89fd,5aa73880,e0641a41) ,S(88bc209c,7342d94c,be3f4215,81383c6c,930f9c19,d09d91b2,a984b6d7,12a1e7c3,acb7d745,76dd8723,89a88866,e287610d,b817ebe6,1581aa23,46ac994c,4c5b3e08) ,S(486c8c68,c81ca88c,df7b93c8,5a1525f4,9bee242,676aae77,c1bd85ce,2a6eb3f8,e0fec94b,35fa97c,d5e64870,6f5e6849,d6249004,fb33e34e,c1add26f,4fe52d54) ,S(4a1efa11,6c588e23,7b5e30fb,5d0ddf37,ba39043d,6e5faf14,e28ceb90,4a681a3,bb196737,3c907165,a8937dd3,1bce476f,65f2acc1,41bd8d53,8fcfbf1a,997b64f4) ,S(d7745c06,c69609ed,db17f30,8efe7bb4,2632e85b,7f7f792f,8da44294,78eb28d2,7575a75,4d1b2bd5,5fc46e11,b1addb1a,5371f007,f702a97c,ad13f082,39b96a73) ,S(bd752f2e,a3db27c6,a6a08ced,df74a87c,dc333d50,fd9995f4,9ca7afa4,2be68def,378f8aaf,67478d20,ba4725ed,26d50c62,ef5c576d,da9c24d7,91dec38b,a5e9491a) ,S(ef588333,15a3c7eb,c6602bff,ace00d5c,55eb304c,7f3301f9,4be457b0,1f224d21,56eb3aab,6253dfbe,3d9a95f7,e843751d,eb52e054,cb5a523f,f46a0c12,b517abd) ,S(2c1de374,7355825d,a09beea4,f42df241,6b495ce,7edf1f1f,c1dc6043,5253727a,98593660,9082f5d8,8f9986bd,f77672a8,5ff92cd0,28d2c588,73a3b1d3,87a150c2) ,S(49f8d71b,23e60140,f50c9001,6f39b2e8,b78e2a22,a88f2535,324ff50f,280daf99,f66bb665,4807e7dc,330ec339,3f6fde20,308111c8,1fe42546,22b93a86,b58b04ec) ,S(365c9f85,754b61ca,2b2a30f9,954f3a52,d18fdf78,db593ceb,6df617ab,189f37be,c43fefe6,aca56bcb,ffa6aced,60a32794,7681b601,22369a3a,f1405a41,5132825e) ,S(1cf2cfe9,e89668ed,c1a446c4,da311cf2,7e2cb53e,1984a310,8e24e8bf,21f1b5af,71e56dac,43c53094,7b78f104,1a685f23,aebc7b12,e2caf803,6731ef5a,20c966b7) ,S(f3303479,62660226,f391c26f,a7e87796,219694f8,e01cbd52,25dce636,b48ca3ec,7dea0bf4,c110e945,dbb59ab8,74f83a42,afa585c8,56a93002,6f48f8fa,62762827) ,S(b689244c,4bc16c88,398664f9,2297ea0,8756a969,1ae7adf0,587c3253,e4b27154,9b488748,1357368c,c97f89a9,b4a75a0,bd7483ae,5c700364,c27d19a8,e450c856) ,S(bf34fcd2,d6b4371c,fef2f874,5e4be021,a78b4302,240d4517,f3eb1140,638cbe41,ce6888d2,7e326eae,8e772914,e1b43bc0,1ef6a238,27f67546,5464e195,5f97ac02) ,S(c2097a6d,231bc796,ce85a594,44c00250,d51ffe63,c45b9cd1,10ed4821,118d74fe,58b06413,fc4ac173,e1e3a85a,ca674885,d1f92b3e,5b99f72b,1350b6a0,bfe4ac87) ,S(874a6222,3d8804f3,a11b1de,3c647aea,e3e81798,40db2618,4d46a330,417afa81,4132a5f6,7986e622,976b181d,5c98f356,b31668e0,ef70f8f,6b13a0ed,af80b429) ,S(ac7c6e8a,1a05d592,8142227a,b0c3ed46,1f28463c,ccaa3b85,b9784e0a,f5bc605c,1a59a195,581e3397,eba60a0a,963f5c71,c107a9db,68794da4,a08b14b3,118a2186) ,S(3f13e2d8,d825a3f6,8875c01,a1715a5f,44bc12b8,2f254a65,575b163a,3333342c,baff6882,fb2c2611,ffef76a6,8b5e2293,6a2e6ecf,d7ba6724,3393fa1c,5825e3b7) ,S(1ebeb354,515e7f39,dc3e2631,51d0630d,aa7e400f,4c9f7cec,4d5f95ec,bfa8fe2d,a2e35cef,c2cdcf,384a2473,c185f3a4,c70724b9,84c72dac,a6ca11f7,ae5c85cf) ,S(c2dcdb65,b211e765,e6c59218,d12b45d8,b47d8f9c,e22b99a0,d2d19a1d,de02b2ab,e0aa5b9c,a960117a,7289326e,9259f886,8722e032,c96b5237,b146f50e,24f3be50) ,S(495d69f7,e2a9d144,8e2ed8a9,c038f6c6,7f360b8,270c9b85,841e8791,64bc0d45,5fb3fe2a,1dabce7b,83b4465d,74fac6f7,c48584be,134283e7,bdf59e0,957088d2) ,S(ceac4569,2139e4f9,701be43d,8da3f515,270a9477,bad5969d,2037ac87,3453bab2,bd1fd9d8,15f4e872,b602f2bd,9604b6b2,f385ea40,d5520b3b,ca32c160,44908070) ,S(7ed1d0b9,3196b8c0,1cd284cb,c0a206af,4e6dba1a,d6cd406,82f55897,9407e0d,e95a3ac9,6ba60be6,22f4ee73,2d75a9c5,11018ec0,d840ce0a,f1bca18a,1d2801c5) ,S(72fb366,4f42cec8,940fd436,5ba7cc97,ac5fe4b2,131250fb,a24b7178,a1040b04,c182b1a,93a211f5,f5de5c9b,4b52ce90,63d551dc,a21ee9bc,dbba2653,c47dce41) ,S(dd06cd8c,9ca91e45,d6720043,d3e6d857,4690192d,59154309,2160f04,6008beea,cdc17327,6eebea3b,f9fa8a7e,e83ebd81,4189705b,900b3ce2,72b85dc6,c41e7ecd) ,S(80f6129,e90a7f0f,1e650439,8bfedb10,3c708c43,2e2c743,da8a9a99,3978cd13,74d97812,145feff4,a3ef594f,85b644a6,d95a3082,3828c00f,e7226d4f,39deb82a) ,S(56af34da,f56b508a,eee970af,bafb9dd2,b48f83c,4c051b24,f5bc27e7,105995b6,d41dfe52,9e788e19,89105a4c,c219dcd3,decca65a,dcc5f34d,8a3ab0de,d1ae68bf) ,S(820225ba,795565b4,c45e29c,4689d91c,148cf693,a1a1c1f6,ca33c44e,4e3f91ee,3622ae5b,c89b9c2e,66bf5a3,17826928,11a0f4f1,4b387334,b24028be,ba4b7db4) ,S(7925fdbf,cfcc202a,895a1b7c,a8c7f09f,ad388db1,5652b703,3bf232be,a2ea57d2,46f7ef01,c9cb7dc9,1559cf5e,c6d3f5f2,1ebcc21c,a8414d0a,9dc37309,4e90525c) ,S(4b224b6a,f38ae731,5b316eb,8dbd2b1e,6638794a,9bff79f6,1027f60d,5d81808,3143ea08,b1633002,bbb2ad2e,11ffe5b4,b6dc6888,1fc669d4,23ff9cb1,595c3dac) ,S(2c0767fa,4135f4eb,602a1a36,e6ce488e,2c1bdd64,aa4113cd,28daf20c,687380ee,ddc3effc,e78d3061,7cc2da71,1373de0,6a65d2b,1050b89a,5f71be3b,fbc16a7) ,S(83837d3e,e7179a84,ef6ed2d9,41a9f835,37b5a2c2,5d511ef1,982d9bba,50a7ae7c,62201e16,60957b4c,a86f1a49,5a6027b5,fe2294f2,7946c8d8,556024b6,e3b66dbe) ,S(cf075b34,e560f057,53a8e011,835bf1da,25e50d9e,1d70dd9b,da427109,5895387a,c73209d0,330ff4d2,38e19f6f,33df38d7,2b11d8dd,180d6a14,4b07184,a2127018) ,S(d583f8ff,9b1875d1,ef468030,e3ebb7,9d06ba2c,1008329d,cb01b883,7c8931a4,f8cfcf1c,3f092ba,6bfcfcc6,9596b508,aaac7c9c,333ba58c,d55be53c,6fae3292) ,S(551fe9b6,21d2389b,fc185372,342edb1b,27568bb2,da1fe220,3431b792,43eaefaa,6c76904a,e48563cc,c6aff505,7f31119f,ff48e5fe,971223d8,c3badd02,563c24e0) ,S(1bb778fc,74062f24,b0962be7,bce7c990,51f06394,bc8e6da9,a9d63f6e,d16a80b2,2754f53d,2f4ed167,3d2700b6,8ff036fa,60e9352f,1dd7bbdb,14be1740,61d88318) ,S(a150af7,1261582f,8949f1a9,3ff8d539,aa0744c4,e97cfbe6,e4a3fe10,e7e364aa,e22a1afe,a68671c2,f9e12471,56e1bf47,100737ed,5f96fab9,9e0df721,eaea4773) ,S(c94ec3df,727fdf91,d7963a03,8e93d68,835ed2bc,2578780b,7242e15a,e72e2a9e,a476a0e9,7bda53c5,46312b35,f0fad09e,11b2810,b3f570d5,a934d21,7152009c) ,S(3366b9db,ebe13231,7c542739,4235a72a,f186bda1,784c7f25,5f8b65f7,f146875a,5ea2478,95f52889,42321383,5439195e,6b620619,20171862,eea32726,1345d3cf) ,S(616c8e6c,e52265ec,cb85ef36,5092b2bb,58bec6be,444c2373,974c38e5,e0e8ba25,4d3d5543,3d6e258c,d8b286f4,5f41249a,724a9890,2f1ef3ca,ba049bf1,cdaa0970) ,S(74df2177,2e38e84e,8b81d86e,f45dc4a7,2617b3a6,32094b1d,432291f,6a651827,4c32baf,30f09527,fc4abc6f,9c9b9a57,2a9ccf1c,6a1b360c,48746d8c,22e01334) ,S(1814a1bf,76b74532,979966d1,5ef42faa,532f8dd9,bee0cce5,d68fc500,21accbd1,5f5df5ff,da9d439,b2205ad2,5fa93b9b,7af1746e,9b2eef3,154bfbad,acd46bdc) ,S(28911e94,98ff7526,badf2287,8e85fbdb,5f444d66,c422a975,c7476c02,b98625cc,5a341cf3,5cf26006,9d869542,fb221ba6,eac150bb,e3809ada,5e4c903c,1e638537) ,S(d5acff71,e82a455c,3a1ce292,689e8686,f441ce1b,e644e79a,bd6d0efe,29270865,aac6d48f,1b46e970,a044971a,ad13f033,ca8cde96,958d870e,dc7d80,1d26d5e8) ,S(5cf51c1b,2210d85,9d765e17,32109514,8f03fc57,51004b6a,91f098e2,e2711596,1eeb19e0,610df459,2c31e58e,aa2a2148,17fe9ee,a3995838,f395bdcf,26d5c3b3) #endif #if WINDOW_G > 14 ,S(21456873,b58e3687,52c75800,8d3bcae,9efaf1f5,c5727842,25e3d854,8fd421cb,a2f2d10,c85e8a0f,4a136ad0,5df991ce,7d3c5585,a263d5cf,da50a4f4,3db76cb0) ,S(c10de5c0,51ae2d73,28ac06ca,cca840b4,ed7ab204,21c6122f,1d68fe7f,7893d38d,ee30e086,a891484,2ad4041,f9ab9c57,cff1a315,f0642d31,b31c2914,faac99e0) ,S(be778032,f12c1b77,9bba3d9e,d290ca90,30ac7050,bdd77a2,7eac09be,eea65c0b,8657348b,a1e27a63,1dd2a54b,e2d5270f,4cca817a,219c5378,4d4f73ba,2c932e63) ,S(a05e7551,f8f090c1,bfc8ffcf,fbf7fd57,9d033163,67d5ee64,b85c4f69,33d0ff6b,8eba561a,f42d43c4,99e1fafd,43b49698,a8f3babc,c9c94c4c,4822cbed,a741b309) ,S(6e4d47f6,b17501b8,f3b220d3,83cf5f11,a395c0a,f0023988,c4e7b8b0,ef66ed23,e01c4330,16e3e6a9,535f1d40,905e9b3f,8be9f05c,b53e6143,e81091f5,4b76b57d) ,S(f626750e,b7eacac1,7cf24afd,43345019,c6c32292,c72503ad,d4125d40,67b7e66e,d669f903,67f407d4,5307578c,ee91fa01,f030bb9c,b66c7111,34b91757,1c993f4d) ,S(437acc60,c555f7c4,778595af,db4676a2,1fc8b3cf,2c8538f,cecbae12,811511f1,985fd2c0,7385fba8,4cf25a1f,46cd2c3e,de8dd359,1c6d20ac,584b4a8d,8a65dd67) ,S(8d50555c,6245e43c,a619fb76,ce45441e,dc585c7c,4fb2f33e,1c07965e,d4e35f5c,ea828c37,331ad0aa,44d168ce,c328a9f1,c7deaa35,47ee4757,c776fc46,439ea5d2) ,S(87f5f6ae,580ebfe7,1b2c19c8,cfe770ce,cf8d4223,62718914,eb853f1b,7f4cbaec,eb61df09,12e06f58,ed6d85da,7240dd72,aad00c3c,6a3a9c11,1f378664,cf359386) ,S(c1cfcacc,b95e6577,4e2a7d12,3cb0071b,3325c27c,5d58beb6,781a30d,ff6306d3,fa9ba55,cd95e721,12d98a19,8e3769ef,8cebb355,dde5b62e,e6f3b8e8,52a3e81d) ,S(d68bf50c,89f25969,a765af90,854bdb89,d67acdf8,f1e16bff,64868338,8b88e311,b62d1866,55835dcf,8064e13d,aca1e896,2157576,a02e178c,78d27c99,9cce81a9) ,S(b8d7c25b,8c20438e,702197cd,a3bfc05d,c6577717,c9b6a527,15ef84a0,2c0df867,316b527d,4be0e62a,2015f15a,17a412fb,72ebbffd,b02e53ab,6e5e9791,b771b45c) ,S(d98b3403,a299106c,9c6fd52a,8abd9ee5,cea9ab0f,17a15b4,7eafc809,c34e356f,bebcd24a,9300c739,9bb3af8c,12fa813c,78c6838,dbfa00a7,4ab09669,4df9700c) ,S(dcd15a1a,7cccd53e,db08c2b2,c6367126,de55cc46,a4eaf5d3,335ccff2,1238bbdc,7de57d26,bf74764d,bcc7e15b,72ec272c,58061f47,cc0715ec,48bcc032,60e63a81) ,S(2f6a844e,e758e3cc,8f299e01,ba5753a9,d35e6c51,6a87a683,8f5ce28a,fca17c62,5c29172f,f907c0ef,95e78768,2625c8ff,27e26eb2,cd86df92,b9371203,8b332e73) ,S(e63add7a,e511eed6,93f62498,17f89221,c7a3a909,253faef9,23f37a64,9e2a2f67,c392df22,5ffa1438,c3d10c6f,813c3956,4f94367d,6fa26c63,1d562049,99a77e0a) ,S(f9955ec9,20fc68b6,cfcd163f,34bd033f,4ed7dc8c,30da7f16,e41adb,908c9b7b,4dfc49e4,ab583975,90bdfae8,56ce97af,91c92f60,a17df9fe,9ee923b9,9fe2cf14) ,S(d974d713,bce1db76,c5ea1143,b63ace02,5a2362ae,fe6b84b0,ebb0c49f,22341d7c,991181fa,3ae5f188,38a94047,9ea9e4dc,e8ff9366,78583189,bc340d2b,40481577) ,S(4f0af691,424d441c,698dfa3e,c3e56bea,e2c52fa3,bfd9ca45,763d7805,33a3037e,caac2486,81590630,b0c67160,89db929d,26a4e15e,b06aa9a5,2e19c92f,a9f9817e) ,S(ef6300a0,70060df2,3f9818c1,6ff4d315,fb1c7d4d,fef41e85,c96760d1,3cea49e7,a0622360,2def9738,d87803e8,6405bc00,88afa82e,39666246,10f5d935,993334fd) ,S(fef30954,1cd2a90e,1d473ae3,699ea7cc,ef69fe75,54f7d710,33b1f23,c9e96886,c2479c48,59423c87,5d76f6b1,5c671ed5,c9489af7,79266341,4ca68675,cab64fec) ,S(457cdf17,b1230409,c3d35a88,390f1bef,859994df,3ba21d2e,ba5f826b,6dcb4fc6,5aff71af,708863df,3074c236,446ddd33,5695c0c1,a45bc482,e0787788,a0e4ede3) ,S(a66e86f,fe0e9cfc,686ab0fa,11b641f4,28499f3,450d69a0,dbce1895,6181ea39,de0cb1e5,ca720556,7c6756ce,868df6b,5174887a,61afd354,653e759d,b3e3ec64) ,S(ddad5a09,c37f0de6,67eab59b,fa2cb47f,b79bf6f5,b8b0403b,f689acfa,627f1014,8aed1b91,c9e567b1,9806082c,79ec433e,1a152279,69df00bd,239fd8f3,f8e8d385) ,S(45c5156b,f1439eaf,16a43b39,5c0a393f,a674e17f,76f96d53,9aa6c99b,49042c42,c9bcc2ed,c5b5c8c4,b17d633c,90d45b9e,1583898e,41bb9d90,1d1b5097,57f5f516) ,S(c83b3c9b,564906dd,60049c3e,9f6ed0fa,b848366c,3b93650b,7923e9ab,8172a8d7,5709dd74,1326ab97,8853304c,a02315f1,1f0bed5e,bffab6f,467816b4,4c60a332) ,S(a857354,dd08dc83,ce7b0324,7594e4c6,99692c95,9a4887e5,344cd0a8,7970174e,becb7001,ddafd72f,1f845579,ca8d56d7,2145c8a9,be816924,957ba324,3c396691) ,S(8bba6b47,88259a19,578adb4b,6f7f51f8,d09eb70,ea790d62,abb2ed45,84f94f33,afa42da3,8526a485,60919f12,d30549e7,1d19608a,81f4cf6e,8e49cb00,2492b143) ,S(bb4d27eb,412e73ca,d2697d6c,46a143ca,e4420ec9,30440025,47aefb71,c99a53d0,9ec07a19,842a1e5c,9cf9f76b,55ad98d1,9485e683,b6b6700b,c905e190,bd9da19) ,S(af6f6827,d197688,f00dd3f5,ded1849c,11fc2abd,f90fc7f2,18b33776,e5753277,f9227693,c9405a2b,10e9b725,aac7ed35,eef4281b,ca04e,bd75b143,89323646) ,S(40453814,445cc67b,e7a4b71a,55e0b993,2b8b3477,f093df6b,f27f55a2,8bad2e1b,ec71d7d5,4e823687,d01d7558,6de9a1a3,7edc927f,e221941f,46051747,a69baab4) ,S(f35a6c29,bd596f0d,93cabc3d,c07b5f68,300f6ab,8ecde5d5,da8299d,112c7bcf,73fe2c46,e1b13112,718526f9,7a39f1f0,3d47ced1,84a2e4cf,1e32c168,1c470121) ,S(ecc7ce7e,bbe5da1a,596bf41c,4d19b51,b77f7019,bc431aba,e5ecea57,b095fa93,1ab89d03,9e7c6ddc,7751c9bc,4eb84ed1,b077cc8e,dc828ffa,37426609,e089c8aa) ,S(559820d6,bb3e47e,f68f48fe,1259da06,cd0b380,1f6bedb7,970c079b,7e373bd9,2373137a,a4d88574,151540cd,ab8cbdbc,5831fb7c,4b901c27,8c9a593,172a64e0) ,S(9c9b7e18,4e76bd16,856addae,9352590e,310d653d,809ec800,415f3c64,149be4a0,182cd167,55eedfc3,21d71199,7543b26b,d08047d7,c9363e23,20bb9516,da37a146) ,S(88e4e3d2,2cc3e6f6,19e62ffa,c7a4aff,63b16733,202e5410,52cedde6,9cda2733,ec6e32aa,498a7a30,e1c47136,5671d356,bf174630,d1b984ec,d9453e24,d275e067) ,S(7f2f8043,8e7d7fcf,593e337,a91b06ad,3ad1c461,fcee7bd5,82df516d,cb1c198f,2cb484f7,5a4472b3,230369f0,79f5e654,8dfdce60,98c4e561,a1310224,13dc1d80) ,S(fe0c5945,c5e67d74,ed498120,dae194cf,33a3fe5b,ef0f1ac,2c64c292,59827d7c,4ebff1a1,7d59c8c,469fad0c,79ef819a,8a897ce4,c0fa1121,741c03f6,cab0f659) ,S(ac0662e0,1be37c28,be457bc9,4af19e72,34a9d3e0,8667c009,ec58ee79,7e539642,b3adc375,bdc81a76,8385c9e7,2ecec61e,9b2b21d2,55f65450,c5956187,837f3767) ,S(15e0f7bc,d74e77a,af933c13,6cdc5b1a,1622de61,251090a8,f8509b05,d7dd527e,4d51a063,1fb81f2,fa1ef534,5fa306c1,a0c64f94,66961cc8,b574b06e,646767ea) ,S(e4119d0f,b79bd8c,e1687abd,4ad63790,814f9972,50fac9a4,f1b52d71,93ce282c,cabde097,8f9a566e,32ab229e,63bdfbd3,89f01378,c7d27b0b,f101cc3b,36bf3fe6) ,S(27a5b030,2005a21,5d89c0b3,4e4ee323,5e94742c,262a89b9,29e286c0,ab8e3c24,4548d58c,3792f7fb,18238cfc,993fdb26,f755379c,e0ed1b0,4df26132,8f987a02) ,S(a18ec59f,7621c8a0,59bcad5a,12d3f536,142d5c94,4c7a54d8,b9206132,d993e08,abd8204e,867035ac,8cde70cc,f7daa29b,d47b888e,1faa9be9,b20744e6,ec5a43a) ,S(9bcc19a6,71b787cb,9da72c91,8d7b2264,b9497ab6,313de85d,c3efbeaa,2f492219,4bea790f,67b8100b,9ad9a301,61e3bd9e,583daec8,b77f4628,568ed554,70894bbc) ,S(7ccb2731,cc3eb3a3,36d36af7,f44a0a64,e23aa0b1,12ba0e6a,11280c5e,1ab36205,8d60552,1813ede4,dcfcbe46,c75c5aef,7ec40c69,99cf301b,28b0e875,3031c6af) ,S(94107245,fa13427a,7d21f7c7,cfe0c4e3,2943821f,da0f77b4,23fde091,ba596939,89846c62,7868b1c7,4c546492,dd4821d0,cfe15fae,36896af4,547deea9,295ccf84) ,S(959bf7d3,989d3460,5f4b8f3c,cd12ed86,cd0a2a93,a8d4e1fa,aeb5d6bf,24f1115d,7cc703f3,5417d7b2,b7229626,558be68c,66a915fd,7cc52829,dc98c81e,c0162b7f) ,S(8e92173,ff2de4bd,f468e2cb,fbf6264c,5fff8f23,2fb57e1d,2a07ee75,3b45e7ac,2655133c,8833040e,4ef4c98c,e5c75818,be781f42,cc0b7314,7baa3ef7,99cc017d) ,S(4acbd2e6,98f349cc,42998c5c,53de7b6,3dc29b1,c2b8a569,48cd3489,190f0255,8837f8d4,15b3551,4544878e,1a71922a,ba4a0790,22c74b60,325c6f49,a411b978) ,S(f79cfd2e,b63f6be3,bf0f12d1,fea3524b,1188959a,425f5e38,fa569648,df433fce,9e412cf1,698805e2,a92114de,5694a925,17c31f49,ddca7e0d,b2d83d80,74d92b2b) ,S(41910c81,78f7a61d,7957c065,5d7e2596,a0e6d5e9,a0a9cf23,28f23569,5d818c76,26b318c7,e8a880ec,94c59a6b,d6f1cad,84031d0,e62ded95,1e265ba8,c3603367) ,S(5a864466,9fd276ac,ad8782d3,51bc27b4,9445835b,75f70a80,2ef42a0b,4885cfe3,b2510d98,60be4e66,edb8c935,3c8ff8d,2e008c37,6dd271b0,1f77276b,f3a5a48b) ,S(5e3974b8,1b87348e,e3ae5c83,2dc56d1,85004b16,90445b74,1b8e262b,ecfe0e01,63f644bc,397a1809,a4d57ba8,f18f0372,cd4fd083,1c3d3449,1ef2a654,46275568) ,S(154e9c88,589ff342,6fe2eb5e,dd6e1db,e253498b,2c0b3e0,52e84211,caf9cc4e,3a897093,df7d31c3,754f84c2,68b0594e,85cfd4a7,c2731fce,e01cc3bc,2bbc383e) ,S(b95aa134,e48967f1,bd3a7a48,d89d550e,3c3c3c6b,3c73de48,f2e6fba1,81c93faa,b6f2d3b8,8d0821b0,6b1134d7,ddc898fc,e84898fc,4719f8aa,e3570daf,168b03e8) ,S(316564c4,ff00502c,f159db79,62984516,4d6d24c9,1f20ba73,66669808,95e58b92,6110a6d5,39ddc,d4185b72,cc576b7d,a4577e80,3dd47a92,d4bf346d,ec5905f5) ,S(222b179c,29ff89ee,d6f2a0d2,d38c6246,33237c5f,7803d8c5,e4315f93,6a9bd225,8bddc333,6eeb3cee,a0c3ac01,e7caf4f2,f44a50f2,587e3e31,7046c85b,a57cb6f4) ,S(10347fab,33fb4ee5,6cbf75ac,6cb768dd,f51f9b0c,5498466a,6679439a,32048904,a351f45e,30f32caf,e10d99f6,9e9e4be,c3f4aa22,5388984,bc45bb78,c0c5148e) ,S(7048c0f3,1e600042,4544e9f6,e26783d7,baeb411b,a2c29c7a,5aed8953,bf831629,4683ad69,1d9f14a3,f67131bc,55d28c61,1b78b2aa,329668fa,8fc41736,c95840f7) ,S(a65f7371,b35de05a,78b71171,40ea9e02,7b777785,13fdcc3b,484ad9a0,4bcfa1a3,41d1268a,77b31744,5a270f73,956bbcfa,3f291770,d248d1e3,364b4aba,72b961c6) ,S(dfa35552,8518d1da,ee31f04a,2673d053,11db4eee,cdc81f15,bce79c64,3267a315,19ed047b,4fa52430,18863cd1,d8ade0d7,dad60ecf,10b767ab,52f5cef5,9eea9a8a) ,S(663ec2a0,80564f1f,943a25b7,2f60d3a4,17b62130,3015e17c,85782460,c601a48d,fce25852,5a4dbb52,4057f8fb,a4393116,ebcffea5,5ae3459d,3d8b19b6,a0387232) ,S(cc714eaf,26f9960a,b2cb139b,d2fa0928,7a309c9b,ea852537,e10b6333,2912431a,c1c5c0c,48c98ea9,b57eb13c,fa64146e,67a95569,b45b8643,7752b037,9269d070) ,S(a6ceed6a,bb8f1ac6,13799527,38a19b35,ece44537,e74e9185,a4ce3939,c14f8e77,c0090ebe,d410f2e0,2e56b4b6,adfd5495,488c2930,2c5e7a61,3926880a,88beedae) ,S(e0b0c34c,8d4f77f1,dd09ea34,8b0ec683,cb5ca777,6720546e,27ffcf55,a5e5bded,ed4adb20,ab5da65c,2d1d5d68,9ad63ebd,90170904,65f7ad03,1bf3d811,f407d09f) ,S(2362ff0b,9a2d0f7f,d779a83,8b26da93,65730d32,bc4411ef,fc4fd182,d9e486a6,d3eb4ee4,42bd6157,557e4e9a,dcc9c103,892ca05f,5c5af804,f736ecee,d8a6fc3e) ,S(2f1636ab,a1516634,a00a464b,aa30c507,af25e83,3f7f6fdd,ccf0706e,d5fb57a0,a664c955,c24a54ee,d56f1aaf,fc853c2f,6a81c53f,1ee36c48,46b26452,fcbcc054) ,S(243a8fff,6230829c,73368eed,fb4d62f5,bf478b4f,1752400a,91ac177f,70c303ac,29318b21,9f371dfe,4048c4b1,2f5317cc,b2e9c44f,ed72b537,a2f56d06,65229235) ,S(b17182a8,5f442a65,839230ca,5cc8f67e,835e54b,e0296c6d,e2b62298,74ae804e,11a4fbcb,9f6f8775,9d131a81,939e0125,7f7b4fca,e36ea644,4da3cc16,a161e5aa) ,S(5c9abfd1,9cae1a47,bebdd324,d11cf758,a1224471,6e83795,e42ff5f5,a8142a6f,38a38db6,f64d9d07,4a08a909,28768bdd,adbdd858,79ec847d,28c94dd3,a122e0d) ,S(44a8a4f2,ec3dd02c,226ae0af,d73a12b9,726e03c3,2a41099e,b70cdce2,767e390c,b7e18dd1,e6adcd88,1d1dbead,e1c83ed0,1f1d7b2e,50246539,b6bc2811,d63233b7) ,S(8e477766,c4de01c2,5cc17218,7f3cb6f0,dbc8eb54,fa888911,33131b7c,219e6e13,ba8f447f,10286c86,d1330c82,2647a999,b4b60e56,4131986,a6c05128,a480d83) 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,S(33d9f9f6,c9ba653b,f9c52166,c29e9c06,2cb7700d,ea2f40cd,28520bf,237b4558,dc80f57c,fc0e73ab,bdfc4a8f,f7e8f4c0,3353e889,bd54cf84,6361c1a9,af5a0a79) ,S(e4ca84fe,307c9237,4d39b2bb,b017b5b9,e478b26b,95236b8d,5bdfb220,f44419d,c0cfc7d8,92271c95,7ef235f7,2f310c7c,7d0ac297,97d42ffc,ba37061c,83775507) ,S(8f1f2d2d,cccb07a2,a8716b77,8c74f3fe,22990d36,b951e6dd,92f5896f,51bc23aa,9eaa792b,426d3400,31a862ca,b805d0da,ed9a4c73,591c204f,c5179b17,22aef870) ,S(20f7f6da,86eb5ae6,6a1b7818,43fd7fe4,c458e3e7,bfb590c8,76afb601,257b2ee0,6dfcd6c3,93e7e9dd,32c7e826,42f90d69,ff1e1ffe,18988de2,bc1cb9ba,db246fbc) ,S(3a3df365,8d65d718,2dc05797,8bc48fe1,5c5eb6d8,6bb241e5,9e178ca3,9cf9a010,ffb89791,7435e8c5,4865bc79,52fb7bd4,1578af51,6f611c54,1f7cfd5,651b293) ,S(7aa435,7dbbc5b9,a01b5f94,6b0240a1,36daa942,1ae1a1c9,b50f66c1,c7f15e48,4640c8d1,ace8f69,6b08ba1f,9a46d04c,f75c5914,3339d5a,181a7dfd,bfc92c0f) ,S(198e4848,8176664d,40fc14c7,acca9eb9,aa22599b,b2370959,5856d78b,5e932e94,fb9dcfdf,b27d062e,8ea5246,275d80e5,6fc7cb09,e81bf066,dfca888a,8df1de6e) ,S(25da8876,d3215051,75694915,c25056e1,2c1329b7,7795b7ec,1d4b66f9,3c911cc9,b8cf4a83,db78787a,6d80a157,c7c205f1,3664a71d,a6e78db5,b52b012b,930c4583) ,S(893d2e9c,3b6fa8e2,136994e6,14121842,bb82e577,89826ccb,eef51fab,de32c0b,d7cb9b4a,1d49b34b,f3f743f2,10c32a25,cf8df45d,8552a7f2,1268e270,ee6fed67) ,S(dde2e8a2,988fd777,4959457a,5c14384f,c8248d1b,a32c7ce1,a727af27,7b217688,1fe0272,137e4c9b,1c6df618,41a240a7,be3b5de1,7b93fa24,ccc055f0,e7972b1) ,S(52a73b51,5326198c,81bd988a,3033e1db,abd9ee27,9a91a434,e7a76813,453e27c1,c23130f,c4b8990f,ee308443,1cbeff25,62963b1a,4a5acb4b,a1319b4e,d77c745b) ,S(1b5afdc6,4598bfee,4ef31904,f0d06796,17b0149d,ac19e7ef,a1d4f19b,c5385490,fcc0c62,47d96d4e,430ae0e9,c19dfa2a,3719e66c,ce25a2cf,d7428d4,4c91e96e) 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,S(c2ad6b2d,e84bf60,7fe77b8f,a9fe26ff,bb5e1906,1494e469,8da44a33,25843844,17b92ad9,d3938fef,7a17f543,a169a7ad,8ee65dce,36eeedfb,5e3c0c8e,a1b24fc3) ,S(a53504f,e2286269,427fd2fc,fcb64827,bdefdfd9,feb89d50,12651d2d,c60ae99e,6b9d73e7,e046d11d,ce78b114,8aea837f,770d8267,6642dac8,f3b3c035,c10eab45) ,S(5410db61,40a77b31,9f19c969,34a8364a,4881ab60,ad76a6c9,34f317c1,1b658dec,ac45bb6e,2e5fe23d,57297370,cd04ffdd,dd89a9,15a1e9ad,15d7f9e7,6d8b3aeb) ,S(882cbd69,fbd3e262,5093385e,ab82fc9e,7597c38e,45fa5df7,f98c94a9,3bf25467,2083f00,b25b28b7,f92b040d,a4294dc0,8a3d97e3,d951e724,da0e692a,5737a87a) ,S(3141e0d1,22b4c136,f7793c73,9c48f308,c5ec8043,19db116d,64eb14f5,aee83942,9c2d06cc,d765c6c3,cee09b70,247f8806,227d0178,13becbb6,96c5a344,b68b33b1) ,S(1b2f3686,5a63df41,65caea4e,305d8d66,1de6ccc1,c2a28cf5,2373527e,27cecfc,1239d8c8,d60fdcb9,fcf3f5d4,63305037,6d47fd97,4cd6bc64,99e0e951,2d2209a9) ,S(725168cd,9fd59e41,14918b77,6ea96fc9,6315b4f0,86672dac,1eaf59a5,e61ed25f,946f03a9,84a6735d,e72acb38,dfd21905,fa2358a5,e66e7b0a,2f8836a1,8f5d73c3) ,S(4207faa5,c9dc9622,9644df1b,a099a84d,654ec6d2,aa69efcd,a4a31a3c,61f2e1d4,ea72a92,836d1597,5275c18a,900c0e7d,d0502610,d97b6f79,1f6a28c2,1b3ddfd7) ,S(53900d38,a4740830,a6129a11,9dc90f6d,30f32847,708d48d4,20b77764,ff5b9cc7,66822ed6,ed941eb2,20aefe94,4325daa7,a619dfed,5c76bf75,1fc25342,8178d3fa) ,S(d0204932,a3fb8d33,9779851c,d69f6adf,be1a9957,59fcfce1,b8d4f047,e4e4dd2,8ded18ff,bbfc663a,9c658ae9,286f82e0,9ee9381b,3291f5c9,efabf0d5,fae318f) ,S(3ed8ce15,2d34e621,94b8b16d,55605766,41fb2673,14a08c91,d916fa14,f21abde5,48490fe3,9769c60e,38996370,27b57df7,230060c,2505f414,5a1c7f1,4ba16660) ,S(b7d57614,9b5e2ce5,edef3c30,b8cce79e,6f122c70,351d04fc,ed2b67c7,f5cb2aed,7c8fc1c6,bd42b25d,d45e37c2,5cb06f0a,bd2f7051,4a50e6e1,2a67c0b5,b199eda1) 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,S(68a89a2,62015a57,5f882215,48c6d3a7,b4ad1f92,f5665980,367107a9,f4cc37a,43ea7b7a,79397dea,c8354436,d53e7731,c94773d1,5b067063,b108c559,c05bc46f) ,S(fa6e2972,87a0e97c,35454378,4a76fb0b,56106727,136474d8,a3edf8b4,e03f95f4,1e80751f,9c127fff,ce28ae,8ce5afe2,eea1c566,fb0a9f20,8030cc96,e1197725) ,S(25474cb7,805d22f8,7a641116,34628321,f086d1a0,40404c47,ebee913c,e9e02a6,2b3aac5c,85ce9672,61757c61,d6a72dd,4ff81e00,87f0b8a4,999b927c,7b069609) ,S(6f7051ef,10fc1485,a9c80ae0,8683397d,c0af15b5,f78fec70,fe4c456f,f33b6689,625086ce,ab7a9173,d9c370c4,c336c63d,2aa85ac7,b8391993,7ffe4118,f6a7b849) ,S(f4720462,2f579de0,701f1e90,558c74b4,ab634664,197c03ed,a85b0fe4,50df4951,c66a490f,f9b588c9,2d17b80f,7f66e5fc,a65187b6,d965e81b,c16039f4,477fdb54) ,S(3b718764,7e722fa3,de42fca9,e3ba181e,de982728,5b8b006b,d51a58e5,ed898c8,bf872047,f3cd3ea,d7a439b,9d4f7776,7175f940,d6cae8fc,930aece7,e1b92202) 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,S(63a09087,e237e0c9,686f2a79,af977ba7,26d77118,29c8ed91,4f99dc43,90c64d08,7771ce4,a5e7d43f,e12b5e8b,c819506d,3b85f52c,fdb0f9c2,92c22bad,790d3b93) ,S(77640a42,4ebd84f7,71734050,7ba400cb,9e8462a6,a91fd0a0,b8f152a5,f5f7868b,516688cc,f422e660,15afa46,b5889331,3cf2d622,d6c829b5,f1d11386,bce41640) ,S(963ae02d,62739bbf,e75965f3,d1b7786d,c3dc6fc,5667aebb,5544db3,157f8a17,b3a109d1,b56570cf,2a5e5056,fd9feb05,2e8f53c4,f2ced1a5,27c3311d,87ba9dfb) ,S(81324144,454cb304,36f365d1,c78ea5f8,9a73706,acc49d5f,125fa282,c28ebad5,77a71aa5,54c0da45,31ed307c,c7fdad32,ab82a4b7,2f2a5154,cc405a2a,fddd3cc3) ,S(eadb105,e80bf2d7,cba9b468,6f6b88ad,34008c85,a7ac4d53,d3fff09d,dcd566b4,199ebce5,872f9dd7,6c14821,622fd343,2b7b6437,3484fe84,714b137e,fa782bee) ,S(a030450b,52b387b3,35cfe8ec,683fe625,884ad73e,2fc1c728,c8d9629e,dd2024ed,895545be,a9009f2c,dcb20441,33f2fad7,ac704ab4,9435fffe,b92836f5,57a114fd) ,S(57e8022d,816255a5,f4d577dd,867d65bc,7d7fdfe9,ed8f993e,d9b30531,fa36888b,9b0b7929,3cef66be,c21b6fca,140e6fe7,9b9f2e8d,48555338,868b6c78,d300233b) ,S(74c14e1a,d52761b1,7206b61f,fdff526,f7008f94,b3707a5d,e5c2a600,97b0dd29,18778822,89711679,c5e41fb0,41b1a806,9b12b709,b526ca1c,44839d5e,3b51e72f) ,S(5a9ce7b6,6368077a,73c09869,38656705,c017faa9,2d9cd40c,69d8e57e,63f8e229,f716b144,cebe2907,928f4618,821af2fc,9de249c9,5ac61bd5,99a550d5,e97363d0) ,S(f0fe4fd9,99c66687,3ab4c904,b9b7c0d2,7f033a0c,7e6c1b6b,4488097b,cdb49fdd,1f4643f0,6f700657,90aa51b5,911b4866,c286128e,de489dc2,8e2d6b64,972738e9) ,S(e86c729d,19347238,a9e97433,355530c8,7b701aa7,d710d26e,6b15ebe7,4796857c,d6260d35,466dbe3f,58d2aab2,1c8d76df,18271247,9715bacb,2a76bb95,5b75730d) ,S(b4e3a39c,8fcb0dc,5a23610b,bbb564a6,765c0135,1a8b666e,d680291f,c97df351,3f1eef0a,7a235130,b5236a2f,f8c9d2a5,fe5f1cbe,22326ba0,54557513,82ec651d) ,S(a9c8482d,a54adc98,4db2d7ac,8fac659b,51c1237,eaf1d524,9bcfcf1c,4ae601b5,446ec925,fc148900,8ef10348,ee167a63,a10686f0,7a01772c,10f7592a,2a544a9) ,S(17adc7b2,c36b1ff9,ea40b398,53246d71,bb973bd8,b469f7dd,fce49aa5,e77b8c06,fc3111a3,8dfc5219,7f41ea77,1682bd8,618f9825,bb2f842f,c7de15bb,224bf573) ,S(328e9a6c,e7397c45,617aefee,130cb6a1,dd26e727,efcfc30c,3d8f415c,187d23b5,6320e80f,e4a57574,1fed0624,c0f956f1,d5b30914,b5da88d5,f63e17e5,64f8b927) ,S(22188680,f765065c,360c52d2,851f3081,b2d3eb5,4201dad0,60b536bb,a45a1a41,b1107c8d,430df246,3b3e91fd,904883b5,cb877b,c10b6f,397a0cf1,c4b6eb35) ,S(620f5772,5919db4d,53b8f89c,5669fc6a,5a3f3846,c31faee1,1e93e53f,b1d20bc7,7d739bc7,4becbd29,2784be81,294185fe,db047d4c,c16c764b,678f9d00,6d27feb7) ,S(49b1228b,b624c71b,2c23e334,b098e84e,d3d8fca0,56303057,49dd39bf,5296666c,3f316e5e,ca9c1aa1,fd5d23a2,613e756f,8ac5e819,8ac16650,a9dff05a,1c8d76d7) ,S(97ca98cb,fedaeddd,b13b86cc,4b6bd7d2,140fde57,dae7b847,c51b118e,e3d6b8c5,1b95c9f,1d6c808f,397c3ec2,a2a2b220,6fdf546e,8c70ac2a,78086ad5,ebe28142) ,S(a679e7e7,3df904aa,e80270b4,d5d57dfe,f5ae819,f240369,b773fa3c,609a1ed0,93201a4b,17286928,be5fdfef,473565be,879cad73,24124c6d,6e1614b5,4e6e5124) ,S(fe17af2f,70887958,1b9b176,4d45d76a,afac0afc,ff50ac8d,9179e53a,c5e3777f,f59728d8,67c3ab63,6d387352,a029b5d2,e9f2d531,7a508894,9a0f6515,f5c4d61f) ,S(f7601ed6,fd64cf22,57cc15e8,e554dc8a,e19e4f4d,ad3fb3ea,a7e819f1,98b3946b,a3292ed3,ff088c22,e9a62b85,4ec87dbf,394cd681,501184c0,b841656b,def0fa3) ,S(3dec302f,cad72c11,54c6b588,ad7f77b2,9368557e,77a723ba,6dcf9357,82d9d917,6484365f,537611ff,49f157f8,6c4bbf07,25094f7f,d8db9a2c,b318ab4e,632cbfce) ,S(a847783e,46ccf334,d7b15f1e,d3aa7dd8,c5b3ef4a,7ced2501,c26d1dd9,4358adbd,7c56f1f3,323a500a,a3496729,ace84a91,6bc6dddf,90435a09,8ca51f6f,5fe5fa99) 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,S(b143029e,7f32bd1b,a381fe82,8da79713,b53550e,f3cf867,4ef1e952,d4dff9d,a44a622f,ff5fb466,83b69803,c6ea5c16,8d86c673,3ed94058,81aff0a,2a8edfd2) ,S(4c54d53f,cefac583,6fcf3b87,7202afc4,ccd68695,567c7fe7,6068546f,aa9070d,7f42728d,78193fd5,946f3787,6ab124f9,b1045ae7,45df58bc,cab6f59f,a27c6f18) ,S(6b625111,556e3ff5,db9cd8f3,7f610b3d,718220b,e459f546,47314b04,b2ba9d6e,b3ae66ca,fc58bb7,5a057767,8bf806b2,c204b90a,fd114ae8,4ed51378,53b30a78) ,S(b3fb12d6,e16e4279,5fcdc1ee,23d42f9c,198debdd,56217af,5b76989a,271b473f,d38adb77,4ce1d0b5,e41b65c,7c973a27,10c5621f,594e6f70,d235f5e,a4a89386) ,S(9c7c908,6976b590,ba9c80a5,fe12c5f5,ce6bbdb3,5a4058a,3cc59899,82073ae4,399687af,4d3e221f,6168ded6,31644c35,e41606e,94583429,34693221,9322da67) ,S(28cdf6d0,f0374a35,4dd169a9,1c3beef,fc88dea0,4922f841,401ffe91,8bfbddb2,2b8f1d3a,6f001d60,95aab0d9,d6248cef,cf3b97a4,850d1a43,ad2bbb3e,d2ea4518) 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,S(2350eca0,b4d0c460,12024be,6d458444,b37b20cb,50042830,182b5e41,d564e26b,5909eee2,e3999d60,4cbe0832,58012001,30a344c5,f72ff127,35e66cdd,904623d7) ,S(ea660cfc,45971e57,852d382a,ae8cc6b,1887fe68,dc1b84bf,31f4409,89f89b2d,52297e86,dfec0730,81a280f,9451623f,9e69c320,6f3c205a,f07e56a2,54cd5837) ,S(9cded450,2a7da3bb,77e06ae3,ef398954,7687d21e,df522f3a,cb6b4fd9,d3d49beb,7b13f455,35a49049,277abc34,3cc6f0a,336242e8,7b69815a,e27122e1,d7838a8) ,S(ac8705f2,cf8dcd77,d409a962,f98a6abf,198dd238,3a5eb258,6b0d2def,81daa172,892fa835,a0af6cf9,dd5bf158,44b22cf8,2af258c0,519955dc,ee4966c7,bd5e995c) ,S(fa026b1b,d5e5fe3c,d6b144bc,6b22f7e7,5512ca6c,9525f62,fc7fb4ea,bcd2282c,4ec40de5,7ffc1768,edb20cae,d3a11380,fcc32f45,f410ad9b,8b674d95,6614aad0) ,S(a928eb73,28285c79,5717dc0b,ccb5280f,92f9a4be,5a0b0ed7,67e58eaa,8b9097db,af57cb66,61a9d08f,4d4e9e25,aeeea2dd,e4c88767,c4e177b,37a87ba4,c2bb772e) 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,S(dc65c06,50cc30e4,d759fa93,d4d0ab65,5cb16591,289206d8,7a988290,20c22f9e,be39ae0e,a41a81d0,2175dfd5,5e004e19,fa925a99,2166d862,296899e,2532b6a6) ,S(f659d02f,f2d4bc82,9f816525,24019a88,6ad539da,3f38b083,5d8265cc,bf3a67ed,bc9c7a81,9036c702,338c57ef,26134647,2a22b8cc,5543f4b4,4a4f7d4d,d4339573) ,S(b89bbc05,420a8a65,aa03441e,da1c54da,9ca84f11,e85a393d,47cc54b9,78b8e5c0,5f3a2fba,4cef4457,ca6befe2,7dd3f9af,a5d8b6de,86679eb4,c877c7b4,cf03c08f) ,S(b9bbb789,690b53e6,e42266bb,853cfbbb,f6788b58,b325097,a55470e3,d4cbc3cb,1f984f38,78427212,cbfc8a93,8c1f0d87,59792ca7,17635c75,71b2c4f1,29e35c2e) ,S(d8ae91cf,8a99ef6d,2ca0c15e,3132974,33cd46cc,55a2c8f3,9f909e96,7d50006c,4fe4696a,79d2f269,9fecfce8,8375cc1,81c2c2e5,4109f380,3377a020,5496d733) ,S(35dc2c70,181aea7b,ccf6a15d,1f708c87,cc8bc5af,93671c97,35867367,549357bf,6f27dad,a9abbe5e,5e59141b,78a2e6dc,5b5433ef,dc8c9cde,a6269c2a,68346f87) 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,S(9df72bbf,fbcdc42e,adb71d69,1791f073,7f945e8,bfbf4e2c,68c5e3f6,5f6955f,24d47aa0,1626b0ac,ce77827,fd7daff,7424d4c7,1d76ad3e,b66d22b2,6f7d1df9) ,S(2df6ef96,7c0e1a41,2bb48bdb,f2cdf8f4,22829abb,4b7a42e,95bd9cbe,8b7f860f,bace2e70,7915069a,bdecd097,9d133cad,bcfedbaa,7eb9891e,ad3380e,9ca99401) ,S(82bf2a99,624e408,188da19,59599de0,eb947438,fcd45784,9a731a1c,15796028,3b6c668a,e5b8f394,3ee713c,a8fbfde5,8ef0f9fd,84054a9d,b626e274,37e611aa) ,S(60260fff,1f213916,9261edeb,5f1d2d0c,a143ca69,400b2776,21793c11,fbc89d41,bec4bfeb,9d09f8d5,cdb11e3c,f65c6a7f,d4aa87f4,e41d7f4,69717a64,5dcf9945) ,S(6391ed61,80cc46fc,33481faf,d21151f3,cb678e3f,4d667748,1a24a01a,c5e9180,c48495fb,fa5962b,44bfbc4f,491b89a6,a8588fe,91677b19,b872dea8,8e34026c) ,S(20807816,758361aa,d5f62d25,8e3951c6,da518890,26507a7b,c0ceb7f6,a96c141c,8526d53b,61c8427b,eb141d91,7a338fe9,f7789a60,cc1a4a62,15dc754d,a73903a9) ,S(1ecceb4f,8acc649a,dbff29c0,fbc62c11,498c7cb3,7d29ed15,e0ebdf03,e994b67d,1c701af7,a9f3d870,81efb798,2382bed6,5d56b8d3,f050bfdf,6da32b10,a18fd4d4) ,S(be82742,dcafe3ca,f646cf01,80202cb4,7086e0f8,ccea3c11,dcccd9de,aeae688d,236d1fd2,5e05d6ab,8651d88e,33d18a3b,caa66c06,b2b68c50,f6158717,f23b4866) ,S(15252ce2,3f666836,dfb47b60,1e642abf,6e56ff2b,5d58fc97,ab09f29e,1b4ec3a9,9a6b2658,f52dfc45,32e6b482,fe909e47,ba7b4442,3be4d474,a524df32,d6149913) ,S(b0429186,21f94599,f7032b4c,1b53bc6a,9259f142,27922f42,fe774772,4b0ee9e7,e73c32d9,ede68eab,e77d681,dd4cbd9e,a356fdf3,bf066f33,6ff2c367,59bed08b) ,S(5fe0917c,1bca66f6,f34bdf1f,dad88a5,b3dc5f5e,2e0227e6,5f3a79c8,9e66c888,885dfcee,c0947b01,71dbaf65,52c09ab4,c0414f8c,7373ec5,e3080521,401ed575) ,S(455985e6,44d9b679,85980752,a13a3f94,94bf9cc,8e6f10ba,fc7a70c2,27ce272c,47eadad3,15e88a99,9d3f5ce7,792ebc10,2fc68f18,cdfa1df,564601f6,3b26c22b) ,S(3562aca3,2291c1cc,ed072a4a,85fbf82f,6b3299f5,2626154,2b41840a,1c868d4,ab4b2656,11db5875,10c48284,7f72c75e,f822f46c,2e7760e2,a46070eb,5db7100c) ,S(54225801,f82406ae,74416373,7408e94d,d3990eb0,60581c47,b453a859,cf63042c,43834935,a6a7acb4,9c086391,24e80fde,72c0a876,1c13a340,1a4e48a5,d96f6a2e) ,S(3c253039,fc8278b2,8135e21,700af1e4,dad4263e,ddc867cf,a3532499,c2c1e48e,ee01ce7c,f8c56c74,1b4b3593,b0cb90a5,9c59cbe6,9a48235d,1295c1d1,ac657081) ,S(8adead1,d898eca7,9e043f71,aa735a32,763f75f6,f6ba7a70,bc47a284,4b580972,7a370bda,412df63d,5590b3da,80365c71,1267cf8c,e3fdd1bb,91ddb981,d213bcd) ,S(8361e522,34c8d62b,9051a95,8af3f090,4f15ee35,4b69a560,7155ea4f,69548037,ca2c329f,8cb65e8a,eb6488f2,2131c525,29df97bf,c8847c87,47145767,7f82c954) ,S(97d65162,d96feb36,e8f00221,52c92c06,2e97087c,703a9dd7,7241216,2262807,15a260bd,bd591c7b,91bdcbb4,c2684545,4706f039,8fef8de,9173e7fc,a3f31f44) 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,S(2ca9e4d8,3358ea8a,40bc15b7,8c06169d,ed7a5abd,47147972,45078e94,75264d20,f3324029,9fe328b7,ecd14a11,6fd82bf6,5d925532,85a176a9,b7ec892c,ebb2cd94) ,S(e0db4052,8e3eafca,1f514b26,8b673afd,277c5aa9,e2dbe85a,74478d6a,f2ec1f94,f868c782,40dd75ba,3c6809d2,d62f80f1,ab7fead3,c67a90d4,ecc242c1,687376a7) ,S(d34cd3a5,764d99f3,16a260c,9659955,fda3cd9c,cb305f73,d3aaa61,27d422f3,3f3b80ef,74bec102,2e442e69,8fd4e28e,514d3a9,5011ba18,1299793b,b760da72) ,S(588dadd0,79d2280f,37dbeb16,3e05a70f,48ec61c7,cf3e6455,f3ea312d,4ab2e075,731a5c9d,f803c2fd,b22de461,d51af493,5874b745,4ab8417a,940383b2,9404fa3d) ,S(1731c955,931905d1,ccad3bc6,133f5d9c,9fbb10c5,e800be80,643ed02d,6d7477b1,d7e89b3,1f18ac07,6c7b7380,64d2449d,2d9beac,728ffa8f,6d8a7498,d43baf1d) ,S(e2f990d7,6818c0c6,e73d066d,5644e9e9,29f495ef,507b18cc,594871a5,88e45b46,2ca12307,fb565d0,7c60b6c3,e92c9757,45777970,1733c0ad,2b299a20,8f50925) 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,S(c2a6369e,e2857d2e,fce4ab31,49556c08,3ac6af90,6be418e5,ddc5677c,f2f7ec8d,a7097ae2,9fea3774,11ce3f81,b6b3356c,9a2abb69,986ad81f,46b13f8e,a0e7f0a1) ,S(f5eac1a2,3dc91862,d8022931,3be5c7a5,364c0880,23c0650e,53e22f42,2f91ec98,7dd62b80,3ad606c3,3d8d9bd6,cb397ab8,1cbd688f,8375a405,23bb7315,a3f48c24) ,S(dd94fec9,3bf7ec6f,cfa0ced9,df31a1c,131c39d7,e110b5e7,b988c59c,dd594fec,cb858565,6a32e03e,2eb84732,4bdfe2e6,3601148f,7bc7e56d,22cf9aa4,54f063f4) ,S(d3dfdaab,8f9db2d8,edd3db27,d96be5d0,678e9088,5448222c,5b3171da,38fbd501,6b210554,df32021f,35170e13,42e2da18,72be61e9,481a4b74,ec470ed0,b942025c) ,S(47ff9918,3e452838,f63eb828,a239d95b,62f8a746,8acd0b43,6c149985,2afbe3f9,33b7b8a3,a5b51b15,fadc1f9,baec6b8a,88e0da56,5a54bea6,1b2d728f,eabbdc48) ,S(1e99e92b,aae56401,1cc10c94,dac071a9,27565a17,2d6d4a20,224e1b49,c007660,914b98dd,a92484e5,a43d7de4,7bbf57cb,2346d852,f743fdd9,15dcedca,4393aa21) 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,S(66a82c47,e756062f,6586ece,86911ac2,23b84c9a,e53e5307,4e22bfbd,3eae6b30,ab2051c,4c231a40,c6da6ac3,5ee32b9,b7eeea17,222cb1d5,a3abf9b6,512db8ec) ,S(974ce35a,9d5a4ef5,84d252dc,3c365423,1335c52a,e3daefa2,8ff9b75,56bf3b46,8c82a9a9,c49d167,4f3995c2,90ae06ac,fa0a5c14,b1c5f41e,c1e449d9,5effb2c0) ,S(1139c2f3,60cb8a4c,e020bb8c,3d19bce2,1c6802e8,5fb3df33,8fc9ffbc,8fc231b6,59adaa14,7980b3e4,73801b73,9f1e0248,2e9f1e17,65df2ec0,183d9f81,d57723d6) ,S(c1bd3793,3b03d95a,b17c10bf,c5167556,4294e38c,740fa3ef,9b356be6,71883b94,c68bd82f,5e926a59,95a83f1f,1a8c2f4,5966b073,91ee74a5,ae2ed99,106c6dca) ,S(c7778ce7,ce668003,86db9263,cddcf608,aff769e4,b4755858,20554ecc,8407bbf2,92509200,9c57f224,8f9b4e71,532c698c,88b91b77,4a3907ae,1ef30c51,78d807c3) ,S(14aa1177,51626b67,8f32418f,1855cc34,52d4ec13,d2d900d8,8a22432c,70ec022b,6151fdf4,f4372a2f,e803478c,da340678,c18a0a7c,d540b0bb,4168f9da,2edd6d81) 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,S(b9f80abf,ab86d596,521bf2d9,cf500e15,adedade8,b51fd8fe,c1d8de53,f4191222,82548186,bb97991f,1f28a93,804cd0a6,378355b,f7c7ed41,4cd585ed,af0afdab) ,S(1ab67bc1,50fcd943,f0b3419f,e5de2969,fb4428a0,b90981d1,a3893c6,18aeeae9,56fb8eb4,4671006a,805e161e,6e3f2bb6,b0199659,667967cd,3c72ba65,97a2c39c) ,S(17425974,39a91dd3,72c09b53,68d9821b,2acba5bf,a5440118,ddb5c494,fa0a807c,1b73d3d8,5eaad3c9,b37f7451,2a7ddd17,97e10e71,b640a820,181757a7,6cd27cba) ,S(72b080f4,d8e812fe,b485361b,59213f59,cd708e6f,d2f7ee71,27af3d87,971633a9,5b9c6a0f,d7a6f32e,f26a4584,542c15fd,e3504935,baa7b48a,d67848b9,67229f32) ,S(94e5f999,b8927b65,a2f4d318,8e3f2fee,229e42b9,ae3e6b46,9f7ea373,d3f11beb,aa27336,204738d3,b2a306d0,4c6efad0,2ae3a431,1da988f2,c6c1decd,b1fb3c92) ,S(2f59f652,2f045980,833c45cf,ef8f3a37,d65ed946,9b3beaac,2167eff8,142e8a03,9101d9d0,60f1a770,9f604eae,4b4243c4,6096c041,2f861106,dc4b8d1a,d9f9b170) ,S(95a443a7,22a88b70,32194130,a349a952,67b89786,e33938c9,7bef7fdb,d211b54d,3d80619,399c0975,a67ea7b8,9a5f6427,ac454278,42f54932,cbf71711,3ae460e7) ,S(c8430fa0,2ce95d35,96eef42c,69f68502,100a29c3,6ddd1f46,daca1e14,4f382d0c,f26c4baa,4a6d9711,e6de2b92,5042c6e3,cadfe60b,93d4f385,d759ec72,5a32bc21) ,S(67504cc3,ffaedcd0,c5a2704f,af1aa41b,4cf489d3,5c23b6d1,4529f4f5,c49afa03,b3858859,b3749792,4d01676c,d96fc03b,37be7b82,aee57e64,a44ba433,2fd936c0) ,S(d4fd8a19,6a56052f,71e8d51,ee3db667,7465ea90,f8449939,be9d1814,86fdb56f,7fc64dee,2bf744a5,ba155865,fb722e11,f3087010,b566182e,8a39f718,922953dc) ,S(12810eca,7f3087,944d3dd2,69baabcd,491113de,99b36ed0,65520569,484fa7ad,f25d02ff,81ed030f,1e67e002,6680a3df,3f27edd7,76155966,6f043f85,f82c9e4a) ,S(b347e0a4,102d2954,cf3ebf6b,7c0e5f88,6a823cb4,c134897e,3169b081,8bd35f4,78494910,3eaf28be,b2d9732,f88dc9a4,66a8b5fd,cc50a2b2,8b347436,2e05cc93) ,S(54cf5638,7972ba75,48dcd07f,1bcc47eb,5d99c95c,a18de15e,9d2ac40f,1435b27,48558294,410d7ed9,9fb008c2,32cc6ae5,33bffa9f,3f02f0a,76b1f390,9e78e507) ,S(e75c0831,ab9569f6,4844f67c,3650f691,e1f84366,46a28613,653c354a,3107cdb,5e2da0f6,83cf019a,82e44f84,e7bde49c,5d477f34,fcbfc3dc,2a9a2a4e,3ead0a1a) ,S(f9eb5462,7d88b64,5899b177,99257d92,4570b3fa,59fca83e,1e302f38,5c524693,dd187873,9fe69020,970609f8,ca1ff56c,3aeac075,43e6cc5b,bcf75af0,2932d516) ,S(8890093c,5bbdd22d,69c91acc,5608e19b,59d2b105,b75e054c,8e873b88,59865997,1f18b0bd,e9b546a,9a2955ad,492290c1,a041b61c,7b534e1a,bcd4db3,b5148bee) ,S(76b95d04,88c9bb7d,2cb28589,f7f3f9a,e2ae24a8,33adf557,76bc3132,4bb80168,590b3022,81649af7,bb2cb0cf,fa0e90ee,13b97294,1a7a8748,bc9ce53,88744e53) ,S(8b3526c5,afd2a987,f8a04949,bb5695da,8b073b93,d8418878,28f9d49,2a6ff4f7,387954e7,60f2ce55,17213bf9,c987a9e7,f9b9b05e,c4677911,22e7a28e,777ab4f4) 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,S(94d45ebc,ce92d10a,3294114d,743db35a,8e2ddb7b,7f5bee72,7d093c89,15d98d45,802386db,bd731bbc,5dc793e4,88fcf20d,15be9024,b94d1d19,edf99ea5,ab1c0acd) ,S(46739c9f,6245639b,692a68bb,8587499c,43184d0c,f0ff467,7b264985,b4a2fb62,9f8f41d7,2eb951ff,17d4517a,3fe7dfed,556aeec6,be518188,8c39a57c,913f7da4) ,S(5c9f57b1,baacb2f,67f1bdb5,3fc85aa9,3293a2d9,d85d1f2f,f62ff40e,d26e8c30,6bcc8a89,7ebf12b7,2f397b5d,ba072f3,c91f413f,df14e441,ae2a2155,887c1527) ,S(9ccb3d34,4c813c15,e9b85517,95ddb04d,c3c790a3,a1ae051b,60202b56,b735f3fe,e24525a9,fa784ee6,2576fa15,6ad350b9,eb5802f6,e5d5bbbc,7f4217e8,73f85916) ,S(f0826eec,162f343e,4cd7e135,df33219b,507876ef,5d29fa13,d8fa2326,3e7ca425,649c1d78,6547e29b,d266f2b3,cb70b823,8e71d198,6791fb09,a19ee4fc,1823e02f) ,S(8b672a2e,1b76096c,80b87519,10b6a09e,1b7204e3,ec139cea,46aabe84,4302dfa7,33f05056,ab88de5,e036f8e8,5bcd51f5,423ef431,4faa1015,7eacfd8a,9db71787) 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,S(8e0dba73,12c4afe,8e1bc508,4d9f4944,654a5693,81a64158,d7db7007,3f897cb3,560eb34a,2451905f,2e9daeaa,63dff50f,761bd68a,2321a714,45930de0,4801875) ,S(35d9eaef,6c4ded5c,371a655f,2fdbac45,35471c32,b369955b,f8f30d95,21cd5817,c5a084ba,7b2ea4c2,e3c3d081,dab53c9a,ee40e10f,607ce88c,899f0e3f,5850d75a) ,S(44d1dd16,c42b7811,f78374d8,2ec9983,7fbee7ce,4b3a8ccf,81ae4ed6,3b7d2c73,6a7bd35c,b10c4e89,60e3eba1,8f658510,3be8d1a8,5c4932f9,f1e48d81,e3f66604) ,S(4b7a54a5,e7153a54,e4400ef,9311d6,cc16f641,6695fd92,5fcae9ed,6b2738d5,43a7bf76,ac2f663e,daf0036d,b665291f,cf983c0,791a8a6d,a5ee1956,2dc18850) ,S(add4a15d,d1a350e9,e5df62b5,4a6638d,76ee221a,4007a19e,db5bc93e,87f11ea6,c26d6fcb,3a8bc1fc,f1474c26,31a4216d,740cf94b,a9d7e48c,8f01be28,885ee849) ,S(9b52aafa,119ada49,ce33340d,ff75ac50,ac9a9d87,775e8e45,da58452f,228a23c2,67640253,503b5e3f,89f7ad07,b9379bfe,77c946d,4f61b83d,3fced91b,69e850af) 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,S(d464a300,df9de2ee,220ae23,4d59b6cf,44f4d280,7ab4f588,aa21dd1e,eeb80819,89988349,b1ab280,8b829754,7e5b36cb,e66ddd16,4d7542d1,cb0cf210,44a8be1c) ,S(5e99ed21,9ade424e,25b807c5,bcbeb05,9b638b7a,4ffb3c6d,d3bd054b,b7af9f41,a373ab0c,4aba0b04,878451bb,96807604,7d811fd3,605e8e46,57574efb,21681aae) ,S(805edc92,6fddf92,d33db068,9334d778,4b30f73e,4e65517,42e62c50,fc6ff2a3,170e4317,4361275c,2102aa8f,5406ff9e,7bd35523,8bf1e946,1a6f16c0,38beecdf) ,S(ec6e5a3f,bb96f0af,dd700701,8c046998,49a879ef,5ebcaf67,456748f2,f25fd18a,9401937d,cf584df5,a9399fa7,bb309ffe,80ae015,20933d63,df1fc181,b2979fbf) ,S(94f226aa,a25c710e,2cc68683,2b9124a,ffc5c3fa,179ace52,327c6866,cfdbb3ca,b92762c3,a4c56d95,1ef16db7,b3992e9e,aa2f9c3,ec48f077,62a379f8,408f94a) ,S(8d2668fd,5d46bd4a,fc84183f,4fc31dac,964358b,fa6b03f9,16ac5bec,a619a92d,c24f6815,3e49048c,a461eea8,ce50c8db,7794b10d,d8080236,2af6677b,45e45f95) 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,S(955ffe05,c4653033,c2b4afa1,fcf8d3f1,3b55c9ba,80d67c37,598f6d87,97f11b1f,d3502a31,bb37b950,93b3e594,944d4bac,3314d490,d375e118,4e8c5a7f,2346e6a5) ,S(699392f3,c2baba31,1bfa8aea,180283c1,9036ea92,f287fc08,adb32fa,6785fefa,242acb3f,fcbce5f5,9dba097f,3d358862,11232403,2730700d,724488e,8bee3478) ,S(193d04f3,61eeec14,633c702a,f8e7eb22,2c3de17c,a0130e9b,cbfb3daa,94674d24,39b68a32,79e62533,8bfda780,9f0f8264,ed2ba2b5,ea9c0035,6459882a,a943e088) ,S(564387e1,ed778e70,baf9f876,2a0171a2,6a4e660a,bc6eaf1c,7ef9f00,69794817,7cf553f9,128d0716,e3c81039,3d1ca83f,1cf0fd82,7f7d4ff0,ff538637,34ef42cf) ,S(f0eba12f,b282171f,d20aef8e,192741e5,4469c5c7,bab13f51,7084d293,c3c294cf,bb0211fd,18229247,5238ba93,f6992d34,a41a7ae6,78750b04,fd34f3cf,af61f90e) ,S(a54b91bd,b09d29ab,f4cb354d,283c436f,a8e9cb20,d3a7fd35,e59f59c4,200bc13f,bae1af42,3459a852,bc16d45c,cd35fd94,c0033d89,5c86fdfc,f4fad5e6,3bec2cd2) ,S(a9294788,b2c9d997,18193553,403350af,78008113,ed58cbcf,a2816c80,46f75d47,dea8059,c24c1c84,44a0263b,2896725b,79c2c8a2,6d425479,f44bb7ad,225bed8f) ,S(b6967b59,ea3d2899,c14fd2,cdd4590e,68dce683,de275313,ec94d5d6,1bee65d1,67eb4a27,8813f69f,e5bbc586,15dcab17,11bca30,77327665,2fc333d0,52fd2a0c) ,S(ffc0f3fd,241ebede,ddb0c43a,a9b8fc2a,9e778963,1af8d54b,bf99c64,add0cd7f,203e3aec,321e40fd,414c002c,e5c6cf90,2f3e75d8,ae0e3604,61028ca1,e21da260) ,S(d8f86220,c390bcfc,f714ec3,8b6f6ee3,d37b41da,4026805d,6fbbc798,8a936ab2,7c0ad863,31ab776f,c22b2539,fd65086,2cfd2ba6,2f5d67a1,6eb957b1,8d812bf7) ,S(11295381,19a146b,442c3447,400b6e7e,9b2190ba,dd42a75e,24460ca6,45a3cb88,44950501,75662a98,793416c5,3c55febc,7babcd29,398d6099,23e1c3e1,92dac1ab) ,S(d7cf3779,236c4a8f,d592525,d30dc0a9,a3318c05,1823e0b0,43a6542d,f38d92d4,1f866df2,429a3dcf,1a285265,18308c25,262c1ea7,2aa2267c,39a315c6,dcd22ac) ,S(d2bb0f89,a0897404,25fc85ce,4d8fe24c,ca061808,e426b08f,ff49a525,137449b0,fc4c4bfa,2bf202e,4d10969a,2c4ca383,17a8c179,20dcb965,7de7aaa9,6b97ff33) ,S(832d95a0,cfb91494,5b43d9a0,4f037266,2ad4453d,353f6e78,47d4aefc,449dabc2,6ec0aabd,3c3981b,8ff55747,63bfb800,453f302a,8161de79,b6b623d9,253124f0) ,S(3a224983,f83c41d,33d3aa2a,c9d29ca9,55850388,a968407,664b2830,3967f25c,7cc31841,96c4fb8a,953602ec,3c79ac75,69e1fd1,7a263946,27826a88,7d651f79) ,S(81197d87,1452332c,2fb18793,c0ebeca,3d1b8a4c,f161b709,e3da21f,3917917b,56a0980d,1ed1f77,3c960de3,1ce4aad3,90a5ea76,fc410a2b,107ed82d,b8bdbef9) ,S(b8204012,c77ebdcf,790f48fc,4acb23f0,b03e5d40,6fdcf212,81545200,faa2b4b6,b8718e0,12ed5a02,16485561,8a5fb6c4,ee4db08e,dc9c1842,881287c7,dc7191b3) ,S(766d82f3,b602c418,d020596a,58e61400,20f58fd1,52448443,2f816dc4,8d437750,d17969a3,c71ea79a,3854b526,efd56f8,148b2d79,3ea3c76e,eb14ab7e,de5841d4) ,S(35fe7655,5d4c88c,dacad9ac,1bf125d9,924276c7,8c2ea9c6,a9c1ae87,52d1e323,9ce2d43,ef8fdb37,82a38d69,972229df,9b9c0c98,abad263,1df192f7,e0e75324) ,S(a29581d2,55efc206,4d1d1839,621daef2,ab049724,167ced73,7566f4cc,3a81f5ad,7eced1c0,575b6152,38db2928,964f7713,f65edd4d,c31a4b34,ae20b6a2,babaa8b1) ,S(d7787fd3,75473801,2370e71f,4d2575a5,b9f89e11,aee370ca,2660dff9,dc6a807e,2875ab09,bb1b2a7e,cc6cb39a,939e4a91,2ddb1dbd,5ca43ca7,93ac663,552ae91c) ,S(1fb6cf61,e8be4d39,b36578cd,8853da6a,1e62cc7f,29426838,a7ecf0a2,77395288,1c018114,2dfbefaa,6bfc2957,6b79c91b,16cf03d3,81285e2e,b74f71db,1986e43f) ,S(511e9c97,866e651b,c4e32e41,92f75019,42316ead,6a0cd78d,fa61e0f1,e76aab8a,2e8cd531,d55bb19e,886b86cf,f7105591,68a9507c,7d78d34b,9ec50f92,5485931f) ,S(74afe7a5,6387bd58,d5996a9a,9650730,44141ca3,1f5236e9,da977289,73c9d434,be7311c2,b4566819,12d13546,8ac1e26f,6113b960,3039c24c,5e77edcf,de452567) ,S(5b545191,25d5f8e,cfbae2ed,bb724782,d07ff380,10eca9a9,29ccc9c1,ecd0f04d,21126f87,a0cf1824,1040d707,4d37e8a3,f035471,63de669b,9f502fd8,92322dfb) ,S(5286fb50,1a525e82,a944d1ba,eab49572,52d86693,19af1367,eaa8d5c3,e73ee8d9,f2abec43,68f3800b,30da81de,5b81e564,f94942a4,9409bcb,a9faffd2,51daa0ec) ,S(7b01eb86,c102438,4be1f023,90a5ed7d,beea652d,cf3ef77f,92fd883c,f2993069,becae52a,915d1393,15435d9d,edb72e2f,fb9bda33,4b2e39ed,6e698344,9e1ef819) ,S(3955e911,874fd6d6,74e04ed1,ea3b43a4,486a0ac4,19735114,3b451c3b,3028a674,3552c619,a845adea,64951c82,75994959,8609a3d,2f691d0d,5947b474,4636e06c) ,S(b67801c6,d96aca89,22d8e7a9,96e95729,c4c29d63,180e4f73,dcf013f1,98eb0d29,876e3361,d82f58f3,f1292315,1509ed62,2e2a73af,d063466d,4af5cf1c,1ffbb150) ,S(1efe4004,1c7ddbba,1aade160,cec007e9,8abfcba4,7d292839,4598b5c0,1b763b10,d9f00f5e,d0868390,230168e7,c5839be7,cef8ebe0,b3b70d73,ebd92931,678dadac) ,S(2083d5be,389e4bd0,23f7685f,2ad00b23,e3687672,72183afb,d5d02384,36d122fb,11b6176c,c7554617,935304d0,4e12e8a7,4bacc20d,d438bf77,a1729a15,b424937e) ,S(8a9420d3,93ff0ba0,25bcbb4f,eaaf715e,4ab14281,85b2dd91,f8eede56,f3006e46,f48edd10,dff93031,2b5df63d,ec9c7a2f,ca373d77,65033de3,8a54d37b,2ab1f4c8) ,S(64a2e8bf,b42de0b4,b2dc8fd5,9e3b2c18,753b43dc,e914fbc1,478818f8,145891c5,82583660,40ebc62f,d5526ecb,9f952091,47f7048a,4004a0a4,7b08905,12ac098) ,S(eb97193,28c44e0a,3f2568bc,b99815a7,c5c2e7b7,90e7fcb5,a2e7f7d9,920404f,cfd26c16,e6709873,1219fdc4,aa8ed998,c6fef955,78d7908c,c72c04a4,4bcf305) ,S(cea3219c,e03a2433,f9ad8d93,73a6bef6,c1f30b3f,fa79d7cc,6ced36be,9abc9c03,13ea8ed6,a0dd8fa3,29bd7563,a34f3499,6442b03a,f2eb703b,d8d5228c,cc4c4e7f) ,S(2e1675b4,f00a0843,89b0587b,f0cb723e,1a833539,c024caed,36101cb2,bc4c4774,ec1d76d2,2752a662,5dafb3c9,6235eb94,f9af1286,2b3eff6d,2a0fb965,ad3173c7) ,S(b0eb3277,7c8d1b09,e22c9b9f,1c37e8ab,74be3c49,7ab6d73e,7fb6ec11,10602438,6d44054e,a4cb4a22,3811bbf6,6d2ab2dc,f7263d7d,6421a368,9a9ca4f,97fac66) ,S(48254bd4,8df24e2a,759c5ef9,cee30855,1c1f79da,b0a32695,2196ea1f,987b6d70,9c12a458,f39f4880,ff04b96c,72b8877f,b4ad0020,495626f4,1d9b32a8,84f7a36) ,S(e3c6dc6,cfd0b94a,57b3d34b,3a77f4f4,45328a12,764e4619,efef75f9,f49fe8e9,5c229420,500f2fa2,888d834f,a517188a,207d8f88,c98b7b7d,31484a49,c4d43a31) ,S(a8d9d9cd,def3362c,b260ad0f,3de51aa5,db066c74,4166d9ac,57db782f,656be9e4,bc696df,80eaccdd,bccc9ac8,960325bf,1a0e9aa6,100908b3,cd0c0ce3,43205db2) ,S(38281034,a34cd153,34b6fdc3,26fdc558,555147cb,534a1c31,89beec74,5a2eca97,f4371a13,a65de538,f31ecc5b,50ce4b92,d5dc5645,9e523851,f6fcdac6,5994b5e0) ,S(b745114b,449f0d7a,4521d7e6,728c89ff,54131e6d,8add9f3b,bf18edff,bebc6ca1,18678d66,781a9120,ba33e01c,ee3fb1ac,b7790f18,b30a651a,99b913c,e621eb67) ,S(5987629f,9c26a8cf,ff39955c,3144f4ab,c4d094c8,8270f3de,620fcdaf,93a7fa9,a554b7be,24e49819,f1256c9e,72b8d981,2aa5984a,c942bd81,5709ee03,67894a07) ,S(8fc9dd0,d84cf297,75ece75e,8cfd7c38,dc9f602a,b0152b01,982be4a1,f29b7290,ed128f96,2cf60503,7acdf6d5,9578ca8,9a232a0c,c432364f,2b661ac9,2a3176b5) ,S(c8b5b1af,90d64379,f2c02ac9,51ff715b,2978ef0,bc87f721,3edfd09,983ecc35,c295c0d4,964ef85a,59490ae,dbfd98bb,f6096217,d7633f0,44470b6c,a1816b55) ,S(b4eabf60,c44d78fc,298b2c90,6cdcf7da,a23d095d,867fd304,513f90c5,437775c5,82d906a1,2d10d6d8,e4c843b5,48ab645b,e6f32104,f07d8fd8,c128351b,e7b526bd) ,S(b19350e8,a5163076,bba0b2e7,2159865f,59a8ea83,b0154fb7,64308bc7,4d0bcfa5,29e4ca7a,554269c3,21a12b37,a4fd0fb2,d3e57ed5,4e79423d,f715bd2,ecda9907) ,S(fecf1ff7,663c7921,40f4deac,ced92484,8c66bec6,f4a5550d,c340896c,5543b886,b2621f65,d52538e2,92a50808,9008efa0,8f530fd9,a321bf30,6dd24f26,c9a1208d) ,S(ab70fe2,355d6d6b,5c5a3f5,a6bdb605,86372165,b8f07d2b,ccfd61f4,798dcb7,7adfb6d3,dd44adff,87ce3727,efef0bc,6fdf9f49,44fbd238,822974d6,dd57e8ea) ,S(5ae5d60a,efd1dae2,43df9d7e,ca025c3f,452b6c62,216c1c1e,8b315ceb,b94769b,d90d73b9,6e33cbe3,6d96c45,656f098b,e7e57d25,dd03be95,8b9cb2a1,d00bb434) ,S(fc51f965,bf8dbdde,b5fa4af8,7abee8a9,a380918d,4d8524e6,73f8501a,291eb96b,ceebbb7e,35eda612,47ad8c8a,5d54af8c,9dbc9bd1,194ba5a9,5844fae4,b658496f) ,S(368b51e3,778f8ddc,2d09e9b7,fc2808c8,ac793edd,244fe177,fe3229a,e5a6d919,5b3ff9e5,af4c6ae0,575b553c,c0ce17cf,fc4da66e,e19fc3f6,2d047007,e1716db) ,S(ac9c4efa,5f63ca07,35fafa0e,9612b459,1a764955,d435c14f,91717e42,26ec0186,5d4d3ebf,9a064670,e09f1d48,79bc9e3e,22198188,5610731,29aa403e,73d7777a) ,S(2b5f951f,360dbecb,9eb1d31d,b414aa13,9d9a7d7c,ed952a72,c0f93a61,d52fbc08,8d46f1b9,cb8883e4,cb504715,eae4326f,11187e46,de477dec,2108ccbc,2b3ddd35) ,S(25a3593f,9670924a,a35c2008,bd8278a9,a78d22d6,572841c,98c4399e,26f67cfa,3b07ab0b,8d400f1,af88561d,af8bb7c6,a6e4b7c6,a8bf5915,4cd85291,66ecd965) ,S(3f03be51,b35e265d,d9cb974c,4ac021d9,d22b2291,40016bb4,e9edf52,36193eca,a17df05d,e4b0e5bf,c7ecac3e,e3253017,cc1d47b2,9fd3d1d5,411f2660,c34932f9) ,S(edbe9bd6,f16782a5,a00d7003,488b9291,faa4f22c,9602c736,a3698587,995d25d,64569751,212d2f6e,c2e7a6a8,973be7fb,c49d7a0c,8857fe76,f9c48011,735179ed) ,S(1f477d33,1fb16ac7,45c29e48,77df8c17,83f69e85,5a111a30,e4717fc8,ebf85377,64c947cf,64a66ad,8a417bae,1bbc1cff,56826349,e024d3bc,bc4a9078,f4bda708) ,S(b8ef8b11,901602cc,9fd1559f,c4bd6bdb,22f9bb7d,8b289c6b,fdae85c3,e9aa3e9a,60b3594a,7349c920,33d816fb,295f41b2,7c4d1d86,b4c9d2e2,2cc3f4f,e603f582) ,S(eb6b31eb,198741f7,49e4b69f,85c23e4b,58e3223b,df8537cf,60a94411,f03e0071,576746c8,ba579896,969c228d,67a57cd8,8501e27c,773a3444,35b7e860,bec9f471) ,S(47193aec,aeae207,ad675228,f4506db8,40a316a2,6cdb328c,2af6c24b,bd5e9a8b,dc67bbbd,ca7cfeb5,981571f5,7022986a,4ec3e408,b641c34a,57b7cfd5,5139a1ad) ,S(ae3c9591,c2768a02,f99b0076,9c56fdf3,1a98fae,1eca3680,38698abb,1d44f961,ba9b0c42,90c2fb0a,ad84754b,e1c3fa0d,7e34f737,f3874af0,4ed2824a,46efdb24) ,S(178ef542,8c4cc38f,f088c383,71f0ead1,4e7b4423,6d90bc7e,9ffc3db2,fdbe9b9d,a5f01afd,74aa9324,b10f6041,27ccae19,24da7b23,72269ef,ab984fe6,ba1b347b) ,S(2df7e5c1,3d0fdda3,3ef8f69b,f0ebe1d0,8649b106,8c965d97,37a7e9b3,c13f4c92,eddbf5c6,324853c3,7d478864,a68d0b40,2c28ac46,295c00c2,2359e10d,d0693d94) ,S(671abd13,fe274da6,a5cb6119,f33fc88e,37ee1b75,59adf215,e08fcead,ee946b8,49d7cd3f,3b8162f4,a85787c6,91bc29fd,69eaccb7,1354bbc2,8ba17227,8a8689fc) ,S(b69fbdbe,e72b1418,6fab59f0,6b57d940,fb8cb5cd,92c53727,a0eed42e,532ed39e,71f488d2,e104d21f,c816631e,d774a714,94c0c609,c86ee052,210113d,672ea302) ,S(1d5b8e6a,25fcc50e,a4a5429b,6233e276,47d978d1,28a5f495,a66b1b12,d7cd8714,8428efab,d2bd23c3,2de8da3b,cb630ee7,ebe84541,ec3eff60,645ec4fa,3978a6) ,S(4844a10e,ffce265b,1a5338e6,a10c4f18,b95b0681,bd702e30,9a376e23,7fcefa22,9018e1d0,34bf225,b4826e42,565a76d9,43c868c3,168d74b9,33b34596,98b5192b) ,S(9567ea6e,231a9c9c,3ea5bd83,59b7340c,dff96e3f,d1fa7a5b,c56c88a1,a57d951c,507e21e0,cc59bab1,f2c38cb3,42b9f83b,f291992,a0c83edb,4cb62b49,6c54759b) ,S(60f2f714,71258f56,6de74774,eda196e,46a30d66,3dc0b308,1cbad662,72f07bcc,12588be3,f62dd2c8,1e485efc,76c754d2,de642f53,d3937c68,f058c61b,ed7b6c22) ,S(4276ad32,b33ba53,ef2ab0af,9fc42af6,6c7bb23d,c7b7a9df,9c00e1dd,f76b6283,9c477729,c61fccfc,a2dc0c3,c3a9ac89,b98f437f,bb221be1,268a6f17,5d0dcd9b) ,S(fa3ec157,f8186c36,3419d818,4473745b,fdd2d054,e0c16e1e,fccd514e,95c9336,a7864a68,91aec12c,fe8104a0,eb3cbec4,4a907380,11a3acbb,d5fb6680,289cfa2a) ,S(7d7d2728,b1db5fdc,38ad6a75,3f39df22,88d50838,b106475e,28ba6eb7,5248b600,25d9d454,8b505739,16ec7bcc,877f6aef,e2641eee,8f78f1b1,a7f74c11,40173e1c) ,S(8cb9cc7e,4ec87013,b6994670,aae06b1a,a4785c06,614ca24d,cb6534,6592ffb9,728c4a8b,36bf36b2,a0bedad9,144c3261,71df8448,e87d151b,d8bee067,769113c1) ,S(8a9aadfc,84aa81d4,46442635,d47a9a4e,988e64de,6fe8836,79b8de44,f57c0169,60f39bce,be18abd,10afefa0,2d076d49,73d9615,10017a1f,469eab8a,c15eab60) ,S(3ea01e46,3a9bfcfa,39125216,7b6ce771,5fb309e4,37d495b7,852be3c1,af2a0b5f,2b756a06,75da2633,b8d2650a,a2102738,d5918420,9c57dd64,7b4c6c2c,c5250252) ,S(a0683395,c5245bdc,24b2b275,e8c2a196,5068fda,253343f7,49ab56e8,93672c4c,7f25a7ca,92d25547,975ddfab,fe50c247,6b4855cb,8f9ec4b8,ecbe9271,779431ea) ,S(b8293e68,1e33b654,7d2902ce,3addaeed,2fcc021a,cf7ee396,9be12661,b2abfb5e,7943e6b6,fd0c90fa,824b1e8d,25d63a1b,c01f16fd,3c9e2254,e1dc35fe,416a5afb) ,S(412722e8,ba1809cf,2df25d5a,49c7648d,b19e42c7,3cc30b7e,1107ee4b,f0aabaa1,557a299c,38ef6a75,61d79a10,ea052a52,818ce67e,1b341c1a,d70b984e,8e41fa39) ,S(7a62c6fa,f4a1f6fe,4a45aa48,a854a16d,a2fb19a1,a5647e3e,28a35d0f,619b2844,dab31641,6241ad42,3e7ee774,acb52a96,26b4b6ca,a4ea0b4a,67a513fd,9637dfd4) ,S(c3915b0c,19df99,ac0ef05,3a07b36d,62643630,201073b2,8e3ec588,6714a695,8f21f136,3cb4ff42,a52f74b4,b10f1dc3,5bcd782d,b477ecf6,38866d79,541de3bf) ,S(2a373fd3,ddd12547,3e30efe2,5533316f,355dd52a,6854d7f4,8144d19b,648f4b59,2ba90aa0,b3de3887,c1ba231f,49b28294,677adcb3,2e81c2f0,3c563e0d,221260a3) ,S(d8729e12,46cc8a52,a5c9b7ee,dcdf4d3b,3d0ff8aa,6efafdc5,ddf37480,2dda4476,1966d7a8,7e527a7a,bc1e829f,90e4e3e8,f4a7df30,48f098c0,df8a5eb0,2a8bc40) ,S(ce45fb7d,2ccb83af,dd1662e0,3ffec83b,5173dd2e,448eaa87,edc980f9,10a20dfa,5973238,531c5a84,1388c656,3d4f3579,41283e31,44d84ea3,31374d8d,e2122244) ,S(230a69,f0fff585,a1163702,4b16481f,65bf27a5,3ad7992d,47ec8ff5,edfe073e,61ae3fbd,90f157ba,6332de25,a571777c,30d8144b,e12d9a25,42bc1877,1b6abedd) ,S(d7f91496,1bdd4fe4,7b538429,df2bee94,cc4d66d9,270da392,a85e8c62,1527700b,67ee9184,bb2cb2b,9671aaec,57634814,b6a1a9f5,dd0430e6,6c5e2774,5afa9f13) ,S(4f2e459b,3eac7349,41cb81d9,2d8b3942,ee7b0ded,b2d9d8c1,90ff390c,aff7e4c3,4188f6be,c3526afa,2b29f953,f5044bf3,8e583c27,395c9f8c,979ff539,b4198e17) ,S(8a4a7b6c,3b598e42,851b0913,209a95fd,edf0f8be,6f152b33,1dac61a2,6f9b6997,53c457a9,f8926415,63e85b0c,b39ac9ee,69b31c65,5e3bc200,d37d86ae,d4291997) ,S(a48f69c2,9dbbc922,78a5f8b4,4a2fa2be,f432a4d1,e6fcfda3,8ad60dbe,6d157990,f251873,152f4ec8,fe5fc88b,cdf28ae,acef895b,1d0f0ce4,44105e14,7ac0ff22) ,S(fc0ec54e,20f7e8b1,fed5cc89,d18a5004,b7aa55ba,7520dc18,c9cbd935,7c78eb4c,17374d8d,36116ef6,49b723af,62a48350,4bd47bd4,c17c7990,fb0e119b,47f21ba8) 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,S(4974252f,9c246a45,1187b1b6,546cbf27,af9c21cc,d03c7b37,df7a604b,a3b6859c,276e69e5,b85e3241,33f9ec76,d628fee8,3af37bd8,def6e677,bba19739,9da14305) ,S(311548d2,d9f880a7,17e77608,8574ff4c,185cb0f0,a9660ef6,7a94d090,3e2fd845,82b2dfdc,2d0ca2e1,d403c1db,7593dc01,2043122a,fb50961e,d5f86174,18a3d7b7) ,S(30068568,4497d5d3,2c98d3ee,1136a9af,d5bbc79e,340528cc,4e0b3c55,74e867f4,57c141af,fd650050,79ea563b,e9ebb161,a7725bb8,e41e3c13,ec528b2d,df23430f) ,S(1c223f58,1f03b4fc,68024db4,876b743d,8a2b635f,988340f0,d22c389c,43d130a1,9d99aaea,d3bd3b1a,9891dae7,4a3dd857,3a86b643,6c623c00,6604b211,4e27c133) ,S(a675c89a,5d453821,429109cf,45cac77a,880e0e6,396a0b4f,16053ff9,eabfe4c1,8cda99bf,c3426739,c4888767,113b7f4c,9b321a61,1b63b4d1,2dd50a79,d80b90f7) ,S(e990a236,d7854ca7,3e40c661,93dbf3ab,74198351,1236988b,cca29eef,772b32c3,a3d42c05,851b8138,ef1bbb7b,41510bb6,fc893baa,928c98ac,91127b3b,a100aa12) 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,S(9ebed934,ca30351f,44b7ea4f,f3f6453f,6d0c7f81,869226c,c8f4312f,d413056,766a6f8c,311550eb,a8500ab6,f3466ca3,52e6b960,c4a52cb9,870ff784,4191a2aa) ,S(a2e78d35,d51970c3,42d03a09,bf3286c2,3a131ff9,abc4bea6,352826d4,5fe2da0e,fcb844e0,4bdf8d96,f423c499,44275ac5,8885c384,57975268,ec8cd880,dc640346) ,S(1a49f352,5203a773,9c7cce34,d21c51fe,dfeba5e5,c0f21622,eb954621,e3d6726d,e617de36,7c6a9283,8d4bcfd2,bf2fd21c,15b53007,6a0367b7,6d6ea65b,af032213) ,S(be65c6c,de6c54b6,c0c4d306,65cb4d61,211c97dc,a74c57b7,13f41028,e2d14832,d7875fb7,5cce3a40,9a74e48a,9b577a04,4c09a43a,989606b5,b44fbade,89e6c03f) ,S(a1572e58,60b10c96,bb3e0b6,7a047d4a,9957448d,74bd8a44,823de9cb,50aaa639,5ae37e0d,88c9f6d,173026ac,58ef45fd,17b0a0da,40304954,f9671c56,93946d1b) ,S(21917639,b6ef2333,378bafe5,fed1780b,24d9fa82,17ee49e7,369099a8,8c9baee5,fee39df,4bcb318b,4dcc4017,7f1af605,f22c44ec,d67a15cc,297f02fc,dfec4eb7) 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,S(62da0bf9,8d32519c,16fac809,95869f09,b570b953,e0a7bd83,9623a9c9,bebbdf84,9b9ec74a,c960fa8c,2ea8bd4d,93ff624a,9ce54fa2,4a1822a2,37d962d5,64e9121d) ,S(5caa2062,c25d7df2,23718f9d,ff29a403,e5200d22,bf064b44,c9519742,4c448a5f,6063bf93,1f72f65b,9ca76400,de5f5204,a8a0bdc4,b19cfd12,2664aa33,79a7a27b) ,S(4a81083c,c18dcec3,5825415b,2854250c,9dc651fd,5d897610,2ceb7691,576ebe60,850f48f8,7ffbf26d,eaad1f8b,2c0b8272,5f7c313f,55811b98,408f8f34,8421f241) ,S(ba8baaf4,9d0c194a,4814070c,786fd9f,4b8dc012,c42ed667,7b39f67d,da7fccaa,ceaa8874,10bbe854,9e87af6a,15ae1326,d85bb995,19a8c4d5,dd3a8599,d9ae0ff2) ,S(4c780a0b,886fdcbc,a30f239e,21495f9d,5ea38a6a,7960ecb,ea4dd2dc,9266103e,7e50e1d5,b6c811fc,f86ee651,5d64e06b,26827ba3,656dfd51,1fa64124,224e182a) ,S(50a433f7,f528d66a,961d7123,7e6d2bf6,7321896,5ec6599d,b1f34b0c,db21524c,6bca1083,9ef8d450,e56829d0,cb23ddcc,81e2e7df,e79b53f3,2f8aab9f,e2eec15b) ,S(b98e05de,573e37c2,80d6de1b,fd479bf9,bd23a6b7,2f6ab34f,caf03236,c67ec5fa,d86f07e0,8a4c3d61,f087dff3,a2af2d98,58787d2f,424b49da,de0c584f,4d8756b3) ,S(d0cb5279,e76b8be9,b2e9cdd7,b0c841b3,33398541,24923224,db54a91a,81995433,11fcafb7,28a3307d,2d87f2ae,d107b0b,d64f6030,b89e845e,1f67ce7,4cf7ee6d) ,S(90c89963,619b1593,d5fd7eb6,751ef03f,aa7c6802,46e36bcc,5d0bbae6,25376720,6e8f2a86,75b803f2,c3c87f9a,98318cbc,61b99073,2b8b33b6,62197ec5,73f64a71) ,S(bd3ad39b,989c3a08,e45007d9,116b0d4e,2dcb6a14,26a44dc2,29bff230,6c1a89be,7e633d7,de03e6d6,a7a4a833,f338160b,cb914997,6dc2080,28c3e2dd,b1c1b11a) ,S(1da5082d,a6e4721a,499d5559,91e8d216,f26167b7,d6de224d,17bc4e5b,ac94093f,5f864511,4b89eb63,60ef865e,6eb887c2,bb0b97e3,9a0b7078,888049c1,29f63c77) ,S(19320416,52e24197,d195a0f1,99818925,35c19790,99d15992,8999073b,4028d659,2cf34c91,2d1666fe,1abd3b0,49b12dcc,f7086e58,b7700b23,497bec18,e057059) ,S(79a7b5e0,482523d0,85bf574f,2e6e431d,b3bd6ae8,4e921b87,fff0f683,976efa9a,f713e011,70de0de8,a8cbe229,b147cf82,efc7fe3c,d7171785,c85bbbfa,ef935755) ,S(c2e16cc6,8559a160,9fe16d0a,9be4016d,55fccdc4,2d22ee62,895e0eea,a64436b,22399345,d40c11bb,79b9f036,5fdf6a91,4e1f43e9,bb1f0a87,81d2ede9,fdb6a118) ,S(f76c0f67,bd3c648d,c320125,5c34a93f,ed656378,8c9f61a9,c60933d4,e2d55d7,205c9c5b,83bbf922,8e99191d,e7ef0feb,429050e8,2b9fb3ca,1dbd2d5,cd35f612) ,S(24a3af8f,ee393ae3,2c30230d,ed6f96f2,9797d591,1cc3d934,b16e1304,de7bd75a,302041e9,2ce00cb5,d4a667ea,90df7f90,576865d3,7f462126,400c77a0,a44259b9) ,S(2e8bf897,5f29a6ba,636e6ddc,1e2dcd6a,1373f123,c6f155b3,3c8f46dd,b18baf7c,a93f0c91,258ec64b,d6e18761,872cf0e2,c89f9713,b9008605,b0378f8,1ec867ae) ,S(a5d35483,7f90d71c,8d829897,b3a8fa36,7c38b41c,879a3e6d,52f2988a,b88dcf68,853a586d,9661cd50,12d1ae6a,1501b874,739405c4,c7e32bd4,23ab7c1,62382bfa) 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,S(53b42d75,bccf2203,7252ee9d,25830f3e,36e7ed8d,8e1b6d4c,b2371e14,fd4fdba9,7791453a,dda2ca19,a775d684,9ee60c18,ca495808,6f8b56e5,1bf2b216,9690cd73) ,S(a3f43f6d,eb178109,cf4aaeed,a0666bec,481a1894,c25a4fc7,f4a87e82,680d63b2,d0331e73,7dc25db7,35625621,85073240,3a69a474,d5f78e54,93486b5b,3d1c067a) ,S(b83bea86,b07b217d,ddac9cde,9b42b334,c994cd1f,92beaa87,57a7e7cd,2c71b1eb,b68f8fd,66b45aa0,dd568458,73eb7829,1e613569,58345fba,7dcef9ee,dab957ca) ,S(16ce1de,573b3654,a0c00212,e878811b,25832f36,373da91b,9d9d7c89,d06ff12,264031fc,7441fe5d,4ce8ebc9,232d1837,7fa810a0,a0e19ba7,5ab16ae5,e93d5763) ,S(18fdf98e,93a7e380,8762e819,2b6e634e,f255b2ee,51c65b58,1ab799ff,52409e15,2d71afd6,c6298868,52ea0a1,943dbcc8,ff844ba3,80b177e8,62f92852,97868dad) ,S(3d5f8af4,ff89de18,866f596b,91300a32,a7aedcb2,a9423f4f,e364cf26,e2f53e96,46e9bc8c,ddc56d4d,ba25a2f6,e77a6a70,2e712496,7591725f,1d240e7f,9836548) ,S(69dc1e7c,11516a15,9edfa4bb,1afe0ea3,5be5b7a4,7695df8e,728a8dac,e2997db2,71be8ddd,d4c51c1d,5c13704,3aee6129,9541e929,799f7b6f,da08aee4,52f4ce8f) ,S(4e8278ed,ce9b340,1ddb1c3c,6b208539,164e1ad0,3adc082a,8d9dd5a0,9c63f737,13e6a5ea,7b2e8ebe,babd812f,2579b8bf,56b476ce,dd23c418,9be7b85a,940c5d79) ,S(91157569,7aed20df,771c1f4e,78b73dea,c89b2781,9b8a5ae7,5e2dc12,e6e7d148,e7114d60,218eb1bd,73074957,5b96fd10,50fa2d09,f37c0fe6,2887042,24ca1a28) ,S(3a37e743,bd2fe2f1,3f667abc,b6c03077,fd82722b,859d7bcc,ebeaf1bb,a6087d93,4192a6b7,eef51034,64040fb2,6b8d9928,21e321b8,cd611b4c,8d3e0186,646f5dad) ,S(d45b5787,9e4732ad,ad0996d5,879980a1,fc8dda5c,b628435e,96c3b44b,faf98f09,e4d4f5ac,1e4b039e,731143d7,60e2ef35,dc243097,d2e2382d,b86dc82d,eba0554a) ,S(ae5ff450,aa607a9b,bf4549d8,4d96adbc,6041cb0d,719793f9,2ec53b96,14522a00,2f061b20,e9bca3af,358e8d14,a04f1d82,97d1e1dd,a406d60a,d15727d0,66b2b8fa) ,S(befd3684,32785d19,7709ec42,e3b6407c,7a539b55,d97c8fe7,afd4f96f,d2050e17,65691153,b2efb4af,ebd2dae1,a50fd3aa,b648c7af,f5804d99,5270cc22,c02e151f) ,S(d13626c,bc00cd,36c776c7,8bdb17c8,18a2bc14,9612e0fc,7ab7888b,eab48382,ea4c3fc9,fe2238f7,1023ab83,fe0e09a1,dc167c0e,6aa05933,8f177cbd,241bdd45) ,S(9730fd42,fa9ffdc,414f90dd,ac790110,9619c01b,f43bfcab,e65a341e,2434435e,de61024,6152fb04,c997fd62,961209f9,44badeb3,6ea7774e,30e8c8a0,8bb0b496) ,S(a27e09ee,9dd4e34c,6a92f4be,aa1b8c0b,2a60b33e,99fa981d,afaac623,9f616d15,33e6d8f7,bcaaa24,b6008e44,377b4892,5f88e884,5fe73807,8cd4f405,a2747f14) ,S(d2dc7884,31e5a497,3905876d,bd6ceac7,8246c9d0,73d68872,f54685eb,5970763c,85f96d40,e31ecc47,dc07fea4,4856068d,15d2a999,735aeb3a,4959e4f9,9ecf5fc8) ,S(38fe7a6c,c401daba,981875a0,f0c2f528,30ce31d8,816a1d3d,47a3d96a,664a02f7,e9893a1a,87034596,9d95e644,313d9b65,5896a931,81d36f6c,7e390102,3cb28c74) 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,S(31766ef2,f3531ead,2c7bbaa3,279e81e0,b040182,ab78065f,d193061,2792035b,87b93ca8,91151ee9,775669bd,df2e5bf7,9f728d52,efabf584,352ba4db,8cd6f6d7) ,S(1e8764f1,982a97d8,b65a0a60,53a2fb5d,39f1221e,dd4f532,b007b2c8,c52d39f,8ed84e0a,de68b789,5ecf8c07,80ba0b26,53faeb49,3d23a453,cc23987a,b51f3a18) ,S(e249cd91,4e35f97c,92a07f4d,6f9961bc,d7f6efe5,ccdfd44,cb3bb698,9939fe43,9ee2fb47,4abdac66,5bb0178f,d8ff3bef,6381a90d,bfab05e4,a9e5566c,cc362ffd) ,S(b9a28764,d21db971,f7cb0c1e,87c9db64,ee6a1acc,485a02e4,5d5ffafe,ea1012b9,1b55a989,43ff4fb,25db6aa1,12d5c459,b1ee0fa3,aea913cc,54878682,f625e882) ,S(5d042803,9f8c37b4,dc92a9ba,43bf7213,971488df,be699901,31820bda,c0b6ff03,1ffd5348,88796c6c,a631c3a1,4773f89a,ea6d5914,bcdf27c,38949147,cab8ac1d) ,S(6d817b42,52986e2e,8ecb908e,99011265,df0cff59,61a82b2c,baf0c61e,c8b22326,55cac99a,d6a70b96,5559af1f,c5b67469,5d653662,bce7594e,22916fa,7c4b826c) 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,S(704bf0b5,f564ccef,4d6e5f8b,eb2e90c2,4b46d581,93cc0a41,5bfee2fe,95021b75,44618d17,c54684e,ea1ffe1,53892090,b74201d8,ab3f9312,e7359ed6,5ca94c27) ,S(a898e473,d4b59956,2a905ede,afc78bcc,9f374c6a,f524fc37,86a91375,83d749dd,5452e556,7d72dab5,e085ab72,1168b5e9,c96a0fce,f9d5862b,9c5a0daf,3769395b) ,S(fc4f83da,817b1648,a8a1be3f,dbd0f309,db712225,2988ac8f,64774c29,e8d9d573,57876e31,6a0ea473,3e34f34c,b0df75b1,1194017b,258cc944,7ccded35,19edd00b) ,S(63e97e30,82c36634,d151f0a8,837956d6,16d5d4,64c66373,253bb94,ed5c8236,af68f06a,e045e5be,88242af4,2e314ecc,d719f76e,33092e6d,8b69f791,446c2acf) ,S(4c06073,5107e9fe,f27dfbfd,5df447c,16f1c911,8ec5cfc,8083a588,9dd82b23,8c8508d4,b86e9eac,2058a912,f2581ae7,fe81647e,e27075d4,fd01b051,fe0ab636) ,S(667f609,7b6af1f,cff58520,83175f85,ea01a1d3,c508b12d,a2e19281,c8d8e443,ff9fd0d7,4a0cb42f,3d7ff6d1,67e5a65f,23c34679,caf3f94,ed5d1073,af31607c) 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,S(949a84d8,5f68f70,81f379e1,9d673748,bed14bb8,dba2458c,34327c03,c893067f,1b9fe41c,f474e57f,8497f6f6,76472a28,fba6b259,91297f81,474cb6fc,f31380f0) ,S(6a4bf3ea,5798c8ed,4b35c629,c6cfdc0e,d16d0d27,39f8bcb8,c34a9105,fa35fed,6f69e357,d5123305,56d04946,f9265353,77610fee,20667815,e7f3cb01,e8196b24) ,S(d0a99a37,d1df89c0,99b0dc1c,16f325b9,b2ec1455,21d4f80e,ad67da85,4f2a5357,7a75846d,eaf7c4e3,5c0c87f,83732eaa,7f6903f7,b721648a,87e1909b,53d3e9c) ,S(e2a45683,f3781309,b6223a7a,5ca64c4c,cbc5d45f,29c66082,912568ca,3ec6d3c0,8e386acb,63c52ed6,5aaacecb,fab458b9,9585951e,cd0e35a6,19c0fc39,5ce1c0ab) ,S(9527ae80,10ddd443,7237c2b3,c8f3afb9,f31e1696,5b10fedf,f150c296,3cb8e60,6e0843a,87833be4,f882c417,7198d985,5af8b144,11e78c3c,497fc49f,5f728479) ,S(15f15c4a,2cc43062,d4360a8d,dcf8e0f,52bc4741,c7924f6d,e1dd9f12,a06b9b2,66a127e7,2c55db1b,57050f4c,a0d8abf3,9ccb455d,9785a4f3,2ee67a42,3bfe5ccd) 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,S(b4b1b7c9,932be243,6b06b2c1,e5de312e,4a409498,11a226d8,5bb30c5e,1487c36d,e169a70c,b95988dd,fe1a98df,527fc172,61cc3103,88d41ed3,4bff23bb,31da4dc0) ,S(7a954055,d2d6acda,8dbe81e7,46310113,e26af09b,91cd59dc,92a479c6,d6079ef4,83c6d3ff,4582eea7,becaf8bd,422c0558,a2bc8d6f,cb615c59,7c46982,47cabcb3) ,S(aedd36fa,91a7f95f,2b2f32c9,1be77860,75783bcf,8fcb20b5,f20ca664,dd89474b,c747f32a,174ec6a7,936f13a4,7e80a2e9,324b7f5,e163b396,218c4c35,9391e565) ,S(41052d48,54402d09,a813492a,2f9362ee,9799ffa,3d270200,45a0ae07,9f913f60,97cbdcf9,b60518c9,74ddd987,386d60d1,3d10defc,8fe64511,843d5bf7,13774178) ,S(886e5afb,69f6debc,c1c5be6f,b636eea8,7314ff1f,975cd96,9070e376,c1a9973c,6a8ec4b7,98fec5e,b4a8d645,c7b72663,d6bf4aff,8f4f4b36,c064bf3b,f6e7b5ef) ,S(c93adec2,ddf85ba8,d9147c91,82ee4fbb,5727081e,a6938c0,a4bcfbfe,6856dee8,9ebef5d,2b2253e9,4474331d,b52739c1,71214093,aeab11e4,e51a2be4,e201dfb1) ,S(d97166fa,94a4e51b,ad21e1d9,76e01011,655ce24f,5f5afdb8,feda67bf,8ae65a83,815ac894,57f83bf9,5579fed2,ea470ad2,ac1c83f8,546ef3f8,bc383701,1bc62a48) ,S(c23cf94f,c5a93aa1,719ea8d4,4f426fd3,d48220cc,10ea558e,e4680c1a,dc91b18a,64a4dd89,8f36efa6,efce9354,fa30f506,be3766f3,a31839e,1fba56b,5a07ebd3) ,S(7236b1df,88751e98,2689e049,c5084b71,b8d7979c,2c412a3c,995e61c7,2440929a,67155955,bf5d1916,9e36636e,ba56fe44,f7cef6d1,b0afd3c2,beb59b26,5e3b67a6) ,S(d1890a85,df4f7933,ff72fad6,5b95f5c,c9fd8683,3c1bd2fd,56a3b7c3,e90428d,8b4896ad,4b4469d8,af074eba,ac38563a,ca68888c,5411ce0e,b3701ced,75d4f87e) ,S(41ae85b1,9fcaf4a6,13901d2,3cd2376,62f299c9,7cb306ee,8ffc13fc,75d54e15,20d99cc3,215f0b1c,20922ffc,6e111b53,e88ffb39,bb6e118c,61b9e3ee,fa7d01f1) ,S(d125489c,4e07c44f,35d39008,e4e29c43,c28ca505,3e370570,a7bd34c7,57e673f5,d142e19e,825ff93e,b6661160,b60d4e06,b4393388,43500b29,2d4d62a9,28db2bd2) ,S(8c50b3d3,667b2aa1,a60c425d,1128d389,f2786b3d,656ee126,dd57af96,ebaad9e4,55eb7ca1,c2bb5881,7f82cfc,c8b5ca35,5c2aec5c,68dd479d,948261ee,d342fce1) ,S(3e77a3c8,a2e995b7,582f502f,9bb1230b,35311af4,dc8d0744,9211a13b,444fd42,99c427f5,8365ca18,75272508,7dc57985,d59d72ed,aedfd5f9,d61517c6,1fb8679d) ,S(73ffde64,80547448,658ae5a8,529755d7,2ad7ec84,5711f0b3,20acc53e,a15ab609,786de118,c6a0daee,48f3f585,d10b9f2c,b4947661,b844ed51,59903ce5,f2cc8d18) ,S(8f2ec78b,47c61a39,c2ed1110,902b3a43,4fc9ddfc,b11b1ed,75c675be,5b8a172c,441686b5,c1327f0f,d2bee35c,5d8f2aef,b6da72ac,e6206982,6d6812a0,5b937346) ,S(c36c0376,d360f87d,28069511,7eddf1fc,75ae7118,5fd5a82b,b47d8fcf,519ae4d4,44c31c56,cda1c2d4,41161ab7,45f3c0,25c4ada3,72396658,cca23f93,bdb6a303) ,S(1ff06490,3cc7e686,d408909,4812a7d8,531c4188,ab8aaf4f,f10bcc5a,9cac352c,87af78d5,3122ad89,9a6a1297,fcc87c1f,252bbf9c,d8cfbf57,f64cb6ad,fe77f3a8) 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,S(d89159a6,d5447ab1,bd03d44a,a8db3410,c86305b4,4f06b25,b88c4244,5ab1e929,c539ee3a,e7dec645,810c4a02,e1777977,d98ddba2,281d5701,2ed2a4c5,85057013) ,S(c91267af,4c303e07,ad82c1e6,2ddd45d7,cfae00a8,d27a34f1,eea8d15c,1add920,975967db,347415ae,24b427a1,b8f7229f,8db0758a,7ea13f7c,582c260,c0711b85) ,S(c860be31,18ce92b0,39b27a50,960d3caf,88e24bae,6e45fd8c,5a253a78,e3d0e6cb,15b8374,922f44f3,adaa213d,5e3facdc,9de1ff6,4da677d3,d89f6e0a,a800413f) ,S(eb8b5f4,2fa90313,b3dd7d4b,d47338e2,9861e52c,b492e9dd,6a1897ec,4da14c14,9d1c4d0d,56c570b,8835e188,517fe7db,490aa6b2,bfbe1564,579e7af9,c0647bf) ,S(151e39fd,d5961da7,44ac5871,94081a88,666d3dda,6507404b,607d449f,1b3c005f,476bca6d,6bfc5e2b,2c183794,563d35ac,aa8d38bd,ec3846b0,22831bda,38fa28fe) ,S(b46d2d52,b764f922,7ead0399,c391a9db,1737c9ab,35394951,5a57c76c,c3c05c59,8aeb78db,db1e52bb,a8030a3f,b9f57f6,644332be,6d0ad41c,34b7fbd3,13c6eccf) 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,S(69e26679,f103a1f9,8a9a4d88,c973874e,db7c82ca,99e48554,37284445,b55517b,cab62aa5,13b41a9c,56ea455b,6a880b95,9d400bba,74e7a203,7b60ccb0,4a89b8c8) ,S(3acf827d,81e39933,64e99fa5,63f89305,dcc60b62,44ecc0a6,b101c6f6,ecd5bdab,77e3bd28,40a99c45,30ab7767,4d8ed17f,f57a4f1a,4ab91732,7059114c,c06fadbf) ,S(2e5125bf,9e263d80,7a220063,434f928,d9a4907f,68601eb9,829041e1,a7b89bc4,9810022a,d7d3c333,d7c022d9,d0779b9b,5807226c,9fd41e65,c3fc8e1a,a7a0b51f) ,S(7b68da4a,197f6bdf,56948023,d2baf10c,9449d6b0,b18addc,49385125,e62506bf,85a92b7a,190aec87,bdcb9df8,42e93917,9254ae6f,b45e6764,32e410ef,4b28434b) ,S(60d4b53,9a29562e,8fab8ad7,3b699550,3fe7d6c1,e2ba1465,f05c92b1,61dc829f,2c2ad439,8fc7c836,5b2efcf2,1e4d0156,1a753f5e,d945ef2,bb1a3394,203d07eb) ,S(5a3a1bd,30250a40,d22aed42,71892b88,3c03ea0a,baba458,6b65cc50,4c79b107,9bf3bf42,df1637cb,80c1fef2,cb9bfaef,dcbff761,89cf9f5e,d00f0f4a,e551e31b) 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,S(cb4ec0aa,c1cddaf1,c7a67507,5cad6762,cf8ffce7,6a06f76a,38bb88c4,5181ca3d,7f15e726,5092287c,d2ccf3c5,dfcda0c1,8c63f2ad,21c06a2b,469bba5a,d9e4ff36) ,S(aee1c436,6b923847,40127dc4,150c6dcc,ea62864f,394415ed,9a39d539,adda44e6,2496d2da,97990e6f,5fb1526d,b93e92e7,8a011c33,61218d,c3d3c56d,952f8666) ,S(a099ce61,d950fa1f,19abc21a,79c74021,472c46ab,d8f67798,34df0429,ba785491,c4dc483d,6d61ab1d,7578ee0d,7548e0b4,295891a1,39774c22,7d073232,f2f3ecfb) ,S(6c57db5f,b194dde1,b8cc9686,fdb65fd4,eaf8aba1,84434344,7a770ddc,9055e429,2dfb48f1,58663b3,6a7747e8,4b5a9001,163ea20e,f07649f7,1d7a21b9,b11995e2) ,S(f6efa15f,20b2e91b,cd7323a6,51e5d7b7,a8b323df,924c616f,21a7d6e0,e34d3c76,ed48a439,2bb4d596,58e75757,95a0a4d2,7443415d,7662a535,a6246d64,3804fc1e) ,S(e7983476,a900be4,e9dfed94,42f575e6,4d9af362,1e874a99,576e06e5,d31485f8,9d21080a,8b0534f,6b2dfff8,9eb8172b,cb5388ff,d910fdfa,405ead29,9df779be) ,S(88ffff0d,7b415f76,8c515d80,9c607949,b469b07f,3978caff,1ba64e,ce198ba1,6816bd9,ab0e773c,38b73787,2881e96b,8eaf381,b155b205,79b24a39,eb9e0fad) ,S(e5fd2c3c,a1c85b03,3d93a3c1,261a5c1e,c4adb72a,7700405e,7c0bb108,d8fec1fe,97bdee17,50801ab9,a96e3fd4,ec4860,e59034e5,c02f9168,79b1e654,5a65fd39) ,S(fb010f18,146336ff,30dee37,b25aa384,9588b83a,bf943125,613d2c72,c2f5b3c4,4b0ff7e,7a6f15c4,d377e92e,73c8935b,d2d9f7b3,5be91cec,da891f61,c7631bbb) ,S(9be574b2,c28b1460,a1d67d94,43e4bb85,c46a6bcd,a957499a,179cc8f9,7ed33c2a,16aada1a,367def6e,d4f34409,e0ff5d41,f3854494,6a764040,e1109574,109bb310) ,S(358e97b7,6799ae09,b80b6797,90e34630,3d61fd4e,71733d6b,3c90fdee,2ad44bf1,3eeb5209,175677af,c16a3869,5ff7d3a5,e9704201,b802ec33,50c6c2ba,c0ff4144) ,S(2ed930c1,c941b209,b6e7cf3e,83971e70,9e36bed7,a4d3884a,faaf013d,5b589b59,ff6a5a5,e601377b,9dd974bc,4fe71e36,403f2cc,90b16834,b1beb6a0,98553d2e) ,S(d86110c0,6e8b20a2,e6da1930,fbda70a0,d8c022e3,e68255f7,262168f3,2bd58986,34dd600f,9b7157cb,2ec545e5,c50b3f95,2f422b21,4afe255,b7337815,1f3dc048) ,S(4e7ffdde,305ea002,f7dfadbe,e2da926e,6d2c2714,596fb052,7eddfe92,81d4fefd,fb4dc1e9,476cb2d1,3bef4548,9ab7ca86,6ccbdd71,4cfc937d,bf024f12,ff04eaef) ,S(6ba04fe,47c4c99f,849fbd68,7e1ca6f6,3e00179,3ba3a08f,86acf668,df0afdfd,dad78b7a,9d34c738,31112801,91476b92,b8eff31f,fcaa6d,a0704244,5fe32e37) ,S(bda2c2c4,86029d0d,b804f1ea,e9215150,34276a88,179154dd,d5d9f176,cd7f50ba,a70291fa,47b98bf1,fecd9aa5,b53ca619,41d62c9e,c8b02ea7,91c79482,afc8f1c3) ,S(99801a16,4da92a6b,de6ec7a2,69c2798c,b421af01,5ec24c8f,1b090169,18980a5,3af209c7,de27a683,56f242e3,8805a368,66cf7780,60c2806d,76f9eb06,35c18358) ,S(67fcf955,dba84390,638517f9,5792d09b,64c056aa,ba98acf9,d63c2bbd,df5f021f,96f96080,b5758233,ee15e8c4,7ffdc3ae,bbc752a9,d7697e1c,3ec3d479,4f912d2b) 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,S(ec13f2e8,53935ae0,705c2644,d1512bfb,8ea4adaa,d45a454e,f761dc68,c7ace561,54139641,97e2f5c5,5b4b7f5c,5267ea7a,bf36b01d,cbd62765,ff56322,c107f321) ,S(ce8e23cc,aa38e603,70defdd9,37803f02,18ae79a7,3679c363,4dab15a,bd46004a,1ddcf92,92ea77c8,4a1346a,a5f79f13,26c9092f,14ce1992,dfc24bf1,a2da35d5) ,S(77d80689,f7cd8585,fc03cb20,14d02425,3b547962,a282beff,17aee956,88292ee2,466283f6,429248fe,301e18ef,61a89784,47142fd7,fcc5c496,36dca83e,ae8e9f03) ,S(6eed61a1,4e7e7ea5,54a4e43a,61fa7eb8,b8e7fd0d,52de9ad8,e4e9b130,78178a5f,2cb4d228,90af9cb,a3c050ab,12a3dd53,1f1c6d6a,e4393449,219d86e2,6465bbab) ,S(10cb3737,a7916d84,12c955d4,32d1ad46,d8c7a60a,e44936ba,f62b2a26,b698e4f9,35499a5d,11e356ad,fc5960d5,8d6842e8,ea0615f5,e8bf39c1,8c217cc6,7a1faa97) ,S(e866ac84,6040f92b,c52d298a,6ae110da,e16bc797,d6958858,1f63c00f,6cc68211,257803b9,ef7bb5ac,59c6b59d,32a49d53,64c6659a,cb0482e,a9d57530,4e244f90) 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,S(5fa72a54,36b2b7eb,c15b34a,fefbb908,acbada63,23809159,66785d12,fbb3d6e1,1c027ed3,a34e892d,4b3d56fa,7a93ac18,663e475,a16a3d2,fac0ec90,be6d9ce6) ,S(5296b2b3,9f179516,d3cb85bd,5b86a9fb,274da608,be6e95b6,c44267af,187e2371,728aa26,e5869775,9c392558,34d00992,73eb6986,5db38b3e,df87f394,31c75dbb) ,S(b145c8b4,4c3f3c77,658899f0,a5b97c4b,dc2b195c,aa56b328,e0535217,88c80298,c73d96b6,47c2e764,e36caa26,8ebfe40e,c07b1e0,947e392f,be2a9095,7dba2595) ,S(bb585531,3cd05f8f,7fc96d8b,6e5194fd,2a70ff55,e7a7c067,cfbf54bd,129d87c1,31ed0367,8d24c231,8c4295a7,90d31094,e54ca68e,47b289c8,45b2f638,64812607) ,S(c6ebab34,ab48c0aa,aa5243f,c82a90e1,9a2012ad,74c925f2,e4e22f6b,13d6e5e,8107a95f,28e11f9b,bcef4b22,c4228c0,b530cdac,1c977640,53828b8a,15fc065) ,S(92e6ec9f,83dd27e6,3be3b0bc,8ebc521e,d84219bc,177f15cf,1bc840d5,be2b551b,931aabb1,5b3479bf,994f7eeb,34871b04,81efa404,c40e063e,59aabb77,2553ac79) ,S(280280ef,424f01ec,3fff321a,61dde1c3,4e674a56,7142c8e6,643ad1d7,e2dc4d51,84710eb4,5a88503f,b1078d06,26522501,fc165ebc,ce3b90a2,925ab1be,3c9ebfc4) ,S(6326eb72,abc4017e,c3f55af7,6a50a4a8,d0074ce1,2f5c9e08,146682ea,e406d047,53dcc346,7b61d08a,204a70b8,7658e4b3,c4016c8d,b5f03004,af6b545a,60223871) ,S(6e59dc29,408efda3,1bcd7b05,276b9f8e,bd9caffc,7f22c207,61f9fd0,a281ecb8,81c60999,45a6a834,8f2bc7e8,4ee002af,ec5729dc,aeed8187,87060c68,c2763887) ,S(100b0cdb,ed05ba0a,fcfbedde,94ecb25a,5cacfb8f,bbb80fed,1a9d87ab,72e4b5d6,1ac27087,8d6764fc,ce5f036e,ea50294,cf38c4c9,1ca9c3c2,87718505,491e11b5) ,S(95865771,e313a1f8,5629585,7ab9aafc,68a124b,6ae61f1a,a7b6e9f5,fb5de6b4,1c5195a4,338bfee5,9910935a,f5fa6091,7d06a2ff,3908fecb,b3fbe30,b0b52b41) ,S(6962774c,9035ce5e,fbb8e715,9d381004,a1828d67,38082e1f,45307ea2,d1d60eae,e9c36d21,6a2acbe5,5f9f9535,bea4b38e,7b75a149,3a281e4e,11b19064,e282c036) ,S(8e0fb8c0,d2d7977a,23f19efb,aec886a7,5170cd08,6a035386,ac784b15,9fec90eb,1218a3d7,6306cd4a,b3debd20,9bf9238d,ce00984f,47b5fafc,b715e2a,655ca9d9) ,S(6e9ea5e1,127c4c60,a01cd278,ac1dc091,e768acd,41566200,47aaa32a,e9cdf5e4,bfad3214,9a299887,c74bcb20,33e01704,ace7c646,eb00dc71,fd1e0461,af05a6eb) ,S(60fd55,9198e1ce,86c401a1,d31d04a8,fec7da21,4efd01d7,f2081027,1c49206,4f234575,cf4e6150,16ad551c,2f8e7635,3718b626,70ed30c4,a4c15e9a,488e0755) ,S(d413c7fd,2c2bd34e,2ab3e871,38495543,3b5ceb32,cba0e9e5,1e0ce198,cd5ea806,b585f836,7ef44ee1,8e32dd1d,95d6f8eb,555d8e53,451e5d8d,1cfca993,b23e344d) ,S(e26a95ac,c0855b56,b702cba4,abcf2004,c7343cf4,72056bb6,161ac077,bfecf98b,36a4834e,4532fa30,eb1caa21,c1572c46,efe4f7fa,e3c370b8,3f1fc221,632f8c2f) ,S(f0541a0a,d29e3806,e2812aab,ac185a55,687e058a,eb17157,e00a1cae,5a9e3d9a,40e81917,4473fbbb,58d40f1e,ccb2444e,ca4a616d,b0efc710,8f887c09,dd04b4b6) 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,S(282f850d,344e63bd,abc4542c,66cf1f1,a6807b1a,19ed7864,82d06a6f,a03b1e05,de82333,48fc960e,b22f5641,5265c1bc,be290ed9,4ee81fae,248d4676,d38a1a5c) ,S(bdba09b1,c1810ad1,ab2f5da1,b628a44d,a8512221,993c83ee,4a9484fe,6416bd2f,7049aac,e507d6f8,d77587eb,b8759f51,1b7bb2c6,5de0481b,d82a2f82,246d229b) ,S(e7e238af,4639d3f7,e5ec4298,65aade7c,c1127f41,d04b3d11,477456c2,b155a79f,da29edf,1e3c0ede,5546ed8d,cf8fa801,b5bf0dc,720a02dc,d9d706c9,a9c6bdaa) ,S(53a635cc,4e24790f,3ec5c17f,f854e2a1,800b2529,fa882945,50a0d237,58d622f7,ae6bf987,2d3a31a7,4f97299d,2fbae146,58c32dfe,418ee242,2029fff8,166656f8) ,S(10750fa7,df634f7c,7d8bd73d,e056e48a,50c413fc,282748d9,f4d0b485,d0ac5c1b,fdc72a01,883f0ed0,52d97ffa,8e6935b2,3f684f58,5e6c29b3,702f5147,dc645e04) ,S(881e3e57,ed8f639c,5023e45c,4e843bf8,e7d13323,289f92c7,143faf66,a65c3fcd,12f991ee,3390b45b,af1aefa9,dcd20da2,5891ac5d,35073750,47836a0d,e75b4dc) ,S(6be50501,4d72c612,bc0d5df9,13beac50,bafefaf0,aac7d032,824a102f,25bb45f7,4a0e0d0f,f2477287,ebd8c221,5bbf3e33,fff7194b,4217f9c7,57efa361,1b3abfb4) ,S(2ca955ef,23ed3481,615d1f0,db0fe5b3,f0fe5f1f,1b7f96a4,bdf814af,c4a58987,2dffc8f1,ce4ceeaa,d09a7610,7ee08e48,a591a177,9de2c84a,765a53e1,808e3c78) ,S(250da25d,5be3561a,92b56f0a,a7ab8fc2,bf7398d7,aca09237,3d416615,6991a05a,b0e62549,ca492ef2,9ab753e2,62b9c3a0,10df946a,99a982ab,812aa48c,def60c81) ,S(57606839,4791a29f,b66f2314,73b6bc6a,ff383623,c889695a,910c1894,d9c060b3,bac9ea05,7285d6b2,7911b19,b32fec7c,1b25db58,ae39eede,f4aedf09,46c04ae1) ,S(46edba34,d53e958c,c3e4e74a,ba8bb4d7,c6266aa8,9fe804fc,e27bb8eb,cba98e2e,2b85a88f,136b201f,9a1747a6,dc55f59b,41049a69,f824e3e2,f7f00787,f687aa6e) ,S(5d4f6ce9,ac52d698,1a13e73c,3156dff3,918d5b72,5e42f415,a503e573,bd6611fa,4c633703,1de35eed,dfc5e646,e8b0f812,2b951fa5,343d7b59,ceaa5c85,e1ce5c08) ,S(c77db927,f7e637fc,24a38bd7,f605383e,91e4e2de,8ba5b1ca,baed4376,8ae120c7,347f43e9,47b5d13c,c7cb6fc9,fc2caa5,2991a0e1,bbd4bc96,d98ff26f,1a81bc5e) ,S(ebe2ccfd,ce91b78c,95cdd34d,79fc9a28,478c406a,224bfb4,668dd5f,197934f4,d7866df2,d346bd30,84ad837a,a0c65cb4,62cad5cf,3d23b0e4,bd260fbb,f4666ec9) ,S(ddc5f94a,d4420ae4,8ece780e,26940338,294b8929,549fb897,82c06e09,b7935549,25802633,a0127d73,21ef0a12,a2a6eb32,692f2d30,5e7d3cee,f137eac5,8896ff71) ,S(e4000918,46f79f21,71b299ae,6b93108a,9377708a,e7d3f5c3,147a98d0,95e876b4,c8d8c4db,8fdecd8e,fda047f,b92bd9b7,3c999493,27c491ce,df19718b,6152c434) ,S(4add9850,90e16b5c,525de57f,a15a9c38,97527b6d,8683e407,3a978cac,53b29b66,dfa1601,d36d2021,6efe432f,8a335e2f,42b6d645,7fd6f032,d727157,32a85dbf) ,S(8a5536ff,ff9c9dc7,b2a67823,5d60ad10,834c9029,bc243f3a,f10d7e14,4ca0a78f,72ee78e4,e0a618ee,191dc7fb,c1143e4d,70ffd570,bd50ce8f,d368ec29,c22bc926) ,S(9f708795,6233a0e,59757e17,5a87e34b,f7a7485c,94f9aa62,61854b4b,3ac62c05,ff9902b9,6a6cd1cb,6ea35965,3527decc,7827318,97b5c8dc,c24e2399,fb16ff15) ,S(bfa5d3b,e3fd56da,d8e70330,dccb79f5,bcc46cfc,220f4921,4cb8e700,e7cd0ae1,2a4870ce,aa2e001f,567ac21a,79eefe94,8763b5ab,c63fa649,8a5cffa4,126c6d0f) ,S(a965e34,47f07286,b91df55,3e4211af,e6b837ad,a9cc10a4,905975f,1983f2fe,393bb45c,3f6eded,b6de1e70,5a706501,cdd10ea0,2548279e,c75e4dd9,15f0da2b) ,S(e5e38677,c1e4a659,51358301,dbba1e3f,c44f5c23,af7011aa,5ab93ad3,c69b18c1,7939d32,de371524,c3b14f5c,745ea023,34f9222,31f29d8f,c8294802,b334821d) ,S(473453e1,80511622,cbe6df28,46f479c3,b8638efe,9af11beb,21dd093a,24d243e,e2b897f,eec79c08,5afb9daf,c9ead107,57d21019,c655d0a4,e5254a69,941962c7) ,S(fff734d0,e5f24c63,dfbc061b,bac37c88,ec5aeead,4974cefd,77f1eb5e,86219772,ef8a22bb,c29c9756,37c600eb,82ee5873,778d539c,a289a50c,5490b5cd,8ee0bfe2) ,S(d0508f53,85f92779,809a1892,43a58f71,47f643a2,a8f5876,510b191a,fa292dd2,329eae7a,2ee52766,a5a2874c,3912d777,e23c4aee,390aca18,140ced23,b8e82d8) ,S(93170604,98fb43a8,41d09d53,98807f99,23405879,be9f224d,52d21971,130fba89,e84fe72a,cd89fd4f,f7db1817,edab493,5f809b78,6d0c3448,f19505e5,a79e60a) ,S(63634cc3,ce570dfd,8bf90307,f4543528,e26f2637,ce32d690,75cecd2f,63dd127,bd12dd78,7ebe0ea6,661dc389,5bdb6478,7435e9da,5812d06d,d9188b47,e1a31939) ,S(30c7e2a7,925a47a1,5aa1e2a9,6f564e31,61b7a559,3af1a696,91088dc8,9ee64431,5ef4f2d9,cfefe53f,3dc76f96,1a04bd71,6aeca894,73553a0,1faeed0f,6bd2d506) ,S(f7b7e1e,d56b7caa,74f60145,98c18126,d8bf10ad,c37cf1bb,5e6c88ae,f9f6e6e4,a019d45a,7e091a62,8b7125e,d3720f95,dcc091e4,2ff17050,da596fdb,58ebc508) ,S(c6e9b0e1,177dedb1,2e19a0c0,d1167a8d,8095b2fa,1f2dc402,adef0cad,d5d87d3a,64440da5,2b3ec64,4565ad12,6f732ae3,c81276df,5ef15605,3318693c,91c12b43) 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,S(c2a175c7,badbfe95,cf7db594,626a42d0,1247ebe5,160c58a0,2437fcd5,eed8c59,94814fe3,7692ad4f,ef0f4fd3,41c63f84,b282324e,faafbc59,38d88f4f,eff210e) ,S(b1296159,d0651519,d76bffdd,98013d1a,bb17de49,111e3035,5f7a1d40,3d8d9148,ae3c442c,2dac0847,bd8d9052,a5470b9c,80536fd9,feb5f820,e4c54ac1,78aa44e) ,S(d30b1976,b0867b57,84d5e619,a5a63516,13980093,5a9458ed,59e4a3bc,ab69b7c8,1b1eee49,690de06d,7a71c334,4fc0a647,133f2fc2,99a8f096,a8a445bb,27f5b96f) ,S(fb1c3b4,5b0f6f0e,35b93a5e,ea157e60,134b00c5,38a6e429,301962f8,38fe51ae,cf79bafa,d7c3fb08,49e1c2cd,48a90ae4,af507bba,5a42f3fe,bb1e101d,7f5fb818) ,S(2bc4d2c1,d34c6d41,9d97ddc0,c758fac9,ff6489fd,786065a3,61ef442a,fe37199f,5b932f15,9500ef4e,a331be88,7022f42f,5148c54b,30957b0,424a168c,c6d76ceb) ,S(2744c1af,3459c35f,d8e1b27,668ac653,eb25f017,e4fa15d,6c1a6bae,e50f3a99,12f95a25,a87e482c,c647b1a9,f22286cf,3297a354,4c7b575e,aa888dd5,6db2844a) 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,S(d7cfeac2,7fdb5922,a5f534c2,b1d325a2,903217f2,ff41b6ea,1e5d2264,8095d3,19618c66,87bb0d92,52133c84,26fb8aa6,4fe1355c,86aaea97,b9ef49fb,de063e75) ,S(dd795951,27b0ff86,94dd131c,e85ca6ef,9aa2022d,d0c7f053,4c83735c,43096c02,caeb4cdc,2633b01f,1b51f7e6,103ede8c,a0ccef5d,e33a8ece,5ddfba8f,736e2adc) ,S(5b2bf207,9a319707,52496851,68aad1e9,5582408,7e5d361e,87b77900,d9c63939,728df41e,69c939fb,59803668,6c44d0b6,f102dc4d,ee146a33,42e1c04c,9b6e30cc) ,S(d2a26a5c,313aef0d,6ac190cb,11c84771,abf97d8e,c7e6e67,bd3313fd,15c2ba11,84a1fb57,1507d012,9d98ebf5,34fac803,5de7a43e,48868269,d5e9656a,773fe768) ,S(22c22c99,860b2b6c,630487f2,5263e77,91b62450,290e9df,379efa7,1edadb52,d2b227b3,dc85c1a1,ed64a7e5,6dd6b178,ce0ab5e,68647b50,1178ac78,4b7d1c93) ,S(b811b039,d2cf5f3b,95e38e2e,14da67bc,417cfd8,623593ee,1f2e924f,d9a064c4,a860653d,ca39030e,8c1ed7bf,aeab73f2,a68cb8a0,5263aaf2,431b6f8d,9c862a28) ,S(59ee23c9,26b38d6d,d6c091a1,d4adcdca,b3a5a548,a5cdaf92,fee9fe2b,c3cc2957,67462318,96e4f107,67e39d47,b03268af,5b54edb0,9f9e8e0c,3f3f89a3,e9d204cb) ,S(cc79ede7,ca5a9ba5,a7c5114,d2039d5e,c6a54db8,fee6c102,577a20d9,18ba857a,2cdc980,3a06af30,c19b262a,12f54132,933ec985,afbd1598,45c40be3,2e24861a) ,S(1319c7a6,2f3959b4,cfee1223,b225c6e9,9070753,a1ad33d8,8f3a8b78,a886f7da,d8a75f9d,b8266ea4,2b650265,6b6c0ee9,7f3598d6,3d149ad6,9a5829e2,f3c29085) ,S(e4ae90fd,74e9b229,b9100cef,1da59b80,753b4f0a,cd7790f6,34930a92,b1eea356,370f1c98,f72e698,73c8d0a4,e76fb117,d7e5a9a4,d13521f,f4902a1b,ed3688e5) ,S(286a98b7,b0b0527c,310afd37,717b5061,467be24f,8a0b5528,52ff26ee,d658988b,d10699be,f79e800a,519b964a,163cffb9,722c3ba5,b56694a5,c1a9b883,b32965d8) ,S(9b8544b3,79746ba1,8524e084,2d15b853,46577b81,7084e02f,7d0cb820,7448f5d6,8421c0f2,ba15f648,246f9cb7,3b10d6db,1de7aefb,fafd9b52,16234dab,8e70218e) ,S(81efaf7b,50a18c8c,2481299,bbd2adba,f3510ac4,f871c3c0,f849ef6d,4550681a,ea8567a2,9c871ba7,fccea923,fe07e8ba,2071d7db,25d33ce7,a6125c0c,2afacd17) ,S(6680fbdb,dab850c9,115d5765,344f1466,b88cc5dc,8de9fab,549f281e,974ed7b,c7871b4b,2690f4ad,1e67ea81,e2cefac2,988082d8,b1c70e67,4389c79a,bc880368) ,S(4c38ce7b,a8e3d317,6f615d6e,27578edc,746fb80e,4701efae,f7557469,a1dce4bc,f6e73d73,61ff5407,10dc9f1a,4bd5c1eb,a7d8c8d6,45f0427e,a4fc3e45,3990b88c) ,S(767146d6,bc1d5bb9,c73321b5,4cf6bc61,e8209703,fe4dddf7,2b3d6089,da60be69,86df7dc3,6894f88e,fe24a4ee,fc78b1e0,fbb5138d,31666be7,97b8934f,d0b9a37) ,S(bffd4856,360c02ac,ee741a65,486d5a7,44e2a005,9db5ef5f,f87b9e18,3adbed20,c11246aa,3bd4ec3f,71f88d2,cb3b96ba,2c210f90,d8234c21,99bf7781,f96ad781) ,S(ad19b5f7,45556650,eb496450,968d056a,fbcb55b6,8852f510,ac96df54,cdc677c0,f78295f8,59445c52,d6ea285,3fe9baa0,5e453bf0,9b3f4d28,6c99e858,62a04bbe) ,S(5924f679,bb94f6db,d8232b01,ca8dfbcb,37a83d24,d0e7026f,b526162d,c82aaac7,baee6567,6a526460,ec7563ad,42482d37,a42f2fcb,f4a5eb7,b37b515,a6c3f1b9) ,S(dee240ea,c90d5399,89d3b3f5,764e0680,1e601a4d,f2c09226,21eb0b7f,bb53ccc6,12668b,72cc139f,5f9fff4c,ef24b5ec,d0648e03,64c17417,f35bfca8,b819316a) ,S(e288a00b,e18b0987,9765940e,caf8972b,1a09f67b,fdc455c8,8e3b4ed9,dc0dad81,fd81e0a5,adf1df8f,42c64825,6b107d44,887d01da,f4cf89c9,11529124,16a1e4e0) ,S(e747d6c7,3f5366ed,241501a0,ca6dc04a,aca7241d,8effbd94,7d3e6a0d,bb6eadb,9954822b,15f44840,9c9e73d,97722194,1eb6a218,ef1ef4f,269ab118,8f9c773c) ,S(57b8865b,ac78b9a1,c244452e,8057be3b,4fe2c6de,9ca9a295,ded04377,2b61aefa,d0e46172,8828f0d3,f1fa808b,1dea8516,b0c30d93,4acc8c90,6ca2bcad,303f06b7) ,S(abda4b38,47ed5cee,7ace4e8e,e652336f,26a8f4bf,4bd610f6,e87e5936,e4e8339b,8860963b,8f266c30,9c6a00c6,cdb44048,a9a1b76,d0a5a652,b4453f7d,330bdd9f) 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,S(df09dbfb,564515f3,a6d86e05,dca59a0a,c353746f,b291d9c,add27d68,6810cbec,90738e50,6bead3aa,c0cc4a2d,cdfb8529,5e752945,a7b2e357,1a99c901,49017c47) ,S(df9817de,89526a26,c61e4294,f245ce06,8b5e22a6,4937d5f9,6898b9ed,74078989,c4db6e86,c6a44091,23227adc,345d6eb7,d2f12acb,f2df3b44,978a1743,94072f15) ,S(2e713387,7a0419b3,7bf77874,b24fd0,7cae9fb1,59919a50,223437b,7746eada,5dcc4c1e,12502573,b0520817,16fa46d1,8ba43ff7,e7f8c8cc,e3c141ca,6176f805) ,S(99826364,f0061305,1ba033ad,63b95884,97158ee6,9542d06a,f2f86d91,3bea7a2,5f109254,24af4592,2ab30701,464d504d,6006969e,30a9ce5d,76a3b115,6158c6ea) ,S(19222e8b,5fec6d2f,33a35fca,83c3b9eb,effb9e3a,f2ca9c53,929fe5f2,a43bcd32,c79b4f98,4621b2c1,d627dade,f01fe761,8af239e6,b80c23ed,a2dd1b1b,e750549b) ,S(e0ea59f8,6b7925d3,ad511280,8b1ae5ed,c0acf6c6,d4ed0846,d870a663,5573970,bbfa69be,ef531b32,5272ee02,8c880178,57ab2a32,65b5a6b5,38ef81db,83b5de52) ,S(7df189b7,c29c06ab,83f7d849,58ba3d1e,7da3ebcb,feeb9dc4,64b60420,3631fdd0,88e00d45,8287fbea,5c14ab33,6a879948,e81d9798,cb82054b,772728a4,4b69e56) ,S(42b9867e,7cde3ef2,b4b73f3,e4df7504,b7f06cb0,67aedabc,16edb276,97bbca58,eab47aa1,df9af0f5,40d1c6d2,ba7edcc6,fd436f56,c944c872,1e1f4958,63144390) ,S(9ffd9a,5535bd30,a697f61e,e6fd0ffe,b1a7e5c1,9459bd3a,708a7112,3a3da54b,79fb0a7a,8334fe38,64fef8a7,60610920,af2741c1,fa41f582,37e92acc,29644011) ,S(13ea8e5d,1116a57f,8b223a5f,79c750de,6c25511d,558e6878,e92cb134,7b81e393,a41efd37,d35ea994,8175d989,cde449d0,e325b40e,a247edd9,e8f4eef,e6a4d283) ,S(110d401b,d7a1a0c,e484fdb2,34cd839d,5e40cad8,6244cdee,5c4f2ba3,ee1e2eb3,cdd91a5,4dfa47d2,98a46f15,c021a38,975ca108,f2653019,46013427,349d7ca) ,S(48a9f1a2,fe29b05e,d419a14e,8ed288de,46affeb2,296522a1,f2407b76,a8f6b040,f1c5ea7,887c029f,67202b41,198113cc,f1ba5617,79afc1eb,db0e10ec,5b5d2a91) ,S(d8c4d9a,feb94e7f,7b831464,77aa4e3e,a48b6af5,35015941,4047cd01,1beb7176,fb8af9c8,da06c2b8,8787793,bd19d7ca,6cc64508,7713af45,4f5fb4c7,eeda3c2a) ,S(34e84417,2f5ff4a2,70a9064c,d5994327,9cefde94,d295f424,2c491efa,bc1f0839,2da40cc0,5120e4e7,8e84435f,895a3ed7,6c507bda,4d16cd14,b602deb4,366ff9fa) ,S(ea802ca2,f07a4348,791b7df8,99639d06,c6db8d15,74ae8441,b29c2d18,18b7a6c8,ea475a0f,5f74e6fe,ccfca44b,ddc38a4e,3cc19c49,e2bffa49,a9572146,6338a155) ,S(d80542c7,a7be8da6,6346d867,4154f65a,b1cc8e94,19299d81,6a5c874,f25ee43f,5e85d69f,b5c72ae,bd94b1e4,67e0d30,df8da61e,4150f4ec,e3efcfae,78d88d25) ,S(bdb35e49,7c1c0d1d,7a120366,cd259e7,31cb253,1bf804ae,f0c82cdf,561d0c0c,2675a4ee,aea6dfed,8597c08a,69fc251b,7bad9869,e83f485a,73dd1638,605915b0) ,S(5174e27a,9a1eeafe,6411f3af,b627223c,db0da11,6bca0ac3,d39a3080,815e22a7,b1223046,5f58d183,fcda2603,e4593398,51ed87ed,6839d9b0,4c845459,daa3d5bb) 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,S(9509f343,17c15f7,a54cafc7,3d4275bb,41e39183,53858724,4031baaf,97bed951,dec71a0c,7f8108b2,5e296361,2d6623b6,7b2f6d9c,69d7b6cf,d7273503,fc72b4ba) ,S(bbf19e9a,efbee2db,fbd5eef8,492f52be,2e2f9072,6b3adc1,d16f0627,f4f19d25,d9e691de,f2ce976,c66d806b,f35a2b13,56f9fc07,7b7bb239,30668081,4b52cea0) ,S(b5997bb4,5b359516,b28ee935,e4d59c39,ae434c29,5e5d98e2,2ddeff57,4afabc5,fb6d36a6,fb2e1aaf,d9b5d89c,39a854f4,a3cec053,1e1a776c,b4267b4a,d2bd8ac7) ,S(fb746cf0,cbf2f56f,6a3a99dc,71e84cc5,af76899a,3a7d02c,fb272391,b77c8384,d1e4cf27,57373ab2,d1ba3f2d,d5bf8b26,a74d6814,23a5b16c,9621b788,a51e9796) ,S(644facf9,e6290462,1a5278c3,f4a2ff8,84600c23,69eeb557,bc412540,c4966655,5b5ee0cb,449423fb,67c9b542,3868f7b7,6d1968b,9d7dd751,75e7dd5,2f994b88) ,S(c41931cc,9c311617,f77faa3f,6b6f6e21,bd030c2d,9778b065,6ca105f,cdb8658c,8a759dda,8db8a8ed,eb1f2972,12858879,bb2f49c7,468d8edd,14d28525,ca3c0746) 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,S(9f4164f5,4f34a59f,3a7be378,66a8204,def2fd98,8dae6dbf,5d471e0b,caab7017,4b662fde,bf2615c0,8c7b53d0,b2915d50,ddd2916f,a3599d81,bb2eab6d,80e93f57) ,S(c6f3a26b,adab6699,aa08fcf4,6f0ac900,2be3597c,16133225,6a5e6577,11b16ecc,f29db1d6,579d0e36,4528c297,36019f4b,6e8f060d,ad5effe6,d357d709,882a250a) ,S(76a4f5ef,6a869e28,e6494cbc,ffc6eec0,1ca983ad,1b8219cb,d2b84eca,96f8b910,e1d8bd7d,55a297df,32ee185c,c60db286,a2e46cb1,312a8995,5923a068,cd3318d5) ,S(d2c25c8a,cfaa0b2b,3f6e70d5,bf095700,68102f8b,24867970,ef3c8000,b2212d1a,bc907681,9c7926dc,bf81278f,7dbfc4cb,292a8071,177ce8a4,f4e9346b,a2d9e500) ,S(b2fc2ca,5a30c678,61b0bd22,5bf2c088,26d799a5,9c9a680d,dabac9aa,5cb624fe,d4abc7c9,fab915d0,fe9dcf59,a0f83ca,56b27566,6e9841cb,b5b14874,5f6732ee) ,S(110ef531,7824c321,ba7fa94f,ac98de3a,c6cf44af,db92b7be,1006c751,9b425065,cc3daa20,6c0eb83,6bdfe640,1f7461a,261e7233,c70e615f,db82a991,77b83cb7) ,S(fe21a607,7419ed88,12d16ba7,5485e01e,3c063359,f95a8634,3aab1c84,ba6ac00b,d6e08c98,4b7a5282,bc1857b8,82604fc0,692a2fa6,40cf5a5c,d298f344,54c836b7) ,S(c5e45275,ec85bb32,edd32702,7d7d87ac,8394bc51,722e0bd9,58281e61,c454fcef,9b158ee7,89034035,fec4f06f,2fc81755,59f9f762,38742715,92ca6ff9,e5712a8e) ,S(cc68f3f3,36360481,5583d65,7da51968,a4a44a69,1264bac8,289791aa,dc7a4ef4,9db5cab6,7b31f3fb,f3b5fde2,273496f7,93316358,6d14e80b,bbca4613,319df9aa) ,S(6d33be85,5fe8bade,89109a3a,8c089aa3,f7e9d178,969100b7,eee7a693,d83ace80,9312736,87c08455,c43b4cab,afe71408,333fbd69,d330315a,3fc9a52,a9d473d0) ,S(5aa581c2,fc48c38c,2aa2e176,c12f12b5,4810ff6f,862fa17a,196c06e4,812b9e3c,adbff08b,bf6fd5e9,9f91f9f0,9881cfcc,a7b5c2af,709bf838,6055079b,2f75f3c4) ,S(12eb2dde,dc6ea4e8,dfd43067,9d45052b,b882e4d9,bf516b,61edaf00,305fe883,8f948ee0,f8514f9a,1bd8a71f,20c95e4d,e30caa5b,bb3a383d,9561f027,34bb1950) ,S(3d0d7eda,43045e9f,62dc680a,be47e933,74a95d59,945b69cc,60acb89d,e40dcded,45c53d35,e369af07,eb223a79,1d148ea7,1875cd1,8ca066d3,399743f9,65e184b4) ,S(173d4741,5803d266,7ea94abf,319c5917,204256ca,e217647c,c024a9b3,be7b70c,2da6c348,cb066462,eddfe8bd,3dd00ec1,34a0a060,4b7e17d7,e6cda389,dd4d5463) ,S(10659655,e2f1ba5d,db390184,c2d6d1df,1cd2abfa,4cd4bc18,c89decc9,5b5d6319,5ac2793,3a88870e,d5c7752a,459ced45,69435a09,7cd0e030,25608cf4,ac2ae267) ,S(e462be7c,380d7bbe,cd45c6dd,8fe60219,404b0c9,4c5e0e4d,31a23064,2b5b95,872183ec,1ba5b854,1f3f99d8,ceac80c5,9e84756d,cae2e694,9b43ea7e,d1cf752e) ,S(8200badd,1df41faa,19b20cb8,efa424d2,2f39b1f9,26b692c0,2a0ef6e7,feeed67c,8402fa9a,6ef0f83f,42546b05,360296d3,74db551a,d89be995,f2c11866,5be528b3) ,S(760e2457,a3e1a165,526e9fe2,2b5bcad6,e8107581,337cecac,e2ae87dd,a3c54592,c5111ec3,24158a21,56b897a3,82bee2bd,de0f9df,af9ef611,a7fd3fc7,4a635b3e) ,S(ba6229c7,1729cae6,5275719d,9a35691c,f260a003,168f1a25,1ac00b09,aa17872,7d281600,6bd8981,82126d21,70fa0ab1,d5dd0c7b,cc377a88,c43cbf61,70a633c3) ,S(a2cf1392,571e758e,6ec74708,dc45f70f,90833ad4,135e7a34,9d2810a1,8efb5216,2420ffdd,afe96506,9e6f9266,1e3839ba,c9b1db40,d40149ae,3acc8683,86acd175) ,S(f8822204,27cc4b37,33268925,fb80beb5,a52e5391,b2c8e31e,f6e99592,1775af20,6cf6eb9e,b19825da,6edc5d2a,66f3987d,c9eb01e2,b70e6395,abe2903,d43acee) ,S(eea28950,fb676991,444f96c5,7e42ea16,aa380e3d,dde63111,fac35708,a4e45b3c,34d30722,98a686ec,7e1a8095,4e2911f1,5e11d426,ecacf11c,eb45a5cc,7204114c) ,S(7f252a72,6f9a1497,f61bc4ee,7b194a31,432c0178,2f40b16f,2d36e9c3,7279e25f,8edf25c5,f50c6f0d,f8a17f92,611bf024,14e02d0c,de38aced,e96d5a7f,4467c449) ,S(d3da23fa,56881cf3,a42a50a7,42e1067f,54ec24f,2de19921,b1ae7f15,fb90509f,b4ec4b17,8e555cbd,15210f09,bd1ab43,28e458fe,6aa3e800,44bf0093,ea08f90c) ,S(6752f294,f8ad85e9,60b6a88c,cfca7874,5c80ed7a,93f6f05,3782ac73,d96e31e3,976222ef,a6f6358d,42d6289a,4f11bd65,e7e755a3,845ed49e,3c972b5c,5fdb2418) ,S(4fe21b06,24a45b69,7f42aa54,10e6385d,645a8d49,2a61ece5,c8d5b2ad,1fe74efe,f7666c09,7caeea3a,c4b2993b,64f4c0cb,ac934099,8870ade,b7cee48a,c3c2c413) ,S(15af87cf,6dc1acc5,1d323a36,b2daf163,ccc8c201,a92f0677,6a26ae27,7fb9d766,53fe4566,6a975d35,ed20a5a,7bbe63c4,4cf8011d,45e7a171,d5d72e57,5debefbb) ,S(656f3686,c60039b4,4c39a5d3,ee82cd08,e8aa8ed4,b9a943e,42281407,4ab6821b,9f277baf,2da730b3,dacc2a43,512411c0,13ffca65,7092e695,d49c8d24,a4cda4d5) ,S(a13286fd,2c17a61e,6bf8d209,d64f5879,2534b037,cd854470,a09c8c8d,95aa0564,9322d3d4,c735a485,5d76e5d1,fd27fdbb,a8af2fcf,ddf7bdf3,f9e26f97,7f4cd1df) ,S(3b355928,4ddb285a,1eab73c5,6e6bc554,9f40d83a,2b859e01,a30032f3,a5a7109c,780670b5,67755fa5,10fc3385,7745a69c,bbe73e3f,8186b3c1,8a82c51d,5e1d9be0) ,S(b0b15be8,6c2dbfed,6da6e7c6,51c10b17,504070,7d1747c3,ff2dddbb,256fa495,8d2c438a,42750adf,345332d,f02f6c4,55a07fce,afcc51e4,96c270ff,913546e3) ,S(c754130,bd717ab0,fc17e14d,dd6ec50d,aa6bc02c,a338cd9a,798ee62e,72d517db,fddf938b,28500dd,c9f1fe0e,70104564,d1bad398,d3bee900,ff609c8d,f56d3b26) ,S(ee615579,33d877e4,9bb228e3,62766ada,8615d382,c022c333,39f78ff6,5e5d9ceb,3dd38b15,5ce01a1b,3d5434f1,b2e04a26,6a830f47,fe89263c,b0ad1b5e,18bd8b76) ,S(f830dd7,4d03a39,d7f5ba3d,132b40bf,130b33cb,9b6609e2,12b6479a,14287c9,9183a68c,33c2d25d,c237f8ed,b5a63d44,4dd2bffb,d1255631,221edb9a,4c9e9e91) ,S(544fa477,3aa3589d,9e63c8f0,f30cd189,a8b6658e,ba908212,cb1b4caf,2d5f64ca,bbf57d7d,b5c6b8d6,e202a7b9,8ed06edf,e1a9ad01,381da1d8,11405fcb,8ef717c3) ,S(9b270440,132f5b09,6fec6214,dac1e27f,3e6c6f7f,25eb2cab,680c3fea,e0b41b1e,a7e591d,eb990617,6bc87263,6ea19e04,c9a3aea9,59059078,2a757fd7,6d99c6dd) ,S(bbd69c5f,f0b9228b,cfeebb97,32b3c316,c14d9a54,d5a3e9ca,ebb337e1,e33525e4,78cc6c84,8c246e7b,7636949d,4e3f2b94,989c77c4,812b8189,cb857cd1,3457c403) ,S(a920edc1,4ddf5bda,56719c0c,2adaea7c,9aa8aab9,25a5d6fd,41172725,bc65341d,b8afac74,46e560ce,bcaaf438,69dc9287,2805fc14,122cb19a,bb59e51,8336ff80) ,S(3c6e9595,a201956d,ed27e83,41b22822,445148e6,d00b2fcd,ecfdd66b,2405ae3f,2b8ef9a7,d7c37d0,d2b77309,74718eba,16f221a5,f3074678,317f0b6b,7b0841b1) ,S(c35c9e45,3f487f8f,ae5b6010,e1bc1ac3,ebe4ee53,33666876,13cc4b35,5162ed91,7a8e64d4,9f827631,579421ad,3c7f7ea1,f4866432,a341f955,6741c521,c757addf) ,S(8fc84331,a8f8dffe,28f30d71,b39c105a,ec09aca,4876241c,1c81a223,a1953637,aac7257a,cf0fce3a,ff8fc7ea,e8d19606,2ba6d7ad,9b7987bc,35a92b9b,20360174) ,S(b43ca4ce,f1b4a2d0,1a20fc64,2f3e1456,317f729a,1ee69798,4ed88bfc,1c5a2908,39ae1e51,f352c0c9,8a79cca6,cc859eb7,92bad6ae,5318f99d,d62d3bd4,d8fedad5) ,S(7f29c501,75628aee,5d39db41,cc4d89a6,9f133f00,47500f6b,aa7a90cf,e13159d2,cf17c6f2,f6072b50,257f722b,5756d8ad,c7486cc1,d21a925e,8cd29a15,4b514cd1) ,S(3fb93959,55ea2522,61b0488,212e15d6,b28e975e,5ff5f357,15337538,247f2a54,7c3db409,e06d6980,d834639f,e9e357bf,e6a4e9b0,ae6b4fb8,f5e45143,ff625ddd) ,S(945ad871,18199665,a4078a46,a9596bd3,ec7cab84,b6323a0,7ceefc63,d7ba29f5,6eb6d896,a24d02c0,630c909e,65d13d4c,2eacf1ef,6e600b89,1b171594,aa28c206) ,S(513bfa93,57c827c1,b3c0289b,c4ce443b,cadfbef0,b28b32a9,265ab85e,67efaf4d,645c5b3f,d45030f,1aaea514,baba7069,91def89b,56fdc292,4b684241,6653b6d2) ,S(d41b35bd,421ef7bb,1c03c794,477c2851,dee92831,714180e6,6e57e735,caba5835,beea2116,9cf971a5,ffd83596,d9bd77eb,cb1e0c7d,506a45ae,be8c0c7c,22738f9d) ,S(96006d64,fac8f0de,88f93e05,da8e76e6,40afc1b2,8ee09a7d,5633643b,d89ee3e7,1404173d,e96a97e9,ae9bcad5,c9093d05,cba96479,30bfe6d1,96664d0b,13c93618) ,S(ad528227,12257f87,d1ef82c4,4af5f046,648c2a72,497651bc,2327e971,1170e7bb,2ea908a6,c742f542,324be959,4746ee48,4229d497,cc8bd535,e7989525,aa36f079) ,S(b4709a81,c067f6e3,93ef97ab,c26675da,6f01a2f7,e3f35275,e7089ea8,ad5644d6,f655b89b,d6a83838,ffd23f6a,fb944bc0,57fe7f1,1d321a0d,2152568d,91751d99) ,S(3b7bc8ac,5ba85b40,2080612a,84e0226f,3b43c8de,c0e54b6e,ea779b76,812782f0,8405dedc,a02825f3,5a60333f,190001fd,98ea3995,9dc6e61,c28c5e2e,5213fb0e) ,S(2a76b67,d197e7a3,7a38bb10,d49d523d,c4beb4a3,75336974,7e22e407,9e0310ca,6331389f,b9cf9fee,e89b089a,95abca6b,a3c2aba5,38725c1a,6848fa46,997d0e87) ,S(9938e808,77c2baa4,53e0256e,d250439d,b11732de,1abf7555,949a7574,f62819e3,250b061f,bba0faa4,468a080a,fee8264c,f72fc12f,2ac91dd7,13ed92a1,1b281124) ,S(7366eac0,7e5e4573,333291,3e42f111,e53a78a6,5069898,52db2355,de089230,b8dfda33,31646343,bfb60b2f,25050967,e735861e,1654f0f7,ff42ed9,5dd652a4) ,S(10fc632c,cab22fd3,2583599a,a2efaaf1,6e1b01e6,a5a96c59,50871012,33022152,cf53d9ec,c74aef44,7019150f,ddfde494,c2382a07,b2dfd73b,c628478f,7fbae0eb) ,S(785f4da0,240de52d,bb50b1bd,bc53994a,47318076,9a1fe06e,5a40a8e,e677ce63,9b5759d2,f77bbb9,e40ac169,a01500ca,6dd6bd70,6a003871,e7ba4d66,b32db9e6) ,S(a7f20615,593850c3,27aaa06f,c03e0d46,d3ff20a0,9b849810,1759638d,8cbb9cf,13b9ebb6,f0cd59ef,54e0f935,87a14fe1,2337e346,94f5e8f1,10323fbd,d7604d3c) ,S(cf083e4f,e0ed4444,85dbd99d,8e6823bb,483eb749,b94ce672,8671de8,6105aa4a,36eaa305,37378494,17050dc2,8290c74d,d9ff9df4,cbfa434a,2b89de00,e06f3099) ,S(9fb8c370,bca485d1,dcadc251,ee906f58,6f3e177,be37baec,6912e535,f5c7ab0a,df5cf77e,1ad07532,7150136e,7ebe7f35,1db47415,74444b24,e9cf2f4f,31ec683c) ,S(ff9e2f29,170dd456,2c94d48c,eeb0390d,db783702,c13574f,8a8c6a79,6427adca,784c7b68,3c824603,5077911f,957aa33b,47534180,d70a60d9,f248b860,736a24c2) ,S(802343c3,e07f9f9d,ed2ca436,3e455427,367b852c,d23ffd7f,fd690eab,90b4162a,b093f0c5,f0fc7d01,a5dfb7f6,bf9d90d8,8595140a,a13fbfc0,f7d6af2f,54ff5ce0) ,S(ae74ed87,11a1a684,9e558e05,47ff8f9b,f6337551,1dd3d272,ee0597fb,fc2d6914,c304897c,e5afb5b9,a383cb64,e85071a3,cfbb2981,93ea6ce0,55257ba4,cf15bec6) ,S(c099b05a,dceb601a,14892c97,7b267152,f29ea71e,fed6090e,7267249e,43c2390f,6c3ad3eb,8c95c72f,e0030a7d,34329945,fd1eb71d,8c4aa1f9,8fa4656c,6bef067f) ,S(97c6949,a25581f5,945814e9,9d590dff,67d936d5,94101005,4cac33d0,fb3658a5,cdc7faad,5bc387ce,a16a10f6,6971e5ee,6d32756b,596adc14,57081ad4,1dbd2e4e) ,S(14a19edc,a1ec89e9,524548ef,cf3dbc03,81b14b46,928f7425,87b11df1,7aa721f7,f83c4d0,aca08709,63a017b6,8db3434d,6088015c,2ff1d8bd,739fd620,35d1a19e) ,S(4742af63,c7597424,e6d04a8c,cb43142c,54c5b350,175bf5a7,27c39820,2187d00e,bb1f2f72,b21e15f,ec17af32,2147edfe,1ca80ac8,3e030dfe,8be39fdd,f340c56d) ,S(a6597869,4d168b00,d9df41de,fcd48ae9,68313394,db683407,330ffae9,f2559a11,6bf65c42,13317a5d,fb561e8c,872c8b1b,90bdabc8,8a8d2e1e,39919f8e,5043ced3) ,S(9e62e468,1e22abde,4d7a2fa1,2f7867f6,ecbfc15b,54990e26,821a8cde,fed76985,4877297b,a64fa8ed,c039ab1a,e62ac72d,8d7bbf05,7513d1,4237b8dd,9f1acd37) ,S(d24333b4,de55b0f5,d47c72e4,88cee8ee,8c960903,260a64d2,c89bca45,db7352c5,688b20b0,617ac12d,5be38fa2,ab52e785,69766a83,2d8b44d5,cfd6ee88,b19b9f1d) ,S(d203301a,13d1c8ae,a8c79007,1ef8116c,3916bb3e,dd5110a7,304b9145,465be838,a606dcea,398dc313,e61c8fbb,dbbc3874,3c103297,164e66a1,4412a21a,5319e55c) ,S(d1aa98ab,7010146f,16a9d6b,cd911535,2595bfa5,1bccb3d5,5e3a4a87,62666610,3abafa4,999294e8,80e3fae9,edb4206b,9b9786d,bddcaec,e2d01cf1,ab715690) ,S(1e20823e,81051b2,65535085,9aefed6,3631dbe,23b4e79,abd3c17c,21f053f4,e238adb6,86592008,f7fe34b9,9b934060,15c323ec,55981b27,85feae6e,5fde7186) ,S(d878afb8,8527a861,4b4276d8,fba39300,72196017,6f437014,980b7bbf,d4320ffc,7403107b,fca8ac64,baa94a4b,128e72ee,4a015675,845519ba,d5609331,1680e7) ,S(53f86d45,61deef96,ca88a685,38fd35ec,a95740a4,3a52c601,faaad0c2,aa3ab72f,667a6ece,bfb97682,c5e9e5df,b6d29156,9604f63,d9ab00ab,8cb10000,e6b01514) ,S(20990660,f1055420,b885fb0a,38824740,3b141c37,5aa20dce,8a29191a,e77bbb16,7d434476,9e302e38,9e14c02e,f5fd8a5c,64cfcf3d,e9813f1c,f53bc6d3,4da93559) ,S(1e70619c,381a6adc,e5d925e0,c9c74f97,3c02ff64,ff2662d7,34efc485,d2bce895,c923f771,f543ffed,42935c28,8474aaaf,80a46ad4,3c579ce0,bb5e663d,668b24b3) #endif } #endif ; static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] #ifndef VST = { S(8f68b9d2,f63b5f33,9239c1ad,981f162e,e88c5678,723ea335,1b7b444c,9ec4c0da,662a9f2d,ba063986,de1d90c2,b6be215d,bbea2cfe,95510bfd,f23cbf79,501fff82) #if WINDOW_G > 2 ,S(38381dbe,2e509f22,8ba93363,f2451f08,fd845cb3,51d954be,18e2b8ed,d23809fa,e4a32d0a,fb917dc,b09405a5,520eb1cc,3681fccb,32d8f24d,bd707518,331fed52) #endif #if WINDOW_G > 3 ,S(49262724,e4372ae6,f6921b82,aa4699a1,f186aea5,40122630,3ea42648,97c2a310,1337e773,bca7abf9,5a2cfa56,9714303b,6d163612,a75ff8ce,c41b681,5e27ded0) ,S(e306568c,1a240c90,d5e253b3,e477e2f8,4dcc1a56,ff06db8d,1384b079,cebd2d31,eac6fe3,78934260,888f2b10,7f7d0db6,ffbc8042,be373826,692b4083,92546e44) #endif #if WINDOW_G > 4 ,S(3b9e100e,2428cefc,271b0e76,23fbd633,74ebf8d9,aab41dd9,c530c39e,363136b0,fafb9815,2d16bb71,df1533eb,8f475b26,a2ae28a3,3ad31f81,953ec16f,6cdbbc8a) ,S(bb0aad49,712ac9a9,2b76ca80,f5dedef7,17ca0768,8107beee,9608f047,2f485d3f,ea699c53,c5835479,8ecd201f,7297da34,895a5afa,31670bff,e7939250,3ca2f975) ,S(79090ac8,e4eefcc0,d4e8eb19,7afe0113,e1e58b4d,b01123de,4aeed33a,36718dc9,eaab722b,91905b8f,13d816cb,cd9aaa56,dd36afb7,ba9008b,963322b1,1cfae7c5) ,S(e77c81ad,e9f97b55,1c03dbbc,e549ba66,8dd71de7,cd775ad2,a269694c,7f60c7d1,3acf1478,eef81321,c5fc3b32,3ea81543,631470f7,1c2986d3,4ec581f2,82d72449) #endif #if WINDOW_G > 5 ,S(de2b5ce9,dbce511c,f2d8878e,3ded87cc,3d633dae,a2d45341,501fb3a4,55ccf6b0,f10576f3,d3c3e0e1,bbf717e9,8b1a3744,65b8c45a,c66318bb,34829eb7,11100666) ,S(d07bddff,d491a2fe,1ea59fbd,7c121217,29659ca5,de46658b,26b1460b,13c03c56,b2ad4708,cd3c97dd,f9c40e2,a1de04d5,61d963ff,8cc2eea7,6be3f60c,2b405ce7) ,S(82403e7c,5d3016af,3765ec4c,396ce8e1,f8da45c,434b8257,10edab41,bb6a4d51,d09661b,e27cb767,4456badd,b3e84051,99ab6ccc,4ec67c1b,11e92ead,7b463b19) ,S(eadc3131,fbd626f5,263faa58,c4caf4d9,930f933d,9541c23f,438cb486,750680cf,d3c977b1,c9b4a897,5c64b36c,972d5d01,a388fb9d,c3791a74,36094ff1,2c87a914) ,S(3903ee5f,6758ff24,c518a4b3,86748f4f,36bdd65c,b77e78ac,609f2909,fc7987d9,e92194e,a15241d6,40915934,bd234749,8d222a18,4927a8da,b0cfe2ae,182be83b) ,S(d0803b78,39ab48a3,8475bdcc,f9a9f219,5759c343,dbbf8e93,23e1f882,5be6a5d9,2cc3b180,ff29c97e,a12ec15f,b38bafa4,4ecf06c,e51d1d24,2894a926,64582f0b) ,S(1f56f096,b18a7499,a153a5ae,acf8be05,8496dd23,da8e6c19,215628fb,c0567ed0,fef22b8a,3b52f490,83004436,b65cd69,c94189f4,1a93c0d5,1fc13cb4,379dff58) ,S(1d9f69b1,a4a47432,e386f525,234aa30,79e947cf,cf203297,4e0fc05b,638e213b,d898ec17,949c0761,b38500c3,a2b1da24,5438d5b3,d3f6f720,41f15d6e,e4d4ccbb) #endif #if WINDOW_G > 6 ,S(128c913,4d9dcb78,12fc4361,5c67ad0,55213354,dc8008b1,aeb5a9dc,fb629efd,fee3e54a,dd152610,d9725936,99d662,c160c8e4,ec6f76e4,5ff41818,be67c96) ,S(21ec012f,5a95b94d,244b8d51,9756075c,301f2854,8e2c51fc,49c0e3d9,d1a9685,2def2105,77af497f,4c7fef71,6949f28e,7418eda6,fd5fc162,d128de19,3cde08ae) ,S(688f5202,fb9d8bc0,9e480e89,4c7cfc74,761c3be7,7dafb11c,58422836,3e331cc5,96ba7d59,63b541a7,2ec7cabd,92403434,1a393eaf,89eebd94,62d9c218,c7302cd3) ,S(fb5c9eea,1cb9a8f5,b3314c30,a50d35,744d0ef,e8bbf68,2e4d3ab4,f7f02baf,29fb8844,e18fc551,fb28bd26,95c5e95c,6868e0cc,7e526af0,91157e9d,fb630418) ,S(f1479fe2,2eedae3f,2f5f6a5d,84a9de1d,593168ec,7b52380d,e0b3625c,cac03421,1a642d5d,2fd88b82,13b50d1a,3fbd3419,c0b4630c,48352131,cb856b2e,22764606) ,S(2273edc5,e8199774,93c5b0e0,9fe0effa,f60f7b,2898565a,69f5c7b2,bf1a7950,b3aea238,8fd978d9,29f1a1df,98495358,b64691fc,4f50b530,906ae39e,fe7bda12) ,S(99f8480c,30504378,b47d10b3,2b39da2f,496d59f4,b1462856,56f05ad7,9bef5214,e001d55d,8e224286,8d8bd397,cb5aa99e,d930e437,e4e62151,71da7ae6,6264b2cd) ,S(382257f,e4751280,d74fdfc6,993c8642,9c000d5,87f57635,bc9656ba,996a6f1f,c2dc733d,fe52cb06,265a4f1d,a6b5f1f9,30dbfa39,e3659973,1c672aad,8b51d474) ,S(23a13632,9125386b,e45f4e1b,2acc847a,62e5eaf9,f6d5f452,6e145e7f,ecefb24b,9129777e,643ba22,2bf817a1,af7155f1,413cc370,3734ba6f,49f15f55,996854c0) ,S(6659ea60,58a664de,a35791a1,8c5cded4,8cf5593d,c440b9d4,8a30ac35,79149f0b,2adcc705,a85d836f,b347b69e,742fc6c3,5300d1d8,e534f1ff,c820c6d6,b2f2199d) ,S(52dc3bc6,e1acd3b4,7ece6f6c,89fd2a3e,2899b487,41421033,37a67dd,1ba939fc,5daeb346,32ad107f,bd83d9da,15a3c4ff,1e8f6ba3,ee5193e2,709e89c3,43d05746) ,S(524b2a97,93cd5745,bd9189ba,9c947bc1,693fbceb,75f074f6,17376b10,d5573551,9e8099d6,cb23fb1a,9deb92cc,3e8a2fb5,a6865ac6,3dececa0,2d146e1b,bcc80b71) ,S(732181a8,e2bc5953,923e6c3d,d960e9b7,525b7b95,e5906997,6fe79156,1782756e,2516c6b3,5592eb0a,42ba193c,bae98ab,e3c42d96,148f1d84,edac621a,722e4823) ,S(b8e8942d,926e38fd,f338496a,c2ef6fca,49a7ae3d,f76eb15d,8d570111,e502664b,7990d56e,7dea588e,4d670ba2,2031e6c7,97248641,69e51d77,f792f5ed,befaf8eb) ,S(144e88f6,3e73abff,72cac11e,7ddccf79,19e744e6,278941ae,18d1b797,e098e4e5,63cdbf3,5df3c655,c58197f,ea54633d,158705cf,7dc2eb3b,4e09f83c,3021837c) ,S(9436e3dc,489ecd8e,2d16a739,c9c73e3d,60e5bc93,68157039,75b8efbd,5c3a9081,1460531f,50cb6ebf,d1aa7806,ea84e7f7,8e8d76b2,b3a66d5e,3a0bf60,39a7e59c) #endif #if WINDOW_G > 7 ,S(9d3c2561,7a56d10b,46d9b01a,1710d193,e840e005,df669e76,1936c275,20890db9,6bbdc0bc,4c4ae9bc,c2dfee9b,82da9b94,1f89ffcd,e8af2aca,4467ce3,78521ea3) ,S(29f98e50,f51b7f8b,e18c6ae0,b453c4f2,d0aca5a8,b0e61d2d,dda8506,3fdb76c8,daf3bcdc,ae8e031c,73eb8b21,14058063,58a6ec30,ad379186,df80e3c7,f0e5d28f) ,S(d67d30c2,c71daa36,1805e31,1dd6046e,17a89752,94d76e1a,538af074,4dc22c94,48b9b0e7,12c807b0,b92e690a,a2e068cc,e87ebbbe,aaf4bd96,9c1114bb,a54f670c) ,S(f22c2ba8,8ce9c2e4,b772c9b7,6d03a017,59aa7b9,97a78334,83566027,2fc81649,6aa9e710,f190be16,243a4e0f,1570270a,2d92dca9,8cf99a3,cbc06fdd,f9b7028f) ,S(c5e718d,6b94c83,e52533c9,ef3234f,36b722ed,cfc074a5,eff30969,9ac5f894,24961051,ccfc6619,dd64e810,fa9c504b,f7f8ce9e,cc445d7e,642b3166,eeef436) ,S(26a8bcaa,c836eb7d,57618999,ef87ee4e,c291dc8b,333554a2,c1f66f73,7944d611,c20051ba,7236663,ace2da29,c1e0763c,e57192d0,e199e7a6,c69cc65d,bbbcecc9) ,S(388e3570,fb7b1545,9bf01ba1,7a6496d5,6bcf65e1,764e7aa,2c083346,2dfa098c,2d4e0d22,a2eb0ff0,545561e5,ae344be6,99120d12,45db6bde,a9500f5f,a07be798) ,S(68189bab,b5a0783e,23227efa,4eab2c6e,da2d1c,2ea57fca,7a7f8f72,15250709,bd30bd83,3694d3fa,a14954f6,251445f8,3e42d517,30d30855,a0eb834d,3c7ae856) ,S(642e0823,bb347795,967b7aa9,418a25,ea6ff683,fd7b3d42,b88d90d1,292190ab,db73dea7,86ec052f,e3674892,639daf39,286b4690,63b68903,210639c7,f3b4000f) ,S(9ab6ea81,e5bf5505,751addea,5896afab,7f4eff2f,d3986027,f916835c,64924afa,38c06aa7,4870a5e7,2ff29efc,bce4b3e7,dd951c9b,29966f2b,47d007ac,7629bb6c) ,S(b09805ae,e567f69c,71a98248,e89e64f9,e059e015,bde01a62,dd18158e,e94a8ee7,62aea16a,7ec912ef,cc5382eb,6d220ac3,dea885a8,e3da12c,8147b28e,1983d221) ,S(3d632a5b,636ed5a3,4a58bfbc,9831691a,91d6b5f0,975bfb5a,82b4c1bc,107e6e5,577a449e,75bf16d9,2eb6ba0f,9cb4d496,7a7ee09c,f1605aef,682cfa31,cf395a1c) ,S(6b821bf0,f70d5ff2,ceedb69d,d96ac8bb,b51e3635,3a36d50a,b1c1a697,40cef707,5212ce11,993fc120,88028674,5cddea94,6371b4,dfa2f47a,6d83b789,c6d12e5d) ,S(bf294951,4496fe0b,8527740b,5cd9394e,dc33b330,c91d996c,789db854,45728b23,790aede5,da35ce7a,343f745c,410de38f,4c53bc2a,bb41bbae,c13272b1,e912782c) ,S(a55354c3,82bf968a,16668267,c4498946,4906f69b,114f6f06,742b6035,1d75ec80,2809bddc,45661a5f,28b31967,6cdfb5b1,9dd6d296,d1828c88,179a630c,ca5962e8) ,S(fc015036,abcd8311,bbfa1574,ffb4980f,b893f8af,84f519f4,5a6fa344,2649a693,d0f6a278,1946e04b,385cd004,29acd3f6,f5542aca,3e7c789,657f676b,f19db819) ,S(6164410d,9f81f352,272a799f,b4afbe24,59caea6c,511fa4ea,b7578980,d9a7aae,92bc1480,ba19fcd,3cbee69c,95b9396f,4982fff5,d4e7dac0,abec7153,ee5a7966) ,S(ef816535,8de9d737,728f9a9b,3182b4f5,6e25917d,1ec05fc6,faa0fc85,170b5f2d,dc372426,403ca9c4,50649df8,8b6fd32d,f1721dc,cb1c7d7e,155c83ea,747ec595) ,S(428c34b9,89a436dd,dc704e68,170d2c40,178c5646,841eb2e2,642c0a48,8987a8ed,b1f24158,251c4646,ca04dc3e,64369634,3836f97e,71945f4f,51237abd,3aeebe06) ,S(6eb61782,f909157b,415e6243,7bebbd6a,5f19da73,7eda64a5,5acfe206,65417a9e,4fe7c546,baedf2b1,6c92f168,f99c42f6,af03edee,290ecc39,4c4efff,e8577b72) ,S(992e0af1,466d4fec,5ef83009,98ce31df,cb6f9573,d14c1646,e4371c62,a376fa4b,d0e3da69,1e4396b2,eb01e3a9,964365,50d000e6,31d79ae3,871690d5,29f9e825) ,S(fedb564b,adc70078,f20f31d1,12496934,513e9903,8cf5b9c3,1084383,5721d11,1a8e2a49,57e8420c,f2d5d97d,657f1602,ba26ae87,d5408b2f,a9448def,38157a39) ,S(f3f2068a,4dd89d18,1247088d,3c424916,3e683226,6274b575,e54430d0,73b24bd,f2aabd19,a7f462,1426ab1e,e0aa7e33,12381c5f,e1f1cf0e,75c1a7f7,7ba2bfa8) ,S(32b9225e,4217a359,8de4e7c1,476a8581,5b6aa458,d93dae02,b3d30772,3ca13680,7466e804,26856340,12985683,dd071e97,53246214,733808a3,96f35d0e,5a133802) ,S(85008a87,385ed6b0,4ff89979,2eb592f9,ee6c6b93,fa24dc7f,c6299b9f,dae64a8a,1f279e2b,8a5b0576,fb9569f6,c0825876,84b5b38f,a250e362,2ae6e284,a504a2df) ,S(4dac7833,ebbeab0b,ec8edac7,cfc49bfd,b835362,f0130e9,e44452f6,a82effd4,fc9d1970,f230aa68,6114ada5,7b4237dd,133dc3b5,db8ec1f0,ccd09aa,23c740a) ,S(9b755881,45a65d54,19b40226,e535df5b,4b44de41,1b93d71,31f3102,d56dbeeb,d0324171,d6937b7,c9b38290,7dbba3b5,c1516061,59e7ce1f,a1ed9d11,e089a02d) ,S(1bd6ceb9,2592a7d7,a66e6e8b,1b645db5,98b525ca,461dc4bd,b583ed9a,cbbc8bdd,9a59de87,84a98bea,48b7abb1,a5b7055,5a1c4ce5,551cde4e,7b790ac4,9a29944c) ,S(25a8b2b9,3b360941,6525b08a,7fe786e9,6b3a3c7d,8b444637,268f5355,bd5b56ee,3c58ccf7,5734687f,dbd027e6,3ec6c550,45f131ae,df71a40a,c45e4e8b,965f22ec) ,S(244b2833,27c33efb,221a5767,15225d6a,bf5a1caa,8da543c0,d88b21e5,17ed9f5f,220036ac,e48d8953,5aecec92,a29f5012,37f83ce6,44380db,c229f0bf,c1f53d7d) ,S(6f97ac0f,27b87905,6b442d13,e566978e,91f0cc1d,d6ac1e64,e9764a35,325dd1b7,83c6e70c,fac6c707,226ce1cc,691b38a0,7e937f5a,5f2d9c81,4dd0d3ff,9f433d32) ,S(72c5d60f,eb014e2d,ba8265ca,d454f261,2d6abcd4,b2236bad,c94c4801,561dce1f,e3119a19,7ef91963,b3b28216,3c5d3acb,97b281b6,d246cbf0,690b40da,63978fe2) #endif #if WINDOW_G > 8 ,S(a96d2da0,1b10186,6998659d,f441a1b0,2af32b94,aae8c6ea,707d9ed0,d5f33825,660d7d83,5da5235,9f7cfd41,28c370aa,5659ea71,16a91690,6c0e8108,a513f9f) ,S(2cce6f63,4d815ecc,1981d200,87616677,d906aa27,990c4875,17314dc5,5be3c4fa,615210dd,bd599e91,1b6f997a,fd05475,b33cb274,c9ecb6e5,d3c23323,beba4b50) ,S(992b0084,525dd399,d98602d9,8b8d53b2,4558fafc,758a2f46,60e89bd6,a645f0c4,83ca98d2,26545a29,8c45f40b,11420602,f5a5c70e,595eea57,2da64d61,a4e2f98d) ,S(434efb45,3089619f,cc761ee4,3fd4b77d,c6b0c69e,b45eb88e,44ef766e,9beb7357,3dbb0d6d,1c0b92e,5965586d,236c0be9,26967ac8,830b9bd0,1e9efc2,2a9291ea) ,S(a2179ad,2c683306,a2e4735,93efe304,f0dbf589,c4dc2b88,4bddc5c7,e3fbc156,ee4539f8,ab980176,a18e6dfa,bdb609d2,88a2d223,86dcb20,19207afa,f6033c1f) ,S(3934081e,d3e1e147,aa52bb40,9221ef6,a445f22a,66718f14,6d63907a,ef05a2e1,bc370656,31391b7a,209e79d4,9f1e959b,d3a9fefe,752c6062,14fab290,a7b5b3c7) ,S(35bc24e1,59a2b939,438354,6cc4255f,f1f3f7e2,105293db,39688e07,df95d8ef,dee1fc70,a9698da,f7abeb5c,56724f8,e87e0cd3,8849edfa,246ed0a8,9223ae15) ,S(f5d1e75c,251fb473,8552a0ee,f05d8e65,63aa14e1,bcae5b48,bc7e5258,b948127d,e260c1bc,7044f058,8f409134,d298528b,e7d586f4,bf7b6fe,92d212a8,6f7170fe) ,S(ee0a76d3,6fed282f,a1170dd,6acb7743,f9617bb3,60350f54,d12da1cc,7eb121c,f8cfc2db,eba6960f,e6135ef,ff9e10ca,4e56c458,4b42b516,6dbf7af1,420ba5b1) ,S(9e3b87cf,78927664,15cab377,f1774d14,4d1879f6,16da5676,f94790d1,9ca689d8,f8f34522,da3ca2ac,b273b0c2,b1b1f26a,7a9c2d96,b4547482,266a8e6d,bab3b577) ,S(e26f256f,d08942c0,3c85b89e,e66b8b50,12f409c7,4f625152,86e5b310,eb4868f0,bab3c4d9,6fea49fa,6d08c656,23c9b127,3552c23f,3c4f12f2,1bbe8bfb,56f210f9) ,S(8ac74046,a5d38398,d14b6763,4f07abc5,a3f5c852,ea8c421c,f0858980,11da6c2,d20ca793,f56e3198,854f5916,35402c2,4a71af95,c84288e,1495d324,7229b3dc) ,S(5b00e095,634694cc,93d531a8,6e81d29e,753928bf,b2c83a83,ac677a92,55932bd0,8d2f267a,8071c48c,616daf18,d587e,42882b33,748032d6,4bc3efd6,60a99656) ,S(162190c4,80c5d7b,ab1ae4ba,7b2a6611,546ffb9a,b4e9ea87,2c0357f8,9e11f0b1,db5e2104,12448a9c,e586d7a3,13bdcc6d,bb84192e,98c5d9d8,79693030,92423525) ,S(f6a84421,b4b383e8,87f8520,e06017db,476774dc,9aff636c,f26a676c,85b145b1,504c71a9,596770ed,7a2da8,2e8fe1ee,93717215,bf88e0a8,ed74a80,4037a3b3) ,S(1f02d142,f0b5d3d8,b3f8937d,a49f908d,83e5919e,55c9c134,55a759a9,932dd6e5,e6a5cb33,8ed36df7,50ec2eae,5db7c9ff,fbc9035f,48ae0348,fb3882da,39863e65) ,S(61f4d96b,c326a1fe,a2ae38c3,73484a56,68e29bf5,12d77a04,34a62278,1d78899f,651ef738,62005ac7,64f97021,6180c25e,2172724b,375e6b38,b3a37ad2,d7b4aab8) ,S(ba7d5c0d,623c5e79,8088a71f,8d2916e0,7c7ebe2b,1afa19c1,9c917cae,31c11616,da409f40,d7e3f6c,78655153,fb35595,a1ec37e7,e66c8958,ce45b07d,bd5f5a51) ,S(8b90a590,eacb977c,6e6a68ee,6dbc3e19,fe5a92a6,9abc43c3,bb16f9d1,925bdb09,a5cf5f42,ef655d59,ae734e1,f746a752,4d01ef75,d829b9a9,2a035180,fb5df718) ,S(87f35227,21914cfd,ce8294a3,cb5ae171,f0d994ff,f55b25b7,1c9e9aac,dff4fe4c,cc71d1af,530bc5e1,eae7c1ef,b9a91335,f26b283f,222a3552,dda24c28,64babb2f) ,S(aeea4d36,ba405159,bf0ffe8a,5530f1f3,83d5509f,187ef58b,6c1eee4a,cb77a15d,db563dea,e7403df8,7d3031c2,48aaa28d,96958f7d,ce36b3f7,8d55607a,60d3ac1a) ,S(300fe98d,3996eb9d,57c6f1ef,8058d4c,d8dda436,5774edb6,2a338a59,afcc7111,d148a017,8fdda40c,f937913c,143b76fd,d2e6e226,d27225e3,a49658b2,38c40e77) ,S(c700af5e,22cd146e,839095a1,f6743e4f,d01e9c1b,76d4c73a,a5005f42,99c19fdb,3fe00181,b1f01c27,27ab1fc6,bb6ea569,d4a3092,c2d511d2,8b5546aa,194b32c0) ,S(d03d08e1,17b94138,1aa147af,38448539,94228f75,f96bb4a5,941c3748,cf50bc60,5b119ffd,2785bcc5,2e0bfbfd,c541da8d,f47dd076,e91440fa,10e071b3,a896e31d) ,S(6c6710fa,17a520b8,56d7fadb,6af81a5f,ea9c983e,c94cf832,b395da5f,c22bd361,db4efd26,36e281ea,419964f3,c0897b05,b036a408,25ed4ad6,4fba393c,f2804941) ,S(d7b5c239,9df47a16,6b6cb900,d08a5d9a,5ea3bfe9,94f861d9,b46f3fbd,a3d91bbb,ed791f4e,4ab1c25e,9c83494d,794ffe1f,a3c8a065,29c0b710,cffd597d,64efe8ba) ,S(90f699ab,8f728152,e2deb8dc,ceaaa3ee,53ff2f23,2341a952,4aba9e8e,50f66c06,8bd0c3a7,7f5312bb,9d46d80e,c36921f8,561558ce,6e63c08e,641c82c9,fefce91d) ,S(4d0eae3e,3d7adc34,c91eaead,6a16f569,37557dce,2b68744a,bb9ae71a,8dfb65cc,816b0806,a9508731,ba99a685,142aa52e,6e874c99,5096a53,52c6e2f2,1fa3de5a) ,S(46cd9edd,ec318498,dfb4f815,3315185d,689a2399,8e06b1d0,2438f7c9,b2f7de62,3b5bc1a3,d5fd7874,8c964a8b,b813388b,e0d5d168,1247d008,10a846fa,561f29bc) ,S(4aac80e,3f6eaab7,1c576297,b4552e40,653748fe,21a580ae,bce4eb83,2ff730b,3d42a00d,8014f46a,80fe2dd5,bac6a046,40d331a9,4f1de050,9e435398,6c8c7954) ,S(59bea661,b73d9c09,131e4573,199937a,e03e96f6,2ecbc637,4bb681a5,582a4114,31a20be8,ee8a2c2e,81d062e7,8e891504,d9f2639a,bd5db5c1,30be3d2c,b1afa47d) ,S(7fe9065,88b2ee92,2b19acd3,fec7a4de,9ee089a4,a4e1c338,5e293567,90ca6037,dfb45d90,c5f43eeb,1f5eb326,20763ff4,2659b763,e7ec72a7,c69e9369,35e5c128) ,S(db390f91,32277889,784b5e4a,cf8f2fd1,f3a5fc47,f2c8262f,19dc9518,95322157,4364955b,241c831f,94fd7d4,da63db19,2aaeb5c0,ade82dc8,d5d61cac,d690bbad) ,S(34dd0266,e5fc19ac,7daa9e61,5ae8f78c,985732a6,1c53c29,e6e5d407,7391ebc8,c2d6b6d8,e73fe00,e6013b1d,2c2b48bc,77a5db6b,45232ddb,6611ea1f,c5dd797b) ,S(eea7f72b,7e31608d,d3dfcfbe,16e2ef95,5e6c7ec5,328f84db,336e3df1,9d1772ab,9662c8f1,ccdea4c3,48ea6d94,739aa747,17219556,c6be9b8,8af0d30d,514004bb) ,S(c6af087a,f1b10eb3,93de412d,de856129,9376d264,36d907fc,10d3e7a3,88c391f2,ba99d62e,31856457,8ad8847a,9cfeaba5,e5ff9824,2c614959,eeeb4ae7,50825144) ,S(eae34735,6c715740,ab73d034,bcb43f5a,aff37fbf,50d35518,1364c999,feccefc7,b9386c75,da8bf645,cd6f15d8,4944f74b,9685256d,b61fda98,79fe6639,92fe4703) ,S(4a548c25,f4d8f54,4f9a27e,64e49626,41b68ae3,1d90461,65c24ff7,fb40438f,ae9f2c85,bd608cf6,ef5e40c6,7e29a63d,4c274215,c2a0d578,38252f28,196f6d10) ,S(61925679,dd6545a8,ea19743d,7cb3c0bf,453318d9,e180da53,f43af2b0,ecf744af,a0682d84,d7215372,e9ec062c,a3e4aa1f,47fc551d,44e3d1a1,7260a44f,2bcb184d) ,S(e1db5e86,9574ab76,d4fa260d,2425ef62,50267ab8,52ff04fe,25f0150,9137ea2a,c8eaf421,9fd5f7a3,6c1a99a1,d0c61250,836e204b,fb496774,83f43c81,511905a8) ,S(3062cbca,73923842,2a0ab862,a1fd84f0,38e63691,cfc204a7,d2f9d263,d248c7f1,8f112e57,e3f2970,dce89eee,1e184310,721a85f1,cc9feb2c,f55c047f,dd9670cb) ,S(67c393cc,aa9736fc,eec7a861,eb53f953,9da74ff2,97764f4e,4e814004,4da4f739,93d329d0,9a165fe2,2f8009d5,ad59b524,33ac24d5,46c7d394,2d147c4d,49853203) ,S(c67471f2,36cf2187,ee5a5619,d581cc7d,ac5bc5b1,e8bb728,f943084f,e899bf5e,75c90c9c,787b318d,943c3247,74cbbcc8,3a533f37,fb684aea,62fe6848,8de2c513) ,S(d5015fef,d5938dd9,2133d7a4,25aaac5,12143acc,6547070,1827e98a,e4ed1b52,44305616,a02236f1,5c37c0d6,51d845dc,e9966860,b798f79f,4006c25d,7cf03d6b) ,S(aebcbf65,aaa89615,cb48ed56,4002ed9a,243ca309,1cf503b7,3c1929ce,8164f2d2,4fc1f25d,1a30ee2b,4220305b,a9c88e86,a6ee7f55,55399ee5,35e7d37f,e4b3f019) ,S(15cb1617,1727deef,49ad6821,932a39d1,bb8f980b,b5370d81,5ef00ff,ebb30e43,64ad8c82,87fc053f,ee35c1b9,9734b34d,2dfff86b,490ead93,b1fe7d2b,f80ebd7a) ,S(d404209e,8530d674,9bb88a5,525211a1,19fb2523,63e2698,6bd03080,4c49c123,3763fd68,fdb85d19,e8506275,3b5a327c,46ef87be,8a3432c5,62bcc622,40a7a128) ,S(f3abf8cf,c232849,58e330c2,fc327ac4,d40b4497,f422aa4e,d42e9381,9bffdd96,50861f05,d831327c,3e907643,2d7a7621,d1dfe9ec,7ccf2061,cc720e9a,7d5b0d5d) ,S(78a32893,2ee9dbfb,3f84755a,651b9d23,5cf92b46,c3e4bb4e,57b7ff6f,7c874dea,925b783a,966721f4,6eaccd87,495eab7d,b3c36eb2,92c1a473,b4617f6b,9ac85895) ,S(8165210f,5d146f8a,1ac1ed91,a7bb678d,1b7d15e4,3ed55e8d,f6503209,a750cd4a,fe390d3a,19e22bdc,cbd45875,e396c713,85954166,a1edb63a,384b8587,915d260d) ,S(75269de8,6c2f3d34,cdf17dd6,f3efa198,ba73431f,cf0072f3,633ca57f,7dfe3f09,b162a65f,d19927ec,4446e3db,d5ee8850,f463f39f,1df1a0b1,f5ed153e,704805bd) ,S(5e36ce8f,b393949e,5b9c4e10,44fb2ff7,c520a7b7,a9016b38,9544e512,427145b0,7c40e718,292f96a4,1d9822ce,d54aea90,22074c5c,c82ba4e,7d39a4e0,7811614c) ,S(c8cc7129,fdebbfc6,c0576edc,6ac983e5,c249d360,76da7d25,b05c0b6b,16632746,48a8cce3,a77e4498,76d1a332,c539feba,2653fbaf,d4f75e68,e4674d78,4c716fb1) ,S(9fe1db36,f1ee3e6d,3924d2a9,ae3ddcaf,fa85798b,7383a1dd,2d6c0c14,ea46973f,1d35b6a8,607045c0,95ed9658,80212b63,43dc55ec,beb3223e,7c2e76ce,2c74f6d2) ,S(4ca8ab8a,3d45748e,6e19e02d,dc351279,e23648db,d26d2465,7c9713f5,bc8ecda2,8a5866ad,9bb7db92,273c9f23,c0876c95,13b8a68d,bb20c5cf,164a9a39,4e3e73da) ,S(c8d0150,e4a989ec,5cdbc724,21b1e29f,f1f30818,1d8117b1,3d376f58,b72060c0,5c5880a4,c5a73a4a,1ae42a9d,f0b20032,7ac4a732,cb26e717,49e63365,5082ebd1) ,S(3d61557b,b4b9fde6,49fe1b7c,981c9883,9e368444,f130bfea,fc1e1a0c,12f2aa31,933167ff,62cd840b,3a960c90,e6b1c37e,1e233695,318ea286,71c87992,de5b56f9) ,S(67569f9f,fd44ca09,5b478dbb,85c3ed1f,feaadaed,cb624552,ccfaf169,24e69e2a,62bb2948,230fbd2c,aa941288,7adfb24b,d16619de,af0fc102,feb1b26d,67eb7fcc) ,S(6313d13e,debf1401,eb7d279,2c66daa8,6e3075d0,3cf0daf7,f3b753e,7372fbc2,44621230,50eb1245,86975455,63e06e2f,2839f874,beaff9c2,f65e26ad,d3573ef3) ,S(6f8ec9e7,fbbe6e8c,d0e3085b,47c6cb2b,88529f2,15f13195,5e2fde24,4dd23968,1fb61e14,523b3fae,b543b215,dc46eeeb,23e1950a,8301c78d,c510c76f,ed36cd79) ,S(56613dac,3c5aa1ac,bd9a0ec2,f839b4c3,36f0ae58,e0e02244,7bec0546,710b7f6c,247263ab,86c398f9,3b23319,4434af8b,530908bd,dd7f716c,f7b73aa9,8eca79e8) ,S(c9de15e7,b4147219,137e6e57,c5a7ddd6,17e91ab0,6859dda0,41eb3c21,87aee08c,c7178ea5,cfa056d0,dfd11c87,715591cc,40cc5db1,f5e4b70f,d8ffbfc4,3f8b0009) ,S(7590a4a,627d5e90,e42a4b0f,6be6497a,f906182d,d2dddc48,a8b6bbfd,f56c0504,d611e21a,b5498760,5c97e878,baa464bc,cc5bd875,353b69f8,1f93ce2a,a6c38587) ,S(94b1da0f,b310e056,db0dff72,81db3362,1fcc555d,bf3c973b,76097908,7fe19d6a,8318893d,d5b41a56,33a2ab4,ae4b953c,45c42e9c,8f2fd159,85286de3,fd4fc217) #endif #if WINDOW_G > 9 ,S(b5af4299,bcdacef1,e07d081,daec2cfa,d6f8f821,38e151a5,f20e6d52,84c9a6cb,c0984407,8a7db82d,f572987e,b137dc09,c8cf65fd,aedcb20,43b2479b,ab95448d) ,S(5f49ad43,70744587,3980a153,c851829b,f8ef6141,9889bb0c,3c476847,6939c3e3,5c40d385,20f56c3d,ba08ae1,b40fc24a,2ae25c94,45cae0f7,d01d1800,747e04eb) ,S(f6bb067f,88ccc11c,64e30d1a,e6893942,16bea3bf,26ec9c64,5cde1b9e,487da385,315a476d,7268978c,d89d4ec8,adde4a83,28dbfdd9,f2bf44fe,ad4ed721,78288f55) ,S(7b47cede,c02b19e0,94daea0e,ec000455,52690b49,44b3f10,beeed2bf,f9df6950,1bcda5f4,9beedec9,6ebac5a7,957918af,53b7ccd8,c211330,280ed93b,e0efe9a6) ,S(ba69d7f3,82d56d9,eb65e1ab,2d70f52d,18223621,c0029035,a78fd660,9940876d,5f44a2fd,56d5289c,f36bdb9,50ee2538,1d1cf935,ae1aec76,84b6d11f,975d393d) ,S(a3b70894,d226c195,223713bf,330ba39,fe7ec35f,9743347d,1d3dfdb9,7bd929ff,5d0cbdf,42755aa0,355ad2e1,ab39479,495edf2c,20bb0aa5,93cc04cd,56ae6135) ,S(c756e23e,bb2d81fd,91fe73b5,20eb3bfe,5ae602b3,448cf84f,e8da37d,d1c804e5,89f4b6fa,edf86b9b,ca9f52b2,9864a982,5a4faba9,d4fb35f8,98511210,34df49ff) ,S(36327c35,6fab94ab,f791c234,1c39049c,65410e9c,6cdfaa00,d172ee84,3671822c,fe3588a4,698c8d35,f0e01f04,e94f7039,eb745631,8c25927a,be7d061f,d3ed4c6d) ,S(3b75bfbe,8e372311,f46ecf6f,c5eb2af4,b66051b1,874b0c32,1189e106,37dd21bb,b9144a33,e3c3339a,4595e248,87940b4e,2e42a095,d7d1bc2a,ea50aa29,5a879908) ,S(44a61f10,57b4e88a,c55ed72,1f8f4477,5f0272bd,379a97b4,d92a7f75,f0d3c5e2,e870ea65,80340464,9716ec1f,5b79392,18162306,6dc14086,111de144,82d80141) ,S(11ae02f7,663c0a,24c6fe5,ce9206ed,1ebed2e6,ca294acb,74c9a227,97fefd,635a1b87,a262fb30,5008737a,e70422cd,a4e35766,940e424b,d697d28c,dfd6a36f) ,S(c751310a,dfb25d14,2e6ab1b0,ab31b37c,8e987af2,105d5981,69085ca,3e142f5c,a4630dd8,ed2717a9,f10485a4,be685c5a,ccca851d,4bcc1886,4df943ba,ee821014) ,S(fff4d7c6,4009f39c,41757b17,3eb2536c,a639b72b,e15af7f,790bddb7,efefe46a,694a798e,ffe22d1,1030697a,292a4bb1,4c110d6b,dad7edc6,e8976450,ce5080e5) ,S(7d76ea39,c13c9f46,e931e8bc,1cd43707,932b1a,31254d18,c06c8ce9,c3f90534,bc14b2ba,8f0a3d8f,34c7cf7c,3458c916,4cee438b,39a5a6d4,d2a1c9fe,8be415bb) ,S(b6efcad2,ca6ae4f3,6f080707,530aaaad,625fda5e,825f77e8,a6730e95,5e07ad39,4868d8ef,8a56d327,3f6f4a3,23ea6ad6,4694301a,1f6405f0,a421939,bdb1c765) ,S(1a04b12a,a889c4a6,d37f9050,e75406d3,48e38faa,c0d2ab4a,e30caa6e,3633a32e,f43a0c8f,fad38d90,6c817dca,3e7ea09e,21e1c801,7af86966,c246ebc8,dc75911d) ,S(adaeb0fe,9b345190,4e878b12,6c8edddf,b70e2500,5a4d6a6c,531aad51,83209b7e,2b26b16d,dd4d29a7,8cc6b4e,198e6ede,b1c59def,c6793173,f33cb039,d37522ad) ,S(4e4ca02,3931f3fc,b512121d,2d632764,d97fa125,8460d0d1,9a94eb88,2c6e0679,ef90eecd,3704a6c9,454c6860,928eb332,cc917b17,f2594348,515822d1,84537467) ,S(a1f3c279,df69c13a,711b5ee4,139f603b,5654ecac,adc02a22,a7c2087,c11e2971,57249794,54cb78dd,7ef69916,5efe2326,e8aafad7,a8a923b2,252523ad,b6a16b2d) ,S(aac76f81,488668e6,f4b0c911,bc9675ff,c19424c8,6a6903c4,f4b13e0c,e798c7a5,24ae16df,dd6c7d6c,1391df3f,73609bc2,c3759536,eb277189,588a72d1,84dd2978) ,S(70e94171,e59622f0,de360166,6498e6c9,ddce496,a15e30a2,a5bdb701,d0034769,d6d7c0a7,75a9cbef,2b84d4e8,200f92a,446111bb,cf46a57d,5e244f1a,1103b757) ,S(ca17e5e7,11d44492,496fa849,c6ab1c47,3426706b,5b8282b6,f288e096,8ec78890,b3ddd632,2ce577b8,ddb9f501,e17d32cc,e6c58fee,4e283410,5e32f3e8,8bce2c2e) ,S(1a16a58d,8d70fde8,6ac0700f,3a43ab9c,255ec001,8d5fe571,7ec6324a,2faa62e8,f2cb2eba,65aff0a3,dd7bc137,257c1d30,dc2eb6f3,7a3897e1,16c0eb1d,1a710c27) ,S(8f2dde65,b4ddf10,c29c6bbf,5ab2ac11,2dd3357a,e3e5f01e,98190e32,94b9d4f2,e06b8cf7,e5a736d5,4e954bd,8591f7cd,79df335b,d3279f5d,80493fe4,df4c6afb) ,S(3314b553,f8213e7c,80d4562e,cdb3564,ba1d7285,6c88d8c5,a3adda90,4950162,33e83c5e,e3f7c550,f94a7434,e3cad51e,b4dab462,13acc24,fc4aa1f9,fc43532d) ,S(7c107ef4,65ac0c2f,fc5b11a3,348a7cc3,fa589554,ee2b6606,2af3c5ba,25304000,6b5bcf12,2e8a0705,d067fe78,e56d365e,89b5a979,c23f124b,508e63ee,975702c5) ,S(e918a829,325adf67,511e257e,e5596d08,19be4605,36b20cb9,7b76a54a,5be4f8b3,1a92f0a0,b46152c3,e1ba8f0d,12119c15,b70af0ef,3ff0ebf,a9dc9207,cf2fa8ae) ,S(8770da03,d4f3a4b9,e92dd2e3,be309c81,c346c97d,2cea15d1,e3fc94cf,41b9b079,d025430f,dc633d57,18d372fe,64f57fac,53f96461,1fb5005a,10ce842d,ab123c03) ,S(c6b4ad3f,ae2b2557,b126a57f,6bbc039d,a6589f70,c6283ea1,7314aad5,acd8b22b,e8523dcd,2c1c3412,35df278d,e49c38df,85f2888e,cf3c76fb,46e1affa,d8d29bfe) ,S(9aced948,6ffbf984,373b1e91,ff871619,4622741b,1e1ab968,9c88cb70,37a86e14,d7a7eb1f,1b4c31df,ff43cc32,1949c1d3,16e1e7ec,a6a852cd,e8e7f592,8b352d9) ,S(af51536f,fccbdab4,c4f4015b,1e8aca69,b08bf055,e038b22b,87c54f5f,1b9007f3,b6bb0b4c,95c07ecf,49ffa85b,abb1d308,cbe813b7,703a27ef,cf849e,47130f7b) ,S(ec5306df,3ea0abb5,6fc45a09,25c1c925,56e02ffa,18238c3e,5bb2ee53,11823ce2,c950cdb6,720f65f4,18065352,43c90bd8,9457f4bf,d941c9f6,89812840,2dee8b99) ,S(293b1ca5,be127bc6,1a397ecd,59164363,587f468c,81de4d87,6c5d9bae,e72d90a0,4821030f,238e9f05,e93d81d9,1764863d,443a524,3d18e61b,ae26f74d,ba35d821) ,S(ebe54b7d,99876ab6,b2951f0e,e68bfc10,16877142,22ef83c1,2561f486,b4865488,2a1d651c,caf8802f,fa699d91,b8242f51,58d84fa0,d481bc47,9246eeb8,6d381c07) ,S(88f77523,3ab0d69b,ed220109,b29d0d99,33ac8325,445d19df,d38d9c69,3464acdc,8f915122,fbd95ef5,31ea2cb1,aec6bebf,8e059059,459c0d5b,79a282cb,cb276702) ,S(1d84753d,e7210dd8,9db6cfa0,8ebe9797,c7fa40b9,6e94439f,b8117359,a2b3bb01,f7360b5a,ba53a4d8,7440b6d6,f540c485,2e889c33,9f34260d,abfa7861,f1f41ad6) ,S(19e69df5,176f82c1,cf1ae032,cb388ce3,36f82a3e,5e741e1c,27fcefb5,311d4b2f,c401f4fe,c9ba53be,be175dc8,cc1d17b3,9d9f7af,5bb496e0,b95bba6,cbd5c143) ,S(73189e02,c1f125ff,df1a9399,57f29aa5,19b04f5e,42adf729,53d354cc,aee3f2c9,52b8e88f,1c6e7cf8,621d21b0,1e406038,d901de1c,4101d424,1009c01,a537f704) ,S(c5ebe082,8ff1a8bf,52f8956c,b747f1d3,278fd2b0,a5ae7669,1c256e9,2887a74f,ce58cb9,62e74b98,1ab97dc9,2d736b5e,c506e51d,6c09b382,3eff1cdb,cd259860) ,S(783c1621,f7990e01,4296feed,3bc883d5,1a780867,c83b9166,435a0562,4982da76,370b3e2,c9a189c6,9c565c3e,8eb8019d,f5224574,bd5ffbc6,22f563e1,8a36da30) ,S(555e7e80,ccc6a46,1724cbd6,4a53721d,fad66fcb,2c71d579,4d799f6f,fa2b3305,67bbf165,d39d7042,18f5ed31,28fe6dd6,db9b4809,b3270eb,63bda603,f44e9e41) ,S(40c49a26,ab1cd46c,f1e8467e,242c6b1b,faa40a4,cacdd50a,4b0213a5,40243471,16950b00,5002622f,e0b9fdb4,c34224c3,ad55bf30,67f4e96b,dc2813f6,2fdadf86) ,S(eb6b3be5,db098d18,9c810b9f,5593c746,47306226,d77e162,7c8b62f6,d7935298,3d295584,3f356f5c,1f990231,701cedc8,c84e9671,44be22fb,9bd74f0e,15c5bc8) ,S(177218a4,2b55c169,1ca0a073,4d061b53,a0683536,9a04fca9,3f670ce,5eb26091,9611661a,a8a3bc73,7717f243,e5e8b97a,57e0e72,759f0f4e,cedb690c,b3a5fa42) ,S(841a8fa2,f3bc5f8a,7d028c00,127c267a,ea0c3762,8b07ebe3,7f883a67,8fd2a680,579bf37d,b2fd1f77,a0057712,88dbbdcc,526938c,4f9ba89d,9a42d4f3,452cf1b0) ,S(b01ef554,3a377f1e,c801421d,a399c53c,3585789c,d7e51691,32250a61,6edea82d,28f30ce9,7e29b2f1,3af626a0,7a37f14,82e119d1,e66389eb,9620200b,25a90265) ,S(b93e014e,8e3cc643,17ee70d6,ef8c9918,ba344e7c,b38a9a6,2591b0ac,4f38904,129c185,5bdfd10c,6bf152e1,2ff89b4,d0b368ed,c0ae01f7,2b29fc95,240ac3d3) ,S(e0f426f2,43c50d9a,ff80a1dd,26d63189,a00601c6,8ac81373,5fbf548,7acd522,96d883e0,951adc5e,304bd848,ccf39c2a,1c19382a,eb24ad1e,1430d705,deb749fc) ,S(e11e9c74,40e897ad,2870adda,63b9ec04,d5379f14,b3bbbdf2,147ea9b7,9c73233c,49d6e54b,29197532,3f5a9df0,3e22e359,e125e34d,d9f3d6c5,cb9f0a20,6dc1f019) ,S(91ad584b,c5ef145,3b796eca,20027cc2,ae38ee70,9ac4591c,79cf67a7,a96b2c2b,d815a213,a620c531,11f79e5d,b5d9c3c5,565dfd97,ece841e2,3e9c1ca7,530bac2a) ,S(3e725392,f4fa34f2,7413785,cb322f35,1032971c,2303f3da,bfe40461,4299f8d2,8e323a51,5addeed5,f3548217,6907efa5,4e0c1d57,7895839e,42223e5,7708ae85) ,S(5e87bec2,1a589ab,483c00ac,fa863f35,91d9119b,9a0239bc,ed4f5790,45a98160,a88a3b84,33c75c1f,9eaf3c15,9fc39a6e,33625f1c,d0cd7263,3a825023,f2e7d47b) ,S(c2e08613,2cb93b35,749cb652,44e99909,da18260e,d252cf32,489fa1c8,d268a0ed,d3f2e3ad,1f16365d,d47038d6,854e0773,28e02e64,d05a4764,4ed0d82a,8c8a5761) ,S(99304c5e,ccf09869,7b2193c2,31dd9432,3b9053d0,e4b9025c,74517ba7,f1978af,ee77fa7b,638b1396,6f7e77e3,43dd04a0,ba1324f3,1e0da111,338019aa,209dc789) ,S(40e108c5,59adfb37,651f04f7,9ef895b,25a79f03,650d6b1d,1c21322a,b4c5c6bc,8980ab38,5733e648,84aff3f8,c47fef44,210eb2ab,a094eb2c,fc5e464b,679db653) ,S(98c88257,2d190721,20c31528,7f508df4,6d6276dd,c9711aca,5bbeacdc,88c6a78a,5d1aa976,1f5c5ffb,d12ea7f4,8d0510e8,b57f270e,e08c3256,f3ee676b,41a61c92) ,S(389aba7a,25e92306,b84eeab7,a16c37ae,d7b4cf09,806ff740,c05dab20,60af6fed,673ab0c9,ec48e2e8,d372ed60,812b2990,49c32637,35f61c13,d6f0ecf6,d065707e) ,S(9dc64fba,832c956e,93efda62,e5f11b3a,6619eaaa,e539b732,61453eea,ca53df17,180b38a9,3c56ab10,a4267ad8,d8a358ef,8f60a9c9,9483889f,956bafda,f45990ac) ,S(71118e18,e758c2c3,6203528b,8b6707ab,b3439b0c,d3d508a9,6759c155,fe4921f7,c2f61af1,2c1b4e9c,64908719,f11b52d1,76bf22f7,e1cc800b,5ec79e28,aa104ee0) ,S(33bcedee,11b9f3c4,924e0990,9adc5fd1,46218b23,6531a242,45cbb2a8,3ec3d096,15f4bd1a,6c22c673,941a71f6,f4694fdb,f83b3e8d,5e317e9d,655057d5,acfbad0a) ,S(4b599b3a,4ab5e9f1,f161e5cb,62fdba55,fbd97740,759871d0,e66b20dc,4e13ccb4,635039da,9035272b,8b706411,9b342144,6c96019a,2c6df423,2b18299d,4a3fb523) ,S(19f6bf4c,dae54ca9,41b8f642,95136026,decb8dda,35e97627,5694365b,21269d10,a24c3fdc,90b06dc,264bca48,db27502f,6cb31a6b,609d3f3d,a1c92c64,cf3c95d7) ,S(bc3df1a9,8027d14d,f6629adf,7ad073ae,8a270875,b177a67a,58dd46f,1b01314c,99dd3a91,54f51d07,2ee33e89,8d915189,93445065,770745e7,b6bb30ab,808d1f76) ,S(977a4264,521a70e8,4d25f5b5,ac1ae5f6,c34ef31e,4dda285e,1ea4a9e5,7dd72c3c,f1bfc819,7aab2fe4,d0425b61,cd403fc9,dbf44f68,32e1c41b,4fce9b2a,2b9f5a0c) ,S(5fdfde4a,85fc5a53,3ed4a7f5,8adc7b1c,98b2611,3e271b47,a1c12c69,dc9b339,3edf2baf,bd6a94e6,951bad5,26fb24b9,731c2588,b2f6eb1c,e9744f49,16c6555a) ,S(b8bcd72c,dcd28afc,eeac1ac5,fb7db8c,afc17abf,82268747,6ce01423,e9e9c50d,82633c5,2e6dc057,9bbd9f2f,3771a53f,9cb6d0e3,6a7566db,f2c45125,3c55e9d) ,S(6c20b999,133bc37b,c65d01eb,6e946565,721bc2e9,da735c72,8be8a41c,1f75c77,20caf674,d8ad036e,25f42aa4,7a5ae475,5e36f44a,79c5ff20,cf6df115,40b71e53) ,S(bbe49141,69655f15,39ce4bf2,f2e919df,f877b5fa,163b7a70,22bc91ad,315adb07,8cd3e025,6618d23c,8c6b5ff6,db8fc0a5,a77b847f,ec876ac,40f76e9c,cbf93a1e) ,S(748b3078,e38374bf,7f39bbb,c5641737,bf6dfeae,d3980c75,2fe14c68,65e73786,7f7cae0a,61a7dfa2,471f2c80,217fc847,ea86b6b0,6297aeb2,8f3c94cf,2a811ac8) ,S(fa63c7c5,b89a2559,4615728b,2272cf68,5d39d592,d052c0bc,d23d48be,c764e4b4,c4c32ba2,77519d60,e1e38a50,6d67d041,804724d6,5cb4dd31,fbe7d692,8ca47c8a) ,S(c2ed7197,d014e380,a365ea13,d948314b,86978eb0,70e3e444,6c953871,cc56c91c,5c73c293,e7c1cd18,f7854a09,d8b9b0fb,3404bdb7,737dc070,9bdc01e,466a595e) ,S(2514c1ef,cb1e0bd6,c2f34e84,6f3e8006,6c2b3a04,c0d9fab5,f22fe872,6fc266be,c5a0ac6c,7bbb2d9,ff844346,65f66ec6,507c35dd,8ccf9ad0,69a1ec94,c64e3eb3) ,S(5bc07f05,11647f2,58dd2e28,9a3843c8,e2318bff,c96a081d,f6b6ef94,4e286350,213ce093,1217ef04,8d87d059,f2584db5,7a91c465,1e112c66,a41f85ab,ebbcbea4) ,S(edb56e42,97375b03,8a573f70,67ae464f,db9c1335,f6a03dd8,862a1731,9a3cad8a,d3e61a70,16f8d546,61b8414a,426f3be4,35862053,1d981f2e,5314447f,15ef5fa7) ,S(2925276e,78266481,3bf60998,2e028646,6849088e,d0d77d55,817c8d9d,73d5d732,f53157a6,a97c989d,ceb2d755,dbb0cee1,84b33213,20dd6d22,62213fe4,9a87296f) ,S(2c4579d5,bda0f4a5,37209882,937019e9,91286379,c3afb37f,a69e409e,9bc0a034,e150bf4d,d889c3c4,655acd23,f3107bca,a319d467,b1b9b15c,336ca934,5ef7d99c) ,S(5f260a00,11f9f876,bbe29587,af31832,25f21b8,42698b3d,5688545,a8808904,6ad33a32,164caa1f,7a4d2ce0,6eac3d,736fe64e,d83a3a9b,53473a89,8ee02350) ,S(3bbbbcc6,12095ec9,52fd430,f3fb3d6a,9d1f2c69,e8885100,d65a4d7,b6ac4b8b,328e828,3846a6e7,db5b090f,8c9581da,40d244cb,aa3b5948,7e4f9faa,550b0c97) ,S(4985027b,dd0fd8ef,fec9af44,bc222f4a,343e80ca,662d917d,affb9d81,956acff0,58befd2e,37a36e41,305561b5,f2716a23,460b1014,fe814654,68c16c22,3b8affda) ,S(214638e8,d2e30891,9b5eb2d8,803b3dcc,6e826ecc,e1b59b,92e263d5,67959de7,9dd8921,6f131e29,35ae0454,ff5fc9c2,dc22c0f1,c8de7dd8,ad9d41e4,f632342a) ,S(6ced8705,5ced2d6a,f3e3532b,965e0a31,6876c110,69155f35,444004f6,e6f3cfdd,f51b1aab,c86f556f,8b7ba4e2,a1e6aee7,55b17c01,997fcac0,a83eb56f,7e546ec6) ,S(95016e67,876c936c,e3263498,7859d1ad,7fc3ade4,4219727,30a1c886,c9dcfacb,299e78c4,e6e266ee,ffbd284b,81005bab,4df7232f,2e43f160,742bb392,6af4f660) ,S(4bec66c8,30401c39,c42a8019,fc398cf0,c513d20f,9db30763,51315319,ee6f23f2,f1dffe92,3b7d4609,871aa916,28929c63,4fcdeda1,543fc3d5,8e8b2735,938514fc) ,S(b50513d1,40513b97,6ac0015a,60e53ae5,9088c4ef,5ab27bb2,7f3eda78,848a59c7,9c41cae5,1182e6c2,3fb254c5,1b786ccd,dc9282c9,a6674841,29a5894b,99c36399) ,S(59792653,3989a039,6a69bda3,8a920ac9,d1df3845,26f30c00,3e415593,b690708d,7f2c14b7,274887db,5e656192,19ee6737,4c750cb3,97ae4bab,3a3ed02f,1aba648f) ,S(7ba2b766,cf012a93,478fe2b3,e916d665,251cc7f9,3ec16dd3,4db37056,5eacf6f,14fd8938,f950798c,37121286,5e8bdd14,3dcc7e8c,2c84aa69,3fb311f,856404bb) ,S(3062f2fe,f69c90d9,fc947af8,a9e839cd,7f9e9d22,566bd3a7,1c43df9b,eab5d6bb,db84a833,49916d41,7fde7b71,9d92a716,64047d4,21a36bba,ad9972bc,6f5ee58) ,S(ed5f949d,69dbec8a,77f4d695,cb446700,f6fae687,e327cce3,db38c2fd,54b06e74,4724e060,57b3d50,65104ff9,29950bcb,2a690723,f15999fd,ee62febf,2d8930e3) ,S(4d655e03,30028276,e9312fe,a6acc010,30e12950,9ebd68d3,d7170e46,61b7cdc,90efc122,6c27549b,2f5e046b,69e97f04,4399579e,278ccd0b,7bcee523,10ea99bb) ,S(f6b60756,b888efec,d0a9edf4,a483f95b,68e05e80,c351a60d,bf166faa,eaf1b35d,27bedebd,aa781584,6a896b24,1afaf9b0,cb57e98f,bce5df6,bfd22a3d,38a5fb8c) ,S(cc592caa,942ba237,72c4db94,58d6ea2c,8c81c538,8fc7cb51,6ca30188,a3c55748,36e2f7cd,358e5608,36e77d10,361c3f1,bb6bd2b1,d640307c,63d512d1,db288158) ,S(4acba9dc,a5bb4698,21a3acb8,cedf4304,f9372161,976d0edf,6a7a032f,f6c1a456,b36e983a,b2ab47f3,3e72287e,9bbd02cd,d6fb302a,972f2166,9cae4e85,52262437) ,S(c8a5185e,42279d3,2b50e0c6,1b9ce961,7be3633d,84a9472d,97446ddb,eb061f91,cfaa50b7,445e189b,d64c1df7,4668eeb1,cdb7cbd1,ff65c0ff,3c38d22d,9bd4b5cb) ,S(c1c95567,7f4f611,365168a8,89de10ad,535faf08,65f8d20e,52b1041,d35f18f9,34f7bc3b,3d956b63,9afc1eb,956f4472,543919e1,3708e7eb,537ab941,48033749) ,S(8df4fbb7,36f6736e,b4a09370,33f7d256,8bb68d68,f3e1f8fa,8df1ae51,d236a8f3,3d7185fe,8e9a2d00,3987af26,71bb3850,cef6b0f7,70770c81,22977764,5d02122c) ,S(d635f0,e35c7cb8,f2aa1ec0,c475011d,c2c8bbb6,d1ebc297,c2baa5e6,aa5af3dd,926ebd,c588e8b3,1a990a5b,5907ae5f,441e5a99,1853c643,5e36803c,7ba51a2f) ,S(b58d12d,5f865375,7514ea38,30e38e05,3678b525,e8b51923,d6460720,b46a4bc,f7b59183,5b0ebab3,935d587c,e995c0b4,d77c9e40,ea4837f6,48e44841,7438d3e) ,S(bb7c6a8c,b4013640,ecfad075,578e89ae,12cb4253,6461d780,11ba76db,da9a7f36,7dda0258,3774d618,68995b83,5708295a,3c2f5c40,306dcba7,d1c20da1,4836581c) ,S(14f6f0f7,92cc8cef,9dca990a,7fa5b7aa,f116b819,722cfb91,9683b298,3514a9e6,88c35f92,7a07598c,90ce5aac,4b3fecb5,2261045f,f23800b9,7b96f210,3a4d7055) ,S(4b95e5f4,eb9fa118,5ddad896,457f4aa2,fb60f4d0,496ad4fa,76bbbce7,77448541,1e100787,513acb31,ba087f51,201201ed,502d1f08,f7e2b8f4,d27706d1,45e71d21) ,S(e9a17fc0,67f75b2c,6384aa31,223355a3,a7af5366,4d85dc16,dcecbd2a,364b63ae,420a2388,ad674523,62f8fcf0,12b601ab,a40e06a,1b4dac1,9560c085,de7fb8c7) ,S(39d8536,f320ec81,4ee3d066,c0834130,96d4ff43,8331a81c,f10ad544,43ff9169,70ee89e9,1478e898,60d66a55,6054abd0,c7434535,13a7a3be,7a76e367,c28ca248) ,S(9779a0c8,8624d6c,beb1dc72,f371ce26,9f95b993,c49ff20e,1daa3c,2fb636e8,9d9e27cc,67296c50,9da4b0e,6037920b,369684d8,a64cb907,d230a4ab,a0c2712e) ,S(cd4c584a,1dabb48f,6a5c09de,9caf36ff,4a97471f,d1565586,bd78b4fb,66f0b401,95902ab1,eff06e2,b3e104b0,cad2c28e,6fd60eed,c47657f0,bc433411,273446f1) ,S(46ca11f4,142362cb,513164f7,c72b776e,dbeb3f65,5d527196,88eabeea,2561aba4,8060431a,2a2ad442,dfb6d3cb,d6263c61,bcfd0946,6204e2f5,e832c4d5,a434c9ff) ,S(dfebd179,1ffb63f5,76f5c753,50031a21,eb712de5,7e8f83b4,75ac39d8,8a94a513,cfed6c7e,39b2b54c,206aa0e2,2f7c610c,6576af2d,ecb28f0a,a71cb1ad,c7be75de) ,S(c71c6532,82fd063b,44633d9d,7a3b94f9,43daf1a1,7967ffcf,e1238087,5d2c2469,62fcd7cd,e006a10,38df8aed,33abe940,f18a4736,52adeba8,620d1b54,a9d376d0) ,S(63ebbb4d,dc8ba09a,4e2640fb,f48fb75a,6864ec41,fc1647b1,e9f8aef7,34c0ff37,e59d034b,fe16f4b,41d090e1,97360a85,dbf1ae4f,719c62df,77261205,da4ae28e) ,S(650498c8,cb51bf16,58eeac61,61b5892d,ce6e5c1c,271d40bc,eea14db9,dd12814a,e7e66785,5d8e0193,24457769,bbd5d14a,7a614585,70ad5e6e,e3058af9,64a65279) ,S(14a1e03f,14c00863,81599c07,b816df44,90815a8,40c1032a,c41225a8,47c43fd5,35244a59,bc6ba88f,46f66bac,9bb8ef5e,4926da38,50532ddb,6d6d606f,35fe98de) ,S(1c9f6eb2,f6a8a1e8,ecf9a16,71154fff,a4f14c15,bbd50f08,4d6f5315,b6903c5c,e6bde1f5,2ca4ff63,9b66fc51,150eee99,5386383e,402f987d,d266065d,2a03a033) ,S(1de71eed,bade7b1,7c80966,4b00d56c,b43ea61a,c0e069d9,7cff0218,f970f8bf,8d4b2de,77edeeae,d78d42e1,6b7bc94d,ea99d65d,985769bb,5c67da66,18ee1434) ,S(f4432a80,ce954d2e,baa2f062,8bbab706,479f7a39,838d8c3,5a96eaab,5f5cb4b1,96fe6ead,ac34a40c,3cabf47,6fc09382,91f3d077,29c6302c,c67a189c,bed579bf) ,S(8f71e74d,17964af4,5623d3f9,68424119,cb37e1ca,c1524737,4828b5e9,2519fb21,6990f0df,d7f0ca4b,a77678e4,ebf6946e,5b6b1720,869c91c,ec07854d,604865ab) ,S(22293157,5e3dc25e,665546e2,96a83a0,5a09d052,cef701a1,20019c49,c6a6745e,aad8f887,42585607,c792bfae,8a941caa,83d05082,defea859,86a6ead8,e5c423b0) ,S(6585fe63,2ef3a69a,816bf5f2,9e627650,cc57d069,3ac217c6,3b73aa2a,f248a096,820aa3bb,20281afe,edd9ca57,76ecc55f,dc8a893f,de11f7cc,12f37a83,6cfd9f8b) ,S(22232479,e55c51ca,b2963ce5,abf06281,aaec472f,e610d339,1951e41f,93f67bf8,e192fab,2cf22d7f,e67f0514,bc1329a2,888a8f18,a8d6504b,b7c5a9bb,ebf927d2) ,S(da8d02fd,e4ba069e,bccaba08,2b396c94,4460148b,70e98f60,8267db02,5ddf16fc,1a30213d,e337084a,47d67e7c,17a2e64d,579756d0,8b66f4d0,59a76021,e63fa2bb) ,S(a6f72c62,854e82de,f1b8a006,64c4e8b9,ad49e092,78ee6501,708a9f18,92202ebf,8355972d,b08c8104,b7c56ab,c2318ef4,2e270989,1a83837e,daa35537,1d03ba4) ,S(2074fd3a,309e85a0,5c6f8c35,937dcc56,a15077ce,99f5a8ee,8d55ae2a,3bc7db68,e11c02ea,cb783c94,2e58fc0e,806a9816,3061a4e9,aea9582e,53ae1f08,322cff97) ,S(49ed5666,fae9aa2b,70cd316f,62a4b62e,29aa59f3,1826106c,8611c50c,79a1a5e3,5ca7e49a,ae144e2b,dcc0b19e,f986967a,1477c209,2a8368b6,324bac6c,807643f7) ,S(2289ec7e,a1f7e4e9,85f472a7,13722335,b582c4e9,8e191468,3ed13622,5d6c1b1f,11e2b18,689a0867,517bff6,77fe40f7,b03f898b,d70e8902,61a512ca,d9cbbeb1) ,S(ea852ebe,23f1efbe,d8ac64a5,58ba2ba3,fbed0e52,ffc70635,bc49cebf,85859164,bde2ef41,fe97a639,73266583,c7a4e415,25ef1351,5b25cfaf,c97aa635,41cbb824) ,S(5718f0e6,7cc07d3f,1ac1a954,8fef08a4,290b257d,a4179855,3fe9be1b,d302f0ea,98ec4d5b,fca65d7e,e72d8bd5,3645a6af,a6ffcaa0,a2eb894f,d4e40ecf,69acbe90) ,S(df62a2ab,d77afd7d,ee8f0650,b75458e3,10269c3f,780cdad5,50bebd92,4b810a4c,6a6606cc,e384d27b,80bea2e9,588663e0,8d39fe8e,9fc8a8cd,54c4829b,8e4c034) ,S(1010fc45,4b0c268b,c339bd19,809508e7,9ea7dc0e,efd779aa,4974cdae,805e6668,686a3adb,681b597,2b30a323,c6b6bd2a,d51194f1,9d3d801c,3fa65fab,e96410e1) ,S(8ac79852,75673818,69fe93c9,6141493e,72ca344,790487b,d5425ed6,9f5c5c18,bb314248,fcbfc867,d1972e04,b9ef1f90,775375f9,9d25bcec,684c72c9,bdd1c08e) ,S(560e9711,88cbc7ce,c61f3bf4,45f0ade3,6f3f174d,219a160,5f9c8692,3f848b9d,9e92dace,6775cc67,bfbbf21f,c64e6e9d,4d133f8a,c18ee277,bc80ef6d,d1b9cd2f) #endif #if WINDOW_G > 10 ,S(8c464204,4b95eb66,cc95ca08,8469a1c0,28eea52f,7f709fe,e6d90700,f5fb943a,bf10fc5d,7bc25181,301b3a61,5ebea597,a3492025,953c3aa5,1a11271e,689d0223) ,S(d293f74c,f3578b71,35377247,cd8b0367,7f2245da,f87453cb,4d8d1cc2,871eb5aa,86c2013a,61dfea14,63e45931,eb09050f,f080e3d4,ae357423,ba7afbed,a64a6f26) ,S(35997241,ae757b1f,c767611e,c76eb935,fefbf7a7,33666aff,4c6bd744,d7687d35,bcbea61f,246bcd4c,c3c7fd35,7bd393da,2f36e0ef,cca0df9c,5994f96f,c44b2aa0) ,S(d096097,7467197d,3c1a0ef8,44ee35dc,285a17c5,bd9e06de,15f36025,7f6464eb,342af6a5,1e06db96,692954bf,c79cde9e,3dd44869,9e88b03c,d144b70b,bd3e8783) ,S(8e875c99,2aeaead6,7033a375,521b0f85,62125797,23a25470,bfdf898c,ae41a777,24aa273d,2d2f19bb,4e0ba10,13127ad2,a5ee6686,1ec6d0c6,53f7a989,73c0bbd8) ,S(bf51d1f3,2703a4c,d1ef47d8,172c5bb8,d622f444,8569aee,d2de1b9,ae541855,8f81e352,b6c60acf,bbde6e40,99353d84,5918d931,4433c30f,3c60a710,cf9aa484) ,S(6fb6b462,9726856,22b2d141,5083ef56,2ebb115b,6cdcbaee,696a8d4c,8341c26f,9c08f7bf,f9cfcd9e,cca923b3,e578ba45,468f2530,baca2032,a899f060,b83c9c73) ,S(75583ac1,8b5cf78d,7de6a21f,aff045fb,1db56f68,6b2cf89d,678df62,93617438,8259a22c,b08546ff,e237c7d,9c669c96,71fe014,9840082d,f6790340,9b69f900) ,S(42611933,a5d759ac,7ec51c89,31b76e95,4aabc2e3,61010f36,cdd8ff9c,b4c0ef92,88a644ce,6b8acbce,a378e2bd,54eb84c5,58cde403,f99cbf8,7830151d,21ed4261) ,S(243a6dbf,6128f964,bdae776c,a716bdc5,6dff9c95,24baf845,8a43ade3,af520d2,262a2e8a,5ce4db48,d0401850,e92bdfa8,3dda744d,a3d9025d,6091f1a5,201b7e50) ,S(212bd175,1548c6d2,41e9307,a7df15bc,46e57e2c,5a76bd58,82b1291,d8c2ac76,82461bc7,6cc97273,267cc788,a8b24082,57f04ef4,719a9aaa,e33cbd77,79391bc) ,S(da6d030b,21f96d2a,aa0b3e56,28ae0ec8,8ca8a546,10bd61fb,c1a7c16b,4d61177b,5b5bc635,8fab0287,4a2b8596,1b49ec29,2c2aad1e,1eabbd0a,1cebdbe7,2e3f9fde) ,S(dc230af0,55a243b0,a581e101,2eea48fc,4a43137e,cfe80108,86a9f4e3,f6c1f01f,d0f98e1b,e70a458d,7030120d,a3d7feed,2eb5a9ab,601718bb,950fa03e,568180ca) ,S(82c2de3a,c815c686,98ce73b5,6f232684,ee9c5972,f0a44797,dc16d04b,a9089df1,1c847065,c6c2cc18,fa253b8e,c1fe178d,c859844,2c1fa432,54462d97,93b8573d) ,S(6ca2de88,74e4916e,e1965dfa,200af89a,cc439f20,6a4077f6,67076149,e20494a3,6ef0b344,97aa85dd,a43cc1aa,57dc7ce6,cd51119d,ae96ae06,99b5119a,9a662043) ,S(ba2687c4,1728fb65,206448f8,28400efb,cf1149a4,90bd31f8,8d33af53,7851d97f,96ad25f1,1f2ce7aa,e8b803bb,3c62cd32,3345500,243b1de5,d61f20b1,86b4c0c4) ,S(ac362040,1947f301,16032d5a,4b303323,d311f533,e46a1aa5,f1ea2f08,d553e0d,53839f95,fef32884,5a75881f,a17db91c,1d5b981b,7b20937f,df171c3f,2cb30a22) ,S(6780ecee,5b1b7205,68d4241e,c3b35c9e,4158c7c2,2dbba46b,ac769476,79049e13,9ac115f0,31e0888d,2dc90b9f,3562e732,46520d57,ecc7ae4e,e0fbf401,3057d9a8) ,S(95377a47,e7a2d5d5,30510d62,2bbd3439,c0f7653a,ab294254,cbb10390,d2a63732,57ac9110,9dafb62c,fe1abe4d,fc64557b,bb01f76a,36649d7b,91be523,f8195fc0) ,S(4f195bf,98fd83bf,7ee97c5,9bd42af5,486a8507,3327415e,85f17a17,2add8921,a56acf25,1c82323,6327cae3,6b1cadd,1a057bbc,f1ef3b59,a865c7b8,691cf3dc) ,S(eccd1fd1,efe8299f,d2208240,adbaabce,cc0510d2,d7b6f6ba,d9e291b1,4cbcb53f,ec2ff321,6da50fa5,c57d6f2d,3198e019,2d9b6f8b,ffc26b29,13580447,a42c667c) ,S(c757444a,f2c3425c,728ff41c,f7cb7475,502e7601,c1edf2b,1eec84e1,b058f438,e1d481b6,169f143e,29701105,bc8b6657,9cd267fc,685014b8,fd070283,6362e53a) ,S(3562837e,bff50776,58d99662,7a11a367,aef3255c,1c470ac6,36f1b57c,645250b8,cdcf4a0d,97aa58fc,ccd374bb,bcafc00,fa1d0d35,ca7fab9c,f4d72d66,299234d8) ,S(ce9dc245,f62e97ab,d2d339e9,7fac18b7,b1f2f07d,fb654a82,b113317c,86d4a3a1,f6e1e325,342afb8e,64fe8520,ec37abde,fcaf1b30,be6ecb79,27ba5615,f0d184d5) ,S(ac022f3b,48ee44ba,9d271a8c,1a01fa8a,aab4818c,e5383dd5,42d9d6e3,2c858a12,1e0563a8,91f8d11f,1989e091,739611de,191e497e,66055aaf,45db9ba9,72ca76fa) ,S(d1d4f682,cb12cfaa,e46e57e6,db6f2277,55a83782,88cca4ff,3a999c0b,a651d9f9,1b19bfe5,870e1931,4c23b4b0,71672233,1607264,acb8e960,488598e7,85e71a36) ,S(79962171,bbddaf94,45fbacd4,f9bdd1a8,892e754b,2d0052ee,2435303a,ff1c8a37,b8ac27de,2a952beb,45472f77,b34c1354,fe47b6a9,daf0720a,b8515be3,7bb98a7d) ,S(445a17c4,2390b604,bb3c3573,b061a2f1,20ecb3b1,83a0f8d8,cf032e3c,509d3b90,b75f4088,7c07fe5c,a0c057c8,7eff4966,4ea76941,e409a6aa,e34ad4b1,693f97b1) ,S(6166b5f9,63a9f47f,5fac49a7,8d175763,8c39cd49,11d16ccf,b0e83bc3,f402051,ba337661,8302aeb2,213e4620,4ec57492,933d6df5,5a045d7e,5317ddf,e92430b3) ,S(cd666e74,28901afe,8e67d0e4,48de7e3,30b6dbdb,a34db4a9,29315d3f,8b251531,af72d8b9,43cba540,e42398e7,49fc89ed,44095951,f11b24f9,e5451810,3802304b) ,S(c833be8c,fd2f6fe0,46d837a1,1d990355,5a6285bc,d7b8814e,e839cbad,523ac72,7ea8f90b,44112363,a8d75153,150c3b4e,b6c07dbe,fe8c8ed6,3a24984,c9a6af03) ,S(cc185f36,3036d385,d890ac1f,5e95b162,e40e4a4f,e8427613,98200369,f25ea477,e0768836,146d9c98,98aaabe5,a9ce12ef,f66d0775,4055eb42,832eeb9f,26338236) ,S(148e0863,24bbc2ba,b67c9be7,407b809,77ccd910,e92c9770,47943c29,8c9c4a5a,89e83c85,9cddfc80,9de733ae,6138e97d,b706a331,fb7176ee,55dfe3ba,c2408797) ,S(9b1539c1,aba5b583,5c88d9b1,92a3761d,cf8b649,54f53a7e,460e0122,bec95c76,391cde19,45be59da,d4c895f1,3aa1ce24,d8472e42,a232795b,967f21d5,acefdc18) ,S(68a2e6c1,75fb01d3,76a9e575,ff427cc7,a6032774,a974bdd3,e93b8a73,e4495cd,153e6484,c8c30dde,5f269b74,1c599647,666cab7,e273d4f2,5573dc4e,78e00752) ,S(58fe9049,35a5a40c,3b633440,533cccac,7669e9a2,e7c2f0b6,6c36c228,61dfb04e,b36905c5,92450e2d,71d06e2a,2d599a77,71ac1e27,15a79555,b39fbb60,5536e1bb) ,S(823c0f96,dcbdd9b0,bfdaff2a,19b6027d,3e9bca6,e298378,3375a783,5eac7080,d91546cc,f34d9a58,babeb6d5,43bf3c36,8831a2b0,d9043db8,895cd208,f2ad0a7f) ,S(4a56aeae,e908f908,55fe7b71,3013ee7,d6812152,4f7decaf,533cde20,2d14537,7e60c801,33b718d2,119995b3,3790eb9a,3129a7fb,2e030d8d,21af90a,c622b7a2) ,S(6c0f3855,e6c4f5f2,c4594e2b,8881319b,82a64bf4,9fe0968a,71f6ca3b,f9240334,5c8e7b6d,a9efbba8,4b5ade85,305aead3,e1478ad1,b4d56fc8,3acfe34d,23b5203c) ,S(d9cf8f2c,d1704907,15dde21c,f172e648,496e40b,5248f331,3aeba2a3,35ac9632,92a7c251,b440f930,bd98299,c35d57f7,15867e90,b6c3e8e6,b073815c,3c934344) ,S(4bfcb492,8b91dc7b,afa7ed43,d9af3039,77592728,fcf1b9e2,7c6767f7,b993d898,276a06f1,ecd9d410,b34c9a4a,e3aa33b8,1854a4e9,e4703dda,7bfca949,a45d14f7) ,S(abde5893,ac4032f4,4ed93dee,8156596e,7cdcc575,e5928792,944019ac,23c434e8,5e03a809,2b9e6044,e942af7a,7cef02fb,46162cb2,4c19916e,d774b00d,8195c40a) ,S(205d6307,7a98a8e1,178814b4,9281da20,4482f1ae,31be20a8,3b3b0fd,526e1cc5,4bbe295c,943e3560,6b95cb19,d6e64bfc,b9cab7d2,55657614,7a79ff50,6fe4d780) ,S(cb4c4c83,e6673a1c,6c228a42,36e6031d,b59653bc,45bf4b7c,3b98cdd2,441c43bd,142e0276,39267ea0,f7c2ff39,75afe714,62f3340c,1fea5149,cfe4e8ea,e31a2769) ,S(25a1f4b2,7ff5bdfb,3af54a4b,493356ef,92ccf0b2,dec7c4f2,b5abb225,2cca77a7,1b25dd93,153f8341,7df3b3af,c991f2d9,36c32e8b,288a7fe9,3e9ff97b,335c3c38) ,S(222f76a7,7eeca0d6,a511c863,a657cb89,5a1b7154,957b66dc,89ca77aa,2a54237b,a8f2bee0,64eff88d,87a598a,8665d295,a205c884,2f6a3492,7945a02f,2cb0b289) ,S(32d4328d,1ad2651b,41bf1015,6936b406,379f5c26,99f1c2da,ec3cbd8f,3b4dfa8d,9f6de6e2,3294a33b,5f4d4062,3e478096,df5de0a1,d069290d,204ce930,7988261d) ,S(cde9ecbe,6948cd70,3b193790,6662b7d,187d0830,cf991b14,e8265691,81f1d3f0,84887b32,e1218d2,9b77794c,e8ad56c5,f5abe8ff,f95515e2,4bce81b1,5b029720) ,S(bc89f45c,3baaef4c,a8343582,6506a006,509f4e7e,265e4b80,11d53d3,a748947d,eff5bca2,714db146,7a272fce,534f79be,9fa15af,7226ba49,51129f5e,6fe68475) ,S(62678cc0,eea2bbfe,2bd4ba65,5434a9ad,39b409b9,b57efdf0,9940f748,ddb51d4f,8d384f4f,d234d31d,1c161245,ef6dd54e,a5cc8ab9,e7bcc883,6735051c,37a74acf) ,S(15e01d39,c63ae225,63dc89cf,3dfa2736,df7c0ac3,4fe86f8a,f219f933,86bc93d0,1f563532,314fcb81,c1725133,49769861,e7efb999,fa317ef4,2bc75588,10cfb13b) ,S(4f8d2b49,3493258d,ff98e813,e428ae9c,52c60103,1bdbeb9,7b8f364b,2bac10e3,8c7d117b,67955db6,c0058028,3f919f57,1e8c58e4,216ca1bc,d66b264e,169b73f) ,S(d14ce31a,2bf16b60,983e397c,ddd3588c,3b0d77b4,f449136f,1a789276,b56f1d61,9a15f620,b227d83a,3722ca6e,4dd7bbf5,833f24c7,2584f356,11ef3734,ad3f0910) ,S(35221b4e,b8c275f5,c10d656c,9bfea000,24c1aa2,c4130841,9c3e8e3b,66f780f1,3d1c5a02,5274afcb,bd78382b,b2778657,6888d46,1b5dffa0,f8ec5dd9,3bf8e808) ,S(82ed9c3b,1c76c1b8,f44ff6f2,9f443b20,83f68617,7270843c,49eac0aa,34a8ddc8,262e9e6b,c2ab2b86,7342081d,90002690,e81f5a58,aefd6fc4,8a91dc5d,e95f1340) ,S(919e960e,acf2aa36,e86342f7,742e97c4,9c49b64a,ff5c6118,d181e349,10717b85,4b51a94e,a3ea1679,cd9ce9d5,ac329f13,ef530d42,c7821650,5a082fe4,d945b861) ,S(cdacae3e,20ce551a,beeabcaf,a643ce62,edca3de1,acf06c30,65ffd366,5bc3ec7d,aaacbb13,872b076a,e28c326d,fa54f4ee,235df4a4,b341c9b1,3d322071,6eb95bb6) ,S(1a4508e2,1bd05c09,f3d80f82,90726f08,de3a62ff,b663d5a8,f949ce26,92a5f2ab,52780ff0,976eb033,760459bf,4bf02994,c6e672c5,6d25d3e6,2b320f5,2cca97ba) ,S(8e46eeed,5686f25c,a94f73d1,3f26c98a,e9129f77,f3aa18dd,d5214262,803a0b45,ee56d38d,7041eea7,c87f2ed1,e7f0aeb6,7253d556,610e8200,782c9af6,1dedcf4d) ,S(782910fa,3bd6b309,dad797c1,5b618469,68d6171e,7a0a0532,a92e5bb3,697e4031,ff178365,c44c2a28,e84c31b8,946b0a80,717914ff,6d3f22dd,ee409753,44e4b3f4) ,S(2ab9e8c,c5a710ca,6cc2d0a2,94f1d7d2,65c50aa8,f9069041,ae93c91a,e5f64e8a,aabcd0f,a2254bad,67cf23d,a5934947,18536602,a13d81c9,db23afc9,a7f89b9b) ,S(d04667c4,4fb25b22,8320cc53,35252937,a094ddc2,4610f7a5,fcb1bd1d,6382c9e5,7c93613f,8bf048e7,86af436e,cac4fa86,6e5a91d8,3064f5c,e31d4794,b2b0f74e) ,S(b9c476f9,799cdda4,a51b0476,c5838994,f157bd29,c9361252,def4af83,6e86b0f7,2ec7619b,c77948b3,f25cefbc,46845527,d1a9b0da,a90529ef,f13aab4a,ca97932e) ,S(90bdedab,f13f9940,4b9d8c56,5d64739c,4ef765ff,dee2ae0d,64fda841,286eee85,a9f47882,d9a848ab,4be812a4,8187d26c,7f8bb8dd,b94f7725,5c628104,e0cf21f5) ,S(a0c394a8,2177734,c02b8310,74ebf0ff,ff4208cd,dcd59e7b,a680737a,fc485c84,c4f08932,b4c62f34,fc82434f,e9b7b164,e835cab6,2f34ee3f,d640e5d7,d09364b) ,S(1b0319bd,3896e8c6,284f949c,72e7694e,bd3c2923,ebeac273,b9aab50d,30294c3e,15dbfe9b,17c3aae7,e5f8233d,703b7b1a,1401b672,1da32080,53ed52f,a2ee339d) ,S(9914ef0f,e92f16be,a27a9354,518dcc0,1210eb3b,3a90f2ab,6992e3d9,bfdc719d,7a0bd065,cea0b11,e8df3629,faf65a30,5e671d2c,86332b83,98ddc2b1,b3c4086b) ,S(3a68fa19,5599f638,7dafa176,395c9615,5798ad6d,7ace7810,daaedd13,ddf60d3e,74575ae6,a3f569db,394faef1,e0641ca4,de158eee,9a8ac54f,5cd96bf7,d4e71a89) ,S(b7361d41,e2b67e31,f1872b1,b1bffc8e,41193dec,7f012385,9da69c60,5e88b2e5,fa9d6b95,66d49bca,73cf5890,f6e7acd0,315347bd,f10be9c2,9b0907e1,80668344) ,S(341e9987,42d84640,f6fd1354,3fb7ff9e,aa93a4d3,12e99bc6,37b85b83,25174e81,c49608dc,91b46187,611cbcff,762e5fc1,e95b4e9a,6ed747ac,8612b6b9,8bfcfc95) ,S(83d6a445,de34f557,40084909,402c9718,1f6420bf,af87426e,2a0f75da,c483e6f6,7a86db44,58c8fb53,5edcf48a,14a94dd8,e9fbed09,277db0fd,787c121b,a1dddfc1) ,S(4f11235a,14bcae9,89082bf1,c6a499d8,32d17686,2fcffbdd,a40b84b9,26ac351b,b50624f1,5f31269d,168021c8,37739cb7,8678ded,be59e288,6e963339,e94a2acf) ,S(8fbb5727,21cfe12c,ea685907,ab6e3d7e,eafb3892,c082115b,998e9a9c,d3ee2b89,da7fe685,c8148e1a,5cd8de8e,2a5b5aa4,ef1bb1a5,af8bfab7,91c923a3,66906680) ,S(804ca63c,b9243f5f,76605b1f,53f5989d,286023f2,fc672bd6,3f52c59f,5496c3de,372912,eedb1156,a1b8300e,eaeb44f8,865fab6d,49c89fd8,43170b05,d75233c6) ,S(b2795c6a,b83ca824,6b18de87,5660d04,60b48ed7,1de9bbf5,8cc1769c,2d2a5365,66e8c2b5,88530b6b,4d351044,186a8a01,db684157,9bdc041f,90d0935b,2a49d820) 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,S(c86f10,7bfa6dcc,b9f00ca3,465049de,5c8a3e6c,d85bdfb8,1ada1d39,303a2eb9,e64f7066,7e910814,ae18c6a,7323474d,9dcb277e,4aaa7ed8,88bae4ae,7c34219d) ,S(bed8eb6e,cda14299,e4cd94cc,202be7b8,9201c2ab,302a5cdb,83e5f5ba,db6cd710,15736cfa,b375a40c,5d367b9f,6692746d,16a1f03c,20941256,708489a5,5d411aac) ,S(b3efa7f2,c5f6ad10,41f171b5,ad759480,665e0a52,de82a881,da1926e0,8f64d38f,3df63c84,32761a24,eb0dfa,ae98e034,b6dbd361,3fb53ff,c535fac8,ff1677e6) ,S(b0460da0,cd869b5f,235213a8,49e143e1,8fa9afc1,651ee921,ebdc525d,2715cbd2,c11a3ead,f3541877,ce73b4c0,2b57b299,46b4725e,cf630eee,865bb121,b86fd7ee) ,S(28b09517,a17452be,b2c19187,12d600d4,b4969253,a7d0d52a,49cec3ce,d73bc071,36696708,73c7591,11163518,40af594,40ffd6d0,690ddae7,fce7a43d,e920a326) ,S(521becd8,192acb58,7ae76b7,c0bf17fa,ad86afc,47157753,6b1a51b0,fbb5f136,648a54c6,d7aff13e,cccf399e,15451682,ee06710e,edf32669,1dc7fe83,75ac858d) ,S(b7bc19d0,b7fd9d65,26c9bca1,b587d84e,a2a200a7,76d39082,368b761f,79f6cf67,5adefabe,e0d0c8cf,4252c29a,773163b6,4a1e9ffe,ffbfe3ad,2f796e8d,1f70acae) ,S(e48e3be5,1b6ca8d5,41f0c241,21558cec,66db7b6d,c13e7114,dc931f0d,397aea8b,dbcf6357,5b16e2f1,30f064bf,ff12b465,f6cb3a3e,f9f74431,4bf41e7e,e0f28ac) ,S(395c6de,71c692a6,a3247596,8e28f2a5,4ec795b5,9759e890,9b2f4290,9f455751,ee5e0118,3c7dda2,c1eed4e1,5aca155f,b5b097e4,499bc3c3,fcfc2c85,a669a13d) ,S(28938ac3,b1184399,22741291,9c0fec36,663da3aa,8a4e89a8,1a66052b,ca808d99,4ae8de7a,b1ebc1be,a2beadb1,80cb9a10,da168295,ba1ea5f8,310b986,4f174603) ,S(5c0f618,95e88cf6,205472f2,3e27e853,be3af64f,d0a376f5,8523ee6b,5248f5a4,be5c3c55,cd09ebb3,b7363456,9fdb50fb,8473e3d8,3441e624,b41b1c3d,e44be51b) ,S(abe1f7bf,22d0f733,ed28e125,f7ed05ba,ae2e8f13,1eba2ec0,1554dac,5e3ca1d7,2a5a48db,3de31f6a,9708ffe4,b996cb33,e553e6b5,95aeaffc,918aa2c4,1ab0ab4e) ,S(c3042427,57d370b3,79124907,ea609129,5f1dbeec,442a6349,bccfd29c,e08d8be7,67a64eb3,3e0fda75,535b35e2,f8c9811d,528959c1,29e8f144,8bb75ce9,b1868934) ,S(65a59946,356f219d,77af0b6a,9e1a43f7,3152746,6af41c21,c81532fe,3140f5b8,64e7128d,5d3e4fa0,518cf27f,c070da20,1692b059,3d84641f,2463a61c,74f35918) ,S(6c7d2e3b,48428c87,46b066f2,bb99da10,60311cb7,d4dae19e,de2eb53f,141413e2,4ba47bf,c2e7c670,4de2864d,1ed7b383,286292fe,28f7c7ab,2a664bcb,6cb7e3a1) ,S(dd257bd,b99c89c2,b47798a9,bc93ff57,5655797f,a45399cf,44acf58e,93fdcdd9,f8d670f2,a9207f25,52e7e0d7,14289103,e8194f81,6390e0cc,1af2ae36,c1b3e4af) ,S(2516034e,b8ddc424,42952b8f,acd47c62,6827b87c,b08f263e,b2aab5e6,ecc23d7b,ad8e8879,f5feea07,ad3545bc,a731dd30,bd2ab534,4b486826,433c75a1,6216ac9e) ,S(7e723054,27b591e3,b19834b3,8211edc1,7f075215,6591980b,907dce0a,d934246d,5c91fcbb,d8c184a6,f21671df,1098760b,2506bee8,e32474e3,3b080147,4e63a71f) ,S(1b1f9d16,ac3c0d2a,4b87691,45a6f6bb,8d4fb57f,ef9df33e,72b5d399,6dd1898b,6442bf1e,5ffe450,b14a399e,16241a5a,15e94453,94519bd1,24d0a67,f35b4b1b) ,S(e0f1fa4e,57cdea43,a3b9f671,596631c6,65b5144d,93c51a23,e9006c63,fc872f2b,c83851fb,54890d14,2f605617,151dd47,74f9a3de,cd27d864,a49c176,af32e564) ,S(ae95bbb,697c820a,251a3667,b2a0a078,40efa027,99d7bd0b,3e9a12eb,32728c3a,e0dbba97,280096d,86ea4da9,45ae509d,1140e0dc,7b803f10,e685b148,6baebb41) ,S(fc8ff885,d52ef42c,1fe529ea,853ff8c3,afad1ae,6e7f1b30,69e34076,682aed31,525eced4,b26e8f62,7b904f1b,3356d01a,9cced71,432ac850,433e0a64,b1e3dd14) ,S(6613136a,459d625a,d5b5753,3a965a0c,ed68d63c,13652546,c629cab3,32c8e810,10f29ff8,24d30a94,b3d732b4,3b168bd2,28b4cb01,4012469b,93a9853b,655b65cb) ,S(45085915,7b683327,c76309b3,96ef3b63,19dda841,f6be1b91,f24f5a37,ddea56f0,b9a71446,584a88e4,6a155e34,f08d5a6b,2b6ebbbf,b4b1aa12,bbc7654f,91956821) ,S(168ee3bd,8f10ba0d,deb82576,cd5e1711,be58af4c,2274464f,e32f3f7,7c8a4325,6eef1e63,43ff409f,a916891c,982f8700,465fb184,5820b886,68b74202,6678b34c) ,S(b3191d97,763c2341,4eb4db8d,eb2003e4,fdd86b4c,6077931b,71802714,ef048c04,b4ac3085,59f975ca,be7d53d8,3ebdd5c3,ce6860d6,37710a04,f885a83c,c2152edd) ,S(da9d5c5b,4e73dc93,3c72acca,1e93f4bb,3ec477fc,f201096a,51ea0226,3a2f8738,7fb6a2da,65f966c3,689b93b0,d6366511,400c05d0,8b0a15b5,b4b3209,a812f8aa) ,S(140e55d2,a7e75678,1791730f,c526470,8d1cfaa0,954e215c,1e65bcc,e4b0dd66,4bfba0d8,63ea2597,91e470d8,1ef36318,87e2d5e5,c897918b,ce805941,953d5b3) ,S(15a9ccf6,4b95cc87,cee9bd01,bfe3d8bf,b438f7f8,66344a1c,f3f399eb,16b173d8,4f5472cd,bdebed25,605e51fb,f0b31a93,5d0ba59a,6e51bf90,e0363c8d,9bb33f3b) ,S(e86e364b,6776701d,b7b3d3d8,fad181bc,c7ed5e91,2d0a888f,814caa3d,88af6e06,22fd460,afc040d,3e995518,c6286989,24a466d1,4a624915,f834c357,4dea7b92) ,S(3c261a98,cd25f0db,2321134c,723ebce7,b1f81d3a,a6d5bddb,fc282fae,5a500eb6,2b8d2145,5e498211,8a4b6ed7,ec96a66c,4027a506,deaeecbc,45535fc5,77abd9c1) ,S(49b6a811,4d55b517,6cbb1f6c,177aacfc,368c3b5d,238300b,d66546ed,f4c955c8,d1b124a4,9f0e7c1,6b8e001,7f1b0b2a,ab94411,391d5bca,5b535838,a3815b94) ,S(6ec8e861,f0d3e5a5,3f9deab6,20cc4b81,6cee801f,f7a43f71,f34a8dac,c525f6b9,42e0545b,68ccafbd,3309c4f7,eb6b5eb1,1e01a871,c63fae27,782001ab,a6dcfd6a) ,S(7342b341,59aca5cf,d305a2e2,a8f14da4,4b527e57,4640fe1a,c08898aa,4595b9ac,b5261302,d2442ee2,363969a8,4ea61281,27f64f40,ac86dac1,21b5d234,53160124) ,S(842b30bd,54ef350b,65dcfc43,df26967c,b2747757,a609c54b,687d30b9,5a686fa9,4ffa9e92,2caa36b9,ecf31f63,f5c8de57,7d594f7c,71e7e77b,9cc5ac83,f336ead6) ,S(2dba435d,d589a7c7,bc3fb60d,495757ef,7c13bb0a,3e91a153,9998e04c,19f94862,c440720e,a4b23cb9,d238eca1,6775e500,931d3e5c,7df853ed,55cd4889,5e8cc0a1) ,S(9d1e8524,8f84ce5b,2a75a457,819390be,bb284fbd,3d035c07,998d3c45,c73bec02,8e40ee4c,c935ccac,2338bbc8,4a8063f3,6d62e8cf,849bff40,1298074c,94eb9ead) ,S(d2735ac5,d1fba75b,d4f63912,11549755,9a7f8623,62e25cf4,e76562d2,d8b441af,bd2ac36,19f9f339,77b7cb0e,5b52f3e5,b4ade86d,1c9fb31d,a1d8fb36,7dafc081) ,S(b0130e38,f46cff13,ad1a68d3,15729395,b27c2b96,e0a957cd,ca63adfe,b0a3e11a,3d9f697f,4a61401c,87eff844,3b11776a,610f1516,4366c1b5,535599a0,c6aa3c4) ,S(e0aa062f,15306af8,b662d8f3,3b89de8b,f59faa78,29942caa,ed82e668,35ec76a7,c5f5f0b5,6ea77304,a5dffb8a,cac98387,34305b54,25fc6181,79a4457e,c15e6f2e) ,S(ed1626c1,a8e6d1c9,187e15c4,ae9875ec,2156d685,997ac413,9f44bd0b,19432d5,3c0d895b,9dcb4a3f,4235e531,ee7373f7,7f0fad46,c5938d7e,69d50429,71f0c35d) ,S(a2cccc31,4e18fdaf,8cc25aa6,74c974f8,664744db,86e04be8,431d2ed0,4dc92833,b6410e49,d6d471ee,d20e5536,8672f5e4,2e1b9c88,c06438a8,46c3a74f,c759d71c) ,S(5bfc192f,db15f62c,4af19119,b2d96a88,b3b24e06,3d54b31f,a35f675b,f668bf27,46774374,acb4e140,90431bb3,9f62a38a,dbe0dc62,4021e23b,6099e198,47d99051) ,S(66842a89,da73c404,32a2e553,97efb009,61eb2155,886ac90e,97dab5f0,9227028,3a8e83c3,511ea048,88d2dc9d,f1016cd9,da171bc6,89c9af4e,90b18091,21941de9) ,S(ec823197,3ba95f98,d45f8991,3ee8b92b,e3a4a84d,d59342f7,1810766b,cdc516e8,532d3c79,f5113f4e,1973bc88,2a953b5d,77d5476d,ac9972ae,f1d25e19,ab7206fe) ,S(3b65fe78,bc516176,aed5e5b6,5f3ed39f,e8e8e26c,32ab07ad,1ac2519f,72fc140b,856d36de,5190eb9c,13f7f976,466f95de,566a1fd7,314cec1b,9c9f7adf,98208d98) ,S(3ac0eca,51c43525,e9e545ce,83fdd009,f9f31eb3,2722b945,18262036,d18cc346,dc72018b,c3b2a4cf,3244ef31,340e0944,325bebc8,b134de50,9ab3024a,a213a7e6) ,S(4929658d,6c50ece6,edd2db7c,217d9be0,bcdac8b9,bb50972f,fbe53a04,2ee23508,e5aca42c,61aabbd4,b8555980,a2328741,6dfc8df8,d7a10c3a,7284bd90,aacec38a) ,S(9d16e76f,4bc96492,f0e9e748,8c6d2297,7830e2ab,491a6278,1d60ab5b,153a6291,e6590f00,e4ac6922,5436318,9770aef5,5eaa988a,44e9711,da7266ec,895ac7ab) ,S(b0649c4a,1327e7fa,f52a9bbe,7ff97add,4e13b36a,27c0676d,5e09b2b8,1f5df94d,991c8316,a6f36848,e072a080,77f75a8a,d79fdd08,1a606d12,b355c3c,3891acdd) ,S(8f194a21,f6303ded,2c9ce51c,44a4a16b,eb39a8f6,5fe13c9,6b7c12bd,b052235d,bd1df3d0,c9af82e2,545afb23,e9a2dc85,c635172c,edfe70f1,bd755d26,9730739e) ,S(1da71a97,cc7a4cd9,4777f6c3,dd5e665b,3872b721,c6c2262a,60e87f1d,efe21ff0,78d17a41,39036e1a,7af2b9af,1273afeb,a4d30e8,66a3e6e8,7f0d0468,4be6a06) ,S(9fed363,e493f262,d3efabb1,c52291c7,e04e401b,b181290f,7a37af3c,df86aa45,130cc33e,e164adff,bedb1827,6a5c965f,53a54f36,90dfcd6c,b3fff836,703de729) ,S(d166eccd,221c3568,199ebc38,fcbb6140,7a601a3a,c1e7a98f,ebb75a87,a7a1e49f,262222b7,e7c200bd,5dcec562,85485434,b0628c7c,ce5483c9,93795f76,a072f06e) ,S(e7853cbd,3e3770c1,cc307839,294a2e8e,b998a56e,393435cc,2930920a,8ddbe0fd,7977e6ca,67147cc4,965d2918,1023c3bc,cff1e7b1,8fa4850b,80a140f6,980e5a8e) ,S(a8b0feb1,cb140201,2bea3cd5,6b1a1f02,51036ce7,423f511,480f49c5,6227a17f,ccd7c3db,9d3ab6db,6cceedd6,d3801c8f,67afe792,c8977b5,27c9dcfa,75ba8a9f) ,S(57ce5dd9,e1815755,31e90579,74f58b98,6d02e406,a846ab26,c9059f6c,56d617d7,cc34c090,4399f316,269598f8,aa8f9aed,829f61f2,5efc9bc4,e851ac63,fe142d14) ,S(479790b6,4f60fc6d,befbbc1d,365ab3e4,8077b6c6,cbf02f2d,6c8b986f,d0f9c858,157f4982,e3581925,dd25382a,e3e48fa6,5cff911a,95e9bf43,5df8b356,87f2f9b) ,S(55abc7b,1ffe0a41,2181b622,813be76c,8ee0a0ca,3cb37b1c,cb265087,fff17c68,bd134249,23e94c53,4cf9e603,a1dd259,606272bf,8283f2d6,69bedd4c,a971d99f) ,S(6ca7e032,8bf5d67a,b804d431,e5f709e,bd3156e0,1d4511da,1dc67394,24d2e659,c428b133,f3683909,6551c2ff,2f870d80,d80aaaf4,6d2b1a69,7722057,5eca2647) ,S(60df19a9,83e9086c,4cbd20ba,fbafa8b2,346ae4ee,9c1ad4dd,99959e91,2df530d3,dae7b854,29f817a0,421c2f1e,e4e8e4d,a09d60f8,84701e31,d7a8b7b0,3b79cc48) #endif #if WINDOW_G > 11 ,S(6f18d50e,5ef5f2ad,bad80ea1,c59a3847,5c22ff05,6ba52c7,e1d26d6d,d3686bce,d1d7ea0f,a166efd0,facf5c83,bc3786e0,d3f3405d,5b4578f5,13a336ad,f0d7d7a9) ,S(b634dc9d,5ed51336,4ac9569a,8ddee9d9,fcdfe00e,65e59233,b3be8a07,2fd949e0,d72e46e2,c61b2575,f25a505c,bdc3456e,fdf18976,6562a1a7,e86d036,eb31db69) ,S(5a37fcf0,2dba24f3,e6646171,43dbc5ab,40d91983,69f5cf0e,4fc566fd,97445910,a960d1d8,13f8746c,662a9582,614c7847,33e6153d,2975cb59,c3342463,75c69d1e) ,S(8aaf16a7,37318032,c60201b6,b196d8fd,eeeb8f8f,1aab29e1,1b83ae1b,f112661c,c461ef56,66a3a4a7,563cc0c2,845f2ae7,6d03a795,987c615d,611bab48,ab9a8e44) ,S(456f0ba5,a05f15ef,d93e7f49,e0729c45,1d85a693,42c2804d,9cd4b8ae,af5e3434,a680f4a9,99221a8b,7f46da13,13041e16,13f616bd,84b9135b,b0f7ecb2,7311cad5) ,S(f89c36a1,f1905409,75f146d9,31e12cb9,4bfdc90f,a178970a,9d0b34cb,38f5c741,3b562c80,58e31b92,a1186615,9c1ffa3b,4b1df38c,eb4a1646,579d2375,9c44099b) ,S(7f6beb11,2e1d8600,d8c4903,1d69cfb4,e23876e6,32f30428,9d2c2503,41f3f76a,a1937407,c0925afc,be994b9b,51627b98,8d98ed6,e8cf6fb9,cddd0ec,a4ff4a9b) ,S(905ad0aa,b585c7c3,78b7130b,ad1d5001,1010f543,194f40d3,827dc606,12d73511,bfce0701,c3ddcd38,150130ae,e91d16d4,a447821f,a2e098aa,b83b8025,b7177a9) ,S(f559c2d1,62122fca,7201e7a3,b6033d1,e54187f4,7550b2ae,f1d51521,f7408b6c,3f10d622,dfd0eb14,7f6f04dc,43108273,7695ea42,38ced7f2,5dc167ad,34154481) ,S(19b328a4,fa17149c,ccae5830,a8bedf53,7c0d8a0c,c3616345,6f4d91d0,718ce8b4,9a1ce80a,2a4e6923,69925883,8e786779,fdff7f09,25d68855,12644d04,9e582f64) ,S(afab98a0,e75619bc,ebcabc24,c1a6a0bf,2743d4f4,921fe53,3a393648,adad5d4a,bf1b3a87,759139a5,79741c09,21f29a10,7c8e5be3,13d75715,7dfd39be,923a32db) ,S(c2cabf7c,1d86a34d,addb36d9,c83a8ec9,b2dfe0ee,8176d085,cca91fd8,ee4181c7,5b32b724,53f1335c,724465bd,6eceb8f5,159ab150,e9c972ac,f51d27aa,4d91070f) ,S(92839424,8e847452,29a8c534,7c14355e,4f6e9cfa,2c1a2be4,f5ad6cfc,2a89f593,bb9c585d,fd41ee06,99ca7b4a,146faf68,51983b15,d652e996,c888a171,7c8c3a07) ,S(bca2853c,389ef184,208cba64,617bd7ad,55e55f12,d0c9fb4a,a8dc30d0,c73c7dfa,9f41289e,f32aeded,3d45952b,16a62fba,fe9a142e,1e65340,17588d79,e1df63a2) ,S(a4ea7bda,94b565a8,ebf53aea,5ce672c5,5745b7bd,37ca77e4,a0e4f281,71bf56fd,c9507485,1405ea90,9b9e1a28,42c5953e,629eef31,37bb0fb0,970cce6a,893e96bc) ,S(71707d45,af71139e,d7327ced,89a2403,da57c18a,8527bb1f,f754e78c,60d5e169,24b36484,fe4da6f3,a3f4e4a8,55a477dd,3eef0f39,fd3c585f,1b9de9d7,10223ef9) ,S(52c1de03,296f591,9d5cf4d2,36b8ff51,5b1f5ff6,d73228c0,7dda706e,4fdf9a05,db958d59,d73d574,384066e4,fda3b785,c9509714,90607c51,35d1d34d,5a344d0e) 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,S(a54aa2d5,95cfa325,38d2e483,70ba86af,d3c3b53d,2141b0fd,cc68a729,a5cc713e,bf74dc6e,63c02b2e,e676b9c8,6a851a48,7e9552b9,a32eabaf,4e1faa06,8bb8a159) ,S(d45fec3c,e2df54eb,844ad145,fb8884ac,420ce2ad,85cd55ea,4cc19e1f,da9fd956,ed8cfb00,65aecb6a,6901dbf9,b8c208d4,bf6be1e7,ee74a08d,205c48bf,8cb81bd6) ,S(f4b44e98,f728b318,ca959829,d4cd836c,5c0136ab,8e433101,87be24ad,53192172,ef5521b3,960bce49,2c841fd8,8cf7b8dd,2febdd8b,f0aa64e8,4d3c2a09,89ea9fa1) ,S(dec6d1bf,d349110,faa0cd40,e8533078,dcec40c6,e260b9e2,8412d424,353d67e3,73a16f81,3609c901,71efe44f,32ffc90f,9451b0b3,24107b72,54ca2fba,65095895) ,S(1fbcdd53,72e17c41,9310b9c0,2273534d,265f1c24,bc1a6039,238b5b7a,b3ff013e,9cf4ff4a,6a61c11,20c4d14b,97275547,b2358f75,8a2a774f,22bc77f2,4c6c27ca) ,S(d9cef0cb,38c6ed7,7aed53f4,93a31daa,50ea1ff9,aa43b890,357012fb,e2ab593b,32a416fe,246872d5,b68e6654,7f19dda5,e161cd13,ed041486,4d0c2dd,3653303f) 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,S(50a764d2,a0d8741b,95ec84a2,feda6df8,1dbe987c,31861166,32c40c3d,e6db251c,b28203f0,233917c1,4b67632a,ce9b512d,76a8c7e2,430a4a40,85cfb422,7fe41055) ,S(c2c314b1,5ef9df1d,26856c9f,a6e39cf9,1bd9c584,582893a9,423746ca,1ab51ef9,a27f9286,ff7fdfaa,b949a9f5,d59f08b7,a22f1e31,e7175d44,93e219a4,e92ab759) ,S(ba655585,da44c8d1,2b3ce375,e220a4c3,64868b75,370fdb75,dbf6bb92,76a9d3df,3d64e16b,a03a385b,def18f61,432cc49c,bdd9d04e,6fc8873b,e51663bb,ca4fda50) ,S(3d45fa49,d4d100a4,b5a76a65,1a5100e,56bd0d13,b9e141c2,aca5cfef,a46e600e,92953c,38eeee42,e1da93b1,3c75ba48,da30390e,731801ec,ed5bdc2b,58059176) ,S(e464c346,e40dc3e2,40e5d96e,1fb2c10c,83e5ab7f,45138596,4ca46b04,bc8c3a8c,63f14b46,182950bd,282205aa,374cd67b,ca364a4,f57cf90f,c7ac90d6,5204cf4e) ,S(14a7e12f,e235b307,5b0d218,bd3dc720,d56f3fe4,c73841e3,fdf42dd5,aea42688,d79683cc,40cef482,ed6a22d4,8137a4f0,eac31249,9ae13809,9eebf3a3,15e9ff2a) 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,S(af588dab,3839e85c,6dc84aa6,c1e05294,a9708951,8006b390,c2ffe0ef,f6ed9b8a,a3d37640,1b06548f,2794131f,5e002aad,616ca135,8cf0c81d,87015416,37d9cff0) ,S(bd91dc60,31706ffb,19b61796,995728b0,5f869d07,6f0b6537,35c46e10,d9b42dc6,3c963ed1,5a74f5c6,1a28db8e,de070870,cdce2cf7,d6525a6d,16171076,44f153b2) ,S(e625c4a5,91460bbf,5c3aa583,c4cb1e1f,c202c82,7debb82d,985732ed,ede98f47,d026c5f9,a9035396,1de50534,8e4ac600,812a461,c913299d,7fddccc1,5970b72e) ,S(6bd227fe,d4b193af,8b94553c,718357e4,122cd057,d95980e8,ebc8fe5c,7fdaac1c,5f3fe540,a98b044,9ed835d3,b0a2b4e7,c66a0549,e4b7b9f0,22fd5249,c621a9f9) ,S(27707a25,895e6f38,523d3872,c5b34e7c,68a0f0f9,54c6ef49,5cff6664,1edb2609,ef6f4f8e,c893d697,69f34b38,f7f677e9,e5de5c91,48cdf35e,3a18022,3ea777ee) ,S(6052248e,3359414e,bb7770ea,4284d7c,c01770c0,e75466db,1f314e0f,cff0ebde,3d982058,5cf0d546,9fa62e02,aa556fb,1a1ac7d3,1cb9712c,8b118e2a,e3f7b7a2) ,S(f2cb5b53,4fa6124c,16d82506,8b229857,4d4fc666,9b45550e,6c75a114,f370f6bc,5cde5707,63a5cad2,13952def,43cc779f,8ec9dcbb,c5fac8a0,ad7a740b,7241112e) ,S(77ad8215,9fe6b9f9,e08030c7,a75c601f,4989b51,4ef6db20,aa9d0b23,e87a502e,9268a1ee,ffc24932,74856add,2ba1ebb3,c13678,99af932a,87fc680d,ea9b703d) ,S(4418748d,171cf80f,a7f80fd7,c2d7891b,5cc9aa0f,ba4ec1c8,a114cbc9,4a8fd29d,5130285,79f01b7f,72f18322,b279fe7a,9916c16a,a67c6aee,babbb418,fb1835c1) ,S(16af4960,6f89c87b,7e5901b4,d11a826d,126e59ff,df7d0883,1d37d7e6,367355e0,1a138440,537223c9,e8e131ca,8ea3b38c,12c8e8ea,50ee09f6,8ca4c2cd,4cb04c2e) ,S(22d2043c,ab4431b8,cf77ba0c,ad81848c,730a730,35277e4a,ae6392f9,de120f9d,d7795dad,5e5b46d0,9c36520a,c7fccf9f,4d71f9c9,8ed3d45a,432f4f6b,991b8acd) ,S(57e7a8b,34826533,7e203360,2f6244b6,41d92c8b,b2419734,9fbb3271,57676302,4d9238e8,ba4bc8b2,c3abd2eb,6bb2e545,5146afdd,3d1ce2a0,9752803b,4599b83a) 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,S(d64e69e9,54e81ec4,7446327f,55e5a82d,3b83eb46,2a92af12,f0b2694,c88f4052,aa7ed55f,284c3ca2,9be75565,f66ea54a,27a8f00d,afaff0d5,8f394797,3dc8622a) ,S(f4cdbaee,d4b01db1,f0b5b0c9,d6178235,483fb58c,5421ba54,17bbcd4f,e4e7b028,66d590eb,29d69904,deb9f48c,5a250089,b2b92447,8ea91302,1ddbab19,6c63b47) ,S(8ff94c4a,6c46e334,feca809,79d21a0,761fc1cd,1de76f4c,7243ff0a,93c9dca5,123ddc33,5f3c68e3,29f42d4f,187fdcc5,77207134,a8bb777c,2ab08dae,f149abf7) ,S(c7869b4,6e34186b,7e87c0e6,23b64fb0,efed70c4,f2af5e70,5c33ecd1,27cf267a,66295439,36620898,2f17d95d,7da2bbd7,29aefa4,69005a59,629720a7,5c11f48a) ,S(e0ea76c6,ad5dc87,bd26ba9e,25b5041b,9836f72,6eec0142,351b2431,6cce1a4,8bd724e6,632049ab,88aa620a,78922b65,6a3a4417,c8af7dbc,5a03d4b8,d4eff928) ,S(2fa63ac7,3e5f8982,36419f1f,4883f52c,e8e357d2,4b4aa7bf,c6aa7eb1,29e30159,57e1601c,d6323fa8,f5a5b314,6b5e5c44,7251db28,6f79d51,7d0b038e,b8d8c3fd) ,S(74ed4038,d4c50930,22e783fc,1bb7a671,49d00877,b202012f,6aa6d32d,c73026a1,5b74f70e,65d009e8,8cc618e4,9f7bfda6,58234f80,38e9835e,80e6fd42,6b28476f) ,S(71d6aca6,e38713dc,6ded1f93,4fdf20fa,16ce75dc,dc405148,eaefd2d8,f0025f97,b4314533,7d48dfc8,278c6c4f,b19f69d2,72ffd4d,a22dabae,dd3e60a,7067e302) ,S(28fb47f1,6e91bc9f,9a2d5720,f40297ae,ee617ec6,897044ac,8a174acc,5bed5292,d04b6961,d72472be,4fcdb605,9943c1b4,ef8e7aed,2ba7859e,bdb84a4,f8b498f7) ,S(68fcd5f5,c8655b5f,5d2fca79,59a7b32f,828c5a5d,e262f6f8,94270ee2,1f47a37a,57480650,33627166,c372bc4e,7a710275,7aa1ad4e,5460dfb6,d3d27f32,778d74ab) ,S(c7617ad2,f423abc4,7ed7f8a8,a7a6002d,17c9744d,1ac6be97,49110685,95aa36da,d9904b67,fba96cad,cbe7a9db,833c614a,69e330fc,a06ca2e8,d597f657,b7121d9d) ,S(a7ef4e9d,2396fe16,c0e78b95,5259a9d1,474fdc21,8b24e8c8,df566192,a6487cdd,d6782604,91c6be04,98c3f7e6,86f22f37,23c1e4dd,4f7655c1,f40509ef,5af67f28) ,S(f3be7846,7ff03676,4ace420f,4091bb2e,71856d18,9e24890,eab6b436,771e2578,f3027657,45cbf3e5,67a6966f,6b27ffc1,dc58f3a,6811f309,434662bb,636dbc5) ,S(5c947f95,5bd9ce29,5214c30,3ebf4f35,6c8d9e2a,4e173470,94d3f755,36f0259c,b6b7b775,3e7552a3,d2dfdf49,8578a24d,90a81d8d,68ef39c4,68fb5ca7,b75e76cc) ,S(236fd960,c3b1735e,279b8702,8c25a074,2c54c189,d1040c13,4e4cf40b,bd8b2c68,9ab59bf7,c0bac18d,d0d9360e,b79a76cd,b44bacbe,b425d181,873ac390,59bbc279) ,S(c92c9f26,17cce2f7,659d0243,8b9d8932,c1a9e9ff,ca8b0d99,cd7613b3,b1947b31,abdea94c,1a5e64eb,65e70769,51ace2b2,e4804ddf,1539d50b,725fe09b,52357a51) ,S(986087c9,142c608c,33783a12,4d22c316,733c2ae8,bc1fbd2,8bd1a142,6da94fc0,14925bf5,fd76b51d,6be82c65,4562cdf,8f5baddc,eb26c68d,3fa6113f,ab42a1cd) ,S(465a1f74,f4f6baad,7c644e21,f35650b6,22424e93,83b421bf,91478621,a48a1d43,26da71e4,179430bd,ee6698d5,7db01553,d41c147b,83247157,9f2fe923,c788cb48) ,S(dd7658cd,f28117c4,4ff3c88b,d0b46adb,c7aa2ed9,1590ca00,785cee6f,5c9796b4,32317c0d,1e10e997,a74935a,8e45d27f,9a9b8ac0,f77dcf37,c1c7b340,cfcc43be) ,S(55bd2abf,a803c49e,b4548b17,725f52fc,6222af8b,dd9aed09,715ceb87,57c72033,34ad33b3,9d7344b3,abfc603b,8dcf2a54,96b991b8,41564e35,53adfc85,3d3ebf43) ,S(77be5c06,d10c226c,8c9616d3,15b1e1c,44006876,4189fc36,db0c88a5,ec12fcde,ccf2cbca,5c474949,88f27ae1,b0361b9c,20e8b55e,d965f7f6,ec8fd9e0,429ba01b) ,S(fab72486,3eb6f261,f0460b19,bea7dbdd,80b890ee,d4bb5618,30db6af2,f52ab21c,914f03a,408a2e2e,aa9174ed,99d80e68,b67f6afa,fa9da5c1,5d22f74c,8876d0b0) ,S(232a2039,fafe8b86,50a671f8,de78314a,510db65d,5cf105a1,9db8082,2a0b2f66,14ca7082,510bc1e3,533b9f6e,e216ec13,3be3a6e2,64d2e218,d95f3ec2,ad78576a) ,S(b3482839,612a4ff7,a0584752,68f13e69,deee9fa2,894a8cfc,64e39054,1b7f58e7,722d02ed,df30025b,eb4e9fa,f7c58de1,653b8224,66b1193a,3f2fb71d,5d26ae44) ,S(d3873a57,b0a7587,cab10871,a9322712,cf6fd84a,226dd7b2,85823996,5a353210,3b7e4984,59c7e706,cdff95b1,c55e3351,f1f45d0c,c9fc11d6,60e5e27f,5160f186) ,S(8828788c,eeebb2b7,71d289a7,147c0a7a,26a049c3,26dcb281,cc9b2dba,162c20ad,e428a195,87425f22,3d798922,b4971c26,5da2fa2d,de4a364c,c8c65f48,c07b71a7) ,S(79fee531,26d0c00d,74986c18,993fa174,52f8dbb4,ea75680a,37f0b3f4,ea7e537d,fde50071,3143f994,b4d7b4a1,43ab3abd,525cebbe,93d5b5a4,560017a8,802cb5b6) ,S(f44f39f0,5a9f5f79,5f0f3a8c,e03ab50b,3672429c,bf699cba,ac1e58a8,66814e91,b95e45d1,e4de1300,950a27af,bab28bba,ff75a246,46ac70e3,fc09da30,d59a1dd4) ,S(1138e209,baf9c9b7,b89d7d78,832cf7be,da45afbf,3c2fa148,50426ec2,80aa9abb,15c28d6a,3965b2af,ea28520,7e67f2eb,ac7d5917,9672f88,3727e499,f06a0d6e) ,S(29d3e942,1b98d78c,60e4685a,aa503130,dcd3d3f1,5afc2620,472b83f9,34912c1e,90a514f8,49680969,215d46b6,db7c53b9,411c8c67,c88bace1,a6d45ca7,d2bf5825) ,S(a8a36a94,5fdd33e0,4f0c18d7,cd2d4709,d6efeb88,a53fa0c7,e90969c0,84ff3eb8,1dd7f905,edbfcd70,26aedbe,1cee1cae,23db1fcd,479f02a9,bb596af5,f56ab564) ,S(5a048ece,b3fa944f,90eab4f0,c3e7a06c,3c35f2ca,81263fd5,3670c212,6a981eff,124f1bae,b70fed65,d53caf7b,5e88077c,8e330d05,692199b2,4b3d6d4b,b7c886ff) ,S(32070282,c5ebc2f,665ee579,c645fac4,fd1eb4ec,d7297158,3dc81288,e932b8ba,8f69662d,d68407e,dafb11ee,8842707,c17eda9a,803cbd55,b86dadf2,85bdaa17) ,S(7c22865b,fb04d3f1,bb988a7b,80a49fe,c7810593,27a19786,db77a47e,57afe787,a02eb26e,30f599d7,d5599734,439f19cb,d0830b72,60e70d53,97f06e1,d036bd3b) ,S(a0ba4c13,30ad8252,c06c8269,a3dcc365,fd842e5a,aaf33a4,22de13cb,b9385cc,58ecab13,5cfdbbf7,f3b6d2ce,277b9e84,940fdb14,47568960,c13290e5,fe239bc8) ,S(42ae6042,c8a2ba5d,c8fe47a4,12e2c0cf,7be448,70e67819,4e31ec23,44f76309,72ad69ac,7ba38bf2,2210a6e7,53c64467,36ea3a23,cbc96c3c,e19f209b,dea1542e) ,S(8f3ae8b6,45507a2e,3ea5d82f,47020739,d8f35f0c,8fc11e7c,6e802d5b,87b2a19,61bb8e35,3028ed54,1b83420e,fb9b1473,60425927,d3f9b6a5,d1d2b80,ee5b4cfe) ,S(3a84ba4b,1e151920,a0e4fb4f,30953e6c,a7ba1e12,62ae44c0,d91b437,b05df32f,b20f6579,43525f14,7b23abe9,c90e1d0f,32c44eeb,cddc6ce7,d3cbad9e,7d3e20c0) ,S(6481fe6c,b04a503,3ecc102b,de462e7d,7b87d181,2bc145b6,2d25fd88,e7316210,bcc1b4ab,f5f32ad0,9176538b,808c9187,d4e88b0e,aef31075,b26e5c27,8f64560d) ,S(5340174,722c583f,af9cd365,1f73b33f,8e4bd1ca,cac0af4d,1ff13064,d551a094,e4902135,448a616d,e435180,f85d0a95,d9e4655b,aebf8a41,a3bbe221,1a66a8e) ,S(c0693eae,a5825c4d,6c24e08b,d57bc32d,6c9ee2a7,90dcb49b,b350f852,4e2867cc,da20fb4b,7627411e,5c6c601,bcb8fb55,f4f6178a,efe0ca04,62c85d86,33b9a05e) ,S(c51d0f73,72fd0502,d17f9200,ca189821,e63e581a,8356735c,a91b6e93,3cfa0d9d,8d10e6b2,7ed7edd,2cfff134,54eb979b,a2797a7d,3c6fb413,b3bad4c2,2e352655) ,S(16811856,4d2d99ae,2daf79f8,58b52ad3,3666008e,d9d2c59d,be3160df,bec3290c,2bebf1a1,45617848,e81dbac3,4522cd0b,3e9cc84a,3c08602d,1adf77ba,292e7460) ,S(7ae94933,e1438525,b2ce1622,5654aa6f,b15999a,57835a09,20a49748,7c0afeb5,91912e37,830a645a,138282a5,1e3331bd,a13b87b6,f443f901,95a2f4f5,bd9b95f5) ,S(e7792d97,d02b76ab,2414c5f6,c2d1bf0a,c27709b0,55b2c36b,179599a1,3019d4ac,9f4d9689,5fceb179,b98c75a0,d5d56cc1,dd274614,a2816e8d,16fb98e0,ed3f2b52) ,S(2ffb9d4,946fd63f,24cff64f,4ac79450,3d97d706,eea6c4f7,69d9e34d,3247bde1,66b1c74,34881531,2bd6907a,6e3608ea,cff18832,5576fa9f,f32257b7,eb81014f) ,S(4544ba32,f90ceeb1,1412aafa,b4ae7351,aeb6f4ba,12e00ea3,c165c8b1,ecbb2fbe,62fbd7b4,c2a5cee8,bfb9ede9,b02dbbfc,2bba538b,834797b3,948887cb,9f8f6736) ,S(250b01b9,25d9ffa2,75eb156d,d8c67b5e,5d981ce7,8824d37a,1b09e3e6,7918980f,ba1d924a,32f0da86,e532bcbe,6766259f,eb185161,4042c0ff,261eb81d,3e09c481) ,S(9cf30e54,1f2a5fdc,73046807,32e962ee,62e0b813,901e30f5,ecbe1fee,abeb4d2,7cb246cd,1281b77b,19601d14,baa8ff62,848259eb,6567c741,c6bd54a3,b5510723) ,S(edc9e8b1,3c61a1e0,8f93be12,495084ed,b5a90eca,4f11dc03,cd217b1a,56285a2c,66c2fd21,7e8fac7,4fd43b1b,58c80661,b0e8df85,a2fddfda,5e9f99fe,621e1f3d) ,S(dd94295f,8388a498,2aaa4164,927b81ba,cae9d002,b3ddb6b6,97082c70,f1e2c66e,838c060c,d409c1ea,9bcd9e8c,b1fac83f,3b08c2b2,482d8f4b,fd3ebc18,8d6706b) #endif #if WINDOW_G > 12 ,S(7e068e04,dfc0be48,e5c0d3b3,5bfc734e,96e96ddd,d0ac4876,92f74535,685ab7e,df2cd146,90d225c8,d04052e6,93f14bf,69351e08,79883646,2c88401e,4ec70d0a) ,S(73a9bfcf,d10aac9b,46e659f,76c439a0,b7c2a073,7dec217a,21f43f39,949a5052,73b91529,3ea7b052,682062c,8f86cbf,bf379df6,91a9cec2,4a1424a9,b3be10dd) ,S(efddff84,c8cc754,e6e34678,d85809bc,55cc224b,f69be05a,daa847ec,d408c55b,65dd8f41,8264aab2,efe6ed7e,c45b4ac,8aac218a,3b6713fc,1736dd6d,c2f188d5) ,S(46a94585,7118384d,8d23d6df,a4386dd9,dc264f5b,171a7585,7565688e,bfd73f4b,3de5af7e,a298c18f,4dbf16cb,38e7f617,1e684ee8,e8df2a6d,256c011a,65aaf35c) ,S(6890edb2,7ce3c265,d4afa17b,be160a94,45dd0c8c,9ad6d93b,910ea47f,3821cd3f,60f47c5b,10ef5494,cd8810a7,ca8802ab,7c24beea,eb67b852,dd22040f,77cbd1ab) ,S(8cc9eb6,340b886a,81ec4b32,87a251c1,e33e68c2,1f55688d,952b44b4,2a05f5ae,9b176b0d,90e38290,8911981a,3bc475b9,f0323870,150c9c95,5078bf02,307fb6eb) ,S(2b062f5a,da48de0b,58001cca,e96cde15,227875e0,26c94e0b,fd1fe2a,495b0475,537f1c68,3d5170c5,8097bad,4bf17276,da9de994,8eff6805,48b35390,2f1eab0d) ,S(dd55b91a,84b3d53f,4332ff7f,224e9231,cd358bdf,27f30082,52d7a8be,bb7240f9,e6f1a08,a40b6530,ed737609,4deef969,774d2173,a3ac158b,ff681908,192a5c94) ,S(ac5127e0,40b1a979,46c0cdb1,c782ee2c,8986fd80,d7151e75,16fc964a,f2c59c70,849e2249,323d0539,dda0a82e,1764593f,8afbb097,880af8e2,4765ea01,b7ae5db9) ,S(df2f2eda,f0b6ce9a,3784e9ce,1e1ddae7,9d136423,153174bf,f72212c1,b5311123,b9d98f8e,bd78bc20,316da64f,46644026,fde6ab44,162027be,dbac75f6,e86d46a5) ,S(fd83b387,d630c176,23b85e21,62113610,97bdc5f4,3fb08027,73ff93d7,a373e5f9,9a962a7d,375f35a5,9d7503d4,c0fddc9,115805bc,38438837,d3c670b6,ab6cd2ee) ,S(d8fbdfc1,155ec8ac,8bead443,ba3feaa8,d565ca1e,4206cc95,5feb8e1,32cac4df,f9453c0f,ccb99cb4,739258ed,febf7642,7fb1fcd6,1f963abc,9cb9a5ea,751f73ac) ,S(9fc9749a,20a3e8c0,1b309389,16aaf3d6,85f00872,b82350dd,c89110c0,dfbf86d6,a2f679a7,6c92ac59,5773bca7,8f0f18,75c85cba,e75a6379,1094a799,863e19df) ,S(29e0e346,71a91ce9,bdabcf25,2e2196bb,65b81092,d3728f62,b58c815f,2f476a3f,2f440c61,b82e0ae4,798a35fb,9c66b261,1ce5ad0a,ab42f9d4,174bd698,d4d0c0e6) ,S(e4068a15,398955a0,f27e6f92,9cc3dfb8,7fbee70b,a86ee78f,8736b519,ae102d7,a3f2f2ad,550f9cb6,aed99943,84a9a350,16b91143,747d4e7,7d69e698,8f165086) ,S(51b45e10,bb1bd989,8bb156c8,a4c81978,10f16364,d3d55092,48a42028,726c9f2c,e30719d0,4225de63,281ac479,70010cc0,8a1f1d51,48c57f6b,b478c95b,e3e141a2) ,S(14cd5d29,7b8ab6b5,e92ec2e6,6c63b3d,64dc492f,d5a0c5ac,f6fcbfa5,aaa0b83e,5bf307d7,7cdcc866,349ad1fa,fb1c7d8d,5be19270,2a46b327,9b72bd77,e3666805) ,S(a5a8a711,49d6d146,c32254ca,e9c18288,45e9f2df,419ed68f,8c3cddb5,d22c4da6,9f47d887,7bc3d345,af4ae693,35639bf0,b003f481,7833d2d5,49c0bbad,3cbf6c2e) ,S(359328d2,4baa4232,d75b13dd,d146624d,bda494e5,2cc778f9,99a4c0c4,1f9372cb,d31556b5,71df399e,99084afe,c8f680b,b6695d7d,648f7050,a7881acf,241af6d8) ,S(c9eb81ca,4f2a5a2c,17268a12,d901edb0,c8fdacc1,d26c5e8,91af95bd,e673e7fd,6d4a512f,c974fe9a,711ae19c,d9bfbd6b,5acb73e5,355608df,76ed2942,488adb66) ,S(e26631f8,16f3b308,ac4c9f90,eb6102e2,48e55730,24f41f38,6ccde5e6,c2ca8e2c,16e0b2a8,823aecd0,165e2f10,20518253,96cfb814,bd5a248,58a4615f,eb9306bd) ,S(f76e9af3,65c0e7e5,7807b24,269c4732,677e5af9,a3b0a965,8db8355f,f99110ba,80cbf439,d26f164e,bdaf2542,385f9d65,9d174c62,96ada102,8a0cb013,bd2a9407) ,S(dcc8145b,af891483,295d6ab6,9a88fce0,bc333d54,841e7421,e65f6270,852c5dd9,cedb3770,a620e7a9,b40d6cd1,60363bb0,296155cd,80d89480,ccac619a,f31e2a19) ,S(7645e13a,6a1c4d0f,a56a199e,cae93018,7660bc40,41edb847,ed33fad3,c603e4fd,7c8ea51b,7990e5d5,125eccbb,5da890d2,bcfc5353,b22c42ee,1864c22c,be91e713) ,S(ba26886e,d74cbcef,afe7210d,51c1b6bd,4658225d,45e20fb4,4222b318,9e2f3f25,fd885db2,23ddadee,9e65fa64,abba326d,e0b89627,7359e893,bdf50db8,a2b3409d) ,S(68b500e1,31005b1d,901bda65,4a525e80,fc6578d,5e792c92,299d21a5,19050fe1,71ef7d7a,b3544a94,f3dac8e8,77da5468,8df9b127,83e02022,7e05d5f,6b12f96b) ,S(2ccca7e2,613fa83c,27ff851f,12c6fa07,5b19f7c9,940a5064,b84ea75a,da7996ff,5ab70a22,22dd1ad0,d0db2d2f,c59390b,cf37af8f,bed4570,3c6ae0f3,27d7707f) ,S(6d797d2d,6a56a45a,1b5af718,3cb6dca4,383ad9c0,4d5cf3c1,827f4da6,f7179f14,aae34e5,d203d18d,99e84bee,7d6f5a8b,b80e541e,15a3aea6,7b162551,e80edf3f) ,S(aa6997c4,37be76b1,9553751a,d96a53e4,9a565a58,55f67b5,11605996,e98ee327,6034a421,9cdb40e0,9698a15b,2e2f5f1b,6532e277,a1f4f4cb,3cc0c33c,c684835) ,S(56c40fbf,fb8e1d70,a345d53a,7b0f897e,1e62484,dc01adea,d010c5be,ba2a0f48,e9d06789,78b9290,27ba0e09,173d8ca9,676a4a78,7e299f4c,458cb6aa,46f0bd01) ,S(db6ff6a8,3963ed7b,dc262be0,8b52c3dd,b6e1e237,2a535073,1d2903d5,17918d89,a40112fa,f30fd44,b42f6b18,c144ca0f,e248d65,d757bdc,162b7118,7d951769) ,S(8df55701,a46f63e2,338e730d,4a543013,dcdd1173,754e5de4,151ca180,63402c6d,64cf9c9a,64b63ff0,1396ddaf,b48bbf62,b3e69665,bc89ea93,b9dd12dd,57a1c3df) ,S(9d10bc2c,51018f57,407ae460,e5dd5e45,66485cce,de258af3,7bef48a0,1b0588a1,38ea3c08,b2a4e171,7edebe44,e03dfeb9,726b302e,aea0eac2,fcbc9389,84922c04) 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,S(223d3d13,6bca94fd,9b3fcae8,6bb2ddeb,3cc33c8d,3ccff556,fa93938c,c27ffe4f,87e19106,e317187c,c256f7dd,83d6219b,27f6cd8a,53bb4ec0,9c74ca58,51512915) ,S(5591d8e8,291161b6,43df3a3e,9b4f495c,b614432b,a0f3aabf,517834ad,9e8f7b2e,2c8d6a35,f6267e52,d9bd454e,bba4719d,30b3fe7e,c40a1416,673ef594,e6d07c2) ,S(eb2cfc4a,d15d1a14,870cbaec,b9e9aefb,4141841e,2e4e6252,c8e93751,45f29a29,78810e08,10bfd992,b7b04c79,c7650150,e62f210d,6d35cb95,5bc67215,7052e5ac) ,S(6112c3f9,9680a818,5e4b1d4c,539cc436,bdcdb47d,2e19f927,d5e3e9,eca3f74b,6e860bdd,723c8bfa,dac8f9d4,1f6ca96,f2579d7c,6a690f35,3b8da52b,98da4403) ,S(892120d8,d552d8b0,c42c23b,9a0f17c3,b9b32914,d7e31579,7b391ded,a7d58b16,e62523ac,b3c778f2,f913d1f6,4bdcc037,cc4a9496,ccf0cedf,32502316,b5cf7941) ,S(4758b456,217ad3be,2315583,963044a5,60ca4a49,168461c5,ecbd1e91,1fc4dc0a,99e4255a,4f30973f,57eec6a,1c30ac1b,bb74987b,3c4e7ca,9604878c,d9d83679) 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,S(a1fcc983,7e720096,7203e2cc,11450716,f2fe6484,f681b2ec,5e42e9b8,eedfd862,1e16b6c3,17e8fb89,dfffa79a,722de49e,a419affd,bc17fa96,4ba6c316,31ed4fd7) ,S(d85a314e,69617e50,18df1e82,21cf738b,60485cf3,3abe8838,472b32b9,7f0ceae0,71a0ffee,e92dde66,66b4b5da,a88a79b4,fbbcbacf,3308a4e8,6e1aa367,e00a52f1) ,S(189226fa,688c70e,415b20e3,1356eac2,f5a53b5e,8043e24e,4ee03faa,f20c2e7f,d9bfd8ac,40c7d53e,7bcbe575,9987cf62,fc2bba7f,952e4eaa,1a0587de,f1515aa6) ,S(d3542e0a,6a931162,d7a674e6,32cf2135,32465d25,4d2d9241,ff70709a,559e1330,25e8f51,e2664234,34cbe5ed,622bbd83,dbd42784,4b1f2bf,9a079917,4b57c369) ,S(514d9e86,fb2cb612,1ec6e6b8,25875856,9a8c0a5a,adbfe45f,2876be18,753a2bc5,700785c0,be5423c4,341918d9,f65f79d9,1b8370bc,48629791,45ca8418,57cbf261) ,S(c9f86365,12e9ccfd,e1f1db33,5ae606ab,43f9aa62,2d723f6a,d6d684a3,ea3fe495,30d3a631,3868a01c,9c6f9445,ddcbe3b9,b7b80b58,f31f5db3,a3b3beb2,1e30270b) 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,S(d7d03a92,95064981,1cdc6503,588d157c,88c861d9,43fa9cab,e2e3301c,994adf7b,8c820bfe,933c2c05,1ca3042d,5ce781e6,ef419c8f,d9aa83ef,2a915e36,382f9627) ,S(5b2c9504,f645ac90,24e25c4a,e880ce7b,f33aed77,e45518d9,1c6f2652,ddcf11b0,500b37bc,c7764f32,11d681e5,e8f2a407,440e1da2,4eaec354,fc289c76,29296449) ,S(d18e26ed,d2c78bbc,16982675,9d59eec3,bab1a64d,f579dc2d,6284add4,8cfbd761,1a1e0172,37a3e78,8fd8989a,a5bb6944,685915da,1392e1a4,4a6c7ef5,7d0770c3) ,S(5f6b1416,9bbc4795,8ca21e88,df252546,dc9e46bf,85d64772,24f34ce2,8e58222d,3a8e7616,4d5a0501,947ca0bf,163e64bb,3a57918d,e383c600,e02aadaf,4b7fd6a6) ,S(d7a625e8,dcc8b456,69802023,8fe85691,ec2e050a,25421373,39bdbc8a,f762bc7,8f1f9935,a8ce2607,abd7bcbc,fec1fd8c,208683a7,10000806,20d50b4d,36ea3643) ,S(a56a5419,72aea4f7,15dc891b,3a1b34ea,7ffb42c9,5e02a771,6bac663e,8d5913f9,47b3dfcd,ad785671,180f7bbf,a7f5d144,59b44023,640e3897,1e999a90,6bc3f994) ,S(1ebb89d7,e574cbd1,37b1a3cd,4a306b44,30325db3,361b7c3a,d93116fa,baade31e,2039c52f,bd30c84b,4983d118,5422a342,ee020c33,49357e6c,b9550075,38da4dc7) ,S(b5728208,931a6575,4b5cd1a4,a798ec27,e189effa,3ee4f0c5,ad493a88,b49706fe,aba785e7,2da3d301,cb29a612,562078bf,358f680a,317836c2,14ddf7d1,bede9ee) ,S(56661670,d67b7c77,202a00de,effc1ef6,f5162a97,47afca8a,a2457c85,85a775c9,adaf08e1,83bc5107,4c55122,e549d3c1,4de8a893,39f199b2,ea044a25,4d8803f6) ,S(18ab56e1,ecc86b69,77104243,35737b51,c18521d1,b170a3e9,3fd068f0,ddf2704d,cc694c3f,43bfba9b,20c9572c,acb30563,df74f07e,ce1ff9ff,46b8259e,8119e94a) ,S(bc12a874,48270360,1575b754,bf5f50f,6e945185,2e0f27c3,c1aa0f1b,ce0ac357,9c6ce76b,ac175ce1,d667783c,7204ace4,abe12d56,62ff36f9,5de017c6,f1ada1e9) ,S(a4494c26,99b2da0d,6edbdd6c,353eca75,75666796,5ddbe457,2c27ac46,79054584,589804d5,8360a9e7,d3e2a914,61d5b1ba,e8f0cf69,3b8add03,5545386d,5082d621) ,S(1ff846f9,6d0e4e7e,be34de77,d036a027,f1baf9e2,ea3dc9c7,8284ac9c,ce3aea6e,8a0a336b,9f0e3560,31f5d1a8,d4c0b68f,27ba3eef,a52dc974,8d03e12d,653f2e6a) ,S(33181aae,91573ddc,728839e0,4173f716,6862d724,35744099,ffa8f1f2,9510b374,1252129a,8cc8ce4c,1ddaaa0a,4c34c4a5,f01ee26b,3e1a9fed,ad0e7c9f,bdc5223e) ,S(e687832d,fb0e44ae,f7649b15,77274a94,64426406,fe4c6ae5,7028c9e5,78012594,5e5b3897,6b734b7,b65caec8,c77ffb7f,c5de4f98,eecab002,8cac0c4a,a513b7c0) ,S(354bbec3,ed9371ac,58174b5e,2a18c76c,c22951,df4c6aa5,755c72f3,94b37def,40d0c876,9283416d,b3613ac7,37401e3f,3c2f4def,bbaba44b,5c2a83fc,c614c29a) ,S(fa46ac6c,5205b81f,3c9e8aa6,8b5ebef2,a8bc68bf,fa2f4511,ae36f726,7439a485,3853f9fa,b016d2a8,1cde37b,13f91185,f25657a,765fbb35,c1b4d52e,3f67d180) ,S(426f86b7,33255f8e,1e85263c,923fb86e,56a53d77,945f6688,5627ed43,3024328c,92ec0168,5301c89d,5b13c4c4,57b22215,658c6341,6aff9148,6a2efbcd,4e8c4fdf) 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,S(47484548,d4b2acd9,bb2cef9d,bed4bd0f,f1fddf4f,e1561a51,891464fa,cf5007db,ea61e154,f011cfe0,46fa2539,7fb444fd,b93e223b,ed882bce,3ddaa3c8,328f44a8) ,S(331f17ff,b14d43f,ec69a6fe,b41a8021,dd8ef56d,2540234a,b466ac85,e6c5b8f1,ba20bca1,8d774731,b6b64a0f,8a19311f,37d8c061,2c4699b,68d569b0,9eec144b) ,S(6aba62d,200bd2c6,4ab88ce9,80530e56,5b8971c,f9c427f1,5e9b146d,dbdc68ce,e4c936d7,d7d98919,acd26ef0,cf071f2d,fcf65fd7,78dd8c5b,ab026,e9f832c8) ,S(c76b6c35,e72fa19c,621022b4,d9ec6ece,c0cfee8d,c73254fc,f52cbc69,23ca19c5,5b0ffa7a,48ee8599,9b74d0a1,d7fa0289,b49dba85,7b21bfb1,ee7ba831,fa13efc9) ,S(c056ea3d,43f33df9,b01590fa,429c14a6,aaa438ed,415254a4,4a93854,ce1bb77a,d5b194e3,2337a9f1,2c479e7f,576a571e,58355a02,8ba0231c,c337b8c7,eb3dca7b) ,S(3d688ccc,8ddf0ef1,137bb897,e6b8f3b7,7df652c4,93cac3a1,47e88b3d,bdac938a,bca94788,4d7ae1f2,960daead,111558f7,38b6bc9a,7af3bb4a,691af22d,4d5879fc) ,S(4faffaf6,69ce1180,a9145f0c,df6fd834,c59d7a9f,5f2e49cf,3924b33d,8d2a179,9e015cac,2dca2ec2,5580c16d,8c910abb,dcbad872,79bcc485,b71f5561,60159d2) ,S(47578e3,7cd7eb78,6b5a44eb,3decc7c4,e8ba0c7,6699ef61,4ac30579,a24aecad,948ac817,a6bee00b,c68eab83,fb628ed8,7fd0066,9ebc8569,45eef8c9,67171651) ,S(9aade275,3eaa646a,24ad1a35,f74887db,8c72fda7,77b59dfe,103e1a95,dc618836,b651c384,8f4625f3,1e6e7a05,c94483f,ceef2fed,dc7f4256,87e0373d,d02bca96) ,S(b1b0c3e0,b1c6ee75,55a81852,447b2bcf,321c9b9f,629caf9a,276133af,63aed711,493accfd,624e6ff3,dfc1d0dc,aff17113,c2c74167,58cbd571,759bab24,300ac827) ,S(c557758f,b192a058,eaec5762,ff391a9b,2a0ce462,7bae01c,156dcf3e,bf2a8ff6,1d4e9b53,d209e195,9f10f671,b1bfdbf3,98921284,a7719766,39947969,6d1bd3b3) ,S(73522ded,5120ed4f,b49b5ca6,df5a1b6,edcc082,48df4d07,cc9ad923,2b7b5e0e,47569d94,cdf0270e,d1d299ce,d5bcfdc7,7f87db4e,c9725a96,e4388cf8,dee08d74) ,S(16571c0d,66328963,2a3ae46d,fc2bee50,fd6fbc0c,f0ec73ad,72bb9c2f,e8323506,65de9d86,9e001c60,ced57911,e7ce6150,a936d684,d759f143,d2224448,4bec68d2) ,S(f5fe5564,2eb630a5,c860cc8d,7c9ef86d,b1810d2e,82dcb343,dbe2f958,98e5f090,5cee7a1f,bea9dac8,ca340dcd,fc2c097a,eec2dabd,d7ed7504,e20c913e,9fadfa87) ,S(ef09db32,70d09043,43da67a0,b87cedaf,7aece017,58d78591,8814e3ca,396e3592,5934f805,ba246e9f,965c6161,cefdf4e3,7df14271,2ae076ea,80ca239a,c7b675e2) ,S(886cdbd7,27d2f099,9852b102,bf201ed2,5e174622,f974b0c1,3edfe523,373a54e8,dacb328a,7fca6e5a,e5351825,564e4f89,5166f687,38d46142,6eea7b09,dca73b2b) ,S(b7d86bcd,4f7bf2e,8529ff84,88d9f3e9,62071308,9bbd91f9,6e4ef82a,ce237cff,c6b0aff1,375a547e,a8546dc4,17574843,3acf2a4,ed0d002e,e32fd88f,3b702f0e) ,S(d7d171b2,8132ab85,30791059,395d94ec,c24f5e99,67bc6c4d,22bfc7ba,eb388c67,983770e0,2421e2b6,55d3c135,1bb39bf7,7be39682,97088744,bfe6543d,dc1a8f8f) ,S(ffe712fd,881e30e7,229f1cfa,833dad90,f01a1896,c1493502,a429080a,9794b1be,f4299e03,75d084a,10b11ae5,8f2fa2be,f18b037a,53165586,cdac18ce,54505da8) ,S(563c92b3,3226951,cd7cd10b,3f7b35c7,dff3f0de,6f03d66,9f664655,57d13f7c,dca1eef4,85bef41,80b0ccfb,2416f948,9bb21094,854f5f43,769cb37,33ec10c1) ,S(b8e76ef3,3a2cebce,614056d7,efa47c15,dd52c228,66a7d3dd,9a0d4d64,68f32437,4454e79d,652ae799,a3a539ba,42619a1c,3076ccc2,109dc4a2,2aa41a28,918651c2) ,S(36db2304,f60703a2,df2e429f,b8a99841,7b4a4f3,e08642d2,c5675460,aaf1c971,a0536e8f,5cc30aa3,d9b859ee,e26b1abb,ecf7f9b4,8c8fef0,f842fc9,a684b5cc) ,S(c5d4e51d,1521637d,d6055e52,9e9ae2a4,d537c1a1,b7c6a314,f9d558a1,88d9a5ab,c841eeed,6a13782c,fbf65b08,c6570994,aaf7093c,4b48ad0d,e04db33a,6feb3f6d) ,S(50c03dc2,985859f6,ffb79ed3,f635e17a,b0561533,600af220,7cd98f9f,71c4bffd,c68c8797,a7ed229a,f59a2bd7,451c748a,5c425528,8b7f6b0a,68b64a77,d7137720) 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,S(5abf5528,2f87ad04,202b62c5,8ff7440c,64f9ba39,e6989df3,e31d665a,73a50216,71dc4e16,f2705c02,2ca1b37,edc5ce0,610b6f57,282d69c5,d3269295,5a1fabf) ,S(419495d,9a121cad,41887fc2,82c2c7e6,f359cbc,d24093ec,57399c3d,a801843a,9152e197,40295094,11afefc7,83990732,d5e6617c,d8e389d2,956536aa,f73e0c31) ,S(fca38482,ea2be49c,3c27979a,5acbb158,a902bc4e,226f7eae,4165ab7a,29fbc3af,1260735e,5fe62664,90a35f0f,7296c441,bad50a75,7b00e34f,28856a6d,cf46f5f4) ,S(bcf05123,3d703688,aca13530,55bc3ab2,d499ec40,8c912de1,4b7af456,55065d06,f32657f1,645690b,35484e63,a3456885,c16d4991,7670e71d,5f5cb65f,a5fb8bf9) ,S(4e70b42f,6391b424,b159cf74,f5fc96b2,68bf6cc4,a26658e4,79dd8a4b,8e9a92e1,8ba78811,1af31c06,77b24fa4,4b6ce356,66c595b2,3fe4fd36,591b33f7,e53b3688) ,S(3fe853d7,331c60ea,c213703c,a7628dc1,3cdb83f3,8a25ce6e,1be84f0d,e921742f,fb7dbb77,c2c6dc13,6f596154,f24dd3,f27b5125,9b60476d,b230e54,5ddca5d6) 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,S(ae5b648a,c5817a86,cfb06a26,d62691ab,8a9cc554,d0eaa86f,839f4a51,b43ba7cc,1ea8ab0d,b665c22a,ab0a48c3,da17c629,66e75212,a6fe9983,d5e925d,432db311) ,S(3b9bacd0,a092856d,98eea5c5,ccc9abb4,4f2e0d3,27e578f0,42102148,890178d2,b681e88e,9603ba1c,57b628d7,ea929ae0,b79be447,f181a491,1fdc65df,21bd5052) ,S(524df580,a74066da,d522f827,95e415ab,f6dfbf7a,1c1f6d7e,e8d05a86,4659fef4,3facc728,5f3bc1e1,a6fc210c,ad302ef1,9c72c5f9,e358b9c1,ed2aba72,2652f35f) ,S(2e0637f2,ade775c4,87d09a38,3480b875,599a34ea,7fc70cdf,f6ed309d,450e4363,e3c6eb08,7e2f4e49,cc78e903,e4ad55f3,1aafb7ee,ada72369,6da8a0a0,f764738e) ,S(f7fec6ad,beafbd3b,e413fb33,587b9427,3f785728,226f764b,bda6130b,aa0cc483,f646a974,8eb457c7,fc8fefd8,e63b976b,dd42093a,e59fc544,c66531d1,9e08c68d) ,S(75f94ce0,6af64c43,2b6c95b1,2d892dc8,cd6eb497,4d826299,29ad8bc4,8a3608be,bf8716d0,a2b7906a,69316b32,21ec0076,6e32c892,2c7be6c6,22e8877b,b1958a29) 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,S(4c76030f,e85cfc92,64f16cad,99dfa541,fc23b8c7,2b558574,ac6f26cd,d4f55e85,44b352d8,9a31b4ec,c8f9a574,51855f7d,e98c63aa,98aec090,2d959be8,a12b7bb6) ,S(dcba96a3,59103c35,aa2c9ef,538c13a0,2f0e8997,3663d580,fe454762,5fbaed2e,af9e205f,727698a,de9f91bd,75bfb73c,b13053d2,db2d83de,b4d14c22,176544b4) ,S(fd0497d8,f75fff9a,cbfd3e03,6c9edc73,e682427f,e9b66a43,3b5b2b31,f2dc7883,d23014b6,9c8d1077,ab3fb2fc,c0bde4a9,44576289,896de135,9c0badf,fcd62d79) ,S(5bb401bb,b38e413,43d1b779,54e83f9e,e705009a,eb8a1077,542cc6ed,edf48040,431fccb5,acec1391,f68ea628,378e3ca8,ca944573,ecfa5e,e7a82bf8,82599c14) ,S(1fa96a4f,f9cc6ad8,b2741c38,b35c377e,3acac704,67bc5d20,a262db5b,48bb283b,c3448c92,ffc65afc,f1eaf7f1,f9e149eb,6404dcc7,1b222ac8,bfca8feb,eeb963eb) ,S(9534aef,1ae551d2,7a638453,171d0a63,697ea420,2fec8f11,61432291,642f86ea,cd0c943c,38837dd0,33d48a4e,ca13e96f,46fd7f21,2cbff849,6432aac0,ef729591) ,S(ea72afed,43300390,bc98d08f,3aa4ff4a,138440bf,1a8f8b7,b57032a0,d01b8ceb,e174dd8c,3692cc2,9ca856a4,4eae7e94,af4fb044,85172809,25ea66d2,d858663e) ,S(39593534,3ca2523a,603801f2,abf3a1d3,16569862,35d79fa9,a01f86d4,5c122327,acd3e3e9,2cd76dc8,551cbf0e,94475125,42a5b887,ac6c975b,45d2e000,9953dd96) ,S(d57b2a2a,375e5a0f,6967d4b5,3dfbb51b,4f74eff8,72742a3f,246e3e09,ec2d4721,12d6f848,4d107ec3,10ec2091,3482781d,c0aeeb94,71ae7b03,6a0d2551,d3ed306) ,S(9f2dfc5,1b99eef6,e6c781a,fe0135d5,fc5def8f,d520119c,59bbaaf6,442f1082,8f20962,fd273048,fa3ca6e4,ea96fe0d,7ad1d758,99e25a77,e0f8b56e,5b20dd0d) ,S(b1c30bc6,f030c913,49b36c1f,9c0deda1,afa58776,58c5a16a,9352c1bd,229884b,f8a459d1,6e77888d,cd5c63d1,8a2e28cb,5563e727,f53b59f1,939390c6,1eecdfc3) ,S(8a663e7,40cad237,12dad6f9,1bb5d266,30542933,853e02eb,665e198d,a5c6e53b,e206b399,51175d15,daccf711,63b0918c,786a8fe,2077812,c0c1eee6,bb5c1e99) ,S(2b0956cb,e0ca91ee,f44fac0a,76cc0b00,5f4a5ae8,27e63696,fe1aa8b4,a92941a1,a31e6fa8,dd454eaf,90ee1e11,62627e3,3f84b8fe,da29f423,ddf2a962,386cffd2) #endif #if WINDOW_G > 13 ,S(e0144151,7a2ac970,eb6381df,7e11fb4c,6b009980,6a0d330,d5429126,e662c3bd,8238ce9b,a691c80c,21563934,18d18dbf,aeb3fd34,48863a1e,7f4ba360,408dfcee) ,S(be3213e,8b062f33,caf16c53,5a0b666,f344e0d7,1e28aeba,8b215a3,7ec86c37,552523ba,eaca38a4,cd795683,852a2643,550fb83d,d1db0adc,3f1b29c9,7d51cd1f) ,S(623393b6,bfbfbd64,fc7aa1db,9e58e274,1c18eb6d,b5eb30ab,c4fe167e,a9e8ff2b,7c0e4174,f0fd5bf2,a025e316,fa3b7b97,1339a197,b52b0b50,bad4dfe,34e42cd3) ,S(dadeb702,dd0a1e87,669eb624,b8cf40bd,bffe79aa,8afab26f,bc6215b1,dcfe97a,930890ca,e4c29b41,2d660acb,8cd39bca,5a522599,a1ab0bb4,8fbc38df,17253490) ,S(b528d3b7,83179b82,bb1c9cfe,c26184cd,ac98ad5,8e253c13,627fb778,c9362f33,63203af,1545122a,63940676,ba2d18a1,aa902e08,8bb444f0,47c2bd52,db8babab) ,S(2ff223e0,93986e22,ae418a5c,804e9e81,7a4de562,d7436e0,2d025ab7,11734a6a,c5c8d188,ec9cda19,bda76d8a,97838ab7,81990475,d4a00096,5efa79c0,100f678) ,S(cb8731d5,e1e53c9,ccfd2c39,3c8ab1cd,9ec839f6,99fc712f,f946e74b,99eb1742,cd2f9df8,38fec504,dd125248,92ce8a4,a9db3848,e487076d,8c18e53c,f6d19fb5) ,S(1377ac45,d776a5cb,76ec265a,af272690,6dac52dd,be987799,36bb1271,e0cf4a2e,a4b3330d,d5954932,d5a7a818,7d9493e0,25ab2155,d4ed0d4,f34aca1e,c2a04670) ,S(984b9bf2,f140c75f,e03489bd,88041faa,22fbac73,7ac10724,c511a253,641a5ccd,c474f639,9733eecb,a750ea82,ac4d50c7,d82f4c9a,942a2bb5,90b1431f,c8d14ff3) ,S(4b8fd000,74f57cf9,b135d56a,c002bf99,d5050479,7298cc4d,857960d7,afbdcb06,7c044103,1df0f6f7,721937a4,c60cf76c,95560ee9,4c6d097e,3a8e37b3,34c703bf) ,S(57316653,68412236,619250b2,58bd0ddb,34fc751b,8becc0b6,60585683,218b6079,d1d56e4f,30f01c57,48972898,b8afe142,16f8335b,e3a39c37,da64050a,91652904) ,S(c9a00197,a0ff16f2,fbf2cb59,767d43f4,60737367,4f2bbbd2,53c7220f,db69f286,177c6783,d739117c,1de074b0,c605cabc,6b4dfeed,a531f4e4,9cc518,40142f0b) ,S(e23416da,91df23a9,db161618,579b3008,c87b9ef5,7ee8bff6,45eec6ce,a61881cb,e556417f,84043691,e7ec82e0,e1718296,e42fbcf4,a3de0137,93772dd5,70b8da15) ,S(9f96e3f2,369d753c,e6614c45,77bd8a9,14293eee,8a749c1e,3b0e2955,638e9ad8,f5cd1268,1567a4da,71650d10,e413e0eb,9b01a396,e529cff6,b494b2b9,a21ddff1) ,S(48657ba4,b24b0123,cd54317d,de6a3245,ae488078,5ba43d5f,1d94fbf6,b9301fd2,191edec0,6eb53781,2813ca77,2a9021b0,dd4931a0,929a7e36,a4a8c66f,aef0d890) ,S(67b322e9,d72e864d,8cb15511,11402d7a,c6c858c8,77832d4,e0187e69,6a36f24a,cfeb12c2,6b58bf15,3bf87058,c5faa833,e15c867,f7f9a208,c3dfdf3a,c7f6946a) ,S(42e8068,542bdd98,fcce8925,52002db,c545ba13,16082d40,fbde06f0,a44ded15,1645a9b0,c1f33cf5,27364915,8c4f261d,a1ee814e,7aac6402,bf644451,bfc4aae5) ,S(8ee7dce1,339c50dd,55619107,9bbac005,3e058cca,4a8c8e30,7588c105,fe90d4c7,ffbd0af4,8aae8279,2cda6170,5dbe9fe0,98e102ff,1e6f11d2,b4669a81,6ec9d5f9) ,S(abc9504,12926a71,6adaaaf2,7b209216,37a935f0,cc66eece,55978a82,1fa368e6,72e54935,e9b461e7,9fb75c48,4dae4fd2,155a4a48,d3a467c9,624c5f6d,71f79203) ,S(bd250320,81e0e9b5,3b00568d,40378fcc,fd72fd8d,783f2f3b,433ddd1b,a6976ba8,5adb8bdb,85855498,994ca879,717b8e7a,e8c4c87d,29d6a1ca,4c3c6395,6c3ceb39) ,S(b4fb262,fbeee84e,49ae9167,7e7aa0d9,b31609e0,48888740,c018a5e1,8ae25f71,34df3f86,dc091d51,258ecbe4,1cf616e9,265d6d36,8ea3403b,24cdc7f8,e176e5fc) ,S(d1ba9b67,66f24eaf,a145ad14,81063b5f,e4604817,21b361c4,95de8833,be605c01,e80a6cbd,17de2f1e,663ce7f2,8917e3a9,f871943c,a4b8ba75,68476a3,d9e8400a) ,S(5c98b6b0,3a3e5a8d,2d46652d,5eb9e2ab,a80c6702,69dc5ba8,3732752e,922639b3,81e2f9a,145d0cdd,2c51bd13,f907a04,6a35efb6,635292e0,6b8f6513,c50f4a54) ,S(c1fa4688,f75fb86f,61cb7071,4fb25f2e,908abf0e,a87aa84,c8db5dd,4c2618f8,f2f74a77,6d4bf26d,17f55d0b,1aa913cb,9db869e5,ab861d9b,2043ccb9,ca8397ea) ,S(5e806e9,a644eb32,51c62ba2,f09a755b,96aec78b,4405df76,dc22ba6c,f7227ec1,b88c8118,d6a1829d,6aecaa05,742313a,b871d2eb,72f31bba,9d84f87f,a73e614b) ,S(f9d147fe,fd2c1a7b,f623d965,bc7901bd,968636d,eff54c14,34c6326e,d1c8de9a,c7887249,ab6686c7,93a7d77b,41173060,40de44cb,84980c33,cd548d72,d29caffd) ,S(b98cc956,85f6d11f,a8d38a1f,50799634,9f7020ae,3171023b,abea0fec,a70ccdb1,f074d495,3689e8a3,6ee4cc0d,40882355,3dcbdf21,70975f49,5712adbc,990ecf7f) ,S(f161cad4,100817e7,ef9091dc,714bcba6,18458493,f3bb6b03,4648a649,6817b474,b7eeb92e,396af324,22881eb2,45e62515,c4410af9,fa519ffd,61289f6d,9b740904) ,S(7c8b6c89,2ea4061e,456abac2,46edc08b,fb54aff6,8a2678fb,1b7b1c08,5326914c,f08e1f02,6ea1d2c2,9ff5eacd,2b34682,2960723d,cdab95b1,d69c8af,5e7692f8) ,S(4668c29f,16334658,195b93cc,ef71a076,3ab2078f,724dde5d,d3635eed,24f28729,5db228c9,8391ec52,324c723,39d99514,8fd22f7c,2f61cfa1,29ee7400,4c74ea4f) ,S(3443d0f3,9dd6da5c,19a39f8c,f3672652,96fa6729,c9290b2f,4e21c7e5,3167b65e,4b6db639,9a088ddc,8ed31f63,7c079451,14a4320b,b7ed94b9,2a87c0e8,97429234) ,S(d3ce3501,17a04e95,58281e69,3574c096,458dbca9,afac20e8,ffec7810,8bc227b4,bcfc77b9,628f6ee9,3541e47f,8d556ad0,7696ee6e,90ce384a,9b77fcab,6eb9908) ,S(c4dc6363,ad772452,221f8640,9de0ac28,f2bc1ac3,cd2d7080,23301560,f95127af,78c9ba8f,d789a666,439bc949,38345250,38a79c5,97f6a71b,3e096b8b,752d3038) ,S(c771f94,221a47ec,fcd78d7a,123d2e0e,1bf4edcc,bbcdd075,b23d29da,6d5ac666,4dee3b30,829f5aae,f4471924,65de293f,f2ec526f,5b8f5980,d9155f71,ce8d6091) ,S(bff88ce8,96338f7f,5b6516e6,448a1f25,36a1e9bf,275afd50,e772517d,79e6e199,8f3f0c7a,b62010a4,eb0b6211,7e9761d9,c1552629,bb55bf68,53274158,a788c206) ,S(4afcd064,5d57bf24,e850e7e3,d3cac224,6a467e76,f2ce02da,576a1f2a,9a3b97a,52f23b54,87b2af93,6cc692f6,1876d6c0,ef927d3b,c06df93,984ae54e,4d10f0a2) ,S(c4bc122c,b9bf0e20,57f933fd,94db012f,79e23c34,98007abd,f8a8ba21,32b1f373,e40c47b6,a31d81ba,dc45d427,3ab56d77,1daf76bd,7bdf8ce1,a8778861,66fbfc6d) ,S(487a19b1,d1be7791,ce223d27,bab11aca,837a0f8a,7d34d9dd,b4c68f18,51f821a8,a53cd743,16ff4e9a,8633554,45415e35,5552403,7b25ce67,f519e44a,a5d0ef98) ,S(274a3cec,be06c748,7603516,588ccffd,f4ac3d80,a85887f8,10632cb8,4301a326,17a24be3,afbe8b45,9a72cab,5385cb6f,5d06b47a,63bf19b3,ff4989c4,85a9f40d) ,S(32b31f77,b0cb99ac,3bfc34e,7558f9d3,e82fcc6a,be2c4,8a079106,33afa9e8,447b44c,c191da90,e0eb3f71,db804472,17f422d5,b1732a8,993da80a,5d8f5bc2) ,S(78c39dcf,55561468,dc339d46,ffd09337,945285e1,66dfc29,25d8b85a,24a2752,d691ddbb,4e41ca85,eebdf63d,5c023e62,a6680931,5e1109ce,89088467,7ba3ac55) ,S(5fc75911,a4920777,c4502116,deefc1a8,d2f21f96,2b1e725f,a04d6fb3,9d34e5ff,59f36f7f,18f5885c,dff524d9,6a139749,f3fe1662,4b728d50,7a460bb3,497512f2) ,S(ca1590e9,152b2b49,a6d0fc16,4e346e19,fa62dde6,f693b64a,e38289d3,ad08fa8a,46a7bb3c,1174ed75,49e9eae1,7126455d,535ea744,936947f5,24a8ff30,8046dc8c) ,S(5c715266,5ff0bdeb,a7f6e660,bf66d5ad,743d94bc,5ba9b7f1,f3d50cdd,9d11fa1f,7da23b15,56e995c3,a21ee9dd,ccccca4e,e41684a4,f208c39,b31ffe9c,4473a03e) ,S(c7f71da3,6361c73a,55dc3877,4f2e1033,fa0c09ce,1c9557c8,c29d8684,e4177e82,8d6e47f,b5c2cecb,6b22dbf9,a04f0f95,77c6f50c,3429df92,78edb85,59b0dedf) ,S(6e91bd9f,5264a13e,37925900,433b7536,4130b4cc,e6fa716d,a0101c2b,dc58afab,5baa7455,506b5849,5d820c20,f209aa01,ee0f9434,1df5b449,9ed23a51,b4fd604f) ,S(1f00de8e,69ac7cbf,c75c789d,f3322813,244907a0,35059072,68954196,baef0d33,2892ce90,f32330ed,2800c30b,4482b67a,e65fec8,41ba6fea,b2e83703,dae040f4) ,S(c00133f5,7d8c469,421efa3a,d71d8d58,1a2f5b0b,2324de10,91d79145,7d300638,3c76b182,d3ee982,dd05ea45,59e8e31b,1aa3dc12,fdcb67a2,f86434ed,34f18895) ,S(af639e7,95e8269e,12cef756,4bbf970,cdb172e0,66cde48d,2f8e9083,c60cad49,1bd01179,ce92cd29,e414a74,cd1de487,c479daf,5673b219,8082c474,2426abb4) ,S(e6dbd27d,5447c044,18fa0a5d,8ebcb9a0,ede58538,8b73ccd5,4e979797,31f4c9a1,77f38524,f2848320,3d4c780a,d0cf8bd,a2071037,348db8ee,6b5deabe,3d242153) ,S(f51a8d23,c95b70aa,d02dd904,ec1119ea,8d1e3e1e,e405646e,4c2dfd53,336360a9,426b2c9a,1d703cf6,c748871,4959acda,ae5c6aab,51945138,73e4b1a9,c0f46c57) ,S(e12f11e7,fe437b7,f578d8fc,33ae3a60,a3e4d1ac,1ee45863,42944d50,a0f6bcf4,22d15d58,35fa89ab,563985b1,4114c957,8bfec8d6,6dc7d253,e3c6d900,4419f5d2) ,S(e758860a,8ec762d0,62f51e56,d958a14f,ac619351,9d890bb9,bf6bc7ed,e988e14c,42d9e0ef,10b84f21,fb88d780,dcb4750f,10438682,3b003b23,ec41c297,567ecd78) ,S(3c933fe9,ba21e5c,d822b90c,78a54b7a,d4799882,ef91f2c6,e423a398,20a64163,c1eaa0be,531922e2,ca5b23a5,6700b4ad,7fc16135,11f67f96,b672ddf3,669080df) ,S(4757576a,83c9066c,b6eb6b08,e91a79c0,df828e4e,3c09ce07,939134fd,ea857872,13f22fb2,62d77f15,de3e8388,d9270c45,818248e8,9d950d7b,58ee6c6,c38277a) ,S(35e63903,70085140,b19df903,9a7fff42,46570fcd,8661caa8,129d6b4,31045c7,2855f4bc,aa9d60d8,6a44f022,b3c28e84,53cfb3ad,a58691f1,b0e9cae5,e5b9e8c9) ,S(ad446e01,1f118207,3565f031,6d0a85f6,ad5330dc,6a8be4fe,82be632e,32126fa3,240382f1,decee3f5,1f92b2f8,1ac0eab2,1d8acb54,2f730d43,15c194f6,28e83e39) ,S(fbe9e5f3,eb01ac37,820af752,9c4221a6,89164ef5,d77461af,f82d6400,6a718815,f2f30cad,d85a2e0c,e393e088,44de9215,ba207384,2abf8468,47801ff6,12d088e6) ,S(1e675320,d81ff430,a0549aa2,482cc9b8,b9b585f6,32d32916,6e952f13,3b038135,ca0f1276,c9c7d995,c5baa5de,2988700c,2e2c7f1b,366d1db1,b44b4c9a,f0686aa7) ,S(176dc770,23b0e52b,a2eb8068,ad27924b,94c3f643,30e0e85f,3593917c,d6267718,d2dc6288,5df75b06,f450686f,df660950,548d4f6,85d1a701,d510f3fe,297ca8d9) ,S(3c8536c2,32a02b3a,b36feadb,ccc7c541,7ac83942,3cfc8dd,99a0ab7b,41a9c938,a684eea5,249cd12a,d24dd8f1,73022ad1,8ebc7f52,d6a3bd9d,bdc4f5ad,a25186b5) ,S(48aa73ab,c61a76b6,e54c446f,ba881198,ec6ea003,d63c54a5,605a322d,7af006fd,c28c5eee,ffb20882,2d018506,5cf3ddf3,5977fab7,40e4d4e,cdbf9935,8e403a64) ,S(74732762,abd028d,9dad2b36,38baca49,263d170d,ca7e4cb,d83a3a1b,53cc1ff1,ca11df0c,e8dfa09f,3f2ef7ce,5c023b6c,927a88fe,60ba9f3f,ddfbd69d,e536c2c6) ,S(eb71ab09,520e5915,767dc918,814fe901,a4042725,5247c02e,b8672c5b,95698522,5fad7ae0,a7e95b38,ed6563cb,2023b2a9,c81b6901,c007f1eb,8749f56e,4d48e995) ,S(2b101bf6,c7763df5,72eda74b,eb179cc6,af5e8695,965761ce,f8444371,7ef5be6b,dd16c8,4e1d1a3d,98d4629f,ef258421,f6664719,7f89a597,67fe862,3f140ce9) 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,S(2119f233,8efa4e0e,2204bbe7,84e9de01,4e1e4c43,450d5910,960ebc38,6b78b935,9f219dc3,778544c6,7a337db9,69c513a8,52acb469,34a71957,11c36913,b8e7bb93) ,S(11fc3e1b,9491be9,d7de53ca,a2558d36,c5227498,3f5c1b32,57f0fe5b,b1295bbf,1c69c74d,ecb05933,6aa6b6c0,231105ad,91b8d188,d109ced6,2198c528,844cf6f5) ,S(34b6ce6f,ea6e5143,95091bc8,67e606ad,5e64ac18,99085821,80abea3b,dfd2a908,5b6ed904,f4bdbef3,fb9e41a1,32c7a313,28e9f325,4e180694,40339642,2bccad6d) ,S(6c225dca,b45768ab,3b1c567d,97ef745c,b326fb3d,2db6ae2e,22a40c95,3610a84c,7e85d752,2180fd8c,ebf63cfa,2d843bdb,912fe042,d00ea29c,d72fd768,402a1084) ,S(5f776e5,41dd95c2,32fcc757,14b688b,cbfd2020,e7043e3,2a707144,5a8ed7d7,3b8c5c78,fc6d8354,3a09de0b,9a64d529,c116803f,6d0d62ff,2a20b369,8b273c0e) ,S(3e26d8c5,531543ef,5e37eaa6,3244faa5,d5371e48,16fd94e9,b8bbd932,891b0e23,30a09d1b,43a4a036,ee1a53bc,6c3ebfa,a5b4c70f,6d8af4b0,c70faabe,b79bb65) 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,S(bfaf95aa,eb55d378,7210033d,b352372e,6a64f2ac,a420b877,586b684d,9cd33f36,7d22bb13,bb61e76e,2a2fce3e,bbf9ec83,78c6ed2e,5f143b0f,60803cda,b0a3d8ee) ,S(78cdd360,4eaba890,da793c9e,f589cca5,faacb6a9,14a29f6a,6add7d8d,74f31421,ed7e9c15,5b801d1,16b0d60e,fb5e2287,76430c8e,faff4bfd,327a38dc,ea19a634) ,S(f2ebcfa9,50a391f,c7b97713,566a8a49,edb8944c,7cb68276,d9843c22,8d213d2e,b1c7630d,956f9f13,c53a180c,569d534f,9513d16,4f3dd900,bb3f5e78,b0fa4eaa) ,S(43cd60d,83bfcbb3,cc19943,34552eae,857593aa,e8158adf,ca850b9d,1aaf4c2b,ff64bab1,f721e6b,9e23d659,224998cd,996230c,4fccd302,47e9e110,607e8f62) ,S(41925ce0,c01a49dd,7be0c3a3,b27f13b7,2168dfb,a5ec1315,f9209709,f38ea93c,5346b95e,cb6a0ac0,1a2f49c1,9b02d9a9,a725a676,f144ac26,c48f0d8b,94f77110) ,S(fd231210,6c762d82,a851bb47,8d0ee0d8,fa1c232,7e26feee,3e6ece5b,323877e5,39763316,f5a6ece8,baf748d6,234eedc1,4bf33462,1db3e66e,7eb2fab4,f96fa162) 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,S(13f1f692,682d04b7,b7e7381b,8c5c13b1,32baac0e,b7f8c8aa,c9ffd77d,3aadd47f,572a05e4,9622ff88,9eb36852,85d1400f,43372533,38c47ce2,282aa4ae,26e99f0e) ,S(79fa13c1,4f0de8f1,ed98e7b3,3edb77f5,a2700707,e54ce522,a516634b,d2804330,a094bd88,e1969ee7,3f41e40e,60f7198,cf2484ab,5a2efaa0,96e891ee,d5987c65) ,S(df1ff6db,d2c61bf7,c273f735,a6dab3d,fb08377d,bb3dd101,9dda03db,e533130a,2fdc7ad,68c58689,92e5c969,d8d14a94,cd0061b7,5ab0e824,fd19611d,923f886e) ,S(a8223280,5f5939ad,180f8776,810cc7,2bff651b,df7972ec,51d86d2a,1acbdb34,9681590f,982e3632,b2aea9b4,40043751,e7f2ef2a,d4b125b5,2784ffb5,17c2dfba) ,S(406b0cc0,49f3bf58,6990ada1,63c73932,b3780fad,ba3fd8c4,79e6a688,484c7c44,aab0e4ef,f2508e54,79074fe0,218aee7e,8b217932,859192d3,1bb20817,df6503dd) ,S(4e7043fd,5783479c,3dcf103d,bc4d9bc8,523c81ea,dbac9460,4b73300c,f516bcc8,196287b7,3ed01bd1,e8033ead,66c92625,77c859b6,73a4c7fa,98f53d69,e82d1133) 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,S(a9ab2512,5df78835,ffbd08c0,9e07b632,81ebb3ef,3fe2fb3e,1a3e5ff6,28439b70,58ff55db,56e015aa,9aa43698,acc35df1,f2eaadb5,4e950c7e,3501a5b5,85877514) ,S(ce058f84,90813dec,c184dc83,915c6d5,53df174a,41ed6521,f2cff46c,460466eb,414d38c4,58817414,5a815a7,84f4f71a,28237741,97b37d47,c7646b2f,8af3e745) ,S(991fab65,30a2b36a,ab385c7f,31644de9,afe9253,9db603d4,737beaa9,6e406299,2a29b576,77c544bd,f156dc9d,44da01f4,5d373cfb,7ada94df,4f82af9f,e48eed57) ,S(ee6cc81f,bd034eef,cc841921,5ab4817,ddfdd2fe,a13f1e14,e91c3f2,af715d8e,b8f79ffe,48c3e965,21c7358d,ea5cbc04,df8fd847,a97bca3f,6893af3b,e386d8be) ,S(66a2d372,d6426657,5544d5cc,5141e003,16ff2dfe,813357a3,c5daccda,159c5ef2,b57d2d6b,91c6f48d,389423b9,af265e04,780000d0,598229a0,5bada3f7,4dbc8929) ,S(20a02dd9,f697de3a,15043e73,fc7f36a3,7a5798e5,acb4cac6,adf5c692,3a421da9,1e6cf100,d162361e,aa6ab61e,711e3dca,ab4ab538,2fcc6b97,33836c30,cdcf34f7) ,S(a0b8ca43,7818e81f,6be98b15,4da25331,9f92b79a,1ceda110,92e3a303,cb7bf552,4541bceb,f447d990,50663ca1,10fce2da,218508e6,48b630ba,a1abfe5a,3d543be6) ,S(51714ead,73dce488,7e15c25f,b5cba9cd,e0d5018d,db5b8ffb,9e4174eb,1cc52c63,47b794a0,82ef561e,bee272c7,d66dd201,a5c24831,99977097,73b9141f,9bdafebf) ,S(18ea2763,1fe4de07,3e7c41f6,a9921e91,7da195a4,13417a2f,ba74ac2c,d6451c59,398a0b37,fff6bba9,b33e0428,e8d7c93c,d31b3b83,2e955e6b,106aed50,d64df316) ,S(e1d58b4f,c39e1834,a61ec341,acfa985f,c3d1f0a5,9d75b0cd,e8b9057,17c5a87e,1b62ee02,15fdfdec,8fe2ab3,bb7f99e5,af82153a,dd9c7f2,cf299225,9c6b3c47) ,S(39793917,30d3c125,7dff5ba8,eb253dc3,2c19c541,11caf9a3,bbdec3e7,716c5a84,d6a1fb50,189f36d9,912cded5,c851da8c,be7b4ebd,41c2a1e3,f78aa4a7,f5f18015) ,S(49b49e4b,601b406d,381dbf88,8b02519e,1d57360b,24f2aef1,5520f17a,5b9ede88,fcf3ccca,2f2d7b3,59be7be1,9e45a3,a0a76e9c,d0e42fad,bff7e772,f969a38d) 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,S(7fdce1ec,3c57b949,44166918,b48af352,759636f7,2eafd744,642e0f7e,5078506d,d7785aef,c19a76e3,73b786ed,1e2d2ce7,53cfb979,65d3d46b,2e313a2a,d7baabd2) ,S(6f13205c,958c83f0,f170906b,d77c79ab,5f51654d,88195b04,a70d4e06,93989c57,8ac9a15b,b386e483,b268d4f1,c950da35,33deb99,55116c99,e848f13f,73b55ee0) ,S(f955a35d,833c69be,40a0665,f4dffbfb,cd405f4f,5b4247e6,e50cd4b6,3697654e,89f4fbce,22468389,a4af2407,f40eb37c,f56e80b2,7da1983e,4e2fa4f5,8bc9ee44) ,S(dbcd152d,619646a3,42a25743,1df9798d,b58b8d1,89238132,e65fb6a8,26248007,66fa717e,c1948fd3,e4425e9e,2e6830f7,e57d23e3,d0219dce,c02b4d36,32d8ba13) ,S(f1aebce8,e57b909f,ac7cfb1d,a2e7953f,99f713b2,8b35b5cc,71eea153,5e6e8ebe,8755fa14,3e77e5aa,60dc24d0,92e4f596,88b0bfd9,585fd57e,1b7f610b,e5d9d516) ,S(a202164d,941f84bf,f89ceab6,50430905,c002bc5a,91d505f5,fef6e48a,4b55187,e0cd42b,2bc268b5,1e572e97,8b9bce4d,b6d4b095,ade884c1,bee3b3ef,c2f057ff) ,S(572e1657,46fde7de,9480eccb,287f8b9a,b1344da5,8026861,e784047d,ca8ad68a,c174ade7,c066abb4,8d2461eb,405dad76,39eda86b,a0fd170,47569617,31eb5d9f) ,S(f4e2c907,fee4d753,c08b1052,b76e49e8,b67047ca,59e64dac,58acce9a,5beba31d,b243aa2d,3a92d2d8,e48b8317,ca8fe897,2b76d134,248070f8,f41bf871,2c11c42c) ,S(a6fc6aec,84455716,f5e9e436,d68809b2,26698781,f24d0463,e06963a5,fdf06dd5,dc16a615,548efd18,6ae135fd,f748d9f0,a96b7f4e,918513d5,73900aa,1818ca8d) ,S(bd806817,5fde9652,9ccd8eec,937f2cbc,c4ffb3ce,b04cc9bc,c00cde2d,5a05f026,b2791ae7,8e014328,e0fe6a0d,8b6bddc6,db048274,5152bf76,bce228b3,64a26216) ,S(f888a667,6f8c3d20,b9d5e810,ecae6b8f,2d8614b2,3a5da51e,16386dd3,5c0165ef,fb4ee20f,e429f3ef,f6f4bfe3,9c7b1ebb,57978853,de242239,42a3dadc,909a0dea) ,S(7c8d1e05,5adbaa71,ec9023a4,8d160fcd,c3182ee6,bda76fd2,3ba8877c,409ae200,8a3b820b,ec595523,d96936f4,fce83779,c489b9a4,f2c8c524,f16e1764,2f907ceb) ,S(18886ea4,ee257120,610ccd71,593baf72,6dfd9bb7,5229959e,75c14e76,26fabf43,266c6695,f57068b0,d33ad3f,7d02b7a,898a3184,39889d31,ffa98d86,e091531d) ,S(fea70f1e,38c8adbd,3339a44e,cac036b9,1242a099,506789a3,184fdcfa,6be52cba,9dff6df5,ba8c1b9,ddc58093,a36670b6,76c0e2f,d745c468,83e26ece,3b9e7915) ,S(4de30389,45aa3c90,76d99142,e79451b8,96dcbf7b,fe420c8f,b1dc4b4a,37d1365a,cee74e9e,9093de64,2401eb2e,201b3377,992ac0a2,13b0b16d,35664ed8,d287cba4) ,S(67d09dd1,eafebe79,c63b8c40,1c102982,8c2d8e6b,6b5bfda3,73988830,1a104fb2,10eb5508,92660d96,8e99049e,818f89bc,d4f03558,d9f2c984,61ffaa5b,bd360a5f) ,S(2b5d70fe,186834f8,d3b96d4d,87031cd5,325e55f4,ffa31b5a,f5ffdd77,40e6010f,646e7e53,24d2a373,78b1f54a,fb2081b4,38439890,c9f53b1f,7bda4d47,a895ed02) ,S(cb426299,8700a76c,193f7b44,6aed0ad0,5d600b23,ca24c752,527f62df,e17be248,92843e13,f3eb60c9,e5f74eb,8cce7723,bcfd0250,4c2186e6,5ace939e,5819a8b6) ,S(3ee6ab7e,75b3bc57,135ce4d0,1e6de88b,22d0b853,fd8e0d25,f9b04ded,418e4e41,69c83f98,4e52519b,931b6afc,933f5200,6ee1ab4f,680ee768,9ad55368,1b4bcc87) ,S(583774b0,a95a5143,17232df6,f17d7829,6918acc7,2a385724,e904085f,c887e7be,33bb1e66,ee8cf17,30c16073,665c353,f8f047fe,150b4424,18c736aa,807c3e7b) ,S(af32e1ef,39822787,79082b77,2a643ea3,eb334100,9a7a3fcb,a8838e0,7079dc1a,6985e28d,c660123e,73aee7e8,b1a36697,16938331,e4b4b7f8,b3a9ecb7,4e95fd4c) ,S(6edf7fdd,32667551,9b60c740,efbfc3f5,50f7249c,deabbf9c,948adc16,e034d0c4,f08c5f18,5def7da7,5fb0de81,9b092691,64534f14,bb7d96d4,bb4513d,ef46026) ,S(3b9a6645,5d268f94,6c504120,a81821e0,86257a60,b3fd9f00,72a0a4f0,1f16b42,ed583a15,aedf6c08,95f60109,6190106,3dfa4848,645b0117,e2e1bddd,2cfe7c7b) ,S(bd035b08,2b5cfdb0,d17cbdf0,7a012b0f,27b52943,82e8bae2,d683ad0a,747a1039,6494cbad,ed4ad7e8,aa135ccd,572be8ac,e94a23c3,8b62bf61,ac90f9a3,9bb2ef54) ,S(e25fbf19,fe9b180b,ae3316ef,89e0382,4dda59b1,41022ff7,a8c45b44,f15338c3,45ec47f6,58a3dd52,34241258,1852e694,7c2c8f11,9f4fbbe6,f6388363,174c7cf2) ,S(2e231dcd,8ffd7356,52ebea7,50165405,f30f595c,3871ee6c,7c072e64,ecffc9b8,c664452,db15961a,8458f3d3,ea24ade2,7610d4cb,ee51927d,29cf3164,6f59317a) ,S(7c0f29c9,3932626f,1b1ae126,316e065,fd2a4174,a66a6048,3b458660,f5338fc8,27ef533d,df6f1272,c0255d7a,587f56a9,b76e2c4f,98c98162,350233ba,75cd037f) ,S(e702d61c,ea6f9fef,fb43e014,4794fb32,7bd857e1,70b299ba,31bb6a20,7cd5bb48,c4779881,c924ee3e,7f228a71,2de07794,ee5e28af,ca63af21,12ec0eb3,1a3f79c9) ,S(f1780044,eadec1b5,bee75c11,7c1647ed,c362c5a4,35a66d8,cc2ae45f,66c852a8,5f8de9f0,f31b3977,f08f63ac,1380310d,e8b7a304,85c9f0f8,9a677572,329e1c18) ,S(7a41b37f,22ec5b18,d4952c53,326665a5,1582ccb7,1660b69f,8d00701f,1f12dd9e,8440be13,2c57259c,80cd74d,2a2f1e01,3448865e,2429c2b9,db750951,607fc443) ,S(94fff7d,8111d69e,198f4e16,57c3551a,a5ce6316,d520a779,ca4ccd0b,282db6d3,482c9270,26c0c05,578a75d3,8b1d8ed7,42541d30,3a933b90,9c3249bc,505c6fc0) ,S(d6a6d44e,8a3ffaa9,56cac76b,1b05a4a9,d3775989,2f70e560,a54c9440,17f4e9d1,48c3bb22,cd839de9,9163bbe7,83a8a057,c7b93e87,de388b6c,dc57ba57,90863e1a) ,S(cc0e25c0,8e24edab,1e5dbc47,71543b92,c47c0993,95b93d53,699204f9,50cdf80c,20c52cb3,7170cf3b,43b76ab2,cb4a6d3b,1a977c55,2431b8c8,220282bd,51fb70b) ,S(cf953f68,4cb7d1af,a125d0ea,cfb83cb5,efddb6a4,41079be3,db72573b,62f8d827,70cfe366,a45d11b1,a847a7b,8e3e50a3,b302fa50,1afc89ac,b89eddb,30909c0c) ,S(1ac22694,2b34ab06,ff16b711,2fd5fe1e,f8ce6975,143ab19f,bff99d6b,6815d5dc,a43d457e,2bd0975,4e9b7fdd,d9e16681,1bd823d2,24476615,4d9e3fa5,ab6539fc) ,S(d02bbbff,1153804a,f0f800bc,f959406c,496349fd,a412e9e9,bb9f7232,7a4d65c2,5de80de,3c7832f7,1d744f9b,9ef08b56,d41e682,1c20f2f2,876fffc1,b802a384) ,S(3ccad347,8d464ee3,42e1cc2b,2c4b299e,d8a60326,4837a040,25a8525b,4f1831a7,35ea2a4c,a59b55b6,ac79fdd,6ceb3401,47492f3e,49b5035a,f3036b26,d02691c0) ,S(eac4d554,3e69c3ce,d762e90,fff84b3d,b3a758b3,419d06b,80f7ba43,36033688,aa64fada,c54374bb,fe8449aa,ddaa1846,ee00fb6d,c9435dbf,17f6a12f,d1deacbe) ,S(3d2879b1,73d93713,3326d0c6,133be281,5df62465,d3dbb7a9,a028e0cc,63fca753,576ce64d,9b95b5e8,a9e3eecb,34cdb8d1,fd38a08c,2a6a8c9d,8f0a7296,68d6e0f0) ,S(3f58ab8d,56a9682e,25137087,ca8c766a,72358a56,99ebbce4,cf74e304,6976ca14,3c9053d1,1a2a8a8,1f30f45f,1b480dad,f6bce20a,15e6315,447405a7,b321f29d) ,S(4f5f1289,b48dcd19,41a9df0f,a8aeae42,2a4ed913,58845b97,3145ddb1,13fd12d7,b5c3e32c,c40c6577,3e286ed,a233ddf,42ac0d6a,5a3c3e86,77f8256,e0dc1428) ,S(a64a29e2,a52dc6fa,e74e70dd,da2bacd7,e4a9dcdf,f9a0bbc5,ad0392dc,93376a76,ade2f8a6,faa9b1b7,7baefe87,33ddc365,c776f2cc,b0e5730b,4ebb0166,418a9590) 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,S(b64180db,3b926481,74a0b743,1f84af72,f1118e9d,6cc1fe02,f0bfb72a,97c441f6,b394f997,83d00816,267a4f0f,8c95a05c,33cc19db,eac704d9,9e1f0c2c,4fb25fd2) ,S(2173f38c,f47377c6,d977fc08,ebb67f29,37e96fbe,e46b2115,b260f03a,216b5c56,bda02a78,3c4a684,fd88c6df,6becf56,3bd1c61a,4e79d36f,27e22fb3,212e2abf) ,S(9dd9ecd3,f3732f0d,864df0b4,8cf35e06,ea2b89a6,a8a2756a,222e266d,fc5c5214,e42ea720,2ba68242,ed9256a,57db94ad,dcf00b1a,50ded06f,a70d712e,17e921fe) ,S(705f9fed,5cebb62e,dd549526,af729092,9d398232,604d136b,2a121cf,e7af71a9,bb2cb17d,aa4472eb,12e69a4a,57a7863c,2b32c100,a1601d2c,44d2cc29,750d30a8) ,S(f1a908d1,807169bd,7fb7fcd8,cfc125e3,3fbcdaa2,8d8df1a2,17b84c2b,2cef4410,e86cc08,804c6c56,f81cfa75,9851e67a,d792bbe4,87812cc1,4e7aa468,b8911512) ,S(db0c5d79,35693c81,c752a475,6852260c,5625e434,5247cd5f,d40cdc24,e1355f57,120c5ea9,fb00d295,37721f1e,2539ebe5,d0de9bd5,354ce629,fe8c2e8d,c683daea) ,S(5e4d5935,56007e92,1b158f68,3411da86,e979d470,7b53caf5,9a2ed94b,ca423ec6,71588b00,1a0e9ed3,27862fb3,7ce6aefd,c309b5a0,928766dc,b947773e,6272d935) ,S(1a79ee08,3c46e5f8,8e97fd11,22410164,a264d106,7ecfabcd,4872af40,4fec7f28,f928dbfc,49bf7553,356289f,18a5c8fe,54f94bd4,d9406aac,c4df7a32,32349111) ,S(e693f88b,e3be0c46,cb40a2d7,f3a0a435,1c3a1812,4abdf46e,86ca3af3,6cac5468,55f0b7bd,24ab2a2b,aef2db89,d8aec5af,fb4f354d,66538efb,78f094a6,dd649cc4) ,S(6d15e8b1,f3c73c76,f73b12d4,f5e96e28,43bb6157,5d0d7e58,1bcc551a,329ca25e,f21f3ee1,84386427,32a0d05e,419f8a59,173f8cbe,6e3b765d,b74c3588,2d7f069d) ,S(48b8f127,b2614af4,95303f2c,f6593d16,20dd98e4,ff536dc4,8a5aaade,3bddb682,8ed1b9ba,ec137c62,5127e23b,55d786d6,a50d191d,6803ae99,c7ce57ec,2f546e3f) ,S(2ec32631,ee1e4510,94719f29,1a32e0a0,8c29fca4,8ff7e3d4,170a7c0f,5aeb3028,eb861d9f,e21b536e,58d0ee35,9d07d09a,491572f8,13eaac91,6105785c,697aa945) ,S(f7960ecb,3b35d4d4,5ed2c13f,b55cc944,7ab72f66,ea1857b6,776b8ca0,afafce3a,90245cf8,d40f6b40,a7140334,da02eea7,d8f7cf7f,8f87c510,cd6d9ae7,8410f08a) ,S(a94ccc3e,4b22f7e6,ef385780,d58f3aa1,139b29b8,c7dcb5af,7a247125,ba613ef2,ef7050fa,dd6afa0d,a89ba357,cbc6a66e,782471cb,8cfa4c45,e94d445d,a2845409) ,S(e48a7ff8,6d80f430,d3d6f57,6c56f026,8c42b3ed,17086399,56d62f54,f5485c38,b1695229,b4997b0b,229e3c65,c7ffb42b,e429b702,47b98231,a7bd9c5a,5e9a6255) ,S(df99488c,7d46c83a,cda5b422,b2a633d6,cccb09bb,f6488d9e,ac79e9bb,7f22d2ae,89490280,a958f45c,4501a878,5bd3c72b,aaf83a45,d91a38c3,e0477562,f345fd4b) ,S(a150c6c0,4db9f9f4,6f64368e,bba348ef,2bb4e43e,29b27770,553ef41a,ef22fd84,61dfaa74,e1525a0e,c3922ab0,20e3ed1c,e7b5397e,b4485cca,e1f64f29,19c5c201) ,S(9b7dedfa,452ec6f9,1d7aa167,bc984a28,937392ff,d856a4e1,204aa541,f3aa0edd,a37f4912,2f5168de,bca0ef6e,7c9b31ab,b4262c09,ccadbe79,10a4a844,ffd2c74a) ,S(c7d77a51,6d0cea71,b20f75c5,579a5906,ad1aa83c,f9209a23,d38ed358,28e51904,399a7c7d,9e1a3660,37b0a7a1,49b0dae9,8e5a288,cb5ece7f,56de4d8d,74a44bd6) ,S(d313a829,8e4de5b9,a166c2b0,f73d9812,fc1d1dec,b3b86e8d,8062794b,42fe73fd,6524463a,7eb26e2f,34f062c5,dbbdb4db,b8514c9c,60af6a16,fc9a8830,1f708fe4) ,S(4bbf363b,4d66c693,6469b8e,83c4f18e,2e6c2a3c,498f38b9,787607fe,97211e5f,9e42ca4b,243872c5,8c7b6406,11817743,82bb0d59,c0de2562,9f26e8c0,7d1c60c3) ,S(3be10ed,23a0ce86,d4a7ef1d,a667cf19,d471bd37,7467403e,3f84535f,861e9cf2,bb959378,cb317c0,6534748a,49bb9fa8,edfd2090,cb95cead,a7b0433,4066d885) ,S(fcd1f880,d723963c,829074ec,8d29eec4,946da198,cba5d96,b169cdb3,5dca2076,9489bce3,a31362e1,c4cec275,5fa5fc86,d3b105ae,25bed346,7c0919d3,b2a87b01) ,S(b5fb358,993d3662,b2e7114c,d8ea0681,f39f42a8,52cd217c,f0ec0271,fab317c4,89d88eb8,ee622cbc,f0dbfa82,8b04ac27,80a653c5,14df734a,791b3bbb,f3a71b43) ,S(a86bbad1,7fca460a,4740f39b,d2ccab3f,30fc137f,604e77c9,55624815,8fe274e7,c26dc259,ba969ac7,8d294742,e4962c07,1394ede1,263f5a0b,d03b7a29,30753fb) ,S(ed321f6,348cbc96,7e34bc7b,a935d129,9dd3fc94,c27d1467,88792180,1330d29a,b4078360,832b5de1,c77b44d6,cf07bdc8,fc5ac402,15002135,1be0d251,a3f7c3b5) ,S(c8179275,e4ddb936,f55e827e,de094c4a,2c425b8f,701fc979,96ed7194,1ad17dea,d99f1c5b,e241d165,eb49b0b9,266486af,8ce5e963,c52b2622,e16fe99d,d82553a7) ,S(6f08f13f,23b9b383,49274328,3f8dfcfd,eeaf82e,1d91e512,df1d0d7d,de84985b,96b6a829,f99f433a,6ee58ed0,50370ac5,665d61e,22cc7a76,a4a3fe08,d8bd602e) ,S(9443a7e3,410f9d4f,ef9f8b60,9eac3e5f,e6ab5d6c,a11855e4,b35c7e67,9f8f9d5a,d8c507b5,78188c3f,31bc93e6,d07abc22,ac9b2add,5a11db53,8fa0f936,3beded57) ,S(432ea8ca,3ed53681,ad3afcfa,570056ed,d38c8848,de293d2,e37703f5,133c502b,9e19228b,70b52bb0,8e66a49,826c6a61,965dddc,64270118,faa3389b,6bedff71) ,S(1d17589a,42f82fd8,c5a584a3,d3c7fed8,5e22ffea,e2b732c1,30f903fe,1982403b,9f7bcfb4,8f18d208,26564ed0,245f0c6b,511e965f,be5e0e94,54e0f552,78c39ceb) ,S(743399b5,cd84846f,65e778ea,790412ce,1ab8c6ff,ff7c098b,55436a1f,e18e6b2d,dc6cc81a,82801be4,e6566d3f,c01b6fd1,e84ff49c,e5ccf145,fb1f49b2,d8b784bc) ,S(e4378558,3b2848c1,62e3e80e,3b5f9242,5330d232,e05f871f,a279a0da,7910b2a7,c39b4171,aa4978e4,7d3f99f,8179a189,d5e2421b,d076d1f0,80cdacf0,55624b68) ,S(eef768a3,1b1639a8,f1755ac7,d00a6463,8f8a99ce,f5f42a10,664026b3,6718d63e,2a9005f4,cbf4e686,1af0043a,fe97b065,878efcb8,8be29ef5,ee648473,1e24a991) ,S(15db4687,2504612c,f40dce1b,d601d848,fc2afa9f,b2de929a,1800caa1,bfc91fe9,a8b6e64e,7d508d9a,504678a9,d90b82ca,1e72360b,95a2f515,f17710cc,4e7eded8) ,S(ad45facf,2529a84b,9d28d2a0,456a1fd9,d2b3303e,fc78e2a0,c7757bad,d4a4191,1a78e571,473f3035,16ef5867,8f77d5ad,bf8d8109,60f9925a,a6b4a88d,3654f069) ,S(41a03744,6e027b4c,eb775050,a892bac2,1c19b66d,5fa4bd89,58c949b5,b9151824,ed7c44dd,fa96d38f,a721cb2e,60e07a84,27c53acd,6435ce74,bb45437d,95140317) ,S(2020b869,58f4c7ff,2cf64589,f1043d,5a70d5d6,dac0740,56011f1d,27217ae0,111959e2,2757f431,a1994617,124eb1c6,b37f5961,29d52aa0,490b94f7,e1c4e9e0) ,S(2f99a946,859f74a9,50f3bf27,d85a169e,99c5f755,71000180,283383a9,eabd4ba1,3e622182,d3caeaa2,47a4ed24,6e608592,36ecba9d,4e8d79fa,12854f74,df89fc53) ,S(ddcf3989,57f65390,167688c,2e227f29,e7c5675,d4a83a3c,177ebdd1,9e369baa,a700c63f,3fa6833a,239a3cee,a90dd021,c3c3428c,f2b11b87,3da1dc01,2f4b2431) ,S(9863a7b8,4252360,19e2fa9e,9319c5b,92df1eaa,c0b7917b,73bd1042,191ace4f,49a499a9,281dab21,4bf09f8c,724a30ea,3a1fa7ae,4f1b2b6a,3bf63562,e03b69e6) ,S(6c5465f9,ea2c5917,34f3734a,64b8e92e,19cb4def,3c6d5d2e,467a8f58,dd733886,57e22bb,179df35d,15aa2616,a319ab3f,768f655f,a1c07c8d,3dafc443,1e0e733c) ,S(ab375513,360b3beb,d0ca387,fb0a0690,25acb654,fe703a53,d979f14,50f3fcdd,3e9c1149,309a2de5,9b7842f4,3c37a6ed,57f0f776,503ee7c5,46445c2f,6c41be4a) ,S(6acbe3ea,4a72eeb0,b23aee37,905b22d0,ff0878a9,e9143111,4821207a,4c2603d2,1ecefcbe,9f934d96,a163dad7,6c9e6806,ac2ca23c,e495a533,aecb19d,df0d32b9) ,S(7955d144,58fd0c42,5e4ac9f9,c766e253,b4ddd105,7f1c8c3,653f95cf,3a955d89,8fa9c5f7,304387f0,94a89225,53a20287,40c6723b,d25245,84735024,9650aaca) ,S(b5972d0c,90433f,702b25a2,27bd3da2,d488ebbf,e5782132,28c20cd8,35ace377,235470bf,7fbc3de5,279ef70e,d174b2fc,e3e78f84,5c0bf212,cf3d64cb,42b008fa) ,S(a266a810,33a5fa68,a204f3bc,53cc79f2,cc500d7e,4495f8e4,d9cb48bd,4bcf886,31a8b1a1,958d15b7,664390e6,a46f3e37,d52b7824,5b0b91ec,b568b7bd,f55949f8) ,S(1c6412ec,21191b63,5bbbf47e,1e9f7c21,ae7f4f3f,7de0f123,451e421d,44b9cc15,833f8a2c,1111c4f3,f5973851,d0256309,6e7fec1b,22ff969d,82a62284,c42c685a) ,S(ee3532ab,17575b57,9c19ccbe,fee04ff3,8172677c,5e625f68,a7462107,3e0b7fda,f12e10c8,b2fd987b,83dff04d,cc48ee6b,4b704b4,92b2cf53,a9af4510,6e7e8718) ,S(5ed10fbe,4867937,2ed2765a,f7f5b4bd,52ef9a4b,96515e,37944d9f,ee1a3838,8c4eb9b4,9fbe3924,ed8ac641,25dce66,a4bffd7b,5fbc68af,2a8c8633,b4080573) ,S(fe348a21,f04c85ed,69fe7345,f73420e1,b8f6b859,7082152a,15a1d535,d01378d2,d595d446,c9f5abf4,5ceabd10,3e38e423,5069473d,7d9f9911,7fa9cfd2,81f2b7b) ,S(7140369,b7b64ba0,861e1c0,b5ba3973,b573679c,c091623d,bda88745,fb2436e9,f0770350,f9799607,28c3bc21,30c6672e,40dfa362,72c50ad,1f376a54,83a12b2d) ,S(6d14c4e4,8e981e3a,e7ec6b88,b1230096,a7465db,a8381bd4,aa82157,99dad15d,25e4d2aa,a5f2d12a,a4e635f6,db58b2d5,f9c6de8f,b5bea99a,50e5b050,e7e0f841) ,S(7931b9c6,a6837d7e,3620558e,55504e88,4dffe071,5bb628d,aeadb0af,1a4383da,586caa73,320925c6,ddd12128,bf3bd38d,96b7a904,8422c2ff,9d5cfede,fbe80c0b) ,S(149e9d6a,35b83d43,5d0e1f32,a1518b88,88dca145,27aabd95,b0ecd0bd,e5cec834,45807aa0,fd84cc65,e91d49b3,8d012fb4,f87b11cc,1906e1f,cbc74c5a,ce5606f5) ,S(656b276e,b4b351a8,222f2b59,d7949010,1bf6e696,c284bff7,b809bd27,d297394,8746f309,5f8643a2,928ebfa9,a0e35893,905eb6d3,faa8e5d9,b6473281,7b763291) ,S(60f399e3,68086989,ee62370f,f7852e1f,3656a720,539880a6,9884b60a,f1eb02e,55dca05a,8347be14,85251676,d20b779f,9e5976fe,4def267d,4f1b2b6f,d444ad59) ,S(4dbda303,a67a41c,a46f417,54f9bdc1,34a305a,9018ce0d,4cadbe41,886eaa13,e062cc86,fec33458,d65f9fe6,4433b745,909a3b95,d23d7970,c22585b8,3fa48fc4) ,S(816ae1ca,4d64cd9,5a7c10c8,fd819c6b,f8c8b1c4,f495b111,d07f2a00,dd0363d1,c09f6bff,c331d6fd,56ea5520,8e9d13bb,b12187f2,d49366b,2dfd1c18,66526009) ,S(45839f9c,983fe0a7,c3b2b8fa,e5e288ad,87202944,c16d60a0,f18daf,8081b52b,f9368e07,4de74eb4,81f7beb,30835af9,aff40c6b,cda104db,2a785a6a,65dd8649) ,S(50ae4a48,3a49203b,1e04c482,ec2454f2,44b7157d,b23bcd50,63c5b6e8,d4223465,e1b8cfd7,e7bd2e1f,65f2031e,c583bda5,a619028,5c364658,36dba37e,7d5f3008) ,S(df77b231,60395089,19edde15,b21ace77,c5d8bb4b,ed26f9db,a694195f,616b72d6,8a4b75b8,9ecebfbc,b88cff82,2673665c,c99e270c,b33f3037,17dc9500,8b4344a4) ,S(ec6c0e19,978e2f18,b74419d6,70274075,6d2d238d,63b2d345,437b0b8e,f233277d,f90dab9a,2dfc4cc,62571dc1,35bfe4c6,96bd3968,173ced8a,4a363f0b,2636e553) ,S(2874416f,90e7fce6,a6d4eacb,1a722218,5af2a885,4852be4b,a4619011,617b3329,1f323675,f6ced648,8ba4c9af,7912ad7f,b8628e49,5b4da82d,448dd265,eaeb4466) ,S(872367ec,586d3a80,f8c87f3e,83b6dd3e,529de5cb,897c9d2b,e7dacf3f,70ff4247,e5bb60e0,fae0843b,788768b5,e427e009,7dc571c9,e4b62eec,eef68512,a6a3ac05) ,S(c10f2004,baffd30,ae430ce9,40c4af34,4339a0b2,13bf1f48,91b8da3e,424713cc,37be9055,f0c39b36,c546d456,b3f82edf,bf6dbf79,6343ee59,c3537fbd,8631c7ee) ,S(14e12ee1,91c83005,6bdf0f15,3353e80,733b8bb3,b93bc59d,a356dd94,70d847c5,e9707b8e,e00c1781,12b32ba7,c66d7245,d487f032,18d20da,b1550e3a,9befcfb2) ,S(dac3ba1e,2583379d,d2cdd89f,6ad053e4,3687eab4,ae804305,7b57823c,489fdf36,45e3da4d,88211519,55c20ab1,c2d1ec4e,d13a6942,fd37bfa4,7614745c,6fe2c041) ,S(d9bfc67a,5c086ae,e879fad0,b03a5a2c,a2507dbb,fdd2cb09,2644dcfe,bf800bf4,e015dd4b,5a39f5bd,1536c8b1,e93490f6,e5bb4e8e,b23e6ca4,2fc14634,2be6730) ,S(de6f3452,2f04ca0f,170d7e58,1d965982,8a9a981c,12f6cb34,761873,7996c61e,1ec16f3b,28d74fa9,43b9c251,f34e15f1,2fc6d814,ff024e3b,826054ee,f72a0cc7) ,S(432ab355,338e17ae,884a15ef,2365283e,b35c873a,4fa8cd93,f54bf828,a0e30eaf,f56066a1,a130dbf,8a3e076,720c10a5,caa9af0a,7d86ab9e,8703dcff,95447807) ,S(3d2e3507,cfa127c3,a350f546,d95431d4,8d96990d,b5beaafa,35a408d6,7f7c4d99,da60885f,4711c373,145655ca,b0f8a235,7f4a0508,2bbd2ac5,1b255593,a35f74f2) ,S(7f3f431c,b96dd4be,37c29d0a,55f3b71b,f781c7c6,191983f,4576e518,24ba87ef,f4df4345,7649d24c,2b8259f6,f7177b96,cfdb08c2,4e9161c1,695c8027,60b8bfec) ,S(4270bf59,f2c87000,44b6cdd8,b558e6ae,6f7b67d5,f128d716,3d604a7f,2f687143,358cef,2e8ff919,6865da0a,15a25524,6c4a180d,ed25174e,d08eabd,4da99315) ,S(c663722b,9930fc9c,4113af50,d51c6539,b7931cab,ebe2ebd,46f95b8c,7f603852,3443e7b3,2cdf23d8,eb532a31,3ca4b32,b94768c,78f8f13f,719708de,925ecfab) ,S(b0014864,e396ff02,cebd7b65,c66e57f9,168e8f3,95ae614f,21f8f162,c86c4e14,3f6c99d7,e2ec94de,ee65007d,ab501230,4a80b69e,a0e0672c,b7dbe4ba,182eb876) ,S(64c9cd93,98fe9da3,5d3329f0,ccb82e43,c2d735f4,d2467b2e,1250c410,da84f41a,d24b50ab,71bf6033,d1206fc6,dcedf049,c223ef78,ff50905e,c8d95115,564372e9) ,S(ffe0841d,51e05862,4f759706,b27db960,ecccfad4,cf326736,ab4fd9db,cd29b766,6bd1f1c9,f6956c10,4fec1595,24d8064f,eb5d8391,30b34a01,77c07491,79cf2562) ,S(d1dd0c0,c053c597,bad38d63,c40d1e7,4b451861,cf0f20fa,47fd3f9b,77ca7432,34aa97fd,b59495f0,3e7b5628,daaaf66b,5c9dc5ad,de929032,80ba23bd,6c55976f) ,S(87a436e8,c76bd7f7,a3e49cd3,af996f1d,9153f704,1b185d8d,f99eca45,ae8e5779,8d2cf3f9,12553844,ff905d5b,2a1fc36c,369ea4ff,6a89a027,b6dbe797,f11006f3) ,S(a54500a7,4899c440,384f707d,a8fd62ec,1801070d,cd5396e4,b59e9ecb,df27c379,e216444a,6d26bb06,5f5b5e5,72c927f8,5315df3f,11da2cae,2f334572,33cb2668) ,S(937ea4f7,99a319f4,fa5aea85,b48d6323,28417b72,8690a9c,88fbd51a,57d8187b,2931a7fc,9eb4aec8,b7dce4af,d14438ac,fce77bda,a7d3e7bb,b24c8554,cfdc9d9d) ,S(50793c76,bb914aa3,204dbc96,cb04ff26,c7060863,8d497f07,a1eb05d9,b7fa6f36,afaafc78,b5e30762,b68940df,41de9ef3,d963b603,6bb1ffbd,eb13fd67,4bdab21) ,S(8b600630,fadae564,dcd1c570,9bfe1ad5,f8da5282,61d55bf1,3a29766f,6d8bb5a,fbf1b64a,3bd0439a,ec45a7c3,859374c1,7885389b,9c201f4d,c1142120,6b2916c0) 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,S(2feb76eb,ff5d47e9,7289c38d,7d1535ff,74bd3b57,264c5844,9edfd36e,6e81ca1b,45bd4e4a,7ba3a823,dfae18cd,1f9cabc7,bb462e74,7899c899,378c33bb,89f93b74) ,S(14d0d90,faef5a77,f5372ab6,2e4f5efd,3eef1b39,498653c0,6372fe0b,b0682573,517f169a,80c2b930,4f530f51,d7196831,601a4f97,72ba1312,36ba92f6,36081453) ,S(7306a7a5,728f91c3,384bd9ad,b10b39b2,ad094137,46d2e476,fd522abf,ff313321,215e22ab,a5b9e87b,35bbd4e4,f492f1b1,574c85ed,25b86a85,a8e17b81,b7a915a2) ,S(85d8454f,870cdb8c,b32873a0,698fad20,fd24067a,737e9719,76d4d362,6a55aaba,36d63c0a,36eb9e8e,522a0715,cb9c833d,539fe7ee,111af3bb,951434b1,3117e4a2) ,S(c68f6782,993067aa,259b21cb,9e19122a,2f7da28,96d8cdff,c1f0a0e4,b34384c3,74e6e96a,331c3387,7ea484fb,995d6a3,8dcd493,6b2994ff,b7dc3681,3079e94a) ,S(81448111,5dbe5550,846d5c9c,3351c89c,e29cd850,6870a17f,e18e3184,4214dd3,75dd78b3,d4cdc29c,697740e9,2478689d,540ea33e,5edd6785,210abcb1,670d19a8) 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,S(344663ef,8b8b52c9,1aa548e9,8b7e1c48,933cbfa3,59644318,5ea973ae,9264121e,73d099c8,9dfe8eec,b957e624,bea5673,6fe3885c,e2f72b06,dfeae760,514d9efd) ,S(37ff484d,dbd22a98,333038d4,7949b4f3,f411d3d5,7ca319e3,5c788bbd,a0de6648,55a5394b,51618d81,d2fb1455,4ec1f5c3,a45cf086,83980bfb,a9aae6a9,20547c67) ,S(cf3bcddb,ad5066b,909339d1,4cc6d3d8,d2881f70,d6f12e1,4d795b06,17556ca5,e12686bc,99e20f20,6220e402,32760224,b61b90f7,8b7c0b1,3c197a47,11678a6f) ,S(961d02e7,db8fd1ac,a38f9110,13d74a5b,d35e47a1,49818d41,49f02edf,5da73402,9462eaac,d698677c,16515ca3,bff217e9,765dc8ad,fe2fa82a,1db05158,71fed240) ,S(43e62f90,574a8e65,25d22ca6,74814ac,3648b724,45a535c,5e1af97e,b46ec3ba,6def0a56,17c1cf17,9369e20e,d18d0503,e141dc85,9edc73a3,18f6a35b,3d939734) ,S(9e682b79,9d79018c,352113cf,98de93b2,457e4b4,a962d160,33b80052,57dfdbb7,9db9cb16,bfe96343,89c468a0,6405d2c9,b2983354,ee9a81e9,3f23ec5d,5049041b) 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,S(ad33e77a,3316eb8e,1a764849,13915e81,edb69518,8ce7507,2e2b6088,4cef8672,fa0161e2,4bc88bd9,da5157fd,7950c75d,6c4f4f89,f158f13f,16ca5e4c,af7ccd90) ,S(444a81ef,7620afe7,91d96ee9,b1c34485,cdb51e1f,6022dba0,69ededb3,d9d8c2bc,a88017d9,a49d4ebc,2ee811c7,fbfcd9ba,bd268329,1efafb52,e641af11,9751e2fd) ,S(5b1e07a3,9530f8b6,60787e9d,26503a2f,77af3ad1,24ac8aa5,1d10b663,ceaa5c51,fcf4c0d3,8d55e0fb,2731e59b,686a806a,e87cb510,7bbd013b,4500c470,f77810b9) ,S(3e8c17,e986a86,57b4c403,3317e67d,b1d42e7d,9625e844,ba533ed1,73174309,deebe49f,f4f5a35d,ea0f396,63c7ee0e,9db702f5,c296fe5e,696f5521,94cd6caa) ,S(a1096eee,5e9bcb19,9d24c078,b46b528b,6432af90,7f1d57e5,746e83d8,4d112c1,bd13e4fe,699436cd,656b3019,acd54f3c,97eace0f,e1e92fc1,3f08a76d,d2e7c6d4) ,S(54758579,4218de75,db40a6d8,99a75ee8,36861093,4ded0938,98c071b7,6665f2f0,3bd55642,13e1c689,70cdcd94,fddaa656,6bcde4bf,29c761b5,c6f613f6,19174548) 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,S(5b7c4750,542df0c4,c4606db4,6861925a,da7423a5,66d6c108,77838f65,5f297695,42811366,1ae1889f,d6ccb1a2,4cd9a6a5,de04db2d,5e805079,5f922b9e,791f784d) ,S(af1a5fe6,40cb2ee,d36982dd,1e7882fe,bd5da168,8005838c,b379b986,bc012042,71570549,305fa634,a63d12ed,1fcfc8a2,5768778e,863d4778,b7e41215,ad3e6224) ,S(727443a2,46787e70,f83cd1be,1189c4cb,e1e8b18b,1d57746a,9a319676,9366b1d2,86357826,9bba3e89,a12565cc,1770e5b4,4df56ac0,d202fdea,d68928d0,6d16d540) ,S(967979,db34e62a,149e6835,213991f7,ae2c9a2b,abf3d255,6c5e198a,12640b8d,99dc1d4f,52445651,3cee44ac,3bf3d1ed,8547b827,251b3b01,4d4c07c1,fd9edcc4) ,S(794009db,8f3491e,27ef9d73,905b06b2,be56937d,be57b8b1,59dfb883,af203601,5a6ad64d,7ee5e1cd,15a6a087,289d86b4,5db60d24,243917e7,50eca61e,2ada40b6) ,S(87cbda39,6f90b090,dba9470b,1fb0dd1f,d2f4212f,50791511,cf6297e,a9851d10,9ca095f3,a2a4f997,501fb4c9,c5585dc7,fb8f7952,e11cd3e7,73a92005,a41b63f0) ,S(9ed57b03,475d1752,58c20772,1be7e12,cd1f3ada,5b95fa8,4b245b01,b910acb0,d58c9054,43bd81af,85c58a7b,d0cb3e8b,25310644,8e1ef50d,324eea36,a3bbd5eb) ,S(ef8d0a22,92ca4498,2dac77e3,86113363,35fd9521,fd266be7,d5d354e6,28b0402,e55c4b4a,556881da,a4a23e5b,677c1a9a,f2f547d2,e2b4037f,f9758a74,3cb58b6b) ,S(6dba21f5,a274f29d,502d369f,4fa4ed08,2299f6e1,b12f5c75,abd01597,d127e3d9,7685f72f,a0ce41e,8c4302de,3e6e9c81,c951f69d,d2df0f3c,930da77a,51a39d94) ,S(8cdc3ebf,857ac235,7dc1b0f4,26ed2a52,7841969b,7fb332aa,6ba44693,c8399a3d,234dd3c1,915ac714,6cd8724,9b68a19b,df250dab,2748abec,a5876fa4,b7f910ca) ,S(a00829c8,caa665b4,7e3391b6,f4706898,a9c790fa,29344de1,e88fd882,b5eca2da,b7c8fcc7,1e834cce,5884b129,98318254,23486297,6068eaa8,184b5316,fd424110) ,S(5872f762,446cbeb1,4a12e54a,1d4f22d6,a4ed5b2e,eff7c5f5,640801dd,2149ce6a,8aacd3e8,862757fa,1a70c29e,24364ef4,4c37d5d8,bbacde2a,c75a0c1c,28ee198f) ,S(b70ed5c0,5dba7150,f22677d2,e5b532cf,53e7ceac,919d3b2f,ec4cc6b9,2fd34f2,7e43f528,cc74171c,a2fcee0b,18d8fcb,76c3d69b,8560831,26bd4482,a4d28cf8) ,S(4beaa213,3c6161d0,c7da6d7c,8eb09cba,2e8ca505,a790a7d3,9d0c16b,8053bb52,da4c083c,9cbdda2e,c6626d8f,e4b2ee13,703496c,c298bffa,db1acdca,99d4f6d5) ,S(a8d31ec6,53ce1834,a78de363,c5f9abd1,8594b34,4d34f5fc,8a10e81f,5804831,b4d6a9cd,7cbbe370,9edb5601,cb7c8ba4,8c462c18,594a4bce,64f4c286,dac5cff9) #endif #if WINDOW_G > 14 ,S(a8f11586,f3df4945,a753c485,ee0fd4d,e410771d,bddc1b26,c9ff10e0,77b915b7,a4ad6f16,dbd741bc,71b2dfd2,dd2d340,3816bf73,4e73cc10,abcfa6bb,d0f161a4) ,S(13e697c3,812d4772,254082da,372892d4,e1a66e1a,eb16bbd4,f7a0d531,c979cb2,87fa7baa,f6def12d,31e42c14,f672c0d6,a9d0e2e1,ceee2546,d65bd01,c18df57f) ,S(3cae4590,821a9697,a5963269,b44f0222,98f60021,b6048b3f,49c6fd4d,8650c7a,e03f8745,60418449,ad97f28,41664745,349329d,268c1c43,86e25147,6e44b234) ,S(6f42f6b1,cb6bbe13,cf081480,766cbb36,9d2e63e,e691722e,ac81621c,66e0fccd,e5d8f8eb,67702ed9,e33c7b71,e3cd7b25,cc9cd315,314815b0,b67e8622,fd35f022) ,S(43d24bc8,469cfdb7,51ca7d82,98727059,6fac14e2,11d37041,370f3bec,90e411eb,2129d618,fb1f7030,9715b2ee,d8e70aad,8b172b74,425cd747,3a3fe40,d7c50dea) ,S(259170e1,d48b6f36,6a281592,3474f0de,434f4ccc,e45126e4,a15c503e,c1f8b97c,9ec06188,dc194bc2,be131217,bb862943,aa9cf36b,7703c45f,b1ffd282,c3c12549) ,S(18d547f0,426139b8,7837d1c1,ca0f5f06,883581b2,c001e8e7,2565c9fa,80fa2719,26d9dc3,e1145ccd,23ae36e0,5c133f6a,5ebaa9fd,bb954792,3e762a8a,9fb60260) ,S(23b5936b,f2dc961f,2fc93814,4c96232d,dceb477a,753253cf,1bf05713,1b9e58be,9b678070,1bd976e8,8d66e740,2c00bec8,e4fbdaf4,976289a4,4391b28d,45519b07) ,S(46de46fc,209df62,6185387,938724fb,702c3239,fcf29113,2807894d,148774f6,cdc2ab0b,5d37a348,1b44de55,d9c50ce5,4322f8be,6f284ed1,ee49f04b,65f4f2d8) ,S(d3b78208,f5876faa,c4d3c970,3a87a586,e897c11f,dca9a7cb,6573c814,9b5d5da9,112ecaec,9f4451ae,23485579,9cfee804,ee053df7,8e65713a,cd43d953,471863e1) ,S(52d51f46,ac86afc,391e6a1d,8ab1d862,2492ae18,b3e86f13,5e42fed9,4cf3735a,cea47627,e7eefa90,7b8bfd12,f3212ea0,bfaf9e00,f407bb4,8a86039,d4815215) ,S(46451d04,48f3f959,e133723e,b9138a73,b3877adf,f294ff15,6303a845,65a4c39a,fd1c4a00,bbd9aa06,afb14790,5c0530e1,d6c3b5da,c9001b9f,8ec76df3,c7bf3c76) ,S(a12f5e51,16c58aae,90d8532a,9182d54,f539014e,e2d8357e,5ac7854,26fc78db,3db94e9b,f37ced91,7c9f466d,2a6db2bb,21725e9f,f4dc1482,3e6e384a,265e0cad) ,S(98999fcc,38fe6b71,97ebfd61,fe8942dd,be944f98,6f139c4b,7bd6bd3,28ac250c,48adfd3e,c348281d,c23335bb,8702cf8,acbdfc84,9ee34a3a,14bf36ca,b7dd0ae8) ,S(8ac22420,f9b9aa05,705b31f,bdb57d05,218ad72,ce09b489,4d0b515b,4e5940a8,37a7e2ca,442b2446,686f91da,db6975b,6f63454,e3a96df3,de8c62a4,364d30b6) ,S(cd0804d7,b1aea00c,13a94a33,f75f3736,f5759080,96a2d418,c5b54c72,de31d619,c7f68576,10df1c38,6e677bb,dd6dc121,b3d9e9ca,e54d22bc,a5ce1184,a3dc755e) ,S(b6c4bde6,2f8fe3d7,3c32e641,573098c1,c559e847,e40f60c3,49d40050,49b0411e,62c691f1,68510458,3e5191b3,758d7e3a,b2cfa31e,7a00d7b,97e39f88,786f9a9) ,S(c20990dc,70134917,42cec766,8b725c26,d918cb46,6cbf7ebe,7b1f37bd,63d5df0a,6f1e71ce,e28b22e1,9c6f180a,4d7a48be,9fc696f4,cfd418d,134c1196,6e285d1f) ,S(ebf16672,45ac7f7,385b5356,dbf977a9,3602a11,40ada114,7face805,dd93f9fb,24b15faf,3b3ac9f9,833882db,b81a976,9a37e6ad,1a4228c9,a4f7d0aa,fcca3400) ,S(1c620657,63199ded,804deefc,c33822f9,cf3d4c1d,72f2022f,37714eb3,83367621,600221e1,48f74ad4,dae118d1,b6dca782,e00117d4,92881c23,b5a7cb79,86cad767) ,S(40b300d0,7520348,38bec63e,f155b527,286db841,754702d1,d512c183,345d492d,29305ffb,31b1feba,abe027b5,f432679c,e265a57a,3960b8b5,a66e6de9,5a10fee6) ,S(5768ffa5,c8b56772,1e10c2ea,421afef5,dfd84120,a8d40e13,751a895a,fccc6c2d,52ee5ce2,e60ec485,7ee62e81,fb2eb118,4d2a6ecf,d8ab7e09,dd728d16,5e508d30) ,S(d906e71a,b6bc6697,858c66d6,82aa85af,e8d80ced,5f470ac0,8158b5aa,4cabf2b7,c75ace8c,74552756,8cad89e2,201dd954,bc6f4ae6,3a671d2c,9bed78f6,40b7e70c) ,S(f71937e,f4553a81,a3f155d2,2f81a5b6,e080c0ac,bd8f5c5a,fd437960,6a63460d,d6e4e57d,422df901,e6292a28,c83c3bf4,136b5700,f6da0351,33099feb,f1228b19) ,S(3c498699,da858f1b,364c464f,b4317b76,5d085393,1c187888,83072cfb,39ee337c,cf3033a8,9749a0f4,fd4ad867,67b919a1,c946dc67,cc46524b,af5c0015,833daa0c) ,S(c416570e,cbc5576f,97090660,438dc3ec,be269c42,6e36fc44,45d53b0e,b2c5d54d,cf6380d8,76e20ce9,5cc181ac,4fdd42c4,b91d7132,d1b1c19c,4cc0db01,4ed782e) ,S(8f97b2bd,344fcf8,62846992,e826f5b6,7fe7d103,28f34231,8a9f7de9,20d71110,e296632,fe41f8cd,b3da3ca,e1c356a4,2424c649,11dcdd58,c21aa1f8,cee07ec0) ,S(6283f371,8e67e917,5b8c1bf,28e66bd8,470dc4a0,1a720a8f,cf1df325,fcb0e10f,5e80225c,87c0d6fe,3432db79,e8cf4365,8640ad4f,21efd2a4,333eb6ae,a46bd342) ,S(9e29c616,ba66db06,bb71e56a,2a049727,e07b83ff,cdbff6ab,898a73a2,f2f9d58d,b5997133,bdfa29e4,431494f2,8444f186,7c4fcc1a,516ca195,c8eb6fe3,f5693dfe) ,S(7a0db51d,56a2b33b,8ab33329,a1d41454,a30e34fc,3db33a31,45c1cb07,923ca061,334164ab,64cdd8fe,9a106f2d,156a16c1,5da4f07,fbd7f1ad,e9d1fd7a,c8630fc9) ,S(5994233c,13ba74ea,19c1c65a,c3653a6c,cef79c4b,bbb827af,e736545e,33ac05bc,2175bea7,3090437c,9af6f994,b33023b0,5fdb278d,c0c59063,eb3b805e,a6b6bf6e) ,S(11e13de,2371f715,4d15373d,d52c504e,50811146,10ebeaa3,f47a3335,ee4e17de,fa961827,b81e71fd,60696d97,17820d67,ec86e8b8,74d3d4bb,f50df644,61f738b2) ,S(787099cb,c8896328,dad08bca,4e682e4,90461574,29aaf740,23795a1a,47f25ccc,1ea5755,bd653ed,ee7ee8d0,b3e6214,df2e31d7,731a1c9e,47a95f46,8c3c8ac5) ,S(c644c88a,fa42bae1,27bec7d9,528cd695,7bf7d906,942baa4e,14ac960f,46469cd,9d7b39cd,22007b04,f61c5905,3a3b7614,81dd45a1,532d395c,baf8ffff,377f2644) ,S(79d1abe5,cdc8b0c4,9508a87d,46163d1f,ada43640,ca1a5e89,d2f1c07,8c58820a,465cdc,983f1be8,948b850e,a9a4d9bd,f3898781,65d5a186,1c94d3d0,3fb9289) ,S(e8d4fa8e,db2a1612,d7b6fd8c,d6aa2f1e,a8f1ba1,32572d6e,dd0826ce,bede0e55,92aa3d43,e944d032,afa03d23,dcdb4604,56cb0363,1fe2f8fc,404dd9f3,f832f065) ,S(6f99e75e,b09110e7,3d5e304f,bf569037,577554e,51861356,40c2c69f,4a92e88e,63b5bf05,c554aa30,261a09e3,b292b9ce,8f1bcbf0,ad91c35,aed04f31,567757bd) ,S(cb089170,d912f8ae,e59f21f8,8860c0d5,182b5252,3b2cdf35,b9795d1f,20c37815,4e8c5b3b,6d79cab9,9f2570de,8c58c34e,6b6f5e19,b285bc4,6988ac86,20e645b5) ,S(5c248793,51e487d3,af1b6d16,b25367fd,9d2b7185,9923c565,5d7567d8,ffd621f0,5806bb36,ac3cca86,2624401c,27c54e90,c76fc747,7e83e6f6,ac89f22,35c84211) ,S(f1d10f0a,2ce54b90,ee71ccdd,eb6dc4d4,c2cab0c9,5cd35bea,5f20d3b3,51d15896,7bdb4d3e,cc613f8a,8fb84d25,541970e0,6c7385e3,c04022d5,82e2efb8,4998eead) ,S(536a5966,b594b460,bd27b4f3,aea6b555,95940f06,311970a0,36dc0fa2,3a274519,c44b0b54,cdb4eb87,b5d70d9f,bfd4a601,5c34182a,31a882c9,880878,7910b3d4) ,S(7f8165ce,ed27a393,41d542e,ba9ae875,554265f6,1c1c56c6,cc0bbd66,2ff88686,6993724,26c18b1b,dd1207e2,f3bcc0b8,673f481a,e7638d5d,45134835,9b4e39d6) ,S(12214607,c610d012,83b9265b,c59d7458,4e0a79f6,8a4e8535,a72809fe,11a6830a,5d26e498,9e3edaf6,27cc4bb7,105ba8de,3344e506,d9bc9a33,8f1e3219,e473e609) ,S(9ad7f097,1d1c326b,8ac468ef,706f53a1,9e8fff25,8e599f0e,72acaa15,b21d58b7,2e7c0921,2199c7cb,da8d3645,a5bd7831,4234849c,41a238c2,a3dd7fad,fdb8a880) ,S(355f75a4,9df69d8e,4ccad41b,1fb0445f,619ba9aa,34697a5e,24ec8e92,f5b41068,9ca83421,4622ad8a,90a09469,d155bbec,717295ec,c071894c,6c91a7b6,e1345f24) ,S(bcde8058,8336a996,fa6af5bb,5ebf7441,ed3bda73,4802ab5d,5c0eac31,8017c706,49e40844,78cf1912,ddc91907,26411814,a782a3c1,452117c9,993d9e8b,4f247563) ,S(372cbbc3,3417320e,21ac4ba5,f286a9ed,273b6425,e8ed22b,d0c352e4,f0a97270,6e05363c,bbbd6b11,8f2842d1,243dd629,247e90d8,4e7c9d02,c3677f93,d1d01bca) ,S(a1122e8d,82e97ff6,ce9fd024,cd4ff32c,76aa0aac,c1c2849d,887240a7,a368e064,ef97035e,1df99943,1139cb88,e03bdcf0,8b3a5c86,d4b42d13,9b3acb12,e4e7df3d) ,S(e0101d71,1d0c7b60,8093997c,229bbbed,63b05224,53c0079a,518826f9,2bfc9d5c,a0acb9e9,c3d3d384,7f2d38bf,29da71c9,af0b5a41,5bf738fc,be24e367,c8db2fcc) ,S(6df3e575,4b62c92,41f8aba4,12804ddb,74ec864a,12076a34,d9cdf9ce,be336e8b,bc66fbf9,276fc85d,767c2155,ef481295,963cf371,c0ae6b48,50140d1f,c32f80d6) ,S(e5794801,97d3eb68,fd859d0a,a616912f,a2a52a7e,f3881969,626f43ae,4ac20586,3ba69743,176c43f7,7afdabef,a06eabf5,94b9d0ec,1114f352,7cb1b127,697a5275) ,S(7b290c31,de7dcb10,177313f1,9a15d751,c128bb2,16823c5d,69298baf,575657cc,9d3b3707,d8f2b17f,e14b6b1d,80c55d14,b747c3e0,8c79d55a,bb54809f,d96f99e2) ,S(4ce2adcc,18632b7a,560bfc3,beb7138d,8ab210de,6cc7f6cb,47171b45,13e991f7,5aa8204b,689d8f69,a42e08d,5ecd2936,97ba76b2,1bae122c,e9252659,25a874c6) ,S(dd798cc9,97530af7,d7ce96d1,a6a93aba,c29056db,c69eebca,f4649648,4942bcb3,e9ed537e,7b679852,88bab4bf,36ed677c,14db982c,9ce8714,b4f3a32b,56609e49) ,S(356f4414,9da655e7,c9ea5a3a,5c4847a9,f908c608,aa492efb,15e7cb00,8b065b79,2adb4e6a,ce059ee,44ee8962,b4aa8c71,a4d55f31,28f56877,6c70c4c7,19fa6332) ,S(b607a62b,c16ffea9,b30f61d9,c711adb1,d110c6b4,357b1e0b,dc71c8e9,4d06668b,6b933ae0,9ba42b06,96419a90,e6579a33,8f4f3fc7,5134abf,70cef838,efc5270e) ,S(77fec5c9,24fbca2f,f564bdc2,96ebbfdf,d52f0dfb,15011792,57085c0a,8fec498e,6c7729a7,c92a6626,44f33fd3,1ad5142a,b521720,24e31308,dc11f73c,ee29d69) ,S(804dd2d9,8014a95b,7fea2651,195585ac,acab7a46,1f3134ad,f2c4403b,3de98461,66fae33c,458de63b,dd04fce8,1c425938,dc13194c,ac03205a,c278c071,918a4e84) ,S(65866c36,90a6cf74,95ef54a4,f222bf9e,3ea803a8,98eebc19,2214133e,9ad35234,8cecbc5f,4a152864,6350711f,c4df57dd,8a2c44d,4133ec17,c95e00d8,b49c62ee) ,S(eaccdd6f,2a9616ed,d6f8c3dd,bcb04c1d,49f0c4c3,8d8c34fa,d47174f9,2323e15d,15a435eb,e23d23fb,2313b59e,2fe0367b,17b6d9d,e900332a,20430362,19c4591b) ,S(860d382,8ccde42e,b27652d1,c159d9db,57a0b9de,f290b071,e93e36aa,f730c53e,b4688879,ef616c7b,87bd37,641e0381,115dd487,d5fa3e87,99257afd,26906aeb) ,S(fe446d0e,8d174570,49394416,9c332f9c,eb47e70,3f214d83,2777398a,dc8189bd,d4cb299e,760ef11e,a3846dd3,9a49f34,4d5c10bd,ba66dccb,a43e3647,718e598d) ,S(e4e6bb03,528f913b,bc34d910,2a96385e,bd0b8aa9,a07a863f,9d5d41c7,b982a578,46ed6885,471b4806,aca3c265,d0c40535,4bd63da0,af35a89c,e8a86896,63d38690) 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,S(15553b6b,defdbee,532599ab,9e0de23,b4954dcc,912f49e8,f084ebb5,af6088e5,8dbaf203,351a1119,16e8aeb2,e5eeaade,b0ee5d9c,2f5020,62b9f5cc,ca40cbf5) ,S(ae84a42d,49dad25f,f0a5320b,d6a33f8d,79c9f2c7,2871f41e,f8b02cc2,c469452a,9b23f07a,234782b1,cfa524b1,ad539ea7,b8fac3cd,e9bfb867,799a2587,95a48ca8) ,S(eecfc7a7,a41f75dd,43e2b85b,5af33ad5,f017e0d4,8f9b9bee,f0cf4499,a3c762d0,65526d26,73b9e5b2,8ec256bc,a524e376,f0e40f62,2db6e492,e1c53820,a3180d11) ,S(35e427f6,d0be7dc1,2d306ecf,be9fd8ff,107a044f,81c38c8c,5b9a181d,f4565440,de09eefd,27a8bb89,d8fc38e8,d32aecb,5c6bdc57,5cdf91ca,2f18e926,dfcca94e) ,S(d27cec9d,11130024,7f71fadd,4ace1139,cbe3168d,174c93d,4c756c42,89cef3da,5747fbf8,c4040895,fded5c00,e1f60403,40e07827,8924ca96,2f83b3f,e50ed701) ,S(df30926a,ca9062bd,7bbef9d9,e312a1cc,49442ebd,9994b93f,dc652e68,25efe5b9,8d1ffe08,de113447,5c3adb77,ee5aa58c,593486f9,c3f27c32,a20df570,6ff5c572) ,S(c2602b7b,56d0eb73,ab494934,5eb77e88,787e54c,79558ea3,dafe3f50,84f96682,45885bf4,65996b12,993efe44,39861b39,84d5fa89,5242ea8,f498695,57391182) ,S(d6d606e6,28c55e08,61a37803,72c17b1,6a2fe04b,e68a0cc7,60fdf7ac,85c8816c,76b299fb,9e716eed,7f09c879,ea8256bc,a953454e,490edabe,c90a2e5,dd277da8) ,S(d1bb671a,10ec5393,9d67f6aa,3b09e1b,57bb6414,e1f707dc,b832ff67,56289c4,47559cac,311f20cd,55760ed6,2e1e87ac,cd8603e4,c1d0cba9,79f6802,6b294a94) ,S(739ab4bd,6b6132f8,2659fcda,5fb46836,7adf2133,37f897fd,70a9552e,786dcb91,b562e798,2bf508ba,1b932deb,3e6b5962,70bba4ca,402db3b4,d806da6e,fbf6670d) ,S(a710cd7b,2aef0005,6d8db954,2abe6cba,2a6c6132,a48a6670,c501fa82,4de21388,4a6037d1,87db5b52,2996bb0e,47fc7509,1ad9eda8,e15faa56,92d56006,e72fb220) ,S(cdbf59c9,b38e40cc,d63b36b8,b6e894a,c6baa22a,93a1382c,9d7fd070,58e69b7a,3e836c78,6954d509,348314df,8ce08f0b,59967aef,4e5f0136,9c6d0f91,2682d77) ,S(1d32e93f,6e5e138e,7d226636,d5e0946b,8117f91b,bd59efb1,560a15bc,657e4dd3,82c43daa,bc1e23d6,3632e167,6bbca422,9797551f,f729cb5d,c8ac1460,46ed20f7) ,S(2730066,cbe72e84,304e3563,a18689a1,c6c8e0b3,e92d8c0,d63a96c7,e3573337,8804d5cc,6aa91f7a,1ae23506,17332f7d,811b8f1f,752fea43,5208b770,94e67c58) ,S(44624ea,a1607e8b,8bcbd736,9c67f86e,6b0f5226,4cc76a3d,b40042cd,bc621cc4,95867a99,d110d9d9,e382d3d8,a5dff78c,d8db012a,972a87ae,ac24bb42,b2747e53) ,S(8ba805d8,864774eb,4494ca5b,f8257bf6,980466f8,30028340,8aafd665,7f1ef49e,1a1164e3,c1b243cc,57507b07,7348495,95cf67c7,b40d4d7f,f10ad096,3f3866b4) ,S(297d0130,25bdd2d3,f4a008d0,d8c51a3c,7b16b605,95958d9e,93e427a8,7ac01267,56361e70,22138026,683b7bf3,1a6bedaa,988d3938,cf8399aa,e0f3175e,61d7e2bc) ,S(d866bb84,23527208,e66f34bc,e26a8ac0,daea9d03,27c9dccd,cdf0e2a,a0588f52,5e16262d,3564736f,30f26e68,1c5ea26a,b6f63429,f0b25dd2,5635a3b3,1fc45584) ,S(ab1e9d8e,b18e016c,d8ec49e4,388636d,5dd2ab55,8b3dbaa2,433a976a,ad8f16a2,a14cbcec,6327451b,15d47fac,d3f3cbbe,fef828c4,6ea07a0a,9c7155cf,2a2f291c) ,S(cf2f035a,ce393efd,3032cb05,4f4e92ae,5311dd04,bf8f3653,5197748d,2094cd30,75b38e90,9f02bb50,7a778243,35a1c97d,75bc653f,c6dcffcf,615bf8c2,ec6b32f5) ,S(a801d552,e63ba120,2c3ff08b,8fb025df,e545ed35,1adf00f,1a08d982,9e8bf9bd,bdb9274d,f5298fab,4cb08f42,252639e4,a24b553e,892cd1ea,93499c47,41c23165) ,S(f7ad7a63,eb2b90aa,3de2a80e,844e5336,287984f0,6075d9f1,26f24108,f4a5869b,d151e7d,9766a81,1db45134,7cc22654,c5ac40f4,a1d82d96,2de02c58,d46cda31) ,S(732541be,26fcc3e8,c824d539,28282611,96717b00,2af01bc8,57f4c0ac,cded0a80,d44adf28,f26370a8,3c9eee24,4e870dab,3fa7a508,bd14a56f,17c9a845,5055f8ca) ,S(892ee5f2,a5266a86,5bf2094,14c31225,b92dffda,7a3ec00c,ee53dc0b,8c3a3367,21bef833,3b983665,7d243b85,c0b4e2cb,6a5b339d,831cfef5,d676c7d8,87a0df00) ,S(1a4597e3,77569fed,70875f9b,f8f5531e,6bd3b363,b96a345f,9275365c,e1e64424,bd142738,fff7b9db,cbff1c,93a968b1,f0ef3e63,8279b745,21aa53a7,6e611f7a) ,S(c7306404,4b4a3a00,6a584193,e915a174,631c8a2e,ac45973,c815a2f4,aee82f35,280adb29,4f9642cc,cbcc4345,28bacdc5,74beb7df,84c06216,68cc2fec,d78731e6) ,S(c06d9d55,264e4ea9,e160fa78,78a7e4fb,1757f6db,fe610966,503ae03,b4723f2e,c0d82600,ae072564,b29373a1,ff1a036a,45f68f22,9d1594ad,1c9584cc,ab732743) ,S(e878c0b2,bf38b500,6c309a51,5121a3c4,5b13440d,74ff6e27,5bfe71d7,51e6926a,4b8be149,11432ff6,c5169731,1c1db30b,c921cc95,b4c98a39,5228c08,b99b6229) ,S(d1f6621f,89ac4421,7ef39a54,a0922c77,dc7addf4,78b15796,2558ae72,9b24f65e,657556fe,e02492c1,97c9c97a,67bf1d6c,eb689415,80a1ce6a,1e4d98d9,64902f3a) ,S(f9199ae3,ae51f441,d88d72d6,9c1ff64a,d5cc4979,b5fd6a23,c514e9b4,66ea0a5a,3c484bb8,8ec31009,eb95b971,69c7ae03,c20dd833,eef53cdf,fdab8cd5,7a82d4eb) ,S(4e059bc7,516d5fe2,510ae63,d3ca9543,f840bff5,710a744d,62de3965,af6a657f,222309ca,242c5858,5a792045,bbfb3e55,b61daa3c,afedd1ee,19a0038b,f929a47) ,S(c1673413,d8b4298f,6ca04741,a3c32d79,83a7d5b3,dd39ada2,53013d3c,9750ac65,333b1660,7b998e8e,fa7e3d32,2d51c052,1de24d3e,9e389f0e,9a00015d,6cc32d54) ,S(c078723d,8abfbc03,63f12766,cf9c6261,9c31173,5f3a9654,b653a8f9,e08f551c,880fa5d0,be09cb8e,4f145749,1c7f54e1,ceef1477,ba7ed718,5f27013e,32deb89) ,S(c77f3351,4b44b047,3835e3ff,abe8d7ac,ae5f912d,aea4e6e0,4ed03feb,78c41ce5,cade531d,26ee668b,5e2fc7ce,421de2f,d9a14dfb,87286c22,c840144e,1290e910) ,S(90e14c45,4ba40739,10f800b2,bcc7b017,ec58660,bdb1e72,16cc6afb,8320277e,61dfb75d,f5f74d47,287f828d,c4ff46d7,fa351a1f,66da99da,40e74758,2c6bd4b2) ,S(34c65f34,23f2474b,7e2f294c,ed4da6b5,c05d19ef,a2b5a792,103b681a,be1a3f68,d0fba1a3,b12d3e4e,f18acdbc,68fc285b,8ef1365,6aa900c8,c86ae191,37f028ee) ,S(fdcc63b0,aa5017ce,215735cc,2802eee6,aa5ef53a,6a258dd7,a128ed7b,9a5df38d,217ea863,5c9b88c7,19c7f9e6,1286844b,d4f4b758,81535954,7b24df0,1fd5bf03) ,S(10624260,58bb9f6,a5e83740,59595ffd,e7013492,4392c753,15853f4d,9c7070f8,84a92509,e809874f,86e60bdf,85c75d7f,2cab596e,185f56d9,262b06e4,e79cf785) ,S(e21f29c6,70cfc7e8,b104921,bb524414,53acdc5f,fd80066,39417966,ca235c9d,41be8bdb,969ddd53,9093dc1,b85dbd4c,a78f7e68,67fa916c,36136d24,b6c4af38) ,S(154a85d8,60b532cc,16bfdcb2,2769fdf3,6dac818e,cd2daeb0,864eee0c,f78a5c5b,15f2dfc9,3e5e08e4,9d340ce4,bb805afd,79f940dc,f97456eb,c73b47ea,5098e429) ,S(ae6f8b12,d52907e8,4ae5063a,114f8e2a,da7be317,454ea505,571f2132,5e4acf42,49376af9,1aea68bd,cdcd637a,909b639c,b7ff8800,ee003fe6,540d6797,f0f296d1) ,S(de42ac26,47fece4e,69341582,7e3c5b7d,a19dbbd6,22da9fa8,58a3be29,8a47bb65,e57cc346,b83b33cb,79a34805,42811d1d,4178805b,a2b88de6,d90b4fe0,ba8e2740) 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,S(34787098,f0df9eb5,e4825449,6fd7eb6b,3118dd45,aa0ccea9,f606a794,126b9ad3,85c30ff1,c8dbde4b,88fe9ff8,20c9908a,a35a0c53,c2175524,a5929eea,5566a564) ,S(6599b07b,5d31c19e,ee02e287,ccaa1bce,70890b14,cd739140,6f1d862b,39d794a6,d18396df,27e6fc21,a9c36a1,8d8f73ef,c79e6c56,ecbab9cb,83750220,a816d5ff) ,S(27b50b15,c92c010c,60feb473,5ac6ae0f,9ec0af75,81e41a90,a3a940da,a1a44ee8,31c2c3c8,61e64b7c,df8ca011,bd4002ba,5373ec63,8c3608fd,619bbb92,3552c1b5) ,S(40aed5af,953f3a17,f5d17622,127f16bd,4cc5bbee,33e23443,5f49c4f7,a48e7a32,e47011ee,96c702a1,1eff428d,2940ddab,d17b76cc,6765d5ed,126876ea,2496f6e6) ,S(cb56977d,f69956da,cf40909b,69fe44c1,4a5ad547,a025d684,c9815ff1,b5331ef8,9904de7a,9ce0f656,2f025ffc,79e8b3a4,2e410ad5,8f0caa16,62a13e29,f0b00bd2) ,S(11dc40ff,58c6d2a5,9768a776,41c611a8,2aa651c1,15e9d36c,bd3ebd18,ac7a0df9,4717af95,274f820,28592bc7,4a84e467,9d168dfd,826a292,5789edf4,a06e0e50) 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,S(bc239122,b0cb1f43,2ed0c2ec,bb3c5391,b7eebafc,c4190fc5,8f62d313,7f58c1bd,5b3cd401,d9cf971a,6b9f70a4,b6f8fab2,d0026a24,cceaea2,a86aef0e,a76a3cfa) ,S(90b7138d,5d2e11b2,86d29b78,521aa9d7,205351f0,1451e134,8a593b78,fe5f1778,77cdd3f5,829af7d9,937ac98f,58a78b99,b54fe9d7,593415f2,18dde880,b5039a37) ,S(631d0fd3,27bca9a6,aec8eff9,54fdde7b,df43edb7,b1f602fd,a32c387,825841e7,d6e8af71,273702a3,a2a767af,3c438f0,b07ab614,2fd0f67d,74a9d358,74e29100) ,S(ac2a0153,d810371c,6a7bc097,ed09be67,14ae9935,4a9910ad,7ee77ab9,6d54cdee,39707795,a4f01640,87b5e149,2ec8fc1e,be11d8f7,c43555ac,6f4674fb,8ac5b0b0) ,S(89751ec3,c1aeb288,1953d3d3,f2f634ee,29b1aa18,c55b8b62,59d5cadc,852ac99e,8b4d51e7,e2f94c0e,ef80e16d,9b62c935,2ac91394,902537f1,e93744c9,72f22a3) ,S(849a6cfe,5e3ab81,2e21f491,4c6ec76b,5233d405,7ffd487d,bb0b5091,2ac499d2,a490b967,b5fcea21,d0135ec3,c9ed5efe,ecf7ac6c,81e06648,66cdca60,a1be7037) 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,S(eaed18ba,83238fa5,ce4e6c82,edaef108,b1f9929,3148f3e6,2d3a6d4b,535455be,1017291b,805f7b1f,eba367f5,9a1a10b5,f7501355,7e6eb921,20838c50,aab0d29b) ,S(91ca8ba1,da9c2625,66a135ad,81f57b10,65ea4632,5bec5d42,ca1ad62b,826f04fe,2d5d619e,84fac3c1,e30343ba,a61d3bfd,e1c4a9a9,8d968e92,d560956e,138e34ee) ,S(8a31ad57,12e32254,7d0d2907,cb73adfb,a9a1ed5f,fe98d645,22082e6f,1cdb1364,8ecc3fea,886737f4,f94a2984,e6edba9,8128b2d3,bc79a209,2b2c1a7b,b00bff9e) ,S(123acd6b,ca673170,400bfc4,1071cca5,4e03daf3,e1ed1458,88470c04,568b972e,e97dc60e,cfec2d5,c6a6e173,9d60f7e9,838ad723,ad0fc7e1,52b5e70d,b48b853b) ,S(d7c26043,ad647f0f,d056c10b,4ac932c6,6a545bbd,509de346,d4391942,52e69df7,6bbf2f04,2c9459cb,c72e6aa3,1b6d8e4d,e606eeb7,d5d4e0f5,7f729a79,ab1f5e9e) ,S(67c4eb00,548e2cdf,50626c8b,1aec1173,8370da41,9280c9b0,1c8783ee,91e018d0,ffff201d,91a4538a,97ceb50b,c9aac646,bedda1d1,3f22a121,c709bfc6,23b95a67) ,S(7e1264ea,486b08c5,19c7d8e6,5c80e1d4,d2994bb0,95185c72,63172b1f,ead93428,1797609c,816f10a2,e82afe39,65112a35,798b0874,b24503a8,f57c983b,6ce7ef6) ,S(912cb164,5f7d7bfe,5ea443af,1c458500,a95ff22b,212109e3,12fa01c2,41319cf8,bab658b0,111c48f8,a2f620a5,fd130d53,e1c70e7,62e33dec,55b22d87,38c1eb99) ,S(1d60694f,15577a40,f6b9f299,be5eb62d,251f62ad,b9b5651b,df804e27,df919fb7,3799eb92,e18335b0,bdbc29b1,f8ce07ff,3f7cd409,5840d5,dd324bca,2f902a14) ,S(8166b50b,811bf53,4a94af10,7672ab4a,4e154b2f,c5cebee8,c8ef6ebc,18cc3906,6dea31f3,343e5b45,f5b08c19,903491f9,349f4ca,29818fa9,16f5e02d,85e09ef) ,S(4852393,e42d0821,6664d5d,f85eee60,9660eaf9,54ccc6d,fb1c31f9,da17923,e4cadcab,17f64d8a,f5dd74da,eaeab7f7,13be1de9,600d4db1,a781a058,5ed2006d) ,S(f40031b5,ba171b26,e02be47a,c34173aa,18ec3850,1b1d529e,a922a418,1c3491c9,c2db89ec,2e50105c,4074b729,a53ef0a7,9371d2a3,354d2d23,8fb39bf4,bcb5028c) 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,S(21ccbdab,f6902a86,d368d445,dfba0f31,4f80de6c,c7f05f7e,9fd1818d,45a174de,eda0b8b8,7f40e9f1,bdd5ded,e65bd72b,6cbe049c,bb1575c9,6b779818,a67251d4) ,S(c3e58ebe,36b0e5b7,2e15c47e,cca6848f,5312369d,d270dd18,93b589b0,56ff7082,212df92d,d724e3aa,c42e293e,b1a2de5,3c340712,7ebba791,b901ff87,9fce94b0) ,S(f19961ea,da1d77df,2fb9d976,7d7c664e,c0400066,2ecd7244,12b72dc3,c5de133,74f321a9,1287943a,8ed14d02,96b05ada,1a24fb52,a09d467e,8e8175ef,8f04a2c9) ,S(3aecbe48,2aaf6af,35e63dda,fc919adc,f974e89e,765c4437,69ef535e,cdc05e01,92b854b9,30e5e4a8,85397592,fde89d3a,601c733f,d88d230a,a1168e36,ee367273) ,S(55fdd639,b87de7c3,9acb95ed,33222935,bd4217c0,fee1c924,f1060f54,fd22055d,81f4ef46,16e51585,cb443bce,f16ad8e2,36d6ed18,87ddfa60,ddba2089,f4b83c4d) ,S(b86a6272,ceed47d2,4ef4cc67,bef0b117,c0761b4c,29548c8a,367d8ae7,bf90744,1c0de18c,d5f3331c,5439020c,5964404,be582f88,3feec4c3,112396ce,b657c4fb) ,S(d141a7ae,9d92913a,26deec5d,d2acb7a2,115da997,63be5a76,c5a0a415,8b5b8170,de784bc0,9308c82b,ce3be9c8,9abe41a,4ed9b9dd,cf817aab,3785e344,dfdc2ecb) ,S(af340559,6902ad5b,e3fe3464,3cbcea5e,7a478a32,b1bde828,ec966837,192344e4,3f65050d,13e7b969,35b013c4,9df385d9,833d419f,aac0f754,5c395ca3,75ae8965) ,S(b70dce7f,870d3d12,472d3c5,481a1288,cccfdb2d,12637a9d,973f4e12,b026cefd,4b4f733d,e5322132,80a36e4,ba57894d,a563f4ac,b1a55a9c,83c8dbc8,96a7fdf5) ,S(14fa3dee,44dafb00,d2e71c91,5d217cd7,a9c2b50a,edcd0025,f7aad2d5,b6c62ce4,67c3a65a,65bd4292,d271fe13,9a8c9d84,343bdf68,cc16e50,11676580,6bc30d8f) ,S(baaa6a53,26a7fc36,e519d9a2,48dd3aca,f6f0628d,a6406021,caf0d0c,56d9bb3d,4fe9c638,c1078c39,a0fc39cb,e9a81bc3,4b15840b,631ecbd3,8ca4a2bc,10d1f3a) ,S(ffe2afcb,5e53bc7c,9ee07740,c8094a3a,32c8e627,4dec7eb8,cf2673a2,dba11725,68d7092e,2b8b56da,1653dfd6,42de49c1,799d3ad5,864e052c,8829815d,b2ad952a) ,S(a25d7c5e,83a0659c,5ead610e,b581d325,adfdd3b8,af03736e,4039ee1f,40612431,679ecfcb,b1da355f,d73d02e8,b79fc949,bdc9fb5b,5a4e28c,5e68c244,7599c806) ,S(1c5d082b,3121c4b0,2e0e2244,88e53b8d,ac5500b,bd396f0,7fc218dc,7311b299,a2a435af,4838d028,4d459216,f3955427,59f1f51e,9a15f28e,d83987dd,9c09e5b1) ,S(d8d21200,2cf2ceae,6c9a90db,89f7d0e0,42a2e97c,458b9024,437e28ed,a775ca26,b31b6a02,4b01de6b,6159ee51,3c118921,f61a536d,c1442525,cc613290,364b9df2) ,S(b5265664,54579771,947bee20,f8e7bc48,1e15d07,2adcecbc,3aae7b91,a4d0f3b3,170ad05a,da7f67ee,f7c611ba,3c55c835,f054bcf2,445e5c1a,399c7cd7,640ba8be) ,S(1d0d2a24,8982635,18a28203,b78cb089,acd5c296,98b86b7b,48fd4db6,3c80812b,71e2e1a2,7bff3bf,9e85e145,7f446048,7643f154,1cbe829e,f600d861,dbb752e0) ,S(cbbd4ee6,33aec586,ec7ba712,c3bbffaf,a0e6497b,8618a476,b64c660b,340046da,d792753f,c73090ac,177ec5e3,40aada73,3b31dcf3,a1f46952,625dab85,7e9b9795) 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,S(cf886295,d1eca9f3,4c95acfa,b86a5061,82e30324,ba5b495c,70318cf7,9e910d70,59bb7068,3147c26e,45c76e7b,e018e467,1f47f488,2c044484,62a5053,8023fd40) ,S(38723d58,ffc69ea0,9a8f2655,dc225da3,78b9224a,f8d81e7a,bf8f29ee,292ddd24,c41d67bb,e699e504,3198adb8,ff11a5e0,4033b66,98d3ec18,256bab11,93db5535) ,S(5b41d5f8,1e2443db,d13521e6,e7b7fdf2,4a226cce,f369279,22b353ef,107f759d,8ad730a5,bfb9f01f,853434b,24866a49,912fc756,e086e781,a07ff2e7,98ef38d3) ,S(4f3c24c7,7dc7e41,843e9018,400d3bc7,5d1dc958,2895c11d,3855b80f,4709373d,a485adae,c547a5a4,e0695913,c4c2fb5d,ea16a3c,5211c162,4819d704,5b0d8d6b) ,S(f603e0c2,8b40c8b0,a6a0378b,c4289059,5a4cf4c9,2b74199a,4e4e231f,a6b458a6,a73aa12d,76572041,f01c33ea,ca599a30,9ba0b838,f1d67fd,67a9a5d5,c3ffe258) ,S(84ef0a98,229c7af,9404cc25,60f4fe1b,4c8e66d9,1aa96118,53fc4f25,eac78a61,653df937,3640b28b,2c2c4061,1d79c4c4,a2d577af,b572f5f9,e50cf3fd,2b2dbcd5) ,S(e675d998,6b3bcd4a,d098ec95,c386be9b,4e96e448,ce6c9371,15c5dedf,d97941b6,4319799e,c4103d65,18590091,e333cd58,9901b020,a62565b7,f84219bf,e31003fb) ,S(10837b33,3603f33b,e528f391,b5b672c8,93fbd813,99c5dfea,f6126e6c,2a2633bd,cdee9534,2456a261,8a293b49,d91ed2ae,f620addb,ed83fc66,d169da3a,a6d0e2f6) ,S(4cb1ddb6,6ad3c1b,68c6b0ea,408ba1d7,dafdbe54,89c22d47,7a62dcc7,77a8e013,6c005484,29e789f7,5c34d8cd,a473270d,75eb8f1c,3db13856,87cda96e,5cd4b370) ,S(db72d671,ff3e0102,b1c52481,b66ea142,8f7fcd43,15e2792,eae234a9,291926e6,71c55f71,68a088f9,980bdb6b,79b052d7,4edd0b19,7ab7359d,9a2f9ce9,f1c5a5d9) ,S(99f92125,162e18ce,7493e6e3,91cd06fd,681371b3,2e147ab0,24ae3799,15f586d3,9286b3de,12ee578a,12ded341,75bdb712,d939b7e5,555e86c1,82f1f283,3c1b1d40) ,S(a2b8b63c,8984a666,2b09c18d,b2d7f263,796660f4,3bd78eaf,af7c63b,986c92d9,2003787b,2af02879,642b0a2c,f716f4d5,85dac86f,e58c7d41,d1959763,310a67e1) ,S(9292ef40,21bbe6dd,8c26a862,c9b7da54,4292e479,a9e89264,618e3a47,9773b446,d1a51e4,65bdfdd0,dbf74fd3,d449f6bb,ea862eed,ad369c52,34a695f1,d229ead2) ,S(8d5a920,547d838f,90159068,ceeab220,cc6aa126,d423edd0,2e136cc0,1cea5d4,c3334a69,f7694e9,43ccb182,2caf2abf,f4caa83b,a006af52,bc010bab,8710b596) ,S(7b62f4a7,7b79c09,76dd2f74,4ec08d9d,21511fa0,7891ff5c,52b8dfa4,ae3430bc,70ab2073,cb3a7cea,350e6aed,dd0c9a6c,ff8e02eb,69bd14a8,a09e9b8e,ccb19a0a) ,S(e18a9c02,5829b47,cdd34c11,f97f2edb,a7fb9b9d,fa4777a6,dbdc3cd6,85245b12,7386fa51,881fe49a,adbd5327,8d6cd0c5,1063dab0,aa830b7d,88c7a4d7,9998e743) ,S(ab9b68ad,61335dea,767c763e,3294d414,74a6d4ce,e4ab9a78,7fbb6749,7307d0f,aab48fbf,53f365ad,bf94f823,ea973a25,f6ddd341,397bd81f,8e825f60,c916852b) ,S(3412531e,8423364d,8d8bac05,bb78973d,7b8d375a,9e52d81e,bed48027,2abdedeb,1b9f5eae,59ea3385,9de752f5,db973a86,4c735e69,fa8882ec,e1ca8350,77d77335) ,S(6a6425bb,af9f65d0,1a401330,46053b50,7ac8d45a,77b30de3,69eed52b,956799b0,7cbdae81,93368c60,5671ae9,faead4ca,2887bd8,9a06062b,dd6707fe,f849f484) ,S(87860648,af9ffbad,50871c2f,29bce0b3,e9693835,8a067201,5c1156a6,7107a4cf,8660c0d8,f1aea58a,c613f6f3,5b27baf5,53835493,fbc0e203,f024ee36,27bbfa53) ,S(35733610,71c55057,5392c685,3cadd8a3,6618443,d80b3625,53a2f197,d3c52539,42935628,adab5bd4,e0aad0dd,a7d76627,58524b2f,34ded1cc,d3e44249,6d213630) ,S(82d21949,2fd48d51,65bea027,6ac15cf5,d27bd736,45e03271,24f0f689,8a2f4a25,f13d9063,fed02a94,1b4e5c67,f42d82b5,33f18ff9,ca4622f6,79c6aabc,ea454c21) ,S(ba1a1c83,6dabf825,e517ff65,549e1d5e,729944a1,d7b17cea,aa4466ac,39ec6eba,f01dd751,3557249,d2fb224b,40ea19e0,57b4052e,adc46787,af587ad1,458bb4f0) ,S(5cfeac36,6bbe58d8,45a36cd7,de6601c8,56943a07,522364b2,23a1718e,6df8de8a,6651d3d5,a344af69,25fe039,c9e29e77,95544b96,66752f4f,c9a3bb57,c5586c32) 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,S(601cc630,47ce63d2,c1fbbc49,f3b2dbe5,6edbca09,17ac41e9,b39f7ac4,5cb3ff8,a773b9b6,d98c7b35,458e956f,f9cc71e0,8539b118,bc2529f0,fd496e54,efc2b25f) ,S(a31ffa07,e16fd36d,2edd7d1d,944ecdb8,2da2641e,cc6ccfe1,88219a67,5677a740,c2253d87,59ab43d7,c919710,9e9ecdae,df1f2d82,d34c5d82,d113958f,cbf1e3f) ,S(131060f1,ba302b06,b26360ad,de531db3,422a6bc9,6ca1e9e2,98b5da8a,c8266249,4dae16bd,40159bfc,96665d6a,d64c6c5,3ce90fe0,95a316a6,8cb84844,ec183cf9) ,S(f4a29fd7,90f35f1f,4b3240d6,c0cbb983,3e701a9b,ca241d3d,bb7630a6,da2de25a,b2ecd794,5afa51e0,1caf3c21,5334dd9e,9f9a1f6b,8f35767f,c63a3f00,69c01382) ,S(b30546b7,c5e45266,854b90ba,53afdab8,be115251,5ae22f1b,5e0c472b,a3b44042,f14a6b95,178fbb85,5aeb9cc3,a4e65560,3e8b18c1,4cc54cb4,1e059597,faad7f4) ,S(b6cbbb5,10ff83fb,c8bdd55f,cfafeae8,947f5e83,4cc78eef,dce45dee,2014e175,d0e29276,a14cfda6,f518a3fc,ac6a4163,13666f91,ce5ae7b9,7abfdff4,925cd415) ,S(fcaed74f,19199482,564ce4b0,7e1033ca,c17bd418,769981bb,6547caa3,b61bafd1,c52c08e,f5331ccc,271b108d,5e7794ee,4a493ce4,f6665773,f97902d6,ffcf40e0) ,S(c6d1ed83,29ade032,c9924945,189ff23a,c6b1befa,e4a33794,8b1b4126,6d14344d,6e1c0e9f,da231092,86d23cb3,2c588799,507368b8,8c0628de,b8a79c97,e4ba817f) ,S(ac7d0edb,a7b86cdb,60963277,cac43674,19dc5d85,ccd9a649,bd335dd5,eea2a9e2,61790bc0,ddf5307a,56fce870,4bc9eed6,9d61d857,f4d2fd34,d53a97f2,4c4c5206) ,S(fd9d0c61,d3dc3ff9,bc3735e2,b2c7d5d6,4a740b1a,bcd46a7a,860816f9,84a64645,701e082a,5e59460e,c3e3ca21,40137ed1,5bf9ef49,fb4673c7,4fa5e4ff,2ad8b762) ,S(82ce7d44,87101716,6ee31310,11bdf02b,336fe44c,88572c37,930a33ff,5bdcea1c,d7fdb097,3961ba18,b53b421b,21c0424b,7b4807ae,256d883e,2e3a6f22,9bc44c0b) ,S(5e507c80,bbd32e0b,efc31714,b464580e,f7ccd3a5,2004f2f1,9fb9b0f6,dad1a767,95facec8,a3b5c996,e0bc9d5f,77c11407,d0ee071b,9cf5af3d,ed625025,3aecc75b) 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,S(85138ec5,a5d3f0a7,881ce23f,e34fbb80,fc3038e,bb7c2a24,ccfeb2ae,5ef07b74,8eb9e80d,8664b11b,d24753f2,bba612bf,c06bf9f2,a4bd061e,82ce9037,895b084d) ,S(3b4c1149,1d98483,9ff33b31,39da0341,f430175a,d5800c80,37e35dfc,a68ec256,574d6475,e225aeea,dace647a,1489b2ea,873175ea,83cff3f2,fec684b3,fd2ad143) ,S(2ea17f9c,6a028f58,396474bc,8c51b1e3,cb9ac0c6,7f73f533,a428281d,4101b04a,19d1f021,8b8cc0c1,bbfb8925,77087caf,ebed3409,69dc2281,3a1dd6eb,9d6c44a8) ,S(67839592,2fcc7ffb,627486db,e1d98a45,25ee1338,5a98c01d,6b3b9f8d,f64c507a,e13ed82a,a1adf761,7cce3760,d049a72c,7572508a,5ecd0615,1bbb589f,17e10a7a) ,S(54a0d2ed,39778fc1,237ab423,1e4384e6,4156c1a7,d5e999fb,2c92ba42,ef40ee68,3d879ff8,c25ed54d,df848e5c,49e3eeda,e8eccf33,afcb1c1f,67440810,8b3e979f) ,S(263ff1ed,726d0ff3,8b47b398,c713455a,3030d499,3a77ffac,b9cde4a2,cd12f7f3,a5f3fb33,c739bc93,c442508b,ac70884f,d90c3699,34fd698d,bc27f7b0,ca48a0ac) 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,S(1ad2aae4,f571c6ff,1abfd45,35b3d085,1aeabdbd,b3a340f6,7bef0f78,f7afa954,1c394b1c,94539758,85d72498,b36a3be5,56b4f80,8ef52977,b0157885,649549b5) ,S(2403f66c,a6a7d60a,254b51e9,32cfb700,f37ad73d,193f25df,6024bd51,d0f337dc,9ad75d44,24517aff,7df86c,9bf4f315,cb40199d,4a2a5d5c,74044c4a,9c79d69f) ,S(f3139f4b,50dba596,87080a7e,b19bcc34,2b58df9,26576bc7,dfdc8e7,4914c524,fbaad228,ab34e8d4,451cf6b3,a1dbe225,bd46bfc4,8a4bcd94,10c150fc,5636c687) ,S(ec415f8a,81b1f559,714dd790,2441eb9b,c5c7bcbd,e87190c,c109ca04,a3e75149,9b90bd46,d27e0200,369fe995,3b50752f,d00b9472,fd31383a,f01bb88f,b223bc5b) ,S(5e336f17,264a53e7,d0899bf8,6f676440,f83ea0c1,5d53fae4,f19a71f6,998a3ca2,2a86fd9a,8358daac,828d42e7,9c6c0fa5,bf977cfe,56899db3,27ea32fc,cdf09f3d) ,S(98828ad8,a6ee9ca1,37f9ec2f,f0cac84f,5e664e09,68455773,3f8fbab3,ec38570d,ae7ba3cb,e617e9e1,6e67f34,f69af863,3e69c9ca,1f46b182,88126f16,9ec0e548) 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,S(318939cc,fb2eb0f8,30d30079,7e209f00,6e28b899,8aecb548,b3b97900,9ea6aab7,5308df9d,10c7d151,cbcbe417,91b627ad,b7204db4,dbd2e01a,c5698e61,bdbda375) ,S(ff9e4851,d3f0c9cd,818facdf,4781cecb,7f622039,c23e236a,7e4b7368,64af1a8b,fd69f241,bac1c6b9,a52d6dd0,6e7bcb6,4a4a79a4,9c3881be,6ef8c83d,3f462c5e) ,S(497113be,a88d4888,2c98ac14,ba0bd0aa,d3c75c8a,58d374cc,86a7fd0a,b6259cc5,9029d9bb,96076d69,a264d2bb,6fea2f15,423ff1f6,ff47c02d,4699943c,9cbfbc4e) ,S(2b2cdb82,6653f563,dfc4c373,96d738e8,3d1dcc5a,ec5f4886,2d5ca84c,2ba69103,d1985cb3,f42e4ae1,7da33b7f,f8563236,6e2f5c89,b849ac73,afc3a7a8,1d049d85) ,S(c55dcffe,fe63e948,af77c8c8,32cb6c0a,c09ced5,5c338bef,fc27fd21,dc63b6c8,edef9fcd,b00fb62f,cc97c03f,26253069,de6f8d00,c13a5666,f574feb7,fabcab6a) ,S(52a0dbfd,371bcfb0,e2c69160,c9cca2b7,8dcf679f,774c9d99,706d306a,30eeb3c8,fe01f320,781275bc,a6c031e6,d71df467,56473d8a,780fc54a,6f8eb1ae,5640bf65) 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,S(961d0144,1618561d,c3504859,7e1701bf,35412ad3,2d04486,704e5593,b9278734,7e137d6b,2060572b,ef66f8b4,c8ce535f,b858327e,26dc2295,6ee6c94b,c83859bc) ,S(2814918a,115ca2d,688f4358,9010b7d8,b8b560f3,6a3dce2,8fcc05e,acd4845b,dbf76f51,ef80e324,8820cb0b,bc7f0c2,4d50ae48,6387d206,c333222c,5f959dd1) ,S(6c4f3b00,c02c19a5,ddb0ab1,798929ca,222a9538,b641cb3c,dd61736,77c9442f,a91d13a4,d3888b82,eaba5173,3ff76fae,8022fb10,8cd61f19,206cd78,7d1c99cc) ,S(8f48304c,ac37d495,fa1a2ff,2178f442,4af030ca,70662a1d,c750bde,5f5d8dd4,ccff6176,47cbdd3c,3d0c588c,37a98723,c2b2aa14,fd17cf9f,ea45ec72,eda8defc) ,S(ae3da559,e3fce253,f5c1fbad,8e12a52d,ee989ea9,8552a192,93f7db0,eaac9405,430b86d1,322191c7,9aed5bb,12eece79,f2519bab,17998346,8aa13b69,94032ef7) ,S(90c093fc,27fa9de,66a1fdc4,d921e5da,6f4fa049,81cb6f91,e085f89b,96561471,1bdad536,4ae198ae,bbb0ff88,3bd5dd2e,dfbaa91d,e989f45a,30befa9,76f2db23) 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,S(394efbbb,fa740f53,b1e70eb9,d12671e7,55337357,b982921a,79915acf,ddd18218,8f1f1980,6c1d631e,6519aadf,b563dbf2,37b75db1,54baf06f,6fde8218,a0a68eb6) ,S(e6c3e152,27453d32,cd4449d1,ab1ad78d,58f5bb6,f29d813c,e7c6628f,b284399f,89d87957,4b640a87,abadc6a,dc51a533,838a83f,53de4448,9ff0640a,502dfd62) ,S(e2480000,9db30642,f925ef8a,e31c54fb,1340e88d,b6d633f8,415ceac5,f583cee6,39ad28f1,8ecd8302,5cc1fa72,ae4e9897,81318cea,9e506794,50abd959,f19758c0) ,S(1c134120,3c2e7e21,f5b10ecf,402d52bd,33db3278,70cdfcec,f3b277e4,78f551f4,cd6907b,57cfad79,5e14e7c3,b2a06a46,17b7a27c,ff476bfe,38d68d0f,1470dd63) ,S(6b2fbbb1,515c261c,954a0be0,279a1cd6,63daa083,1fbd58c9,c69b7be7,ee6047dd,d38ef59b,4e276fe5,6f1f2fe6,74b6974d,5ef1f4a9,74abb2c8,17cc68cf,78a164a) ,S(dd5098a,8cc8ccf0,7db82096,b52d1fa3,6bd26c2b,57f0cbe6,2ca954db,1773e9cb,a198ec1e,71c53d73,5b50000d,678d7d93,de64a72e,8ad018bb,f515b4f7,c7840aff) 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,S(698f8b8,66093996,e2e357d4,d671d21b,230726a8,84079fbd,766332a5,4e7f18f3,5925e34e,dcab3458,ed959aa,3903ac93,c39b8ebd,1c562691,3f844150,d41ad20a) ,S(37274120,6cb7047d,aa97274f,b12aa8d2,e5eabca2,f3ab0b4b,daa3fd7a,3d5365df,30d36bad,c10337a2,db6c30f2,e8876226,5ccc6a1,7104460a,6f438a9d,3e8e9300) ,S(4e8c8df7,30f5d411,77355739,84a530b3,8ca4012d,3d4c8ce,f6c00689,b72cbeca,d9f7aed1,f5073c8a,8d2948d7,86ce6dd9,93a405ba,393a20a8,719287ce,797163) ,S(1e62c3c7,16e4f6ca,77b6d325,8553a5fd,59f67df,f7295115,cd6e4bb1,19b4b5aa,7df17da2,a7397df9,e314fd8b,6b03d293,ff7325e2,769d7477,ef3802a5,7d8010a0) ,S(c79f25a4,664cae13,d0971832,fee6a316,ff338f15,40c1f3e5,95c707c0,6e035db,5ef7879,c46266ca,7b342264,1594e81,5c189ce0,f057f187,e43a61fa,10330e85) ,S(768a47a3,64304a44,34b097e5,132edab2,b9840584,6e543dd4,755038da,e355cb9b,79896b63,eed7e866,32c33041,d037554e,551f2a73,6f2c2b35,4dd7d7ac,f6562344) 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,S(593c7afd,c178edf,9eae7fb0,85984992,bc5ca489,16a2a155,a0314d8e,31fed706,ef39bd47,64f3b3b4,cd505e3a,628197df,5aa74126,30d83793,75c85b27,76a1073f) ,S(6622a6ea,569856b4,23e9f68a,78bab680,759a0089,3f6f645b,2e0eae60,f5dc9d3d,e84d491a,1bfc3127,3cfecf5b,65621213,bdf1af30,2dd39d26,d756e75c,4f9bc86d) ,S(d7149e32,fb34d956,1f5b25d0,650409f7,33a28fc1,fa4ad822,eabe98c6,74b3437d,2c249dbd,a1a82561,51b6eca8,a44bad96,1b2d37c6,d01c1d1a,70ceaa38,9b3f5039) ,S(64058ff8,7cadb65,8efbf32f,a68b7b3f,19915f5f,b434830f,bd5ca208,a4a09b6f,71c6dc90,f4d8082f,72d5697e,48fb380b,8486d7e1,5f113cc,28365ef7,d3ee9999) ,S(6a6cbb7f,5b571865,d70ec29d,425115a0,82d1fc1,f0209e8d,47be5e5,a9965dfc,fbf10d18,f3af0e94,b2a6ed30,c610f17f,5bd571a,41d073c4,2b2a4dce,c98ced0c) ,S(3f9a9be2,9a72cf7f,2086d9ff,3701a35a,94a7f81d,4b34a364,916a45e0,d8652874,25b12751,5ff033c1,70feaee1,189a35d8,ba0b8da,d4c943bb,4fdcebd2,1cffdf72) ,S(873be5e6,3cca17ca,95980167,9568b487,3d34c5ce,68abd305,169917a7,30dd206f,6ea148c1,280396a0,7ea5c5a4,17980f48,d076bdab,3df1628a,89da4c45,14bcbd4c) ,S(17865995,f28d4c4f,43e2e9f5,9b20edfd,830a65cd,d632cf9e,e7024ec3,4da0834a,6773c06d,478f3822,86c749c,5ae09a10,910b5666,5b6df747,36d20adc,af58332c) ,S(efe91146,fdfc4865,bd784853,ef79b8d4,d2f020db,3f901f45,38c74c80,bef49172,a81a34a8,dc3a229,8348109c,14d367c8,7abe6753,50d013e0,b1b0372d,2a6ee5ba) ,S(7ee6fb63,36cc88be,3b3c2821,1552031f,d017aa4e,192bc122,973545bf,924e8a8e,a656fe25,846e8173,327ab11b,d8ecd2ed,9d1909fb,21d1f789,588b4fa9,a8ceb0d8) ,S(449677d0,2a78e9a,ce374016,e19e7fae,46efd0d6,4839680a,4d5cbc42,173ee605,47017ad3,3357db8b,ceca2513,c6477157,f3daa99,9cccb709,bbe88340,29312013) ,S(ca9db080,12b9fd4a,cef2255e,83f35fb,e20806f3,9839c2a1,699c5d03,d7b5762,6a1a811,3d82a60b,677d61c0,af995bd1,4c598f08,f915e971,d9f17e9f,8398487b) ,S(d040da2,8dd69fc,67414651,714d4e94,5a27c4a2,9fb44612,d6d87f4f,80e2ba45,a1a72b85,957a01ca,8c8d5d3e,d9ae6a2b,31d2d192,cd7afb9a,4d1e4629,aeb9f356) ,S(27eeb708,fd2d52a9,47f69872,3706b67a,1d6e29b,cc0c86e8,111057f1,e3655608,7f67db4c,25b2e88e,275e53c1,c52eb47f,c2dab668,64b91236,522229d3,1b001a94) ,S(3bc82484,daab22ad,6d887a01,ea9f4b38,bb70e272,b15a7b4d,ab5e3dd2,439d8a23,b0ec952e,6cfe3ed7,4e6246d1,46c9c354,dacbc024,45b1af9a,6a668f0f,6fd52ded) ,S(d0a00060,13596198,8f070ff6,7ea731be,7f97a51f,68faf899,95eb0ad7,746aec69,dde4a735,d6dd08cc,28e2588e,9af0eed7,57017b38,790d381f,74748f30,9717a989) ,S(8efc4c50,51c65e10,56f5ccb6,a4be2014,a9dd043b,641b7690,cae2a8a9,1bbe8ecb,26fd1112,e1aa603c,91eb458e,3874d010,db58efab,5dd9ed20,e156886a,5f39fc13) ,S(e42271b8,881306ce,f166138,7d14f0d,da0db64a,b379368e,fa79969f,432cb110,d2b9999e,7ce9f3c5,8a6c77ce,a97cb9f5,f2860299,9bacdc7a,b7d5487f,8b5c9f5b) ,S(bb068f3f,8e7fbd31,f3aaf96f,de53d134,e3a88b63,9d8d43c6,4b3a2b45,2f8de740,574410bf,903c173e,23d88fb1,3f7534fe,566984c1,aa10f0d0,f54eea9e,7883819b) ,S(a3d0bd11,d728bee1,b166dff1,81c3682d,650fde7f,285ed5ef,b2ac5033,5327cd66,3e290c2a,42afb4ed,8b5a685f,69bdd379,44215104,17a61d8d,bd3dd2cd,805c5f44) ,S(9884434,78bfd51b,d27d04df,b5282a72,4cf82c21,487a8733,9347e560,994debdc,545574c4,359fe553,b694803c,5a07339b,b4e1a95a,b9fc72c7,5d4c8f5d,ec6ce4df) ,S(8cc104b8,58b8fb94,e0771dce,a103a7ae,adfc50cc,dea4cf93,a5f4ec9a,d44acea3,ad73883f,57c470cf,d477f228,8badab99,938b6723,516f97b1,22578f2b,f893b506) ,S(1627b08d,a822d244,ec8fe2e7,d8f02094,111fa362,e7190cbc,11229a4c,2043c626,41f6b029,80fb1370,c1e800de,39507798,8b6f315c,f910bb00,423ff727,e9e04c3c) ,S(459d4b1f,2676fd9c,2aac5937,376dc18c,fd4244d9,dc937407,d641e0d5,491df69,6f22ce37,a6ea6a5d,c9823197,22b0085a,e61fe140,d7558fcf,7bb44976,5de7aae6) 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,S(4d18c5c7,51639d86,b21712fe,b2333d52,5f4bd3f5,e4208537,e1e3bf7a,9343475f,2a60352a,4d8fcb6a,ce01b4c7,63619f16,156868c2,d85e882e,a2e7fb80,16f6500d) ,S(8e473caf,d74fb06,b483d955,ba3e35ec,e99a4495,cc86485,a8b6fada,c4c8eb4f,41708d5d,ae2de832,c7c38389,d0ae46c4,46add069,8e83990f,52a545f1,6ef66942) ,S(91366f76,48ed27a9,2ab639ac,f37aba5c,44e8bea6,1402e075,e307c4fa,ea2cefa8,868fe0f5,565092ad,677eb1c9,8959affe,5af504a0,c929bb58,2f5c3263,114ea371) ,S(1eab20f6,51b63685,a0a8489b,4e3247ce,1592c4db,40cb2f90,7eff1c58,c6609915,c142e9f4,b9522b0f,1db90912,c6f83c7,add6d8a,6bd1de4b,c54503a8,4e873cce) ,S(a0652eda,796ff72a,eaf8cfef,371594fb,e1528929,1320230d,2bc6a252,f4b49484,67e6d40e,8aaca7cd,f2a2047a,fc0a59c3,b4eddc1f,d3d5662f,45bb5792,9e4dc9a3) ,S(83915afa,c936886a,3deb8958,70e926e9,7ee4a6ab,1a5c66b,a1602c13,c4f959f1,86dad7b8,e870dba7,712ca968,1ab63524,2ed55fe0,36a148fe,25b1bdb1,1ac2da4c) ,S(293f0bc4,11454959,86b19fb8,6f738d2c,814523f8,b75b280,f8f9021f,95db6061,12d98ddc,894669fa,86b073e6,5855a0a1,760733e7,b7c5bf5e,868dd977,82a4fdbd) ,S(a829b1c0,d6780732,321871da,2d28ecdf,18d13311,4ddc33aa,8ff4caf0,58fb9ad,c5375298,501294a4,dc38d1f,a8c96f9b,789ee9c5,6533643e,1142bce6,8e1ef5ef) ,S(48133900,866a344,68309fc0,cc18f79,c0e01dfd,ed6a7bb4,e5a4697d,4b9cd462,335b7188,ccea4687,50fcdfc9,a6fa6034,c239fe6b,27cf6460,182a1c0e,c8c96707) ,S(7fe9d310,bbdaa101,b28c1e71,137a7ab5,181dca39,aa8d1469,bc06c856,3c7a70ec,18006c39,538a5141,2371828a,4d73e02,f4699a34,7e887318,57e394fe,75c8143c) ,S(1bd5b65b,d79c3eb,54ee1ce2,541b4352,1b7d6c37,d2a26f21,b51d2c07,103ebd8b,66e81b90,a120f04b,340adb2c,42143ef6,5d8a383,46e71856,673090ef,291d7bf2) ,S(237374f9,306e5714,5f37a1ce,1418a238,73938fa0,8bb971ab,fb5d97e8,e5fa0206,d8410815,fd4049e,f54abd51,fe2053a9,bde7f3ac,f40fe992,21bdcf8d,4b9808a5) ,S(33279bf7,38cee621,c17f75eb,bf78af4,58c1a4ef,a7197456,b57ee679,f2c34bfd,d63a21a4,5dc29462,13750d88,ea5e12c9,900b110b,ce433c49,e9b37382,7de327ac) ,S(ee274c71,b1f43251,11d7e100,5d7e9d97,ed1590d8,95cc6504,3e8ed6e5,5a87a9b,73f2bd1b,1baec4f8,ebbcf9ec,f613869e,8a262d99,7bdee49c,c5b2fb22,b652e9dd) ,S(2f49f0ab,c24536a3,3bb0857d,57c35846,f5dd036,3851a873,46f93d0e,53ab8de2,66b3dcd,d367958f,fd06121b,e42237a0,a9edaf21,79ded853,e8bf3c5,b6a81531) ,S(2d122193,ea92ca9b,46eec10e,2a23268e,9b1f972e,91821489,8cb12571,1e3094b0,b54d4b85,a02f77a1,57a48001,c0a26c81,2c038d0f,b91575cd,835183ff,3a0b7071) ,S(9047eae7,841f346a,374131ee,d4299fef,970f59e1,e4bb1fab,819fecb7,3026ad44,d59d3d2a,2c03be1e,553a54d,2dc61c9,e13364bf,3338a5f0,4e4466b6,86695061) ,S(f689480d,c0ddd61c,ba5aefe3,17aaa497,c2d051ed,d527cc20,16877986,12d7c8f,dac41495,a948d83e,37a9f310,18cd7abf,6d5608f2,213aa5cb,7a2b8f90,98d87398) ,S(4a01c418,be472958,5bae0c45,cf6233b9,ad0177ef,eb6e74ca,ded59788,a22d083a,8a12550b,83de095f,22411b16,937a85b5,a079c7ea,b8137f80,ffa66116,2a1c53f2) ,S(a6c715ad,cdc77020,febc4ae7,c6caf5a1,107147ba,8281d3f3,7945682e,72a5da7c,69b4ce46,2634da4e,e9e43559,72f87511,a26718d1,d232f726,577f0d5,6b49d165) ,S(68ecec4f,aa19ac3d,dd8b928e,8362ed53,3be24406,15f5ddf8,4b8a376b,cbff327d,f725f978,f6129f28,49a1c9fe,b07bc2b2,78fcdf4a,96a6ee3a,70b9b943,98a89f3d) ,S(5701d52e,2cdb7b71,a9ed91e6,95396487,1b656bc7,271299b,62ce0a4a,78dc69ee,eb8e4539,be99cbf0,ad730fa5,fcf785b7,35e1f5ad,f5c16c72,85abfeee,4058ea1b) ,S(8210f0c4,4b2f54b0,62de4761,b7c62d87,42424b13,ca0448ca,ba999eab,73b26409,1c79890,e4149248,b9dcd496,1da563f1,517275ec,79949969,8c6b864f,c03f8050) ,S(64cb2793,4ee57641,9d52cd81,6144543b,e4319d16,fdde7a7e,2bd824c,113bc1b7,c3144c3a,518eaebb,51a55bba,d87aba0a,12d3add5,5a5e00c0,94a2e227,80f0f6b7) ,S(37eb1010,acb889,932d8536,b86648e7,c124a8f5,1005c0fd,ec40bdd3,6369c82a,1da5703f,b387312d,d5a337c2,2d3f63b7,33dcc994,38109c2c,4807fc45,c02a2717) ,S(84bbf980,b54d60e1,ccfacb7,e861aded,b4cd7bd1,a3f7baa0,9a1898fa,22144d2b,3820c4d2,7b545166,2515064c,dc9b4cf,813c2435,e84a4a67,ba47068a,e6e09045) ,S(29e74c02,6b43add6,939ae05b,dc0a5e0e,b7d05bc0,536e23f8,8fed55e0,6f93f1f7,f0f6fd9c,798732c2,1dd1c550,3cfbd56a,71b335d3,aaa22359,75fb0c89,9571186c) ,S(98f3530,1122a0d2,629e5adc,579acbf8,8c0aea34,c3450ea6,784c4ce5,ee9672f1,427b899e,74e0c5cc,c289304d,b9a874c5,1d401369,55dc5b03,e0713bb0,8c3ec3ac) ,S(16af2e5c,4c37b50f,5f2b6e94,341e365c,90548d68,2bd9af37,1d849126,ad2c6c6b,1dd1bef1,6077f6df,32054335,c81ff474,33b7c1c7,d6243dbf,6a2564b0,fb9d8502) ,S(56998d6,bd5b2da6,d452f951,5343a9bc,4ed64463,adc6b8df,6a3edd64,e75e1cbc,ccd52462,9dbda3a3,10f3beac,7b3d3bb2,f1bf3c50,bca242ba,224861c8,1f26760f) ,S(f1732044,ec59c52,86273115,3c53aee0,c7f1c4df,e6e55cb0,e7e37d62,c1e11ce9,16a547b9,a61a6c10,4df1d1a9,de99f54,b42e0ad1,104a6a30,e6e616c4,dcadb2a2) ,S(6e5fcc4d,2df77b2b,8d2f95dc,56ddb885,6030f9af,aa51d86e,20d4772a,854b8973,11939a24,26c1ad6f,90db151e,c5c9f036,3f0b6898,2464fe92,c33aeedc,77347660) ,S(74a3ff02,98c3cbde,ba066554,d6def895,3954af05,f0f72365,680b7b8,4c5e9fc8,23b5f011,e50dd2b6,9c5ad6b,b4dad524,9c6a8abd,f134c232,f40de18c,3c65206) ,S(12a40a59,169e806c,8e32deb6,7e64c615,77a3ca,5c56723d,ebc98ed3,11983bc1,9d97709a,9c644c8e,3fcda745,a70cf3be,c405d230,eedac78f,96792bce,a715c081) ,S(f25dcc0c,5ae3f442,7fc17acc,bf888557,82673050,c3594abf,cea7eec4,7a4662af,52a20297,bb9213cd,d1b4f1f3,4f6168aa,ec2d326e,d9aef5eb,5b497c39,e0642e0b) ,S(fe31ac7b,ee45ffd7,99941eb1,8d65cb2d,38618938,c6278e45,4b87e41b,3c7d0f90,a5f1be4b,e0373cea,c3137a8a,c5b5cab3,e1209c93,2d49b245,eb99a0c6,469c3e64) ,S(c0ff7403,2855c2c9,ba06c2fc,6c9a8fc5,29b4ebb8,be082951,475196b0,ca4d6711,2c53707e,540e0c03,27a10980,25e356a,81fa6a48,b1e41d78,b7fe5515,b022173f) ,S(5b23e392,b87bef43,a3c08956,e1930c10,cae049e,b6f041f9,1bf3de75,4a84f984,c905adbc,337b9e7d,78781dd5,deaa0590,18e20bc3,5114c842,72343879,7a37987e) ,S(2100a6c5,b6b96ad6,37e13430,8d92e2cd,97902da4,7a016ccb,63a20cef,e72ac25c,a1fdc3cf,93560ea3,8418c470,679c5389,7bcc12aa,dc87ee6c,3429c68f,690f7e11) ,S(d57874e,509198e9,ee6ac826,b101ab2d,fe952895,ab288184,55f2d85a,eb2c3387,1c7bd36b,cdb6debc,99228b,341abac2,94dfd768,c9e00e73,8aa58339,d226f940) ,S(ff91057a,e46817be,b3874656,42afecb2,a290d31d,f18c6da3,d6313565,99657c4d,a2bb1559,96ca6cbe,2a375c3e,510df603,69d0cd8,f66d6571,9f9866f8,c6e73675) ,S(7f20e461,ee306c4d,7db625b3,49906235,14aca551,21b7890f,244de5e5,84d18b7f,8cc69fd1,eeb89a9f,9e126be4,3983ed45,d88c22fc,89f47006,ecd57431,4eb5d1c5) ,S(7ca32320,75421226,257670e4,5f277f4d,32cc7b4d,53588423,317203cc,b787696d,1e940799,8f25b7da,8f1212ba,c1dceaae,ca7b1952,26655535,6a98769c,b3da15fd) ,S(bcb7060e,f2685623,9aac249b,f603ce7d,b5c253a2,c998e44c,4ed60db6,730d5450,e03df58e,6d279025,955a4f52,dfce586b,f427e376,ca72e09,36d80c31,5047f57) ,S(30387990,3157ac6,fed71113,a004284e,82fdfc7a,3e08c0ff,1ff5dbc5,dbdfc04c,7132084a,1230ecfb,200ded60,9a1666a5,2f574014,d29475e1,6a061330,fbe19e7f) ,S(c5b3aa24,1147d664,a0b80f33,5dfefed8,a8f7c1a8,c6258686,cb16e3c,c365a249,fb5143c6,5f8907b9,a44f10fd,27064fef,93ee588f,9e77a65b,1cf64e4f,956f5748) ,S(11d8bdb2,b750146d,d78d8c55,6e6ac45f,4d34f1ae,35332673,cbb46bdd,3d76d9a9,1ea28ad5,c92761b8,7df96987,6e5b3243,9fe97661,87b5978a,d7515288,f30a5970) ,S(d6db4c60,742914e,c9c7bfa0,7a716cc5,f5492aa8,5381f31d,f76d089d,a773814d,b0ca5fa3,bc5d1fa2,c62a657d,77215b49,82f72e89,b138552d,bdea8166,359b6a3d) ,S(d28a6123,3b4e073,f1242c4f,5292bf70,9e1ae15e,a654bae3,4239133c,4a8a86e8,89519c8,8c44b38e,ad5c2ace,52d01de1,d74ee0de,5365567,cf1b21b2,2ae8b95) ,S(ff32042b,6a943772,d6f5794a,43420218,2ed31ac2,447167ba,ec82d19b,86751337,16961368,e20f2550,383268c3,9fe62fe3,b5d356b1,da2e4231,8f9618e3,13655f0e) ,S(f2c6177,30a9870f,5999ed69,d34efac3,589baa96,9f660cf9,ac839eee,a10e374c,fbb2480e,b6f191c0,15ee3c58,bd950aa6,7bee7569,1681250e,502e1d76,b6ec9069) ,S(dca14b70,e5e33022,eb559d90,1cf3a533,4c40bd45,7a43df85,e87acd40,90342539,7d038e51,30f77ec7,efe84748,4145594f,87d613bb,85a95715,9d0cd377,91678d23) ,S(9cbb407d,acc7c2df,2d86a258,d5ab2b43,31a18bea,9480f5e3,7727aef7,644416cf,7ab9fb64,c5f54f6a,4e5529b6,eb7834ae,80283bcd,c3f6b24a,8a014d02,b3b80b57) ,S(4552c48f,2d96ef41,aaf27778,a7ab4945,e4f2a2fb,7e1564ee,c375e50e,3516f555,e63da54e,28b70a99,5f35a1ac,3a25e384,6efafcbe,4e8f73fe,d84e095f,126524ac) ,S(b4cfb90b,168dc850,36559181,3d2d084a,9866512,9396f76,879280f2,38e4af3f,cfca0080,37006c35,7fd89c5a,1d444d19,5fd72d4,17fee670,e7b743dd,57f71b00) ,S(8e264996,e4e8a858,a1e32c59,b0df640b,a096401c,e77be6ee,ccd228d9,67dada3f,c9f5a8bc,89322e56,838c6d8d,859b6012,6d0a40f2,8377aca6,b5b4dacd,44931d0e) ,S(34ea02ae,49a4dce2,5ec2dc07,c71e3400,390b3054,83b8f30a,81021eef,5761ed99,b4b6f9ea,c41bf9d6,c4bba143,4639fd57,b8735d27,6098e374,d9324319,3def4c1b) ,S(bd391dfd,8569db85,b567c36c,5e6c378c,c152ad9b,c23d1fd6,1af23e29,543a56c3,9bf167d2,77e6bca3,a8d3cce7,61a36abe,91fcad0d,8d6ce398,877d3748,f2f13bf) ,S(67b295aa,440c8807,95369b98,c67d1d5c,1b9265af,58541994,7353c0bc,47ea8483,c94a0287,f2983c42,14f3baca,a8c5c791,d4d88fb7,30eb5b3d,4309f5cb,c5706f23) ,S(755e0335,284ad31b,5afb5775,fa191486,32b29c84,f38cafce,1b0b3b4f,2d073a42,c4506c75,c8cc96d2,8e31766e,a8ed1cf,531f4f7c,73888831,65f825d2,2b74c47d) 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,S(596db19c,38d91452,ad238f05,453bb773,9883df63,a0b545e2,47e5947c,d9f52a2e,bcb35b45,b172aeff,9e4fc5d1,714d6743,46bb4073,6f571291,e6575d34,f8b0d929) ,S(4cfbd998,f9544921,e5f1658d,e3ee95c6,df85b3f9,309f7a85,f6e4d08b,7e535497,ccd54e2e,437e4aff,7fc2ef17,3bed5ce6,b7d6e34b,4b386f36,72140d72,ceba71e9) ,S(c3f056d2,357ffe13,4403cee,6dd5ba3a,a7d2d0d,91d83f25,cb2cee44,34e57f94,1c31cee1,595b3682,fd85840e,312a61e4,40cbbf68,55418b30,bd6b24ab,c3bbf7b) ,S(e272370b,82ffc486,53274eb8,898409c5,9338e024,202be5e7,e18b5ec5,7f824680,d2f4e6c,619f0d,71e38990,f4e52881,de27ee31,ff7ad9cb,11a7f735,80a546cb) ,S(81537bc4,6a5fe897,827aeba4,6e66d576,6cd05a35,cd3fe1cd,9c06a2d7,194be59f,6706c254,125be3c5,92ad55f,6fa6289,4298f23f,2f4f397f,3bc84f50,79bcb8ae) ,S(50e161e2,6bc89d2c,816030ad,45559a3b,49c8606c,b28b6307,6ac6a051,9226d2b2,98478bc6,3f8d6be9,2db02910,67e5e359,e865d046,a5dd853a,fccb7592,72985c67) ,S(76ce7272,fcff02f9,bfc355eb,24286fab,88ba08ad,b15e099,22724b84,315be56,88f98fe7,62e37fdb,b72c1526,59528cdc,fc4c4203,c465e772,38dc8618,78a5a14d) ,S(77935c1,3a7f5f47,13098101,6e10ec54,d5ca10eb,492d4025,365d5265,ef7e6ebb,3c15e7c9,cf230340,44444126,5e74456a,4f3b72dd,7aff0ac1,aa76c67b,ce77dd0a) ,S(b37c3ecf,5813b5a5,2f52fc4,42049653,991d9241,e8677d2a,f9779fda,43c7a255,4361c742,c070b356,387fef42,1a9cdf79,58dd47a0,b7c9add5,57fa425d,626a1786) ,S(90c64aa3,28d43534,271e2f37,3460d8af,d17f9585,516b909a,6a7bea2f,1b12d2c6,79394191,a37a451f,e439e538,5e876c2d,ac397f0e,dfe29114,d14b9363,b76823c4) ,S(a314f637,2362ef7c,c4bec6a7,9396c318,568d9f05,9b6ca38a,c5f56090,c33e5e5e,b3a401e4,f7741130,95179507,2ce3b0e,53d2f51,f2dcaa9,d289e25a,8de01519) ,S(15c25f4e,80a7de90,8c49fc7b,649afd24,4c5a4be4,dfc15b2f,70099f73,6ad003dd,4aa9fb98,39855fca,c9f8bb26,b6322c95,e5d7adae,5aca9bf6,de073949,eb364b86) ,S(445e6d34,90f4ce76,22b6713f,584065a5,e0998d47,1b7603a,2527ed85,5d67d7a0,ecf994bd,7ba618b7,6eaca0,b852e0eb,be7b7f86,70d028e3,f52d1b2,846ce8ea) ,S(def695be,1ded66c3,650e9918,e942e4c,bd420fab,3a4708c2,43ab4e3f,1bf2101b,63569e13,532bf299,a0cf8d0e,a4addffc,1e782a1e,98a2f7c0,e0b64f50,8dd0afc5) ,S(eb364f1b,89938b48,2d32271,551f9529,5013185e,3ee2b534,bf01a288,9a534a88,9e6091fa,b439d0,d96f6a9d,cb468573,881234c1,6bbf4c50,32a6c950,99e6e6c1) ,S(7efe80e6,5c0134b8,49b6c58c,7d4c54ac,873e43fd,1b47f9d2,1d33f9c8,ee26646b,5411262d,63357cc8,d8280243,41d1767f,c25a0972,4c8c7a7f,3ddf6701,d12478e7) ,S(5f412876,3774e9de,6f2f25d8,a1d98de9,edf959a8,884643a4,fa18ac7a,26d6308,d3f6eff0,e336d4f5,abe35a12,4c47ed4e,5dbbe6d8,7d563fb1,8ea89242,aa454411) ,S(c63e3b34,bafd384b,2b60328b,4aee3a28,c7b3ed30,8a7cde45,87aa6c75,6c49c2dd,724fbbfc,11d05623,a5cb449e,a2f9f65f,a3de167a,a811bfcb,6ab9c3d0,3b123ad7) ,S(cc92795e,a0be5e79,757a86b5,147429eb,ca7a7c7,d51a8d3c,93650178,4f6ba5b5,92053ab3,db369d61,3af1093f,50829c73,4618c1d3,610ebc57,420d2824,935ae2ff) ,S(ba73d310,b5170cd1,57bbe14,63bfe944,ce7cea80,1b1aedb2,da3db11d,f1c7ea5c,4114e55,15806ca6,323edc6b,f0b75a92,834c72ff,9579d1f2,27fdadd6,d773c577) ,S(6047bc6,fd3a1c7b,9a36036a,94139542,7d9432c0,f652259e,1d52d709,e5088b22,bb119bf4,5d8ac9bb,1a918e6b,95cdf23e,6e2ccbf0,171579f7,ecfc9126,6d236b8a) ,S(a0600a7c,484559cf,3da255c4,935d2d97,1628fe8a,e75b88bb,1f3c4eca,e68f78d5,a439ac58,42bc6ee8,be096973,d87598da,349929c6,92e37852,e57ac941,eedef402) ,S(bfdef77e,1efac235,c1c49f04,290f89aa,c2e4632c,85f40481,dfdf5c59,d479e2a,e6e451cf,d76433ab,1de85511,9abaa5c7,8e4499a5,fa48ad77,f098c825,206dc7fc) ,S(81ff778c,373975,fb041cf8,ce4bc337,e2c977f2,d6bb2c61,9122240b,8e21234,3fc02add,e92c9928,e94e0ad0,218d6204,d71ef295,4c32227d,96b30b5b,9a61f640) ,S(84c4653c,d1af54f3,fc59dab4,5bbaa470,48f8eb13,4afc8f5b,60a8974a,cbf03933,98ff808b,a4682139,68b73ecb,67fe0a32,85dace7a,19d300dd,bd517e3d,b04ddba9) ,S(9d7ed86a,69f39ecd,c448de07,55197029,f81ee886,7c9a61b9,62d13eb3,abce35ae,d9b27e39,41c6bd1d,87dab6e9,32e8ba57,1dcd2c58,67177ce8,e7ef0fdc,668fccd5) ,S(540b7fe1,ee263e6b,3610bb96,1071d817,b9cdd162,77aaf28,87e7e5fd,df72f5b5,6638015d,591305c1,7a598a44,ba6871cb,8d1d3628,3ea25c5c,846bab2b,cd910340) ,S(4799c5ec,f1fb2112,f479abab,217ed0dc,e936c6bd,14215eee,6bbbb34f,d811cbe0,abfdeb73,4ac738cf,f607cd93,de58c0a3,237201eb,da47a808,3bccaee6,da5c5515) ,S(70a58362,b360c280,626a8698,7e4f2aa1,abdc9f8,f0b8c216,bb88b0cc,133c2312,5e37daac,d2835f3,1d924659,e51858ab,68e3a874,947360eb,c520767f,ce4d46d0) ,S(f345a0ca,857102b6,e225dfc5,7ae1cbbb,dd5c2737,116adbd8,b3d1f74,7d132b01,16fcaf2d,f7cae2ec,ef25da7b,3d51afd2,8f5e9920,5c0d74f0,c1e7b360,17eb2fb8) ,S(c3f4282b,29f253d4,fae8deb7,941484e3,9d2555d3,f96889b4,551e7d8a,eb2a209d,fc562248,8a6e83f1,6bb1530d,2a35629d,b25c8280,2eea7057,d22d109d,4263ac1d) ,S(5542218f,606e7cf3,9cf646a1,3677b0ed,4ff61aac,1dcea3f5,da5dd4a7,d4727632,f1bce63e,a11d5176,f47e576f,66817f45,4b51840b,a79695e6,3a1a1cd6,fb6c07db) ,S(65e81ed2,7d6b839e,5c3829f9,24beda63,98264de8,b2223479,43881582,4d124b35,2a17e09c,e4dd6e6a,32d85d71,e6cc2378,b53b9356,ee5790f6,8fc3040c,e6b6179f) ,S(5066b022,e43a5f83,c4290064,9e2b611e,750a5ded,7c89b8f5,892126f1,e112edf3,381e92b3,e407c6c5,d1c0ab40,6fbe1a99,57643da9,a2118cb1,3b8c6243,9328d9e8) ,S(8df78ac5,c5ff1cc6,df1e1dfb,58ef889b,17886433,61bea73b,a805c3ae,a83e2373,dc668ddf,5b39eebb,7b692997,f22140c1,8347e14b,edb6d343,96017e09,d37ca4d3) ,S(426c1767,7d7b00ee,af8d7d30,1bb11cea,1cebfa58,fc54bf0f,de719937,fb484434,4fcfa5b9,ab7b71fd,560ecbfa,985db2f2,418465f7,cbf8acd8,fdd71af5,7f9519d8) ,S(4f7f0061,bb90e396,63f6aadf,70dd3312,f781b2a2,3867df3c,566e18f9,b4a511e1,1308473f,d8956b35,97d904c6,cf73c05c,fd7c075d,c83848b8,571e666d,dc44b3df) ,S(7393002d,d2e85925,3b23db69,6c140258,8272a847,d834982c,5b22b256,93685107,b61532fc,6706f7ad,78548e76,b334a836,c899a49c,46afa1f4,4579b5cd,27641528) ,S(c41dff65,e88e5c6f,fca3b0ab,6ae69bde,c4215194,cd7c57ca,fd9b38be,feab4e05,9a9ba27b,a0b7e217,d31340cb,acd8506,7f052d8b,f92a4be1,cf59fbe9,6241f0c9) ,S(f619dc9d,6dcc39d2,9155082c,2ed9bc60,99296a8a,982327f0,60fd6208,5765c518,87961d3e,2b850ffd,f080d5aa,cceb1912,120ddbc3,4e0ad8d7,96e74afc,aa4871fd) ,S(6becdd5d,f02a7bbc,d1cc811c,fb83901c,46aa8207,35e81c29,a8d4d4ea,3f5cf99a,a45f7dd1,8949f842,2905c7ee,836004a6,5bb106d2,fb623d68,c2690c14,f181e39d) ,S(cd2390,db1e7c53,f424a893,c2529660,69a8f151,6f60722a,524578e3,e5427196,b817ed1b,457633ab,a3439454,6ed410cd,8140b9d2,e7e679b6,3322eae5,f3466e90) 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,S(8852fd51,1e5f5e93,c6c3c7b8,4b0544af,cdb7d0b8,497d4bfc,90cb7322,28a77040,b0ea5bb9,c338a6de,7333b4cf,ac29f997,36c248,405facd2,6ce438f9,cb997a13) ,S(59105318,491ab266,2fb94506,532ed81b,74c8f82e,a13581ae,ef6c0c77,80696ad9,3417191f,bdcc1dd1,43323ff8,6e6051ee,921dcf69,9eda369a,afec66ff,a06097ec) ,S(c78bb701,8e96901d,3f13681e,ecc24df9,65b124b6,43f72904,ddf00ce8,bd28a127,ef07ce8,1b9c1cf1,26108dd5,f96ff86b,e0d49bdf,ad3d518b,1004b3c9,4c79bea0) ,S(9eb55ba5,2b5d11ae,3d419ede,5a5480b6,c2aee921,6f9aeb4a,96e51934,e8e4c11d,50094963,25b94022,2642ca89,1fb4697a,5e643e50,19670934,99937432,f020eaf) ,S(79ca2986,d40c7786,dc4d3e6f,71c33233,ad0b65fd,96822383,c11949f1,ab42f5e1,275db48a,fab1f0db,188e1298,4b391ce,6872e216,85c04c0f,3e62d42,d1e6d310) ,S(a2cf65b8,fe2a7abc,b78bcdf3,f25db18f,432ada89,1ce7d99f,faccefe8,e9673463,418e9be4,f6a1dce9,200823f0,5a6a0e31,7924a0f9,44c18b2f,1602a2fd,1ef13a72) ,S(7f6881f3,9f4684d1,3bf35c4b,c350b64b,28eb3c44,2adf05fb,c5e2c1e0,307fef19,20ac47a9,b954e805,db6fa20a,4e1a04f3,36c058f2,1946aff4,d4c24f63,6bd608eb) ,S(abf40dcf,72704e6c,65502d17,aa384bca,5834a802,62ec0de2,fd46ca2d,d9316ef,f605192b,a8c56b66,f3bdb35d,9c1df4d9,94662b41,85e8e6c2,9fde9d27,45039564) ,S(4fbb0d5d,ada948f6,2877c665,9cfe5f57,c6d5be5c,8cbb7bee,71cc575a,f4c92989,d2290911,45c718d5,243e1ef,92b8f7bc,2c77af95,f8666ce8,15900462,35d1c3dc) ,S(6c62710d,d0ce5eb9,5196e202,7c3c1d12,5a25f329,878b1f38,fa883146,b8ccffa4,c70ee1dc,174a6a4b,908b54d,69c94ec,5829bc8d,f6513c82,b0fc02ce,f566dde7) ,S(83ac175e,e220c800,a40adc87,df8450a3,963015a5,2c9e9497,602f930c,37af6c12,b7dd932,95601178,f6db7b5f,98046d7c,e42371ab,34e5f11,31f7cb31,59d37994) ,S(c823727a,348e275b,f52c18b1,43653c3f,8f0a5c0a,e8f48432,a8016486,ec3674b5,760237f6,2222cf21,fe1813da,4cfe9437,edca8286,cf3be63b,5bb05560,fa71235f) ,S(388b02ce,506784cf,2ec7e315,e765f126,23f764a,7d1ef836,fe360355,cb3f0517,ed0998cc,9069f336,c938b639,d6a74e8c,672a7d2a,2fe1dd1a,d7e18969,e7e57b20) ,S(517d4da9,e25f9eaf,7ab6efcd,cc00e6eb,7bfb975d,e8287b2b,d7d15914,4b7a981a,2ea7196b,a14b60c0,78444a20,2b67fedf,8fd119a3,7a39738b,17694cd4,c0dd712d) ,S(eac89275,54b0f71c,4ee80260,4945c5e5,578fdd50,ad68c478,2295670a,80432bee,dfe1ac53,dc9e18b7,1a930e73,cea36af2,8c8326eb,3615f858,fa1d3884,446f59a7) ,S(f77a0877,e7ffd2e2,cba9f0b2,c419e886,73711125,7cee4480,f6529851,6013ce29,fb245db7,29acfa2c,145011f4,42c9d480,5fcb0be8,b7f27dd9,9d532f6,aee2d57c) ,S(747d96af,94b3ae3,4cbcec25,fe8f4b74,e8d2077e,31ca2520,6d0d5613,3a49bd7e,b13d780b,8d322848,de5463af,3dc9c6fb,4cee70e0,da4731db,14916252,4b6d8d4f) ,S(9bf6ae06,6db68c50,4ef9b1cd,6d123efe,1d8608c5,3a1a2276,f1f44493,f8b5bf72,5b0080f7,694a756,f306714,aa9d8b3e,617b7c5e,84d862be,470df13d,e79c8994) 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,S(4225728f,ee2495d6,73f64d5a,cee2e372,2713a3b4,dbd2f098,d20415c9,3ab513e6,76c17939,461504e6,e1420d53,c5b07449,ce7f976a,e4de178e,69552755,75e92412) ,S(669c2815,b3357084,bf7bab89,63753b0b,ebbea33e,5b731ba7,5f969890,3a281eb6,23fcf486,e2839e2d,91fb08a9,11ed7361,81de7406,54c13306,575c576c,d0459c28) ,S(7b29749b,393869b0,d7f0977b,340b9e07,76a20ceb,ff6d8f8e,f4650348,11773665,a0d68cd,b6033ab6,a4c92113,c8f07110,aa5cf600,2335d2d5,2ca9b956,2874832b) ,S(6f096ed8,56f38c26,25200774,77ef7ade,19fb616e,30ed560a,ee5b4987,5f43a7db,54453b3d,1ffce3dc,b5e72ec9,3f15b57c,6725b271,d3fe8b7d,8f30ed00,35845b6d) ,S(1354de01,ef040d5c,681318c5,a6dfe7af,5c8eba0e,ab581674,acd5335c,e33c4bec,4002513f,ed215b53,c65686ad,8366cd7e,38711fd9,98d27750,bfce7e24,dda317b) ,S(5f8afb0b,3800c535,47cdf93d,61ae5c67,233c2525,17f99c38,8e97e7a9,1a90b561,7dad53b7,a64b7068,967fc0dc,e7178a43,a06e56f7,7aab1a57,7910d69c,23540671) 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,S(c631f4ec,f205b1b4,6bc0fce5,3680e6a7,27f9e64d,5ee3fe24,c37291a0,d3a69b53,f0de9e0,e4bea2a9,cc01a5d,2f9aad2,f5af7ab2,7c2ff98b,983dd2b6,38dced4c) ,S(9326d449,4fcb3049,8badc221,6d3a90c0,131d31ea,cbca74f7,2cf7da2c,bb6aa2b8,c3f268ba,4c9a9ab5,3f9edb88,74f2786c,4e4c065e,ab58487e,cd8101b,7132511a) ,S(538c52d4,8fa6c492,cf546349,675d6a2c,ba10b442,8827dfeb,69f0303b,1b7ac774,c1b1db4f,d6d50f3e,c7533ee8,cea0d47,883b57e6,dd4137c8,2132f846,3b81ebf9) ,S(5e58a25d,8bdb4576,d178fdb7,23158d26,508f8486,ad553727,907901d5,6e99a680,97c1f814,8880cd85,51c9f1e4,9ae58eb3,d1a01285,bfa8248,44bc794b,7d83ec62) ,S(1e9830ee,b75d6c6d,c70989d4,ccb85e62,34a1cf94,ef81b65a,49b25753,cb6c13c4,d0780a7f,9607e530,d80dc068,68b1cf8b,82d3047a,2977d204,65187ed3,13c94c6c) ,S(c5b441c2,f7e97a03,dd690cbc,ac605772,1524dce7,fb5068f3,f73d78ce,50fe0183,9bdd2242,e35008dd,4f907600,64eb3b29,427ee9b2,bbeeb548,62878688,a916e410) ,S(a5f56816,e9448d0a,aaa7593e,e3145678,3be74521,b129f13,f11a276e,d419492,8406662,65c275da,76ef289e,d36f8af6,6ead9be1,48cec081,7c21987e,9e8af9fc) ,S(c5e85955,44004f79,2260d553,25628858,ce50c95b,9362d868,90fdfd20,8d1184c4,6a5f02f1,c0f381f2,7fd21eb,928f03a,c8524dc5,9bfc1bca,d025a290,7cf939d1) ,S(d5dd810,9e691f5,8694c87b,59907ed5,ec18d37b,8554799c,1481ac78,825d2ac9,ffbaef54,fd35a5ab,a49f9946,a11e5ad9,2f29590c,20e28180,9f4be3e4,b156dbe0) ,S(ee5d42a2,c705bae5,a11d9d09,af3217d,2ec16588,64a60a56,d8e4a1cd,4313c61a,f08f0e08,89c015f5,3a2a74c3,3dd625da,b329181d,1d0f4fa0,14ec01e9,5d113d88) ,S(90409eee,78af819e,249f62ea,3b4d70a9,26557f8,731e50ed,532c0b30,4616d615,17aa7a7f,8af635c9,c4ea353c,56c89da9,70df599a,faec8916,ec9a6d82,cdf957f2) ,S(5f19aa1b,a6d6e3d6,9445e8cd,71c95e3f,a3ddad6c,ff0dcb4b,9e09aee5,65ba9e46,f82b3170,c2953397,a6cd29fc,9c87bcd9,76cbc7a3,5f953948,5a57a940,63c2e570) 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,S(6f019691,def39afb,103e524a,598bca92,3c99e44d,7dff4866,f76fb6c4,47e6b40b,a225b484,cda916f3,559e5782,3b519827,8bd7300a,c31dace1,7a797582,2a2e2a31) ,S(cb9a979f,c4e8d887,f03956da,9ac89637,579813b0,c3b27874,82961a54,e54c16a5,ff42bdc3,1a837d98,b7d37a38,db3c74ee,6109e868,d06b7c33,d5562dde,b11ddbf2) ,S(2ccee51c,9d63f3e8,99314da1,656cbb15,635928bd,309cde4b,69699860,c0e28736,dff9a128,adb8b4fb,7bcaa1eb,6bfb390f,226b2ae0,b72443a4,5982d559,91d379eb) ,S(a239538c,c5e0b53e,879f484f,7202a52b,d52d1cdb,ca7ae7d0,639850cd,b2c4f57c,6cc1f9c5,8998e347,2c6db0b8,6b1d9092,d3cd0c84,267bea8e,75a172f9,f4879dd5) ,S(e77796ac,c619974a,63476635,7bb3bf33,6ad1e87e,8496bac3,378db956,7beaee90,3eaa4b63,c9679050,59d8cf67,7b7095c,4064534,1c592ccd,ddb7626c,10586f0c) ,S(52c332cf,37646a2c,c1bf25cd,26a6131c,3b243688,9c44d804,d2762fae,618250c6,2279bab0,a19f78a9,43e695d4,53a0dc3c,f0312987,6ccbb70b,1d61eae1,e92729bb) ,S(d68826da,36e5f78c,bf728468,88bbe6ef,f6e55d34,f8b47a9c,8296e662,4ad9bbb3,88ffeb15,5f70c6ab,9b83f9e8,30e2f449,7e661dac,889803a6,d30a2ddb,11bfca5f) ,S(af92bd8a,2a5b0034,ea074d69,a1d7a517,808d3b61,58f5f7c2,d3fb08e4,eb825cf3,2fef9245,a4a3c837,d4b57ded,52009294,c077a801,8f633313,b6db2d4c,92c724b7) ,S(df86fa3f,63d95d73,98872011,c7545b3c,f5f27fc6,a821bff4,5d09afd1,bf76d895,a891e766,12953c4f,37a463c5,ce449574,b1906c63,c192ba4c,67f4f78e,d1e93a35) ,S(a049a35e,119e27f6,e272774e,f470ca50,9a1da9b,a4e5d781,6e64a13a,23383c24,4cb8e2eb,ccc82ca4,a2f82841,34eb3a05,f85a2335,a3b1b117,92886029,96fb3fd6) ,S(b3193cbb,f3c8f3b0,b47b1a0e,5689461a,8da801c2,4c8d51ab,fc2e67b,1d9f331,2032a290,3f0cf0ad,21b63de1,565170a3,edee470,a4dbbabe,5f3d459a,3827c7ff) ,S(ff3cd387,554fb3a,89142ff7,3e97fdd8,884964bb,2f457283,e45b79ae,ef1d692d,24475b62,c1ade1b0,ba36ad93,27916e19,637071c,22fb59c1,f2108fb8,d38ec5b2) ,S(c095d24c,42b058d,c2f77e2b,463a2c7f,1ddd1dae,dd6f6111,11ba78db,26763204,d2648519,61974d6c,cf66de22,1028943d,ceccb181,ae03cd38,fb5aec22,fae54326) ,S(5365a446,389f54dd,8279826c,e1e7df5d,b4a9699d,b8208efe,80d1eff,2d883ee,74625a49,b7856c1f,b157776c,cd79270a,2957862c,a437bfc8,75986264,401e714e) ,S(4c073085,e96134b7,75248412,c36b3b33,77afa275,24c83369,a2477b8c,9851f15e,fed40d9f,a44f64b1,59c290e1,63d1add6,92bd2782,51de71db,e302cbfa,67e508aa) ,S(71edf152,ab95a066,2b7e5190,8af75f38,d03d27b0,3a3b6607,4f472b7,706a3114,c3e6f145,dad44a3d,5cf056d6,2c608b4c,840608bb,aa15a101,c9bd3cca,e511741d) ,S(1b7d41a9,3cba67ad,c145962e,7b2c6353,bfbc8eed,34eb4c27,bfc181d3,1ac0a802,b165e7e4,23c5d880,1bc3bd1,ee0c6778,50986b35,9dbad06e,aabb2f57,dbe553bf) ,S(ce997626,cb41ab98,58f591ca,c89f7a73,bc1df836,716ee74c,45c4c781,eef4ccc9,be76f81f,a8e4b053,f63be23a,5e72ad6b,7aa359aa,e9407b60,98bdcadf,e367b167) ,S(5b0cfa70,aeccd544,cd634d10,a2bcccdc,33e4525a,54259ba9,92c40100,698bbf2f,ec50e655,163994b6,4881369f,b3aab550,65df1a5b,dc6037a7,7c01e56,904660d2) ,S(a03873b9,695ee82a,42b72a90,f0cdfc68,dbedbd2e,a50d5ff6,e120d811,ce8d5097,5947c8e3,56e64f71,b36fc1f7,7ecfc7f,a31c0f0b,cbb05102,775648bc,f2435758) ,S(d6b91cc6,6dd31e59,f04c6e58,bd7448a3,fac62753,68579214,11a8b42c,66084ed1,fec7fa6d,778c0b63,e7dfd72f,ef044da0,903ccfc7,1786f0b1,85edd004,f691a0f2) ,S(896a1313,e0a96d35,9fd42841,7790baef,a40647cc,f56264a,ac3b72df,687b5692,831d4b47,52f5fcd3,4942ca26,95dc86d8,4fe49c73,7c2bd46a,f892eef7,304117e6) ,S(779e7400,8e564167,56795a4f,9d2021b7,94aa9689,eaa37780,8e3a6061,b5bdc04d,739ea3a9,4f38be31,df57c052,362d1872,333d2777,c6704c2,e69271d2,9f78b123) ,S(f20988a9,3a3273a5,a015866a,c4de930e,507b5b48,cc5ba52f,a2a71e9c,185e72a5,6c861907,8fadd612,c0535163,dfa4cf39,648b59d6,4b056bb0,4e06695b,3b51213a) ,S(7e8520e2,3151c78f,9f48bd10,5aff4087,dd90f9c4,2ac33e24,19499ab6,8e5b21aa,995827b,43c276dd,61403388,27b2fb9d,9fbb46ec,af10b65a,a8025971,608f38c9) ,S(98f0e4b0,9e72ec0f,d80ce3ad,eab29913,fe84fa49,1786bd79,7f6832cd,7ed4dc6a,58c42bdd,7ca43579,b45df8f,b2a6db3d,41f75a3f,89dfab0e,e000383,c9e04a54) ,S(31cf38d3,dec1162e,e75eeac6,6827aad,22fa3ee9,abfda002,b6956600,6fe596ec,ceeb4b04,fc6c31e7,7a6260ca,bdf92569,92841221,d60ca74e,81309472,8fff4442) ,S(60766d5b,50cc4d46,a1234c92,1baeec1d,29900e23,4493f174,2f06ada3,ed9dfbea,13debdc8,9795f421,6f796a53,74b87aaa,bca4f73e,fda2ecf,7d151870,179c44a4) ,S(1b0ebbaa,35e8ecb5,a76d9c30,ab88fa10,b211ce3,e7c2b428,117645b6,881c7895,a312adef,e1c4a34c,d9f75d10,bb2ceb29,79184181,bb955439,e317cde4,202b2f83) ,S(b3129f71,c3438602,c9c24ee3,2f997341,26dbd76c,60cf7713,200ffb68,e486fc94,bd4beeb5,70966285,6a15002e,a25046cf,996a1cc7,9a570549,467ac179,b4f145f9) ,S(2925ca17,662f0905,3927d40f,f2fdee1f,66cc5c13,c3587e78,fe48effc,40cc075f,6d37757e,64f0438d,7bfb3658,5df58dbe,a8ab8cdd,89871670,dbe221b7,4c416185) ,S(8d55b85e,fce6bd0f,ff8906d1,6497d35e,4b69e701,da7845f2,aec1a049,39c9ec45,435416dd,9fd01388,b717ba9a,df574456,785cc0fa,c115dc04,8a242270,4a3c77dd) ,S(a660a9bd,b419e19b,16823b5e,dc3fcdde,f1021b71,4debd17a,9a0619a3,aabc23c9,ef6d4bbc,e963bb1c,2edffa5c,ef70e330,bddccb4b,3b23cc52,d5b4a689,e0c76c32) ,S(8896427f,c92bdbfd,59699ec2,222b4bbf,2198e160,94945c77,1f207bbe,4cdd6b0b,bc6081fa,abd2df26,b087acbd,a2c67c63,2eb1a8dd,6fae2454,6f3fa747,be421ff1) ,S(47e5d9b2,3f429484,61ee9f38,2f14babb,f93e318f,32d67063,ed20e917,9894e993,bd17f8b5,6084d3f6,62facae,24e93e3e,29205f21,68903ade,4f7476a5,ba70e8b1) ,S(ff352870,69bf1131,6f530ef3,b32a487b,3f11e6e,f8518c15,b1202a18,4e6d5487,8920338,ccf36f98,4afde38e,1a74528e,86fddfc7,8d7a6964,cad4286f,231462b6) 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,S(aaa18fe1,25e781a8,901ac351,38d2bffa,83cf7c3c,99a4c7d8,54b30c70,c9483e8,6a8f9e1e,a40f6383,6008a0c3,596f7644,c044bf53,9700a142,ec5e3c97,c075b03c) ,S(d473950a,8465711f,71a6f1f0,22f4bfcc,1c16ba81,4bf73c2c,1eca244a,da4999f1,6eccf9c8,aafb09df,46ca0d36,ee9028dd,1df62bdc,6ade77b8,a5d410d1,a69bc775) ,S(d7e2b17c,f8e1895c,cf9fb163,b56f4be8,ad99133f,f00f2ce8,8ce911d3,3b8e36cc,b6557693,ed9371ce,69bf397b,56c0b566,21d38958,ebdc0b96,ca488570,1561e6bc) ,S(3f1e73f2,a2192809,acaecea1,71d175af,683e796,e1337db2,11b6b34,8ba924f0,a593bd94,96308bb7,76b63703,bc11e30a,c5f01c17,c8b9748f,3b4c8015,56f52c3f) ,S(4cbb68b4,27899c92,1c0d969c,94341d8d,161f3b8b,3fe4cfca,2b583a63,eb383dd2,6b3c29d4,97728ac7,b45cf7ce,ea618789,95935bea,bd146e1,6c756f61,4698b6cb) ,S(e41b826b,52ff9bea,354af41e,3004b7b9,edd01e13,8cbd466c,ba4cbab8,d63bb4e0,75d5b642,47388aa1,51d4d8d5,2568a804,fcf66ba2,42b3f56b,dee0350d,ecc527ed) ,S(d508dd5b,ec38f795,88bf2d9b,6bcc9f8,aa96689e,91c1381b,9f8db311,94588028,9b144547,1a2ee559,6584c927,2d779fa3,123a760d,9faeabfa,1e39d3b5,ddac2595) ,S(5276f127,3bad7149,ee5ff022,2769dd6e,973018e2,a9948070,fdc82148,ac637de0,73f778c2,caca737f,acd3d877,14e24d83,964dd47c,f22915e6,212bfb09,8e804e21) ,S(2e9ebbb5,9d108d21,71d28c27,32af659d,b534cd10,c5457cea,3fcef018,4d7761a,229d20ba,cbf0104f,b385621f,dfe386df,4f40c287,7d956046,60eb3923,46937bff) ,S(ad819539,5b94bb1f,4e60ab85,932b24cf,2c79c20b,79a972bd,db1e4201,c49f1d1f,9226c45f,4d161a1a,c5c3c0ba,a0536def,3c6052a4,ec22dd24,cc803a37,b5d791a1) ,S(f5d4baf3,93ee5acd,944b2057,78cae170,8a622f30,68d3147b,62bef05a,88fee96f,9a187396,9eeba528,9f5fca32,6bbb922,2eeff5f6,6d205a0c,78b77dea,ee17d1db) ,S(1a0f5e1c,b2fb5d01,fbcbfddc,da83693e,9619ea60,1669c728,7710733a,e6ca778c,3074e8d1,61da2d34,38be57cc,fc437742,533e415e,5f0c888b,834a2fe5,5d4fd6bf) ,S(a78f6f7a,110cd16f,99fbe16e,9be52782,248518d8,e621f478,2167887,f81cdae4,e3f78e8d,507f9af8,11653ab8,5f2286dc,db34d9dc,8106e9f0,57610267,411f02a0) ,S(c53e4243,b26ebe40,a1abffdf,3c42129c,47e92cb7,32bd66c0,3d4a4290,c68b1c25,bd4f96b5,b5801b82,300b2132,2c39fd2c,65b2d084,e657ba2d,7db5df15,ab960e34) ,S(a3a1ddc8,56957468,2e9b8a57,50bbc738,f72dc60a,1c09c95e,a6559b2a,736535e4,94887a0f,a4381d9e,dcc4faf5,1525ce98,fc43116d,29f68c99,236e4940,6842a741) ,S(8160ee7f,738f54a0,698806b8,35ed4bca,113bb568,b23fd331,ef5f1cc2,80b6230b,382ff30b,f13f1e28,95a38af3,13fcd099,249b195c,96ac42a6,6a929fc7,a907b17b) ,S(68552ddc,6b219554,dbabd276,e0f2a5d9,33610bcc,776bc40d,7efdc1c6,1b992e35,eee09352,c82dec92,b0ae8d8c,d6918ac6,df620dec,86a0e4ac,abfe8025,52a0ab5e) ,S(919fef57,f308255e,1fa802cb,5acab880,c1810c62,c79a4ecf,c2251a2c,cc02ef51,cb38c163,8f7890f2,d61a980f,ed712ca8,97296366,7927ff7,39de824d,207ab566) ,S(d7e493e2,e2c33635,ee8d22f3,76fa8de9,31ed4eb0,9771746,f48ba201,307e04d1,ff7e6d72,f712f2be,2bfffb43,2764f677,62917509,3cf6bfe5,eb5cb7ce,85c1a8b4) ,S(6b642a8d,f4131ddf,7f31dc9f,c26b96c9,286e1f80,de2af96d,52e383d1,ffa73a41,1e55e667,5f0ee13e,76818c02,ce424d8f,48cbc930,b25dbb85,363019c5,fc29979c) ,S(7ade4aa8,1df8c53d,1e64655f,bfe0ad88,4057e0b2,1c88bb2b,4c8d5f19,34794191,cb0e9802,fbf1027f,dd8d2167,f4f4680c,f9e18f4c,3bc3310a,c4014745,530a06fa) ,S(6d578cb3,1ed19dc,812fd360,a367996b,91a7ba42,7d2f74c3,e2a1721d,72e1c017,4ac9ad2e,aab987ed,dc994b74,733fc710,19301e1,f691999a,5161cb15,ba11e9b4) ,S(df95b5f7,7bb79814,21892d72,743abe4e,828a7544,f9f0e774,b1f5ada7,a054978c,4ccd011f,a966604b,32f70bd6,1a3c1515,c6d1b261,a3ce5c59,7078cc9d,f723b32) ,S(d7392d17,1cf72e1e,ddea0be,a242edf2,c418e9eb,7dcbe1b3,aa07ae7f,a11ef08c,4b696f78,20a9ac8d,a5f52c8e,9d1a39c,bbb3d3d9,fb5b38c8,1b46bcfc,90e869ef) ,S(f01f2aa9,82842315,98f414ae,f87c9d7b,6eaf21be,c4dddea1,3967677f,5d2a1032,7c3be753,da5485bf,13a4cd72,a9e3fbe2,28fc6a22,c502b19d,1b6f7d18,149e2b3e) ,S(cee8f811,4b1829ab,a47e9b5a,54de7cba,1f6edfe,624f30e2,ec4979f8,3145242,4b01f7b4,cebb1125,20bb0ab2,7013af9d,11d19c4,14b0c29f,d142c7d,5b903a09) ,S(f4215bb,973b5586,ec051388,203b1c99,cf69b555,6b1591d2,fc711842,759e9832,5d8a5ce3,ece7c011,df3d414d,e62ecd4,2d716c73,cab02e29,621307e0,658e6fe5) ,S(e39ecc23,90c9464c,32b08759,9a44586a,da09af95,ba8a3b30,2cb015d6,4a49b18a,bd7957c6,e1feb061,f5535231,4f5c5e5e,c8245f28,4638f390,d079cffe,bd2eea7a) ,S(9e6bbe6c,402e4cbf,e298e789,458fa9a6,68cfd407,3efb3d25,4699278,760589,989bf3f,9912b242,419c848c,f82c3fb6,8690ab05,bc23372f,eb9a850f,b4dd44ba) ,S(67504bbf,57824cd9,8a3bd82d,34fcb59,3d20590c,a90b5652,c4ea4695,1f48905d,93ebbf6d,3678478f,56ae5a54,cde812f7,d8d40928,21b5e82,71669dd3,f0b263d3) ,S(4e5bee50,503a28c0,9252b9bc,dd28af66,cecae127,2128e88e,fc431373,7324657d,d6891df5,3a4cdf2a,d7ab610b,817b0f60,c2502442,2e40269,a7da80dd,2672e0f3) ,S(7481d5a5,bef3d397,533e01b3,640b0809,fd6ff946,a1e5481f,b90f0b3d,dd05c21,21ee7275,9c217d19,3999df2b,e3cddff6,fe59f26a,e570e0ae,58868441,f37e342b) ,S(778dff4f,dd32f251,6defcd94,188f2440,26b9f789,ff4eefd5,84b2c15e,2bc61d62,996a2edc,f43e10d6,93cc2d00,c6f4506f,45be1dc5,c762fe20,3dce124e,34e320e0) ,S(cf531271,3d65d471,929f6108,12db63ac,b1c52203,eb879ca4,a8ee9f62,774580,38e28f4c,881391e0,55fa7148,2c92c097,c842dd,74a58d6b,5753d6e1,2f773b19) ,S(99702d01,9420286e,723625b5,62c8152a,2dd5f1a,eff84437,8a182cf4,25582031,8c4af2b2,654f1631,82d08bd6,e7f8b6ca,d5365b9e,d869fd23,e5a3c4d4,7e5990c) ,S(68614c88,6b59c198,c49245c1,e1232cb0,b4bcce31,e0a2aa15,9fb2331d,ff1dce66,49c870bc,7ac78e22,b635c2b9,6f29e641,3b29c6ec,8ec8b3b7,8fa6597c,90180c7c) 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,S(d24ad71e,81de43d5,7096e101,6bd4d99a,46e52e56,782d99ee,838217a0,dfea0f5b,ae574f68,e07cead9,f214976,67a18c2f,fbbcbddf,2bfb6c95,3b7ba673,7d08903b) ,S(ac96889a,f0b46b7,6896b763,8e1a13f3,dd24459e,8601f892,c3367c7d,8b52931a,b68a8631,8672c378,d99b0b20,44b06190,876ab100,eadb12e6,c16c2ba7,c1ee2381) ,S(36b4da52,4f4ad5da,d7396445,1e79bd5c,20973df0,efa82bb2,da4bf68c,55afeeb7,5cb7598b,576f0db4,db1093c5,e6c9723c,f493bb91,450a0017,9f79c8e9,92dd6136) ,S(98c7bc3a,7054f928,d062ae65,b4140dd6,293f2fb6,cd16fbba,e00d39d0,b11befd2,82d134ac,3e614e4e,62b1b475,bbb5fd80,a5e6d3e4,e4572dc5,7cb666c9,a06131da) ,S(95bb18cd,991cdf72,1c627d62,aee4655e,aaed0b6a,b1e64537,fa89a0ac,f60b4a52,c37e37ee,5b87a5a5,e61824a3,ea519f03,dc3b0a77,f755485,d337ac79,f1f9e8c9) ,S(41e45ca2,b88a4679,6df9106b,c8b53180,81674c34,9646545,e5ad9b6d,e5f6cdc6,151ba666,b0fdb7a7,18110f62,83e3cb8f,8e40fb8b,fa1a1854,75958a3b,ec10d197) ,S(32d15f16,dda923d5,c2f1bf5c,9c003b33,b77d2450,95e5ad31,2ec62956,ae092805,58d64c72,96ba6976,d61774f,f37a0d1,6316cd19,3ac0d930,bdcf4924,cd904095) ,S(41c4e029,817de516,8dc04b2a,9bde3850,7ae48602,dab08db0,3272c694,6cf099eb,303738a8,7b888601,2f9e2053,5bb8b610,92f6222e,96968afb,98940d85,98181458) ,S(28b8ccf,b14a86a1,84fc3c3c,a6a7dbd8,763415,91a67d8b,4109f026,1dd964c5,899f98fd,5e0c59be,69150d8c,5a917d6e,864fa15c,63072769,f75f6353,8cb276e6) ,S(f2776367,762d6468,c9cc0e38,d3921813,16dd394c,eaeea519,786b4353,a5044586,1a873421,1b170183,a117e420,c41d2725,84acf219,a415778a,4eb0c34b,bee9a68c) ,S(7a1a5f53,6e96ee57,e10b1337,6bb1e895,d0703c6,5adfa4bd,f24937da,98bd7144,860921d5,67fbdd1f,11aa3ced,103453af,8c3f5037,b92ff10b,ee70ddc,e4323206) ,S(d82e79dc,5d6de6ff,8863e039,60401bd1,610500f1,57fd2b41,f20689d8,889c3f76,f1947dc2,ca625df3,af5ec97d,32e62c09,2139d108,948795ba,5cb164b9,351bbf34) ,S(6a2e184c,23ee235f,93f036c4,3875db01,22416a6d,26ef54bd,85a2b465,defd0351,6c44297d,724eb2d3,2f58a197,2f52a7ad,ee49d30f,c8f8424d,7f26c6e1,73dc6868) ,S(ea0d5281,bd1417c7,2dbedbd4,dff37c49,bf143417,d2a40dc2,573b4b3b,2ccddcde,c7a35ef7,685faf18,c5a4cfcb,2eca27b7,46b21d65,ed71aae9,15185cc2,6d2b54ee) ,S(d5432c9f,8ed0b4a4,c3e42dd8,28098f13,11d2cdf3,94672331,51fddbf2,a6030974,1e047ebb,8cc01a43,2ee6ea04,578513aa,17ad2bef,7fc7653e,936b2d22,bf8f6c3) ,S(c99ee053,655c9d53,1fdd2298,3cc03756,299f47bb,5e1d0a4,d7b861fa,c3b5e332,61c5187e,4e12f8fc,617a5fd8,746f28c3,368b6b19,1189172d,8c56e2f4,679f6b7a) ,S(f41ee431,170be2d7,fd488c3f,5f21f3f3,aae5e501,1a3c4ebe,d0f6db8f,63e11e55,f767b289,118391c4,4d27c1e0,76b7c70d,110cb938,e9c5c62f,1af200ad,7e9976cc) ,S(505a65a4,29388bcd,55561f5e,fb3090b2,2d553bac,2f8cee97,6c0685da,40006e41,c72c9e86,6b4de925,3d463d7,e7bcf7d3,d6e7c351,1fe6c4b4,7fc436f6,d793e0ae) ,S(ca34be0d,48bc2931,cabe71d7,9cd2bc23,ffa928a,5d532d67,f3665acd,375dc01e,263008ca,4dcf002f,8fdd580a,65701694,bf4530e8,baa0438d,b77ec246,75b4db4c) ,S(d52c25e,9a76600,b16dfa93,cf9c2df3,38c806a7,d8cff18a,1d262662,5fed6d7,80309810,6055c3a4,d5d1e5ac,945aa815,bb8ca3ed,10b5d54f,156e4336,39c4ac77) ,S(83e43bbe,62e39426,a0a74ef3,831cb4d2,776d7ea3,d5a2d57a,8280bae6,ae0bd8d7,a1c2c1b4,ea1140c8,cb4ec2a6,98a3f727,666eaf81,1ae9b89a,9e09db39,d1a257d2) ,S(12326a97,ad8dbe89,3181d76c,6d7507e2,74d62cca,1f0a3517,30e9ddd7,198de84f,79e7823e,7cfa4df0,bb31e9dc,ac415297,edc6e061,4fca2f18,1ac7fd46,d27fff48) ,S(1ad3375e,c82aa917,88bd787c,37fef8a0,2071509e,aef62e8a,dd5c5e4c,b096cea4,f9f9f10e,efc1fa79,454c6d55,b894d65b,ff5c445b,f4e9e46b,8c82a4c2,a94d5a71) ,S(8e8bf9c3,a752258c,278bcf19,7aeebae6,fcc198f9,2310b13d,d114c1a7,d10fd2c9,e2f41d5,b7d94378,5f61f572,763e6e88,df7b321e,9baf0445,482d9f22,f1160195) ,S(c44cd33a,144e2926,b7ebfb93,d7d9ab56,3888f6d2,694efbbf,a5665e10,f6e0ff7,c2d4afed,f77c22d2,88f9cf38,a057df90,baae8ca3,1e074d11,bb8f89f4,e9e1bf4b) ,S(b960f0cc,bd7d3431,4138accd,aadc2efa,d5b60071,7c69f1c5,92900a40,ea68b24a,e0cbda14,801794eb,19401935,3f8ab80a,f525b8eb,2b64e5ee,62afaa5a,da4680b1) ,S(f7104560,8fe120fe,5d036260,5bc3de58,76e24b6,20684413,a440cf56,6520559b,2e208f0f,fea3f78a,9a283f9a,6b601ce,db4df4b,b2fda7b6,306dc8b7,3d514f35) ,S(83a31aa2,cb10fc14,ca8cb2cd,b21cc163,41cc9862,67a5f1cb,75f3f90e,1a92c59c,be18918,400a6e32,b4fa3469,ea6e3613,251ceabb,29cbbfaf,2c16af07,fc5413ac) ,S(3d7b800f,8802e521,341f83a5,efdb355a,b60669d0,adc15531,72c62097,8106f6ab,f9b179a3,aae98427,e02d4f00,89b3cee7,250e30e5,ed72d59c,198d5ae7,1d639e72) ,S(7bef4e27,9064400c,48d4f27a,a754deaf,8af74b10,d5dfc497,98c38216,803f50e8,bab0d71f,d02c67e6,b274693f,6a4f402f,831aa4a3,5fd83014,fb07c5c2,e62d561d) ,S(e6b2c83f,2a6ea201,f56a024c,482a8076,2f2053b4,2e4d2901,4a5178d2,3361bcc,75d1f7b5,209cafe4,f98e63ac,53052a40,487b3390,e4ab73eb,ac63acb5,cc3dc88c) ,S(eb4f3b95,f12c16a8,e5e13446,d9b8ca7e,92c56bdf,565aa4f9,bc1c47af,914fd145,e3776908,e3f3228b,ba0c0523,7eaf1963,1835797b,ffd7eff5,61b30fb3,9fcd6307) ,S(e2926c0a,858b9732,82c1b34b,4c4ba4b0,3099797d,d29c5fb7,4447f28d,ff962e54,2730f3b,e59e862b,37ac50,e5375d08,920cb62,b87ee8d2,f5ec9975,886359e2) ,S(8bf4efd6,c11d7251,b06a5e08,99ff2e80,349f8022,387f3200,6d9de060,bfbf3f68,5514395,457848e,a79ba6c4,39a7c151,b497751a,a4a1784f,114686e,e351afb) ,S(4ea97c1b,920d2ec5,3c2182ce,d6f7e1f3,df49e673,1a14ecd7,d67aba0f,fd077c78,5e958afc,d3894757,e0aa89ed,ba26e035,f06e4b11,da13675e,29d382c7,b21fa9e) ,S(1b12e81,3c7c19be,18576f93,69d938f4,bc81bbfd,7e9eb443,cf2b9ef2,b8e2b3ee,47220a1f,718c36af,8eb8a9e7,ecee3899,ddc49127,91421438,8760d6d1,699a5ad1) ,S(7c6c144d,4f839904,ba40fba8,b739913,54f40bf0,f5810329,c4e3b961,ee6a101d,6eebb976,3ceae5f4,f1ef2473,a50b795b,a6375c72,df67d15,f310b5ca,9706b5eb) ,S(ec637ec6,bea71803,2bae7631,9227ae58,9581d3a7,131323ec,35f0d9fa,27a3e285,c12b830f,f273fe72,4f3bfdef,4279ce4a,8ae6d0a6,de5cbad2,b0a7b4ab,643c79db) ,S(33c8d6fc,d2b37103,2426910,6b9adb76,6c76f788,9627a9,6807572,e0af0f84,b3f01db0,7ed82f45,252d494c,af735e6d,3934ff78,c89c57e6,6c42a663,e5d6a792) ,S(35ee32e5,f7204f0d,d48b1a80,cea0a418,1d71205e,c373827b,2afc25eb,e3ab7e20,d57bc815,684adacc,756291c6,87d0eab1,63067976,a7c3a2a1,98ef1d8e,bad12935) ,S(97362395,200d807e,623826e8,3bdfa37b,e98793fd,6d7057f6,370720b7,5089a6b0,c908e9de,cd1d54a,172973b9,1706fc6c,c3367d75,2216c2d8,1085dffa,5627f06b) ,S(bd37e01,eb944b32,b379b195,16256ad7,4061760e,4eb44361,5e8e5fd4,34eae9a,dadb545e,2a613e54,6067cb6c,179fbdf6,d94b7b8b,c799adef,391b2957,2b93f57) 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,S(61b3a7a0,53c477b9,e03d0a96,8ba38de0,b02e42df,162a13fe,8ad538c2,840eed06,94c07520,fa19457e,8d98fdbd,d9a9bf93,57642cd8,1b48fa58,b4b14a89,cb6142ce) ,S(cbd26d0e,a00f7dd,4b0b26ba,7358b2c7,587e233c,3a13c86a,d5022ecf,c865e4ba,50e832c9,d84ff55b,7ba79035,559bc889,53700622,59dec3cd,8b3eda3f,1f2b6e67) ,S(17a6f57e,d3d729d,c5ec018e,1b69394b,1ed78e59,6c7a5e31,bfe5dc43,f9c67e56,34f16cdb,c23e46e6,bda5db2,7538d7e1,f66751de,3eb05543,96c66a54,36bdfe9b) ,S(eaeb62d,93fa13e1,ff9d9a4,9eda40ce,dd6006e5,ced0e8b8,c02f7ab9,98f06f31,7e225365,b4b39204,b01c8890,4476c141,1c166f75,1726718,8ad917c4,9a719ad3) ,S(d09999b6,c35d5d71,55605a17,e7f82d3c,dd8d68ce,9be252e6,99493031,a39c7487,9165e761,8dfec3d7,cf733fcc,e548f672,362637aa,8687f47c,b1eb5c18,a780b061) ,S(2b4cf8d,7fb166d8,a6931bce,e67f580,870c61c7,635632a0,71166fc7,4a11c693,7974e2d5,164771d5,2e7a121e,2b015565,b3a874d,d6313721,ec69d3aa,b44d473e) ,S(d5c0045f,a411cdea,470d85a6,66aafa44,49ed682f,a1903c5b,c9594d19,5cbebea6,ffeebc77,5b24e736,8a8b46a3,64837466,85df5c8c,b40bf2b2,291f370e,94c6eca4) ,S(1eed08dd,d9569712,6c0a4039,c6aa5ae5,ab4aabe2,a88142c3,b9aa763c,632b5e38,d180547e,c4640035,ca86d925,10a70a64,5dcbf2b5,d3add4b0,3f6d0fba,5f4c2f8a) ,S(9591b04e,3de43104,3a6982e1,29a2e79f,f525888,846689f0,44e50b18,ce14413e,cc4cc696,73279c51,4aa4fd63,474050b1,930e627e,a1bd9d55,867d700e,fccf8155) ,S(690a17c1,b2dc7ff,520aecaa,380b19d6,d4a28669,83dc5df5,8ab2bfb7,6c7b0600,bdd8a858,e2d989ca,79fbfd46,60ffdc0b,e0231562,711b13d3,47cfd37b,7a53d4d) ,S(800a632a,aca6b505,f9fddc22,14efe53e,4e7ad2a1,a6c07d90,27d8109d,893851ab,bf242683,e0c1a24c,9220c6ab,deae8baa,12c6203c,a0080856,bc5e5ac6,4c3f3261) ,S(6dceb824,c48159d8,57a92334,4c72b4e5,cf2005c5,6fadedaf,5a8b780d,3ceeeab7,e6b961f7,6162ab6a,d44f3fb4,5aefc843,bf0d714a,1a50d13c,68036f42,30a1ad10) ,S(3ef5eff1,2b76432c,4bdfd1f8,23bdfdee,f60b5d0f,5d0b4051,2a3e22bb,665f2b0,8741e43e,9f78066e,d57d317b,d50252fb,11d8d235,3c2c9d57,76191c21,8798b0a9) ,S(4ce8d33f,a53f2e1d,aa696e9a,2de694df,2192db5f,8e6fe88e,b5d51340,83791c17,a023ff40,69587bb9,49ebb15a,d047f141,9985b521,ae915f54,bebc6dbf,5320558f) ,S(da030efd,a3f6363,926abcd1,182f183c,43c4a6d8,8bcb0519,3d137827,6dcd3fbe,c14f27d3,2251248e,3c4b8613,481e7c48,f1493b6e,5c0716c7,8d5e3b97,876ccf3a) ,S(65c12034,87b729bc,3709759d,beabdd79,ee7f50d7,ed2cedfe,f2c2b7e9,97192f40,f440d69e,d59adfbe,e087ef70,9b75b95d,13ac0e06,20683d3c,6d49762,ddf68a01) ,S(82c052fd,dbd6aceb,1f429f21,eed34d44,f915e949,7190aa6a,d487bd6e,68d91c20,90dfd944,c7c20ec4,4ce35d2d,4036eb97,894f5b93,6bef62a0,f2f65082,b0f7678d) ,S(43e2f20e,cab47065,e71abd8b,aa511163,e17e3efd,3e17d790,ba924de5,ab402255,6b1ff657,e37b65e0,bf2c5e60,47e36c8a,2b7ba965,79bdc711,c3ae5935,d2c47bed) 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,S(3a9635b0,b82585d2,37068f72,76291c4f,cd3d211f,80fa7256,58e28dfe,920e3e93,a1711c74,ba4e1a1f,f0a9b6d2,12c8b995,7b6c8c0f,f71da246,154f13f4,719f0713) ,S(ce6dc56e,6f5c496,71a900c1,ae531e3a,a8246877,98044497,fc543013,2572bff8,1af98ef7,3703f8a7,6fc88e9e,c9134aa8,a9e24326,314bf4d8,2a0c85ed,af291f8) ,S(a945a79f,1627e79c,9ce1cc5b,79ad02b7,c07263a9,11f8f78a,ad314049,92bea11f,f41aa315,4049b7c8,c9bef95,f3462336,ccfadf0e,16c1f129,26a5c9e3,7a443bf5) ,S(3debe447,a5f793d4,210e1607,642abdc3,c3a8d446,5a553a45,d73ede0f,20819dae,c0463782,dc5383b4,f7f81557,efddb90d,30138670,858c4197,5a47e6a5,565e339e) ,S(dba32245,a37b5636,9d7120fb,a99880a5,aa590299,601c6cff,d33238a0,395f8d2f,d589ab1f,ff442551,12aa1283,3deb9b43,947059bc,9cb1b32,4d8a29e1,1da82b2e) ,S(9c52bd5d,1fd61e1f,8e75f23f,f6e8baea,a8b7b5e1,5e780870,ea9f8dea,2b75cd56,e6d0a620,c116a7d2,2b2f797c,da7119be,556cd834,caab1007,e9a8ac02,f8945859) 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,S(6223ee77,4e56b9e3,da6e008a,eb3ba06a,40bafa1e,84383ff5,65f98286,d9095d37,ebcec7ec,f750cde,9ff7972d,172340c3,c324d843,f31db269,c3f35a62,c5f15f36) ,S(326943a5,5e7b7ca6,951a78dd,afd00e10,c8ca7f6f,3c01a038,ffc4fc7a,20fe2c63,b3bc5a8b,c87ba023,ee22bb4d,3f92cd81,787f2af2,4ecaebe2,67fe0a86,21c5d201) ,S(f69b5d4a,eb0b550f,851f601c,92698789,f9f94821,47a0ade8,c8a19fe0,5742731f,2a74e8bd,94469645,c8a328b4,24975dc4,93adc83e,4baddba,6c41e10,3b58e90c) ,S(f69a5a88,b8f13bef,a987194d,6b00a79b,7e576749,3d180fe0,32a1868a,26d853ba,6eb589cc,9c51900e,a6d99110,206f60dd,cbdc368f,5ae8dd48,cea05218,3415cbfa) ,S(c00ffc9d,8a57cfcf,9624a812,dd2181f7,195f459c,3b858a19,864393bb,1d1a269e,3097e10a,d6abfc0a,3fa039fe,952034e7,6bda4fc5,c5614092,b124ee3b,bf55f87a) ,S(9c021c49,d6671103,cfddcc3d,8e54848a,addfefa1,d6de5455,e5bda021,126dd183,4fa1ad18,81362f4f,f0587b52,a7a1b483,2d14127,434ffc4,c5bb90e4,fce50834) 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,S(d255c1e7,ccc88c4c,33887c9c,b9c15a2b,52b08471,90ad1420,5fb5909e,d36059c7,83e3e1ca,99a386e8,4b119391,2c20593c,f9573996,d42cb7c3,6db24a5f,cb413080) ,S(aca6c69b,9ea17803,4af67422,71b8062f,77e6dbe5,1df2a570,65fb3057,ea185b8c,40cb09f2,adef414c,816b22f8,d7a59f8c,f5197fb9,b31614d9,ac172436,d0f54647) ,S(fbc19c84,3b656fcb,21d99c3,5289d3e3,2bc58fdb,c2404309,a9d8831a,f2365f24,cc22999f,203a4fae,59eac72c,28bed6d9,291f204b,707bffca,ca6d8359,1e403124) ,S(ea308c88,c366677d,5e575457,cd3e6978,5b491a02,c542dcae,5dd5e149,2f839c55,c1916831,2f48555f,b80845fc,ba89eee7,a7967807,d10c6f6e,b516c190,94873ac9) ,S(d911d62a,33fefc48,abfd4409,7ee2d32f,d7e85816,2a8a00d1,342646ac,8dda6cd2,f160f933,41bb32f7,401d153b,4a2decf8,b793fb5b,4d5520c9,6d9cb9e,cba79aa3) ,S(bb75b497,7d698442,7b0ac74b,939ab3d8,fb94304f,602e102,1fdacf22,27022a4e,ee3cc171,8e9190df,9b45d8d3,54eeef9e,11639423,dc091128,ae09e451,fffe3468) ,S(358e7639,b4031852,b983b5c0,a6c0d33e,5edb304a,3f8bd15c,35d35794,e2cf90f0,5da4be1d,2e9bef5a,5da3cc59,d3c4f85a,e6624ee3,17395ded,398147a,12c56c45) ,S(e098fb9c,440a5cdf,bc570270,4b57eeed,f3087b7,e196522e,4b194618,f3c874fe,9a5b80e6,b22dd111,1f824c36,4830e723,18b7825e,2f2a0fe6,ca460d0c,34eb6449) ,S(62d607b2,d1a16e4e,cf60480a,be9416a7,15d70b5c,56734e7d,1498ba03,7632528e,70c5f4d1,4f5c900a,96291a4e,d0f795ff,439d35d5,2c5bddd2,ab10571b,1d7d20c2) ,S(a630c5bd,ec76f869,40842391,cba6cdfb,9109940b,e1034b87,c6a1e5e6,9662857c,8f28f55e,beed2883,3e347b10,92ff8938,133558c3,bfeac1f6,a6b938a4,c783b79f) ,S(e2a164aa,e17cb0c4,8ae1e911,872b0b3a,7c0e29f0,93cd5e18,97145211,d72147b,23ccf99c,afd1bfbf,a7ce1ade,1590d609,9a423b26,381f5761,c19ba373,290e6193) ,S(742526f5,b95051cf,2ee34994,8385fa72,425162e7,e46bba3,febe5ce8,595a8b37,d106a3be,638987e6,870acf8d,26d4f78c,e6aa0e9b,63e4eb19,114fc97a,eee3a12f) 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,S(be40166a,60ad9af2,d1bdfc7d,9b0660c1,640d4f1b,640ce485,8fb22eda,65d15a21,78c49afc,1d992bdc,b70bab6d,d3619305,a32fe90a,2f2b1b43,38d77c80,b208cf90) ,S(2fd5831e,6bd5a79b,35bc75f,92e83e4c,9acff5cf,61eaad7e,dacb149f,46d5e6ba,82f38222,4b6be0f2,f52318eb,7fe44a4c,4c0c1b05,8eae3f99,dbdea80f,a70ca3d0) ,S(32fc3fb,4574a651,472e0328,c15a71e3,bf9a12ca,15d341f1,c5102dab,2ee6de37,7e9398a6,760df809,e5eb57df,8fdc3234,eff1aa8,bef57008,c36e7953,c07f25a9) ,S(b9018d98,3452e952,7944f2fb,3354487d,a82f8b90,e52689d4,edb2a91a,a8faa6bf,e9cd0e4e,5c5efcbf,9ca25cf9,f271f9c,a2c46b4a,322cc966,e7789607,324348f8) ,S(a74ba662,32afb3e7,d5c22ad1,c792da33,f1bc88dc,244a8ce5,d4d582bb,b16ced23,444c5512,b49c2c63,4cc0328d,20f7321,a88db1ee,6d525be3,5d2de8df,cc381377) ,S(40f6df83,6d5e8c94,332174e2,2fa43556,d06f48a8,f52cfd69,820c2c46,2185dbfa,852c5b98,15ba4ef0,18f5d231,195fb62d,afafc08d,fbf9159a,eb5f6063,ca353424) 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,S(9dfe808f,cf7f574a,ddb251c0,4b053d00,8915f8fa,5a975479,d43c719a,b67aa4ad,4d40cc00,ea6720db,ff1f1339,7bb26c0b,281686a8,726fa430,bce0e4e4,ff01b01d) ,S(835f1c87,cf8d4420,72728601,ab6aef63,cd0d73a1,80f81f07,f5d57cc6,bab5ef7d,bac2d1d4,c8541f65,be0644c9,40a18f7f,d2c30360,2083a455,4d70a111,1c5bf07c) ,S(9562dc71,33c48e4,b46d73ac,d42db4c0,b0222c4d,dcd0e76e,b4f84969,348fa46,7cfe0965,96f691de,d358c00e,a292975d,465ef064,e9437556,40bc1d4a,33c3a0ba) ,S(21afe3b9,4237473c,dc032588,c4c1b7ec,853987a6,dcd1fce,2c48bbb6,8d0f3b45,1751c5ef,674cf88d,d5385943,b40a20a4,6d20cbd3,9876adc4,a4a4bba8,477e78a7) ,S(89809c4d,572cc5c1,2241ae09,fe1cee6f,71aaa292,c9ff8d6e,c3eb8a92,8e144ebe,462c023e,1710ed77,bd47d22e,e222598c,68cd7c56,b004369,a9356a47,ed6809d) ,S(b7c6164f,b9e175c1,5724c596,988b496a,b9f5b0d9,dd45d0e6,4a0f08cb,9000e3e9,1a13e8e5,a23b40a0,aba44bad,5cb4d37d,a6061157,aeab7a0d,d327242,ab2ad11f) ,S(62088450,24eef2d5,4fabe8f8,fabf519,72908ac3,23596378,c377c458,9719bba8,26216b3,a353295e,a1877547,b826c240,351f227e,293abcd2,e3967fed,30391f5a) ,S(dcfe82df,4049089,f3f8b275,120ca438,998fb22f,e11d40e0,9d09c4ce,c12ad036,388f9754,39b1c412,10014136,c3b58fe3,30ab524d,d7d3524b,37ce9133,5cb3bf3f) ,S(324ec5b0,12de7919,2f27f5ed,166344e1,934b3527,2b197d28,9a634044,5dd4bce1,99944794,579e12e8,c5c0c11f,a8eae5f1,88cb8cdb,3ce7814c,f89e3f1b,a3d3de0f) ,S(b3a70b0f,af96cb56,7dc4245,13ab7c6c,bbc38634,faa0c286,b81b9754,454a363f,b507745b,97843c90,170f8ffb,f731fee8,4532c1d0,6b2a077c,2aba5d94,189545ed) ,S(c4a6ff4e,cdf1ac83,29a1cdb7,b5165d88,2a1f1823,d1c38006,1b53144f,56187fce,6f7d0fc0,c08a7ba7,386f9a59,330996ef,b13d9d21,eb6d3915,4c8fb919,66159919) ,S(61d9ee96,1ef58634,5c4a73e3,a8c3df82,eac28aa2,6d740cbe,1833dcf6,d5a38811,c9e4a482,1700107,f2d4af3d,fcc74e68,8123b589,4da1c2bb,1fd926e7,11330892) ,S(67ecbd0f,4f4fe300,49390655,5289c9a5,cb6ac090,dff38502,75f7751,a84c6172,e422b1dd,10467cfe,921028f6,71cc75cd,2be5d8a6,75e644e5,d3c40b3a,2836726d) ,S(47f6c669,70898fa8,16dcd4d7,4553c644,2ce5bbe9,cda91324,ee3bba7a,868ff0f7,e56b9590,838bdfaa,1c2be1c3,95f775e,4a0b3982,d0eee531,26ec7ddc,9e3f77a6) ,S(e39ec9af,c8dccd35,4b155dd3,1d1750cb,ab096807,f89c8afc,fe61e6d2,e348cfa3,df3fca08,99158319,b93bac62,88c302f8,a59e175a,cda9fbf7,6f0ad59,8358088) ,S(2d1aae84,500037f9,8e08b64,341eab03,e0f1cdf,5a079b46,738746c2,18b3a0,747c23ac,8173adcc,de767d2e,ac156384,ddf40797,131a6167,c32486aa,12c89e5) ,S(ed1bbf04,d4570df5,8f584158,1fc47665,481ebf59,cb88322e,497d128a,678c2b4a,a40765c4,772da2d0,b3c8f107,22ec3931,ab3fc8cc,c28b003c,bea1a0da,279c8fba) ,S(bcbc3e1f,7bd268,93f377b2,eee4b76d,49a8a603,738de309,5353fde3,deff55f3,fb697a08,2f2570bd,1e9e4ec3,fc7f6c81,2a27a7e6,f7b8a53e,30da80ef,f59ef2cc) ,S(4f98b2d9,2f0b5d57,51ed3784,94cf4de5,65cf632e,982a270b,2746a5a6,3da9333d,43857e7e,437bdc02,6dcdbe68,d056784f,a2cc606d,7ce09a0e,12978a74,5b67e529) ,S(9dbb995d,d0667371,1731bf05,c8029035,2b413411,45318de8,2236df5c,87728582,c0a90e4c,6fbc0665,f8cd9fb6,fd59ea3e,f6ae9a16,9bfb71fc,5fe73e3a,4d665f86) ,S(83692208,1d099344,3d979c51,90940e44,5465624d,3a945c05,7885cd00,5ce6b9e,49be5e40,2e1d05e0,67b16279,855bc1de,6f0d8aad,35d8bc0e,142dbe87,33a14e13) ,S(f713e920,7a699b68,12d7ee9d,1475ba85,a6c56af2,8b73ace7,cf67ed6b,55650e97,a5a2c2a2,45012812,29fc71c8,103db717,48a51f88,61765d31,4b9ec278,3d0aab45) ,S(919f2d21,256ae682,fe514320,9c6551cc,d165de1b,8213fdbc,9c06578d,ef705725,9780da96,eeaac4e8,c96f3d6a,89c222cc,9b16b4c2,e8faad4d,96cc0136,a06021d3) ,S(1738093d,197a5ce3,cedd1fa7,e2a8ff03,959a6c23,6aedf9e8,9dbd74c4,d82b6e48,74363112,d16b829,d371a0c,f1b3bcd1,2000254e,196ea80c,a9d46570,1ee4a1d8) ,S(41242a81,35811b36,d4ffc40d,bbdeaa7c,cce36135,3c4fc9f2,d23191a4,b9c46379,7b894326,789f3071,374983c7,cd2a5ad7,e0ee49c5,e740dd33,817a31ed,97c388ba) ,S(894a6ec9,96eaa8e0,9e077b34,7b4f1e1,a387c930,a526c469,aaefc0c5,402d41a,a080fb43,c8e6bc6,388fa766,2398e096,b65032e8,26c5a9a8,47793924,4dcf5e41) ,S(a71f2131,3599cb7e,8c1058c9,52a5712e,661d01d5,79bc7ee5,1fbadd35,34ca5d5f,afe5b47b,663ebd7c,d788e0f,d3f963c9,ac63ee24,b7495e61,4a5d6553,9ab5f859) ,S(8f330e77,82eb62e4,4ea389f5,7f1c58b3,458c5d39,127d9783,6ddef8c1,27fa390,894e6142,bc359171,999489e1,1ed08224,4a46100,136fba84,e2b8732,e9bb626b) ,S(d2f0700d,6124c46f,a64cb709,1181cea9,34fe0406,21267334,c85ace2,cf05fc6f,8dc30ae9,83a95b74,2d800490,fbd8c290,bda64daf,f82d8fa5,e69243cb,43556cb4) ,S(c2478e89,8c075873,ba6cd5e9,6a730e1c,b6ade2f2,7fc9e7ec,93da9201,63f88c32,c6412063,9921d8c5,77dced53,76907410,82b1b4ff,4434bd,9a55b6c,8591ed5c) 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,S(5136c2e4,5004c1fd,615fe81a,e4463153,2753c670,86d1bba0,b3a35bdc,47bbec08,1743f5c5,d0a58608,a66fab55,69f7134d,7fe49fad,2dbee1a6,d01c581d,18f97d85) ,S(b65423af,618b242b,71e258e8,c22f975b,621a8900,9e0a3f12,f9f8314d,7fc6ca54,e3c39b1c,e4159306,e730c2ad,4ecec430,720355a2,815b63a9,720ef623,b91e4230) ,S(d6db49c6,4e68f6b0,59cb5a00,3c826a59,bea1e9fe,7622a2e,6eca605e,fe9a7858,cff0a39d,83e246f1,efad5dad,72c5df0d,62e9cf8f,4da81a5a,68586187,3dfd758f) ,S(ff2f739,8e5aaae1,a589a82f,e8e36315,34ff1081,cb083933,d08473b4,bd16f03,1559e2e8,49dc5aeb,50f3de13,1478fa99,e110627,aa0c4c5d,43ab03ca,dde04cdf) ,S(a7c9398c,5938a3ca,e32d2947,d8e3a58,e42a669f,5cd9b219,d8acf6f5,2cef9bf5,43e2a5a3,dae4bd5e,64a30861,7056fce6,cf86d0b7,41c3b46e,3a3ed90e,98d2d51c) ,S(faa9724a,357b6806,7be30aa6,4fb85879,1969191e,346d5d73,8a85b27c,c6608d72,ea1f8a66,8f4881fc,4ecfc556,f0ca4e12,b93ee6ca,54a0fce,b2fe51ca,174d9713) ,S(28301cf8,328171c0,74cd585f,6e5870ac,815de8d0,9c9f15c5,5540de9a,b29a86df,31910e6f,15585710,74e87f41,e5cc9c73,4ddd15bd,4436ec8f,59806afe,7901c2e4) ,S(fbde2380,ae0cccc4,e044ca59,92be8e11,5fc782eb,c1d49bc2,cbdfd1f5,d7908a09,c1a1d67c,74777fbb,68919bf4,11de555a,6485436f,7e34062b,480b7516,8a03dba3) ,S(59d8ba7b,6c71ba1d,191d4cce,662483cb,9784ede7,d1908e81,815d0a48,4b84bf7d,8a32e968,1ecf963b,3c23a9d2,f382490b,1f229b27,a663f4a6,9819c33b,f9f6149f) ,S(6c3a61d7,1c999ae0,604511ad,23f620ad,dfc7891b,925eeed1,6a5ca37f,b41b47e4,f7115905,c696c2b3,e2b82a30,9728923e,b8eba53c,363f1456,73676b59,9b50b9c0) ,S(8e53027f,8e137bfa,73eb5167,35382ba,ab3468f4,d4227b19,a45c51c2,ef3d8339,2b5ea7b9,542a83ab,a1c402ba,be13437b,c621067,96e83b7a,2cdedc52,2bcff513) ,S(113aa35e,6a5f794b,a56b04a3,d639b1e1,64a790b5,8ff310c,fbeab588,f93be16a,227c17e7,d95583e7,fdcc3ab7,b24182b5,1bb11e91,9f28fd7b,3a2e4a40,4f333962) ,S(16c4c83f,5a06b2de,9d3f39e7,1f0a9de7,af6e8fc7,b0fecaf3,2c82f1aa,fe9a5343,b4cbf71e,c3ad4635,87f8e355,cffe1ea,a19f1dc6,d233d617,776a69a9,ab8dec03) ,S(4d97594c,613de84a,e685199a,ac639a56,e5c15a0e,c00282bd,197cc2ea,90f8fbb0,b9f39a44,24cbb1e2,f77afa90,ec7266ee,64ea987e,80a32b34,483c1f2e,b0c5844a) ,S(b679693a,b3fecff0,819e0598,65406521,1f9aee9c,1ea44417,eba86ebe,32414ac3,7bfe1ba0,ae17291d,71aac3f3,66e5a927,56b53312,a6818d1a,78b7d9ef,a5d01b2f) ,S(a97c2730,a78cf5b7,538b518a,87d8fc55,f95a367d,4e021d23,79f163eb,98b6eb9a,aed1e51c,3ce7e35e,ff69e7d9,3fd3a968,59f0f23a,7bbab9d8,3b60cabd,cebd34f) ,S(7dd4e84f,6547d66b,5e0b204c,ed1d0258,4fe92ed8,6b504ae4,eb1b3d66,d43b8ca4,7956148f,de975510,5e3b5126,f82e77b,89a77b68,ffc9364c,bfb596e8,187ea99b) ,S(5e856d1d,25acc306,e8c1a2b7,a9ccea1,beb3008d,c224b38f,e2f31376,65d07c3f,7dccf6b1,55c12be2,f3da02c9,12fdb666,816558b1,11a2a545,9d88aa28,9d855e6c) ,S(c85ee868,7f507429,e5c26af6,7ef1fe45,e782661c,1fa03aa3,ee9dd9c9,302e5dd6,732de6ad,d071a0b0,b77e47bc,14e176d4,c85b39d0,ac5b4ea,55f0d367,dba5ab5d) ,S(a97ba3a5,cc2d5148,3f65c65b,483b3e4f,3c68e46b,87bcfea1,42aeed8,4c42e42b,f4eb1271,3024d1,b7612c3b,7dc3dff8,ca336f23,5db7daf9,3ca6f7d8,1bdb4a21) ,S(3c0396cf,6ff0150c,5b6bd528,4a05d0a5,3b735c85,125bd49c,f62db5b6,4eaf54a7,6ec02c02,f8d9a61e,6bb38d64,daaf3c7d,5324462e,37e2df8d,4ad12bfa,37fd2cb2) ,S(e36fcebc,e406d2a4,ad42f7dd,cc00e9f3,cf385eeb,58cee004,5aab8174,82d84f94,7c98182f,6edd358e,76d66de0,b45ae9f6,5eb75092,1a25194c,1911bd9f,7e6a1a6b) ,S(171ea2ec,b9641746,7d7edcf,ecd6d85,8577322e,6ebac130,5ab57f33,62eb4e37,9f219970,753a7b9c,e4f0c6ce,5745596a,aca8df7b,a73660c9,10add5a9,d4c533d6) ,S(a81d720a,bf8047e8,ef67bf2,71a13f47,636a5f9e,ec425649,1cbdad65,39652f9e,92b37c88,275c022b,635df6b,9246edf5,5dbd8284,eaa4cd7e,3d3ce6d1,c0ca3794) ,S(fa3b6973,4bd9939c,4b6ecd3b,f0a06327,2dc11345,1bddd717,f17b745f,bc3f99b3,f38a4e1a,bcb35097,7acc8f2e,d7f73f75,d406e7f2,22fdeea,2c12d8b9,e5d2dfa3) ,S(c117681e,b55bff67,feda80a1,ae88b4be,c806860d,91916619,288a7ce0,b31aef86,d94ae124,dca678bc,b69c9421,f295405f,d6dc1fac,de96a2b4,58ba5fd2,72faa032) ,S(5ccc0619,92744a57,683de5e3,7b956fa1,fd7287d,b4516fc9,f8635be3,a0db42a9,af1f73ea,4d2168e1,7550ffc,dcbba288,8397931b,e457ce6f,3f8082f8,cfc5f03) ,S(858b019c,8a93524f,6c86738d,cb10b534,d8caaf86,5c0ce75c,fc9b83b0,7c661a0a,7c59d30,1ffc8ce1,b0767ed7,91f84bc5,60bb8ca,ed3464ba,698a53c,160ec570) ,S(e1e217b8,69da0c77,599dcc38,40fa1d8c,a8d08b1a,4ac9a882,da1476cc,cc76fa56,83f0ef77,905f0801,4bd86e17,63b8c2cf,ab2018a8,9586620a,b49a15,9fc314ca) ,S(15a1ae40,b4fc51dc,554b75d4,db0c2bfd,62dfbbfc,dede18e1,4edbb689,91525cff,4f0453b7,e4e0e99d,9663e5c6,bb018007,b52c8e14,d78a28d,c4a888e4,8c4326c2) ,S(1b9a142f,fc4d03ea,4b079f2d,b05fad98,8ddb2d32,b359967f,c173801f,63320825,59bda7ed,5b691c20,4fc8f8ac,f53be298,ae628954,a8134d0f,dd097e67,be9ff9b6) #endif } #endif ; #undef S #endif /* SECP256K1_PRECOMPUTED_ECMULT_H */ ================================================ FILE: C/secp256k1/scalar.h ================================================ /*********************************************************************** * Copyright (c) 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_SCALAR_H #define SECP256K1_SCALAR_H #include "util.h" #if defined(SECP256K1_WIDEMUL_INT128) #include "scalar_4x64.h" #else #error "Please select wide multiplication implementation" #endif /** Clear a scalar to prevent the leak of sensitive data. */ static void secp256k1_scalar_clear(secp256k1_scalar *r); #if 0 /** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */ static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count); /** Access bits from a scalar. Not constant time. */ static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count); #endif /** Set a scalar from a big endian byte array. The scalar will be reduced modulo group order `n`. * In: bin: pointer to a 32-byte array. * Out: r: scalar to be set. * overflow: non-zero if the scalar was bigger or equal to `n` before reduction, zero otherwise (can be NULL). */ static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow); #if 0 /** Set a scalar from a big endian byte array and returns 1 if it is a valid * seckey and 0 otherwise. */ static int secp256k1_scalar_set_b32_seckey(secp256k1_scalar *r, const unsigned char *bin); #endif /** Set a scalar to an unsigned integer. */ static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v); /** Convert a scalar to a byte array. */ static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a); /** Add two scalars together (modulo the group order). Returns whether it overflowed. */ static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); /** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */ static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag); /** Multiply two scalars (modulo the group order). */ static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); #if 0 /** Shift a scalar right by some amount strictly between 0 and 16, returning * the low bits that were shifted off */ static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n); /** Compute the inverse of a scalar (modulo the group order). */ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a); #endif /** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */ static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a); /** Compute the complement of a scalar (modulo the group order). */ static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a); /** Check whether a scalar equals zero. */ static int secp256k1_scalar_is_zero(const secp256k1_scalar *a); #if 0 /** Check whether a scalar equals one. */ static int secp256k1_scalar_is_one(const secp256k1_scalar *a); /** Check whether a scalar, considered as an nonnegative integer, is even. */ static int secp256k1_scalar_is_even(const secp256k1_scalar *a); /** Check whether a scalar is higher than the group order divided by 2. */ static int secp256k1_scalar_is_high(const secp256k1_scalar *a); /** Conditionally negate a number, in constant time. * Returns -1 if the number was negated, 1 otherwise */ static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag); /** Compare two scalars. */ static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b); #endif /** Find r1 and r2 such that r1+r2*2^128 = k. */ static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k); /** Find r1 and r2 such that r1+r2*lambda = k, where r1 and r2 or their * negations are maximum 128 bits long (see secp256k1_ge_mul_lambda). It is * required that r1, r2, and k all point to different objects. */ static void secp256k1_scalar_split_lambda(secp256k1_scalar * SECP256K1_RESTRICT r1, secp256k1_scalar * SECP256K1_RESTRICT r2, const secp256k1_scalar * SECP256K1_RESTRICT k); /** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */ static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift); #if 0 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag); #endif #endif /* SECP256K1_SCALAR_H */ ================================================ FILE: C/secp256k1/scalar_4x64.h ================================================ /*********************************************************************** * Copyright (c) 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_SCALAR_REPR_H #define SECP256K1_SCALAR_REPR_H #include /** A scalar modulo the group order of the secp256k1 curve. */ typedef struct { uint64_t d[4]; } secp256k1_scalar; #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}} #endif /* SECP256K1_SCALAR_REPR_H */ ================================================ FILE: C/secp256k1/scalar_4x64_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_SCALAR_REPR_IMPL_H #define SECP256K1_SCALAR_REPR_IMPL_H #include "int128.h" #include "modinv64_impl.h" /* Limbs of the secp256k1 order. */ #define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL) #define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL) #define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL) #define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) /* Limbs of 2^256 minus the secp256k1 order. */ #define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1) #define SECP256K1_N_C_1 (~SECP256K1_N_1) #define SECP256K1_N_C_2 (1) /* Limbs of half the secp256k1 order. */ #define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL) #define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL) #define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) #define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL) SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { r->d[0] = 0; r->d[1] = 0; r->d[2] = 0; r->d[3] = 0; } SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { r->d[0] = v; r->d[1] = 0; r->d[2] = 0; r->d[3] = 0; } SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6); return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1); } SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { VERIFY_CHECK(count < 32); VERIFY_CHECK(offset + count <= 256); if ((offset + count - 1) >> 6 == offset >> 6) { return secp256k1_scalar_get_bits(a, offset, count); } else { VERIFY_CHECK((offset >> 6) + 1 < 4); return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1); } } SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { int yes = 0; int no = 0; no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */ no |= (a->d[2] < SECP256K1_N_2); yes |= (a->d[2] > SECP256K1_N_2) & ~no; no |= (a->d[1] < SECP256K1_N_1); yes |= (a->d[1] > SECP256K1_N_1) & ~no; yes |= (a->d[0] >= SECP256K1_N_0) & ~no; return yes; } SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) { secp256k1_uint128 t; VERIFY_CHECK(overflow <= 1); secp256k1_u128_from_u64(&t, r->d[0]); secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_0); r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[1]); secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_1); r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[2]); secp256k1_u128_accum_u64(&t, overflow * SECP256K1_N_C_2); r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[3]); r->d[3] = secp256k1_u128_to_u64(&t); return overflow; } static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { int overflow; secp256k1_uint128 t; secp256k1_u128_from_u64(&t, a->d[0]); secp256k1_u128_accum_u64(&t, b->d[0]); r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, a->d[1]); secp256k1_u128_accum_u64(&t, b->d[1]); r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, a->d[2]); secp256k1_u128_accum_u64(&t, b->d[2]); r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, a->d[3]); secp256k1_u128_accum_u64(&t, b->d[3]); r->d[3] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); overflow = secp256k1_u128_to_u64(&t) + secp256k1_scalar_check_overflow(r); VERIFY_CHECK(overflow == 0 || overflow == 1); secp256k1_scalar_reduce(r, overflow); return overflow; } static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { secp256k1_uint128 t; VERIFY_CHECK(bit < 256); bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 6) > 3 makes this a noop */ secp256k1_u128_from_u64(&t, r->d[0]); secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F)); r->d[0] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[1]); secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F)); r->d[1] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[2]); secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F)); r->d[2] = secp256k1_u128_to_u64(&t); secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[3]); secp256k1_u128_accum_u64(&t, ((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F)); r->d[3] = secp256k1_u128_to_u64(&t); #ifdef VERIFY VERIFY_CHECK(secp256k1_u128_hi_u64(&t) == 0); #endif } static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { int over; r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56; r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56; r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56; r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56; over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r)); if (overflow) { *overflow = over; } } static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3]; bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2]; bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1]; bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0]; } SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0; } static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0); secp256k1_uint128 t; secp256k1_u128_from_u64(&t, ~a->d[0]); secp256k1_u128_accum_u64(&t, SECP256K1_N_0 + 1); r->d[0] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, ~a->d[1]); secp256k1_u128_accum_u64(&t, SECP256K1_N_1); r->d[1] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, ~a->d[2]); secp256k1_u128_accum_u64(&t, SECP256K1_N_2); r->d[2] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, ~a->d[3]); secp256k1_u128_accum_u64(&t, SECP256K1_N_3); r->d[3] = secp256k1_u128_to_u64(&t) & nonzero; } #if 0 SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0; } static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { int yes = 0; int no = 0; no |= (a->d[3] < SECP256K1_N_H_3); yes |= (a->d[3] > SECP256K1_N_H_3) & ~no; no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */ no |= (a->d[1] < SECP256K1_N_H_1) & ~yes; yes |= (a->d[1] > SECP256K1_N_H_1) & ~no; yes |= (a->d[0] > SECP256K1_N_H_0) & ~no; return yes; } static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { /* If we are flag = 0, mask = 00...00 and this is a no-op; * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */ uint64_t mask = !flag - 1; uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1; secp256k1_uint128 t; secp256k1_u128_from_u64(&t, r->d[0] ^ mask); secp256k1_u128_accum_u64(&t, (SECP256K1_N_0 + 1) & mask); r->d[0] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[1] ^ mask); secp256k1_u128_accum_u64(&t, SECP256K1_N_1 & mask); r->d[1] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[2] ^ mask); secp256k1_u128_accum_u64(&t, SECP256K1_N_2 & mask); r->d[2] = secp256k1_u128_to_u64(&t) & nonzero; secp256k1_u128_rshift(&t, 64); secp256k1_u128_accum_u64(&t, r->d[3] ^ mask); secp256k1_u128_accum_u64(&t, SECP256K1_N_3 & mask); r->d[3] = secp256k1_u128_to_u64(&t) & nonzero; return 2 * (mask == 0) - 1; } #endif /* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */ /** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ #define muladd(a,b) { \ uint64_t tl, th; \ { \ secp256k1_uint128 t; \ secp256k1_u128_mul(&t, a, b); \ th = secp256k1_u128_hi_u64(&t); /* at most 0xFFFFFFFFFFFFFFFE */ \ tl = secp256k1_u128_to_u64(&t); \ } \ c0 += tl; /* overflow is handled on the next line */ \ th += (c0 < tl); /* at most 0xFFFFFFFFFFFFFFFF */ \ c1 += th; /* overflow is handled on the next line */ \ c2 += (c1 < th); /* never overflows by contract (verified in the next line) */ \ VERIFY_CHECK((c1 >= th) || (c2 != 0)); \ } /** Add a*b to the number defined by (c0,c1). c1 must never overflow. */ #define muladd_fast(a,b) { \ uint64_t tl, th; \ { \ secp256k1_uint128 t; \ secp256k1_u128_mul(&t, a, b); \ th = secp256k1_u128_hi_u64(&t); /* at most 0xFFFFFFFFFFFFFFFE */ \ tl = secp256k1_u128_to_u64(&t); \ } \ c0 += tl; /* overflow is handled on the next line */ \ th += (c0 < tl); /* at most 0xFFFFFFFFFFFFFFFF */ \ c1 += th; /* never overflows by contract (verified in the next line) */ \ VERIFY_CHECK(c1 >= th); \ } /** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ #define sumadd(a) { \ unsigned int over; \ c0 += (a); /* overflow is handled on the next line */ \ over = (c0 < (a)); \ c1 += over; /* overflow is handled on the next line */ \ c2 += (c1 < over); /* never overflows by contract */ \ } /** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */ #define sumadd_fast(a) { \ c0 += (a); /* overflow is handled on the next line */ \ c1 += (c0 < (a)); /* never overflows by contract (verified the next line) */ \ VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \ VERIFY_CHECK(c2 == 0); \ } /** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */ #define extract(n) { \ (n) = c0; \ c0 = c1; \ c1 = c2; \ c2 = 0; \ } /** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */ #define extract_fast(n) { \ (n) = c0; \ c0 = c1; \ c1 = 0; \ VERIFY_CHECK(c2 == 0); \ } static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) { #ifdef USE_ASM_X86_64 /* Reduce 512 bits into 385. */ uint64_t m0, m1, m2, m3, m4, m5, m6; uint64_t p0, p1, p2, p3, p4; uint64_t c; __asm__ __volatile__( /* Preload. */ "movq 32(%%rsi), %%r11\n" "movq 40(%%rsi), %%r12\n" "movq 48(%%rsi), %%r13\n" "movq 56(%%rsi), %%r14\n" /* Initialize r8,r9,r10 */ "movq 0(%%rsi), %%r8\n" "xorq %%r9, %%r9\n" "xorq %%r10, %%r10\n" /* (r8,r9) += n0 * c0 */ "movq %8, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" /* extract m0 */ "movq %%r8, %q0\n" "xorq %%r8, %%r8\n" /* (r9,r10) += l1 */ "addq 8(%%rsi), %%r9\n" "adcq $0, %%r10\n" /* (r9,r10,r8) += n1 * c0 */ "movq %8, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* (r9,r10,r8) += n0 * c1 */ "movq %9, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* extract m1 */ "movq %%r9, %q1\n" "xorq %%r9, %%r9\n" /* (r10,r8,r9) += l2 */ "addq 16(%%rsi), %%r10\n" "adcq $0, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += n2 * c0 */ "movq %8, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += n1 * c1 */ "movq %9, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += n0 */ "addq %%r11, %%r10\n" "adcq $0, %%r8\n" "adcq $0, %%r9\n" /* extract m2 */ "movq %%r10, %q2\n" "xorq %%r10, %%r10\n" /* (r8,r9,r10) += l3 */ "addq 24(%%rsi), %%r8\n" "adcq $0, %%r9\n" "adcq $0, %%r10\n" /* (r8,r9,r10) += n3 * c0 */ "movq %8, %%rax\n" "mulq %%r14\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* (r8,r9,r10) += n2 * c1 */ "movq %9, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* (r8,r9,r10) += n1 */ "addq %%r12, %%r8\n" "adcq $0, %%r9\n" "adcq $0, %%r10\n" /* extract m3 */ "movq %%r8, %q3\n" "xorq %%r8, %%r8\n" /* (r9,r10,r8) += n3 * c1 */ "movq %9, %%rax\n" "mulq %%r14\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* (r9,r10,r8) += n2 */ "addq %%r13, %%r9\n" "adcq $0, %%r10\n" "adcq $0, %%r8\n" /* extract m4 */ "movq %%r9, %q4\n" /* (r10,r8) += n3 */ "addq %%r14, %%r10\n" "adcq $0, %%r8\n" /* extract m5 */ "movq %%r10, %q5\n" /* extract m6 */ "movq %%r8, %q6\n" : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6) : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc"); /* Reduce 385 bits into 258. */ __asm__ __volatile__( /* Preload */ "movq %q9, %%r11\n" "movq %q10, %%r12\n" "movq %q11, %%r13\n" /* Initialize (r8,r9,r10) */ "movq %q5, %%r8\n" "xorq %%r9, %%r9\n" "xorq %%r10, %%r10\n" /* (r8,r9) += m4 * c0 */ "movq %12, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" /* extract p0 */ "movq %%r8, %q0\n" "xorq %%r8, %%r8\n" /* (r9,r10) += m1 */ "addq %q6, %%r9\n" "adcq $0, %%r10\n" /* (r9,r10,r8) += m5 * c0 */ "movq %12, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* (r9,r10,r8) += m4 * c1 */ "movq %13, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* extract p1 */ "movq %%r9, %q1\n" "xorq %%r9, %%r9\n" /* (r10,r8,r9) += m2 */ "addq %q7, %%r10\n" "adcq $0, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += m6 * c0 */ "movq %12, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += m5 * c1 */ "movq %13, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += m4 */ "addq %%r11, %%r10\n" "adcq $0, %%r8\n" "adcq $0, %%r9\n" /* extract p2 */ "movq %%r10, %q2\n" /* (r8,r9) += m3 */ "addq %q8, %%r8\n" "adcq $0, %%r9\n" /* (r8,r9) += m6 * c1 */ "movq %13, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" /* (r8,r9) += m5 */ "addq %%r12, %%r8\n" "adcq $0, %%r9\n" /* extract p3 */ "movq %%r8, %q3\n" /* (r9) += m6 */ "addq %%r13, %%r9\n" /* extract p4 */ "movq %%r9, %q4\n" : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4) : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc"); /* Reduce 258 bits into 256. */ __asm__ __volatile__( /* Preload */ "movq %q5, %%r10\n" /* (rax,rdx) = p4 * c0 */ "movq %7, %%rax\n" "mulq %%r10\n" /* (rax,rdx) += p0 */ "addq %q1, %%rax\n" "adcq $0, %%rdx\n" /* extract r0 */ "movq %%rax, 0(%q6)\n" /* Move to (r8,r9) */ "movq %%rdx, %%r8\n" "xorq %%r9, %%r9\n" /* (r8,r9) += p1 */ "addq %q2, %%r8\n" "adcq $0, %%r9\n" /* (r8,r9) += p4 * c1 */ "movq %8, %%rax\n" "mulq %%r10\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" /* Extract r1 */ "movq %%r8, 8(%q6)\n" "xorq %%r8, %%r8\n" /* (r9,r8) += p4 */ "addq %%r10, %%r9\n" "adcq $0, %%r8\n" /* (r9,r8) += p2 */ "addq %q3, %%r9\n" "adcq $0, %%r8\n" /* Extract r2 */ "movq %%r9, 16(%q6)\n" "xorq %%r9, %%r9\n" /* (r8,r9) += p3 */ "addq %q4, %%r8\n" "adcq $0, %%r9\n" /* Extract r3 */ "movq %%r8, 24(%q6)\n" /* Extract c */ "movq %%r9, %q0\n" : "=g"(c) : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) : "rax", "rdx", "r8", "r9", "r10", "cc", "memory"); #else secp256k1_uint128 c128; uint64_t c, c0, c1, c2; uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7]; uint64_t m0, m1, m2, m3, m4, m5; uint32_t m6; uint64_t p0, p1, p2, p3; uint32_t p4; /* Reduce 512 bits into 385. */ /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */ c0 = l[0]; c1 = 0; c2 = 0; muladd_fast(n0, SECP256K1_N_C_0); extract_fast(m0); sumadd_fast(l[1]); muladd(n1, SECP256K1_N_C_0); muladd(n0, SECP256K1_N_C_1); extract(m1); sumadd(l[2]); muladd(n2, SECP256K1_N_C_0); muladd(n1, SECP256K1_N_C_1); sumadd(n0); extract(m2); sumadd(l[3]); muladd(n3, SECP256K1_N_C_0); muladd(n2, SECP256K1_N_C_1); sumadd(n1); extract(m3); muladd(n3, SECP256K1_N_C_1); sumadd(n2); extract(m4); sumadd_fast(n3); extract_fast(m5); VERIFY_CHECK(c0 <= 1); m6 = c0; /* Reduce 385 bits into 258. */ /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */ c0 = m0; c1 = 0; c2 = 0; muladd_fast(m4, SECP256K1_N_C_0); extract_fast(p0); sumadd_fast(m1); muladd(m5, SECP256K1_N_C_0); muladd(m4, SECP256K1_N_C_1); extract(p1); sumadd(m2); muladd(m6, SECP256K1_N_C_0); muladd(m5, SECP256K1_N_C_1); sumadd(m4); extract(p2); sumadd_fast(m3); muladd_fast(m6, SECP256K1_N_C_1); sumadd_fast(m5); extract_fast(p3); p4 = c0 + m6; VERIFY_CHECK(p4 <= 2); /* Reduce 258 bits into 256. */ /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */ secp256k1_u128_from_u64(&c128, p0); secp256k1_u128_accum_mul(&c128, SECP256K1_N_C_0, p4); r->d[0] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64); secp256k1_u128_accum_u64(&c128, p1); secp256k1_u128_accum_mul(&c128, SECP256K1_N_C_1, p4); r->d[1] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64); secp256k1_u128_accum_u64(&c128, p2); secp256k1_u128_accum_u64(&c128, p4); r->d[2] = secp256k1_u128_to_u64(&c128); secp256k1_u128_rshift(&c128, 64); secp256k1_u128_accum_u64(&c128, p3); r->d[3] = secp256k1_u128_to_u64(&c128); c = secp256k1_u128_hi_u64(&c128); #endif /* Final reduction of r. */ secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r)); } static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) { #ifdef USE_ASM_X86_64 const uint64_t *pb = b->d; __asm__ __volatile__( /* Preload */ "movq 0(%%rdi), %%r15\n" "movq 8(%%rdi), %%rbx\n" "movq 16(%%rdi), %%rcx\n" "movq 0(%%rdx), %%r11\n" "movq 8(%%rdx), %%r12\n" "movq 16(%%rdx), %%r13\n" "movq 24(%%rdx), %%r14\n" /* (rax,rdx) = a0 * b0 */ "movq %%r15, %%rax\n" "mulq %%r11\n" /* Extract l0 */ "movq %%rax, 0(%%rsi)\n" /* (r8,r9,r10) = (rdx) */ "movq %%rdx, %%r8\n" "xorq %%r9, %%r9\n" "xorq %%r10, %%r10\n" /* (r8,r9,r10) += a0 * b1 */ "movq %%r15, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* (r8,r9,r10) += a1 * b0 */ "movq %%rbx, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* Extract l1 */ "movq %%r8, 8(%%rsi)\n" "xorq %%r8, %%r8\n" /* (r9,r10,r8) += a0 * b2 */ "movq %%r15, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* (r9,r10,r8) += a1 * b1 */ "movq %%rbx, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* (r9,r10,r8) += a2 * b0 */ "movq %%rcx, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* Extract l2 */ "movq %%r9, 16(%%rsi)\n" "xorq %%r9, %%r9\n" /* (r10,r8,r9) += a0 * b3 */ "movq %%r15, %%rax\n" "mulq %%r14\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* Preload a3 */ "movq 24(%%rdi), %%r15\n" /* (r10,r8,r9) += a1 * b2 */ "movq %%rbx, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += a2 * b1 */ "movq %%rcx, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* (r10,r8,r9) += a3 * b0 */ "movq %%r15, %%rax\n" "mulq %%r11\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" "adcq $0, %%r9\n" /* Extract l3 */ "movq %%r10, 24(%%rsi)\n" "xorq %%r10, %%r10\n" /* (r8,r9,r10) += a1 * b3 */ "movq %%rbx, %%rax\n" "mulq %%r14\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* (r8,r9,r10) += a2 * b2 */ "movq %%rcx, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* (r8,r9,r10) += a3 * b1 */ "movq %%r15, %%rax\n" "mulq %%r12\n" "addq %%rax, %%r8\n" "adcq %%rdx, %%r9\n" "adcq $0, %%r10\n" /* Extract l4 */ "movq %%r8, 32(%%rsi)\n" "xorq %%r8, %%r8\n" /* (r9,r10,r8) += a2 * b3 */ "movq %%rcx, %%rax\n" "mulq %%r14\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* (r9,r10,r8) += a3 * b2 */ "movq %%r15, %%rax\n" "mulq %%r13\n" "addq %%rax, %%r9\n" "adcq %%rdx, %%r10\n" "adcq $0, %%r8\n" /* Extract l5 */ "movq %%r9, 40(%%rsi)\n" /* (r10,r8) += a3 * b3 */ "movq %%r15, %%rax\n" "mulq %%r14\n" "addq %%rax, %%r10\n" "adcq %%rdx, %%r8\n" /* Extract l6 */ "movq %%r10, 48(%%rsi)\n" /* Extract l7 */ "movq %%r8, 56(%%rsi)\n" : "+d"(pb) : "S"(l), "D"(a->d) : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory"); #else /* 160 bit accumulator. */ uint64_t c0 = 0, c1 = 0; uint32_t c2 = 0; /* l[0..7] = a[0..3] * b[0..3]. */ muladd_fast(a->d[0], b->d[0]); extract_fast(l[0]); muladd(a->d[0], b->d[1]); muladd(a->d[1], b->d[0]); extract(l[1]); muladd(a->d[0], b->d[2]); muladd(a->d[1], b->d[1]); muladd(a->d[2], b->d[0]); extract(l[2]); muladd(a->d[0], b->d[3]); muladd(a->d[1], b->d[2]); muladd(a->d[2], b->d[1]); muladd(a->d[3], b->d[0]); extract(l[3]); muladd(a->d[1], b->d[3]); muladd(a->d[2], b->d[2]); muladd(a->d[3], b->d[1]); extract(l[4]); muladd(a->d[2], b->d[3]); muladd(a->d[3], b->d[2]); extract(l[5]); muladd_fast(a->d[3], b->d[3]); extract_fast(l[6]); VERIFY_CHECK(c1 == 0); l[7] = c0; #endif } #undef sumadd #undef sumadd_fast #undef muladd #undef muladd_fast #undef extract #undef extract_fast static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { uint64_t l[8]; secp256k1_scalar_mul_512(l, a, b); secp256k1_scalar_reduce_512(r, l); } #if 0 static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { int ret; VERIFY_CHECK(n > 0); VERIFY_CHECK(n < 16); ret = r->d[0] & ((1 << n) - 1); r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n)); r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n)); r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n)); r->d[3] = (r->d[3] >> n); return ret; } #endif static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) { r1->d[0] = k->d[0]; r1->d[1] = k->d[1]; r1->d[2] = 0; r1->d[3] = 0; r2->d[0] = k->d[2]; r2->d[1] = k->d[3]; r2->d[2] = 0; r2->d[3] = 0; } #if 0 SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0; } #endif SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) { uint64_t l[8]; unsigned int shiftlimbs; unsigned int shiftlow; unsigned int shifthigh; VERIFY_CHECK(shift >= 256); secp256k1_scalar_mul_512(l, a, b); shiftlimbs = shift >> 6; shiftlow = shift & 0x3F; shifthigh = 64 - shiftlow; r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0; r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0; r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0; r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0; secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1); } #if 0 static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { uint64_t mask0, mask1; SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d)); mask0 = flag + ~((uint64_t)0); mask1 = ~mask0; r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1); r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1); r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1); r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1); } #endif static void secp256k1_scalar_from_signed62(secp256k1_scalar *r, const secp256k1_modinv64_signed62 *a) { const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4]; /* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and * have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4). */ VERIFY_CHECK(a0 >> 62 == 0); VERIFY_CHECK(a1 >> 62 == 0); VERIFY_CHECK(a2 >> 62 == 0); VERIFY_CHECK(a3 >> 62 == 0); VERIFY_CHECK(a4 >> 8 == 0); r->d[0] = a0 | a1 << 62; r->d[1] = a1 >> 2 | a2 << 60; r->d[2] = a2 >> 4 | a3 << 58; r->d[3] = a3 >> 6 | a4 << 56; #ifdef VERIFY VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); #endif } static void secp256k1_scalar_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_scalar *a) { const uint64_t M62 = UINT64_MAX >> 2; const uint64_t a0 = a->d[0], a1 = a->d[1], a2 = a->d[2], a3 = a->d[3]; #ifdef VERIFY VERIFY_CHECK(secp256k1_scalar_check_overflow(a) == 0); #endif r->v[0] = a0 & M62; r->v[1] = (a0 >> 62 | a1 << 2) & M62; r->v[2] = (a1 >> 60 | a2 << 4) & M62; r->v[3] = (a2 >> 58 | a3 << 6) & M62; r->v[4] = a3 >> 56; } static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_scalar = { {{0x3FD25E8CD0364141LL, 0x2ABB739ABD2280EELL, -0x15LL, 0, 256}}, 0x34F20099AA774EC1LL }; #if 0 static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { secp256k1_modinv64_signed62 s; #ifdef VERIFY int zero_in = secp256k1_scalar_is_zero(x); #endif secp256k1_scalar_to_signed62(&s, x); secp256k1_modinv64(&s, &secp256k1_const_modinfo_scalar); secp256k1_scalar_from_signed62(r, &s); #ifdef VERIFY VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in); #endif } #endif static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { secp256k1_modinv64_signed62 s; #ifdef VERIFY int zero_in = secp256k1_scalar_is_zero(x); #endif secp256k1_scalar_to_signed62(&s, x); secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_scalar); secp256k1_scalar_from_signed62(r, &s); #ifdef VERIFY VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in); #endif } #if 0 SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { return !(a->d[0] & 1); } #endif #endif /* SECP256K1_SCALAR_REPR_IMPL_H */ ================================================ FILE: C/secp256k1/scalar_impl.h ================================================ /*********************************************************************** * Copyright (c) 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_SCALAR_IMPL_H #define SECP256K1_SCALAR_IMPL_H #ifdef VERIFY #include #endif #include "scalar.h" #include "util.h" #if defined(SECP256K1_WIDEMUL_INT128) #include "scalar_4x64_impl.h" #else #error "Please select wide multiplication implementation" #endif static const secp256k1_scalar secp256k1_scalar_one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); static const secp256k1_scalar secp256k1_scalar_zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); #if 0 static int secp256k1_scalar_set_b32_seckey(secp256k1_scalar *r, const unsigned char *bin) { int overflow; secp256k1_scalar_set_b32(r, bin, &overflow); return (!overflow) & (!secp256k1_scalar_is_zero(r)); } #endif /** * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where * lambda is: */ static const secp256k1_scalar secp256k1_const_lambda = SECP256K1_SCALAR_CONST( 0x5363AD4CUL, 0xC05C30E0UL, 0xA5261C02UL, 0x8812645AUL, 0x122E22EAUL, 0x20816678UL, 0xDF02967CUL, 0x1B23BD72UL ); #ifdef VERIFY static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, const secp256k1_scalar *r2, const secp256k1_scalar *k); #endif /* * Both lambda and beta are primitive cube roots of unity. That is lambda^3 == 1 mod n and * beta^3 == 1 mod p, where n is the curve order and p is the field order. * * Furthermore, because (X^3 - 1) = (X - 1)(X^2 + X + 1), the primitive cube roots of unity are * roots of X^2 + X + 1. Therefore lambda^2 + lambda == -1 mod n and beta^2 + beta == -1 mod p. * (The other primitive cube roots of unity are lambda^2 and beta^2 respectively.) * * Let l = -1/2 + i*sqrt(3)/2, the complex root of X^2 + X + 1. We can define a ring * homomorphism phi : Z[l] -> Z_n where phi(a + b*l) == a + b*lambda mod n. The kernel of phi * is a lattice over Z[l] (considering Z[l] as a Z-module). This lattice is generated by a * reduced basis {a1 + b1*l, a2 + b2*l} where * * - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} * - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3} * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8} * - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} * * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1 * and k2 are small in absolute value. * * The algorithm computes c1 = round(b2 * k / n) and c2 = round((-b1) * k / n), and gives * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and * compute r2 = k2 mod n, and r1 = k1 mod n = (k - r2 * lambda) mod n, avoiding the need for * the constants a1 and a2. * * g1, g2 are precomputed constants used to replace division with a rounded multiplication * when decomposing the scalar for an endomorphism-based point multiplication. * * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5. * * The derivation is described in the paper "Efficient Software Implementation of Public-Key * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez), * Section 4.3 (here we use a somewhat higher-precision estimate): * d = a1*b2 - b1*a2 * g1 = round(2^384 * b2/d) * g2 = round(2^384 * (-b1)/d) * * (Note that d is also equal to the curve order, n, here because [a1,b1] and [a2,b2] * can be found as outputs of the Extended Euclidean Algorithm on inputs n and lambda). * * The function below splits k into r1 and r2, such that * - r1 + lambda * r2 == k (mod n) * - either r1 < 2^128 or -r1 mod n < 2^128 * - either r2 < 2^128 or -r2 mod n < 2^128 * * See proof below. */ static void secp256k1_scalar_split_lambda(secp256k1_scalar * SECP256K1_RESTRICT r1, secp256k1_scalar * SECP256K1_RESTRICT r2, const secp256k1_scalar * SECP256K1_RESTRICT k) { secp256k1_scalar c1, c2; static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST( 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL ); static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST( 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL ); static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST( 0x3086D221UL, 0xA7D46BCDUL, 0xE86C90E4UL, 0x9284EB15UL, 0x3DAA8A14UL, 0x71E8CA7FUL, 0xE893209AUL, 0x45DBB031UL ); static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST( 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C4UL, 0x221208ACUL, 0x9DF506C6UL, 0x1571B4AEUL, 0x8AC47F71UL ); VERIFY_CHECK(r1 != k); VERIFY_CHECK(r2 != k); VERIFY_CHECK(r1 != r2); /* these _var calls are constant time since the shift amount is constant */ secp256k1_scalar_mul_shift_var(&c1, k, &g1, 384); secp256k1_scalar_mul_shift_var(&c2, k, &g2, 384); secp256k1_scalar_mul(&c1, &c1, &minus_b1); secp256k1_scalar_mul(&c2, &c2, &minus_b2); secp256k1_scalar_add(r2, &c1, &c2); secp256k1_scalar_mul(r1, r2, &secp256k1_const_lambda); secp256k1_scalar_negate(r1, r1); secp256k1_scalar_add(r1, r1, k); #ifdef VERIFY secp256k1_scalar_split_lambda_verify(r1, r2, k); #endif } #ifdef VERIFY /* * Proof for secp256k1_scalar_split_lambda's bounds. * * Let * - epsilon1 = 2^256 * |g1/2^384 - b2/d| * - epsilon2 = 2^256 * |g2/2^384 - (-b1)/d| * - c1 = round(k*g1/2^384) * - c2 = round(k*g2/2^384) * * Lemma 1: |c1 - k*b2/d| < 2^-1 + epsilon1 * * |c1 - k*b2/d| * = * |c1 - k*g1/2^384 + k*g1/2^384 - k*b2/d| * <= {triangle inequality} * |c1 - k*g1/2^384| + |k*g1/2^384 - k*b2/d| * = * |c1 - k*g1/2^384| + k*|g1/2^384 - b2/d| * < {rounding in c1 and 0 <= k < 2^256} * 2^-1 + 2^256 * |g1/2^384 - b2/d| * = {definition of epsilon1} * 2^-1 + epsilon1 * * Lemma 2: |c2 - k*(-b1)/d| < 2^-1 + epsilon2 * * |c2 - k*(-b1)/d| * = * |c2 - k*g2/2^384 + k*g2/2^384 - k*(-b1)/d| * <= {triangle inequality} * |c2 - k*g2/2^384| + |k*g2/2^384 - k*(-b1)/d| * = * |c2 - k*g2/2^384| + k*|g2/2^384 - (-b1)/d| * < {rounding in c2 and 0 <= k < 2^256} * 2^-1 + 2^256 * |g2/2^384 - (-b1)/d| * = {definition of epsilon2} * 2^-1 + epsilon2 * * Let * - k1 = k - c1*a1 - c2*a2 * - k2 = - c1*b1 - c2*b2 * * Lemma 3: |k1| < (a1 + a2 + 1)/2 < 2^128 * * |k1| * = {definition of k1} * |k - c1*a1 - c2*a2| * = {(a1*b2 - b1*a2)/n = 1} * |k*(a1*b2 - b1*a2)/n - c1*a1 - c2*a2| * = * |a1*(k*b2/n - c1) + a2*(k*(-b1)/n - c2)| * <= {triangle inequality} * a1*|k*b2/n - c1| + a2*|k*(-b1)/n - c2| * < {Lemma 1 and Lemma 2} * a1*(2^-1 + epslion1) + a2*(2^-1 + epsilon2) * < {rounding up to an integer} * (a1 + a2 + 1)/2 * < {rounding up to a power of 2} * 2^128 * * Lemma 4: |k2| < (-b1 + b2)/2 + 1 < 2^128 * * |k2| * = {definition of k2} * |- c1*a1 - c2*a2| * = {(b1*b2 - b1*b2)/n = 0} * |k*(b1*b2 - b1*b2)/n - c1*b1 - c2*b2| * = * |b1*(k*b2/n - c1) + b2*(k*(-b1)/n - c2)| * <= {triangle inequality} * (-b1)*|k*b2/n - c1| + b2*|k*(-b1)/n - c2| * < {Lemma 1 and Lemma 2} * (-b1)*(2^-1 + epslion1) + b2*(2^-1 + epsilon2) * < {rounding up to an integer} * (-b1 + b2)/2 + 1 * < {rounding up to a power of 2} * 2^128 * * Let * - r2 = k2 mod n * - r1 = k - r2*lambda mod n. * * Notice that r1 is defined such that r1 + r2 * lambda == k (mod n). * * Lemma 5: r1 == k1 mod n. * * r1 * == {definition of r1 and r2} * k - k2*lambda * == {definition of k2} * k - (- c1*b1 - c2*b2)*lambda * == * k + c1*b1*lambda + c2*b2*lambda * == {a1 + b1*lambda == 0 mod n and a2 + b2*lambda == 0 mod n} * k - c1*a1 - c2*a2 * == {definition of k1} * k1 * * From Lemma 3, Lemma 4, Lemma 5 and the definition of r2, we can conclude that * * - either r1 < 2^128 or -r1 mod n < 2^128 * - either r2 < 2^128 or -r2 mod n < 2^128. * * Q.E.D. */ static void secp256k1_scalar_split_lambda_verify(const secp256k1_scalar *r1, const secp256k1_scalar *r2, const secp256k1_scalar *k) { secp256k1_scalar s; unsigned char buf1[32]; unsigned char buf2[32]; /* (a1 + a2 + 1)/2 is 0xa2a8918ca85bafe22016d0b917e4dd77 */ static const unsigned char k1_bound[32] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xa2, 0xa8, 0x91, 0x8c, 0xa8, 0x5b, 0xaf, 0xe2, 0x20, 0x16, 0xd0, 0xb9, 0x17, 0xe4, 0xdd, 0x77 }; /* (-b1 + b2)/2 + 1 is 0x8a65287bd47179fb2be08846cea267ed */ static const unsigned char k2_bound[32] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x8a, 0x65, 0x28, 0x7b, 0xd4, 0x71, 0x79, 0xfb, 0x2b, 0xe0, 0x88, 0x46, 0xce, 0xa2, 0x67, 0xed }; secp256k1_scalar_mul(&s, &secp256k1_const_lambda, r2); secp256k1_scalar_add(&s, &s, r1); VERIFY_CHECK(secp256k1_scalar_eq(&s, k)); secp256k1_scalar_negate(&s, r1); secp256k1_scalar_get_b32(buf1, r1); secp256k1_scalar_get_b32(buf2, &s); VERIFY_CHECK(secp256k1_memcmp_var(buf1, k1_bound, 32) < 0 || secp256k1_memcmp_var(buf2, k1_bound, 32) < 0); secp256k1_scalar_negate(&s, r2); secp256k1_scalar_get_b32(buf1, r2); secp256k1_scalar_get_b32(buf2, &s); VERIFY_CHECK(secp256k1_memcmp_var(buf1, k2_bound, 32) < 0 || secp256k1_memcmp_var(buf2, k2_bound, 32) < 0); } #endif /* VERIFY */ #endif /* SECP256K1_SCALAR_IMPL_H */ ================================================ FILE: C/secp256k1/schnorrsig.h ================================================ #ifndef SECP256K1_SCHNORRSIG_H #define SECP256K1_SCHNORRSIG_H #include "secp256k1.h" #include "extrakeys.h" /** This module implements a variant of Schnorr signatures compliant with * Bitcoin Improvement Proposal 340 "Schnorr Signatures for secp256k1" * (https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki). */ /** Verify a Schnorr signature. * * Returns: 1: correct signature * 0: incorrect signature * In: sig64: pointer to the 64-byte signature to verify. * msg: the message being verified. Can only be NULL if msglen is 0. * msglen: length of the message * pubkey: pointer to an x-only public key to verify with (cannot be NULL) */ static SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorrsig_verify( const unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_xonly_pubkey *pubkey ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(4); #endif /* SCHNORRSIG_H */ ================================================ FILE: C/secp256k1/schnorrsig_impl.h ================================================ /*********************************************************************** * Copyright (c) 2018-2020 Andrew Poelstra, Jonas Nick * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_SCHNORRSIG_IMPL_H #define SECP256K1_SCHNORRSIG_IMPL_H #include "secp256k1.h" #include "schnorrsig.h" #include "../sha256.h" /* Initializes SHA256 with fixed midstate. This midstate was computed by applying * SHA256 to SHA256("BIP0340/challenge")||SHA256("BIP0340/challenge"). */ static sha256_context secp256k1_schnorrsig_sha256_tagged(uint32_t* output) { output[0] = 0x9cecba11ul; output[1] = 0x23925381ul; output[2] = 0x11679112ul; output[3] = 0xd1627e0ful; output[4] = 0x97c87550ul; output[5] = 0x003cc765ul; output[6] = 0x90f61164ul; output[7] = 0x33e9b66aul; return (sha256_context){ .output = output, .counter = 64 }; } static void secp256k1_schnorrsig_challenge(secp256k1_scalar* e, const unsigned char *r32, const unsigned char *msg, size_t msglen, const unsigned char *pubkey32) { unsigned char buf[32]; sha256_midstate sha_buf; /* tagged hash(r.x, pk.x, msg32) */ sha256_context sha = secp256k1_schnorrsig_sha256_tagged(sha_buf.s); sha256_uchars(&sha, r32, 32); sha256_uchars(&sha, pubkey32, 32); sha256_uchars(&sha, msg, msglen); sha256_finalize(&sha); sha256_fromMidstate(buf, sha_buf.s); /* Set scalar e to the challenge hash modulo the curve order as per * BIP340. */ secp256k1_scalar_set_b32(e, buf, NULL); } static int secp256k1_schnorrsig_verify(const unsigned char *sig64, const unsigned char *msg, size_t msglen, const secp256k1_xonly_pubkey *pubkey) { secp256k1_scalar s; secp256k1_scalar e; secp256k1_gej rj; secp256k1_ge pk; secp256k1_gej pkj; secp256k1_fe rx; secp256k1_ge r; unsigned char buf[32]; int overflow; ARG_CHECK(sig64 != NULL); ARG_CHECK(msg != NULL || msglen == 0); ARG_CHECK(pubkey != NULL); if (!secp256k1_fe_set_b32(&rx, &sig64[0])) { return 0; } secp256k1_scalar_set_b32(&s, &sig64[32], &overflow); if (overflow) { return 0; } if (!secp256k1_xonly_pubkey_load(&pk, pubkey)) { return 0; } /* Compute e. */ secp256k1_fe_get_b32(buf, &pk.x); secp256k1_schnorrsig_challenge(&e, &sig64[0], msg, msglen, buf); /* Compute rj = s*G + (-e)*pkj */ secp256k1_scalar_negate(&e, &e); secp256k1_gej_set_ge(&pkj, &pk); secp256k1_ecmult(&rj, &pkj, &e, &s); secp256k1_ge_set_gej_var(&r, &rj); if (secp256k1_ge_is_infinity(&r)) { return 0; } secp256k1_fe_normalize_var(&r.y); return !secp256k1_fe_is_odd(&r.y) && secp256k1_fe_equal_var(&rx, &r.x); } #endif ================================================ FILE: C/secp256k1/secp256k1.h ================================================ #ifndef SECP256K1_H #define SECP256K1_H #include /** Unless explicitly stated all pointer arguments must not be NULL. * * The following rules specify the order of arguments in API calls: * * 1. Context pointers go first, followed by output arguments, combined * output/input arguments, and finally input-only arguments. * 2. Array lengths always immediately follow the argument whose length * they describe, even if this violates rule 1. * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated * later go first. This means: signatures, public nonces, secret nonces, * messages, public keys, secret keys, tweaks. * 4. Arguments that are not data pointers go last, from more complex to less * complex: function pointers, algorithm names, messages, void pointers, * counts, flags, booleans. * 5. Opaque data pointers follow the function pointer they are to be passed to. */ /** Opaque data structure that holds a parsed and valid public key. * * The exact representation of data inside is implementation defined and not * guaranteed to be portable between different platforms or versions. It is * however guaranteed to be 64 bytes in size, and can be safely copied/moved. * If you need to convert to a format suitable for storage or transmission, * use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse. To * compare keys, use secp256k1_ec_pubkey_cmp. */ typedef struct { unsigned char data[64]; } secp256k1_pubkey; # if !defined(SECP256K1_GNUC_PREREQ) # if defined(__GNUC__)&&defined(__GNUC_MINOR__) # define SECP256K1_GNUC_PREREQ(_maj,_min) \ ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min)) # else # define SECP256K1_GNUC_PREREQ(_maj,_min) 0 # endif # endif #define SECP256K1_INLINE inline /* Warning attributes * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out * some paranoid null checks. */ # if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) # define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__)) # else # define SECP256K1_WARN_UNUSED_RESULT # endif # if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) # define SECP256K1_ARG_NONNULL(_x) __attribute__ ((__nonnull__(_x))) # else # define SECP256K1_ARG_NONNULL(_x) # endif #endif /* SECP256K1_H */ ================================================ FILE: C/secp256k1/secp256k1_impl.h ================================================ /*********************************************************************** * Copyright (c) 2013-2015 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_IMPL_H #define SECP256K1_IMPL_H #define SECP256K1_BUILD #include "secp256k1.h" #include "assumptions.h" #include "util.h" #include "field_impl.h" #include "scalar_impl.h" #include "group_impl.h" #include "ecmult_impl.h" #include "eckey_impl.h" #include "int128_impl.h" #ifdef SECP256K1_NO_BUILD # error "secp256k1.h processed without SECP256K1_BUILD defined while building secp256k1.c" #endif #define ARG_CHECK(cond) do { \ if (EXPECT(!(cond), 0)) { \ return 0; \ } \ } while(0) static int secp256k1_pubkey_load(secp256k1_ge* ge, const secp256k1_pubkey* pubkey) { if (sizeof(secp256k1_ge_storage) == 64) { /* When the secp256k1_ge_storage type is exactly 64 byte, use its * representation inside secp256k1_pubkey, as conversion is very fast. * Note that secp256k1_pubkey_save must use the same representation. */ secp256k1_ge_storage s; memcpy(&s, &pubkey->data[0], sizeof(s)); secp256k1_ge_from_storage(ge, &s); } else { /* Otherwise, fall back to 32-byte big endian for X and Y. */ secp256k1_fe x, y; secp256k1_fe_set_b32(&x, pubkey->data); secp256k1_fe_set_b32(&y, pubkey->data + 32); secp256k1_ge_set_xy(ge, &x, &y); } ARG_CHECK(!secp256k1_fe_is_zero(&ge->x)); return 1; } static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) { if (sizeof(secp256k1_ge_storage) == 64) { secp256k1_ge_storage s; secp256k1_ge_to_storage(&s, ge); memcpy(&pubkey->data[0], &s, sizeof(s)); } else { VERIFY_CHECK(!secp256k1_ge_is_infinity(ge)); secp256k1_fe_normalize_var(&ge->x); secp256k1_fe_normalize_var(&ge->y); secp256k1_fe_get_b32(pubkey->data, &ge->x); secp256k1_fe_get_b32(pubkey->data + 32, &ge->y); } } static int secp256k1_ec_pubkey_tweak_add_helper(secp256k1_ge *p, const unsigned char *tweak32) { secp256k1_scalar term; int overflow = 0; secp256k1_scalar_set_b32(&term, tweak32, &overflow); return !overflow && secp256k1_eckey_pubkey_tweak_add(p, &term); } #include "extrakeys_impl.h" #include "schnorrsig_impl.h" #include "generator_impl.h" #endif ================================================ FILE: C/secp256k1/util.h ================================================ /*********************************************************************** * Copyright (c) 2013, 2014 Pieter Wuille * * Distributed under the MIT software license, see the accompanying * * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ #ifndef SECP256K1_UTIL_H #define SECP256K1_UTIL_H #include #include #include #ifdef DETERMINISTIC #define TEST_FAILURE(msg) do { \ fprintf(stderr, "%s\n", msg); \ abort(); \ } while(0); #else #define TEST_FAILURE(msg) do { \ fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \ abort(); \ } while(0) #endif #if SECP256K1_GNUC_PREREQ(3, 0) #define EXPECT(x,c) __builtin_expect((x),(c)) #else #define EXPECT(x,c) (x) #endif #ifdef DETERMINISTIC #define CHECK(cond) do { \ if (EXPECT(!(cond), 0)) { \ TEST_FAILURE("test condition failed"); \ } \ } while(0) #else #define CHECK(cond) do { \ if (EXPECT(!(cond), 0)) { \ TEST_FAILURE("test condition failed: " #cond); \ } \ } while(0) #endif /* Like assert(), but when VERIFY is defined, and side-effect safe. */ #if defined(COVERAGE) #define VERIFY_CHECK(check) #define VERIFY_SETUP(stmt) #elif defined(VERIFY) #define VERIFY_CHECK CHECK #define VERIFY_SETUP(stmt) do { stmt; } while(0) #else #define VERIFY_CHECK(cond) do { (void)(cond); } while(0) #define VERIFY_SETUP(stmt) #endif /* Macro for restrict, when available and not in a VERIFY build. */ #if defined(SECP256K1_BUILD) && defined(VERIFY) # define SECP256K1_RESTRICT #else # define SECP256K1_RESTRICT restrict #endif #if defined(__GNUC__) # define SECP256K1_GNUC_EXT __extension__ #else # define SECP256K1_GNUC_EXT #endif /** Semantics like memcmp. Variable-time. * * We use this to avoid possible compiler bugs with memcmp, e.g. * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=95189 */ static SECP256K1_INLINE int secp256k1_memcmp_var(const void *s1, const void *s2, size_t n) { const unsigned char *p1 = s1, *p2 = s2; size_t i; for (i = 0; i < n; i++) { int diff = p1[i] - p2[i]; if (diff != 0) { return diff; } } return 0; } #if defined(USE_FORCE_WIDEMUL_INT128_STRUCT) /* If USE_FORCE_WIDEMUL_INT128_STRUCT is set, use int128_struct. */ # define SECP256K1_WIDEMUL_INT128 1 # define SECP256K1_INT128_STRUCT 1 #elif defined(USE_FORCE_WIDEMUL_INT128) /* If USE_FORCE_WIDEMUL_INT128 is set, use int128. */ # define SECP256K1_WIDEMUL_INT128 1 # define SECP256K1_INT128_NATIVE 1 #elif defined(USE_FORCE_WIDEMUL_INT64) /* If USE_FORCE_WIDEMUL_INT64 is set, use int64. */ # error WIDEMUL_INT64 not supported in Simplicity. #elif defined(UINT128_MAX) || defined(__SIZEOF_INT128__) /* If a native 128-bit integer type exists, use int128. */ # define SECP256K1_WIDEMUL_INT128 1 # define SECP256K1_INT128_NATIVE 1 #elif defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) /* On 64-bit MSVC targets (x86_64 and arm64), use int128_struct * (which has special logic to implement using intrinsics on those systems). */ # define SECP256K1_WIDEMUL_INT128 1 # define SECP256K1_INT128_STRUCT 1 #elif SIZE_MAX > 0xffffffff /* Systems with 64-bit pointers (and thus registers) very likely benefit from * using 64-bit based arithmetic (even if we need to fall back to 32x32->64 based * multiplication logic). */ # define SECP256K1_WIDEMUL_INT128 1 # define SECP256K1_INT128_STRUCT 1 #else /* Lastly, fall back to int128 structure based arithmetic. */ # define SECP256K1_WIDEMUL_INT128 1 # define SECP256K1_INT128_STRUCT 1 /* Even though these 3 last branches all have the same body, we keep it this way so that it is easy to compare Simplicity's libsecp256k1 with the original libsepc256k1. */ #endif #ifndef __has_builtin #define __has_builtin(x) 0 #endif /* Determine the number of trailing zero bits in a (non-zero) 64-bit x. * This function is only intended to be used as fallback for * secp256k1_ctz64_var, but permits it to be tested separately. */ static SECP256K1_INLINE int secp256k1_ctz64_var_debruijn(uint64_t x) { static const uint8_t debruijn[64] = { 0, 1, 2, 53, 3, 7, 54, 27, 4, 38, 41, 8, 34, 55, 48, 28, 62, 5, 39, 46, 44, 42, 22, 9, 24, 35, 59, 56, 49, 18, 29, 11, 63, 52, 6, 26, 37, 40, 33, 47, 61, 45, 43, 21, 23, 58, 17, 10, 51, 25, 36, 32, 60, 20, 57, 16, 50, 31, 19, 15, 30, 14, 13, 12 }; return debruijn[(uint64_t)((x & -x) * 0x022FDD63CC95386DU) >> 58]; } /* Determine the number of trailing zero bits in a (non-zero) 64-bit x. */ static SECP256K1_INLINE int secp256k1_ctz64_var(uint64_t x) { VERIFY_CHECK(x != 0); #if (__has_builtin(__builtin_ctzl) || SECP256K1_GNUC_PREREQ(3,4)) /* If the unsigned long type is sufficient to represent the largest uint64_t, consider __builtin_ctzl. */ if (((unsigned long)UINT64_MAX) == UINT64_MAX) { return __builtin_ctzl((unsigned long)x); } #endif #if (__has_builtin(__builtin_ctzll) || SECP256K1_GNUC_PREREQ(3,4)) /* Otherwise consider __builtin_ctzll (the unsigned long long type is always at least 64 bits). */ return __builtin_ctzll(x); #else /* If no suitable CTZ builtin is available, use a (variable time) software emulation. */ return secp256k1_ctz64_var_debruijn(x); #endif } #endif /* SECP256K1_UTIL_H */ ================================================ FILE: C/sha256.c ================================================ /* Parts translated from Bitcoin Core's C++ project: * src/crypto/sha256.cpp commit eb7daf4d600eeb631427c018a984a77a34aca66e * * Copyright (c) 2014-2018 The Bitcoin Core developers * Distributed under the MIT software license, see the accompanying * file COPYING or http://www.opensource.org/licenses/mit-license.php. */ #include "sha256.h" #include #include "simplicity_assert.h" /* Multiplying a uint32_t by 1U promotes a value's type to the wider of unsigned int and uint32_t, * avoiding any possible issues with signed integer promotions causing havoc with unsigned modular arithmetic. */ static inline uint32_t Ch(uint32_t x, uint32_t y, uint32_t z) { return z ^ (x & (y ^ z)); } static inline uint32_t Maj(uint32_t x, uint32_t y, uint32_t z) { return (x & y) | (z & (x | y)); } static inline uint32_t Sigma0(uint32_t x) { return (x >> 2 | 1U * x << 30) ^ (x >> 13 | 1U * x << 19) ^ (x >> 22 | 1U * x << 10); } static inline uint32_t Sigma1(uint32_t x) { return (x >> 6 | 1U * x << 26) ^ (x >> 11 | 1U * x << 21) ^ (x >> 25 | 1U * x << 7); } static inline uint32_t sigma0(uint32_t x) { return (x >> 7 | 1U * x << 25) ^ (x >> 18 | 1U * x << 14) ^ (x >> 3); } static inline uint32_t sigma1(uint32_t x) { return (x >> 17 | 1U * x << 15) ^ (x >> 19 | 1U * x << 13) ^ (x >> 10); } /* One round of SHA-256. * * Precondition: NULL != d * NULL != h * d != h */ static inline void Round(uint32_t a, uint32_t b, uint32_t c, uint32_t* d, uint32_t e, uint32_t f, uint32_t g, uint32_t* h, uint32_t k) { uint32_t t1 = 1U * *h + Sigma1(e) + Ch(e, f, g) + k; uint32_t t2 = 1U * Sigma0(a) + Maj(a, b, c); *d = 1U * *d + t1; *h = 1U * t1 + t2; } /* Given a 256-bit 's' and a 512-bit 'chunk', then 's' becomes the value of the SHA-256 compression function ("added" to the original 's' value). * * Precondition: uint32_t s[8]; * uint32_t chunk[16] */ static void sha256_compression_portable(uint32_t* s, const uint32_t* chunk) { uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7]; uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15; Round(a, b, c, &d, e, f, g, &h, 0x428a2f98U + (w0 = chunk[0])); Round(h, a, b, &c, d, e, f, &g, 0x71374491U + (w1 = chunk[1])); Round(g, h, a, &b, c, d, e, &f, 0xb5c0fbcfU + (w2 = chunk[2])); Round(f, g, h, &a, b, c, d, &e, 0xe9b5dba5U + (w3 = chunk[3])); Round(e, f, g, &h, a, b, c, &d, 0x3956c25bU + (w4 = chunk[4])); Round(d, e, f, &g, h, a, b, &c, 0x59f111f1U + (w5 = chunk[5])); Round(c, d, e, &f, g, h, a, &b, 0x923f82a4U + (w6 = chunk[6])); Round(b, c, d, &e, f, g, h, &a, 0xab1c5ed5U + (w7 = chunk[7])); Round(a, b, c, &d, e, f, g, &h, 0xd807aa98U + (w8 = chunk[8])); Round(h, a, b, &c, d, e, f, &g, 0x12835b01U + (w9 = chunk[9])); Round(g, h, a, &b, c, d, e, &f, 0x243185beU + (w10 = chunk[10])); Round(f, g, h, &a, b, c, d, &e, 0x550c7dc3U + (w11 = chunk[11])); Round(e, f, g, &h, a, b, c, &d, 0x72be5d74U + (w12 = chunk[12])); Round(d, e, f, &g, h, a, b, &c, 0x80deb1feU + (w13 = chunk[13])); Round(c, d, e, &f, g, h, a, &b, 0x9bdc06a7U + (w14 = chunk[14])); Round(b, c, d, &e, f, g, h, &a, 0xc19bf174U + (w15 = chunk[15])); Round(a, b, c, &d, e, f, g, &h, 0xe49b69c1U + (w0 = 1U * w0 + sigma1(w14) + w9 + sigma0(w1))); Round(h, a, b, &c, d, e, f, &g, 0xefbe4786U + (w1 = 1U * w1 + sigma1(w15) + w10 + sigma0(w2))); Round(g, h, a, &b, c, d, e, &f, 0x0fc19dc6U + (w2 = 1U * w2 + sigma1(w0) + w11 + sigma0(w3))); Round(f, g, h, &a, b, c, d, &e, 0x240ca1ccU + (w3 = 1U * w3 + sigma1(w1) + w12 + sigma0(w4))); Round(e, f, g, &h, a, b, c, &d, 0x2de92c6fU + (w4 = 1U * w4 + sigma1(w2) + w13 + sigma0(w5))); Round(d, e, f, &g, h, a, b, &c, 0x4a7484aaU + (w5 = 1U * w5 + sigma1(w3) + w14 + sigma0(w6))); Round(c, d, e, &f, g, h, a, &b, 0x5cb0a9dcU + (w6 = 1U * w6 + sigma1(w4) + w15 + sigma0(w7))); Round(b, c, d, &e, f, g, h, &a, 0x76f988daU + (w7 = 1U * w7 + sigma1(w5) + w0 + sigma0(w8))); Round(a, b, c, &d, e, f, g, &h, 0x983e5152U + (w8 = 1U * w8 + sigma1(w6) + w1 + sigma0(w9))); Round(h, a, b, &c, d, e, f, &g, 0xa831c66dU + (w9 = 1U * w9 + sigma1(w7) + w2 + sigma0(w10))); Round(g, h, a, &b, c, d, e, &f, 0xb00327c8U + (w10 = 1U * w10 + sigma1(w8) + w3 + sigma0(w11))); Round(f, g, h, &a, b, c, d, &e, 0xbf597fc7U + (w11 = 1U * w11 + sigma1(w9) + w4 + sigma0(w12))); Round(e, f, g, &h, a, b, c, &d, 0xc6e00bf3U + (w12 = 1U * w12 + sigma1(w10) + w5 + sigma0(w13))); Round(d, e, f, &g, h, a, b, &c, 0xd5a79147U + (w13 = 1U * w13 + sigma1(w11) + w6 + sigma0(w14))); Round(c, d, e, &f, g, h, a, &b, 0x06ca6351U + (w14 = 1U * w14 + sigma1(w12) + w7 + sigma0(w15))); Round(b, c, d, &e, f, g, h, &a, 0x14292967U + (w15 = 1U * w15 + sigma1(w13) + w8 + sigma0(w0))); Round(a, b, c, &d, e, f, g, &h, 0x27b70a85U + (w0 = 1U * w0 + sigma1(w14) + w9 + sigma0(w1))); Round(h, a, b, &c, d, e, f, &g, 0x2e1b2138U + (w1 = 1U * w1 + sigma1(w15) + w10 + sigma0(w2))); Round(g, h, a, &b, c, d, e, &f, 0x4d2c6dfcU + (w2 = 1U * w2 + sigma1(w0) + w11 + sigma0(w3))); Round(f, g, h, &a, b, c, d, &e, 0x53380d13U + (w3 = 1U * w3 + sigma1(w1) + w12 + sigma0(w4))); Round(e, f, g, &h, a, b, c, &d, 0x650a7354U + (w4 = 1U * w4 + sigma1(w2) + w13 + sigma0(w5))); Round(d, e, f, &g, h, a, b, &c, 0x766a0abbU + (w5 = 1U * w5 + sigma1(w3) + w14 + sigma0(w6))); Round(c, d, e, &f, g, h, a, &b, 0x81c2c92eU + (w6 = 1U * w6 + sigma1(w4) + w15 + sigma0(w7))); Round(b, c, d, &e, f, g, h, &a, 0x92722c85U + (w7 = 1U * w7 + sigma1(w5) + w0 + sigma0(w8))); Round(a, b, c, &d, e, f, g, &h, 0xa2bfe8a1U + (w8 = 1U * w8 + sigma1(w6) + w1 + sigma0(w9))); Round(h, a, b, &c, d, e, f, &g, 0xa81a664bU + (w9 = 1U * w9 + sigma1(w7) + w2 + sigma0(w10))); Round(g, h, a, &b, c, d, e, &f, 0xc24b8b70U + (w10 = 1U * w10 + sigma1(w8) + w3 + sigma0(w11))); Round(f, g, h, &a, b, c, d, &e, 0xc76c51a3U + (w11 = 1U * w11 + sigma1(w9) + w4 + sigma0(w12))); Round(e, f, g, &h, a, b, c, &d, 0xd192e819U + (w12 = 1U * w12 + sigma1(w10) + w5 + sigma0(w13))); Round(d, e, f, &g, h, a, b, &c, 0xd6990624U + (w13 = 1U * w13 + sigma1(w11) + w6 + sigma0(w14))); Round(c, d, e, &f, g, h, a, &b, 0xf40e3585U + (w14 = 1U * w14 + sigma1(w12) + w7 + sigma0(w15))); Round(b, c, d, &e, f, g, h, &a, 0x106aa070U + (w15 = 1U * w15 + sigma1(w13) + w8 + sigma0(w0))); Round(a, b, c, &d, e, f, g, &h, 0x19a4c116U + (w0 = 1U * w0 + sigma1(w14) + w9 + sigma0(w1))); Round(h, a, b, &c, d, e, f, &g, 0x1e376c08U + (w1 = 1U * w1 + sigma1(w15) + w10 + sigma0(w2))); Round(g, h, a, &b, c, d, e, &f, 0x2748774cU + (w2 = 1U * w2 + sigma1(w0) + w11 + sigma0(w3))); Round(f, g, h, &a, b, c, d, &e, 0x34b0bcb5U + (w3 = 1U * w3 + sigma1(w1) + w12 + sigma0(w4))); Round(e, f, g, &h, a, b, c, &d, 0x391c0cb3U + (w4 = 1U * w4 + sigma1(w2) + w13 + sigma0(w5))); Round(d, e, f, &g, h, a, b, &c, 0x4ed8aa4aU + (w5 = 1U * w5 + sigma1(w3) + w14 + sigma0(w6))); Round(c, d, e, &f, g, h, a, &b, 0x5b9cca4fU + (w6 = 1U * w6 + sigma1(w4) + w15 + sigma0(w7))); Round(b, c, d, &e, f, g, h, &a, 0x682e6ff3U + (w7 = 1U * w7 + sigma1(w5) + w0 + sigma0(w8))); Round(a, b, c, &d, e, f, g, &h, 0x748f82eeU + (w8 = 1U * w8 + sigma1(w6) + w1 + sigma0(w9))); Round(h, a, b, &c, d, e, f, &g, 0x78a5636fU + (w9 = 1U * w9 + sigma1(w7) + w2 + sigma0(w10))); Round(g, h, a, &b, c, d, e, &f, 0x84c87814U + (w10 = 1U * w10 + sigma1(w8) + w3 + sigma0(w11))); Round(f, g, h, &a, b, c, d, &e, 0x8cc70208U + (w11 = 1U * w11 + sigma1(w9) + w4 + sigma0(w12))); Round(e, f, g, &h, a, b, c, &d, 0x90befffaU + (w12 = 1U * w12 + sigma1(w10) + w5 + sigma0(w13))); Round(d, e, f, &g, h, a, b, &c, 0xa4506cebU + (w13 = 1U * w13 + sigma1(w11) + w6 + sigma0(w14))); Round(c, d, e, &f, g, h, a, &b, 0xbef9a3f7U + (1U * w14 + sigma1(w12) + w7 + sigma0(w15))); Round(b, c, d, &e, f, g, h, &a, 0xc67178f2U + (1U * w15 + sigma1(w13) + w8 + sigma0(w0))); s[0] = 1U * s[0] + a; s[1] = 1U * s[1] + b; s[2] = 1U * s[2] + c; s[3] = 1U * s[3] + d; s[4] = 1U * s[4] + e; s[5] = 1U * s[5] + f; s[6] = 1U * s[6] + g; s[7] = 1U * s[7] + h; } void (*simplicity_sha256_compression)(uint32_t* midstate, const uint32_t* block) = sha256_compression_portable; /* For information purposes only. * Returns true if the sha256_compression implementation has been optimized for the CPU. * Otherwise returns false. */ bool simplicity_sha256_compression_is_optimized(void) { return sha256_compression_portable != simplicity_sha256_compression; }; /* Given a SHA-256 midstate, 'h', of 'len / 512' blocks, and * a 'block' with 'len % 512' bits set and with the remaining bits set to 0, * finalize the SHA-256 computation by adding SHA-256 padding and set 'h' to the resulting SHA-256 hash. * * Precondition: uint32_t h[8]; * uint32_t block[16]; */ static void sha256_end(uint32_t* h, uint32_t* block, const uint_fast64_t len) { block[len / 32 % 16] |= (uint32_t)1 << (31 - len % 32); if (448 <= len % 512) { simplicity_sha256_compression(h, block); memset(block, 0, sizeof(uint32_t[14])); } block[14] = (uint32_t)(len >> 32); block[15] = (uint32_t)len; simplicity_sha256_compression(h, block); } /* Compute the SHA-256 hash, 'h', of the bitstring represented by 's'. * * Precondition: uint32_t h[8]; * '*s' is a valid bitstring; * 's->len < 2^64; */ void simplicity_sha256_bitstring(uint32_t* h, const bitstring* s) { /* This static assert should never fail if uint32_t exists. * But for more certainty, we note that the correctness of this implementation depends on CHAR_BIT being no more than 32. */ static_assert(CHAR_BIT <= 32, "CHAR_BIT has to be less than 32 for uint32_t to even exist."); uint32_t block[16] = { 0 }; size_t count = 0; sha256_iv(h); if (s->len) { block[0] = s->arr[s->offset / CHAR_BIT]; if (s->len < CHAR_BIT - s->offset % CHAR_BIT) { /* s->len is so short that we don't even use a whole char. * Zero out the low bits. */ block[0] = block[0] >> (CHAR_BIT - s->offset % CHAR_BIT - s->len) << (CHAR_BIT - s->offset % CHAR_BIT - s->len); count = s->len; } else { count = CHAR_BIT - s->offset % CHAR_BIT; } block[0] = 1U * block[0] << (32 - CHAR_BIT + s->offset % CHAR_BIT); while (count < s->len) { unsigned char ch = s->arr[(s->offset + count)/CHAR_BIT]; size_t delta = CHAR_BIT; if (s->len - count < CHAR_BIT) { delta = s->len - count; /* Zero out any extra low bits that 'ch' may have. */ ch = (unsigned char)(ch >> (CHAR_BIT - delta) << (CHAR_BIT - delta)); } if (count / 32 != (count + CHAR_BIT) / 32) { /* The next character from s->arr straddles (or almost straddles) the boundary of two elements of the block array. */ block[count / 32 % 16] |= (uint32_t)((uint_fast32_t)ch >> (count + CHAR_BIT) % 32); if (count / 512 != (count + delta) / 512) { simplicity_sha256_compression(h, block); memset(block, 0, sizeof(uint32_t[16])); } } if ((count + CHAR_BIT) % 32) { block[(count + CHAR_BIT) / 32 % 16] |= (uint32_t)(1U * (uint_fast32_t)ch << (32 - (count + CHAR_BIT) % 32)); } count += delta; } } simplicity_assert(count == s->len); sha256_end(h, block, s->len); } #ifndef NO_SHA_NI_FLAG #include "sha256_x86.inc" #endif ================================================ FILE: C/sha256.h ================================================ #ifndef SIMPLICITY_SHA256_H #define SIMPLICITY_SHA256_H #include #include #include #include "bitstring.h" /* A struct holding the 256-bit array of a SHA-256 hash or midstate. */ typedef struct sha256_midstate { uint32_t s[8]; } sha256_midstate; /* Packs (the 8 least significant bits of) 8 'unsigned char's into a 'uint_fast64_t' in "big endian" order. * * Precondition: unsigned char b[8] */ static inline uint_fast64_t ReadBE64(const unsigned char* b) { return (uint_fast64_t)(b[0] & 0xff) << 56 | (uint_fast64_t)(b[1] & 0xff) << 48 | (uint_fast64_t)(b[2] & 0xff) << 40 | (uint_fast64_t)(b[3] & 0xff) << 32 | (uint_fast64_t)(b[4] & 0xff) << 24 | (uint_fast64_t)(b[5] & 0xff) << 16 | (uint_fast64_t)(b[6] & 0xff) << 8 | (uint_fast64_t)(b[7] & 0xff); } /* Packs (the 8 least significant bits of) 4 'unsigned char's into a 'uint32_t' in "big endian" order. * * Precondition: unsigned char b[4] */ static inline uint32_t ReadBE32(const unsigned char* b) { return (uint32_t)(b[0]) << 24 | (uint32_t)(b[1] & 0xff) << 16 | (uint32_t)(b[2] & 0xff) << 8 | (uint32_t)(b[3] & 0xff); } /* Unpacks the 8 least significant bytes from a 'uint_fast64_t' into an 'unsigned char' array in "big endian" order. * * Precondition: unsigned char ptr[8] */ static inline void WriteBE64(unsigned char* ptr, uint_fast64_t x) { ptr[0] = (unsigned char)(0xff & x >> 56); ptr[1] = 0xff & x >> 48; ptr[2] = 0xff & x >> 40; ptr[3] = 0xff & x >> 32; ptr[4] = 0xff & x >> 24; ptr[5] = 0xff & x >> 16; ptr[6] = 0xff & x >> 8; ptr[7] = 0xff & x; } /* Unpacks 4 bytes from a 'uint_fast32_t' into an 'unsigned char' array in "big endian" order. * * Precondition: unsigned char ptr[4] */ static inline void WriteBE32(unsigned char* ptr, uint_fast32_t x) { ptr[0] = (unsigned char)(x >> 24); ptr[1] = (x >> 16) & 0xff; ptr[2] = (x >> 8) & 0xff; ptr[3] = x & 0xff; } /* Unpacks 4 bytes from a 'uint_fast32_t' into an 'unsigned char' array in "little endian" order. * * Precondition: unsigned char ptr[4] */ static inline void WriteLE32(unsigned char* ptr, uint_fast32_t x) { ptr[3] = (unsigned char)(0xff & x >> 24); ptr[2] = 0xff & x >> 16; ptr[1] = 0xff & x >> 8; ptr[0] = 0xff & x; } /* Converts a given 'midstate' value to a 'hash' value as 32 bytes stored in an unsigned char array. * * Precondition: unsigned char hash[32]; * uint32_t midstate[8] */ static inline void sha256_fromMidstate(unsigned char* hash, const uint32_t* midstate) { WriteBE32(hash + 0*4, midstate[0]); WriteBE32(hash + 1*4, midstate[1]); WriteBE32(hash + 2*4, midstate[2]); WriteBE32(hash + 3*4, midstate[3]); WriteBE32(hash + 4*4, midstate[4]); WriteBE32(hash + 5*4, midstate[5]); WriteBE32(hash + 6*4, midstate[6]); WriteBE32(hash + 7*4, midstate[7]); } /* Converts a given 'hash' value as 32 bytes stored in an unsigned char array to a 'midstate' value. * * Precondition: uint32_t midstate[8]; * unsigned char hash[32] */ static inline void sha256_toMidstate(uint32_t* midstate, const unsigned char* hash) { midstate[0] = ReadBE32(hash + 0*4); midstate[1] = ReadBE32(hash + 1*4); midstate[2] = ReadBE32(hash + 2*4); midstate[3] = ReadBE32(hash + 3*4); midstate[4] = ReadBE32(hash + 4*4); midstate[5] = ReadBE32(hash + 5*4); midstate[6] = ReadBE32(hash + 6*4); midstate[7] = ReadBE32(hash + 7*4); } /* Sets the value of 'iv' to SHA-256's initial value. * * Precondition: uint32_t iv[8] */ static inline void sha256_iv(uint32_t* iv) { iv[0] = 0x6a09e667ul; iv[1] = 0xbb67ae85ul; iv[2] = 0x3c6ef372ul; iv[3] = 0xa54ff53aul; iv[4] = 0x510e527ful; iv[5] = 0x9b05688cul; iv[6] = 0x1f83d9abul; iv[7] = 0x5be0cd19ul; } /* Given a 256-bit 'midstate' and a 512-bit 'block', then 'midstate' becomes the value of the SHA-256 compression function ("added" to the original 'midstate' value). * * Precondition: uint32_t midstate[8]; * uint32_t block[16] */ extern void (*simplicity_sha256_compression)(uint32_t* midstate, const uint32_t* block); /* For information purposes only. * Returns true if the sha256_compression implementation has been optimized for the CPU. * Otherwise returns false. */ bool simplicity_sha256_compression_is_optimized(void); /* Compute the SHA-256 hash, 'h', of the bitstring represented by 's'. * * Precondition: uint32_t h[8]; * '*s' is a valid bitstring; */ void simplicity_sha256_bitstring(uint32_t* h, const bitstring* s); /* Given a 256-bit 's' and a 512-bit 'chunk', then 's' becomes the value of the SHA-256 compression function ("added" to the original 's' value). * * Precondition: uint32_t s[8]; * unsigned char chunk[64] */ static void sha256_compression_uchar(uint32_t* s, const unsigned char* chunk) { simplicity_sha256_compression(s, (const uint32_t[16]) { ReadBE32(chunk + 4*0) , ReadBE32(chunk + 4*1) , ReadBE32(chunk + 4*2) , ReadBE32(chunk + 4*3) , ReadBE32(chunk + 4*4) , ReadBE32(chunk + 4*5) , ReadBE32(chunk + 4*6) , ReadBE32(chunk + 4*7) , ReadBE32(chunk + 4*8) , ReadBE32(chunk + 4*9) , ReadBE32(chunk + 4*10) , ReadBE32(chunk + 4*11) , ReadBE32(chunk + 4*12) , ReadBE32(chunk + 4*13) , ReadBE32(chunk + 4*14) , ReadBE32(chunk + 4*15) }); } /* This next section implements a (typical) byte-oriented interface to SHA-256 that consumes the 8 least significant bits of * an 'unsigned char' in big endian order. */ /* This is the context structure for an ongoing SHA-256 evaluation. * It has a pointer to the output buffer, which is modified during evaluation to also hold the current SHA-256 midstate. * It has a counter to track the number of bytes consumed so far. * It has a block of bytes that are queued up that have been consumed but not digested. * * Invariant: uint32_t output[8] */ typedef struct sha256_context { uint32_t* const output; uint_fast64_t counter; unsigned char block[64]; bool overflow; } sha256_context; /* SHA-256 is limited to strictly less than 2^64 bits or 2^56 bytes of data. * This limit cannot be reached in practice under proper use of the SHA-256 interface. * However some jets in simplicity load and store this context and it is easy to synthesize contexts with absurdly large counter values. */ static const uint_fast64_t sha256_max_counter = 0x2000000000000000; /* Initialize a sha256_context given a buffer in which the final output will be written to. * Note that the 'output' buffer may be updated during the computation to hold a SHA-256 midstate. * * Precondition: unit32_t output[8] */ static inline sha256_context sha256_init(uint32_t* output) { sha256_iv(output); return (sha256_context){ .output = output }; } /* Initialize a sha256_context given a buffer in which the final output will be written to, * and the midstate of a tagged hash. * * Note that the 'output' buffer may be updated during the computation to hold a SHA-256 midstate. * Precondition: unit32_t output[8] * unit32_t iv[8] */ static inline sha256_context sha256_tagged_init(uint32_t* output, const sha256_midstate* iv) { memcpy(output, iv->s, sizeof(uint32_t[8])); return (sha256_context){ .output = output, .counter = 64 }; } /* Add an array of bytes to be consumed by an ongoing SHA-256 evaluation. * Returns false if the counter overflows. * * Precondition: NULL != ctx; * if 0 < len then unsigned char arr[len]; */ static inline bool sha256_uchars(sha256_context* ctx, const unsigned char* arr, size_t len) { size_t delta = 64 - ctx->counter % 64; unsigned char *block = ctx->block + ctx->counter % 64; ctx->overflow = ctx->overflow || sha256_max_counter - ctx->counter <= len; ctx->counter += len; while (delta <= len) { memcpy(block, arr, delta); arr += delta; len -= delta; sha256_compression_uchar(ctx->output, ctx->block); block = ctx->block; delta = 64; } if (len) memcpy(block, arr, len); return !ctx->overflow; } /* Add one byte to be consumed by an ongoing SHA-256 evaluation. * * Returns false if the counter overflows. * * Precondition: NULL != ctx; */ static inline bool sha256_uchar(sha256_context* ctx, unsigned char x) { return sha256_uchars(ctx, &x, 1); } /* Add a 64-bit word to be consumed in big endian order by an ongoing SHA-256 evaluation. * For greater certainty, only the least 64 bits of 'x' are consumed. * * Returns false if the counter overflows. * * Precondition: NULL != ctx; */ static inline bool sha256_u64be(sha256_context* ctx, uint_fast64_t x) { unsigned char buf[8]; WriteBE64(buf, x); return sha256_uchars(ctx, buf, sizeof(buf)); } /* Add a 32-bit word to be consumed in little endian byte-order by an ongoing SHA-256 evaluation. * For greater certainty, only the least 32 bits of 'x' are consumed. * Furthermore the bits within each byte are consumed in big endian order. * * Returns false if the counter overflows. * * Precondition: NULL != ctx; */ static inline bool sha256_u32le(sha256_context* ctx, uint_fast32_t x) { unsigned char buf[4]; WriteLE32(buf, x); return sha256_uchars(ctx, buf, sizeof(buf)); } /* Add a 32-bit word to be consumed in big endian byte-order by an ongoing SHA-256 evaluation. * For greater certainty, only the least 32 bits of 'x' are consumed. * Furthermore the bits within each byte are consumed in big endian order. * * Returns false if the counter overflows. * * Precondition: NULL != ctx; */ static inline bool sha256_u32be(sha256_context* ctx, uint_fast32_t x) { unsigned char buf[4]; WriteBE32(buf, x); return sha256_uchars(ctx, buf, sizeof(buf)); } /* Finish the SHA-256 computation by consuming and digesting the SHA-256 padding. * The final result is stored in the original 'output' buffer that was given to 'sha256_init'. * * Returns false if the counter had overflowed. * * Precondition: NULL != ctx; */ static inline bool sha256_finalize(sha256_context* ctx) { bool result = !ctx->overflow; uint_fast64_t length = ctx->counter * 8; sha256_uchars(ctx, (const unsigned char[64]){0x80}, 1 + (64 + 56 - ctx->counter % 64 - 1) % 64); sha256_u64be(ctx, length); return result; } /* Add a 256-bit hash to be consumed by an ongoing SHA-256 evaluation. * * Precondition: NULL != ctx; * NULL != h; */ static inline void sha256_hash(sha256_context* ctx, const sha256_midstate* h) { unsigned char buf[32]; sha256_fromMidstate(buf, h->s); sha256_uchars(ctx, buf, sizeof(buf)); } /* Compare two hash interprted as big endian values. * * Precondition: NULL != a; * NULL != b; */ static inline int sha256_cmp_be(const sha256_midstate* a, const sha256_midstate* b) { if (a->s[0] != b->s[0]) return a->s[0] < b->s[0] ? -1 : 1; if (a->s[1] != b->s[1]) return a->s[1] < b->s[1] ? -1 : 1; if (a->s[2] != b->s[2]) return a->s[2] < b->s[2] ? -1 : 1; if (a->s[3] != b->s[3]) return a->s[3] < b->s[3] ? -1 : 1; if (a->s[4] != b->s[4]) return a->s[4] < b->s[4] ? -1 : 1; if (a->s[5] != b->s[5]) return a->s[5] < b->s[5] ? -1 : 1; if (a->s[6] != b->s[6]) return a->s[6] < b->s[6] ? -1 : 1; if (a->s[7] != b->s[7]) return a->s[7] < b->s[7] ? -1 : 1; return 0; } #endif ================================================ FILE: C/sha256_x86.inc ================================================ #if defined(__SHA__) && defined(__SSE4_1__) && (defined(__x86_64__) || defined(__amd64__) || defined(__i386__)) #include #include #include #include "sha256.h" static bool cpu_has_sha_ni(void) { const uint32_t sse4_flag = (uint32_t)1 << 19; const uint32_t sha_ni_flag = (uint32_t)1 << 29; bool sse4, sha_ni; uint32_t eax, ebx, ecx, edx; __cpuid(0, eax, ebx, ecx, edx); if (eax < 7) return false; __cpuid_count(1, 0, eax, ebx, ecx, edx); sse4 = ecx & sse4_flag; __cpuid_count(7, 0, eax, ebx, ecx, edx); sha_ni = ebx & sha_ni_flag; return sse4 && sha_ni; } /* sha256_compression_x86_sha_ni based on */ /* Given a 256-bit 'midstate' and a 512-bit 'block', then 'midstate' becomes the value of the SHA-256 compression function ("added" to the original 'midstate' value). * * Precondition: uint32_t midstate[8]; * uint32_t block[16] */ static void sha256_compression_x86_sha_ni(uint32_t* midstate, const uint32_t* block) { __m128i msg, t1, t2, m0, m1, m2, m3, s0, s1, so0, so1; /* Load state */ s0 = _mm_loadu_si128((const __m128i*)(midstate + 0)); s1 = _mm_loadu_si128((const __m128i*)(midstate + 4)); t1 = _mm_shuffle_epi32(s0, 0xB1); t2 = _mm_shuffle_epi32(s1, 0x1B); s0 = _mm_alignr_epi8(t1, t2, 0x08); s1 = _mm_blend_epi16(t2, t1, 0xF0); /* Remember old state */ so0 = s0; so1 = s1; /* Rounds 0 - 3 */ m0 = _mm_shuffle_epi32(_mm_loadu_si128((const __m128i*)(block + 0)), 0xE4); msg = _mm_add_epi32(m0, _mm_set_epi64x(0xE9B5DBA5B5C0FBCFULL, 0x71374491428A2F98ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); /* Rounds 4 - 7 */ m1 = _mm_shuffle_epi32(_mm_loadu_si128((const __m128i*)(block + 4)), 0xE4); msg = _mm_add_epi32(m1, _mm_set_epi64x(0xAB1C5ED5923F82A4ULL, 0x59F111F13956C25BULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m0 = _mm_sha256msg1_epu32(m0, m1); /* Rounds 8 - 11 */ m2 = _mm_shuffle_epi32(_mm_loadu_si128((const __m128i*)(block + 8)), 0xE4); msg = _mm_add_epi32(m2, _mm_set_epi64x(0x550C7DC3243185BEULL, 0x12835B01D807AA98ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m1 = _mm_sha256msg1_epu32(m1, m2); /* Rounds 12 - 15 */ m3 = _mm_shuffle_epi32(_mm_loadu_si128((const __m128i*)(block + 12)), 0xE4); msg = _mm_add_epi32(m3, _mm_set_epi64x(0xC19BF1749BDC06A7ULL, 0x80DEB1FE72BE5D74ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m0 = _mm_sha256msg2_epu32(_mm_add_epi32(m0, _mm_alignr_epi8(m3, m2, 4)), m3); m2 = _mm_sha256msg1_epu32(m2, m3); /* Rounds 16 - 19 */ msg = _mm_add_epi32(m0, _mm_set_epi64x(0x240CA1CC0FC19DC6ULL, 0xEFBE4786E49B69C1ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m1 = _mm_sha256msg2_epu32(_mm_add_epi32(m1, _mm_alignr_epi8(m0, m3, 4)), m0); m3 = _mm_sha256msg1_epu32(m3, m0); /* Rounds 20 - 23 */ msg = _mm_add_epi32(m1, _mm_set_epi64x(0x76F988DA5CB0A9DCULL, 0x4A7484AA2DE92C6FULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m2 = _mm_sha256msg2_epu32(_mm_add_epi32(m2, _mm_alignr_epi8(m1, m0, 4)), m1); m0 = _mm_sha256msg1_epu32(m0, m1); /* Rounds 24 - 27 */ msg = _mm_add_epi32(m2, _mm_set_epi64x(0xBF597FC7B00327C8ULL, 0xA831C66D983E5152ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m3 = _mm_sha256msg2_epu32(_mm_add_epi32(m3, _mm_alignr_epi8(m2, m1, 4)), m2); m1 = _mm_sha256msg1_epu32(m1, m2); /* Rounds 28 - 31 */ msg = _mm_add_epi32(m3, _mm_set_epi64x(0x1429296706CA6351ULL, 0xD5A79147C6E00BF3ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m0 = _mm_sha256msg2_epu32(_mm_add_epi32(m0, _mm_alignr_epi8(m3, m2, 4)), m3); m2 = _mm_sha256msg1_epu32(m2, m3); /* Rounds 32 - 35 */ msg = _mm_add_epi32(m0, _mm_set_epi64x(0x53380D134D2C6DFCULL, 0x2E1B213827B70A85ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m1 = _mm_sha256msg2_epu32(_mm_add_epi32(m1, _mm_alignr_epi8(m0, m3, 4)), m0); m3 = _mm_sha256msg1_epu32(m3, m0); /* Rounds 36 - 39 */ msg = _mm_add_epi32(m1, _mm_set_epi64x(0x92722C8581C2C92EULL, 0x766A0ABB650A7354ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m2 = _mm_sha256msg2_epu32(_mm_add_epi32(m2, _mm_alignr_epi8(m1, m0, 4)), m1); m0 = _mm_sha256msg1_epu32(m0, m1); /* Rounds 40 - 43 */ msg = _mm_add_epi32(m2, _mm_set_epi64x(0xC76C51A3C24B8B70ULL, 0xA81A664BA2BFE8A1ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m3 = _mm_sha256msg2_epu32(_mm_add_epi32(m3, _mm_alignr_epi8(m2, m1, 4)), m2); m1 = _mm_sha256msg1_epu32(m1, m2); /* Rounds 44 - 47 */ msg = _mm_add_epi32(m3, _mm_set_epi64x(0x106AA070F40E3585ULL, 0xD6990624D192E819ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m0 = _mm_sha256msg2_epu32(_mm_add_epi32(m0, _mm_alignr_epi8(m3, m2, 4)), m3); m2 = _mm_sha256msg1_epu32(m2, m3); /* Rounds 48 - 51 */ msg = _mm_add_epi32(m0, _mm_set_epi64x(0x34B0BCB52748774CULL, 0x1E376C0819A4C116ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m1 = _mm_sha256msg2_epu32(_mm_add_epi32(m1, _mm_alignr_epi8(m0, m3, 4)), m0); m3 = _mm_sha256msg1_epu32(m3, m0); /* Rounds 52 - 55 */ msg = _mm_add_epi32(m1, _mm_set_epi64x(0x682E6FF35B9CCA4FULL, 0x4ED8AA4A391C0CB3ULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m2 = _mm_sha256msg2_epu32(_mm_add_epi32(m2, _mm_alignr_epi8(m1, m0, 4)), m1); /* Rounds 56 - 59 */ msg = _mm_add_epi32(m2, _mm_set_epi64x(0x8CC7020884C87814ULL, 0x78A5636F748F82EEULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); m3 = _mm_sha256msg2_epu32(_mm_add_epi32(m3, _mm_alignr_epi8(m2, m1, 4)), m2); /* Rounds 60 - 63 */ msg = _mm_add_epi32(m3, _mm_set_epi64x(0xC67178F2BEF9A3F7ULL, 0xA4506CEB90BEFFFAULL)); s1 = _mm_sha256rnds2_epu32(s1, s0, msg); s0 = _mm_sha256rnds2_epu32(s0, s1, _mm_shuffle_epi32(msg, 0x0e)); /* Combine with old state */ s0 = _mm_add_epi32(s0, so0); s1 = _mm_add_epi32(s1, so1); /* Store state */ t1 = _mm_shuffle_epi32(s0, 0x1B); t2 = _mm_shuffle_epi32(s1, 0xB1); s0 = _mm_blend_epi16(t1, t2, 0xF0); s1 = _mm_alignr_epi8(t2, t1, 0x08); _mm_storeu_si128((__m128i*)(midstate + 0), s0); _mm_storeu_si128((__m128i*)(midstate + 4), s1); } /* This function inspects the CPU's capabilities and enables the use of some optimized instructions, if they are known and available. */ extern void simplicity_sha256_cpu_optimize_not_thread_safe(void) __attribute__((constructor)); extern void simplicity_sha256_cpu_optimize_not_thread_safe(void) { if (cpu_has_sha_ni()) { simplicity_sha256_compression = sha256_compression_x86_sha_ni; } } #endif ================================================ FILE: C/simplicity_alloc.h ================================================ #ifndef SIMPLICITY_SIMPLICITY_ALLOC_H #define SIMPLICITY_SIMPLICITY_ALLOC_H #include /* Allocate with malloc by default. */ #define simplicity_malloc malloc /* Allocate+zero initialize with calloc by default. */ #define simplicity_calloc calloc /* Deallocate with free by default. */ #define simplicity_free free #endif /* SIMPLICITY_SIMPLICITY_ALLOC_H */ ================================================ FILE: C/simplicity_assert.h ================================================ #ifndef SIMPLICITY_SIMPLICITY_ASSERT_H #define SIMPLICITY_SIMPLICITY_ASSERT_H #include /* Disable NDEBUG mode. */ #if (defined NDEBUG) && (!defined RECKLESS) # error "Don't be RECKLESS. Turn off NDEBUG when building. For production builds use PRODUCTION." #endif /* Set a PRODUCTION_FLAG value based on whether PRODUCTION mode is enabled or not. */ #ifdef PRODUCTION # define PRODUCTION_FLAG 1 #else # define PRODUCTION_FLAG 0 #endif /* Currently Simplicity's assert is the same a C's assert. */ #define simplicity_assert assert /* simplicity_debug_assert is for assertions to be removed in PRODUCTION mode. * We use an if statement instead of conditional compilation to ensure the condition is type checked, even in PRODUCTION mode. */ #define simplicity_debug_assert(cond) do { if (!PRODUCTION_FLAG) { assert(cond); } } while(0) /* Defines an UNREACHABLE macro that, if you manage to get into NDEBUG mode, calls '__builtin_unreachable' if it exists. */ #if (defined NDEBUG) && (defined __hasbuiltin) # if __has_builtin(__builtin_unreachable) # define SIMPLICITY_UNREACHABLE() __builtin_unreachable() # endif #endif #ifndef SIMPLICITY_UNREACHABLE # define SIMPLICITY_UNREACHABLE assert(NULL == "SIMPLICITY_UNCREACHABLE was reached") #endif #endif /* SIMPLICITY_SIMPLICITY_ASSERT_H */ ================================================ FILE: C/taptweak.h ================================================ #ifndef SIMPLICITY_TAPTWEAK_H #define SIMPLICITY_TAPTWEAK_H #include "frame.h" /* This is a generic taptweak jet implementation parameterized by the tag used in the hash. * It is designed to be specialized to implement slightly different taptweak operations for Bitcoin and Elements. * * PUBKEY * TWO^256 |- PUBKEY * * Precondition: unsigned char[tagLen] tag */ bool simplicity_generic_taptweak(frameItem* dst, frameItem *src, const unsigned char *tag, size_t tagLen); #endif ================================================ FILE: C/test.c ================================================ #include #include #include #include #include #include #include #include #include "ctx8Pruned.h" #include "ctx8Unpruned.h" #include "dag.h" #include "deserialize.h" #include "eval.h" #include "hashBlock.h" #include "rsort.h" #include "sha256.h" #include "schnorr0.h" #include "schnorr6.h" #include "regression4.h" #include "typeSkipTest.h" #include "simplicity_alloc.h" #include "typeInference.h" #include "elements/checkSigHashAllTx1.h" #include "elements/primitive.h" _Static_assert(CHAR_BIT == 8, "Buffers passed to fmemopen presume 8 bit chars"); /* Bitcoin's (old-school) sigop limit is 80,000. Ecdsa signature verification takes approximately 50 microseconds, * meaning a block for of sigops would take 4 seconds to verify. * Post-taproot, there is a block size limit of 4,000,000 WU. * To verify the worst case block full of simplicity programs, in the same 4 second limit * we need to limit Simplicity programs so they take no more than 1 microsecond per WU to run. */ static const double secondsPerWU = 1 / 1000. / 1000.; static int successes = 0; static int failures = 0; #ifdef TIMING_FLAG static int timing_flag = 1; #else static int timing_flag = 0; #endif static void fprint_cmr(FILE* stream, const uint32_t* cmr) { fprintf(stream, "0x%08x, 0x%08x, 0x%08x, 0x%08x, 0x%08x, 0x%08x, 0x%08x, 0x%08x", cmr[0], cmr[1], cmr[2], cmr[3], cmr[4], cmr[5], cmr[6], cmr[7] ); } static void test_decodeUptoMaxInt(void) { printf("Test decodeUptoMaxInt\n"); const unsigned char buf[] = { 0x4b, 0x86, 0x39, 0xe8, 0xdf, 0xc0, 0x38, 0x0f, 0x7f, 0xff, 0xff, 0x00 , 0x00, 0x00, 0xf0, 0xe0, 0x00, 0x00, 0x00, 0x3c, 0x3b, 0xff, 0xff, 0xff , 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00 }; const int32_t expected[] = { 1, 2, 3, 4, 5, 7, 8, 15, 16, 17 , 0xffff, 0x10000, 0x40000000, 0x7fffffff, SIMPLICITY_ERR_DATA_OUT_OF_RANGE }; bitstream stream = initializeBitstream(buf, sizeof(buf)); for (size_t i = 0; i < sizeof(expected)/sizeof(expected[0]); ++i) { int32_t result = simplicity_decodeUptoMaxInt(&stream); if (expected[i] == result) { successes++; } else { failures++; printf("Unexpected result during parsing. Expected %d and received %d\n", expected[i], result); } } } static void test_hashBlock(void) { printf("Test hashBlock\n"); dag_node* dag; combinator_counters census; int_fast32_t len; simplicity_err error; { bitstream stream = initializeBitstream(hashBlock, sizeof_hashBlock); len = simplicity_decodeMallocDag(&dag, simplicity_elements_decodeJet, &census, &stream); if (!dag) { simplicity_assert(len < 0); error = (simplicity_err)len; failures++; printf("Error parsing dag: %d\n", error); } else { simplicity_assert(0 < len); error = simplicity_closeBitstream(&stream); if (!IS_OK(error)) { failures++; printf("Error closing dag stream for hashblock\n"); } } } if (dag && IS_OK(error)) { successes++; if (0 == memcmp(hashBlock_cmr, dag[len-1].cmr.s, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected CMR of hashblock\n"); } type* type_dag; bitstream witness = initializeBitstream(hashBlock_witness, sizeof_hashBlock_witness); if (!IS_OK(simplicity_mallocTypeInference(&type_dag, simplicity_elements_mallocBoundVars, dag, (uint_fast32_t)len, &census)) || !type_dag || type_dag[dag[len-1].sourceType].bitSize != 768 || type_dag[dag[len-1].targetType].bitSize != 256) { failures++; printf("Unexpected failure of type inference for hashblock\n"); } else if (!IS_OK(simplicity_fillWitnessData(dag, type_dag, (uint_fast32_t)len, &witness))) { failures++; printf("Unexpected failure of fillWitnessData for hashblock\n"); } else if (!IS_OK(simplicity_closeBitstream(&witness))) { failures++; printf("Unexpected failure of witness stream for hashblock\n"); } else { { analyses analysis[len]; simplicity_computeAnnotatedMerkleRoot(analysis, dag, type_dag, (uint_fast32_t)len); if (0 == memcmp(hashBlock_amr, analysis[len-1].annotatedMerkleRoot.s, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected AMR of hashblock\n"); } } { sha256_midstate ihr; if (IS_OK(simplicity_verifyNoDuplicateIdentityHashes(&ihr, dag, type_dag, (uint_fast32_t)len)) && 0 == memcmp(hashBlock_ihr, ihr.s, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected IHR of hashblock\n"); } } ubounded inputBitSize = type_dag[dag[len-1].sourceType].bitSize; ubounded outputBitSize = type_dag[dag[len-1].targetType].bitSize; UWORD input[ROUND_UWORD(inputBitSize)]; UWORD output[ROUND_UWORD(outputBitSize)]; { frameItem frame = initWriteFrame(inputBitSize, &input[ROUND_UWORD(inputBitSize)]); simplicity_assert(256+512 == inputBitSize); /* Set SHA-256's initial value. */ write32s(&frame, (uint32_t[8]) { 0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19 } , 8); /* Set the block to be compressed to "abc" with padding. */ write32s(&frame, (uint32_t[16]){ [0] = 0x61626380, [15] = 0x18 }, 16); } { ubounded cellsBound, UWORDBound, frameBound, costBound; if (IS_OK(simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, UBOUNDED_MAX, 0, UBOUNDED_MAX, dag, type_dag, (uint_fast32_t)len)) && hashBlock_cost == costBound) { successes++; } else { failures++; printf("Expected %d for cost, but got %d instead.\n", hashBlock_cost, costBound); } } simplicity_err err = simplicity_evalTCOExpression(CHECK_NONE, output, input, dag, type_dag, (uint_fast32_t)len, 0, NULL, NULL); if (IS_OK(err)) { /* The expected result is the value 'SHA256("abc")'. */ const uint32_t expectedHash[8] = { 0xba7816bful, 0x8f01cfeaul, 0x414140deul, 0x5dae2223ul , 0xb00361a3ul, 0x96177a9cul, 0xb410ff61ul, 0xf20015adul }; frameItem frame = initReadFrame(outputBitSize, &output[0]); uint32_t result[8]; simplicity_assert(256 == outputBitSize); read32s(result, 8, &frame); if (0 == memcmp(expectedHash, result, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected output of hashblock computation.\n"); } } else { failures++; printf("Unexpected failure of hashblock evaluation: %d\n", err); } } simplicity_free(type_dag); } simplicity_free(dag); } static void test_program(char* name, const unsigned char* program, size_t program_len, const unsigned char* witness, size_t witness_len, simplicity_err expectedResult, const uint32_t* expectedCMR, const uint32_t* expectedIHR, const uint32_t* expectedAMR, const ubounded *expectedCost) { printf("Test %s\n", name); dag_node* dag; combinator_counters census; int_fast32_t len; simplicity_err error; { bitstream stream = initializeBitstream(program, program_len); len = simplicity_decodeMallocDag(&dag, simplicity_elements_decodeJet, &census, &stream); if (!dag) { simplicity_assert(len < 0); error = (simplicity_err)len; failures++; printf("Error parsing dag: %d\n", error); } else { simplicity_assert(0 < len); error = simplicity_closeBitstream(&stream); if (!IS_OK(error)) { if (expectedResult == error) { successes++; } else { failures++; printf("Error closing dag stream: %d\n", error); } } } } if (dag && IS_OK(error)) { successes++; if (expectedCMR) { if (0 == memcmp(expectedCMR, dag[len-1].cmr.s, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected CMR. Expected\n{"); fprint_cmr(stdout, expectedCMR); printf("}, but received\n{"); fprint_cmr(stdout, dag[len-1].cmr.s); printf("}\n"); } } type* type_dag; bitstream witness_stream = initializeBitstream(witness, witness_len); if (!IS_OK(simplicity_mallocTypeInference(&type_dag, simplicity_elements_mallocBoundVars, dag, (uint_fast32_t)len, &census)) || !type_dag || dag[len-1].sourceType != 0 || dag[len-1].targetType != 0) { failures++; printf("Unexpected failure of type inference.\n"); } else if (!IS_OK(simplicity_fillWitnessData(dag, type_dag, (uint_fast32_t)len, &witness_stream))) { failures++; printf("Unexpected failure of fillWitnessData.\n"); } else if (!IS_OK(simplicity_closeBitstream(&witness_stream))) { failures++; printf("Unexpected failure closing witness_stream\n"); } else { if (expectedAMR) { analyses analysis[len]; simplicity_computeAnnotatedMerkleRoot(analysis, dag, type_dag, (uint_fast32_t)len); if (0 == memcmp(expectedAMR, analysis[len-1].annotatedMerkleRoot.s, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected AMR.\n"); } } { sha256_midstate ihr; if (IS_OK(simplicity_verifyNoDuplicateIdentityHashes(&ihr, dag, type_dag, (uint_fast32_t)len)) && (!expectedIHR || 0 == memcmp(expectedIHR, ihr.s, sizeof(uint32_t[8])))) { successes++; } else { failures++; printf("Unexpected IHR.\n"); } } if (expectedCost) { ubounded cellsBound, UWORDBound, frameBound, costBound; if (IS_OK(simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, UBOUNDED_MAX, 0, UBOUNDED_MAX, dag, type_dag, (uint_fast32_t)len)) && 0 < costBound && *expectedCost == costBound) { successes++; } else { failures++; printf("Expected %u for cost, but got %u instead.\n", *expectedCost, costBound); } /* Analysis should pass when computed bounds are used. */ if (IS_OK(simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, cellsBound, costBound-1, costBound, dag, type_dag, (uint_fast32_t)len)) && *expectedCost == costBound) { successes++; } else { failures++; printf("Analysis with computed bounds failed.\n"); } /* if cellsBound is non-zero, analysis should fail when smaller cellsBound is used. */ if (0 < cellsBound) { if (SIMPLICITY_ERR_EXEC_MEMORY == simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, cellsBound-1, 0, UBOUNDED_MAX, dag, type_dag, (uint_fast32_t)len)) { successes++; } else { failures++; printf("Analysis with too small cells bounds failed. \n"); } } /* Analysis should fail when smaller costBound is used. */ if (0 < *expectedCost && SIMPLICITY_ERR_EXEC_BUDGET == simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, UBOUNDED_MAX, 0, *expectedCost-1, dag, type_dag, (uint_fast32_t)len) ) { successes++; } else { failures++; printf("Analysis with too small cost bounds failed.\n"); } /* Analysis should fail when overweight. */ if (0 < *expectedCost && SIMPLICITY_ERR_OVERWEIGHT == simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, UBOUNDED_MAX, *expectedCost, UBOUNDED_MAX, dag, type_dag, (uint_fast32_t)len) ) { successes++; } else { failures++; printf("Analysis with too large minCost failed.\n"); } } simplicity_err actualResult = evalTCOProgram(dag, type_dag, (uint_fast32_t)len, 0, NULL, NULL); if (expectedResult == actualResult) { successes++; } else { failures++; printf("Expected %d from evaluation, but got %d instead.\n", expectedResult, actualResult); } } simplicity_free(type_dag); } simplicity_free(dag); } static void test_occursCheck(void) { printf("Test occursCheck\n"); /* The untyped Simplicity term (case (drop iden) iden) ought to cause an occurs check failure. */ const unsigned char buf[] = { 0xc1, 0x07, 0x20, 0x30 }; dag_node* dag; combinator_counters census; int_fast32_t len; { bitstream stream = initializeBitstream(buf, sizeof(buf)); len = simplicity_decodeMallocDag(&dag, simplicity_elements_decodeJet, &census, &stream); } if (!dag) { simplicity_assert(len < 0); printf("Error parsing dag: %" PRIdFAST32 "\n", len); } else { type* type_dag; simplicity_assert(0 < len); if (SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK == simplicity_mallocTypeInference(&type_dag, simplicity_elements_mallocBoundVars, dag, (uint_fast32_t)len, &census) && !type_dag) { successes++; } else { printf("Unexpected occurs check success\n"); failures++; } simplicity_free(type_dag); } simplicity_free(dag); } static void test_elements(void) { unsigned char cmr[32], amr[32]; sha256_fromMidstate(cmr, elementsCheckSigHashAllTx1_cmr); sha256_fromMidstate(amr, elementsCheckSigHashAllTx1_amr); unsigned char genesisHash[32] = {0x0f, 0x91, 0x88, 0xf1, 0x3c, 0xb7, 0xb2, 0xc7, 0x1f, 0x2a, 0x33, 0x5e, 0x3a, 0x4f, 0xc3, 0x28, 0xbf, 0x5b, 0xeb, 0x43, 0x60, 0x12, 0xaf, 0xca, 0x59, 0x0b, 0x1a, 0x11, 0x46, 0x6e, 0x22, 0x06}; rawElementsTapEnv rawTaproot = (rawElementsTapEnv) { .controlBlock = (unsigned char [33]){0xbe, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x3b, 0x78, 0xce, 0x56, 0x3f, 0x89, 0xa0, 0xed, 0x94, 0x14, 0xf5, 0xaa, 0x28, 0xad, 0x0d, 0x96, 0xd6, 0x79, 0x5f, 0x9c, 0x63} , .pathLen = 0 , .scriptCMR = cmr }; elementsTapEnv* taproot = simplicity_elements_mallocTapEnv(&rawTaproot); printf("Test elements\n"); { rawElementsTransaction testTx1 = (rawElementsTransaction) { .txid = (unsigned char[32]){0xdb, 0x9a, 0x3d, 0xe0, 0xb6, 0xb8, 0xcc, 0x74, 0x1e, 0x4d, 0x6c, 0x8f, 0x19, 0xce, 0x75, 0xec, 0x0d, 0xfd, 0x01, 0x02, 0xdb, 0x9c, 0xb5, 0xcd, 0x27, 0xa4, 0x1a, 0x66, 0x91, 0x66, 0x3a, 0x07} , .input = (rawElementsInput[]) { { .annex = NULL , .prevTxid = (unsigned char[32]){0xeb, 0x04, 0xb6, 0x8e, 0x9a, 0x26, 0xd1, 0x16, 0x04, 0x6c, 0x76, 0xe8, 0xff, 0x47, 0x33, 0x2f, 0xb7, 0x1d, 0xda, 0x90, 0xff, 0x4b, 0xef, 0x53, 0x70, 0xf2, 0x52, 0x26, 0xd3, 0xbc, 0x09, 0xfc} , .prevIx = 0 , .sequence = 0xfffffffe , .issuance = {0} , .scriptSig = {0} , .txo = { .asset = (unsigned char[33]){0x01, 0x23, 0x0f, 0x4f, 0x5d, 0x4b, 0x7c, 0x6f, 0xa8, 0x45, 0x80, 0x6e, 0xe4, 0xf6, 0x77, 0x13, 0x45, 0x9e, 0x1b, 0x69, 0xe8, 0xe6, 0x0f, 0xce, 0xe2, 0xe4, 0x94, 0x0c, 0x7a, 0x0d, 0x5d, 0xe1, 0xb2} , .value = (unsigned char[9]){0x01, 0x00, 0x00, 0x00, 0x02, 0x54, 0x0b, 0xe4, 0x00} , .scriptPubKey = {0} } } } , .output = (rawElementsOutput[]) { { .asset = (unsigned char[33]){0x01, 0x23, 0x0f, 0x4f, 0x5d, 0x4b, 0x7c, 0x6f, 0xa8, 0x45, 0x80, 0x6e, 0xe4, 0xf6, 0x77, 0x13, 0x45, 0x9e, 0x1b, 0x69, 0xe8, 0xe6, 0x0f, 0xce, 0xe2, 0xe4, 0x94, 0x0c, 0x7a, 0x0d, 0x5d, 0xe1, 0xb2} , .value = (unsigned char[9]){0x01, 0x00, 0x00, 0x00, 0x02, 0x54, 0x0b, 0xd7, 0x1c} , .nonce = NULL , .scriptPubKey = { .buf = (unsigned char [26]){0x19, 0x76, 0xa9, 0x14, 0x48, 0x63, 0x3e, 0x2c, 0x0e, 0xe9, 0x49, 0x5d, 0xd3, 0xf9, 0xc4, 0x37, 0x32, 0xc4, 0x7f, 0x47, 0x02, 0xa3, 0x62, 0xc8, 0x88, 0xac} , .len = 26 } } , { .asset = (unsigned char[33]){0x01, 0x23, 0x0f, 0x4f, 0x5d, 0x4b, 0x7c, 0x6f, 0xa8, 0x45, 0x80, 0x6e, 0xe4, 0xf6, 0x77, 0x13, 0x45, 0x9e, 0x1b, 0x69, 0xe8, 0xe6, 0x0f, 0xce, 0xe2, 0xe4, 0x94, 0x0c, 0x7a, 0x0d, 0x5d, 0xe1, 0xb2} , .value = (unsigned char[9]){0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0c, 0xe4} , .nonce = NULL , .scriptPubKey = {0} } } , .numInputs = 1 , .numOutputs = 2 , .version = 0x00000002 , .lockTime = 0x00000000 }; elementsTransaction* tx1 = simplicity_elements_mallocTransaction(&testTx1); if (tx1) { successes++; simplicity_err execResult; { unsigned char cmrResult[32]; if (simplicity_elements_computeCmr(&execResult, cmrResult, elementsCheckSigHashAllTx1, sizeof_elementsCheckSigHashAllTx1) && IS_OK(execResult)) { if (0 == memcmp(cmrResult, cmr, sizeof(unsigned char[8]))) { successes++; } else { failures++; printf("Unexpected CMR of elementsCheckSigHashAllTx1\n"); } } else { failures++; printf("simplicity_elements_computeCmr of elementsCheckSigHashAllTx1 unexpectedly produced %d.\n", execResult); } } { unsigned char ihrResult[32]; if (simplicity_elements_execSimplicity(&execResult, ihrResult, tx1, 0, taproot, genesisHash, 0, (elementsCheckSigHashAllTx1_cost + 999)/1000, amr, elementsCheckSigHashAllTx1, sizeof_elementsCheckSigHashAllTx1, elementsCheckSigHashAllTx1_witness, sizeof_elementsCheckSigHashAllTx1_witness) && IS_OK(execResult)) { sha256_midstate ihr; sha256_toMidstate(ihr.s, ihrResult); if (0 == memcmp(ihr.s, elementsCheckSigHashAllTx1_ihr, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Unexpected IHR of elementsCheckSigHashAllTx1\n"); } } else { failures++; printf("execSimplicity of elementsCheckSigHashAllTx1 on tx1 unexpectedly produced %d.\n", execResult); } if (elementsCheckSigHashAllTx1_cost){ /* test the same transaction without adequate budget. */ simplicity_assert(elementsCheckSigHashAllTx1_cost); if (simplicity_elements_execSimplicity(&execResult, ihrResult, tx1, 0, taproot, genesisHash, 0, (elementsCheckSigHashAllTx1_cost - 1)/1000, amr, elementsCheckSigHashAllTx1, sizeof_elementsCheckSigHashAllTx1, elementsCheckSigHashAllTx1_witness, sizeof_elementsCheckSigHashAllTx1_witness) && SIMPLICITY_ERR_EXEC_BUDGET == execResult) { successes++; } else { failures++; printf("execSimplicity of elementsCheckSigHashAllTx1 on tx1 unexpectedly produced %d.\n", execResult); } } } { /* test the same transaction with a erroneous signature. */ unsigned char brokenSig[sizeof_elementsCheckSigHashAllTx1_witness]; memcpy(brokenSig, elementsCheckSigHashAllTx1_witness, sizeof_elementsCheckSigHashAllTx1_witness); brokenSig[sizeof_elementsCheckSigHashAllTx1_witness - 1] ^= 0x80; if (simplicity_elements_execSimplicity(&execResult, NULL, tx1, 0, taproot, genesisHash, 0, BUDGET_MAX, NULL, elementsCheckSigHashAllTx1, sizeof_elementsCheckSigHashAllTx1, brokenSig, sizeof_elementsCheckSigHashAllTx1_witness) && SIMPLICITY_ERR_EXEC_JET == execResult) { successes++; } else { failures++; printf("execSimplicity of brokenSig on tx1 unexpectedly produced %d.\n", execResult); } } } else { printf("mallocTransaction(&rawTx1) failed\n"); failures++; } simplicity_elements_freeTransaction(tx1); } /* test a modified transaction with the same signature. */ { rawElementsTransaction testTx2 = (rawElementsTransaction) { .txid = (unsigned char[32]){0xdb, 0x9a, 0x3d, 0xe0, 0xb6, 0xb8, 0xcc, 0x74, 0x1e, 0x4d, 0x6c, 0x8f, 0x19, 0xce, 0x75, 0xec, 0x0d, 0xfd, 0x01, 0x02, 0xdb, 0x9c, 0xb5, 0xcd, 0x27, 0xa4, 0x1a, 0x66, 0x91, 0x66, 0x3a, 0x07} , .input = (rawElementsInput[]) { { .prevTxid = (unsigned char[32]){0xeb, 0x04, 0xb6, 0x8e, 0x9a, 0x26, 0xd1, 0x16, 0x04, 0x6c, 0x76, 0xe8, 0xff, 0x47, 0x33, 0x2f, 0xb7, 0x1d, 0xda, 0x90, 0xff, 0x4b, 0xef, 0x53, 0x70, 0xf2, 0x52, 0x26, 0xd3, 0xbc, 0x09, 0xfc} , .prevIx = 0 , .sequence = 0xffffffff /* Here is the modification. */ , .issuance = {0} , .txo = { .asset = (unsigned char[33]){0x01, 0x23, 0x0f, 0x4f, 0x5d, 0x4b, 0x7c, 0x6f, 0xa8, 0x45, 0x80, 0x6e, 0xe4, 0xf6, 0x77, 0x13, 0x45, 0x9e, 0x1b, 0x69, 0xe8, 0xe6, 0x0f, 0xce, 0xe2, 0xe4, 0x94, 0x0c, 0x7a, 0x0d, 0x5d, 0xe1, 0xb2} , .value = (unsigned char[9]){0x01, 0x00, 0x00, 0x00, 0x02, 0x54, 0x0b, 0xe4, 0x00} , .scriptPubKey = {0} } } } , .output = (rawElementsOutput[]) { { .asset = (unsigned char[33]){0x01, 0x23, 0x0f, 0x4f, 0x5d, 0x4b, 0x7c, 0x6f, 0xa8, 0x45, 0x80, 0x6e, 0xe4, 0xf6, 0x77, 0x13, 0x45, 0x9e, 0x1b, 0x69, 0xe8, 0xe6, 0x0f, 0xce, 0xe2, 0xe4, 0x94, 0x0c, 0x7a, 0x0d, 0x5d, 0xe1, 0xb2} , .value = (unsigned char[9]){0x01, 0x00, 0x00, 0x00, 0x02, 0x54, 0x0b, 0xd7, 0x1c} , .nonce = NULL , .scriptPubKey = { .buf = (unsigned char [26]){0x19, 0x76, 0xa9, 0x14, 0x48, 0x63, 0x3e, 0x2c, 0x0e, 0xe9, 0x49, 0x5d, 0xd3, 0xf9, 0xc4, 0x37, 0x32, 0xc4, 0x7f, 0x47, 0x02, 0xa3, 0x62, 0xc8, 0x88, 0xac} , .len = 26 } } , { .asset = (unsigned char[33]){0x01, 0x23, 0x0f, 0x4f, 0x5d, 0x4b, 0x7c, 0x6f, 0xa8, 0x45, 0x80, 0x6e, 0xe4, 0xf6, 0x77, 0x13, 0x45, 0x9e, 0x1b, 0x69, 0xe8, 0xe6, 0x0f, 0xce, 0xe2, 0xe4, 0x94, 0x0c, 0x7a, 0x0d, 0x5d, 0xe1, 0xb2} , .value = (unsigned char[9]){0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0c, 0xe4} , .nonce = NULL , .scriptPubKey = {0} } } , .numInputs = 1 , .numOutputs = 2 , .version = 0x00000002 , .lockTime = 0x00000000 }; elementsTransaction* tx2 = simplicity_elements_mallocTransaction(&testTx2); if (tx2) { successes++; simplicity_err execResult; { if (simplicity_elements_execSimplicity(&execResult, NULL, tx2, 0, taproot, genesisHash, 0, BUDGET_MAX, NULL, elementsCheckSigHashAllTx1, sizeof_elementsCheckSigHashAllTx1, elementsCheckSigHashAllTx1_witness, sizeof_elementsCheckSigHashAllTx1_witness) && SIMPLICITY_ERR_EXEC_JET == execResult) { successes++; } else { failures++; printf("execSimplicity of elementsCheckSigHashAllTx1 on tx2 unexpectedly produced %d.\n", execResult); } } } else { printf("mallocTransaction(&testTx2) failed\n"); failures++; } simplicity_elements_freeTransaction(tx2); } simplicity_elements_freeTapEnv(taproot); } static sha256_midstate hashint(uint_fast32_t n) { sha256_midstate result; sha256_context ctx = sha256_init(result.s); sha256_u32le(&ctx, n); sha256_finalize(&ctx); return result; } static sha256_midstate rsort_no_duplicates(uint_fast32_t i) { return hashint(i); } static sha256_midstate rsort_all_duplicates(uint_fast32_t i) { (void)i; return hashint(0); } static sha256_midstate rsort_one_duplicate(uint_fast32_t i) { return hashint(i ? i : 1); } /* Tests a worst-case conditions for stack usage in rsort. */ static sha256_midstate rsort_diagonal(uint_fast32_t i) { sha256_midstate result = {0}; unsigned char *alias = (unsigned char *)(result.s); for (uint_fast32_t j = 0; j < sizeof(result.s); ++j) { alias[j] = j == i ? 0 : 0xff; } return result; } static void test_hasDuplicates(const char* name, int expected, sha256_midstate (*f)(uint_fast32_t), uint_fast32_t n) { sha256_midstate hashes[n]; printf("Test %s\n", name); for(uint_fast32_t i = 0; i < n; ++i) { hashes[i] = f(i); } int actual = simplicity_hasDuplicates(hashes, n); if (expected == actual) { successes++; } else if (actual < 0) { failures++; printf("Unexpected failure of hasDuplicates\n"); } else if (0 == expected) { failures++; printf("Expected no duplicate but found some.\n"); } else { failures++; printf("Expected duplicates but found none.\n"); } } static void regression_tests(void) { { /* word("2^23 zero bits") ; unit */ size_t sizeof_regression3 = ((size_t)1 << 20) + 4; unsigned char *regression3 = simplicity_calloc(sizeof_regression3, 1); clock_t start, end; double diff, bound; const uint32_t cmr[] = { 0x872d12eeu, 0x631ae2e7u, 0xffb8b06au, 0xc54ef77fu, 0x693adbffu, 0xb229e760u, 0x111b8fd9u, 0x13d88b7au }; simplicity_assert(regression3); regression3[0] = 0xb7; regression3[1] = 0x08; regression3[sizeof_regression3 - 2] = 0x48; regression3[sizeof_regression3 - 1] = 0x20; start = clock(); test_program("regression3", regression3, sizeof_regression3, NULL, 0, SIMPLICITY_ERR_EXEC_MEMORY, cmr, NULL, NULL, NULL); end = clock(); diff = (double)(end - start) / CLOCKS_PER_SEC; bound = (double)(sizeof_regression3) * secondsPerWU; printf("cpu_time_used by regression3: %f s. (Should be less than %f s.)\n", diff, bound); if (timing_flag) { if (diff <= bound) { successes++; } else { failures++; printf("regression3 took too long.\n"); } } simplicity_free(regression3); } { clock_t start, end; double diff, bound; start = clock(); test_program("regression4", regression4, sizeof_regression4, NULL, 0, SIMPLICITY_NO_ERROR, NULL, NULL, NULL, NULL); end = clock(); diff = (double)(end - start) / CLOCKS_PER_SEC; bound = (double)(sizeof_regression4) * secondsPerWU; printf("cpu_time_used by regression4: %f s. (Should be less than %f s.)\n", diff, bound); if (timing_flag) { if (diff <= bound) { successes++; } else { failures++; printf("regression4 took too long.\n"); } } } } static void iden8mebi_test(void) { /* iden composed with itself 2^23 times. */ const unsigned char iden8mebi[23] = {0xe1, 0x08}; const ubounded expectedCost = 1677721500; /* in milliWU */ clock_t start, end; double diff, bound; start = clock(); test_program("iden8mebi", iden8mebi, sizeof(iden8mebi), NULL, 0, SIMPLICITY_NO_ERROR, NULL, NULL, NULL, &expectedCost); end = clock(); diff = (double)(end - start) / CLOCKS_PER_SEC; bound = (double)expectedCost / 1000. * secondsPerWU; printf("cpu_time_used by iden8mebi: %f s. (Should be less than %f s.)\n", diff, bound); if (timing_flag) { if (diff <= bound) { successes++; } else { failures++; printf("iden8mebi took too long.\n"); } } } static void exactBudget_test(void) { /* Core Simplicity program with a cost that is exactly 410000 milliWU */ const unsigned char program[] = { 0xe0, 0x09, 0x40, 0x81, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x81, 0x02, 0x05, 0xb4, 0x6d, 0xa0, 0x80 }; const ubounded expectedCost = 410; /* in WU */ printf("Test exactBudget\n"); dag_node* dag; type* type_dag; combinator_counters census; int_fast32_t len; simplicity_err error, expected; sha256_midstate ihr; { bitstream stream = initializeBitstream(program, sizeof(program)); len = simplicity_decodeMallocDag(&dag, simplicity_elements_decodeJet, &census, &stream); simplicity_assert(dag); simplicity_assert(0 < len); error = simplicity_closeBitstream(&stream); simplicity_assert(IS_OK(error)); } error = simplicity_mallocTypeInference(&type_dag, simplicity_elements_mallocBoundVars, dag, (uint_fast32_t)len, &census); simplicity_assert(IS_OK(error)); simplicity_assert(type_dag); simplicity_assert(!dag[len-1].sourceType); simplicity_assert(!dag[len-1].targetType); { bitstream stream = initializeBitstream(NULL, 0); error = simplicity_fillWitnessData(dag, type_dag, (uint_fast32_t)len, &stream); simplicity_assert(IS_OK(error)); } error = simplicity_verifyNoDuplicateIdentityHashes(&ihr, dag, type_dag, (uint_fast32_t)len); simplicity_assert(IS_OK(error)); { ubounded cellsBound, UWORDBound, frameBound, costBound; error = simplicity_analyseBounds(&cellsBound, &UWORDBound, &frameBound, &costBound, UBOUNDED_MAX, 0, UBOUNDED_MAX, dag, type_dag, (uint_fast32_t)len); simplicity_assert(IS_OK(error)); simplicity_assert(1000*expectedCost == costBound); } error = evalTCOProgram(dag, type_dag, (uint_fast32_t)len, expectedCost, &expectedCost, NULL); expected = SIMPLICITY_ERR_OVERWEIGHT; if (expected == error) { successes++; } else { failures++; printf("Expected %d from evaluation, but got %d instead.\n", expected, error); } error = evalTCOProgram(dag, type_dag, (uint_fast32_t)len, expectedCost-1, &(ubounded){expectedCost-1}, NULL); expected = SIMPLICITY_ERR_EXEC_BUDGET; if (expected == error) { successes++; } else { failures++; printf("Expected %d from evaluation, but got %d instead.\n", expected, error); } error = evalTCOProgram(dag, type_dag, (uint_fast32_t)len, expectedCost, &(ubounded){expectedCost+1}, NULL); expected = SIMPLICITY_ERR_OVERWEIGHT; if (expected == error) { successes++; } else { failures++; printf("Expected %d from evaluation, but got %d instead.\n", expected, error); } error = evalTCOProgram(dag, type_dag, (uint_fast32_t)len, expectedCost-1, &expectedCost, NULL); expected = SIMPLICITY_NO_ERROR; if (expected == error) { successes++; } else { failures++; printf("Expected %d from evaluation, but got %d instead.\n", expected, error); } simplicity_free(type_dag); simplicity_free(dag); } int main(int argc, char **argv) { while (true) { static struct option long_options[] = { /* These options set a flag. */ {"timing", no_argument, &timing_flag, 1}, {"no-timing", no_argument, &timing_flag, 0}, {0, 0, 0, 0} }; int opt_result = getopt_long(argc, argv, "", long_options, NULL); if (-1 == opt_result) break; if (0 == opt_result) continue; exit(EXIT_FAILURE); } if (simplicity_sha256_compression_is_optimized()) { printf("Sha optimization enabled.\n"); if (timing_flag) { printf("Timings are checked.\n"); } else { printf("Timings not checked.\n"); } } else { printf("Sha optimization disabled.\n"); if (timing_flag) { printf("Timings cannot be checked.\n"); } else { printf("Timings not checked.\n"); } timing_flag = 0; } test_decodeUptoMaxInt(); test_hashBlock(); test_occursCheck(); test_hasDuplicates("hasDuplicates no duplicates testcase", 0, rsort_no_duplicates, 10000); test_hasDuplicates("hasDuplicates all duplicates testcase", 1, rsort_all_duplicates, 10000); test_hasDuplicates("hasDuplicates one duplicate testcase", 1, rsort_one_duplicate, 10000); test_hasDuplicates("hasDuplicates diagonal testcase", 0, rsort_diagonal, 33); test_program("ctx8Pruned", ctx8Pruned, sizeof_ctx8Pruned, ctx8Pruned_witness, sizeof_ctx8Pruned_witness, SIMPLICITY_NO_ERROR, ctx8Pruned_cmr, ctx8Pruned_ihr, ctx8Pruned_amr, &ctx8Pruned_cost); test_program("ctx8Unpruned", ctx8Unpruned, sizeof_ctx8Unpruned, ctx8Unpruned_witness, sizeof_ctx8Unpruned_witness, SIMPLICITY_ERR_ANTIDOS, ctx8Unpruned_cmr, ctx8Unpruned_ihr, ctx8Unpruned_amr, &ctx8Unpruned_cost); if (0 == memcmp(ctx8Pruned_cmr, ctx8Unpruned_cmr, sizeof(uint32_t[8]))) { successes++; } else { failures++; printf("Pruned and Unpruned CMRs are not the same.\n"); } test_program("schnorr0", schnorr0, sizeof_schnorr0, schnorr0_witness, sizeof_schnorr0_witness, SIMPLICITY_NO_ERROR, schnorr0_cmr, schnorr0_ihr, schnorr0_amr, &schnorr0_cost); test_program("schnorr6", schnorr6, sizeof_schnorr6, schnorr6_witness, sizeof_schnorr6_witness, SIMPLICITY_ERR_EXEC_JET, schnorr6_cmr, schnorr6_ihr, schnorr6_amr, &schnorr0_cost); test_program("typeSkipTest", typeSkipTest, sizeof_typeSkipTest, typeSkipTest_witness, sizeof_typeSkipTest_witness, SIMPLICITY_NO_ERROR, NULL, NULL, NULL, NULL); test_elements(); exactBudget_test(); regression_tests(); iden8mebi_test(); printf("Successes: %d\n", successes); printf("Failures: %d\n", failures); return (0 == failures) ? EXIT_SUCCESS : EXIT_FAILURE; } ================================================ FILE: C/type.c ================================================ #include "type.h" #include #include "precomputed.h" #include "simplicity_assert.h" /* Given a the 'kind' of a Simplicity type, return the SHA-256 hash of its associated TMR tag. * This is the "initial value" for computing the type Merkle root for that type. */ static sha256_midstate tmrIV(typeName kind) { switch (kind) { case ONE: return unitIV; case SUM: return sumIV; case PRODUCT: return prodIV; } /* Impossible to reach here (unless you call with uninitialized values). */ SIMPLICITY_UNREACHABLE; } /* Given a well-formed 'type_dag', compute the bitSizes, skips, and type Merkle roots of all subexpressions. * For all 'i', 0 <= 'i' < 'len', * 'type_dag[i].typeMerkleRoot' will be the TMR * and 'type_dag[i].bitSize' will be the bitSize of the subexpression denoted by the slice * * (type_dag[i + 1])type_dag. * * and when 'type_dag[i]' represents a non-trivial 'PRODUCT' type, where one of the two type arguments a trivial type. * then 'type_dag[i].skip' is the index of the largest subexpression of 'type_dag[i]' such that * either 'type_dag[type_dag[i].skip]' is a 'SUM' type * or 'type_dag[type_dag[i].skip]' is a 'PRODUCT' type of two non-trivial types. * * Precondition: type type_dag[len] and 'type_dag' is well-formed. */ void simplicity_computeTypeAnalyses(type* type_dag, const size_t len) { for (size_t i = 0; i < len; ++i) { type_dag[i].skip = i; switch (type_dag[i].kind) { case ONE: type_dag[i].bitSize = 0; break; case SUM: type_dag[i].bitSize = bounded_max(type_dag[type_dag[i].typeArg[0]].bitSize, type_dag[type_dag[i].typeArg[1]].bitSize); bounded_inc(&type_dag[i].bitSize); break; case PRODUCT: type_dag[i].bitSize = bounded_add(type_dag[type_dag[i].typeArg[0]].bitSize, type_dag[type_dag[i].typeArg[1]].bitSize); if (0 == type_dag[type_dag[i].typeArg[0]].bitSize) { type_dag[i].skip = type_dag[type_dag[i].typeArg[1]].skip; } else if (0 == type_dag[type_dag[i].typeArg[1]].bitSize) { type_dag[i].skip = type_dag[type_dag[i].typeArg[0]].skip; } } type_dag[i].typeMerkleRoot = tmrIV(type_dag[i].kind); uint32_t block[16]; switch (type_dag[i].kind) { case ONE: break; case SUM: case PRODUCT: memcpy(block, type_dag[type_dag[i].typeArg[0]].typeMerkleRoot.s, sizeof(uint32_t[8])); memcpy(block + 8, type_dag[type_dag[i].typeArg[1]].typeMerkleRoot.s, sizeof(uint32_t[8])); simplicity_sha256_compression(type_dag[i].typeMerkleRoot.s, block); } } } ================================================ FILE: C/type.h ================================================ /* This module defines the structure for Simplicity type DAGs and computes type Merkle roots. */ #ifndef SIMPLICITY_TYPE_H #define SIMPLICITY_TYPE_H #include #include "bounded.h" #include "sha256.h" #include "simplicity_assert.h" typedef enum typeName { ONE, SUM, PRODUCT } typeName; /* A structure for Simplicity type DAGs. */ /* :TODO: when 'back' is used as "mutable" scratch space, concurrent evaluation of Simplicity expressions that share * subexpressions and typing information is not possible. * Consider instead implementing static analysis to determine a maximum stack size needed for traversing types in an expression * in order to remove uses of 'back'. */ typedef struct type { size_t typeArg[2]; union { size_t skip; /* Used by 'typeSkip'. */ size_t back; /* Sometimes used as scratch space when traversing types. */ }; sha256_midstate typeMerkleRoot; ubounded bitSize; typeName kind; } type; /* We say a Simplicity type is trivial if it is the 'ONE' type, or the 'PRODUCT' of two trivial types. * A Simplicity type is a trivial type if and only if its bitSize is 0. */ /* A well-formed type DAG is an array of 'type's, * * type type_dag[n], * * such that * * 0 < n * * and * * type_dag[0].kind == ONE. * * and for all 'i', 1 <= 'i' < 'n' and for all 'j', 0 <= 'j' < 2. * * type_dag[i].kind \in { SUM, PRODUCT } and type_dag[i].typeArg[j] < i. */ /* Given a well-formed 'type_dag', compute the bitSizes, skips, and type Merkle roots of all subexpressions. * For all 'i', 0 <= 'i' < 'len', * 'type_dag[i].typeMerkleRoot' will be the TMR * and 'type_dag[i].bitSize' will be the bitSize of the subexpression denoted by the slice * * (type_dag[i + 1])type_dag. * * and when 'type_dag[i]' represents a non-trivial 'PRODUCT' type, where one of the two type arguments a trivial type. * then 'type_dag[i].skip' is the index of the largest subexpression of 'type_dag[i]' such that * either 'type_dag[type_dag[i].skip]' is a 'SUM' type * or 'type_dag[type_dag[i].skip]' is a 'PRODUCT' type of two non-trivial types. * * Precondition: type type_dag[len] and 'type_dag' is well-formed. */ void simplicity_computeTypeAnalyses(type* type_dag, size_t len); /* Return the index of the largest subexpression of 'type_dag[i]' (possibly 'i' itself) that is either * (1) a 'SUM' type; * (2) a 'PRODUCT' type of two non-trivial type arguments. * * If there is no such subexpression at all, i.e. when 'type_dag[i]' is a trivial type, return 0 * (which is the index of the 'ONE' type). * * This functions is used for fast traversals of type expressions, skipping over trivial subexpressions, * as this function runs in in constant time. */ static inline size_t typeSkip(size_t i, const type* type_dag) { if (0 == type_dag[i].bitSize) return 0; if (PRODUCT == type_dag[i].kind && (0 == type_dag[type_dag[i].typeArg[0]].bitSize || 0 == type_dag[type_dag[i].typeArg[1]].bitSize)) { return type_dag[i].skip; } return i; } /* Precondition: type type_dag[i] and 'type_dag' is well-formed. * if type_dag[i] is a non-trival 'PRODUCT', then both of its two type arguments are non-trival. * Postconditon: value == type_dag[i] */ static inline void setTypeBack(size_t i, type* type_dag, size_t value) { /* .back cannot be used if .skip is in use. Specifically it cannot be a non-trivial 'PRODUCT' type where one of its two type arguments is a trivial type. */ simplicity_assert((PRODUCT != type_dag[i].kind || 0 == type_dag[i].bitSize || (0 != type_dag[type_dag[i].typeArg[0]].bitSize && 0 != type_dag[type_dag[i].typeArg[1]].bitSize))); type_dag[i].back = value; } #endif ================================================ FILE: C/typeInference.c ================================================ #include "typeInference.h" #include #include "bounded.h" #include "limitations.h" #include "simplicity_alloc.h" #include "simplicity_assert.h" static_assert(DAG_LEN_MAX <= (SIZE_MAX - NUMBER_OF_TYPENAMES_MAX) / 4, "TYPE_DAG_LEN_MAX doesn't fit in size_t."); #define TYPE_DAG_LEN_MAX (NUMBER_OF_TYPENAMES_MAX + 4*DAG_LEN_MAX) /* Every subexpression in a Simplicity expression has a unification variable for its inferred source and target type. */ typedef struct unification_arrow { unification_var source, target; } unification_arrow; /* Returns the representative of this variable's equivalence class. * Note: the 'parent' pointers of some variables within this equivalence class may be adjusted (to point more directly to the * representative). * * Precondition: NULL != alpha * * Postcondition: NULL == result_value->parent */ static unification_var* findRoot(unification_var* alpha) { /* During unification, when '.rank' fields are active, the value of 'alpha->rank' strictly increases during this loop. * If 'alpha->rank' = 'i', then there must be at least 2^'i' unification variables referencing (indirectly) 'alpha'. * Therefore, this loop terminates in at most log_2('n')/2 steps where 'n' is the number of unification variables in 'alpha's * equivalence class. * This bound holds even during freezing when 'alpha->rank' may not be activated. * * Note: the total number of unification variables created for type inference is linearly bounded by the number of nodes * in the Simplicity expression being inferred's DAG. * * According to ``Worst-Case Analysis of Set Union Algorithms'' by Robert E. Tarjan and Jan van Leeuwen (1984) * the "path halving" method used in this implementation is adequate to ensure that the amortized time complexity is * O(InvAck('n')) and ``for all practical purposes InvAck('n') a constant no larger than four''. */ while (alpha->parent != NULL) { if (alpha->parent->parent != NULL) alpha->parent = alpha->parent->parent; alpha = alpha->parent; } return alpha; } /* Begin attempt to add a new binding, 'bound', to a unification variable 'alpha' representing its equivalence class. * If 'alpha' is a free variable, it becomes a bound to a copy of 'bound' and 'true' is returned. * If 'alpha' is already bound to the same kind of type, new unification constraints may be added by overwriting '**cont' * and putting more elements into the '*cont' stack and 'true' is returned. * Hence, '*cont' must be a non-empty stack whose top element is scratch space available to be overwritten. * If 'alpha' is already bound to the same kind of non-trivial binding then '*bindings_used' is decremented * and 'bound->cont' may become active. * * In cases where no new unification constraints are need, the top element of '*cont' is popped off the stack, * removing the scratch item. * * If 'alpha' is already bound to a different kind of type, then 'false' is returned. * * If 'false' is returned, then '*alpha', '*bound', '*cont', '*bindings_used', * and values referenced by these structures may be modified. * * Preconditon: NULL != alpha and NULL == alpha->parent; * NULL != bound; * &alpha->bound != bound * NULL != cont and '*cont' is a non-empty stack; * NULL != bindings_used */ static bool applyBinding_cont(unification_var* alpha, binding* bound, unification_cont** cont, size_t* bindings_used) { if (!alpha->isBound) { /* alpha is currently a free variable. Copy the provided binding. */ alpha->isBound = true; alpha->bound = *bound; *cont = (*cont)->next; return true; } if (&alpha->bound == bound) { simplicity_assert(false); /* The algorithm should never try to bind an already bound variable to it's own binding. */ /* However, if it does happen then just return successfully without pushing any new unification constraints. */ *cont = (*cont)->next; return true; } if (alpha->bound.kind != bound->kind) return false; /* Unification failure */ /* Otherwise 'bound' is bound to the same kind of type as 'alpha's. */ if (ONE == bound->kind) { /* 'bound' is a trivial binding. */ *cont = (*cont)->next; return true; } else { /* 'bound' is a non-trivial binding. * Push two new pairs of the 'alpha->bound' and 'bound' type's unification variables to the stack of variables to be unified * by overwriting the top of the stack and slipping a new stack item underneath it. */ (*cont)->alpha = alpha->bound.arg[0]; (*cont)->beta = bound->arg[0]; /* 'bound' will not be used further, so it is safe to activate 'bound->cont'. */ bound->cont = (unification_cont){ .alpha = alpha->bound.arg[1] , .beta = bound->arg[1] , .next = (*cont)->next }; (*cont)->next = &(bound->cont); simplicity_assert(0 < *bindings_used); (*bindings_used)--; } return true; } /* Unify a stack of pairs of unification variables. * If any unification fails, then NULL is returned. * If all unifications are successful, the representative of the equivalence class of the top pair of unified variables * from the stack is returned. * '*bindings_used' is decremented by the number of pairs of (non-trivial) bindings that are successfully unified. * * If 'NULL' is returned, then '*cont', '*bindings_used', and values referenced by these structures may be modified. * * Precondition: 'cont' is a non-empty stack; * All of the 'unification_var's accessible through 'cont' have their '.rank' fields active; * NULL != bindings_used */ static unification_var* unify_cont(unification_cont* cont, size_t* bindings_used) { unification_var* result = NULL; /* Each time we go through this loop, the stack size of 'cont' either increases by 1 or decreases by 1. * Whenever the stack size increases by 1, at the same time '*bindings_used' decreases by 1. * * For the above reason, the total number of times this loop iterates summed over all calls to 'unify_cont' cannot exceed * * (2 * the total number of bindings created + the number of times 'unify_cont' is called). * * The total number of bindings created is bounded linearly in the number of nodes in the Simplicity expression's DAG. * The total number of calls to 'unify_cont' (via 'unify' and 'applyBinding') is bounded * linearly in the number of nodes in the Simplicity expression's DAG. * Therefore the total number of times this loop iterates summed over all calls to 'unify_cont' is bounded * linearly in the number of nodes in the Simplicity DAG. */ while (cont) { unification_var* alpha = findRoot(cont->alpha); unification_var* beta = findRoot(cont->beta); if (alpha == beta) { /* 'cont->alpha' and 'cont->beta' are already equivalent. */ cont = cont->next; } else { /* We will be making 'alpha' a parent of 'beta', so swap the variables to ensure that 'alpha's rank * is at least as large as 'beta'. */ if (alpha->rank < beta->rank) { unification_var* tmp = beta; beta = alpha; alpha = tmp; } /* Make 'beta' equivalent to 'alpha'. */ beta->parent = alpha; if (beta->isBound) { /* Copy/unify 'beta's binding to/with 'alpha'. */ if (!applyBinding_cont(alpha, &beta->bound, &cont, bindings_used)) return NULL; /* Unification failure */ } else { /* 'beta' used to be a free variable. */ cont = cont->next; } /* Ensure 'alpha's rank exceeds 'beta's rank. * Note that if 'alpha->rank' == 'beta->rank' then the two variables equivalence classes each had at least * 2^'alpha->rank' variables in each of them. * Therefore the unified equivalence classes will now have at least 2^'alpha->rank + 1' variables, * which will be compatible with 'alpha's increased rank. */ if (alpha->rank == beta->rank) alpha->rank++; } /* Return the representative of the unified variable of the two inputs that was on the top of the stack * (as long as all other unifications are successful). */ if (!result) result = alpha; } return result; } /* Add a new binding, 'bound', to a unification variable 'alpha'. * If 'alpha' is already bound to a type that doesn't unify with 'bound', then 'false' is returned. * Otherwise variables of 'bound's bindings and 'alpha's bindings (if any) are recursively unified and 'true' is returned. * '*bindings_used' is decremented by the number of pairs of (non-trivial) bindings that are successfully unified. * * If 'false' is returned, then '*alpha', '*bound', '*bindings_used', and values referenced by these structures may be modified. * * Precondition: NULL != alpha; * NULL != bound; * All of the 'unification_var's accessible through 'alpha' and 'bound' (including 'alpha' itself) * have their '.rank' fields active; * NULL != bindings_used */ static bool applyBinding(unification_var* alpha, binding* bound, size_t* bindings_used) { unification_cont scratch = {0}; unification_cont* cont = &scratch; if (!applyBinding_cont(findRoot(alpha), bound, &cont, bindings_used)) return false; return NULL == cont || unify_cont(cont, bindings_used); } /* Unify a pair of unification variables. * If unification fails, then NULL is returned. * If unification is successful, the representative of the equivalence class of unified pair of variables is returned. * If alpha or beta is NULL, then NULL is returned. This allows you to chain calls to 'unify'. * * '*bindings_used' is decremented by the number of pairs of (non-trivial) bindings that are successfully unified. * * If unification fails, then '*alpha', '*beta', '*bindings_used', and values referenced by these structures may be modified. * * Precondition: NULL != bindings_used; * All of the 'unification_var's accessible through 'alpha' and 'beta' (including themselves if they are not NULL) * have their '.rank' fields active. */ static unification_var* unify(unification_var* alpha, unification_var* beta, size_t* bindings_used) { return alpha && beta ? unify_cont(&(unification_cont){ .alpha = alpha, .beta = beta }, bindings_used) : NULL; } /* Given a census containing a tally of the different tags that occurs in some Simplicity DAG, * return an upper bound on number of extra unification variables, 'extra_var', * that the 'typeInference' function will end up needing for that DAG. * * Precondition: NULL != census */ static size_t max_extra_vars(const combinator_counters* census) { return 4*(census->case_cnt) + (census->disconnect_cnt) + (census->injl_cnt) + (census->injr_cnt) + (census->take_cnt) + (census->drop_cnt); } /* Solve the constraints of source and target types of each subexpression in a Simplicity DAG. * * If the Simplicity DAG, 'dag', has a principal type (including constraints due to sharing of subexprssions), * then 'arrow[i]'s and 'source' and 'target' fields are set to unification variables * that are bound to the principal source and target types of subexpression denoted by the slice '(dag_nodes[i + 1])dag'. * If the 'dag' does not have a principal type then either 'SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION' is returned * or there will be a cycle in the graph of the bindings of the unification variables accessible from the resulting 'arrows' array. * * If 'SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION' is not returned, then 'SIMPLICITY_NO_ERR' is returned. * * If 'SIMPLICITY_NO_ERR' is not returned, * then '*arrow', '*extra_var', '*word256Type', '*bindings_used', and values referenced by these structures may be modified. * * Precondition: unification_arrow arrow[len]; * dag_node dag[len] is well-formed; * unification_var extra_var[max_extra_vars(&census)] * where 'census' contains a tally of the different tags that occur in 'dag'; * unification_var bound_var[N]; * forall '0 <= i < len', if 'dag[i].tag == JET' * then 'dag[i].sourceIx < N' and 'dag[i].targetIx < N' * and if 'jet[i].tag == WORD' * then 'dag[i].targetIx < N' * word256_ix < N and 'bound_var[word256_ix]' is bound to the type 'TWO^256'; * '*bindings_used' is at least the number of unification variables that have * non-trivial bindings that are accessible from the 'bound_var' array. * * Postcondition: if 'SIMPLICITY_NO_ERR' is returned * then '*bindings_used' is at least the number of unification variables that have non-trivial bindings * that are accessible from the 'arrow' array and 'bound_var' array. * and 'arrow' is a graph of bindings that satisfies the typing constraints of imposed by 'dag'. */ static simplicity_err typeInference( unification_arrow* arrow, const dag_node* dag, const uint_fast32_t len, unification_var* extra_var, unification_var* bound_var, size_t word256_ix, size_t* bindings_used ) { for (uint_fast32_t i = 0; i < len; ++i) { switch (dag[i].tag) { #define UNIFY(a, b) { if (!unify((a), (b), bindings_used)) return SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION; } #define APPLY_BINDING(a, b) { if (!applyBinding((a), (b), bindings_used)) return SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION; } case COMP: arrow[i] = (unification_arrow){0}; UNIFY(&(arrow[dag[i].child[0]].source), &(arrow[i].source)); UNIFY(&(arrow[dag[i].child[1]].target), &(arrow[i].target)); UNIFY(&(arrow[dag[i].child[0]].target), &(arrow[dag[i].child[1]].source)); break; case ASSERTL: case ASSERTR: case CASE: *bindings_used += 2; extra_var[0] = extra_var[1] = extra_var[2] = (unification_var){0}; extra_var[3] = (unification_var) { .isBound = true , .bound = { .kind = SUM , .arg = { &extra_var[0], &extra_var[1] } } }; arrow[i] = (unification_arrow){ .source = { .isBound = true , .bound = { .kind = PRODUCT , .arg = { &extra_var[3], &extra_var[2] } } } }; if (ASSERTR != dag[i].tag) { *bindings_used += 1; APPLY_BINDING(&(arrow[dag[i].child[0]].source), &((binding) { .kind = PRODUCT , .arg = { &extra_var[0], &extra_var[2] } })); UNIFY(&(arrow[dag[i].child[0]].target), &(arrow[i].target)); } if (ASSERTL != dag[i].tag) { *bindings_used += 1; APPLY_BINDING(&(arrow[dag[i].child[1]].source), &((binding) { .kind = PRODUCT , .arg = { &extra_var[1], &extra_var[2] } })); UNIFY(&(arrow[dag[i].child[1]].target), &(arrow[i].target)); } extra_var += 4; break; case PAIR: *bindings_used += 1; arrow[i] = (unification_arrow){ .target = { .isBound = true , .bound = { .kind = PRODUCT , .arg = { &(arrow[dag[i].child[0]].target), &(arrow[dag[i].child[1]].target) } } } }; UNIFY(unify(&(arrow[dag[i].child[0]].source), &(arrow[dag[i].child[1]].source), bindings_used), &(arrow[i].source)); break; case DISCONNECT: *bindings_used += 3; *extra_var = (unification_var){0}; arrow[i] = (unification_arrow){ .target = { .isBound = true , .bound = { .kind = PRODUCT , .arg = { extra_var, &(arrow[dag[i].child[1]].target) } } } }; APPLY_BINDING(&(arrow[dag[i].child[0]].source), &((binding) { .kind = PRODUCT , .arg = { &(bound_var[word256_ix]), &(arrow[i].source) } })); APPLY_BINDING(&(arrow[dag[i].child[0]].target), &((binding) { .kind = PRODUCT , .arg = { extra_var, &(arrow[dag[i].child[1]].source) } })); extra_var++; break; case INJL: case INJR: *bindings_used += 1; *extra_var = (unification_var){0}; arrow[i] = (unification_arrow){ .target = { .isBound = true , .bound = { .kind = SUM , .arg = { INJL == dag[i].tag ? &(arrow[dag[i].child[0]].target) : extra_var , INJL == dag[i].tag ? extra_var : &(arrow[dag[i].child[0]].target) } } } }; UNIFY(&(arrow[dag[i].child[0]].source), &(arrow[i].source)); extra_var++; break; case TAKE: case DROP: *bindings_used += 1; *extra_var = (unification_var){0}; arrow[i] = (unification_arrow){ .source = { .isBound = true , .bound = { .kind = PRODUCT , .arg = { TAKE == dag[i].tag ? &(arrow[dag[i].child[0]].source) : extra_var , TAKE == dag[i].tag ? extra_var : &(arrow[dag[i].child[0]].source) } } } }; UNIFY(&(arrow[dag[i].child[0]].target), &(arrow[i].target)); extra_var++; break; case IDEN: arrow[i] = (unification_arrow){0}; UNIFY(&(arrow[i].source), &(arrow[i].target)); break; case UNIT: /* UNIT only imposes trivial bindings, so we do not increment 'bindings_used'. */ arrow[i] = (unification_arrow){ .target = { .isBound = true, .bound = { .kind = ONE } } }; break; case HIDDEN: case WITNESS: arrow[i] = (unification_arrow){0}; break; case JET: arrow[i] = (unification_arrow){0}; UNIFY(&(bound_var[dag[i].sourceIx]),&arrow[i].source); UNIFY(&(bound_var[dag[i].targetIx]),&arrow[i].target); break; case WORD: /* WORD only imposes trivial bindings, so we do not increment 'bindings_used'. */ arrow[i] = (unification_arrow){ .source = { .isBound = true, .bound = { .kind = ONE } } }; UNIFY(&(bound_var[dag[i].targetIx]),&arrow[i].target); #undef APPLY_BINDING #undef UNIFY } } return SIMPLICITY_NO_ERROR; } /* Determine if the representative of an equivalence class of unification variables already has a reference * to a frozen version of its bound type. * * Note that free variables and variables bound to the 'ONE' type are automatically always frozen. * * Precondition: NULL == var->parent */ static bool isFrozen(unification_var* var) { simplicity_assert(!var->isBound || ONE != var->bound.kind || 0 == var->bound.frozen_ix); return !var->isBound || ONE == var->bound.kind || var->bound.frozen_ix; } /* Given the representative of an equivalence class of unification variables that already has a reference to a frozen version * of its bound type, return that reference. * * Precondition: NULL == var->parent; * isFrozen(var) */ static size_t getFrozenIx(unification_var* var) { return var->isBound ? var->bound.frozen_ix : 0; } /* Set '*result' to the index within 'type_dag' that contains an instance type bound by 'var' where free variables are instantiated * at the ONE type, recursively adding new nodes to 'type_dag' as necessary. * '*type_dag_used' will be incremented by the number of new 'type_dag' nodes created. * * If it is impossible to create a required instance (due to a cycle in the bindings reachable by 'var'), then 'false' is returned, * otherwise 'true' is returned. * * If 'false' is returned, then '*result', '*type_dag', '*type_dag_used', and values referenced by these structures may be modified. * * Precondition: NULL != result; * type type_dag[*type_dag_used + n] * where 'n' is the number of unfrozen unification variables that have non-trivial bindings * that are accessible from 'var' array; * type type_dag[*type_dag_used] is well-formed; * NULL != type_dag_used; * NULL != var * * Postcondition: If 'true' is returned, then type type_dag[*type_dag_used] is well-formed */ static bool freeze(size_t* result, type* type_dag, size_t* type_dag_used, unification_var* var) { var = findRoot(var); if (isFrozen(var)) { *result = getFrozenIx(var); return true; } /* 'var' is not frozen, and therefore it must have a non-trivial binding. * Create a one item stack of unification variables 'var' to be frozen. */ var->next = NULL; simplicity_assert(!var->bound.occursCheck); var->bound.occursCheck = true; /* Attempt to freeze all variables on the stack, pushing new variables onto the stack to recursively freeze them if needed. * * All variables in the stack are representatives of their equivalence class and have just had their 'occursCheck' flag changed * from 'false' to 'true'. * Variables never change their 'occursCheck' flag back from 'true' to 'false'. * Variables are only removed from the stack after being frozen. * Each time we go through this loop, the stack size either increases by 1 or decreases by 1. * Therefore the total number of times this loop iterates summed over all calls to 'freeze' is bounded by * twice the number of unification variable (representatives) with non-trivial bindings. * ("twice" because once to add the variable to the stack and once to remove the variable from the stack). * * Note that number of unification_variables is bound linearly in the number of nodes in the Simplicity DAG. */ while (var) { unification_var* typeArg[2] = { findRoot(var->bound.arg[0]), findRoot(var->bound.arg[1]) }; if (!isFrozen(typeArg[0])) { /* The first type argument's representative isn't frozen. Add it to the stack and immediately attempt to freeze it. */ if (typeArg[0]->bound.occursCheck) return false; /* Occurs check failure. */ typeArg[0]->bound.occursCheck = true; typeArg[0]->next = var; var = typeArg[0]; } else if (!isFrozen(typeArg[1])) { /* The second type argument's representative isn't frozen. Add it to the stack and immediately attempt to freeze it. */ if (typeArg[1]->bound.occursCheck) return false; /* Occurs check failure. */ typeArg[1]->bound.occursCheck = true; typeArg[1]->next = var; var = typeArg[1]; } else { /* Both the type argument's representatives are frozen. * Create a new entry in the 'type_dag' for 'var's binding and freeze 'var'. */ *result = var->bound.frozen_ix = (*type_dag_used)++; type_dag[var->bound.frozen_ix] = (type) { .kind = var->bound.kind , .typeArg = { getFrozenIx(typeArg[0]), getFrozenIx(typeArg[1]) } }; var = var->next; } } return true; } /* Create a type DAG that supports all the type annotations of the Simplicity expression, 'dag', * and the input and output types of whole expression. * * If the Simplicity DAG, 'dag', has a principal type (including constraints due to sharing of subexpressions), * and 'arrow[i]'s and 'source' and 'target' field's unification variables are bound to the principal source and target types * of subexpression denoted by the slice '(dag_nodes[i + 1])dag', then we create a well-formed 'type_dag' (see 'type.h') * that includes the input and output types for every subexpression in 'dag', with all free type variables instantiated to the type * 'ONE' and add references to these type annotations to 'dag' * and returns 'SIMPLICITY_NO_ERROR'. * * The type Merkle roots of the 'type_dag' are also filled in. * * We say 'dag' is "well-typed" if it is a well-formed 'dag' with source and target types on all subexpressions, * referencing a well-formed 'type_dag', that satisfies all the typing constraints of Simplicity. * Hidden nodes are not actually typed and are instead assigned references to the type 'ONE' for their input and output types. * * If the Simplicity DAG, 'dag' does not have a principal type, yet the precondition on 'arrow' below is still satisfied, * then there must be a cycle in the graph of bindings accessible through the 'arrow' array, * and in this case we return 'SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK'. * * In either case, '*arrow', and values referenced by these structures may be modified. * * If 'SIMPLICITY_NO_ERROR' is not returned, then the 'type_dag' array, and the '.sourceType', '.targetType' within the 'dag' array may be modified. * * Precondition: type type_dag[1 + n] * where 'n' is the number of unification variables that have non-trivial bindings * that are accessible from the 'arrow' array; * dag_node dag[len] is well-formed; * unification_arrow arrow[len] is a graph of bindings that satisfies the typing constraints of imposed by 'dag'. */ static simplicity_err freezeTypes(type* type_dag, dag_node* dag, unification_arrow* arrow, const size_t len) { /* First entry of type_dag gets assigned to the ONE type. */ type_dag[0] = (type){ .kind = ONE }; size_t type_dag_used = 1; for (size_t i = 0; i < len; ++i) { if (!(freeze(&(dag[i].sourceType), type_dag, &type_dag_used, &(arrow[i].source)) && freeze(&(dag[i].targetType), type_dag, &type_dag_used, &(arrow[i].target)))) { return SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK; } } simplicity_computeTypeAnalyses(type_dag, type_dag_used); return SIMPLICITY_NO_ERROR; } /* If the Simplicity DAG, 'dag', has a principal type (including constraints due to sharing of subexpressions), * then allocate a well-formed type DAG containing all the types needed for all the subexpressions of 'dag', * with all free type variables instantiated at ONE, and set '*type_dag' to this allocation, * and update the '.sourceType' and '.targetType' fields within each node of the 'dag' 'type_dag[dag[i].sourceType]' * and 'type_dag[dag[i].targetType]' are the inferred types of the Simplicity subexpression at dag[i]. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * If the Simplicity DAG, 'dag', has no principal type (because it has a type error), then '*type_dag' is set to NULL, * and either 'SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION' or 'SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK' is returned. * Otherwise 'SIMPLICITY_NO_ERROR' is returned. * * Precondition: NULL != type_dag; * dag_node dag[len] is well-formed; * '*census' contains a tally of the different tags that occur in 'dag'. * * Postcondition: if the return value is 'SIMPLICITY_NO_ERROR' * then either NULL == '*type_dag' * or 'dag' is well-typed with '*type_dag' and without witness values * if the return value is not 'SIMPLICITY_NO_ERROR' then 'NULL == *type_dag' */ simplicity_err simplicity_mallocTypeInference(type** type_dag, simplicity_callback_mallocBoundVars mallocBoundVars, dag_node* dag, const uint_fast32_t len, const combinator_counters* census) { *type_dag = NULL; static_assert(DAG_LEN_MAX <= SIZE_MAX / sizeof(unification_arrow), "arrow array too large."); static_assert(1 <= DAG_LEN_MAX, "DAG_LEN_MAX is zero."); static_assert(DAG_LEN_MAX - 1 <= UINT32_MAX, "arrow array index does not fit in uint32_t."); simplicity_assert(1 <= len); simplicity_assert(len <= DAG_LEN_MAX); unification_arrow* arrow = simplicity_malloc(len * sizeof(unification_arrow)); unification_var* bound_var = NULL; size_t word256_ix, extra_var_start; const size_t orig_bindings_used = mallocBoundVars(&bound_var, &word256_ix, &extra_var_start, max_extra_vars(census)); size_t bindings_used = orig_bindings_used; static_assert(1 <= NUMBER_OF_TYPENAMES_MAX, "NUMBER_OF_TYPENAMES_MAX is zero."); simplicity_assert(orig_bindings_used <= NUMBER_OF_TYPENAMES_MAX - 1); simplicity_err result = arrow && bound_var ? SIMPLICITY_NO_ERROR : SIMPLICITY_ERR_MALLOC; if (IS_OK(result)) { result = typeInference(arrow, dag, len, bound_var + extra_var_start, bound_var, word256_ix, &bindings_used); } if (IS_OK(result)) { /* :TODO: constrain the root of the dag to be a Simplicity program: ONE |- ONE */ static_assert(TYPE_DAG_LEN_MAX <= SIZE_MAX / sizeof(type), "type_dag array too large."); static_assert(1 <= TYPE_DAG_LEN_MAX, "TYPE_DAG_LEN_MAX is zero."); static_assert(TYPE_DAG_LEN_MAX - 1 <= UINT32_MAX, "type_dag array index does not fit in uint32_t."); /* 'bindings_used' is at most 4*len plus the initial value of 'bindings_used' set by 'mallocBoundVars'. */ simplicity_assert(bindings_used <= orig_bindings_used + 4*len); *type_dag = simplicity_malloc((1 + bindings_used) * sizeof(type)); result = *type_dag ? SIMPLICITY_NO_ERROR : SIMPLICITY_ERR_MALLOC; if (IS_OK(result)) { result = freezeTypes(*type_dag, dag, arrow, len); } if (!IS_OK(result)) { simplicity_free(*type_dag); *type_dag = NULL; } } simplicity_free(arrow); simplicity_free(bound_var); return result; } ================================================ FILE: C/typeInference.h ================================================ /* This module provides function for running monomorphic type inference over Simplicity DAGs. */ #ifndef SIMPLICITY_TYPEINFERENCE_H #define SIMPLICITY_TYPEINFERENCE_H #include "dag.h" #include "type.h" /* Forward declarations for recursive data structures. */ typedef struct unification_cont unification_cont; typedef struct unification_var unification_var; /* 'unification_cont' is a stack element holding a pair of variables to be unified. * 'next' points to the rest of the stack or NULL if this is the bottom of the stack. */ struct unification_cont { unification_var* alpha; unification_var* beta; unification_cont* next; }; /* We say that a value 'cont' of type 'unification_cont*' is a stack when * (a) 'NULL == cont', in which case we say 'cont' is an empty stack, * or * (b) 'NULL != cont', 'NULL != cont->alpha', 'NULL != cont->beta', and 'cont->next' is a stack, * in which case we say 'cont' is a non-empty stack. */ /* A binding for a bound unification variable. * 'kind' is the kind of Simplicity type for this binding. * When 'kind' is 'ONE' then this is a called "trivial" binding and 'arg' is not used. * When 'kind' is in { 'SUM', 'PRODUCT' } then this is called a "non-trivial" binding * and 'arg[0]' and 'arg[1]' are pointers to variables for the type's arguments. * * During freezing, the 'occursCheck' flag may be set to help detect occurs check failures (a.k.a cyclic types). * After freezing, 'frozen_ix' refers to the index within some 'type' array that holds the frozen version of this binding. * * When a binding is unused (e.g. when a unification_var has a non-NULL 'parent'), unification may activate 'cont' as scratch space; */ typedef union binding { struct { unification_var* arg[2]; size_t frozen_ix; typeName kind; bool occursCheck; }; unification_cont cont; /* unification uses this field as scratch space. */ } binding; /* A unification variable. * When 'NULL == parent' then this variable is the representative of its equivalence class. * When 'NULL == parent' and '!isBound' this (and all equivalent variables) is a free unification variable. * When 'NULL == parent' and 'isBound' this (and all equivalent variables) is a bound unification variable * with 'bound' holding its binding (and bound.kind is active). * When 'NULL != parent' then this variable is equivalent to '*parent' and 'isBound' and 'bound' are not used. * * During unification 'rank' is active and when 'NULL != parent' then 'rank < parent->rank'. * Also when 'rank' is active, there are at least 2^'rank' unification variables in this unification variable's equivalence class. * * After unification is completed, the freeze function may activate 'next' as scratch space. * * This structure is designed so that initializing it with '{0}' / implicit static initialization * produces a fresh free unification variable. */ struct unification_var { unification_var* parent; binding bound; union { int rank; unification_var* next; /* freezing uses this field as scratch space. */ }; bool isBound; }; /* Allocate a fresh set of unification variables bound to at least all the types necessary * for all the jets that can be created by 'simplicity_callbac_decodeJet', and also the type 'TWO^256', * and also allocate space for 'extra_var_len' many unification variables. * Return the number of non-trivial bindings created. * * However, if malloc fails, then return 0. * * Precondition: NULL != bound_var; * NULL != word256_ix; * NULL != extra_var_start; * extra_var_len <= 6*DAG_LEN_MAX; * * Postcondition: Either '*bound_var == NULL' and the function returns 0 * or 'unification_var (*bound_var)[*extra_var_start + extra_var_len]' is an array of unification variables * such that for any 'jet : A |- B' there is some 'i < *extra_var_start' and 'j < *extra_var_start' such that * '(*bound_var)[i]' is bound to 'A' and '(*bound_var)[j]' is bound to 'B' * and, '*word256_ix < *extra_var_start' and '(*bound_var)[*word256_ix]' is bound the type 'TWO^256' */ typedef size_t (*simplicity_callback_mallocBoundVars)(unification_var** bound_var, size_t* word256_ix, size_t* extra_var_start, size_t extra_var_len); /* If the Simplicity DAG, 'dag', has a principal type (including constraints due to sharing of subexpressions), * then allocate a well-formed type DAG containing all the types needed for all the subexpressions of 'dag', * with all free type variables instantiated at ONE, and set '*type_dag' to this allocation, * and update the '.sourceType' and '.targetType' fields within each node of the 'dag' 'type_dag[dag[i].sourceType]' * and 'type_dag[dag[i].targetType]' are the inferred types of the Simplicity subexpression at dag[i]. * * If malloc fails, returns 'SIMPLICITY_ERR_MALLOC'. * If the Simplicity DAG, 'dag', has no principal type (because it has a type error), then '*type_dag' is set to NULL, * and either 'SIMPLICITY_ERR_TYPE_INFERENCE_UNIFICATION' or 'SIMPLICITY_ERR_TYPE_INFERENCE_OCCURS_CHECK' is returned. * Otherwise 'SIMPLICITY_NO_ERROR' is returned. * * Precondition: NULL != type_dag; * dag_node dag[len] is well-formed; * '*census' contains a tally of the different tags that occur in 'dag'. * * Postcondition: if the return value is 'SIMPLICITY_NO_ERROR' * then either NULL == '*type_dag' * or 'dag' is well-typed with '*type_dag' and without witness values * if the return value is not 'SIMPLICITY_NO_ERROR' then 'NULL == *type_dag' */ simplicity_err simplicity_mallocTypeInference(type** type_dag, simplicity_callback_mallocBoundVars mallocBoundVars, dag_node* dag, const uint_fast32_t len, const combinator_counters* census); #endif ================================================ FILE: C/typeSkipTest.c ================================================ #include "typeSkipTest.h" /* A length-prefixed encoding of the following Simplicity program: * witness (runIdentity (getValue (return True))) >>> mn >>> unit * where * l1 = take l0 &&& drop l0 * l2 = take l1 &&& drop l1 * l3 = take l2 &&& drop l2 * ltop = l3 * m1 = copair l3 l3 * m2 = take l1 &&& drop m1 * m3 = take m2 &&& drop l2 * m4 = take l3 &&& drop m3 * m5 = copair (injl m4) (injr ltop) * m6 = take l1 &&& drop m5 * m7 = take m6 &&& drop l2 * m8 = take l3 &&& drop m7 * n1 = copair l3 l3 * n2 = take n1 &&& drop l1 * n3 = take l2 &&& drop n2 * n4 = take n3 &&& drop l3 * n5 = copair (injl ltop) (injr n4) * n6 = take n5 &&& drop l0 * n7 = take l1 &&& drop n6 * n8 = take n7 &&& drop l2 * mn = copair (injl m8) (injr n8) */ const unsigned char typeSkipTest[] = { 0xe3, 0x77, 0x42, 0x45, 0x0c, 0xb5, 0xf0, 0xec, 0x6e, 0x61, 0xbb, 0x47, 0xa7, 0x00, 0x47, 0x8f, 0xc4, 0xd3, 0x00, 0x4b, 0x65, 0x5d, 0xb7, 0x70, 0x69, 0xf6, 0x7a, 0x99, 0x73, 0x8f, 0x03, 0x8f, 0x08, 0x94, 0x6b, 0x10, 0x8a, 0x83, 0x0f, 0x05, 0x06, 0x1e, 0x0a, 0x0c, 0x36, 0x84, 0x24, 0x50, 0xc3, 0xff, 0xf7, 0x0a, 0xf7, 0xbb, 0x16, 0x15, 0x3b, 0x42, 0x52, 0x00, 0x81, 0xa2, 0xc0, 0x81, 0xb1, 0x19, 0xa7, 0x90, 0xd6, 0x0c, 0x30, 0x8b, 0xd2, 0x37, 0xb6, 0xd8, 0x47, 0x5e, 0x0b, 0x4a, 0x66, 0xcd, 0x09, 0x14, 0x37, 0x9e, 0x40, 0x52, 0x60, 0x02, 0xb3, 0xf3, 0x3f, 0xc5, 0x2a, 0xba, 0xbd, 0x6f, 0x3d, 0x92, 0x1d, 0xc9, 0x30, 0x79, 0xe6, 0xe1, 0x2b, 0x6f, 0xdb, 0x7e, 0x6d, 0x62, 0x7f, 0x23, 0xc7, 0x9a, 0x81, 0xb6, 0x1f, 0x68, 0xa0, 0xc0, 0xe2, 0x06, 0x63, 0x0f, 0xc1, 0x85, 0x07, 0x0b, 0x78, 0xc3, 0xea, 0x14, 0x14, 0x60, 0x78, 0x30, 0x1c, 0x20, 0x70, 0xb8, 0x68, 0xc3, 0xf1, 0x20, 0xa0, 0xe1, 0x71, 0x18, 0xa3, 0x03, 0xc5, 0xc0, 0x71, 0x81, 0x20, 0x80, 0x71, 0xb0 }; const size_t sizeof_typeSkipTest = sizeof(typeSkipTest); const unsigned char typeSkipTest_witness[] = { 0xe0 }; const size_t sizeof_typeSkipTest_witness = sizeof(typeSkipTest_witness); /* The commitment Merkle root of the above typeSkipTest Simplicity expression. */ const uint32_t typeSkipTest_cmr[] = { 0x2a791cd8u, 0xf1e2beeau, 0x883e53f2u, 0xce36db2bu, 0x246b3156u, 0xcc40f91bu, 0xb2f59059u, 0xb601ac4au }; /* The identity hash of the root of the above typeSkipTest Simplicity expression. */ const uint32_t typeSkipTest_ihr[] = { 0xbadac773u, 0x19e9cabau, 0x7fe49174u, 0x54d0e25eu, 0x7d4c4a7eu, 0x4867c392u, 0x20bf409au, 0xc6e6bf10u }; /* The annotated Merkle root of the above typeSkipTest Simplicity expression. */ const uint32_t typeSkipTest_amr[] = { 0xbf18694du, 0x9b6a4b10u, 0xe4facc4du, 0xf8718387u, 0x2998f5dau, 0x1b0adc45u, 0x1f58fc4du, 0x924de2c9u }; /* The cost of the above typeSkipTest Simplicity expression in milli weight units. */ const ubounded typeSkipTest_cost = 13720; ================================================ FILE: C/typeSkipTest.h ================================================ #ifndef SIMPLICITY_TYPESKIPTEST_H #define SIMPLICITY_TYPESKIPTEST_H #include #include #include "bounded.h" /* A length-prefixed encoding of the following Simplicity program: * witness (runIdentity (getValue (return True))) >>> mn >>> unit * where * l1 = take l0 &&& drop l0 * l2 = take l1 &&& drop l1 * l3 = take l2 &&& drop l2 * ltop = l3 * m1 = copair l3 l3 * m2 = take l1 &&& drop m1 * m3 = take m2 &&& drop l2 * m4 = take l3 &&& drop m3 * m5 = copair (injl m4) (injr ltop) * m6 = take l1 &&& drop m5 * m7 = take m6 &&& drop l2 * m8 = take l3 &&& drop m7 * n1 = copair l3 l3 * n2 = take n1 &&& drop l1 * n3 = take l2 &&& drop n2 * n4 = take n3 &&& drop l3 * n5 = copair (injl ltop) (injr n4) * n6 = take n5 &&& drop l0 * n7 = take l1 &&& drop n6 * n8 = take n7 &&& drop l2 * mn = copair (injl m8) (injr n8) */ extern const unsigned char typeSkipTest[]; extern const size_t sizeof_typeSkipTest; extern const unsigned char typeSkipTest_witness[]; extern const size_t sizeof_typeSkipTest_witness; /* The commitment Merkle root of the above typeSkipTest Simplicity expression. */ extern const uint32_t typeSkipTest_cmr[]; /* The identity hash of the root of the above typeSkipTest Simplicity expression. */ extern const uint32_t typeSkipTest_ihr[]; /* The annotated Merkle root of the above typeSkipTest Simplicity expression. */ extern const uint32_t typeSkipTest_amr[]; /* The cost of the above typeSkipTest Simplicity expression in milli weight units. */ extern const ubounded typeSkipTest_cost; #endif ================================================ FILE: C/uword.h ================================================ #ifndef SIMPLICITY_UWORD_H #define SIMPLICITY_UWORD_H #include #include #include /* Number of bits for any value of the form 2^b - 1 where 0 <= b < 0x3fffffff * 30. * From: https://stackoverflow.com/a/4589384/727983 * * A correctness proof can be found at * * https://wiki.sei.cmu.edu/confluence/display/c/INT35-C.+Use+correct+integer+precisions?focusedCommentId=88018664#comment-88018664 */ #define UMAX_BITS(m) ((m) / ((m) % 0x3fffffffu + 1) / 0x3fffffffu % 0x3fffffffu * 30 \ + (m)%0x3fffffffu / ((m) % 31 + 1) / 31 % 31 * 5 \ + 4 - 12 / ((m) % 31 + 3)) /* UWORD can be any unsigned integer type. * The default ought to be 'unsigned int', but unfortunately that tends to be 32-bits on 64-bit platforms. * Instead we select 'uint_fast16_t' as our default (with the disadvantage that it is again 32-bits for the x32 target). */ #ifndef UWORD #define UWORD uint_fast16_t #endif _Static_assert((UWORD)1 <= (UWORD)(-1), "UWORD must be an unsigned type"); _Static_assert(sizeof(UWORD) < 0x3fffffffu * 30 / CHAR_BIT, "UWORD must have fewer than 32 billion bits for UMAX_BITS."); #define UWORD_MAX ((UWORD)-1) #define UWORD_BIT UMAX_BITS(UWORD_MAX) _Static_assert(UWORD_BIT <= SIZE_MAX, "UWORD_BIT must fit into size_t."); /* For all 'x' and 'y', * * 'x <= UWORD_BIT * y' if and only if 'ROUND_UWORD(x) <= y' * * Precondition: 0 <= bitSize */ #define ROUND_UWORD(bitSize) ((bitSize) / UWORD_BIT + !!((bitSize) % UWORD_BIT)) /* Clear the 'n' least significant bits of a UWORD. * Precondition: 0 < n <= UWORD_BIT */ static inline UWORD LSBclear(UWORD x, size_t n) { return (UWORD)(x >> 1 >> (n - 1) << 1 << (n - 1)); } /* Clear all but the 'n' least significant bits of a UWORD. * Precondition: 0 < n <= UWORD_BIT */ static inline UWORD LSBkeep(UWORD x, size_t n) { return (UWORD)(x & (UWORD_MAX >> (UWORD_BIT - n))); } #endif ================================================ FILE: Coq/C/divstep.v ================================================ Require Import ZArith. Require Import ZArith.Znumtheory. Require Import ZArith.Zpow_facts. Require Import Lia. Require Import List. Require Import divsteps.divsteps_def. Require Import extraMath. Require Import modinv. Open Scope list_scope. Open Scope Z_scope. Arguments Z.add !x !y. Arguments Z.sub !m !n. Arguments Z.mul !x !y. Definition Zodd_irr z (Hz1 Hz2 : Zodd z) : Hz1 = Hz2. Proof. revert Hz1 Hz2. destruct z as [|p|p]; try destruct p; try contradiction; intros [] []; reflexivity. Defined. Module Step. Inductive Step : Set := | D : Step | S : Step | H : Step. End Step. Definition Step := Step.Step. Definition INC : Z := 1. Record State : Set := { delta : Z ; f : Z ; g : Z ; oddF : Zodd f }. Definition eta (st : State) := Z.opp (delta st). Definition init f g oddF := {| delta := 1 ; f := f ; g := g ; oddF := oddF |}. Definition step (st : State) : State * Step := match Zeven_odd_dec (g st) with | left _ => ({| delta := INC + delta st ; f := f st ; g := g st / 2 ; oddF := oddF st |} , Step.H) | right oddG => if (0 State * list Step := match n with | O => fun st => (st, nil) | (S n) => fun st => let (st0, xs) := stepN n st in let (st1, x) := step st0 in (st1, x :: xs) end. Inductive Spec : State -> (State * Step) -> Set := | specH : forall d f' g', Spec {| delta := d; f := 2*f'+1; g := 2*g'; oddF := Zodd_2p_plus_1 f' |} ({| delta := INC + d; f := 2*f'+1; g := g'; oddF := Zodd_2p_plus_1 f' |}, Step.H) | specD : forall d f' g', Spec {| delta := Z.pos d; f := 2*f'+1; g := 2*g'+1; oddF := Zodd_2p_plus_1 f' |} ({| delta := INC - Z.pos d; f := 2*g'+1; g := g' - f'; oddF := Zodd_2p_plus_1 g' |}, Step.D) | specS : forall d f' g', (d <= 0) -> Spec {| delta := d; f := 2*f'+1; g := 2*g'+1; oddF := Zodd_2p_plus_1 f' |} ({| delta := INC + d; f := 2*f'+1; g := g' + f' + 1; oddF := Zodd_2p_plus_1 f' |}, Step.S). Lemma spec st : Spec st (step st). Proof. destruct st as [d0 f0 g0 Hf0]. unfold step; cbn -[Z.div]. destruct (Zeven_odd_dec g0) as [Hg0|Hg0]. generalize Hf0. apply Zodd_bool_iff in Hf0. rewrite (Zdiv2_odd_eqn f0), Hf0. rewrite (Zeven_div2 g0) by auto. replace (2 * Z.div2 g0 / 2) with (Z.div2 g0) by (rewrite Z.mul_comm, Z.div_mul by lia; reflexivity). intros Hf0'. replace Hf0' with (Zodd_2p_plus_1 (Z.div2 f0)) by apply Zodd_irr. apply specH. generalize Hf0 Hg0. apply Zodd_bool_iff in Hf0. apply Zodd_bool_iff in Hg0. rewrite (Zdiv2_odd_eqn f0), Hf0. rewrite (Zdiv2_odd_eqn g0), Hg0. destruct (0 -b - Z.of_nat n <= eta (fst (stepN n st)) < b + Z.of_nat n. Proof. induction n; simpl; [lia|]. destruct (stepN n st). rewrite Zpos_P_of_succ_nat. revert IHn. elim (spec s); intros d f' g'; try generalize (Z.pos d); unfold eta; cbn; try lia. Qed. Lemma gHs n st : (2^(Z.of_nat n) | g st) -> g (fst (stepN n st)) = g st / 2^(Z.of_nat n). Proof. induction n;[intros;rewrite Z.div_1_r; reflexivity|]. rewrite Nat2Z.inj_succ, Z.pow_succ_r by lia. simpl (fst _). destruct (stepN n st). intros Hg. assert (Hdivide : (2 ^ Z.of_nat n | g st)) by (etransitivity;[|apply Hg]; auto with *). apply Zdivide_mod in Hg. apply (f_equal (fun x => x / 2 ^ (Z.of_nat n))) in Hg. rewrite Z.mul_comm, Z.rem_mul_r, Z.mul_comm, Z_div_plus_full, Z.mod_div, Z.add_0_l in Hg by lia. rewrite <- IHn in Hg by assumption. destruct (spec s); simpl in Hg; try solve [rewrite Zmod_odd, Z.add_comm, Z.odd_add_mul_2 in Hg; discriminate]. simpl (g _). simpl (g _) in IHn. apply Z.mul_cancel_l with 2; try lia. rewrite !(Z.mul_comm 2), <- Zdiv_Zdiv by lia. rewrite <- IHn by assumption. rewrite !(Z.mul_comm 2), Z.div_mul; lia. Qed. Lemma fHs n st : (2^(Z.of_nat n) | g st) -> f (fst (stepN n st)) = f st. Proof. induction n;[intros; reflexivity|]. rewrite Nat2Z.inj_succ, Z.pow_succ_r by lia. intros Hg. simpl (fst _). assert (Hg' : (2 ^ Z.of_nat n | g st)) by (etransitivity;[|apply Hg]; auto with *). apply Zdivide_mod in Hg. apply (f_equal (fun x => x / 2 ^ (Z.of_nat n))) in Hg. rewrite Z.mul_comm, Z.rem_mul_r, Z.mul_comm, Z_div_plus_full, Z.mod_div, Z.add_0_l in Hg by lia. rewrite <- gHs in Hg by assumption. destruct (stepN n st). rewrite <- IHn by assumption. destruct (spec s); simpl in Hg; try solve [rewrite Zmod_odd, Z.add_comm, Z.odd_add_mul_2 in Hg; discriminate]. reflexivity. Qed. Lemma etaHs n st : (2^(Z.of_nat n) | g st) -> eta (fst (stepN n st)) = eta st - (Z.of_nat n). Proof. induction n;[intros;cbn;ring|]. rewrite Nat2Z.inj_succ, Z.pow_succ_r by lia. intros Hg. simpl (fst _). assert (Hg' : (2 ^ Z.of_nat n | g st)) by (etransitivity;[|apply Hg]; auto with *). apply Zdivide_mod in Hg. apply (f_equal (fun x => x / 2 ^ (Z.of_nat n))) in Hg. rewrite Z.mul_comm, Z.rem_mul_r, Z.mul_comm, Z_div_plus_full, Z.mod_div, Z.add_0_l in Hg by lia. rewrite <- gHs in Hg by assumption. destruct (stepN n st). replace (eta st - _) with (eta st - (Z.of_nat n) - 1) by lia. rewrite <- IHn by assumption. destruct (spec s); simpl in Hg; try solve [rewrite Zmod_odd, Z.add_comm, Z.odd_add_mul_2 in Hg; discriminate]. unfold eta, INC. simpl. ring. Qed. Lemma etaSs n st : 0 <= eta st -> Z.of_nat n <= 1 + eta st -> eta (fst (stepN n st)) = eta st - Z.of_nat n. Proof. induction n;[intros;cbn;ring|]. rewrite Nat2Z.inj_succ, <- Z.add_1_l. intros Heta Hn. simpl (fst _). destruct (stepN n st) as [s l]. transitivity (eta st - Z.of_nat n - 1);[|ring]. assert (Hs : eta (fst (s, l)) = eta st - Z.of_nat n) by (apply IHn; lia). rewrite <- Hs. unfold eta in *. destruct (spec s); cbn; try ring. cbn in Hs. lia. Qed. Lemma stepN_app (n m : nat) st : stepN (n + m) st = let st1 := stepN m st in (fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1). Proof. induction n;[destruct (stepN _ _);reflexivity|]. cbn. rewrite IHn. cbn. destruct (stepN n _). cbn. destruct (step s). reflexivity. Qed. Lemma stepN_app_fst (n m : nat) st : fst (stepN (n + m) st) = fst (stepN n (fst (stepN m st))). Proof. rewrite stepN_app. reflexivity. Qed. Lemma stepN_app_snd (n m : nat) st : snd (stepN (n + m) st) = snd (stepN n (fst (stepN m st))) ++ snd (stepN m st). Proof. rewrite stepN_app. reflexivity. Qed. Lemma etaDs n st : Zodd (g st) -> eta st < 0 -> 0 < Z.of_nat n <= 1 - eta st -> eta (fst (stepN n st)) = -eta st - Z.of_nat n. Proof. intros Hodd Heta Hn. destruct n;[lia|]. rewrite <- Nat.add_1_r. rewrite stepN_app_fst. simpl (stepN 1 st). destruct (spec st);[elim (Zodd_not_Zeven _ Hodd); apply Zeven_2p| |unfold eta in *;cbn in *;lia]. rewrite etaSs; unfold eta in *; cbn in *; change (Z.pos_sub 1 d) with (1 - Z.pos d); try lia. change (0 < Z.of_nat (S n) <= 1 - -(Z.pos d)) in Hn. lia. Qed. Lemma stepN_mod n st1 st2 : eqm (2^Z.of_nat n) (f st1) (f st2) -> eqm (2^Z.of_nat n) (g st1) (g st2) -> delta st1 = delta st2 -> delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\ snd (stepN n st1) = snd (stepN n st2). Proof. revert st1 st2. induction n;[simpl;repeat split;congruence|]. intros st1 st2 Hf Hg Hdelta. replace (S n) with (n + 1)%nat by lia. rewrite !stepN_app_fst, !stepN_app_snd. simpl (stepN 1 st1); simpl (stepN 1 st2). unfold step; rewrite Hdelta. assert (Hdiv2 : forall x y, eqm (2 ^ Z.of_nat (S n)) x y -> eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)). 1:{ intros x y. unfold eqm. rewrite <-!Z.land_ones, <-!(Z.shiftr_div_pow2 _ 1) by lia. replace (Z.of_nat n) with (Z.of_nat (S n) - 1) by lia. rewrite <-!extraMath.Z_shiftr_ones, <-!Z.shiftr_land by lia. congruence. } destruct (Zeven_odd_dec (g st1)); destruct (Zeven_odd_dec (g st2)); try solve [exfalso; rewrite <-?Zeven_bool_iff, <-?Zodd_bool_iff, ?Zeven_mod, ?Zodd_mod in *; apply Zeq_bool_eq in z, z0; apply (extraMath.eqm_2_pow_le 1) in Hg; try lia; change (2^1) with 2 in *; rewrite Hg in z; congruence ];[|destruct (0 Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\ Z.abs (g (fst (stepN n st))) < Z.max (Z.abs (f st)) (Z.abs (g st)). Proof. induction n;[cbn; lia|]. cbn. assert (Hf := fStepBounds (fst (stepN n st))). assert (Hg := gStepBounds (fst (stepN n st))). destruct (stepN n st) as [st' xs]. cbn in *. destruct (step st') as [st'' xs']. cbn in *. lia. Qed. Lemma fixed st n : g st = 0 -> f (fst (stepN n st)) = f st /\ g (fst (stepN n st)) = 0. Proof. intros Hg. induction n;[auto|]. cbn. destruct (stepN n st) as [[eta f g Hf] l]. unfold step. cbn in *. destruct IHn as [-> ->]. cbn. auto. Qed. Lemma fixed_f st n : g st = 0 -> f (fst (stepN n st)) = f st. Proof. intros Hg. destruct (fixed st n Hg). assumption. Qed. Lemma fixed_g st n : g st = 0 -> g (fst (stepN n st)) = 0. Proof. intros Hg. destruct (fixed st n Hg). assumption. Qed. Lemma gcd st d n : Zis_gcd (f st) (g st) d -> Zis_gcd (f (fst (stepN n st))) (g (fst (stepN n st))) d. Proof. intros Hgcd. induction n;[auto|]. cbn. destruct (stepN n st) as [st0 l]. cbn in IHn. destruct (spec st0);cbn in *; revert IHn; apply Zis_gcd_ind; intros Hd1 Hd2 Hdx; apply Zis_gcd_intro; try assumption. * assert (Hodd : Z.odd d = true). 1:{ destruct Hd1 as [z1 Hd1]. apply (f_equal Z.odd) in Hd1. rewrite Z.add_comm, Z.odd_add_mul_2, Z.mul_comm, Z.odd_mul in Hd1. destruct (Z.odd d);auto. } eapply Gauss;[apply Hd2|]. apply rel_prime_mod_rev;[lia|]. rewrite Zmod_odd, Hodd. apply rel_prime_1. * intros x Hxf Hxg. apply Hdx; try assumption. auto with *. * assert (Hodd : Z.odd d = true). 1:{ destruct Hd1 as [z1 Hd1]. apply (f_equal Z.odd) in Hd1. rewrite Z.add_comm, Z.odd_add_mul_2, Z.mul_comm, Z.odd_mul in Hd1. destruct (Z.odd d);auto. } apply Gauss with 2. + replace (2 * (g' - f')) with ((2 * g' + 1) - (2 * f' + 1)) by ring. apply Z.divide_sub_r; assumption. + apply rel_prime_mod_rev;[lia|]. rewrite Zmod_odd, Hodd. apply rel_prime_1. * intros x Hxf Hxg. apply Hdx; try assumption. replace (2 * f' + 1) with ((2 * g' + 1) - (2*(g' - f'))) by ring. apply Z.divide_sub_r; try assumption. auto with *. * assert (Hodd : Z.odd d = true). 1:{ destruct Hd1 as [z1 Hd1]. apply (f_equal Z.odd) in Hd1. rewrite Z.add_comm, Z.odd_add_mul_2, Z.mul_comm, Z.odd_mul in Hd1. destruct (Z.odd d);auto. } apply Gauss with 2. + replace (2 * (g' + f' + 1)) with ((2 * g' + 1) + (2 * f' + 1)) by ring. apply Z.divide_add_r; assumption. + apply rel_prime_mod_rev;[lia|]. rewrite Zmod_odd, Hodd. apply rel_prime_1. * intros x Hxf Hxg. apply Hdx; try assumption. replace (2 * g' + 1) with ((2*(g' + f' + 1)) - (2 * f' + 1)) by ring. apply Z.divide_sub_r; try assumption. auto with *. Qed. Lemma Translate_divsteps n fi gi (Hf : Zodd fi) : delta (fst (stepN n (init fi gi Hf))) = divsteps.delta (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)) /\ f (fst (stepN n (init fi gi Hf))) = divsteps.f (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)) /\ g (fst (stepN n (init fi gi Hf))) = divsteps.g (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)). Proof. induction n;[cbn;auto|]. destruct IHn as [IHdelta [IHf IHg]]. rewrite Nnat.Nat2N.inj_succ, N.iter_succ. destruct (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)). simpl. destruct (stepN n (init fi gi Hf)) as [st0 l]. simpl in *. subst delta0 f0 g0. destruct (spec st0); unfold divsteps.step; cbn -[Z.div]. * rewrite Z.even_mul; cbn -[Z.div]. rewrite (Z.mul_comm 2 g'), Z.div_mul; lia. * rewrite Z.add_comm, Z.even_add_mul_2; cbn -[Z.div]. repeat (split;try reflexivity). replace (1 + 2 * g' - (2 * f' + 1)) with ((g' - f') * 2) by ring. rewrite Z.div_mul; lia. * rewrite (Z.add_comm _ 1), Z.even_add_mul_2; cbn -[Z.div]. elim Z.ltb_spec;[lia|intros _];cbn -[Z.div]. repeat (split;try reflexivity). replace (1 + 2 * g' + (2 * f' + 1)) with ((g' + f' + 1) * 2) by ring. rewrite Z.div_mul; lia. Qed. Lemma Translate_divsteps_g n fi gi (Hf : Zodd fi) : g (fst (stepN n (init fi gi Hf))) = divsteps.g (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)). Proof. destruct (Translate_divsteps n fi gi Hf). tauto. Qed. Module Trans. Record V2 := { x : Z; y : Z }. Definition scale (c : Z) (vec : V2) := {| x := c * (x vec) ; y := c * (y vec) |}. Lemma scale_mul c1 c2 vec : scale (c1 * c2) vec = scale c1 (scale c2 vec). Proof. destruct vec. unfold scale; simpl; f_equal; ring. Qed. Record M2x2 := { u : Z; v : Z; q : Z; r : Z}. Definition I : M2x2 := {| u := 1 ; v := 0 ; q := 0 ; r := 1 |}. Definition ap (m : M2x2) (vec : V2) : V2 := {| x := (u m) * (x vec) + (v m) * (y vec) ; y := (q m) * (x vec) + (r m) * (y vec) |}. Lemma ap_scale m c vec : ap m (scale c vec) = scale c (ap m vec). Proof. destruct m, vec. unfold ap, scale; simpl; f_equal; ring. Qed. Definition mul (m1 m2: M2x2) : M2x2 := {| u := (u m1) * (u m2) + (v m1) * (q m2) ; v := (u m1) * (v m2) + (v m1) * (r m2) ; q := (q m1) * (u m2) + (r m1) * (q m2) ; r := (q m1) * (v m2) + (r m1) * (r m2) |}. Lemma mul_assoc m1 m2 m3 : mul m1 (mul m2 m3) = mul (mul m1 m2) m3. Proof. destruct m1, m2, m3. unfold mul; simpl; f_equal; ring. Qed. Lemma ap_mul m1 m2 vec : ap (mul m1 m2) vec = ap m1 (ap m2 vec). Proof. destruct m1, m2, vec. unfold ap, mul; simpl; f_equal; ring. Qed. Definition det (m: M2x2) : Z := (u m) * (r m) - (v m) * (q m). Lemma det_mul m1 m2 : det (mul m1 m2) = det m1 * det m2. Proof. destruct m1, m2. cbn. ring. Qed. Definition prod : list M2x2 -> M2x2 := fold_right mul I. Lemma prod_app l1 l2 : prod (l1 ++ l2) = mul (prod l1) (prod l2). Proof. induction l1. 1:cbn; destruct (prod l2); unfold mul; cbn; f_equal; ring. cbn. rewrite IHl1. destruct (prod l1); destruct (prod l2); unfold mul; cbn; f_equal; ring. Qed. Lemma det_prod ms : det (prod ms) = fold_right Z.mul 1 (map det ms). Proof. induction ms; try reflexivity. simpl. rewrite det_mul. congruence. Qed. Definition bounded (b : Z) (m : M2x2) := (Z.abs (u m) + Z.abs (v m) <= b /\ -b < u m + v m) /\ (Z.abs (q m) + Z.abs (r m) <= b /\ -b < q m + r m). Lemma bounded_I : bounded 1 I. Proof. unfold bounded. simpl. lia. Qed. Definition trans (s : Step) : M2x2 := match s with | Step.H => {| u := 2; v := 0; q := 0; r := 1 |} | Step.D => {| u := 0; v := 2; q := -1; r := 1 |} | Step.S => {| u := 2; v := 0; q := 1; r := 1 |} end. Definition fg st := {| x := f st; y := g st |}. Lemma trans_step st : scale 2 (fg (fst (step st))) = ap (trans (snd (step st))) (fg st). Proof. destruct (spec st); unfold scale,ap, fg; cbn; f_equal; ring. Qed. Lemma det_trans s : det (trans s) = 2. Proof. destruct s; reflexivity. Qed. Lemma bounded_mul_trans b m s : bounded b m -> bounded (2*b) (mul (trans s) m). Proof. destruct m as [u v q r]. intros [Huv Hqr]; simpl in *. destruct s; unfold bounded; simpl; lia. Qed. Definition transN (n : nat) (st : State) : M2x2 := prod (map trans (snd (stepN n st))). Lemma transN_S n st : {x | transN (S n) st = mul (trans x) (transN n st)}. Proof. unfold transN. simpl. destruct (stepN n st) as [st0 xs] eqn:Hxs. destruct (step st0) as [st1 x]. exists x. reflexivity. Qed. Lemma transN_step n st : scale (2^(Z.of_nat n)) (fg (fst (stepN n st))) = ap (transN n st) (fg st). Proof. induction n. rewrite Z.pow_0_r. destruct st; unfold scale, fg, ap; cbn. f_equal; ring. rewrite Nat2Z.inj_succ, Z.pow_succ_r by lia. unfold transN in *. simpl. destruct (stepN n st) as [st0 xs]; simpl in *. assert (Htrans := trans_step st0). destruct (step st0) as [st1 x]; simpl in *. rewrite ap_mul, <- IHn, ap_scale, Z.mul_comm, scale_mul by auto. f_equal. apply Htrans. Qed. Lemma det_transN n st : det (transN n st) = 2^(Z.of_nat n). Proof. revert st. induction n; try reflexivity. intros st. destruct (transN_S n st) as [x ->]. rewrite det_mul, det_trans, Nat2Z.inj_succ, Z.pow_succ_r by lia. congruence. Qed. Lemma bounded_transN n st : bounded (2^(Z.of_nat n)) (transN n st). Proof. induction n; try apply bounded_I. destruct (transN_S n st) as [x ->]. rewrite Nat2Z.inj_succ, Z.pow_succ_r by lia. auto using bounded_mul_trans. Qed. Lemma transN_stepN (n m : nat) (st : State) : mul (transN n (fst (stepN m st))) (transN m st) = transN (n + m) st. Proof. unfold transN. rewrite stepN_app_snd, map_app, prod_app. reflexivity. Qed. Lemma transHs n st : (2^(Z.of_nat n) | g st) -> transN n st = {| u := 2^(Z.of_nat n); v := 0; q := 0; r := 1 |}. Proof. induction n;[intros; reflexivity|]. rewrite Nat2Z.inj_succ, Z.pow_succ_r by lia. intros Hg. unfold transN in *. simpl (snd _). assert (Hg' : (2 ^ Z.of_nat n | g st)) by (etransitivity;[|apply Hg]; auto with *). apply Zdivide_mod in Hg. apply (f_equal (fun x => x / 2 ^ (Z.of_nat n))) in Hg. rewrite Z.mul_comm, Z.rem_mul_r, Z.mul_comm, Z_div_plus_full, Z.mod_div, Z.add_0_l in Hg by lia. rewrite <- gHs in Hg by assumption. destruct (stepN n st). transitivity (mul (trans Step.H) {| u := 2^(Z.of_nat n); v := 0; q := 0; r := 1 |}). 2:unfold mul;cbn;f_equal; ring. rewrite <- IHn by assumption. destruct (spec s); simpl in Hg; try solve [rewrite Zmod_odd, Z.add_comm, Z.odd_add_mul_2 in Hg; discriminate]. reflexivity. Qed. Lemma transSs n st : delta st <= 0 -> Z.of_nat n <= 1 - delta st -> transN n st = {| u := 2^(Z.of_nat n); v := 0; q := (modInv (-f st) (2^(Z.of_nat n)) * g st) mod (2^(Z.of_nat n)); r := 1 |}. Proof. intros Hdelta Hn. assert (Hrel_prime : rel_prime (f st) 2). 1:{ apply rel_prime_mod_rev; try lia. assert (Hfodd := oddF st). apply <- Zodd_bool_iff in Hfodd. rewrite Zmod_odd, Hfodd. apply rel_prime_1. } assert (Hgcd : forall x, 0 <= x -> Z.gcd (f st) (2 ^ x) = 1). 1:{ intros x Hx. apply Zgcd_1_rel_prime. apply Zpow_facts.rel_prime_Zpower_r; try lia. assumption. } replace ((modInv (-f st) (2 ^ Z.of_nat n) * g st) mod 2 ^ Z.of_nat n) with ((-modInv (f st) (2 ^ Z.of_nat n) * g st) mod 2 ^ Z.of_nat n). 2:{ apply Zmult_eqm;[|reflexivity]. unfold eqm. symmetry. rewrite <- (Z.mul_1_l (modInv _ _)). rewrite <- (Hgcd (Z.of_nat n)), <- Zmult_mod_idemp_l, <- modInv_mul_l, Zmult_mod_idemp_l, <- Z.mul_assoc by lia. rewrite <- (Z.opp_involutive (f st)) at 2. rewrite Z.mul_opp_l, Z.mul_opp_r, <- Z.mul_opp_l. rewrite <- Zmult_mod_idemp_r, modInv_mul_r, Z.gcd_opp_l, Hgcd, Zmult_mod_idemp_r by lia. rewrite Z.mul_1_r. reflexivity. } set (w := _ mod _). apply proj1 with ( (2^(Z.of_nat n) | f st * w + g st) /\ (delta (fst (stepN n st)) = Z.of_nat n + delta st)). revert w Hn; induction n; intros w Hn; [repeat split;[unfold w;rewrite Z.mod_1_r;reflexivity|apply Z.divide_1_l]|]. destruct IHn as [IHn1 [IHn2 IHn3]];[lia|]. rewrite <- (transN_stepN 1 n), IHn1. change (stepN (S n) st) with (stepN (1 + n) st). rewrite stepN_app. unfold transN. simpl (fst (_,_)). simpl (stepN 1 _). set (st' := fst _). assert (Hst' := eq_refl st'). revert Hst'. unfold st' at 2. assert (Hbound : forall a, 0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n) by auto using Z.mod_pos_bound with *. assert (Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)). 1:{ apply Z.mod_divide; try lia. unfold w. rewrite <- Zplus_mod_idemp_l, Zmult_mod_idemp_r, Z.mul_assoc, Z.mul_opp_r, Z.mul_opp_l, <-Z.mul_opp_r, <- Zmult_mod_idemp_l, modInv_mul_r. replace (Z.gcd _ _) with 1. 2:{ symmetry. apply Zgcd_1_rel_prime. apply Zpow_facts.rel_prime_Zpower_r; try lia. assumption. } rewrite Zmult_mod_idemp_l, Zplus_mod_idemp_l. ring_simplify (1 * -g st + g st). reflexivity. } elim (spec);intros d f' g' Hst'. * repeat split. + replace (Z.of_nat (S n)) with (1 + Z.of_nat n) by lia. rewrite Z.pow_add_r by lia. unfold mul; cbn. f_equal; try ring. ring_simplify. unfold w. symmetry. apply Zdivide_mod_minus. - specialize (Hbound ((-modInv (f st) (2 ^ Z.of_nat n) * g st))). replace (Z.of_nat (S n)) with (1 + Z.of_nat n) by lia. rewrite Z.pow_add_r; lia. - set (w0 := (-modInv (f st) (2 ^ Z.of_nat n) * g st) mod 2 ^ Z.of_nat n) in *. apply Z.mod_divide; try lia. rewrite <- Zminus_mod_idemp_r. replace w0 with (1 * w0) by ring. rewrite <- Zmult_mod_idemp_l, <- (Hgcd (Z.of_nat (S n))) by lia. rewrite <- modInv_mul_l, Zmult_mod_idemp_l, Zminus_mod_idemp_r. replace (-modInv (f st) (2 ^ Z.of_nat (S n)) * g st - modInv (f st) (2 ^ Z.of_nat (S n)) * f st * w0) with (-modInv (f st) (2 ^ Z.of_nat (S n)) * (w0 * f st + 1 * g st)) by ring. assert (HtransN := transN_step n st). rewrite <- Hst', IHn1 in HtransN. unfold fg, scale, ap in HtransN. simpl in HtransN. injection HtransN; clear HtransN. intros Hg' Hf'. rewrite <- Hg'. replace (2 ^ Z.of_nat n * (2 * g')) with (g' * (2 ^ Z.of_nat n * 2^1)) by ring. rewrite <- Z.pow_add_r, Z.mul_assoc by lia. replace (Z.of_nat n + 1) with (Z.of_nat (S n)) by lia. apply Z_mod_mult. + assumption. + replace (Z.of_nat (S n) + delta st) with (1 + (Z.of_nat n + delta st)) by lia. rewrite <- IHn3. simpl. rewrite <- Hst'. reflexivity. * rewrite <- Hst' in IHn3. unfold delta at 1 in IHn3. lia. * repeat split. + replace (Z.of_nat (S n)) with (1 + Z.of_nat n) by lia. rewrite Z.pow_add_r by lia. unfold mul; cbn. f_equal; try ring. ring_simplify. unfold w. symmetry. apply Zdivide_mod_minus. - specialize (Hbound ((-modInv (f st) (2 ^ Z.of_nat n) * g st))). replace (Z.of_nat (S n)) with (1 + Z.of_nat n) by lia. rewrite Z.pow_add_r; lia. - set (w0 := (-modInv (f st) (2 ^ Z.of_nat n) * g st) mod 2 ^ Z.of_nat n) in *. apply Z.mod_divide; try lia. rewrite <- Zminus_mod_idemp_r. replace (2 ^ Z.of_nat n + w0) with (1 * (2 ^ Z.of_nat n + w0)) by ring. rewrite <- Zmult_mod_idemp_l, <- (Hgcd (Z.of_nat (S n))) by lia. rewrite <- modInv_mul_l, Zmult_mod_idemp_l, Zminus_mod_idemp_r. replace (-modInv (f st) (2 ^ Z.of_nat (S n)) * g st - modInv (f st) (2 ^ Z.of_nat (S n)) * f st * (2 ^ Z.of_nat n + w0)) with (-modInv (f st) (2 ^ Z.of_nat (S n)) * (2 ^ Z.of_nat n * f st + 0 * g st + (w0 * f st + 1 * g st))) by ring. assert (HtransN := transN_step n st). rewrite <- Hst'0, IHn1 in HtransN. unfold fg, scale, ap in HtransN; simpl in HtransN. injection HtransN; clear HtransN. intros Hg' Hf'. rewrite <- Hg', <- Hf'. replace (2 ^ Z.of_nat n * (2 * f' + 1) + 2 ^ Z.of_nat n * (2 * g' + 1)) with ((f' + g' + 1) * (2 ^ Z.of_nat n * 2^1)) by ring. rewrite <- Z.pow_add_r, Z.mul_assoc by lia. replace (Z.of_nat n + 1) with (Z.of_nat (S n)) by lia. apply Z_mod_mult. + assumption. + replace (Z.of_nat (S n) + delta st) with (1 + (Z.of_nat n + delta st)) by lia. rewrite <- IHn3. simpl. rewrite <- Hst'0. reflexivity. Qed. Lemma transDs n st : Zodd (g st) -> 0 < delta st -> 0 < Z.of_nat n <= 1 + delta st -> transN n st = {| u := 0; v := 2^(Z.of_nat n); q := -1; r := (modInv (-g st) (2^(Z.of_nat n)) * (-f st)) mod (2^(Z.of_nat n)) |}. Proof. intros Hodd Hdelta [Hn0 Hn]. destruct n;[lia|]. rewrite <- Nat.add_1_r, <- transN_stepN. unfold transN at 2; cbn. revert Hodd Hdelta Hn. elim (spec);cbn;intros d f' g' Hodd Hdelta Hn; [elim (Zeven_not_Zodd _ (Zeven_2p _) Hodd)| |lia]. change (Z.of_nat (S n) <= 1 + Z.pos d) in Hn. change (Z.pos_sub 1 d) with (1 - Z.pos d). set (dZ := Z.pos d) in *; clearbody dZ; clear d. change (mul {| u := 0; v := 2; q := -1; r := 1 |} I) with (mul (trans Step.S) {| u := 0; v := 1; q := -1; r := 0 |}). rewrite !mul_assoc. clear st. pose (st0 := {| delta := - dZ; f := 2 * g' + 1; g := - 2 * f' - 1; oddF := Zodd_2p_plus_1 g' |}). set (st1 := Build_State _ _ _ _). assert (Hst01 : step st0 = (st1, Step.S)). 1:{ unfold step. assert (Hoddg : Zodd (g st0)) by (replace (g st0) with (2*(-f' - 1) + 1) by (cbn;ring); apply Zodd_2p_plus_1). destruct Zeven_odd_dec as [Heveng'|Hoddg']; [elim (Zodd_not_Zeven _ Hoddg Heveng')|]. elim (Z.ltb_spec); intros Hd0; cbn in Hd0; try lia. simpl (g st0 + f st0). replace (-2 * f' - 1 + (2 * g' + 1)) with ((g' - f')*2) by ring. rewrite Z_div_mult by lia. reflexivity. } replace (trans Step.S) with (transN 1 st0) by (unfold transN;cbn;rewrite Hst01;reflexivity). replace st1 with (fst (stepN 1 st0)) by (unfold transN;cbn;rewrite Hst01;reflexivity). rewrite transN_stepN, transSs; cbn; try lia. unfold mul; cbn. f_equal; try ring. ring_simplify. do 1 f_equal. ring. Qed. End Trans. Definition pre_div62Modulo (M a : Z) : Z := a - (((modInv M (2^62))*a) mod 2^62) * M. Lemma pre_div62Modulo_mod (M a : Z) : pre_div62Modulo M a mod M = a mod M. Proof. unfold pre_div62Modulo, Z.sub. rewrite <- Z.mul_opp_l. apply Z_mod_plus_full. Qed. Lemma pre_div62Modulo_divide M a : Zodd M -> (2^62 | pre_div62Modulo M a). Proof. intros HM. apply Z.mod_divide;[lia|]. unfold pre_div62Modulo. rewrite <- Zminus_mod_idemp_r, Zmult_mod_idemp_l. replace (modInv M (2 ^ 62) * a * M) with (modInv M (2 ^ 62) * M * a) by ring. rewrite <- Zmult_mod_idemp_l, modInv_mul_l. replace (Z.gcd M (2 ^ 62)) with 1; [rewrite Z.mul_1_l, Zminus_mod_idemp_r, Z.sub_diag; reflexivity|]. symmetry. apply Zgcd_1_rel_prime. apply Zpow_facts.rel_prime_Zpower_r;[lia|]. apply Zgcd_1_rel_prime. apply Z.bezout_1_gcd. apply Zodd_ex_iff in HM. destruct HM as [m HMm]. exists 1; exists (-m). lia. Qed. Definition update_de (M d e : Z) (mtx : Trans.M2x2) : (Z * Z) := let vec := Trans.ap mtx {| Trans.x := d + if d Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <= 2 ^ 62 -> Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <= 2 ^ 62 -> -2 * m < d < m -> -2 * m < e < m -> -2 * m < fst (update_de m d e mtx) < m /\ -2 * m < snd (update_de m d e mtx) < m. Proof. intros Hoddm Huv Hqr Hmd Hme. unfold update_de. set (x := Trans.x _). set (y := Trans.y _). assert (Hm1 : 1 <= m) by lia. assert (Hxbound : Z.abs x <= 2^62 * (m - 1)). 1:{ cbn. eapply Z.le_trans;[apply Z.abs_triangle|]. rewrite !Z.abs_mul. apply Z.le_trans with ((Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx))*(m - 1));[|nia]. destruct (Z.ltb_spec0 d 0); destruct (Z.ltb_spec0 e 0); rewrite Z.mul_add_distr_r; apply Z.add_le_mono; apply Zmult_le_compat_l; lia. } assert (Hybound : Z.abs y <= 2^62 * (m - 1)). 1:{ cbn. eapply Z.le_trans;[apply Z.abs_triangle|]. rewrite !Z.abs_mul. apply Z.le_trans with ((Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx))*(m - 1));[|nia]. destruct (Z.ltb_spec0 d 0); destruct (Z.ltb_spec0 e 0); rewrite Z.mul_add_distr_r; apply Z.add_le_mono; apply Zmult_le_compat_l; lia. } cbn -[Z.div Z.pow x y]. unfold pre_div62Modulo. assert (Hxmod : 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 < 2^62) by (apply Z.mod_pos_bound;lia). assert (Hymod : 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 < 2^62) by (apply Z.mod_pos_bound;lia). rewrite <- !Z.shiftr_div_pow2 by lia. split. * cut (-2*m + 1 <= Z.shiftr (x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m) 62 < m);[lia|apply shiftr_bounds;nia]. * cut (-2*m + 1 <= Z.shiftr (y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m) 62 < m);[lia|apply shiftr_bounds;nia]. Qed. Lemma update_de_eqm m x d e st : Zodd m -> eqm m (x * d) (f st) -> eqm m (x * e) (g st) -> eqm m (x * fst (update_de m d e (Trans.transN 62 st))) (f (fst (stepN 62 st))) /\ eqm m (x * snd (update_de m d e (Trans.transN 62 st))) (g (fst (stepN 62 st))). Proof. intros Hoddm Hf Hg. unfold update_de. generalize (fun a => pre_div62Modulo_divide m a Hoddm). generalize (pre_div62Modulo_mod m). generalize (Trans.transN_step 62 st). change (2^62) with (2^Z.of_nat 62). generalize 62%nat; intros n. intros X; injection X; clear X. intros Hgqr Hfuv Hpre1 Hpre2. destruct (Trans.transN n st) as [u v q r]. cbn -[Z.div pre_div62Modulo] in *. assert (Hn : 0 < 2^Z.of_nat n) by lia. assert (Hinv : modInv (2^Z.of_nat n) m * (2^Z.of_nat n) mod m = 1 mod m). 1:{ rewrite modInv_mul_l. f_equal. rewrite Zgcd_1_rel_prime. apply rel_prime_sym. apply Zpow_facts.rel_prime_Zpower_r;[lia|]. apply rel_prime_sym. apply prime_rel_prime;[apply prime_2|]. rewrite Zodd_equiv in Hoddm. destruct Hoddm as [b ->]. intros Hdivide. apply (Z.divide_add_cancel_r _ _ _ (Z.divide_factor_l _ _)) in Hdivide. apply Z.divide_1_r_abs in Hdivide. discriminate. } unfold eqm. rewrite <- !(Zmult_mod_idemp_l x). replace x with (x*1) by ring. rewrite <- !(Zmult_mod_idemp_r 1), <-Hinv, !Zmult_mod_idemp_r, !Zmult_mod_idemp_l. rewrite <-!Z.mul_assoc, <-!Zdivide_Zdiv_eq by auto. rewrite !Z.mul_assoc, <-!(Zmult_mod_idemp_r (pre_div62Modulo m _)), !Hpre1. assert (Hab : forall a b, eqm m (a * (d + (if d B) (b:bool) x y: f (if b then x else y) = if b then f x else f y. Proof. destruct b; reflexivity. Qed. Lemma div_bounds a b c d : 0 < d -> d * a <= b < d * c <-> a <= b / d < c. Proof. intros Hd. split; intros Hb. * split;[apply Z.div_le_lower_bound|apply Z.div_lt_upper_bound];tauto. * split. - etransitivity;[apply Zmult_le_compat_l|apply Z.mul_div_le];lia. - eapply Z.lt_le_trans;[apply Z.mul_succ_div_gt|apply Zmult_le_compat_l];try lia. Qed. Lemma Z_shiftr_neg1_l: forall n : Z, 0 <= n -> Z.shiftr (-1) n = -1. Proof. apply natlike_rec. reflexivity. intros x Hx Hrec. rewrite <- Z.add_1_r, <- Z.shiftr_shiftr, Hrec by auto with zarith. reflexivity. Qed. Lemma mod_add_carry m a b : 0 < m -> (a mod m + b mod m) / m = Z.b2z ((a + b) mod m (a + b) / m = a / m + b / m + Z.b2z ((a + b) mod m Z.shiftr (a mod (2^n) + b mod (2^n)) n = Z.b2z ((a + b) mod (2^n) Z.shiftr (a + b) n = Z.shiftr a n + Z.shiftr b n + Z.b2z ((a + b) mod (2^n) (a mod m - b mod m) / m = - Z.b2z (a mod m (a - b) / m = a / m - b / m - Z.b2z (a mod m a <= Z.shiftr b n < c. Proof. intros Hb. assert (Hn : 0 <= n). destruct (Z.neg_nonneg_cases n); auto. rewrite (Z.pow_neg_r 2 n) in Hb; lia. rewrite Z.shiftr_div_pow2 by assumption. apply div_bounds; auto with *. Qed. Lemma shiftr_mod_sub_borrow n a b : 0 <= n -> Z.shiftr (a mod (2^n) - b mod (2^n)) n = - Z.b2z (a mod (2^n) Z.shiftr (a - b) n = Z.shiftr a n - Z.shiftr b n - Z.b2z (a mod (2^n) Z.shiftr a n = 0. Proof. intros [Ha0 Ha1]. apply Zle_lt_or_eq in Ha0. destruct Ha0 as [Ha0| <-]. apply Z.shiftr_eq_0. lia. apply Z.log2_lt_pow2; assumption. apply Z.shiftr_0_l. Qed. Lemma shiftr_small_iff a n : 0 <= n -> Z.shiftr a n = 0 <-> 0 <= a < 2^n. Proof. intros Hn. split;[|apply shiftr_small]. rewrite Z.shiftr_eq_0_iff. intros [->|[Ha Hlog]];[lia|]. rewrite <- Z.log2_lt_pow2 in Hlog; lia. Qed. Lemma shiftr_small_neg a n : -2^n <= a < 0 -> Z.shiftr a n = -1. Proof. intros Ha. cut (-1 <= Z.shiftr a n < 0);[lia|]. apply shiftr_bounds. lia. Qed. Lemma shiftr_small_neg_iff a n : 0 <= n -> Z.shiftr a n = -1 <-> -2^n <= a < 0. Proof. intros Hn. split;[|apply shiftr_small_neg]. intros Ha. split;[|apply (Z.shiftr_neg _ n);lia]. rewrite Z.shiftr_div_pow2 in Ha by assumption. rewrite (Z_div_mod_eq_full a (2^n)), Ha. assert (X := Z.mod_pos_bound a (2^n)). lia. Qed. Lemma shiftr_small_signed a n m : -2^n <= a < 2^n -> 0 < m -> Z.shiftr a (n + m) = Z.shiftr a n. Proof. intros [Ha0 Ha1] Hm. rewrite <- Z.shiftr_shiftr by lia. destruct (Z.neg_nonneg_cases a); [|rewrite (shiftr_small _ n), Z.shiftr_0_l by lia; reflexivity]. replace (Z.shiftr a n) with (-1); [rewrite Z_shiftr_neg1_l by lia; reflexivity|]. cut (-1 <= Z.shiftr a n < 0);[lia|]. apply shiftr_bounds. lia. Qed. Lemma shiftl_mod_eqb_unique n a b c d : 0 <= n -> Z.shiftl a n + b mod 2^n =? Z.shiftl c n + d mod 2^n = ((a =? c) && (b mod 2^n =? d mod 2^n))%bool. Proof. intros Hn. rewrite !Z.shiftl_mul_pow2 by auto. symmetry; rewrite andb_comm. case Z.eqb_spec;[case Z.eqb_spec|]. - intros -> ->. symmetry. apply Z.eqb_eq. reflexivity. - intros Hac ->. symmetry. apply Z.eqb_neq. rewrite Z.add_cancel_r. intros Hneq. apply Z.mul_reg_r in Hneq; auto with *. - intros Hbd. symmetry. apply Z.eqb_neq. intros Hneq. apply Hbd. rewrite <- Z.mod_mod by auto with *. rewrite <- (Z_mod_plus_full _ a), Z.add_comm, Hneq, Z.add_comm, Z_mod_plus_full. rewrite Z.mod_mod by auto with *. reflexivity. Qed. Lemma Z_mod_eq_bounded a b m x y : 0 < m -> b - a <= m -> a <= x <= b - 1 -> a <= y <= b - 1 -> x mod m = y mod m -> x = y. Proof. intros Hm Hab Hx Hy Hxym. cut (x - a = y - a);[lia|]. rewrite (Z_div_mod_eq_full (x - a) m), (Z_div_mod_eq_full (y - a) m), <- Zminus_mod_idemp_l, Hxym, Zminus_mod_idemp_l. do 2 f_equal. assert (Hx' : 0 <= (x - a)/m < 1) by (apply div_bounds; lia). assert (Hy' : 0 <= (y - a)/m < 1) by (apply div_bounds; lia). lia. Qed. Lemma Z_lor_pos (a b : Z) : 0 <= a -> 0 < b -> 0 < Z.lor a b. Proof. intros Ha Hb. cut (0 <= Z.lor a b). * intros Hab. apply Z.le_lteq in Hab. destruct Hab; try assumption. cut (false = true);[discriminate|]. rewrite <- (Z.bits_0 (Z.log2 b)), H, Z.lor_spec, Z.bit_log2, orb_true_r; auto. * apply Z.lt_le_incl in Hb. rewrite Z.bits_iff_nonneg_ex in *. destruct Ha as [ka Ha]. destruct Hb as [kb Hb]. exists (Z.max ka kb). intros m Hm. rewrite Z.lor_spec, Ha, Hb; lia. Qed. Lemma Z_log2_lt_pow2 (a b : Z) : 0 < b -> a < 2 ^ b <-> Z.log2 a < b. Proof. intros Hb. destruct a as [|a|a];[|apply Z.log2_lt_pow2;lia|];auto with *. Qed. Lemma Z_shiftr_ones a n : 0 <= n <= a -> (Z.shiftr (Z.ones a) n) = Z.ones (a - n). Proof. intros Hn. apply Z.bits_inj. intros i. destruct (Z.neg_nonneg_cases i) as [Hi|Hi]; [rewrite !Z.testbit_neg_r by lia; reflexivity|]. rewrite Z.shiftr_spec, !Z.testbit_ones_nonneg; lia. Qed. Lemma Z_land_ones_min a b : 0 <= a -> 0 <= b -> (Z.land (Z.ones a) (Z.ones b)) = Z.ones (Z.min a b). intros Ha fhb. apply Z.bits_inj. intros i. destruct (Z.neg_nonneg_cases i) as [Hi|Hi]; [rewrite !Z.testbit_neg_r by lia; reflexivity|]. rewrite Z.land_spec; rewrite !Z.testbit_ones_nonneg; lia. Qed. Lemma eqm_2_pow_le m n a b : 0 <= m <= n -> eqm (2^n) a b -> eqm (2^m) a b. Proof. intros Hmn. unfold eqm. rewrite <- !Z.land_ones by lia. replace m with (Z.min n m) by lia. rewrite <- !Z_land_ones_min, !Z.land_assoc by lia. intros ->. reflexivity. Qed. Lemma Z_shiftr_mod_2 a i j : 0 <= i -> 0 <= j -> Z.shiftr a i mod 2^j = Z.shiftr (a mod 2^(j + i)) i. Proof. intros Hi Hj. rewrite <-!Z.land_ones by lia. rewrite Z.shiftr_land, Z_shiftr_ones by lia. repeat f_equal. lia. Qed. Definition Z_of_comparison (c : Datatypes.comparison) : Z := match c with | Gt => 1 | Eq => 0 | Lt => -1 end. Lemma comp_Z_of_comparison c : Z_of_comparison c ?= 0 = c. Proof. destruct c; reflexivity. Qed. Lemma Z_of_comparison_bounds c : -1 <= Z_of_comparison c <= 1. Proof. destruct c; cbn; lia. Qed. Fixpoint Pos_ctz (p : positive) : nat := match p with | xO p0 => Nat.succ (Pos_ctz p0) | _ => 0 end. (* ctz 0 is normally undefined. We simply return 0 in this case. *) Definition Z_ctz (a : Z) : Z := match a with | Z0 => 0 | Zpos p => Z.of_nat (Pos_ctz p) | Zneg p => Z.of_nat (Pos_ctz p) end. Lemma Z_ctz_non_neg a : 0 <= Z_ctz a. Proof. destruct a; cbn; lia. Qed. Lemma Z_ctz_bound_aux a n : Z.pos a < 2^(Z.of_nat n) -> (Pos_ctz a < n)%nat. Proof. destruct n; try lia. revert n. induction a; auto with *. intros n Hn. rewrite Nat2Z.inj_succ, Z.pow_succ_r, Pos2Z.inj_xO, <- Z.mul_lt_mono_pos_l in Hn by lia. simpl. rewrite <- Nat.succ_lt_mono. destruct n; try lia. auto. Qed. Lemma Z_ctz_bound a n : a <> 0 -> -2^n < a < 2^n -> Z_ctz a < n. Proof. intros Ha0 Ha. destruct (Z.neg_nonneg_cases n);[rewrite Z.pow_neg_r in Ha;lia|]. destruct a; try lia; simpl; rewrite <- (Z2Nat.id _ H); apply Nat2Z.inj_lt; apply Z_ctz_bound_aux; rewrite (Z2Nat.id _ H); lia. Qed. Lemma Z_ctz_testbit_false a i : i < Z_ctz a -> Z.testbit a i = false. Proof. revert i. destruct a; try induction p; simpl in *; try lia; try solve [auto using Z.testbit_neg_r]; intros i Hi; [rewrite Pos2Z.pos_xO|rewrite Pos2Z.neg_xO]; rewrite Z.double_bits; apply IHp; rewrite Z.lt_pred_lt_succ, <- Zpos_P_of_succ_nat; assumption. Qed. Lemma Z_ctz_testbit_true a : a <> 0 -> Z.testbit a (Z_ctz a) = true. Proof. destruct a; try lia; intros _; induction p; try reflexivity; simpl (Z_ctz _); rewrite Zpos_P_of_succ_nat; [rewrite Pos2Z.pos_xO|rewrite Pos2Z.neg_xO]; rewrite Z.double_bits_succ; apply IHp. Qed. Lemma Z_neg_lnot a : -a = Z.lnot a + 1. Proof. cut (a + Z.lnot a = -1);[lia|]. apply Z.add_lnot_diag. Qed. Lemma Z_testbit_neg_low_aux a i : i <= Z_ctz (Z.pos a) -> Z.testbit (-(Z.pos a)) i = Z.testbit (Z.pos a) i. Proof. destruct (Z.neg_nonneg_cases i); [rewrite !Z.testbit_neg_r; auto|]. revert i H a. apply (natlike_ind (fun i => forall a, i <= Z_ctz (Z.pos a) -> Z.testbit (-(Z.pos a)) i = Z.testbit (Z.pos a) i)). * intros a _. rewrite Z_neg_lnot, Z.add_bit0, Z.lnot_spec, xorb_true_r by lia. apply negb_involutive. * intros i H Hrec a Hi. destruct a; try solve [simpl in Hi; lia]. rewrite Pos2Z.inj_xO, <- Z.mul_opp_r, !Z.double_bits_succ. apply Hrec. simpl in *. lia. Qed. Lemma Z_testbit_neg_low a i : i <= Z_ctz a -> Z.testbit (-a) i = Z.testbit a i. Proof. intros Hi. destruct a. * reflexivity. * auto using Z_testbit_neg_low_aux. * symmetry; apply Z_testbit_neg_low_aux. assumption. Qed. Lemma Z_testbit_neg_high_aux a i : Z_ctz (Z.pos a) < i -> Z.testbit (-(Z.pos a)) i = negb (Z.testbit (Z.pos a) i). Proof. revert i. induction a. * intros i Hi. simpl in Hi. rewrite Z_neg_lnot, Z.add_nocarry_lxor, Z.lxor_spec, Z.lnot_spec; try lia. 1:{ change (Z.testbit 1) with (Z.testbit (Z.ones 1)). rewrite (Z.ones_spec_high 1 i), xorb_false_r by lia. reflexivity. } apply Z.bits_inj_iff'. intros n Hn. rewrite Z.bits_0, Z.land_comm, Z.land_spec, Z.lnot_spec by lia. apply Zle_lt_or_eq in Hn. destruct Hn as [Hn|<-];[|reflexivity]. change (Z.testbit 1) with (Z.testbit (Z.ones 1)). rewrite (Z.ones_spec_high 1 n) by lia. reflexivity. * intros i Hi. rewrite Pos2Z.inj_xO, <- Z.mul_opp_r, !Z.double_bits. apply IHa. cbn in Hi. rewrite Zpos_P_of_succ_nat, Z.lt_succ_lt_pred in Hi. assumption. * cbn. intros i Hi. change (Z.testbit 1) with (Z.testbit (Z.ones 1)). rewrite Z.bits_m1, (Z.ones_spec_high 1 i) by lia. reflexivity. Qed. Lemma Z_testbit_neg_high a i : a <> 0 -> Z_ctz a < i -> Z.testbit (-a) i = negb (Z.testbit a i). Proof. intros Ha Hi. destruct a. * lia. * auto using Z_testbit_neg_high_aux. * rewrite <- (negb_involutive (Z.testbit (-Z.neg p) i)). f_equal; symmetry. apply (Z_testbit_neg_high_aux p). assumption. Qed. Lemma Z_x_and_opp_x a : a <> 0 -> Z.land a (-a) = 2^(Z_ctz a). Proof. intros Ha. apply Z.bits_inj'. intros n Hn. rewrite Z.land_spec, Z.pow2_bits_eqb by apply Z_ctz_non_neg. destruct (Z.le_gt_cases n (Z_ctz a)); [|rewrite Z_testbit_neg_high, andb_negb_r by auto;lia]. rewrite Z_testbit_neg_low, andb_diag by auto. apply Z.le_lteq in H. destruct H as [H| ->]; [rewrite Z_ctz_testbit_false|rewrite Z_ctz_testbit_true]; lia. Qed. Lemma Z_testbit_false_ctz a i : a <> 0 -> (forall j, 0 <= j <= i -> Z.testbit a j = false) -> i < Z_ctz a. Proof. intros Ha0 Ha. apply Z.nle_gt. intros Hi. assert (Htest : Z.testbit a (Z_ctz a) = false). * apply Ha. auto using Z_ctz_non_neg. * rewrite Z_ctz_testbit_true in Htest by assumption. discriminate. Qed. Lemma Z_ctz_lor_l a b : a <> 0 -> Z_ctz (Z.lor a b) <= Z_ctz a. Proof. intros Ha. cut (forall i, i < Z_ctz (Z.lor a b) -> i < Z_ctz a). * intros H. apply Z.lt_pred_le. apply H. lia. * intros i Hi. apply Z_testbit_false_ctz;[assumption|]. intros j Hj. eapply proj1. apply orb_false_iff. rewrite <- Z.lor_spec. apply Z_ctz_testbit_false. eapply Z.le_lt_trans;[|apply Hi]. tauto. Qed. ================================================ FILE: Coq/C/jets_secp256k1.v ================================================ (* clightgen -normalize -I secp256k1 -U__has_builtin -D USE_FORCE_WIDEMUL_INT128_STRUCT -D VERIFY -D VST -fstruct-passing jets-secp256k1.c *) From Coq Require Import String List ZArith. From compcert Require Import Coqlib Integers Floats AST Ctypes Cop Clight Clightdefs. Import Clightdefs.ClightNotations. Local Open Scope Z_scope. Local Open Scope string_scope. Local Open Scope clight_scope. Module Info. Definition version := "22.10-sources". Definition build_number := "11868730". Definition build_tag := "auto/2022/10/17/2029". Definition build_branch := "auto/2022/10". Definition arch := "x86". Definition model := "64". Definition abi := "standard". Definition bitsize := 64. Definition big_endian := false. Definition source_file := "jets-secp256k1.c". Definition normalized := true. End Info. Definition _LSBclear : ident := $"LSBclear". Definition _M : ident := $"M". Definition _M52 : ident := $"M52". Definition _M62 : ident := $"M62". Definition _R : ident := $"R". Definition _ReadBE32 : ident := $"ReadBE32". Definition _SECP256K1_SIGNED62_ONE : ident := $"SECP256K1_SIGNED62_ONE". Definition _WriteBE32 : ident := $"WriteBE32". Definition _WriteBE64 : ident := $"WriteBE64". Definition _Z : ident := $"Z". Definition __2064 : ident := $"_2064". Definition __2380 : ident := $"_2380". Definition __2382 : ident := $"_2382". Definition __2843 : ident := $"_2843". Definition __3154 : ident := $"_3154". Definition __3156 : ident := $"_3156". Definition __3158 : ident := $"_3158". Definition __3626 : ident := $"_3626". Definition __3711 : ident := $"_3711". Definition __IO_FILE : ident := $"_IO_FILE". Definition __IO_backup_base : ident := $"_IO_backup_base". Definition __IO_buf_base : ident := $"_IO_buf_base". Definition __IO_buf_end : ident := $"_IO_buf_end". Definition __IO_codecvt : ident := $"_IO_codecvt". Definition __IO_marker : ident := $"_IO_marker". Definition __IO_read_base : ident := $"_IO_read_base". Definition __IO_read_end : ident := $"_IO_read_end". Definition __IO_read_ptr : ident := $"_IO_read_ptr". Definition __IO_save_base : ident := $"_IO_save_base". Definition __IO_save_end : ident := $"_IO_save_end". Definition __IO_wide_data : ident := $"_IO_wide_data". Definition __IO_write_base : ident := $"_IO_write_base". Definition __IO_write_end : ident := $"_IO_write_end". Definition __IO_write_ptr : ident := $"_IO_write_ptr". Definition ___assert_fail : ident := $"__assert_fail". Definition ___builtin_addl : ident := $"__builtin_addl". Definition ___builtin_ais_annot : ident := $"__builtin_ais_annot". Definition ___builtin_annot : ident := $"__builtin_annot". Definition ___builtin_annot_intval : ident := $"__builtin_annot_intval". Definition ___builtin_bswap : ident := $"__builtin_bswap". Definition ___builtin_bswap16 : ident := $"__builtin_bswap16". Definition ___builtin_bswap32 : ident := $"__builtin_bswap32". Definition ___builtin_bswap64 : ident := $"__builtin_bswap64". Definition ___builtin_clz : ident := $"__builtin_clz". Definition ___builtin_clzl : ident := $"__builtin_clzl". Definition ___builtin_clzll : ident := $"__builtin_clzll". Definition ___builtin_ctz : ident := $"__builtin_ctz". Definition ___builtin_ctzl : ident := $"__builtin_ctzl". Definition ___builtin_ctzll : ident := $"__builtin_ctzll". Definition ___builtin_debug : ident := $"__builtin_debug". Definition ___builtin_expect : ident := $"__builtin_expect". Definition ___builtin_fabs : ident := $"__builtin_fabs". Definition ___builtin_fabsf : ident := $"__builtin_fabsf". Definition ___builtin_fmadd : ident := $"__builtin_fmadd". Definition ___builtin_fmax : ident := $"__builtin_fmax". Definition ___builtin_fmin : ident := $"__builtin_fmin". Definition ___builtin_fmsub : ident := $"__builtin_fmsub". Definition ___builtin_fnmadd : ident := $"__builtin_fnmadd". Definition ___builtin_fnmsub : ident := $"__builtin_fnmsub". Definition ___builtin_fsqrt : ident := $"__builtin_fsqrt". Definition ___builtin_isfinite : ident := $"__builtin_isfinite". Definition ___builtin_isfinitef : ident := $"__builtin_isfinitef". Definition ___builtin_isinf : ident := $"__builtin_isinf". Definition ___builtin_isinff : ident := $"__builtin_isinff". Definition ___builtin_isnan : ident := $"__builtin_isnan". Definition ___builtin_isnanf : ident := $"__builtin_isnanf". Definition ___builtin_membar : ident := $"__builtin_membar". Definition ___builtin_memcpy_aligned : ident := $"__builtin_memcpy_aligned". Definition ___builtin_mull : ident := $"__builtin_mull". Definition ___builtin_nan : ident := $"__builtin_nan". Definition ___builtin_nanf : ident := $"__builtin_nanf". Definition ___builtin_nans : ident := $"__builtin_nans". Definition ___builtin_nansf : ident := $"__builtin_nansf". Definition ___builtin_negl : ident := $"__builtin_negl". Definition ___builtin_nop : ident := $"__builtin_nop". Definition ___builtin_read16_reversed : ident := $"__builtin_read16_reversed". Definition ___builtin_read32_reversed : ident := $"__builtin_read32_reversed". Definition ___builtin_sel : ident := $"__builtin_sel". Definition ___builtin_sqrt : ident := $"__builtin_sqrt". Definition ___builtin_subl : ident := $"__builtin_subl". Definition ___builtin_unreachable : ident := $"__builtin_unreachable". Definition ___builtin_va_arg : ident := $"__builtin_va_arg". Definition ___builtin_va_copy : ident := $"__builtin_va_copy". Definition ___builtin_va_end : ident := $"__builtin_va_end". Definition ___builtin_va_start : ident := $"__builtin_va_start". Definition ___builtin_write16_reversed : ident := $"__builtin_write16_reversed". Definition ___builtin_write32_reversed : ident := $"__builtin_write32_reversed". Definition ___compcert_i64_dtos : ident := $"__compcert_i64_dtos". Definition ___compcert_i64_dtou : ident := $"__compcert_i64_dtou". Definition ___compcert_i64_ftos : ident := $"__compcert_i64_ftos". Definition ___compcert_i64_ftou : ident := $"__compcert_i64_ftou". Definition ___compcert_i64_sar : ident := $"__compcert_i64_sar". Definition ___compcert_i64_sdiv : ident := $"__compcert_i64_sdiv". Definition ___compcert_i64_shl : ident := $"__compcert_i64_shl". Definition ___compcert_i64_shr : ident := $"__compcert_i64_shr". Definition ___compcert_i64_smod : ident := $"__compcert_i64_smod". Definition ___compcert_i64_smulh : ident := $"__compcert_i64_smulh". Definition ___compcert_i64_stod : ident := $"__compcert_i64_stod". Definition ___compcert_i64_stof : ident := $"__compcert_i64_stof". Definition ___compcert_i64_udiv : ident := $"__compcert_i64_udiv". Definition ___compcert_i64_umod : ident := $"__compcert_i64_umod". Definition ___compcert_i64_umulh : ident := $"__compcert_i64_umulh". Definition ___compcert_i64_utod : ident := $"__compcert_i64_utod". Definition ___compcert_i64_utof : ident := $"__compcert_i64_utof". Definition ___compcert_va_composite : ident := $"__compcert_va_composite". Definition ___compcert_va_float32 : ident := $"__compcert_va_float32". Definition ___compcert_va_float64 : ident := $"__compcert_va_float64". Definition ___compcert_va_int32 : ident := $"__compcert_va_int32". Definition ___compcert_va_int64 : ident := $"__compcert_va_int64". Definition ___compound : ident := $"__compound". Definition ___func__ : ident := $"__func__". Definition ___func____1 : ident := $"__func____1". Definition ___stringlit_1 : ident := $"__stringlit_1". Definition ___stringlit_10 : ident := $"__stringlit_10". Definition ___stringlit_100 : ident := $"__stringlit_100". Definition ___stringlit_101 : ident := $"__stringlit_101". Definition ___stringlit_102 : ident := $"__stringlit_102". Definition ___stringlit_103 : ident := $"__stringlit_103". Definition ___stringlit_104 : ident := $"__stringlit_104". Definition ___stringlit_105 : ident := $"__stringlit_105". Definition ___stringlit_106 : ident := $"__stringlit_106". Definition ___stringlit_107 : ident := $"__stringlit_107". Definition ___stringlit_108 : ident := $"__stringlit_108". Definition ___stringlit_109 : ident := $"__stringlit_109". Definition ___stringlit_11 : ident := $"__stringlit_11". Definition ___stringlit_110 : ident := $"__stringlit_110". Definition ___stringlit_111 : ident := $"__stringlit_111". Definition ___stringlit_112 : ident := $"__stringlit_112". Definition ___stringlit_113 : ident := $"__stringlit_113". Definition ___stringlit_114 : ident := $"__stringlit_114". Definition ___stringlit_115 : ident := $"__stringlit_115". Definition ___stringlit_116 : ident := $"__stringlit_116". Definition ___stringlit_117 : ident := $"__stringlit_117". Definition ___stringlit_118 : ident := $"__stringlit_118". Definition ___stringlit_119 : ident := $"__stringlit_119". Definition ___stringlit_12 : ident := $"__stringlit_12". Definition ___stringlit_120 : ident := $"__stringlit_120". Definition ___stringlit_121 : ident := $"__stringlit_121". Definition ___stringlit_122 : ident := $"__stringlit_122". Definition ___stringlit_123 : ident := $"__stringlit_123". Definition ___stringlit_124 : ident := $"__stringlit_124". Definition ___stringlit_125 : ident := $"__stringlit_125". Definition ___stringlit_126 : ident := $"__stringlit_126". Definition ___stringlit_127 : ident := $"__stringlit_127". Definition ___stringlit_128 : ident := $"__stringlit_128". Definition ___stringlit_129 : ident := $"__stringlit_129". Definition ___stringlit_13 : ident := $"__stringlit_13". Definition ___stringlit_130 : ident := $"__stringlit_130". Definition ___stringlit_131 : ident := $"__stringlit_131". Definition ___stringlit_132 : ident := $"__stringlit_132". Definition ___stringlit_133 : ident := $"__stringlit_133". Definition ___stringlit_134 : ident := $"__stringlit_134". Definition ___stringlit_135 : ident := $"__stringlit_135". Definition ___stringlit_136 : ident := $"__stringlit_136". Definition ___stringlit_137 : ident := $"__stringlit_137". Definition ___stringlit_138 : ident := $"__stringlit_138". Definition ___stringlit_139 : ident := $"__stringlit_139". Definition ___stringlit_14 : ident := $"__stringlit_14". Definition ___stringlit_140 : ident := $"__stringlit_140". Definition ___stringlit_141 : ident := $"__stringlit_141". Definition ___stringlit_142 : ident := $"__stringlit_142". Definition ___stringlit_143 : ident := $"__stringlit_143". Definition ___stringlit_144 : ident := $"__stringlit_144". Definition ___stringlit_145 : ident := $"__stringlit_145". Definition ___stringlit_146 : ident := $"__stringlit_146". Definition ___stringlit_147 : ident := $"__stringlit_147". Definition ___stringlit_148 : ident := $"__stringlit_148". Definition ___stringlit_149 : ident := $"__stringlit_149". Definition ___stringlit_15 : ident := $"__stringlit_15". Definition ___stringlit_150 : ident := $"__stringlit_150". Definition ___stringlit_151 : ident := $"__stringlit_151". Definition ___stringlit_152 : ident := $"__stringlit_152". Definition ___stringlit_153 : ident := $"__stringlit_153". Definition ___stringlit_154 : ident := $"__stringlit_154". Definition ___stringlit_155 : ident := $"__stringlit_155". Definition ___stringlit_156 : ident := $"__stringlit_156". Definition ___stringlit_157 : ident := $"__stringlit_157". Definition ___stringlit_158 : ident := $"__stringlit_158". Definition ___stringlit_159 : ident := $"__stringlit_159". Definition ___stringlit_16 : ident := $"__stringlit_16". Definition ___stringlit_160 : ident := $"__stringlit_160". Definition ___stringlit_161 : ident := $"__stringlit_161". Definition ___stringlit_162 : ident := $"__stringlit_162". Definition ___stringlit_163 : ident := $"__stringlit_163". Definition ___stringlit_164 : ident := $"__stringlit_164". Definition ___stringlit_165 : ident := $"__stringlit_165". Definition ___stringlit_166 : ident := $"__stringlit_166". Definition ___stringlit_167 : ident := $"__stringlit_167". Definition ___stringlit_168 : ident := $"__stringlit_168". Definition ___stringlit_169 : ident := $"__stringlit_169". Definition ___stringlit_17 : ident := $"__stringlit_17". Definition ___stringlit_170 : ident := $"__stringlit_170". Definition ___stringlit_171 : ident := $"__stringlit_171". Definition ___stringlit_172 : ident := $"__stringlit_172". Definition ___stringlit_18 : ident := $"__stringlit_18". Definition ___stringlit_19 : ident := $"__stringlit_19". Definition ___stringlit_2 : ident := $"__stringlit_2". Definition ___stringlit_20 : ident := $"__stringlit_20". Definition ___stringlit_21 : ident := $"__stringlit_21". Definition ___stringlit_22 : ident := $"__stringlit_22". Definition ___stringlit_23 : ident := $"__stringlit_23". Definition ___stringlit_24 : ident := $"__stringlit_24". Definition ___stringlit_25 : ident := $"__stringlit_25". Definition ___stringlit_26 : ident := $"__stringlit_26". Definition ___stringlit_27 : ident := $"__stringlit_27". Definition ___stringlit_28 : ident := $"__stringlit_28". Definition ___stringlit_29 : ident := $"__stringlit_29". Definition ___stringlit_3 : ident := $"__stringlit_3". Definition ___stringlit_30 : ident := $"__stringlit_30". Definition ___stringlit_31 : ident := $"__stringlit_31". Definition ___stringlit_32 : ident := $"__stringlit_32". Definition ___stringlit_33 : ident := $"__stringlit_33". Definition ___stringlit_34 : ident := $"__stringlit_34". Definition ___stringlit_35 : ident := $"__stringlit_35". Definition ___stringlit_36 : ident := $"__stringlit_36". Definition ___stringlit_37 : ident := $"__stringlit_37". Definition ___stringlit_38 : ident := $"__stringlit_38". Definition ___stringlit_39 : ident := $"__stringlit_39". Definition ___stringlit_4 : ident := $"__stringlit_4". Definition ___stringlit_40 : ident := $"__stringlit_40". Definition ___stringlit_41 : ident := $"__stringlit_41". Definition ___stringlit_42 : ident := $"__stringlit_42". Definition ___stringlit_43 : ident := $"__stringlit_43". Definition ___stringlit_44 : ident := $"__stringlit_44". Definition ___stringlit_45 : ident := $"__stringlit_45". Definition ___stringlit_46 : ident := $"__stringlit_46". Definition ___stringlit_47 : ident := $"__stringlit_47". Definition ___stringlit_48 : ident := $"__stringlit_48". Definition ___stringlit_49 : ident := $"__stringlit_49". Definition ___stringlit_5 : ident := $"__stringlit_5". Definition ___stringlit_50 : ident := $"__stringlit_50". Definition ___stringlit_51 : ident := $"__stringlit_51". Definition ___stringlit_52 : ident := $"__stringlit_52". Definition ___stringlit_53 : ident := $"__stringlit_53". Definition ___stringlit_54 : ident := $"__stringlit_54". Definition ___stringlit_55 : ident := $"__stringlit_55". Definition ___stringlit_56 : ident := $"__stringlit_56". Definition ___stringlit_57 : ident := $"__stringlit_57". Definition ___stringlit_58 : ident := $"__stringlit_58". Definition ___stringlit_59 : ident := $"__stringlit_59". Definition ___stringlit_6 : ident := $"__stringlit_6". Definition ___stringlit_60 : ident := $"__stringlit_60". Definition ___stringlit_61 : ident := $"__stringlit_61". Definition ___stringlit_62 : ident := $"__stringlit_62". Definition ___stringlit_63 : ident := $"__stringlit_63". Definition ___stringlit_64 : ident := $"__stringlit_64". Definition ___stringlit_65 : ident := $"__stringlit_65". Definition ___stringlit_66 : ident := $"__stringlit_66". Definition ___stringlit_67 : ident := $"__stringlit_67". Definition ___stringlit_68 : ident := $"__stringlit_68". Definition ___stringlit_69 : ident := $"__stringlit_69". Definition ___stringlit_7 : ident := $"__stringlit_7". Definition ___stringlit_70 : ident := $"__stringlit_70". Definition ___stringlit_71 : ident := $"__stringlit_71". Definition ___stringlit_72 : ident := $"__stringlit_72". Definition ___stringlit_73 : ident := $"__stringlit_73". Definition ___stringlit_74 : ident := $"__stringlit_74". Definition ___stringlit_75 : ident := $"__stringlit_75". Definition ___stringlit_76 : ident := $"__stringlit_76". Definition ___stringlit_77 : ident := $"__stringlit_77". Definition ___stringlit_78 : ident := $"__stringlit_78". Definition ___stringlit_79 : ident := $"__stringlit_79". Definition ___stringlit_8 : ident := $"__stringlit_8". Definition ___stringlit_80 : ident := $"__stringlit_80". Definition ___stringlit_81 : ident := $"__stringlit_81". Definition ___stringlit_82 : ident := $"__stringlit_82". Definition ___stringlit_83 : ident := $"__stringlit_83". Definition ___stringlit_84 : ident := $"__stringlit_84". Definition ___stringlit_85 : ident := $"__stringlit_85". Definition ___stringlit_86 : ident := $"__stringlit_86". Definition ___stringlit_87 : ident := $"__stringlit_87". Definition ___stringlit_88 : ident := $"__stringlit_88". Definition ___stringlit_89 : ident := $"__stringlit_89". Definition ___stringlit_9 : ident := $"__stringlit_9". Definition ___stringlit_90 : ident := $"__stringlit_90". Definition ___stringlit_91 : ident := $"__stringlit_91". Definition ___stringlit_92 : ident := $"__stringlit_92". Definition ___stringlit_93 : ident := $"__stringlit_93". Definition ___stringlit_94 : ident := $"__stringlit_94". Definition ___stringlit_95 : ident := $"__stringlit_95". Definition ___stringlit_96 : ident := $"__stringlit_96". Definition ___stringlit_97 : ident := $"__stringlit_97". Definition ___stringlit_98 : ident := $"__stringlit_98". Definition ___stringlit_99 : ident := $"__stringlit_99". Definition __chain : ident := $"_chain". Definition __codecvt : ident := $"_codecvt". Definition __cur_column : ident := $"_cur_column". Definition __fileno : ident := $"_fileno". Definition __flags : ident := $"_flags". Definition __flags2 : ident := $"_flags2". Definition __freeres_buf : ident := $"_freeres_buf". Definition __freeres_list : ident := $"_freeres_list". Definition __lock : ident := $"_lock". Definition __markers : ident := $"_markers". Definition __mode : ident := $"_mode". Definition __offset : ident := $"_offset". Definition __old_offset : ident := $"_old_offset". Definition __prevchain : ident := $"_prevchain". Definition __res : ident := $"_res". Definition __res__1 : ident := $"_res__1". Definition __shortbuf : ident := $"_shortbuf". Definition __unused2 : ident := $"_unused2". Definition __vtable_offset : ident := $"_vtable_offset". Definition __wide_data : ident := $"_wide_data". Definition _a : ident := $"a". Definition _a0 : ident := $"a0". Definition _a1 : ident := $"a1". Definition _a2 : ident := $"a2". Definition _a3 : ident := $"a3". Definition _a4 : ident := $"a4". Definition _a__1 : ident := $"a__1". Definition _abort : ident := $"abort". Definition _abs : ident := $"abs". Definition _accum : ident := $"accum". Definition _add : ident := $"add". Definition _ai : ident := $"ai". Definition _alen : ident := $"alen". Definition _alphain : ident := $"alphain". Definition _alphaquad : ident := $"alphaquad". Definition _am : ident := $"am". Definition _arr : ident := $"arr". Definition _aux : ident := $"aux". Definition _ax : ident := $"ax". Definition _ay : ident := $"ay". Definition _az : ident := $"az". Definition _b : ident := $"b". Definition _b32 : ident := $"b32". Definition _betain : ident := $"betain". Definition _betaquad : ident := $"betaquad". Definition _bin : ident := $"bin". Definition _bit : ident := $"bit". Definition _bits : ident := $"bits". Definition _bits_na_1 : ident := $"bits_na_1". Definition _bits_na_lam : ident := $"bits_na_lam". Definition _bits_ng_1 : ident := $"bits_ng_1". Definition _bits_ng_128 : ident := $"bits_ng_128". Definition _blind : ident := $"blind". Definition _blind32 : ident := $"blind32". Definition _block : ident := $"block". Definition _bm : ident := $"bm". Definition _buf : ident := $"buf". Definition _buf1 : ident := $"buf1". Definition _buf2 : ident := $"buf2". Definition _bx : ident := $"bx". Definition _by : ident := $"by". Definition _bzinv : ident := $"bzinv". Definition _bzinv2 : ident := $"bzinv2". Definition _bzinv3 : ident := $"bzinv3". Definition _c : ident := $"c". Definition _c0 : ident := $"c0". Definition _c1 : ident := $"c1". Definition _c128 : ident := $"c128". Definition _c2 : ident := $"c2". Definition _carry : ident := $"carry". Definition _cd : ident := $"cd". Definition _ce : ident := $"ce". Definition _cf : ident := $"cf". Definition _cg : ident := $"cg". Definition _chunk : ident := $"chunk". Definition _cond : ident := $"cond". Definition _cond_add : ident := $"cond_add". Definition _cond_negate : ident := $"cond_negate". Definition _count : ident := $"count". Definition _counter : ident := $"counter". Definition _ctx : ident := $"ctx". Definition _ctx__1 : ident := $"ctx__1". Definition _d : ident := $"d". Definition _d0 : ident := $"d0". Definition _d1 : ident := $"d1". Definition _d2 : ident := $"d2". Definition _d3 : ident := $"d3". Definition _d4 : ident := $"d4". Definition _d_ge : ident := $"d_ge". Definition _data : ident := $"data". Definition _debruijn : ident := $"debruijn". Definition _delta : ident := $"delta". Definition _diff : ident := $"diff". Definition _dst : ident := $"dst". Definition _dst_ptr : ident := $"dst_ptr". Definition _e : ident := $"e". Definition _e0 : ident := $"e0". Definition _e1 : ident := $"e1". Definition _e2 : ident := $"e2". Definition _e3 : ident := $"e3". Definition _e4 : ident := $"e4". Definition _edge : ident := $"edge". Definition _env : ident := $"env". Definition _eta : ident := $"eta". Definition _f : ident := $"f". Definition _f0 : ident := $"f0". Definition _factor : ident := $"factor". Definition _fi : ident := $"fi". Definition _flag : ident := $"flag". Definition _fn : ident := $"fn". Definition _fprintf : ident := $"fprintf". Definition _frame : ident := $"frame". Definition _frameItem : ident := $"frameItem". Definition _g : ident := $"g". Definition _g0 : ident := $"g0". Definition _g1 : ident := $"g1". Definition _g2 : ident := $"g2". Definition _gammain : ident := $"gammain". Definition _ge : ident := $"ge". Definition _gen : ident := $"gen". Definition _gi : ident := $"gi". Definition _gn : ident := $"gn". Definition _h : ident := $"h". Definition _h2 : ident := $"h2". Definition _h3 : ident := $"h3". Definition _hash : ident := $"hash". Definition _hh : ident := $"hh". Definition _hi : ident := $"hi". Definition _hl : ident := $"hl". Definition _i : ident := $"i". Definition _inf : ident := $"inf". Definition _infinity : ident := $"infinity". Definition _input32 : ident := $"input32". Definition _input_hash : ident := $"input_hash". Definition _input_pubkey : ident := $"input_pubkey". Definition _internal_pubkey : ident := $"internal_pubkey". Definition _iv : ident := $"iv". Definition _j : ident := $"j". Definition _jinv : ident := $"jinv". Definition _k : ident := $"k". Definition _k1_bound : ident := $"k1_bound". Definition _k2_bound : ident := $"k2_bound". Definition _key : ident := $"key". Definition _key32 : ident := $"key32". Definition _l : ident := $"l". Definition _last_set_bit : ident := $"last_set_bit". Definition _len : ident := $"len". Definition _length : ident := $"length". Definition _lh : ident := $"lh". Definition _limit : ident := $"limit". Definition _ll : ident := $"ll". Definition _lo : ident := $"lo". Definition _m : ident := $"m". Definition _m0 : ident := $"m0". Definition _m1 : ident := $"m1". Definition _m2 : ident := $"m2". Definition _m3 : ident := $"m3". Definition _m4 : ident := $"m4". Definition _m5 : ident := $"m5". Definition _m6 : ident := $"m6". Definition _magnitude : ident := $"magnitude". Definition _main : ident := $"main". Definition _mask : ident := $"mask". Definition _mask0 : ident := $"mask0". Definition _mask1 : ident := $"mask1". Definition _md : ident := $"md". Definition _me : ident := $"me". Definition _memcpy : ident := $"memcpy". Definition _memset : ident := $"memset". Definition _mid34 : ident := $"mid34". Definition _midstate : ident := $"midstate". Definition _minus_b1 : ident := $"minus_b1". Definition _minus_b2 : ident := $"minus_b2". Definition _modinfo : ident := $"modinfo". Definition _modulus : ident := $"modulus". Definition _modulus_inv62 : ident := $"modulus_inv62". Definition _msg : ident := $"msg". Definition _msglen : ident := $"msglen". Definition _n : ident := $"n". Definition _n0 : ident := $"n0". Definition _n1 : ident := $"n1". Definition _n2 : ident := $"n2". Definition _n3 : ident := $"n3". Definition _na : ident := $"na". Definition _na_1 : ident := $"na_1". Definition _na__1 : ident := $"na__1". Definition _na_lam : ident := $"na_lam". Definition _negc : ident := $"negc". Definition _ng : ident := $"ng". Definition _ng_1 : ident := $"ng_1". Definition _ng_128 : ident := $"ng_128". Definition _ng__1 : ident := $"ng__1". Definition _ng__2 : ident := $"ng__2". Definition _no : ident := $"no". Definition _nonzero : ident := $"nonzero". Definition _normalized : ident := $"normalized". Definition _now : ident := $"now". Definition _np : ident := $"np". Definition _num : ident := $"num". Definition _odd : ident := $"odd". Definition _offset : ident := $"offset". Definition _one : ident := $"one". Definition _output : ident := $"output". Definition _output32 : ident := $"output32". Definition _output_hash : ident := $"output_hash". Definition _output_pubkey : ident := $"output_pubkey". Definition _over : ident := $"over". Definition _over__1 : ident := $"over__1". Definition _over__2 : ident := $"over__2". Definition _over__3 : ident := $"over__3". Definition _over__4 : ident := $"over__4". Definition _over__5 : ident := $"over__5". Definition _over__6 : ident := $"over__6". Definition _overflow : ident := $"overflow". Definition _p : ident := $"p". Definition _p0 : ident := $"p0". Definition _p1 : ident := $"p1". Definition _p2 : ident := $"p2". Definition _p3 : ident := $"p3". Definition _p4 : ident := $"p4". Definition _peekBit : ident := $"peekBit". Definition _pk : ident := $"pk". Definition _pk_parity : ident := $"pk_parity". Definition _pkj : ident := $"pkj". Definition _pre : ident := $"pre". Definition _pre_a : ident := $"pre_a". Definition _prefix1 : ident := $"prefix1". Definition _prefix2 : ident := $"prefix2". Definition _ps : ident := $"ps". Definition _pt : ident := $"pt". Definition _ptr : ident := $"ptr". Definition _pubkey : ident := $"pubkey". Definition _pubkey32 : ident := $"pubkey32". Definition _q : ident := $"q". Definition _r : ident := $"r". Definition _r0 : ident := $"r0". Definition _r1 : ident := $"r1". Definition _r2 : ident := $"r2". Definition _r3 : ident := $"r3". Definition _r32 : ident := $"r32". Definition _r4 : ident := $"r4". Definition _read32s : ident := $"read32s". Definition _read8s : ident := $"read8s". Definition _readBit : ident := $"readBit". Definition _read_fe : ident := $"read_fe". Definition _read_ge : ident := $"read_ge". Definition _read_gej : ident := $"read_gej". Definition _read_scalar : ident := $"read_scalar". Definition _result : ident := $"result". Definition _ret : ident := $"ret". Definition _rj : ident := $"rj". Definition _rx : ident := $"rx". Definition _rzr : ident := $"rzr". Definition _s : ident := $"s". Definition _s1 : ident := $"s1". Definition _s2 : ident := $"s2". Definition _sd : ident := $"sd". Definition _se : ident := $"se". Definition _secp256k1_const_beta : ident := $"secp256k1_const_beta". Definition _secp256k1_const_lambda : ident := $"secp256k1_const_lambda". Definition _secp256k1_const_modinfo_fe : ident := $"secp256k1_const_modinfo_fe". Definition _secp256k1_const_modinfo_scalar : ident := $"secp256k1_const_modinfo_scalar". Definition _secp256k1_ctz64_var : ident := $"secp256k1_ctz64_var". Definition _secp256k1_ctz64_var_debruijn : ident := $"secp256k1_ctz64_var_debruijn". Definition _secp256k1_ec_pubkey_tweak_add_helper : ident := $"secp256k1_ec_pubkey_tweak_add_helper". Definition _secp256k1_eckey_pubkey_tweak_add : ident := $"secp256k1_eckey_pubkey_tweak_add". Definition _secp256k1_ecmult : ident := $"secp256k1_ecmult". Definition _secp256k1_ecmult_odd_multiples_table : ident := $"secp256k1_ecmult_odd_multiples_table". Definition _secp256k1_ecmult_strauss_wnaf : ident := $"secp256k1_ecmult_strauss_wnaf". Definition _secp256k1_ecmult_table_get_ge : ident := $"secp256k1_ecmult_table_get_ge". Definition _secp256k1_ecmult_table_get_ge_lambda : ident := $"secp256k1_ecmult_table_get_ge_lambda". Definition _secp256k1_ecmult_table_get_ge_storage : ident := $"secp256k1_ecmult_table_get_ge_storage". Definition _secp256k1_ecmult_wnaf : ident := $"secp256k1_ecmult_wnaf". Definition _secp256k1_extrakeys_ge_even_y : ident := $"secp256k1_extrakeys_ge_even_y". Definition _secp256k1_fe_add : ident := $"secp256k1_fe_add". Definition _secp256k1_fe_add_int : ident := $"secp256k1_fe_add_int". Definition _secp256k1_fe_clear : ident := $"secp256k1_fe_clear". Definition _secp256k1_fe_cmov : ident := $"secp256k1_fe_cmov". Definition _secp256k1_fe_equal_var : ident := $"secp256k1_fe_equal_var". Definition _secp256k1_fe_from_signed62 : ident := $"secp256k1_fe_from_signed62". Definition _secp256k1_fe_from_storage : ident := $"secp256k1_fe_from_storage". Definition _secp256k1_fe_get_b32 : ident := $"secp256k1_fe_get_b32". Definition _secp256k1_fe_half : ident := $"secp256k1_fe_half". Definition _secp256k1_fe_inv_var : ident := $"secp256k1_fe_inv_var". Definition _secp256k1_fe_is_odd : ident := $"secp256k1_fe_is_odd". Definition _secp256k1_fe_is_zero : ident := $"secp256k1_fe_is_zero". Definition _secp256k1_fe_mul : ident := $"secp256k1_fe_mul". Definition _secp256k1_fe_mul_inner : ident := $"secp256k1_fe_mul_inner". Definition _secp256k1_fe_mul_int : ident := $"secp256k1_fe_mul_int". Definition _secp256k1_fe_negate : ident := $"secp256k1_fe_negate". Definition _secp256k1_fe_normalize_var : ident := $"secp256k1_fe_normalize_var". Definition _secp256k1_fe_normalize_weak : ident := $"secp256k1_fe_normalize_weak". Definition _secp256k1_fe_normalizes_to_zero : ident := $"secp256k1_fe_normalizes_to_zero". Definition _secp256k1_fe_normalizes_to_zero_var : ident := $"secp256k1_fe_normalizes_to_zero_var". Definition _secp256k1_fe_set_b32 : ident := $"secp256k1_fe_set_b32". Definition _secp256k1_fe_set_int : ident := $"secp256k1_fe_set_int". Definition _secp256k1_fe_sqr : ident := $"secp256k1_fe_sqr". Definition _secp256k1_fe_sqr_inner : ident := $"secp256k1_fe_sqr_inner". Definition _secp256k1_fe_sqrt_var : ident := $"secp256k1_fe_sqrt_var". Definition _secp256k1_fe_to_signed62 : ident := $"secp256k1_fe_to_signed62". Definition _secp256k1_fe_to_storage : ident := $"secp256k1_fe_to_storage". Definition _secp256k1_fe_verify : ident := $"secp256k1_fe_verify". Definition _secp256k1_ge_from_storage : ident := $"secp256k1_ge_from_storage". Definition _secp256k1_ge_is_in_correct_subgroup : ident := $"secp256k1_ge_is_in_correct_subgroup". Definition _secp256k1_ge_is_infinity : ident := $"secp256k1_ge_is_infinity". Definition _secp256k1_ge_is_valid_var : ident := $"secp256k1_ge_is_valid_var". Definition _secp256k1_ge_neg : ident := $"secp256k1_ge_neg". Definition _secp256k1_ge_set_gej_var : ident := $"secp256k1_ge_set_gej_var". Definition _secp256k1_ge_set_gej_zinv : ident := $"secp256k1_ge_set_gej_zinv". Definition _secp256k1_ge_set_infinity : ident := $"secp256k1_ge_set_infinity". Definition _secp256k1_ge_set_xo_var : ident := $"secp256k1_ge_set_xo_var". Definition _secp256k1_ge_set_xy : ident := $"secp256k1_ge_set_xy". Definition _secp256k1_ge_table_set_globalz : ident := $"secp256k1_ge_table_set_globalz". Definition _secp256k1_ge_to_storage : ident := $"secp256k1_ge_to_storage". Definition _secp256k1_gej_add_ge_var : ident := $"secp256k1_gej_add_ge_var". Definition _secp256k1_gej_add_var : ident := $"secp256k1_gej_add_var". Definition _secp256k1_gej_add_zinv_var : ident := $"secp256k1_gej_add_zinv_var". Definition _secp256k1_gej_double : ident := $"secp256k1_gej_double". Definition _secp256k1_gej_double_var : ident := $"secp256k1_gej_double_var". Definition _secp256k1_gej_eq_ge_var : ident := $"secp256k1_gej_eq_ge_var". Definition _secp256k1_gej_eq_var : ident := $"secp256k1_gej_eq_var". Definition _secp256k1_gej_eq_x_var : ident := $"secp256k1_gej_eq_x_var". Definition _secp256k1_gej_is_infinity : ident := $"secp256k1_gej_is_infinity". Definition _secp256k1_gej_neg : ident := $"secp256k1_gej_neg". Definition _secp256k1_gej_rescale : ident := $"secp256k1_gej_rescale". Definition _secp256k1_gej_set_ge : ident := $"secp256k1_gej_set_ge". Definition _secp256k1_gej_set_infinity : ident := $"secp256k1_gej_set_infinity". Definition _secp256k1_generator_generate : ident := $"secp256k1_generator_generate". Definition _secp256k1_generator_generate_internal : ident := $"secp256k1_generator_generate_internal". Definition _secp256k1_generator_load : ident := $"secp256k1_generator_load". Definition _secp256k1_generator_save : ident := $"secp256k1_generator_save". Definition _secp256k1_i128_accum_mul : ident := $"secp256k1_i128_accum_mul". Definition _secp256k1_i128_check_pow2 : ident := $"secp256k1_i128_check_pow2". Definition _secp256k1_i128_det : ident := $"secp256k1_i128_det". Definition _secp256k1_i128_dissip_mul : ident := $"secp256k1_i128_dissip_mul". Definition _secp256k1_i128_eq_var : ident := $"secp256k1_i128_eq_var". Definition _secp256k1_i128_from_i64 : ident := $"secp256k1_i128_from_i64". Definition _secp256k1_i128_mul : ident := $"secp256k1_i128_mul". Definition _secp256k1_i128_rshift : ident := $"secp256k1_i128_rshift". Definition _secp256k1_i128_to_i64 : ident := $"secp256k1_i128_to_i64". Definition _secp256k1_i128_to_u64 : ident := $"secp256k1_i128_to_u64". Definition _secp256k1_memcmp_var : ident := $"secp256k1_memcmp_var". Definition _secp256k1_modinv64_abs : ident := $"secp256k1_modinv64_abs". Definition _secp256k1_modinv64_det_check_pow2 : ident := $"secp256k1_modinv64_det_check_pow2". Definition _secp256k1_modinv64_divsteps_62_var : ident := $"secp256k1_modinv64_divsteps_62_var". Definition _secp256k1_modinv64_modinfo : ident := $"secp256k1_modinv64_modinfo". Definition _secp256k1_modinv64_mul_62 : ident := $"secp256k1_modinv64_mul_62". Definition _secp256k1_modinv64_mul_cmp_62 : ident := $"secp256k1_modinv64_mul_cmp_62". Definition _secp256k1_modinv64_normalize_62 : ident := $"secp256k1_modinv64_normalize_62". Definition _secp256k1_modinv64_signed62 : ident := $"secp256k1_modinv64_signed62". Definition _secp256k1_modinv64_signed62_assign : ident := $"secp256k1_modinv64_signed62_assign". Definition _secp256k1_modinv64_trans2x2 : ident := $"secp256k1_modinv64_trans2x2". Definition _secp256k1_modinv64_update_de_62 : ident := $"secp256k1_modinv64_update_de_62". Definition _secp256k1_modinv64_update_fg_62_var : ident := $"secp256k1_modinv64_update_fg_62_var". Definition _secp256k1_modinv64_var : ident := $"secp256k1_modinv64_var". Definition _secp256k1_mul128 : ident := $"secp256k1_mul128". Definition _secp256k1_pre_g : ident := $"secp256k1_pre_g". Definition _secp256k1_pre_g_128 : ident := $"secp256k1_pre_g_128". Definition _secp256k1_pubkey_load : ident := $"secp256k1_pubkey_load". Definition _secp256k1_pubkey_save : ident := $"secp256k1_pubkey_save". Definition _secp256k1_scalar_add : ident := $"secp256k1_scalar_add". Definition _secp256k1_scalar_cadd_bit : ident := $"secp256k1_scalar_cadd_bit". Definition _secp256k1_scalar_check_overflow : ident := $"secp256k1_scalar_check_overflow". Definition _secp256k1_scalar_eq : ident := $"secp256k1_scalar_eq". Definition _secp256k1_scalar_from_signed62 : ident := $"secp256k1_scalar_from_signed62". Definition _secp256k1_scalar_get_b32 : ident := $"secp256k1_scalar_get_b32". Definition _secp256k1_scalar_get_bits : ident := $"secp256k1_scalar_get_bits". Definition _secp256k1_scalar_get_bits_var : ident := $"secp256k1_scalar_get_bits_var". Definition _secp256k1_scalar_inverse_var : ident := $"secp256k1_scalar_inverse_var". Definition _secp256k1_scalar_is_zero : ident := $"secp256k1_scalar_is_zero". Definition _secp256k1_scalar_mul : ident := $"secp256k1_scalar_mul". Definition _secp256k1_scalar_mul_512 : ident := $"secp256k1_scalar_mul_512". Definition _secp256k1_scalar_mul_shift_var : ident := $"secp256k1_scalar_mul_shift_var". Definition _secp256k1_scalar_negate : ident := $"secp256k1_scalar_negate". Definition _secp256k1_scalar_reduce : ident := $"secp256k1_scalar_reduce". Definition _secp256k1_scalar_reduce_512 : ident := $"secp256k1_scalar_reduce_512". Definition _secp256k1_scalar_set_b32 : ident := $"secp256k1_scalar_set_b32". Definition _secp256k1_scalar_set_int : ident := $"secp256k1_scalar_set_int". Definition _secp256k1_scalar_split_128 : ident := $"secp256k1_scalar_split_128". Definition _secp256k1_scalar_split_lambda : ident := $"secp256k1_scalar_split_lambda". Definition _secp256k1_scalar_split_lambda_verify : ident := $"secp256k1_scalar_split_lambda_verify". Definition _secp256k1_scalar_to_signed62 : ident := $"secp256k1_scalar_to_signed62". Definition _secp256k1_schnorrsig_challenge : ident := $"secp256k1_schnorrsig_challenge". Definition _secp256k1_schnorrsig_sha256_tagged : ident := $"secp256k1_schnorrsig_sha256_tagged". Definition _secp256k1_schnorrsig_verify : ident := $"secp256k1_schnorrsig_verify". Definition _secp256k1_strauss_point_state : ident := $"secp256k1_strauss_point_state". Definition _secp256k1_strauss_state : ident := $"secp256k1_strauss_state". Definition _secp256k1_u128_accum_mul : ident := $"secp256k1_u128_accum_mul". Definition _secp256k1_u128_accum_u64 : ident := $"secp256k1_u128_accum_u64". Definition _secp256k1_u128_check_bits : ident := $"secp256k1_u128_check_bits". Definition _secp256k1_u128_from_u64 : ident := $"secp256k1_u128_from_u64". Definition _secp256k1_u128_hi_u64 : ident := $"secp256k1_u128_hi_u64". Definition _secp256k1_u128_mul : ident := $"secp256k1_u128_mul". Definition _secp256k1_u128_rshift : ident := $"secp256k1_u128_rshift". Definition _secp256k1_u128_to_u64 : ident := $"secp256k1_u128_to_u64". Definition _secp256k1_uint128 : ident := $"secp256k1_uint128". Definition _secp256k1_umul128 : ident := $"secp256k1_umul128". Definition _secp256k1_xonly_pubkey_from_pubkey : ident := $"secp256k1_xonly_pubkey_from_pubkey". Definition _secp256k1_xonly_pubkey_load : ident := $"secp256k1_xonly_pubkey_load". Definition _secp256k1_xonly_pubkey_parse : ident := $"secp256k1_xonly_pubkey_parse". Definition _secp256k1_xonly_pubkey_save : ident := $"secp256k1_xonly_pubkey_save". Definition _secp256k1_xonly_pubkey_serialize : ident := $"secp256k1_xonly_pubkey_serialize". Definition _secp256k1_xonly_pubkey_tweak_add : ident := $"secp256k1_xonly_pubkey_tweak_add". Definition _sha : ident := $"sha". Definition _sha256_buf : ident := $"sha256_buf". Definition _sha256_compression_uchar : ident := $"sha256_compression_uchar". Definition _sha256_context : ident := $"sha256_context". Definition _sha256_ctx : ident := $"sha256_ctx". Definition _sha256_ctx__1 : ident := $"sha256_ctx__1". Definition _sha256_finalize : ident := $"sha256_finalize". Definition _sha256_fromMidstate : ident := $"sha256_fromMidstate". Definition _sha256_hash : ident := $"sha256_hash". Definition _sha256_init : ident := $"sha256_init". Definition _sha256_iv : ident := $"sha256_iv". Definition _sha256_max_counter : ident := $"sha256_max_counter". Definition _sha256_midstate : ident := $"sha256_midstate". Definition _sha256_tagged_init : ident := $"sha256_tagged_init". Definition _sha256_u64be : ident := $"sha256_u64be". Definition _sha256_uchars : ident := $"sha256_uchars". Definition _sha_buf : ident := $"sha_buf". Definition _shallue_van_de_woestijne : ident := $"shallue_van_de_woestijne". Definition _shift : ident := $"shift". Definition _shifthigh : ident := $"shifthigh". Definition _shiftlimbs : ident := $"shiftlimbs". Definition _shiftlow : ident := $"shiftlow". Definition _sig : ident := $"sig". Definition _sig64 : ident := $"sig64". Definition _sign : ident := $"sign". Definition _signatureIV : ident := $"signatureIV". Definition _simplicity_bip_0340_verify : ident := $"simplicity_bip_0340_verify". Definition _simplicity_check_sig_verify : ident := $"simplicity_check_sig_verify". Definition _simplicity_decompress : ident := $"simplicity_decompress". Definition _simplicity_fe_add : ident := $"simplicity_fe_add". Definition _simplicity_fe_invert : ident := $"simplicity_fe_invert". Definition _simplicity_fe_is_odd : ident := $"simplicity_fe_is_odd". Definition _simplicity_fe_is_zero : ident := $"simplicity_fe_is_zero". Definition _simplicity_fe_multiply : ident := $"simplicity_fe_multiply". Definition _simplicity_fe_multiply_beta : ident := $"simplicity_fe_multiply_beta". Definition _simplicity_fe_negate : ident := $"simplicity_fe_negate". Definition _simplicity_fe_normalize : ident := $"simplicity_fe_normalize". Definition _simplicity_fe_square : ident := $"simplicity_fe_square". Definition _simplicity_fe_square_root : ident := $"simplicity_fe_square_root". Definition _simplicity_ge_is_on_curve : ident := $"simplicity_ge_is_on_curve". Definition _simplicity_ge_negate : ident := $"simplicity_ge_negate". Definition _simplicity_gej_add : ident := $"simplicity_gej_add". Definition _simplicity_gej_double : ident := $"simplicity_gej_double". Definition _simplicity_gej_equiv : ident := $"simplicity_gej_equiv". Definition _simplicity_gej_ge_add : ident := $"simplicity_gej_ge_add". Definition _simplicity_gej_ge_add_ex : ident := $"simplicity_gej_ge_add_ex". Definition _simplicity_gej_ge_equiv : ident := $"simplicity_gej_ge_equiv". Definition _simplicity_gej_infinity : ident := $"simplicity_gej_infinity". Definition _simplicity_gej_is_infinity : ident := $"simplicity_gej_is_infinity". Definition _simplicity_gej_is_on_curve : ident := $"simplicity_gej_is_on_curve". Definition _simplicity_gej_is_valid_var : ident := $"simplicity_gej_is_valid_var". Definition _simplicity_gej_negate : ident := $"simplicity_gej_negate". Definition _simplicity_gej_normalize : ident := $"simplicity_gej_normalize". Definition _simplicity_gej_rescale : ident := $"simplicity_gej_rescale". Definition _simplicity_gej_x_equiv : ident := $"simplicity_gej_x_equiv". Definition _simplicity_gej_y_is_odd : ident := $"simplicity_gej_y_is_odd". Definition _simplicity_generate : ident := $"simplicity_generate". Definition _simplicity_generic_taptweak : ident := $"simplicity_generic_taptweak". Definition _simplicity_hash_to_curve : ident := $"simplicity_hash_to_curve". Definition _simplicity_linear_combination_1 : ident := $"simplicity_linear_combination_1". Definition _simplicity_linear_verify_1 : ident := $"simplicity_linear_verify_1". Definition _simplicity_off_curve_linear_combination_1 : ident := $"simplicity_off_curve_linear_combination_1". Definition _simplicity_off_curve_scale : ident := $"simplicity_off_curve_scale". Definition _simplicity_point_verify_1 : ident := $"simplicity_point_verify_1". Definition _simplicity_read32 : ident := $"simplicity_read32". Definition _simplicity_read8 : ident := $"simplicity_read8". Definition _simplicity_scalar_add : ident := $"simplicity_scalar_add". Definition _simplicity_scalar_invert : ident := $"simplicity_scalar_invert". Definition _simplicity_scalar_is_zero : ident := $"simplicity_scalar_is_zero". Definition _simplicity_scalar_multiply : ident := $"simplicity_scalar_multiply". Definition _simplicity_scalar_multiply_lambda : ident := $"simplicity_scalar_multiply_lambda". Definition _simplicity_scalar_negate : ident := $"simplicity_scalar_negate". Definition _simplicity_scalar_normalize : ident := $"simplicity_scalar_normalize". Definition _simplicity_scalar_square : ident := $"simplicity_scalar_square". Definition _simplicity_scale : ident := $"simplicity_scale". Definition _simplicity_sha256_compression : ident := $"simplicity_sha256_compression". Definition _simplicity_swu : ident := $"simplicity_swu". Definition _simplicity_write8 : ident := $"simplicity_write8". Definition _skipBits : ident := $"skipBits". Definition _skip_fe : ident := $"skip_fe". Definition _skip_ge : ident := $"skip_ge". Definition _src : ident := $"src". Definition _state : ident := $"state". Definition _stderr : ident := $"stderr". Definition _succeed : ident := $"succeed". Definition _t : ident := $"t". Definition _t0 : ident := $"t0". Definition _t1 : ident := $"t1". Definition _t2 : ident := $"t2". Definition _t3 : ident := $"t3". Definition _t4 : ident := $"t4". Definition _t__1 : ident := $"t__1". Definition _t__10 : ident := $"t__10". Definition _t__11 : ident := $"t__11". Definition _t__12 : ident := $"t__12". Definition _t__13 : ident := $"t__13". Definition _t__14 : ident := $"t__14". Definition _t__15 : ident := $"t__15". Definition _t__2 : ident := $"t__2". Definition _t__3 : ident := $"t__3". Definition _t__4 : ident := $"t__4". Definition _t__5 : ident := $"t__5". Definition _t__6 : ident := $"t__6". Definition _t__7 : ident := $"t__7". Definition _t__8 : ident := $"t__8". Definition _t__9 : ident := $"t__9". Definition _tagLen : ident := $"tagLen". Definition _tagName : ident := $"tagName". Definition _taptweakTag : ident := $"taptweakTag". Definition _term : ident := $"term". Definition _th : ident := $"th". Definition _th__1 : ident := $"th__1". Definition _th__10 : ident := $"th__10". Definition _th__11 : ident := $"th__11". Definition _th__12 : ident := $"th__12". Definition _th__13 : ident := $"th__13". Definition _th__14 : ident := $"th__14". Definition _th__15 : ident := $"th__15". Definition _th__2 : ident := $"th__2". Definition _th__3 : ident := $"th__3". Definition _th__4 : ident := $"th__4". Definition _th__5 : ident := $"th__5". Definition _th__6 : ident := $"th__6". Definition _th__7 : ident := $"th__7". Definition _th__8 : ident := $"th__8". Definition _th__9 : ident := $"th__9". Definition _tl : ident := $"tl". Definition _tl__1 : ident := $"tl__1". Definition _tl__10 : ident := $"tl__10". Definition _tl__11 : ident := $"tl__11". Definition _tl__12 : ident := $"tl__12". Definition _tl__13 : ident := $"tl__13". Definition _tl__14 : ident := $"tl__14". Definition _tl__15 : ident := $"tl__15". Definition _tl__2 : ident := $"tl__2". Definition _tl__3 : ident := $"tl__3". Definition _tl__4 : ident := $"tl__4". Definition _tl__5 : ident := $"tl__5". Definition _tl__6 : ident := $"tl__6". Definition _tl__7 : ident := $"tl__7". Definition _tl__8 : ident := $"tl__8". Definition _tl__9 : ident := $"tl__9". Definition _tmp : ident := $"tmp". Definition _tmpa : ident := $"tmpa". Definition _tweak : ident := $"tweak". Definition _tweak32 : ident := $"tweak32". Definition _tx : ident := $"tx". Definition _txEnv : ident := $"txEnv". Definition _u : ident := $"u". Definition _u0 : ident := $"u0". Definition _u1 : ident := $"u1". Definition _u2 : ident := $"u2". Definition _v : ident := $"v". Definition _verify_bit : ident := $"verify_bit". Definition _w : ident := $"w". Definition _wd : ident := $"wd". Definition _wnaf : ident := $"wnaf". Definition _wnaf_na_1 : ident := $"wnaf_na_1". Definition _wnaf_na_lam : ident := $"wnaf_na_lam". Definition _wnaf_ng_1 : ident := $"wnaf_ng_1". Definition _wnaf_ng_128 : ident := $"wnaf_ng_128". Definition _word : ident := $"word". Definition _write8s : ident := $"write8s". Definition _writeBit : ident := $"writeBit". Definition _write_fe : ident := $"write_fe". Definition _write_ge : ident := $"write_ge". Definition _write_gej : ident := $"write_gej". Definition _write_scalar : ident := $"write_scalar". Definition _x : ident := $"x". Definition _x1 : ident := $"x1". Definition _x11 : ident := $"x11". Definition _x176 : ident := $"x176". Definition _x2 : ident := $"x2". Definition _x22 : ident := $"x22". Definition _x220 : ident := $"x220". Definition _x223 : ident := $"x223". Definition _x3 : ident := $"x3". Definition _x3d : ident := $"x3d". Definition _x44 : ident := $"x44". Definition _x6 : ident := $"x6". Definition _x88 : ident := $"x88". Definition _x9 : ident := $"x9". Definition _xonly_pubkey : ident := $"xonly_pubkey". Definition _y : ident := $"y". Definition _y1 : ident := $"y1". Definition _y2 : ident := $"y2". Definition _y3 : ident := $"y3". Definition _y_parity : ident := $"y_parity". Definition _yes : ident := $"yes". Definition _z : ident := $"z". Definition _z0 : ident := $"z0". Definition _z1 : ident := $"z1". Definition _z12 : ident := $"z12". Definition _z2 : ident := $"z2". Definition _z22 : ident := $"z22". Definition _z3 : ident := $"z3". Definition _z6 : ident := $"z6". Definition _zero : ident := $"zero". Definition _zero_in : ident := $"zero_in". Definition _zeros : ident := $"zeros". Definition _zi : ident := $"zi". Definition _zi2 : ident := $"zi2". Definition _zi3 : ident := $"zi3". Definition _zr : ident := $"zr". Definition _zs : ident := $"zs". Definition _zz : ident := $"zz". Definition _t'1 : ident := 128%positive. Definition _t'10 : ident := 137%positive. Definition _t'100 : ident := 227%positive. Definition _t'101 : ident := 228%positive. Definition _t'102 : ident := 229%positive. Definition _t'103 : ident := 230%positive. Definition _t'104 : ident := 231%positive. Definition _t'105 : ident := 232%positive. Definition _t'106 : ident := 233%positive. Definition _t'107 : ident := 234%positive. Definition _t'108 : ident := 235%positive. Definition _t'109 : ident := 236%positive. Definition _t'11 : ident := 138%positive. Definition _t'110 : ident := 237%positive. Definition _t'111 : ident := 238%positive. Definition _t'112 : ident := 239%positive. Definition _t'113 : ident := 240%positive. Definition _t'114 : ident := 241%positive. Definition _t'115 : ident := 242%positive. Definition _t'116 : ident := 243%positive. Definition _t'117 : ident := 244%positive. Definition _t'118 : ident := 245%positive. Definition _t'119 : ident := 246%positive. Definition _t'12 : ident := 139%positive. Definition _t'120 : ident := 247%positive. Definition _t'121 : ident := 248%positive. Definition _t'122 : ident := 249%positive. Definition _t'123 : ident := 250%positive. Definition _t'124 : ident := 251%positive. Definition _t'125 : ident := 252%positive. Definition _t'126 : ident := 253%positive. Definition _t'13 : ident := 140%positive. Definition _t'14 : ident := 141%positive. Definition _t'15 : ident := 142%positive. Definition _t'16 : ident := 143%positive. Definition _t'17 : ident := 144%positive. Definition _t'18 : ident := 145%positive. Definition _t'19 : ident := 146%positive. Definition _t'2 : ident := 129%positive. Definition _t'20 : ident := 147%positive. Definition _t'21 : ident := 148%positive. Definition _t'22 : ident := 149%positive. Definition _t'23 : ident := 150%positive. Definition _t'24 : ident := 151%positive. Definition _t'25 : ident := 152%positive. Definition _t'26 : ident := 153%positive. Definition _t'27 : ident := 154%positive. Definition _t'28 : ident := 155%positive. Definition _t'29 : ident := 156%positive. Definition _t'3 : ident := 130%positive. Definition _t'30 : ident := 157%positive. Definition _t'31 : ident := 158%positive. Definition _t'32 : ident := 159%positive. Definition _t'33 : ident := 160%positive. Definition _t'34 : ident := 161%positive. Definition _t'35 : ident := 162%positive. Definition _t'36 : ident := 163%positive. Definition _t'37 : ident := 164%positive. Definition _t'38 : ident := 165%positive. Definition _t'39 : ident := 166%positive. Definition _t'4 : ident := 131%positive. Definition _t'40 : ident := 167%positive. Definition _t'41 : ident := 168%positive. Definition _t'42 : ident := 169%positive. Definition _t'43 : ident := 170%positive. Definition _t'44 : ident := 171%positive. Definition _t'45 : ident := 172%positive. Definition _t'46 : ident := 173%positive. Definition _t'47 : ident := 174%positive. Definition _t'48 : ident := 175%positive. Definition _t'49 : ident := 176%positive. Definition _t'5 : ident := 132%positive. Definition _t'50 : ident := 177%positive. Definition _t'51 : ident := 178%positive. Definition _t'52 : ident := 179%positive. Definition _t'53 : ident := 180%positive. Definition _t'54 : ident := 181%positive. Definition _t'55 : ident := 182%positive. Definition _t'56 : ident := 183%positive. Definition _t'57 : ident := 184%positive. Definition _t'58 : ident := 185%positive. Definition _t'59 : ident := 186%positive. Definition _t'6 : ident := 133%positive. Definition _t'60 : ident := 187%positive. Definition _t'61 : ident := 188%positive. Definition _t'62 : ident := 189%positive. Definition _t'63 : ident := 190%positive. Definition _t'64 : ident := 191%positive. Definition _t'65 : ident := 192%positive. Definition _t'66 : ident := 193%positive. Definition _t'67 : ident := 194%positive. Definition _t'68 : ident := 195%positive. Definition _t'69 : ident := 196%positive. Definition _t'7 : ident := 134%positive. Definition _t'70 : ident := 197%positive. Definition _t'71 : ident := 198%positive. Definition _t'72 : ident := 199%positive. Definition _t'73 : ident := 200%positive. Definition _t'74 : ident := 201%positive. Definition _t'75 : ident := 202%positive. Definition _t'76 : ident := 203%positive. Definition _t'77 : ident := 204%positive. Definition _t'78 : ident := 205%positive. Definition _t'79 : ident := 206%positive. Definition _t'8 : ident := 135%positive. Definition _t'80 : ident := 207%positive. Definition _t'81 : ident := 208%positive. Definition _t'82 : ident := 209%positive. Definition _t'83 : ident := 210%positive. Definition _t'84 : ident := 211%positive. Definition _t'85 : ident := 212%positive. Definition _t'86 : ident := 213%positive. Definition _t'87 : ident := 214%positive. Definition _t'88 : ident := 215%positive. Definition _t'89 : ident := 216%positive. Definition _t'9 : ident := 136%positive. Definition _t'90 : ident := 217%positive. Definition _t'91 : ident := 218%positive. Definition _t'92 : ident := 219%positive. Definition _t'93 : ident := 220%positive. Definition _t'94 : ident := 221%positive. Definition _t'95 : ident := 222%positive. Definition _t'96 : ident := 223%positive. Definition _t'97 : ident := 224%positive. Definition _t'98 : ident := 225%positive. Definition _t'99 : ident := 226%positive. Definition v___stringlit_1 := {| gvar_info := (tarray tschar 8); gvar_init := (Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_2 := {| gvar_info := (tarray tschar 18); gvar_init := (Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_3 := {| gvar_info := (tarray tschar 19); gvar_init := (Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_4 := {| gvar_info := (tarray tschar 30); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_5 := {| gvar_info := (tarray tschar 17); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_6 := {| gvar_info := (tarray tschar 11); gvar_init := (Init_int8 (Int.repr 37) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 37) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 37) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 10) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_7 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 84) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_8 := {| gvar_info := (tarray tschar 26); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_9 := {| gvar_info := (tarray tschar 53); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 113) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_10 := {| gvar_info := (tarray tschar 42); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_20 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_30 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_40 := {| gvar_info := (tarray tschar 63); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_50 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_60 := {| gvar_info := (tarray tschar 30); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_70 := {| gvar_info := (tarray tschar 42); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_80 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_90 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_11 := {| gvar_info := (tarray tschar 42); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_21 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_31 := {| gvar_info := (tarray tschar 85); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_41 := {| gvar_info := (tarray tschar 89); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_51 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_61 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_71 := {| gvar_info := (tarray tschar 43); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_81 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_91 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_12 := {| gvar_info := (tarray tschar 39); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_22 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_32 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_42 := {| gvar_info := (tarray tschar 89); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_52 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_62 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_72 := {| gvar_info := (tarray tschar 43); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_82 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_92 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_13 := {| gvar_info := (tarray tschar 38); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_23 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_33 := {| gvar_info := (tarray tschar 85); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_43 := {| gvar_info := (tarray tschar 89); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_53 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_63 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_73 := {| gvar_info := (tarray tschar 43); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_83 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_93 := {| gvar_info := (tarray tschar 41); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_14 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_24 := {| gvar_info := (tarray tschar 58); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_34 := {| gvar_info := (tarray tschar 101); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_44 := {| gvar_info := (tarray tschar 88); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_54 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_64 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_74 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_84 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_94 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 67) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_15 := {| gvar_info := (tarray tschar 85); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_25 := {| gvar_info := (tarray tschar 58); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 113) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_35 := {| gvar_info := (tarray tschar 101); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 113) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_45 := {| gvar_info := (tarray tschar 32); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_55 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_65 := {| gvar_info := (tarray tschar 43); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_75 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_85 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 57) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_95 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_16 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_26 := {| gvar_info := (tarray tschar 49); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_36 := {| gvar_info := (tarray tschar 63); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_46 := {| gvar_info := (tarray tschar 95); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 67) :: Init_int8 (Int.repr 80) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 75) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 71) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 68) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 79) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_56 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_66 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_76 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_86 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_96 := {| gvar_info := (tarray tschar 86); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_17 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_27 := {| gvar_info := (tarray tschar 48); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_37 := {| gvar_info := (tarray tschar 63); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_47 := {| gvar_info := (tarray tschar 459); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 67) :: Init_int8 (Int.repr 80) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 75) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 71) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 68) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 79) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 67) :: Init_int8 (Int.repr 80) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 75) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 71) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 68) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 79) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 67) :: Init_int8 (Int.repr 80) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 75) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 71) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 68) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 79) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 67) :: Init_int8 (Int.repr 80) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 75) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 83) :: Init_int8 (Int.repr 73) :: Init_int8 (Int.repr 71) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 68) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 79) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 69) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_57 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_67 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_77 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_87 := {| gvar_info := (tarray tschar 30); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_97 := {| gvar_info := (tarray tschar 30); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_18 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_28 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_38 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_48 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_58 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_68 := {| gvar_info := (tarray tschar 43); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_78 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_88 := {| gvar_info := (tarray tschar 28); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_98 := {| gvar_info := (tarray tschar 35); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_19 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_29 := {| gvar_info := (tarray tschar 67); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_39 := {| gvar_info := (tarray tschar 63); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 77) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_49 := {| gvar_info := (tarray tschar 35); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_59 := {| gvar_info := (tarray tschar 30); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_69 := {| gvar_info := (tarray tschar 61); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_79 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_89 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 57) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_99 := {| gvar_info := (tarray tschar 41); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_100 := {| gvar_info := (tarray tschar 41); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_110 := {| gvar_info := (tarray tschar 23); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_120 := {| gvar_info := (tarray tschar 32); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_130 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_140 := {| gvar_info := (tarray tschar 116); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_150 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_160 := {| gvar_info := (tarray tschar 142); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_170 := {| gvar_info := (tarray tschar 27); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_101 := {| gvar_info := (tarray tschar 41); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_111 := {| gvar_info := (tarray tschar 64); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_121 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_131 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_141 := {| gvar_info := (tarray tschar 116); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_151 := {| gvar_info := (tarray tschar 46); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_161 := {| gvar_info := (tarray tschar 139); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_171 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_102 := {| gvar_info := (tarray tschar 39); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_112 := {| gvar_info := (tarray tschar 29); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_122 := {| gvar_info := (tarray tschar 50); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_132 := {| gvar_info := (tarray tschar 63); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_142 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_152 := {| gvar_info := (tarray tschar 33); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_162 := {| gvar_info := (tarray tschar 141); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_172 := {| gvar_info := (tarray tschar 27); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_103 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_113 := {| gvar_info := (tarray tschar 34); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_123 := {| gvar_info := (tarray tschar 47); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_133 := {| gvar_info := (tarray tschar 63); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_143 := {| gvar_info := (tarray tschar 23); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_153 := {| gvar_info := (tarray tschar 41); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_163 := {| gvar_info := (tarray tschar 140); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 120) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_104 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_114 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_124 := {| gvar_info := (tarray tschar 48); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_134 := {| gvar_info := (tarray tschar 62); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_144 := {| gvar_info := (tarray tschar 35); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 78) :: Init_int8 (Int.repr 85) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 76) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_154 := {| gvar_info := (tarray tschar 34); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_164 := {| gvar_info := (tarray tschar 47); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_105 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_115 := {| gvar_info := (tarray tschar 45); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_125 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_135 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_145 := {| gvar_info := (tarray tschar 48); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_155 := {| gvar_info := (tarray tschar 73); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_165 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_106 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_116 := {| gvar_info := (tarray tschar 37); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_126 := {| gvar_info := (tarray tschar 48); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_136 := {| gvar_info := (tarray tschar 24); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_146 := {| gvar_info := (tarray tschar 24); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_156 := {| gvar_info := (tarray tschar 54); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 57) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_166 := {| gvar_info := (tarray tschar 47); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_107 := {| gvar_info := (tarray tschar 36); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_117 := {| gvar_info := (tarray tschar 54); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 118) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_127 := {| gvar_info := (tarray tschar 48); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_137 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_147 := {| gvar_info := (tarray tschar 38); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_157 := {| gvar_info := (tarray tschar 56); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 93) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 57) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_167 := {| gvar_info := (tarray tschar 53); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_108 := {| gvar_info := (tarray tschar 99); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 122) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_118 := {| gvar_info := (tarray tschar 33); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 98) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_128 := {| gvar_info := (tarray tschar 48); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 124) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_138 := {| gvar_info := (tarray tschar 32); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_148 := {| gvar_info := (tarray tschar 52); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_158 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_168 := {| gvar_info := (tarray tschar 27); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_109 := {| gvar_info := (tarray tschar 30); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_119 := {| gvar_info := (tarray tschar 54); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_129 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_139 := {| gvar_info := (tarray tschar 50); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 113) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_149 := {| gvar_info := (tarray tschar 51); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_159 := {| gvar_info := (tarray tschar 31); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 117) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 109) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 104) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v___stringlit_169 := {| gvar_info := (tarray tschar 52); gvar_init := (Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 108) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 99) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 95) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 102) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_ReadBE32 := {| fn_return := tuint; fn_callconv := cc_default; fn_params := ((_b, (tptr tuchar)) :: nil); fn_vars := nil; fn_temps := ((_t'4, tuchar) :: (_t'3, tuchar) :: (_t'2, tuchar) :: (_t'1, tuchar) :: nil); fn_body := (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Etempvar _b (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Etempvar _b (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Etempvar _b (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Etempvar _b (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar)) (Sreturn (Some (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oshl (Ecast (Etempvar _t'1 tuchar) tuint) (Econst_int (Int.repr 24) tint) tuint) (Ebinop Oshl (Ecast (Ebinop Oand (Etempvar _t'2 tuchar) (Econst_int (Int.repr 255) tint) tint) tuint) (Econst_int (Int.repr 16) tint) tuint) tuint) (Ebinop Oshl (Ecast (Ebinop Oand (Etempvar _t'3 tuchar) (Econst_int (Int.repr 255) tint) tint) tuint) (Econst_int (Int.repr 8) tint) tuint) tuint) (Ecast (Ebinop Oand (Etempvar _t'4 tuchar) (Econst_int (Int.repr 255) tint) tint) tuint) tuint))))))) |}. Definition f_WriteBE64 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_ptr, (tptr tuchar)) :: (_x, tulong) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Ecast (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 56) tint) tulong) tulong) tuchar)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 48) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 40) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 32) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 24) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 16) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 8) tint) tulong) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Econst_int (Int.repr 255) tint) (Etempvar _x tulong) tulong))))))))) |}. Definition f_WriteBE32 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_ptr, (tptr tuchar)) :: (_x, tulong) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Ecast (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 24) tint) tulong) tuchar)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 16) tint) tulong) (Econst_int (Int.repr 255) tint) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 8) tint) tulong) (Econst_int (Int.repr 255) tint) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _ptr (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Etempvar _x tulong) (Econst_int (Int.repr 255) tint) tulong))))) |}. Definition f_sha256_fromMidstate := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_hash, (tptr tuchar)) :: (_midstate, (tptr tuint)) :: nil); fn_vars := nil; fn_temps := ((_t'8, tuint) :: (_t'7, tuint) :: (_t'6, tuint) :: (_t'5, tuint) :: (_t'4, tuint) :: (_t'3, tuint) :: (_t'2, tuint) :: (_t'1, tuint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 0) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 0) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'8 tuint) :: nil))) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 1) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 1) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'7 tuint) :: nil))) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 2) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 2) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'6 tuint) :: nil))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 3) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 3) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'5 tuint) :: nil))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 4) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'4 tuint) :: nil))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 5) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'3 tuint) :: nil))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 6) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 6) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'2 tuint) :: nil))) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Etempvar _midstate (tptr tuint)) (Econst_int (Int.repr 7) tint) (tptr tuint)) tuint)) (Scall None (Evar _WriteBE32 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Ebinop Oadd (Etempvar _hash (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 7) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: (Etempvar _t'1 tuint) :: nil)))))))))) |}. Definition f_sha256_iv := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_iv, (tptr tuint)) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 0) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 1779033703) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 1) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 3144134277) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 2) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 1013904242) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 3) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 2773480762) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 4) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 1359893119) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 5) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 2600822924) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 6) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 528734635) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _iv (tptr tuint)) (Econst_int (Int.repr 7) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 1541459225) tulong))))))))) |}. Definition v_simplicity_sha256_compression := {| gvar_info := (tptr (Tfunction (Tcons (tptr tuint) (Tcons (tptr tuint) Tnil)) tvoid cc_default)); gvar_init := nil; gvar_readonly := false; gvar_volatile := false |}. Definition f_sha256_compression_uchar := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_s, (tptr tuint)) :: (_chunk, (tptr tuchar)) :: nil); fn_vars := ((___compound, (tarray tuint 16)) :: nil); fn_temps := ((_t'16, tuint) :: (_t'15, tuint) :: (_t'14, tuint) :: (_t'13, tuint) :: (_t'12, tuint) :: (_t'11, tuint) :: (_t'10, tuint) :: (_t'9, tuint) :: (_t'8, tuint) :: (_t'7, tuint) :: (_t'6, tuint) :: (_t'5, tuint) :: (_t'4, tuint) :: (_t'3, tuint) :: (_t'2, tuint) :: (_t'1, tuint) :: (_t'17, (tptr (Tfunction (Tcons (tptr tuint) (Tcons (tptr tuint) Tnil)) tvoid cc_default))) :: nil); fn_body := (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Scall (Some _t'1) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 0) tint) tint) (tptr tuchar)) :: nil)) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 0) tint) (tptr tuint)) tuint) (Etempvar _t'1 tuint))) (Scall (Some _t'2) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 1) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 1) tint) (tptr tuint)) tuint) (Etempvar _t'2 tuint))) (Scall (Some _t'3) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 2) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 2) tint) (tptr tuint)) tuint) (Etempvar _t'3 tuint))) (Scall (Some _t'4) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 3) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 3) tint) (tptr tuint)) tuint) (Etempvar _t'4 tuint))) (Scall (Some _t'5) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 4) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 4) tint) (tptr tuint)) tuint) (Etempvar _t'5 tuint))) (Scall (Some _t'6) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 5) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 5) tint) (tptr tuint)) tuint) (Etempvar _t'6 tuint))) (Scall (Some _t'7) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 6) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 6) tint) (tptr tuint)) tuint) (Etempvar _t'7 tuint))) (Scall (Some _t'8) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 7) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 7) tint) (tptr tuint)) tuint) (Etempvar _t'8 tuint))) (Scall (Some _t'9) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 8) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 8) tint) (tptr tuint)) tuint) (Etempvar _t'9 tuint))) (Scall (Some _t'10) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 9) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 9) tint) (tptr tuint)) tuint) (Etempvar _t'10 tuint))) (Scall (Some _t'11) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 10) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 10) tint) (tptr tuint)) tuint) (Etempvar _t'11 tuint))) (Scall (Some _t'12) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 11) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 11) tint) (tptr tuint)) tuint) (Etempvar _t'12 tuint))) (Scall (Some _t'13) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 12) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 12) tint) (tptr tuint)) tuint) (Etempvar _t'13 tuint))) (Scall (Some _t'14) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 13) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 13) tint) (tptr tuint)) tuint) (Etempvar _t'14 tuint))) (Scall (Some _t'15) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 14) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 14) tint) (tptr tuint)) tuint) (Etempvar _t'15 tuint))) (Scall (Some _t'16) (Evar _ReadBE32 (Tfunction (Tcons (tptr tuchar) Tnil) tuint cc_default)) ((Ebinop Oadd (Etempvar _chunk (tptr tuchar)) (Ebinop Omul (Econst_int (Int.repr 4) tint) (Econst_int (Int.repr 15) tint) tint) (tptr tuchar)) :: nil))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuint 16)) (Econst_int (Int.repr 15) tint) (tptr tuint)) tuint) (Etempvar _t'16 tuint))) (Ssequence (Sset _t'17 (Evar _simplicity_sha256_compression (tptr (Tfunction (Tcons (tptr tuint) (Tcons (tptr tuint) Tnil)) tvoid cc_default)))) (Scall None (Etempvar _t'17 (tptr (Tfunction (Tcons (tptr tuint) (Tcons (tptr tuint) Tnil)) tvoid cc_default))) ((Etempvar _s (tptr tuint)) :: (Evar ___compound (tarray tuint 16)) :: nil)))) |}. Definition v_sha256_max_counter := {| gvar_info := tulong; gvar_init := (Init_int64 (Int64.repr 2305843009213693952) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_sha256_init := {| fn_return := tvoid; fn_callconv := {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|}; fn_params := ((__res, (tptr (Tstruct _sha256_context noattr))) :: (_output, (tptr tuint)) :: nil); fn_vars := ((___compound, (Tstruct _sha256_context noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _sha256_iv (Tfunction (Tcons (tptr tuint) Tnil) tvoid cc_default)) ((Etempvar _output (tptr tuint)) :: nil)) (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _output (tptr tuint)) (Etempvar _output (tptr tuint))) (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _counter tulong) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 33) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 34) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 35) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 36) tint) (tptr 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(Int.repr 41) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 42) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 43) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 44) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 45) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 46) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 47) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 48) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 49) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 50) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context 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(Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 56) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 57) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 58) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 59) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 60) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 61) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 62) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 63) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _overflow tbool) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Etempvar __res (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) (Evar ___compound (Tstruct _sha256_context noattr)))) (Sreturn None))) |}. Definition f_sha256_tagged_init := {| fn_return := tvoid; fn_callconv := {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|}; fn_params := ((__res, (tptr (Tstruct _sha256_context noattr))) :: (_output, (tptr tuint)) :: (_iv, (tptr (Tstruct _sha256_midstate noattr))) :: nil); fn_vars := ((___compound, (Tstruct _sha256_context noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _memcpy (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _output (tptr tuint)) :: (Efield (Ederef (Etempvar _iv (tptr (Tstruct _sha256_midstate noattr))) (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: (Esizeof (tarray tuint 8) tulong) :: nil)) (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _output (tptr tuint)) (Etempvar _output (tptr tuint))) (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _counter tulong) (Econst_int (Int.repr 64) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 33) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 34) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 35) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 36) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 37) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 38) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 39) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 40) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 41) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 42) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 43) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 44) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 45) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 46) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 47) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 48) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 49) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 50) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 51) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 52) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 53) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 54) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 55) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 56) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 57) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 58) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 59) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 60) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 61) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 62) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 63) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _overflow tbool) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Etempvar __res (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) (Evar ___compound (Tstruct _sha256_context noattr)))) (Sreturn None))) |}. Definition f_sha256_uchars := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_ctx, (tptr (Tstruct _sha256_context noattr))) :: (_arr, (tptr tuchar)) :: (_len, tulong) :: nil); fn_vars := nil; fn_temps := ((_delta, tulong) :: (_block, (tptr tuchar)) :: (_t'1, tint) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tbool) :: (_t'4, tulong) :: (_t'3, (tptr tuint)) :: (_t'2, tbool) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'9 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong)) (Sset _delta (Ebinop Osub (Econst_int (Int.repr 64) tint) (Ebinop Omod (Etempvar _t'9 tulong) (Econst_int (Int.repr 64) tint) tulong) tulong))) (Ssequence (Ssequence (Sset _t'8 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong)) (Sset _block (Ebinop Oadd (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Ebinop Omod (Etempvar _t'8 tulong) (Econst_int (Int.repr 64) tint) tulong) (tptr tuchar)))) (Ssequence (Ssequence (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _overflow tbool)) (Sifthenelse (Etempvar _t'5 tbool) (Sset _t'1 (Econst_int (Int.repr 1) tint)) (Ssequence (Sset _t'6 (Evar _sha256_max_counter tulong)) (Ssequence (Sset _t'7 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong)) (Sset _t'1 (Ecast (Ebinop Ole (Ebinop Osub (Etempvar _t'6 tulong) (Etempvar _t'7 tulong) tulong) (Etempvar _len tulong) tint) tbool)))))) (Sassign (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _overflow tbool) (Etempvar _t'1 tint))) (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong)) (Sassign (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong) (Ebinop Oadd (Etempvar _t'4 tulong) (Etempvar _len tulong) tulong))) (Ssequence (Swhile (Ebinop Ole (Etempvar _delta tulong) (Etempvar _len tulong) tint) (Ssequence (Scall None (Evar _memcpy (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _block (tptr tuchar)) :: (Etempvar _arr (tptr tuchar)) :: (Etempvar _delta tulong) :: nil)) (Ssequence (Sset _arr (Ebinop Oadd (Etempvar _arr (tptr tuchar)) (Etempvar _delta tulong) (tptr tuchar))) (Ssequence (Sset _len (Ebinop Osub (Etempvar _len tulong) (Etempvar _delta tulong) tulong)) (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _output (tptr tuint))) (Scall None (Evar _sha256_compression_uchar (Tfunction (Tcons (tptr tuint) (Tcons (tptr tuchar) Tnil)) tvoid cc_default)) ((Etempvar _t'3 (tptr tuint)) :: (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) :: nil))) (Ssequence (Sset _block (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _block (tarray tuchar 64))) (Sset _delta (Ecast (Econst_int (Int.repr 64) tint) tulong)))))))) (Ssequence (Sifthenelse (Etempvar _len tulong) (Scall None (Evar _memcpy (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _block (tptr tuchar)) :: (Etempvar _arr (tptr tuchar)) :: (Etempvar _len tulong) :: nil)) Sskip) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _overflow tbool)) (Sreturn (Some (Eunop Onotbool (Etempvar _t'2 tbool) tint)))))))))) |}. Definition f_sha256_u64be := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_ctx, (tptr (Tstruct _sha256_context noattr))) :: (_x, tulong) :: nil); fn_vars := ((_buf, (tarray tuchar 8)) :: nil); fn_temps := ((_t'1, tbool) :: nil); fn_body := (Ssequence (Scall None (Evar _WriteBE64 (Tfunction (Tcons (tptr tuchar) (Tcons tulong Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 8)) :: (Etempvar _x tulong) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) :: (Evar _buf (tarray tuchar 8)) :: (Esizeof (tarray tuchar 8) tulong) :: nil)) (Sreturn (Some (Etempvar _t'1 tbool))))) |}. Definition f_sha256_finalize := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_ctx, (tptr (Tstruct _sha256_context noattr))) :: nil); fn_vars := ((___compound, (tarray tuchar 64)) :: nil); fn_temps := ((_result, tbool) :: (_length, tulong) :: (_t'3, tbool) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _overflow tbool)) (Sset _result (Ecast (Eunop Onotbool (Etempvar _t'3 tbool) tint) tbool))) (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong)) (Sset _length (Ebinop Omul (Etempvar _t'2 tulong) (Econst_int (Int.repr 8) tint) tulong))) (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 128) tint)) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 33) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 34) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 35) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 36) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 37) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 38) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 39) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 40) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 41) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 42) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 43) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 44) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 45) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 46) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 47) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 48) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 49) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 50) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 51) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 52) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 53) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 54) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 55) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 56) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 57) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 58) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 59) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 60) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 61) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 62) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Evar ___compound (tarray tuchar 64)) (Econst_int (Int.repr 63) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) _counter tulong)) (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) :: (Evar ___compound (tarray tuchar 64)) :: (Ebinop Oadd (Econst_int (Int.repr 1) tint) (Ebinop Omod (Ebinop Osub (Ebinop Osub (Ebinop Oadd (Econst_int (Int.repr 64) tint) (Econst_int (Int.repr 56) tint) tint) (Ebinop Omod (Etempvar _t'1 tulong) (Econst_int (Int.repr 64) tint) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) (Econst_int (Int.repr 64) tint) tulong) tulong) :: nil)))) (Ssequence (Scall None (Evar _sha256_u64be (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons tulong Tnil)) tbool cc_default)) ((Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _length tulong) :: nil)) (Sreturn (Some (Etempvar _result tbool))))))) |}. Definition f_sha256_hash := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_ctx, (tptr (Tstruct _sha256_context noattr))) :: (_h, (tptr (Tstruct _sha256_midstate noattr))) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _sha256_fromMidstate (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuint) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Efield (Ederef (Etempvar _h (tptr (Tstruct _sha256_midstate noattr))) (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Etempvar _ctx (tptr (Tstruct _sha256_context noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Esizeof (tarray tuchar 32) tulong) :: nil))) |}. Definition f_LSBclear := {| fn_return := tulong; fn_callconv := cc_default; fn_params := ((_x, tulong) :: (_n, tulong) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Sreturn (Some (Ecast (Ebinop Oshl (Ebinop Oshl (Ebinop Oshr (Ebinop Oshr (Etempvar _x tulong) (Econst_int (Int.repr 1) tint) tulong) (Ebinop Osub (Etempvar _n tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) (Ebinop Osub (Etempvar _n tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) tulong))) |}. Definition f_peekBit := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_frame, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, (tptr tulong)) :: nil); fn_body := (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _edge (tptr tulong))) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Ssequence (Sset _t'3 (Ederef (Ebinop Osub (Ebinop Osub (Etempvar _t'1 (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) (Ebinop Odiv (Etempvar _t'2 tulong) (Ebinop Osub (Ebinop Oadd (Ebinop Oadd (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 5) tint) tulong) tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Odiv (Econst_int (Int.repr 12) tint) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 3) tint) tulong) tulong) tulong) tulong) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sreturn (Some (Ebinop Oand (Econst_int (Int.repr 1) tint) (Ebinop Oshr (Etempvar _t'3 tulong) (Ebinop Osub (Ebinop Osub (Ebinop Osub (Ebinop Oadd (Ebinop Oadd (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 5) tint) tulong) tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Odiv (Econst_int (Int.repr 12) tint) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 3) tint) tulong) tulong) tulong) (Ebinop Omod (Etempvar _t'4 tulong) (Ebinop Osub (Ebinop Oadd (Ebinop Oadd (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 5) tint) tulong) tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Odiv (Econst_int (Int.repr 12) tint) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 3) tint) tulong) tulong) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) tulong))))))) |}. Definition f_readBit := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_frame, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := ((_result, tbool) :: (_t'1, tbool) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _peekBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tbool cc_default)) ((Etempvar _frame (tptr (Tstruct _frameItem noattr))) :: nil)) (Sset _result (Ecast (Etempvar _t'1 tbool) tbool))) (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sassign (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong) (Ebinop Oadd (Etempvar _t'2 tulong) (Econst_int (Int.repr 1) tint) tulong))) (Sreturn (Some (Etempvar _result tbool))))) |}. Definition v___func__ := {| gvar_info := (tarray tschar 9); gvar_init := (Init_int8 (Int.repr 119) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 66) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_writeBit := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_frame, (tptr (Tstruct _frameItem noattr))) :: (_bit, tbool) :: nil); fn_vars := nil; fn_temps := ((_dst_ptr, (tptr tulong)) :: (_t'1, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, (tptr tulong)) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Econst_int (Int.repr 0) tint) tint) (Ssequence (Sset _t'9 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sifthenelse (Ebinop Olt (Econst_int (Int.repr 0) tint) (Etempvar _t'9 tulong) tint) Sskip (Scall None (Evar ___assert_fail (Tfunction (Tcons (tptr tschar) (Tcons (tptr tschar) (Tcons tuint (Tcons (tptr tschar) Tnil)))) tvoid cc_default)) ((Evar ___stringlit_2 (tarray tschar 18)) :: (Evar ___stringlit_1 (tarray tschar 8)) :: (Econst_int (Int.repr 81) tint) :: (Evar ___func__ (tarray tschar 9)) :: nil)))) Sskip) Sbreak) (Ssequence (Ssequence (Sset _t'8 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sassign (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong) (Ebinop Osub (Etempvar _t'8 tulong) (Econst_int (Int.repr 1) tint) tulong))) (Ssequence (Ssequence (Sset _t'6 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _edge (tptr tulong))) (Ssequence (Sset _t'7 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sset _dst_ptr (Ebinop Oadd (Etempvar _t'6 (tptr tulong)) (Ebinop Odiv (Etempvar _t'7 tulong) (Ebinop Osub (Ebinop Oadd (Ebinop Oadd (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 5) tint) tulong) tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Odiv (Econst_int (Int.repr 12) tint) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 3) tint) tulong) tulong) tulong) tulong) (tptr tulong))))) (Ssequence (Sifthenelse (Etempvar _bit tbool) (Ssequence (Sset _t'4 (Ederef (Etempvar _dst_ptr (tptr tulong)) tulong)) (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sassign (Ederef (Etempvar _dst_ptr (tptr tulong)) tulong) (Ebinop Oor (Etempvar _t'4 tulong) (Ecast (Ebinop Oshl (Ecast (Econst_int (Int.repr 1) tint) tulong) (Ebinop Omod (Etempvar _t'5 tulong) (Ebinop Osub (Ebinop Oadd (Ebinop Oadd (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 5) tint) tulong) tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Odiv (Econst_int (Int.repr 12) tint) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 3) tint) tulong) tulong) tulong) tulong) tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Etempvar _dst_ptr (tptr tulong)) tulong)) (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Scall (Some _t'1) (Evar _LSBclear (Tfunction (Tcons tulong (Tcons tulong Tnil)) tulong cc_default)) ((Etempvar _t'2 tulong) :: (Ebinop Oadd (Ebinop Omod (Etempvar _t'3 tulong) (Ebinop Osub (Ebinop Oadd (Ebinop Oadd (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Omul (Ebinop Omod (Ebinop Odiv (Ebinop Odiv (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 1073741823) tuint) tulong) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 5) tint) tulong) tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Odiv (Econst_int (Int.repr 12) tint) (Ebinop Oadd (Ebinop Omod (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tulong) (Econst_int (Int.repr 31) tint) tulong) (Econst_int (Int.repr 3) tint) tulong) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) :: nil)))) (Sassign (Ederef (Etempvar _dst_ptr (tptr tulong)) tulong) (Etempvar _t'1 tulong)))) (Sreturn (Some (Etempvar _bit tbool))))))) |}. Definition v___func____1 := {| gvar_info := (tarray tschar 9); gvar_init := (Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 107) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 112) :: Init_int8 (Int.repr 66) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_skipBits := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_frame, (tptr (Tstruct _frameItem noattr))) :: (_n, tulong) :: nil); fn_vars := nil; fn_temps := ((_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Econst_int (Int.repr 0) tint) tint) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sifthenelse (Ebinop Ole (Etempvar _n tulong) (Etempvar _t'2 tulong) tint) Sskip (Scall None (Evar ___assert_fail (Tfunction (Tcons (tptr tschar) (Tcons (tptr tschar) (Tcons tuint (Tcons (tptr tschar) Tnil)))) tvoid cc_default)) ((Evar ___stringlit_3 (tarray tschar 19)) :: (Evar ___stringlit_1 (tarray tschar 8)) :: (Econst_int (Int.repr 105) tint) :: (Evar ___func____1 (tarray tschar 9)) :: nil)))) Sskip) Sbreak) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong)) (Sassign (Efield (Ederef (Etempvar _frame (tptr (Tstruct _frameItem noattr))) (Tstruct _frameItem noattr)) _offset tulong) (Ebinop Osub (Etempvar _t'1 tulong) (Etempvar _n tulong) tulong)))) |}. Definition f_read8s := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_x, (tptr tuchar)) :: (_n, tulong) :: (_frame, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'2, tuchar) :: (_t'1, (tptr tuchar)) :: nil); fn_body := (Sloop (Ssequence (Sifthenelse (Etempvar _n tulong) Sskip Sbreak) (Ssequence (Ssequence (Ssequence (Sset _t'1 (Etempvar _x (tptr tuchar))) (Sset _x (Ebinop Oadd (Etempvar _t'1 (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)))) (Scall (Some _t'2) (Evar _simplicity_read8 (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tuchar cc_default)) ((Etempvar _frame (tptr (Tstruct _frameItem noattr))) :: nil))) (Sassign (Ederef (Etempvar _t'1 (tptr tuchar)) tuchar) (Ecast (Etempvar _t'2 tuchar) tuchar)))) (Sset _n (Ebinop Osub (Etempvar _n tulong) (Econst_int (Int.repr 1) tint) tulong))) |}. Definition f_write8s := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_frame, (tptr (Tstruct _frameItem noattr))) :: (_x, (tptr tuchar)) :: (_n, tulong) :: nil); fn_vars := nil; fn_temps := ((_t'1, (tptr tuchar)) :: (_t'2, tuchar) :: nil); fn_body := (Sloop (Ssequence (Sifthenelse (Etempvar _n tulong) Sskip Sbreak) (Ssequence (Ssequence (Sset _t'1 (Etempvar _x (tptr tuchar))) (Sset _x (Ebinop Oadd (Etempvar _t'1 (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)))) (Ssequence (Sset _t'2 (Ederef (Etempvar _t'1 (tptr tuchar)) tuchar)) (Scall None (Evar _simplicity_write8 (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tuchar Tnil)) tvoid cc_default)) ((Etempvar _frame (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'2 tuchar) :: nil))))) (Sset _n (Ebinop Osub (Etempvar _n tulong) (Econst_int (Int.repr 1) tint) tulong))) |}. Definition f_read32s := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_x, (tptr tuint)) :: (_n, tulong) :: (_frame, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'2, tulong) :: (_t'1, (tptr tuint)) :: nil); fn_body := (Sloop (Ssequence (Sifthenelse (Etempvar _n tulong) Sskip Sbreak) (Ssequence (Ssequence (Ssequence (Sset _t'1 (Etempvar _x (tptr tuint))) (Sset _x (Ebinop Oadd (Etempvar _t'1 (tptr tuint)) (Econst_int (Int.repr 1) tint) (tptr tuint)))) (Scall (Some _t'2) (Evar _simplicity_read32 (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tulong cc_default)) ((Etempvar _frame (tptr (Tstruct _frameItem noattr))) :: nil))) (Sassign (Ederef (Etempvar _t'1 (tptr tuint)) tuint) (Ecast (Etempvar _t'2 tulong) tuint)))) (Sset _n (Ebinop Osub (Etempvar _n tulong) (Econst_int (Int.repr 1) tint) tulong))) |}. Definition v_signatureIV := {| gvar_info := (Tstruct _sha256_midstate noattr); gvar_init := (Init_int32 (Int.repr (-303315125)) :: Init_int32 (Int.repr 2001476530) :: Init_int32 (Int.repr (-882122114)) :: Init_int32 (Int.repr 953564290) :: Init_int32 (Int.repr 1863085798) :: Init_int32 (Int.repr 37330614) :: Init_int32 (Int.repr 1211883153) :: Init_int32 (Int.repr 654973851) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_stderr := {| gvar_info := (tptr (Tstruct __IO_FILE noattr)); gvar_init := nil; gvar_readonly := false; gvar_volatile := false |}. Definition f_secp256k1_memcmp_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_s1, (tptr tvoid)) :: (_s2, (tptr tvoid)) :: (_n, tulong) :: nil); fn_vars := nil; fn_temps := ((_p1, (tptr tuchar)) :: (_p2, (tptr tuchar)) :: (_i, tulong) :: (_diff, tint) :: (_t'2, tuchar) :: (_t'1, tuchar) :: nil); fn_body := (Ssequence (Sset _p1 (Etempvar _s1 (tptr tvoid))) (Ssequence (Sset _p2 (Etempvar _s2 (tptr tvoid))) (Ssequence (Ssequence (Sset _i (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tulong) (Etempvar _n tulong) tint) Sskip Sbreak) (Ssequence (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Etempvar _p1 (tptr tuchar)) (Etempvar _i tulong) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Etempvar _p2 (tptr tuchar)) (Etempvar _i tulong) (tptr tuchar)) tuchar)) (Sset _diff (Ebinop Osub (Etempvar _t'1 tuchar) (Etempvar _t'2 tuchar) tint)))) (Sifthenelse (Ebinop One (Etempvar _diff tint) (Econst_int (Int.repr 0) tint) tint) (Sreturn (Some (Etempvar _diff tint))) Sskip))) (Sset _i (Ebinop Oadd (Etempvar _i tulong) (Econst_int (Int.repr 1) tint) tulong)))) (Sreturn (Some (Econst_int (Int.repr 0) tint)))))) |}. Definition v_debruijn := {| gvar_info := (tarray tuchar 64); gvar_init := (Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 1) :: Init_int8 (Int.repr 2) :: Init_int8 (Int.repr 53) :: Init_int8 (Int.repr 3) :: Init_int8 (Int.repr 7) :: Init_int8 (Int.repr 54) :: Init_int8 (Int.repr 27) :: Init_int8 (Int.repr 4) :: Init_int8 (Int.repr 38) :: Init_int8 (Int.repr 41) :: Init_int8 (Int.repr 8) :: Init_int8 (Int.repr 34) :: Init_int8 (Int.repr 55) :: Init_int8 (Int.repr 48) :: Init_int8 (Int.repr 28) :: Init_int8 (Int.repr 62) :: Init_int8 (Int.repr 5) :: Init_int8 (Int.repr 39) :: Init_int8 (Int.repr 46) :: Init_int8 (Int.repr 44) :: Init_int8 (Int.repr 42) :: Init_int8 (Int.repr 22) :: Init_int8 (Int.repr 9) :: Init_int8 (Int.repr 24) :: Init_int8 (Int.repr 35) :: Init_int8 (Int.repr 59) :: Init_int8 (Int.repr 56) :: Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 18) :: Init_int8 (Int.repr 29) :: Init_int8 (Int.repr 11) :: Init_int8 (Int.repr 63) :: Init_int8 (Int.repr 52) :: Init_int8 (Int.repr 6) :: Init_int8 (Int.repr 26) :: Init_int8 (Int.repr 37) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 33) :: Init_int8 (Int.repr 47) :: Init_int8 (Int.repr 61) :: Init_int8 (Int.repr 45) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 21) :: Init_int8 (Int.repr 23) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 17) :: Init_int8 (Int.repr 10) :: Init_int8 (Int.repr 51) :: Init_int8 (Int.repr 25) :: Init_int8 (Int.repr 36) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 60) :: Init_int8 (Int.repr 20) :: Init_int8 (Int.repr 57) :: Init_int8 (Int.repr 16) :: Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 31) :: Init_int8 (Int.repr 19) :: Init_int8 (Int.repr 15) :: Init_int8 (Int.repr 30) :: Init_int8 (Int.repr 14) :: Init_int8 (Int.repr 13) :: Init_int8 (Int.repr 12) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_ctz64_var_debruijn := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_x, tulong) :: nil); fn_vars := nil; fn_temps := ((_t'1, tuchar) :: nil); fn_body := (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Evar _debruijn (tarray tuchar 64)) (Ebinop Oshr (Ecast (Ebinop Omul (Ebinop Oand (Etempvar _x tulong) (Eunop Oneg (Etempvar _x tulong) tulong) tulong) (Econst_long (Int64.repr 157587932685088877) tulong) tulong) tulong) (Econst_int (Int.repr 58) tint) tulong) (tptr tuchar)) tuchar)) (Sreturn (Some (Etempvar _t'1 tuchar)))) |}. Definition f_secp256k1_ctz64_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_x, tulong) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _x tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_5 (tarray tschar 17)) :: (Econst_int (Int.repr 141) tint) :: (Evar ___stringlit_4 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_ctz64_var_debruijn (Tfunction (Tcons tulong Tnil) tint cc_default)) ((Etempvar _x tulong) :: nil)) (Sreturn (Some (Etempvar _t'1 tint))))) |}. Definition v_secp256k1_const_beta := {| gvar_info := (Tstruct __2380 noattr); gvar_init := (Init_int64 (Int64.repr 2652195750478318) :: Init_int64 (Int64.repr 2059588628732947) :: Init_int64 (Int64.repr 3435101582848073) :: Init_int64 (Int64.repr 124274446989802) :: Init_int64 (Int64.repr 135142927197564) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_modinv64_signed62_assign := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_src, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'5, tlong) :: (_t'4, tlong) :: (_t'3, tlong) :: (_t'2, tlong) :: (_t'1, tlong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _src (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _dst (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Etempvar _t'5 tlong))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _src (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _dst (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Etempvar _t'4 tlong))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _src (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _dst (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Etempvar _t'3 tlong))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _src (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _dst (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Etempvar _t'2 tlong))) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _src (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _dst (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Etempvar _t'1 tlong))))))) |}. Definition f_secp256k1_modinv64_abs := {| fn_return := tlong; fn_callconv := cc_default; fn_params := ((_v, tlong) :: nil); fn_vars := nil; fn_temps := ((_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _v tlong) (Ebinop Osub (Eunop Oneg (Econst_long (Int64.repr 9223372036854775807) tlong) tlong) (Econst_int (Int.repr 1) tint) tlong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 33) tint) :: (Evar ___stringlit_7 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _v tlong) (Econst_int (Int.repr 0) tint) tint) (Sreturn (Some (Eunop Oneg (Etempvar _v tlong) tlong))) Sskip) (Sreturn (Some (Etempvar _v tlong))))) |}. Definition v_SECP256K1_SIGNED62_ONE := {| gvar_info := (Tstruct _secp256k1_modinv64_signed62 noattr); gvar_init := (Init_int64 (Int64.repr 1) :: Init_space 32 :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_modinv64_mul_62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_a, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_alen, tint) :: (_factor, tlong) :: nil); fn_vars := ((_c, (Tstruct _secp256k1_uint128 noattr)) :: (_d, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_M62, tulong) :: (_i, tint) :: (_t'4, tlong) :: (_t'3, tint) :: (_t'2, tlong) :: (_t'1, tulong) :: (_t'7, tlong) :: (_t'6, tlong) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _M62 (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Scall None (Evar _secp256k1_i128_from_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Ssequence (Ssequence (Sset _i (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Econst_int (Int.repr 4) tint) tint) Sskip Sbreak) (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _alen tint) tint) (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'7 tlong) :: (Etempvar _factor tlong) :: nil))) Sskip) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'1 tulong) (Etempvar _M62 tulong) tulong))) (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil))))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Sifthenelse (Ebinop Olt (Econst_int (Int.repr 4) tint) (Etempvar _alen tint) tint) (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'6 tlong) :: (Etempvar _factor tlong) :: nil))) Sskip) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_i128_to_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tlong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_i128_from_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'2 tlong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'3) (Evar _secp256k1_i128_eq_var (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'3 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 52) tint) :: (Evar ___stringlit_9 (tarray tschar 53)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall (Some _t'4) (Evar _secp256k1_i128_to_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tlong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Etempvar _t'4 tlong))))))))) |}. Definition f_secp256k1_modinv64_mul_cmp_62 := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_alen, tint) :: (_b, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_factor, tlong) :: nil); fn_vars := ((_am, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: (_bm, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: nil); fn_temps := ((_i, tint) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, tlong) :: (_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, tlong) :: (_t'4, tlong) :: (_t'3, tlong) :: (_t'2, tlong) :: (_t'1, tlong) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_modinv64_mul_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons tlong Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _am (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _alen tint) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_modinv64_mul_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons tlong Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _bm (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _b (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Etempvar _factor tlong) :: nil)) (Ssequence (Ssequence (Sset _i (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Econst_int (Int.repr 4) tint) tint) Sskip Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Evar _am (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'7 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 64) tint) :: (Evar ___stringlit_10 (tarray tschar 42)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sloop (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Evar _bm (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'5 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 65) tint) :: (Evar ___stringlit_11 (tarray tschar 42)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Ssequence (Sset _i (Econst_int (Int.repr 4) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _i tint) (Econst_int (Int.repr 0) tint) tint) Sskip Sbreak) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Evar _am (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Evar _bm (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Sifthenelse (Ebinop Olt (Etempvar _t'3 tlong) (Etempvar _t'4 tlong) tint) (Sreturn (Some (Eunop Oneg (Econst_int (Int.repr 1) tint) tint))) Sskip))) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Evar _am (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Evar _bm (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Sifthenelse (Ebinop Ogt (Etempvar _t'1 tlong) (Etempvar _t'2 tlong) tint) (Sreturn (Some (Econst_int (Int.repr 1) tint))) Sskip))))) (Sset _i (Ebinop Osub (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Sreturn (Some (Econst_int (Int.repr 0) tint))))))) |}. Definition f_secp256k1_modinv64_det_check_pow2 := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_t, (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: (_n, tuint) :: (_abs, tint) :: nil); fn_vars := ((_a, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'7, tlong) :: (_t'6, tlong) :: (_t'5, tlong) :: (_t'4, tlong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _u tlong)) (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _v tlong)) (Ssequence (Sset _t'6 (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _q tlong)) (Ssequence (Sset _t'7 (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _r tlong)) (Scall None (Evar _secp256k1_i128_det (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong (Tcons tlong (Tcons tlong Tnil))))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'4 tlong) :: (Etempvar _t'5 tlong) :: (Etempvar _t'6 tlong) :: (Etempvar _t'7 tlong) :: nil)))))) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_i128_check_pow2 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint (Tcons tint Tnil))) tint cc_default)) ((Eaddrof (Evar _a (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _n tuint) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Etempvar _t'1 tint) (Sreturn (Some (Econst_int (Int.repr 1) tint))) Sskip)) (Ssequence (Ssequence (Sifthenelse (Etempvar _abs tint) (Ssequence (Scall (Some _t'3) (Evar _secp256k1_i128_check_pow2 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint (Tcons tint Tnil))) tint cc_default)) ((Eaddrof (Evar _a (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _n tuint) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sset _t'2 (Ecast (Etempvar _t'3 tint) tbool))) (Sset _t'2 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'2 tint) (Sreturn (Some (Econst_int (Int.repr 1) tint))) Sskip)) (Sreturn (Some (Econst_int (Int.repr 0) tint)))))) |}. Definition f_secp256k1_modinv64_normalize_62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_sign, tlong) :: (_modinfo, (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil); fn_vars := nil; fn_temps := ((_M62, tlong) :: (_r0, tlong) :: (_r1, tlong) :: (_r2, tlong) :: (_r3, tlong) :: (_r4, tlong) :: (_cond_add, tlong) :: (_cond_negate, tlong) :: (_i, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'27, (tptr (Tstruct __IO_FILE noattr))) :: (_t'26, tlong) :: (_t'25, (tptr (Tstruct __IO_FILE noattr))) :: (_t'24, tlong) :: (_t'23, (tptr (Tstruct __IO_FILE noattr))) :: (_t'22, (tptr (Tstruct __IO_FILE noattr))) :: (_t'21, tlong) :: (_t'20, tlong) :: (_t'19, tlong) :: (_t'18, tlong) :: (_t'17, tlong) :: (_t'16, tlong) :: (_t'15, tlong) :: (_t'14, tlong) :: (_t'13, tlong) :: (_t'12, tlong) :: (_t'11, (tptr (Tstruct __IO_FILE noattr))) :: (_t'10, (tptr (Tstruct __IO_FILE noattr))) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: (_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _M62 (Ecast (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 2) tint) tulong) tlong)) (Ssequence (Sset _r0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _r1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Ssequence (Sset _r2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Ssequence (Sset _r3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Ssequence (Sset _r4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Ssequence (Ssequence (Sset _i (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Econst_int (Int.repr 5) tint) tint) Sskip Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'26 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _t'26 tlong) (Eunop Oneg (Etempvar _M62 tlong) tlong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'27 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'27 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 97) tint) :: (Evar ___stringlit_12 (tarray tschar 39)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sloop (Ssequence (Sset _t'24 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'24 tlong) (Etempvar _M62 tlong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'25 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'25 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 98) tint) :: (Evar ___stringlit_13 (tarray tschar 38)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 2) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'1 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'23 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'23 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 100) tint) :: (Evar ___stringlit_14 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'2 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'22 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'22 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 101) tint) :: (Evar ___stringlit_15 (tarray tschar 85)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _cond_add (Ebinop Oshr (Etempvar _r4 tlong) (Econst_int (Int.repr 63) tint) tlong)) (Ssequence (Ssequence (Sset _t'21 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Sset _r0 (Ebinop Oadd (Etempvar _r0 tlong) (Ebinop Oand (Etempvar _t'21 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'20 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Sset _r1 (Ebinop Oadd (Etempvar _r1 tlong) (Ebinop Oand (Etempvar _t'20 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'19 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Sset _r2 (Ebinop Oadd (Etempvar _r2 tlong) (Ebinop Oand (Etempvar _t'19 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Sset _r3 (Ebinop Oadd (Etempvar _r3 tlong) (Ebinop Oand (Etempvar _t'18 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Sset _r4 (Ebinop Oadd (Etempvar _r4 tlong) (Ebinop Oand (Etempvar _t'17 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Sset _cond_negate (Ebinop Oshr (Etempvar _sign tlong) (Econst_int (Int.repr 63) tint) tlong)) (Ssequence (Sset _r0 (Ebinop Osub (Ebinop Oxor (Etempvar _r0 tlong) (Etempvar _cond_negate tlong) tlong) (Etempvar _cond_negate tlong) tlong)) (Ssequence (Sset _r1 (Ebinop Osub (Ebinop Oxor (Etempvar _r1 tlong) (Etempvar _cond_negate tlong) tlong) (Etempvar _cond_negate tlong) tlong)) (Ssequence (Sset _r2 (Ebinop Osub (Ebinop Oxor (Etempvar _r2 tlong) (Etempvar _cond_negate tlong) tlong) (Etempvar _cond_negate tlong) tlong)) (Ssequence (Sset _r3 (Ebinop Osub (Ebinop Oxor (Etempvar _r3 tlong) (Etempvar _cond_negate tlong) tlong) (Etempvar _cond_negate tlong) tlong)) (Ssequence (Sset _r4 (Ebinop Osub (Ebinop Oxor (Etempvar _r4 tlong) (Etempvar _cond_negate tlong) tlong) (Etempvar _cond_negate tlong) tlong)) (Ssequence (Sset _r1 (Ebinop Oadd (Etempvar _r1 tlong) (Ebinop Oshr (Etempvar _r0 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r0 (Ebinop Oand (Etempvar _r0 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _r2 (Ebinop Oadd (Etempvar _r2 tlong) (Ebinop Oshr (Etempvar _r1 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r1 (Ebinop Oand (Etempvar _r1 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _r3 (Ebinop Oadd (Etempvar _r3 tlong) (Ebinop Oshr (Etempvar _r2 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r2 (Ebinop Oand (Etempvar _r2 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _r4 (Ebinop Oadd (Etempvar _r4 tlong) (Ebinop Oshr (Etempvar _r3 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r3 (Ebinop Oand (Etempvar _r3 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _cond_add (Ebinop Oshr (Etempvar _r4 tlong) (Econst_int (Int.repr 63) tint) tlong)) (Ssequence (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Sset _r0 (Ebinop Oadd (Etempvar _r0 tlong) (Ebinop Oand (Etempvar _t'16 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Sset _r1 (Ebinop Oadd (Etempvar _r1 tlong) (Ebinop Oand (Etempvar _t'15 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Sset _r2 (Ebinop Oadd (Etempvar _r2 tlong) (Ebinop Oand (Etempvar _t'14 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Sset _r3 (Ebinop Oadd (Etempvar _r3 tlong) (Ebinop Oand (Etempvar _t'13 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Sset _r4 (Ebinop Oadd (Etempvar _r4 tlong) (Ebinop Oand (Etempvar _t'12 tlong) (Etempvar _cond_add tlong) tlong) tlong))) (Ssequence (Sset _r1 (Ebinop Oadd (Etempvar _r1 tlong) (Ebinop Oshr (Etempvar _r0 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r0 (Ebinop Oand (Etempvar _r0 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _r2 (Ebinop Oadd (Etempvar _r2 tlong) (Ebinop Oshr (Etempvar _r1 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r1 (Ebinop Oand (Etempvar _r1 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _r3 (Ebinop Oadd (Etempvar _r3 tlong) (Ebinop Oshr (Etempvar _r2 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r2 (Ebinop Oand (Etempvar _r2 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sset _r4 (Ebinop Oadd (Etempvar _r4 tlong) (Ebinop Oshr (Etempvar _r3 tlong) (Econst_int (Int.repr 62) tint) tlong) tlong)) (Ssequence (Sset _r3 (Ebinop Oand (Etempvar _r3 tlong) (Etempvar _M62 tlong) tlong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Etempvar _r0 tlong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Etempvar _r1 tlong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Etempvar _r2 tlong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Etempvar _r3 tlong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Etempvar _r4 tlong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _r0 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'11 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'11 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 148) tint) :: (Evar ___stringlit_16 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _r1 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'10 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'10 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 149) tint) :: (Evar ___stringlit_17 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _r2 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 150) tint) :: (Evar ___stringlit_18 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _r3 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 151) tint) :: (Evar ___stringlit_19 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _r4 tlong) (Econst_int (Int.repr 62) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 152) tint) :: (Evar ___stringlit_20 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'3) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _t'3 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 153) tint) :: (Evar ___stringlit_21 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sloop (Ssequence (Scall (Some _t'4) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'4 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 154) tint) :: (Evar ___stringlit_15 (tarray tschar 85)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))))))))))))))))))))))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_modinv64_divsteps_62_var := {| fn_return := tlong; fn_callconv := cc_default; fn_params := ((_eta, tlong) :: (_f0, tulong) :: (_g0, tulong) :: (_t, (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: nil); fn_vars := nil; fn_temps := ((_u, tulong) :: (_v, tulong) :: (_q, tulong) :: (_r, tulong) :: (_f, tulong) :: (_g, tulong) :: (_m, tulong) :: (_w, tuint) :: (_i, tint) :: (_limit, tint) :: (_zeros, tint) :: (_tmp, tulong) :: (_t'7, tint) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'16, (tptr (Tstruct __IO_FILE noattr))) :: (_t'15, (tptr (Tstruct __IO_FILE noattr))) :: (_t'14, (tptr (Tstruct __IO_FILE noattr))) :: (_t'13, (tptr (Tstruct __IO_FILE noattr))) :: (_t'12, (tptr (Tstruct __IO_FILE noattr))) :: (_t'11, (tptr (Tstruct __IO_FILE noattr))) :: (_t'10, (tptr (Tstruct __IO_FILE noattr))) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _u (Ecast (Econst_int (Int.repr 1) tint) tulong)) (Ssequence (Sset _v (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Sset _q (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Sset _r (Ecast (Econst_int (Int.repr 1) tint) tulong)) (Ssequence (Sset _f (Etempvar _f0 tulong)) (Ssequence (Sset _g (Etempvar _g0 tulong)) (Ssequence (Sset _i (Econst_int (Int.repr 62) tint)) (Ssequence (Sloop (Ssequence Sskip (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_ctz64_var (Tfunction (Tcons tulong Tnil) tint cc_default)) ((Ebinop Oor (Etempvar _g tulong) (Ebinop Oshl (Econst_long (Int64.repr (-1)) tulong) (Etempvar _i tint) tulong) tulong) :: nil)) (Sset _zeros (Etempvar _t'1 tint))) (Ssequence (Sset _g (Ebinop Oshr (Etempvar _g tulong) (Etempvar _zeros tint) tulong)) (Ssequence (Sset _u (Ebinop Oshl (Etempvar _u tulong) (Etempvar _zeros tint) tulong)) (Ssequence (Sset _v (Ebinop Oshl (Etempvar _v tulong) (Etempvar _zeros tint) tulong)) (Ssequence (Sset _eta (Ebinop Osub (Etempvar _eta tlong) (Etempvar _zeros tint) tlong)) (Ssequence (Sset _i (Ebinop Osub (Etempvar _i tint) (Etempvar _zeros tint) tint)) (Ssequence (Sifthenelse (Ebinop Oeq (Etempvar _i tint) (Econst_int (Int.repr 0) tint) tint) Sbreak Sskip) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _f tulong) (Econst_int (Int.repr 1) tint) tulong) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'16 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'16 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 258) tint) :: (Evar ___stringlit_22 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _g tulong) (Econst_int (Int.repr 1) tint) tulong) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'15 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'15 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 259) tint) :: (Evar ___stringlit_23 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oadd (Ebinop Omul (Etempvar _u tulong) (Etempvar _f0 tulong) tulong) (Ebinop Omul (Etempvar _v tulong) (Etempvar _g0 tulong) tulong) tulong) (Ebinop Oshl (Etempvar _f tulong) (Ebinop Osub (Econst_int (Int.repr 62) tint) (Etempvar _i tint) tint) tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'14 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'14 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 260) tint) :: (Evar ___stringlit_24 (tarray tschar 58)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oadd (Ebinop Omul (Etempvar _q tulong) (Etempvar _f0 tulong) tulong) (Ebinop Omul (Etempvar _r tulong) (Etempvar _g0 tulong) tulong) tulong) (Ebinop Oshl (Etempvar _g tulong) (Ebinop Osub (Econst_int (Int.repr 62) tint) (Etempvar _i tint) tint) tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'13 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'13 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 261) tint) :: (Evar ___stringlit_25 (tarray tschar 58)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _eta tlong) (Eunop Oneg (Econst_int (Int.repr 745) tint) tint) tint) (Sset _t'2 (Ecast (Ebinop Ole (Etempvar _eta tlong) (Econst_int (Int.repr 745) tint) tint) tbool)) (Sset _t'2 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'12 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'12 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 263) tint) :: (Evar ___stringlit_26 (tarray tschar 49)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _eta tlong) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Sset _eta (Eunop Oneg (Etempvar _eta tlong) tlong)) (Ssequence (Sset _tmp (Etempvar _f tulong)) (Ssequence (Sset _f (Etempvar _g tulong)) (Ssequence (Sset _g (Eunop Oneg (Etempvar _tmp tulong) tulong)) (Ssequence (Sset _tmp (Etempvar _u tulong)) (Ssequence (Sset _u (Etempvar _q tulong)) (Ssequence (Sset _q (Eunop Oneg (Etempvar _tmp tulong) tulong)) (Ssequence (Sset _tmp (Etempvar _v tulong)) (Ssequence (Sset _v (Etempvar _r tulong)) (Ssequence (Sset _r (Eunop Oneg (Etempvar _tmp tulong) tulong)) (Ssequence (Ssequence (Sifthenelse (Ebinop Ogt (Ebinop Oadd (Ecast (Etempvar _eta tlong) tint) (Econst_int (Int.repr 1) tint) tint) (Etempvar _i tint) tint) (Sset _t'3 (Ecast (Etempvar _i tint) tint)) (Sset _t'3 (Ecast (Ebinop Oadd (Ecast (Etempvar _eta tlong) tint) (Econst_int (Int.repr 1) tint) tint) tint))) (Sset _limit (Etempvar _t'3 tint))) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Ogt (Etempvar _limit tint) (Econst_int (Int.repr 0) tint) tint) (Sset _t'4 (Ecast (Ebinop Ole (Etempvar _limit tint) (Econst_int (Int.repr 62) tint) tint) tbool)) (Sset _t'4 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Eunop Onotbool (Etempvar _t'4 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'11 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'11 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 275) tint) :: (Evar ___stringlit_27 (tarray tschar 48)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _m (Ebinop Oand (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Ebinop Osub (Econst_int (Int.repr 64) tint) (Etempvar _limit tint) tint) tulong) (Econst_int (Int.repr 63) tuint) tulong)) (Sset _w (Ecast (Ebinop Oand (Ebinop Omul (Ebinop Omul (Etempvar _f tulong) (Etempvar _g tulong) tulong) (Ebinop Osub (Ebinop Omul (Etempvar _f tulong) (Etempvar _f tulong) tulong) (Econst_int (Int.repr 2) tint) tulong) tulong) (Etempvar _m tulong) tulong) tuint))))))))))))))) (Ssequence (Ssequence (Sifthenelse (Ebinop Ogt (Ebinop Oadd (Ecast (Etempvar _eta tlong) tint) (Econst_int (Int.repr 1) tint) tint) (Etempvar _i tint) tint) (Sset _t'5 (Ecast (Etempvar _i tint) tint)) (Sset _t'5 (Ecast (Ebinop Oadd (Ecast (Etempvar _eta tlong) tint) (Econst_int (Int.repr 1) tint) tint) tint))) (Sset _limit (Etempvar _t'5 tint))) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Ogt (Etempvar _limit tint) (Econst_int (Int.repr 0) tint) tint) (Sset _t'6 (Ecast (Ebinop Ole (Etempvar _limit tint) (Econst_int (Int.repr 62) tint) tint) tbool)) (Sset _t'6 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Eunop Onotbool (Etempvar _t'6 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'10 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'10 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 285) tint) :: (Evar ___stringlit_27 (tarray tschar 48)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _m (Ebinop Oand (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Ebinop Osub (Econst_int (Int.repr 64) tint) (Etempvar _limit tint) tint) tulong) (Econst_int (Int.repr 15) tuint) tulong)) (Ssequence (Sset _w (Ecast (Ebinop Oadd (Etempvar _f tulong) (Ebinop Oshl (Ebinop Oand (Ebinop Oadd (Etempvar _f tulong) (Econst_int (Int.repr 1) tint) tulong) (Econst_int (Int.repr 4) tint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) tuint)) (Sset _w (Ecast (Ebinop Oand (Ebinop Omul (Eunop Oneg (Etempvar _w tuint) tuint) (Etempvar _g tulong) tulong) (Etempvar _m tulong) tulong) tuint))))))) (Ssequence (Sset _g (Ebinop Oadd (Etempvar _g tulong) (Ebinop Omul (Etempvar _f tulong) (Etempvar _w tuint) tulong) tulong)) (Ssequence (Sset _q (Ebinop Oadd (Etempvar _q tulong) (Ebinop Omul (Etempvar _u tulong) (Etempvar _w tuint) tulong) tulong)) (Ssequence (Sset _r (Ebinop Oadd (Etempvar _r tulong) (Ebinop Omul (Etempvar _v tulong) (Etempvar _w tuint) tulong) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _g tulong) (Etempvar _m tulong) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 296) tint) :: (Evar ___stringlit_28 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))))))))))))))))) Sskip) (Ssequence (Sassign (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _u tlong) (Ecast (Etempvar _u tulong) tlong)) (Ssequence (Sassign (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _v tlong) (Ecast (Etempvar _v tulong) tlong)) (Ssequence (Sassign (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _q tlong) (Ecast (Etempvar _q tulong) tlong)) (Ssequence (Sassign (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _r tlong) (Ecast (Etempvar _r tulong) tlong)) (Ssequence (Sloop (Ssequence (Scall (Some _t'7) (Evar _secp256k1_modinv64_det_check_pow2 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr)) (Tcons tuint (Tcons tint Tnil))) tint cc_default)) ((Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: (Econst_int (Int.repr 62) tint) :: (Econst_int (Int.repr 0) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'7 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 308) tint) :: (Evar ___stringlit_29 (tarray tschar 67)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sreturn (Some (Etempvar _eta tlong)))))))))))))))) |}. Definition f_secp256k1_modinv64_update_de_62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_d, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_e, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_t, (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: (_modinfo, (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil); fn_vars := ((_cd, (Tstruct _secp256k1_uint128 noattr)) :: (_ce, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_M62, tulong) :: (_d0, tlong) :: (_d1, tlong) :: (_d2, tlong) :: (_d3, tlong) :: (_d4, tlong) :: (_e0, tlong) :: (_e1, tlong) :: (_e2, tlong) :: (_e3, tlong) :: (_e4, tlong) :: (_u, tlong) :: (_v, tlong) :: (_q, tlong) :: (_r, tlong) :: (_md, tlong) :: (_me, tlong) :: (_sd, tlong) :: (_se, tlong) :: (_t'26, tint) :: (_t'25, tint) :: (_t'24, tint) :: (_t'23, tint) :: (_t'22, tlong) :: (_t'21, tlong) :: (_t'20, tulong) :: (_t'19, tulong) :: (_t'18, tulong) :: (_t'17, tulong) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tulong) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tulong) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tlong) :: (_t'7, tlong) :: (_t'6, tlong) :: (_t'5, tlong) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'53, (tptr (Tstruct __IO_FILE noattr))) :: (_t'52, (tptr (Tstruct __IO_FILE noattr))) :: (_t'51, (tptr (Tstruct __IO_FILE noattr))) :: (_t'50, (tptr (Tstruct __IO_FILE noattr))) :: (_t'49, (tptr (Tstruct __IO_FILE noattr))) :: (_t'48, (tptr (Tstruct __IO_FILE noattr))) :: (_t'47, tulong) :: (_t'46, tulong) :: (_t'45, tlong) :: (_t'44, tlong) :: (_t'43, (tptr (Tstruct __IO_FILE noattr))) :: (_t'42, (tptr (Tstruct __IO_FILE noattr))) :: (_t'41, tlong) :: (_t'40, tlong) :: (_t'39, tlong) :: (_t'38, tlong) :: (_t'37, tlong) :: (_t'36, tlong) :: (_t'35, tlong) :: (_t'34, tlong) :: (_t'33, tlong) :: (_t'32, tlong) :: (_t'31, tlong) :: (_t'30, (tptr (Tstruct __IO_FILE noattr))) :: (_t'29, (tptr (Tstruct __IO_FILE noattr))) :: (_t'28, (tptr (Tstruct __IO_FILE noattr))) :: (_t'27, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _M62 (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Sset _d0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _d1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Ssequence (Sset _d2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Ssequence (Sset _d3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Ssequence (Sset _d4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Ssequence (Sset _e0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _e1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Ssequence (Sset _e2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Ssequence (Sset _e3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Ssequence (Sset _e4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Ssequence (Sset _u (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _u tlong)) (Ssequence (Sset _v (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _v tlong)) (Ssequence (Sset _q (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _q tlong)) (Ssequence (Sset _r (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _r tlong)) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 2) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'1 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'53 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'53 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 422) tint) :: (Evar ___stringlit_30 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'2 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'52 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'52 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 423) tint) :: (Evar ___stringlit_31 (tarray tschar 85)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'3) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 2) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'3 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'51 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'51 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 424) tint) :: (Evar ___stringlit_32 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'4) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'4 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'50 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'50 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 425) tint) :: (Evar ___stringlit_33 (tarray tschar 85)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Ssequence (Scall (Some _t'5) (Evar _secp256k1_modinv64_abs (Tfunction (Tcons tlong Tnil) tlong cc_default)) ((Etempvar _u tlong) :: nil)) (Scall (Some _t'6) (Evar _secp256k1_modinv64_abs (Tfunction (Tcons tlong Tnil) tlong cc_default)) ((Etempvar _v tlong) :: nil))) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'5 tlong) (Ebinop Osub (Ebinop Oshl (Ecast (Econst_int (Int.repr 1) tint) tlong) (Econst_int (Int.repr 62) tint) tlong) (Etempvar _t'6 tlong) tlong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'49 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'49 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 426) tint) :: (Evar ___stringlit_34 (tarray tschar 101)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Ssequence (Scall (Some _t'7) (Evar _secp256k1_modinv64_abs (Tfunction (Tcons tlong Tnil) tlong cc_default)) ((Etempvar _q tlong) :: nil)) (Scall (Some _t'8) (Evar _secp256k1_modinv64_abs (Tfunction (Tcons tlong Tnil) tlong cc_default)) ((Etempvar _r tlong) :: nil))) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'7 tlong) (Ebinop Osub (Ebinop Oshl (Ecast (Econst_int (Int.repr 1) tint) tlong) (Econst_int (Int.repr 62) tint) tlong) (Etempvar _t'8 tlong) tlong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'48 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'48 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 427) tint) :: (Evar ___stringlit_35 (tarray tschar 101)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _sd (Ebinop Oshr (Etempvar _d4 tlong) (Econst_int (Int.repr 63) tint) tlong)) (Ssequence (Sset _se (Ebinop Oshr (Etempvar _e4 tlong) (Econst_int (Int.repr 63) tint) tlong)) (Ssequence (Sset _md (Ebinop Oadd (Ebinop Oand (Etempvar _u tlong) (Etempvar _sd tlong) tlong) (Ebinop Oand (Etempvar _v tlong) (Etempvar _se tlong) tlong) tlong)) (Ssequence (Sset _me (Ebinop Oadd (Ebinop Oand (Etempvar _q tlong) (Etempvar _sd tlong) tlong) (Ebinop Oand (Etempvar _r tlong) (Etempvar _se tlong) tlong) tlong)) (Ssequence (Scall None (Evar _secp256k1_i128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _d0 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _e0 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _d0 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _e0 tlong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'9) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Ssequence (Sset _t'47 (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus_inv62 tulong)) (Sset _md (Ebinop Osub (Etempvar _md tlong) (Ebinop Oand (Ebinop Oadd (Ebinop Omul (Etempvar _t'47 tulong) (Etempvar _t'9 tulong) tulong) (Etempvar _md tlong) tulong) (Etempvar _M62 tulong) tulong) tulong)))) (Ssequence (Ssequence (Scall (Some _t'10) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Ssequence (Sset _t'46 (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus_inv62 tulong)) (Sset _me (Ebinop Osub (Etempvar _me tlong) (Ebinop Oand (Ebinop Oadd (Ebinop Omul (Etempvar _t'46 tulong) (Etempvar _t'10 tulong) tulong) (Etempvar _me tlong) tulong) (Etempvar _M62 tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'45 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'45 tlong) :: (Etempvar _md tlong) :: nil))) (Ssequence (Ssequence (Sset _t'44 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'44 tlong) :: (Etempvar _me tlong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'11) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _t'11 tulong) (Etempvar _M62 tulong) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'43 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'43 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 446) tint) :: (Evar ___stringlit_36 (tarray tschar 63)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'12) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _t'12 tulong) (Etempvar _M62 tulong) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'42 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'42 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 447) tint) :: (Evar ___stringlit_37 (tarray tschar 63)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _d1 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _e1 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _d1 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _e1 tlong) :: nil)) (Ssequence (Ssequence (Sset _t'39 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Sifthenelse (Etempvar _t'39 tlong) (Ssequence (Ssequence (Sset _t'41 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'41 tlong) :: (Etempvar _md tlong) :: nil))) (Ssequence (Sset _t'40 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'40 tlong) :: (Etempvar _me tlong) :: nil)))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'13) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'13 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'14) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'14 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _d2 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _e2 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _d2 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _e2 tlong) :: nil)) (Ssequence (Ssequence (Sset _t'36 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Sifthenelse (Etempvar _t'36 tlong) (Ssequence (Ssequence (Sset _t'38 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'38 tlong) :: (Etempvar _md tlong) :: nil))) (Ssequence (Sset _t'37 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'37 tlong) :: (Etempvar _me tlong) :: nil)))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'15) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cd (Tstruct 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(Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'16 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _d3 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _e3 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _d3 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _e3 tlong) :: nil)) (Ssequence (Ssequence (Sset _t'33 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Sifthenelse (Etempvar _t'33 tlong) (Ssequence (Ssequence (Sset _t'35 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'35 tlong) :: (Etempvar _md tlong) :: nil))) (Ssequence (Sset _t'34 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'34 tlong) :: (Etempvar _me tlong) :: nil)))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'17) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'17 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'18) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'18 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _d4 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _e4 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _d4 tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _e4 tlong) :: nil)) (Ssequence (Ssequence (Sset _t'32 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'32 tlong) :: (Etempvar _md tlong) :: nil))) (Ssequence (Ssequence (Sset _t'31 (Ederef (Ebinop Oadd (Efield (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'31 tlong) :: (Etempvar _me tlong) :: nil))) (Ssequence (Ssequence (Scall (Some _t'19) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'19 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'20) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'20 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'21) (Evar _secp256k1_i128_to_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tlong cc_default)) ((Eaddrof (Evar _cd (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Etempvar _t'21 tlong))) (Ssequence (Ssequence (Scall (Some _t'22) (Evar _secp256k1_i128_to_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tlong cc_default)) ((Eaddrof (Evar _ce (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Etempvar _t'22 tlong))) (Ssequence (Sloop (Ssequence (Scall (Some _t'23) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 2) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'23 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'30 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'30 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 494) tint) :: (Evar ___stringlit_30 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'24) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _d (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'24 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'29 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'29 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 495) tint) :: (Evar ___stringlit_31 (tarray tschar 85)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'25) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 2) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'25 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'28 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'28 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 496) tint) :: (Evar ___stringlit_32 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sloop (Ssequence (Scall (Some _t'26) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _e (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'26 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'27 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'27 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 497) tint) :: (Evar ___stringlit_33 (tarray tschar 85)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_modinv64_update_fg_62_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_len, tint) :: (_f, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_g, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_t, (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: nil); fn_vars := ((_cf, (Tstruct _secp256k1_uint128 noattr)) :: (_cg, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_M62, tulong) :: (_u, tlong) :: (_v, tlong) :: (_q, tlong) :: (_r, tlong) :: (_fi, tlong) :: (_gi, tlong) :: (_i, tint) :: (_t'6, tlong) :: (_t'5, tlong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _M62 (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Sset _u (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _u tlong)) (Ssequence (Sset _v (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _v tlong)) (Ssequence (Sset _q (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _q tlong)) (Ssequence (Sset _r (Efield (Ederef (Etempvar _t (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) (Tstruct _secp256k1_modinv64_trans2x2 noattr)) _r tlong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _len tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 566) tint) :: (Evar ___stringlit_38 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sset _fi (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _f (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _gi (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _g (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Scall None (Evar _secp256k1_i128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _fi tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _gi tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _fi tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _gi tlong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _t'1 tulong) (Etempvar _M62 tulong) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 575) tint) :: (Evar ___stringlit_39 (tarray tschar 63)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _t'2 tulong) (Etempvar _M62 tulong) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 576) tint) :: (Evar ___stringlit_40 (tarray tschar 63)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Ssequence (Sset _i (Econst_int (Int.repr 1) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _len tint) tint) Sskip Sbreak) (Ssequence (Sset _fi (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _f (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Ssequence (Sset _gi (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _g (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _i tint) (tptr tlong)) tlong)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u tlong) :: (Etempvar _fi tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _v tlong) :: (Etempvar _gi tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _q tlong) :: (Etempvar _fi tlong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_i128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _r tlong) :: (Etempvar _gi tlong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _f (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'3 tulong) (Etempvar _M62 tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _g (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _t'4 tulong) (Etempvar _M62 tulong) tulong))) (Scall None (Evar _secp256k1_i128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)))))))))))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Ssequence (Scall (Some _t'5) (Evar _secp256k1_i128_to_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tlong cc_default)) ((Eaddrof (Evar _cf (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _f (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong) (Etempvar _t'5 tlong))) (Ssequence (Scall (Some _t'6) (Evar _secp256k1_i128_to_i64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tlong cc_default)) ((Eaddrof (Evar _cg (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _g (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong) (Etempvar _t'6 tlong))))))))))))))))))))) |}. Definition f_secp256k1_modinv64_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_x, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_modinfo, (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil); fn_vars := ((_d, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: (_e, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: (_f, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: (_g, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: (_t, (Tstruct _secp256k1_modinv64_trans2x2 noattr)) :: nil); fn_temps := ((_i, tint) :: (_j, tint) :: (_len, tint) :: (_eta, tlong) :: (_cond, tlong) :: (_fn, tlong) :: (_gn, tlong) :: (_t'20, tint) :: (_t'19, tint) :: (_t'18, tint) :: (_t'17, tint) :: (_t'16, tint) :: (_t'15, tint) :: (_t'14, tint) :: (_t'13, tint) :: (_t'12, tint) :: (_t'11, tint) :: (_t'10, tint) :: (_t'9, tint) :: (_t'8, tint) :: (_t'7, tint) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tlong) :: (_t'38, tlong) :: (_t'37, tlong) :: (_t'36, (tptr (Tstruct __IO_FILE noattr))) :: (_t'35, (tptr (Tstruct __IO_FILE noattr))) :: (_t'34, (tptr (Tstruct __IO_FILE noattr))) :: (_t'33, (tptr (Tstruct __IO_FILE noattr))) :: (_t'32, tlong) :: (_t'31, tlong) :: (_t'30, tlong) :: (_t'29, tlong) :: (_t'28, (tptr (Tstruct __IO_FILE noattr))) :: (_t'27, (tptr (Tstruct __IO_FILE noattr))) :: (_t'26, (tptr (Tstruct __IO_FILE noattr))) :: (_t'25, (tptr (Tstruct __IO_FILE noattr))) :: (_t'24, (tptr (Tstruct __IO_FILE noattr))) :: (_t'23, (tptr (Tstruct __IO_FILE noattr))) :: (_t'22, (tptr (Tstruct __IO_FILE noattr))) :: (_t'21, tlong) :: nil); fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _e (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _e (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _e (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _e (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _e (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Econst_int (Int.repr 0) tint)) (Ssequence (Scall None (Evar _secp256k1_modinv64_signed62_assign (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_modinv64_signed62_assign (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _x (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil)) (Ssequence (Sset _i (Econst_int (Int.repr 0) tint)) (Ssequence (Sset _len (Econst_int (Int.repr 5) tint)) (Ssequence (Sset _eta (Ecast (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tlong)) (Ssequence (Sloop (Ssequence Sskip (Ssequence (Ssequence (Ssequence (Sset _t'37 (Ederef (Ebinop Oadd (Efield (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _t'38 (Ederef (Ebinop Oadd (Efield (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Scall (Some _t'1) (Evar _secp256k1_modinv64_divsteps_62_var (Tfunction (Tcons tlong (Tcons tulong (Tcons tulong (Tcons (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr)) Tnil)))) tlong cc_default)) ((Etempvar _eta tlong) :: (Etempvar _t'37 tlong) :: (Etempvar _t'38 tlong) :: (Eaddrof (Evar _t (Tstruct _secp256k1_modinv64_trans2x2 noattr)) (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: nil)))) (Sset _eta (Etempvar _t'1 tlong))) (Ssequence (Scall None (Evar _secp256k1_modinv64_update_de_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_modinfo noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _e (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _t (Tstruct _secp256k1_modinv64_trans2x2 noattr)) (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'2 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'36 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'36 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 674) tint) :: (Evar ___stringlit_41 (tarray tschar 89)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'3) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'3 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'35 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'35 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 675) tint) :: (Evar ___stringlit_42 (tarray tschar 89)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'4) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'4 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'34 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'34 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 676) tint) :: (Evar ___stringlit_43 (tarray tschar 89)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'5) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'5 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'33 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'33 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 677) tint) :: (Evar ___stringlit_44 (tarray tschar 88)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_modinv64_update_fg_62_var (Tfunction (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr)) Tnil)))) tvoid cc_default)) ((Etempvar _len tint) :: (Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _t (Tstruct _secp256k1_modinv64_trans2x2 noattr)) (tptr (Tstruct _secp256k1_modinv64_trans2x2 noattr))) :: nil)) (Ssequence (Ssequence (Sset _t'31 (Ederef (Ebinop Oadd (Efield (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Sifthenelse (Ebinop Oeq (Etempvar _t'31 tlong) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Sset _cond (Ecast (Econst_int (Int.repr 0) tint) tlong)) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 1) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Etempvar _len tint) tint) Sskip Sbreak) (Ssequence (Sset _t'32 (Ederef (Ebinop Oadd (Efield (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Etempvar _j tint) (tptr tlong)) tlong)) (Sset _cond (Ebinop Oor (Etempvar _cond tlong) (Etempvar _t'32 tlong) tlong)))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Sifthenelse (Ebinop Oeq (Etempvar _cond tlong) (Econst_int (Int.repr 0) tint) tint) Sbreak Sskip))) Sskip)) (Ssequence (Sset _fn (Ederef (Ebinop Oadd (Efield (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong)) (Ssequence (Sset _gn (Ederef (Ebinop Oadd (Efield (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong)) (Ssequence (Sset _cond (Ebinop Oshr (Ebinop Osub (Ecast (Etempvar _len tint) tlong) (Econst_int (Int.repr 2) tint) tlong) (Econst_int (Int.repr 63) tint) tlong)) (Ssequence (Sset _cond (Ebinop Oor (Etempvar _cond tlong) (Ebinop Oxor (Etempvar _fn tlong) (Ebinop Oshr (Etempvar _fn tlong) (Econst_int (Int.repr 63) tint) tlong) tlong) tlong)) (Ssequence (Sset _cond (Ebinop Oor (Etempvar _cond tlong) (Ebinop Oxor (Etempvar _gn tlong) (Ebinop Oshr (Etempvar _gn tlong) (Econst_int (Int.repr 63) tint) tlong) tlong) tlong)) (Ssequence (Sifthenelse (Ebinop Oeq (Etempvar _cond tlong) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Ssequence (Sset _t'30 (Ederef (Ebinop Oadd (Efield (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 2) tint) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 2) tint) tint) (tptr tlong)) tlong) (Ebinop Oor (Etempvar _t'30 tlong) (Ebinop Oshl (Ecast (Etempvar _fn tlong) tulong) (Econst_int (Int.repr 62) tint) tulong) tulong))) (Ssequence (Ssequence (Sset _t'29 (Ederef (Ebinop Oadd (Efield (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 2) tint) tint) (tptr tlong)) tlong)) (Sassign (Ederef (Ebinop Oadd (Efield (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 2) tint) tint) (tptr tlong)) tlong) (Ebinop Oor (Etempvar _t'29 tlong) (Ebinop Oshl (Ecast (Etempvar _gn tlong) tulong) (Econst_int (Int.repr 62) tint) tulong) tulong))) (Sset _len (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 1) tint) tint)))) Sskip) (Ssequence (Sloop (Ssequence (Ssequence (Sset _t'6 (Ecast (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint) tint)) (Sset _i (Etempvar _t'6 tint))) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'6 tint) (Econst_int (Int.repr 12) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'28 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'28 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 704) tint) :: (Evar ___stringlit_45 (tarray tschar 32)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'7) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'7 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'27 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'27 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 705) tint) :: (Evar ___stringlit_41 (tarray tschar 89)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'8) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'8 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'26 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'26 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 706) tint) :: (Evar ___stringlit_42 (tarray tschar 89)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'9) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Ogt (Etempvar _t'9 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'25 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'25 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 707) tint) :: (Evar ___stringlit_43 (tarray tschar 89)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sloop (Ssequence (Scall (Some _t'10) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'10 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'24 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'24 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 708) tint) :: (Evar ___stringlit_44 (tarray tschar 88)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))))))))))))))))) Sskip) (Ssequence (Sloop (Ssequence (Scall (Some _t'11) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _g (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Evar _SECP256K1_SIGNED62_ONE (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'11 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'23 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'23 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 716) tint) :: (Evar ___stringlit_46 (tarray tschar 95)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Ssequence (Ssequence (Scall (Some _t'12) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Evar _SECP256K1_SIGNED62_ONE (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sifthenelse (Ebinop Oeq (Etempvar _t'12 tint) (Econst_int (Int.repr 0) tint) tint) (Sset _t'13 (Econst_int (Int.repr 1) tint)) (Ssequence (Scall (Some _t'14) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Evar _SECP256K1_SIGNED62_ONE (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sset _t'13 (Ecast (Ebinop Oeq (Etempvar _t'14 tint) (Econst_int (Int.repr 0) tint) tint) tbool))))) (Sifthenelse (Etempvar _t'13 tint) (Sset _t'15 (Econst_int (Int.repr 1) tint)) (Ssequence (Ssequence (Scall (Some _t'16) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Etempvar _x (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Evar _SECP256K1_SIGNED62_ONE (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Sifthenelse (Ebinop Oeq (Etempvar _t'16 tint) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Scall (Some _t'18) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 5) tint) :: (Eaddrof (Evar _SECP256K1_SIGNED62_ONE (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Sset _t'17 (Ecast (Ebinop Oeq (Etempvar _t'18 tint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sset _t'17 (Econst_int (Int.repr 0) tint)))) (Sifthenelse (Etempvar _t'17 tint) (Ssequence (Scall (Some _t'19) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Ebinop Oeq (Etempvar _t'19 tint) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Sset _t'15 (Ecast (Econst_int (Int.repr 1) tint) tbool)) (Sset _t'15 (Ecast (Etempvar _t'15 tint) tbool))) (Ssequence (Ssequence (Ssequence (Scall (Some _t'20) (Evar _secp256k1_modinv64_mul_cmp_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tint (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong Tnil)))) tint cc_default)) ((Eaddrof (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _len tint) :: (Eaddrof (Efield (Ederef (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) (Tstruct _secp256k1_modinv64_modinfo noattr)) _modulus (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) :: nil)) (Sset _t'15 (Ecast (Ebinop Oeq (Etempvar _t'20 tint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sset _t'15 (Ecast (Etempvar _t'15 tint) tbool))) (Sset _t'15 (Ecast (Etempvar _t'15 tint) tbool))))) (Sset _t'15 (Ecast (Econst_int (Int.repr 0) tint) tbool)))))) (Sifthenelse (Eunop Onotbool (Etempvar _t'15 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'22 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'22 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_8 (tarray tschar 26)) :: (Econst_int (Int.repr 718) tint) :: (Evar ___stringlit_47 (tarray tschar 459)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'21 (Ederef (Ebinop Oadd (Efield (Evar _f (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Ebinop Osub (Etempvar _len tint) (Econst_int (Int.repr 1) tint) tint) (tptr tlong)) tlong)) (Scall None (Evar _secp256k1_modinv64_normalize_62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons tlong (Tcons (tptr (Tstruct _secp256k1_modinv64_modinfo noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _t'21 tlong) :: (Etempvar _modinfo (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil))) (Scall None (Evar _secp256k1_modinv64_signed62_assign (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _x (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _d (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil))))))))))))))))))))) |}. Definition f_secp256k1_fe_mul_inner := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr tulong)) :: (_a, (tptr tulong)) :: (_b, (tptr tulong)) :: nil); fn_vars := ((_c, (Tstruct _secp256k1_uint128 noattr)) :: (_d, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_t3, tulong) :: (_t4, tulong) :: (_tx, tulong) :: (_u0, tulong) :: (_a0, tulong) :: (_a1, tulong) :: (_a2, tulong) :: (_a3, tulong) :: (_a4, tulong) :: (_M, tulong) :: (_R, tulong) :: (_t'38, tulong) :: (_t'37, tint) :: (_t'36, tulong) :: (_t'35, tint) :: (_t'34, tulong) :: (_t'33, tint) :: (_t'32, tulong) :: (_t'31, tint) :: (_t'30, tint) :: (_t'29, tulong) :: (_t'28, tint) :: (_t'27, tint) :: (_t'26, tint) :: (_t'25, tulong) :: (_t'24, tint) :: (_t'23, tint) :: (_t'22, tulong) :: (_t'21, tint) :: (_t'20, tint) :: (_t'19, tint) :: (_t'18, tulong) :: (_t'17, tint) :: (_t'16, tint) :: (_t'15, tulong) :: (_t'14, tint) :: (_t'13, tint) :: (_t'12, tint) :: (_t'11, tulong) :: (_t'10, tint) :: (_t'9, tulong) :: (_t'8, tint) :: (_t'7, tint) :: (_t'6, tulong) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tulong) :: (_t'2, tint) :: (_t'1, tint) :: (_t'126, (tptr (Tstruct __IO_FILE noattr))) :: (_t'125, tulong) :: (_t'124, (tptr (Tstruct __IO_FILE noattr))) :: (_t'123, tulong) :: (_t'122, (tptr (Tstruct __IO_FILE noattr))) :: (_t'121, tulong) :: (_t'120, (tptr (Tstruct __IO_FILE noattr))) :: (_t'119, tulong) :: (_t'118, (tptr (Tstruct __IO_FILE noattr))) :: (_t'117, tulong) :: (_t'116, (tptr (Tstruct __IO_FILE noattr))) :: (_t'115, tulong) :: (_t'114, (tptr (Tstruct __IO_FILE noattr))) :: (_t'113, tulong) :: (_t'112, (tptr (Tstruct __IO_FILE noattr))) :: (_t'111, tulong) :: (_t'110, (tptr (Tstruct __IO_FILE noattr))) :: (_t'109, tulong) :: (_t'108, (tptr (Tstruct __IO_FILE noattr))) :: (_t'107, tulong) :: (_t'106, (tptr (Tstruct __IO_FILE noattr))) :: (_t'105, (tptr (Tstruct __IO_FILE noattr))) :: (_t'104, tulong) :: (_t'103, tulong) :: (_t'102, tulong) :: (_t'101, tulong) :: (_t'100, (tptr (Tstruct __IO_FILE noattr))) :: (_t'99, tulong) :: (_t'98, (tptr (Tstruct __IO_FILE noattr))) :: (_t'97, (tptr (Tstruct __IO_FILE noattr))) :: (_t'96, (tptr (Tstruct __IO_FILE noattr))) :: (_t'95, (tptr (Tstruct __IO_FILE noattr))) :: (_t'94, (tptr (Tstruct __IO_FILE noattr))) :: (_t'93, tulong) :: (_t'92, tulong) :: (_t'91, tulong) :: (_t'90, tulong) :: (_t'89, tulong) :: (_t'88, (tptr (Tstruct __IO_FILE noattr))) :: (_t'87, (tptr (Tstruct __IO_FILE noattr))) :: (_t'86, (tptr (Tstruct __IO_FILE noattr))) :: (_t'85, (tptr (Tstruct __IO_FILE noattr))) :: (_t'84, (tptr (Tstruct __IO_FILE noattr))) :: (_t'83, (tptr (Tstruct __IO_FILE noattr))) :: (_t'82, tulong) :: (_t'81, (tptr (Tstruct __IO_FILE noattr))) :: (_t'80, tulong) :: (_t'79, tulong) :: (_t'78, tulong) :: (_t'77, tulong) :: (_t'76, (tptr (Tstruct __IO_FILE noattr))) :: (_t'75, (tptr (Tstruct __IO_FILE noattr))) :: (_t'74, (tptr (Tstruct __IO_FILE noattr))) :: (_t'73, (tptr (Tstruct __IO_FILE noattr))) :: (_t'72, (tptr (Tstruct __IO_FILE noattr))) :: (_t'71, (tptr (Tstruct __IO_FILE noattr))) :: (_t'70, tulong) :: (_t'69, (tptr (Tstruct __IO_FILE noattr))) :: (_t'68, tulong) :: (_t'67, tulong) :: (_t'66, (tptr (Tstruct __IO_FILE noattr))) :: (_t'65, tulong) :: (_t'64, tulong) :: (_t'63, tulong) :: (_t'62, (tptr (Tstruct __IO_FILE noattr))) :: (_t'61, (tptr (Tstruct __IO_FILE noattr))) :: (_t'60, (tptr (Tstruct __IO_FILE noattr))) :: (_t'59, (tptr (Tstruct __IO_FILE noattr))) :: (_t'58, tulong) :: (_t'57, (tptr (Tstruct __IO_FILE noattr))) :: (_t'56, tulong) :: (_t'55, tulong) :: (_t'54, tulong) :: (_t'53, (tptr (Tstruct __IO_FILE noattr))) :: (_t'52, tulong) :: (_t'51, tulong) :: (_t'50, (tptr (Tstruct __IO_FILE noattr))) :: (_t'49, (tptr (Tstruct __IO_FILE noattr))) :: (_t'48, (tptr (Tstruct __IO_FILE noattr))) :: (_t'47, (tptr (Tstruct __IO_FILE noattr))) :: (_t'46, tulong) :: (_t'45, (tptr (Tstruct __IO_FILE noattr))) :: (_t'44, (tptr (Tstruct __IO_FILE noattr))) :: (_t'43, (tptr (Tstruct __IO_FILE noattr))) :: (_t'42, tulong) :: (_t'41, (tptr (Tstruct __IO_FILE noattr))) :: (_t'40, (tptr (Tstruct __IO_FILE noattr))) :: (_t'39, tulong) :: nil); fn_body := (Ssequence (Sset _a0 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a1 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a2 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a3 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a4 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _M (Econst_long (Int64.repr 4503599627370495) tulong)) (Ssequence (Sset _R (Econst_long (Int64.repr 68719492368) tulong)) (Ssequence (Sloop (Ssequence (Sset _t'125 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'125 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'126 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'126 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 28) tint) :: (Evar ___stringlit_48 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'123 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'123 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'124 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'124 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 29) tint) :: (Evar ___stringlit_50 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'121 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'121 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'122 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'122 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 30) tint) :: (Evar ___stringlit_51 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'119 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'119 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'120 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'120 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 31) tint) :: (Evar ___stringlit_52 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'117 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'117 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'118 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'118 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 32) tint) :: (Evar ___stringlit_53 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'115 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'115 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'116 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'116 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 33) tint) :: (Evar ___stringlit_54 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'113 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'113 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'114 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'114 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 34) tint) :: (Evar ___stringlit_55 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'111 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'111 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'112 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'112 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 35) tint) :: (Evar ___stringlit_56 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'109 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'109 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'110 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'110 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 36) tint) :: (Evar ___stringlit_57 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'107 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'107 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'108 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'108 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 37) tint) :: (Evar ___stringlit_58 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _r (tptr tulong)) (Etempvar _b (tptr tulong)) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'106 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'106 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 38) tint) :: (Evar ___stringlit_59 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _a (tptr tulong)) (Etempvar _b (tptr tulong)) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'105 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'105 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 39) tint) :: (Evar ___stringlit_60 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Ssequence (Sset _t'104 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _t'104 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'103 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _t'103 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'102 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _t'102 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'101 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _t'101 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'100 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'100 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 51) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'99 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a4 tulong) :: (Etempvar _t'99 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 112) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'98 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'98 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 54) tint) :: (Evar ___stringlit_62 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _R tulong) :: (Etempvar _t'3 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'4 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'97 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'97 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 57) tint) :: (Evar ___stringlit_63 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'5) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 48) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'5 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'96 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'96 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 58) tint) :: (Evar ___stringlit_64 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'6) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _t3 (Ebinop Oand (Etempvar _t'6 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t3 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'95 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'95 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 61) tint) :: (Evar ___stringlit_65 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'7) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'7 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'94 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'94 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 62) tint) :: (Evar ___stringlit_66 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'93 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _t'93 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'92 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _t'92 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'91 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _t'91 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'90 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _t'90 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'89 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a4 tulong) :: (Etempvar _t'89 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'8) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'8 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'88 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'88 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 70) tint) :: (Evar ___stringlit_63 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'9) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Etempvar _R tulong) (Econst_int (Int.repr 12) tint) tulong) :: (Etempvar _t'9 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'10) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 116) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'10 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'87 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'87 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 73) tint) :: (Evar ___stringlit_67 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'11) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _t4 (Ebinop Oand (Etempvar _t'11 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'86 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'86 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 76) tint) :: (Evar ___stringlit_68 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'12) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'12 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'85 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'85 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 77) tint) :: (Evar ___stringlit_69 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _tx (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong)) (Ssequence (Sset _t4 (Ebinop Oand (Etempvar _t4 tulong) (Ebinop Oshr (Etempvar _M tulong) (Econst_int (Int.repr 4) tint) tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _tx tulong) (Econst_int (Int.repr 4) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'84 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'84 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 80) tint) :: (Evar ___stringlit_70 (tarray tschar 42)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'83 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'83 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 81) tint) :: (Evar ___stringlit_71 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Ssequence (Sset _t'82 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _t'82 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'13) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 112) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'13 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'81 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'81 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 85) tint) :: (Evar ___stringlit_62 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'80 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _t'80 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'79 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _t'79 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'78 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _t'78 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'77 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a4 tulong) :: (Etempvar _t'77 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'14) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'14 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'76 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'76 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 91) tint) :: (Evar ___stringlit_63 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'15) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _u0 (Ebinop Oand (Etempvar _t'15 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _u0 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'75 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'75 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 94) tint) :: (Evar ___stringlit_72 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'16) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'16 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'74 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'74 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 95) tint) :: (Evar ___stringlit_66 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _u0 (Ebinop Oor (Ebinop Oshl (Etempvar _u0 tulong) (Econst_int (Int.repr 4) tint) tulong) (Etempvar _tx tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _u0 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'73 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'73 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 99) tint) :: (Evar ___stringlit_73 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u0 tulong) :: (Ebinop Oshr (Etempvar _R tulong) (Econst_int (Int.repr 4) tint) tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'17) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'17 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'72 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'72 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 102) tint) :: (Evar ___stringlit_74 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'18) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'18 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'70 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'70 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'71 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'71 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 105) tint) :: (Evar ___stringlit_75 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'19) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 61) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'19 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'69 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'69 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 106) tint) :: (Evar ___stringlit_76 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'68 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _t'68 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'67 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _t'67 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'20) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'20 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'66 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'66 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 111) tint) :: (Evar ___stringlit_77 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'65 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _t'65 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'64 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _t'64 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'63 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a4 tulong) :: (Etempvar _t'63 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'21) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'21 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'62 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'62 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 116) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'22) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oand (Etempvar _t'22 tulong) (Etempvar _M tulong) tulong) :: (Etempvar _R tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'23) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'23 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'61 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'61 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 119) tint) :: (Evar ___stringlit_74 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'24) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'24 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'60 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'60 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 120) tint) :: (Evar ___stringlit_78 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'25) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'25 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'58 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'58 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'59 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'59 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 123) tint) :: (Evar ___stringlit_79 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'26) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'26 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'57 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'57 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 124) tint) :: (Evar ___stringlit_80 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'56 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _t'56 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'55 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _t'55 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'54 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _t'54 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'27) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'27 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'53 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'53 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 130) tint) :: (Evar ___stringlit_77 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'52 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _t'52 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'51 (Ederef (Ebinop Oadd (Etempvar _b (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a4 tulong) :: (Etempvar _t'51 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'28) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'28 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'50 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'50 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 134) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'29) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _R tulong) :: (Etempvar _t'29 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'30) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'30 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'49 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'49 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 137) tint) :: (Evar ___stringlit_74 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'31) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 50) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'31 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'48 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'48 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 138) tint) :: (Evar ___stringlit_81 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'32) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'32 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'46 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'46 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'47 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'47 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 142) tint) :: (Evar ___stringlit_82 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'33) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'33 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'45 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'45 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 143) tint) :: (Evar ___stringlit_80 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'34) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Etempvar _R tulong) (Econst_int (Int.repr 12) tint) tulong) :: (Etempvar _t'34 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t3 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'35) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 100) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'35 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'44 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'44 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 147) tint) :: (Evar ___stringlit_83 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'36) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'36 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'42 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'42 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'43 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'43 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 150) tint) :: (Evar ___stringlit_84 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'37) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 48) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'37 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'41 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'41 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 151) tint) :: (Evar ___stringlit_64 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'38) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'38 tulong) (Etempvar _t4 tulong) tulong))) (Sloop (Ssequence (Sset _t'39 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'39 tulong) (Econst_int (Int.repr 49) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'40 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'40 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 154) tint) :: (Evar ___stringlit_85 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_fe_sqr_inner := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr tulong)) :: (_a, (tptr tulong)) :: nil); fn_vars := ((_c, (Tstruct _secp256k1_uint128 noattr)) :: (_d, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_a0, tulong) :: (_a1, tulong) :: (_a2, tulong) :: (_a3, tulong) :: (_a4, tulong) :: (_t3, tlong) :: (_t4, tlong) :: (_tx, tlong) :: (_u0, tlong) :: (_M, tulong) :: (_R, tulong) :: (_t'38, tulong) :: (_t'37, tint) :: (_t'36, tulong) :: (_t'35, tint) :: (_t'34, tulong) :: (_t'33, tint) :: (_t'32, tulong) :: (_t'31, tint) :: (_t'30, tint) :: (_t'29, tulong) :: (_t'28, tint) :: (_t'27, tint) :: (_t'26, tint) :: (_t'25, tulong) :: (_t'24, tint) :: (_t'23, tint) :: (_t'22, tulong) :: (_t'21, tint) :: (_t'20, tint) :: (_t'19, tint) :: (_t'18, tulong) :: (_t'17, tint) :: (_t'16, tint) :: (_t'15, tulong) :: (_t'14, tint) :: (_t'13, tint) :: (_t'12, tint) :: (_t'11, tulong) :: (_t'10, tint) :: (_t'9, tulong) :: (_t'8, tint) :: (_t'7, tint) :: (_t'6, tulong) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tulong) :: (_t'2, tint) :: (_t'1, tint) :: (_t'89, (tptr (Tstruct __IO_FILE noattr))) :: (_t'88, tulong) :: (_t'87, (tptr (Tstruct __IO_FILE noattr))) :: (_t'86, tulong) :: (_t'85, (tptr (Tstruct __IO_FILE noattr))) :: (_t'84, tulong) :: (_t'83, (tptr (Tstruct __IO_FILE noattr))) :: (_t'82, tulong) :: (_t'81, (tptr (Tstruct __IO_FILE noattr))) :: (_t'80, tulong) :: (_t'79, (tptr (Tstruct __IO_FILE noattr))) :: (_t'78, (tptr (Tstruct __IO_FILE noattr))) :: (_t'77, (tptr (Tstruct __IO_FILE noattr))) :: (_t'76, (tptr (Tstruct __IO_FILE noattr))) :: (_t'75, (tptr (Tstruct __IO_FILE noattr))) :: (_t'74, (tptr (Tstruct __IO_FILE noattr))) :: (_t'73, (tptr (Tstruct __IO_FILE noattr))) :: (_t'72, (tptr (Tstruct __IO_FILE noattr))) :: (_t'71, (tptr (Tstruct __IO_FILE noattr))) :: (_t'70, (tptr (Tstruct __IO_FILE noattr))) :: (_t'69, (tptr (Tstruct __IO_FILE noattr))) :: (_t'68, (tptr (Tstruct __IO_FILE noattr))) :: (_t'67, (tptr (Tstruct __IO_FILE noattr))) :: (_t'66, (tptr (Tstruct __IO_FILE noattr))) :: (_t'65, (tptr (Tstruct __IO_FILE noattr))) :: (_t'64, (tptr (Tstruct __IO_FILE noattr))) :: (_t'63, (tptr (Tstruct __IO_FILE noattr))) :: (_t'62, (tptr (Tstruct __IO_FILE noattr))) :: (_t'61, (tptr (Tstruct __IO_FILE noattr))) :: (_t'60, tulong) :: (_t'59, (tptr (Tstruct __IO_FILE noattr))) :: (_t'58, (tptr (Tstruct __IO_FILE noattr))) :: (_t'57, (tptr (Tstruct __IO_FILE noattr))) :: (_t'56, (tptr (Tstruct __IO_FILE noattr))) :: (_t'55, (tptr (Tstruct __IO_FILE noattr))) :: (_t'54, (tptr (Tstruct __IO_FILE noattr))) :: (_t'53, tulong) :: (_t'52, (tptr (Tstruct __IO_FILE noattr))) :: (_t'51, (tptr (Tstruct __IO_FILE noattr))) :: (_t'50, (tptr (Tstruct __IO_FILE noattr))) :: (_t'49, (tptr (Tstruct __IO_FILE noattr))) :: (_t'48, (tptr (Tstruct __IO_FILE noattr))) :: (_t'47, (tptr (Tstruct __IO_FILE noattr))) :: (_t'46, tulong) :: (_t'45, (tptr (Tstruct __IO_FILE noattr))) :: (_t'44, (tptr (Tstruct __IO_FILE noattr))) :: (_t'43, (tptr (Tstruct __IO_FILE noattr))) :: (_t'42, tulong) :: (_t'41, (tptr (Tstruct __IO_FILE noattr))) :: (_t'40, (tptr (Tstruct __IO_FILE noattr))) :: (_t'39, tulong) :: nil); fn_body := (Ssequence (Sset _a0 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a1 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a2 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a3 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a4 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _M (Econst_long (Int64.repr 4503599627370495) tulong)) (Ssequence (Sset _R (Econst_long (Int64.repr 68719492368) tulong)) (Ssequence (Sloop (Ssequence (Sset _t'88 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'88 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'89 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'89 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 164) tint) :: (Evar ___stringlit_48 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'86 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'86 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'87 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'87 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 165) tint) :: (Evar ___stringlit_50 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'84 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'84 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'85 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'85 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 166) tint) :: (Evar ___stringlit_51 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'82 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'82 tulong) (Econst_int (Int.repr 56) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'83 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'83 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 167) tint) :: (Evar ___stringlit_52 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'80 (Ederef (Ebinop Oadd (Etempvar _a (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'80 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'81 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'81 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 168) tint) :: (Evar ___stringlit_53 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _a0 tulong) (Econst_int (Int.repr 2) tint) tulong) :: (Etempvar _a3 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _a1 tulong) (Econst_int (Int.repr 2) tint) tulong) :: (Etempvar _a2 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'79 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'79 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 177) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a4 tulong) :: (Etempvar _a4 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 112) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'78 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'78 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 180) tint) :: (Evar ___stringlit_62 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _R tulong) :: (Etempvar _t'3 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'4 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'77 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'77 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 183) tint) :: (Evar ___stringlit_63 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'5) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 48) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'5 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'76 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'76 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 184) tint) :: (Evar ___stringlit_64 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'6) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _t3 (Ebinop Oand (Etempvar _t'6 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t3 tlong) (Econst_int (Int.repr 52) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'75 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'75 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 187) tint) :: (Evar ___stringlit_65 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'7) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'7 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'74 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'74 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 188) tint) :: (Evar ___stringlit_66 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _a4 (Ebinop Omul (Etempvar _a4 tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _a4 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _a1 tulong) (Econst_int (Int.repr 2) tint) tulong) :: (Etempvar _a3 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _a2 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'8) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'8 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'73 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'73 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 195) tint) :: (Evar ___stringlit_63 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'9) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Etempvar _R tulong) (Econst_int (Int.repr 12) tint) tulong) :: (Etempvar _t'9 tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'10) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 116) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'10 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'72 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'72 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 198) tint) :: (Evar ___stringlit_67 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'11) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _t4 (Ebinop Oand (Etempvar _t'11 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tlong) (Econst_int (Int.repr 52) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'71 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'71 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 201) tint) :: (Evar ___stringlit_68 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'12) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'12 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'70 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'70 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 202) tint) :: (Evar ___stringlit_69 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _tx (Ebinop Oshr (Etempvar _t4 tlong) (Econst_int (Int.repr 48) tint) tlong)) (Ssequence (Sset _t4 (Ebinop Oand (Etempvar _t4 tlong) (Ebinop Oshr (Etempvar _M tulong) (Econst_int (Int.repr 4) tint) tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _tx tlong) (Econst_int (Int.repr 4) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'69 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'69 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 205) tint) :: (Evar ___stringlit_70 (tarray tschar 42)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tlong) (Econst_int (Int.repr 48) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'68 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'68 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 206) tint) :: (Evar ___stringlit_71 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _a0 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'13) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 112) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'13 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'67 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'67 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 210) tint) :: (Evar ___stringlit_62 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _a4 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _a2 tulong) (Econst_int (Int.repr 2) tint) tulong) :: (Etempvar _a3 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'14) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'14 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'66 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'66 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 214) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'15) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _u0 (Ebinop Oand (Etempvar _t'15 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _u0 tlong) (Econst_int (Int.repr 52) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'65 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'65 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 217) tint) :: (Evar ___stringlit_72 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'16) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'16 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'64 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'64 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 218) tint) :: (Evar ___stringlit_78 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _u0 (Ebinop Oor (Ebinop Oshl (Etempvar _u0 tlong) (Econst_int (Int.repr 4) tint) tlong) (Etempvar _tx tlong) tlong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _u0 tlong) (Econst_int (Int.repr 56) tint) tlong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'63 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'63 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 222) tint) :: (Evar ___stringlit_73 (tarray tschar 43)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _u0 tlong) :: (Ebinop Oshr (Etempvar _R tulong) (Econst_int (Int.repr 4) tint) tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'17) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 113) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'17 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'62 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'62 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 225) tint) :: (Evar ___stringlit_86 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'18) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'18 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'60 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'60 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'61 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'61 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 228) tint) :: (Evar ___stringlit_75 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'19) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 61) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'19 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'59 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'59 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 229) tint) :: (Evar ___stringlit_76 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _a0 (Ebinop Omul (Etempvar _a0 tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _a1 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'20) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'20 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'58 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'58 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 234) tint) :: (Evar ___stringlit_77 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a2 tulong) :: (Etempvar _a4 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _a3 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'21) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'21 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'57 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'57 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 238) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'22) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oand (Etempvar _t'22 tulong) (Etempvar _M tulong) tulong) :: (Etempvar _R tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'23) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'23 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'56 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'56 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 241) tint) :: (Evar ___stringlit_74 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'24) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 62) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'24 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'55 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'55 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 242) tint) :: (Evar ___stringlit_78 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'25) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'25 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'53 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'53 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'54 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'54 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 245) tint) :: (Evar ___stringlit_79 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'26) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'26 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'52 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'52 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 246) tint) :: (Evar ___stringlit_80 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a0 tulong) :: (Etempvar _a2 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a1 tulong) :: (Etempvar _a1 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'27) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'27 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'51 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'51 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 251) tint) :: (Evar ___stringlit_77 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a3 tulong) :: (Etempvar _a4 tulong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'28) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 114) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'28 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'50 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'50 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 254) tint) :: (Evar ___stringlit_61 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'29) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _R tulong) :: (Etempvar _t'29 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'30) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 115) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'30 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'49 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'49 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 257) tint) :: (Evar ___stringlit_74 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'31) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 50) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'31 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'48 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'48 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 258) tint) :: (Evar ___stringlit_81 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'32) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'32 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'46 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'46 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'47 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'47 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 261) tint) :: (Evar ___stringlit_82 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'33) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 63) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'33 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'45 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'45 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 262) tint) :: (Evar ___stringlit_80 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'34) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _d (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Etempvar _R tulong) (Econst_int (Int.repr 12) tint) tulong) :: (Etempvar _t'34 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t3 tlong) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'35) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 100) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'35 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'44 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'44 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 267) tint) :: (Evar ___stringlit_83 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'36) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'36 tulong) (Etempvar _M tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 52) tint) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'42 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'42 tulong) (Econst_int (Int.repr 52) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'43 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'43 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 270) tint) :: (Evar ___stringlit_84 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Scall (Some _t'37) (Evar _secp256k1_u128_check_bits (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 48) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'37 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'41 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'41 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 271) tint) :: (Evar ___stringlit_64 (tarray tschar 61)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'38) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'38 tulong) (Etempvar _t4 tlong) tulong))) (Sloop (Ssequence (Sset _t'39 (Ederef (Ebinop Oadd (Etempvar _r (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t'39 tulong) (Econst_int (Int.repr 49) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'40 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'40 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_49 (tarray tschar 35)) :: (Econst_int (Int.repr 274) tint) :: (Evar ___stringlit_85 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_fe_verify := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_d, (tptr tulong)) :: (_m, tint) :: (_r, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'20, tint) :: (_t'19, tint) :: (_t'18, tulong) :: (_t'17, tulong) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tulong) :: (_t'13, tint) :: (_t'12, tint) :: (_t'11, tint) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tint) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _d (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5))) (Ssequence (Ssequence (Ssequence (Sset _t'19 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Etempvar _t'19 tint) (Sset _t'1 (Ecast (Econst_int (Int.repr 1) tint) tint)) (Ssequence (Sset _t'20 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sset _t'1 (Ecast (Ebinop Omul (Econst_int (Int.repr 2) tint) (Etempvar _t'20 tint) tint) tint))))) (Sset _m (Etempvar _t'1 tint))) (Ssequence (Sset _r (Econst_int (Int.repr 1) tint)) (Ssequence (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'18 tulong) (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Etempvar _m tint) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'17 tulong) (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Etempvar _m tint) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'16 tulong) (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Etempvar _m tint) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'15 tulong) (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Etempvar _m tint) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'14 tulong) (Ebinop Omul (Econst_long (Int64.repr 281474976710655) tulong) (Etempvar _m tint) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'13 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Oge (Etempvar _t'13 tint) (Econst_int (Int.repr 0) tint) tint) tint))) (Ssequence (Ssequence (Sset _t'12 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'12 tint) (Econst_int (Int.repr 2048) tint) tint) tint))) (Ssequence (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Etempvar _t'5 tint) (Ssequence (Ssequence (Sset _t'11 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Ole (Etempvar _t'11 tint) (Econst_int (Int.repr 1) tint) tint) tint))) (Ssequence (Ssequence (Sifthenelse (Etempvar _r tint) (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sset _t'2 (Ecast (Ebinop Oeq (Etempvar _t'10 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tint) tbool))) (Sset _t'2 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sset _t'3 (Ecast (Ebinop Oeq (Ebinop Oand (Ebinop Oand (Etempvar _t'7 tulong) (Etempvar _t'8 tulong) tulong) (Etempvar _t'9 tulong) tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tint) tbool))))) (Sset _t'3 (Econst_int (Int.repr 0) tint)))) (Sifthenelse (Etempvar _t'3 tint) (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Etempvar _d (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sset _r (Ebinop Oand (Etempvar _r tint) (Ebinop Olt (Etempvar _t'6 tulong) (Econst_long (Int64.repr 4503595332402223) tulong) tint) tint))) Sskip))) Sskip)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _r tint) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 53) tint) :: (Evar ___stringlit_87 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))))))))))) |}. Definition f_secp256k1_fe_normalize_weak := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t0, tulong) :: (_t1, tulong) :: (_t2, tulong) :: (_t3, tulong) :: (_t4, tulong) :: (_x, tulong) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _t0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _x (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong)) (Ssequence (Sset _t4 (Ebinop Oand (Etempvar _t4 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tulong)) (Ssequence (Sset _t0 (Ebinop Oadd (Etempvar _t0 tulong) (Ebinop Omul (Etempvar _x tulong) (Econst_long (Int64.repr 4294968273) tulong) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oadd (Etempvar _t1 tulong) (Ebinop Oshr (Etempvar _t0 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t0 (Ebinop Oand (Etempvar _t0 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oadd (Etempvar _t2 tulong) (Ebinop Oshr (Etempvar _t1 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oand (Etempvar _t1 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oadd (Etempvar _t3 tulong) (Ebinop Oshr (Etempvar _t2 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oand (Etempvar _t2 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t4 (Ebinop Oadd (Etempvar _t4 tulong) (Ebinop Oshr (Etempvar _t3 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oand (Etempvar _t3 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 49) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 131) tint) :: (Evar ___stringlit_89 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t0 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t1 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t2 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t3 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Etempvar _t4 tulong)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))))))))))))))))))))) |}. Definition f_secp256k1_fe_normalize_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t0, tulong) :: (_t1, tulong) :: (_t2, tulong) :: (_t3, tulong) :: (_t4, tulong) :: (_m, tulong) :: (_x, tulong) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _t0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _x (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong)) (Ssequence (Sset _t4 (Ebinop Oand (Etempvar _t4 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tulong)) (Ssequence (Sset _t0 (Ebinop Oadd (Etempvar _t0 tulong) (Ebinop Omul (Etempvar _x tulong) (Econst_long (Int64.repr 4294968273) tulong) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oadd (Etempvar _t1 tulong) (Ebinop Oshr (Etempvar _t0 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t0 (Ebinop Oand (Etempvar _t0 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oadd (Etempvar _t2 tulong) (Ebinop Oshr (Etempvar _t1 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oand (Etempvar _t1 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _m (Etempvar _t1 tulong)) (Ssequence (Sset _t3 (Ebinop Oadd (Etempvar _t3 tulong) (Ebinop Oshr (Etempvar _t2 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oand (Etempvar _t2 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _m (Ebinop Oand (Etempvar _m tulong) (Etempvar _t2 tulong) tulong)) (Ssequence (Sset _t4 (Ebinop Oadd (Etempvar _t4 tulong) (Ebinop Oshr (Etempvar _t3 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oand (Etempvar _t3 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _m (Ebinop Oand (Etempvar _m tulong) (Etempvar _t3 tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 49) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 156) tint) :: (Evar ___stringlit_89 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sset _x (Ebinop Oor (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong) (Ebinop Oand (Ebinop Oand (Ebinop Oeq (Etempvar _t4 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tint) (Ebinop Oeq (Etempvar _m tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tint) tint) (Ebinop Oge (Etempvar _t0 tulong) (Econst_long (Int64.repr 4503595332402223) tulong) tint) tint) tulong)) (Ssequence (Sifthenelse (Etempvar _x tulong) (Ssequence (Sset _t0 (Ebinop Oadd (Etempvar _t0 tulong) (Econst_long (Int64.repr 4294968273) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oadd (Etempvar _t1 tulong) (Ebinop Oshr (Etempvar _t0 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t0 (Ebinop Oand (Etempvar _t0 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oadd (Etempvar _t2 tulong) (Ebinop Oshr (Etempvar _t1 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oand (Etempvar _t1 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oadd (Etempvar _t3 tulong) (Ebinop Oshr (Etempvar _t2 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oand (Etempvar _t2 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _t4 (Ebinop Oadd (Etempvar _t4 tulong) (Ebinop Oshr (Etempvar _t3 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oand (Etempvar _t3 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong) (Etempvar _x tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 170) tint) :: (Evar ___stringlit_90 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sset _t4 (Ebinop Oand (Etempvar _t4 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tulong)))))))))))) Sskip) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t0 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t1 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t2 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t3 tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Etempvar _t4 tulong)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_fe_normalizes_to_zero_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t0, tulong) :: (_t1, tulong) :: (_t2, tulong) :: (_t3, tulong) :: (_t4, tulong) :: (_z0, tulong) :: (_z1, tulong) :: (_x, tulong) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _t0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _x (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 48) tint) tulong)) (Ssequence (Sset _t0 (Ebinop Oadd (Etempvar _t0 tulong) (Ebinop Omul (Etempvar _x tulong) (Econst_long (Int64.repr 4294968273) tulong) tulong) tulong)) (Ssequence (Sset _z0 (Ebinop Oand (Etempvar _t0 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _z1 (Ebinop Oxor (Etempvar _z0 tulong) (Econst_long (Int64.repr 4294968272) tulong) tulong)) (Ssequence (Sifthenelse (Ebinop Oand (Ebinop One (Etempvar _z0 tulong) (Econst_long (Int64.repr 0) tulong) tint) (Ebinop One (Etempvar _z1 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) (Ssequence (Sset _t1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t4 (Ebinop Oand (Etempvar _t4 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oadd (Etempvar _t1 tulong) (Ebinop Oshr (Etempvar _t0 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oadd (Etempvar _t2 tulong) (Ebinop Oshr (Etempvar _t1 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oand (Etempvar _t1 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _z0 (Ebinop Oor (Etempvar _z0 tulong) (Etempvar _t1 tulong) tulong)) (Ssequence (Sset _z1 (Ebinop Oand (Etempvar _z1 tulong) (Etempvar _t1 tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oadd (Etempvar _t3 tulong) (Ebinop Oshr (Etempvar _t2 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oand (Etempvar _t2 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _z0 (Ebinop Oor (Etempvar _z0 tulong) (Etempvar _t2 tulong) tulong)) (Ssequence (Sset _z1 (Ebinop Oand (Etempvar _z1 tulong) (Etempvar _t2 tulong) tulong)) (Ssequence (Sset _t4 (Ebinop Oadd (Etempvar _t4 tulong) (Ebinop Oshr (Etempvar _t3 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oand (Etempvar _t3 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong)) (Ssequence (Sset _z0 (Ebinop Oor (Etempvar _z0 tulong) (Etempvar _t3 tulong) tulong)) (Ssequence (Sset _z1 (Ebinop Oand (Etempvar _z1 tulong) (Etempvar _t3 tulong) tulong)) (Ssequence (Sset _z0 (Ebinop Oor (Etempvar _z0 tulong) (Etempvar _t4 tulong) tulong)) (Ssequence (Sset _z1 (Ebinop Oand (Etempvar _z1 tulong) (Ebinop Oxor (Etempvar _t4 tulong) (Econst_long (Int64.repr 4222124650659840) tulong) tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 49) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 246) tint) :: (Evar ___stringlit_89 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sreturn (Some (Ebinop Oor (Ebinop Oeq (Etempvar _z0 tulong) (Econst_int (Int.repr 0) tint) tint) (Ebinop Oeq (Etempvar _z1 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tint) tint)))))))))))))))))))))))))))))) |}. Definition f_secp256k1_fe_set_int := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, tint) :: nil); fn_vars := nil; fn_temps := ((_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tint) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Ole (Econst_int (Int.repr 0) tint) (Etempvar _a tint) tint) (Sset _t'1 (Ecast (Ebinop Ole (Etempvar _a tint) (Econst_int (Int.repr 32767) tint) tint) tbool)) (Sset _t'1 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 252) tint) :: (Evar ___stringlit_91 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _a tint)) (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'2 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Etempvar _t'2 tulong))) (Sset _t'3 (Ecast (Etempvar _t'2 tulong) tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t'3 tulong))) (Sset _t'4 (Ecast (Etempvar _t'3 tulong) tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Ebinop One (Etempvar _a tint) (Econst_int (Int.repr 0) tint) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))) |}. Definition f_secp256k1_fe_is_zero := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t, (tptr tulong)) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: (_t'6, tint) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sset _t (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5))) (Ssequence (Sloop (Ssequence (Sset _t'6 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'6 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 265) tint) :: (Evar ___stringlit_92 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Etempvar _t (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Etempvar _t (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Etempvar _t (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Etempvar _t (tptr tulong)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Etempvar _t (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sreturn (Some (Ebinop Oeq (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Etempvar _t'1 tulong) (Etempvar _t'2 tulong) tulong) (Etempvar _t'3 tulong) tulong) (Etempvar _t'4 tulong) tulong) (Etempvar _t'5 tulong) tulong) (Econst_int (Int.repr 0) tint) tint))))))))))) |}. Definition f_secp256k1_fe_is_odd := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, tint) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 273) tint) :: (Evar ___stringlit_92 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sreturn (Some (Ebinop Oand (Etempvar _t'1 tulong) (Econst_int (Int.repr 1) tint) tulong)))))) |}. Definition f_secp256k1_fe_clear := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_i, tint) :: nil); fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sset _i (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Econst_int (Int.repr 5) tint) tint) Sskip Sbreak) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Etempvar _i tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))))) |}. Definition f_secp256k1_fe_set_b32 := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr tuchar)) :: nil); fn_vars := nil; fn_temps := ((_ret, tint) :: (_t'39, tuchar) :: (_t'38, tuchar) :: (_t'37, tuchar) :: (_t'36, tuchar) :: (_t'35, tuchar) :: (_t'34, tuchar) :: (_t'33, tuchar) :: (_t'32, tuchar) :: (_t'31, tuchar) :: (_t'30, tuchar) :: (_t'29, tuchar) :: (_t'28, tuchar) :: (_t'27, tuchar) :: (_t'26, tuchar) :: (_t'25, tuchar) :: (_t'24, tuchar) :: (_t'23, tuchar) :: (_t'22, tuchar) :: (_t'21, tuchar) :: (_t'20, tuchar) :: (_t'19, tuchar) :: (_t'18, tuchar) :: (_t'17, tuchar) :: (_t'16, tuchar) :: (_t'15, tuchar) :: (_t'14, tuchar) :: (_t'13, tuchar) :: (_t'12, tuchar) :: (_t'11, tuchar) :: (_t'10, tuchar) :: (_t'9, tuchar) :: (_t'8, tuchar) :: (_t'7, tuchar) :: (_t'6, tuchar) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'33 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'34 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'35 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'36 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'37 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'38 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'39 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'33 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'34 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'35 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'36 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'37 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'38 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong) (Ebinop Oshl (Ecast (Ebinop Oand (Etempvar _t'39 tuchar) (Econst_int (Int.repr 15) tint) tint) tulong) (Econst_int (Int.repr 48) tint) tulong) tulong))))))))) (Ssequence (Ssequence (Sset _t'26 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'27 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'28 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'29 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'30 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'31 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'32 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Ebinop Oand (Ebinop Oshr (Etempvar _t'26 tuchar) (Econst_int (Int.repr 4) tint) tint) (Econst_int (Int.repr 15) tint) tint) tulong) (Ebinop Oshl (Ecast (Etempvar _t'27 tuchar) tulong) (Econst_int (Int.repr 4) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'28 tuchar) tulong) (Econst_int (Int.repr 12) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'29 tuchar) tulong) (Econst_int (Int.repr 20) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'30 tuchar) tulong) (Econst_int (Int.repr 28) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'31 tuchar) tulong) (Econst_int (Int.repr 36) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'32 tuchar) tulong) (Econst_int (Int.repr 44) tint) tulong) tulong))))))))) (Ssequence (Ssequence (Sset _t'19 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'20 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'21 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'22 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'23 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'24 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'25 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'19 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'20 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'21 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'22 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'23 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'24 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong) (Ebinop Oshl (Ecast (Ebinop Oand (Etempvar _t'25 tuchar) (Econst_int (Int.repr 15) tint) tint) tulong) (Econst_int (Int.repr 48) tint) tulong) tulong))))))))) (Ssequence (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Ebinop Oand (Ebinop Oshr (Etempvar _t'12 tuchar) (Econst_int (Int.repr 4) tint) tint) (Econst_int (Int.repr 15) tint) tint) tulong) (Ebinop Oshl (Ecast (Etempvar _t'13 tuchar) tulong) (Econst_int (Int.repr 4) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'14 tuchar) tulong) (Econst_int (Int.repr 12) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'15 tuchar) tulong) (Econst_int (Int.repr 20) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'16 tuchar) tulong) (Econst_int (Int.repr 28) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'17 tuchar) tulong) (Econst_int (Int.repr 36) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'18 tuchar) tulong) (Econst_int (Int.repr 44) tint) tulong) tulong))))))))) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Etempvar _a (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'6 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'7 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'8 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'9 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'10 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'11 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong)))))))) (Ssequence (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sset _ret (Eunop Onotbool (Ebinop Oand (Ebinop Oand (Ebinop Oeq (Etempvar _t'1 tulong) (Econst_long (Int64.repr 281474976710655) tulong) tint) (Ebinop Oeq (Ebinop Oand (Ebinop Oand (Etempvar _t'2 tulong) (Etempvar _t'3 tulong) tulong) (Etempvar _t'4 tulong) tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tint) tint) (Ebinop Oge (Etempvar _t'5 tulong) (Econst_long (Int64.repr 4503595332402223) tulong) tint) tint) tint))))))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sifthenelse (Etempvar _ret tint) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint))) (Sreturn (Some (Etempvar _ret tint))))))))))) |}. Definition f_secp256k1_fe_get_b32 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr tuchar)) :: (_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'36, (tptr (Tstruct __IO_FILE noattr))) :: (_t'35, tint) :: (_t'34, tulong) :: (_t'33, tulong) :: (_t'32, tulong) :: (_t'31, tulong) :: (_t'30, tulong) :: (_t'29, tulong) :: (_t'28, tulong) :: (_t'27, tulong) :: (_t'26, tulong) :: (_t'25, tulong) :: (_t'24, tulong) :: (_t'23, tulong) :: (_t'22, tulong) :: (_t'21, tulong) :: (_t'20, tulong) :: (_t'19, tulong) :: (_t'18, tulong) :: (_t'17, tulong) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tulong) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tulong) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'35 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'35 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'36 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'36 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 363) tint) :: (Evar ___stringlit_92 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Sset _t'34 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'34 tulong) (Econst_int (Int.repr 40) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'33 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'33 tulong) (Econst_int (Int.repr 32) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'32 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'32 tulong) (Econst_int (Int.repr 24) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'31 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'31 tulong) (Econst_int (Int.repr 16) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'30 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'30 tulong) (Econst_int (Int.repr 8) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'29 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Etempvar _t'29 tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'28 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'28 tulong) (Econst_int (Int.repr 44) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'27 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'27 tulong) (Econst_int (Int.repr 36) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'26 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'26 tulong) (Econst_int (Int.repr 28) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'25 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'25 tulong) (Econst_int (Int.repr 20) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'24 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'24 tulong) (Econst_int (Int.repr 12) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'23 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'23 tulong) (Econst_int (Int.repr 4) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'21 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'22 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar) (Ebinop Oor (Ebinop Oand (Ebinop Oshr (Etempvar _t'21 tulong) (Econst_int (Int.repr 48) tint) tulong) (Econst_int (Int.repr 15) tint) tulong) (Ebinop Oshl (Ebinop Oand (Etempvar _t'22 tulong) (Econst_int (Int.repr 15) tint) tulong) (Econst_int (Int.repr 4) tint) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'20 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'20 tulong) (Econst_int (Int.repr 40) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'19 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'19 tulong) (Econst_int (Int.repr 32) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'18 tulong) (Econst_int (Int.repr 24) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'17 tulong) (Econst_int (Int.repr 16) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'16 tulong) (Econst_int (Int.repr 8) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Etempvar _t'15 tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'14 tulong) (Econst_int (Int.repr 44) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'13 tulong) (Econst_int (Int.repr 36) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'12 tulong) (Econst_int (Int.repr 28) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'11 tulong) (Econst_int (Int.repr 20) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'10 tulong) (Econst_int (Int.repr 12) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'9 tulong) (Econst_int (Int.repr 4) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar) (Ebinop Oor (Ebinop Oand (Ebinop Oshr (Etempvar _t'7 tulong) (Econst_int (Int.repr 48) tint) tulong) (Econst_int (Int.repr 15) tint) tulong) (Ebinop Oshl (Ebinop Oand (Etempvar _t'8 tulong) (Econst_int (Int.repr 15) tint) tulong) (Econst_int (Int.repr 4) tint) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'6 tulong) (Econst_int (Int.repr 40) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'5 tulong) (Econst_int (Int.repr 32) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'4 tulong) (Econst_int (Int.repr 24) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'3 tulong) (Econst_int (Int.repr 16) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Ebinop Oshr (Etempvar _t'2 tulong) (Econst_int (Int.repr 8) tint) tulong) (Econst_int (Int.repr 255) tint) tulong))) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _r (tptr tuchar)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar) (Ebinop Oand (Etempvar _t'1 tulong) (Econst_int (Int.repr 255) tint) tulong)))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_fe_negate := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: (_m, tint) :: nil); fn_vars := nil; fn_temps := ((_t'10, (tptr (Tstruct __IO_FILE noattr))) :: (_t'9, tint) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: (_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'9 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'9 tint) (Etempvar _m tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'10 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'10 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 402) tint) :: (Evar ___stringlit_93 (tarray tschar 41)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503595332402223) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Econst_int (Int.repr 2) tint) tulong) (Etempvar _m tint) tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 404) tint) :: (Evar ___stringlit_94 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Econst_int (Int.repr 2) tint) tulong) (Etempvar _m tint) tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 405) tint) :: (Evar ___stringlit_95 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 281474976710655) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 281474976710655) tulong) (Econst_int (Int.repr 2) tint) tulong) (Etempvar _m tint) tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 406) tint) :: (Evar ___stringlit_96 (tarray tschar 86)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Osub (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503595332402223) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Etempvar _t'5 tulong) tulong))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Osub (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Etempvar _t'4 tulong) tulong))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Osub (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Etempvar _t'3 tulong) tulong))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Osub (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 4503599627370495) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Etempvar _t'2 tulong) tulong))) (Ssequence (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Osub (Ebinop Omul (Ebinop Omul (Econst_long (Int64.repr 281474976710655) tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint) tulong) (Etempvar _t'1 tulong) tulong))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Ebinop Oadd (Etempvar _m tint) (Econst_int (Int.repr 1) tint) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)))))))))))))) |}. Definition f_secp256k1_fe_mul_int := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, tint) :: nil); fn_vars := nil; fn_temps := ((_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Omul (Etempvar _t'6 tulong) (Etempvar _a tint) tulong))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Omul (Etempvar _t'5 tulong) (Etempvar _a tint) tulong))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Omul (Etempvar _t'4 tulong) (Etempvar _a tint) tulong))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Omul (Etempvar _t'3 tulong) (Etempvar _a tint) tulong))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Omul (Etempvar _t'2 tulong) (Etempvar _a tint) tulong))) (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Ebinop Omul (Etempvar _t'1 tint) (Etempvar _a tint) tint))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))))) |}. Definition f_secp256k1_fe_add_int := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, tint) :: nil); fn_vars := nil; fn_temps := ((_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, tulong) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _a tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 436) tint) :: (Evar ___stringlit_97 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _a tint) (Econst_int (Int.repr 32767) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 437) tint) :: (Evar ___stringlit_98 (tarray tschar 35)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'2 tulong) (Etempvar _a tint) tulong))) (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Ebinop Oadd (Etempvar _t'1 tint) (Econst_int (Int.repr 1) tint) tint))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)))))))) |}. Definition f_secp256k1_fe_add := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'12, tulong) :: (_t'11, tulong) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'11 tulong) (Etempvar _t'12 tulong) tulong)))) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'9 tulong) (Etempvar _t'10 tulong) tulong)))) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'7 tulong) (Etempvar _t'8 tulong) tulong)))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'5 tulong) (Etempvar _t'6 tulong) tulong)))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oadd (Etempvar _t'3 tulong) (Etempvar _t'4 tulong) tulong)))) (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Ebinop Oadd (Etempvar _t'1 tint) (Etempvar _t'2 tint) tint)))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)))))))))) |}. Definition f_secp256k1_fe_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: (_b, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, tint) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'5 tint) (Econst_int (Int.repr 8) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 465) tint) :: (Evar ___stringlit_99 (tarray tschar 41)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _b (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'3 tint) (Econst_int (Int.repr 8) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 466) tint) :: (Evar ___stringlit_100 (tarray tschar 41)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _b (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _r (tptr (Tstruct __2380 noattr))) (Etempvar _b (tptr (Tstruct __2380 noattr))) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 469) tint) :: (Evar ___stringlit_59 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _a (tptr (Tstruct __2380 noattr))) (Etempvar _b (tptr (Tstruct __2380 noattr))) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 470) tint) :: (Evar ___stringlit_60 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_mul_inner (Tfunction (Tcons (tptr tulong) (Tcons (tptr tulong) (Tcons (tptr tulong) Tnil))) tvoid cc_default)) ((Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) :: (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) :: (Efield (Ederef (Etempvar _b (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) :: nil)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))))))) |}. Definition f_secp256k1_fe_sqr := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'1 tint) (Econst_int (Int.repr 8) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 482) tint) :: (Evar ___stringlit_99 (tarray tschar 41)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr_inner (Tfunction (Tcons (tptr tulong) (Tcons (tptr tulong) Tnil)) tvoid cc_default)) ((Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) :: (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) :: nil)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))) |}. Definition f_secp256k1_fe_cmov := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: (_flag, tint) :: nil); fn_vars := nil; fn_temps := ((_mask0, tulong) :: (_mask1, tulong) :: (_t'12, tulong) :: (_t'11, tulong) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sset _mask0 (Ebinop Oadd (Etempvar _flag tint) (Eunop Onotint (Ecast (Econst_int (Int.repr 0) tint) tulong) tulong) tulong)) (Ssequence (Sset _mask1 (Eunop Onotint (Etempvar _mask0 tulong) tulong)) (Ssequence (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oand (Etempvar _t'11 tulong) (Etempvar _mask0 tulong) tulong) (Ebinop Oand (Etempvar _t'12 tulong) (Etempvar _mask1 tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oand (Etempvar _t'9 tulong) (Etempvar _mask0 tulong) tulong) (Ebinop Oand (Etempvar _t'10 tulong) (Etempvar _mask1 tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oand (Etempvar _t'7 tulong) (Etempvar _mask0 tulong) tulong) (Ebinop Oand (Etempvar _t'8 tulong) (Etempvar _mask1 tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oand (Etempvar _t'5 tulong) (Etempvar _mask0 tulong) tulong) (Ebinop Oand (Etempvar _t'6 tulong) (Etempvar _mask1 tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oand (Etempvar _t'3 tulong) (Etempvar _mask0 tulong) tulong) (Ebinop Oand (Etempvar _t'4 tulong) (Etempvar _mask1 tulong) tulong) tulong)))) (Sifthenelse (Etempvar _flag tint) (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Etempvar _t'2 tint))) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Etempvar _t'1 tint)))) Sskip)))))))) |}. Definition f_secp256k1_fe_half := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t0, tulong) :: (_t1, tulong) :: (_t2, tulong) :: (_t3, tulong) :: (_t4, tulong) :: (_one, tulong) :: (_mask, tulong) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sset _t0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _one (Ecast (Econst_int (Int.repr 1) tint) tulong)) (Ssequence (Sset _mask (Ebinop Oshr (Eunop Oneg (Ebinop Oand (Etempvar _t0 tulong) (Etempvar _one tulong) tulong) tulong) (Econst_int (Int.repr 12) tint) tulong)) (Ssequence (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sloop (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _t'3 tint) (Econst_int (Int.repr 32) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 520) tint) :: (Evar ___stringlit_101 (tarray tschar 41)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sset _t0 (Ebinop Oadd (Etempvar _t0 tulong) (Ebinop Oand (Econst_long (Int64.repr 4503595332402223) tulong) (Etempvar _mask tulong) tulong) tulong)) (Ssequence (Sset _t1 (Ebinop Oadd (Etempvar _t1 tulong) (Etempvar _mask tulong) tulong)) (Ssequence (Sset _t2 (Ebinop Oadd (Etempvar _t2 tulong) (Etempvar _mask tulong) tulong)) (Ssequence (Sset _t3 (Ebinop Oadd (Etempvar _t3 tulong) (Etempvar _mask tulong) tulong)) (Ssequence (Sset _t4 (Ebinop Oadd (Etempvar _t4 tulong) (Ebinop Oshr (Etempvar _mask tulong) (Econst_int (Int.repr 4) tint) tulong) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _t0 tulong) (Etempvar _one tulong) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 539) tint) :: (Evar ___stringlit_102 (tarray tschar 39)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oadd (Ebinop Oshr (Etempvar _t0 tulong) (Econst_int (Int.repr 1) tint) tulong) (Ebinop Oshl (Ebinop Oand (Etempvar _t1 tulong) (Etempvar _one tulong) tulong) (Econst_int (Int.repr 51) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oadd (Ebinop Oshr (Etempvar _t1 tulong) (Econst_int (Int.repr 1) tint) tulong) (Ebinop Oshl (Ebinop Oand (Etempvar _t2 tulong) (Etempvar _one tulong) tulong) (Econst_int (Int.repr 51) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oadd (Ebinop Oshr (Etempvar _t2 tulong) (Econst_int (Int.repr 1) tint) tulong) (Ebinop Oshl (Ebinop Oand (Etempvar _t3 tulong) (Etempvar _one tulong) tulong) (Econst_int (Int.repr 51) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oadd (Ebinop Oshr (Etempvar _t3 tulong) (Econst_int (Int.repr 1) tint) tulong) (Ebinop Oshl (Ebinop Oand (Etempvar _t4 tulong) (Etempvar _one tulong) tulong) (Econst_int (Int.repr 51) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oshr (Etempvar _t4 tulong) (Econst_int (Int.repr 1) tint) tulong)) (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Ebinop Oadd (Ebinop Oshr (Etempvar _t'1 tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 1) tint) tint))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)))))))))))))))))))))))) |}. Definition f_secp256k1_fe_to_storage := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2382 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'10, (tptr (Tstruct __IO_FILE noattr))) :: (_t'9, tint) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'9 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'9 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'10 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'10 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 593) tint) :: (Evar ___stringlit_92 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oor (Etempvar _t'7 tulong) (Ebinop Oshl (Etempvar _t'8 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _t'5 tulong) (Econst_int (Int.repr 12) tint) tulong) (Ebinop Oshl (Etempvar _t'6 tulong) (Econst_int (Int.repr 40) tint) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _t'3 tulong) (Econst_int (Int.repr 24) tint) tulong) (Ebinop Oshl (Etempvar _t'4 tulong) (Econst_int (Int.repr 28) tint) tulong) tulong)))) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _t'1 tulong) (Econst_int (Int.repr 36) tint) tulong) (Ebinop Oshl (Etempvar _t'2 tulong) (Econst_int (Int.repr 16) tint) tulong) tulong)))))))) |}. Definition f_secp256k1_fe_from_storage := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2382 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'8 tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong))) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _t'6 tulong) (Econst_int (Int.repr 52) tint) tulong) (Ebinop Oand (Ebinop Oshl (Etempvar _t'7 tulong) (Econst_int (Int.repr 12) tint) tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _t'4 tulong) (Econst_int (Int.repr 40) tint) tulong) (Ebinop Oand (Ebinop Oshl (Etempvar _t'5 tulong) (Econst_int (Int.repr 24) tint) tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _t'2 tulong) (Econst_int (Int.repr 28) tint) tulong) (Ebinop Oand (Ebinop Oshl (Etempvar _t'3 tulong) (Econst_int (Int.repr 36) tint) tulong) (Econst_long (Int64.repr 4503599627370495) tulong) tulong) tulong)))) (Ssequence (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2382 noattr))) (Tstruct __2382 noattr)) _n (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oshr (Etempvar _t'1 tulong) (Econst_int (Int.repr 16) tint) tulong))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil))))))))) |}. Definition f_secp256k1_fe_from_signed62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil); fn_vars := nil; fn_temps := ((_M52, tulong) :: (_a0, tulong) :: (_a1, tulong) :: (_a2, tulong) :: (_a3, tulong) :: (_a4, tulong) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _M52 (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 12) tint) tulong)) (Ssequence (Sset _a0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a0 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 621) tint) :: (Evar ___stringlit_103 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a1 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 622) tint) :: (Evar ___stringlit_104 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a2 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 623) tint) :: (Evar ___stringlit_105 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a3 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 624) tint) :: (Evar ___stringlit_106 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a4 tulong) (Econst_int (Int.repr 8) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 625) tint) :: (Evar ___stringlit_107 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _a0 tulong) (Etempvar _M52 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a0 tulong) (Econst_int (Int.repr 52) tint) tulong) (Ebinop Oshl (Etempvar _a1 tulong) (Econst_int (Int.repr 10) tint) tulong) tulong) (Etempvar _M52 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a1 tulong) (Econst_int (Int.repr 42) tint) tulong) (Ebinop Oshl (Etempvar _a2 tulong) (Econst_int (Int.repr 20) tint) tulong) tulong) (Etempvar _M52 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a2 tulong) (Econst_int (Int.repr 32) tint) tulong) (Ebinop Oshl (Etempvar _a3 tulong) (Econst_int (Int.repr 30) tint) tulong) tulong) (Etempvar _M52 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _a3 tulong) (Econst_int (Int.repr 22) tint) tulong) (Ebinop Oshl (Etempvar _a4 tulong) (Econst_int (Int.repr 40) tint) tulong) tulong)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Scall None (Evar _secp256k1_fe_verify (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)))))))))))))))))))) |}. Definition f_secp256k1_fe_to_signed62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_M62, tulong) :: (_a0, tulong) :: (_a1, tulong) :: (_a2, tulong) :: (_a3, tulong) :: (_a4, tulong) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sset _M62 (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Sset _a0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sloop (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) _normalized tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 645) tint) :: (Evar ___stringlit_92 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Etempvar _a0 tulong) (Ebinop Oshl (Etempvar _a1 tulong) (Econst_int (Int.repr 52) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a1 tulong) (Econst_int (Int.repr 10) tint) tulong) (Ebinop Oshl (Etempvar _a2 tulong) (Econst_int (Int.repr 42) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a2 tulong) (Econst_int (Int.repr 20) tint) tulong) (Ebinop Oshl (Etempvar _a3 tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a3 tulong) (Econst_int (Int.repr 30) tint) tulong) (Ebinop Oshl (Etempvar _a4 tulong) (Econst_int (Int.repr 22) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Ebinop Oshr (Etempvar _a4 tulong) (Econst_int (Int.repr 40) tint) tulong))))))))))))) |}. Definition v_secp256k1_const_modinfo_fe := {| gvar_info := (Tstruct _secp256k1_modinv64_modinfo noattr); gvar_init := (Init_int64 (Int64.repr (-4294968273)) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 256) :: Init_int64 (Int64.repr 2866531139136965327) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_fe_inv_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_x, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_tmp, (Tstruct __2380 noattr)) :: (_s, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sassign (Evar _tmp (Tstruct __2380 noattr)) (Ederef (Etempvar _x (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_to_signed62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _tmp (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_modinv64_var (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_modinfo noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _secp256k1_const_modinfo_fe (Tstruct _secp256k1_modinv64_modinfo noattr)) (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_from_signed62 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil)) (Sloop (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_normalizes_to_zero (Tfunction Tnil tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) (Scall (Some _t'2) (Evar _secp256k1_fe_normalizes_to_zero (Tfunction Tnil tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) ((Eaddrof (Evar _tmp (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'1 tint) (Etempvar _t'2 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_88 (tarray tschar 28)) :: (Econst_int (Int.repr 688) tint) :: (Evar ___stringlit_108 (tarray tschar 99)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) |}. Definition f_secp256k1_fe_equal_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2380 noattr))) :: (_b, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_na, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _na (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _a (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _b (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _na (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))) |}. Definition f_secp256k1_fe_sqrt_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_x2, (Tstruct __2380 noattr)) :: (_x3, (Tstruct __2380 noattr)) :: (_x6, (Tstruct __2380 noattr)) :: (_x9, (Tstruct __2380 noattr)) :: (_x11, (Tstruct __2380 noattr)) :: (_x22, (Tstruct __2380 noattr)) :: (_x44, (Tstruct __2380 noattr)) :: (_x88, (Tstruct __2380 noattr)) :: (_x176, (Tstruct __2380 noattr)) :: (_x220, (Tstruct __2380 noattr)) :: (_x223, (Tstruct __2380 noattr)) :: (_t1, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_j, tint) :: (_t'1, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _r (tptr (Tstruct __2380 noattr))) (Etempvar _a (tptr (Tstruct __2380 noattr))) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_110 (tarray tschar 23)) :: (Econst_int (Int.repr 47) tint) :: (Evar ___stringlit_109 (tarray tschar 30)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x6 (Tstruct __2380 noattr)) (Evar _x3 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 3) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x9 (Tstruct __2380 noattr)) (Evar _x6 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 3) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x9 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x9 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x9 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x9 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x11 (Tstruct __2380 noattr)) (Evar _x9 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 2) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x11 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x11 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x11 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x11 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x22 (Tstruct __2380 noattr)) (Evar _x11 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 11) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x11 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x44 (Tstruct __2380 noattr)) (Evar _x22 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 22) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x44 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x44 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x44 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x44 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x88 (Tstruct __2380 noattr)) (Evar _x44 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 44) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x88 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x88 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x88 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x88 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x44 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x176 (Tstruct __2380 noattr)) (Evar _x88 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 88) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x176 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x176 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x176 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x176 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x88 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x220 (Tstruct __2380 noattr)) (Evar _x176 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 44) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x220 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x220 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x220 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x220 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x44 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x223 (Tstruct __2380 noattr)) (Evar _x220 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 3) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x223 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x223 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x223 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x223 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _t1 (Tstruct __2380 noattr)) (Evar _x223 (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 23) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Sset _j (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _j tint) (Econst_int (Int.repr 6) tint) tint) Sskip Sbreak) (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) (Sset _j (Ebinop Oadd (Etempvar _j tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_equal_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _t1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _a (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))))))))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_scalar_set_int := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_v, tuint) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _v tuint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint))))) |}. Definition f_secp256k1_scalar_get_bits := {| fn_return := tuint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2843 noattr))) :: (_offset, tuint) :: (_count, tuint) :: nil); fn_vars := nil; fn_temps := ((_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Ebinop Osub (Ebinop Oadd (Etempvar _offset tuint) (Etempvar _count tuint) tuint) (Econst_int (Int.repr 1) tint) tuint) (Econst_int (Int.repr 6) tint) tuint) (Ebinop Oshr (Etempvar _offset tuint) (Econst_int (Int.repr 6) tint) tuint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 45) tint) :: (Evar ___stringlit_111 (tarray tschar 64)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Ebinop Oshr (Etempvar _offset tuint) (Econst_int (Int.repr 6) tint) tuint) (tptr tulong)) tulong)) (Sreturn (Some (Ebinop Oand (Ebinop Oshr (Etempvar _t'1 tulong) (Ebinop Oand (Etempvar _offset tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) (Ebinop Osub (Ebinop Oshl (Ecast (Econst_int (Int.repr 1) tint) tulong) (Etempvar _count tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong))))) |}. Definition f_secp256k1_scalar_get_bits_var := {| fn_return := tuint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2843 noattr))) :: (_offset, tuint) :: (_count, tuint) :: nil); fn_vars := nil; fn_temps := ((_t'1, tuint) :: (_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, tulong) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _count tuint) (Econst_int (Int.repr 32) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 50) tint) :: (Evar ___stringlit_113 (tarray tschar 34)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Ebinop Oadd (Etempvar _offset tuint) (Etempvar _count tuint) tuint) (Econst_int (Int.repr 256) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 51) tint) :: (Evar ___stringlit_114 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sifthenelse (Ebinop Oeq (Ebinop Oshr (Ebinop Osub (Ebinop Oadd (Etempvar _offset tuint) (Etempvar _count tuint) tuint) (Econst_int (Int.repr 1) tint) tuint) (Econst_int (Int.repr 6) tint) tuint) (Ebinop Oshr (Etempvar _offset tuint) (Econst_int (Int.repr 6) tint) tuint) tint) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_get_bits (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint (Tcons tuint Tnil))) tuint cc_default)) ((Etempvar _a (tptr (Tstruct __2843 noattr))) :: (Etempvar _offset tuint) :: (Etempvar _count tuint) :: nil)) (Sreturn (Some (Etempvar _t'1 tuint)))) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Ebinop Oadd (Ebinop Oshr (Etempvar _offset tuint) (Econst_int (Int.repr 6) tint) tuint) (Econst_int (Int.repr 1) tint) tuint) (Econst_int (Int.repr 4) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 55) tint) :: (Evar ___stringlit_115 (tarray tschar 45)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Ebinop Oshr (Etempvar _offset tuint) (Econst_int (Int.repr 6) tint) tuint) (tptr tulong)) tulong)) (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Ebinop Oadd (Ebinop Oshr (Etempvar _offset tuint) (Econst_int (Int.repr 6) tint) tuint) (Econst_int (Int.repr 1) tint) tuint) (tptr tulong)) tulong)) (Sreturn (Some (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _t'2 tulong) (Ebinop Oand (Etempvar _offset tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) (Ebinop Oshl (Etempvar _t'3 tulong) (Ebinop Osub (Econst_int (Int.repr 64) tint) (Ebinop Oand (Etempvar _offset tuint) (Econst_int (Int.repr 63) tint) tuint) tuint) tulong) tulong) (Ebinop Osub (Ebinop Oshl (Ecast (Econst_int (Int.repr 1) tint) tulong) (Etempvar _count tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong))))))))) |}. Definition f_secp256k1_scalar_check_overflow := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := nil; fn_temps := ((_yes, tint) :: (_no, tint) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sset _yes (Econst_int (Int.repr 0) tint)) (Ssequence (Sset _no (Econst_int (Int.repr 0) tint)) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sset _no (Ebinop Oor (Etempvar _no tint) (Ebinop Olt (Etempvar _t'6 tulong) (Ecast (Econst_long (Int64.repr (-1)) tulong) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sset _no (Ebinop Oor (Etempvar _no tint) (Ebinop Olt (Etempvar _t'5 tulong) (Ecast (Econst_long (Int64.repr (-2)) tulong) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sset _yes (Ebinop Oor (Etempvar _yes tint) (Ebinop Oand (Ebinop Ogt (Etempvar _t'4 tulong) (Ecast (Econst_long (Int64.repr (-2)) tulong) tulong) tint) (Eunop Onotint (Etempvar _no tint) tint) tint) tint))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sset _no (Ebinop Oor (Etempvar _no tint) (Ebinop Olt (Etempvar _t'3 tulong) (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) tint) tint))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sset _yes (Ebinop Oor (Etempvar _yes tint) (Ebinop Oand (Ebinop Ogt (Etempvar _t'2 tulong) (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) tint) (Eunop Onotint (Etempvar _no tint) tint) tint) tint))) (Ssequence (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sset _yes (Ebinop Oor (Etempvar _yes tint) (Ebinop Oand (Ebinop Oge (Etempvar _t'1 tulong) (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) tint) (Eunop Onotint (Etempvar _no tint) tint) tint) tint))) (Sreturn (Some (Etempvar _yes tint))))))))))) |}. Definition f_secp256k1_scalar_reduce := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_overflow, tuint) :: nil); fn_vars := ((_t, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _overflow tuint) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 74) tint) :: (Evar ___stringlit_116 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_from_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'8 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _overflow tuint) (Ebinop Oadd (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'1 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'7 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _overflow tuint) (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) tulong) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'2 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'6 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Omul (Etempvar _overflow tuint) (Econst_int (Int.repr 1) tint) tuint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t'3 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'5 tulong) :: nil))) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Sreturn (Some (Etempvar _overflow tuint)))))))))))))))))) |}. Definition f_secp256k1_scalar_add := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_a, (tptr (Tstruct __2843 noattr))) :: (_b, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_t, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_overflow, tint) :: (_t'7, tint) :: (_t'6, tint) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tulong) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tulong) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_from_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'16 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'15 tulong) :: nil))) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'1 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'14 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'13 tulong) :: nil))) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'2 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'12 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'11 tulong) :: nil))) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t'3 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'10 tulong) :: nil))) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'9 tulong) :: nil))) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Ssequence (Scall (Some _t'5) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Scall (Some _t'6) (Evar _secp256k1_scalar_check_overflow (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: nil))) (Sset _overflow (Ecast (Ebinop Oadd (Etempvar _t'5 tulong) (Etempvar _t'6 tint) tulong) tint))) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Oeq (Etempvar _overflow tint) (Econst_int (Int.repr 0) tint) tint) (Sset _t'7 (Econst_int (Int.repr 1) tint)) (Sset _t'7 (Ecast (Ebinop Oeq (Etempvar _overflow tint) (Econst_int (Int.repr 1) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'7 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 105) tint) :: (Evar ___stringlit_117 (tarray tschar 54)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_scalar_reduce (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Etempvar _overflow tint) :: nil)) (Sreturn (Some (Etempvar _overflow tint)))))))))))))))))))))) |}. Definition f_secp256k1_scalar_cadd_bit := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_bit, tuint) :: (_flag, tint) :: nil); fn_vars := ((_t, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: (_t'11, (tptr (Tstruct __IO_FILE noattr))) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _bit tuint) (Econst_int (Int.repr 256) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'11 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'11 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 112) tint) :: (Evar ___stringlit_118 (tarray tschar 33)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sset _bit (Ebinop Oadd (Etempvar _bit tuint) (Ebinop Oand (Ebinop Osub (Ecast (Etempvar _flag tint) tuint) (Econst_int (Int.repr 1) tint) tuint) (Econst_int (Int.repr 256) tint) tuint) tuint)) (Ssequence (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_from_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'10 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Ecast (Ebinop Oeq (Ebinop Oshr (Etempvar _bit tuint) (Econst_int (Int.repr 6) tint) tuint) (Econst_int (Int.repr 0) tint) tint) tulong) (Ebinop Oand (Etempvar _bit tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'1 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'9 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Ecast (Ebinop Oeq (Ebinop Oshr (Etempvar _bit tuint) (Econst_int (Int.repr 6) tint) tuint) (Econst_int (Int.repr 1) tint) tint) tulong) (Ebinop Oand (Etempvar _bit tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'2 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'8 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Ecast (Ebinop Oeq (Ebinop Oshr (Etempvar _bit tuint) (Econst_int (Int.repr 6) tint) tuint) (Econst_int (Int.repr 2) tint) tint) tulong) (Ebinop Oand (Etempvar _bit tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t'3 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'7 tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oshl (Ecast (Ebinop Oeq (Ebinop Oshr (Etempvar _bit tuint) (Econst_int (Int.repr 6) tint) tuint) (Econst_int (Int.repr 3) tint) tint) tulong) (Ebinop Oand (Etempvar _bit tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Sloop (Ssequence (Scall (Some _t'5) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'5 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 127) tint) :: (Evar ___stringlit_119 (tarray tschar 54)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))))))))))))))) |}. Definition f_secp256k1_scalar_set_b32 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_b32, (tptr tuchar)) :: (_overflow, (tptr tint)) :: nil); fn_vars := nil; fn_temps := ((_over, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'34, tuchar) :: (_t'33, tuchar) :: (_t'32, tuchar) :: (_t'31, tuchar) :: (_t'30, tuchar) :: (_t'29, tuchar) :: (_t'28, tuchar) :: (_t'27, tuchar) :: (_t'26, tuchar) :: (_t'25, tuchar) :: (_t'24, tuchar) :: (_t'23, tuchar) :: (_t'22, tuchar) :: (_t'21, tuchar) :: (_t'20, tuchar) :: (_t'19, tuchar) :: (_t'18, tuchar) :: (_t'17, tuchar) :: (_t'16, tuchar) :: (_t'15, tuchar) :: (_t'14, tuchar) :: (_t'13, tuchar) :: (_t'12, tuchar) :: (_t'11, tuchar) :: (_t'10, tuchar) :: (_t'9, tuchar) :: (_t'8, tuchar) :: (_t'7, tuchar) :: (_t'6, tuchar) :: (_t'5, tuchar) :: (_t'4, tuchar) :: (_t'3, tuchar) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'27 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'28 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'29 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'30 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'31 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'32 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'33 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'34 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'27 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'28 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'29 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'30 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'31 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'32 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'33 tuchar) tulong) (Econst_int (Int.repr 48) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'34 tuchar) tulong) (Econst_int (Int.repr 56) tint) tulong) tulong)))))))))) (Ssequence (Ssequence (Sset _t'19 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'20 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'21 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'22 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'23 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'24 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'25 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'26 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'19 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'20 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'21 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'22 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'23 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'24 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'25 tuchar) tulong) (Econst_int (Int.repr 48) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'26 tuchar) tulong) (Econst_int (Int.repr 56) tint) tulong) tulong)))))))))) (Ssequence (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'11 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'12 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'13 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'14 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'15 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'16 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'17 tuchar) tulong) (Econst_int (Int.repr 48) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'18 tuchar) tulong) (Econst_int (Int.repr 56) tint) tulong) tulong)))))))))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar)) (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Etempvar _b32 (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ebinop Oor (Ecast (Etempvar _t'3 tuchar) tulong) (Ebinop Oshl (Ecast (Etempvar _t'4 tuchar) tulong) (Econst_int (Int.repr 8) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'5 tuchar) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'6 tuchar) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'7 tuchar) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'8 tuchar) tulong) (Econst_int (Int.repr 40) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'9 tuchar) tulong) (Econst_int (Int.repr 48) tint) tulong) tulong) (Ebinop Oshl (Ecast (Etempvar _t'10 tuchar) tulong) (Econst_int (Int.repr 56) tint) tulong) tulong)))))))))) (Ssequence (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_check_overflow (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: nil)) (Scall (Some _t'2) (Evar _secp256k1_scalar_reduce (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sset _over (Etempvar _t'2 tint))) (Sifthenelse (Etempvar _overflow (tptr tint)) (Sassign (Ederef (Etempvar _overflow (tptr tint)) tint) (Etempvar _over tint)) Sskip)))))) |}. Definition f_secp256k1_scalar_get_b32 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_bin, (tptr tuchar)) :: (_a, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'32, tulong) :: (_t'31, tulong) :: (_t'30, tulong) :: (_t'29, tulong) :: (_t'28, tulong) :: (_t'27, tulong) :: (_t'26, tulong) :: (_t'25, tulong) :: (_t'24, tulong) :: (_t'23, tulong) :: (_t'22, tulong) :: (_t'21, tulong) :: (_t'20, tulong) :: (_t'19, tulong) :: (_t'18, tulong) :: (_t'17, tulong) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tulong) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tulong) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'32 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'32 tulong) (Econst_int (Int.repr 56) tint) tulong))) (Ssequence (Ssequence (Sset _t'31 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'31 tulong) (Econst_int (Int.repr 48) tint) tulong))) (Ssequence (Ssequence (Sset _t'30 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'30 tulong) (Econst_int (Int.repr 40) tint) tulong))) (Ssequence (Ssequence (Sset _t'29 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'29 tulong) (Econst_int (Int.repr 32) tint) tulong))) (Ssequence (Ssequence (Sset _t'28 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'28 tulong) (Econst_int (Int.repr 24) tint) tulong))) (Ssequence (Ssequence (Sset _t'27 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'27 tulong) (Econst_int (Int.repr 16) tint) tulong))) (Ssequence (Ssequence (Sset _t'26 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'26 tulong) (Econst_int (Int.repr 8) tint) tulong))) (Ssequence (Ssequence (Sset _t'25 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Etempvar _t'25 tulong))) (Ssequence (Ssequence (Sset _t'24 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'24 tulong) (Econst_int (Int.repr 56) tint) tulong))) (Ssequence (Ssequence (Sset _t'23 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'23 tulong) (Econst_int (Int.repr 48) tint) tulong))) (Ssequence (Ssequence (Sset _t'22 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'22 tulong) (Econst_int (Int.repr 40) tint) tulong))) (Ssequence (Ssequence (Sset _t'21 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'21 tulong) (Econst_int (Int.repr 32) tint) tulong))) (Ssequence (Ssequence (Sset _t'20 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'20 tulong) (Econst_int (Int.repr 24) tint) tulong))) (Ssequence (Ssequence (Sset _t'19 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'19 tulong) (Econst_int (Int.repr 16) tint) tulong))) (Ssequence (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'18 tulong) (Econst_int (Int.repr 8) tint) tulong))) (Ssequence (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar) (Etempvar _t'17 tulong))) (Ssequence (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'16 tulong) (Econst_int (Int.repr 56) tint) tulong))) (Ssequence (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'15 tulong) (Econst_int (Int.repr 48) tint) tulong))) (Ssequence (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'14 tulong) (Econst_int (Int.repr 40) tint) tulong))) (Ssequence (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'13 tulong) (Econst_int (Int.repr 32) tint) tulong))) (Ssequence (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'12 tulong) (Econst_int (Int.repr 24) tint) tulong))) (Ssequence (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'11 tulong) (Econst_int (Int.repr 16) tint) tulong))) (Ssequence (Ssequence (Sset _t'10 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'10 tulong) (Econst_int (Int.repr 8) tint) tulong))) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar) (Etempvar _t'9 tulong))) (Ssequence (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'8 tulong) (Econst_int (Int.repr 56) tint) tulong))) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'7 tulong) (Econst_int (Int.repr 48) tint) tulong))) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'6 tulong) (Econst_int (Int.repr 40) tint) tulong))) (Ssequence (Ssequence (Sset _t'5 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'5 tulong) (Econst_int (Int.repr 32) tint) tulong))) (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'4 tulong) (Econst_int (Int.repr 24) tint) tulong))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'3 tulong) (Econst_int (Int.repr 16) tint) tulong))) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar) (Ebinop Oshr (Etempvar _t'2 tulong) (Econst_int (Int.repr 8) tint) tulong))) (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Etempvar _bin (tptr tuchar)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar) (Etempvar _t'1 tulong)))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_scalar_is_zero := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sreturn (Some (Ebinop Oeq (Ebinop Oor (Ebinop Oor (Ebinop Oor (Etempvar _t'1 tulong) (Etempvar _t'2 tulong) tulong) (Etempvar _t'3 tulong) tulong) (Etempvar _t'4 tulong) tulong) (Econst_int (Int.repr 0) tint) tint))))))) |}. Definition f_secp256k1_scalar_negate := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_a, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_t, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_nonzero, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tint) :: (_t'9, tulong) :: (_t'8, tulong) :: (_t'7, tulong) :: (_t'6, tulong) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_is_zero (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _a (tptr (Tstruct __2843 noattr))) :: nil)) (Sset _nonzero (Ebinop Omul (Econst_long (Int64.repr (-1)) tulong) (Ebinop Oeq (Etempvar _t'1 tint) (Econst_int (Int.repr 0) tint) tint) tulong))) (Ssequence (Ssequence (Sset _t'9 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_from_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Eunop Onotint (Etempvar _t'9 tulong) tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oadd (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'2 tulong) (Etempvar _nonzero tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'8 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Eunop Onotint (Etempvar _t'8 tulong) tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'3 tulong) (Etempvar _nonzero tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'7 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Eunop Onotint (Etempvar _t'7 tulong) tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ecast (Econst_long (Int64.repr (-2)) tulong) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'4 tulong) (Etempvar _nonzero tulong) tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Ssequence (Sset _t'6 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Eunop Onotint (Etempvar _t'6 tulong) tulong) :: nil))) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ecast (Econst_long (Int64.repr (-1)) tulong) tulong) :: nil)) (Ssequence (Scall (Some _t'5) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oand (Etempvar _t'5 tulong) (Etempvar _nonzero tulong) tulong)))))))))))))))))) |}. Definition f_secp256k1_scalar_reduce_512 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_l, (tptr tulong)) :: nil); fn_vars := ((_c128, (Tstruct _secp256k1_uint128 noattr)) :: (_t, (Tstruct _secp256k1_uint128 noattr)) :: (_t__1, (Tstruct _secp256k1_uint128 noattr)) :: (_t__2, (Tstruct _secp256k1_uint128 noattr)) :: (_t__3, (Tstruct _secp256k1_uint128 noattr)) :: (_t__4, (Tstruct _secp256k1_uint128 noattr)) :: (_t__5, (Tstruct _secp256k1_uint128 noattr)) :: (_t__6, (Tstruct _secp256k1_uint128 noattr)) :: (_t__7, (Tstruct _secp256k1_uint128 noattr)) :: (_t__8, (Tstruct _secp256k1_uint128 noattr)) :: (_t__9, (Tstruct _secp256k1_uint128 noattr)) :: (_t__10, (Tstruct _secp256k1_uint128 noattr)) :: (_t__11, (Tstruct _secp256k1_uint128 noattr)) :: (_t__12, (Tstruct _secp256k1_uint128 noattr)) :: (_t__13, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_c, tulong) :: (_c0, tulong) :: (_c1, tulong) :: (_c2, tulong) :: (_n0, tulong) :: (_n1, tulong) :: (_n2, tulong) :: (_n3, tulong) :: (_m0, tulong) :: (_m1, tulong) :: (_m2, tulong) :: (_m3, tulong) :: (_m4, tulong) :: (_m5, tulong) :: (_m6, tuint) :: (_p0, tulong) :: (_p1, tulong) :: (_p2, tulong) :: (_p3, tulong) :: (_p4, tuint) :: (_tl, tulong) :: (_th, tulong) :: (_tl__1, tulong) :: (_th__1, tulong) :: (_tl__2, tulong) :: (_th__2, tulong) :: (_over, tuint) :: (_tl__3, tulong) :: (_th__3, tulong) :: (_tl__4, tulong) :: (_th__4, tulong) :: (_over__1, tuint) :: (_over__2, tuint) :: (_tl__5, tulong) :: (_th__5, tulong) :: (_tl__6, tulong) :: (_th__6, tulong) :: (_over__3, tuint) :: (_tl__7, tulong) :: (_th__7, tulong) :: (_over__4, tuint) :: (_tl__8, tulong) :: (_th__8, tulong) :: (_tl__9, tulong) :: (_th__9, tulong) :: (_tl__10, tulong) :: (_th__10, tulong) :: (_over__5, tuint) :: (_tl__11, tulong) :: (_th__11, tulong) :: (_tl__12, tulong) :: (_th__12, tulong) :: (_over__6, tuint) :: (_tl__13, tulong) :: (_th__13, tulong) :: (_t'45, tint) :: (_t'44, tulong) :: (_t'43, tulong) :: (_t'42, tulong) :: (_t'41, tulong) :: (_t'40, tulong) :: (_t'39, tulong) :: (_t'38, tulong) :: (_t'37, tint) :: (_t'36, tulong) :: (_t'35, tulong) :: (_t'34, tint) :: (_t'33, tulong) :: (_t'32, tulong) :: (_t'31, tint) :: (_t'30, tulong) :: (_t'29, tulong) :: (_t'28, tint) :: (_t'27, tulong) :: (_t'26, tulong) :: (_t'25, tulong) :: (_t'24, tulong) :: (_t'23, tint) :: (_t'22, tulong) :: (_t'21, tulong) :: (_t'20, tint) :: (_t'19, tulong) :: (_t'18, tulong) :: (_t'17, tint) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tint) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tint) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tint) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tint) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: (_t'82, (tptr (Tstruct __IO_FILE noattr))) :: (_t'81, (tptr (Tstruct __IO_FILE noattr))) :: (_t'80, tulong) :: (_t'79, tulong) :: (_t'78, (tptr (Tstruct __IO_FILE noattr))) :: (_t'77, tulong) :: (_t'76, (tptr (Tstruct __IO_FILE noattr))) :: (_t'75, (tptr (Tstruct __IO_FILE noattr))) :: (_t'74, (tptr (Tstruct __IO_FILE noattr))) :: (_t'73, tulong) :: (_t'72, tulong) :: (_t'71, (tptr (Tstruct __IO_FILE noattr))) :: (_t'70, (tptr (Tstruct __IO_FILE noattr))) :: (_t'69, tulong) :: (_t'68, tulong) :: (_t'67, (tptr (Tstruct __IO_FILE noattr))) :: (_t'66, (tptr (Tstruct __IO_FILE noattr))) :: (_t'65, (tptr (Tstruct __IO_FILE noattr))) :: (_t'64, (tptr (Tstruct __IO_FILE noattr))) :: (_t'63, (tptr (Tstruct __IO_FILE noattr))) :: (_t'62, (tptr (Tstruct __IO_FILE noattr))) :: (_t'61, (tptr (Tstruct __IO_FILE noattr))) :: (_t'60, (tptr (Tstruct __IO_FILE noattr))) :: (_t'59, (tptr (Tstruct __IO_FILE noattr))) :: (_t'58, (tptr (Tstruct __IO_FILE noattr))) :: (_t'57, (tptr (Tstruct __IO_FILE noattr))) :: (_t'56, (tptr (Tstruct __IO_FILE noattr))) :: (_t'55, (tptr (Tstruct __IO_FILE noattr))) :: (_t'54, (tptr (Tstruct __IO_FILE noattr))) :: (_t'53, (tptr (Tstruct __IO_FILE noattr))) :: (_t'52, (tptr (Tstruct __IO_FILE noattr))) :: (_t'51, (tptr (Tstruct __IO_FILE noattr))) :: (_t'50, (tptr (Tstruct __IO_FILE noattr))) :: (_t'49, (tptr (Tstruct __IO_FILE noattr))) :: (_t'48, (tptr (Tstruct __IO_FILE noattr))) :: (_t'47, (tptr (Tstruct __IO_FILE noattr))) :: (_t'46, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _n0 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong)) (Ssequence (Sset _n1 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 5) tint) (tptr tulong)) tulong)) (Ssequence (Sset _n2 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 6) tint) (tptr tulong)) tulong)) (Ssequence (Sset _n3 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 7) tint) (tptr tulong)) tulong)) (Ssequence (Sset _c0 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _c1 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Sset _c2 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Ssequence (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _n0 tulong) :: (Ebinop Oadd (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th (Etempvar _t'1 tulong))) (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl (Etempvar _t'2 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl tulong) tulong)) (Ssequence (Sset _th (Ebinop Oadd (Etempvar _th tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th tulong) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'82 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'82 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 524) tint) :: (Evar ___stringlit_120 (tarray tschar 32)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak))))) (Ssequence (Ssequence (Sset _m0 (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'81 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'81 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 525) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Ssequence (Ssequence (Sset _t'80 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _t'80 tulong) tulong))) (Ssequence (Ssequence (Sset _t'79 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _t'79 tulong) tint) tulong))) (Ssequence (Sloop (Ssequence (Sset _t'77 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oor (Ebinop One (Etempvar _c1 tulong) (Econst_int (Int.repr 0) tint) tint) (Ebinop Oge (Etempvar _c0 tulong) (Etempvar _t'77 tulong) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'78 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'78 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 526) tint) :: (Evar ___stringlit_122 (tarray tschar 50)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'76 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'76 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 526) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Ssequence (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__1 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _n1 tulong) :: (Ebinop Oadd (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__1 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__1 (Etempvar _t'3 tulong))) (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__1 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__1 (Etempvar _t'4 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__1 tulong) tulong)) (Ssequence (Sset _th__1 (Ebinop Oadd (Etempvar _th__1 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__1 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__1 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tulong) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__1 tulong) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__1 tulong) tint) (Sset _t'5 (Econst_int (Int.repr 1) tint)) (Sset _t'5 (Ecast (Ebinop One (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'5 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'75 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'75 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 527) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__2 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _n0 tulong) :: (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'6) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__2 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__2 (Etempvar _t'6 tulong))) (Ssequence (Scall (Some _t'7) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__2 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__2 (Etempvar _t'7 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__2 tulong) tulong)) (Ssequence (Sset _th__2 (Ebinop Oadd (Etempvar _th__2 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__2 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__2 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tulong) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__2 tulong) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__2 tulong) tint) (Sset _t'8 (Econst_int (Int.repr 1) tint)) (Sset _t'8 (Ecast (Ebinop One (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'8 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'74 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'74 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 528) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Sset _m1 (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Etempvar _c2 tulong)) (Sset _c2 (Ecast (Econst_int (Int.repr 0) tint) tulong))))) (Ssequence (Ssequence (Ssequence (Sset _t'73 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _t'73 tulong) tulong))) (Ssequence (Ssequence (Sset _t'72 (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sset _over (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _t'72 tulong) tint))) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _over tuint) tulong)) (Sset _c2 (Ebinop Oadd (Etempvar _c2 tulong) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _over tuint) tint) tulong))))) (Ssequence (Ssequence (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__3 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _n2 tulong) :: (Ebinop Oadd (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'9) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__3 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__3 (Etempvar _t'9 tulong))) (Ssequence (Scall (Some _t'10) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__3 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__3 (Etempvar _t'10 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__3 tulong) tulong)) (Ssequence (Sset _th__3 (Ebinop Oadd (Etempvar _th__3 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__3 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__3 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tulong) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__3 tulong) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__3 tulong) tint) (Sset _t'11 (Econst_int (Int.repr 1) tint)) (Sset _t'11 (Ecast (Ebinop One (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'11 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'71 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'71 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 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(Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'52 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 562) tint) :: (Evar ___stringlit_127 (tarray tschar 48)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'51 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'51 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 562) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Ssequence (Ssequence (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__13 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _m6 tuint) :: (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'38) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__13 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__13 (Etempvar _t'38 tulong))) (Ssequence (Scall (Some _t'39) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__13 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__13 (Etempvar _t'39 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__13 tulong) tulong)) (Ssequence (Sset _th__13 (Ebinop Oadd (Etempvar _th__13 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__13 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__13 tulong) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__13 tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'50 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'50 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 563) tint) :: (Evar ___stringlit_120 (tarray tschar 32)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak))))) (Ssequence (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _m5 tulong) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _m5 tulong) tint) tulong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oor (Ebinop One (Etempvar _c1 tulong) (Econst_int (Int.repr 0) tint) tint) (Ebinop Oge (Etempvar _c0 tulong) (Etempvar _m5 tulong) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'49 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'49 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 564) tint) :: (Evar ___stringlit_128 (tarray tschar 48)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'48 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'48 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 564) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Ssequence (Sset _p3 (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'47 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'47 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 565) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Sset _p4 (Ecast (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _m6 tuint) tulong) tuint)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _p4 tuint) (Econst_int (Int.repr 2) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'46 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'46 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 567) tint) :: (Evar ___stringlit_129 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_u128_from_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _p0 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Ebinop Oadd (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4624529908474429119)) tulong) tulong) tulong) (Econst_int (Int.repr 1) tint) tulong) :: (Etempvar _p4 tuint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'40) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'40 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _p1 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Eunop Onotint (Ecast (Econst_long (Int64.repr (-4994812053365940165)) tulong) tulong) tulong) :: (Etempvar _p4 tuint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'41) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'41 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _p2 tulong) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _p4 tuint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'42) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t'42 tulong))) (Ssequence (Scall None (Evar _secp256k1_u128_rshift (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_u128_accum_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _p3 tulong) :: nil)) (Ssequence (Ssequence (Scall (Some _t'43) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t'43 tulong))) (Ssequence (Ssequence (Scall (Some _t'44) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _c128 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _c (Etempvar _t'44 tulong))) (Ssequence (Scall (Some _t'45) (Evar _secp256k1_scalar_check_overflow (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: nil)) (Scall None (Evar _secp256k1_scalar_reduce (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint Tnil)) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Ebinop Oadd (Etempvar _c tulong) (Etempvar _t'45 tint) tulong) :: nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_scalar_mul_512 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_l, (tptr tulong)) :: (_a, (tptr (Tstruct __2843 noattr))) :: (_b, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_t, (Tstruct _secp256k1_uint128 noattr)) :: (_t__1, (Tstruct _secp256k1_uint128 noattr)) :: (_t__2, (Tstruct _secp256k1_uint128 noattr)) :: (_t__3, (Tstruct _secp256k1_uint128 noattr)) :: (_t__4, (Tstruct _secp256k1_uint128 noattr)) :: (_t__5, (Tstruct _secp256k1_uint128 noattr)) :: (_t__6, (Tstruct _secp256k1_uint128 noattr)) :: (_t__7, (Tstruct _secp256k1_uint128 noattr)) :: (_t__8, (Tstruct _secp256k1_uint128 noattr)) :: (_t__9, (Tstruct _secp256k1_uint128 noattr)) :: (_t__10, (Tstruct _secp256k1_uint128 noattr)) :: (_t__11, (Tstruct _secp256k1_uint128 noattr)) :: (_t__12, (Tstruct _secp256k1_uint128 noattr)) :: (_t__13, (Tstruct _secp256k1_uint128 noattr)) :: (_t__14, (Tstruct _secp256k1_uint128 noattr)) :: (_t__15, (Tstruct _secp256k1_uint128 noattr)) :: nil); fn_temps := ((_c0, tulong) :: (_c1, tulong) :: (_c2, tuint) :: (_tl, tulong) :: (_th, tulong) :: (_tl__1, tulong) :: (_th__1, tulong) :: (_tl__2, tulong) :: (_th__2, tulong) :: (_tl__3, tulong) :: (_th__3, tulong) :: (_tl__4, tulong) :: (_th__4, tulong) :: (_tl__5, tulong) :: (_th__5, tulong) :: (_tl__6, tulong) :: (_th__6, tulong) :: (_tl__7, tulong) :: (_th__7, tulong) :: (_tl__8, tulong) :: (_th__8, tulong) :: (_tl__9, tulong) :: (_th__9, tulong) :: (_tl__10, tulong) :: (_th__10, tulong) :: (_tl__11, tulong) :: (_th__11, tulong) :: (_tl__12, tulong) :: (_th__12, tulong) :: (_tl__13, tulong) :: (_th__13, tulong) :: (_tl__14, tulong) :: (_th__14, tulong) :: (_tl__15, tulong) :: (_th__15, tulong) :: (_t'46, tulong) :: (_t'45, tulong) :: (_t'44, tint) :: (_t'43, tulong) :: (_t'42, tulong) :: (_t'41, tint) :: (_t'40, tulong) :: (_t'39, tulong) :: (_t'38, tint) :: (_t'37, tulong) :: (_t'36, tulong) :: (_t'35, tint) :: (_t'34, tulong) :: (_t'33, tulong) :: (_t'32, tint) :: (_t'31, tulong) :: (_t'30, tulong) :: (_t'29, tint) :: (_t'28, tulong) :: (_t'27, tulong) :: (_t'26, tint) :: (_t'25, tulong) :: (_t'24, tulong) :: (_t'23, tint) :: (_t'22, tulong) :: (_t'21, tulong) :: (_t'20, tint) :: (_t'19, tulong) :: (_t'18, tulong) :: (_t'17, tint) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tint) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tint) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tint) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tint) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: (_t'97, tulong) :: (_t'96, tulong) :: (_t'95, (tptr (Tstruct __IO_FILE noattr))) :: (_t'94, (tptr (Tstruct __IO_FILE noattr))) :: (_t'93, tulong) :: (_t'92, tulong) :: (_t'91, (tptr (Tstruct __IO_FILE noattr))) :: (_t'90, tulong) :: (_t'89, tulong) :: (_t'88, (tptr (Tstruct __IO_FILE noattr))) :: (_t'87, tulong) :: (_t'86, tulong) :: (_t'85, (tptr (Tstruct __IO_FILE noattr))) :: (_t'84, tulong) :: (_t'83, tulong) :: (_t'82, (tptr (Tstruct __IO_FILE noattr))) :: (_t'81, tulong) :: (_t'80, tulong) :: (_t'79, (tptr (Tstruct __IO_FILE noattr))) :: (_t'78, tulong) :: (_t'77, tulong) :: (_t'76, (tptr (Tstruct __IO_FILE noattr))) :: (_t'75, tulong) :: (_t'74, tulong) :: (_t'73, (tptr (Tstruct __IO_FILE noattr))) :: (_t'72, tulong) :: (_t'71, tulong) :: (_t'70, (tptr (Tstruct __IO_FILE noattr))) :: (_t'69, tulong) :: (_t'68, tulong) :: (_t'67, (tptr (Tstruct __IO_FILE noattr))) :: (_t'66, tulong) :: (_t'65, tulong) :: (_t'64, (tptr (Tstruct __IO_FILE noattr))) :: (_t'63, tulong) :: (_t'62, tulong) :: (_t'61, (tptr (Tstruct __IO_FILE noattr))) :: (_t'60, tulong) :: (_t'59, tulong) :: (_t'58, (tptr (Tstruct __IO_FILE noattr))) :: (_t'57, tulong) :: (_t'56, tulong) :: (_t'55, (tptr (Tstruct __IO_FILE noattr))) :: (_t'54, tulong) :: (_t'53, tulong) :: (_t'52, (tptr (Tstruct __IO_FILE noattr))) :: (_t'51, tulong) :: (_t'50, tulong) :: (_t'49, (tptr (Tstruct __IO_FILE noattr))) :: (_t'48, (tptr (Tstruct __IO_FILE noattr))) :: (_t'47, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _c0 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Sset _c1 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Sset _c2 (Econst_int (Int.repr 0) tint)) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'96 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'97 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'96 tulong) :: (Etempvar _t'97 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th (Etempvar _t'1 tulong))) (Ssequence (Scall (Some _t'2) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl (Etempvar _t'2 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl tulong) tulong)) (Ssequence (Sset _th (Ebinop Oadd (Etempvar _th tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th tulong) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'95 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'95 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 728) tint) :: (Evar ___stringlit_120 (tarray tschar 32)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak))))) (Ssequence (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'94 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'94 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 729) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'92 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'93 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__1 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'92 tulong) :: (Etempvar _t'93 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__1 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__1 (Etempvar _t'3 tulong))) (Ssequence (Scall (Some _t'4) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__1 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__1 (Etempvar _t'4 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__1 tulong) tulong)) (Ssequence (Sset _th__1 (Ebinop Oadd (Etempvar _th__1 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__1 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__1 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__1 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__1 tulong) tint) (Sset _t'5 (Econst_int (Int.repr 1) tint)) (Sset _t'5 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'5 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'91 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'91 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 730) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'89 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'90 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__2 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'89 tulong) :: (Etempvar _t'90 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'6) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__2 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__2 (Etempvar _t'6 tulong))) (Ssequence (Scall (Some _t'7) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__2 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__2 (Etempvar _t'7 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__2 tulong) tulong)) (Ssequence (Sset _th__2 (Ebinop Oadd (Etempvar _th__2 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__2 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__2 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__2 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__2 tulong) tint) (Sset _t'8 (Econst_int (Int.repr 1) tint)) (Sset _t'8 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'8 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'88 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'88 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 731) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Etempvar _c2 tuint) tulong)) (Sset _c2 (Econst_int (Int.repr 0) tint))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'86 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'87 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__3 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'86 tulong) :: (Etempvar _t'87 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'9) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__3 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__3 (Etempvar _t'9 tulong))) (Ssequence (Scall (Some _t'10) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__3 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__3 (Etempvar _t'10 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__3 tulong) tulong)) (Ssequence (Sset _th__3 (Ebinop Oadd (Etempvar _th__3 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__3 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__3 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__3 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__3 tulong) tint) (Sset _t'11 (Econst_int (Int.repr 1) tint)) (Sset _t'11 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'11 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'85 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'85 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 733) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'83 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'84 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__4 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'83 tulong) :: (Etempvar _t'84 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'12) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__4 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__4 (Etempvar _t'12 tulong))) (Ssequence (Scall (Some _t'13) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__4 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__4 (Etempvar _t'13 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__4 tulong) tulong)) (Ssequence (Sset _th__4 (Ebinop Oadd (Etempvar _th__4 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__4 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__4 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__4 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__4 tulong) tint) (Sset _t'14 (Econst_int (Int.repr 1) tint)) (Sset _t'14 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'14 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'82 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); 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cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'64 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 742) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'62 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'63 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__11 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'62 tulong) :: (Etempvar _t'63 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'33) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__11 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__11 (Etempvar _t'33 tulong))) (Ssequence (Scall (Some _t'34) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__11 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__11 (Etempvar _t'34 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__11 tulong) tulong)) (Ssequence (Sset _th__11 (Ebinop Oadd (Etempvar _th__11 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__11 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__11 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__11 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__11 tulong) tint) (Sset _t'35 (Econst_int (Int.repr 1) tint)) (Sset _t'35 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'35 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'61 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'61 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 743) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'59 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'60 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__12 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'59 tulong) :: (Etempvar _t'60 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'36) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__12 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__12 (Etempvar _t'36 tulong))) (Ssequence (Scall (Some _t'37) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__12 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__12 (Etempvar _t'37 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__12 tulong) tulong)) (Ssequence (Sset _th__12 (Ebinop Oadd (Etempvar _th__12 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__12 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__12 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__12 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__12 tulong) tint) (Sset _t'38 (Econst_int (Int.repr 1) tint)) (Sset _t'38 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'38 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'58 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'58 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 744) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Etempvar _c2 tuint) tulong)) (Sset _c2 (Econst_int (Int.repr 0) tint))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'56 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'57 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__13 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'56 tulong) :: (Etempvar _t'57 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'39) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__13 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__13 (Etempvar _t'39 tulong))) (Ssequence (Scall (Some _t'40) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__13 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__13 (Etempvar _t'40 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__13 tulong) tulong)) (Ssequence (Sset _th__13 (Ebinop Oadd (Etempvar _th__13 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__13 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__13 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__13 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__13 tulong) tint) (Sset _t'41 (Econst_int (Int.repr 1) tint)) (Sset _t'41 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'41 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'55 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'55 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 746) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'53 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'54 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__14 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'53 tulong) :: (Etempvar _t'54 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'42) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__14 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__14 (Etempvar _t'42 tulong))) (Ssequence (Scall (Some _t'43) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__14 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__14 (Etempvar _t'43 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__14 tulong) tulong)) (Ssequence (Sset _th__14 (Ebinop Oadd (Etempvar _th__14 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__14 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__14 tulong) tulong)) (Ssequence (Sset _c2 (Ebinop Oadd (Etempvar _c2 tuint) (Ebinop Olt (Etempvar _c1 tulong) (Etempvar _th__14 tulong) tint) tuint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__14 tulong) tint) (Sset _t'44 (Econst_int (Int.repr 1) tint)) (Sset _t'44 (Ecast (Ebinop One (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'44 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'52 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'52 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 747) tint) :: (Evar ___stringlit_123 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak)))))) (Ssequence (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 5) tint) (tptr tulong)) tulong) (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Etempvar _c2 tuint) tulong)) (Sset _c2 (Econst_int (Int.repr 0) tint))))) (Ssequence (Ssequence (Ssequence (Ssequence (Sset _t'50 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sset _t'51 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _b (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_u128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tulong (Tcons tulong Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t__15 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _t'50 tulong) :: (Etempvar _t'51 tulong) :: nil)))) (Ssequence (Ssequence (Scall (Some _t'45) (Evar _secp256k1_u128_hi_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__15 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _th__15 (Etempvar _t'45 tulong))) (Ssequence (Scall (Some _t'46) (Evar _secp256k1_u128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Eaddrof (Evar _t__15 (Tstruct _secp256k1_uint128 noattr)) (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sset _tl__15 (Etempvar _t'46 tulong))))) (Ssequence (Sset _c0 (Ebinop Oadd (Etempvar _c0 tulong) (Etempvar _tl__15 tulong) tulong)) (Ssequence (Sset _th__15 (Ebinop Oadd (Etempvar _th__15 tulong) (Ebinop Olt (Etempvar _c0 tulong) (Etempvar _tl__15 tulong) tint) tulong)) (Ssequence (Sset _c1 (Ebinop Oadd (Etempvar _c1 tulong) (Etempvar _th__15 tulong) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _c1 tulong) (Etempvar _th__15 tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'49 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'49 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 749) tint) :: (Evar ___stringlit_120 (tarray tschar 32)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak))))) (Ssequence (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 6) tint) (tptr tulong)) tulong) (Etempvar _c0 tulong)) (Ssequence (Sset _c0 (Etempvar _c1 tulong)) (Ssequence (Sset _c1 (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c2 tuint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'48 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'48 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 750) tint) :: (Evar ___stringlit_121 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak)))) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _c1 tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'47 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'47 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 751) tint) :: (Evar ___stringlit_130 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sassign (Ederef (Ebinop Oadd (Etempvar _l (tptr tulong)) (Econst_int (Int.repr 7) tint) (tptr tulong)) tulong) (Etempvar _c0 tulong))))))))))))))))))))))))))))) |}. Definition f_secp256k1_scalar_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_a, (tptr (Tstruct __2843 noattr))) :: (_b, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_l, (tarray tulong 8)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _secp256k1_scalar_mul_512 (Tfunction (Tcons (tptr tulong) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Evar _l (tarray tulong 8)) :: (Etempvar _a (tptr (Tstruct __2843 noattr))) :: (Etempvar _b (tptr (Tstruct __2843 noattr))) :: nil)) (Scall None (Evar _secp256k1_scalar_reduce_512 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tulong) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Evar _l (tarray tulong 8)) :: nil))) |}. Definition f_secp256k1_scalar_split_128 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r1, (tptr (Tstruct __2843 noattr))) :: (_r2, (tptr (Tstruct __2843 noattr))) :: (_k, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _k (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r1 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Ssequence (Ssequence (Sset _t'3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _k (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r1 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'3 tulong))) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r1 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r1 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint)) (Ssequence (Ssequence (Sset _t'2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _k (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r2 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'2 tulong))) (Ssequence (Ssequence (Sset _t'1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _k (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r2 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'1 tulong))) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r2 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r2 (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Econst_int (Int.repr 0) tint))))))))) |}. Definition f_secp256k1_scalar_mul_shift_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_a, (tptr (Tstruct __2843 noattr))) :: (_b, (tptr (Tstruct __2843 noattr))) :: (_shift, tuint) :: nil); fn_vars := ((_l, (tarray tulong 8)) :: nil); fn_temps := ((_shiftlimbs, tuint) :: (_shiftlow, tuint) :: (_shifthigh, tuint) :: (_t'10, tulong) :: (_t'9, tulong) :: (_t'8, tint) :: (_t'7, tulong) :: (_t'6, tulong) :: (_t'5, tint) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tint) :: (_t'1, tulong) :: (_t'19, (tptr (Tstruct __IO_FILE noattr))) :: (_t'18, tulong) :: (_t'17, tulong) :: (_t'16, tulong) :: (_t'15, tulong) :: (_t'14, tulong) :: (_t'13, tulong) :: (_t'12, tulong) :: (_t'11, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _shift tuint) (Econst_int (Int.repr 256) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'19 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'19 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 805) tint) :: (Evar ___stringlit_131 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_scalar_mul_512 (Tfunction (Tcons (tptr tulong) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Evar _l (tarray tulong 8)) :: (Etempvar _a (tptr (Tstruct __2843 noattr))) :: (Etempvar _b (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Sset _shiftlimbs (Ebinop Oshr (Etempvar _shift tuint) (Econst_int (Int.repr 6) tint) tuint)) (Ssequence (Sset _shiftlow (Ebinop Oand (Etempvar _shift tuint) (Econst_int (Int.repr 63) tint) tuint)) (Ssequence (Sset _shifthigh (Ebinop Osub (Econst_int (Int.repr 64) tint) (Etempvar _shiftlow tuint) tuint)) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 512) tint) tint) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 448) tint) tint) (Sset _t'2 (Ecast (Etempvar _shiftlow tuint) tbool)) (Sset _t'2 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 1) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'3 (Ecast (Ebinop Oshl (Etempvar _t'18 tulong) (Etempvar _shifthigh tuint) tulong) tulong))) (Sset _t'3 (Ecast (Econst_int (Int.repr 0) tint) tulong)))) (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 0) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'1 (Ecast (Ebinop Oor (Ebinop Oshr (Etempvar _t'17 tulong) (Etempvar _shiftlow tuint) tulong) (Etempvar _t'3 tulong) tulong) tulong)))) (Sset _t'1 (Ecast (Econst_int (Int.repr 0) tint) tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Etempvar _t'1 tulong))) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 448) tint) tint) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 384) tint) tint) (Sset _t'5 (Ecast (Etempvar _shiftlow tuint) tbool)) (Sset _t'5 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'5 tint) (Ssequence (Sset _t'16 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 2) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'6 (Ecast (Ebinop Oshl (Etempvar _t'16 tulong) (Etempvar _shifthigh tuint) tulong) tulong))) (Sset _t'6 (Ecast (Econst_int (Int.repr 0) tint) tulong)))) (Ssequence (Sset _t'15 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 1) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'4 (Ecast (Ebinop Oor (Ebinop Oshr (Etempvar _t'15 tulong) (Etempvar _shiftlow tuint) tulong) (Etempvar _t'6 tulong) tulong) tulong)))) (Sset _t'4 (Ecast (Econst_int (Int.repr 0) tint) tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Etempvar _t'4 tulong))) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 384) tint) tint) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 320) tint) tint) (Sset _t'8 (Ecast (Etempvar _shiftlow tuint) tbool)) (Sset _t'8 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'8 tint) (Ssequence (Sset _t'14 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 3) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'9 (Ecast (Ebinop Oshl (Etempvar _t'14 tulong) (Etempvar _shifthigh tuint) tulong) tulong))) (Sset _t'9 (Ecast (Econst_int (Int.repr 0) tint) tulong)))) (Ssequence (Sset _t'13 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 2) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'7 (Ecast (Ebinop Oor (Ebinop Oshr (Etempvar _t'13 tulong) (Etempvar _shiftlow tuint) tulong) (Etempvar _t'9 tulong) tulong) tulong)))) (Sset _t'7 (Ecast (Econst_int (Int.repr 0) tint) tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Etempvar _t'7 tulong))) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _shift tuint) (Econst_int (Int.repr 320) tint) tint) (Ssequence (Sset _t'12 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oadd (Econst_int (Int.repr 3) tint) (Etempvar _shiftlimbs tuint) tuint) (tptr tulong)) tulong)) (Sset _t'10 (Ecast (Ebinop Oshr (Etempvar _t'12 tulong) (Etempvar _shiftlow tuint) tulong) tulong))) (Sset _t'10 (Ecast (Econst_int (Int.repr 0) tint) tulong))) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Etempvar _t'10 tulong))) (Ssequence (Sset _t'11 (Ederef (Ebinop Oadd (Evar _l (tarray tulong 8)) (Ebinop Oshr (Ebinop Osub (Etempvar _shift tuint) (Econst_int (Int.repr 1) tint) tuint) (Econst_int (Int.repr 6) tint) tuint) (tptr tulong)) tulong)) (Scall None (Evar _secp256k1_scalar_cadd_bit (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint (Tcons tint Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 0) tint) :: (Ebinop Oand (Ebinop Oshr (Etempvar _t'11 tulong) (Ebinop Oand (Ebinop Osub (Etempvar _shift tuint) (Econst_int (Int.repr 1) tint) tuint) (Econst_int (Int.repr 63) tint) tuint) tulong) (Econst_int (Int.repr 1) tint) tulong) :: nil)))))))))))) |}. Definition f_secp256k1_scalar_from_signed62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_a, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil); fn_vars := nil; fn_temps := ((_a0, tulong) :: (_a1, tulong) :: (_a2, tulong) :: (_a3, tulong) :: (_a4, tulong) :: (_t'1, tint) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: (_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _a0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong)) (Ssequence (Sset _a4 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a0 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 836) tint) :: (Evar ___stringlit_103 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a1 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 837) tint) :: (Evar ___stringlit_104 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a2 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 838) tint) :: (Evar ___stringlit_105 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a3 tulong) (Econst_int (Int.repr 62) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 839) tint) :: (Evar ___stringlit_106 (tarray tschar 37)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oshr (Etempvar _a4 tulong) (Econst_int (Int.repr 8) tint) tulong) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 840) tint) :: (Evar ___stringlit_107 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oor (Etempvar _a0 tulong) (Ebinop Oshl (Etempvar _a1 tulong) (Econst_int (Int.repr 62) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _a1 tulong) (Econst_int (Int.repr 2) tint) tulong) (Ebinop Oshl (Etempvar _a2 tulong) (Econst_int (Int.repr 60) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _a2 tulong) (Econst_int (Int.repr 4) tint) tulong) (Ebinop Oshl (Etempvar _a3 tulong) (Econst_int (Int.repr 58) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Etempvar _a3 tulong) (Econst_int (Int.repr 6) tint) tulong) (Ebinop Oshl (Etempvar _a4 tulong) (Econst_int (Int.repr 56) tint) tulong) tulong)) (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_check_overflow (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'1 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 848) tint) :: (Evar ___stringlit_132 (tarray tschar 63)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))))))))))))))) |}. Definition f_secp256k1_scalar_to_signed62 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (_a, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := nil; fn_temps := ((_M62, tulong) :: (_a0, tulong) :: (_a1, tulong) :: (_a2, tulong) :: (_a3, tulong) :: (_t'1, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _M62 (Ebinop Oshr (Econst_long (Int64.repr (-1)) tulong) (Econst_int (Int.repr 2) tint) tulong)) (Ssequence (Sset _a0 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a1 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a2 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong)) (Ssequence (Sset _a3 (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr)) _d (tarray tulong 4)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong)) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_check_overflow (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _a (tptr (Tstruct __2843 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'1 tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 857) tint) :: (Evar ___stringlit_133 (tarray tschar 63)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 0) tint) (tptr tlong)) tlong) (Ebinop Oand (Etempvar _a0 tulong) (Etempvar _M62 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 1) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a0 tulong) (Econst_int (Int.repr 62) tint) tulong) (Ebinop Oshl (Etempvar _a1 tulong) (Econst_int (Int.repr 2) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 2) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a1 tulong) (Econst_int (Int.repr 60) tint) tulong) (Ebinop Oshl (Etempvar _a2 tulong) (Econst_int (Int.repr 4) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 3) tint) (tptr tlong)) tlong) (Ebinop Oand (Ebinop Oor (Ebinop Oshr (Etempvar _a2 tulong) (Econst_int (Int.repr 58) tint) tulong) (Ebinop Oshl (Etempvar _a3 tulong) (Econst_int (Int.repr 6) tint) tulong) tulong) (Etempvar _M62 tulong) tulong)) (Sassign (Ederef (Ebinop Oadd (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) (Tstruct _secp256k1_modinv64_signed62 noattr)) _v (tarray tlong 5)) (Econst_int (Int.repr 4) tint) (tptr tlong)) tlong) (Ebinop Oshr (Etempvar _a3 tulong) (Econst_int (Int.repr 56) tint) tulong)))))))))))) |}. Definition v_secp256k1_const_modinfo_scalar := {| gvar_info := (Tstruct _secp256k1_modinv64_modinfo noattr); gvar_init := (Init_int64 (Int64.repr 4598842128380346689) :: Init_int64 (Int64.repr 3079181878673178862) :: Init_int64 (Int64.repr (-21)) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 256) :: Init_int64 (Int64.repr 3815112494326173377) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_scalar_inverse_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_x, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_s, (Tstruct _secp256k1_modinv64_signed62 noattr)) :: nil); fn_temps := ((_zero_in, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_is_zero (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _x (tptr (Tstruct __2843 noattr))) :: nil)) (Sset _zero_in (Etempvar _t'1 tint))) (Ssequence (Scall None (Evar _secp256k1_scalar_to_signed62 (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Etempvar _x (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_modinv64_var (Tfunction (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_modinfo noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: (Eaddrof (Evar _secp256k1_const_modinfo_scalar (Tstruct _secp256k1_modinv64_modinfo noattr)) (tptr (Tstruct _secp256k1_modinv64_modinfo noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_from_signed62 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _secp256k1_modinv64_signed62 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _s (Tstruct _secp256k1_modinv64_signed62 noattr)) (tptr (Tstruct _secp256k1_modinv64_signed62 noattr))) :: nil)) (Sloop (Ssequence (Scall (Some _t'2) (Evar _secp256k1_scalar_is_zero (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'2 tint) (Etempvar _zero_in tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_112 (tarray tschar 29)) :: (Econst_int (Int.repr 898) tint) :: (Evar ___stringlit_134 (tarray tschar 62)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))))) |}. Definition v_secp256k1_const_lambda := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr (-2377172193522762382)) :: Init_int64 (Int64.repr 1310022930574435960) :: Init_int64 (Int64.repr (-6546514211138018214)) :: Init_int64 (Int64.repr 6008836872998760672) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_minus_b1 := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr 8022177200260244675) :: Init_int64 (Int64.repr (-1998614352016537560)) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_minus_b2 := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr (-2925706260434037204)) :: Init_int64 (Int64.repr (-8491525256057179027)) :: Init_int64 (Int64.repr (-2)) :: Init_int64 (Int64.repr (-1)) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_g1 := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr (-1687969588364726223)) :: Init_int64 (Int64.repr 4443515802769476223) :: Init_int64 (Int64.repr (-1698823648040391915)) :: Init_int64 (Int64.repr 3496713202691238861) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_g2 := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr 1545214808910233457) :: Init_int64 (Int64.repr 2455034284347819718) :: Init_int64 (Int64.repr 8022177200260244676) :: Init_int64 (Int64.repr (-1998614352016537560)) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_scalar_split_lambda := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r1, (tptr (Tstruct __2843 noattr))) :: (_r2, (tptr (Tstruct __2843 noattr))) :: (_k, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_c1, (Tstruct __2843 noattr)) :: (_c2, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _r1 (tptr (Tstruct __2843 noattr))) (Etempvar _k (tptr (Tstruct __2843 noattr))) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_136 (tarray tschar 24)) :: (Econst_int (Int.repr 114) tint) :: (Evar ___stringlit_135 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _r2 (tptr (Tstruct __2843 noattr))) (Etempvar _k (tptr (Tstruct __2843 noattr))) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_136 (tarray tschar 24)) :: (Econst_int (Int.repr 115) tint) :: (Evar ___stringlit_137 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _r1 (tptr (Tstruct __2843 noattr))) (Etempvar _r2 (tptr (Tstruct __2843 noattr))) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_136 (tarray tschar 24)) :: (Econst_int (Int.repr 116) tint) :: (Evar ___stringlit_138 (tarray tschar 32)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Scall None (Evar _secp256k1_scalar_mul_shift_var (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _c1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _k (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _g1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 384) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul_shift_var (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _c2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _k (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _g2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 384) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _c1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _minus_b1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _c2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _c2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _minus_b2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_add (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tint cc_default)) ((Etempvar _r2 (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _c1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _c2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: (Etempvar _r2 (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _secp256k1_const_lambda (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_negate (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: (Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_add (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tint cc_default)) ((Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: (Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: (Etempvar _k (tptr (Tstruct __2843 noattr))) :: nil)) (Scall None (Evar _secp256k1_scalar_split_lambda_verify (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: (Etempvar _r2 (tptr (Tstruct __2843 noattr))) :: (Etempvar _k (tptr (Tstruct __2843 noattr))) :: nil))))))))))))) |}. Definition v_k1_bound := {| gvar_info := (tarray tuchar 32); gvar_init := (Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 162) :: Init_int8 (Int.repr 168) :: Init_int8 (Int.repr 145) :: Init_int8 (Int.repr 140) :: Init_int8 (Int.repr 168) :: Init_int8 (Int.repr 91) :: Init_int8 (Int.repr 175) :: Init_int8 (Int.repr 226) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 22) :: Init_int8 (Int.repr 208) :: Init_int8 (Int.repr 185) :: Init_int8 (Int.repr 23) :: Init_int8 (Int.repr 228) :: Init_int8 (Int.repr 221) :: Init_int8 (Int.repr 119) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_k2_bound := {| gvar_info := (tarray tuchar 32); gvar_init := (Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 0) :: Init_int8 (Int.repr 138) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 40) :: Init_int8 (Int.repr 123) :: Init_int8 (Int.repr 212) :: Init_int8 (Int.repr 113) :: Init_int8 (Int.repr 121) :: Init_int8 (Int.repr 251) :: Init_int8 (Int.repr 43) :: Init_int8 (Int.repr 224) :: Init_int8 (Int.repr 136) :: Init_int8 (Int.repr 70) :: Init_int8 (Int.repr 206) :: Init_int8 (Int.repr 162) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 237) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_scalar_split_lambda_verify := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r1, (tptr (Tstruct __2843 noattr))) :: (_r2, (tptr (Tstruct __2843 noattr))) :: (_k, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_s, (Tstruct __2843 noattr)) :: (_buf1, (tarray tuchar 32)) :: (_buf2, (tarray tuchar 32)) :: nil); fn_temps := ((_t'7, tint) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'10, (tptr (Tstruct __IO_FILE noattr))) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _secp256k1_const_lambda (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _r2 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_add (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tint cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_eq (Tfunction Tnil tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _k (tptr (Tstruct __2843 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'10 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'10 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_136 (tarray tschar 24)) :: (Econst_int (Int.repr 256) tint) :: (Evar ___stringlit_139 (tarray tschar 50)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_scalar_negate (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf1 (tarray tuchar 32)) :: (Etempvar _r1 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf2 (tarray tuchar 32)) :: (Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Sloop (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_memcmp_var (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) tint cc_default)) ((Evar _buf1 (tarray tuchar 32)) :: (Evar _k1_bound (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Sifthenelse (Ebinop Olt (Etempvar _t'2 tint) (Econst_int (Int.repr 0) tint) tint) (Sset _t'3 (Econst_int (Int.repr 1) tint)) (Ssequence (Scall (Some _t'4) (Evar _secp256k1_memcmp_var (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) tint cc_default)) ((Evar _buf2 (tarray tuchar 32)) :: (Evar _k1_bound (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Sset _t'3 (Ecast (Ebinop Olt (Etempvar _t'4 tint) (Econst_int (Int.repr 0) tint) tint) tbool))))) (Sifthenelse (Eunop Onotbool (Etempvar _t'3 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_136 (tarray tschar 24)) :: (Econst_int (Int.repr 261) tint) :: (Evar ___stringlit_140 (tarray tschar 116)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_scalar_negate (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _r2 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf1 (tarray tuchar 32)) :: (Etempvar _r2 (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf2 (tarray tuchar 32)) :: (Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sloop (Ssequence (Ssequence (Scall (Some _t'5) (Evar _secp256k1_memcmp_var (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) tint cc_default)) ((Evar _buf1 (tarray tuchar 32)) :: (Evar _k2_bound (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Sifthenelse (Ebinop Olt (Etempvar _t'5 tint) (Econst_int (Int.repr 0) tint) tint) (Sset _t'6 (Econst_int (Int.repr 1) tint)) (Ssequence (Scall (Some _t'7) (Evar _secp256k1_memcmp_var (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) tint cc_default)) ((Evar _buf2 (tarray tuchar 32)) :: (Evar _k2_bound (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Sset _t'6 (Ecast (Ebinop Olt (Etempvar _t'7 tint) (Econst_int (Int.repr 0) tint) tint) tbool))))) (Sifthenelse (Eunop Onotbool (Etempvar _t'6 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_136 (tarray tschar 24)) :: (Econst_int (Int.repr 266) tint) :: (Evar ___stringlit_141 (tarray tschar 116)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak))))))))))) |}. Definition f_secp256k1_ge_set_gej_zinv := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_zi, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_zi2, (Tstruct __2380 noattr)) :: (_zi3, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'2 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_143 (tarray tschar 23)) :: (Econst_int (Int.repr 58) tint) :: (Evar ___stringlit_142 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _zi2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _zi (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _zi3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _zi2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _zi (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _zi2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _zi3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Etempvar _t'1 tint)))))))) |}. Definition f_secp256k1_ge_set_xy := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_x, (tptr (Tstruct __2380 noattr))) :: (_y, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (Ederef (Etempvar _x (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr))) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (Ederef (Etempvar _y (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr))))) |}. Definition f_secp256k1_ge_is_infinity := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sreturn (Some (Etempvar _t'1 tint)))) |}. Definition f_secp256k1_ge_neg := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_a, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)))) |}. Definition f_secp256k1_ge_set_gej_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := ((_z2, (Tstruct __2380 noattr)) :: (_z3, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'1 tint) (Ssequence (Scall None (Evar _secp256k1_ge_set_infinity (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn None)) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_inv_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _z3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))))))) |}. Definition f_secp256k1_ge_table_set_globalz := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_len, tulong) :: (_a, (tptr (Tstruct __3154 noattr))) :: (_zr, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_zs, (Tstruct __2380 noattr)) :: (_tmpa, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_i, tulong) :: nil); fn_body := (Ssequence (Sset _i (Ebinop Osub (Etempvar _len tulong) (Econst_int (Int.repr 1) tint) tulong)) (Sifthenelse (Ebinop Ogt (Etempvar _len tulong) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Ebinop Oadd (Etempvar _a (tptr (Tstruct __3154 noattr))) (Etempvar _i tulong) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _zs (Tstruct __2380 noattr)) (Ederef (Ebinop Oadd (Etempvar _zr (tptr (Tstruct __2380 noattr))) (Etempvar _i tulong) (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr))) (Swhile (Ebinop Ogt (Etempvar _i tulong) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Sifthenelse (Ebinop One (Etempvar _i tulong) (Ebinop Osub (Etempvar _len tulong) (Econst_int (Int.repr 1) tint) tulong) tint) (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _zs (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _zs (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Etempvar _zr (tptr (Tstruct __2380 noattr))) (Etempvar _i tulong) (tptr (Tstruct __2380 noattr))) :: nil)) Sskip) (Ssequence (Sset _i (Ebinop Osub (Etempvar _i tulong) (Econst_int (Int.repr 1) tint) tulong)) (Ssequence (Sassign (Efield (Evar _tmpa (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (Efield (Ederef (Ebinop Oadd (Etempvar _a (tptr (Tstruct __3154 noattr))) (Etempvar _i tulong) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Sassign (Efield (Evar _tmpa (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (Efield (Ederef (Ebinop Oadd (Etempvar _a (tptr (Tstruct __3154 noattr))) (Etempvar _i tulong) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr))) (Ssequence (Sassign (Efield (Evar _tmpa (Tstruct __3156 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)) (Scall None (Evar _secp256k1_ge_set_gej_zinv (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Ebinop Oadd (Etempvar _a (tptr (Tstruct __3154 noattr))) (Etempvar _i tulong) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _tmpa (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _zs (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))))))))) Sskip)) |}. Definition f_secp256k1_gej_set_infinity := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))) |}. Definition f_secp256k1_ge_set_infinity := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))) |}. Definition f_secp256k1_ge_set_xo_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_x, (tptr (Tstruct __2380 noattr))) :: (_odd, tint) :: nil); fn_vars := ((_x2, (Tstruct __2380 noattr)) :: (_x3, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (Ederef (Etempvar _x (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _x (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _x (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 7) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_sqrt_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_is_odd (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Ebinop One (Etempvar _t'2 tint) (Etempvar _odd tint) tint) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) Sskip)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))))))) |}. Definition f_secp256k1_gej_set_ge := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Etempvar _t'2 tint))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr))) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eunop Onotbool (Etempvar _t'1 tint) tint) :: nil)))))) |}. Definition f_secp256k1_gej_eq_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __3156 noattr))) :: (_b, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := ((_tmp, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_gej_neg (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Etempvar _b (tptr (Tstruct __3156 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))) |}. Definition f_secp256k1_gej_eq_ge_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __3156 noattr))) :: (_b, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := ((_tmp, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_gej_neg (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Etempvar _b (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))) |}. Definition f_secp256k1_gej_eq_x_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_x, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := ((_r, (Tstruct __2380 noattr)) :: (_r2, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, tint) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'2 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_143 (tarray tschar 23)) :: (Econst_int (Int.repr 249) tint) :: (Evar ___stringlit_142 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _r (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _x (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _r2 (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _r2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_equal_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _r (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _r2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint))))))))) |}. Definition f_secp256k1_gej_neg := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Etempvar _t'1 tint))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr))) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil))))))) |}. Definition f_secp256k1_gej_is_infinity := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sreturn (Some (Etempvar _t'1 tint)))) |}. Definition f_secp256k1_ge_is_valid_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := ((_y2, (Tstruct __2380 noattr)) :: (_x3, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: (_t'2, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'2 tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _y2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 7) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_equal_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _y2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))))))) |}. Definition f_secp256k1_gej_double := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := ((_l, (Tstruct __2380 noattr)) :: (_s, (Tstruct __2380 noattr)) :: (_t, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Etempvar _t'1 tint))) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _l (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _l (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 3) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_half (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _l (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _l (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _l (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 2) tint) :: nil))))))))))))))))) |}. Definition f_secp256k1_gej_double_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_rzr, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: (_t'2, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Scall None (Evar _secp256k1_gej_set_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) Sskip) (Sreturn None))) Sskip)) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Ssequence (Sassign (Ederef (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr))) (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: nil))) Sskip) (Ssequence (Scall None (Evar _secp256k1_gej_double (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Etempvar _t'1 tint)))))) |}. Definition f_secp256k1_gej_add_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_b, (tptr (Tstruct __3156 noattr))) :: (_rzr, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_z22, (Tstruct __2380 noattr)) :: (_z12, (Tstruct __2380 noattr)) :: (_u1, (Tstruct __2380 noattr)) :: (_u2, (Tstruct __2380 noattr)) :: (_s1, (Tstruct __2380 noattr)) :: (_s2, (Tstruct __2380 noattr)) :: (_h, (Tstruct __2380 noattr)) :: (_i, (Tstruct __2380 noattr)) :: (_h2, (Tstruct __2380 noattr)) :: (_h3, (Tstruct __2380 noattr)) :: (_t, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, tint) :: (_t'3, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'4 tint) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_143 (tarray tschar 23)) :: (Econst_int (Int.repr 346) tint) :: (Evar ___stringlit_144 (tarray tschar 35)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr))) (Sreturn None))) Sskip)) (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'3 tint) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) Sskip) (Ssequence (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr))) (Sreturn None))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _u2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z22 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tint) (Scall None (Evar _secp256k1_gej_double_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: (Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) Sskip) (Scall None (Evar _secp256k1_gej_set_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: nil))))) (Sreturn None)) Sskip)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Sassign (Ederef (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) (Evar _t (Tstruct __2380 noattr))) Sskip) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_gej_add_ge_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_b, (tptr (Tstruct __3154 noattr))) :: (_rzr, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_z12, (Tstruct __2380 noattr)) :: (_u1, (Tstruct __2380 noattr)) :: (_u2, (Tstruct __2380 noattr)) :: (_s1, (Tstruct __2380 noattr)) :: (_s2, (Tstruct __2380 noattr)) :: (_h, (Tstruct __2380 noattr)) :: (_i, (Tstruct __2380 noattr)) :: (_h2, (Tstruct __2380 noattr)) :: (_h3, (Tstruct __2380 noattr)) :: (_t, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, tint) :: (_t'3, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'4 tint) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_143 (tarray tschar 23)) :: (Econst_int (Int.repr 405) tint) :: (Evar ___stringlit_144 (tarray tschar 35)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: nil)) Sskip) (Ssequence (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _b (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn None)))) Sskip)) (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'3 tint) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) Sskip) (Ssequence (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr))) (Sreturn None))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _u1 (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _u2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _s1 (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tint) (Scall None (Evar _secp256k1_gej_double_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: (Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Etempvar _rzr (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) Sskip) (Scall None (Evar _secp256k1_gej_set_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: nil))))) (Sreturn None)) Sskip)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Sifthenelse (Ebinop One (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Sassign (Ederef (Etempvar _rzr (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) (Evar _h (Tstruct __2380 noattr))) Sskip) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_gej_add_zinv_var := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_b, (tptr (Tstruct __3154 noattr))) :: (_bzinv, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_az, (Tstruct __2380 noattr)) :: (_z12, (Tstruct __2380 noattr)) :: (_u1, (Tstruct __2380 noattr)) :: (_u2, (Tstruct __2380 noattr)) :: (_s1, (Tstruct __2380 noattr)) :: (_s2, (Tstruct __2380 noattr)) :: (_h, (Tstruct __2380 noattr)) :: (_i, (Tstruct __2380 noattr)) :: (_h2, (Tstruct __2380 noattr)) :: (_h3, (Tstruct __2380 noattr)) :: (_t, (Tstruct __2380 noattr)) :: (_bzinv2, (Tstruct __2380 noattr)) :: (_bzinv3, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'4 tint) (Ssequence (Ssequence (Sset _t'6 (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Etempvar _t'6 tint))) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _bzinv2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _bzinv (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _bzinv3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _bzinv2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _bzinv (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _bzinv2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _bzinv3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eunop Onotbool (Etempvar _t'5 tint) tint) :: nil))) (Sreturn None))))))) Sskip)) (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sifthenelse (Etempvar _t'3 tint) (Ssequence (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr))) (Sreturn None)) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _az (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _bzinv (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _az (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _u1 (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _u2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _s1 (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_weak (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _b (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z12 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _az (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_normalizes_to_zero_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tint) (Scall None (Evar _secp256k1_gej_double_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Scall None (Evar _secp256k1_gej_set_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: nil)))) (Sreturn None)) Sskip)) (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _u1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _i (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _s1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _h3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))))))))))))))))))))))))))))) |}. Definition f_secp256k1_gej_rescale := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_s, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_zz, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_is_zero (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Etempvar _s (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_143 (tarray tschar 23)) :: (Econst_int (Int.repr 663) tint) :: (Evar ___stringlit_145 (tarray tschar 48)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _zz (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _s (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _zz (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _zz (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _s (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _s (tptr (Tstruct __2380 noattr))) :: nil))))))) |}. Definition f_secp256k1_ge_to_storage := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3158 noattr))) :: (_a, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := ((_x, (Tstruct __2380 noattr)) :: (_y, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_143 (tarray tschar 23)) :: (Econst_int (Int.repr 673) tint) :: (Evar ___stringlit_142 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sassign (Evar _x (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _y (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_to_storage (Tfunction (Tcons (tptr (Tstruct __2382 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3158 noattr))) (Tstruct __3158 noattr)) _x (Tstruct __2382 noattr)) (tptr (Tstruct __2382 noattr))) :: (Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_to_storage (Tfunction (Tcons (tptr (Tstruct __2382 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3158 noattr))) (Tstruct __3158 noattr)) _y (Tstruct __2382 noattr)) (tptr (Tstruct __2382 noattr))) :: (Eaddrof (Evar _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))))))) |}. Definition f_secp256k1_ge_from_storage := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_a, (tptr (Tstruct __3158 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_from_storage (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2382 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3158 noattr))) (Tstruct __3158 noattr)) _x (Tstruct __2382 noattr)) (tptr (Tstruct __2382 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_from_storage (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2382 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3158 noattr))) (Tstruct __3158 noattr)) _y (Tstruct __2382 noattr)) (tptr (Tstruct __2382 noattr))) :: nil)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)))) |}. Definition f_secp256k1_ge_is_in_correct_subgroup := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_ge, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Sreturn (Some (Econst_int (Int.repr 1) tint))) |}. Definition v_secp256k1_pre_g := {| gvar_info := (tarray (Tstruct __3158 noattr) 8192); gvar_init := (Init_space 524288 :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_secp256k1_pre_g_128 := {| gvar_info := (tarray (Tstruct __3158 noattr) 8192); gvar_init := (Init_space 524288 :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_ecmult_odd_multiples_table := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_n, tint) :: (_pre_a, (tptr (Tstruct __3154 noattr))) :: (_zr, (tptr (Tstruct __2380 noattr))) :: (_z, (tptr (Tstruct __2380 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := ((_d, (Tstruct __3156 noattr)) :: (_ai, (Tstruct __3156 noattr)) :: (_d_ge, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_i, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 78) tint) :: (Evar ___stringlit_142 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_gej_double_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _d_ge (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Efield (Evar _d (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Evar _d (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_gej_zinv (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Ebinop Oadd (Etempvar _pre_a (tptr (Tstruct __3154 noattr))) (Econst_int (Int.repr 0) tint) (tptr (Tstruct __3154 noattr))) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Efield (Evar _d (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ai (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Ebinop Oadd (Etempvar _pre_a (tptr (Tstruct __3154 noattr))) (Econst_int (Int.repr 0) tint) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Sassign (Efield (Evar _ai (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr))) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _zr (tptr (Tstruct __2380 noattr))) (Econst_int (Int.repr 0) tint) (tptr (Tstruct __2380 noattr))) (Tstruct __2380 noattr)) (Efield (Evar _d (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr))) (Ssequence (Ssequence (Sset _i (Econst_int (Int.repr 1) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _n tint) tint) Sskip Sbreak) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _ai (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _ai (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _d_ge (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _zr (tptr (Tstruct __2380 noattr))) (Etempvar _i tint) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Ebinop Oadd (Etempvar _pre_a (tptr (Tstruct __3154 noattr))) (Etempvar _i tint) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Efield (Evar _ai (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Evar _ai (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _z (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Evar _ai (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Evar _d (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))))))))) |}. Definition f_secp256k1_ecmult_table_get_ge := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_pre, (tptr (Tstruct __3154 noattr))) :: (_n, tint) :: (_w, tint) :: nil); fn_vars := nil; fn_temps := ((_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 123) tint) :: (Evar ___stringlit_147 (tarray tschar 38)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _n tint) (Eunop Oneg (Ebinop Osub (Ebinop Oshl (Econst_int (Int.repr 1) tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 123) tint) :: (Evar ___stringlit_148 (tarray tschar 52)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _n tint) (Ebinop Osub (Ebinop Oshl (Econst_int (Int.repr 1) tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 123) tint) :: (Evar ___stringlit_149 (tarray tschar 51)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sifthenelse (Ebinop Ogt (Etempvar _n tint) (Econst_int (Int.repr 0) tint) tint) (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) (Ederef (Ebinop Oadd (Etempvar _pre (tptr (Tstruct __3154 noattr))) (Ebinop Odiv (Ebinop Osub (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr))) (Ssequence (Sassign (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) (Ederef (Ebinop Oadd (Etempvar _pre (tptr (Tstruct __3154 noattr))) (Ebinop Odiv (Ebinop Osub (Eunop Oneg (Etempvar _n tint) tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr))) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil))))))) |}. Definition f_secp256k1_ecmult_table_get_ge_lambda := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_pre, (tptr (Tstruct __3154 noattr))) :: (_x, (tptr (Tstruct __2380 noattr))) :: (_n, tint) :: (_w, tint) :: nil); fn_vars := nil; fn_temps := ((_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 133) tint) :: (Evar ___stringlit_147 (tarray tschar 38)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _n tint) (Eunop Oneg (Ebinop Osub (Ebinop Oshl (Econst_int (Int.repr 1) tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 133) tint) :: (Evar ___stringlit_148 (tarray tschar 52)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _n tint) (Ebinop Osub (Ebinop Oshl (Econst_int (Int.repr 1) tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 133) tint) :: (Evar ___stringlit_149 (tarray tschar 51)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sifthenelse (Ebinop Ogt (Etempvar _n tint) (Econst_int (Int.repr 0) tint) tint) (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _x (tptr (Tstruct __2380 noattr))) (Ebinop Odiv (Ebinop Osub (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Ebinop Oadd (Etempvar _pre (tptr (Tstruct __3154 noattr))) (Ebinop Odiv (Ebinop Osub (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _x (tptr (Tstruct __2380 noattr))) (Ebinop Odiv (Ebinop Osub (Eunop Oneg (Etempvar _n tint) tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Ebinop Oadd (Etempvar _pre (tptr (Tstruct __3154 noattr))) (Ebinop Odiv (Ebinop Osub (Eunop Oneg (Etempvar _n tint) tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil))))))) |}. Definition f_secp256k1_ecmult_table_get_ge_storage := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_pre, (tptr (Tstruct __3158 noattr))) :: (_n, tint) :: (_w, tint) :: nil); fn_vars := nil; fn_temps := ((_t'3, (tptr (Tstruct __IO_FILE noattr))) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: (_t'1, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Ebinop Oand (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 143) tint) :: (Evar ___stringlit_147 (tarray tschar 38)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oge (Etempvar _n tint) (Eunop Oneg (Ebinop Osub (Ebinop Oshl (Econst_int (Int.repr 1) tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 143) tint) :: (Evar ___stringlit_148 (tarray tschar 52)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _n tint) (Ebinop Osub (Ebinop Oshl (Econst_int (Int.repr 1) tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'1 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'1 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 143) tint) :: (Evar ___stringlit_149 (tarray tschar 51)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sifthenelse (Ebinop Ogt (Etempvar _n tint) (Econst_int (Int.repr 0) tint) tint) (Scall None (Evar _secp256k1_ge_from_storage (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3158 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _pre (tptr (Tstruct __3158 noattr))) (Ebinop Odiv (Ebinop Osub (Etempvar _n tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __3158 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_from_storage (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3158 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _pre (tptr (Tstruct __3158 noattr))) (Ebinop Odiv (Ebinop Osub (Eunop Oneg (Etempvar _n tint) tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 2) tint) tint) (tptr (Tstruct __3158 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil))))))) |}. Definition f_secp256k1_ecmult_wnaf := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_wnaf, (tptr tint)) :: (_len, tint) :: (_a, (tptr (Tstruct __2843 noattr))) :: (_w, tint) :: nil); fn_vars := ((_s, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_last_set_bit, tint) :: (_bit, tint) :: (_sign, tint) :: (_carry, tint) :: (_now, tint) :: (_word, tint) :: (_verify_bit, tint) :: (_t'6, tuint) :: (_t'5, tuint) :: (_t'4, tuint) :: (_t'3, tuint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'12, (tptr (Tstruct __IO_FILE noattr))) :: (_t'11, (tptr (Tstruct __IO_FILE noattr))) :: (_t'10, (tptr (Tstruct __IO_FILE noattr))) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _last_set_bit (Eunop Oneg (Econst_int (Int.repr 1) tint) tint)) (Ssequence (Sset _bit (Econst_int (Int.repr 0) tint)) (Ssequence (Sset _sign (Econst_int (Int.repr 1) tint)) (Ssequence (Sset _carry (Econst_int (Int.repr 0) tint)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _wnaf (tptr tint)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'12 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'12 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 166) tint) :: (Evar ___stringlit_150 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Ole (Econst_int (Int.repr 0) tint) (Etempvar _len tint) tint) (Sset _t'1 (Ecast (Ebinop Ole (Etempvar _len tint) (Econst_int (Int.repr 256) tint) tint) tbool)) (Sset _t'1 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'11 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'11 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 167) tint) :: (Evar ___stringlit_151 (tarray tschar 46)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _a (tptr (Tstruct __2843 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'10 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'10 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 168) tint) :: (Evar ___stringlit_152 (tarray tschar 33)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Ole (Econst_int (Int.repr 2) tint) (Etempvar _w tint) tint) (Sset _t'2 (Ecast (Ebinop Ole (Etempvar _w tint) (Econst_int (Int.repr 31) tint) tint) tbool)) (Sset _t'2 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 169) tint) :: (Evar ___stringlit_153 (tarray tschar 41)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _memset (Tfunction (Tcons (tptr tvoid) (Tcons tint (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _wnaf (tptr tint)) :: (Econst_int (Int.repr 0) tint) :: (Ebinop Omul (Etempvar _len tint) (Esizeof tint tulong) tulong) :: nil)) (Ssequence (Sassign (Evar _s (Tstruct __2843 noattr)) (Ederef (Etempvar _a (tptr (Tstruct __2843 noattr))) (Tstruct __2843 noattr))) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_scalar_get_bits (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint (Tcons tuint Tnil))) tuint cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 255) tint) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Etempvar _t'3 tuint) (Ssequence (Scall None (Evar _secp256k1_scalar_negate (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sset _sign (Eunop Oneg (Econst_int (Int.repr 1) tint) tint))) Sskip)) (Ssequence (Swhile (Ebinop Olt (Etempvar _bit tint) (Etempvar _len tint) tint) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_scalar_get_bits (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint (Tcons tuint Tnil))) tuint cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _bit tint) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Ebinop Oeq (Etempvar _t'4 tuint) (Ecast (Etempvar _carry tint) tuint) tint) (Ssequence (Sset _bit (Ebinop Oadd (Etempvar _bit tint) (Econst_int (Int.repr 1) tint) tint)) Scontinue) Sskip)) (Ssequence (Sset _now (Etempvar _w tint)) (Ssequence (Sifthenelse (Ebinop Ogt (Etempvar _now tint) (Ebinop Osub (Etempvar _len tint) (Etempvar _bit tint) tint) tint) (Sset _now (Ebinop Osub (Etempvar _len tint) (Etempvar _bit tint) tint)) Sskip) (Ssequence (Ssequence (Scall (Some _t'5) (Evar _secp256k1_scalar_get_bits_var (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint (Tcons tuint Tnil))) tuint cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _bit tint) :: (Etempvar _now tint) :: nil)) (Sset _word (Ebinop Oadd (Etempvar _t'5 tuint) (Etempvar _carry tint) tuint))) (Ssequence (Sset _carry (Ebinop Oand (Ebinop Oshr (Etempvar _word tint) (Ebinop Osub (Etempvar _w tint) (Econst_int (Int.repr 1) tint) tint) tint) (Econst_int (Int.repr 1) tint) tint)) (Ssequence (Sset _word (Ebinop Osub (Etempvar _word tint) (Ebinop Oshl (Etempvar _carry tint) (Etempvar _w tint) tint) tint)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _wnaf (tptr tint)) (Etempvar _bit tint) (tptr tint)) tint) (Ebinop Omul (Etempvar _sign tint) (Etempvar _word tint) tint)) (Ssequence (Sset _last_set_bit (Etempvar _bit tint)) (Sset _bit (Ebinop Oadd (Etempvar _bit tint) (Etempvar _now tint) tint))))))))))) (Ssequence (Ssequence (Sset _verify_bit (Etempvar _bit tint)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _carry tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 206) tint) :: (Evar ___stringlit_154 (tarray tschar 34)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Swhile (Ebinop Olt (Etempvar _verify_bit tint) (Econst_int (Int.repr 256) tint) tint) (Ssequence (Sloop (Ssequence (Scall (Some _t'6) (Evar _secp256k1_scalar_get_bits (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint (Tcons tuint Tnil))) tuint cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _verify_bit tint) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'6 tuint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 209) tint) :: (Evar ___stringlit_155 (tarray tschar 73)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Sset _verify_bit (Ebinop Oadd (Etempvar _verify_bit tint) (Econst_int (Int.repr 1) tint) tint)))))) (Sreturn (Some (Ebinop Oadd (Etempvar _last_set_bit tint) (Econst_int (Int.repr 1) tint) tint)))))))))))))))) |}. Definition f_secp256k1_ecmult_strauss_wnaf := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_state, (tptr (Tstruct _secp256k1_strauss_state noattr))) :: (_r, (tptr (Tstruct __3156 noattr))) :: (_num, tulong) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_na, (tptr (Tstruct __2843 noattr))) :: (_ng, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_tmpa, (Tstruct __3154 noattr)) :: (_Z, (Tstruct __2380 noattr)) :: (_ng_1, (Tstruct __2843 noattr)) :: (_ng_128, (Tstruct __2843 noattr)) :: (_wnaf_ng_1, (tarray tint 129)) :: (_wnaf_ng_128, (tarray tint 129)) :: (_tmp, (Tstruct __3156 noattr)) :: (_na_1, (Tstruct __2843 noattr)) :: (_na_lam, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_bits_ng_1, tint) :: (_bits_ng_128, tint) :: (_i, tint) :: (_bits, tint) :: (_np, tulong) :: (_no, tulong) :: (_n, tint) :: (_t'15, tint) :: (_t'14, tint) :: (_t'13, tint) :: (_t'12, tint) :: (_t'11, tint) :: (_t'10, tint) :: (_t'9, tint) :: (_t'8, tint) :: (_t'7, tint) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'53, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'52, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'51, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'50, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'49, (tptr (Tstruct __IO_FILE noattr))) :: (_t'48, tint) :: (_t'47, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'46, (tptr (Tstruct __IO_FILE noattr))) :: (_t'45, tint) :: (_t'44, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'43, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'42, tint) :: (_t'41, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'40, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'39, tint) :: (_t'38, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'37, (tptr (Tstruct __2380 noattr))) :: (_t'36, (tptr (Tstruct __3154 noattr))) :: (_t'35, (tptr (Tstruct __2380 noattr))) :: (_t'34, (tptr (Tstruct __2380 noattr))) :: (_t'33, (tptr (Tstruct __2380 noattr))) :: (_t'32, (tptr (Tstruct __3154 noattr))) :: (_t'31, (tptr (Tstruct __3154 noattr))) :: (_t'30, (tptr (Tstruct __2380 noattr))) :: (_t'29, tint) :: (_t'28, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'27, tint) :: (_t'26, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'25, (tptr (Tstruct __3154 noattr))) :: (_t'24, tint) :: (_t'23, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'22, tint) :: (_t'21, (tptr (Tstruct _secp256k1_strauss_point_state noattr))) :: (_t'20, (tptr (Tstruct __2380 noattr))) :: (_t'19, (tptr (Tstruct __3154 noattr))) :: (_t'18, tint) :: (_t'17, tint) :: (_t'16, tint) :: nil); fn_body := (Ssequence (Sset _bits_ng_1 (Econst_int (Int.repr 0) tint)) (Ssequence (Sset _bits_ng_128 (Econst_int (Int.repr 0) tint)) (Ssequence (Sset _bits (Econst_int (Int.repr 0) tint)) (Ssequence (Sset _no (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Ssequence (Scall None (Evar _secp256k1_fe_set_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Ssequence (Sset _np (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _np tulong) (Etempvar _num tulong) tint) Sskip Sbreak) (Ssequence (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_is_zero (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Ebinop Oadd (Etempvar _na (tptr (Tstruct __2843 noattr))) (Etempvar _np tulong) (tptr (Tstruct __2843 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tint) (Sset _t'2 (Econst_int (Int.repr 1) tint)) (Ssequence (Scall (Some _t'3) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Ebinop Oadd (Etempvar _a (tptr (Tstruct __3156 noattr))) (Etempvar _np tulong) (tptr (Tstruct __3156 noattr))) :: nil)) (Sset _t'2 (Ecast (Etempvar _t'3 tint) tbool))))) (Sifthenelse (Etempvar _t'2 tint) Scontinue Sskip)) (Ssequence (Scall None (Evar _secp256k1_scalar_split_lambda (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _na_1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _na_lam (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Ebinop Oadd (Etempvar _na (tptr (Tstruct __2843 noattr))) (Etempvar _np tulong) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Ssequence (Ssequence (Sset _t'53 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Scall (Some _t'4) (Evar _secp256k1_ecmult_wnaf (Tfunction (Tcons (tptr tint) (Tcons tint (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tint Tnil)))) tint cc_default)) ((Efield (Ederef (Ebinop Oadd (Etempvar _t'53 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _wnaf_na_1 (tarray tint 129)) :: (Econst_int (Int.repr 129) tint) :: (Eaddrof (Evar _na_1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 5) tint) :: nil))) (Ssequence (Sset _t'52 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Sassign (Efield (Ederef (Ebinop Oadd (Etempvar _t'52 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_1 tint) (Etempvar _t'4 tint)))) (Ssequence (Ssequence (Ssequence (Sset _t'51 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Scall (Some _t'5) (Evar _secp256k1_ecmult_wnaf (Tfunction (Tcons (tptr tint) (Tcons tint (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tint Tnil)))) tint cc_default)) ((Efield (Ederef (Ebinop Oadd (Etempvar _t'51 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _wnaf_na_lam (tarray tint 129)) :: (Econst_int (Int.repr 129) tint) :: (Eaddrof (Evar _na_lam (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 5) tint) :: nil))) (Ssequence (Sset _t'50 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Sassign (Efield (Ederef (Ebinop Oadd (Etempvar _t'50 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_lam tint) (Etempvar _t'5 tint)))) (Ssequence (Sloop (Ssequence (Sset _t'47 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'48 (Efield (Ederef (Ebinop Oadd (Etempvar _t'47 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_1 tint)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'48 tint) (Econst_int (Int.repr 129) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'49 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'49 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 258) tint) :: (Evar ___stringlit_156 (tarray tschar 54)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip))) Sbreak) (Ssequence (Sloop (Ssequence (Sset _t'44 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'45 (Efield (Ederef (Ebinop Oadd (Etempvar _t'44 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_lam tint)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'45 tint) (Econst_int (Int.repr 129) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'46 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'46 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_146 (tarray tschar 24)) :: (Econst_int (Int.repr 259) tint) :: (Evar ___stringlit_157 (tarray tschar 56)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip))) Sbreak) (Ssequence (Ssequence (Sset _t'41 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'42 (Efield (Ederef (Ebinop Oadd (Etempvar _t'41 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_1 tint)) (Sifthenelse (Ebinop Ogt (Etempvar _t'42 tint) (Etempvar _bits tint) tint) (Ssequence (Sset _t'43 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Sset _bits (Efield (Ederef (Ebinop Oadd (Etempvar _t'43 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_1 tint))) Sskip))) (Ssequence (Ssequence (Sset _t'38 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'39 (Efield (Ederef (Ebinop Oadd (Etempvar _t'38 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_lam tint)) (Sifthenelse (Ebinop Ogt (Etempvar _t'39 tint) (Etempvar _bits tint) tint) (Ssequence (Sset _t'40 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Sset _bits (Efield (Ederef (Ebinop Oadd (Etempvar _t'40 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _no tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_lam tint))) Sskip))) (Ssequence (Sassign (Evar _tmp (Tstruct __3156 noattr)) (Ederef (Ebinop Oadd (Etempvar _a (tptr (Tstruct __3156 noattr))) (Etempvar _np tulong) (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr))) (Ssequence (Sifthenelse (Etempvar _no tulong) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_gej_rescale (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) Sskip) (Ssequence (Ssequence (Sset _t'36 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _pre_a (tptr (Tstruct __3154 noattr)))) (Ssequence (Sset _t'37 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr)))) (Scall None (Evar _secp256k1_ecmult_odd_multiples_table (Tfunction (Tcons tint (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil))))) tvoid cc_default)) ((Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) :: (Ebinop Oadd (Etempvar _t'36 (tptr (Tstruct __3154 noattr))) (Ebinop Omul (Etempvar _no tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _t'37 (tptr (Tstruct __2380 noattr))) (Ebinop Omul (Etempvar _no tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _tmp (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)))) (Ssequence (Sifthenelse (Etempvar _no tulong) (Ssequence (Sset _t'34 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr)))) (Ssequence (Sset _t'35 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr)))) (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Ebinop Oadd (Etempvar _t'34 (tptr (Tstruct __2380 noattr))) (Ebinop Omul (Etempvar _no tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Etempvar _t'35 (tptr (Tstruct __2380 noattr))) (Ebinop Omul (Etempvar _no tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Ebinop Oadd (Etempvar _a (tptr (Tstruct __3156 noattr))) (Etempvar _np tulong) (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))) Sskip) (Sset _no (Ebinop Oadd (Etempvar _no tulong) (Econst_int (Int.repr 1) tint) tulong))))))))))))))) (Sset _np (Ebinop Oadd (Etempvar _np tulong) (Econst_int (Int.repr 1) tint) tulong)))) (Ssequence (Ssequence (Sset _t'32 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _pre_a (tptr (Tstruct __3154 noattr)))) (Ssequence (Sset _t'33 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr)))) (Scall None (Evar _secp256k1_ge_table_set_globalz (Tfunction (Tcons tulong (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Ebinop Omul (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) (Etempvar _no tulong) tulong) :: (Etempvar _t'32 (tptr (Tstruct __3154 noattr))) :: (Etempvar _t'33 (tptr (Tstruct __2380 noattr))) :: nil)))) (Ssequence (Ssequence (Sset _np (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _np tulong) (Etempvar _no tulong) tint) Sskip Sbreak) (Ssequence (Sset _i (Econst_int (Int.repr 0) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tint) Sskip Sbreak) (Ssequence (Sset _t'30 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr)))) (Ssequence (Sset _t'31 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _pre_a (tptr (Tstruct __3154 noattr)))) (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Ebinop Oadd (Etempvar _t'30 (tptr (Tstruct __2380 noattr))) (Ebinop Oadd (Ebinop Omul (Etempvar _np tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (Etempvar _i tint) tulong) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Ebinop Oadd (Etempvar _t'31 (tptr (Tstruct __3154 noattr))) (Ebinop Oadd (Ebinop Omul (Etempvar _np tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (Etempvar _i tint) tulong) (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _secp256k1_const_beta (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))) (Sset _i (Ebinop Oadd (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint))))) (Sset _np (Ebinop Oadd (Etempvar _np tulong) (Econst_int (Int.repr 1) tint) tulong)))) (Ssequence (Sifthenelse (Etempvar _ng (tptr (Tstruct __2843 noattr))) (Ssequence (Scall None (Evar _secp256k1_scalar_split_128 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _ng_1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng_128 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _ng (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'6) (Evar _secp256k1_ecmult_wnaf (Tfunction (Tcons (tptr tint) (Tcons tint (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tint Tnil)))) tint cc_default)) ((Evar _wnaf_ng_1 (tarray tint 129)) :: (Econst_int (Int.repr 129) tint) :: (Eaddrof (Evar _ng_1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 15) tint) :: nil)) (Sset _bits_ng_1 (Etempvar _t'6 tint))) (Ssequence (Ssequence (Scall (Some _t'7) (Evar _secp256k1_ecmult_wnaf (Tfunction (Tcons (tptr tint) (Tcons tint (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tint Tnil)))) tint cc_default)) ((Evar _wnaf_ng_128 (tarray tint 129)) :: (Econst_int (Int.repr 129) tint) :: (Eaddrof (Evar _ng_128 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 15) tint) :: nil)) (Sset _bits_ng_128 (Etempvar _t'7 tint))) (Ssequence (Sifthenelse (Ebinop Ogt (Etempvar _bits_ng_1 tint) (Etempvar _bits tint) tint) (Sset _bits (Etempvar _bits_ng_1 tint)) Sskip) (Sifthenelse (Ebinop Ogt (Etempvar _bits_ng_128 tint) (Etempvar _bits tint) tint) (Sset _bits (Etempvar _bits_ng_128 tint)) Sskip))))) Sskip) (Ssequence (Scall None (Evar _secp256k1_gej_set_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Ssequence (Sset _i (Ebinop Osub (Etempvar _bits tint) (Econst_int (Int.repr 1) tint) tint)) (Sloop (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _i tint) (Econst_int (Int.repr 0) tint) tint) Sskip Sbreak) (Ssequence (Scall None (Evar _secp256k1_gej_double_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Ssequence (Sset _np (Ecast (Econst_int (Int.repr 0) tint) tulong)) (Sloop (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _np tulong) (Etempvar _no tulong) tint) Sskip Sbreak) (Ssequence (Ssequence (Ssequence (Sset _t'26 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'27 (Efield (Ederef (Ebinop Oadd (Etempvar _t'26 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _np tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_1 tint)) (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _t'27 tint) tint) (Ssequence (Ssequence (Ssequence (Sset _t'28 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'29 (Ederef (Ebinop Oadd (Efield (Ederef (Ebinop Oadd (Etempvar _t'28 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _np tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _wnaf_na_1 (tarray tint 129)) (Etempvar _i tint) (tptr tint)) tint)) (Sset _t'9 (Ecast (Etempvar _t'29 tint) tint)))) (Sset _n (Etempvar _t'9 tint))) (Sset _t'8 (Ecast (Etempvar _t'9 tint) tbool))) (Sset _t'8 (Econst_int (Int.repr 0) tint))))) (Sifthenelse (Etempvar _t'8 tint) (Ssequence (Ssequence (Sset _t'25 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _pre_a (tptr (Tstruct __3154 noattr)))) (Scall None (Evar _secp256k1_ecmult_table_get_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons tint (Tcons tint Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _t'25 (tptr (Tstruct __3154 noattr))) (Ebinop Omul (Etempvar _np tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __3154 noattr))) :: (Etempvar _n tint) :: (Econst_int (Int.repr 5) tint) :: nil))) (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil))) Sskip)) (Ssequence (Ssequence (Sset _t'21 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'22 (Efield (Ederef (Ebinop Oadd (Etempvar _t'21 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _np tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _bits_na_lam tint)) (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _t'22 tint) tint) (Ssequence (Ssequence (Ssequence (Sset _t'23 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)))) (Ssequence (Sset _t'24 (Ederef (Ebinop Oadd (Efield (Ederef (Ebinop Oadd (Etempvar _t'23 (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Etempvar _np tulong) (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Tstruct _secp256k1_strauss_point_state noattr)) _wnaf_na_lam (tarray tint 129)) (Etempvar _i tint) (tptr tint)) tint)) (Sset _t'11 (Ecast (Etempvar _t'24 tint) tint)))) (Sset _n (Etempvar _t'11 tint))) (Sset _t'10 (Ecast (Etempvar _t'11 tint) tbool))) (Sset _t'10 (Econst_int (Int.repr 0) tint))))) (Sifthenelse (Etempvar _t'10 tint) (Ssequence (Ssequence (Sset _t'19 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _pre_a (tptr (Tstruct __3154 noattr)))) (Ssequence (Sset _t'20 (Efield (Ederef (Etempvar _state (tptr (Tstruct _secp256k1_strauss_state noattr))) (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr)))) (Scall None (Evar _secp256k1_ecmult_table_get_ge_lambda (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint (Tcons tint Tnil))))) tvoid cc_default)) ((Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _t'19 (tptr (Tstruct __3154 noattr))) (Ebinop Omul (Etempvar _np tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __3154 noattr))) :: (Ebinop Oadd (Etempvar _t'20 (tptr (Tstruct __2380 noattr))) (Ebinop Omul (Etempvar _np tulong) (Ebinop Oshl (Econst_long (Int64.repr 1) tlong) (Ebinop Osub (Econst_int (Int.repr 5) tint) (Econst_int (Int.repr 2) tint) tint) tlong) tulong) (tptr (Tstruct __2380 noattr))) :: (Etempvar _n tint) :: (Econst_int (Int.repr 5) tint) :: nil)))) (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil))) Sskip)))) (Sset _np (Ebinop Oadd (Etempvar _np tulong) (Econst_int (Int.repr 1) tint) tulong)))) (Ssequence (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _bits_ng_1 tint) tint) (Ssequence (Ssequence (Ssequence (Sset _t'18 (Ederef (Ebinop Oadd (Evar _wnaf_ng_1 (tarray tint 129)) (Etempvar _i tint) (tptr tint)) tint)) (Sset _t'13 (Ecast (Etempvar _t'18 tint) tint))) (Sset _n (Etempvar _t'13 tint))) (Sset _t'12 (Ecast (Etempvar _t'13 tint) tbool))) (Sset _t'12 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'12 tint) (Ssequence (Scall None (Evar _secp256k1_ecmult_table_get_ge_storage (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3158 noattr)) (Tcons tint (Tcons tint Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Evar _secp256k1_pre_g (tarray (Tstruct __3158 noattr) 8192)) :: (Etempvar _n tint) :: (Econst_int (Int.repr 15) tint) :: nil)) (Scall None (Evar _secp256k1_gej_add_zinv_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) Sskip)) (Ssequence (Sifthenelse (Ebinop Olt (Etempvar _i tint) (Etempvar _bits_ng_128 tint) tint) (Ssequence (Ssequence (Ssequence (Sset _t'17 (Ederef (Ebinop Oadd (Evar _wnaf_ng_128 (tarray tint 129)) (Etempvar _i tint) (tptr tint)) tint)) (Sset _t'15 (Ecast (Etempvar _t'17 tint) tint))) (Sset _n (Etempvar _t'15 tint))) (Sset _t'14 (Ecast (Etempvar _t'15 tint) tbool))) (Sset _t'14 (Econst_int (Int.repr 0) tint))) (Sifthenelse (Etempvar _t'14 tint) (Ssequence (Scall None (Evar _secp256k1_ecmult_table_get_ge_storage (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3158 noattr)) (Tcons tint (Tcons tint Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Evar _secp256k1_pre_g_128 (tarray (Tstruct __3158 noattr) 8192)) :: (Etempvar _n tint) :: (Econst_int (Int.repr 15) tint) :: nil)) (Scall None (Evar _secp256k1_gej_add_zinv_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _tmpa (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) Sskip)))))) (Sset _i (Ebinop Osub (Etempvar _i tint) (Econst_int (Int.repr 1) tint) tint)))) (Ssequence (Sset _t'16 (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'16 tint) tint) (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _Z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) Sskip))))))))))))) |}. Definition f_secp256k1_ecmult := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_a, (tptr (Tstruct __3156 noattr))) :: (_na, (tptr (Tstruct __2843 noattr))) :: (_ng, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_aux, (tarray (Tstruct __2380 noattr) 8)) :: (_pre_a, (tarray (Tstruct __3154 noattr) 8)) :: (_ps, (tarray (Tstruct _secp256k1_strauss_point_state noattr) 1)) :: (_state, (Tstruct _secp256k1_strauss_state noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Efield (Evar _state (Tstruct _secp256k1_strauss_state noattr)) _aux (tptr (Tstruct __2380 noattr))) (Evar _aux (tarray (Tstruct __2380 noattr) 8))) (Ssequence (Sassign (Efield (Evar _state (Tstruct _secp256k1_strauss_state noattr)) _pre_a (tptr (Tstruct __3154 noattr))) (Evar _pre_a (tarray (Tstruct __3154 noattr) 8))) (Ssequence (Sassign (Efield (Evar _state (Tstruct _secp256k1_strauss_state noattr)) _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr))) (Evar _ps (tarray (Tstruct _secp256k1_strauss_point_state noattr) 1))) (Scall None (Evar _secp256k1_ecmult_strauss_wnaf (Tfunction (Tcons (tptr (Tstruct _secp256k1_strauss_state noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons tulong (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))))) tvoid cc_default)) ((Eaddrof (Evar _state (Tstruct _secp256k1_strauss_state noattr)) (tptr (Tstruct _secp256k1_strauss_state noattr))) :: (Etempvar _r (tptr (Tstruct __3156 noattr))) :: (Econst_int (Int.repr 1) tint) :: (Etempvar _a (tptr (Tstruct __3156 noattr))) :: (Etempvar _na (tptr (Tstruct __2843 noattr))) :: (Etempvar _ng (tptr (Tstruct __2843 noattr))) :: nil))))) |}. Definition f_secp256k1_eckey_pubkey_tweak_add := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_key, (tptr (Tstruct __3154 noattr))) :: (_tweak, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_pt, (Tstruct __3156 noattr)) :: (_one, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _pt (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Etempvar _key (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_set_int (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons tuint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _one (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _pt (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _pt (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _one (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _tweak (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _pt (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_ge_set_gej_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _key (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _pt (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_secp256k1_umul128 := {| fn_return := tulong; fn_callconv := cc_default; fn_params := ((_a, tulong) :: (_b, tulong) :: (_hi, (tptr tulong)) :: nil); fn_vars := nil; fn_temps := ((_ll, tulong) :: (_lh, tulong) :: (_hl, tulong) :: (_hh, tulong) :: (_mid34, tulong) :: nil); fn_body := (Ssequence (Sset _ll (Ebinop Omul (Ecast (Ecast (Etempvar _a tulong) tuint) tulong) (Ecast (Etempvar _b tulong) tuint) tulong)) (Ssequence (Sset _lh (Ebinop Omul (Ecast (Etempvar _a tulong) tuint) (Ebinop Oshr (Etempvar _b tulong) (Econst_int (Int.repr 32) tint) tulong) tulong)) (Ssequence (Sset _hl (Ebinop Omul (Ebinop Oshr (Etempvar _a tulong) (Econst_int (Int.repr 32) tint) tulong) (Ecast (Etempvar _b tulong) tuint) tulong)) (Ssequence (Sset _hh (Ebinop Omul (Ebinop Oshr (Etempvar _a tulong) (Econst_int (Int.repr 32) tint) tulong) (Ebinop Oshr (Etempvar _b tulong) (Econst_int (Int.repr 32) tint) tulong) tulong)) (Ssequence (Sset _mid34 (Ebinop Oadd (Ebinop Oadd (Ebinop Oshr (Etempvar _ll tulong) (Econst_int (Int.repr 32) tint) tulong) (Ecast (Etempvar _lh tulong) tuint) tulong) (Ecast (Etempvar _hl tulong) tuint) tulong)) (Ssequence (Sassign (Ederef (Etempvar _hi (tptr tulong)) tulong) (Ebinop Oadd (Ebinop Oadd (Ebinop Oadd (Etempvar _hh tulong) (Ebinop Oshr (Etempvar _lh tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshr (Etempvar _hl tulong) (Econst_int (Int.repr 32) tint) tulong) tulong) (Ebinop Oshr (Etempvar _mid34 tulong) (Econst_int (Int.repr 32) tint) tulong) tulong)) (Sreturn (Some (Ebinop Oadd (Ebinop Oshl (Etempvar _mid34 tulong) (Econst_int (Int.repr 32) tint) tulong) (Ecast (Etempvar _ll tulong) tuint) tulong))))))))) |}. Definition f_secp256k1_mul128 := {| fn_return := tulong; fn_callconv := cc_default; fn_params := ((_a, tlong) :: (_b, tlong) :: (_hi, (tptr tlong)) :: nil); fn_vars := nil; fn_temps := ((_ll, tulong) :: (_lh, tlong) :: (_hl, tlong) :: (_hh, tlong) :: (_mid34, tulong) :: nil); fn_body := (Ssequence (Sset _ll (Ebinop Omul (Ecast (Ecast (Etempvar _a tlong) tuint) tulong) (Ecast (Etempvar _b tlong) tuint) tulong)) (Ssequence (Sset _lh (Ebinop Omul (Ecast (Etempvar _a tlong) tuint) (Ebinop Oshr (Etempvar _b tlong) (Econst_int (Int.repr 32) tint) tlong) tlong)) (Ssequence (Sset _hl (Ebinop Omul (Ebinop Oshr (Etempvar _a tlong) (Econst_int (Int.repr 32) tint) tlong) (Ecast (Etempvar _b tlong) tuint) tlong)) (Ssequence (Sset _hh (Ebinop Omul (Ebinop Oshr (Etempvar _a tlong) (Econst_int (Int.repr 32) tint) tlong) (Ebinop Oshr (Etempvar _b tlong) (Econst_int (Int.repr 32) tint) tlong) tlong)) (Ssequence (Sset _mid34 (Ebinop Oadd (Ebinop Oadd (Ebinop Oshr (Etempvar _ll tulong) (Econst_int (Int.repr 32) tint) tulong) (Ecast (Etempvar _lh tlong) tuint) tulong) (Ecast (Etempvar _hl tlong) tuint) tulong)) (Ssequence (Sassign (Ederef (Etempvar _hi (tptr tlong)) tlong) (Ebinop Oadd (Ebinop Oadd (Ebinop Oadd (Etempvar _hh tlong) (Ebinop Oshr (Etempvar _lh tlong) (Econst_int (Int.repr 32) tint) tlong) tlong) (Ebinop Oshr (Etempvar _hl tlong) (Econst_int (Int.repr 32) tint) tlong) tlong) (Ecast (Ebinop Oshr (Etempvar _mid34 tulong) (Econst_int (Int.repr 32) tint) tulong) tlong) tlong)) (Sreturn (Some (Ebinop Oadd (Ebinop Oshl (Etempvar _mid34 tulong) (Econst_int (Int.repr 32) tint) tulong) (Ecast (Etempvar _ll tulong) tuint) tulong))))))))) |}. Definition f_secp256k1_u128_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tulong) :: (_b, tulong) :: nil); fn_vars := nil; fn_temps := ((_t'1, tulong) :: nil); fn_body := (Ssequence (Scall (Some _t'1) (Evar _secp256k1_umul128 (Tfunction (Tcons tulong (Tcons tulong (Tcons (tptr tulong) Tnil))) tulong cc_default)) ((Etempvar _a tulong) :: (Etempvar _b tulong) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (tptr tulong)) :: nil)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Etempvar _t'1 tulong))) |}. Definition f_secp256k1_u128_accum_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tulong) :: (_b, tulong) :: nil); fn_vars := ((_hi, tulong) :: nil); fn_temps := ((_lo, tulong) :: (_t'1, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_umul128 (Tfunction (Tcons tulong (Tcons tulong (Tcons (tptr tulong) Tnil))) tulong cc_default)) ((Etempvar _a tulong) :: (Etempvar _b tulong) :: (Eaddrof (Evar _hi tulong) (tptr tulong)) :: nil)) (Sset _lo (Etempvar _t'1 tulong))) (Ssequence (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Oadd (Etempvar _t'5 tulong) (Etempvar _lo tulong) tulong))) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'3 (Evar _hi tulong)) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ebinop Oadd (Etempvar _t'2 tulong) (Ebinop Oadd (Etempvar _t'3 tulong) (Ebinop Olt (Etempvar _t'4 tulong) (Etempvar _lo tulong) tint) tulong) tulong))))))) |}. Definition f_secp256k1_u128_accum_u64 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tulong) :: nil); fn_vars := nil; fn_temps := ((_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Oadd (Etempvar _t'3 tulong) (Etempvar _a tulong) tulong))) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ebinop Oadd (Etempvar _t'1 tulong) (Ebinop Olt (Etempvar _t'2 tulong) (Etempvar _a tulong) tint) tulong))))) |}. Definition f_secp256k1_u128_rshift := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_n, tuint) :: nil); fn_vars := nil; fn_temps := ((_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _n tuint) (Econst_int (Int.repr 128) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 79) tint) :: (Evar ___stringlit_158 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sifthenelse (Ebinop Oge (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tint) (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Oshr (Etempvar _t'4 tulong) (Ebinop Osub (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tuint) tulong))) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Econst_int (Int.repr 0) tint))) (Sifthenelse (Ebinop Ogt (Etempvar _n tuint) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Oor (Ebinop Oshl (Ebinop Omul (Econst_int (Int.repr 1) tuint) (Etempvar _t'2 tulong) tulong) (Ebinop Osub (Econst_int (Int.repr 64) tint) (Etempvar _n tuint) tuint) tulong) (Ebinop Oshr (Etempvar _t'3 tulong) (Etempvar _n tuint) tulong) tulong)))) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ebinop Oshr (Etempvar _t'1 tulong) (Etempvar _n tuint) tulong)))) Sskip))) |}. Definition f_secp256k1_u128_to_u64 := {| fn_return := tulong; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tulong) :: nil); fn_body := (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sreturn (Some (Etempvar _t'1 tulong)))) |}. Definition f_secp256k1_u128_hi_u64 := {| fn_return := tulong; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tulong) :: nil); fn_body := (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sreturn (Some (Etempvar _t'1 tulong)))) |}. Definition f_secp256k1_u128_from_u64 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tulong) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Econst_int (Int.repr 0) tint)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Etempvar _a tulong))) |}. Definition f_secp256k1_u128_check_bits := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_n, tuint) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: (_t'5, (tptr (Tstruct __IO_FILE noattr))) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _n tuint) (Econst_int (Int.repr 128) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'5 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'5 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 103) tint) :: (Evar ___stringlit_158 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tint) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sset _t'1 (Ecast (Ebinop Oeq (Ebinop Oshr (Etempvar _t'4 tulong) (Ebinop Osub (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tuint) tulong) (Econst_int (Int.repr 0) tint) tint) tint))) (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Oeq (Etempvar _t'2 tulong) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sset _t'1 (Ecast (Ebinop Oeq (Ebinop Oshr (Etempvar _t'3 tulong) (Etempvar _n tuint) tulong) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sset _t'1 (Ecast (Etempvar _t'1 tint) tint))) (Sset _t'1 (Ecast (Econst_int (Int.repr 0) tint) tint))))) (Sreturn (Some (Etempvar _t'1 tint))))) |}. Definition f_secp256k1_i128_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tlong) :: (_b, tlong) :: nil); fn_vars := ((_hi, tlong) :: nil); fn_temps := ((_t'1, tulong) :: (_t'2, tlong) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_mul128 (Tfunction (Tcons tlong (Tcons tlong (Tcons (tptr tlong) Tnil))) tulong cc_default)) ((Etempvar _a tlong) :: (Etempvar _b tlong) :: (Eaddrof (Evar _hi tlong) (tptr tlong)) :: nil)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Etempvar _t'1 tulong))) (Ssequence (Sset _t'2 (Evar _hi tlong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ecast (Etempvar _t'2 tlong) tulong)))) |}. Definition f_secp256k1_i128_accum_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tlong) :: (_b, tlong) :: nil); fn_vars := ((_hi, tlong) :: nil); fn_temps := ((_lo, tulong) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tulong) :: (_t'18, tulong) :: (_t'17, tulong) :: (_t'16, tlong) :: (_t'15, tlong) :: (_t'14, tulong) :: (_t'13, (tptr (Tstruct __IO_FILE noattr))) :: (_t'12, tlong) :: (_t'11, tulong) :: (_t'10, tlong) :: (_t'9, tulong) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, tlong) :: (_t'6, tulong) :: (_t'5, tlong) :: (_t'4, tulong) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_mul128 (Tfunction (Tcons tlong (Tcons tlong (Tcons (tptr tlong) Tnil))) tulong cc_default)) ((Etempvar _a tlong) :: (Etempvar _b tlong) :: (Eaddrof (Evar _hi tlong) (tptr tlong)) :: nil)) (Sset _lo (Etempvar _t'1 tulong))) (Ssequence (Ssequence (Sset _t'18 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Oadd (Etempvar _t'18 tulong) (Etempvar _lo tulong) tulong))) (Ssequence (Ssequence (Sset _t'16 (Evar _hi tlong)) (Ssequence (Sset _t'17 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Evar _hi tlong) (Ebinop Oadd (Etempvar _t'16 tlong) (Ebinop Olt (Etempvar _t'17 tulong) (Etempvar _lo tulong) tint) tlong)))) (Ssequence (Sloop (Ssequence (Ssequence (Sset _t'14 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Ole (Etempvar _t'14 tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) (Ssequence (Sset _t'15 (Evar _hi tlong)) (Sset _t'2 (Ecast (Ebinop Ole (Ecast (Etempvar _t'15 tlong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tbool))) (Sset _t'2 (Econst_int (Int.repr 0) tint)))) (Ssequence (Sset _t'11 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'12 (Evar _hi tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'2 tint) (Ebinop Ole (Ebinop Oadd (Etempvar _t'11 tulong) (Ecast (Etempvar _t'12 tlong) tulong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'13 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'13 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 129) tint) :: (Evar ___stringlit_160 (tarray tschar 142)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)))) Sbreak) (Ssequence (Sloop (Ssequence (Ssequence (Sset _t'9 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Ogt (Etempvar _t'9 tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) (Ssequence (Sset _t'10 (Evar _hi tlong)) (Sset _t'3 (Ecast (Ebinop Ogt (Ecast (Etempvar _t'10 tlong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tbool))) (Sset _t'3 (Econst_int (Int.repr 0) tint)))) (Ssequence (Sset _t'6 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'7 (Evar _hi tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'3 tint) (Ebinop Ogt (Ebinop Oadd (Etempvar _t'6 tulong) (Ecast (Etempvar _t'7 tlong) tulong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 134) tint) :: (Evar ___stringlit_161 (tarray tschar 139)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)))) Sbreak) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'5 (Evar _hi tlong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ebinop Oadd (Etempvar _t'4 tulong) (Ecast (Etempvar _t'5 tlong) tulong) tulong))))))))) |}. Definition f_secp256k1_i128_dissip_mul := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tlong) :: (_b, tlong) :: nil); fn_vars := ((_hi, tlong) :: nil); fn_temps := ((_lo, tulong) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tulong) :: (_t'18, tulong) :: (_t'17, tlong) :: (_t'16, tlong) :: (_t'15, tulong) :: (_t'14, (tptr (Tstruct __IO_FILE noattr))) :: (_t'13, tlong) :: (_t'12, tulong) :: (_t'11, tlong) :: (_t'10, tulong) :: (_t'9, (tptr (Tstruct __IO_FILE noattr))) :: (_t'8, tlong) :: (_t'7, tulong) :: (_t'6, tlong) :: (_t'5, tulong) :: (_t'4, tulong) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_mul128 (Tfunction (Tcons tlong (Tcons tlong (Tcons (tptr tlong) Tnil))) tulong cc_default)) ((Etempvar _a tlong) :: (Etempvar _b tlong) :: (Eaddrof (Evar _hi tlong) (tptr tlong)) :: nil)) (Sset _lo (Etempvar _t'1 tulong))) (Ssequence (Ssequence (Sset _t'17 (Evar _hi tlong)) (Ssequence (Sset _t'18 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Evar _hi tlong) (Ebinop Oadd (Etempvar _t'17 tlong) (Ebinop Olt (Etempvar _t'18 tulong) (Etempvar _lo tulong) tint) tlong)))) (Ssequence (Sloop (Ssequence (Ssequence (Sset _t'15 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Ole (Etempvar _t'15 tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) (Ssequence (Sset _t'16 (Evar _hi tlong)) (Sset _t'2 (Ecast (Ebinop Ogt (Ecast (Etempvar _t'16 tlong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tbool))) (Sset _t'2 (Econst_int (Int.repr 0) tint)))) (Ssequence (Sset _t'12 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'13 (Evar _hi tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'2 tint) (Ebinop Ole (Ebinop Osub (Etempvar _t'12 tulong) (Ecast (Etempvar _t'13 tlong) tulong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'14 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'14 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 146) tint) :: (Evar ___stringlit_162 (tarray tschar 141)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)))) Sbreak) (Ssequence (Sloop (Ssequence (Ssequence (Sset _t'10 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Ogt (Etempvar _t'10 tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) (Ssequence (Sset _t'11 (Evar _hi tlong)) (Sset _t'3 (Ecast (Ebinop Ole (Ecast (Etempvar _t'11 tlong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tbool))) (Sset _t'3 (Econst_int (Int.repr 0) tint)))) (Ssequence (Sset _t'7 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'8 (Evar _hi tlong)) (Sifthenelse (Eunop Onotbool (Ebinop Ole (Etempvar _t'3 tint) (Ebinop Ogt (Ebinop Osub (Etempvar _t'7 tulong) (Ecast (Etempvar _t'8 tlong) tulong) tulong) (Econst_long (Int64.repr 9223372036854775807) tulong) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'9 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'9 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 151) tint) :: (Evar ___stringlit_163 (tarray tschar 140)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)))) Sbreak) (Ssequence (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'6 (Evar _hi tlong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ebinop Osub (Etempvar _t'5 tulong) (Ecast (Etempvar _t'6 tlong) tulong) tulong)))) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Osub (Etempvar _t'4 tulong) (Etempvar _lo tulong) tulong)))))))) |}. Definition f_secp256k1_i128_det := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tlong) :: (_b, tlong) :: (_c, tlong) :: (_d, tlong) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _secp256k1_i128_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _a tlong) :: (Etempvar _d tlong) :: nil)) (Scall None (Evar _secp256k1_i128_dissip_mul (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) (Tcons tlong (Tcons tlong Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) :: (Etempvar _b tlong) :: (Etempvar _c tlong) :: nil))) |}. Definition f_secp256k1_i128_rshift := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_n, tuint) :: nil); fn_vars := nil; fn_temps := ((_t'6, (tptr (Tstruct __IO_FILE noattr))) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: (_t'1, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _n tuint) (Econst_int (Int.repr 128) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'6 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'6 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 165) tint) :: (Evar ___stringlit_158 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sifthenelse (Ebinop Oge (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tint) (Ssequence (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ecast (Ebinop Oshr (Ecast (Etempvar _t'5 tulong) tlong) (Ebinop Osub (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tuint) tlong) tulong))) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ecast (Ebinop Oshr (Ecast (Etempvar _t'4 tulong) tlong) (Econst_int (Int.repr 63) tint) tlong) tulong)))) (Sifthenelse (Ebinop Ogt (Etempvar _n tuint) (Econst_int (Int.repr 0) tint) tint) (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ebinop Oor (Ebinop Oshl (Ebinop Omul (Econst_int (Int.repr 1) tuint) (Etempvar _t'2 tulong) tulong) (Ebinop Osub (Econst_int (Int.repr 64) tint) (Etempvar _n tuint) tuint) tulong) (Ebinop Oshr (Etempvar _t'3 tulong) (Etempvar _n tuint) tulong) tulong)))) (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ecast (Ebinop Oshr (Ecast (Etempvar _t'1 tulong) tlong) (Etempvar _n tuint) tlong) tulong)))) Sskip))) |}. Definition f_secp256k1_i128_to_u64 := {| fn_return := tulong; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tulong) :: nil); fn_body := (Ssequence (Sset _t'1 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sreturn (Some (Etempvar _t'1 tulong)))) |}. Definition f_secp256k1_i128_to_i64 := {| fn_return := tlong; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tulong) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, tulong) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sifthenelse (Eunop Onotbool (Ebinop Oeq (Etempvar _t'2 tulong) (Eunop Oneg (Ebinop Oshr (Etempvar _t'3 tulong) (Econst_int (Int.repr 63) tint) tulong) tulong) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 181) tint) :: (Evar ___stringlit_164 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip))) Sbreak) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_i128_to_u64 (Tfunction (Tcons (tptr (Tstruct _secp256k1_uint128 noattr)) Tnil) tulong cc_default)) ((Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil)) (Sreturn (Some (Ecast (Etempvar _t'1 tulong) tlong))))) |}. Definition f_secp256k1_i128_from_i64 := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_a, tlong) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong) (Ecast (Ebinop Oshr (Etempvar _a tlong) (Econst_int (Int.repr 63) tint) tlong) tulong)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong) (Ecast (Etempvar _a tlong) tulong))) |}. Definition f_secp256k1_i128_eq_var := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_b, (tptr (Tstruct _secp256k1_uint128 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: (_t'2, tulong) :: nil); fn_body := (Ssequence (Ssequence (Sset _t'2 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _b (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Oeq (Etempvar _t'2 tulong) (Etempvar _t'3 tulong) tint) (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _a (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _b (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sset _t'1 (Ecast (Ebinop Oeq (Etempvar _t'4 tulong) (Etempvar _t'5 tulong) tint) tbool)))) (Sset _t'1 (Econst_int (Int.repr 0) tint))))) (Sreturn (Some (Etempvar _t'1 tint)))) |}. Definition f_secp256k1_i128_check_pow2 := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct _secp256k1_uint128 noattr))) :: (_n, tuint) :: (_sign, tint) :: nil); fn_vars := nil; fn_temps := ((_t'2, tint) :: (_t'1, tint) :: (_t'8, (tptr (Tstruct __IO_FILE noattr))) :: (_t'7, (tptr (Tstruct __IO_FILE noattr))) :: (_t'6, tulong) :: (_t'5, tulong) :: (_t'4, tulong) :: (_t'3, tulong) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop Olt (Etempvar _n tuint) (Econst_int (Int.repr 127) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'8 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'8 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 195) tint) :: (Evar ___stringlit_165 (tarray tschar 31)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop Oeq (Etempvar _sign tint) (Econst_int (Int.repr 1) tint) tint) (Sset _t'1 (Econst_int (Int.repr 1) tint)) (Sset _t'1 (Ecast (Ebinop Oeq (Etempvar _sign tint) (Eunop Oneg (Econst_int (Int.repr 1) tint) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'7 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'7 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_159 (tarray tschar 31)) :: (Econst_int (Int.repr 196) tint) :: (Evar ___stringlit_166 (tarray tschar 47)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Sifthenelse (Ebinop Oge (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tint) (Ssequence (Sset _t'5 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Oeq (Etempvar _t'5 tulong) (Ebinop Oshl (Ecast (Etempvar _sign tint) tulong) (Ebinop Osub (Etempvar _n tuint) (Econst_int (Int.repr 64) tint) tuint) tulong) tint) (Ssequence (Ssequence (Sset _t'6 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sset _t'2 (Ecast (Ebinop Oeq (Etempvar _t'6 tulong) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sset _t'2 (Ecast (Etempvar _t'2 tint) tint))) (Sset _t'2 (Ecast (Econst_int (Int.repr 0) tint) tint)))) (Ssequence (Sset _t'3 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _hi tulong)) (Sifthenelse (Ebinop Oeq (Etempvar _t'3 tulong) (Ecast (Ebinop Oshr (Ebinop Osub (Etempvar _sign tint) (Econst_int (Int.repr 1) tint) tint) (Econst_int (Int.repr 1) tint) tint) tulong) tint) (Ssequence (Ssequence (Sset _t'4 (Efield (Ederef (Etempvar _r (tptr (Tstruct _secp256k1_uint128 noattr))) (Tstruct _secp256k1_uint128 noattr)) _lo tulong)) (Sset _t'2 (Ecast (Ebinop Oeq (Etempvar _t'4 tulong) (Ebinop Oshl (Ecast (Etempvar _sign tint) tulong) (Etempvar _n tuint) tulong) tint) tbool))) (Sset _t'2 (Ecast (Etempvar _t'2 tint) tint))) (Sset _t'2 (Ecast (Econst_int (Int.repr 0) tint) tint))))) (Sreturn (Some (Etempvar _t'2 tint)))))) |}. Definition f_secp256k1_pubkey_load := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_ge, (tptr (Tstruct __3154 noattr))) :: (_pubkey, (tptr (Tstruct __2064 noattr))) :: nil); fn_vars := ((_s, (Tstruct __3158 noattr)) :: (_x, (Tstruct __2380 noattr)) :: (_y, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sifthenelse (Ebinop Oeq (Esizeof (Tstruct __3158 noattr) tulong) (Econst_int (Int.repr 64) tint) tint) (Ssequence (Scall None (Evar _memcpy (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Eaddrof (Evar _s (Tstruct __3158 noattr)) (tptr (Tstruct __3158 noattr))) :: (Ebinop Oadd (Efield (Ederef (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Tstruct __2064 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) :: (Esizeof (Tstruct __3158 noattr) tulong) :: nil)) (Scall None (Evar _secp256k1_ge_from_storage (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3158 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _ge (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _s (Tstruct __3158 noattr)) (tptr (Tstruct __3158 noattr))) :: nil))) (Ssequence (Scall None (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Efield (Ederef (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Tstruct __2064 noattr)) _data (tarray tuchar 64)) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Efield (Ederef (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Tstruct __2064 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) :: nil)) (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _ge (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_is_zero (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) Sbreak) (Sreturn (Some (Econst_int (Int.repr 1) tint))))) |}. Definition f_secp256k1_pubkey_save := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_pubkey, (tptr (Tstruct __2064 noattr))) :: (_ge, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := ((_s, (Tstruct __3158 noattr)) :: nil); fn_temps := ((_t'1, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Sifthenelse (Ebinop Oeq (Esizeof (Tstruct __3158 noattr) tulong) (Econst_int (Int.repr 64) tint) tint) (Ssequence (Scall None (Evar _secp256k1_ge_to_storage (Tfunction (Tcons (tptr (Tstruct __3158 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __3158 noattr)) (tptr (Tstruct __3158 noattr))) :: (Etempvar _ge (tptr (Tstruct __3154 noattr))) :: nil)) (Scall None (Evar _memcpy (Tfunction (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Ebinop Oadd (Efield (Ederef (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Tstruct __2064 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) :: (Eaddrof (Evar _s (Tstruct __3158 noattr)) (tptr (Tstruct __3158 noattr))) :: (Esizeof (Tstruct __3158 noattr) tulong) :: nil))) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_ge_is_infinity (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Etempvar _ge (tptr (Tstruct __3154 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_168 (tarray tschar 27)) :: (Econst_int (Int.repr 59) tint) :: (Evar ___stringlit_167 (tarray tschar 53)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Efield (Ederef (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Tstruct __2064 noattr)) _data (tarray tuchar 64)) :: (Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Ebinop Oadd (Efield (Ederef (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Tstruct __2064 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) :: (Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))))))) |}. Definition f_secp256k1_ec_pubkey_tweak_add_helper := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_p, (tptr (Tstruct __3154 noattr))) :: (_tweak32, (tptr tuchar)) :: nil); fn_vars := ((_term, (Tstruct __2843 noattr)) :: (_overflow, tint) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: (_t'3, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _overflow tint) (Econst_int (Int.repr 0) tint)) (Ssequence (Scall None (Evar _secp256k1_scalar_set_b32 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tint) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _term (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _tweak32 (tptr tuchar)) :: (Eaddrof (Evar _overflow tint) (tptr tint)) :: nil)) (Ssequence (Ssequence (Sset _t'3 (Evar _overflow tint)) (Sifthenelse (Eunop Onotbool (Etempvar _t'3 tint) tint) (Ssequence (Scall (Some _t'2) (Evar _secp256k1_eckey_pubkey_tweak_add (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tint cc_default)) ((Etempvar _p (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _term (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sset _t'1 (Ecast (Etempvar _t'2 tint) tbool))) (Sset _t'1 (Econst_int (Int.repr 0) tint)))) (Sreturn (Some (Etempvar _t'1 tint)))))) |}. Definition f_secp256k1_xonly_pubkey_load := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_ge, (tptr (Tstruct __3154 noattr))) :: (_pubkey, (tptr (Tstruct __3626 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall (Some _t'1) (Evar _secp256k1_pubkey_load (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2064 noattr)) Tnil)) tint cc_default)) ((Etempvar _ge (tptr (Tstruct __3154 noattr))) :: (Ecast (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) (tptr (Tstruct __2064 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))) |}. Definition f_secp256k1_xonly_pubkey_save := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_pubkey, (tptr (Tstruct __3626 noattr))) :: (_ge, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Scall None (Evar _secp256k1_pubkey_save (Tfunction (Tcons (tptr (Tstruct __2064 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Ecast (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) (tptr (Tstruct __2064 noattr))) :: (Etempvar _ge (tptr (Tstruct __3154 noattr))) :: nil)) |}. Definition f_secp256k1_xonly_pubkey_parse := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_pubkey, (tptr (Tstruct __3626 noattr))) :: (_input32, (tptr tuchar)) :: nil); fn_vars := ((_pk, (Tstruct __3154 noattr)) :: (_x, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Scall None (Evar _memset (Tfunction (Tcons (tptr tvoid) (Tcons tint (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _pubkey (tptr (Tstruct __3626 noattr))) :: (Econst_int (Int.repr 0) tint) :: (Esizeof (Tstruct __3626 noattr) tulong) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _input32 (tptr tuchar)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _input32 (tptr tuchar)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_ge_set_xo_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_ge_is_in_correct_subgroup (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'3 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_xonly_pubkey_save (Tfunction (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _pubkey (tptr (Tstruct __3626 noattr))) :: (Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))))) |}. Definition f_secp256k1_xonly_pubkey_serialize := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_output32, (tptr tuchar)) :: (_pubkey, (tptr (Tstruct __3626 noattr))) :: nil); fn_vars := ((_pk, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _output32 (tptr tuchar)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Scall None (Evar _memset (Tfunction (Tcons (tptr tvoid) (Tcons tint (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _output32 (tptr tuchar)) :: (Econst_int (Int.repr 0) tint) :: (Econst_int (Int.repr 32) tint) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_xonly_pubkey_load (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3626 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _output32 (tptr tuchar)) :: (Eaddrof (Efield (Evar _pk (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_secp256k1_extrakeys_ge_even_y := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := ((_y_parity, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sset _y_parity (Econst_int (Int.repr 0) tint)) (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_ge_is_infinity (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Etempvar _r (tptr (Tstruct __3154 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_170 (tarray tschar 27)) :: (Econst_int (Int.repr 61) tint) :: (Evar ___stringlit_169 (tarray tschar 52)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_is_odd (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Sset _y_parity (Econst_int (Int.repr 1) tint))) Sskip)) (Sreturn (Some (Etempvar _y_parity tint)))))) |}. Definition f_secp256k1_xonly_pubkey_from_pubkey := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_xonly_pubkey, (tptr (Tstruct __3626 noattr))) :: (_pk_parity, (tptr tint)) :: (_pubkey, (tptr (Tstruct __2064 noattr))) :: nil); fn_vars := ((_pk, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_tmp, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _xonly_pubkey (tptr (Tstruct __3626 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_pubkey_load (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2064 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Etempvar _pubkey (tptr (Tstruct __2064 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_extrakeys_ge_even_y (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sset _tmp (Etempvar _t'2 tint))) (Ssequence (Sifthenelse (Ebinop One (Etempvar _pk_parity (tptr tint)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Sassign (Ederef (Etempvar _pk_parity (tptr tint)) tint) (Etempvar _tmp tint)) Sskip) (Ssequence (Scall None (Evar _secp256k1_xonly_pubkey_save (Tfunction (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _xonly_pubkey (tptr (Tstruct __3626 noattr))) :: (Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))))) |}. Definition f_secp256k1_xonly_pubkey_tweak_add := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_output_pubkey, (tptr (Tstruct __2064 noattr))) :: (_internal_pubkey, (tptr (Tstruct __3626 noattr))) :: (_tweak32, (tptr tuchar)) :: nil); fn_vars := ((_pk, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _output_pubkey (tptr (Tstruct __2064 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Scall None (Evar _memset (Tfunction (Tcons (tptr tvoid) (Tcons tint (Tcons tulong Tnil))) (tptr tvoid) cc_default)) ((Etempvar _output_pubkey (tptr (Tstruct __2064 noattr))) :: (Econst_int (Int.repr 0) tint) :: (Esizeof (Tstruct __2064 noattr) tulong) :: nil)) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _internal_pubkey (tptr (Tstruct __3626 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _tweak32 (tptr tuchar)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_xonly_pubkey_load (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3626 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Etempvar _internal_pubkey (tptr (Tstruct __3626 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sset _t'2 (Econst_int (Int.repr 1) tint)) (Ssequence (Scall (Some _t'3) (Evar _secp256k1_ec_pubkey_tweak_add_helper (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Etempvar _tweak32 (tptr tuchar)) :: nil)) (Sset _t'2 (Ecast (Eunop Onotbool (Etempvar _t'3 tint) tint) tbool))))) (Sifthenelse (Etempvar _t'2 tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_pubkey_save (Tfunction (Tcons (tptr (Tstruct __2064 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _output_pubkey (tptr (Tstruct __2064 noattr))) :: (Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))))) |}. Definition f_secp256k1_schnorrsig_sha256_tagged := {| fn_return := tvoid; fn_callconv := {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|}; fn_params := ((__res, (tptr (Tstruct _sha256_context noattr))) :: (_output, (tptr tuint)) :: nil); fn_vars := ((___compound, (Tstruct _sha256_context noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 0) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 2632759825) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 1) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 596792193) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 2) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 292000018) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 3) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 3512892943) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 4) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 2546496848) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 5) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 3983205) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 6) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 2432045412) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Etempvar _output (tptr tuint)) (Econst_int (Int.repr 7) tint) (tptr tuint)) tuint) (Econst_long (Int64.repr 870954602) tulong)) (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Ssequence (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _output (tptr tuint)) (Etempvar _output (tptr tuint))) (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _counter tulong) (Econst_int (Int.repr 64) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 1) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 2) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 3) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 4) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 5) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 6) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 7) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 8) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 9) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 10) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 11) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 12) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 13) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 14) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 15) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 16) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 17) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 18) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 19) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 20) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 21) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 22) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 23) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 24) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 25) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 26) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 27) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 28) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 29) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 30) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 31) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 33) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 34) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 35) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 36) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 37) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 38) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 39) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 40) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 41) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 42) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 43) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 44) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 45) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 46) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 47) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 48) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 49) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 50) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 51) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 52) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 53) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 54) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 55) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 56) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 57) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 58) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 59) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 60) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 61) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 62) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Ebinop Oadd (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _block (tarray tuchar 64)) (Econst_int (Int.repr 63) tint) (tptr tuchar)) tuchar) (Econst_int (Int.repr 0) tint))) (Sassign (Efield (Evar ___compound (Tstruct _sha256_context noattr)) _overflow tbool) (Econst_int (Int.repr 0) tint))) (Sassign (Ederef (Etempvar __res (tptr (Tstruct _sha256_context noattr))) (Tstruct _sha256_context noattr)) (Evar ___compound (Tstruct _sha256_context noattr)))) (Sreturn None)))))))))) |}. Definition f_secp256k1_schnorrsig_challenge := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_e, (tptr (Tstruct __2843 noattr))) :: (_r32, (tptr tuchar)) :: (_msg, (tptr tuchar)) :: (_msglen, tulong) :: (_pubkey32, (tptr tuchar)) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: (_sha_buf, (Tstruct _sha256_midstate noattr)) :: (_sha, (Tstruct _sha256_context noattr)) :: (__res, (Tstruct _sha256_context noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Ssequence (Scall None (Evar _secp256k1_schnorrsig_sha256_tagged (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuint) Tnil)) tvoid {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|})) ((Eaddrof (Evar __res (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Efield (Evar _sha_buf (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Sassign (Evar _sha (Tstruct _sha256_context noattr)) (Evar __res (Tstruct _sha256_context noattr)))) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _r32 (tptr tuchar)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _pubkey32 (tptr tuchar)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _msg (tptr tuchar)) :: (Etempvar _msglen tulong) :: nil)) (Ssequence (Scall None (Evar _sha256_finalize (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _sha (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_fromMidstate (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuint) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Efield (Evar _sha_buf (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Scall None (Evar _secp256k1_scalar_set_b32 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tint) Tnil))) tvoid cc_default)) ((Etempvar _e (tptr (Tstruct __2843 noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)))))))) |}. Definition f_secp256k1_schnorrsig_verify := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_sig64, (tptr tuchar)) :: (_msg, (tptr tuchar)) :: (_msglen, tulong) :: (_pubkey, (tptr (Tstruct __3626 noattr))) :: nil); fn_vars := ((_s, (Tstruct __2843 noattr)) :: (_e, (Tstruct __2843 noattr)) :: (_rj, (Tstruct __3156 noattr)) :: (_pk, (Tstruct __3154 noattr)) :: (_pkj, (Tstruct __3156 noattr)) :: (_rx, (Tstruct __2380 noattr)) :: (_r, (Tstruct __3154 noattr)) :: (_buf, (tarray tuchar 32)) :: (_overflow, tint) :: nil); fn_temps := ((_t'7, tint) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'8, tint) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _sig64 (tptr tuchar)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Sloop (Ssequence (Sifthenelse (Ebinop One (Etempvar _msg (tptr tuchar)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) (Sset _t'1 (Econst_int (Int.repr 1) tint)) (Sset _t'1 (Ecast (Ebinop Oeq (Etempvar _msglen tulong) (Econst_int (Int.repr 0) tint) tint) tbool))) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _rx (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Etempvar _sig64 (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_scalar_set_b32 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tint) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Ebinop Oadd (Etempvar _sig64 (tptr tuchar)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) :: (Eaddrof (Evar _overflow tint) (tptr tint)) :: nil)) (Ssequence (Ssequence (Sset _t'8 (Evar _overflow tint)) (Sifthenelse (Etempvar _t'8 tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_xonly_pubkey_load (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3626 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Etempvar _pubkey (tptr (Tstruct __3626 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'3 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Eaddrof (Efield (Evar _pk (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_schnorrsig_challenge (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr tuchar) Tnil))))) tvoid cc_default)) ((Eaddrof (Evar _e (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Ebinop Oadd (Etempvar _sig64 (tptr tuchar)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) :: (Etempvar _msg (tptr tuchar)) :: (Etempvar _msglen tulong) :: (Evar _buf (tarray tuchar 32)) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_negate (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _e (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _e (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _pkj (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _pk (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _rj (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _pkj (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _e (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _s (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_gej_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _rj (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_ge_is_infinity (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _r (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sifthenelse (Etempvar _t'4 tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Evar _r (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'5) (Evar _secp256k1_fe_is_odd (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Evar _r (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'5 tint) tint) (Ssequence (Scall (Some _t'7) (Evar _secp256k1_fe_equal_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _rx (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Evar _r (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sset _t'6 (Ecast (Etempvar _t'7 tint) tbool))) (Sset _t'6 (Econst_int (Int.repr 0) tint)))) (Sreturn (Some (Etempvar _t'6 tint))))))))))))))))))) |}. Definition f_secp256k1_generator_load := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_ge, (tptr (Tstruct __3154 noattr))) :: (_gen, (tptr (Tstruct __3711 noattr))) :: nil); fn_vars := nil; fn_temps := ((_succeed, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'4, (tptr (Tstruct __IO_FILE noattr))) :: (_t'3, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Efield (Ederef (Etempvar _gen (tptr (Tstruct __3711 noattr))) (Tstruct __3711 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) :: nil)) (Sset _succeed (Etempvar _t'1 tint))) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _succeed tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'4 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'4 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_172 (tarray tschar 27)) :: (Econst_int (Int.repr 43) tint) :: (Evar ___stringlit_171 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Efield (Ederef (Etempvar _gen (tptr (Tstruct __3711 noattr))) (Tstruct __3711 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) :: nil)) (Sset _succeed (Etempvar _t'2 tint))) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _succeed tint) (Econst_int (Int.repr 0) tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'3 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'3 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_172 (tarray tschar 27)) :: (Econst_int (Int.repr 45) tint) :: (Evar ___stringlit_171 (tarray tschar 36)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip) Sbreak) (Sassign (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)))))) |}. Definition f_secp256k1_generator_save := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_gen, (tptr (Tstruct __3711 noattr))) :: (_ge, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: (_t'2, (tptr (Tstruct __IO_FILE noattr))) :: nil); fn_body := (Ssequence (Sloop (Ssequence (Scall (Some _t'1) (Evar _secp256k1_ge_is_infinity (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Etempvar _ge (tptr (Tstruct __3154 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Eunop Onotbool (Etempvar _t'1 tint) tint) tint) (Sloop (Ssequence (Ssequence (Sset _t'2 (Evar _stderr (tptr (Tstruct __IO_FILE noattr)))) (Scall None (Evar _fprintf (Tfunction (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) ((Etempvar _t'2 (tptr (Tstruct __IO_FILE noattr))) :: (Evar ___stringlit_6 (tarray tschar 11)) :: (Evar ___stringlit_172 (tarray tschar 27)) :: (Econst_int (Int.repr 51) tint) :: (Evar ___stringlit_167 (tarray tschar 53)) :: nil))) (Scall None (Evar _abort (Tfunction Tnil tvoid cc_default)) nil)) Sbreak) Sskip)) Sbreak) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Ebinop Oadd (Efield (Ederef (Etempvar _gen (tptr (Tstruct __3711 noattr))) (Tstruct __3711 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 0) tint) (tptr tuchar)) :: (Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Ebinop Oadd (Efield (Ederef (Etempvar _gen (tptr (Tstruct __3711 noattr))) (Tstruct __3711 noattr)) _data (tarray tuchar 64)) (Econst_int (Int.repr 32) tint) (tptr tuchar)) :: (Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))))) |}. Definition v_negc := {| gvar_info := (Tstruct __2380 noattr); gvar_init := (Init_int64 (Int64.repr 800791873586141) :: Init_int64 (Int64.repr 4119177257465895) :: Init_int64 (Int64.repr 2366603538325650) :: Init_int64 (Int64.repr 248548893979605) :: Init_int64 (Int64.repr 270285854395128) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_d := {| gvar_info := (Tstruct __2380 noattr); gvar_init := (Init_int64 (Int64.repr 1851399581923904) :: Init_int64 (Int64.repr 2444010998637548) :: Init_int64 (Int64.repr 1068498044522422) :: Init_int64 (Int64.repr 4379325180380693) :: Init_int64 (Int64.repr 146332049513091) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_shallue_van_de_woestijne := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_ge, (tptr (Tstruct __3154 noattr))) :: (_t, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_wd, (Tstruct __2380 noattr)) :: (_x3d, (Tstruct __2380 noattr)) :: (_jinv, (Tstruct __2380 noattr)) :: (_tmp, (Tstruct __2380 noattr)) :: (_x1, (Tstruct __2380 noattr)) :: (_x2, (Tstruct __2380 noattr)) :: (_x3, (Tstruct __2380 noattr)) :: (_alphain, (Tstruct __2380 noattr)) :: (_betain, (Tstruct __2380 noattr)) :: (_gammain, (Tstruct __2380 noattr)) :: (_y1, (Tstruct __2380 noattr)) :: (_y2, (Tstruct __2380 noattr)) :: (_y3, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_alphaquad, tint) :: (_betaquad, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _wd (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _t (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _negc (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _wd (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x3d (Tstruct __2380 noattr)) (Evar _wd (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_mul_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3d (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 3) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3d (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3d (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 3) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _wd (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oadd (Econst_int (Int.repr 7) tint) (Econst_int (Int.repr 1) tint) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _jinv (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _wd (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3d (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_inv_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _jinv (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _jinv (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3d (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _jinv (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _d (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sassign (Evar _x2 (Tstruct __2380 noattr)) (Evar _x1 (Tstruct __2380 noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 3) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _wd (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _wd (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _jinv (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _alphain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _alphain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _alphain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _alphain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 7) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _betain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _betain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _betain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _betain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 7) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _gammain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _gammain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _gammain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _gammain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 7) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_sqrt_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _y1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _alphain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sset _alphaquad (Etempvar _t'1 tint))) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_sqrt_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _y2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _betain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sset _betaquad (Etempvar _t'2 tint))) (Ssequence (Scall None (Evar _secp256k1_fe_sqrt_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _y3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _gammain (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_cmov (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oand (Eunop Onotbool (Etempvar _alphaquad tint) tint) (Etempvar _betaquad tint) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_cmov (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _y1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _y2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oand (Eunop Onotbool (Etempvar _alphaquad tint) tint) (Etempvar _betaquad tint) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_cmov (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oand (Eunop Onotbool (Etempvar _alphaquad tint) tint) (Eunop Onotbool (Etempvar _betaquad tint) tint) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_cmov (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _y1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _y3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Ebinop Oand (Eunop Onotbool (Etempvar _alphaquad tint) tint) (Eunop Onotbool (Etempvar _betaquad tint) tint) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_xy (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Etempvar _ge (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _x1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _y1 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _tmp (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall (Some _t'3) (Evar _secp256k1_fe_is_odd (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Etempvar _t (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _secp256k1_fe_cmov (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _ge (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _tmp (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _t'3 tint) :: nil))))))))))))))))))))))))))))))))))))))) |}. Definition v_prefix1 := {| gvar_info := (tarray tuchar 17); gvar_init := (Init_int8 (Int.repr 49) :: Init_int8 (Int.repr 115) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_prefix2 := {| gvar_info := (tarray tuchar 17); gvar_init := (Init_int8 (Int.repr 50) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 100) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 103) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 101) :: Init_int8 (Int.repr 114) :: Init_int8 (Int.repr 97) :: Init_int8 (Int.repr 116) :: Init_int8 (Int.repr 105) :: Init_int8 (Int.repr 111) :: Init_int8 (Int.repr 110) :: Init_int8 (Int.repr 58) :: Init_int8 (Int.repr 32) :: Init_int8 (Int.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_inf := {| gvar_info := (Tstruct __3156 noattr); gvar_init := (Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_space 4 :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_zero := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_secp256k1_generator_generate_internal := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_gen, (tptr (Tstruct __3711 noattr))) :: (_key32, (tptr tuchar)) :: (_blind32, (tptr tuchar)) :: nil); fn_vars := ((_t, (Tstruct __2380 noattr)) :: (_add, (Tstruct __3154 noattr)) :: (_accum, (Tstruct __3156 noattr)) :: (_overflow, tint) :: (_sha256_buf, (Tstruct _sha256_midstate noattr)) :: (_b32, (tarray tuchar 32)) :: (_blind, (Tstruct __2843 noattr)) :: (_sha256_ctx, (Tstruct _sha256_context noattr)) :: (_sha256_ctx__1, (Tstruct _sha256_context noattr)) :: (__res, (Tstruct _sha256_context noattr)) :: (__res__1, (Tstruct _sha256_context noattr)) :: nil); fn_temps := ((_ret, tint) :: (_t'2, tint) :: (_t'1, tint) :: (_t'3, tint) :: nil); fn_body := (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _t (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 0) tint) (tptr tulong)) tulong) (Ebinop Oor (Econst_int (Int.repr 4) tint) (Ebinop Oshl (Ebinop Oand (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_long (Int64.repr 1048575) tulong) tulong) (Econst_int (Int.repr 32) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _t (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 1) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oshr (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 20) tint) tulong) (Ebinop Oshl (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 12) tint) tulong) tulong) (Ebinop Oshl (Ebinop Oand (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_long (Int64.repr 255) tulong) tulong) (Econst_int (Int.repr 44) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _t (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 2) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 8) tint) tulong) (Ebinop Oshl (Ebinop Oand (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_long (Int64.repr 268435455) tulong) tulong) (Econst_int (Int.repr 24) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _t (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 3) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oor (Ebinop Oshr (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 28) tint) tulong) (Ebinop Oshl (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 4) tint) tulong) tulong) (Ebinop Oshl (Ebinop Oand (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_long (Int64.repr 65535) tulong) tulong) (Econst_int (Int.repr 36) tint) tulong) tulong)) (Ssequence (Sassign (Ederef (Ebinop Oadd (Efield (Evar _t (Tstruct __2380 noattr)) _n (tarray tulong 5)) (Econst_int (Int.repr 4) tint) (tptr tulong)) tulong) (Ebinop Oor (Ebinop Oshr (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 16) tint) tulong) (Ebinop Oshl (Ecast (Econst_int (Int.repr 0) tint) tulong) (Econst_int (Int.repr 16) tint) tulong) tulong)) (Ssequence (Sassign (Efield (Evar _t (Tstruct __2380 noattr)) _magnitude tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sassign (Efield (Evar _t (Tstruct __2380 noattr)) _normalized tint) (Econst_int (Int.repr 1) tint)) (Ssequence (Sset _ret (Econst_int (Int.repr 1) tint)) (Ssequence (Sifthenelse (Etempvar _blind32 (tptr tuchar)) (Ssequence (Scall None (Evar _secp256k1_scalar_set_b32 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tint) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _blind (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Etempvar _blind32 (tptr tuchar)) :: (Eaddrof (Evar _overflow tint) (tptr tint)) :: nil)) (Ssequence (Ssequence (Sset _t'3 (Evar _overflow tint)) (Sset _ret (Eunop Onotbool (Etempvar _t'3 tint) tint))) (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _inf (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _zero (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _blind (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)))) Sskip) (Ssequence (Ssequence (Ssequence (Scall None (Evar _sha256_init (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuint) Tnil)) tvoid {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|})) ((Eaddrof (Evar __res__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Efield (Evar _sha256_buf (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Sassign (Evar _sha256_ctx (Tstruct _sha256_context noattr)) (Evar __res__1 (Tstruct _sha256_context noattr)))) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha256_ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Evar _prefix1 (tarray tuchar 17)) :: (Econst_int (Int.repr 16) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha256_ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _key32 (tptr tuchar)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_finalize (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _sha256_ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: nil)) (Scall None (Evar _sha256_fromMidstate (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuint) Tnil)) tvoid cc_default)) ((Evar _b32 (tarray tuchar 32)) :: (Efield (Evar _sha256_buf (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)))))) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Evar _b32 (tarray tuchar 32)) :: nil)) (Sset _ret (Ebinop Oand (Etempvar _ret tint) (Etempvar _t'1 tint) tint))) (Ssequence (Scall None (Evar _shallue_van_de_woestijne (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Sifthenelse (Etempvar _blind32 (tptr tuchar)) (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil))) (Ssequence (Ssequence (Ssequence (Scall None (Evar _sha256_init (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuint) Tnil)) tvoid {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|})) ((Eaddrof (Evar __res (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Efield (Evar _sha256_buf (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Sassign (Evar _sha256_ctx__1 (Tstruct _sha256_context noattr)) (Evar __res (Tstruct _sha256_context noattr)))) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha256_ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Evar _prefix2 (tarray tuchar 17)) :: (Econst_int (Int.repr 16) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _sha256_ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _key32 (tptr tuchar)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_finalize (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _sha256_ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: nil)) (Scall None (Evar _sha256_fromMidstate (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuint) Tnil)) tvoid cc_default)) ((Evar _b32 (tarray tuchar 32)) :: (Efield (Evar _sha256_buf (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)))))) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Evar _b32 (tarray tuchar 32)) :: nil)) (Sset _ret (Ebinop Oand (Etempvar _ret tint) (Etempvar _t'2 tint) tint))) (Ssequence (Scall None (Evar _shallue_van_de_woestijne (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_gej_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _accum (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_generator_save (Tfunction (Tcons (tptr (Tstruct __3711 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _gen (tptr (Tstruct __3711 noattr))) :: (Eaddrof (Evar _add (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Etempvar _ret tint)))))))))))))))))))))) |}. Definition f_secp256k1_generator_generate := {| fn_return := tint; fn_callconv := cc_default; fn_params := ((_gen, (tptr (Tstruct __3711 noattr))) :: (_key32, (tptr tuchar)) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _gen (tptr (Tstruct __3711 noattr))) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Sloop (Sifthenelse (Eunop Onotbool (Ebinop One (Etempvar _key32 (tptr tuchar)) (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip) Sbreak) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_generator_generate_internal (Tfunction (Tcons (tptr (Tstruct __3711 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tuchar) Tnil))) tint cc_default)) ((Etempvar _gen (tptr (Tstruct __3711 noattr))) :: (Etempvar _key32 (tptr tuchar)) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))) |}. Definition f_simplicity_gej_is_valid_var := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_a, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := ((_x3, (Tstruct __2380 noattr)) :: (_y2, (Tstruct __2380 noattr)) :: (_z6, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _y2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _a (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul_int (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil)) tvoid cc_default)) ((Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 7) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _z6 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_equal_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _y2 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _x3 (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))))))))) |}. Definition f_read_fe := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2380 noattr))) :: (_src, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_set_b32 (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: (Evar _buf (tarray tuchar 32)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) Sskip))) |}. Definition f_write_fe := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_r, (tptr (Tstruct __2380 noattr))) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Etempvar _r (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _write8s (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)))) |}. Definition f_skip_fe := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Scall None (Evar _skipBits (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tulong Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Econst_int (Int.repr 256) tint) :: nil)) |}. Definition f_read_ge := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3154 noattr))) :: (_src, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _infinity tint) (Econst_int (Int.repr 0) tint)))) |}. Definition f_write_ge := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_r, (tptr (Tstruct __3154 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3154 noattr))) (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil))) |}. Definition f_skip_ge := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _skip_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: nil)) (Scall None (Evar _skip_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: nil))) |}. Definition f_read_gej := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __3156 noattr))) :: (_src, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := nil; fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_is_zero (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sassign (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _infinity tint) (Etempvar _t'1 tint)))))) |}. Definition f_write_gej := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_r, (tptr (Tstruct __3156 noattr))) :: nil); fn_vars := nil; fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Efield (Ederef (Etempvar _r (tptr (Tstruct __3156 noattr))) (Tstruct __3156 noattr)) _z (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)))) |}. Definition f_read_scalar := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_r, (tptr (Tstruct __2843 noattr))) :: (_src, (tptr (Tstruct _frameItem noattr))) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Scall None (Evar _secp256k1_scalar_set_b32 (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr tuchar) (Tcons (tptr tint) Tnil))) tvoid cc_default)) ((Etempvar _r (tptr (Tstruct __2843 noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil))) |}. Definition f_write_scalar := {| fn_return := tvoid; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_r, (tptr (Tstruct __2843 noattr))) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: nil); fn_temps := nil; fn_body := (Ssequence (Scall None (Evar _secp256k1_scalar_get_b32 (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Etempvar _r (tptr (Tstruct __2843 noattr))) :: nil)) (Scall None (Evar _write8s (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil))) |}. Definition f_simplicity_fe_normalize := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_fe_negate := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_negate (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Econst_int (Int.repr 1) tint) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_fe_add := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: (_b, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_add (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _b (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_fe_square := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_sqr (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_fe_multiply := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: (_b, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _b (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_fe_multiply_beta := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_mul (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _secp256k1_const_beta (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_fe_invert := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_inv_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_fe_square_root := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_r, (Tstruct __2380 noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_result, tint) :: (_t'2, tbool) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_sqrt_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _r (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Sset _result (Etempvar _t'1 tint))) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _result tint) :: nil)) (Sifthenelse (Etempvar _t'2 tbool) (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _skip_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: nil)))) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_fe_is_zero := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_is_zero (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_fe_is_odd := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2380 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_is_odd (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_scalar_normalize := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_scalar_negate := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_negate (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_scalar_add := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: (_b, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_add (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _b (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_scalar_square := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_scalar_multiply := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: (_b, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _b (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_scalar_multiply_lambda := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_mul (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _secp256k1_const_lambda (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_scalar_invert := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_scalar_inverse_var (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_scalar (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_scalar_is_zero := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_scalar_is_zero (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_gej_infinity := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _secp256k1_gej_set_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_gej_rescale := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_c, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _c (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_rescale (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _c (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_gej_normalize := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_r, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'2, tbool) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Scall (Some _t'2) (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eunop Onotbool (Etempvar _t'1 tint) tint) :: nil))) (Sifthenelse (Etempvar _t'2 tbool) (Ssequence (Scall None (Evar _secp256k1_ge_set_gej_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Scall None (Evar _write_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil))) (Scall None (Evar _skip_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: nil)))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_gej_negate := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_neg (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_ge_negate := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3154 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_neg (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _a (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_gej_double := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_double_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_gej_add := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_b, (Tstruct __3156 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_gej_ge_add_ex := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_b, (Tstruct __3154 noattr)) :: (_rzr, (Tstruct __2380 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _secp256k1_fe_clear (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Evar _rzr (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _rzr (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_fe (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _rzr (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))))) |}. Definition f_simplicity_gej_ge_add := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_b, (Tstruct __3154 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_gej_is_infinity := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_gej_equiv := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_b, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_eq_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_gej_ge_equiv := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_b, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_eq_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_gej_x_equiv := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_x, (Tstruct __2380 noattr)) :: (_a, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Ssequence (Scall (Some _t'3) (Evar _secp256k1_gej_eq_x_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tint cc_default)) ((Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sset _t'2 (Ecast (Etempvar _t'3 tint) tbool))) (Sset _t'2 (Econst_int (Int.repr 0) tint)))) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'2 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_gej_y_is_odd := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_b, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sifthenelse (Etempvar _t'2 tint) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Econst_int (Int.repr 0) tint) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_set_gej_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_fe_normalize_var (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tvoid cc_default)) ((Eaddrof (Efield (Evar _b (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_fe_is_odd (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) Tnil) tint cc_default)) ((Eaddrof (Efield (Evar _b (Tstruct __3154 noattr)) _y (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))))))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_gej_is_on_curve := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'1, tbool) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _simplicity_gej_is_valid_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tbool) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition f_simplicity_ge_is_on_curve := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_ge_is_valid_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Scall None (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'1 tint) :: nil))) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))) |}. Definition v_ng := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_simplicity_off_curve_scale := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_na, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition v_ng__1 := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_simplicity_scale := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_a, (Tstruct __3156 noattr)) :: (_na, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_t'1, tbool) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _simplicity_gej_is_valid_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tbool) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))) (Sreturn (Some (Econst_int (Int.repr 0) tint)))))))) |}. Definition v_a := {| gvar_info := (Tstruct __3156 noattr); gvar_init := (Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_int32 (Int.repr 1) :: Init_space 4 :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition v_na := {| gvar_info := (Tstruct __2843 noattr); gvar_init := (Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: Init_int64 (Int64.repr 0) :: nil); gvar_readonly := true; gvar_volatile := false |}. Definition f_simplicity_generate := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_ng__2, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_off_curve_linear_combination_1 := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_a__1, (Tstruct __3156 noattr)) :: (_na__1, (Tstruct __2843 noattr)) :: (_ng__2, (Tstruct __2843 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a__1 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a__1 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))))) |}. Definition f_simplicity_linear_combination_1 := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_a__1, (Tstruct __3156 noattr)) :: (_na__1, (Tstruct __2843 noattr)) :: (_ng__2, (Tstruct __2843 noattr)) :: nil); fn_temps := ((_t'1, tbool) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_gej (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a__1 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _simplicity_gej_is_valid_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _a__1 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sifthenelse (Etempvar _t'1 tbool) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a__1 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_gej (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3156 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))) (Sreturn (Some (Econst_int (Int.repr 0) tint))))))))) |}. Definition f_simplicity_linear_verify_1 := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_a__1, (Tstruct __3154 noattr)) :: (_b, (Tstruct __3154 noattr)) :: (_na__1, (Tstruct __2843 noattr)) :: (_ng__2, (Tstruct __2843 noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_a0, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a__1 (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_ge (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_ge_is_valid_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _a__1 (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sifthenelse (Etempvar _t'2 tint) (Ssequence (Scall (Some _t'4) (Evar _secp256k1_ge_is_valid_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sset _t'3 (Ecast (Etempvar _t'4 tint) tbool))) (Sset _t'3 (Econst_int (Int.repr 0) tint)))) (Sifthenelse (Etempvar _t'3 tint) (Ssequence (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a0 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a__1 (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_neg (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a0 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall (Some _t'1) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'1 tint)))))))) (Sreturn (Some (Econst_int (Int.repr 0) tint)))))))))) |}. Definition f_simplicity_decompress := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_x, (Tstruct __2380 noattr)) :: (_r, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_y, tbool) :: (_t'3, tbool) :: (_t'2, tint) :: (_t'1, tbool) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _readBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Sset _y (Ecast (Etempvar _t'1 tbool) tbool))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_ge_set_xo_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tint cc_default)) ((Eaddrof (Evar _r (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _x (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _y tbool) :: nil)) (Scall (Some _t'3) (Evar _writeBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tbool Tnil)) tbool cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Etempvar _t'2 tint) :: nil))) (Sifthenelse (Etempvar _t'3 tbool) (Scall None (Evar _write_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _r (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Scall None (Evar _skip_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: nil)))) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_point_verify_1 := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_ax, (Tstruct __2380 noattr)) :: (_bx, (Tstruct __2380 noattr)) :: (_a__1, (Tstruct __3154 noattr)) :: (_b, (Tstruct __3154 noattr)) :: (_na__1, (Tstruct __2843 noattr)) :: (_ng__2, (Tstruct __2843 noattr)) :: (_r, (Tstruct __3156 noattr)) :: (_a0, (Tstruct __3156 noattr)) :: nil); fn_temps := ((_ay, tbool) :: (_by, tbool) :: (_t'6, tint) :: (_t'5, tint) :: (_t'4, tint) :: (_t'3, tint) :: (_t'2, tbool) :: (_t'1, tbool) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _readBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Sset _ay (Ecast (Etempvar _t'1 tbool) tbool))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ax (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read_scalar (Tfunction (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _readBit (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Sset _by (Ecast (Etempvar _t'2 tbool) tbool))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _bx (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_ge_set_xo_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tint cc_default)) ((Eaddrof (Evar _a__1 (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _ax (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _ay tbool) :: nil)) (Sifthenelse (Etempvar _t'4 tint) (Ssequence (Scall (Some _t'6) (Evar _secp256k1_ge_set_xo_var (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) (Tcons tint Tnil))) tint cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _bx (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Etempvar _by tbool) :: nil)) (Sset _t'5 (Ecast (Etempvar _t'6 tint) tbool))) (Sset _t'5 (Econst_int (Int.repr 0) tint)))) (Sifthenelse (Etempvar _t'5 tint) (Ssequence (Scall None (Evar _secp256k1_gej_set_ge (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _a0 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a__1 (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ge_neg (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_ecmult (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) (Tcons (tptr (Tstruct __2843 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _a0 (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _na__1 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: (Eaddrof (Evar _ng__2 (Tstruct __2843 noattr)) (tptr (Tstruct __2843 noattr))) :: nil)) (Ssequence (Scall None (Evar _secp256k1_gej_add_ge_var (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3156 noattr)) (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)))) tvoid cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: (Eaddrof (Evar _b (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: nil)) (Ssequence (Scall (Some _t'3) (Evar _secp256k1_gej_is_infinity (Tfunction (Tcons (tptr (Tstruct __3156 noattr)) Tnil) tint cc_default)) ((Eaddrof (Evar _r (Tstruct __3156 noattr)) (tptr (Tstruct __3156 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'3 tint)))))))) (Sreturn (Some (Econst_int (Int.repr 0) tint)))))))))))) |}. Definition f_simplicity_bip_0340_verify := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_buf, (tarray tuchar 32)) :: (_pubkey, (Tstruct __3626 noattr)) :: (_msg, (tarray tuchar 32)) :: (_sig, (tarray tuchar 64)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_xonly_pubkey_parse (Tfunction (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: (Evar _buf (tarray tuchar 32)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _msg (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _sig (tarray tuchar 64)) :: (Econst_int (Int.repr 64) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall (Some _t'2) (Evar _secp256k1_schnorrsig_verify (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct __3626 noattr)) Tnil)))) tint cc_default)) ((Evar _sig (tarray tuchar 64)) :: (Evar _msg (tarray tuchar 32)) :: (Esizeof (tarray tuchar 32) tulong) :: (Eaddrof (Evar _pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'2 tint))))))))) |}. Definition f_simplicity_check_sig_verify := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_buf, (tarray tuchar 32)) :: (_pubkey, (Tstruct __3626 noattr)) :: (_msg, (tarray tuchar 64)) :: (_sig, (tarray tuchar 64)) :: (_output, (Tstruct _sha256_midstate noattr)) :: (_ctx, (Tstruct _sha256_context noattr)) :: (__res, (Tstruct _sha256_context noattr)) :: nil); fn_temps := ((_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_xonly_pubkey_parse (Tfunction (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: (Evar _buf (tarray tuchar 32)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Ssequence (Scall None (Evar _sha256_tagged_init (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuint) (Tcons (tptr (Tstruct _sha256_midstate noattr)) Tnil))) tvoid {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|})) ((Eaddrof (Evar __res (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Efield (Evar _output (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: (Eaddrof (Evar _signatureIV (Tstruct _sha256_midstate noattr)) (tptr (Tstruct _sha256_midstate noattr))) :: nil)) (Sassign (Evar _ctx (Tstruct _sha256_context noattr)) (Evar __res (Tstruct _sha256_context noattr)))) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _msg (tarray tuchar 64)) :: (Econst_int (Int.repr 64) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Evar _msg (tarray tuchar 64)) :: (Econst_int (Int.repr 64) tint) :: nil)) (Ssequence (Scall None (Evar _sha256_finalize (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: nil)) (Scall None (Evar _sha256_fromMidstate (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuint) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Efield (Evar _output (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)))))) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _sig (tarray tuchar 64)) :: (Econst_int (Int.repr 64) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall (Some _t'2) (Evar _secp256k1_schnorrsig_verify (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct __3626 noattr)) Tnil)))) tint cc_default)) ((Evar _sig (tarray tuchar 64)) :: (Evar _buf (tarray tuchar 32)) :: (Esizeof (tarray tuchar 32) tulong) :: (Eaddrof (Evar _pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: nil)) (Sreturn (Some (Etempvar _t'2 tint))))))))) |}. Definition f_simplicity_swu := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_t, (Tstruct __2380 noattr)) :: (_ge, (Tstruct __3154 noattr)) :: nil); fn_temps := nil; fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read_fe (Tfunction (Tcons (tptr (Tstruct __2380 noattr)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _shallue_van_de_woestijne (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __2380 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ge (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _t (Tstruct __2380 noattr)) (tptr (Tstruct __2380 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _ge (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint))))))) |}. Definition f_simplicity_hash_to_curve := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (Tstruct _frameItem noattr)) :: (_env, (tptr (Tstruct _txEnv noattr))) :: nil); fn_vars := ((_src, (Tstruct _frameItem noattr)) :: (_key, (tarray tuchar 32)) :: (_gen, (Tstruct __3711 noattr)) :: (_ge, (Tstruct __3154 noattr)) :: nil); fn_temps := ((_t'1, tint) :: nil); fn_body := (Ssequence (Sassign (Evar _src (Tstruct _frameItem noattr)) (Etempvar _src (Tstruct _frameItem noattr))) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _key (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Eaddrof (Evar _src (Tstruct _frameItem noattr)) (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_generator_generate (Tfunction (Tcons (tptr (Tstruct __3711 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _gen (Tstruct __3711 noattr)) (tptr (Tstruct __3711 noattr))) :: (Evar _key (tarray tuchar 32)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _secp256k1_generator_load (Tfunction (Tcons (tptr (Tstruct __3154 noattr)) (Tcons (tptr (Tstruct __3711 noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ge (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: (Eaddrof (Evar _gen (Tstruct __3711 noattr)) (tptr (Tstruct __3711 noattr))) :: nil)) (Ssequence (Scall None (Evar _write_ge (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr (Tstruct __3154 noattr)) Tnil)) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Eaddrof (Evar _ge (Tstruct __3154 noattr)) (tptr (Tstruct __3154 noattr))) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))) |}. Definition f_simplicity_generic_taptweak := {| fn_return := tbool; fn_callconv := cc_default; fn_params := ((_dst, (tptr (Tstruct _frameItem noattr))) :: (_src, (tptr (Tstruct _frameItem noattr))) :: (_tagName, (tptr tuchar)) :: (_tagLen, tulong) :: nil); fn_vars := ((_buf, (tarray tuchar 32)) :: (_input_pubkey, (Tstruct __3626 noattr)) :: (_output_pubkey, (Tstruct __3626 noattr)) :: (_pubkey, (Tstruct __2064 noattr)) :: (_taptweakTag, (Tstruct _sha256_midstate noattr)) :: (_input_hash, (Tstruct _sha256_midstate noattr)) :: (_output_hash, (Tstruct _sha256_midstate noattr)) :: (_ctx, (Tstruct _sha256_context noattr)) :: (_ctx__1, (Tstruct _sha256_context noattr)) :: (__res, (Tstruct _sha256_context noattr)) :: (__res__1, (Tstruct _sha256_context noattr)) :: nil); fn_temps := ((_t'4, tint) :: (_t'3, tint) :: (_t'2, tint) :: (_t'1, tint) :: nil); fn_body := (Ssequence (Ssequence (Ssequence (Scall None (Evar _sha256_init (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuint) Tnil)) tvoid {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|})) ((Eaddrof (Evar __res__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Efield (Evar _taptweakTag (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Sassign (Evar _ctx (Tstruct _sha256_context noattr)) (Evar __res__1 (Tstruct _sha256_context noattr)))) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Etempvar _tagName (tptr tuchar)) :: (Etempvar _tagLen tulong) :: nil)) (Scall None (Evar _sha256_finalize (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _ctx (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: nil)))) (Ssequence (Ssequence (Scall None (Evar _sha256_init (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuint) Tnil)) tvoid {|cc_vararg:=None; cc_unproto:=false; cc_structret:=true|})) ((Eaddrof (Evar __res (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Efield (Evar _output_hash (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Sassign (Evar _ctx__1 (Tstruct _sha256_context noattr)) (Evar __res (Tstruct _sha256_context noattr)))) (Ssequence (Scall None (Evar _sha256_hash (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr (Tstruct _sha256_midstate noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Eaddrof (Evar _taptweakTag (Tstruct _sha256_midstate noattr)) (tptr (Tstruct _sha256_midstate noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_hash (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr (Tstruct _sha256_midstate noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Eaddrof (Evar _taptweakTag (Tstruct _sha256_midstate noattr)) (tptr (Tstruct _sha256_midstate noattr))) :: nil)) (Ssequence (Scall None (Evar _read8s (Tfunction (Tcons (tptr tuchar) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_uchars (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tbool cc_default)) ((Eaddrof (Evar _ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Ssequence (Ssequence (Scall (Some _t'1) (Evar _secp256k1_xonly_pubkey_parse (Tfunction (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr tuchar) Tnil)) tint cc_default)) ((Eaddrof (Evar _input_pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: (Evar _buf (tarray tuchar 32)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'1 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _read32s (Tfunction (Tcons (tptr tuint) (Tcons tulong (Tcons (tptr (Tstruct _frameItem noattr)) Tnil))) tvoid cc_default)) ((Efield (Evar _input_hash (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: (Econst_int (Int.repr 8) tint) :: (Etempvar _src (tptr (Tstruct _frameItem noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_hash (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) (Tcons (tptr (Tstruct _sha256_midstate noattr)) Tnil)) tvoid cc_default)) ((Eaddrof (Evar _ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: (Eaddrof (Evar _input_hash (Tstruct _sha256_midstate noattr)) (tptr (Tstruct _sha256_midstate noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_finalize (Tfunction (Tcons (tptr (Tstruct _sha256_context noattr)) Tnil) tbool cc_default)) ((Eaddrof (Evar _ctx__1 (Tstruct _sha256_context noattr)) (tptr (Tstruct _sha256_context noattr))) :: nil)) (Ssequence (Scall None (Evar _sha256_fromMidstate (Tfunction (Tcons (tptr tuchar) (Tcons (tptr tuint) Tnil)) tvoid cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Efield (Evar _output_hash (Tstruct _sha256_midstate noattr)) _s (tarray tuint 8)) :: nil)) (Ssequence (Ssequence (Scall (Some _t'2) (Evar _secp256k1_xonly_pubkey_tweak_add (Tfunction (Tcons (tptr (Tstruct __2064 noattr)) (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr tuchar) Tnil))) tint cc_default)) ((Eaddrof (Evar _pubkey (Tstruct __2064 noattr)) (tptr (Tstruct __2064 noattr))) :: (Eaddrof (Evar _input_pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: (Evar _buf (tarray tuchar 32)) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'2 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'3) (Evar _secp256k1_xonly_pubkey_from_pubkey (Tfunction (Tcons (tptr (Tstruct __3626 noattr)) (Tcons (tptr tint) (Tcons (tptr (Tstruct __2064 noattr)) Tnil))) tint cc_default)) ((Eaddrof (Evar _output_pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: (Ecast (Econst_int (Int.repr 0) tint) (tptr tvoid)) :: (Eaddrof (Evar _pubkey (Tstruct __2064 noattr)) (tptr (Tstruct __2064 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'3 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Ssequence (Scall (Some _t'4) (Evar _secp256k1_xonly_pubkey_serialize (Tfunction (Tcons (tptr tuchar) (Tcons (tptr (Tstruct __3626 noattr)) Tnil)) tint cc_default)) ((Evar _buf (tarray tuchar 32)) :: (Eaddrof (Evar _output_pubkey (Tstruct __3626 noattr)) (tptr (Tstruct __3626 noattr))) :: nil)) (Sifthenelse (Eunop Onotbool (Etempvar _t'4 tint) tint) (Sreturn (Some (Econst_int (Int.repr 0) tint))) Sskip)) (Ssequence (Scall None (Evar _write8s (Tfunction (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons (tptr tuchar) (Tcons tulong Tnil))) tvoid cc_default)) ((Etempvar _dst (tptr (Tstruct _frameItem noattr))) :: (Evar _buf (tarray tuchar 32)) :: (Econst_int (Int.repr 32) tint) :: nil)) (Sreturn (Some (Econst_int (Int.repr 1) tint)))))))))))))))))) |}. Definition composites : list composite_definition := (Composite _sha256_midstate Struct (Member_plain _s (tarray tuint 8) :: nil) noattr :: Composite _sha256_context Struct (Member_plain _output (tptr tuint) :: Member_plain _counter tulong :: Member_plain _block (tarray tuchar 64) :: Member_plain _overflow tbool :: nil) noattr :: Composite _frameItem Struct (Member_plain _edge (tptr tulong) :: Member_plain _offset tulong :: nil) noattr :: Composite __2064 Struct (Member_plain _data (tarray tuchar 64) :: nil) noattr :: Composite __IO_FILE Struct (Member_plain __flags tint :: Member_plain __IO_read_ptr (tptr tschar) :: Member_plain __IO_read_end (tptr tschar) :: Member_plain __IO_read_base (tptr tschar) :: Member_plain __IO_write_base (tptr tschar) :: Member_plain __IO_write_ptr (tptr tschar) :: Member_plain __IO_write_end (tptr tschar) :: Member_plain __IO_buf_base (tptr tschar) :: Member_plain __IO_buf_end (tptr tschar) :: Member_plain __IO_save_base (tptr tschar) :: Member_plain __IO_backup_base (tptr tschar) :: Member_plain __IO_save_end (tptr tschar) :: Member_plain __markers (tptr (Tstruct __IO_marker noattr)) :: Member_plain __chain (tptr (Tstruct __IO_FILE noattr)) :: Member_plain __fileno tint :: Member_plain __flags2 tint :: Member_plain __old_offset tlong :: Member_plain __cur_column tushort :: Member_plain __vtable_offset tschar :: Member_plain __shortbuf (tarray tschar 1) :: Member_plain __lock (tptr tvoid) :: Member_plain __offset tlong :: Member_plain __codecvt (tptr (Tstruct __IO_codecvt noattr)) :: Member_plain __wide_data (tptr (Tstruct __IO_wide_data noattr)) :: Member_plain __freeres_list (tptr (Tstruct __IO_FILE noattr)) :: Member_plain __freeres_buf (tptr tvoid) :: Member_plain __prevchain (tptr (tptr (Tstruct __IO_FILE noattr))) :: Member_plain __mode tint :: Member_plain __unused2 (tarray tschar 20) :: nil) noattr :: Composite __2380 Struct (Member_plain _n (tarray tulong 5) :: Member_plain _magnitude tint :: Member_plain _normalized tint :: nil) noattr :: Composite __2382 Struct (Member_plain _n (tarray tulong 4) :: nil) noattr :: Composite _secp256k1_uint128 Struct (Member_plain _lo tulong :: Member_plain _hi tulong :: nil) noattr :: Composite _secp256k1_modinv64_signed62 Struct (Member_plain _v (tarray tlong 5) :: nil) noattr :: Composite _secp256k1_modinv64_modinfo Struct (Member_plain _modulus (Tstruct _secp256k1_modinv64_signed62 noattr) :: Member_plain _modulus_inv62 tulong :: nil) noattr :: Composite _secp256k1_modinv64_trans2x2 Struct (Member_plain _u tlong :: Member_plain _v tlong :: Member_plain _q tlong :: Member_plain _r tlong :: nil) noattr :: Composite __2843 Struct (Member_plain _d (tarray tulong 4) :: nil) noattr :: Composite __3154 Struct (Member_plain _x (Tstruct __2380 noattr) :: Member_plain _y (Tstruct __2380 noattr) :: Member_plain _infinity tint :: nil) noattr :: Composite __3156 Struct (Member_plain _x (Tstruct __2380 noattr) :: Member_plain _y (Tstruct __2380 noattr) :: Member_plain _z (Tstruct __2380 noattr) :: Member_plain _infinity tint :: nil) noattr :: Composite __3158 Struct (Member_plain _x (Tstruct __2382 noattr) :: Member_plain _y (Tstruct __2382 noattr) :: nil) noattr :: Composite _secp256k1_strauss_point_state Struct (Member_plain _wnaf_na_1 (tarray tint 129) :: Member_plain _wnaf_na_lam (tarray tint 129) :: Member_plain _bits_na_1 tint :: Member_plain _bits_na_lam tint :: nil) noattr :: Composite _secp256k1_strauss_state Struct (Member_plain _aux (tptr (Tstruct __2380 noattr)) :: Member_plain _pre_a (tptr (Tstruct __3154 noattr)) :: Member_plain _ps (tptr (Tstruct _secp256k1_strauss_point_state noattr)) :: nil) noattr :: Composite __3626 Struct (Member_plain _data (tarray tuchar 64) :: nil) noattr :: Composite __3711 Struct (Member_plain _data (tarray tuchar 64) :: nil) noattr :: nil). Definition global_definitions : list (ident * globdef fundef type) := ((___compcert_va_int32, Gfun(External (EF_runtime "__compcert_va_int32" (mksignature (AST.Tlong :: nil) AST.Tint cc_default)) (Tcons (tptr tvoid) Tnil) tuint cc_default)) :: (___compcert_va_int64, Gfun(External (EF_runtime "__compcert_va_int64" (mksignature (AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons (tptr tvoid) Tnil) tulong cc_default)) :: (___compcert_va_float64, Gfun(External (EF_runtime "__compcert_va_float64" (mksignature (AST.Tlong :: nil) AST.Tfloat cc_default)) (Tcons (tptr tvoid) Tnil) tdouble cc_default)) :: (___compcert_va_float32, Gfun(External (EF_runtime "__compcert_va_float32" (mksignature (AST.Tlong :: nil) AST.Tsingle cc_default)) (Tcons (tptr tvoid) Tnil) tfloat cc_default)) :: (___compcert_va_composite, Gfun(External (EF_runtime "__compcert_va_composite" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons (tptr tvoid) (Tcons tulong Tnil)) (tptr tvoid) cc_default)) :: (___compcert_i64_dtos, Gfun(External (EF_runtime "__compcert_i64_dtos" (mksignature (AST.Tfloat :: nil) AST.Tlong cc_default)) (Tcons tdouble Tnil) tlong cc_default)) :: (___compcert_i64_dtou, Gfun(External (EF_runtime "__compcert_i64_dtou" (mksignature (AST.Tfloat :: nil) AST.Tlong cc_default)) (Tcons tdouble Tnil) tulong cc_default)) :: (___compcert_i64_ftos, Gfun(External (EF_runtime "__compcert_i64_ftos" (mksignature (AST.Tsingle :: nil) AST.Tlong cc_default)) (Tcons tfloat Tnil) tulong cc_default)) :: (___compcert_i64_ftou, Gfun(External (EF_runtime "__compcert_i64_ftou" (mksignature (AST.Tsingle :: nil) AST.Tlong cc_default)) (Tcons tfloat Tnil) tlong cc_default)) :: (___compcert_i64_stod, Gfun(External (EF_runtime "__compcert_i64_stod" (mksignature (AST.Tlong :: nil) AST.Tfloat cc_default)) (Tcons tlong Tnil) tdouble cc_default)) :: (___compcert_i64_utod, Gfun(External (EF_runtime "__compcert_i64_utod" (mksignature (AST.Tlong :: nil) AST.Tfloat cc_default)) (Tcons tulong Tnil) tdouble cc_default)) :: (___compcert_i64_stof, Gfun(External (EF_runtime "__compcert_i64_stof" (mksignature (AST.Tlong :: nil) AST.Tsingle cc_default)) (Tcons tlong Tnil) tfloat cc_default)) :: (___compcert_i64_utof, Gfun(External (EF_runtime "__compcert_i64_utof" (mksignature (AST.Tlong :: nil) AST.Tsingle cc_default)) (Tcons tulong Tnil) tfloat cc_default)) :: (___compcert_i64_sdiv, Gfun(External (EF_runtime "__compcert_i64_sdiv" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___compcert_i64_udiv, Gfun(External (EF_runtime "__compcert_i64_udiv" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tulong (Tcons tulong Tnil)) tulong cc_default)) :: (___compcert_i64_smod, Gfun(External (EF_runtime "__compcert_i64_smod" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___compcert_i64_umod, Gfun(External (EF_runtime "__compcert_i64_umod" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tulong (Tcons tulong Tnil)) tulong cc_default)) :: (___compcert_i64_shl, Gfun(External (EF_runtime "__compcert_i64_shl" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tint Tnil)) tlong cc_default)) :: (___compcert_i64_shr, Gfun(External (EF_runtime "__compcert_i64_shr" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tlong cc_default)) (Tcons tulong (Tcons tint Tnil)) tulong cc_default)) :: (___compcert_i64_sar, Gfun(External (EF_runtime "__compcert_i64_sar" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tint Tnil)) tlong cc_default)) :: (___compcert_i64_smulh, Gfun(External (EF_runtime "__compcert_i64_smulh" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___compcert_i64_umulh, Gfun(External (EF_runtime "__compcert_i64_umulh" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tulong (Tcons tulong Tnil)) tulong cc_default)) :: (___stringlit_1, Gvar v___stringlit_1) :: (___stringlit_2, Gvar v___stringlit_2) :: (___stringlit_3, Gvar v___stringlit_3) :: (___stringlit_4, Gvar v___stringlit_4) :: (___stringlit_5, Gvar v___stringlit_5) :: (___stringlit_6, Gvar v___stringlit_6) :: (___stringlit_7, Gvar v___stringlit_7) :: (___stringlit_8, Gvar v___stringlit_8) :: (___stringlit_9, Gvar v___stringlit_9) :: (___stringlit_10, Gvar v___stringlit_10) :: (___stringlit_20, Gvar v___stringlit_20) :: (___stringlit_30, Gvar v___stringlit_30) :: (___stringlit_40, Gvar v___stringlit_40) :: (___stringlit_50, Gvar v___stringlit_50) :: (___stringlit_60, Gvar v___stringlit_60) :: (___stringlit_70, Gvar v___stringlit_70) :: (___stringlit_80, Gvar v___stringlit_80) :: (___stringlit_90, Gvar v___stringlit_90) :: (___stringlit_11, Gvar v___stringlit_11) :: (___stringlit_21, Gvar v___stringlit_21) :: (___stringlit_31, Gvar v___stringlit_31) :: (___stringlit_41, Gvar v___stringlit_41) :: (___stringlit_51, Gvar v___stringlit_51) :: (___stringlit_61, Gvar v___stringlit_61) :: (___stringlit_71, Gvar v___stringlit_71) :: (___stringlit_81, Gvar v___stringlit_81) :: (___stringlit_91, Gvar v___stringlit_91) :: (___stringlit_12, Gvar v___stringlit_12) :: (___stringlit_22, Gvar v___stringlit_22) :: (___stringlit_32, Gvar v___stringlit_32) :: (___stringlit_42, Gvar v___stringlit_42) :: (___stringlit_52, Gvar v___stringlit_52) :: (___stringlit_62, Gvar v___stringlit_62) :: (___stringlit_72, Gvar v___stringlit_72) :: (___stringlit_82, Gvar v___stringlit_82) :: (___stringlit_92, Gvar v___stringlit_92) :: (___stringlit_13, Gvar v___stringlit_13) :: (___stringlit_23, Gvar v___stringlit_23) :: (___stringlit_33, Gvar v___stringlit_33) :: (___stringlit_43, Gvar v___stringlit_43) :: (___stringlit_53, Gvar v___stringlit_53) :: (___stringlit_63, Gvar v___stringlit_63) :: (___stringlit_73, Gvar v___stringlit_73) :: (___stringlit_83, Gvar v___stringlit_83) :: (___stringlit_93, Gvar v___stringlit_93) :: (___stringlit_14, Gvar v___stringlit_14) :: (___stringlit_24, Gvar v___stringlit_24) :: (___stringlit_34, Gvar v___stringlit_34) :: (___stringlit_44, Gvar v___stringlit_44) :: (___stringlit_54, Gvar v___stringlit_54) :: (___stringlit_64, Gvar v___stringlit_64) :: (___stringlit_74, Gvar v___stringlit_74) :: (___stringlit_84, Gvar v___stringlit_84) :: (___stringlit_94, Gvar v___stringlit_94) :: (___stringlit_15, Gvar v___stringlit_15) :: (___stringlit_25, Gvar v___stringlit_25) :: (___stringlit_35, Gvar v___stringlit_35) :: (___stringlit_45, Gvar v___stringlit_45) :: (___stringlit_55, Gvar v___stringlit_55) :: (___stringlit_65, Gvar v___stringlit_65) :: (___stringlit_75, Gvar v___stringlit_75) :: (___stringlit_85, Gvar v___stringlit_85) :: (___stringlit_95, Gvar v___stringlit_95) :: (___stringlit_16, Gvar v___stringlit_16) :: (___stringlit_26, Gvar v___stringlit_26) :: (___stringlit_36, Gvar v___stringlit_36) :: (___stringlit_46, Gvar v___stringlit_46) :: (___stringlit_56, Gvar v___stringlit_56) :: (___stringlit_66, Gvar v___stringlit_66) :: (___stringlit_76, Gvar v___stringlit_76) :: (___stringlit_86, Gvar v___stringlit_86) :: (___stringlit_96, Gvar v___stringlit_96) :: (___stringlit_17, Gvar v___stringlit_17) :: (___stringlit_27, Gvar v___stringlit_27) :: (___stringlit_37, Gvar v___stringlit_37) :: (___stringlit_47, Gvar v___stringlit_47) :: (___stringlit_57, Gvar v___stringlit_57) :: (___stringlit_67, Gvar v___stringlit_67) :: (___stringlit_77, Gvar v___stringlit_77) :: (___stringlit_87, Gvar v___stringlit_87) :: (___stringlit_97, Gvar v___stringlit_97) :: (___stringlit_18, Gvar v___stringlit_18) :: (___stringlit_28, Gvar v___stringlit_28) :: (___stringlit_38, Gvar v___stringlit_38) :: (___stringlit_48, Gvar v___stringlit_48) :: (___stringlit_58, Gvar v___stringlit_58) :: (___stringlit_68, Gvar v___stringlit_68) :: (___stringlit_78, Gvar v___stringlit_78) :: (___stringlit_88, Gvar v___stringlit_88) :: (___stringlit_98, Gvar v___stringlit_98) :: (___stringlit_19, Gvar v___stringlit_19) :: (___stringlit_29, Gvar v___stringlit_29) :: (___stringlit_39, Gvar v___stringlit_39) :: (___stringlit_49, Gvar v___stringlit_49) :: (___stringlit_59, Gvar v___stringlit_59) :: (___stringlit_69, Gvar v___stringlit_69) :: (___stringlit_79, Gvar v___stringlit_79) :: (___stringlit_89, Gvar v___stringlit_89) :: (___stringlit_99, Gvar v___stringlit_99) :: (___stringlit_100, Gvar v___stringlit_100) :: (___stringlit_110, Gvar v___stringlit_110) :: (___stringlit_120, Gvar v___stringlit_120) :: (___stringlit_130, Gvar v___stringlit_130) :: (___stringlit_140, Gvar v___stringlit_140) :: (___stringlit_150, Gvar v___stringlit_150) :: (___stringlit_160, Gvar v___stringlit_160) :: (___stringlit_170, Gvar v___stringlit_170) :: (___stringlit_101, Gvar v___stringlit_101) :: (___stringlit_111, Gvar v___stringlit_111) :: (___stringlit_121, Gvar v___stringlit_121) :: (___stringlit_131, Gvar v___stringlit_131) :: (___stringlit_141, Gvar v___stringlit_141) :: (___stringlit_151, Gvar v___stringlit_151) :: (___stringlit_161, Gvar v___stringlit_161) :: (___stringlit_171, Gvar v___stringlit_171) :: (___stringlit_102, Gvar v___stringlit_102) :: (___stringlit_112, Gvar v___stringlit_112) :: (___stringlit_122, Gvar v___stringlit_122) :: (___stringlit_132, Gvar v___stringlit_132) :: (___stringlit_142, Gvar v___stringlit_142) :: (___stringlit_152, Gvar v___stringlit_152) :: (___stringlit_162, Gvar v___stringlit_162) :: (___stringlit_172, Gvar v___stringlit_172) :: (___stringlit_103, Gvar v___stringlit_103) :: (___stringlit_113, Gvar v___stringlit_113) :: (___stringlit_123, Gvar v___stringlit_123) :: (___stringlit_133, Gvar v___stringlit_133) :: (___stringlit_143, Gvar v___stringlit_143) :: (___stringlit_153, Gvar v___stringlit_153) :: (___stringlit_163, Gvar v___stringlit_163) :: (___stringlit_104, Gvar v___stringlit_104) :: (___stringlit_114, Gvar v___stringlit_114) :: (___stringlit_124, Gvar v___stringlit_124) :: (___stringlit_134, Gvar v___stringlit_134) :: (___stringlit_144, Gvar v___stringlit_144) :: (___stringlit_154, Gvar v___stringlit_154) :: (___stringlit_164, Gvar v___stringlit_164) :: (___stringlit_105, Gvar v___stringlit_105) :: (___stringlit_115, Gvar v___stringlit_115) :: (___stringlit_125, Gvar v___stringlit_125) :: (___stringlit_135, Gvar v___stringlit_135) :: (___stringlit_145, Gvar v___stringlit_145) :: (___stringlit_155, Gvar v___stringlit_155) :: (___stringlit_165, Gvar v___stringlit_165) :: (___stringlit_106, Gvar v___stringlit_106) :: (___stringlit_116, Gvar v___stringlit_116) :: (___stringlit_126, Gvar v___stringlit_126) :: (___stringlit_136, Gvar v___stringlit_136) :: (___stringlit_146, Gvar v___stringlit_146) :: (___stringlit_156, Gvar v___stringlit_156) :: (___stringlit_166, Gvar v___stringlit_166) :: (___stringlit_107, Gvar v___stringlit_107) :: (___stringlit_117, Gvar v___stringlit_117) :: (___stringlit_127, Gvar v___stringlit_127) :: (___stringlit_137, Gvar v___stringlit_137) :: (___stringlit_147, Gvar v___stringlit_147) :: (___stringlit_157, Gvar v___stringlit_157) :: (___stringlit_167, Gvar v___stringlit_167) :: (___stringlit_108, Gvar v___stringlit_108) :: (___stringlit_118, Gvar v___stringlit_118) :: (___stringlit_128, Gvar v___stringlit_128) :: (___stringlit_138, Gvar v___stringlit_138) :: (___stringlit_148, Gvar v___stringlit_148) :: (___stringlit_158, Gvar v___stringlit_158) :: (___stringlit_168, Gvar v___stringlit_168) :: (___stringlit_109, Gvar v___stringlit_109) :: (___stringlit_119, Gvar v___stringlit_119) :: (___stringlit_129, Gvar v___stringlit_129) :: (___stringlit_139, Gvar v___stringlit_139) :: (___stringlit_149, Gvar v___stringlit_149) :: (___stringlit_159, Gvar v___stringlit_159) :: (___stringlit_169, Gvar v___stringlit_169) :: (___builtin_ais_annot, Gfun(External (EF_builtin "__builtin_ais_annot" (mksignature (AST.Tlong :: nil) AST.Tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) (Tcons (tptr tschar) Tnil) tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) :: (___builtin_bswap64, Gfun(External (EF_builtin "__builtin_bswap64" (mksignature (AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tulong Tnil) tulong cc_default)) :: (___builtin_bswap, Gfun(External (EF_builtin "__builtin_bswap" (mksignature (AST.Tint :: nil) AST.Tint cc_default)) (Tcons tuint Tnil) tuint cc_default)) :: (___builtin_bswap32, Gfun(External (EF_builtin "__builtin_bswap32" (mksignature (AST.Tint :: nil) AST.Tint cc_default)) (Tcons tuint Tnil) tuint cc_default)) :: (___builtin_bswap16, Gfun(External (EF_builtin "__builtin_bswap16" (mksignature (AST.Tint :: nil) AST.Tint16unsigned cc_default)) (Tcons tushort Tnil) tushort cc_default)) :: (___builtin_clz, Gfun(External (EF_builtin "__builtin_clz" (mksignature (AST.Tint :: nil) AST.Tint cc_default)) (Tcons tuint Tnil) tint cc_default)) :: (___builtin_clzl, Gfun(External (EF_builtin "__builtin_clzl" (mksignature (AST.Tlong :: nil) AST.Tint cc_default)) (Tcons tulong Tnil) tint cc_default)) :: (___builtin_clzll, Gfun(External (EF_builtin "__builtin_clzll" (mksignature (AST.Tlong :: nil) AST.Tint cc_default)) (Tcons tulong Tnil) tint cc_default)) :: (___builtin_ctz, Gfun(External (EF_builtin "__builtin_ctz" (mksignature (AST.Tint :: nil) AST.Tint cc_default)) (Tcons tuint Tnil) tint cc_default)) :: (___builtin_ctzl, Gfun(External (EF_builtin "__builtin_ctzl" (mksignature (AST.Tlong :: nil) AST.Tint cc_default)) (Tcons tulong Tnil) tint cc_default)) :: (___builtin_ctzll, Gfun(External (EF_builtin "__builtin_ctzll" (mksignature (AST.Tlong :: nil) AST.Tint cc_default)) (Tcons tulong Tnil) tint cc_default)) :: (___builtin_negl, Gfun(External (EF_builtin "__builtin_negl" (mksignature (AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong Tnil) tlong cc_default)) :: (___builtin_addl, Gfun(External (EF_builtin "__builtin_addl" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___builtin_subl, Gfun(External (EF_builtin "__builtin_subl" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___builtin_mull, Gfun(External (EF_builtin "__builtin_mull" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___builtin_fabs, Gfun(External (EF_builtin "__builtin_fabs" (mksignature (AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble Tnil) tdouble cc_default)) :: (___builtin_fabsf, Gfun(External (EF_builtin "__builtin_fabsf" (mksignature (AST.Tsingle :: nil) AST.Tsingle cc_default)) (Tcons tfloat Tnil) tfloat cc_default)) :: (___builtin_fsqrt, Gfun(External (EF_builtin "__builtin_fsqrt" (mksignature (AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble Tnil) tdouble cc_default)) :: (___builtin_sqrt, Gfun(External (EF_builtin "__builtin_sqrt" (mksignature (AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble Tnil) tdouble cc_default)) :: (___builtin_nanf, Gfun(External (EF_builtin "__builtin_nanf" (mksignature (AST.Tlong :: nil) AST.Tsingle cc_default)) (Tcons (tptr tschar) Tnil) tfloat cc_default)) :: (___builtin_nansf, Gfun(External (EF_builtin "__builtin_nansf" (mksignature (AST.Tlong :: nil) AST.Tsingle cc_default)) (Tcons (tptr tschar) Tnil) tfloat cc_default)) :: (___builtin_nan, Gfun(External (EF_builtin "__builtin_nan" (mksignature (AST.Tlong :: nil) AST.Tfloat cc_default)) (Tcons (tptr tschar) Tnil) tdouble cc_default)) :: (___builtin_nans, Gfun(External (EF_builtin "__builtin_nans" (mksignature (AST.Tlong :: nil) AST.Tfloat cc_default)) (Tcons (tptr tschar) Tnil) tdouble cc_default)) :: (___builtin_isnanf, Gfun(External (EF_builtin "__builtin_isnanf" (mksignature (AST.Tsingle :: nil) AST.Tint cc_default)) (Tcons tfloat Tnil) tint cc_default)) :: (___builtin_isnan, Gfun(External (EF_builtin "__builtin_isnan" (mksignature (AST.Tfloat :: nil) AST.Tint cc_default)) (Tcons tdouble Tnil) tint cc_default)) :: (___builtin_isinff, Gfun(External (EF_builtin "__builtin_isinff" (mksignature (AST.Tsingle :: nil) AST.Tint cc_default)) (Tcons tfloat Tnil) tint cc_default)) :: (___builtin_isinf, Gfun(External (EF_builtin "__builtin_isinf" (mksignature (AST.Tfloat :: nil) AST.Tint cc_default)) (Tcons tdouble Tnil) tint cc_default)) :: (___builtin_isfinitef, Gfun(External (EF_builtin "__builtin_isfinitef" (mksignature (AST.Tsingle :: nil) AST.Tint cc_default)) (Tcons tfloat Tnil) tint cc_default)) :: (___builtin_isfinite, Gfun(External (EF_builtin "__builtin_isfinite" (mksignature (AST.Tfloat :: nil) AST.Tint cc_default)) (Tcons tdouble Tnil) tint cc_default)) :: (___builtin_memcpy_aligned, Gfun(External (EF_builtin "__builtin_memcpy_aligned" (mksignature (AST.Tlong :: AST.Tlong :: AST.Tlong :: AST.Tlong :: nil) AST.Tvoid cc_default)) (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong (Tcons tulong Tnil)))) tvoid cc_default)) :: (___builtin_sel, Gfun(External (EF_builtin "__builtin_sel" (mksignature (AST.Tint :: nil) AST.Tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) (Tcons tbool Tnil) tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) :: (___builtin_annot, Gfun(External (EF_builtin "__builtin_annot" (mksignature (AST.Tlong :: nil) AST.Tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) (Tcons (tptr tschar) Tnil) tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) :: (___builtin_annot_intval, Gfun(External (EF_builtin "__builtin_annot_intval" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tint cc_default)) (Tcons (tptr tschar) (Tcons tint Tnil)) tint cc_default)) :: (___builtin_membar, Gfun(External (EF_builtin "__builtin_membar" (mksignature nil AST.Tvoid cc_default)) Tnil tvoid cc_default)) :: (___builtin_debug, Gfun(External (EF_builtin "__builtin_debug" (mksignature (AST.Tint :: nil) AST.Tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) (Tcons tint Tnil) tvoid {|cc_vararg:=(Some 1); cc_unproto:=false; cc_structret:=false|})) :: (___builtin_nop, Gfun(External (EF_builtin "__builtin_nop" (mksignature nil AST.Tvoid cc_default)) Tnil tvoid cc_default)) :: (___builtin_va_start, Gfun(External (EF_builtin "__builtin_va_start" (mksignature (AST.Tlong :: nil) AST.Tvoid cc_default)) (Tcons (tptr tvoid) Tnil) tvoid cc_default)) :: (___builtin_va_arg, Gfun(External (EF_builtin "__builtin_va_arg" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tvoid cc_default)) (Tcons (tptr tvoid) (Tcons tuint Tnil)) tvoid cc_default)) :: (___builtin_va_copy, Gfun(External (EF_builtin "__builtin_va_copy" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tvoid cc_default)) (Tcons (tptr tvoid) (Tcons (tptr tvoid) Tnil)) tvoid cc_default)) :: (___builtin_va_end, Gfun(External (EF_builtin "__builtin_va_end" (mksignature (AST.Tlong :: nil) AST.Tvoid cc_default)) (Tcons (tptr tvoid) Tnil) tvoid cc_default)) :: (___builtin_unreachable, Gfun(External (EF_builtin "__builtin_unreachable" (mksignature nil AST.Tvoid cc_default)) Tnil tvoid cc_default)) :: (___builtin_expect, Gfun(External (EF_builtin "__builtin_expect" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons tlong (Tcons tlong Tnil)) tlong cc_default)) :: (___builtin_fmax, Gfun(External (EF_builtin "__builtin_fmax" (mksignature (AST.Tfloat :: AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble (Tcons tdouble Tnil)) tdouble cc_default)) :: (___builtin_fmin, Gfun(External (EF_builtin "__builtin_fmin" (mksignature (AST.Tfloat :: AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble (Tcons tdouble Tnil)) tdouble cc_default)) :: (___builtin_fmadd, Gfun(External (EF_builtin "__builtin_fmadd" (mksignature (AST.Tfloat :: AST.Tfloat :: AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble (Tcons tdouble (Tcons tdouble Tnil))) tdouble cc_default)) :: (___builtin_fmsub, Gfun(External (EF_builtin "__builtin_fmsub" (mksignature (AST.Tfloat :: AST.Tfloat :: AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble (Tcons tdouble (Tcons tdouble Tnil))) tdouble cc_default)) :: (___builtin_fnmadd, Gfun(External (EF_builtin "__builtin_fnmadd" (mksignature (AST.Tfloat :: AST.Tfloat :: AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble (Tcons tdouble (Tcons tdouble Tnil))) tdouble cc_default)) :: (___builtin_fnmsub, Gfun(External (EF_builtin "__builtin_fnmsub" (mksignature (AST.Tfloat :: AST.Tfloat :: AST.Tfloat :: nil) AST.Tfloat cc_default)) (Tcons tdouble (Tcons tdouble (Tcons tdouble Tnil))) tdouble cc_default)) :: (___builtin_read16_reversed, Gfun(External (EF_builtin "__builtin_read16_reversed" (mksignature (AST.Tlong :: nil) AST.Tint16unsigned cc_default)) (Tcons (tptr tushort) Tnil) tushort cc_default)) :: (___builtin_read32_reversed, Gfun(External (EF_builtin "__builtin_read32_reversed" (mksignature (AST.Tlong :: nil) AST.Tint cc_default)) (Tcons (tptr tuint) Tnil) tuint cc_default)) :: (___builtin_write16_reversed, Gfun(External (EF_builtin "__builtin_write16_reversed" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tvoid cc_default)) (Tcons (tptr tushort) (Tcons tushort Tnil)) tvoid cc_default)) :: (___builtin_write32_reversed, Gfun(External (EF_builtin "__builtin_write32_reversed" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tvoid cc_default)) (Tcons (tptr tuint) (Tcons tuint Tnil)) tvoid cc_default)) :: (_memcpy, Gfun(External (EF_external "memcpy" (mksignature (AST.Tlong :: AST.Tlong :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons (tptr tvoid) (Tcons (tptr tvoid) (Tcons tulong Tnil))) (tptr tvoid) cc_default)) :: (_memset, Gfun(External (EF_external "memset" (mksignature (AST.Tlong :: AST.Tint :: AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons (tptr tvoid) (Tcons tint (Tcons tulong Tnil))) (tptr tvoid) cc_default)) :: (___assert_fail, Gfun(External (EF_external "__assert_fail" (mksignature (AST.Tlong :: AST.Tlong :: AST.Tint :: AST.Tlong :: nil) AST.Tvoid cc_default)) (Tcons (tptr tschar) (Tcons (tptr tschar) (Tcons tuint (Tcons (tptr tschar) Tnil)))) tvoid cc_default)) :: (_ReadBE32, Gfun(Internal f_ReadBE32)) :: (_WriteBE64, Gfun(Internal f_WriteBE64)) :: (_WriteBE32, Gfun(Internal f_WriteBE32)) :: (_sha256_fromMidstate, Gfun(Internal f_sha256_fromMidstate)) :: (_sha256_iv, Gfun(Internal f_sha256_iv)) :: (_simplicity_sha256_compression, Gvar v_simplicity_sha256_compression) :: (_sha256_compression_uchar, Gfun(Internal f_sha256_compression_uchar)) :: (_sha256_max_counter, Gvar v_sha256_max_counter) :: (_sha256_init, Gfun(Internal f_sha256_init)) :: (_sha256_tagged_init, Gfun(Internal f_sha256_tagged_init)) :: (_sha256_uchars, Gfun(Internal f_sha256_uchars)) :: (_sha256_u64be, Gfun(Internal f_sha256_u64be)) :: (_sha256_finalize, Gfun(Internal f_sha256_finalize)) :: (_sha256_hash, Gfun(Internal f_sha256_hash)) :: (_LSBclear, Gfun(Internal f_LSBclear)) :: (_peekBit, Gfun(Internal f_peekBit)) :: (_readBit, Gfun(Internal f_readBit)) :: (___func__, Gvar v___func__) :: (_writeBit, Gfun(Internal f_writeBit)) :: (___func____1, Gvar v___func____1) :: (_skipBits, Gfun(Internal f_skipBits)) :: (_simplicity_read8, Gfun(External (EF_external "simplicity_read8" (mksignature (AST.Tlong :: nil) AST.Tint8unsigned cc_default)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tuchar cc_default)) :: (_simplicity_read32, Gfun(External (EF_external "simplicity_read32" (mksignature (AST.Tlong :: nil) AST.Tlong cc_default)) (Tcons (tptr (Tstruct _frameItem noattr)) Tnil) tulong cc_default)) :: (_simplicity_write8, Gfun(External (EF_external "simplicity_write8" (mksignature (AST.Tlong :: AST.Tint :: nil) AST.Tvoid cc_default)) (Tcons (tptr (Tstruct _frameItem noattr)) (Tcons tuchar Tnil)) tvoid cc_default)) :: (_read8s, Gfun(Internal f_read8s)) :: (_write8s, Gfun(Internal f_write8s)) :: (_read32s, Gfun(Internal f_read32s)) :: (_signatureIV, Gvar v_signatureIV) :: (_abort, Gfun(External (EF_external "abort" (mksignature nil AST.Tvoid cc_default)) Tnil tvoid cc_default)) :: (_stderr, Gvar v_stderr) :: (_fprintf, Gfun(External (EF_external "fprintf" (mksignature (AST.Tlong :: AST.Tlong :: nil) AST.Tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) (Tcons (tptr (Tstruct __IO_FILE noattr)) (Tcons (tptr tschar) Tnil)) tint {|cc_vararg:=(Some 2); cc_unproto:=false; cc_structret:=false|})) :: (_secp256k1_memcmp_var, Gfun(Internal f_secp256k1_memcmp_var)) :: (_debruijn, Gvar v_debruijn) :: (_secp256k1_ctz64_var_debruijn, Gfun(Internal f_secp256k1_ctz64_var_debruijn)) :: (_secp256k1_ctz64_var, Gfun(Internal f_secp256k1_ctz64_var)) :: (_secp256k1_const_beta, Gvar v_secp256k1_const_beta) :: (_secp256k1_modinv64_signed62_assign, Gfun(Internal f_secp256k1_modinv64_signed62_assign)) :: (_secp256k1_modinv64_abs, Gfun(Internal f_secp256k1_modinv64_abs)) :: (_SECP256K1_SIGNED62_ONE, Gvar v_SECP256K1_SIGNED62_ONE) :: (_secp256k1_modinv64_mul_62, Gfun(Internal f_secp256k1_modinv64_mul_62)) :: (_secp256k1_modinv64_mul_cmp_62, Gfun(Internal f_secp256k1_modinv64_mul_cmp_62)) :: (_secp256k1_modinv64_det_check_pow2, Gfun(Internal f_secp256k1_modinv64_det_check_pow2)) :: (_secp256k1_modinv64_normalize_62, Gfun(Internal f_secp256k1_modinv64_normalize_62)) :: (_secp256k1_modinv64_divsteps_62_var, Gfun(Internal f_secp256k1_modinv64_divsteps_62_var)) :: (_secp256k1_modinv64_update_de_62, Gfun(Internal f_secp256k1_modinv64_update_de_62)) :: (_secp256k1_modinv64_update_fg_62_var, Gfun(Internal f_secp256k1_modinv64_update_fg_62_var)) :: (_secp256k1_modinv64_var, Gfun(Internal f_secp256k1_modinv64_var)) :: (_secp256k1_fe_mul_inner, Gfun(Internal f_secp256k1_fe_mul_inner)) :: (_secp256k1_fe_sqr_inner, Gfun(Internal f_secp256k1_fe_sqr_inner)) :: (_secp256k1_fe_verify, Gfun(Internal f_secp256k1_fe_verify)) :: (_secp256k1_fe_normalize_weak, Gfun(Internal f_secp256k1_fe_normalize_weak)) :: (_secp256k1_fe_normalize_var, Gfun(Internal f_secp256k1_fe_normalize_var)) :: (_secp256k1_fe_normalizes_to_zero_var, Gfun(Internal f_secp256k1_fe_normalizes_to_zero_var)) :: (_secp256k1_fe_set_int, Gfun(Internal f_secp256k1_fe_set_int)) :: (_secp256k1_fe_is_zero, Gfun(Internal f_secp256k1_fe_is_zero)) :: (_secp256k1_fe_is_odd, Gfun(Internal f_secp256k1_fe_is_odd)) :: (_secp256k1_fe_clear, Gfun(Internal f_secp256k1_fe_clear)) :: (_secp256k1_fe_set_b32, Gfun(Internal f_secp256k1_fe_set_b32)) :: (_secp256k1_fe_get_b32, Gfun(Internal f_secp256k1_fe_get_b32)) :: (_secp256k1_fe_negate, Gfun(Internal f_secp256k1_fe_negate)) :: (_secp256k1_fe_mul_int, Gfun(Internal f_secp256k1_fe_mul_int)) :: (_secp256k1_fe_add_int, Gfun(Internal f_secp256k1_fe_add_int)) :: (_secp256k1_fe_add, Gfun(Internal f_secp256k1_fe_add)) :: (_secp256k1_fe_mul, Gfun(Internal f_secp256k1_fe_mul)) :: (_secp256k1_fe_sqr, Gfun(Internal f_secp256k1_fe_sqr)) :: (_secp256k1_fe_cmov, Gfun(Internal f_secp256k1_fe_cmov)) :: (_secp256k1_fe_half, Gfun(Internal f_secp256k1_fe_half)) :: (_secp256k1_fe_to_storage, Gfun(Internal f_secp256k1_fe_to_storage)) :: (_secp256k1_fe_from_storage, Gfun(Internal f_secp256k1_fe_from_storage)) :: (_secp256k1_fe_from_signed62, Gfun(Internal f_secp256k1_fe_from_signed62)) :: (_secp256k1_fe_to_signed62, Gfun(Internal f_secp256k1_fe_to_signed62)) :: (_secp256k1_const_modinfo_fe, Gvar v_secp256k1_const_modinfo_fe) :: (_secp256k1_fe_normalizes_to_zero, Gfun(External (EF_external "secp256k1_fe_normalizes_to_zero" (mksignature nil AST.Tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) Tnil tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) :: (_secp256k1_fe_inv_var, Gfun(Internal f_secp256k1_fe_inv_var)) :: (_secp256k1_fe_equal_var, Gfun(Internal f_secp256k1_fe_equal_var)) :: (_secp256k1_fe_sqrt_var, Gfun(Internal f_secp256k1_fe_sqrt_var)) :: (_secp256k1_scalar_set_int, Gfun(Internal f_secp256k1_scalar_set_int)) :: (_secp256k1_scalar_get_bits, Gfun(Internal f_secp256k1_scalar_get_bits)) :: (_secp256k1_scalar_get_bits_var, Gfun(Internal f_secp256k1_scalar_get_bits_var)) :: (_secp256k1_scalar_check_overflow, Gfun(Internal f_secp256k1_scalar_check_overflow)) :: (_secp256k1_scalar_reduce, Gfun(Internal f_secp256k1_scalar_reduce)) :: (_secp256k1_scalar_add, Gfun(Internal f_secp256k1_scalar_add)) :: (_secp256k1_scalar_cadd_bit, Gfun(Internal f_secp256k1_scalar_cadd_bit)) :: (_secp256k1_scalar_set_b32, Gfun(Internal f_secp256k1_scalar_set_b32)) :: (_secp256k1_scalar_get_b32, Gfun(Internal f_secp256k1_scalar_get_b32)) :: (_secp256k1_scalar_is_zero, Gfun(Internal f_secp256k1_scalar_is_zero)) :: (_secp256k1_scalar_negate, Gfun(Internal f_secp256k1_scalar_negate)) :: (_secp256k1_scalar_reduce_512, Gfun(Internal f_secp256k1_scalar_reduce_512)) :: (_secp256k1_scalar_mul_512, Gfun(Internal f_secp256k1_scalar_mul_512)) :: (_secp256k1_scalar_mul, Gfun(Internal f_secp256k1_scalar_mul)) :: (_secp256k1_scalar_split_128, Gfun(Internal f_secp256k1_scalar_split_128)) :: (_secp256k1_scalar_mul_shift_var, Gfun(Internal f_secp256k1_scalar_mul_shift_var)) :: (_secp256k1_scalar_from_signed62, Gfun(Internal f_secp256k1_scalar_from_signed62)) :: (_secp256k1_scalar_to_signed62, Gfun(Internal f_secp256k1_scalar_to_signed62)) :: (_secp256k1_const_modinfo_scalar, Gvar v_secp256k1_const_modinfo_scalar) :: (_secp256k1_scalar_inverse_var, Gfun(Internal f_secp256k1_scalar_inverse_var)) :: (_secp256k1_const_lambda, Gvar v_secp256k1_const_lambda) :: (_minus_b1, Gvar v_minus_b1) :: (_minus_b2, Gvar v_minus_b2) :: (_g1, Gvar v_g1) :: (_g2, Gvar v_g2) :: (_secp256k1_scalar_split_lambda, Gfun(Internal f_secp256k1_scalar_split_lambda)) :: (_k1_bound, Gvar v_k1_bound) :: (_k2_bound, Gvar v_k2_bound) :: (_secp256k1_scalar_eq, Gfun(External (EF_external "secp256k1_scalar_eq" (mksignature nil AST.Tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) Tnil tint {|cc_vararg:=None; cc_unproto:=true; cc_structret:=false|})) :: (_secp256k1_scalar_split_lambda_verify, Gfun(Internal f_secp256k1_scalar_split_lambda_verify)) :: (_secp256k1_ge_set_gej_zinv, Gfun(Internal f_secp256k1_ge_set_gej_zinv)) :: (_secp256k1_ge_set_xy, Gfun(Internal f_secp256k1_ge_set_xy)) :: (_secp256k1_ge_is_infinity, Gfun(Internal f_secp256k1_ge_is_infinity)) :: (_secp256k1_ge_neg, Gfun(Internal f_secp256k1_ge_neg)) :: (_secp256k1_ge_set_gej_var, Gfun(Internal f_secp256k1_ge_set_gej_var)) :: (_secp256k1_ge_table_set_globalz, Gfun(Internal f_secp256k1_ge_table_set_globalz)) :: (_secp256k1_gej_set_infinity, Gfun(Internal f_secp256k1_gej_set_infinity)) :: (_secp256k1_ge_set_infinity, Gfun(Internal f_secp256k1_ge_set_infinity)) :: (_secp256k1_ge_set_xo_var, Gfun(Internal f_secp256k1_ge_set_xo_var)) :: (_secp256k1_gej_set_ge, Gfun(Internal f_secp256k1_gej_set_ge)) :: (_secp256k1_gej_eq_var, Gfun(Internal f_secp256k1_gej_eq_var)) :: (_secp256k1_gej_eq_ge_var, Gfun(Internal f_secp256k1_gej_eq_ge_var)) :: (_secp256k1_gej_eq_x_var, Gfun(Internal f_secp256k1_gej_eq_x_var)) :: (_secp256k1_gej_neg, Gfun(Internal f_secp256k1_gej_neg)) :: (_secp256k1_gej_is_infinity, Gfun(Internal f_secp256k1_gej_is_infinity)) :: (_secp256k1_ge_is_valid_var, Gfun(Internal f_secp256k1_ge_is_valid_var)) :: (_secp256k1_gej_double, Gfun(Internal f_secp256k1_gej_double)) :: (_secp256k1_gej_double_var, Gfun(Internal f_secp256k1_gej_double_var)) :: (_secp256k1_gej_add_var, Gfun(Internal f_secp256k1_gej_add_var)) :: (_secp256k1_gej_add_ge_var, Gfun(Internal f_secp256k1_gej_add_ge_var)) :: (_secp256k1_gej_add_zinv_var, Gfun(Internal f_secp256k1_gej_add_zinv_var)) :: (_secp256k1_gej_rescale, Gfun(Internal f_secp256k1_gej_rescale)) :: (_secp256k1_ge_to_storage, Gfun(Internal f_secp256k1_ge_to_storage)) :: (_secp256k1_ge_from_storage, Gfun(Internal f_secp256k1_ge_from_storage)) :: (_secp256k1_ge_is_in_correct_subgroup, Gfun(Internal f_secp256k1_ge_is_in_correct_subgroup)) :: (_secp256k1_pre_g, Gvar v_secp256k1_pre_g) :: (_secp256k1_pre_g_128, Gvar v_secp256k1_pre_g_128) :: (_secp256k1_ecmult_odd_multiples_table, Gfun(Internal f_secp256k1_ecmult_odd_multiples_table)) :: (_secp256k1_ecmult_table_get_ge, Gfun(Internal f_secp256k1_ecmult_table_get_ge)) :: (_secp256k1_ecmult_table_get_ge_lambda, Gfun(Internal f_secp256k1_ecmult_table_get_ge_lambda)) :: (_secp256k1_ecmult_table_get_ge_storage, Gfun(Internal f_secp256k1_ecmult_table_get_ge_storage)) :: (_secp256k1_ecmult_wnaf, Gfun(Internal f_secp256k1_ecmult_wnaf)) :: (_secp256k1_ecmult_strauss_wnaf, Gfun(Internal f_secp256k1_ecmult_strauss_wnaf)) :: (_secp256k1_ecmult, Gfun(Internal f_secp256k1_ecmult)) :: (_secp256k1_eckey_pubkey_tweak_add, Gfun(Internal f_secp256k1_eckey_pubkey_tweak_add)) :: (_secp256k1_umul128, Gfun(Internal f_secp256k1_umul128)) :: (_secp256k1_mul128, Gfun(Internal f_secp256k1_mul128)) :: (_secp256k1_u128_mul, Gfun(Internal f_secp256k1_u128_mul)) :: (_secp256k1_u128_accum_mul, Gfun(Internal f_secp256k1_u128_accum_mul)) :: (_secp256k1_u128_accum_u64, Gfun(Internal f_secp256k1_u128_accum_u64)) :: (_secp256k1_u128_rshift, Gfun(Internal f_secp256k1_u128_rshift)) :: (_secp256k1_u128_to_u64, Gfun(Internal f_secp256k1_u128_to_u64)) :: (_secp256k1_u128_hi_u64, Gfun(Internal f_secp256k1_u128_hi_u64)) :: (_secp256k1_u128_from_u64, Gfun(Internal f_secp256k1_u128_from_u64)) :: (_secp256k1_u128_check_bits, Gfun(Internal f_secp256k1_u128_check_bits)) :: (_secp256k1_i128_mul, Gfun(Internal f_secp256k1_i128_mul)) :: (_secp256k1_i128_accum_mul, Gfun(Internal f_secp256k1_i128_accum_mul)) :: (_secp256k1_i128_dissip_mul, Gfun(Internal f_secp256k1_i128_dissip_mul)) :: (_secp256k1_i128_det, Gfun(Internal f_secp256k1_i128_det)) :: (_secp256k1_i128_rshift, Gfun(Internal f_secp256k1_i128_rshift)) :: (_secp256k1_i128_to_u64, Gfun(Internal f_secp256k1_i128_to_u64)) :: (_secp256k1_i128_to_i64, Gfun(Internal f_secp256k1_i128_to_i64)) :: (_secp256k1_i128_from_i64, Gfun(Internal f_secp256k1_i128_from_i64)) :: (_secp256k1_i128_eq_var, Gfun(Internal f_secp256k1_i128_eq_var)) :: (_secp256k1_i128_check_pow2, Gfun(Internal f_secp256k1_i128_check_pow2)) :: (_secp256k1_pubkey_load, Gfun(Internal f_secp256k1_pubkey_load)) :: (_secp256k1_pubkey_save, Gfun(Internal f_secp256k1_pubkey_save)) :: (_secp256k1_ec_pubkey_tweak_add_helper, Gfun(Internal f_secp256k1_ec_pubkey_tweak_add_helper)) :: (_secp256k1_xonly_pubkey_load, Gfun(Internal f_secp256k1_xonly_pubkey_load)) :: (_secp256k1_xonly_pubkey_save, Gfun(Internal f_secp256k1_xonly_pubkey_save)) :: (_secp256k1_xonly_pubkey_parse, Gfun(Internal f_secp256k1_xonly_pubkey_parse)) :: (_secp256k1_xonly_pubkey_serialize, Gfun(Internal f_secp256k1_xonly_pubkey_serialize)) :: (_secp256k1_extrakeys_ge_even_y, Gfun(Internal f_secp256k1_extrakeys_ge_even_y)) :: (_secp256k1_xonly_pubkey_from_pubkey, Gfun(Internal f_secp256k1_xonly_pubkey_from_pubkey)) :: (_secp256k1_xonly_pubkey_tweak_add, Gfun(Internal f_secp256k1_xonly_pubkey_tweak_add)) :: (_secp256k1_schnorrsig_sha256_tagged, Gfun(Internal f_secp256k1_schnorrsig_sha256_tagged)) :: (_secp256k1_schnorrsig_challenge, Gfun(Internal f_secp256k1_schnorrsig_challenge)) :: (_secp256k1_schnorrsig_verify, Gfun(Internal f_secp256k1_schnorrsig_verify)) :: (_secp256k1_generator_load, Gfun(Internal f_secp256k1_generator_load)) :: (_secp256k1_generator_save, Gfun(Internal f_secp256k1_generator_save)) :: (_negc, Gvar v_negc) :: (_d, Gvar v_d) :: (_shallue_van_de_woestijne, Gfun(Internal f_shallue_van_de_woestijne)) :: (_prefix1, Gvar v_prefix1) :: (_prefix2, Gvar v_prefix2) :: (_inf, Gvar v_inf) :: (_zero, Gvar v_zero) :: (_secp256k1_generator_generate_internal, Gfun(Internal f_secp256k1_generator_generate_internal)) :: (_secp256k1_generator_generate, Gfun(Internal f_secp256k1_generator_generate)) :: (_simplicity_gej_is_valid_var, Gfun(Internal f_simplicity_gej_is_valid_var)) :: (_read_fe, Gfun(Internal f_read_fe)) :: (_write_fe, Gfun(Internal f_write_fe)) :: (_skip_fe, Gfun(Internal f_skip_fe)) :: (_read_ge, Gfun(Internal f_read_ge)) :: (_write_ge, Gfun(Internal f_write_ge)) :: (_skip_ge, Gfun(Internal f_skip_ge)) :: (_read_gej, Gfun(Internal f_read_gej)) :: (_write_gej, Gfun(Internal f_write_gej)) :: (_read_scalar, Gfun(Internal f_read_scalar)) :: (_write_scalar, Gfun(Internal f_write_scalar)) :: (_simplicity_fe_normalize, Gfun(Internal f_simplicity_fe_normalize)) :: (_simplicity_fe_negate, Gfun(Internal f_simplicity_fe_negate)) :: (_simplicity_fe_add, Gfun(Internal f_simplicity_fe_add)) :: (_simplicity_fe_square, Gfun(Internal f_simplicity_fe_square)) :: (_simplicity_fe_multiply, Gfun(Internal f_simplicity_fe_multiply)) :: (_simplicity_fe_multiply_beta, Gfun(Internal f_simplicity_fe_multiply_beta)) :: (_simplicity_fe_invert, Gfun(Internal f_simplicity_fe_invert)) :: (_simplicity_fe_square_root, Gfun(Internal f_simplicity_fe_square_root)) :: (_simplicity_fe_is_zero, Gfun(Internal f_simplicity_fe_is_zero)) :: (_simplicity_fe_is_odd, Gfun(Internal f_simplicity_fe_is_odd)) :: (_simplicity_scalar_normalize, Gfun(Internal f_simplicity_scalar_normalize)) :: (_simplicity_scalar_negate, Gfun(Internal f_simplicity_scalar_negate)) :: (_simplicity_scalar_add, Gfun(Internal f_simplicity_scalar_add)) :: (_simplicity_scalar_square, Gfun(Internal f_simplicity_scalar_square)) :: (_simplicity_scalar_multiply, Gfun(Internal f_simplicity_scalar_multiply)) :: (_simplicity_scalar_multiply_lambda, Gfun(Internal f_simplicity_scalar_multiply_lambda)) :: (_simplicity_scalar_invert, Gfun(Internal f_simplicity_scalar_invert)) :: (_simplicity_scalar_is_zero, Gfun(Internal f_simplicity_scalar_is_zero)) :: (_simplicity_gej_infinity, Gfun(Internal f_simplicity_gej_infinity)) :: (_simplicity_gej_rescale, Gfun(Internal f_simplicity_gej_rescale)) :: (_simplicity_gej_normalize, Gfun(Internal f_simplicity_gej_normalize)) :: (_simplicity_gej_negate, Gfun(Internal f_simplicity_gej_negate)) :: (_simplicity_ge_negate, Gfun(Internal f_simplicity_ge_negate)) :: (_simplicity_gej_double, Gfun(Internal f_simplicity_gej_double)) :: (_simplicity_gej_add, Gfun(Internal f_simplicity_gej_add)) :: (_simplicity_gej_ge_add_ex, Gfun(Internal f_simplicity_gej_ge_add_ex)) :: (_simplicity_gej_ge_add, Gfun(Internal f_simplicity_gej_ge_add)) :: (_simplicity_gej_is_infinity, Gfun(Internal f_simplicity_gej_is_infinity)) :: (_simplicity_gej_equiv, Gfun(Internal f_simplicity_gej_equiv)) :: (_simplicity_gej_ge_equiv, Gfun(Internal f_simplicity_gej_ge_equiv)) :: (_simplicity_gej_x_equiv, Gfun(Internal f_simplicity_gej_x_equiv)) :: (_simplicity_gej_y_is_odd, Gfun(Internal f_simplicity_gej_y_is_odd)) :: (_simplicity_gej_is_on_curve, Gfun(Internal f_simplicity_gej_is_on_curve)) :: (_simplicity_ge_is_on_curve, Gfun(Internal f_simplicity_ge_is_on_curve)) :: (_ng, Gvar v_ng) :: (_simplicity_off_curve_scale, Gfun(Internal f_simplicity_off_curve_scale)) :: (_ng__1, Gvar v_ng__1) :: (_simplicity_scale, Gfun(Internal f_simplicity_scale)) :: (_a, Gvar v_a) :: (_na, Gvar v_na) :: (_simplicity_generate, Gfun(Internal f_simplicity_generate)) :: (_simplicity_off_curve_linear_combination_1, Gfun(Internal f_simplicity_off_curve_linear_combination_1)) :: (_simplicity_linear_combination_1, Gfun(Internal f_simplicity_linear_combination_1)) :: (_simplicity_linear_verify_1, Gfun(Internal f_simplicity_linear_verify_1)) :: (_simplicity_decompress, Gfun(Internal f_simplicity_decompress)) :: (_simplicity_point_verify_1, Gfun(Internal f_simplicity_point_verify_1)) :: (_simplicity_bip_0340_verify, Gfun(Internal f_simplicity_bip_0340_verify)) :: (_simplicity_check_sig_verify, Gfun(Internal f_simplicity_check_sig_verify)) :: (_simplicity_swu, Gfun(Internal f_simplicity_swu)) :: (_simplicity_hash_to_curve, Gfun(Internal f_simplicity_hash_to_curve)) :: (_simplicity_generic_taptweak, Gfun(Internal f_simplicity_generic_taptweak)) :: nil). Definition public_idents : list ident := (_simplicity_generic_taptweak :: _simplicity_hash_to_curve :: _simplicity_swu :: _simplicity_check_sig_verify :: _simplicity_bip_0340_verify :: _simplicity_point_verify_1 :: _simplicity_decompress :: _simplicity_linear_verify_1 :: _simplicity_linear_combination_1 :: _simplicity_off_curve_linear_combination_1 :: _simplicity_generate :: _simplicity_scale :: _simplicity_off_curve_scale :: _simplicity_ge_is_on_curve :: _simplicity_gej_is_on_curve :: _simplicity_gej_y_is_odd :: _simplicity_gej_x_equiv :: _simplicity_gej_ge_equiv :: _simplicity_gej_equiv :: _simplicity_gej_is_infinity :: _simplicity_gej_ge_add :: _simplicity_gej_ge_add_ex :: _simplicity_gej_add :: _simplicity_gej_double :: _simplicity_ge_negate :: _simplicity_gej_negate :: _simplicity_gej_normalize :: _simplicity_gej_rescale :: _simplicity_gej_infinity :: _simplicity_scalar_is_zero :: _simplicity_scalar_invert :: _simplicity_scalar_multiply_lambda :: _simplicity_scalar_multiply :: _simplicity_scalar_square :: _simplicity_scalar_add :: _simplicity_scalar_negate :: _simplicity_scalar_normalize :: _simplicity_fe_is_odd :: _simplicity_fe_is_zero :: _simplicity_fe_square_root :: _simplicity_fe_invert :: _simplicity_fe_multiply_beta :: _simplicity_fe_multiply :: _simplicity_fe_square :: _simplicity_fe_add :: _simplicity_fe_negate :: _simplicity_fe_normalize :: _secp256k1_scalar_eq :: _secp256k1_fe_normalizes_to_zero :: _fprintf :: _stderr :: _abort :: _simplicity_write8 :: _simplicity_read32 :: _simplicity_read8 :: _simplicity_sha256_compression :: ___assert_fail :: _memset :: _memcpy :: ___builtin_write32_reversed :: ___builtin_write16_reversed :: ___builtin_read32_reversed :: ___builtin_read16_reversed :: ___builtin_fnmsub :: ___builtin_fnmadd :: ___builtin_fmsub :: ___builtin_fmadd :: ___builtin_fmin :: ___builtin_fmax :: ___builtin_expect :: ___builtin_unreachable :: ___builtin_va_end :: ___builtin_va_copy :: ___builtin_va_arg :: ___builtin_va_start :: ___builtin_nop :: ___builtin_debug :: ___builtin_membar :: ___builtin_annot_intval :: ___builtin_annot :: ___builtin_sel :: ___builtin_memcpy_aligned :: ___builtin_isfinite :: ___builtin_isfinitef :: ___builtin_isinf :: ___builtin_isinff :: ___builtin_isnan :: ___builtin_isnanf :: ___builtin_nans :: ___builtin_nan :: ___builtin_nansf :: ___builtin_nanf :: ___builtin_sqrt :: ___builtin_fsqrt :: ___builtin_fabsf :: ___builtin_fabs :: ___builtin_mull :: ___builtin_subl :: ___builtin_addl :: ___builtin_negl :: ___builtin_ctzll :: ___builtin_ctzl :: ___builtin_ctz :: ___builtin_clzll :: ___builtin_clzl :: ___builtin_clz :: ___builtin_bswap16 :: ___builtin_bswap32 :: ___builtin_bswap :: ___builtin_bswap64 :: ___builtin_ais_annot :: ___compcert_i64_umulh :: ___compcert_i64_smulh :: ___compcert_i64_sar :: ___compcert_i64_shr :: ___compcert_i64_shl :: ___compcert_i64_umod :: ___compcert_i64_smod :: ___compcert_i64_udiv :: ___compcert_i64_sdiv :: ___compcert_i64_utof :: ___compcert_i64_stof :: ___compcert_i64_utod :: ___compcert_i64_stod :: ___compcert_i64_ftou :: ___compcert_i64_ftos :: ___compcert_i64_dtou :: ___compcert_i64_dtos :: ___compcert_va_composite :: ___compcert_va_float32 :: ___compcert_va_float64 :: ___compcert_va_int64 :: ___compcert_va_int32 :: nil). Definition prog : Clight.program := mkprogram composites global_definitions public_idents _main Logic.I. ================================================ FILE: Coq/C/modinv.v ================================================ Require Import ZArith. Require Import Coq.ZArith.Znumtheory. Require Import Lia. Require Import Coq.Logic.Eqdep_dec. Open Scope Z_scope. Arguments Z.add !x !y. Arguments Z.sub !m !n. Arguments Z.mul !x !y. Record Bezout (a b d : Z) := { uBezout : Z ; vBezout : Z ; HBezout : uBezout * a + vBezout * b = d }. Arguments uBezout [a b d]. Arguments vBezout [a b d]. Definition Bezout_normalize [a b d] (H: Bezout a b d) : Bezout a b d. exists (uBezout H) (vBezout H). match goal with |- ?x = ?y => destruct (Z.eq_dec x y);[assumption|] end. abstract (destruct H;contradiction). Defined. Lemma Bezout_normalize_eq a b d (H: Bezout a b d) : Bezout_normalize H = H. Proof. destruct H as [u v H]. unfold Bezout_normalize. destruct (Z.eq_dec _ _);try contradiction. replace e with H; try reflexivity. apply UIP_dec. apply Z.eq_dec. Qed. Definition Bezout_0b b : Bezout 0 b (Z.abs b). exists 0 (Z.sgn b). abstract (rewrite <- Z.sgn_abs;ring). Defined. Definition Bezout_a0 a : Bezout a 0 (Z.abs a). exists (Z.sgn a) 0. abstract (rewrite <- Z.sgn_abs;ring). Defined. Definition Bezout_aba a b : Bezout a b a. exists 1 0. abstract ring. Defined. Definition Bezout_abb a b : Bezout a b b. exists 0 1. abstract ring. Defined. Definition Bezout_b_minus_a a b d : Bezout (b - a) a d -> Bezout a b d. intros bezout. exists (vBezout bezout - uBezout bezout) (uBezout bezout). abstract (destruct bezout as [u v <-];simpl;ring). Defined. Definition Bezout_a_minus_b a b d : Bezout (a - b) b d -> Bezout a b d. intros bezout. exists (uBezout bezout) (vBezout bezout - uBezout bezout). abstract (destruct bezout as [u v <-];simpl;ring). Defined. Definition Bezout_even a b d : Bezout a b d -> Bezout (2*a) (2*b) (2*d). intros bezout. exists (uBezout bezout) (vBezout bezout). abstract (destruct bezout as [u v <-];simpl;ring). Defined. Definition Bezout_flip a b d : Bezout a b d -> Bezout b a d. intros bezout. exists (vBezout bezout) (uBezout bezout). abstract (destruct bezout as [u v <-];simpl;ring). Defined. Definition Bezout_2a a b d : Z.Odd b -> Bezout a b d -> Bezout (2*a) b d. intros Hodd [u v Huv]. destruct (Z.odd u) eqn:H. exists (Z.div2 (u + b)) (v - a). abstract ( rewrite <- Z.odd_spec in Hodd; rewrite (Zdiv2_odd_eqn u), (Zdiv2_odd_eqn b) in Huv|-*; rewrite <- Huv, H, Hodd; rewrite Z.div2_div; replace (2 * Z.div2 u + 1 + (2 * Z.div2 b + 1)) with ((Z.div2 u + Z.div2 b + 1) * 2) by ring; rewrite Z.div_mul by lia; ring ). exists (Z.div2 u) v. abstract ( rewrite (Zdiv2_odd_eqn u) in Huv; rewrite <- Huv, H; ring ). Defined. Definition Bezout_2b a b d : Z.Odd a -> Bezout a b d -> Bezout a (2*b) d. intros Hodd bezout. apply Bezout_flip. apply Bezout_2a; try assumption. apply Bezout_flip. assumption. Defined. Lemma Pos_size_nat_sub a b : (Pos.size_nat (a - b) <= Pos.size_nat a)%nat. Proof. destruct (Pos.lt_total a b) as [H|[->|H]]. * rewrite (Pos.sub_lt _ _ H); destruct a; simpl; lia. * rewrite Pos.sub_diag; destruct b; simpl; lia. * apply Pos.size_nat_monotone; apply Pos.sub_decr; assumption. Qed. Definition Pos_Bezoutn : forall n a b, (Pos.size_nat a + Pos.size_nat b <= n)%nat -> Bezout (Z.pos a) (Z.pos b) (Z.pos (Pos.gcdn n a b)). fix Pos_Bezoutn 1. intros [|n]. * abstract (intros a b Hn; destruct a; destruct b; simpl in Hn; lia). * intros [a'|a0|]. + intros [b'|b0|] Hsize;simpl. - destruct (a' ?= b')%positive eqn:Hcmp; simpl. apply Bezout_aba. apply Bezout_b_minus_a;simpl;apply Bezout_2a; [abstract (rewrite <- Z.odd_spec; reflexivity)|]. destruct (Z.eq_dec (Z.pos_sub b' a') (Z.pos (b' - a'))) as [->|Hneq]; [apply (Pos_Bezoutn n);abstract(assert (H:=Pos_size_nat_sub b' a'); simpl in *;lia)|]. abstract (rewrite Pos.compare_lt_iff in Hcmp;apply Z.pos_sub_gt in Hcmp;contradiction). apply Bezout_a_minus_b;simpl;apply Bezout_2a; [abstract (rewrite <- Z.odd_spec; reflexivity)|]. destruct (Z.eq_dec (Z.pos_sub a' b') (Z.pos (a' - b'))) as [->|Hneq]; [apply (Pos_Bezoutn n);abstract(assert (H:=Pos_size_nat_sub a' b'); simpl in *;lia)|]. abstract (rewrite Pos.compare_gt_iff in Hcmp;apply Z.pos_sub_gt in Hcmp;contradiction). - change (Z.pos b0~0) with (2*Z.pos b0);apply Bezout_2b; [abstract (rewrite <- Z.odd_spec; reflexivity)|]. apply (Pos_Bezoutn n). abstract(simpl in *;lia). - apply Bezout_abb. + intros [b'|b0|] Hsize;simpl. - change (Z.pos a0~0) with (2*Z.pos a0);apply Bezout_2a; [abstract (rewrite <- Z.odd_spec; reflexivity)|]. apply (Pos_Bezoutn n). abstract(simpl in *;lia). - apply (Bezout_even (Z.pos a0) (Z.pos b0) (Z.pos (Pos.gcdn n a0 b0))). apply (Pos_Bezoutn n). abstract(simpl in *;lia). - apply Bezout_abb. + intros b _. apply Bezout_aba. Defined. Definition Pos_Bezout a b : Bezout (Z.pos a) (Z.pos b) (Z.pos (Pos.gcd a b)). apply Bezout_normalize. apply Pos_Bezoutn. abstract lia. Defined. Definition Bezout_neg_a a b d : Bezout (-a) b d -> Bezout a b d. intros bezout. exists (- uBezout bezout) (vBezout bezout). abstract (destruct bezout as [u v <-];simpl;ring). Defined. Definition Bezout_neg_b a b d : Bezout a (-b) d -> Bezout a b d. intros bezout. exists (uBezout bezout) (- vBezout bezout). abstract (destruct bezout as [u v <-];simpl;ring). Defined. Definition Bezout_gcd a b : Bezout a b (Z.gcd a b). apply Bezout_normalize. destruct a; try apply Bezout_0b; destruct b; try apply Bezout_a0. * apply Pos_Bezout. * apply Bezout_neg_b; apply Pos_Bezout. * apply Bezout_neg_a; apply Pos_Bezout. * apply Bezout_neg_a; apply Bezout_neg_b; apply Pos_Bezout. Defined. Definition modInv a b := Z.modulo (uBezout (Bezout_gcd (Z.modulo a b) b)) b. Lemma modInv_zero b : modInv 0 b = 0. Proof. reflexivity. Qed. Lemma modInv_divide a b : (b | a) -> modInv a b = 0. Proof. intros Hba. unfold modInv. rewrite (Zdivide_mod _ _ Hba). apply (modInv_zero b). Qed. Lemma modInv_mul_l a b : modInv a b * a mod b = Z.gcd a b mod b. Proof. unfold modInv. destruct (Bezout_gcd (a mod b) b) as [u v Huv]; simpl. rewrite Zmult_mod_idemp_l, <- Zmult_mod_idemp_r. replace (u * (a mod b)) with (Z.gcd (a mod b) b + (- v) * b) by lia. destruct (Z.eq_dec b 0) as [->|Hb]. * rewrite !Zmod_0_r; ring. * rewrite Z.gcd_mod, Z.gcd_comm by assumption. apply Z_mod_plus_full. Qed. Lemma modInv_mul_r a b : a * modInv a b mod b = Z.gcd a b mod b. Proof. rewrite Z.mul_comm. apply modInv_mul_l. Qed. Lemma modInv_mul_unique_l a b x : x * a mod b = 1 -> x mod b = modInv a b. Proof. intros Hx. destruct (Z_dec' b 0) as [[Hb0|Hb0]| ->]. * apply (Z.mod_neg_bound (x*a)) in Hb0. lia. * apply Zmod_divide_minus in Hx;[|assumption]. destruct (Hx) as [c Hc]. unfold modInv. symmetry. apply Zdivide_mod_minus;[apply Z.mod_pos_bound;assumption|]. replace (uBezout (Bezout_gcd (a mod b) b) - x mod b) with ((uBezout (Bezout_gcd (a mod b) b) - x) + (x - x mod b)) by ring. apply Z.divide_add_r;[|apply Zmod_divide_minus;lia]. destruct (Bezout_gcd (a mod b) b) as [u v Huv]; simpl. rewrite Z.gcd_mod, Zmod_eq in Huv by lia. assert (Hgcd : Z.gcd b a = 1). 1:{ apply Z.bezout_1_gcd. exists (-c); exists x. lia. } rewrite Hgcd in Huv. apply Z.gauss with a;[|lia]. exists (-c - v + u*(a/b)). lia. * assert (Hmodinv := modInv_mul_r a 0). rewrite !Zmod_0_r, Z.gcd_0_r in *. rewrite Z.mul_comm in Hx. destruct (Z.mul_eq_1 _ _ Hx) as [->| ->];lia. Qed. Lemma modInv_mul_unique_r a b x : a * x mod b = 1 -> x mod b = modInv a b. Proof. rewrite Z.mul_comm. apply modInv_mul_unique_l. Qed. Lemma modInv_eqm N a b : eqm N a b -> modInv a N = modInv b N. Proof. intros Hab. unfold modInv. rewrite Hab. reflexivity. Qed. Transparent Z.shiftr Z.pow. Lemma HackersDelightA a : Z.Odd a -> Z.land (-(a + (Z.shiftl (Z.land (a + 1) 4)) 1)) (Z.ones 4) = modInv (-a) (2^4). Proof. rewrite <- Z.odd_spec. intros Hodd. rewrite Z.land_ones by lia. rewrite <- Z.sub_0_l, <- Zminus_mod_idemp_r, Z.sub_0_l. rewrite <- Zplus_mod_idemp_l. change (Z.land (a + 1) 4) with (Z.land (a + 1) (Z.land (Z.ones 4) 4)). rewrite Z.land_assoc, Z.land_ones by lia. rewrite <- (Zplus_mod_idemp_l a). unfold modInv. symmetry. rewrite <- Z.sub_0_l, <- Zminus_mod_idemp_r, Z.sub_0_l. assert (Ha : 0 <= a mod 2^4 < 2^4) by (apply Z.mod_pos_bound;lia). assert (Hodd0 : Z.odd (a mod 2 ^ 4) = true). 1:{ rewrite <- Z.bit0_odd in *|-*. rewrite <- Z.land_ones by lia. rewrite Z.land_spec, Hodd. reflexivity. } destruct (a mod 2^4) as [|b|b]; try discriminate; try lia. do 4 (destruct b; try reflexivity; try discriminate; try lia). Qed. Lemma HackersDelightB a : Z.Odd a -> Z.land (a * (a * a - 2)) (Z.ones 6) = modInv (-a) (2^6). Proof. rewrite <- Z.odd_spec. intros Hodd. rewrite Z.land_ones by lia. rewrite <- Zmult_mod_idemp_l, <- Zmult_mod_idemp_r, <- Zminus_mod_idemp_l. rewrite <- (Zmult_mod_idemp_l a), <- (Zmult_mod_idemp_r a). rewrite Zminus_mod_idemp_l, Zmult_mod_idemp_r. unfold modInv. symmetry. rewrite <- Z.sub_0_l, <- Zminus_mod_idemp_r, Z.sub_0_l. assert (Ha : 0 <= a mod 2^6 < 2^6) by (apply Z.mod_pos_bound;lia). assert (Hodd0 : Z.odd (a mod 2 ^ 6) = true). 1:{ rewrite <- Z.bit0_odd in *|-*. rewrite <- Z.land_ones by lia. rewrite Z.land_spec, Hodd. reflexivity. } destruct (a mod 2^6) as [|b|b]; try discriminate; try lia. do 6 (destruct b; try reflexivity; try discriminate; try lia). Qed. ================================================ FILE: Coq/C/progressC.v ================================================ Require Import VST.floyd.proofauto. Require Import extraMath. Lemma Int64_low_is_nonneg (x : Z) : Int64.min_signed <= x <= Int64.max_signed -> x mod 2 ^ 64 <= Int64.max_signed -> 0 <= x <= Int64.max_signed. Proof. intros [Hx0 Hx1] Hxmod. destruct (Z.neg_nonneg_cases x) as [Hneg|Hpos]. * apply Zlt_not_le in Hxmod. elim Hxmod. change x with (2^64 mod 2^64 + x). rewrite Zplus_mod_idemp_l. rewrite Z.mod_small; rep_lia. * rewrite Z.mod_small in Hxmod; rep_lia. Qed. Lemma Int64_high_is_neg (x : Z) : Int64.min_signed <= x <= Int64.max_signed -> Int64.max_signed < x mod 2 ^ 64 -> Int64.min_signed <= x < 0. Proof. intros [Hx0 Hx1] Hxmod. destruct (Z.neg_nonneg_cases x) as [Hneg|Hpos]. * change x with (2^64 mod 2^64 + x) in Hxmod. rewrite Zplus_mod_idemp_l in Hxmod. rewrite Z.mod_small in Hxmod; rep_lia. * apply Zle_not_lt in Hxmod;[contradiction|]. rewrite Z.mod_small; rep_lia. Qed. Lemma umul_bounds_tight a x y : 0 <= x <= a -> 0 <= y <= a -> 0 <= x * y <= a * a. Proof. intros Hx Hy. split;[lia|]. transitivity (x * a);[apply Zmult_le_compat_l|apply Zmult_le_compat_r]; try tauto. lia. Qed. Lemma umul64_bounds_tight x y : 0 <= x <= 2^32 - 1 -> 0 <= y <= 2^32-1 -> 0 <= x * y <= 2^64 - 2^33 + 1. Proof. apply (umul_bounds_tight (2^32-1)). Qed. Lemma smul_bounds_tight a b x y : 0 <= a <= b -> -b <= x <= a -> -b <= y <= a -> -(a * b) <= x * y <= b * b. Proof. intros Hab. destruct (Z.neg_nonneg_cases y). split. rewrite <- Z.mul_opp_r. etransitivity;[apply Z.mul_le_mono_nonneg_l|apply Z.mul_le_mono_nonpos_r];lia. etransitivity;[apply (Z.mul_le_mono_nonpos_r (-b)) |rewrite Z.mul_opp_comm;apply Z.mul_le_mono_nonneg_l];lia. split. rewrite Z.mul_comm, <- Z.mul_opp_l. etransitivity;[apply Z.mul_le_mono_nonpos_l|apply Z.mul_le_mono_nonneg_r];lia. etransitivity;[apply (Z.mul_le_mono_nonneg_r _ b)|apply Z.mul_le_mono_nonneg_l];lia. Qed. Lemma smul_bounds a b x y : -a <= x <= a-1 -> -b <= y <= b-1 -> -(a * b) <= x * y <= a * b. Proof. intros Hab. destruct (Z.neg_nonneg_cases y). split. rewrite <- Z.mul_opp_r. etransitivity;[apply Z.mul_le_mono_nonneg_l|apply Z.mul_le_mono_nonpos_r];lia. etransitivity;[apply (Z.mul_le_mono_nonpos_r (-a)) |rewrite Z.mul_opp_comm;apply Z.mul_le_mono_nonneg_l]; lia. split. transitivity (-a*(b-1));[lia|]. etransitivity;[apply Z.mul_le_mono_nonpos_l|apply Z.mul_le_mono_nonneg_r]; lia. transitivity ((a-1)*(b-1));[|lia]. etransitivity;[apply (Z.mul_le_mono_nonneg_r _ (a-1))|apply Z.mul_le_mono_nonneg_l];lia. Qed. Lemma usmul_bounds_tight a b x y : 0 <= x <= a -> -b <= y <= b-1 -> a * (-b) <= x * y <= a * (b - 1). Proof. destruct (Z.neg_nonneg_cases y). split. etransitivity;[apply Z.mul_le_mono_nonneg_l|apply Z.mul_le_mono_nonpos_r];lia. etransitivity;[apply Z.mul_le_mono_nonneg_l|apply Z.mul_le_mono_nonneg_r];lia. split. rewrite Z.mul_opp_r, <- Z.mul_opp_l. etransitivity;[apply Z.mul_le_mono_nonpos_l|apply Z.mul_le_mono_nonneg_r]; lia. etransitivity;[apply Z.mul_le_mono_nonneg_l|apply Z.mul_le_mono_nonneg_r];lia. Qed. Lemma smul64_bounds_tight x y : -2^31 <= x <= 2^31 - 1 -> -2^31 <= y <= 2^31 - 1 -> -2^62+2^31 <= x * y <= 2^62. Proof. assert (H := smul_bounds_tight (2^31 - 1) (2^31) x y). lia. Qed. Lemma smul128_bounds_tight x y : -2^63 <= x <= 2^63 - 1 -> -2^63 <= y <= 2^63 - 1 -> -2^126+2^63 <= x * y <= 2^126. Proof. assert (H := smul_bounds_tight (2^63 - 1) (2^63) x y). lia. Qed. Lemma sumul64_bounds x y : -2^31 <= x <= 2^31 - 1 -> 0 <= y <= 2^32-1 -> -2^63 <= x * y <= 2^63 - 1. Proof. intros Hx Hy. change (2^63) with (2^31 * 2^32). split. rewrite <- Z.mul_opp_l. transitivity (-2^31 * y);[|apply Z.mul_le_mono_nonneg_r];lia. transitivity ((2^31 - 1)*(2^32));[|lia]. transitivity ((2^31 - 1) * y);[apply Z.mul_le_mono_nonneg_r|];lia. Qed. Lemma usmul64_bounds x y : -2^31 <= y <= 2^31 - 1 -> 0 <= x <= 2^32-1 -> -2^63 <= x * y <= 2^63 - 1. Proof. rewrite Z.mul_comm. auto using sumul64_bounds. Qed. (* Lemma add_bounds ax ay az cx cy cz : ax <= ay <= az -> cx <= cy <= cz -> ax + cx <= ay + cy <= az + cz. Proof. lia. Qed. *) Lemma unadd_bounds_unsigned_32 ax ay az b : 0 <= b <= 2^32-1 -> ax <= ay <= az - 2^32 + 1 -> ax <= ay + b <= az. Proof. lia. Qed. Lemma unadd_bounds_signed_32 ax ay az b : -2^31 <= b <= 2^31-1 -> ax + 2^31 <= ay <= az - 2^31 + 1 -> ax <= ay + b <= az. Proof. lia. Qed. Lemma unadd_bounds_unsigned_62 ax ay az b : 0 <= b <= 2^62-1 -> ax <= ay <= az - 2^62 + 1 -> ax <= ay + b <= az. Proof. lia. Qed. Lemma unadd_bounds_shiftr_62 ax ay az b : -2^63 <= b <= 2^63 - 1 -> ax + 2 <= ay <= az - 1 -> ax <= ay + (Z.shiftr b 62) <= az. Proof. intros Hay Hb. assert (-2 <= Z.shiftr b 62 < 2) by (apply shiftr_bounds;lia). lia. Qed. Lemma unadd_bounds_b2z ax ay az b : ax <= ay <= az - 1 -> ax <= ay + Z.b2z b <= az. Proof. destruct b;simpl;lia. Qed. Lemma unadd_bounds_small b ax ay az : ax - b <= ay <= az - b -> ax <= ay + b <= az. Proof. lia. Qed. Lemma opp_bounds x y z : (-z <= y <= -x) -> x <= -y <= z. Proof. lia. Qed. Lemma if_bounds (b : bool) ax ay1 ay2 az : ax <= ay1 <= az -> ax <= ay2 <= az -> ax <= (if b then ay1 else ay2) <= az. Proof. destruct b;lia. Qed. (* Lemma umul64_bounds x y a b : 0 <= x <= 2^32 - 1 -> 0 <= y <= 2^32-1 -> 0 <= a <= 2^32-1 -> 0 <= b <= 2^32-1 -> 0 <= x * y + a + b <= 2^64 - 1. Proof. intros Hx Hy Ha Hb. change (2 ^ 64- 1) with (2^64 - 2^33 + 1 + (2^32 - 1) + (2^32 - 1)). change 0 with (0 + 0 + 0). repeat (apply add_bounds;[|tauto]). apply umul64_bounds_tight; tauto. Qed. *) Lemma strict_bounds a b : a < b <-> a <= b-1. Proof. rep_lia. Qed. Lemma strict_bounds' a b c : a <= b < c+1 <-> a <= b <= c. Proof. rep_lia. Qed. Lemma weaken_bounds a b c d e : b <= c <= d -> a <= b -> d <= e -> a <= c <= e. Proof. rep_lia. Qed. Lemma of_bool_if b : Val.of_bool b = Vint (Int.repr (Z.b2z b)). Proof. destruct b; reflexivity. Qed. (* Lemma Int_unsigned_b2z b : Int.unsigned (Int.repr (Z.b2z b)) = Z.b2z b. Proof. destruct b; reflexivity. Qed. *) Lemma Int_signed_b2z b : Int.signed (Int.repr (Z.b2z b)) = Z.b2z b. Proof. destruct b; reflexivity. Qed. Lemma zlt_ltb a b : (if zlt a b then true else false) = (a solve_bounds_body ..]. Ltac solve_bounds := unfold_C; rewrite ?Z.ones_equiv, <- ?Z.sub_1_r; repeat match goal with |- (?a1 /\ ?a2 /\ ?b) => split end; solve_bounds_body. Ltac clear_mod := repeat match goal with | |- context [ (?a mod ?b)%Z ] => first [change (?a mod ?b)%Z with ?a |rewrite <- Zmod_div_mod by (try lia; change (2^64) with (2^32 * 2^32);auto with *) |rewrite (Z.mod_small a b);[|solve[rewrite strict_bounds;solve_bounds]] ] end. Ltac convert_C_to_math := unfold Int.eq, Int.lt, Int.ltu, Int64.eq, Int64.lt, Int64.ltu; repeat (first [rewrite of_bool_if;simpl (force_val _) |rewrite Int64.signed_zero |rewrite Int64.unsigned_zero |rewrite Int_signed_b2z |rewrite Int.signed_zero |rewrite Int.signed_one by rep_lia |rewrite zlt_ltb |rewrite zeq_eqb |rewrite Zleb_bool |rewrite add64_repr |rewrite Int64.neg_repr |rewrite sub64_repr |rewrite sub_repr |rewrite mul64_repr |rewrite and64_repr |rewrite or64_repr |rewrite xor64_repr |rewrite Int64_shru_shiftr |rewrite Int_shr_shiftr |rewrite Int64_shr_shiftr |rewrite Int64.shl_mul_two_p; try rewrite !two_p_equiv |rewrite Int64.Z_mod_modulus_eq ]); repeat match goal with | |- context [ Int.unsigned (Int.repr ?a) ] => rewrite (Int.unsigned_repr a) by rep_lia | |- context [ Int64.unsigned (Int64.repr ?a) ] => rewrite (Int64.unsigned_repr a) by rep_lia | |- context [ Int.signed (Int.repr ?a) ] => rewrite (Int.signed_repr a) by solve_bounds | |- context [ Int64.signed (Int64.repr ?a) ] => rewrite (Int64.signed_repr a) by solve_bounds end; repeat (first [rewrite (Int.unsigned_repr_eq _) |rewrite (Int64.unsigned_repr_eq _) ]); unfold_C; clear_mod. Ltac progressC := first [forward|forward_if]; try (entailer!!;cbn);convert_C_to_math;try entailer!!;try solve_bounds. Ltac forward_verify_check := match goal with | |- semax _ ?E (Sloop _ _) _ => forward_loop E; [entailer!!|try (forward_if;[elimtype False|forward;entailer!!])] | |- semax _ ?E _ _ => forward_loop E continue:E break:E; [entailer!!|try (forward_if;[elimtype False|forward;entailer!!])|forward;entailer!!|] end. ================================================ FILE: Coq/C/secp256k1/spec_int128.v ================================================ Require Import VST.floyd.proofauto. Require Import VST.msl.iter_sepcon. Require Import jets_secp256k1. #[export] Instance CompSpecs : compspecs. make_compspecs prog. Defined. Definition Int128_modulus : Z := 2^128. Definition Int128_max_unsigned : Z := Int128_modulus - 1. Definition Int128_max_signed : Z := 2^127 - 1. Definition Int128_min_signed : Z := -2^127. Definition t_secp256k1_uint128 := Tstruct _secp256k1_uint128 noattr. (* (secp256k1_uint128_at sh x p) says that the structure pointed to by p * is equivalent to x modulo 2^128. *) Definition secp256k1_uint128_at sh x := data_at sh t_secp256k1_uint128 (Vlong (Int64.repr x), Vlong (Int64.repr (Z.shiftr x 64))). (*/ Definition secp256k1_u128_load_spec : ident * funspec := DECLARE _secp256k1_u128_load WITH r : val, sh : share, hi : Z, lo : Z PRE [ tptr t_secp256k1_uint128, tulong, tulong ] PROP(writable_share sh; 0 <= lo < Int64.modulus) PARAMS(r; Vlong (Int64.repr hi); Vlong (Int64.repr lo)) SEP(data_at_ sh t_secp256k1_uint128 r) POST [ tvoid ] PROP() RETURN() SEP(secp256k1_uint128_at sh (Z.shiftl hi 64 + lo) r). *) Definition secp256k1_u128_mul_spec : ident * funspec := DECLARE _secp256k1_u128_mul WITH r : val, sh : share, a : Z, b : Z PRE [ tptr t_secp256k1_uint128, tulong, tulong ] PROP(writable_share sh; 0 <= a < Int64.modulus; 0 <= b < Int64.modulus) PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b)) SEP(data_at_ sh t_secp256k1_uint128 r) POST [ tvoid ] PROP() RETURN() SEP(secp256k1_uint128_at sh (a * b) r). Definition secp256k1_u128_accum_mul_spec : ident * funspec := DECLARE _secp256k1_u128_accum_mul WITH r : val, sh : share, r0 : Z, a : Z, b : Z PRE [ tptr t_secp256k1_uint128, tulong, tulong ] PROP(writable_share sh; 0 <= a < Int64.modulus; 0 <= b < Int64.modulus) PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b)) SEP(secp256k1_uint128_at sh r0 r) POST [ tvoid ] PROP() RETURN() SEP(secp256k1_uint128_at sh (r0 + a * b) r). Definition secp256k1_u128_accum_u64_spec : ident * funspec := DECLARE _secp256k1_u128_accum_u64 WITH r : val, sh : share, r0 : Z, a : Z PRE [ tptr t_secp256k1_uint128, tulong ] PROP(writable_share sh; 0 <= a < Int64.modulus) PARAMS(r; Vlong (Int64.repr a)) SEP(secp256k1_uint128_at sh r0 r) POST [ tvoid ] PROP() RETURN() SEP(secp256k1_uint128_at sh (r0 + a) r). Definition secp256k1_u128_rshift_spec : ident * funspec := DECLARE _secp256k1_u128_rshift WITH r : val, sh : share, r0 : Z, n : Z PRE [ tptr t_secp256k1_uint128, tuint ] PROP(writable_share sh; 0 <= r0 < Int128_modulus; 0 <= n < 128) PARAMS(r; Vint (Int.repr n)) SEP(secp256k1_uint128_at sh r0 r) POST [ tvoid ] PROP() RETURN() SEP(secp256k1_uint128_at sh (Z.shiftr r0 n) r). Definition secp256k1_u128_to_u64_spec : ident * funspec := DECLARE _secp256k1_u128_to_u64 WITH r : val, sh : share, r0 : Z PRE [ tptr t_secp256k1_uint128 ] PROP(readable_share sh) PARAMS(r) SEP(secp256k1_uint128_at sh r0 r) POST [ tulong ] PROP() RETURN(Vlong (Int64.repr r0)) SEP(secp256k1_uint128_at sh r0 r). Definition secp256k1_u128_hi_u64_spec : ident * funspec := DECLARE _secp256k1_u128_hi_u64 WITH r : val, sh : share, r0 : Z PRE [ tptr t_secp256k1_uint128 ] PROP(readable_share sh) PARAMS(r) SEP(secp256k1_uint128_at sh r0 r) POST [ tulong ] PROP() RETURN(Vlong (Int64.repr (Z.shiftr r0 64))) SEP(secp256k1_uint128_at sh r0 r). Definition secp256k1_u128_from_u64_spec : ident * funspec := DECLARE _secp256k1_u128_from_u64 WITH r : val, sh : share, a : Z PRE [ tptr t_secp256k1_uint128, tulong ] PROP(writable_share sh; 0 <= a < Int64.modulus) PARAMS(r; Vlong (Int64.repr a)) SEP(data_at_ sh t_secp256k1_uint128 r) POST [ tvoid ] PROP() RETURN() SEP(secp256k1_uint128_at sh a r). Definition secp256k1_u128_check_bits_spec : ident * funspec := DECLARE _secp256k1_u128_check_bits WITH r : val, sh : share, r0 : Z, n : Z PRE [ tptr t_secp256k1_uint128, tuint ] PROP(readable_share sh; 0 <= r0 < 2^128; 0 <= n < 128) PARAMS(r; Vint (Int.repr n)) SEP(secp256k1_uint128_at sh r0 r) POST [ tint ] PROP() RETURN(Vint (Int.repr (if r0 0 | (a :: l') => Int64.signed a + 2^62 * signed l' end. Lemma app_signed l1 l2 : signed (l1 ++ l2) = signed l1 + 2^(Zlength l1 * 62) * signed l2. Proof. revert l2. induction l1; intros l2. * rewrite Z.pow_0_r. cbn. ring. * rewrite Zlength_cons. cbn. assert (Hlen := Zlength_nonneg l1). rewrite IHl1, Z.mul_succ_l, Z.pow_add_r; lia. Qed. Fixpoint reprn (n : nat) (a : Z) : list int64 := match n with | 0%nat => [] | 1%nat => [Int64.repr a] | (S n0) => Int64.repr (a mod (2 ^ 62)) :: (reprn n0 (Z.shiftr a 62)) end. Lemma reprn_length n : forall a, length (reprn n a) = n. Proof. induction n;try reflexivity. destruct n;try reflexivity. intro a; simpl in *; rewrite IHn; reflexivity. Qed. Lemma reprn_Zlength n : forall a, Zlength (reprn n a) = Z.of_nat n. Proof. intros a. rewrite Zlength_correct, Signed62.reprn_length; reflexivity. Qed. Lemma reprn_succ n a : reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++ [Int64.repr (Z.shiftr a (62 * Z.of_nat n))]. Proof. revert a; induction n; intros a;[reflexivity|]. pattern (S n). simpl (reprn (S _) a). cbn beta. rewrite IHn, Z.shiftr_shiftr, Nat2Z.inj_succ, Z.mul_succ_r, Z.add_comm by lia. simpl. destruct n;[reflexivity|]. rewrite Z.pow_add_r by lia. rewrite <- Zmod_div_mod, !(Z.shiftr_div_pow2 _ 62) by (try lia; auto with *). rewrite (Z.mul_comm _ (2^62)), Zaux.Zdiv_mod_mult by lia. reflexivity. Qed. Lemma reprn_last : forall a n d, (1 <= n)%nat -> last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1))). Proof. intros a n. revert a. induction n;[lia|]. intros a d Hn. rewrite Nat2Z.inj_succ. unfold Z.succ. replace (Z.of_nat n + 1 - 1) with (Z.of_nat n) by ring. rewrite reprn_succ. apply last_last. Qed. Lemma reprn_nth : forall a n i d, (0 <= i < n - 1)%nat -> nth i (reprn n a) d = Int64.repr ((Z.shiftr a (62 * (Z.of_nat i))) mod (2^62)). Proof. intros a n. revert a. induction n;[intros; lia|]. intros a i d Hi. rewrite reprn_succ. rewrite app_nth1 by (rewrite reprn_length; lia). destruct (Nat.lt_ge_cases i (n - 1)). + rewrite IHn, !Z.shiftr_div_pow2, <- (Nat.sub_add i n), Nat2Z.inj_add, Z.mul_add_distr_l, Z.pow_add_r, Z.mul_comm, Zaux.Zdiv_mod_mult by lia. rewrite !Z.pow_mul_r, <- Zmod_div_mod; try reflexivity; try lia. apply Zpow_facts.Zpower_divide. lia. + set (l := (reprn n _)). replace i with (n - 1)%nat by lia. replace n with (length l) at 1 by apply reprn_length. unfold l. rewrite nth_last, reprn_last by lia. replace (62 * Z.of_nat n) with (62 * (Z.of_nat n - 1) + 62) by ring. rewrite Z.pow_add_r, !Z.shiftr_div_pow2, Zaux.Zdiv_mod_mult by lia. repeat f_equal. lia. Qed. Lemma reprn_Znth : forall a n i, 0 <= i < Z.of_nat n - 1 -> Znth i (reprn n a) = Int64.repr ((Z.shiftr a (62 * i)) mod (2^62)). Proof. intros a n i Hi. rewrite <- nth_Znth by (rewrite reprn_Zlength; lia). rewrite reprn_nth, Z2Nat.id by lia. reflexivity. Qed. Lemma signed_firstn_reprn a i n : (i < n)%nat -> signed (firstn i (reprn n a)) = a mod (2^(62*Z.of_nat i)). Proof. revert a i. induction n;[lia|]. intros a [|i];[simpl; rewrite Z.pow_0_r, Zmod_1_r; reflexivity|]. intros Hi. apply Nat.succ_lt_mono in Hi. destruct n;[lia|]. rewrite Nat2Z.inj_succ, Z.mul_succ_r, Z.pow_add_r by lia. simpl. change (signed _) with (signed (firstn i (reprn (S n) (Z.shiftr a 62)))). rewrite IHn by assumption. rewrite Int64.signed_repr by solve_bounds. rewrite Z.shiftr_div_pow2 by lia. symmetry. rewrite Zmod_recombine by lia. ring. Qed. Lemma signed_reprn a n : (1 <= n)%nat -> -2 ^ (62 * Z.of_nat n + 1) <= a <= 2 ^ (62 * Z.of_nat n + 1) - 1 -> signed (reprn n a) = a. Proof. revert a. induction n;[lia|]. intros a _. rewrite Nat2Z.inj_succ, Z.mul_succ_r. destruct n. * simpl. intros Ha. rewrite Int64.signed_repr;[lia|assumption]. * change (reprn _ a) with (Int64.repr (a mod (2 ^ 62)) :: (reprn (S n) (Z.shiftr a 62))). cbn [signed]. rewrite !Z.pow_add_r in * by lia. intros Ha. rewrite IHn by solve_bounds. rewrite Int64.signed_repr by solve_bounds. rewrite Z.shiftr_div_pow2, Z.add_comm by lia. symmetry. apply Z_div_mod_eq_full. Qed. Lemma reprn_shrink a n1 n2 : (min_signed (Z.of_nat n1) <= a <= max_signed (Z.of_nat n1)) -> (1 <= n1 < n2)%nat -> (firstn n1 (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a) (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a)) (Int64.repr (Z.shiftl (if 0 <=? a then 0 else -1) 62))))) = (reprn n1 a). Proof. intros Ha Hn. apply (nth_eq_ext _ default); rewrite firstn_length, <-ZtoNat_Zlength, Zlength_upd_Znth, ZtoNat_Zlength, !reprn_length; [lia|]. replace (Init.Nat.min n1 n2) with n1 by lia. intros i Hi. rewrite nth_firstn by lia. destruct (Nat.eq_dec i (n1 - 1)) as [->|Hneq];rewrite nth_Znth'; [|rewrite reprn_nth, Znth_upd_Znth_diff, reprn_Znth by lia; reflexivity]. replace (Z.of_nat (n1 - 1)) with (Z.of_nat n1 - 1) by lia. rewrite upd_Znth_same by (rewrite reprn_Zlength; lia). rewrite reprn_Znth by lia. symmetry. replace n1 with (length (reprn n1 a)) at 1 by (rewrite reprn_length;reflexivity). rewrite nth_last. rewrite reprn_last by lia. unfold min_signed, max_signed in Ha. elim Z.leb_spec;intros Ha0. + rewrite Int64.or_zero. symmetry. f_equal. apply Z.mod_small. apply shiftr_bounds. rewrite <-Z.pow_add_r by lia. replace (62 * (Z.of_nat n1 - 1) + 62) with (Z.of_nat n1 * 62) by lia. lia. + rewrite <- Int64.add_is_or. 2:{ apply Int64.same_bits_eq. intros j Hj. rewrite Int64.bits_zero, and64_repr, Int64.testbit_repr by assumption. rewrite <- Z.land_ones, !Z.land_spec, Z.testbit_ones_nonneg, Z.shiftl_spec by lia. elim Z.ltb_spec;[|rewrite andb_false_r;reflexivity]. intro; rewrite (Z.testbit_neg_r _ (j - 62)), !andb_false_r by lia; reflexivity. } rewrite add64_repr. f_equal. change (Z.shiftl (-1) 62) with (-2^62). rewrite <- (Z_mod_plus_full _ 1), Z.mod_small;[ring|]. rewrite strict_bounds. apply unadd_bounds_small. setoid_rewrite <- strict_bounds'. apply shiftr_bounds. rewrite Z.mul_0_r. cut (-(2^62 * 2 ^ (62 * (Z.of_nat n1 - 1))) <= a < 0);[lia|]. rewrite <-Z.pow_add_r by lia. replace (62 + 62 * (Z.of_nat n1 - 1)) with (Z.of_nat n1 * 62); lia. Qed. Definition pad (l : list int64) : list val := map Vlong l ++ repeat Vundef (5 - length l). Lemma pad_nth i (l : list int64) : 0 <= i < Zlength l -> Znth i (pad l) = Vlong (Znth i l). Proof. intros Hi. rewrite <- !nth_Znth; try auto. * assert (Z.to_nat i < length l)%nat by (rewrite <- ZtoNat_Zlength, <- Z2Nat.inj_lt; lia). unfold pad. rewrite app_nth1 by (rewrite map_length; assumption). erewrite nth_indep by (rewrite map_length; assumption). apply map_nth. * unfold pad. rewrite Zlength_app, Zlength_map. assert (Hlen := Zlength_nonneg (repeat Vundef (5 - Datatypes.length l))). lia. Qed. Lemma pad_nth_undef i (l : list int64) : Zlength l <= i -> Znth i (pad l) = Vundef. Proof. intros Hi. pose (Hl := Zlength_nonneg l). rewrite <- (Z2Nat.id i), <- nth_Znth' by lia. rewrite Z2Nat.inj_le, ZtoNat_Zlength in Hi by lia. unfold pad. rewrite app_nth2 by (rewrite map_length; lia). apply nth_repeat. Qed. Lemma pad_length l : (length l <= 5)%nat -> length (pad l) = 5%nat. Proof. intros Hl. unfold pad. rewrite app_length, map_length, repeat_length. lia. Qed. Lemma pad_Zlength l : Zlength l <= 5 -> Zlength (pad l) = 5. Proof. intros Hl. rewrite Zlength_correct, pad_length in *; try lia. Qed. Lemma pad0 : pad nil = repeat Vundef 5. Proof. reflexivity. Qed. Lemma pad5 l : length l = 5%nat -> pad l = map Vlong l. Proof. unfold pad. intros ->. cbn. rewrite app_nil_end. reflexivity. Qed. Lemma pad_upd_Znth a i l : 0 <= i < Zlength l -> upd_Znth i (pad l) (Vlong a) = pad (upd_Znth i l a). Proof. intros Hi. unfold pad. rewrite upd_Znth_app1 by (rewrite Zlength_map; assumption). f_equal. * apply upd_Znth_map. * rewrite <- (ZtoNat_Zlength (upd_Znth _ _ _)), Zlength_upd_Znth, ZtoNat_Zlength. reflexivity. Qed. Lemma pad_upd_Znth_end a l : (length l <= 4)%nat -> upd_Znth (Zlength l) (pad l) (Vlong a) = pad (l++[a]). Proof. intros Hl. rewrite <- ZtoNat_Zlength in Hl. (* assert (Hl' : Zlength l <= 4) by lia. *) apply (nth_ext _ _ default default). * apply Nat2Z.inj. rewrite <- !Zlength_correct, Zlength_upd_Znth, !pad_Zlength; simpl; try lia. rewrite Zlength_app, Zlength_cons; simpl; lia. * intros n Hn. rewrite !nth_Znth'. pose (Hpad := pad_Zlength l). destruct (Z.lt_total (Z.of_nat n) (Zlength l)) as [Hnl|[Hnl|Hnl]]. + rewrite Znth_upd_Znth_diff, pad_nth by lia. rewrite pad_nth by (rewrite Zlength_app, Zlength_cons; simpl; lia). rewrite Znth_app1 by lia. reflexivity. + rewrite Znth_upd_Znth_same by lia. unfold pad. rewrite map_app, Znth_app1, Znth_app2, Zlength_map, Hnl, Z.sub_diag by (rewrite ?Zlength_app, !Zlength_map, ?Zlength_cons; simpl; lia). reflexivity. + rewrite Znth_upd_Znth_diff, pad_nth_undef by lia. rewrite pad_nth_undef by (rewrite Zlength_app, Zlength_cons; simpl; lia). reflexivity. Qed. End Signed62. Definition make_modinfo (m : Z) : (list val * val)%type := (map Vlong (Signed62.reprn 5 m), Vlong (Int64.repr (modInv m (2^62)))). Definition debruijn64_array (sh: share) (gv: globals) : mpred := Eval cbn in let is_all_init_int8 := fix is_all_init_int8 (l : list init_data) := match l with | [] => True | Init_int8 _ :: l' => is_all_init_int8 l' | _ => False end in let uninit_int8s := fix uninit_int8s (l: list init_data) : is_all_init_int8 l -> list int := match l with | [] => fun _ => [] | x :: l' => match x with | Init_int8 i => fun pf => i :: uninit_int8s l' pf | _ => False_rec (list int) end end in data_at sh (gvar_info v_debruijn) (map Vint (uninit_int8s (gvar_init v_debruijn) I)) (gv _debruijn). Lemma data_at_tulong_tlong {cs: compspecs}: forall sh v p, data_at sh tulong v p = data_at sh tlong v p. Proof. intros. unfold data_at, field_at. f_equal. unfold field_compatible. apply ND_prop_ext. assert (align_compatible tulong p <-> align_compatible tlong p); [| tauto]. destruct p; simpl; try tauto. split; intros. + eapply align_compatible_rec_by_value_inv in H; [| reflexivity]. eapply align_compatible_rec_by_value; [reflexivity |]. auto. + eapply align_compatible_rec_by_value_inv in H; [| reflexivity]. eapply align_compatible_rec_by_value; [reflexivity |]. auto. Qed. Lemma SECP256K1_SIGNED62_ONE_global gv : headptr (gv _SECP256K1_SIGNED62_ONE) -> globvar2pred gv (_SECP256K1_SIGNED62_ONE, v_SECP256K1_SIGNED62_ONE) |-- data_at Ers t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE). Proof. intros Hheadptr. unfold globvar2pred. simpl. rewrite sepcon_emp. change (Z.shiftr 1 _) with 0. repeat change (Z.shiftr 0 _) with 0. change (1 mod _) with 1. change (0 mod _) with 0. unfold t_secp256k1_modinv64_signed62. assert (Hptr : isptr (gv _SECP256K1_SIGNED62_ONE)) by (apply headptr_isptr; assumption). unfold data_at. erewrite field_at_Tstruct; [|reflexivity|apply JMeq_refl]. simpl (co_members (get_co _secp256k1_modinv64_signed62)). cbn -[mapsto]. change (0 + _) with 40. unfold withspacer. destruct (Z.eq_dec _ _);[clear e|lia]. rewrite field_at_data_at. assert (Hcompat : field_compatible (Tstruct _secp256k1_modinv64_signed62 noattr) (DOT _v) (gv _SECP256K1_SIGNED62_ONE)). 1:{ apply headptr_field_compatible. - assumption. - reflexivity. - repeat constructor. - reflexivity. - eapply align_compatible_rec_Tstruct. + reflexivity. + reflexivity. + simpl; intros i0 t0 z0 H0 H1. destruct (ident_eq _ _) in H0;[|discriminate]. injection H0; clear H0. intros <-. subst i0. injection H1; clear H1. intros <-. eapply align_compatible_rec_Tarray. * intros i Hi. cut (i = 0 \/ i = 1 \/ i = 2 \/ i = 3 \/ i = 4);[|lia]. clear Hi. intros [->|[->|[->|[->| ->]]]];econstructor;try reflexivity;apply Zmod_divide;try reflexivity;cbn;lia. } rewrite field_address_offset by assumption. rewrite isptr_offset_val_zero by (apply headptr_isptr; assumption). simpl (nested_field_type _ _). unfold tarray. rewrite (split2_data_at_Tarray _ tlong _ 1 _ [Vlong (Int64.repr 1); Vlong (Int64.repr 0); Vlong (Int64.repr 0); Vlong (Int64.repr 0); Vlong (Int64.repr 0)] [Vlong (Int64.repr 1)] [Vlong (Int64.repr 0); Vlong (Int64.repr 0); Vlong (Int64.repr 0); Vlong (Int64.repr 0)]); try solve[cbn;lia]; try reflexivity. apply sepcon_derives. - eapply derives_trans;[|apply data_at_singleton_array];[|reflexivity]. rewrite <-data_at_tulong_tlong. erewrite mapsto_data_at'; try reflexivity; try apply JMeq_refl;try entailer. apply headptr_field_compatible. + assumption. + reflexivity. + repeat constructor. + reflexivity. + econstructor;[reflexivity|apply Z.divide_0_r]. - clear Hcompat. assert (Hcompat : field_compatible (tarray tlong 5) [] (gv _SECP256K1_SIGNED62_ONE)). 1:{ apply headptr_field_compatible. - assumption. - reflexivity. - repeat constructor. - reflexivity. - eapply align_compatible_rec_Tarray. * intros i Hi. cut (i = 0 \/ i = 1 \/ i = 2 \/ i = 3 \/ i = 4);[|lia]. clear Hi. intros [->|[->|[->|[->| ->]]]];econstructor;try reflexivity;apply Zmod_divide;try reflexivity;cbn;lia. } eapply derives_trans;[apply (mapsto_zero_data_at_zero (Tarray tlong (5 - 1) noattr))|]. + apply readable_Ers. + reflexivity. + reflexivity. + apply (field_compatible0_nested_field_array (Tarray tlong 5 noattr) []); try lia; apply arr_field_compatible0; try lia; assumption. + rewrite field_address0_offset by (eapply field_compatible0_cons_Tarray;[reflexivity|assumption|lia]). change (nested_field_offset (Tarray tlong 5 noattr) (SUB 1)) with 8. fold (tarray tlong (5 - 1)). rewrite zero_val_tarray, zero_val_tlong. apply derives_refl. Qed. Definition secp256k1_modinv64_signed62_assign_spec : ident * funspec := DECLARE _secp256k1_modinv64_signed62_assign WITH x : Z, ptr_dst : val, ptr_src : val, sh_dst : share, sh_src : share PRE [ tptr t_secp256k1_modinv64_signed62 , tptr t_secp256k1_modinv64_signed62 ] PROP( writable_share sh_dst ; readable_share sh_src ) PARAMS(ptr_dst; ptr_src) SEP( data_at_ sh_dst t_secp256k1_modinv64_signed62 ptr_dst ; data_at sh_src t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptr_src ) POST [ tvoid ] PROP() RETURN() SEP( data_at sh_dst t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptr_dst ; data_at sh_src t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptr_src ). Definition secp256k1_modinv64_var_spec : ident * funspec := DECLARE _secp256k1_modinv64_var WITH x : Z, m : Z, ptrx : val, modinfo : val, shx : share, sh_modinfo : share, sh_debruijn : share, sh_SECP256K1_SIGNED62_ONE : share, gv : globals PRE [ tptr t_secp256k1_modinv64_signed62 , tptr t_secp256k1_modinv64_modinfo ] PROP( Z.Odd m ; 0 <= x < m ; 1 < m < 2^256 ; x = 0 \/ rel_prime x m ; writable_share shx ; readable_share sh_modinfo ; readable_share sh_debruijn ; readable_share sh_SECP256K1_SIGNED62_ONE ) PARAMS(ptrx; modinfo) GLOBALS(gv) SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx; data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)) POST [ tvoid ] PROP() RETURN() SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 (modInv x m))) ptrx; data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)). Definition secp256k1_modinv64_var_spec_prime : ident * funspec := DECLARE _secp256k1_modinv64_var WITH x : Z, m : Z, ptrx : val, modinfo : val, shx : share, sh_modinfo : share, sh_debruijn : share, sh_SECP256K1_SIGNED62_ONE : share, gv : globals PRE [ tptr t_secp256k1_modinv64_signed62 , tptr t_secp256k1_modinv64_modinfo ] PROP( Z.Odd m ; 0 <= x < m ; m < 2^256 ; prime m ; writable_share shx ; readable_share sh_modinfo ; readable_share sh_debruijn ; readable_share sh_SECP256K1_SIGNED62_ONE ) PARAMS(ptrx; modinfo) GLOBALS(gv) SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx; data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)) POST [ tvoid ] PROP() RETURN() SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 (modInv x m))) ptrx; data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)). (* Use with forward_call secp256k1_modinv64_var_spec_prime_sub (x, m, ptrx, modinfo, shx, sh_modinfo, sh_debruijn, sh_SECP256K1_SIGNED62_ONE, gv) *) Lemma secp256k1_modinv64_var_spec_prime_sub : funspec_sub (snd secp256k1_modinv64_var_spec) (snd secp256k1_modinv64_var_spec_prime). Proof. do_funspec_sub. Exists w emp. destruct w as [[[[[[[[x m] ptrx] modinfo] shx] sh_modinfo] sh_debruinj] sh_SECP256K1_SIGNED62_ONE] gv]. entailer!!. split. * cut (m <> 1);[lia|]. intros Hm; apply not_prime_1. congruence. * destruct (Z.eq_dec x 0) as [Hx0|Hx0];[tauto|]. right. apply rel_prime_le_prime;[assumption|lia]. Qed. ================================================ FILE: Coq/C/secp256k1/verif_int128_impl.v ================================================ Require Import VST.floyd.proofauto. Require Import jets_secp256k1. Require Import spec_int128. Require Import VST.msl.iter_sepcon. Require Import extraMath. Require Import progressC. Opaque Z.shiftl Z.shiftr Z.pow. Definition Vprog : varspecs. mk_varspecs prog. Defined. Definition secp256k1_umul128_spec : ident * funspec := DECLARE _secp256k1_umul128 WITH a : Z, b : Z, hi : val, sh : share PRE [ tulong, tulong, tptr tulong ] PROP(writable_share sh; 0 <= a < Int64.modulus; 0 <= b < Int64.modulus) PARAMS(Vlong (Int64.repr a); Vlong (Int64.repr b); hi) SEP(data_at_ sh tulong hi) POST [ tulong ] PROP() RETURN(Vlong (Int64.repr (a * b))) SEP(data_at sh tulong (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi). Definition secp256k1_mul128_spec : ident * funspec := DECLARE _secp256k1_mul128 WITH a : Z, b : Z, hi : val, sh : share PRE [ tlong, tlong, tptr tlong ] PROP(writable_share sh; Int64.min_signed <= a <= Int64.max_signed; Int64.min_signed <= b <= Int64.max_signed) PARAMS(Vlong (Int64.repr a); Vlong (Int64.repr b); hi) SEP(data_at_ sh tlong hi) POST [ tulong ] PROP() RETURN(Vlong (Int64.repr (a * b))) SEP(data_at sh tlong (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi). Lemma iter_sepcon_wand_in B f (x : B) l (Hl : In x l) : iter_sepcon f l = (f x * (f x -* iter_sepcon f l))%logic. Proof. apply pred_ext;[|apply wand_frame_elim]. apply In_Permutation_cons in Hl. destruct Hl as [l' Hl']. rewrite (iter_sepcon_permutation _ Hl'). simpl. entailer!. apply wand_frame_intro. Qed. Ltac unfold_Int128 := unfold Int128_max_unsigned, Int128_max_signed, Int128_min_signed, Int128_modulus in *|-*. Definition Gprog := ltac:(with_library prog [secp256k1_umul128_spec ;secp256k1_mul128_spec (* ;secp256k1_u128_load_spec *) ;secp256k1_u128_mul_spec ;secp256k1_u128_accum_mul_spec ;secp256k1_u128_accum_u64_spec ;secp256k1_u128_rshift_spec ;secp256k1_u128_to_u64_spec ;secp256k1_u128_hi_u64_spec ;secp256k1_u128_from_u64_spec ;secp256k1_u128_check_bits_spec (* ;secp256k1_i128_load_spec *) ;secp256k1_i128_mul_spec ;secp256k1_i128_accum_mul_spec ;secp256k1_i128_dissip_mul_spec ;secp256k1_i128_det_spec ;secp256k1_i128_rshift_spec ;secp256k1_i128_to_u64_spec ;secp256k1_i128_to_i64_spec ;secp256k1_i128_from_i64_spec ;secp256k1_i128_eq_var_spec ;secp256k1_i128_check_pow2_spec ]). Lemma body_secp256k1_umul128: semax_body Vprog Gprog f_secp256k1_umul128 secp256k1_umul128_spec. Proof. start_function. repeat progressC. * f_equal. apply Int64.eqm_repr_eq. eapply Int64.eqm_trans;[apply Int64.eqm_unsigned_repr|apply Int64.eqm_refl2]. rewrite !Int64.unsigned_repr_eq. change Int64.modulus with (2^64). rewrite !Z.shiftr_div_pow2 by lia. match goal with |- (?x mod 2^64) = _ => replace x with (2 ^ 32 * ((a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32) + 2 ^ 32 * ((a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32) + (2 ^ 32 * (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32) + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) by ring end. rewrite <- Z_div_mod_eq by lia. rewrite <- !(Zmult_mod_distr_l _ _ (2^32)). rewrite <- (Z.mod_small (a mod 2 ^ 32 * (b mod 2 ^ 32)) (2^64)) by (rewrite strict_bounds; solve_bounds). change (2^32 * 2^32) with (2^64). rewrite Zplus_mod_idemp_r, <- Zplus_assoc, Zplus_mod_idemp_l. match goal with |- (?x mod 2^64) = _ => replace x with ((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2^64 + (a mod 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32) + b mod 2 ^ 32)))) by ring end. rewrite <- Z_div_mod_eq by lia. change (2^64) with (2^32 * 2^32) at 1. rewrite Zmult_mod_distr_l, Zmult_mod_idemp_r, <- Zmult_mod_distr_l, Zplus_mod_idemp_l. match goal with |- (?x mod 2^64) = _ => replace x with ((2 ^ 32 * (a / 2 ^ 32) + (a mod 2 ^ 32)) * b) by ring end. rewrite <- Z_div_mod_eq by lia. reflexivity. * rewrite <- (Z.shiftr_shiftr _ 32 32), !Z.shiftr_div_pow2 by lia. rewrite <- Z.div_add_l by lia. match goal with |- context [Int64.repr (?x / 2^32)] => replace x with (((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32) + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32) + (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32)) + (a / 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32)) + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32) + (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) ) by ring end. rewrite <- !Z_div_mod_eq by lia. rewrite <- Z.mul_add_distr_l. rewrite <- Z_div_mod_eq by lia. rewrite <- Z.div_add_l by lia. rewrite <- Z.mul_assoc. rewrite <- Z.mul_add_distr_l. rewrite (Z.mul_comm _ (2^32)). rewrite <- Z_div_mod_eq by lia. rewrite Z.add_comm. rewrite <- Z.div_add_l by lia. rewrite (Z.mul_comm _ (2^32)), Z.mul_assoc. rewrite <- Z.mul_add_distr_r. rewrite <- Z_div_mod_eq by lia. entailer!. Qed. Lemma body_secp256k1_mul128: semax_body Vprog Gprog f_secp256k1_mul128 secp256k1_mul128_spec. Proof. start_function. repeat progressC. * f_equal. apply Int64.eqm_repr_eq. eapply Int64.eqm_trans;[apply Int64.eqm_unsigned_repr|apply Int64.eqm_refl2]. rewrite !Int64.unsigned_repr_eq. change Int64.modulus with (2^64). rewrite !Z.shiftr_div_pow2 by lia. unfold Int64.Z_mod_modulus. match goal with |- (?x mod 2^64) = _ => replace x with (2 ^ 32 * ((a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32) + 2 ^ 32 * ((a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32) + (2 ^ 32 * (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32) + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) by ring end. rewrite <- Z_div_mod_eq by lia. rewrite <- !(Zmult_mod_distr_l _ _ (2^32)). rewrite <- (Z.mod_small (a mod 2 ^ 32 * (b mod 2 ^ 32)) (2^64)) by (rewrite strict_bounds; solve_bounds). change (2^32 * 2^32) with (2^64). rewrite Zplus_mod_idemp_r, <- Zplus_assoc, Zplus_mod_idemp_l. match goal with |- (?x mod 2^64) = _ => replace x with ((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2^64 + (a mod 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32) + b mod 2 ^ 32)))) by ring end. rewrite <- Z_div_mod_eq by lia. change (2^64) with (2^32 * 2^32) at 1. rewrite Zmult_mod_distr_l, Zmult_mod_idemp_r, <- Zmult_mod_distr_l, Zplus_mod_idemp_l. match goal with |- (?x mod 2^64) = _ => replace x with ((2 ^ 32 * (a / 2 ^ 32) + (a mod 2 ^ 32)) * b) by ring end. rewrite <- Z_div_mod_eq by lia. reflexivity. * rewrite <- (Z.shiftr_shiftr _ 32 32), !Z.shiftr_div_pow2 by lia. rewrite <- Z.div_add_l by lia. match goal with |- context [Int64.repr (?x / 2^32)] => replace x with (((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32) + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32) + (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32)) + (a / 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32)) + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32) + (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) ) by ring end. rewrite <- !Z_div_mod_eq by lia. rewrite <- Z.mul_add_distr_l. rewrite <- Z_div_mod_eq by lia. rewrite <- Z.div_add_l by lia. rewrite <- Z.mul_assoc. rewrite <- Z.mul_add_distr_l. rewrite (Z.mul_comm _ (2^32)). rewrite <- Z_div_mod_eq by lia. rewrite Z.add_comm. rewrite <- Z.div_add_l by lia. rewrite (Z.mul_comm _ (2^32)), Z.mul_assoc. rewrite <- Z.mul_add_distr_r. rewrite <- Z_div_mod_eq by lia. entailer!. Qed. (* Lemma body_secp256k1_u128_load: semax_body Vprog Gprog f_secp256k1_u128_load secp256k1_u128_load_spec. Proof. start_function. repeat forward. entailer!. unfold secp256k1_uint128_at. rewrite <- (Int64.repr_unsigned (Int64.repr (_ + lo))), Int64.unsigned_repr_eq. rewrite Z.shiftl_mul_pow2, <- Zplus_mod_idemp_l, <- Zmult_mod_idemp_r, Z_mod_same_full by lia. rewrite Z.mul_0_r, Z.add_0_l. clear_mod. rewrite Z.shiftr_div_pow2, Z.div_add_l by lia. rewrite Z.div_small, Z.add_0_r by solve_bounds. entailer!. Qed. *) Lemma body_secp256k1_u128_mul: semax_body Vprog Gprog f_secp256k1_u128_mul secp256k1_u128_mul_spec. Proof. start_function. unfold_data_at (data_at_ sh t_secp256k1_uint128 r). simpl. rewrite (field_at_data_at _ _ (DOT _hi)). assert_PROP (field_compatible t_secp256k1_uint128 (DOT _hi) r) by entailer!. forward_call (a, b, (field_address t_secp256k1_uint128 (DOT _hi) r), sh). forward. unfold secp256k1_uint128_at. unfold_data_at (data_at sh t_secp256k1_uint128 _ r). entailer!. Qed. Lemma body_secp256k1_u128_accum_mul: semax_body Vprog Gprog f_secp256k1_u128_accum_mul secp256k1_u128_accum_mul_spec. Proof. start_function. forward_call. repeat progressC. unfold secp256k1_uint128_at. rewrite Z.add_assoc. rewrite <- shiftr_add_carry by lia. entailer!. Qed. Lemma body_secp256k1_u128_accum_u64: semax_body Vprog Gprog f_secp256k1_u128_accum_u64 secp256k1_u128_accum_u64_spec. Proof. start_function. repeat progressC. unfold secp256k1_uint128_at. rewrite shiftr_add_carry by lia. rewrite (shiftr_small a), Z.add_0_r, (Z.mod_small a) by solve_bounds. entailer!. Qed. Lemma body_secp256k1_u128_rshift: semax_body Vprog Gprog f_secp256k1_u128_rshift secp256k1_u128_rshift_spec. Proof. start_function. forward_verify_check. revert H1. convert_C_to_math. cbn. case Z.ltb_spec;[discriminate|lia]. unfold secp256k1_uint128_at. unfold_Int128. repeat progressC. * rewrite !Z.shiftr_shiftr by lia. replace (64 + (n - 64)) with n by ring. rewrite (shiftr_small _ (n + 64));[entailer!|]. cut (0 <= r0 < 2^128);[|solve_bounds]. assert (2^128 <= 2^(n+64)) by (apply Z.pow_le_mono_r;lia). lia. * rewrite !Z.shiftr_shiftr by lia. rewrite Z.add_comm. replace (Int64.repr (Z.lor _ _)) with (Int64.repr (Z.shiftr r0 n));[entailer!|]. rewrite <- Z.shiftl_mul_pow2 by lia. apply Int64.eqm_samerepr. apply Int64.eqm_same_bits. change Int64.zwordsize with 64. intros i Hi. rewrite Z.lor_spec, !Z.shiftr_spec, Z.shiftl_spec by lia. destruct (Z.neg_nonneg_cases (i - (64 - n))) as [Hneg|Hpos]. - rewrite (Z.testbit_neg_r _ _ Hneg). rewrite Z.mod_pow2_bits_low by lia. reflexivity. - rewrite Z.shiftr_spec by lia. rewrite Z.mod_pow2_bits_high, orb_false_r by lia. replace (i - (64 - n) + 64) with (i + n) by ring. reflexivity. * replace n with 0 by lia. rewrite Z.shiftr_0_r. entailer!. Qed. Lemma body_secp256k1_u128_to_u64: semax_body Vprog Gprog f_secp256k1_u128_to_u64 secp256k1_u128_to_u64_spec. Proof. start_function. unfold secp256k1_uint128_at. repeat progressC. Qed. Lemma body_secp256k1_u128_hi_u64: semax_body Vprog Gprog f_secp256k1_u128_hi_u64 secp256k1_u128_hi_u64_spec. Proof. start_function. unfold secp256k1_uint128_at. repeat progressC. Qed. Lemma body_secp256k1_u128_from_u64: semax_body Vprog Gprog f_secp256k1_u128_from_u64 secp256k1_u128_from_u64_spec. Proof. start_function. repeat progressC. unfold secp256k1_uint128_at. replace (Z.shiftr a 64) with 0;[entailer!|]. symmetry; auto using shiftr_small. Qed. Lemma body_secp256k1_u128_check_bits: semax_body Vprog Gprog f_secp256k1_u128_check_bits secp256k1_u128_check_bits_spec. Proof. start_function. forward_verify_check. revert H1. convert_C_to_math. cbn. case Z.ltb_spec;[discriminate|lia]. unfold secp256k1_uint128_at. assert (shiftr_small_eq : (r0 . replace (_ + r0 mod 2^64) with (r0 mod 2^64) by ring. reflexivity. - rewrite shiftr_small_eq. case (Z.eqb_spec);[|reflexivity]. intros Hr0. elim H2. replace 64 with (n + (64 - n)) by ring. rewrite <- Z.shiftr_shiftr, Hr0, Z.shiftr_0_l by lia. reflexivity. Qed. (* Lemma body_secp256k1_i128_load: semax_body Vprog Gprog f_secp256k1_i128_load secp256k1_i128_load_spec. Proof. start_function. repeat forward. entailer!. unfold secp256k1_uint128_at. rewrite <- (Int64.repr_unsigned (Int64.repr (_ + lo))), Int64.unsigned_repr_eq. rewrite Z.shiftl_mul_pow2, <- Zplus_mod_idemp_l, <- Zmult_mod_idemp_r, Z_mod_same_full by lia. rewrite Z.mul_0_r, Z.add_0_l. clear_mod. rewrite Z.shiftr_div_pow2, Z.div_add_l by lia. rewrite Z.div_small, Z.add_0_r by solve_bounds. entailer!. Qed. *) Lemma body_secp256k1_i128_mul: semax_body Vprog Gprog f_secp256k1_i128_mul secp256k1_i128_mul_spec. Proof. start_function. forward_call. repeat progressC. Qed. Lemma body_secp256k1_i128_accum_mul: semax_body Vprog Gprog f_secp256k1_i128_accum_mul secp256k1_i128_accum_mul_spec. Proof. start_function. unfold secp256k1_uint128_at. unfold_Int128. forward_call. repeat progressC. forward_verify_check. repeat progressC. set (hi := (_ + Z.b2z _)). forward_if (temp _t'2 (Vint (Int.repr (Z.b2z (((Z.shiftr r0 64) mod 2^64 <=? 9223372036854775807) && (hi mod 2^64 <=? 9223372036854775807))%bool)))); repeat progressC; revert H3; convert_C_to_math; try solve [repeat (first[case (Z.leb_spec _ _)|case (Z.ltb_spec _ _)];try lia;try reflexivity)]. case (Z.leb_spec _ _);try discriminate; intros Hr0. case (Z.leb_spec _ _);try discriminate; intros Hhi. case (Z.ltb_spec _ _);try discriminate; intros Hr0hi. apply Int64_low_is_nonneg in Hr0; [|solve_bounds]. apply Int64_low_is_nonneg in Hhi;[|solve_bounds]. apply Int64_high_is_neg in Hr0hi;[lia|]. unfold hi. rewrite Z.add_assoc, <- shiftr_add_carry by lia. solve_bounds. forward_verify_check. repeat progressC. set (hi := (_ + Z.b2z _)). forward_if (temp _t'3 (Vint (Int.repr (Z.b2z ((2^63-1 . reflexivity. + repeat progressC. apply Int64.eq_false in H. rewrite Hrs. revert H. convert_C_to_math. intros ->. reflexivity. + repeat progressC. Qed. (* Use with forward_call secp256k1_i128_eq_var_spec_alias_sub (r, shr, r0) *) Lemma secp256k1_i128_eq_var_spec_alias_sub : funspec_sub (snd secp256k1_i128_eq_var_spec) (snd secp256k1_i128_eq_var_spec_alias). Proof. do_funspec_sub. destruct w as [[r shr] r0]. entailer!. destruct (slice.split_readable_share _ H0) as [sh1 [sh2 [Hsh1 [Hsh2 Hsh]]]]. Exists (((((r, sh1), r0), r), sh2), r0) emp. unfold secp256k1_uint128_at. rewrite <- (data_at_share_join _ _ _ _ _ _ Hsh), Z.eqb_refl. entailer!. intros. entailer!. Qed. Lemma body_secp256k1_i128_check_pow2: semax_body Vprog Gprog f_secp256k1_i128_check_pow2 secp256k1_i128_check_pow2_spec. Proof. start_function. unfold_Int128. forward_verify_check. revert H2. convert_C_to_math. cbn. case Z.ltb_spec;[discriminate|lia]. forward_verify_check. forward_if (temp _t'1 (Vint (Int.repr 1))); [forward|forward;replace sign with (-1) by lia|]; try entailer!. forward_if;[discriminate|forward;entailer]. unfold secp256k1_uint128_at. forward_if (temp _t'2 (Vint (Int.repr (Z.b2z (r0 =? sign*2^n)))));[| |forward]. * assert (Hr0: r0 =? sign * 2 ^ n = ((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) && (r0 mod 2^64 =? 0))%bool). rewrite (Z_div_mod_eq_full r0 (2^64)) at 1. rewrite Z.mul_comm. replace n with (n - 64 + 64) at 1 by ring. rewrite <- (Z.add_0_r (sign * 2 ^ (n - 64 + 64))). change 0 with (0 mod 2^64). rewrite Z.pow_add_r, Z.mul_assoc, <- !Z.shiftl_mul_pow2, <- Z.shiftr_div_pow2 by lia. apply shiftl_mod_eqb_unique; lia. repeat progressC. - rewrite Hr0. replace (_ =? sign * 2 ^ _) with true;[reflexivity|]. symmetry; rewrite Z.eqb_eq. revert H3. convert_C_to_math. rewrite Z.eqb_eq. apply (Z_mod_eq_bounded (-2^63) (2^63)); try solve_bounds. pose (Hpow := Z.pow_lt_mono_r 2 (n-64) 63). lia. - rewrite Hr0. case Z.eqb_spec; try reflexivity. intros Hr0n. elim H3. convert_C_to_math. congruence. * assert (Hr0: r0 =? sign * 2 ^ n = ((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) && (r0 mod 2^64 =? (sign * 2^n) mod 2^64))%bool). rewrite (Z_div_mod_eq_full r0 (2^64)) at 1. rewrite (Z_div_mod_eq_full (sign * 2^n) (2^64)) at 1. rewrite !(Z.mul_comm (2^64)). rewrite <- (Z.shiftl_mul_pow2 _ n), <- !(Z.shiftl_mul_pow2 _ 64), <- !Z.shiftr_div_pow2, Z.shiftr_shiftl_l by lia. replace (n - 64) with (-(64 - n)) by ring. rewrite Z.shiftl_opp_r. replace (Z.shiftr sign (64 - n)) with (Z.shiftr (sign - 1) 1). apply shiftl_mod_eqb_unique; lia. destruct H1 as [-> | ->]; [rewrite Z_shiftr_neg1_l;[reflexivity|lia]|]. rewrite (shiftr_small 1);[reflexivity|]. split; try apply Z.pow_gt_1; lia. repeat progressC. - rewrite Hr0. replace (_ =? Z.shiftr _ _) with true;[reflexivity|]. symmetry; rewrite Z.eqb_eq. revert H3. convert_C_to_math. rewrite Z.eqb_eq. apply (Z_mod_eq_bounded (-2^63) (2^63)); solve_bounds. - rewrite Hr0. case Z.eqb_spec; try reflexivity. intros Hr0n. elim H3. convert_C_to_math. congruence. Qed. ================================================ FILE: Coq/C/secp256k1/verif_modinv64_impl.v ================================================ Require Import VST.floyd.proofauto. Require Import jets_secp256k1. Require Import spec_int128. Require Import spec_modinv64. Require Import extraMath. Require Import progressC. Require Import divsteps.divsteps_theory. Require Import divsteps.divsteps724. Require Import modinv. Require divstep. Opaque Z.shiftl Z.shiftr Z.pow. Definition Vprog : varspecs. mk_varspecs prog. Defined. Definition t_secp256k1_modinv64_trans2x2 := Tstruct _secp256k1_modinv64_trans2x2 noattr. Definition Trans_repr (m: divstep.Trans.M2x2) : reptype t_secp256k1_modinv64_trans2x2 := ( Vlong (Int64.repr (divstep.Trans.u m)) , (Vlong (Int64.repr (divstep.Trans.v m)) , (Vlong (Int64.repr (divstep.Trans.q m)) , Vlong (Int64.repr (divstep.Trans.r m)) ))). Definition secp256k1_ctz64_var_debruijn_spec : ident * funspec := DECLARE _secp256k1_ctz64_var_debruijn WITH a : Z, sh_debruijn : share, gv : globals PRE [ tulong ] PROP(0 <= a < Int64.modulus; readable_share sh_debruijn) PARAMS(Vlong (Int64.repr a)) GLOBALS(gv) SEP(debruijn64_array sh_debruijn gv) POST [ tint ] PROP() RETURN(Vint (Int.repr (Z_ctz a))) SEP(debruijn64_array sh_debruijn gv). (* secp256k1_ctz64_var is undefined for 0. *) Definition secp256k1_ctz64_var_spec : ident * funspec := DECLARE _secp256k1_ctz64_var WITH a : Z, sh_debruijn : share, gv : globals PRE [ tulong ] PROP(0 < a < Int64.modulus; readable_share sh_debruijn) PARAMS(Vlong (Int64.repr a)) GLOBALS(gv) SEP(debruijn64_array sh_debruijn gv) POST [ tint ] PROP() RETURN(Vint (Int.repr (Z_ctz a))) SEP(debruijn64_array sh_debruijn gv). Definition secp256k1_modinv64_abs_spec : ident * funspec := DECLARE _secp256k1_modinv64_abs WITH a : Z PRE [ tlong ] PROP(Int64.min_signed < a <= Int64.max_signed) PARAMS(Vlong (Int64.repr a)) SEP() POST [ tlong ] PROP() RETURN(Vlong (Int64.repr (Z.abs a))) SEP(). Definition secp256k1_modinv64_mul_62_spec : ident * funspec := DECLARE _secp256k1_modinv64_mul_62 WITH a : Z, alen : nat, factor : Z, ptrr : val, ptra : val, shr : share, sha : share PRE [ tptr t_secp256k1_modinv64_signed62 , tptr t_secp256k1_modinv64_signed62 , tint , tlong ] PROP( (1 <= alen <= 5)%nat ; -2^(62 * Z.of_nat alen + 1) <= a <= 2^(62 * Z.of_nat alen + 1) - 1 ; -2^311 <= a * factor <= 2^311 - 1 ; Int64.min_signed <= factor <= Int64.max_signed ; writable_share shr ; readable_share sha ) PARAMS(ptrr; ptra; Vint (Int.repr (Z.of_nat alen)); Vlong (Int64.repr factor)) SEP( data_at_ shr t_secp256k1_modinv64_signed62 ptrr ; data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ) POST [ tvoid ] PROP() RETURN() SEP( data_at shr t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 (a*factor))) ptrr ; data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ). Definition secp256k1_modinv64_mul_cmp_62_spec : ident * funspec := DECLARE _secp256k1_modinv64_mul_cmp_62 WITH a : Z, alen : nat, b : Z, factor : Z, ptra : val, ptrb : val, sha : share, shb : share PRE [ tptr t_secp256k1_modinv64_signed62 , tint , tptr t_secp256k1_modinv64_signed62 , tlong ] PROP( (1 <= alen <= 5)%nat ; -2^(62 * Z.of_nat alen + 1) <= a <= 2^(62 * Z.of_nat alen + 1) - 1 ; -2^311 <= b <= 2^311 - 1 ; -2^311 <= b * factor <= 2^311 - 1 ; Int64.min_signed <= factor <= Int64.max_signed ; readable_share sha ; readable_share shb ) PARAMS(ptra; Vint (Int.repr (Z.of_nat alen)); ptrb; Vlong (Int64.repr factor)) SEP( data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ; data_at shb t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 b)) ptrb ) POST [ tint ] PROP() RETURN(Vint (Int.repr (Z_of_comparison (a ?= b * factor)))) SEP( data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ; data_at shb t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 b)) ptrb ). Definition secp256k1_modinv64_det_check_pow2_spec : ident * funspec := DECLARE _secp256k1_modinv64_det_check_pow2 WITH m : divstep.Trans.M2x2, t : val, sh : share, n : Z, abs_flag : bool PRE [ tptr t_secp256k1_modinv64_trans2x2, tuint, tint ] PROP(divstep.Trans.bounded (2^62) m; 0 <= n < 127; readable_share sh) PARAMS(t; Vint (Int.repr n); Vint (Int.repr (Z.b2z abs_flag))) SEP(data_at sh t_secp256k1_modinv64_trans2x2 (Trans_repr m) t) POST [ tint ] PROP() RETURN(Vint (Int.repr (Z.b2z ((if abs_flag then Z.abs else id) (divstep.Trans.det m) =? 2^n)))) SEP(data_at sh t_secp256k1_modinv64_trans2x2 (Trans_repr m) t). Definition secp256k1_modinv64_normalize_62_spec : ident * funspec := DECLARE _secp256k1_modinv64_normalize_62 WITH r : Z, sign : int64, m : Z, ptrr : val, ptrm : val, shr : share, shm : share PRE [ tptr t_secp256k1_modinv64_signed62 , tlong , tptr t_secp256k1_modinv64_modinfo ] PROP( 0 <= m <= 2^310 - 2 ^ 248 ; -2^310 + 2^248 <= r ; -2 * m < r < m ; writable_share shr ; readable_share shm ) PARAMS(ptrr; Vlong sign; ptrm) SEP( data_at shr t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 r)) ptrr ; data_at shm t_secp256k1_modinv64_modinfo (make_modinfo m) ptrm ) POST [ tvoid ] PROP() RETURN() SEP( data_at shr t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 ((if Int64.signed sign Signed62.signed (firstn (Z.to_nat i) (Signed62.reprn alen a)) * factor / 2 ^ (62 * i) + Int64.signed (Znth i (Signed62.reprn alen a)) * factor = Signed62.signed (firstn (Z.to_nat (Z.succ i)) (Signed62.reprn alen a)) * factor / 2 ^ (62 * i)). clear - H Hlen HZlen. intros i Hi. rewrite (app_removelast_last (l:=firstn (Z.to_nat (Z.succ i)) _) default) by (rewrite <- length_zero_iff_nil, firstn_length; lia). rewrite Signed62.app_signed. rewrite Z2Nat.inj_succ, <- removelast_firstn, <- nth_last, removelast_firstn_len, Zlength_correct, !firstn_length, !min_l, Nat.sub_1_r, Z.mul_add_distr_r, <- Z.mul_assoc, firstn_firstn, nth_firstn_low by lia. change (Nat.pred (S (Z.to_nat i)))%nat with (Z.to_nat i). rewrite nth_Znth, Z2Nat.id by lia. rewrite (Z.mul_comm i 62), (Z.mul_comm (2^(62*i))), Z_div_plus_full by lia. simpl (Signed62.signed [Znth i (Signed62.reprn alen a)]). rewrite Z.mul_0_r, Z.add_0_r. reflexivity. forward_for_simple_bound 4 (EX i:Z, PROP ( ) LOCAL ( lvar _d (Tstruct _secp256k1_uint128 noattr) v_d ; lvar _c (Tstruct _secp256k1_uint128 noattr) v_c ; temp _M62 (Vlong (Int64.repr (2 ^ 62 - 1))) ; temp _r ptrr ; temp _a ptra ; temp _alen (Vint (Int.repr (Z.of_nat alen))) ; temp _factor (Vlong (Int64.repr factor)) ) SEP( data_at_ Tsh (Tstruct _secp256k1_uint128 noattr) v_d ; secp256k1_uint128_at Tsh ((Signed62.signed (firstn (Z.to_nat i) (Signed62.reprn alen a)))*factor / 2^(62*i)) v_c ; data_at shr t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn (Z.to_nat i) (a*factor mod 2^(62*i)))) ptrr ; data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ) )%assert. 1:{ rewrite Z.div_1_r, Z.mul_0_l. change (Signed62.pad (Signed62.reprn 5 _)) with (repeat Vundef 5). entailer!!. } 1:{ (* TODO Make this an external lemma. *) assert (Hfirst : forall i, 0 <= i -> -2 ^ (62 * i + 1) <= Signed62.signed (firstn (Z.to_nat i) (Signed62.reprn alen a)) <= 2 ^ (62 * i + 1) - 1). 1:{ clear -H0. intros i Hi. destruct (Z.lt_ge_cases i (Z.of_nat alen)). - rewrite Signed62.signed_firstn_reprn, Z2Nat.id, Z.mul_comm, Z.pow_add_r by lia. eapply weaken_bounds;[setoid_rewrite <- strict_bounds;apply Z.mod_pos_bound| |]; try lia. - rewrite firstn_same by (rewrite Signed62.reprn_length; lia). destruct alen;[simpl;lia|]. rewrite Signed62.signed_reprn by lia. eapply weaken_bounds;[apply H0|apply -> Z.opp_le_mono|apply Z.sub_le_mono_r];apply Z.pow_le_mono_r; lia. } forward_if ( PROP ( ) LOCAL ( temp _i (Vint (Int.repr i)) ; lvar _d (Tstruct _secp256k1_uint128 noattr) v_d ; lvar _c (Tstruct _secp256k1_uint128 noattr) v_c ; temp _M62 (Vlong (Int64.repr (2 ^ 62 - 1))) ; temp _r ptrr ; temp _a ptra ; temp _alen (Vint (Int.repr (Z.of_nat alen))) ; temp _factor (Vlong (Int64.repr factor)) ) SEP( data_at_ Tsh (Tstruct _secp256k1_uint128 noattr) v_d ; secp256k1_uint128_at Tsh ((Signed62.signed (firstn (Z.to_nat (Z.succ i)) (Signed62.reprn alen a)))*factor / 2^(62*i)) v_c ; data_at shr t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn (Z.to_nat i) (a*factor mod 2^(62*i)))) ptrr ; data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ) )%assert. 2:{ forward. rewrite !firstn_same by lia. entailer!. } 1:{ forward; rewrite Signed62.pad_nth by lia;[entailer!|]. rewrite <- (Int64.repr_signed (Znth i (Signed62.reprn alen a))). forward_call;rewrite Hstep by lia;[|entailer!]. split; unfold Int128_min_signed, Int128_max_signed; (setoid_rewrite <- strict_bounds';apply div_bounds;rewrite strict_bounds;[lia|]; eapply weaken_bounds;[ apply smul_bounds;[apply Hfirst;lia|apply H2] | |]); rewrite ?Z.mul_succ_r, !Z.pow_add_r; lia. } set (c:= _ / _). forward_call. forward. forward_call. 1:{ unfold c, Int128_min_signed, Int128_max_signed. setoid_rewrite <- strict_bounds';apply div_bounds;rewrite strict_bounds;[lia|]. eapply weaken_bounds;[ apply smul_bounds;[apply Hfirst;lia|apply H2] | |]; rewrite ?Z.mul_succ_r, !Z.pow_add_r; lia. } entailer!. unfold c at 1. rewrite <- Z.add_1_r, Z.shiftr_div_pow2, Zdiv_Zdiv, <- Z.pow_add_r by lia. replace (62 * (i + 1)) with (62 * i + 62) by ring. entailer!. erewrite <- (Z2Nat.id i), <- Signed62.reprn_length, <- Zlength_correct at 1 by lia. rewrite Signed62.pad_upd_Znth_end by (rewrite Signed62.reprn_length; lia). replace (2^62 - 1) with (Z.ones 62) by apply Z.ones_equiv. rewrite Z.land_ones, Z2Nat.inj_add, Nat.add_1_r, Signed62.reprn_succ, Z2Nat.id, Z.pow_add_r by lia. rewrite <- Zmod_div_mod, Z.shiftr_div_pow2 by (try lia; auto with *). destruct (Z.lt_ge_cases (Z.succ i) (Z.of_nat alen)); unfold c. * rewrite Signed62.signed_firstn_reprn, Z2Nat.id, Z.mul_succ_r, Z.pow_add_r, <- Zaux.Zdiv_mod_mult, Zmult_mod_idemp_l by lia. entailer!. * rewrite Zfirstn_same, Signed62.signed_reprn, <- Zaux.Zdiv_mod_mult by lia. entailer!. } forward_if ( PROP ( ) LOCAL ( lvar _d (Tstruct _secp256k1_uint128 noattr) v_d ; lvar _c (Tstruct _secp256k1_uint128 noattr) v_c ; temp _M62 (Vlong (Int64.repr (2 ^ 62 - 1))) ; temp _r ptrr ; temp _a ptra ; temp _alen (Vint (Int.repr (Z.of_nat alen))) ; temp _factor (Vlong (Int64.repr factor)) ) SEP( data_at_ Tsh (Tstruct _secp256k1_uint128 noattr) v_d ; secp256k1_uint128_at Tsh (a*factor / 2^(62*4)) v_c ; data_at shr t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn (Z.to_nat 4) (a*factor mod 2^(62*4)))) ptrr ; data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra ) )%assert. 2:{ forward. entailer!. rewrite Zfirstn_same, Signed62.signed_reprn by lia. entailer!. } 1:{ forward; rewrite Signed62.pad_nth by lia;[entailer|]. rewrite <- (Int64.repr_signed (Znth 4 (Signed62.reprn alen a))). forward_call;rewrite Hstep by lia; [|rewrite Zfirstn_same, Signed62.signed_reprn by lia; entailer!]. rewrite Signed62.signed_firstn_reprn, Zfirstn_same, Signed62.signed_reprn by lia. simpl (62 * _). unfold Int128_min_signed, Int128_max_signed. split;setoid_rewrite <- strict_bounds';apply div_bounds;rewrite strict_bounds; try lia. eapply weaken_bounds;[ apply usmul_bounds_tight;[setoid_rewrite <- strict_bounds; apply Z.mod_pos_bound|apply H2] | |]; lia. } forward_call; [setoid_rewrite <- strict_bounds';apply div_bounds;rewrite strict_bounds; lia|]. rewrite <- Z.shiftr_div_pow2 by lia. forward_call (v_d, Tsh, (Z.shiftr (a * factor) (62 * 4)));[solve_bounds|]. forward_verify_check. 1:{ simpl (62 * 4). set (n := Z.shiftr (a * factor) 248). forward_call. rewrite Z.eqb_refl. unfold n; clear n. forward_if;[discriminate|forward]. entailer!. } forward_call;[solve_bounds|]. forward. unfold secp256k1_uint128_at. replace (upd_Znth 4 _ _) with (map Vlong (Signed62.reprn 5 (a * factor))). * do 2 sep_apply (data_at_data_at_ Tsh t_secp256k1_uint128 (Vlong (Int64.repr (Z.shiftr (a * factor) (62 * 4))), Vlong (Int64.repr (Z.shiftr (Z.shiftr (a * factor) (62 * 4)) 64)))). entailer!!. * unfold Signed62.pad, upd_Znth, sublist. simpl. rewrite !Z.shiftr_shiftr, !Z.shiftr_div_pow2, <- !Zaux.Zdiv_mod_mult, <- !Z.pow_add_r by lia. repeat (rewrite <- Zmod_div_mod; try lia; [|match goal with |- (2 ^ ?a | 2 ^ ?b) => exists (2^(b - a)); reflexivity end]). reflexivity. Qed. Lemma body_secp256k1_modinv64_mul_cmp_62: semax_body Vprog Gprog f_secp256k1_modinv64_mul_cmp_62 secp256k1_modinv64_mul_cmp_62_spec. Proof. start_function. assert (H311: 2 ^ (62 * Z.of_nat alen + 1) <= 2^311) by (apply Z.pow_le_mono_r; lia). forward_call;[lia|]. forward_call (b, 5%nat, factor, v_bm, ptrb, Tsh, shb). change (a * Int.signed (Int.repr 1)) with (a * 1). set (bf := b * factor) in *. rewrite Z.mul_1_r. match goal with | |- semax _ ?E _ _ => forward_for_simple_bound 4 (EX _:Z, E) end. 1: entailer!. 1: { assert (H5a := Signed62.reprn_Zlength 5 a). assert (H5b := Signed62.reprn_Zlength 5 bf). forward_verify_check;[|forward_verify_check];( forward; rewrite Signed62.reprn_Znth by lia; match goal with | |- semax _ ?E _ _ => forward_if E end;try (try forward;entailer!);elimtype False; revert H5; convert_C_to_math; rewrite shiftr_small, Z.eqb_refl;[discriminate|]; apply Z.mod_pos_bound; lia; forward;entailer!). } forward_for (fun i:Z => PROP ( -1 <= i < 5 /\ (i = 4 \/ (i < 4 /\ Z.shiftr a (62*(i + 1)) = Z.shiftr bf (62*(i + 1)))) ) LOCAL (temp _i (Vint (Int.repr i)); lvar _bm (Tstruct _secp256k1_modinv64_signed62 noattr) v_bm; lvar _am (Tstruct _secp256k1_modinv64_signed62 noattr) v_am; temp _a ptra; temp _alen (Vint (Int.repr (Z.of_nat alen))); temp _b ptrb; temp _factor (Vlong (Int64.repr factor))) SEP (data_at shb t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn 5 b)) ptrb; data_at sha t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn alen a)) ptra; data_at Tsh t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 bf)) v_bm; data_at Tsh t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 a)) v_am)). 1: forward; Exists 4; entailer!. 1: entailer!. 2: { forward. replace x with (-1) in * by lia. rewrite !Z.shiftr_0_r in H4. destruct H4 as [_ [|[_ ->]]];[lia|]. rewrite Z.compare_refl. entailer!. } assert (Ha := Signed62.reprn_Zlength 5 a). assert (Hbf := Signed62.reprn_Zlength 5 bf). do 2 forward. destruct H4 as [Hx [H4|[Hx4 H4]]];forward_if;repeat forward;try forward_if;repeat forward;try entailer!!. * unfold Znth in H5; simpl in H5. revert H5;convert_C_to_math;intros H5. rewrite Z.ltb_lt, !Z.shiftr_shiftr in H5 by lia. simpl in H5. rewrite !Z.shiftr_div_pow2 in H5 by lia. rewrite (proj2 (Z.compare_lt_iff _ _));[reflexivity|]. apply Z.nle_gt; intro; revert H5; apply Z.le_ngt. apply Z.div_le_mono; lia. * unfold Znth in H6; simpl in H6. revert H6;convert_C_to_math;intros H6. rewrite Z.ltb_lt, !Z.shiftr_shiftr in H6 by lia. simpl in H6. rewrite !Z.shiftr_div_pow2 in H6 by lia. rewrite (proj2 (Z.compare_gt_iff _ _));[reflexivity|]. apply Z.nle_gt; intro; revert H6; apply Z.le_ngt. apply Z.div_le_mono; lia. * Exists 3. entailer!. right. unfold Znth in H5,H6; simpl in H5,H6. revert H5 H6;convert_C_to_math. rewrite !Z.ltb_ge, !Z.shiftr_shiftr by lia. simpl; unfold bf. lia. * rewrite (proj2 (Z.compare_lt_iff _ _));[reflexivity|]. rewrite (Z_div_mod_eq_full a (2^(62 * (x + 1)))). rewrite (Z_div_mod_eq_full bf (2^(62 * (x + 1)))). change (cons (Int64.repr (a mod 2 ^ 62)) _) with (Signed62.reprn 5 a) in H5. change (cons _ _) with (Signed62.reprn 5 bf) in H5. rewrite !Signed62.reprn_Znth in H5 by lia. revert H5;convert_C_to_math;intros H5. rewrite Z.ltb_lt, !Z.shiftr_div_pow2, <- !Zaux.Zdiv_mod_mult, <- Z.pow_add_r in H5 by lia. replace (62 * x + 62) with (62 * (x + 1)) in H5 by lia. rewrite !Z.shiftr_div_pow2 in H4 by lia. rewrite H4. apply Z.add_le_lt_mono; [lia|]. apply Z.nle_gt; intro; revert H5; apply Z.le_ngt. apply Z.div_le_mono; lia. * rewrite (proj2 (Z.compare_gt_iff _ _));[reflexivity|]. rewrite (Z_div_mod_eq_full a (2^(62 * (x + 1)))). rewrite (Z_div_mod_eq_full bf (2^(62 * (x + 1)))). change (cons (Int64.repr (a mod 2 ^ 62)) _) with (Signed62.reprn 5 a) in H6. change (cons _ _) with (Signed62.reprn 5 bf) in H6. rewrite !Signed62.reprn_Znth in H6 by lia. revert H6;convert_C_to_math;intros H6. rewrite Z.ltb_lt, !Z.shiftr_div_pow2, <- !Zaux.Zdiv_mod_mult, <- Z.pow_add_r in H6 by lia. replace (62 * x + 62) with (62 * (x + 1)) in H6 by lia. rewrite !Z.shiftr_div_pow2 in H4 by lia. rewrite H4. apply Z.add_le_lt_mono; [lia|]. apply Z.nle_gt; intro; revert H6; apply Z.le_ngt. apply Z.div_le_mono; lia. * Exists (x-1). entailer!. right. split;[lia|]. replace (x - 1 + 1) with x by ring. rewrite (Z_div_mod_eq_full (Z.shiftr a _) (2^62)). rewrite (Z_div_mod_eq_full (Z.shiftr bf _) (2^62)). rewrite <- !Z.shiftr_div_pow2, !Z.shiftr_shiftr by lia. replace (62 * x + 62) with (62 * (x + 1)) by lia. change (cons (Int64.repr (a mod 2 ^ 62)) _) with (Signed62.reprn 5 a) in *. change (cons _ _) with (Signed62.reprn 5 bf) in *. rewrite !Signed62.reprn_Znth in H5, H6 by lia. revert H5 H6;convert_C_to_math. rewrite !Z.ltb_ge;lia. Qed. Lemma body_secp256k1_modinv64_det_check_pow2: semax_body Vprog Gprog f_secp256k1_modinv64_det_check_pow2 secp256k1_modinv64_det_check_pow2_spec. Proof. start_function. destruct m as [u v q r]. unfold divstep.Trans.bounded in H. simpl in H. destruct H as [[Huv _] [Hqr _]]. unfold Trans_repr. simpl (data_at _ _ _ _). assert (Hur : -((2 ^ 62 + 1) * (2 ^ 62 + 1)) <= u * r <= (2 ^ 62 + 1) * (2 ^ 62 + 1)) by (apply smul_bounds; lia). assert (Hvq : -((2 ^ 62 + 1) * (2 ^ 62 + 1)) <= v * q <= (2 ^ 62 + 1) * (2 ^ 62 + 1)) by (apply smul_bounds; lia). fastforward 4. forward_call (v_a, Tsh, u, v, q, r). forward_call;[unfold Int128_min_signed, Int128_max_signed; lia|]. forward_if. 1: { unfold secp256k1_uint128_at. sep_apply (data_at_data_at_ Tsh t_secp256k1_uint128 (Vlong (Int64.repr (u * r - v * q)), Vlong (Int64.repr (Z.shiftr (u * r - v * q) 64))) v_a). forward; entailer!!. revert H. elim Z.eqb_spec; cbn; try lia. intros -> _. rewrite Z.mul_1_l. elim Z.eqb_spec; try reflexivity. intros e; elim e. destruct abs_flag; try reflexivity. auto with *. } forward_if (temp _t'2 (Vint (Int.repr (Z.b2z (abs_flag && (u * r - v * q =? -2^n)))))). 1: { forward_call;[unfold Int128_min_signed, Int128_max_signed; lia|]. forward; entailer!. } 1: { forward; entailer!. } forward_if. 1: { unfold secp256k1_uint128_at. sep_apply (data_at_data_at_ Tsh t_secp256k1_uint128 (Vlong (Int64.repr (u * r - v * q)), Vlong (Int64.repr (Z.shiftr (u * r - v * q) 64))) v_a). forward; entailer!!. destruct abs_flag; try discriminate. revert H1. elim Z.eqb_spec; unfold Int.zero; cbn; try congruence. intros -> _. rewrite Z.abs_opp. elim Z.eqb_spec; try reflexivity. intros e; elim e. auto with *. } unfold secp256k1_uint128_at. sep_apply (data_at_data_at_ Tsh t_secp256k1_uint128 (Vlong (Int64.repr (u * r - v * q)), Vlong (Int64.repr (Z.shiftr (u * r - v * q) 64))) v_a). forward; entailer!!. cbn. elim Z.eqb_spec; try reflexivity. destruct abs_flag; [replace (2^n) with (Z.abs (2^n)) by auto with *; intros Habs; destruct (Z.abs_eq_cases _ _ Habs)|cbn; intros H5]; try (rewrite H5, Z.mul_1_l, Z.eqb_refl in H; discriminate). rewrite H5, Z.eqb_refl in H1; discriminate. Qed. Lemma body_secp256k1_modinv64_normalize_62: semax_body Vprog Gprog f_secp256k1_modinv64_normalize_62 secp256k1_modinv64_normalize_62_spec. Proof. start_function. assert (H5r := Signed62.reprn_Zlength 5 r). assert (H5m := Signed62.reprn_Zlength 5 m). assert (Hrbound : -(2 ^ 62 - 1) <= Z.shiftr r 248 <= 2 ^ 62 - 1) by solve_bounds. assert (Hmbound : 0 <= Z.shiftr m 248 <= 2 ^ 62 - 1) by solve_bounds. set (rl := Signed62.reprn 5 r) in *. set (ml := Signed62.reprn 5 m) in *. progressC. change (Z.shiftr (-1 mod 2 ^ 64) 2) with (2^62 - 1). fastforward 5. match goal with |- semax _ ?E _ _ => forward_for_simple_bound 5 (EX i:Z, E) end;[entailer| |]. 1:{ forward_verify_check;[|forward_verify_check]. 1:{ forward; forward_if;[entailer!; cbn; lia| | forward;entailer]. revert H3. change (Znth i _) with (Znth i (Signed62.reprn 5 r)). destruct (Z.lt_ge_cases i 4) as [Hi|Hi]. * rewrite Signed62.reprn_Znth by lia. convert_C_to_math. elim Z.ltb_spec0; try discriminate. intros H3. assert (Hr:=Z.mod_pos_bound (Z.shiftr r (62 * i)) (2 ^ 62)). lia. * replace i with 4 by lia. change 4 with (Zlength (Signed62.reprn 5 r) - 1). rewrite Znth_last, Signed62.reprn_last by lia. convert_C_to_math. elim Z.ltb_spec0; try discriminate. cbn;lia. } 1:{ forward. match goal with |- semax _ ?E _ _ => forward_if E end;[|forward;entailer|forward;entailer]. revert H3. change (Znth i _) with (Znth i (Signed62.reprn 5 r)). destruct (Z.lt_ge_cases i 4) as [Hi|Hi]. * rewrite Signed62.reprn_Znth by lia. convert_C_to_math. elim Z.ltb_spec0; try discriminate. intros H3. assert (Hr:=Z.mod_pos_bound (Z.shiftr r (62 * i)) (2 ^ 62)). lia. * replace i with 4 by lia. change 4 with (Zlength (Signed62.reprn 5 r) - 1). rewrite Znth_last, Signed62.reprn_last by lia. convert_C_to_math. elim Z.ltb_spec0; try discriminate. cbn;lia. } } unfold make_modinfo. assert_PROP (field_compatible t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm) by entailer. forward_verify_check. 1:{ forward_call (r, 5%nat, m, -2, ptrr, (field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm), shr, shm); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ ptrm);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Gt in H3; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ ptrm);entailer!. } forward_verify_check. 1:{ forward_call (r, 5%nat, m, 1, ptrr, (field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm), shr, shm); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ ptrm);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Lt in H3; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ ptrm);entailer!. } progressC. change 4 with (Zlength rl - 1);rewrite Znth_last. unfold rl. rewrite Signed62.reprn_last by lia. repeat (rewrite Signed62.reprn_Znth by lia). convert_C_to_math. rewrite Z.shiftr_shiftr by lia. simpl (62 * (Z.of_nat 5 - 1) + 63). assert (-1 <= Z.shiftr r 311 <= 0) by solve_bounds. replace (Z.shiftr r 311) with (if r ring_simplify x end; solve [auto with *]. } clear t' Ht0 Ht1 Ht2 Ht3 Ht4 t0 t1 t2 t3 t4. do 5 progressC. do 5 (forward_verify_check;[ revert H6; convert_C_to_math; elim Z.eqb_spec; try discriminate; intros H6 _; apply H6; apply shiftr_small; rewrite strict_bounds; solve_bounds |]). change (upd_Znth 4 _ _) with (map Vlong (Signed62.reprn 5 t)). assert (Ht0: 0 <= t < m) by (apply Z.mod_pos_bound; lia). forward_verify_check. 1:{ forward_call (t, 5%nat, m, 0, ptrr, (field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm), shr, shm); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ ptrm);entailer!|]. forward_if. 1:{ revert H6. fold t. elim Z.compare_spec; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ ptrm);entailer!. } forward_verify_check. 1:{ forward_call (t, 5%nat, m, 1, ptrr, (field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm), shr, shm); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ ptrm);entailer!|]. match goal with |- semax _ ?E _ _ => forward_if E end. * revert H6. fold t. rewrite Zaux.Zcompare_Lt; try discriminate. lia. * forward. entailer!. * forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ ptrm);entailer!. } Qed. Lemma body_secp256k1_modinv64_divsteps_62_var: semax_body Vprog Gprog f_secp256k1_modinv64_divsteps_62_var secp256k1_modinv64_divsteps_62_var_spec. Proof. start_function. do 7 forward. forward_loop (EX i:nat, EX j:nat, EX u:Z, EX v:Z, EX f:Z, EX g:Z, PROP ( Z.of_nat j <= Z.of_nat i <= 62 ; divstep.Trans.u (divstep.Trans.transN i st) = (u * 2^(Z.of_nat j))%Z ; divstep.Trans.v (divstep.Trans.transN i st) = (v * 2^(Z.of_nat j))%Z ; eqm (2^(64 - Z.of_nat i)) f (divstep.f (fst (divstep.stepN i st))) ; eqm (2^(64 - Z.of_nat i)) g (divstep.g (fst (divstep.stepN i st))) ) LOCAL (temp _i (Vint (Int.repr (62 - Z.of_nat i + Z.of_nat j))); temp _g (Vlong (Int64.repr (g * 2^(Z.of_nat j)))); temp _f (Vlong (Int64.repr f)); temp _r (Vlong (Int64.repr (divstep.Trans.r (divstep.Trans.transN i st)))); temp _q (Vlong (Int64.repr (divstep.Trans.q (divstep.Trans.transN i st)))); temp _v (Vlong (Int64.repr v)); temp _u (Vlong (Int64.repr u)); gvars gv; temp _eta (Vlong (Int64.repr (divstep.eta (fst (divstep.stepN i st)) + Z.of_nat j))); temp _f0 (Vlong (Int64.repr (divstep.f st))); temp _g0 (Vlong (Int64.repr (divstep.g st))); temp _t t) SEP (data_at_ sh t_secp256k1_modinv64_trans2x2 t; debruijn64_array sh_debruijn gv) )%assert break:( PROP ( ) LOCAL ( temp _r (Vlong (Int64.repr (divstep.Trans.r (divstep.Trans.transN 62 st)))); temp _q (Vlong (Int64.repr (divstep.Trans.q (divstep.Trans.transN 62 st)))); temp _v (Vlong (Int64.repr (divstep.Trans.v (divstep.Trans.transN 62 st)))); temp _u (Vlong (Int64.repr (divstep.Trans.u (divstep.Trans.transN 62 st)))); gvars gv; temp _eta (Vlong (Int64.repr (divstep.eta (fst (divstep.stepN 62 st))))); temp _t t) SEP (data_at_ sh t_secp256k1_modinv64_trans2x2 t; debruijn64_array sh_debruijn gv) )%assert. * Exists 0%nat; Exists 0%nat; Exists (divstep.Trans.u (divstep.Trans.transN 0 st)); Exists (divstep.Trans.v (divstep.Trans.transN 0 st)); Exists (divstep.f (fst (divstep.stepN 0 st)));Exists (divstep.g (fst (divstep.stepN 0 st))); entailer!. * Intros n j u v f g; rename H4 into Hg; rename H3 into Hf; rename H2 into Hv; rename H1 into Hu; rename H0 into Hn. assert (Hmask : 0 <> (-1 * 2 ^ (62 - Z.of_nat n + Z.of_nat j)) mod (2^64)). 1:{ intros Hzero; symmetry in Hzero. apply Zmod_divide in Hzero; try lia. replace 64 with ((2 + Z.of_nat n - Z.of_nat j) + (62 - Z.of_nat n + Z.of_nat j)) in Hzero by ring. rewrite !Z.pow_add_r, Z.mul_divide_cancel_r, (Z.divide_opp_r _ 1) in Hzero by lia. apply Z.divide_1_r_nonneg in Hzero; try lia. replace (2 + Z.of_nat n - Z.of_nat j) with (2 + (Z.of_nat n - Z.of_nat j)) in Hzero by ring. rewrite Z.pow_add_r in Hzero by lia. lia. } assert (Hbound := Z.mod_pos_bound (-1 * 2 ^ (62 - Z.of_nat n + Z.of_nat j)) (2 ^ 64)). assert (Heta := divstep.etaBounds 683 n st H). assert (Hfodd : Zodd f). 1:{ apply Zodd_bool_iff. assert (Hf0 := Zmod_odd f). revert Hf0. destruct (Z.odd f); try reflexivity. assert (H2 : (2 | 2 ^ (64 - Z.of_nat n))) by (apply Zpow_facts.Zpower_divide; lia). rewrite (Zmod_div_mod 2 (2 ^ (64 - Z.of_nat n))), Hf, <- (Zmod_div_mod 2 (2 ^ (64 - Z.of_nat n))) by (try lia; assumption). assert (Hfodd := divstep.oddF (fst (divstep.stepN n st))). apply Zodd_bool_iff in Hfodd. assert (Hmod := Zmod_odd (divstep.f (fst (divstep.stepN n st)))). rewrite Hfodd in Hmod. rewrite Hmod. discriminate. } assert (Hgcd : forall z a, Zodd z -> 0 <= a -> Z.gcd z (2 ^ a) = 1). 1:{ intros z a Hz Ha. apply Zgcd_1_rel_prime. apply Zpow_facts.rel_prime_Zpower_r;[lia|]. apply rel_prime_mod_rev;[lia|]. rewrite Zmod_odd. replace (Z.odd z) with true;[apply rel_prime_1|]. symmetry; apply Zodd_bool_iff. assumption. } forward_call. 1:{ change (Int.unsigned Int64.iwordsize') with 64; lia. } 1:{ split; [|unfold_C; rewrite Z_log2_lt_pow2, Z.log2_lor, Z.max_lub_lt_iff, <- !Z_log2_lt_pow2; rep_lia]. apply Z_lor_pos; try rep_lia. convert_C_to_math. lia. } convert_C_to_math. set (g' := g * _). assert (Hgbound := Z.mod_pos_bound g' (2 ^ 64)). set (zeros := (Z_ctz _)). assert (Hzeros_pos : 0 <= zeros) by apply Z_ctz_non_neg. assert (Hzeros62 : zeros <= 62 - Z.of_nat n + Z.of_nat j). 1:{ unfold zeros. rewrite Z.lor_comm. etransitivity. * apply Z_ctz_lor_l. lia. * apply Z.nlt_ge. intros Hctz. apply Z_ctz_testbit_false in Hctz. rewrite Z.mod_pow2_bits_low, <- two_p_equiv, Z.mul_comm, <- Z.opp_eq_mul_m1, Zbits.Ztestbit_neg_two_p in Hctz by lia. destruct zlt in Hctz; lia. } assert (Hg'zeros : (2^zeros | g')). 1:{ apply Zmod_divide;[auto with *|]. apply Z.bits_inj_0; intros k. destruct (Z_le_lt_dec 0 k);[|auto using Z.testbit_neg_r]. rewrite <- two_p_equiv, Zbits.Ztestbit_mod_two_p by lia. destruct zlt as [Hk|Hk];[|reflexivity]. rewrite <- (Z.mod_pow2_bits_low _ 64) by lia. destruct (Z.eq_dec (g' mod 2^64) 0) as [->|Hne];[apply Z.bits_0|]. apply Z_ctz_testbit_false. eapply Z.lt_le_trans;[apply Hk|]. apply Z_ctz_lor_l; assumption. } assert (Hzeros_opt: forall i, (2^i | g') -> i <= 62 - Z.of_nat n + Z.of_nat j -> i <= zeros). 1:{ intros i Hig Hi62. apply Z.lt_pred_le. apply Z_testbit_false_ctz;[apply Z_lt_neq;apply Z_lor_pos; lia|]. intros k Hk. destruct Hig as [m ->]. rewrite Z.lor_spec, orb_false_iff, !Z.mod_pow2_bits_low, Z.mul_pow2_bits_low by lia. rewrite <- two_p_equiv, Z.mul_comm, <- Z.opp_eq_mul_m1, Zbits.Ztestbit_neg_two_p by lia. elim zlt; lia. } do 5 progressC. unfold g'. replace 64 with (zeros + (64 - zeros)) by ring. rewrite Z.pow_add_r, (Z.shiftr_div_pow2 _ zeros), Zaux.Zdiv_mod_mult by lia. replace zeros with (Z.of_nat j + (zeros - Z.of_nat j)) by ring. set (k := zeros - Z.of_nat j). assert (Hk : 0 <= k). 1:{ apply Z.nlt_ge. intros Hk. cut (zeros + 1 <= zeros);[lia|]. apply Hzeros_opt;[|lia]. etransitivity;[|apply Z.divide_factor_r]. apply Zmod_divide;try lia. replace (Z.of_nat j) with ((-1 - k) + (zeros + 1)) by (unfold k; ring). rewrite Z.pow_add_r by lia. apply Z_mod_mult. } rewrite !Z.pow_add_r, !Z.mul_assoc, <- Hu, <- Hv by lia. clear u v Hu Hv. replace (62 - Z.of_nat n + Z.of_nat j - (Z.of_nat j + k)) with (62 - Z.of_nat n - k) by ring. replace (divstep.eta (fst (divstep.stepN n st)) + Z.of_nat j - (Z.of_nat j + k)) with (divstep.eta (fst (divstep.stepN n st)) - k) by ring. rewrite (Z.mul_comm g), Zdiv_mult_cancel_l by lia. assert (Hkn : (2 ^ k | 2 ^ (64 - Z.of_nat n))). 1:{ replace (64 - Z.of_nat n) with (k + (64 - Z.of_nat n - k)) by ring. rewrite Z.pow_add_r by lia. apply Z.divide_factor_l. } assert (Hgzeros : (2 ^ k | divstep.g (fst (divstep.stepN n st)))). 1:{ apply Zmod_divide; try lia. rewrite (Zmod_div_mod _ (2 ^ (64 - Z.of_nat n))), <- Hg, <-Zmod_div_mod by (try lia; assumption). apply Zdivide_mod. eapply Z.mul_divide_cancel_r;[|etransitivity;[|apply Hg'zeros]];[lia|]. rewrite <- Z.pow_add_r by lia. replace (k + Z.of_nat j) with zeros by (unfold k; ring). reflexivity. } rewrite <- (Z2Nat.id _ Hk) in Hgzeros |- *. rewrite <- divstep.etaHs by assumption. set (g1 := ((g / _) mod _)). assert (Hg1 : eqm (2 ^ (64 - Z.of_nat n - k)) g1 (divstep.g (fst (divstep.stepN (Z.to_nat k) (fst (divstep.stepN n st)))))). 1:{ rewrite divstep.gHs by assumption. unfold eqm, g1. rewrite (Z2Nat.id _ Hk). rewrite <- Zmod_div_mod; try lia. 2:{ replace (64 - (Z.of_nat j + k)) with ((64 - Z.of_nat n - k) + (0 - Z.of_nat j + Z.of_nat n)) by ring. rewrite Z.pow_add_r by lia. apply Z.divide_factor_l. } rewrite <- !Zaux.Zdiv_mod_mult by lia. rewrite <- Z.pow_add_r by lia. replace (k + (64 - Z.of_nat n - k)) with (64 - Z.of_nat n) by ring. f_equal. assumption. } assert (Hf1 : eqm (2 ^ (64 - Z.of_nat n - k)) f (divstep.f (fst (divstep.stepN (Z.to_nat k) (fst (divstep.stepN n st)))))). 1:{ rewrite divstep.fHs by assumption. unfold eqm. rewrite (Zmod_div_mod _ (2 ^ (64 - Z.of_nat n - k + k)) (divstep.f _)), (Zmod_div_mod _ (2 ^ (64 - Z.of_nat n - k + k))) by (try lia;rewrite Z.pow_add_r by lia; apply Z.divide_factor_l). f_equal. replace (64 - Z.of_nat n - k + k) with (64 - Z.of_nat n) by ring. assumption. } rewrite <- divstep.stepN_app_fst in *. assert (trans_n_k := divstep.Trans.transN_stepN (Z.to_nat k) n st). rewrite divstep.Trans.transHs in trans_n_k by assumption. unfold divstep.Trans.mul in trans_n_k. cbn in trans_n_k. rewrite !Z.mul_0_l, !Z.mul_1_l, !Z.add_0_r in trans_n_k. replace (divstep.Trans.v (divstep.Trans.transN n st) * 2 ^ Z.of_nat (Z.to_nat k)) with (divstep.Trans.v (divstep.Trans.transN (Z.to_nat k + n) st)) by (rewrite <- trans_n_k; cbn; ring). replace (divstep.Trans.u (divstep.Trans.transN n st) * 2 ^ Z.of_nat (Z.to_nat k)) with (divstep.Trans.u (divstep.Trans.transN (Z.to_nat k + n) st)) by (rewrite <- trans_n_k; cbn; ring). replace (divstep.Trans.r (divstep.Trans.transN n st)) with (divstep.Trans.r (divstep.Trans.transN (Z.to_nat k + n) st)) by (rewrite <- trans_n_k; reflexivity). replace (divstep.Trans.q (divstep.Trans.transN n st)) with (divstep.Trans.q (divstep.Trans.transN (Z.to_nat k + n) st)) by (rewrite <- trans_n_k; reflexivity). replace (62 - Z.of_nat n - Z.of_nat (Z.to_nat k)) with (62 - Z.of_nat (Z.to_nat k + n)) by lia. replace (64 - Z.of_nat n - k) with (64 - Z.of_nat (Z.to_nat k + n)) in * by lia. set (n1 := (Z.to_nat k + n)%nat) in *. assert (Hn1 : 0 <= Z.of_nat n1 <= 62) by lia. assert (Hg1odd : Zodd g1 \/ n1 = 62%nat). 1:{ destruct (Zeven_odd_dec g1) as [Hg1even|Hg1odd];[|tauto]. right. apply Zeven_div2 in Hg1even. rewrite (Z_div_mod_eq_full g1 2) in Hg1even at 1. rewrite Z.div2_div in Hg1even. assert (Hgeven : g1 mod 2 = 0) by lia. clear Hg1even. unfold g1 in Hgeven. rewrite <- Zmod_div_mod, (* <- Zaux.Zdiv_mod_mult, *) (Z2Nat.id _ Hk) in Hgeven; try lia. 2:apply Zpow_facts.Zpower_divide; lia. cut (2 ^ (zeros + 1) | g'). 1:intros Hg';specialize (Hzeros_opt (zeros + 1) Hg');lia. apply Zmod_divide; try lia. apply Zdivide_mod in Hg'zeros. rewrite Z.pow_add_r, Z.rem_mul_r, Hg'zeros, Z.add_0_l by lia. replace 0 with (2 ^ zeros * 0) by ring. rewrite Z.mul_cancel_l by lia. unfold g'. replace zeros with (k + Z.of_nat j) by lia. rewrite Z.pow_add_r, Zdiv_mult_cancel_r by lia. assumption. } clearbody n1 k g1. clear zeros Hzeros_pos Hzeros62 Hg'zeros Hzeros_opt Hk Hkn Hgzeros g' Hgbound Hf Hg g Hmask Hbound Hn n Heta trans_n_k. forward_if;change (62 - _) with (62 - Z.of_nat n1) in H0. 1:{ rewrite H0. replace n1 with 62%nat by lia. forward. entailer!. } assert (Hn162 : Z.of_nat n1 < 62) by lia. clear H0. destruct Hg1odd as [Hg1odd|Hg1odd];[|lia]. forward_verify_check. 1:{ revert H0. convert_C_to_math. change (Z.land f 1) with (Z.land f (Z.ones 1)). rewrite Z.land_ones by lia. change (2^1) with 2. rewrite (Zmod_div_mod 2 (2 ^ (64 - Z.of_nat n1))) by (try lia; apply Zpow_facts.Zpower_divide; lia). rewrite Hf1. rewrite <- (Zmod_div_mod 2) by (try lia; apply Zpow_facts.Zpower_divide; lia). rewrite Zmod_odd. assert (Hf1odd := divstep.oddF (fst (divstep.stepN n1 st))). rewrite <- Zodd_bool_iff in Hf1odd. rewrite Hf1odd, Z.eqb_refl. cbn. discriminate. } forward_verify_check. 1:{ revert H0. convert_C_to_math. change (Z.land g1 1) with (Z.land g1 (Z.ones 1)). rewrite Z.land_ones by lia. change (2^1) with 2. rewrite Zmod_odd. rewrite <- Zodd_bool_iff in Hg1odd. rewrite Hg1odd, Z.eqb_refl. cbn. discriminate. } assert (Hstepn := divstep.Trans.transN_step n1 st). injection Hstepn; intros Hstepng Hstepnf; clear Hstepn. assert (Hshift : 62 - (62 - Z.of_nat n1) < 64) by lia. forward_verify_check. 1:{ assert (Hfshift : eqm (2^64) (2 ^ Z.of_nat n1 * f) (2 ^ Z.of_nat n1 * divstep.f (fst (divstep.stepN n1 st)))). 1:{ unfold eqm. replace 64 with (Z.of_nat n1 + (64 - Z.of_nat n1)) by ring. rewrite Z.pow_add_r, !Zmult_mod_distr_l, Hf1; lia. } rewrite Hstepnf in Hfshift. revert H0. convert_C_to_math. replace (62 - _) with (Z.of_nat n1) by ring. rewrite <- Hfshift, (Z.mul_comm f), Z.eqb_refl. discriminate. } forward_verify_check. 1:{ assert (Hgshift : eqm (2^64) (2 ^ Z.of_nat n1 * g1) (2 ^ Z.of_nat n1 * divstep.g (fst (divstep.stepN n1 st)))). 1:{ unfold eqm. replace 64 with (Z.of_nat n1 + (64 - Z.of_nat n1)) by ring. rewrite Z.pow_add_r, !Zmult_mod_distr_l, Hg1; lia. } rewrite Hstepng in Hgshift. revert H0. convert_C_to_math. replace (62 - _) with (Z.of_nat n1) by ring. rewrite <- Hgshift, (Z.mul_comm g1), Z.eqb_refl. discriminate. } clear Hstepng Hstepnf. assert (Heta := divstep.etaBounds 683 n1 st H). forward_verify_check. 1:{ forward_if (temp _t'2 (Vint Int.one)); [| |forward_if; try discriminate; forward; entailer!]; forward; entailer!; revert H0; convert_C_to_math; try lia. cbn; convert_C_to_math. elim Z.ltb_spec0; try lia; reflexivity. } forward_if (EX n2 : nat, EX u:Z, EX v:Z, EX f2:Z, EX g2:Z, EX w: int, PROP ( 1 <= Z.of_nat n2 <= 62 - Z.of_nat n1; Z.of_nat n2 <= 32 ; divstep.Trans.u (divstep.Trans.transN (n1 + n2) st) = (u * 2^(Z.of_nat n2))%Z ; divstep.Trans.v (divstep.Trans.transN (n1 + n2) st) = (v * 2^(Z.of_nat n2))%Z ; eqm (2^(64 - Z.of_nat (n1 + n2))) f2 (divstep.f (fst (divstep.stepN (n1 + n2) st))) ; eqm (2^(64 - Z.of_nat (n1 + n2))) g2 (divstep.g (fst (divstep.stepN (n1 + n2) st))) ) LOCAL (temp _i (Vint (Int.repr (62 - Z.of_nat n1))); temp _g (Vlong (Int64.repr (g2 * 2^(Z.of_nat n2) - f2 * Int.unsigned w))); temp _f (Vlong (Int64.repr f2)); temp _r (Vlong (Int64.repr (divstep.Trans.r (divstep.Trans.transN (n1 + n2) st) - v * Int.unsigned w))); temp _q (Vlong (Int64.repr (divstep.Trans.q (divstep.Trans.transN (n1 + n2) st) - u * Int.unsigned w))); temp _v (Vlong (Int64.repr v)); temp _u (Vlong (Int64.repr u)); temp _m (Vlong (Int64.repr (Z.ones (Z.of_nat n2)))); temp _w (Vint w); gvars gv; temp _eta (Vlong (Int64.repr (divstep.eta (fst (divstep.stepN (n1 + n2) st)) + Z.of_nat n2))); temp _f0 (Vlong (Int64.repr (divstep.f st))); temp _g0 (Vlong (Int64.repr (divstep.g st))); temp _t t) SEP (data_at_ sh t_secp256k1_modinv64_trans2x2 t; debruijn64_array sh_debruijn gv) )%assert. 1:{ do 10 progressC. forward_if (temp _t'3 (Vint (Int.repr (Z.min (62 - Z.of_nat n1) ((-divstep.eta (fst (divstep.stepN n1 st))) + 1))))); try (progressC; revert H1; rewrite <- add_repr); try rewrite Int_repr_Int64_Z_mod_modulus; try entailer; try rewrite add_repr; convert_C_to_math; try lia; try (intros H1;first [rewrite Z.min_l by lia|rewrite Z.min_r by lia];reflexivity). progressC. forward_verify_check. 1:{ forward_if (temp _t'4 (Vint Int.one)); try lia. 1:{ progressC. destruct (zlt _ _); try lia. reflexivity. } forward_if; try discriminate. forward; entailer!. } replace ((Z.of_nat j + Z.of_nat (Z.to_nat k) + (64 - (Z.of_nat j + Z.of_nat (Z.to_nat k))))) with 64 by ring. progressC. change 63 with (Z.ones 6). rewrite <- Z.land_ones, Z.land_m1_l, Z_shiftr_ones, subsub1, Z_land_ones_min by lia. set (n2 := (Z.min _ 6)). pose (w := (modInv (-g1) (2^n2) * (-f)) mod (2^n2)). progressC. Exists (Z.to_nat n2) (divstep.Trans.q (divstep.Trans.transN n1 st)) (divstep.Trans.r (divstep.Trans.transN n1 st)) g1 ((-f + g1 * w) / 2^n2) (Int.repr w). entailer!. rewrite Nat.add_comm. rewrite <- divstep.Trans.transN_stepN. assert (Hgn1 : Zodd (divstep.g (fst (divstep.stepN n1 st)))). 1:{ rewrite <- Zodd_bool_iff, <- Z.bit0_odd in *|-*. change (Z.testbit (divstep.g (fst (divstep.stepN n1 st))) 0) with (true && (Z.testbit (divstep.g (fst (divstep.stepN n1 st))) 0))%bool. rewrite <- (Z.ones_spec_low (64 - Z.of_nat n1) 0) at 1 by lia. rewrite <- Z.land_spec, Z.land_comm, Z.land_ones, <- Hg1, <- Z.land_ones, Z.land_comm, Z.land_spec, Z.ones_spec_low by lia. assumption. } rewrite divstep.Trans.transDs; try solve [assumption|unfold divstep.eta in H0; unfold n2, divstep.eta; lia]. split;[cbn; ring|]. split;[cbn; ring|]. rewrite Nat2Z.inj_add, Z2Nat.id, divstep.stepN_app_fst by lia. injection (divstep.Trans.transN_step (Z.to_nat n2) (fst (divstep.stepN n1 st))); intros Hg2 Hf2. rewrite divstep.Trans.transDs in Hf2, Hg2; try solve [assumption|unfold divstep.eta in H0; unfold n2, divstep.eta; lia]. cbn in Hf2, Hg2. ring_simplify in Hf2; ring_simplify in Hg2. assert (Hw : 0 <= w < 2^6). 1:{ assert (0 < 2^n2 <= 2^6) by (split;[|apply Z.pow_le_mono_r];lia). pose (Z.mod_pos_bound (modInv (-g1) (2 ^ n2) * (-f)) (2 ^ n2)). lia. } convert_C_to_math. assert (Hg1fw : (2^n2 | (-f) + g1 * w)). 1: { apply Zmod_divide;[lia|]. unfold w. rewrite <- Zplus_mod_idemp_r, Zmult_mod_idemp_r, Zplus_mod_idemp_r, Z.mul_assoc, <- Z.sub_opp_r, !Zopp_mult_distr_l, <- Zminus_mod_idemp_r, <- Zmult_mod_idemp_l, modInv_mul_r, Z.gcd_opp_l. rewrite Hgcd by assumption || lia. rewrite Zmult_mod_idemp_l, Zminus_mod_idemp_r, Z.mul_1_l, Z.sub_diag, Zmod_0_l; lia. } assert (Hw0 : w = (modInv (-divstep.g (fst (divstep.stepN n1 st))) (2 ^ n2) * (-divstep.f (fst (divstep.stepN n1 st)))) mod 2 ^ n2). 1:{ assert (Hn2 : (2^n2 | 2^((64 - Z.of_nat n1)))) by (exists (2^((64 - Z.of_nat n1) - n2)); rewrite <- Z.pow_add_r by lia; f_equal; ring). apply Zmult_eqm;[|eapply eqm_2_pow_le;[|apply Zopp_eqm;apply Hf1];lia]. unfold eqm; f_equal. apply modInv_eqm. apply Zopp_eqm. eapply eqm_2_pow_le;[|apply Hg1]. lia. } apply Z.mul_cancel_l in Hf2;[|lia]. repeat split. * rewrite Hf2. apply (eqm_2_pow_le _ (64 - Z.of_nat n1));[lia|assumption]. * rewrite Z2Nat.id in Hg2 by lia. unfold eqm. rewrite <- Zaux.Zdiv_mod_mult by lia. symmetry. apply Z.div_unique_exact;[lia|]. rewrite <- Zmult_mod_distr_l, <- Z.pow_add_r, Hg2 by lia. replace (n2 + (64 - (n2 + Z.of_nat n1))) with (64 - (Z.of_nat n1)) by ring. apply Zplus_eqm;[apply Zopp_eqm; assumption|]. rewrite (Z.mul_comm _ (divstep.g (fst (divstep.stepN n1 st)))). apply Zmult_eqm; try assumption. unfold eqm; f_equal. assumption. * repeat f_equal. rewrite Z.mul_comm, <-Z_div_exact_full_2 by (try lia; apply Zdivide_mod; assumption). ring. * repeat f_equal. apply Z.sub_move_r. rewrite <- Hw0 by lia. cbn; ring. * repeat f_equal. apply Z.sub_move_r. rewrite <- Hw0 by lia. cbn; ring. * repeat f_equal. rewrite Z.land_ones by lia. assert (Hn264 : 2^n2 < 2^64) by (apply Z.pow_lt_mono_r; lia). change Int64.modulus with (2^64). assert (Hmod := Z.mod_pos_bound (g1 * -f * (g1 * g1 - 2)) (2^n2)). rewrite Z.mod_small by lia. unfold w. replace (g1 * -f * (g1 * g1 - 2)) with (g1 * (g1 * g1 - 2) * -f) by ring. do 2 (rewrite <- Zmult_mod_idemp_l; symmetry). do 2 f_equal. symmetry. rewrite <- Z.land_ones by lia. replace n2 with (Z.min 6 n2) at 1 by lia. rewrite <- Z_land_ones_min, Z.land_assoc by lia. rewrite HackersDelightB by (apply Zodd_equiv; assumption). rewrite Z.land_ones by lia. rewrite <- (Z.mul_1_l (modInv _ _)), <- Zmult_mod_idemp_l. rewrite <- (Hgcd g1 n2) at 1 by assumption || lia. rewrite <- Z.gcd_opp_l, <- Zmult_mod_idemp_r, <- modInv_mul_l, Zmult_mod_idemp_r, Zmult_mod_idemp_l, <- Z.mul_assoc. rewrite <- Z.land_ones by lia. replace n2 with (Z.min 6 n2) at 2 by lia. rewrite <- Z_land_ones_min, Z.land_assoc by lia. rewrite !Z.land_ones by lia. rewrite <- Zmult_mod_idemp_r, modInv_mul_r, Z.gcd_opp_l, Hgcd, Zmult_mod_idemp_r, Z.mul_1_r by assumption || lia. rewrite <- Zmod_div_mod; try lia. exists (2^(6 - n2)); rewrite <-Z.pow_add_r; try lia; f_equal; ring. * repeat f_equal. rewrite divstep.etaDs by assumption || lia. lia. } 1:{ forward_if (temp _t'5 (Vint (Int.repr (Z.min (62 - Z.of_nat n1) ((divstep.eta (fst (divstep.stepN n1 st))) + 1))))); try (progressC; revert H1; rewrite <- add_repr); try rewrite Int_repr_Int64_Z_mod_modulus; try entailer; try rewrite add_repr; convert_C_to_math; try lia; try (intros H1;first [rewrite Z.min_l by lia|rewrite Z.min_r by lia];reflexivity). progressC. forward_verify_check. 1:{ forward_if (temp _t'6 (Vint Int.one)); try lia. 1:{ progressC. destruct (zlt _ _); try lia. reflexivity. } forward_if; try discriminate. forward; entailer!. } replace ((Z.of_nat j + Z.of_nat (Z.to_nat k) + (64 - (Z.of_nat j + Z.of_nat (Z.to_nat k))))) with 64 by ring. progressC. change 15 with (Z.ones 4). rewrite <- Z.land_ones, Z.land_m1_l, Z_shiftr_ones, subsub1, Z_land_ones_min by lia. set (n2 := (Z.min _ 4)). pose (w := (modInv (-f) (2^n2) * g1) mod (2^n2)). do 2 progressC. Exists (Z.to_nat n2) (divstep.Trans.u (divstep.Trans.transN n1 st)) (divstep.Trans.v (divstep.Trans.transN n1 st)) f ((g1 + f * w) / 2^n2) (Int.repr w). entailer!. rewrite Nat.add_comm. rewrite <- divstep.Trans.transN_stepN. rewrite divstep.Trans.transSs; try solve [unfold divstep.eta in H0; unfold n2, divstep.eta; lia]. split;[cbn; ring|]. split;[cbn; ring|]. rewrite Nat2Z.inj_add, Z2Nat.id, divstep.stepN_app_fst by lia. injection (divstep.Trans.transN_step (Z.to_nat n2) (fst (divstep.stepN n1 st))); intros Hg2 Hf2. rewrite divstep.Trans.transSs in Hf2, Hg2; try solve [unfold divstep.eta in H0; unfold n2, divstep.eta; lia]. cbn in Hf2, Hg2. ring_simplify in Hf2; ring_simplify in Hg2. assert (Hw : 0 <= w < 2^4). 1:{ assert (0 < 2^n2 <= 2^4) by (split;[|apply Z.pow_le_mono_r];lia). pose (Z.mod_pos_bound (modInv (-f) (2 ^ n2) * g1) (2 ^ n2)). lia. } convert_C_to_math. assert (Hg1fw : (2^n2 | g1 + f * w)). 1: { apply Zmod_divide;[lia|]. unfold w. rewrite <- Zplus_mod_idemp_r, Zmult_mod_idemp_r, Zplus_mod_idemp_r, Z.mul_assoc, <- Z.sub_opp_r, !Zopp_mult_distr_l, <- Zminus_mod_idemp_r, <- Zmult_mod_idemp_l, modInv_mul_r, Z.gcd_opp_l. rewrite Hgcd by assumption || lia. rewrite Zmult_mod_idemp_l, Zminus_mod_idemp_r, Z.mul_1_l, Z.sub_diag, Zmod_0_l; lia. } assert (Hw0 : w = (modInv (-divstep.f (fst (divstep.stepN n1 st))) (2 ^ n2) * divstep.g (fst (divstep.stepN n1 st))) mod 2 ^ n2). 1:{ assert (Hn2 : (2^n2 | 2^((64 - Z.of_nat n1)))) by (exists (2^((64 - Z.of_nat n1) - n2)); rewrite <- Z.pow_add_r by lia; f_equal; ring). apply Zmult_eqm;[|eapply eqm_2_pow_le;[|apply Hg1];lia]. unfold eqm; f_equal. apply modInv_eqm. apply Zopp_eqm. eapply eqm_2_pow_le;[|apply Hf1]. lia. } apply Z.mul_cancel_l in Hf2;[|lia]. repeat split. * rewrite Hf2. apply (eqm_2_pow_le _ (64 - Z.of_nat n1));[lia|assumption]. * rewrite Z2Nat.id in Hg2 by lia. unfold eqm. rewrite <- Zaux.Zdiv_mod_mult by lia. symmetry. apply Z.div_unique_exact;[lia|]. rewrite <- Zmult_mod_distr_l, <- Z.pow_add_r, Hg2 by lia. replace (n2 + (64 - (n2 + Z.of_nat n1))) with (64 - (Z.of_nat n1)) by ring. rewrite (Z.add_comm _ (divstep.g (fst (divstep.stepN n1 st)))). apply Zplus_eqm; try assumption. rewrite (Z.mul_comm _ (divstep.f (fst (divstep.stepN n1 st)))). apply Zmult_eqm; try assumption. unfold eqm; f_equal. assumption. * repeat f_equal. rewrite Z.mul_comm, <-Z_div_exact_full_2 by (try lia; apply Zdivide_mod; assumption). ring. * repeat f_equal. apply Z.sub_move_r. rewrite <- Hw0 by lia. cbn; ring. * repeat f_equal. apply Z.sub_move_r. rewrite <- Hw0 by lia. cbn; ring. * repeat f_equal. rewrite Z.land_ones by lia. assert (Hn264 : 2^n2 < 2^64) by (apply Z.pow_lt_mono_r; lia). change Int64.modulus with (2^64). assert (Hmod := Z.mod_pos_bound (-((f + Z.land (f + 1) 4 * 2 ^ 1) mod 2 ^ 64) mod 2 ^ 32 * g1) (2^n2)). rewrite Z.mod_small by lia. unfold w. do 2 (rewrite <- Zmult_mod_idemp_l; symmetry). do 2 f_equal. rewrite <- Zmod_div_mod; try lia. 2:exists (2^(32 - n2)); rewrite <-Z.pow_add_r; try lia; f_equal; ring. rewrite <- (Z.mul_1_l (_ mod (2^64))), <- Z.mul_opp_l, <- Zmult_mod_idemp_r. rewrite <- Zmod_div_mod, Zmult_mod_idemp_r; try lia. 2:exists (2^(64 - n2)); rewrite <-Z.pow_add_r; try lia; f_equal; ring. rewrite (Zmod_div_mod (2^n2) (2^4)); try lia. 2:exists (2^(4 - n2)); rewrite <-Z.pow_add_r; try lia; f_equal; ring. rewrite <- (Z.mul_1_r (modInv (-f) (2 ^ n2))). rewrite <- (Hgcd f 4) at 1 by assumption || lia. rewrite <- Z.gcd_opp_l, <- Zmult_mod_idemp_r, <- modInv_mul_r, Zmult_mod_idemp_r, Z.mul_assoc. rewrite <- Zmod_div_mod; try lia. 2:exists (2^(4 - n2)); rewrite <-Z.pow_add_r; try lia; f_equal; ring. rewrite <- Zmult_mod_idemp_l, modInv_mul_l, Z.gcd_opp_l, Hgcd, Zmult_mod_idemp_l, Z.mul_1_l by assumption || lia. rewrite <- HackersDelightA, Z.land_ones by (try lia; apply Zodd_equiv; assumption). rewrite <- Zmod_div_mod; try lia. 2:exists (2^(4 - n2)); rewrite <-Z.pow_add_r; try lia; f_equal; ring. rewrite Z.mul_opp_l, Z.mul_1_l. do 3 f_equal. rewrite Z.shiftl_mul_pow2; lia. * repeat f_equal. rewrite divstep.etaSs; lia. } Intros n2 u v f2 g2 w. rename H0 into Hn2; rename H1 into Hn232; rename H2 into Hu; rename H3 into Hv; rename H4 into Hf2; rename H5 into Hg2. do 3 progressC. ring_simplify (g2 * 2 ^ Z.of_nat n2 - f2 * Int.unsigned w + f2 * Int.unsigned w). ring_simplify ((divstep.Trans.q (divstep.Trans.transN (n1 + n2) st) - u * Int.unsigned w + u * Int.unsigned w)). ring_simplify ((divstep.Trans.r (divstep.Trans.transN (n1 + n2) st) - v * Int.unsigned w + v * Int.unsigned w)). forward_verify_check. match goal with | |- semax _ ?E _ _ => forward_if E end. 2:(forward;entailer!). 1:{ elimtype False. revert H0. convert_C_to_math. rewrite Z.land_ones, Z_mod_mult, Z.eqb_refl by lia. discriminate. } forward. Exists (n1 + n2)%nat n2 u v f2 g2. rewrite Nat2Z.inj_add in * |- *. replace (62 - (Z.of_nat n1 + Z.of_nat n2) + Z.of_nat n2) with (62 - Z.of_nat n1) by ring. entailer!. * do 4 progressC. forward_verify_check. 1:{ forward_call (divstep.Trans.transN 62 st, t, sh, 62, false); [apply (divstep.Trans.bounded_transN 62)|]. rewrite divstep.Trans.det_transN, Z.eqb_refl. simpl (Z.b2z true). forward_if;[discriminate|forward;entailer!]. } forward. Qed. Lemma body_modinv64_update_de_62: semax_body Vprog Gprog f_secp256k1_modinv64_update_de_62 secp256k1_modinv64_update_de_62_spec. Proof. start_function. assert (Hoddm : forall n, 0 <= n -> Z.gcd m (2^n) = 1). 1:{ intros n Hn. apply Zgcd_1_rel_prime. apply Zpow_facts.rel_prime_Zpower_r;[assumption|]. apply rel_prime_sym. apply prime_rel_prime;[apply prime_2|]. intros [m0 Hm0]. revert H; apply Z.Even_Odd_False. rewrite Hm0, Z.mul_comm. apply Zeven_equiv. apply Zeven_2p. } unfold Trans_repr, Signed62.reprn. fastforward 16. change (Int64.shru (Int64.repr (-1)) (Int64.repr 2)) with (Int64.repr (Z.ones 62)). unfold Znth; simpl (Vlong _). unfold make_modinfo. forward_verify_check. 1:{ unfold_data_at (data_at _ _ _ ptrm). assert_PROP (field_compatible t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm);[entailer!|]. forward_call (d, 5%nat, m, -2, ptrd, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm, shd, shm); [rewrite field_address_offset by assumption;entailer!|]. rewrite Zaux.Zcompare_Gt by lia. forward_if;[discriminate|forward]. unfold_data_at (data_at _ _ _ ptrm). entailer!!. } forward_verify_check. 1:{ unfold_data_at (data_at _ _ _ ptrm). assert_PROP (field_compatible t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm);[entailer!|]. forward_call (d, 5%nat, m, 1, ptrd, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm, shd, shm); [rewrite field_address_offset by assumption;entailer!|]. rewrite Zaux.Zcompare_Lt by lia. forward_if;[discriminate|forward]. unfold_data_at (data_at _ _ _ ptrm). entailer!!. } forward_verify_check. 1:{ unfold_data_at (data_at _ _ _ ptrm). assert_PROP (field_compatible t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm);[entailer!|]. forward_call (e, 5%nat, m, -2, ptre, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm, she, shm); [rewrite field_address_offset by assumption;entailer!|]. rewrite Zaux.Zcompare_Gt by lia. forward_if;[discriminate|forward]. unfold_data_at (data_at _ _ _ ptrm). entailer!!. } forward_verify_check. 1:{ unfold_data_at (data_at _ _ _ ptrm). assert_PROP (field_compatible t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm);[entailer!|]. forward_call (e, 5%nat, m, 1, ptre, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) ptrm, she, shm); [rewrite field_address_offset by assumption;entailer!|]. rewrite Zaux.Zcompare_Lt by lia. forward_if;[discriminate|forward]. unfold_data_at (data_at _ _ _ ptrm). entailer!!. } destruct H3 as [[Huv _] [Hqr _]]. forward_verify_check. 1:{ do 2 forward_call. forward_if;[convert_C_to_math;entailer!!| |forward;entailer!!]. revert H3. convert_C_to_math. replace (_ Z.shiftr x 311 = if x -2^62 <= y <= 2^62 -> -2 ^ 126 <= Z.shiftr x 62 + y * (z mod 2 ^ 62) <= 2 ^ 126 - 1). 1:{ intros x y z Hx Hy. clear -Hx Hy. apply (shiftr_bounds (-2^65) _ (2^65) 62) in Hx. assert (0 <= z mod 2^62 < 2^62) by (apply Z.mod_pos_bound; lia). nia. } assert (HboundB : forall x y0 z0 y1 z1, -2^127 <= x < 2^127 -> -2^62 <= y0 <= 2^62 -> -2^62 <= y1 <= 2^62 -> -2 ^ 126 <= Z.shiftr x 62 + y0 * (z0 mod 2 ^ 62) + y1 * (z1 mod 2 ^ 62) <= 2 ^ 126 - 1). 1:{ intros x y0 z0 y1 z1 Hx Hy0 Hy1. clear -Hx Hy0 Hy1. apply (shiftr_bounds (-2^65) _ (2^65) 62) in Hx. assert (0 <= z0 mod 2^62 < 2^62) by (apply Z.mod_pos_bound; lia). assert (0 <= z1 mod 2^62 < 2^62) by (apply Z.mod_pos_bound; lia). nia. } assert (Hcd1' : -2 ^ 126 <= Z.shiftr cd0' 62 + divstep.Trans.u mtx * (Z.shiftr d 62 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundA;lia). assert (Hcd1'' : -2 ^ 126 <= Z.shiftr cd0' 62 + divstep.Trans.u mtx * (Z.shiftr d 62 mod 2 ^ 62) + divstep.Trans.v mtx * (Z.shiftr e 62 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundB;lia). assert (Hce1' : -2 ^ 126 <= Z.shiftr ce0' 62 + divstep.Trans.q mtx * (Z.shiftr d 62 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundA;lia). assert (Hce1'' : -2 ^ 126 <= Z.shiftr ce0' 62 + divstep.Trans.q mtx * (Z.shiftr d 62 mod 2 ^ 62) + divstep.Trans.r mtx * (Z.shiftr e 62 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundB;lia). do 4 (forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|]). forward;unfold Znth;simpl (temp _ _). set (dval := [Vlong _;Vlong _;Vlong _;Vlong _;Vlong _]). set (eval := [Vlong _;Vlong _;Vlong _;Vlong _;Vlong _]). set (tval := (Vlong _, (Vlong _, (Vlong _, Vlong _)))). set (mval := [Vlong _;Vlong _;Vlong _;Vlong _;Vlong _]). set (minvval := Vlong (Int64.repr (modInv m (2 ^ 62)))). set (m1 := Z.shiftr m 62 mod 2 ^ 62) in *. assert (Hm1 : 0 <= m1 < 2^62) by (apply Z.mod_pos_bound;lia). assert (Hm1md : -2 ^ 125 <= m1 * md <= 2^125) by (clear -Hm1 Hmd;nia). assert (Hm1me : -2 ^ 125 <= m1 * me <= 2^125) by (clear -Hm1 Hme;nia). pose (cd1 := Z.shiftr cd0' 62 + divstep.Trans.u mtx * (Z.shiftr d 62 mod 2 ^ 62) + divstep.Trans.v mtx * (Z.shiftr e 62 mod 2 ^ 62) + m1 * md). pose (ce1 := Z.shiftr ce0' 62 + divstep.Trans.q mtx * (Z.shiftr d 62 mod 2 ^ 62) + divstep.Trans.r mtx * (Z.shiftr e 62 mod 2 ^ 62) + m1 * me). assert (Hcd1 : -2 ^ 127 <= cd1 <= 2 ^ 127 - 1) by lia. assert (Hce1 : -2 ^ 127 <= ce1 <= 2 ^ 127 - 1) by lia. match goal with | |- semax _ (PROPx nil (LOCALx ?L _)) _ _ => forward_if (PROPx nil (LOCALx L (SEPx [ secp256k1_uint128_at Tsh ce1 v_ce; secp256k1_uint128_at Tsh cd1 v_cd; data_at shd t_secp256k1_modinv64_signed62 dval ptrd; data_at she t_secp256k1_modinv64_signed62 eval ptre; data_at sht t_secp256k1_modinv64_trans2x2 tval ptrt; data_at shm t_secp256k1_modinv64_modinfo (mval, minvval) ptrm]))) end. 2:{ forward. unfold cd1, ce1; replace m1 with 0; [rewrite !Z.mul_0_l, !Z.add_0_r;apply ENTAIL_refl|]. symmetry. revert H3. apply repr_inj_unsigned64;rep_lia. } 1:{ do 2( forward;change (Znth 1 mval) with (Vlong (Int64.repr m1)); forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|] ). fold cd1 ce1. clear -m;entailer!!. } do 2 (forward_call;progressC;forward_call). rewrite !Z.land_ones by lia. assert (Hcd2' : -2 ^ 126 <= Z.shiftr cd1 62 + divstep.Trans.u mtx * (Z.shiftr d 124 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundA;lia). assert (Hcd2'' : -2 ^ 126 <= Z.shiftr cd1 62 + divstep.Trans.u mtx * (Z.shiftr d 124 mod 2 ^ 62) + divstep.Trans.v mtx * (Z.shiftr e 124 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundB;lia). assert (Hce2' : -2 ^ 126 <= Z.shiftr ce1 62 + divstep.Trans.q mtx * (Z.shiftr d 124 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundA;lia). assert (Hce2'' : -2 ^ 126 <= Z.shiftr ce1 62 + divstep.Trans.q mtx * (Z.shiftr d 124 mod 2 ^ 62) + divstep.Trans.r mtx * (Z.shiftr e 124 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundB;lia). do 4 (forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|]). forward;unfold Znth;simpl (temp _ _). set (dval1 := (upd_Znth 0 dval (Vlong (Int64.repr (cd1 mod 2 ^ 62))))). set (eval1 := (upd_Znth 0 eval (Vlong (Int64.repr (ce1 mod 2 ^ 62))))). set (m2 := Z.shiftr m 124 mod 2 ^ 62) in *. assert (Hm2 : 0 <= m2 < 2^62) by (apply Z.mod_pos_bound;lia). assert (Hm2md : -2 ^ 125 <= m2 * md <= 2^125) by (clear -Hm2 Hmd;nia). assert (Hm2me : -2 ^ 125 <= m2 * me <= 2^125) by (clear -Hm2 Hme;nia). pose (cd2 := Z.shiftr cd1 62 + divstep.Trans.u mtx * (Z.shiftr d 124 mod 2 ^ 62) + divstep.Trans.v mtx * (Z.shiftr e 124 mod 2 ^ 62) + m2 * md). pose (ce2 := Z.shiftr ce1 62 + divstep.Trans.q mtx * (Z.shiftr d 124 mod 2 ^ 62) + divstep.Trans.r mtx * (Z.shiftr e 124 mod 2 ^ 62) + m2 * me). assert (Hcd2 : -2 ^ 127 <= cd2 <= 2 ^ 127 - 1) by lia. assert (Hce2 : -2 ^ 127 <= ce2 <= 2 ^ 127 - 1) by lia. match goal with | |- semax _ (PROPx nil (LOCALx ?L _)) _ _ => forward_if (PROPx nil (LOCALx L (SEPx [ secp256k1_uint128_at Tsh ce2 v_ce; secp256k1_uint128_at Tsh cd2 v_cd; data_at shd t_secp256k1_modinv64_signed62 dval1 ptrd; data_at she t_secp256k1_modinv64_signed62 eval1 ptre; data_at sht t_secp256k1_modinv64_trans2x2 tval ptrt; data_at shm t_secp256k1_modinv64_modinfo (mval, minvval) ptrm]))) end. 2:{ forward. unfold cd2, ce2; replace m2 with 0; [rewrite !Z.mul_0_l, !Z.add_0_r;apply ENTAIL_refl|]. symmetry. revert H3. apply repr_inj_unsigned64;rep_lia. } 1:{ do 2( forward;change (Znth 2 mval) with (Vlong (Int64.repr m2)); forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|] ). fold cd2 ce2. clear -m;entailer!!. } do 2 (forward_call;progressC;forward_call). rewrite !Z.land_ones by lia. assert (Hcd3' : -2 ^ 126 <= Z.shiftr cd2 62 + divstep.Trans.u mtx * (Z.shiftr d 186 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundA;lia). assert (Hcd3'' : -2 ^ 126 <= Z.shiftr cd2 62 + divstep.Trans.u mtx * (Z.shiftr d 186 mod 2 ^ 62) + divstep.Trans.v mtx * (Z.shiftr e 186 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundB;lia). assert (Hce3' : -2 ^ 126 <= Z.shiftr ce2 62 + divstep.Trans.q mtx * (Z.shiftr d 186 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundA;lia). assert (Hce3'' : -2 ^ 126 <= Z.shiftr ce2 62 + divstep.Trans.q mtx * (Z.shiftr d 186 mod 2 ^ 62) + divstep.Trans.r mtx * (Z.shiftr e 186 mod 2 ^ 62) <= 2 ^ 126 - 1) by (apply HboundB;lia). do 4 (forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|]). forward;unfold Znth;simpl (temp _ _). set (dval2 := (upd_Znth 1 dval1 (Vlong (Int64.repr (cd2 mod 2 ^ 62))))). set (eval2 := (upd_Znth 1 eval1 (Vlong (Int64.repr (ce2 mod 2 ^ 62))))). set (m3 := Z.shiftr m 186 mod 2 ^ 62) in *. assert (Hm3 : 0 <= m3 < 2^62) by (apply Z.mod_pos_bound;lia). assert (Hm3md : -2 ^ 125 <= m3 * md <= 2^125) by (clear -Hm3 Hmd;nia). assert (Hm3me : -2 ^ 125 <= m3 * me <= 2^125) by (clear -Hm3 Hme;nia). pose (cd3 := Z.shiftr cd2 62 + divstep.Trans.u mtx * (Z.shiftr d 186 mod 2 ^ 62) + divstep.Trans.v mtx * (Z.shiftr e 186 mod 2 ^ 62) + m3 * md). pose (ce3 := Z.shiftr ce2 62 + divstep.Trans.q mtx * (Z.shiftr d 186 mod 2 ^ 62) + divstep.Trans.r mtx * (Z.shiftr e 186 mod 2 ^ 62) + m3 * me). assert (Hcd3 : -2 ^ 127 <= cd3 <= 2 ^ 127 - 1) by lia. assert (Hce3 : -2 ^ 127 <= ce3 <= 2 ^ 127 - 1) by lia. match goal with | |- semax _ (PROPx nil (LOCALx ?L _)) _ _ => forward_if (PROPx nil (LOCALx L (SEPx [ secp256k1_uint128_at Tsh ce3 v_ce; secp256k1_uint128_at Tsh cd3 v_cd; data_at shd t_secp256k1_modinv64_signed62 dval2 ptrd; data_at she t_secp256k1_modinv64_signed62 eval2 ptre; data_at sht t_secp256k1_modinv64_trans2x2 tval ptrt; data_at shm t_secp256k1_modinv64_modinfo (mval, minvval) ptrm]))) end. 2:{ forward. unfold cd3, ce3; replace m3 with 0; [rewrite !Z.mul_0_l, !Z.add_0_r;apply ENTAIL_refl|]. symmetry. revert H3. apply repr_inj_unsigned64;rep_lia. } 1:{ do 2( forward;change (Znth 3 mval) with (Vlong (Int64.repr m3)); forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|] ). fold cd3 ce3. clear -m;entailer!!. } do 2 (forward_call;progressC;forward_call). rewrite !Z.land_ones by lia. assert (Hd248 : -2^61 <= Z.shiftr d 248 <= 2^61 - 1) by solve_bounds. assert (He248 : -2^61 <= Z.shiftr e 248 <= 2^61 - 1) by solve_bounds. assert (Hcd4' : -2 ^ 124 <= Z.shiftr cd3 62 + divstep.Trans.u mtx * Z.shiftr d 248 <= 2 ^ 124 - 1). 1:{ rewrite <- strict_bounds in Hcd3. apply (shiftr_bounds (-2^65) _ (2^65) 62) in Hcd3. clear -Hd248 Hcd3 Huv; nia. } assert (Hcd4'' : -2 ^ 124 <= Z.shiftr cd3 62 + divstep.Trans.u mtx * Z.shiftr d 248 + divstep.Trans.v mtx * Z.shiftr e 248 <= 2 ^ 124 - 1). 1:{ rewrite <- strict_bounds in Hcd3. apply (shiftr_bounds (-2^65) _ (2^65) 62) in Hcd3. clear -Hd248 He248 Hcd3 Huv; nia. } assert (Hce4' : -2 ^ 124 <= Z.shiftr ce3 62 + divstep.Trans.q mtx * Z.shiftr d 248 <= 2 ^ 124 - 1) . 1:{ rewrite <- strict_bounds in Hce3. apply (shiftr_bounds (-2^65) _ (2^65) 62) in Hce3. clear -Hd248 Hce3 Hqr; nia. } assert (Hce4'' : -2 ^ 124 <= Z.shiftr ce3 62 + divstep.Trans.q mtx * Z.shiftr d 248 + divstep.Trans.r mtx * Z.shiftr e 248 <= 2 ^ 124 - 1) . 1:{ rewrite <- strict_bounds in Hce3. apply (shiftr_bounds (-2^65) _ (2^65) 62) in Hce3. clear -Hd248 He248 Hce3 Hqr; nia. } do 4 (forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|]). set (dval3 := (upd_Znth 2 dval2 (Vlong (Int64.repr (cd3 mod 2 ^ 62))))). set (eval3 := (upd_Znth 2 eval2 (Vlong (Int64.repr (ce3 mod 2 ^ 62))))). set (m4 := Z.shiftr m 248) in *. assert (Hm4 : 0 <= m4 <= 2^61) by (unfold m4;solve_bounds). assert (Hm4md : -2 ^ 124 <= m4 * md <= 2^124) by (clear -Hm4 Hmd;nia). assert (Hm4me : -2 ^ 124 <= m4 * me <= 2^124) by (clear -Hm4 Hme;nia). pose (cd4 := Z.shiftr cd3 62 + divstep.Trans.u mtx * Z.shiftr d 248 + divstep.Trans.v mtx * Z.shiftr e 248 + m4 * md). pose (ce4 := Z.shiftr ce3 62 + divstep.Trans.q mtx * Z.shiftr d 248 + divstep.Trans.r mtx * Z.shiftr e 248 + m4 * me). assert (Hcd4 : -2 ^ 125 <= cd4 <= 2 ^ 125 - 1) by lia. assert (Hce4 : -2 ^ 125 <= ce4 <= 2 ^ 125 - 1) by lia. do 2( forward;change (Znth 4 mval) with (Vlong (Int64.repr m4)); forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|] ). fold cd4 ce4. do 2 (forward_call;progressC;forward_call;[change Int128_min_signed with (-2^127);change Int128_max_signed with (2^127-1);solve_bounds|]). rewrite !Z.land_ones by lia. do 2 (forward_call;[solve_bounds|forward]). set (dval4 := (upd_Znth 4 _ _)). set (eval4 := (upd_Znth 4 _ _)). assert (Hcarry : forall n a x y z, 0 <= n -> a = Z.shiftr (x * (d mod 2^(n+62)) + y * (e mod 2^(n+62)) + (m mod 2^(n+62)) * z) n -> Z.shiftr a 62 + x * (Z.shiftr d (n+62) mod 2 ^ 62) + y * (Z.shiftr e (n+62) mod 2 ^ 62) + (Z.shiftr m (n+62) mod 2 ^ 62) * z = Z.shiftr (x * (d mod 2^(n+124)) + y * (e mod 2^(n+124)) + (m mod 2^(n+124)) * z) (n+62)). 1:{ intros n a x y z Hn ->. rewrite !Z.shiftr_div_pow2 by lia. rewrite Z.div_div by lia. rewrite <-!Z.add_assoc, Z.add_comm, !Z.add_assoc, <- Z.div_add_l, <-!Z.pow_add_r by lia. replace ((x * ((d / 2 ^ (n + 62)) mod 2 ^ 62) + y * ((e / 2 ^ (n + 62)) mod 2 ^ 62) + (m / 2 ^ (n + 62)) mod 2 ^ 62 * z) * 2 ^ (n + 62) + (x * (d mod 2 ^ (n + 62)) + y * (e mod 2 ^ (n + 62)) + m mod 2 ^ (n + 62) * z)) with (x * (d mod 2 ^ (n + 62) + 2 ^ (n + 62) * ((d / 2 ^ (n + 62)) mod 2 ^ 62)) + y * (e mod 2 ^ (n + 62) + 2 ^ (n + 62) * ((e / 2 ^ (n + 62)) mod 2 ^ 62)) + (m mod 2 ^ (n + 62) + 2 ^ (n + 62) * ((m / 2 ^ (n + 62)) mod 2 ^ 62)) * z) by ring. rewrite <-!Z.rem_mul_r, <-!Z.pow_add_r, <-!Z.add_assoc by lia. reflexivity. } assert (Hcd124 : cd1 = Z.shiftr (divstep.Trans.u mtx * (d mod 2^124) + divstep.Trans.v mtx * (e mod 2^124) + (m mod 2^124) * md) 62) by (apply (Hcarry 0);[lia|reflexivity]). assert (Hce124 : ce1 = Z.shiftr (divstep.Trans.q mtx * (d mod 2^124) + divstep.Trans.r mtx * (e mod 2^124) + (m mod 2^124) * me) 62) by (apply (Hcarry 0);[lia|reflexivity]). assert (Hcd186 : cd2 = Z.shiftr (divstep.Trans.u mtx * (d mod 2^186) + divstep.Trans.v mtx * (e mod 2^186) + (m mod 2^186) * md) 124) by (apply (Hcarry 62);[lia|assumption]). assert (Hce186 : ce2 = Z.shiftr (divstep.Trans.q mtx * (d mod 2^186) + divstep.Trans.r mtx * (e mod 2^186) + (m mod 2^186) * me) 124) by (apply (Hcarry 62);[lia|assumption]). assert (Hcd248 : cd3 = Z.shiftr (divstep.Trans.u mtx * (d mod 2^248) + divstep.Trans.v mtx * (e mod 2^248) + (m mod 2^248) * md) 186) by (apply (Hcarry 124);[lia|assumption]). assert (Hce248 : ce3 = Z.shiftr (divstep.Trans.q mtx * (d mod 2^248) + divstep.Trans.r mtx * (e mod 2^248) + (m mod 2^248) * me) 186) by (apply (Hcarry 124);[lia|assumption]). assert (Hcd310 : cd4 = Z.shiftr (divstep.Trans.u mtx * d + divstep.Trans.v mtx * e + m * md) 248). 1:{ unfold cd4, m4. symmetry. rewrite (Z_div_mod_eq_full d (2^248)) at 1. rewrite (Z_div_mod_eq_full e (2^248)) at 1. rewrite (Z_div_mod_eq_full m (2^248)) at 1. replace (divstep.Trans.u mtx * (2 ^ 248 * (d / 2 ^ 248) + d mod 2 ^ 248) + divstep.Trans.v mtx * (2 ^ 248 * (e / 2 ^ 248) + e mod 2 ^ 248) + (2 ^ 248 * (m / 2 ^ 248) + m mod 2 ^ 248) * md) with ((divstep.Trans.u mtx * (d / 2 ^ 248) + divstep.Trans.v mtx * (e / 2 ^ 248) + (m / 2 ^ 248) * md) * 2^248 + (divstep.Trans.u mtx * (d mod 2 ^ 248) + divstep.Trans.v mtx * (e mod 2 ^ 248) + (m mod 2 ^ 248) * md)) by ring. rewrite Hcd248, Z.shiftr_shiftr, !Z.shiftr_div_pow2, Z.div_add_l by lia. change (186 + 62) with 248. ring. } assert (Hce310 : ce4 = Z.shiftr (divstep.Trans.q mtx * d + divstep.Trans.r mtx * e + m * me) 248). 1:{ unfold ce4, m4. symmetry. rewrite (Z_div_mod_eq_full d (2^248)) at 1. rewrite (Z_div_mod_eq_full e (2^248)) at 1. rewrite (Z_div_mod_eq_full m (2^248)) at 1. replace (divstep.Trans.q mtx * (2 ^ 248 * (d / 2 ^ 248) + d mod 2 ^ 248) + divstep.Trans.r mtx * (2 ^ 248 * (e / 2 ^ 248) + e mod 2 ^ 248) + (2 ^ 248 * (m / 2 ^ 248) + m mod 2 ^ 248) * me) with ((divstep.Trans.q mtx * (d / 2 ^ 248) + divstep.Trans.r mtx * (e / 2 ^ 248) + (m / 2 ^ 248) * me) * 2^248 + (divstep.Trans.q mtx * (d mod 2 ^ 248) + divstep.Trans.r mtx * (e mod 2 ^ 248) + (m mod 2 ^ 248) * me)) by ring. rewrite Hce248, Z.shiftr_shiftr, !Z.shiftr_div_pow2, Z.div_add_l by lia. change (186 + 62) with 248. ring. } set (cd := divstep.Trans.u mtx * d + divstep.Trans.v mtx * e + m * md) in *. set (ce := divstep.Trans.q mtx * d + divstep.Trans.r mtx * e + m * me) in *. replace dval4 with (map Vlong (Signed62.reprn 5 (Z.shiftr cd 62))). 2:{ cbn. rewrite !Z.shiftr_shiftr by lia. change dval4 with [ (Vlong (Int64.repr (cd1 mod 2 ^ 62))) ; (Vlong (Int64.repr (cd2 mod 2 ^ 62))) ; (Vlong (Int64.repr (cd3 mod 2 ^ 62))) ; (Vlong (Int64.repr (cd4 mod 2 ^ 62))) ; (Vlong (Int64.repr (Z.shiftr cd4 62))) ]. cbn. rewrite <-!Z.land_ones by lia. rewrite Hcd124, Hcd186, Hcd248, Hcd310. rewrite <-(Z.shiftr_land _ (Z.ones 124) 62). rewrite <-(Z.shiftr_land _ (Z.ones 186) 124). rewrite <-(Z.shiftr_land _ (Z.ones 248) 186). rewrite <-(Z.shiftr_land _ (Z.ones 310) 248). symmetry. rewrite <-(Z.shiftr_land _ (Z.ones 124) 62). rewrite <-(Z.shiftr_land _ (Z.ones 186) 124). rewrite <-(Z.shiftr_land _ (Z.ones 248) 186). rewrite !Z.land_ones by lia. repeat (apply eqm_refl || apply Zmod_eqm || apply Zplus_eqm || apply Zmult_eqm || f_equal). } replace eval4 with (map Vlong (Signed62.reprn 5 (Z.shiftr ce 62))). 2:{ cbn. rewrite !Z.shiftr_shiftr by lia. change eval4 with [ (Vlong (Int64.repr (ce1 mod 2 ^ 62))) ; (Vlong (Int64.repr (ce2 mod 2 ^ 62))) ; (Vlong (Int64.repr (ce3 mod 2 ^ 62))) ; (Vlong (Int64.repr (ce4 mod 2 ^ 62))) ; (Vlong (Int64.repr (Z.shiftr ce4 62))) ]. cbn. rewrite <-!Z.land_ones by lia. rewrite Hce124, Hce186, Hce248, Hce310. rewrite <-(Z.shiftr_land _ (Z.ones 124) 62). rewrite <-(Z.shiftr_land _ (Z.ones 186) 124). rewrite <-(Z.shiftr_land _ (Z.ones 248) 186). rewrite <-(Z.shiftr_land _ (Z.ones 310) 248). symmetry. rewrite <-(Z.shiftr_land _ (Z.ones 124) 62). rewrite <-(Z.shiftr_land _ (Z.ones 186) 124). rewrite <-(Z.shiftr_land _ (Z.ones 248) 186). rewrite !Z.land_ones by lia. repeat (apply eqm_refl || apply Zmod_eqm || apply Zplus_eqm || apply Zmult_eqm || f_equal). } assert (Hcd' : cd = (divstep.Trans.u mtx * (d + if d forward_if E;[discriminate|forward;entailer!!|] end. forward. unfold_data_at (data_at _ _ _ ptrm). entailer!!. unfold secp256k1_uint128_at, t_secp256k1_uint128. set (X := (_,_)). set (Y := (_,_)). clearbody X Y. clear -X Y. apply sepcon_derives;apply data_at_data_at_. Qed. Lemma body_modinv64_update_fg_62_var: semax_body Vprog Gprog f_secp256k1_modinv64_update_fg_62_var secp256k1_modinv64_update_fg_62_var_spec. Proof. start_function. set (f := divstep.f st). set (g := divstep.g st). unfold Trans_repr. do 5 forward. forward_verify_check. 1:{ revert H2. convert_C_to_math. elim Z.ltb_spec; try discriminate. lia. } assert (HZnth : forall a i, 0 <= i < Z.of_nat len -> Znth i (Signed62.reprn len a) = Int64.repr (Z.shiftr (if Z.of_nat len =? i + 1 then a else a mod 2^(62 * (i + 1))) (62 * i))). 1:{ intros a i Hi. rewrite f_if, (f_if (fun f => f (62 * i))). rewrite Z.mul_add_distr_l, (Z.add_comm (62 * i)), <- Z_shiftr_mod_2 by lia. assert (Ha := Signed62.reprn_Zlength len a). elim (Z.eqb_spec); intros Hlen. * replace i with (Z.of_nat len - 1)%Z by lia. rewrite <- Ha at 1. rewrite Znth_last, Signed62.reprn_last by lia. reflexivity. * rewrite Signed62.reprn_Znth by lia. reflexivity. } assert (HZnth0 : forall a, @Znth _ Vundef 0 (Signed62.pad (Signed62.reprn len a)) = Vlong (Int64.repr (if Z.of_nat len =? 1 then a else a mod 2^62))). 1:{ intros a. specialize (HZnth a 0). rewrite Z.shiftr_0_r in HZnth. assert (Ha := Signed62.reprn_Zlength len a). rewrite Signed62.pad_nth by lia. destruct len;[lia|]. destruct len. * rewrite HZnth by lia. reflexivity. * replace (Z.of_nat (S (S len)) =? 0 + 1) with false in HZnth by (symmetry;apply Z.eqb_neq; lia). rewrite HZnth by lia. rewrite <- zeq_eqb. destruct zeq;try reflexivity. lia. } forward;[rewrite HZnth0;entailer!!|]. forward;[rewrite (HZnth0 g);entailer!!|]. fold t_secp256k1_uint128. rewrite (HZnth0 f), (HZnth0 g). clear HZnth0. pose (fi := fun i => if Z.of_nat len =? i then f else f mod 2^(62*i)). pose (gi := fun i => if Z.of_nat len =? i then g else g mod 2^(62*i)). change (if Z.of_nat len =? 1 then f else _) with (fi 1). change (if Z.of_nat len =? 1 then g else _) with (gi 1). assert (Hfij : forall i j, j <= Z.of_nat len -> 0 <= i < j -> (fi j) mod 2^(62 * i) = fi i). 1:{ intros i j Hj Hij. unfold fi. replace (Z.of_nat len =? i) with false by lia. destruct (Z.of_nat len =? j); try reflexivity. rewrite <- !Z.land_ones, <- Z.land_assoc, Z_land_ones_min, Z.min_r by lia. reflexivity. } assert (Hgij : forall i j, j <= Z.of_nat len -> 0 <= i < j -> (gi j) mod 2^(62 * i) = gi i). 1:{ intros i j Hj Hij. unfold gi. replace (Z.of_nat len =? i) with false by lia. destruct (Z.of_nat len =? j); try reflexivity. rewrite <- !Z.land_ones, <- Z.land_assoc, Z_land_ones_min, Z.min_r by lia. reflexivity. } assert (Hfi : forall i, 0 <= i -> -2 ^ (62*i + 1) <= fi i <= 2 ^ (62*i + 1) - 1). 1:{ intros i Hi. unfold fi. elim Z.eqb_spec;[intros <-; lia|intros _]. cut (0 <= f mod 2 ^ (62 * i) <= 2 ^ (62 * i) - 1); [rewrite Z.pow_add_r;lia|solve_bounds]. } assert (Hgi : forall i, 0 <= i -> -2 ^ (62*i + 1) <= gi i <= 2 ^ (62*i + 1) - 1). 1:{ intros i Hi. unfold gi. elim Z.eqb_spec;[intros <-; lia|intros _]. cut (0 <= g mod 2 ^ (62 * i) <= 2 ^ (62 * i) - 1); [rewrite Z.pow_add_r;lia|solve_bounds]. } assert (Hf1 := Hfi 1). assert (Hg1 := Hgi 1). destruct (divstep.Trans.bounded_transN 62 st) as [[Huv Huv'] [Hqr Hqr']]. set (u := divstep.Trans.u (divstep.Trans.transN 62 st)) in *. set (v := divstep.Trans.v (divstep.Trans.transN 62 st)) in *. set (q := divstep.Trans.q (divstep.Trans.transN 62 st)) in *. set (r := divstep.Trans.r (divstep.Trans.transN 62 st)) in *. set (T := (Vlong (Int64.repr u),(Vlong (Int64.repr v), (Vlong (Int64.repr q), Vlong (Int64.repr r))))). assert (H6262i : forall a b x y, -2 ^ a <= x <= 2 ^ a -> -2 ^ b <= y <= 2 ^ b -> -(2 ^ a * 2 ^ b) <= x * y <= 2 ^ a * 2 ^ b). 1:{ intros a b x y Hx Hy. rewrite <- Z.abs_le in *. rewrite Z.abs_mul. etransitivity;[apply Z.mul_le_mono_nonneg_l;[|apply Hy]|apply Z.mul_le_mono_nonneg_r];lia. } assert (Hufi : forall i, 0 <= i -> -(2 ^ 62 * 2^(62 * i + 1)) <= u * fi i <= 2 ^ 62 * 2^(62 * i + 1)) by (intros;specialize (Hfi i);apply H6262i;lia). assert (Hvgi : forall i, 0 <= i -> -(2 ^ 62 * 2^(62 * i + 1)) <= v * gi i <= 2 ^ 62 * 2^(62 * i + 1)) by (intros;specialize (Hgi i);apply H6262i;lia). assert (Huf1 := Hufi 1). assert (Hvg1 := Hvgi 1). forward_call (v_cf, Tsh, u, fi 1). forward_call. 1: unfold Int128_min_signed, Int128_max_signed;lia. assert (Hqfi : forall i, 0 <= i -> -(2 ^ 62 * 2^(62 * i + 1)) <= q * fi i <= 2 ^ 62 * 2^(62 * i + 1)) by (intros;specialize (Hfi i);apply H6262i;lia). assert (Hrgi : forall i, 0 <= i -> -(2 ^ 62 * 2^(62 * i + 1)) <= r * gi i <= 2 ^ 62 * 2^(62 * i + 1)) by (intros;specialize (Hgi i);apply H6262i;lia). assert (Hqf1 := Hqfi 1). assert (Hrg1 := Hrgi 1). forward_call (v_cg, Tsh, q, fi 1). forward_call. 1: unfold Int128_min_signed, Int128_max_signed;lia. change (Int64.shru _ _) with (Int64.repr (Z.ones 62)). set (f1 := divstep.f (fst (divstep.stepN 62 st))). set (g1 := divstep.g (fst (divstep.stepN 62 st))). assert (Hfg := divstep.Trans.transN_step 62 st). injection Hfg as Htransf Htransg. change (2^62 * f1 = u*f + v*g) in Htransf. change (2^62 * g1 = q*f + r*g) in Htransg. assert (Hfi62 : forall i, 0 <= i -> fi i mod 2^(62*i) = f mod 2^(62*i)) by (intros; unfold fi; destruct Z.eqb; rewrite ?Zmod_mod; reflexivity). assert (Hgi62 : forall i, 0 <= i -> gi i mod 2^(62*i) = g mod 2^(62*i)) by (intros; unfold gi; destruct Z.eqb; rewrite ?Zmod_mod; reflexivity). forward_verify_check. 1:{ forward_call. forward_if;[|forward;entailer!!]. exfalso. revert H2. convert_C_to_math. change (_ + _) with (u*(fi 1) + v*(gi 1)). rewrite <-(Z.land_ones _ 64), <-Z.land_assoc by lia. change (Z.land (Z.ones _) _) with (Z.ones 62). rewrite Z.land_ones by lia. rewrite <- Zplus_mod_idemp_l, <- Zmult_mod_idemp_r, Hfi62, Zmult_mod_idemp_r, Zplus_mod_idemp_l by lia. rewrite <- Zplus_mod_idemp_r, <- Zmult_mod_idemp_r, Hgi62, Zmult_mod_idemp_r, Zplus_mod_idemp_r by lia. rewrite <- Htransf, Z.mul_comm, Z_mod_mult, Z.eqb_refl. discriminate. } forward_call. 1: unfold Int128_min_signed, Int128_max_signed;lia. forward_verify_check. 1:{ forward_call. forward_if;[|forward;entailer!!]. exfalso. revert H2. convert_C_to_math. change (_ + _) with (q*(fi 1) + r*(gi 1)). rewrite <-(Z.land_ones _ 64), <-Z.land_assoc by lia. change (Z.land (Z.ones _) _) with (Z.ones 62). rewrite Z.land_ones by lia. rewrite <- Zplus_mod_idemp_l, <- Zmult_mod_idemp_r, Hfi62, Zmult_mod_idemp_r, Zplus_mod_idemp_l by lia. rewrite <- Zplus_mod_idemp_r, <- Zmult_mod_idemp_r, Hgi62, Zmult_mod_idemp_r, Zplus_mod_idemp_r by lia. rewrite <- Htransg, Z.mul_comm, Z_mod_mult, Z.eqb_refl. discriminate. } forward_call. 1: unfold Int128_min_signed, Int128_max_signed;lia. assert (Hlength_firstn_skipn : forall n m x y, Zlength (firstn (Z.to_nat n) (Signed62.reprn m x) ++ skipn (Z.to_nat n) (Signed62.reprn m y)) = Z.of_nat m) by (intros; rewrite Zlength_app, Zlength_firstn, Zlength_skipn, !Signed62.reprn_Zlength; lia). forward_for_simple_bound (Z.of_nat len) (EX i:Z, PROP ( ) LOCAL (temp _r (Vlong (Int64.repr r)); temp _q (Vlong (Int64.repr q)); temp _v (Vlong (Int64.repr v)); temp _u (Vlong (Int64.repr u)); temp _M62 (Vlong (Int64.repr (Z.ones 62))); lvar _cg t_secp256k1_uint128 v_cg; lvar _cf t_secp256k1_uint128 v_cf; temp _len (Vint (Int.repr (Z.of_nat len))); temp _f ptrf; temp _g ptrg; temp _t ptrt) SEP (secp256k1_uint128_at Tsh (Z.shiftr (q * (fi i) + r * (gi i)) (62*i)) v_cg; secp256k1_uint128_at Tsh (Z.shiftr (u * (fi i) + v * (gi i)) (62*i)) v_cf; data_at shf t_secp256k1_modinv64_signed62 (Signed62.pad (firstn (Z.to_nat (i - 1)) (Signed62.reprn len ((u * f + v * g) / 2^62)) ++ skipn (Z.to_nat (i - 1)) (Signed62.reprn len f))) ptrf; data_at shg t_secp256k1_modinv64_signed62 (Signed62.pad (firstn (Z.to_nat (i - 1)) (Signed62.reprn len ((q * f + r * g) / 2^62)) ++ skipn (Z.to_nat (i - 1)) (Signed62.reprn len g))) ptrg; data_at sht t_secp256k1_modinv64_trans2x2 T ptrt))%assert. * entailer!!. * do 2 (forward;rewrite !Signed62.pad_nth by (rewrite Hlength_firstn_skipn;lia);try entailer). rewrite !Znth_app2;rewrite !Zlength_firstn; try lia. rewrite !Signed62.reprn_Zlength, !Znth_skipn by lia. replace (i - Z.min (Z.max 0 (i - 1)) (Z.of_nat len) + (i - 1)) with i by lia. rewrite !HZnth by lia. fold (fi (i + 1)) (gi (i + 1)). assert (Hi01 : 0 <= i + 1) by lia. assert (Hi0 : 0 <= i) by lia. specialize (Hfi _ Hi01); specialize (Hgi _ Hi01). rewrite !Z.mul_add_distr_l, !Z.pow_add_r in Hfi, Hgi by lia. assert (Hfi_boundA : -2^63 <= Z.shiftr (fi (i + 1)) (62 * i) <= 2^63) by solve_bounds. assert (Hfi_boundB : -(2^62 * 2^63) <= u * Z.shiftr (fi (i + 1)) (62 * i) <= 2^62 * 2^63) by (apply H6262i; lia). assert (Hgi_boundA : -2^63 <= Z.shiftr (gi (i + 1)) (62 * i) <= 2^63) by solve_bounds. assert (Hgi_boundB : -(2^62 * 2^63) <= v * Z.shiftr (gi (i + 1)) (62 * i) <= 2^62 * 2^63) by (apply H6262i; lia). specialize (Hufi _ Hi0); specialize (Hvgi _ Hi0); specialize (Hqfi _ Hi0); specialize (Hrgi _ Hi0). rewrite !Z.pow_add_r in Hufi, Hvgi, Hqfi, Hrgi by lia. assert (Hfgi_boundA : -2^64 <= Z.shiftr (u * fi i + v * gi i) (62 * i) <= 2^64) by solve_bounds. forward_call;[unfold Int128_min_signed, Int128_max_signed;split;solve_bounds|]. forward_call;[unfold Int128_min_signed, Int128_max_signed;split;solve_bounds|]. assert (Hfi_boundC : -(2^62 * 2^63) <= q * Z.shiftr (fi (i + 1)) (62 * i) <= 2^62 * 2^63) by (apply H6262i; lia). assert (Hgi_boundC : -(2^62 * 2^63) <= r * Z.shiftr (gi (i + 1)) (62 * i) <= 2^62 * 2^63) by (apply H6262i; lia). assert (Hfgi_boundB : -2^64 <= Z.shiftr (q * fi i + r * gi i) (62 * i) <= 2^64) by solve_bounds. forward_call;[unfold Int128_min_signed, Int128_max_signed;split;solve_bounds|]. forward_call;[unfold Int128_min_signed, Int128_max_signed;split;solve_bounds|]. forward_call;forward;forward_call;[unfold Int128_min_signed, Int128_max_signed;solve_bounds|]. forward_call;forward;forward_call;[unfold Int128_min_signed, Int128_max_signed;solve_bounds|]. replace (Z.shiftr (u * fi i + v * gi i) (62 * i) + u * Z.shiftr (fi (i + 1)) (62 * i) + v * Z.shiftr (gi (i + 1)) (62 * i)) with (Z.shiftr (u * fi (i + 1) + v * gi (i + 1)) (62 * i)). 2:{ rewrite (Z_div_mod_eq_full (fi (i + 1)) (2^(62 * i))) at 1. rewrite (Z_div_mod_eq_full (gi (i + 1)) (2^(62 * i))) at 1. rewrite Hfij, Hgij by lia. replace (u * ((2^(62 * i)) * (fi (i + 1) / (2^(62 * i))) + fi i) + v * ((2^(62 * i)) * (gi (i + 1) / (2^(62 * i))) + gi i)) with ((u * fi i + v * gi i) + ((u * (fi (i + 1) / (2^(62 * i))) + v * (gi (i + 1) / (2^(62 * i)))) * 2^(62 * i))) by ring. rewrite !Z.shiftr_div_pow2, Z.div_add by lia. ring. } replace (Z.shiftr (q * fi i + r * gi i) (62 * i) + q * Z.shiftr (fi (i + 1)) (62 * i) + r * Z.shiftr (gi (i + 1)) (62 * i)) with (Z.shiftr (q * fi (i + 1) + r * gi (i + 1)) (62 * i)). 2:{ rewrite (Z_div_mod_eq_full (fi (i + 1)) (2^(62 * i))) at 1. rewrite (Z_div_mod_eq_full (gi (i + 1)) (2^(62 * i))) at 1. rewrite Hfij, Hgij by lia. replace (q * ((2^(62 * i)) * (fi (i + 1) / (2^(62 * i))) + fi i) + r * ((2^(62 * i)) * (gi (i + 1) / (2^(62 * i))) + gi i)) with ((q * fi i + r * gi i) + ((q * (fi (i + 1) / (2^(62 * i))) + r * (gi (i + 1) / (2^(62 * i)))) * 2^(62 * i))) by ring. rewrite !Z.shiftr_div_pow2, Z.div_add by lia. ring. } rewrite !Z.shiftr_shiftr by lia. convert_C_to_math. rewrite !Signed62.pad_upd_Znth by (rewrite Hlength_firstn_skipn; lia). rewrite !upd_Znth_app2 by (rewrite Zlength_firstn, Zlength_skipn, Signed62.reprn_Zlength; lia). rewrite !Zlength_firstn, !Signed62.reprn_Zlength. replace (i - 1 - Z.min (Z.max 0 (i - 1)) (Z.of_nat len)) with 0 by lia. rewrite !(skipn_cons (Z.to_nat (i - 1))) by (rewrite Signed62.reprn_length; lia). rewrite !upd_Znth0. replace (S (Z.to_nat (i - 1))) with (Z.to_nat (i + 1 - 1)) by lia. replace (Z.ones 62) with (Z.ones (62 * (i + 1) - 62 * i)) by (f_equal;ring). rewrite <- !Z_shiftr_ones, <- !Z.shiftr_land, !Z.land_ones by lia. rewrite !(Z.add_mod (_*_) (_*_)), <-!(Z.mul_mod_idemp_r _ (fi (i + 1))), <-!(Z.mul_mod_idemp_r _ (gi (i+1))) by lia. rewrite !Hfi62, !Hgi62 by lia. rewrite !Z.mul_mod_idemp_r, <-!Z.add_mod by lia. replace (62 * (i + 1)) with (62 + 62 * i) by ring. rewrite <- !Z_shiftr_mod_2 by lia. replace (62 * i) with (62 + (62 * (i - 1))) by ring. rewrite <- !(Z.shiftr_shiftr _ 62 (62 * (i - 1))), !(Z.shiftr_div_pow2 _ 62) by lia. rewrite <- !(Signed62.reprn_Znth _ len) by lia. rewrite !Znth_cons by (rewrite Signed62.reprn_Zlength; lia). rewrite !app_assoc, !firstn_app, <- Z2Nat.inj_add by lia. replace (i - 1 + 1) with (i + 1 - 1) by lia. rewrite !(Z.add_comm _ 62). entailer!!. * unfold fi, gi. rewrite !Z.eqb_refl. assert (Hcfdg : forall c d, Z.abs c + Z.abs d <= 2^62 -> -2^62 < c + d -> -(2^63 * 2^(62 * Z.of_nat len)) <= c * f + d * g < 2^63 * 2^(62 * Z.of_nat len)). 1:{ intros c d Hcd0 Hcd1. rewrite <- Z.pow_add_r by lia. replace (63 + 62 * Z.of_nat len) with (62 + (62 * Z.of_nat len + 1)) by ring. rewrite Z.pow_add_r by lia. split;[|destruct (Z_le_lt_dec c 0); destruct (Z_le_lt_dec d 0)]. * cut (Z.abs (c * f) + Z.abs (d * g) <= 2 ^ 62 * 2 ^ (62 * Z.of_nat len + 1));[lia|]. transitivity (Z.abs (c * f) + Z.abs (d * g));[lia|]. rewrite !Z.abs_mul. transitivity (Z.abs c * Z.max (Z.abs f) (Z.abs g) + Z.abs d * Z.max (Z.abs f) (Z.abs g)); [apply Z.add_le_mono; apply Zmult_le_compat_l; lia|]. rewrite <- Z.mul_add_distr_r. apply Zmult_le_compat; lia. * apply Z.le_lt_trans with (c * (-2 ^ (62 * Z.of_nat len + 1)) + d * (-2 ^ (62 * Z.of_nat len + 1))); [apply Z.add_le_mono;apply Z.mul_le_mono_nonpos_l;lia|]. replace (c * -2 ^ (62 * Z.of_nat len + 1) + d * -2 ^ (62 * Z.of_nat len + 1)) with (-(c + d) * 2 ^ (62 * Z.of_nat len + 1)) by ring. apply Zmult_lt_compat_r;lia. * apply Z.le_lt_trans with (c * (-2 ^ (62 * Z.of_nat len + 1)) + d * (2 ^ (62 * Z.of_nat len + 1) - 1)); [apply Z.add_le_mono;[apply Z.mul_le_mono_nonpos_l|apply Z.mul_le_mono_nonneg_l];lia|]. replace (c * -2 ^ (62 * Z.of_nat len + 1) + d * (2 ^ (62 * Z.of_nat len + 1) - 1)) with ((d - c) * (2 ^ (62 * Z.of_nat len + 1)) - d) by ring. apply Z.le_lt_trans with (2^62 * (2 ^ (62 * Z.of_nat len + 1)) - d); [apply Z.add_le_mono_r;apply Zmult_le_compat_r;lia|lia]. * apply Z.le_lt_trans with (c * (2 ^ (62 * Z.of_nat len + 1) - 1) + d * (-2 ^ (62 * Z.of_nat len + 1))); [apply Z.add_le_mono;[apply Z.mul_le_mono_nonneg_l|apply Z.mul_le_mono_nonpos_l];lia|]. replace (c * (2 ^ (62 * Z.of_nat len + 1) - 1) + d * (-2 ^ (62 * Z.of_nat len + 1))) with ((c - d) * (2 ^ (62 * Z.of_nat len + 1)) - c) by ring. apply Z.le_lt_trans with (2^62 * (2 ^ (62 * Z.of_nat len + 1)) - c); [apply Z.add_le_mono_r;apply Zmult_le_compat_r;lia|lia]. * apply Z.le_lt_trans with (c * (2 ^ (62 * Z.of_nat len + 1) - 1) + d * (2 ^ (62 * Z.of_nat len + 1) - 1)); [apply Z.add_le_mono; apply Z.mul_le_mono_nonneg_l;lia|]. replace (c * (2 ^ (62 * Z.of_nat len + 1) - 1) + d * (2 ^ (62 * Z.of_nat len + 1) - 1)) with ((c + d) * (2 ^ (62 * Z.of_nat len + 1) - 1)) by ring. apply Z.le_lt_trans with (2^62 * (2 ^ (62 * Z.of_nat len + 1) - 1)); [apply Zmult_le_compat_r;lia|lia]. } assert (Hufvg : -(2 ^ 63 * 2 ^ (62 * Z.of_nat len)) <= u * f + v * g < 2 ^ 63 * 2 ^ (62 * Z.of_nat len)) by (apply Hcfdg; lia). assert (Hqfrg : -(2 ^ 63 * 2 ^ (62 * Z.of_nat len)) <= q * f + r * g < 2 ^ 63 * 2 ^ (62 * Z.of_nat len)) by (apply Hcfdg; lia). forward_call;[solve_bounds|]. forward. forward_call;[solve_bounds|]. forward. rewrite !Signed62.pad_upd_Znth by (rewrite Hlength_firstn_skipn; lia). rewrite !upd_Znth_app2 by (rewrite Zlength_firstn, Zlength_skipn, Signed62.reprn_Zlength; lia). rewrite !Zlength_firstn, !Signed62.reprn_Zlength. replace (Z.of_nat len - 1 - Z.min (Z.max 0 (Z.of_nat len - 1)) (Z.of_nat len)) with 0 by lia. rewrite !(skipn_cons (Z.to_nat (Z.of_nat len - 1))) by (rewrite Signed62.reprn_length; lia). rewrite !upd_Znth0. replace (S (Z.to_nat (Z.of_nat len - 1))) with (len) by lia. rewrite !skipn_short by (rewrite Signed62.reprn_length;lia). replace (62 * Z.of_nat len) with (62 + (62 * (Z.of_nat len - 1))) by ring. rewrite <- !(Z.shiftr_shiftr _ 62 (62 * (Z.of_nat len - 1))), !(Z.shiftr_div_pow2 _ 62) by lia. replace (Z.to_nat (Z.of_nat len - 1)) with (Init.Nat.pred (Datatypes.length (Signed62.reprn len ((u * f + v * g) / 2 ^ 62)))) at 1 by (rewrite Signed62.reprn_length; lia). replace (Z.to_nat (Z.of_nat len - 1)) with (Init.Nat.pred (Datatypes.length (Signed62.reprn len ((q * f + r * g) / 2 ^ 62)))) by (rewrite Signed62.reprn_length; lia). rewrite <- !removelast_firstn_len, <- !(Signed62.reprn_last _ len default) by lia. rewrite <- !app_removelast_last by (rewrite <- length_zero_iff_nil, Signed62.reprn_length; lia). rewrite <- Htransf, <- Htransg, !(Z.mul_comm (2 ^ 62)), !Z.div_mul by lia. unfold secp256k1_uint128_at. sep_apply (data_at_data_at_ Tsh t_secp256k1_uint128 (Vlong (Int64.repr (Z.shiftr f1 (62 * (Z.of_nat len - 1)))), Vlong (Int64.repr (Z.shiftr (Z.shiftr f1 (62 * (Z.of_nat len - 1))) 64))) v_cf). sep_apply (data_at_data_at_ Tsh t_secp256k1_uint128 (Vlong (Int64.repr (Z.shiftr g1 (62 * (Z.of_nat len - 1)))), Vlong (Int64.repr (Z.shiftr (Z.shiftr g1 (62 * (Z.of_nat len - 1))) 64))) v_cg). entailer!!. Qed. Lemma body_secp256k1_modinv64_var: semax_body Vprog Gprog f_secp256k1_modinv64_var secp256k1_modinv64_var_spec. Proof. start_function. fastforward 5. change (upd_Znth 4 _ _) with (map Vlong (Signed62.reprn 5 0)). fastforward 5. change (upd_Znth 4 _ _) with (map Vlong (Signed62.reprn 5 1)). unfold make_modinfo. unfold_data_at (data_at _ _ _ modinfo). assert_PROP (field_compatible t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo) by entailer. forward_call (m, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer!!|]. change (data_at sh_modinfo t_secp256k1_modinv64_signed62) with (data_at sh_modinfo (nested_field_type t_secp256k1_modinv64_modinfo (DOT _modulus))). rewrite <- field_at_data_at. assert (Hmodinfo : ((field_at sh_modinfo t_secp256k1_modinv64_modinfo (DOT _modulus) (map Vlong (Signed62.reprn 5 m)) modinfo) * (field_at sh_modinfo t_secp256k1_modinv64_modinfo (DOT _modulus_inv62) (Vlong (Int64.repr (modInv m (2 ^ 62)))) modinfo) |-- data_at sh_modinfo t_secp256k1_modinv64_modinfo (map Vlong (Signed62.reprn 5 m), Vlong (Int64.repr (modInv m (2 ^ 62)))) modinfo)) by (unfold_data_at (data_at _ _ _ modinfo);entailer!!). sep_apply Hmodinfo. fold (make_modinfo m). clear Hmodinfo. forward_call. fastforward 3. change (Int.neg (Int.repr 1)) with (Int.repr (-1)). rewrite <- Zodd_equiv in H. set (init := divstep.init m x H). assert (HfBound : forall i, -m < divstep.f (fst (divstep.stepN i init)) <= m). 1:{ clear -H0 H1; intro i. injection (divstep.Trans.transN_step i init). intros _. destruct (divstep.Trans.bounded_transN i init) as [[Huv Huv'] _]. nia. } assert (HgBound : forall i, -m < divstep.g (fst (divstep.stepN i init)) < m). 1:{ clear -H0 H1; intro i. case (divstep.fgBoundsStrict init i);[cbn; lia|]. intros _. change (divstep.f init) with m. change (divstep.g init) with x. lia. } set (invariant := fun P f => (EX i:nat, EX len:nat, EX d:Z, EX e:Z, PROP ( 0 <= Z.of_nat i < 12 ; (1 <= len <= 5)%nat ; -2^(62 * Z.of_nat len + 1) <= divstep.f (fst (divstep.stepN (f i) init)) <= 2^(62 * Z.of_nat len + 1) - 1 ; -2^(62 * Z.of_nat len + 1) <= divstep.g (fst (divstep.stepN (f i) init)) <= 2^(62 * Z.of_nat len + 1) - 1 ; -2 * m < d < m ; -2 * m < e < m ; eqm m (x * d) (divstep.f (fst (divstep.stepN (f i) init))) ; eqm m (x * e) (divstep.g (fst (divstep.stepN (f i) init))) ; x = 0 -> d = 0 ; P (divstep.g (fst (divstep.stepN (f i) init))) ) LOCAL (temp _eta (Vlong (Int64.repr (divstep.eta (fst (divstep.stepN (f i) init))))); temp _len (Vint (Int.repr (Z.of_nat len))); temp _i (Vint (Int.repr (Z.of_nat i))); lvar _t (Tstruct _secp256k1_modinv64_trans2x2 noattr) v_t; lvar _g (Tstruct _secp256k1_modinv64_signed62 noattr) v_g; lvar _f (Tstruct _secp256k1_modinv64_signed62 noattr) v_f; lvar _e (Tstruct _secp256k1_modinv64_signed62 noattr) v_e; lvar _d (Tstruct _secp256k1_modinv64_signed62 noattr) v_d; gvars gv; temp _x ptrx; temp _modinfo modinfo) SEP ( data_at (cs := CompSpecs) Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn len (divstep.g (fst (divstep.stepN (f i) init))))) v_g; data_at (cs := CompSpecs) shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx; data_at (cs := CompSpecs) Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn len (divstep.f (fst (divstep.stepN (f i) init))))) v_f; data_at_ (cs := CompSpecs) Tsh (Tstruct _secp256k1_modinv64_trans2x2 noattr) v_t; data_at (cs := CompSpecs) Tsh (Tstruct _secp256k1_modinv64_signed62 noattr) (map Vlong (Signed62.reprn 5 e)) v_e; data_at (cs := CompSpecs) Tsh (Tstruct _secp256k1_modinv64_signed62 noattr) (map Vlong (Signed62.reprn 5 d)) v_d; data_at (cs := CompSpecs) sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at (cs := CompSpecs) sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)) )%assert). forward_loop (invariant (fun g => True) (fun i => 62*i)%nat) break: (invariant (fun g => g = 0) (fun i => 62*(i + 1))%nat); unfold invariant in *; clear invariant. * Exists 0%nat; Exists 5%nat; Exists 0; Exists 1. rewrite !Signed62.pad5 by (rewrite Signed62.reprn_length; reflexivity). simpl (divstep.stepN (62 * 0) init). simpl (divstep.g _). simpl (divstep.f _). entailer!!. split. - unfold eqm; rewrite Z.mod_same, Z.mul_0_r, Z.mod_0_l; lia. - apply eqm_refl. * Intros i len d e. set (sti := (fst (divstep.stepN (62 * i) init))) in *. set (fi := divstep.f sti) in *. set (gi := divstep.g sti) in *. forward;rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength; lia);[entailer!!|]. forward;rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength; lia);[entailer!!|]. assert (Hi0 : forall z, Znth 0 (Signed62.reprn len z) = Int64.repr (if (len =? 1)%nat then z else z mod 2^62)). 1:{ intros z. destruct len;[lia|]. destruct len. - rewrite Nat.eqb_refl. change (Znth 0 (Signed62.reprn 1 z)) with (last (Signed62.reprn 1 z) default). rewrite Signed62.reprn_last by lia. reflexivity. - replace (_ =? _)%nat with false by (symmetry; apply Nat.eqb_neq; lia). rewrite Signed62.reprn_Znth by lia. reflexivity. } rewrite !Hi0. set (fi0 := if (len =? 1)%nat then fi else fi mod 2^62). set (gi0 := if (len =? 1)%nat then gi else gi mod 2^62). assert (Hfi0Odd : Zodd fi0). 1:{ unfold fi0. destruct (len =? 1)%nat; try apply divstep.oddF. apply Zodd_bool_iff. rewrite <- Zbits.Ztestbit_base, <-Z.land_ones, Z.land_spec, Zbits.Ztestbit_base, andb_true_r by lia. apply Zodd_bool_iff. apply divstep.oddF. } set (stCall := {| divstep.delta := divstep.delta sti; divstep.f := _; divstep.g := gi0; divstep.oddF := Hfi0Odd |}). assert (etaStCall : -683 <= divstep.eta stCall < 683). 1:{ assert (etaInit : -(1) <= divstep.eta init < 1) by (cbn;lia). assert (etaBounds := divstep.etaBounds 1 (62*i) init etaInit). fold sti in etaBounds. change (divstep.eta stCall) with (divstep.eta sti). lia. } forward_call (stCall, v_t, Tsh, sh_debruijn, gv). assert (Hi0mod : forall z, eqm (2^62) (if (len =? 1)%nat then z else z mod 2^62) z). 1:{ intros z. destruct (_ =? _)%nat;[reflexivity|]. unfold eqm. rewrite Z.mod_mod by lia. reflexivity. } unfold divstep.eta, divstep.Trans.transN. destruct (divstep.stepN_mod 62 stCall sti (Hi0mod fi) (Hi0mod gi) (eq_refl _)) as [-> ->]. fold (divstep.Trans.transN 62 sti). fold (divstep.eta (fst (divstep.stepN 62 sti))). clear Hi0mod etaStCall stCall. forward. assert (HmOdd : Z.Odd m) by (apply Zodd_equiv; assumption). assert (HstiBounded := divstep.Trans.bounded_transN 62 sti). forward_call (d, e, divstep.Trans.transN 62 sti, m, v_d, v_e, v_t, modinfo, Tsh, Tsh, Tsh, sh_modinfo). destruct HstiBounded as [[Huv Huv'] [Hqr Hqr']]. destruct (divstep.update_de_bound m d e (divstep.Trans.transN 62 sti)) as [Hdm Hem]; try assumption. set (d' := fst (divstep.update_de m d e (divstep.Trans.transN 62 sti))). set (e' := snd (divstep.update_de m d e (divstep.Trans.transN 62 sti))). assert (Hx0d'0 : x = 0 -> d' = 0). 1:{ intros Hx0. specialize (H13 Hx0). unfold d', sti, init. rewrite divstep.Trans.transHs. - rewrite H13. simpl. replace (_ + _) with (0) by ring. unfold divstep.pre_div62Modulo. rewrite Z.mul_0_r. reflexivity. - rewrite divstep.fixed_g;[|assumption]. apply Z.divide_0_r. } clear H13. assert (HfiBound : -m < fi <= m) by apply HfBound. assert (HgiBound : -m < gi < m) by apply HgBound. forward_verify_check. 1:{ unfold make_modinfo. forward_call (fi, len, m, -1, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Gt in H13; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_verify_check. 1:{ unfold make_modinfo. forward_call (fi, len, m, 1, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ revert H13. elim Z.compare_spec; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_verify_check. 1:{ unfold make_modinfo. forward_call (gi, len, m, -1, v_g, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Gt in H13; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_verify_check. 1:{ unfold make_modinfo. forward_call (gi, len, m, 1, v_g, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Lt in H13; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_call (len, sti, v_f, v_g, v_t, Tsh, Tsh, Tsh). sep_apply (data_at_data_at_ Tsh t_secp256k1_modinv64_trans2x2). set (fi' := divstep.f (fst (divstep.stepN 62 sti))). set (gi' := divstep.g (fst (divstep.stepN 62 sti))). assert (Hfgi'Bound : -2 ^ (62 * Z.of_nat len + 1) <= fi' <= 2 ^ (62 * Z.of_nat len + 1) - 1 /\ -2 ^ (62 * Z.of_nat len + 1) <= gi' <= 2 ^ (62 * Z.of_nat len + 1) - 1). 1:{ unfold fi'. remember 62%nat as n62. injection (divstep.Trans.transN_step n62 sti). subst n62. destruct (divstep.Trans.bounded_transN 62 sti) as [[Hb1 Hb2] [Hb3 Hb4]]. clear -Hb1 Hb2 Hb3 Hb4 H7 H8. nia. } destruct Hfgi'Bound as [Hfi'Bound Hgi'Bound]. destruct (divstep.update_de_eqm m x d e sti) as [Hxd' Hxe']; try assumption. fold d' in Hxd'. fold e' in Hxe'. pose (sti' := fst (divstep.stepN (62 * (i + 1)) init)). unfold fi', gi' in *; clear fi' gi'. replace (fst (divstep.stepN 62 sti)) with sti' in * by (unfold sti'; replace (62 * (i + 1))%nat with (62 + 62 * i)%nat by lia; apply divstep.stepN_app_fst). set (fi' := divstep.f sti') in *. set (gi' := divstep.g sti') in *. forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|]. drop_LOCALs [_t'1; _t'38; _t'37]. forward_if (gi' <> 0). 2:{ forward. entailer!!. apply H13. rewrite H14. clear -len. destruct len as [|[|len]];reflexivity. } 1:{ forward. forward_for_simple_bound (Z.of_nat len) (EX j:Z, PROP ( ) LOCAL (temp _cond (Vlong (fold_left (fun x y => Int64.or x y) (firstn (Z.to_nat j) (Signed62.reprn len gi')) Int64.zero)); temp _t'31 (Vlong (Znth 0 (Signed62.reprn len gi'))); temp _eta (Vlong (Int64.repr (divstep.eta sti'))); temp _len (Vint (Int.repr (Z.of_nat len))); temp _i (Vint (Int.repr (Z.of_nat i))); lvar _t (Tstruct _secp256k1_modinv64_trans2x2 noattr) v_t; lvar _g (Tstruct _secp256k1_modinv64_signed62 noattr) v_g; lvar _f (Tstruct _secp256k1_modinv64_signed62 noattr) v_f; lvar _e (Tstruct _secp256k1_modinv64_signed62 noattr) v_e; lvar _d (Tstruct _secp256k1_modinv64_signed62 noattr) v_d; gvars gv; temp _x ptrx; temp _modinfo modinfo) SEP (data_at_ Tsh t_secp256k1_modinv64_trans2x2 v_t; data_at Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn len fi')) v_f; data_at Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn len gi')) v_g; data_at Tsh t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 d')) v_d; data_at Tsh t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 e')) v_e; data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE); data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx))%assert. + entailer!!. rewrite <-sublist_firstn, sublist_one, H13;[reflexivity|lia| |lia]. rewrite Signed62.reprn_Zlength;lia. + forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|]. forward. entailer!!. rewrite <-Zfirstn_app by lia. rewrite (app_nil_end (firstn (Z.to_nat 1) _)), <-(Znth_cons Int64.zero) by (rewrite Signed62.reprn_Zlength;lia). rewrite fold_left_app. cbn. reflexivity. + rewrite Nat2Z.id, firstn_all2 by (rewrite Signed62.reprn_length;lia). rewrite fold_symmetric;intros;[|rewrite Int64.or_assoc|rewrite Int64.or_commut];try reflexivity. forward_if (gi' <> 0);[| |entailer!!]. 2:{ forward;entailer!!. apply H14. rewrite H15. clear -len. induction len;[reflexivity|]. destruct len;[reflexivity|]. cbn in *. rewrite !Z.shiftr_0_l, !Zmod_0_l in *. rewrite IHlen. reflexivity. } forward. Exists i len d' e'. entailer!!. change (gi' = 0). assert (Hgi'0 : Forall (fun x => x = Int64.zero) (Signed62.reprn len gi')). 1:{ revert H14. clear H13. induction (Signed62.reprn len gi');[constructor|]. cbn. intros H14. assert (Horzero : forall a b, Int64.or a b = Int64.zero -> a = Int64.zero). 1:{ clear -l. intros a b Hab. destruct (Int64.bits_size_1 a);[assumption|]. assert (Hsize : 0 < Int64.size a). 1:{ destruct (Z_le_lt_dec 0 (Z.pred (Int64.size a))) as [Hle|Hlt];[lia|]. assert (Hcontra := Int64.bits_below a _ Hlt). congruence. } apply (f_equal (fun x => Int64.testbit x (Z.pred (Int64.size a)))) in Hab. rewrite Int64.bits_zero, Int64.bits_or in Hab by (assert (Hrange := Int64.size_range a); lia). apply orb_false_elim in Hab. destruct Hab;congruence. } constructor;[eapply Horzero; apply H14|]. apply IHl. eapply Horzero; rewrite Int64.or_commut; apply H14. } rewrite <-(Signed62.signed_reprn gi' len);[|lia|assumption]. clear -Hgi'0. induction (Signed62.reprn len gi');[reflexivity|]. cbn. inversion_clear Hgi'0 as [|Ha Hl]. rewrite H0, IHl;[reflexivity|assumption]. } drop_LOCALs [_t'31]. forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|]. replace (Z.of_nat len - 1) with (Zlength (Signed62.reprn len fi') - 1) by (rewrite Signed62.reprn_Zlength; reflexivity). rewrite Znth_last, Signed62.reprn_last by lia. forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|]. replace (Z.of_nat len - 1) with (Zlength (Signed62.reprn len gi') - 1) at 1 by (rewrite Signed62.reprn_Zlength; reflexivity). rewrite Znth_last, Signed62.reprn_last by lia. progressC. replace (Z.shiftr (Z.of_nat len - 2) 63) with (if 2 <=? Z.of_nat len then 0 else -1). 2:{ rewrite Z.shiftr_div_pow2 by lia. elim Z.leb_spec; intros Hlen. + cut (0 <= (Z.of_nat len - 2) / 2 ^ 63 < 1);[lia|]. apply div_bounds; lia. + cut (-1 <= (Z.of_nat len - 2) / 2 ^ 63 < 0);[lia|]. apply div_bounds; lia. } do 2 forward. forward_if (EX len:nat, PROP ( (1 <= len <= 5)%nat ; -2^(62 * Z.of_nat len + 1) <= divstep.f (fst (divstep.stepN (62 * (i + 1)) init)) <= 2^(62 * Z.of_nat len + 1) - 1 ; -2^(62 * Z.of_nat len + 1) <= divstep.g (fst (divstep.stepN (62 * (i + 1)) init)) <= 2^(62 * Z.of_nat len + 1) - 1 ) LOCAL ( temp _eta (Vlong (Int64.repr (divstep.eta sti'))); temp _len (Vint (Int.repr (Z.of_nat len))); temp _i (Vint (Int.repr (Z.of_nat i))); lvar _t (Tstruct _secp256k1_modinv64_trans2x2 noattr) v_t; lvar _g (Tstruct _secp256k1_modinv64_signed62 noattr) v_g; lvar _f (Tstruct _secp256k1_modinv64_signed62 noattr) v_f; lvar _e (Tstruct _secp256k1_modinv64_signed62 noattr) v_e; lvar _d (Tstruct _secp256k1_modinv64_signed62 noattr) v_d; gvars gv; temp _x ptrx; temp _modinfo modinfo) SEP (data_at_ Tsh t_secp256k1_modinv64_trans2x2 v_t; data_at Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn len fi')) v_f; data_at Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn len gi')) v_g; data_at Tsh t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 d')) v_d; data_at Tsh t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 e')) v_e; data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo; debruijn64_array sh_debruijn gv; data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE); data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx))%assert; [|forward;Exists len;entailer!!|Intros len0]. 1:{ assert (Hor0_l : forall x y, Int64.or x y = Int64.zero -> x = Int64.zero). 1:{ clear. intros x y Hxy. apply Int64.same_bits_eq. intros i Hi. apply (f_equal (fun x => Int64.testbit x i)) in Hxy. rewrite Int64.bits_or, Int64.bits_zero, orb_false_iff in Hxy by assumption. rewrite Int64.bits_zero. tauto. } assert (H14ab := Hor0_l _ _ H14). rewrite Int64.or_commut in H14. generalize (Hor0_l _ _ H14). clear H14. assert (H14a := Hor0_l _ _ H14ab). rewrite Int64.or_commut in H14ab. generalize (Hor0_l _ _ H14ab). clear H14ab. convert_C_to_math. assert (Hxor : forall x, -2^63 <= x < 2^63 -> Int64.repr (Z.lxor x (Z.shiftr (Int64.signed (Int64.repr x)) 63)) = Int64.zero -> -1 <= x <= 0). 1:{ clear. intros x Hx Hlxor. rewrite <- xor64_repr in Hlxor. apply Int64.xor_zero_equal in Hlxor. rewrite Int64.signed_repr in Hlxor by rep_lia. assert (Heq : x = Z.shiftr x 63). 1:{ rewrite <- (Int64.signed_repr (Z.shiftr x 63)) by solve_bounds. rewrite <- (Int64.signed_repr x) at 1 by solve_bounds. congruence. } rewrite Heq. solve_bounds. } intros Hfi'last Hgi'last. apply Hxor in Hfi'last, Hgi'last. 2:{ rewrite Z.mul_sub_distr_l, Z.shiftr_div_pow2 by lia. apply div_bounds;[lia|]. clear -Hgi'Bound H5 H6. rewrite Z.mul_opp_r, <- Z.pow_add_r by lia. replace (62 * Z.of_nat len - 62 * 1 + 63) with (62 * Z.of_nat len + 1) by ring. lia. } 2:{ rewrite Z.mul_sub_distr_l, Z.shiftr_div_pow2 by lia. apply div_bounds;[lia|]. clear -Hfi'Bound H5 H6. rewrite Z.mul_opp_r, <- Z.pow_add_r by lia. replace (62 * Z.of_nat len - 62 * 1 + 63) with (62 * Z.of_nat len + 1) by ring. lia. } revert H14a. elim Z.leb_spec;[|discriminate]. intros Hlen2 _. set (fisign := Z.shiftr fi' (62 * (Z.of_nat len - 1))) in *. set (gisign := Z.shiftr gi' (62 * (Z.of_nat len - 1))) in *. forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|forward]. forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|forward]. rewrite !Int64_shl_shiftl, !Signed62.pad_upd_Znth by (rewrite Signed62.reprn_Zlength;lia). change (Int64.unsigned(Int64.repr (Int.unsigned (Int.repr 62)))) with 62. rewrite !Int64.signed_repr by rep_lia. forward. rewrite sub_repr. Exists (len - 1)%nat. rewrite Nat2Z.inj_sub by lia. change (Z.of_nat 1) with 1. assert (Hfi'Bound' : -2 ^ (Z.of_nat (len - 1) * 62) <= fi' < 2 ^ (Z.of_nat (len - 1) * 62)). 1:{ replace (Z.of_nat (len - 1) * 62) with (62 * (Z.of_nat len - 1)) by lia. destruct (Z.eq_dec fisign 0) as [Hfisign0|Hfisign0]; [apply shiftr_small_iff in Hfisign0; lia|]. destruct (Z.eq_dec fisign (-1)) as [Hfisign1|Hfisign1];[|lia]. apply shiftr_small_neg_iff in Hfisign1; lia. } assert (Hgi'Bound' : -2 ^ (Z.of_nat (len - 1) * 62) <= gi' < 2 ^ (Z.of_nat (len - 1) * 62)). 1:{ replace (Z.of_nat (len - 1) * 62) with (62 * (Z.of_nat len - 1)) by lia. destruct (Z.eq_dec gisign 0) as [Hgisign0|Hgisign0]; [apply shiftr_small_iff in Hgisign0; lia|]. destruct (Z.eq_dec gisign (-1)) as [Hgisign1|Hgisign1];[|lia]. apply shiftr_small_neg_iff in Hgisign1; lia. } entailer!!. 1:{ replace (62 * (Z.of_nat len - 1) + 1) with (Z.of_nat (len - 1) * 62 + 1) by lia. rewrite Z.pow_add_r by lia. fold sti' fi' gi'. lia. } assert (Hsign : forall x n, -1 <= Z.shiftr x n <= 0 -> Z.shiftr x n = if 0 <=? x then 0 else -1). 1:{ clear. intros x n Hx. elim Z.leb_spec; intros Hx0. + apply (Z.shiftr_nonneg _ n) in Hx0; lia. + apply (Z.shiftr_neg _ n) in Hx0; lia. } unfold fisign, gisign. rewrite !Hsign by assumption. cut (forall v x, -2 ^ (Z.of_nat (len - 1) * 62) <= x <= 2 ^ (Z.of_nat (len - 1) * 62) - 1 -> data_at Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (upd_Znth (Z.of_nat len - 2) (Signed62.reprn len x) (Int64.or (Znth (Z.of_nat len - 2) (Signed62.reprn len x)) (Int64.repr (Z.shiftl (if 0 <=? x then 0 else -1) 62))))) v |-- data_at Tsh t_secp256k1_modinv64_signed62 (Signed62.pad (Signed62.reprn (len - 1) x)) v). intro K. apply sepcon_derives;apply K;lia. intros v h Hh. unfold Signed62.pad at 2. do 2 unfold_data_at (data_at _ _ _ v). rewrite !field_at_data_at. simpl (nested_field_type t_secp256k1_modinv64_signed62 (DOT _v)). rewrite (split2_data_at_Tarray_app (Z.of_nat len - 1));rewrite ?Signed62.reprn_length;[ |rewrite Zlength_map, Signed62.reprn_Zlength; lia |rewrite Zlength_repeat'; lia ]. rewrite <-(data_at__tarray' _ tlong _ (repeat Vundef (5 - (len - 1)))) by (replace (5 - (len - 1))%nat with (Z.to_nat (5 - (Z.of_nat len - 1))) by lia;apply repeat_Zrepeat). sep_apply (split2_data_at_Tarray_unfold Tsh tlong 5 (Z.of_nat len - 1));[lia|]. entailer!!. unfold Signed62.pad. rewrite sublist0_app1, sublist_map, sublist_firstn by (rewrite Zlength_map, Zlength_upd_Znth, Signed62.reprn_Zlength;lia). replace (Z.to_nat (Z.of_nat len - 1)) with (len - 1)%nat by lia. replace (Z.of_nat len - 2) with ((Z.of_nat (len - 1)) - 1) by lia. rewrite Signed62.reprn_shrink;[entailer!!| |lia]. unfold Signed62.min_signed, Signed62.max_signed. lia. } clear Hgi'Bound Hfi'Bound Hfi0Odd gi0 fi0 Hi0 H8 H7 H6 H5 len. rename len0 into len. assert(Hi0 : (i <> 11)%nat). 1:{ intros ->. apply H13. unfold gi', sti', init. rewrite (divstep.stepN_app_fst 20 724). apply divstep.fixed_g. rewrite divstep.Translate_divsteps_g. apply (processDivstep_correct _ 0x1030596cf6d817d1357f908ef70cdb00b38d047fbba852139babb6c8646fb15b2); try lia;[assumption|]. apply example724. } match goal with | |- semax _ (PROPx (?P) (LOCALx ?Q ?R)) _ _ => let Q' := remove_LOCAL2 [temp _i (Vint (Int.repr (Z.of_nat i)))] Q in forward_loop (PROPx (P) (LOCALx Q R)) break:(PROPx (P) (LOCALx (temp _i (Vint (Int.repr (Z.of_nat i + 1)))::Q') R)) end;[entailer!!| |]. 1:{ forward. rewrite add_repr. forward. forward_if True;[exfalso|forward;entailer!!|forward;entailer!!]. revert H5. convert_C_to_math. case Z.ltb_spec;[discriminate|lia]. } assert (Hfi'Bound : -m < fi' <= m) by apply HfBound. assert (Hgi'Bound : -m < gi' < m) by apply HgBound. forward_verify_check. 1:{ unfold make_modinfo. forward_call (fi', len, m, -1, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Gt in H5; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_verify_check. 1:{ unfold make_modinfo. forward_call (fi', len, m, 1, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ revert H5. elim Z.compare_spec; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_verify_check. 1:{ unfold make_modinfo. forward_call (gi', len, m, -1, v_g, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Gt in H5; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } forward_verify_check. 1:{ unfold make_modinfo. forward_call (gi', len, m, 1, v_g, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ rewrite Zaux.Zcompare_Lt in H5; try discriminate. lia. } forward;unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!. } Exists (i+1)%nat; Exists len; Exists d'; Exists e'. entailer!!. do 2 f_equal. lia. * Intros i len d e. rename H13 into Hx0d0. rename H14 into H13. set (sti := (fst (divstep.stepN (62 * (i + 1)) init))) in *. set (fi := divstep.f sti) in *. set (gi := divstep.g sti) in *. forward_verify_check. 1:{ forward_call (gi, len, 1, 0, v_g, gv _SECP256K1_SIGNED62_ONE, Tsh, sh_SECP256K1_SIGNED62_ONE). rewrite H13 at 1. forward_if;[discriminate|]. forward. entailer!!. } assert (Hverify : (Z.abs fi = 1) \/ (x = 0 /\ fi = m)). 1:{ destruct (Z.eq_dec x 0) as [Hx0|Hx0];[right|left]. - split;[assumption|]. specialize (HfBound (62 * (i + 1))%nat). fold sti fi in HfBound. cut (m = Z.abs fi);[lia|]. etransitivity;[|apply Z.gcd_0_r]. symmetry. apply Zis_gcd_gcd;[lia|]. rewrite <- H13. apply divstep.gcd. subst x. apply Zis_gcd_0. - rewrite <- Z.gcd_0_r. apply Zis_gcd_gcd;[lia|]. rewrite <- H13. apply divstep.gcd. apply Zis_gcd_sym. destruct H2 as [H2|H2];[lia|]. apply H2. } forward_verify_check. 1:{ forward_call (fi, len, 1, -1, v_f, gv _SECP256K1_SIGNED62_ONE, Tsh, sh_SECP256K1_SIGNED62_ONE). forward_if (temp _t'13 (Vint (Int.repr (Z.b2z (Z.abs fi =? 1))))). 1:{ forward. destruct (Z.eq_dec fi (-1)) as [->|Hne];[entailer!!|]. revert H14. elim Zaux.Zcompare_spec;try discriminate. lia. } 1:{ forward_call (fi, len, 1, 1, v_f, gv _SECP256K1_SIGNED62_ONE, Tsh, sh_SECP256K1_SIGNED62_ONE). forward. entailer!!. assert (Hfi1 : fi <> -1) by (revert H14;elim Zaux.Zcompare_spec;try contradiction;lia). elim Z.eqb_spec;intros Habsfi. - replace fi with 1 by lia. reflexivity. - elim Zaux.Zcompare_spec;try reflexivity. lia. } forward_if (temp _t'15 (Vint (Int.repr (Z.b2z ((Z.abs fi =? 1) || (x =? 0) && (d =? 0) && (Z.abs fi =? m)))))). 1:{ forward. entailer!!. rewrite H14. reflexivity. } 1:{ forward_call (x, 5%nat, 1, 0, ptrx, gv _SECP256K1_SIGNED62_ONE, shx, sh_SECP256K1_SIGNED62_ONE). forward_if (temp _t'17 (Vint (Int.repr (Z.b2z ((x =? 0) && (d =? 0)))))). 2:{ forward. entailer!!. elim Z.eqb_spec; try reflexivity. intros ->. contradiction. } 1:{ forward_call (d, 5%nat, 1, 0, v_d, gv _SECP256K1_SIGNED62_ONE, Tsh, sh_SECP256K1_SIGNED62_ONE). forward. entailer!!. elim (Z.eqb_spec d). 2:{ rewrite andb_false_r; simpl. elim Zaux.Zcompare_spec;try reflexivity; lia. } revert H15. elim Zaux.Zcompare_spec;try discriminate. intros -> _ ->. reflexivity. } forward_if. 2:{ forward. entailer!!. } unfold make_modinfo. forward_call (fi, len, m, 1, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer! |unfold_data_at (data_at _ _ _ modinfo);entailer!|]. forward_if. 1:{ fastforward. entailer!!;[| unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!]. revert H16. elim Zaux.Zcompare_spec;try discriminate. rewrite H14, H15. intros -> _. replace (Z.abs (m * 1)) with m by lia. rewrite Z.eqb_refl. reflexivity. } forward_call (fi, len, m, -1, v_f, field_address t_secp256k1_modinv64_modinfo (DOT _modulus) modinfo, Tsh, sh_modinfo); [rewrite field_address_offset by assumption;entailer!|]. fastforward. entailer!!;[| unfold_data_at (data_at _ t_secp256k1_modinv64_modinfo _ modinfo);entailer!]. assert (Hfim : fi <> m). 1:{ revert H16. elim Zaux.Zcompare_spec;try contradiction;lia. } rewrite H14, H15. simpl. elim Z.eqb_spec;elim Zaux.Zcompare_spec;try lia; reflexivity. } forward_if;[|forward;entailer!!]. exfalso. destruct Hverify as [Hverify|[Hx0 Hverify]]. - rewrite Hverify, Z.eqb_refl in H14 by reflexivity;discriminate. - subst x. rewrite orb_comm, Hverify in H14. replace (Z.abs m) with m in H14 by lia. rewrite Hx0d0, !Z.eqb_refl in H14 by reflexivity. discriminate. } forward; rewrite Signed62.pad_nth by (rewrite Signed62.reprn_Zlength;lia); [entailer!!|]. rewrite <- (Signed62.reprn_Zlength len fi), Znth_last, Signed62.reprn_last at 1 by lia. forward_call. assert (Hfibound : 2 ^ (62 * (Z.of_nat len - 1)) * -2 ^ 63 <= fi <= 2 ^ (62 * (Z.of_nat len - 1)) * (2 ^ 63 - 1 + 1) - 1). 1:{ rewrite Z.sub_add, Z.mul_opp_r, <-Z.pow_add_r, Z.mul_sub_distr_l by lia. replace (62 * Z.of_nat len - 62 * 1 + 63) with (62 * Z.of_nat len + 1);lia. } rewrite Int64.signed_repr by solve_bounds. replace (_ Ty -> Type) := Class { iden : forall {A}, term A A ; comp : forall {A B C}, term A B -> term B C -> term A C ; unit : forall {A}, term A Unit ; injl : forall {A B C}, term A B -> term A (B + C) ; injr : forall {A B C}, term A C -> term A (B + C) ; case : forall {A B C D}, term (A * C) D -> term (B * C) D -> term ((A + B) * C) D ; pair : forall {A B C}, term A B -> term A C -> term A (B * C) ; take : forall {A B C}, term A C -> term (A * B) C ; drop : forall {A B C}, term B C -> term (A * B) C }. Structure Algebra := Pack { domain :> Ty -> Ty -> Type; class_of : class domain }. Arguments Pack : clear implicits. Module Combinators. Definition iden {A} {alg : Algebra} : alg A A := iden (class_of alg). Definition comp {A B C} {alg : Algebra} : alg A B -> alg B C -> alg A C := comp (class_of alg). Definition unit {A} {alg : Algebra} : alg A Unit := unit (class_of alg). Definition injl {A B C} {alg : Algebra} : alg A B -> alg A (B + C) := injl (class_of alg). Definition injr {A B C} {alg : Algebra} : alg A C -> alg A (B + C) := injr (class_of alg). Definition case {A B C D} {alg : Algebra} : alg (A * C) D -> alg (B * C) D -> alg ((A + B) * C) D := case (class_of alg). Definition pair {A B C} {alg : Algebra} : alg A B -> alg A C -> alg A (B * C) := pair (class_of alg). Definition take {A B C} {alg : Algebra} : alg A C -> alg (A * B) C := take (class_of alg). Definition drop {A B C} {alg : Algebra} : alg B C -> alg (A * B) C := drop (class_of alg). Definition elimS {A B C D} {alg : Algebra} (r : alg A (B + C)) (s : alg B D) (t : alg C D) : alg A D := comp (pair r unit) (case (take s) (take t)). Definition copair {A B C} {alg : Algebra} : alg A C -> alg B C -> alg (A + B) C := elimS iden. Definition swapS {A B} {alg : Algebra} : alg (A + B) (B + A) := copair (injr iden) (injl iden). Definition swapP {A B} {alg : Algebra} : alg (A * B) (B * A) := pair (drop iden) (take iden). Notation "s &&& t" := (pair s t) (at level 70, right associativity) : term_scope. Notation "s >>> t" := (comp s t) (at level 90, right associativity) : term_scope. Notation "'H'" := iden : term_scope. Notation "'O' x" := (take x) (at level 0, right associativity) : term_scope. Notation "'I' x" := (drop x) (at level 0, right associativity) : term_scope. End Combinators. Module Parametric. Import Combinators. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { _ : forall A, rel iden (@iden A _) ; _ : forall A B C s1 s2 t1 t2 (Hs : rel s1 s2) (Ht : rel t1 t2), rel (comp s1 t1) (@comp A B C _ s2 t2) ; _ : forall A, rel unit (@unit A _) ; _ : forall A B C t1 t2 (Ht : rel t1 t2), rel (injl t1) (@injl A B C _ t2) ; _ : forall A B C t1 t2 (Ht : rel t1 t2), rel (injr t1) (@injr A B C _ t2) ; _ : forall A B C D s1 s2 t1 t2 (Hs : rel s1 s2) (Ht : rel t1 t2), rel (case s1 t1) (@case A B C D _ s2 t2) ; _ : forall A B C s1 s2 t1 t2 (Hs : rel s1 s2) (Ht : rel t1 t2), rel (pair s1 t1) (@pair A B C _ s2 t2) ; _ : forall A B C t1 t2 (Ht : rel t1 t2), rel (take t1) (@take A B C _ t2) ; _ : forall A B C t1 t2 (Ht : rel t1 t2), rel (drop t1) (@drop A B C _ t2) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall {alg : Algebra}, alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B x y. Definition Parametric {A B} (x : forall {alg : Algebra}, alg A B) : Prop := Reynolds (@x) (@x). End Reynolds. Section CoreTerm. Import Combinators. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Fixpoint eval {A B} (x : Simplicity.Core.Term A B) {alg : Algebra} : alg A B := match x in Simplicity.Core.Term A B return alg A B with | Simplicity.Core.iden => iden | Simplicity.Core.comp s t => comp (eval s) (eval t) | Simplicity.Core.unit => unit | Simplicity.Core.injl t => injl (eval t) | Simplicity.Core.injr t => injr (eval t) | Simplicity.Core.case s t => case (eval s) (eval t) | Simplicity.Core.pair s t => pair (eval s) (eval t) | Simplicity.Core.take t => take (eval t) | Simplicity.Core.drop t => drop (eval t) end. Lemma eval_Parametric {A B} (x : Simplicity.Core.Term A B) : Parametric (@eval A B x). Proof. intros alg1 alg2 [R []]. induction x; simpl; auto. Qed. Definition Term_mixin : class Simplicity.Core.Term := {| Core.iden := @Simplicity.Core.iden ; Core.comp := @Simplicity.Core.comp ; Core.unit := @Simplicity.Core.unit ; Core.injl := @Simplicity.Core.injl ; Core.injr := @Simplicity.Core.injr ; Core.case := @Simplicity.Core.case ; Core.pair := @Simplicity.Core.pair ; Core.take := @Simplicity.Core.take ; Core.drop := @Simplicity.Core.drop |}. Canonical Structure Term : Algebra := Pack Simplicity.Core.Term Term_mixin. Lemma eval_Term {A B} (x : Simplicity.Core.Term A B) : eval x = x. Proof. induction x; cbn; congruence. Qed. Lemma term_eval {A B} (x : forall alg : Algebra, alg A B) (Hx : Parametric x) (alg : Algebra) : x alg = eval (x Term). Proof. refine (Hx _ _ (@Parametric.Pack Term alg (fun a b x y => y = eval x) _)); constructor; intros; simpl; congruence. Qed. End CoreTerm. End Core. Export Core.Combinators. Coercion Core.domain : Core.Algebra >-> Funclass. Coercion Core.Parametric.rel : Core.Parametric.Rel >-> Funclass. Canonical Structure Core.Term. Lemma iden_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A} : R A A iden iden. Proof. destruct R as [R []]. cbn; auto. Qed. Lemma comp_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} s1 s2 t1 t2 : R A B s1 s2 -> R B C t1 t2 -> R A C (comp s1 t1) (comp s2 t2). Proof. destruct R as [R []]. cbn; auto. Qed. Lemma unit_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A} : R A Unit unit unit. Proof. destruct R as [R []]. cbn; auto. Qed. Lemma injl_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} t1 t2 : R A B t1 t2 -> R A (B + C) (injl t1) (injl t2). Proof. destruct R as [R []]. cbn; auto. Qed. Lemma injr_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} t1 t2 : R A C t1 t2 -> R A (B + C) (injr t1) (injr t2). Proof. destruct R as [R []]. cbn; auto. Qed. Lemma case_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C D} s1 s2 t1 t2 : R (A * C) D s1 s2 -> R (B * C) D t1 t2 -> R ((A + B) * C) D (case s1 t1) (case s2 t2). Proof. destruct R as [R []]. cbn; auto. Qed. Lemma pair_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} s1 s2 t1 t2 : R A B s1 s2 -> R A C t1 t2 -> R A (B * C) (pair s1 t1) (pair s2 t2). Proof. destruct R as [R []]. cbn; auto. Qed. Lemma take_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} t1 t2 : R A C t1 t2 -> R (A * B) C (take t1) (take t2). Proof. destruct R as [R []]. cbn; auto. Qed. Lemma drop_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} t1 t2 : R B C t1 t2 -> R (A * B) C (drop t1) (drop t2). Proof. destruct R as [R []]. cbn; auto. Qed. Create HintDb parametricity discriminated. #[export] Hint Immediate iden_Parametric : parametricity. #[export] Hint Resolve comp_Parametric : parametricity. #[export] Hint Immediate unit_Parametric : parametricity. #[export] Hint Resolve injl_Parametric : parametricity. #[export] Hint Resolve injr_Parametric : parametricity. #[export] Hint Resolve case_Parametric : parametricity. #[export] Hint Resolve pair_Parametric : parametricity. #[export] Hint Resolve take_Parametric : parametricity. #[export] Hint Resolve drop_Parametric : parametricity. Lemma elimS_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C D} r1 r2 s1 s2 t1 t2 : R A (B + C) r1 r2 -> R B D s1 s2 -> R C D t1 t2 -> R A D (elimS r1 s1 t1) (elimS r2 s2 t2). Proof. unfold elimS. auto with parametricity. Qed. #[export] Hint Resolve elimS_Parametric : parametricity. Lemma copair_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B C} s1 s2 t1 t2 : R A C s1 s2 -> R B C t1 t2 -> R (A + B) C (copair s1 t1) (copair s2 t2). Proof. unfold copair. auto with parametricity. Qed. #[export] Hint Resolve copair_Parametric : parametricity. Lemma swapS_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B} : R (A + B) (B + A) swapS swapS. Proof. unfold swapS. auto with parametricity. Qed. #[export] Hint Resolve swapS_Parametric : parametricity. Lemma swapP_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B} : R (A * B) (B * A) swapP swapP. Proof. unfold swapP. auto with parametricity. Qed. #[export] Hint Resolve swapP_Parametric : parametricity. Section CoreSem. Definition FunSem_mixin : Core.class Arrow := {| Core.iden A a := a ; Core.comp A B C s t (a : A) := t (s a) ; Core.unit A _ := tt ; Core.injl A B C t a := inl (t a) ; Core.injr A B C t a := inr (t a) ; Core.case A B C D s t p := let (ab, c) := p in match ab with | inl a => s (a, c) | inr b => t (b, c) end ; Core.pair A B C s t a := (s a, t a) ; Core.take A B C t ab := t (fst ab) ; Core.drop A B C t ab := t (snd ab) |}. Definition CoreSem_mixin (M : CIMonad) : Core.class (Kleisli M) := {| Core.iden A a := eta a ; Core.comp A B C s t (a : A) := (t <-< s) a ; Core.unit A _ := eta tt ; Core.injl A B C t a := map inl (t a) ; Core.injr A B C t a := map inr (t a) ; Core.case A B C D s t p := let (ab, c) := p in match ab with | inl a => s (a, c) | inr b => t (b, c) end ; Core.pair A B C s t a := phi (s a) (t a) ; Core.take A B C t ab := t (fst ab) ; Core.drop A B C t ab := t (snd ab) |}. End CoreSem. Canonical Structure CoreFunSem : Core.Algebra := Core.Pack Arrow FunSem_mixin. Canonical Structure CoreSem (M : CIMonad) : Core.Algebra := Core.Pack (Kleisli M) (CoreSem_mixin M). Notation "|[ x ]|^ M" := (x : Kleisli M _ _) (at level 0, M at level 0) : semantic_scope. Notation "|[ x ]|" := (x : Arrow _ _) : semantic_scope. Local Open Scope semantic_scope. Local Open Scope monad_scope. Lemma CoreFunSem_correct {A B} {t : forall {alg : Core.Algebra}, alg A B} (Ht : Core.Parametric (@t)) : forall a, Simplicity.Core.eval t a = |[ t ]| a. Proof. set (R A B (x : Simplicity.Core.Term A B) (y : Arrow A B) := forall a, Simplicity.Core.eval x a = |[ y ]| a). refine (Ht _ _ (Core.Parametric.Pack (_ : Core.Parametric.class R))). constructor; unfold R; clear; intros; cbn; try destruct a as [[a|b] c]; try rewrite Hs; try rewrite Ht; try reflexivity. Qed. Lemma CoreSem_initial {M : CIMonad} {A B} {t : forall {alg : Core.Algebra}, alg A B} (Ht : Core.Parametric (@t)) : forall a, |[ t ]|^M a = eta (|[ t ]| a). Proof. set (R A B (x : Kleisli M A B) (y : Arrow A B) := forall a, |[ x ]|^M a = eta (|[ y ]| a)). refine (Ht _ _ (Core.Parametric.Pack (_ : Core.Parametric.class R))). constructor; unfold R; clear; intros; cbn. - reflexivity. - rewrite kleisli_comp_def, Hs, <- kleisli_comp_def. rewrite kleisli_compr; apply Ht. - reflexivity. - rewrite Ht; apply eta_natural. - rewrite Ht; apply eta_natural. - destruct a as [[a|b] c]; [apply Hs|apply Ht]. - rewrite Hs, Ht. apply phi_eta. - apply Ht. - apply Ht. Qed. Section Generic. Fixpoint scribe {A B : Ty} : B -> forall {alg : Core.Algebra}, alg A B := match B with | Unit => fun _ _ => unit | Sum BL BR => fun b => match b with | inl l => fun _ => injl (scribe l) | inr r => fun _ => injr (scribe r) end | Prod B1 B2 => fun b _ => pair (scribe (fst b)) (scribe (snd b)) end. Lemma scribe_correct {A B : Ty} (a : A) (b : B) : |[scribe b]| a = b. Proof. induction B;[destruct b as [] | destruct b as [b|b] | destruct b as [b0 b1]]; cbn; try rewrite IHB1; try rewrite IHB2; reflexivity. Qed. End Generic. Lemma scribe_Parametric {alg1 alg2 : Core.Algebra} (R : Core.Parametric.Rel alg1 alg2) {A B : Ty} (b : B) : R A B (scribe b) (scribe b). Proof. induction B;[|destruct b as [b|b] |]; cbn; auto with parametricity. Qed. #[export] Hint Immediate scribe_Parametric : parametricity. Module Assertion. Record mixin (term : Ty -> Ty -> Type) := Mixin { assertl : forall {A B C D}, term (A * C) D -> hash256 -> term ((A + B) * C) D ; assertr : forall {A B C D}, hash256 -> term (B * C) D -> term ((A + B) * C) D ; fail : forall {A B}, (hash256 * hash256) -> term A B }. Record class (term : Ty -> Ty -> Type) := Class { base :> Core.class term ; ext :> mixin term }. Structure Algebra := _Pack { domain :> Ty -> Ty -> Type; class_of : class domain }. Definition packager dom (a0 : mixin dom) := [find c | Core.domain c ~ dom | "is not a Core algebra" ] [find cc | Core.class_of c ~ cc ] [find a | a ~ a0 | "is not the right mixin" ] @_Pack dom (@Class dom cc a). Notation Pack dom a := (@packager dom a _ id _ id _ id). Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Module Combinators. Definition assertl {A B C D} {alg : Algebra} : alg (A * C) D -> hash256 -> alg ((A + B) * C) D := assertl (class_of alg). Definition assertr {A B C D} {alg : Algebra} : hash256 -> alg (B * C) D -> alg ((A + B) * C) D := assertr (class_of alg). Definition fail {A B} {alg : Algebra} : (hash256 * hash256) -> alg A B := fail (class_of alg). End Combinators. Module Parametric. Import Combinators. Record mixin {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { _ : forall A B C D s1 s2 th, rel s1 s2 -> rel (assertl s1 th) (@assertl A B C D _ s2 th) ; _ : forall A B C D sh t1 t2, rel t1 t2 -> rel (assertr sh t1) (@assertr A B C D _ sh t2) ; _ : forall A B hh, rel (fail hh) (@fail A B _ hh) }. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> Core.Parametric.class (@rel) ; ext :> mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. End Assertion. Export Assertion.Combinators. Coercion Assertion.domain : Assertion.Algebra >-> Funclass. Coercion Assertion.toCore : Assertion.Algebra >-> Core.Algebra. Coercion Assertion.base : Assertion.class >-> Core.class. Coercion Assertion.ext : Assertion.class >-> Assertion.mixin. Coercion Assertion.Parametric.rel : Assertion.Parametric.Rel >-> Funclass. Canonical Structure Assertion.toCore. Lemma assertl_Parametric {alg1 alg2 : Assertion.Algebra} (R : Assertion.Parametric.Rel alg1 alg2) {A B C D} s1 s2 th : R (A * C) D s1 s2 -> R ((A + B) * C) D (assertl s1 th) (assertl s2 th). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. Lemma assertr_Parametric {alg1 alg2 : Assertion.Algebra} (R : Assertion.Parametric.Rel alg1 alg2) {A B C D} sh t1 t2 : R (B * C) D t1 t2 -> R ((A + B) * C) D (assertr sh t1) (assertr sh t2). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. Lemma fail_Parametric {alg1 alg2 : Assertion.Algebra} (R : Assertion.Parametric.Rel alg1 alg2) {A B} hh : R A B (fail hh) (fail hh). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. #[export] Hint Resolve assertl_Parametric : parametricity. #[export] Hint Resolve assertr_Parametric : parametricity. #[export] Hint Immediate fail_Parametric : parametricity. Section AssertionSem. Definition AssertionSem_mixin (M : CIMonadZero) : Assertion.mixin (Kleisli M) := {| Assertion.assertl A B C D s _ (p : tySem ((A + B) * C)):= let (ab, c) := p in match ab with | inl a => s (a, c) | inr b => mzero end ; Assertion.assertr A B C D _ t p := let (ab, c) := p in match ab with | inl a => mzero | inr b => t (b, c) end ; Assertion.fail A B _ := kzero |}. End AssertionSem. Canonical Structure AssertionSem (M : CIMonadZero) : Assertion.Algebra := Assertion.Pack (Kleisli M) (AssertionSem_mixin M). Lemma AssertionSem_initial {M : CIMonadZero} {A B} {t : forall {alg : Assertion.Algebra}, alg A B} (Ht : Assertion.Parametric (@t)) : forall (a : A), |[ t ]|^M a = optionZero (|[ t ]|^option a). Proof. set (R := fun A B (x : AssertionSem M A B) (y : AssertionSem option_Monad_Zero A B) => forall a : A, x a = optionZero (y a)). refine (Ht _ _ (Assertion.Parametric.Pack (_ : Assertion.Parametric.class R))); repeat constructor; unfold R; clear; try reflexivity; cbn. - intros A B C s1 s2 t1 t2 Hs Ht a. symmetry; rewrite kleisli_comp_def. rewrite optionZero_mu, optionZero_natural, map_comp, <- optionZero_natural, <- Hs. erewrite map_ext;[|intros;symmetry;apply Ht]. rewrite <- kleisli_comp_def. reflexivity. - intros A B C t1 t2 Ht a. rewrite Ht; apply optionZero_natural. - intros A B C t1 t2 Ht a. rewrite Ht; apply optionZero_natural. - intros A B C D s1 s2 t1 t2 Hs Ht [[a|b] c]; [apply Hs|apply Ht]. - intros A B C s1 s2 t1 t2 Hs Ht a. rewrite Hs, Ht. symmetry; apply optionZero_phi. - intros A B C t1 t2 Ht a. apply Ht. - intros A B C t1 t2 Ht a. apply Ht. - intros A B C D s1 s2 h Hs [[a|b] c]; [apply Hs|reflexivity]. - intros A B C D h t1 t2 Ht [[a|b] c]; [reflexivity|apply Ht]. Qed. Module Witness. Record mixin (term : Ty -> Ty -> Type) := Mixin { witness : forall {A B : Ty}, B -> term A B }. Record class (term : Ty -> Ty -> Type) := Class { base :> Core.class term ; ext :> mixin term }. Structure Algebra := _Pack { domain :> Ty -> Ty -> Type; class_of : class domain }. Definition packager dom (a0 : mixin dom) := [find c | Core.domain c ~ dom | "is not a Core algebra" ] [find cc | Core.class_of c ~ cc ] [find a | a ~ a0 | "is not the right mixin" ] @_Pack dom (@Class dom cc a). Notation Pack dom a := (@packager dom a _ id _ id _ id). Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Module Combinators. Definition witness {A B : Ty} {alg : Algebra} : B -> alg A B := witness (class_of alg). End Combinators. Module Parametric. Import Combinators. Record mixin {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { _ : forall A B b, rel (witness b) (@witness A B _ b) }. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> Core.Parametric.class (@rel) ; ext :> mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. End Witness. Export Witness.Combinators. Coercion Witness.domain : Witness.Algebra >-> Funclass. Coercion Witness.toCore : Witness.Algebra >-> Core.Algebra. Coercion Witness.base : Witness.class >-> Core.class. Coercion Witness.ext : Witness.class >-> Witness.mixin. Coercion Witness.Parametric.rel : Witness.Parametric.Rel >-> Funclass. Canonical Structure Witness.toCore. Lemma witness_Parametric {alg1 alg2 : Witness.Algebra} (R : Witness.Parametric.Rel alg1 alg2) {A B} b : R A B (witness b) (witness b). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. #[export] Hint Immediate witness_Parametric : parametricity. Section WitnessSem. Definition WitnessFunSem_mixin : Witness.mixin Arrow := {| Witness.witness A B b a := b |}. Definition WitnessSem_mixin (M : CIMonad) : Witness.mixin (Kleisli M) := {| Witness.witness A B b a := eta b |}. End WitnessSem. Canonical Structure WitnessFunSem : Witness.Algebra := Witness.Pack Arrow WitnessFunSem_mixin. Canonical Structure WitnessSem (M : CIMonad) : Witness.Algebra := Witness.Pack (Kleisli M) (WitnessSem_mixin M). Lemma WitnessSem_initial {M : CIMonad} {A B} {t : forall {alg : Witness.Algebra}, alg A B} (Ht : Witness.Parametric (@t)) : forall a, |[ t ]|^M a = eta (|[ t ]| a). Proof. set (R A B (x : Kleisli M A B) (y : Arrow A B) := forall a, |[ x ]|^M a = eta (|[ y ]| a)). refine (Ht _ _ (Witness.Parametric.Pack (_ : Witness.Parametric.class R))). do 2 constructor; unfold R; clear; intros; cbn. - reflexivity. - rewrite kleisli_comp_def, Hs, <- kleisli_comp_def. rewrite kleisli_compr; apply Ht. - reflexivity. - rewrite Ht; apply eta_natural. - rewrite Ht; apply eta_natural. - destruct a as [[a|b] c]; [apply Hs|apply Ht]. - rewrite Hs, Ht. apply phi_eta. - apply Ht. - apply Ht. - reflexivity. Qed. Module AssertionWitness. Record class (term : Ty -> Ty -> Type) := Class { base :> Assertion.class term ; ext :> Witness.mixin term }. Definition base2 term (c : class term) : Witness.class term := Witness.Class (base c) (ext c). Structure Algebra := _Pack { domain :> Ty -> Ty -> Type; class_of : class domain }. Definition packager dom := [find a | Assertion.domain a ~ dom | "is not a Assertion algebra" ] [find ac | Assertion.class_of a ~ ac ] [find w | Witness.domain w ~ dom | "is not a Witness algebra" ] [find wm | Witness.ext (Witness.class_of w) ~ wm ] @_Pack dom (@Class dom ac wm). Notation Pack dom := (@packager dom _ id _ id _ id _ id). Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toAssertion (alg : Algebra) : Assertion.Algebra := Assertion.Pack alg (class_of alg). Canonical Structure toWitness (alg : Algebra) : Witness.Algebra := Witness.Pack alg (class_of alg). Module Parametric. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> Assertion.Parametric.class (@rel) ; ext :> Witness.Parametric.mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. End AssertionWitness. Coercion AssertionWitness.domain : AssertionWitness.Algebra >-> Funclass. Coercion AssertionWitness.toAssertion : AssertionWitness.Algebra >-> Assertion.Algebra. Coercion AssertionWitness.toWitness : AssertionWitness.Algebra >-> Witness.Algebra. Coercion AssertionWitness.base : AssertionWitness.class >-> Assertion.class. Coercion AssertionWitness.base2 : AssertionWitness.class >-> Witness.class. Coercion AssertionWitness.Parametric.rel : AssertionWitness.Parametric.Rel >-> Funclass. Canonical Structure AssertionWitness.toCore. Canonical Structure AssertionWitness.toAssertion. Canonical Structure AssertionWitness.toWitness. Canonical Structure AssertionWitnessSem (M : CIMonadZero) : AssertionWitness.Algebra := AssertionWitness.Pack (Kleisli M). Lemma AssertionWitnessSem_initial {M : CIMonadZero} {A B} {t : forall {alg : AssertionWitness.Algebra}, alg A B} (Ht : AssertionWitness.Parametric (@t)) : forall (a : A), |[ t ]|^M a = optionZero (|[ t ]|^option a). Proof. set (R := fun A B (x : AssertionSem M A B) (y : AssertionSem option_Monad_Zero A B) => forall a : A, x a = optionZero (y a)). refine (Ht _ _ (AssertionWitness.Parametric.Pack (_ : AssertionWitness.Parametric.class R))). repeat constructor; unfold R; clear; try reflexivity; cbn. - intros A B C s1 s2 t1 t2 Hs Ht a. symmetry; rewrite kleisli_comp_def. rewrite optionZero_mu, optionZero_natural, map_comp, <- optionZero_natural, <- Hs. erewrite map_ext;[|intros;symmetry;apply Ht]. rewrite <- kleisli_comp_def. reflexivity. - intros A B C t1 t2 Ht a. rewrite Ht; apply optionZero_natural. - intros A B C t1 t2 Ht a. rewrite Ht; apply optionZero_natural. - intros A B C D s1 s2 t1 t2 Hs Ht [[a|b] c]; [apply Hs|apply Ht]. - intros A B C s1 s2 t1 t2 Hs Ht a. rewrite Hs, Ht. symmetry; apply optionZero_phi. - intros A B C t1 t2 Ht a. apply Ht. - intros A B C t1 t2 Ht a. apply Ht. - intros A B C D s1 s2 h Hs [[a|b] c]; [apply Hs|reflexivity]. - intros A B C D h t1 t2 Ht [[a|b] c]; [reflexivity|apply Ht]. Qed. ================================================ FILE: Coq/Simplicity/Bit.v ================================================ Require Import Simplicity.Ty. Require Import Simplicity.Alg. Set Implicit Arguments. Local Open Scope ty_scope. Local Open Scope term_scope. Notation Bit := (Unit + Unit). Notation "'Bit.zero'" := (inl tt). Notation "'Bit.one'" := (inr tt). Definition toBool (b : Bit) := match b with | inl _ => false | inr _ => true end. Definition fromBool (b : bool) := if b then Bit.one else Bit.zero. Section Definitions. Definition false {A} {term : Core.Algebra} : term A Bit := injl unit. Definition true {A} {term : Core.Algebra} : term A Bit := injr unit. Definition cond {A B} {term : Core.Algebra} (thn els : term A B) : term (Bit * A) B := case (drop els) (drop thn). Definition ch {A} {term : Core.Algebra} : term (Bit * (A * A)) A := cond (O H) (I H). Definition not {A} {term : Core.Algebra} (t : term A Bit) : term A Bit := t &&& unit >>> cond false true. Definition and {A} {term : Core.Algebra} (s t : term A Bit) : term A Bit := s &&& iden >>> cond t false. Definition or {A} {term : Core.Algebra} (s t : term A Bit) : term A Bit := s &&& iden >>> cond true t. Definition xor3 {term : Core.Algebra} : term (Bit * (Bit * Bit)) Bit := cond (cond iden (not iden)) (cond (not iden) iden). Definition maj {term : Core.Algebra} : term (Bit * (Bit * Bit)) Bit := cond (cond true iden) (cond iden false). End Definitions. Lemma false_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} : R A Bit false false. Proof. unfold false. auto with parametricity. Qed. #[export] Hint Immediate false_Parametric : parametricity. Lemma true_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} : R A Bit true true. Proof. unfold true. auto with parametricity. Qed. #[export] Hint Immediate true_Parametric : parametricity. Lemma cond_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A B} s1 s2 t1 t2 : R A B s1 s2 -> R A B t1 t2 -> R (Bit * A) B (cond s1 t1) (cond s2 t2). Proof. unfold cond. auto with parametricity. Qed. #[export] Hint Resolve cond_Parametric : parametricity. Lemma ch_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} : R _ A ch ch. Proof. unfold ch. auto with parametricity. Qed. #[export] Hint Immediate ch_Parametric : parametricity. Lemma not_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} t1 t2 : R A Bit t1 t2 -> R A Bit (not t1) (not t2). Proof. unfold not. auto with parametricity. Qed. #[export] Hint Resolve not_Parametric : parametricity. Lemma and_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} s1 s2 t1 t2 : R A Bit s1 s2 -> R A Bit t1 t2 -> R A Bit (and s1 t1) (and s2 t2). Proof. unfold and. auto with parametricity. Qed. #[export] Hint Resolve and_Parametric : parametricity. Lemma or_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} s1 s2 t1 t2 : R A Bit s1 s2 -> R A Bit t1 t2 -> R A Bit (or s1 t1) (or s2 t2). Proof. unfold or. auto with parametricity. Qed. #[export] Hint Resolve or_Parametric : parametricity. Lemma xor3_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ xor3 xor3. Proof. unfold xor3. auto with parametricity. Qed. #[export] Hint Immediate xor3_Parametric : parametricity. Lemma maj_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ maj maj. Proof. unfold maj. auto with parametricity. Qed. #[export] Hint Immediate maj_Parametric : parametricity. ================================================ FILE: Coq/Simplicity/BitMachine.v ================================================ Require Import PeanoNat. Require Import NArith. Require Import Simplicity.Util.List. Require Import Simplicity.Util.Thrist. Require Import Eqdep_dec. Set Primitive Projections. Set Implicit Arguments. Local Open Scope N_scope. Declare Scope mc_scope. Definition Cell := option bool. (* Write-only frames are append only. We represent the frame by, writeData, * the list of cells before the frame's cursor, and by writeEmpty, which * contains the number of undefined cells after the cursor. * * The writeData store the list of cells in reverse order! This is analogous to * the zipper used in ReadFrame below. *) Record WriteFrame := { writeData : list Cell ; writeEmpty : nat }. Definition writeSize wf := N.of_nat (length (writeData wf)) + N.of_nat (writeEmpty wf). Definition newWriteFrame n : WriteFrame := {| writeData := nil; writeEmpty := n |}. (* Note that fullWriteFrame take a list of cells in forward order and * transforms it into the reverse representation. *) Definition fullWriteFrame l : WriteFrame := {| writeData := rev l; writeEmpty := 0 |}. Lemma fullWriteFrame_size l : writeSize (fullWriteFrame l) = N.of_nat (length l). Proof. unfold writeSize; cbn. rewrite rev_length. ring. Qed. (* Read-only frames are represented in zipper format. The cells before the * cursor are stored in prevData in reverse order. The cells after the cursor * are stored in nextData in forward order. *) Record ReadFrame := { prevData : list Cell ; nextData : list Cell }. Definition readSize rf := N.of_nat (length (prevData rf)) + N.of_nat (length (nextData rf)). Definition setFrame l := {| prevData := nil; nextData := l |}. (* The full running state of the Bit Machine is captured by a list of inactive * read-only and write-only frames. The top of the two stacks are held in the * activeReadFrame and activeWriteFrame. This ensures that both stacks are * non-empty. *) Record RunState := { inactiveReadFrames : list ReadFrame ; activeReadFrame : ReadFrame ; activeWriteFrame : WriteFrame ; inactiveWriteFrames : list WriteFrame }. (* The state of the Bit Machine can either be a running state or a halted * state. *) Inductive State := | Halted : State | Running : RunState -> State. Coercion Running : RunState >-> State. Lemma State_dec (x y : State) : {x = y} + {x <> y}. Proof. repeat (decide equality). Qed. Record RunStateShape := { inactiveReadFrameSizes : list N ; activeReadFrameSize : N ; activeWriteFrameSize : N ; inactiveWriteFrameSizes : list N }. Inductive StateShape := | HaltedSS : StateShape | RunningSS : RunStateShape -> StateShape. Coercion RunningSS : RunStateShape >-> StateShape. Definition runStateShape s := {| inactiveReadFrameSizes := map readSize (inactiveReadFrames s) ; activeReadFrameSize := readSize (activeReadFrame s) ; activeWriteFrameSize := writeSize (activeWriteFrame s) ; inactiveWriteFrameSizes := map writeSize (inactiveWriteFrames s) |}. Definition stateShape s := match s with | Running s0 => RunningSS (runStateShape s0) | Halted => HaltedSS end. Definition stateShapeSize s := match s with | RunningSS s0 => N_sum (inactiveReadFrameSizes s0) + activeReadFrameSize s0 + activeWriteFrameSize s0 + N_sum (inactiveWriteFrameSizes s0) | HaltedSS => 0 end. Definition stateSize s := stateShapeSize (stateShape s). (* Logically, the state of the Bit Machine is commonly divided between the part * of the state that we are focused on and the rest of state. The focused part * consists of some fragment of data after the cursor in the read-only frame, * which contains the encoding of the input to some sub-expression in * Simplicity, and some fragment of data around the cursor in the write-only * frame, which contains the, partially written, output of some sub-expression. * * This focused part of the state is captured by the LocalState type. * The remainder of the state is captured by the Context type, and happens to * be isomorphic to the State type. The fillContext function combines the * LocalState with some context to produce a complete state. *) Definition Context := RunState. Definition emptyCtx : Context := {| inactiveReadFrames := nil ; activeReadFrame := setFrame nil ; activeWriteFrame := newWriteFrame 0 ; inactiveWriteFrames := nil |}. Record LocalState := { readLocalState : list Cell ; writeLocalState : WriteFrame }. Record LocalStateShape := { readLocalStateSize : N ; writeLocalStateSize : N }. Definition localStateShape ls := {| readLocalStateSize := N.of_nat (length (readLocalState ls)) ; writeLocalStateSize := writeSize (writeLocalState ls) |}. Definition localStateShapeSize ls := readLocalStateSize ls + writeLocalStateSize ls. Definition localStateSize ls := localStateShapeSize (localStateShape ls). Definition fillContext (ctx : Context) (h : LocalState) : RunState := {| inactiveReadFrames := inactiveReadFrames ctx ; activeReadFrame := {| prevData := prevData (activeReadFrame ctx) ; nextData := readLocalState h ++ nextData (activeReadFrame ctx) |} ; activeWriteFrame := {| writeData := writeData (writeLocalState h) ++ writeData (activeWriteFrame ctx) ; writeEmpty := writeEmpty (writeLocalState h) + writeEmpty (activeWriteFrame ctx) |} ; inactiveWriteFrames := inactiveWriteFrames ctx |}. Definition fillContextShape (ctx : RunStateShape) (h : LocalStateShape) : StateShape := {| inactiveReadFrameSizes := inactiveReadFrameSizes ctx ; activeReadFrameSize := activeReadFrameSize ctx + readLocalStateSize h ; activeWriteFrameSize := activeWriteFrameSize ctx + writeLocalStateSize h ; inactiveWriteFrameSizes := inactiveWriteFrameSizes ctx |}. Lemma fillContextShape_correct ctx h : stateShape (fillContext ctx h) = fillContextShape (runStateShape ctx) (localStateShape h). Proof. destruct ctx as [irf [prf nrf] awf iwf]. destruct h as [rl wl]. unfold stateShape, runStateShape, fillContextShape; simpl. repeat f_equal; [unfold readSize|unfold writeSize]; simpl; rewrite app_length; repeat rewrite Nat2N.inj_add; ring. Qed. (* Sometimes we need to focus in on part of the LocalState. We can divide the * LocalState into a localer state and its (relative) context. Both the * localer state and its context are isomorphic to the LocalState type and we * do not give them separate types. * We define appendLocalState to combine ls2, a LocalState representing the * localer state, with ls1, a LocalState representing its relative context. * Note that this append operation makes LocalState a monoid. *) Definition appendLocalState (ls1 ls2 : LocalState) : LocalState := {| readLocalState := readLocalState ls2 ++ readLocalState ls1 ; writeLocalState := {| writeData := writeData (writeLocalState ls2) ++ writeData (writeLocalState ls1) ; writeEmpty := writeEmpty (writeLocalState ls2) + writeEmpty (writeLocalState ls1) |} |}. (* The monoid for LocalState above makes fillContext into a (right) monoid * action on Contexts. *) Lemma context_action ctx ls1 ls2 : fillContext (fillContext ctx ls1) ls2 = fillContext ctx (appendLocalState ls1 ls2). Proof. unfold fillContext. cbn. repeat rewrite app_assoc. rewrite Nat.add_assoc. reflexivity. Qed. Definition fillReadFrame (ctx : Context) (h : ReadFrame) : RunState := {| inactiveReadFrames := inactiveReadFrames ctx ; activeReadFrame := {| prevData := prevData h ++ prevData (activeReadFrame ctx) ; nextData := nextData h ++ nextData (activeReadFrame ctx) |} ; activeWriteFrame := activeWriteFrame ctx ; inactiveWriteFrames := inactiveWriteFrames ctx |}. Definition fillReadFrameShape (ctx : RunStateShape) (h : N) : StateShape := {| inactiveReadFrameSizes := inactiveReadFrameSizes ctx ; activeReadFrameSize := activeReadFrameSize ctx + h ; activeWriteFrameSize := activeWriteFrameSize ctx ; inactiveWriteFrameSizes := inactiveWriteFrameSizes ctx |}. Lemma fillReadFrameShape_correct ctx h : stateShape (fillReadFrame ctx h) = fillReadFrameShape (runStateShape ctx) (readSize h). Proof. destruct ctx as [irf [prf nrf] awf iwf]. destruct h as [rl wl]. unfold stateShape, runStateShape, fillReadFrameShape; simpl. repeat f_equal. unfold readSize; simpl. repeat rewrite app_length, Nat2N.inj_add; ring. Qed. Module MachineCode. (* Although the types for the following instructions have the form of a * Proposition (i.e. they have at most one inhabitant) we put them in the Set * universe because we want to compute with the witness values. *) Module NewFrame. Inductive T n ctx : RunState -> Set := op : T n ctx {| inactiveReadFrames := inactiveReadFrames ctx ; activeReadFrame := activeReadFrame ctx ; activeWriteFrame := newWriteFrame n ; inactiveWriteFrames := activeWriteFrame ctx :: inactiveWriteFrames ctx |}. (* This isn't really needed, but we add it for completeness *) Definition chk n s0 : (forall s1, T n s0 s1 -> False)+{s1 : RunState & T n s0 s1}. right. econstructor. constructor. Defined. End NewFrame. Module MoveFrame. Inductive T : RunState -> RunState -> Set := op : forall l ctx, T {| inactiveReadFrames := inactiveReadFrames ctx ; activeReadFrame := activeReadFrame ctx ; activeWriteFrame := fullWriteFrame l ; inactiveWriteFrames := activeWriteFrame ctx :: inactiveWriteFrames ctx |} {| inactiveReadFrames := activeReadFrame ctx :: inactiveReadFrames ctx ; activeReadFrame := setFrame l ; activeWriteFrame := activeWriteFrame ctx ; inactiveWriteFrames := inactiveWriteFrames ctx |}. Definition chk s0 : (forall s1, T s0 s1 -> False)+{s1 : RunState & T s0 s1}. destruct s0 as [irf arf [l n] [|awf iwf]]. left;abstract (inversion 1). destruct n as [|n];[|left;abstract (inversion 1)]. pose (ctx := {| inactiveReadFrames := irf ; activeReadFrame := arf ; activeWriteFrame := awf ; inactiveWriteFrames := iwf |}). right. exists {| inactiveReadFrames := activeReadFrame ctx :: inactiveReadFrames ctx ; activeReadFrame := setFrame (rev l) ; activeWriteFrame := activeWriteFrame ctx ; inactiveWriteFrames := inactiveWriteFrames ctx |}. pattern l at 1. elim (rev_involutive l). exact (op _ ctx). Defined. End MoveFrame. Module DropFrame. Inductive T : RunState -> RunState -> Set := op : forall rf ctx, T {| inactiveReadFrames := activeReadFrame ctx :: inactiveReadFrames ctx ; activeReadFrame := rf ; activeWriteFrame := activeWriteFrame ctx ; inactiveWriteFrames := inactiveWriteFrames ctx |} ctx. Definition chk s0 : (forall s1, T s0 s1 -> False)+{s1 : RunState & T s0 s1}. destruct s0 as [[|arf irf] rf awf iwf]. left;abstract (inversion 1). right. pose (ctx := {| inactiveReadFrames := irf ; activeReadFrame := arf ; activeWriteFrame := awf ; inactiveWriteFrames := iwf |}). exists ctx. exact (op rf ctx). Defined. End DropFrame. Module Write. Inductive T b : RunState -> RunState -> Set := op : forall ctx, T b (fillContext ctx {| readLocalState := nil ; writeLocalState := newWriteFrame 1 |}) (fillContext ctx {| readLocalState := nil ; writeLocalState := fullWriteFrame (Some b :: nil) |}). Definition chk b s0 : (forall s1, T b s0 s1 -> False)+{s1 : RunState & T b s0 s1}. destruct s0 as [irf [rp rn] [wd [|we]] iwf]. left;abstract (inversion 1). right. eexists. exact (op _ {| inactiveReadFrames := irf ; activeReadFrame := {| prevData := rp; nextData := rn |} ; activeWriteFrame := {| writeData := wd; writeEmpty := we |} ; inactiveWriteFrames := iwf |}). Defined. End Write. Module Skip. Inductive T n : RunState -> RunState -> Set := op : forall ctx, T n (fillContext ctx {| readLocalState := nil ; writeLocalState := newWriteFrame n |}) (fillContext ctx {| readLocalState := nil ; writeLocalState := fullWriteFrame (repeat None n) |}). Definition chk n s0 : (forall s1, T n s0 s1 -> False)+{s1 : RunState & T n s0 s1}. destruct s0 as [irf [rp rn] [wd we] iwf]. generalize (Nat.leb_spec n we). destruct (n <=? we)%nat;intros H. right. pose (ctx := {| inactiveReadFrames := irf ; activeReadFrame := {| prevData := rp; nextData := rn |} ; activeWriteFrame := {| writeData := wd; writeEmpty := we - n |} ; inactiveWriteFrames := iwf |}). exists (fillContext ctx {| readLocalState := nil ; writeLocalState := fullWriteFrame (repeat None n) |}). replace we with (n + (we - n))%nat. exact (op _ ctx). abstract (rewrite Nat.add_comm; apply Nat.sub_add; inversion_clear H; assumption). left. abstract( inversion 1; apply (Nat.lt_nge we n); [inversion_clear H; assumption |replace <- we;auto with arith ]). Defined. End Skip. Module Copy. Inductive T n : RunState -> RunState -> Set := op : forall l ctx, length l = n -> T n (fillContext ctx {| readLocalState := l ; writeLocalState := newWriteFrame n |}) (fillContext ctx {| readLocalState := l ; writeLocalState := fullWriteFrame l |}). Definition chk n s0 : (forall s1, T n s0 s1 -> False)+{s1 : RunState & T n s0 s1}. destruct s0 as [irf [rp rn] [wd we] iwf]. generalize (Nat.leb_spec n we). destruct (n <=? we)%nat;intros Hwe. generalize (Nat.leb_spec n (length rn)). destruct (n <=? length rn)%nat;intros Hrn. right. pose (ctx := {| inactiveReadFrames := irf ; activeReadFrame := {| prevData := rp; nextData := skipn n rn |} ; activeWriteFrame := {| writeData := wd; writeEmpty := we - n |} ; inactiveWriteFrames := iwf |}). pose (l := firstn n rn). exists (fillContext ctx {| readLocalState := l ; writeLocalState := fullWriteFrame l |}). elim (firstn_skipn n rn). replace we with (n + (we - n))%nat. refine (op l ctx _). abstract (apply (firstn_length_le _); inversion_clear Hrn; assumption). abstract (rewrite Nat.add_comm; apply Nat.sub_add; inversion_clear Hwe; assumption). left. abstract ( inversion 1; apply (Nat.lt_nge (length rn) n); [inversion_clear Hrn; assumption |replace <- rn; replace <- n; rewrite app_length; auto with arith ]). left. abstract( inversion 1; apply (Nat.lt_nge we n); [inversion_clear Hwe; assumption |replace <- we;auto with arith ]). Defined. End Copy. Module Fwd. Inductive T n : RunState -> RunState -> Set := op : forall l ctx, length l = n -> T n (fillReadFrame ctx {| prevData := nil ; nextData := l |}) (fillReadFrame ctx {| prevData := rev l ; nextData := nil |}). Definition chk n s0 : (forall s1, T n s0 s1 -> False)+{s1 : RunState & T n s0 s1}. Proof. destruct s0 as [irf [rp rn] awf iwf]. generalize (Nat.leb_spec n (length rn)). destruct (n <=? length rn)%nat;intros Hrn. right. pose (ctx := {| inactiveReadFrames := irf ; activeReadFrame := {| prevData := rp; nextData := skipn n rn |} ; activeWriteFrame := awf ; inactiveWriteFrames := iwf |}). pose (l := firstn n rn). exists (fillReadFrame ctx {| prevData := rev l ; nextData := nil |}). elim (firstn_skipn n rn). refine (op l ctx _). abstract (apply (firstn_length_le _); inversion_clear Hrn; assumption). left. abstract ( inversion 1; apply (Nat.lt_nge (length rn) n); [inversion_clear Hrn; assumption |replace <- rn; replace <- n; rewrite app_length; auto with arith ]). Defined. End Fwd. Module Bwd. Inductive T n : RunState -> RunState -> Set := op : forall l ctx, length l = n -> T n (fillReadFrame ctx {| prevData := rev l ; nextData := nil |}) (fillReadFrame ctx {| prevData := nil ; nextData := l |}). Definition chk n s0 : (forall s1, T n s0 s1 -> False)+{s1 : RunState & T n s0 s1}. destruct s0 as [irf [rp rn] awf iwf]. generalize (Nat.leb_spec n (length rp)). destruct (n <=? length rp)%nat;intros Hrp. right. pose (ctx := {| inactiveReadFrames := irf ; activeReadFrame := {| prevData := skipn n rp; nextData := rn |} ; activeWriteFrame := awf ; inactiveWriteFrames := iwf |}). pose (l := rev (firstn n rp)). exists (fillReadFrame ctx {| prevData := nil ; nextData := l |}). elim (firstn_skipn n rp). elim (rev_involutive (firstn n rp)). refine (op l ctx _). abstract (unfold l; rewrite rev_length; apply (firstn_length_le _); inversion_clear Hrp; assumption). left. abstract( inversion 1; apply (Nat.lt_nge (length rp) n); [inversion_clear Hrp; assumption |replace <- rp; replace <- n; rewrite app_length, rev_length; auto with arith ]). Defined. End Bwd. (* This machine code type specifies all legal basic Bit Machine state * transitions. Notice that all legal state transitions begin in a RunState * and only Abort ends in a Halted state. *) Inductive T : State -> State -> Set := | NewFrame : forall s0 s1 n, NewFrame.T n s0 s1 -> T s0 s1 | MoveFrame : forall s0 s1, MoveFrame.T s0 s1 -> T s0 s1 | DropFrame : forall s0 s1, DropFrame.T s0 s1 -> T s0 s1 | Write : forall s0 s1 b, Write.T b s0 s1 -> T s0 s1 | Skip : forall s0 s1 n, Skip.T n s0 s1 -> T s0 s1 | Copy : forall s0 s1 n, Copy.T n s0 s1 -> T s0 s1 | Fwd : forall s0 s1 n, Fwd.T n s0 s1 -> T s0 s1 | Bwd : forall s0 s1 n, Bwd.T n s0 s1 -> T s0 s1 | Abort : forall (s0 : RunState), T s0 Halted. Arguments NewFrame [s0 s1]. Arguments MoveFrame [s0 s1]. Arguments DropFrame [s0 s1]. Arguments Write [s0 s1]. Arguments Skip [s0 s1]. Arguments Copy [s0 s1]. Arguments Fwd [s0 s1]. Arguments Bwd [s0 s1]. Arguments Abort {s0}. Definition newFrame n ctx : T _ _ := NewFrame _ (NewFrame.op n ctx). Definition moveFrame l ctx : T _ _ := MoveFrame (MoveFrame.op l ctx). Definition dropFrame l ctx : T _ _ := DropFrame (DropFrame.op l ctx). Definition write b ctx : T _ _ := Write _ (Write.op b ctx). Definition skip n ctx : T _ _ := Skip _ (Skip.op n ctx). Definition copy l ctx : T _ _ := Copy _ (Copy.op l ctx (refl_equal _)). Definition fwd l ctx : T _ _ := Fwd _ (Fwd.op l ctx (refl_equal _)). Definition bwd l ctx : T _ _ := Bwd _ (Bwd.op l ctx (refl_equal _)). End MachineCode. Local Open Scope thrist_scope. Notation "x ~~> y" := (MachineCode.T x y) (at level 70) : type_scope. Notation "x ->> y" := (Thrst MachineCode.T x y) (at level 70) : type_scope. (* When starting from the Halted state, the final state must also be * Halted, and the only trace possible is the empty trace. *) Inductive nop_trace s0 : forall s1, s0 ->> s1 -> Prop := nop_trace_empty : nop_trace []. Lemma runHalt {s} (tr : Halted ->> s): nop_trace tr. Proof. dependent inversion tr. constructor. inversion t. Qed. (* A Bit Machine programs takes an initial state, x, and tries to produce a * thrist of basic state transformations to some final state, y. However, a * program can potentially crash instead if it encounters an instruction that * cannot execute successfully from the given state. *) Definition Program := forall x : State, option { y : State & x ->> y }. (* runProgram lives in Prop so the witness, tr, isn't directly extractable. * However, the trace function below can be used to (indirectly) extract this * witness value. *) Definition runProgram (p : Program) s0 s1 := exists tr : s0 ->> s1, (p s0) = Some (existT _ _ tr). Notation "s0 >>- p ->> s1" := (runProgram p s0 s1) (at level 70, p at next level) : type_scope. Definition trace {p s0 s1} : s0 >>- p ->> s1 -> s0 ->> s1. unfold runProgram. intros Htr. destruct (p s0) as [[s1' Hs1]|]. replace s1 with s1'. exact Hs1. abstract (destruct Htr as [tr Htr]; inversion_clear Htr; reflexivity). abstract (elimtype False; destruct Htr as [tr Htr]; discriminate). Defined. Lemma trace_correct {p s0 s1} (tr : s0 >>- p ->> s1) : p s0 = Some (existT _ _ (trace tr)). Proof. revert tr. unfold trace, runProgram. destruct (p s0) as [[s1' Hs1]|]. intros tr. set (eq:= trace_subproof _). destruct eq; reflexivity. intros [tr Htr]. discriminate. Qed. (* The nop program has no instructions. *) Definition nop : Program := fun x => Some (existT _ x []). Lemma nop_correct s : s >>- nop ->> s. Proof. eexists. reflexivity. Qed. Lemma nop_complete s1 s2 : s1 >>- nop ->> s2 -> s1 = s2. Proof. intros [tr Htr]. unfold nop, runProgram in Htr. inversion_clear Htr. reflexivity. Qed. (* For each instruction we define a program that executes only that single * instruction. For each instruction we have a correctness lemma that * describes the result of the program when executed with an initial state * that is legal for that instruction. *) (* This function is used to build a program from a single instruction. * When in the Halted state we ignore the instruction and return the * empty trace. *) Definition makeProgram {T : RunState -> RunState -> Set} (inj : forall {s0 s1}, T s0 s1 -> s0 ~~> s1) (dec : forall s0, (forall s1, T s0 s1 -> False)+{s1 : RunState & T s0 s1}) : Program := fun s0 : State => match s0 with | Halted => Some (existT _ _ []) | Running s0' => match dec s0' with | inl _ => None | inr (existT _ s2 t) => Some (existT (fun y : State => s0' ->> y) s2 (inj t <| [])) end end. Inductive complete_spec (T : RunState -> RunState -> Set) : State -> State -> Set := | complete_step : forall s0 s1, T s0 s1 -> complete_spec T s0 s1 | complete_halted : complete_spec T Halted Halted. Lemma op_complete {T : RunState -> RunState -> Set} (inj : forall s0 s1, T s0 s1 -> s0 ~~> s1) (dec : forall s0, (forall s1, T s0 s1 -> False)+{s1 : RunState & T s0 s1}) s0 s1 : s0 >>- makeProgram inj dec ->> s1 -> complete_spec T s0 s1. unfold makeProgram, runProgram. destruct s0 as [|s0]. destruct s1 as [|s1]. intros _; constructor. abstract (intros Htr; elimtype False; destruct Htr; discriminate). destruct (dec s0) as [|[s1' Hs1]]. abstract (intros Htr; elimtype False; destruct Htr; discriminate). intros Htr. replace s1 with (Running s1'). constructor; assumption. abstract( destruct Htr as [tr Htr]; inversion Htr; auto ). Defined. Definition newFrame (n : nat) : Program := makeProgram (fun s0 s1 => @MachineCode.NewFrame s0 s1 n) (MachineCode.NewFrame.chk n). Lemma newFrame_correct n (s : RunState) : s >>- newFrame n ->> {| inactiveReadFrames := inactiveReadFrames s; activeReadFrame := activeReadFrame s; activeWriteFrame := newWriteFrame n; inactiveWriteFrames := activeWriteFrame s :: inactiveWriteFrames s |}. Proof. eexists. reflexivity. Qed. Definition newFrame_complete {n s0 s1} (tr : s0 >>- newFrame n ->> s1) : complete_spec (MachineCode.NewFrame.T n) s0 s1 := op_complete tr. Definition moveFrame : Program := makeProgram MachineCode.MoveFrame MachineCode.MoveFrame.chk. Lemma moveFrame_correct : forall l irf arf awf iwf, {| inactiveReadFrames := irf ; activeReadFrame := arf ; activeWriteFrame := fullWriteFrame l ; inactiveWriteFrames := awf :: iwf |} >>- moveFrame ->> {| inactiveReadFrames := arf :: irf ; activeReadFrame := setFrame l ; activeWriteFrame := awf ; inactiveWriteFrames := iwf |}. Proof. eexists. cbn. generalize (rev_involutive (rev l)). rewrite (rev_involutive l). apply K_dec_set. repeat decide equality. reflexivity. Qed. Definition moveFrame_complete {s0 s1} (tr : s0 >>- moveFrame ->> s1) : complete_spec MachineCode.MoveFrame.T s0 s1 := op_complete tr. Definition dropFrame : Program := makeProgram MachineCode.DropFrame MachineCode.DropFrame.chk. Lemma dropFrame_correct : forall rf s, {| inactiveReadFrames := activeReadFrame s :: inactiveReadFrames s ; activeReadFrame := rf ; activeWriteFrame := activeWriteFrame s ; inactiveWriteFrames := inactiveWriteFrames s |} >>- dropFrame ->> s. Proof. eexists. destruct s; reflexivity. Qed. Definition dropFrame_complete {s0 s1} (tr : s0 >>- dropFrame ->> s1) : complete_spec MachineCode.DropFrame.T s0 s1 := op_complete tr. Definition write (b : bool) : Program := makeProgram (fun s0 s1 => @MachineCode.Write s0 s1 b) (MachineCode.Write.chk b). Lemma write_correct : forall b ctx, fillContext ctx {| readLocalState := nil; writeLocalState := newWriteFrame 1 |} >>- write b ->> fillContext ctx {| readLocalState := nil; writeLocalState := fullWriteFrame (Some b :: nil) |}. Proof. eexists. reflexivity. Qed. Definition write_complete {b s0 s1} (tr : s0 >>- (write b) ->> s1) : complete_spec (MachineCode.Write.T b) s0 s1 := op_complete tr. Definition skip (n : nat) : Program := makeProgram (fun s0 s1 => @MachineCode.Skip s0 s1 n) (MachineCode.Skip.chk n). Lemma skip_correct : forall n ctx, fillContext ctx {| readLocalState := nil; writeLocalState := newWriteFrame n |} >>- skip n ->> fillContext ctx {| readLocalState := nil; writeLocalState := fullWriteFrame (repeat None n) |}. Proof. eexists. unfold skip, makeProgram, MachineCode.Skip.chk. cbn. set (H := Nat.leb_spec _ _). generalize H; clear H. rewrite (Compare_dec.leb_correct n (n + writeEmpty (activeWriteFrame ctx))%nat) by auto with arith. intros H. set (e := MachineCode.Skip.chk_subproof _). generalize e; clear e. replace (n + writeEmpty (activeWriteFrame ctx) - n)%nat with (writeEmpty (activeWriteFrame ctx)). apply (K_dec_set Nat.eq_dec); reflexivity. rewrite Nat.add_comm, Nat.add_sub; reflexivity. Qed. Definition skip_complete {n s0 s1} (tr : s0 >>- (skip n) ->> s1) : complete_spec (MachineCode.Skip.T n) s0 s1 := op_complete tr. Definition copy (n : nat) : Program := makeProgram (fun s0 s1 => @MachineCode.Copy s0 s1 n) (MachineCode.Copy.chk n). Lemma copy_correct : forall l ctx, fillContext ctx {| readLocalState := l; writeLocalState := newWriteFrame (length l) |} >>- copy (length l) ->> fillContext ctx {| readLocalState := l; writeLocalState := fullWriteFrame l |}. Proof. eexists. unfold copy, makeProgram, MachineCode.Copy.chk. cbn. set (H := Nat.leb_spec _ (_ + writeEmpty _)%nat). generalize H; clear H. rewrite (Compare_dec.leb_correct (length l) (length l + writeEmpty (activeWriteFrame ctx))%nat) by auto with arith. intros H. set (H1 := Nat.leb_spec _ _). generalize H1; clear H1. rewrite (Compare_dec.leb_correct (length l) (length (l ++ nextData (activeReadFrame ctx)))) by (rewrite app_length;auto with arith). intros H1. set (e := MachineCode.Copy.chk_subproof0 _). generalize e; clear e. replace (length l + writeEmpty (activeWriteFrame ctx) - length l)%nat with (writeEmpty (activeWriteFrame ctx)) by (rewrite Nat.add_comm, Nat.add_sub; reflexivity). apply (K_dec_set Nat.eq_dec). set (e := firstn_skipn _ _). generalize e; clear e. generalize (MachineCode.Copy.chk_subproof _ H1). rewrite firstn_app_3, skipn_app_3; intros e. apply (K_dec_set). repeat decide equality. revert e. apply (K_dec_set Nat.eq_dec). reflexivity. Qed. Definition copy_complete {n s0 s1} (tr : s0 >>- (copy n) ->> s1) : complete_spec (MachineCode.Copy.T n) s0 s1 := op_complete tr. Definition fwd (n : nat) : Program := makeProgram (fun s0 s1 => @MachineCode.Fwd s0 s1 n) (MachineCode.Fwd.chk n). Lemma fwd_correct : forall l ctx, fillReadFrame ctx {| prevData := nil; nextData := l |} >>- fwd (length l) ->> fillReadFrame ctx {| prevData := rev l; nextData := nil |}. Proof. eexists. unfold fwd, makeProgram, MachineCode.Fwd.chk; cbn. set (H := Nat.leb_spec _ _). generalize H; clear H. rewrite (Compare_dec.leb_correct (length l) (length (l ++ nextData (activeReadFrame ctx)))) by (rewrite app_length;auto with arith). intros H1. set (e := firstn_skipn _ _). generalize e; clear e. generalize (MachineCode.Fwd.chk_subproof _ H1). rewrite firstn_app_3, skipn_app_3; intros e. apply (K_dec_set). repeat decide equality. revert e. apply (K_dec_set Nat.eq_dec). reflexivity. Qed. Definition fwd_complete {n s0 s1} (tr : s0 >>- (fwd n) ->> s1) : complete_spec (MachineCode.Fwd.T n) s0 s1 := op_complete tr. Definition bwd (n : nat) : Program := makeProgram (fun s0 s1 => @MachineCode.Bwd s0 s1 n) (MachineCode.Bwd.chk n). Lemma bwd_correct : forall l ctx, fillReadFrame ctx {| prevData := rev l; nextData := nil |} >>- bwd (length l) ->> fillReadFrame ctx {| prevData := nil; nextData := l |}. Proof. eexists. unfold bwd, makeProgram, MachineCode.Bwd.chk; cbn. set (H := Nat.leb_spec _ _). generalize H; clear H. rewrite (Compare_dec.leb_correct (length l) (length (rev l ++ prevData (activeReadFrame ctx)))) by (rewrite app_length, rev_length;auto with arith). intros H1. set (e := firstn_skipn _ _). generalize e; clear e. generalize (MachineCode.Bwd.chk_subproof _ H1). rewrite <- rev_length. rewrite firstn_app_3, skipn_app_3; intros e. apply K_dec_set. repeat decide equality. set (e1 := rev_involutive (rev l)). generalize e1; clear e1. revert e; rewrite rev_involutive; intros e. apply K_dec_set. repeat decide equality. revert e. rewrite rev_length. apply (K_dec_set Nat.eq_dec). reflexivity. Qed. Definition bwd_complete {n s0 s1} (tr : s0 >>- (bwd n) ->> s1) : complete_spec (MachineCode.Bwd.T n) s0 s1 := op_complete tr. (* The basic instruction abort halts the machine. Of course if the machine * is already halted, it does nothing, like every other program starting from * the halted state. *) Definition abort : Program := fun s0 : State => Some match s0 with | Halted => existT _ _ [] | Running s0' => existT _ _ (MachineCode.Abort <| []) end. (* There are two combinators for building larger programs from smaller ones: * seq runs two programs, one after the other. choice runs one of two programs * depending on whether the Cell value under the cursor on the active read * frame is a 0 or a 1. *) Definition seq (p1 p2 : Program) : Program. intros x. destruct (p1 x) as [[y thr1]|];[|exact None]. destruct (p2 y) as [[z thr2]|];[|exact None]. exact (Some (existT _ _ (thr1 |><| thr2))). Defined. Notation "p1 ;;; p2" := (seq p1 p2) (at level 40, left associativity) : mc_scope. Definition choice (p1 p2 : Program) : Program. intros [|x];[exact (Some (existT _ _ []))|]. destruct (nextData (activeReadFrame x)) as [|[b|] tl];[exact None| |exact None]. exact ((if b then p2 else p1) x). Defined. Notation "p1 ||| p2" := (choice p1 p2) (at level 50, left associativity) : mc_scope. Local Open Scope mc_scope. Lemma seq_correct p q s0 s1 s2 : s0 >>- p ->> s1 -> s1 >>- q ->> s2 -> s0 >>- p ;;; q ->> s2. Proof. intros [trp Hp] [trq Hq]. eexists. unfold seq. rewrite Hp, Hq. reflexivity. Qed. Lemma seq_complete p q s0 s2 : s0 >>- p ;;; q ->> s2 -> { s1 | s0 >>- p ->> s1 & s1 >>- q ->> s2}. unfold seq, runProgram. destruct (p s0) as [[s1 tr1]|]. - intros Hpq. exists s1. exists tr1; reflexivity. abstract ( destruct (q s1) as [[s2' tr2]|]; [destruct Hpq as [tr Htr]; inversion Htr; exists tr2; reflexivity |destruct Hpq; discriminate ]). - abstract (intros Hpq; elimtype False; destruct Hpq; discriminate). Defined. Lemma choice_left_correct p q s0 s1 : head (nextData (activeReadFrame s0)) = Some (Some false) -> s0 >>- p ->> s1 -> s0 >>- p ||| q ->> s1. Proof. unfold choice, runProgram. destruct (nextData _) as [|[[|]|] tl]; try discriminate. auto. Qed. Lemma choice_right_correct p q s0 s1 : head (nextData (activeReadFrame s0)) = Some (Some true) -> s0 >>- q ->> s1 -> s0 >>- p ||| q ->> s1. Proof. unfold choice, runProgram. destruct (nextData _) as [|[[|]|] tl]; try discriminate. auto. Qed. Lemma choice_complete p q : forall (P : State -> State -> Type), (forall (s0 : RunState) s1 b, head (nextData (activeReadFrame s0)) = Some (Some b) -> s0 >>- (if b then q else p) ->> s1 -> P s0 s1) -> P Halted Halted -> forall s0 s1 : State, s0 >>- p ||| q ->> s1 -> P s0 s1. intros P H HHalted s0 s1. unfold choice, runProgram. destruct s0 as [|s0]. destruct s1. intros _; exact HHalted. try abstract (intros Hpq; elimtype False; destruct Hpq; discriminate). specialize (H s0 s1). destruct (nextData _) as [|[b|]]; try abstract (intros Hpq; elimtype False; destruct Hpq; discriminate). intros Htr. apply (H b). reflexivity. assumption. Defined. Lemma trace_left p q (s0 : RunState) s1 (trp : s0 >>- p ->> s1) (trpq : s0 >>- p ||| q ->> s1) : head (nextData (activeReadFrame s0)) = Some (Some false) -> trace trp = trace trpq. Proof. intros H. unfold trace, runProgram, choice in *. destruct (nextData _) as [|b];[discriminate|cbn in *]. revert trpq. inversion_clear H. destruct (p s0) as [[s1' Hs1]|];[|intros [ ]; discriminate]. destruct (trace_subproof trp). intros trpq. generalize (trace_subproof trpq). apply (K_dec_set State_dec). reflexivity. Qed. Lemma trace_right p q (s0 : RunState) s1 (trq : s0 >>- q ->> s1) (trpq : s0 >>- p ||| q ->> s1) : head (nextData (activeReadFrame s0)) = Some (Some true) -> trace trq = trace trpq. Proof. intros H. unfold trace, runProgram, choice in *. destruct (nextData _) as [|b];[discriminate|cbn in *]. revert trpq. inversion_clear H. destruct (q s0) as [[s1' Hs1]|];[|intros [ ]; discriminate]. destruct (trace_subproof trq). intros trpq. generalize (trace_subproof trpq). apply (K_dec_set State_dec). reflexivity. Qed. (* bump is notation for a program that is run where the active read frame's * cursor is temporarily advanced. *) Definition bump n p : Program := fwd n ;;; p ;;; bwd n. Lemma bump_correct p l ctx0 ctx1 : fillReadFrame ctx0 {| prevData := rev l; nextData := nil |} >>- p ->> fillReadFrame ctx1 {| prevData := rev l; nextData := nil |} -> fillReadFrame ctx0 {| prevData := nil; nextData := l |} >>- bump (length l) p ->> fillReadFrame ctx1 {| prevData := nil; nextData := l |}. Proof. intros Hp. unfold bump. repeat eapply seq_correct;[apply fwd_correct|exact Hp|apply bwd_correct]. Qed. Lemma bump_complete p l ctx0 ctx1 : fillReadFrame ctx0 {| prevData := nil; nextData := l |} >>- bump (length l) p ->> fillReadFrame ctx1 {| prevData := nil; nextData := l |} -> fillReadFrame ctx0 {| prevData := rev l; nextData := nil |} >>- p ->> fillReadFrame ctx1 {| prevData := rev l; nextData := nil |}. Proof. unfold bump. intros Hb. apply seq_complete in Hb. destruct Hb as [s2 Hb Hs2]. apply seq_complete in Hb. destruct Hb as [s1 Hs1 Hb]. replace (_ (fillReadFrame _ _)) with s1. replace (_ (fillReadFrame _ _)) with s2. assumption. clear - Hs2. pose (inv := bwd_complete Hs2);inversion_clear inv as [s0 s1 Hs01|]. destruct ctx1; inversion Hs01; unfold fillReadFrame; cbn. replace l0 with l in *. rewrite (app_inv_head _ _ _ H3). congruence. apply (f_equal (firstn (length l0))) in H3. rewrite firstn_app_3 in H3. replace (length l0) in H3. rewrite firstn_app_3 in H3. congruence. clear - Hs1. pose (inv := fwd_complete Hs1);inversion_clear inv as [s0 s1' Hs01|]. destruct ctx0; inversion Hs01; unfold fillReadFrame; cbn. replace l0 with l in *. rewrite (app_inv_head _ _ _ H2). congruence. apply (f_equal (firstn (length l0))) in H2. rewrite firstn_app_3 in H2. replace (length l0) in H2. rewrite firstn_app_3 in H2. congruence. Qed. Lemma stateShape_write b x y : x >>- write b ->> y -> stateShape x = stateShape y. Proof. intros Hxy. destruct (write_complete Hxy) as[x' y' Hxy'|];[|reflexivity]. inversion_clear Hxy'. do 2 rewrite fillContextShape_correct. reflexivity. Qed. Lemma stateShape_skip n x y : x >>- skip n ->> y -> stateShape x = stateShape y. Proof. intros Hxy. destruct (skip_complete Hxy) as [x' y' Hxy'|];[|reflexivity]. inversion_clear Hxy'. do 2 rewrite fillContextShape_correct. f_equal. unfold localStateShape; cbn. rewrite fullWriteFrame_size, repeat_length. reflexivity. Qed. Lemma stateShape_copy n x y : x >>- copy n ->> y -> stateShape x = stateShape y. Proof. intros Hxy. destruct (copy_complete Hxy) as [x' y' Hxy'|];[|reflexivity]. inversion_clear Hxy'. do 2 rewrite fillContextShape_correct. f_equal. unfold localStateShape; cbn. rewrite fullWriteFrame_size. congruence. Qed. Lemma stateShape_fwd n x y : x >>- fwd n ->> y -> stateShape x = stateShape y. Proof. intros Hxy. destruct (fwd_complete Hxy) as [x' y' Hxy'|];[|reflexivity]. inversion_clear Hxy'. do 2 rewrite fillReadFrameShape_correct. f_equal. unfold readSize; cbn. rewrite rev_length. ring. Qed. Lemma stateShape_bwd n x y : x >>- bwd n ->> y -> stateShape x = stateShape y. Proof. intros Hxy. destruct (bwd_complete Hxy) as [x' y' Hxy'|];[|reflexivity]. inversion_clear Hxy'. do 2 rewrite fillReadFrameShape_correct. f_equal. unfold readSize; cbn. rewrite rev_length. ring. Qed. Fixpoint maximumMemoryResidence {x y} (tr : x ->> y) : N := match tr with | Thrist.nil _ _ => stateSize y | Thrist.cons _ _ z _ _ tr0 => N.max (stateSize z) (maximumMemoryResidence tr0) end. Lemma MMR_app {x y z} (tr0 : x ->> y) (tr1 : y ->> z) : maximumMemoryResidence (tr0 |><| tr1) = N.max (maximumMemoryResidence tr0) (maximumMemoryResidence tr1). Proof. induction tr0;cbn. induction tr1;cbn;[|rewrite N.max_assoc];rewrite N.max_id; reflexivity. rewrite <- N.max_assoc, IHtr0. reflexivity. Qed. Lemma MMR_bounds {x y} (tr0 : x ->> y) : N.max (stateSize x) (stateSize y) <= maximumMemoryResidence tr0. Proof. apply N.max_lub. destruct tr0. reflexivity. apply N.le_max_l. induction tr0. reflexivity. etransitivity;[exact IHtr0|apply N.le_max_r]. Qed. Lemma MMR_newFrame n x y (tr : x >>- newFrame n ->> y) : maximumMemoryResidence (trace tr) = stateSize y. Proof. unfold runProgram in tr. unfold trace. unfold newFrame in *. destruct x as [|x];cbn;destruct (trace_subproof tr);[reflexivity|cbn;clear]. apply N.max_r. destruct x. unfold stateSize, stateShape, stateShapeSize. cbn. rewrite N.add_assoc. repeat apply N.add_le_mono_r. rewrite <- N.add_assoc. repeat apply N.add_le_mono_l. apply N.le_add_r. Qed. Lemma MMR_moveFrame x y (tr : x >>- moveFrame ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. unfold runProgram in tr. unfold trace. unfold moveFrame, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.MoveFrame.chk x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);cbn. apply N.max_l. unfold stateSize, stateShape, stateShapeSize. inversion Hy. cbn. rewrite fullWriteFrame_size. apply N.eq_le_incl. ring. Qed. Lemma MMR_dropFrame x y (tr : x >>- dropFrame ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. unfold runProgram in tr. unfold trace. unfold dropFrame, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.DropFrame.chk x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);cbn. apply N.max_l. unfold stateSize, stateShape, stateShapeSize. inversion Hy. cbn. repeat apply N.add_le_mono_r. rewrite N.add_comm, <- N.add_assoc. repeat apply N.add_le_mono_l. apply N.le_add_r. Qed. Lemma MMR_write b x y (tr : x >>- write b ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. assert (Hx := stateShape_write tr). unfold runProgram in tr. unfold trace. unfold write, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.Write.chk b x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);simpl. unfold stateSize. rewrite Hx. apply N.max_id. Qed. Lemma MMR_skip n x y (tr : x >>- skip n ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. assert (Hx := stateShape_skip tr). unfold runProgram in tr. unfold trace. unfold skip, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.Skip.chk n x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);simpl. unfold stateSize. rewrite Hx. apply N.max_id. Qed. Lemma MMR_copy n x y (tr : x >>- copy n ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. assert (Hx := stateShape_copy tr). unfold runProgram in tr. unfold trace. unfold copy, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.Copy.chk n x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);simpl. unfold stateSize. rewrite Hx. apply N.max_id. Qed. Lemma MMR_fwd n x y (tr : x >>- fwd n ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. assert (Hx := stateShape_fwd tr). unfold runProgram in tr. unfold trace. unfold fwd, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.Fwd.chk n x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);simpl. unfold stateSize. rewrite Hx. apply N.max_id. Qed. Lemma MMR_bwd n x y (tr : x >>- bwd n ->> y) : maximumMemoryResidence (trace tr) = stateSize x. Proof. assert (Hx := stateShape_bwd tr). unfold runProgram in tr. unfold trace. unfold bwd, makeProgram in *. destruct x as [|x];[cbn;destruct (trace_subproof tr);reflexivity|]. destruct (MachineCode.Bwd.chk n x) as [|[y' Hy]]in *. destruct tr; discriminate. destruct (trace_subproof tr);simpl. unfold stateSize. rewrite Hx. apply N.max_id. Qed. Lemma MMR_seq (p q : Program) x y z (trp : x >>- p ->> y) (trq : y >>- q ->> z) (trpq : x >>- p ;;; q ->> z) : maximumMemoryResidence (trace trpq) = N.max (maximumMemoryResidence (trace trp)) (maximumMemoryResidence (trace trq)). Proof. unfold runProgram in *. unfold trace. unfold seq in *. destruct (p x) as [[y' Hy]|];[|destruct trp; discriminate]. destruct (trace_subproof trp). destruct (q y') as [[z' Hz]|];[|destruct trq; discriminate]. destruct (trace_subproof trq). destruct (trace_subproof trpq). apply MMR_app. Qed. ================================================ FILE: Coq/Simplicity/Core.v ================================================ Require Import Simplicity.Ty. Set Implicit Arguments. Inductive Term : Ty -> Ty -> Set := | iden : forall {A}, Term A A | comp : forall {A B C}, Term A B -> Term B C -> Term A C | unit : forall {A}, Term A Unit | injl : forall {A B C}, Term A B -> Term A (Sum B C) | injr : forall {A B C}, Term A C -> Term A (Sum B C) | case : forall {A B C D}, Term (Prod A C) D -> Term (Prod B C) D -> Term (Prod (Sum A B) C) D | pair : forall {A B C}, Term A B -> Term A C -> Term A (Prod B C) | take : forall {A B C}, Term A C -> Term (Prod A B) C | drop : forall {A B C}, Term B C -> Term (Prod A B) C. Fixpoint eval {A B} (x : Term A B) : tySem A -> tySem B := match x in Term A B return tySem A -> tySem B with | iden => fun a => a | comp s t => fun a => eval t (eval s a) | unit => fun _ => tt | injl t => fun a => inl (eval t a) | injr t => fun a => inr (eval t a) | case s t => fun p => let (ab, c) := p in match ab with | inl a => eval s (a, c) | inr b => eval t (b, c) end | pair s t => fun a => (eval s a, eval t a) | take t => fun ab => eval t (fst ab) | drop t => fun ab => eval t (snd ab) end. Section Completeness. Fixpoint scribe {A B : Ty} : B -> Term A B := match B with | Unit => fun _ => unit | Sum BL BR => fun b => match b with | inl l => injl (scribe l) | inr r => injr (scribe r) end | Prod B1 B2 => fun b => pair (scribe (fst b)) (scribe (snd b)) end. Lemma scribe_correct (A B : Ty) (a : A) (b : B) : eval (scribe b) a = b. Proof. induction B. - destruct b; reflexivity. - destruct b as [b|b];cbn;f_equal;auto. - destruct b as [b0 b1];cbn;f_equal;auto. Qed. Fixpoint reifyProd {A B C : Ty} : (A -> Term B C) -> Term (Prod A B) C := match A with | Unit => fun f => drop (f tt) | Sum AL AR => fun f => case (reifyProd (fun al => f (inl al))) (reifyProd (fun ar => f (inr ar))) | Prod A1 A2 => fun f => comp (pair (take (take iden)) (pair (take (drop iden)) (drop iden))) (reifyProd (fun a1 => reifyProd (fun a2 => f (a1, a2)))) end. Lemma reifyProd_correct : forall (A B C : Ty) (f : A -> Term B C) (a : A) (b : B), eval (reifyProd f) (a, b) = eval (f a) b. Proof. intros A. induction A; intros B C f a b. - destruct a; reflexivity. - destruct a as [a|a];cbn;[rewrite IHA1|rewrite IHA2];reflexivity. - destruct a as [a1 a2];cbn;rewrite IHA1, IHA2;reflexivity. Qed. Fixpoint reify {A B : Ty} : (A -> B) -> Term A B := match A with | Unit => fun f => scribe (f tt) | Sum AL AR => fun f => comp (pair iden unit) (case (take (reify (fun al => f (inl al)))) (take (reify (fun ar => f (inr ar))))) | Prod A1 A2 => fun f => reifyProd (fun a1 => reify (fun a2 => f (a1, a2))) end. Lemma reify_correct (A B : Ty) (f : A -> B) (a : A) : eval (reify f) a = f a. Proof. induction A. - destruct a; cbn; apply scribe_correct. - destruct a as [a|a];cbn;[apply IHA1|apply IHA2]. - destruct a as [a0 a1]; cbn; rewrite reifyProd_correct; apply IHA2. Qed. Theorem Simplicity_Completeness : forall (A B : Ty) (f : A -> B), { t : Term A B | forall a, eval t a = f a }. Proof. intros A B f. exists (reify f). apply reify_correct. Defined. End Completeness. ================================================ FILE: Coq/Simplicity/Delegation.v ================================================ Require Import Simplicity.Util.PackedClass. Import Coq.Strings.String.StringSyntax. Require Import Simplicity.Alg. Require Import Simplicity.MerkleRoot. Require Import Simplicity.Ty. Require Import Simplicity.Word. Set Implicit Arguments. Local Open Scope ty_scope. Local Open Scope term_scope. Module Delegation. Record mixin (term : Ty -> Ty -> Type) := Mixin { disconnect : forall {A B C D}, term (Word256 * A) (B * C) -> term C D -> term A (B * D) }. Record class (term : Ty -> Ty -> Type) := Class { base :> Witness.class term ; ext :> mixin term }. Structure Algebra := _Pack { domain :> Ty -> Ty -> Type; class_of : class domain }. Definition packager dom (d0 : mixin dom) := [find w | Witness.domain w ~ dom | "is not a Witness algebra" ] [find wc | Witness.class_of w ~ wc ] [find d | d ~ d0 | "is not the right mixin" ] @_Pack dom (@Class dom wc d). Notation Pack dom d := (@packager dom d _ id _ id _ id). Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toWitness (alg : Algebra) : Witness.Algebra := Witness.Pack alg (class_of alg). Module Combinators. Definition disconnect {A B C D : Ty} {alg : Algebra} : alg (Word256 * A) (B * C) -> alg C D -> alg A (B * D) := disconnect (class_of alg). End Combinators. Module Parametric. Import Combinators. Record mixin {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { _ : forall A B C D s1 s2 t1 t2 (Hs : rel s1 s2) (Ht : rel t1 t2), rel (disconnect s1 t1) (@disconnect A B C D _ s2 t2) }. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> Witness.Parametric.class (@rel) ; ext :> mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. End Delegation. Export Delegation.Combinators. Coercion Delegation.domain : Delegation.Algebra >-> Funclass. Coercion Delegation.toWitness : Delegation.Algebra >-> Witness.Algebra. Coercion Delegation.base : Delegation.class >-> Witness.class. Coercion Delegation.ext : Delegation.class >-> Delegation.mixin. Coercion Delegation.Parametric.rel : Delegation.Parametric.Rel >-> Funclass. Canonical Structure Delegation.toCore. Canonical Structure Delegation.toWitness. Lemma disconnect_Parametric {alg1 alg2 : Delegation.Algebra} (R : Delegation.Parametric.Rel alg1 alg2) {A B C D} s1 s2 t1 t2 : R (Word256 * A) (B * C) s1 s2 -> R C D t1 t2 -> R A (B * D) (disconnect s1 t1) (disconnect s2 t2). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. #[export] Hint Resolve disconnect_Parametric : parametricity. Module AssertionDelegation. Record class (term : Ty -> Ty -> Type) := Class { base :> AssertionWitness.class term ; ext :> Delegation.mixin term }. Definition base2 term (c : class term) := Delegation.Class (base c) (ext c). Structure Algebra := _Pack { domain :> Ty -> Ty -> Type; class_of : class domain }. Definition packager dom := [find aw | AssertionWitness.domain aw ~ dom | "is not a AssertionWitness algebra" ] [find awc | AssertionWitness.class_of aw ~ awc ] [find d | Delegation.domain d ~ dom | "is not a Delegation algebra" ] [find dm | Delegation.ext (Delegation.class_of d) ~ dm ] @_Pack dom (@Class dom awc dm). Notation Pack dom := (@packager dom _ id _ id _ id _ id). Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toAssertion (alg : Algebra) : Assertion.Algebra := Assertion.Pack alg (class_of alg). Canonical Structure toWitness (alg : Algebra) : Witness.Algebra := Witness.Pack alg (class_of alg). Canonical Structure toAssertionWitness (alg : Algebra) : AssertionWitness.Algebra := AssertionWitness.Pack alg. Canonical Structure toDelegation (alg : Algebra) : Delegation.Algebra := Delegation.Pack alg (class_of alg). Module Parametric. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> AssertionWitness.Parametric.class (@rel) ; ext :> Delegation.Parametric.mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. End AssertionDelegation. Coercion AssertionDelegation.domain : AssertionDelegation.Algebra >-> Funclass. Coercion AssertionDelegation.toAssertionWitness : AssertionDelegation.Algebra >-> AssertionWitness.Algebra. Coercion AssertionDelegation.toDelegation : AssertionDelegation.Algebra >-> Delegation.Algebra. Coercion AssertionDelegation.base : AssertionDelegation.class >-> AssertionWitness.class. Coercion AssertionDelegation.base2 : AssertionDelegation.class >-> Delegation.class. Coercion AssertionDelegation.Parametric.rel : AssertionDelegation.Parametric.Rel >-> Funclass. Canonical Structure AssertionDelegation.toCore. Canonical Structure AssertionDelegation.toAssertion. Canonical Structure AssertionDelegation.toWitness. Canonical Structure AssertionDelegation.toAssertionWitness. Canonical Structure AssertionDelegation.toDelegation. Section MerkleRoot. Let disconnectTag := Eval vm_compute in commitmentTag "disconnect". Definition CommitmentRoot_Delegation_mixin : Delegation.mixin CommitmentRoot := {| Delegation.disconnect A B C D s _ := compress_half disconnectTag s |}. End MerkleRoot. Canonical Structure CommitmentRoot_Delegation_alg : Delegation.Algebra := Delegation.Pack CommitmentRoot CommitmentRoot_Delegation_mixin. Canonical Structure CommitmentRoot_AssertionDelegation_alg : AssertionDelegation.Algebra := AssertionDelegation.Pack CommitmentRoot. Section Delegator. Record Delegator (Arrow : Ty -> Ty -> Type) (A B : Ty) := { delegatorRoot : CommitmentRoot A B ; runDelegator : Arrow A B }. Definition CoreDelegator_mixin (alg : Core.Algebra) : Core.class (Delegator alg) := {| Core.iden A := {| delegatorRoot := iden ; runDelegator := iden |} ; Core.comp A B C s t := {| delegatorRoot := comp (delegatorRoot s) (delegatorRoot t) ; runDelegator := comp (runDelegator s) (runDelegator t) |} ; Core.unit A := {| delegatorRoot := unit ; runDelegator := unit |} ; Core.injl A B C t := {| delegatorRoot := injl (delegatorRoot t) ; runDelegator := injl (runDelegator t) |} ; Core.injr A B C t := {| delegatorRoot := injr (delegatorRoot t) ; runDelegator := injr (runDelegator t) |} ; Core.case A B C D s t := {| delegatorRoot := case (delegatorRoot s) (delegatorRoot t) ; runDelegator := case (runDelegator s) (runDelegator t) |} ; Core.pair A B C s t := {| delegatorRoot := pair (delegatorRoot s) (delegatorRoot t) ; runDelegator := pair (runDelegator s) (runDelegator t) |} ; Core.take A B C t := {| delegatorRoot := take (delegatorRoot t) ; runDelegator := take (runDelegator t) |} ; Core.drop A B C t := {| delegatorRoot := drop (delegatorRoot t) ; runDelegator := drop (runDelegator t) |} |}. Definition AssertionDelegator_mixin (alg : Assertion.Algebra) : Assertion.mixin (Delegator alg) := {| Assertion.assertl A B C D s ht := {| delegatorRoot := assertl (delegatorRoot s) ht ; runDelegator := assertl (runDelegator s) ht |} ; Assertion.assertr A B C D hs t := {| delegatorRoot := assertr hs (delegatorRoot t) ; runDelegator := assertr hs (runDelegator t) |} ; Assertion.fail A B h := {| delegatorRoot := fail h ; runDelegator := @fail A B alg h |} |}. Definition WitnessDelegator_mixin (alg : Witness.Algebra) : Witness.mixin (Delegator alg) := {| Witness.witness A B b := {| delegatorRoot := witness b ; runDelegator := witness b |} |}. Definition DelegationDelegator_mixin (alg : Core.Algebra) : Delegation.mixin (Delegator alg) := {| Delegation.disconnect A B C D s t := {| delegatorRoot := @disconnect A B C D _ (delegatorRoot s) (delegatorRoot t) ; runDelegator := scribe (from_hash256 (delegatorRoot t)) &&& iden >>> runDelegator s >>> take iden &&& drop (runDelegator t) |} |}. End Delegator. Canonical Structure CoreDelegator (alg : Core.Algebra) : Core.Algebra := Core.Pack (Delegator alg) (CoreDelegator_mixin alg). Canonical Structure AssertionDelegator (alg : Assertion.Algebra) : Assertion.Algebra := Assertion.Pack (Delegator alg) (AssertionDelegator_mixin alg). Canonical Structure WitnessDelegator (alg : Witness.Algebra) : Witness.Algebra := Witness.Pack (Delegator alg) (WitnessDelegator_mixin alg). Canonical Structure AssertionWitnessDelegator (alg : AssertionWitness.Algebra) : AssertionWitness.Algebra := AssertionWitness.Pack (Delegator alg). Canonical Structure DelegationDelegator (alg : Witness.Algebra) : Delegation.Algebra := Delegation.Pack (Delegator alg) (DelegationDelegator_mixin alg). Canonical Structure AssertionDelegationDelegator (alg : AssertionWitness.Algebra) : AssertionDelegation.Algebra := AssertionDelegation.Pack (Delegator alg). Lemma delegatorRoot_correctness A B (t : forall alg : AssertionDelegation.Algebra, alg A B) (Ht : AssertionDelegation.Parametric t) alg : delegatorRoot (t (AssertionDelegationDelegator alg)) = t _. Proof. set (R := fun A B (x : Delegator alg A B) (y : CommitmentRoot A B) => delegatorRoot x = y). refine (Ht _ _ (AssertionDelegation.Parametric.Pack (_ : AssertionDelegation.Parametric.class R))). repeat constructor; unfold R; clear; intros; cbn; repeat f_equal; assumption. Qed. Lemma runDelegator_correctness A B (t : forall alg : AssertionWitness.Algebra, alg A B) (Ht : AssertionWitness.Parametric t) alg : runDelegator (t (AssertionWitnessDelegator alg)) = t alg. Proof. set (R := fun A B (x : Delegator alg A B) (y : alg A B) => runDelegator x = y). refine (Ht _ _ (AssertionWitness.Parametric.Pack (_ : AssertionWitness.Parametric.class R))). repeat constructor; unfold R; clear; intros; cbn; repeat f_equal; assumption. Qed. ================================================ FILE: Coq/Simplicity/Digest.v ================================================ Require Import Logic.Eqdep_dec. Require Import Strings.String. Require Import List. Require BinInt. Import Coq.ZArith.BinIntDef. Require compcert.lib.Integers. Require sha.SHA256. Require Import sha.functional_prog. Require Import sha.general_lemmas. Global Unset Asymmetric Patterns. (* the VST library does a Global Set so we must unset it. *) Set Implicit Arguments. Record hash256 : Set := Hash256 { hash256_reg :> SHA256.registers ; hash256_len : length hash256_reg = 8 }. Definition hash256_to_bytelist (x : hash256) := intlist_to_bytelist (hash256_reg x). (* The normalizeInt and normalizeHash functions are extensionally the identity * function. Operationally they work by replacing the internal proof * obligations of their inputs with canonical versions of those proofs. When * evaluated in the empty context, this has the effect of pruning away any * opaque proof terms. This will also work whenever the internal data values * of the inputs are independent of the context. *) Definition normalizeInt (x : Integers.Int.int) : Integers.Int.int. set (v := Integers.Int.intval x). exists v. assert (Hv := Integers.Int.intrange x). fold v in Hv. unfold BinInt.Z.lt in *. split; [destruct (BinInt.Z.compare (-1) v) |destruct (BinInt.Z.compare v Integers.Int.modulus) ]; solve [reflexivity|destruct Hv; discriminate]. Defined. Lemma normalizeInt_correct x : normalizeInt x = x. Proof. destruct x; apply Integers.Int.mkint_eq. reflexivity. Qed. Definition normalizeHash (x : hash256) : hash256. exists (map normalizeInt (hash256_reg x)). assert (Heq := hash256_len x). rewrite <- (map_length normalizeInt) in Heq. destruct (length (map normalizeInt (hash256_reg x))) as [|n]; try discriminate. repeat (destruct n as [|n]; try reflexivity; try discriminate). Defined. Lemma normalizeHash_correct x : normalizeHash x = x. Proof. destruct x as [x Hx]. unfold normalizeHash;cbn. set (Heq:= eq_ind_r _ _ _). generalize Heq; clear Heq. replace (map normalizeInt x) with x by (clear; induction x; cbn;[|rewrite normalizeInt_correct, <- IHx]; auto). intros Heq. f_equal. apply UIP_dec; decide equality. Qed. Definition byteStringHash (x : list Integers.byte) : hash256 := Hash256 (process_msg SHA256.init_registers (generate_and_pad_alt x)) (length_process_msg _). Definition stringHash (x : string) : hash256 := byteStringHash (SHA256.str_to_bytes x). Definition sha256_iv : hash256 := Hash256 SHA256.init_registers refl_equal. Definition compress (iv h1 h2 : hash256) : hash256 := Hash256 (process_block iv (List.rev (hash256_reg h1 ++ hash256_reg h2))) (length_process_block _ _ (hash256_len iv)). Definition compress_half (iv h: hash256) : hash256 := Hash256 (process_block iv (List.rev (hash256_reg h) ++ repeat Integers.Int.zero 8)) (length_process_block _ _ (hash256_len iv)). ================================================ FILE: Coq/Simplicity/MerkleRoot.v ================================================ Require Import List. Require Import Coq.Strings.String. Import Coq.Strings.Ascii.AsciiSyntax. Require Import Simplicity.Alg. Require Export Simplicity.Digest. Require Import Simplicity.Ty. Set Implicit Arguments. Import ListNotations. Definition tag (ws : list string) := let str := concat (String "031" EmptyString) ws in let tagDigest := normalizeHash (stringHash str) in normalizeHash (compress sha256_iv tagDigest tagDigest). Definition prefix := ["Simplicity"%string]. Definition typePrefix := prefix ++ ["Type"%string]. Definition commitmentPrefix := prefix ++ ["Commitment"%string]. Definition identityPrefix := prefix ++ ["Identity"%string]. Section TypeRoot. Let typeTag tg := tag (typePrefix ++ [tg]). Let unitTag := Eval vm_compute in typeTag "unit". Let sumTag := Eval vm_compute in typeTag "sum". Let prodTag := Eval vm_compute in typeTag "prod". Definition typeRootAlg : tyAlg hash256 := {| unitA := unitTag ; sumA := compress sumTag ; prodA := compress prodTag |}. End TypeRoot. (* :TODO: memoize the computation of type roots. *) Definition typeRoot : Ty -> hash256 := tyCata typeRootAlg. Definition commitmentTag tg := tag (commitmentPrefix ++ [tg]). Section CommitmentRoot. Let idenTag := Eval vm_compute in commitmentTag "iden". Let compTag := Eval vm_compute in commitmentTag "comp". Let unitTag := Eval vm_compute in commitmentTag "unit". Let injlTag := Eval vm_compute in commitmentTag "injl". Let injrTag := Eval vm_compute in commitmentTag "injr". Let caseTag := Eval vm_compute in commitmentTag "case". Let pairTag := Eval vm_compute in commitmentTag "pair". Let takeTag := Eval vm_compute in commitmentTag "take". Let dropTag := Eval vm_compute in commitmentTag "drop". Let failTag := Eval vm_compute in commitmentTag "fail". Let witnessTag := Eval vm_compute in commitmentTag "witness". Definition CommitmentRoot (A B:Ty) := hash256. Definition commitmentRoot {A B} (x : CommitmentRoot A B) : hash256 := x. Definition CommitmentRoot_Core_mixin : Core.class CommitmentRoot := {| Core.iden A := idenTag ; Core.comp A B C hs ht := compress compTag hs ht ; Core.unit A := unitTag ; Core.injl A B C ht := compress_half injlTag ht ; Core.injr A B C ht := compress_half injrTag ht ; Core.case A B C D hs ht := compress caseTag hs ht ; Core.pair A B C hs ht := compress pairTag hs ht ; Core.take A B C ht := compress_half takeTag ht ; Core.drop A B C ht := compress_half dropTag ht |}. Definition CommitmentRoot_Assertion_mixin : Assertion.mixin CommitmentRoot := {| Assertion.assertl A B C D hs ht := compress caseTag hs ht ; Assertion.assertr A B C D hs ht := compress caseTag hs ht ; Assertion.fail A B h := compress failTag (fst h) (snd h) |}. Definition CommitmentRoot_Witness_mixin : Witness.mixin CommitmentRoot := {| Witness.witness A B b := witnessTag |}. End CommitmentRoot. Canonical Structure CommitmentRoot_Core_alg : Core.Algebra := Core.Pack CommitmentRoot CommitmentRoot_Core_mixin. Canonical Structure CommitmentRoot_Assertion_alg : Assertion.Algebra := Assertion.Pack CommitmentRoot CommitmentRoot_Assertion_mixin. Canonical Structure CommitmentRoot_Witness_alg : Witness.Algebra := Witness.Pack CommitmentRoot CommitmentRoot_Witness_mixin. Canonical Structure CommitmentRoot_AssertionWitness_alg : AssertionWitness.Algebra := AssertionWitness.Pack CommitmentRoot. Definition identityHashTag := tag identityPrefix. Section IdentityRoot. Definition IdentityRoot (A B:Ty) := hash256. Definition identityHash {A B} (x : IdentityRoot A B) : hash256 := compress (compress_half identityHashTag x) (typeRoot A) (typeRoot B). Definition IdentityRoot_Core_mixin : Core.class IdentityRoot := CommitmentRoot_Core_mixin. Definition IdentityRoot_Assertion_mixin : Assertion.mixin IdentityRoot := CommitmentRoot_Assertion_mixin. End IdentityRoot. Canonical Structure IdentityRoot_Core_alg : Core.Algebra := Core.Pack IdentityRoot IdentityRoot_Core_mixin. Canonical Structure IdentityRoot_Assertion_alg : Assertion.Algebra := Assertion.Pack IdentityRoot IdentityRoot_Assertion_mixin. ================================================ FILE: Coq/Simplicity/Primitive/Bitcoin.v ================================================ Require Import ZArith. Require Import String. Require Import Simplicity.Util.List. Require Import compcert.lib.Integers. Global Unset Asymmetric Patterns. (* the VST library does a Global Set so we must unset it. *) Require Import Simplicity.Digest. Require Simplicity.MerkleRoot. Require Import Simplicity.Primitive. Require Import Simplicity.Ty. Require Import Simplicity.Word. Set Primitive Projections. Set Implicit Arguments. Import ListNotations. Section DataTypes. Definition MAX_MONEY : Z := 21000000 * 10^8. Notation moneyRange x := (-1 < x < Z.succ MAX_MONEY)%Z. Definition lock := int. Definition script := list byte. Record outpoint : Set := { opHash : hash256 ; opIndex : int }. Record sigTxInput : Set := { sigTxiPreviousOutpoint : outpoint ; sigTxiValue : int64 ; sigTxiSequence : int ; sigTxiValue_bound : moneyRange (Int64.signed sigTxiValue) }. Record txOutput : Set := { txoValue : int64 ; txoScript : script ; txoValue_bound : moneyRange (Int64.signed txoValue) ; txoScript_bound : (Zlength txoScript < Int.modulus)%Z }. Record sigTx : Set := { sigTxVersion : int ; sigTxIn : list sigTxInput ; sigTxOut : list txOutput ; sigTxLock : lock ; sigTxInBounds : (0 < Zlength sigTxIn < Int.modulus)%Z ; sigTxOutBounds : (0 < Zlength sigTxOut < Int.modulus)%Z ; sigTxTotalInValue : Z := Z_sum (map (fun i => Int64.signed (sigTxiValue i)) sigTxIn) ; sigTxTotalOutValue : Z := Z_sum (map (fun i => Int64.signed (txoValue i)) sigTxOut) ; sigTxFee : Z := sigTxTotalOutValue - sigTxTotalInValue ; sigTxTotalInValue_bound : moneyRange sigTxTotalInValue ; sigTxTotalOutValue_bound : moneyRange sigTxTotalOutValue ; sigTxFee_bound : moneyRange sigTxFee }. End DataTypes. Section Serialization. Definition putHash256 (x : hash256) : list byte := hash256_to_bytelist x. Definition putInt64le (x : Int64.int) : list byte := let z := Int64.unsigned x in map (fun i => Byte.repr (z / two_power_nat (i*Byte.wordsize))%Z) (seq 0 8). Definition putInt32le (x : Int.int) : list byte := let z := Int.unsigned x in map (fun i => Byte.repr (z / two_power_nat (i*Byte.wordsize))%Z) (seq 0 4). Definition putOutpoint (x : outpoint) : list byte := putHash256 (opHash x) ++ putInt32le (opIndex x). End Serialization. Module Bitcoin <: PrimitiveSig. Inductive prim : Ty -> Ty -> Set := | Version : prim Unit Word32 | LockTime : prim Unit Word32 | InputsHash : prim Unit Word256 | OutputsHash : prim Unit Word256 | NumInputs : prim Unit Word32 | TotalInputValue : prim Unit Word64 | CurrentPrevOutpoint : prim Unit (Prod Word256 Word32) | CurrentValue : prim Unit Word64 | CurrentSequence : prim Unit Word32 | CurrentIndex : prim Unit Word32 | InputPrevOutpoint : prim Word32 (Sum Unit (Prod Word256 Word32)) | InputValue : prim Word32 (Sum Unit Word64) | InputSequence : prim Word32 (Sum Unit Word32) | NumOutputs : prim Unit Word32 | TotalOutputValue : prim Unit Word64 | OutputValue : prim Word32 (Sum Unit Word64) | OutputScriptHash : prim Word32 (Sum Unit Word256) | ScriptCMR : prim Unit Word256. Definition t := prim. Definition primName : string := "Bitcoin". Definition name {a b} (p : t a b) : string := match p with | Version => "version" | LockTime => "locktime" | InputsHash => "inputsHash" | OutputsHash => "outputsHash" | NumInputs => "numInputs" | TotalInputValue => "totalInputValue" | CurrentPrevOutpoint => "currentPrevOutpoint" | CurrentValue => "currentValue" | CurrentSequence => "currentSequence" | CurrentIndex => "currentIndex" | InputPrevOutpoint => "inputPrevOutpoint" | InputValue => "inputValue" | InputSequence => "inputSequence" | NumOutputs => "numOutputs" | TotalOutputValue => "totalOutputValue" | OutputValue => "outputValue" | OutputScriptHash => "outputScriptHash" | ScriptCMR => "scriptCMR" end. Section Tag. Let tag_def {A B} (p : t A B) : hash256. pose (nm := name p). revert p nm; intros [] nm; exact (MerkleRoot.tag (primitivePrefix primName ++ [nm])). Defined. (* Using Eval vm_compute lets us precompute all the tags for all our primitives *) Definition tag {A B} (p : t A B) := Eval vm_compute in (tag_def p). (* Try running *) (* Print tag. *) End Tag. Record environment := { envTx : sigTx ; envIx : nat ; envScriptCMR : hash256 ; envIxBounded : envIx < length (sigTxIn envTx) }. Definition env := environment. Section primSem. Let cast {A : Ty} (x : option A) : tySem (Unit + A) := match x with | Some a => inr a | None => inl tt end. Let encodeOutpoint (op : outpoint) : tySem (Word256 * Word32) := (from_hash256 (opHash op), fromZ (Int.unsigned (opIndex op)) : Word32). Definition sem {A B} (p : t A B) (a : A) (e : env) : option B := let tx := envTx e in let ix := envIx e in let currentInput {A : Ty} (f : sigTxInput -> A) := option_map f (nth_error (sigTxIn tx) ix) in let atInput {A : Ty} (f : sigTxInput -> A) (i : Word32) := Some (cast (option_map f (nth_error (sigTxIn tx) (Z.to_nat (toZ i))))) in let atOutput {A : Ty} (f : txOutput -> A) (i : Word32) := Some (cast (option_map f (nth_error (sigTxOut tx) (Z.to_nat (toZ i))))) in let outputsHash := let go i := putInt64le (txoValue i) ++ putHash256 (byteStringHash (txoScript i)) in byteStringHash (concat (map go (sigTxOut tx))) in let inputsHash := let go i := putOutpoint (sigTxiPreviousOutpoint i) ++ putInt64le (sigTxiValue i) ++ putInt32le (sigTxiSequence i) in byteStringHash (concat (map go (sigTxIn tx))) in (match p in prim A B return A -> option B with | Version => fun _ => Some (fromZ (Int.signed (sigTxVersion tx))) | LockTime => fun _ => Some (fromZ (Int.unsigned (sigTxLock tx))) | InputsHash => fun _ => Some (from_hash256 inputsHash) | OutputsHash => fun _ => Some (from_hash256 outputsHash) | NumInputs => fun _ => Some (fromZ (Zlength (sigTxIn tx))) | TotalInputValue => fun _ => Some (fromZ (sigTxTotalInValue tx)) | CurrentPrevOutpoint => fun _ => currentInput (fun txi => encodeOutpoint (sigTxiPreviousOutpoint txi)) | CurrentValue => fun _ => currentInput (fun txi => fromZ (Int64.signed (sigTxiValue txi))) | CurrentSequence => fun _ => currentInput (fun txi => fromZ (Int.unsigned (sigTxiSequence txi))) | CurrentIndex => fun _ => Some (fromZ (Z.of_nat ix)) | InputPrevOutpoint => atInput (fun txi => encodeOutpoint (sigTxiPreviousOutpoint txi)) | InputValue => atInput (fun txi => fromZ (Int64.signed (sigTxiValue txi))) | InputSequence => atInput (fun txi => fromZ (Int.unsigned (sigTxiSequence txi))) | NumOutputs => fun _ => Some (fromZ (Zlength (sigTxOut tx))) | TotalOutputValue => fun _ => Some (fromZ (sigTxTotalOutValue tx)) | OutputValue => atOutput (fun txout => fromZ (Int64.signed (txoValue txout))) | OutputScriptHash => atOutput (fun txout => from_hash256 (byteStringHash (txoScript txout))) | ScriptCMR => fun _ => Some (from_hash256 (envScriptCMR e)) end ) a. End primSem. End Bitcoin. Module Export PrimitiveBitcoin := PrimitiveModule Bitcoin. ================================================ FILE: Coq/Simplicity/Primitive.v ================================================ Require Import Simplicity.Util.List. Require Import Strings.String. Require Import Simplicity.Util.PackedClass. Require Import Simplicity.Util.Monad. Require Import Simplicity.Util.Monad.Reader. Require Import Simplicity.Util.Option. Require Import Simplicity.Alg. Require Import Simplicity.Delegation. Require Import Simplicity.MerkleRoot. Require Import Simplicity.Ty. Set Implicit Arguments. Import ListNotations. Definition primitivePrefix primName := (MerkleRoot.prefix ++ ["Primitive"%string; primName])%list. Definition jetTag := Eval vm_compute in tag (MerkleRoot.prefix ++ ["Jet"%string]). Module Type PrimitiveSig. Parameter t : Ty -> Ty -> Set. Parameter tag : forall {A B}, t A B -> hash256. Parameter env : Set. Parameter sem : forall {A B}, t A B -> A -> env -> option B. End PrimitiveSig. Module PrimitiveModule (Prim : PrimitiveSig). Module Primitive. Record mixin (term : Ty -> Ty -> Type) := Mixin { prim : forall {A B}, Prim.t A B -> term A B }. Record class (term : Ty -> Ty -> Type) := Class { base : Assertion.class term ; ext : mixin term }. Structure Algebra := _Pack { domain : Ty -> Ty -> Type; class_of : class domain }. Definition packager dom (p0 : mixin dom) := [find a | Assertion.domain a ~ dom | "is not a Assertion algebra" ] [find ac | Assertion.class_of a ~ ac ] [find p | p ~ p0 | "is not the right mixin" ] @_Pack dom (@Class dom ac p). Notation Pack dom p := (@packager dom p _ id _ id _ id). Module Coercions. Coercion domain : Algebra >-> Funclass. Coercion base : class >-> Assertion.class. Coercion ext : class >-> mixin. End Coercions. Module CanonicalStructures. Export Coercions. Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toAssertion (alg : Algebra) : Assertion.Algebra := Assertion.Pack alg (class_of alg). End CanonicalStructures. Module Combinators. Export CanonicalStructures. Definition prim {A B} {alg : Algebra} : Prim.t A B -> alg A B := prim (class_of alg). End Combinators. Module Parametric. Import Combinators. Record mixin {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { _ : forall A B (p : Prim.t A B), rel (prim p) (prim p) }. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base : Assertion.Parametric.class (@rel) ; ext : mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Import Combinators. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. Module Theory. Export Combinators. Coercion Parametric.rel : Parametric.Rel >-> Funclass. Lemma prim_Parametric {alg1 alg2 : Algebra} (R : Parametric.Rel alg1 alg2) {A B} (p : Prim.t A B) : R A B (prim p) (prim p). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. #[export] Hint Immediate prim_Parametric : parametricity. Definition primSem M A B := Kleisli (ReaderT Prim.env M) A B. Definition PrimSem_mixin (M : CIMonadZero) : mixin (primSem M) := {| Primitive.prim A B p := fun a e => optionZero (Prim.sem p a e) |}. Canonical Structure CorePrimSem (M : CIMonad) : Core.Algebra := Core.Pack (primSem M) (CoreSem_mixin (ReaderT_CIMonad Prim.env M)). Canonical Structure AssertionPrimSem (M : CIMonadZero) : Assertion.Algebra := Assertion.Pack (primSem M) (AssertionSem_mixin (ReaderT_CIMonadZero Prim.env M)). Canonical Structure PrimitivePrimSem (M : CIMonadZero) : Algebra := Pack (primSem M) (PrimSem_mixin M). Canonical Structure WitnessPrimSem (M : CIMonad) : Witness.Algebra := Witness.Pack (primSem M) (WitnessSem_mixin (ReaderT_CIMonad Prim.env M)). Canonical Structure AssertionWitnessPrimSem (M : CIMonadZero) : AssertionWitness.Algebra := AssertionWitness.Pack (primSem M). Definition CommitmentRoot_Primitive_mixin : mixin CommitmentRoot := {| Primitive.prim A B p := Prim.tag p |}. Canonical Structure CommitmentRoot_Primitive_alg : Algebra := Pack CommitmentRoot CommitmentRoot_Primitive_mixin. Definition IdentityRoot_Primitive_mixin : mixin IdentityRoot := {| Primitive.prim A B p := Prim.tag p |}. Canonical Structure IdentityRoot_Primitive_alg : Algebra := Pack IdentityRoot IdentityRoot_Primitive_mixin. Definition Delegator_Primitive_mixin (alg : Algebra) : mixin (Delegator alg) := {| Primitive.prim A B p := {| delegatorRoot := prim p ; runDelegator := prim p |} |}. Canonical Structure Delegator_Primitive_alg (alg : Algebra) : Algebra := Pack (Delegator alg) (Delegator_Primitive_mixin alg). End Theory. End Primitive. Export Primitive.Theory. Module Jet. Record mixin (term : Ty -> Ty -> Type) := Mixin { jet : forall {A B} (t : forall (term : Primitive.Algebra), term A B), Primitive.Parametric t -> term A B }. Record class (term : Ty -> Ty -> Type) := Class { base : Primitive.class term ; ext : mixin term }. Structure Algebra := _Pack { domain : Ty -> Ty -> Type; class_of : class domain }. Definition packager dom (p0 : mixin dom) := [find a | Primitive.domain a ~ dom | "is not a Primitive algebra" ] [find ac | Primitive.class_of a ~ ac ] [find p | p ~ p0 | "is not the right mixin" ] @_Pack dom (@Class dom ac p). Notation Pack dom p := (@packager dom p _ id _ id _ id). Module Coercions. Coercion domain : Algebra >-> Funclass. Coercion base : class >-> Primitive.class. Coercion ext : class >-> mixin. End Coercions. Module CanonicalStructures. Export Coercions. Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toAssertion (alg : Algebra) : Assertion.Algebra := Assertion.Pack alg (class_of alg). Canonical Structure toPrimitive (alg : Algebra) : Primitive.Algebra := Primitive.Pack alg (class_of alg). End CanonicalStructures. Module Combinators. Export CanonicalStructures. Definition jet {A B} {alg : Algebra} : forall (t : _), Primitive.Parametric t -> alg A B := jet (class_of alg). End Combinators. Module Parametric. Import Combinators. Record mixin {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { _ : forall A B (t : _) (p : Primitive.Parametric t), @rel A B (jet p) (jet p) }. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base : Assertion.Parametric.class (@rel) ; ext : mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Import Combinators. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. Module Theory. Export Combinators. Coercion Parametric.rel : Parametric.Rel >-> Funclass. Lemma jet_Parametric {alg1 alg2 : Algebra} (R : Parametric.Rel alg1 alg2) {A B} {t : _} (p : Primitive.Parametric t) : R A B (jet p) (jet p). Proof. destruct R as [R [Rb []]]. cbn; auto. Qed. #[export] Hint Resolve jet_Parametric : parametricity. Definition PrimSem_jet_mixin (M : CIMonadZero) : mixin (primSem M) := {| Jet.jet A B t p := t (PrimitivePrimSem M) |}. Canonical Structure JetPrimSem (M : CIMonadZero) : Algebra := Pack (primSem M) (PrimSem_jet_mixin M). Definition CommitmentRoot_Jet_mixin : mixin CommitmentRoot := {| Jet.jet A B t p := compress_half jetTag (identityHash (t _)) |}. Canonical Structure CommitmentRoot_Jet_alg : Algebra := Pack CommitmentRoot CommitmentRoot_Jet_mixin. Definition IdentityRoot_Jet_mixin : mixin IdentityRoot := {| Jet.jet A B t p := compress_half jetTag (identityHash (t _)) |}. Canonical Structure IdentityRoot_Jet_alg : Algebra := Pack IdentityRoot IdentityRoot_Jet_mixin. Definition Delegator_Jet_mixin (alg : Algebra) : mixin (Delegator alg) := {| Jet.jet A B t p := {| delegatorRoot := jet p ; runDelegator := jet p |} |}. Canonical Structure Delegator_Jet_alg (alg : Algebra) : Algebra := Pack (Delegator alg) (Delegator_Jet_mixin alg). End Theory. End Jet. Export Jet.Theory. Module FullSimplicity. Record class (term : Ty -> Ty -> Type) := Class { base : Jet.class term ; ext : Witness.mixin term }. Definition base2 term (c : class term) : AssertionWitness.class term := AssertionWitness.Class (base c) (ext c). Structure Algebra := _Pack { domain : Ty -> Ty -> Type; class_of : class domain }. Definition packager dom := [find j | Jet.domain j ~ dom | "is not a Jet algebra" ] [find jc | Jet.class_of j ~ jc ] [find aw | AssertionWitness.domain aw ~ dom | "is not a AssertionWitness algebra" ] [find awm | AssertionWitness.ext (AssertionWitness.class_of aw) ~ awm ] @_Pack dom (@Class dom jc awm). Notation Pack dom := (@packager dom _ id _ id _ id _ id). Module Coercions. Coercion domain : Algebra >-> Funclass. Coercion base : class >-> Jet.class. Coercion base2 : class >-> AssertionWitness.class. End Coercions. Module CanonicalStructures. Export Coercions. Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toAssertion (alg : Algebra) : Assertion.Algebra := Assertion.Pack alg (class_of alg). Canonical Structure toPrimitive (alg : Algebra) : Primitive.Algebra := Primitive.Pack alg (class_of alg). Canonical Structure toJet (alg : Algebra) : Jet.Algebra := Jet.Pack alg (class_of alg). Canonical Structure toWitiness (alg : Algebra) : Witness.Algebra := Witness.Pack alg (class_of alg). Canonical Structure toAssertionWitiness (alg : Algebra) : AssertionWitness.Algebra := AssertionWitness.Pack alg. End CanonicalStructures. Module Parametric. Import CanonicalStructures. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> Jet.Parametric.class (@rel) ; ext :> Witness.Parametric.mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Import CanonicalStructures. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. Module Theory. Export CanonicalStructures. Coercion Parametric.rel : Parametric.Rel >-> Funclass. Canonical Structure SimplicityPrimSem (M : CIMonadZero) : Algebra := Pack (primSem M). Canonical Structure CommitmentRoot_Simplicity_alg : Algebra := Pack CommitmentRoot. Canonical Structure Delegator_Simplicity_alg (alg : Algebra) : Algebra := Pack (Delegator alg). Lemma runDelegator_correctness A B (t : forall alg : Algebra, alg A B) (Ht : Parametric t) alg : runDelegator (t (Delegator_Simplicity_alg alg)) = t alg. Proof. set (R := fun A B (x : Delegator alg A B) (y : alg A B) => runDelegator x = y). refine (Ht _ _ (Parametric.Pack (_ : Parametric.class R))). repeat constructor; unfold R; clear; intros; cbn; repeat f_equal; assumption. Qed. End Theory. End FullSimplicity. Export FullSimplicity.Theory. Module FullSimplicityWithDelegation. Record class (term : Ty -> Ty -> Type) := Class { base : FullSimplicity.class term ; ext : Delegation.mixin term }. Definition base2 term (c : class term) : AssertionDelegation.class term := AssertionDelegation.Class (base c) (ext c). Structure Algebra := _Pack { domain : Ty -> Ty -> Type; class_of : class domain }. Definition packager dom := [find fs | FullSimplicity.domain fs ~ dom | "is not a FullSimplicity algebra" ] [find fsc | FullSimplicity.class_of fs ~ fsc ] [find ad | AssertionDelegation.domain ad ~ dom | "is not a AssertionDelegation algebra" ] [find adm | AssertionDelegation.ext (AssertionDelegation.class_of ad) ~ adm ] @_Pack dom (@Class dom fsc adm). Notation Pack dom := (@packager dom _ id _ id _ id _ id). Module Coercions. Coercion domain : Algebra >-> Funclass. Coercion base : class >-> FullSimplicity.class. Coercion base2 : class >-> AssertionDelegation.class. End Coercions. Module CanonicalStructures. Export Coercions. Canonical Structure toCore (alg : Algebra) : Core.Algebra := Core.Pack alg (class_of alg). Canonical Structure toAssertion (alg : Algebra) : Assertion.Algebra := Assertion.Pack alg (class_of alg). Canonical Structure toPrimitive (alg : Algebra) : Primitive.Algebra := Primitive.Pack alg (class_of alg). Canonical Structure toJet (alg : Algebra) : Jet.Algebra := Jet.Pack alg (class_of alg). Canonical Structure toWitiness (alg : Algebra) : Witness.Algebra := Witness.Pack alg (class_of alg). Canonical Structure toAssertionWitiness (alg : Algebra) : AssertionWitness.Algebra := AssertionWitness.Pack alg. Canonical Structure toFullSimplicity (alg : Algebra) : FullSimplicity.Algebra := FullSimplicity.Pack alg. Canonical Structure toDelegation (alg : Algebra) : Delegation.Algebra := Delegation.Pack alg (class_of alg). Canonical Structure toAssertionDelegation (alg : Algebra) : AssertionDelegation.Algebra := AssertionDelegation.Pack alg. End CanonicalStructures. Module Parametric. Import CanonicalStructures. Record class {alg1 alg2 : Algebra} (rel : forall {A B}, alg1 A B -> alg2 A B -> Prop) := { base :> FullSimplicity.Parametric.class (@rel) ; ext :> Delegation.Parametric.mixin (@rel) }. Record Rel (alg1 alg2 : Algebra) := Pack { rel :> forall {A B}, alg1 A B -> alg2 A B -> Prop ; class_of : class (@rel) }. End Parametric. Section Reynolds. Import CanonicalStructures. Local Coercion Parametric.rel : Parametric.Rel >-> Funclass. Definition Reynolds {A B} (x y : forall (alg : Algebra), alg A B) : Prop := forall alg1 alg2 (R : Parametric.Rel alg1 alg2), R A B (x alg1) (y alg2). Definition Parametric {A B} (x : forall (alg : Algebra), alg A B) : Prop := Reynolds x x. End Reynolds. Module Theory. Export CanonicalStructures. Coercion Parametric.rel : Parametric.Rel >-> Funclass. Canonical Structure CommitmentRoot_Simplicity_alg : Algebra := Pack CommitmentRoot. Canonical Structure SimplicityDelegationDelegator (alg : FullSimplicity.Algebra) : Algebra := Pack (Delegator alg). Lemma delegatorRoot_correctness A B (t : forall alg : Algebra, alg A B) (Ht : Parametric t) alg : delegatorRoot (t (SimplicityDelegationDelegator alg)) = t _. Proof. set (R := fun A B (x : Delegator alg A B) (y : CommitmentRoot A B) => delegatorRoot x = y). refine (Ht _ _ (Parametric.Pack (_ : Parametric.class R))). repeat constructor; unfold R; clear; intros; cbn; repeat f_equal; assumption. Qed. End Theory. End FullSimplicityWithDelegation. Export FullSimplicityWithDelegation.Theory. End PrimitiveModule. ================================================ FILE: Coq/Simplicity/SHA256.v ================================================ Require Import ZArith. Require Import List. Require Import Lia. Require sha.SHA256. Require Import compcert.lib.Integers. Global Unset Asymmetric Patterns. (* the VST library does a Global Set so we must unset it. *) Import Coq.Strings.String.StringSyntax. Require Import Simplicity.Alg. Require Import Simplicity.Bit. Require Import Simplicity.Digest. Require Import Simplicity.Ty. Require Import Simplicity.Word. Set Implicit Arguments. Import ListNotations. Local Open Scope list_scope. Local Open Scope ty_scope. Local Open Scope term_scope. Local Open Scope semantic_scope. Local Tactic Notation "introLet" := match goal with |- context f [let N := ?V in (@?b N)] => let N0 := fresh N in set (N0 := V); let Y := eval cbv beta in (b N0) in let X := context f[Y] in change X end. Local Tactic Notation "clearLet" := match goal with |- context f [let N := ?V in (@?b N)] => let Y := eval cbv beta in (b V) in let X := context f[Y] in change X end. Definition repr_Block (b : Word512) : list int := let (b0,b1) := b in hash256_reg (to_hash256 b0) ++ hash256_reg (to_hash256 b1). Definition repr_Block_inv (l : list int) : Word512 := match l with | [b0; b1; b2; b3; b4; b5; b6; b7; b8; b9; ba; bb; bc; bd; be; bf] => (from_hash256 (Hash256 [b0; b1; b2; b3; b4; b5; b6; b7] refl_equal) ,from_hash256 (Hash256 [b8; b9; ba; bb; bc; bd; be; bf] refl_equal)) | _ => fromZ 0%Z end. Lemma repr_Block_inj (b : Word512) : repr_Block_inv (repr_Block b) = b. Proof. assert (H32 : forall x : Word32, (0 <= toZ x <= Int.max_unsigned)%Z). intros x. change Int.max_unsigned with (Z.pred Int.modulus). rewrite <- Z.lt_le_pred, toZ_mod. apply Z.mod_pos_bound. reflexivity. destruct b as [[[[b0 b1][b2 b3]][[b4 b5][b6 b7]]] [[[b8 b9][ba bb]][[bc bd][be bf]]]]. simpl. unfold from_hash256. simpl map. cbv iota beta. repeat rewrite Int.unsigned_repr by auto. repeat rewrite from_toZ. reflexivity. Qed. Lemma repr_Block_length (b : Word512) : length (repr_Block b) = 16. Proof. destruct b as [b0 b1];cbn. rewrite app_length, !hash256_len. reflexivity. Qed. Section Definitions. Definition scribe32 (z : Z) {A} {term : Core.Algebra} : term A Word32 := scribe (fromZ z). Definition add32 {term : Core.Algebra} : term (Word32 * Word32) Word32 := adder >>> I H. Definition xor3Word32 {term : Core.Algebra} : term (Word32 * (Word32 * Word32)) Word32 := bitwiseTri xor3. Definition chWord32 {term : Core.Algebra} : term (Word32 * (Word32 * Word32)) Word32 := bitwiseTri ch. Definition majWord32 {term : Core.Algebra} : term (Word32 * (Word32 * Word32)) Word32 := bitwiseTri maj. Definition shift32 z {term : Core.Algebra} : term Word32 Word32 := shift_const z. Definition rotate32 z {term : Core.Algebra} : term Word32 Word32 := rotate_const z. Definition hashBlock {term : Core.Algebra} : term (Word256 * Word512) Word256 := let a32 := add32 in let x32 := xor3Word32 in let diag := O I H &&& I O H in let odiag := O diag in let idiag := I diag in let bigDiag := O I I H &&& I O O H in let part1Schedule := odiag &&& bigDiag in let smallSigma0 := rotate32 (-7) &&& rotate32 (-18) &&& shift32 (-3) >>> x32 in let smallSigma1 := rotate32 (-17) &&& rotate32 (-19) &&& shift32 (-10) >>> x32 in let smallSigma := (O O O (O H &&& (I H >>> smallSigma0)) >>> a32) &&& (I (O O I H &&& (I I O H >>> smallSigma1)) >>> a32) >>> a32 in let schedule := (O part1Schedule &&& (O idiag &&& (O I I I H &&& I (O O O H)))) &&& (I part1Schedule &&& (I idiag &&& (I I I I H &&& smallSigma))) in let bigSigma0 := rotate32 (-2) &&& rotate32 (-13) &&& rotate32 (-22) >>> x32 in let bigSigma1 := rotate32 (-6) &&& rotate32 (-11) &&& rotate32 (-25) >>> x32 in let t1 := (O H &&& I I O O O O H >>> a32) &&& I O (I (I I H &&& ((O O H >>> bigSigma1) &&& (O O H &&& diag >>> chWord32) >>> a32)) >>> a32) >>> a32 in let t12 := O ((O I H &&& I H >>> majWord32) &&& (O (O H &&& (I H >>> bigSigma0)) >>> a32)) >>> a32 in let t1d := O O O H &&& I O O H >>> a32 in let part1Round := ((t1 &&& I O O O O H) &&& I O odiag) &&& I O (bigDiag &&& idiag) in let part2Round := ((t12 &&& O O I H) &&& O I H) &&& ((t1d &&& I O I H) &&& I I H) in let round := part1Round >>> part2Round in let step := round &&& I I schedule in let k0 := 1116352408%Z in let ks := [ 1899447441; 3049323471; 3921009573; 961987163 ; 1508970993; 2453635748; 2870763221; 3624381080; 310598401; 607225278; 1426881987; 1925078388; 2162078206; 2614888103; 3248222580; 3835390401; 4022224774; 264347078; 604807628; 770255983; 1249150122; 1555081692; 1996064986; 2554220882; 2821834349; 2952996808; 3210313671; 3336571891; 3584528711; 113926993; 338241895; 666307205; 773529912; 1294757372; 1396182291; 1695183700; 1986661051; 2177026350; 2456956037; 2730485921; 2820302411; 3259730800; 3345764771; 3516065817; 3600352804; 4094571909; 275423344; 430227734; 506948616; 659060556; 883997877; 958139571; 1322822218; 1537002063; 1747873779; 1955562222; 2024104815; 2227730452; 2361852424; 2428436474; 2756734187; 3204031479; 3329325298]%Z in let compression := scribe32 k0 &&& iden >>> fold_right (fun k (rec : term (Word32 * (Word256 * Word512)) Word256) => scribe32 k &&& step >>> rec) round ks in let collate (x : term Word256 Word32) := O x &&& I x >>> a32 in O H &&& compression >>> ((collate (O O O H) &&& collate (O O I H)) &&& (collate (O I O H) &&& collate (O I I H))) &&& ((collate (I O O H) &&& collate (I O I H)) &&& (collate (I I O H) &&& collate (I I I H))). End Definitions. Lemma add32_correct (x y : Word32) : Int.repr (toZ (|[add32]| (x,y))) = Int.add (Int.repr (toZ x)) (Int.repr (toZ y)). Proof. rewrite coqlib3.add_repr. change (_ (x, y)) with (|[I H]| (|[adder (n:=5)]| (x,y))). rewrite <- (adder_correct _ x y). destruct (|[adder (n:=5)]| (x,y)) as [c z]. rewrite toZ_Pair, two_power_nat_equiv. rewrite <- Int.repr_unsigned, Int.unsigned_repr_eq. rewrite Zplus_comm, Z_mod_plus_full. rewrite toZ_mod. reflexivity. Qed. Lemma xor3Word32_xor (x y z : Word32) : Int.repr (toZ (|[xor3Word32]| (x,(y,z)))) = Int.xor (Int.xor (Int.repr (toZ x)) (Int.repr (toZ y))) (Int.repr (toZ z)). Proof. apply Int.same_bits_eq; intros i Hi. repeat rewrite Int.bits_xor by auto. repeat rewrite Int.testbit_repr by auto. set (f a b c := xorb (xorb a b) c). apply (bitwiseTri_correct f);[|intros [[] | []] [[] | []] [[] | []]]; reflexivity. Qed. Lemma chWord32_Ch (x y z : Word32) : Int.repr (toZ (|[chWord32]| (x,(y,z)))) = SHA256.Ch (Int.repr (toZ x)) (Int.repr (toZ y)) (Int.repr (toZ z)). Proof. apply Int.same_bits_eq; intros i Hi. unfold SHA256.Ch. rewrite Int.bits_xor by auto. repeat rewrite Int.bits_and by auto. rewrite Int.bits_not by auto. repeat rewrite Int.testbit_repr by auto. set (f a b c := xorb (a && b) (negb a && c)). apply (bitwiseTri_correct f);[|intros [[] | []] [[] | []] [[] | []]]; reflexivity. Qed. Lemma majWord32_Maj (x y z : Word32) : Int.repr (toZ (|[majWord32]| (x,(y,z)))) = SHA256.Maj (Int.repr (toZ x)) (Int.repr (toZ y)) (Int.repr (toZ z)). Proof. apply Int.same_bits_eq; intros i Hi. unfold SHA256.Maj. repeat rewrite Int.bits_xor by auto. repeat rewrite Int.bits_and by auto. repeat rewrite Int.testbit_repr by auto. set (f a b c := xorb (xorb (a && c) (b && c)) (a && b)). apply (bitwiseTri_correct f);[|intros [[] | []] [[] | []] [[] | []]]; reflexivity. Qed. Lemma shift32_correct z (Hz : (0 <= (-z) <= Int.max_unsigned)%Z) (x : Word32) : Int.repr (toZ (|[shift32 z]| x)) = general_lemmas.Shr (-z) (Int.repr (toZ x)). Proof. unfold general_lemmas.Shr. apply Int.same_bits_eq; intros i Hi. rewrite Int.testbit_repr by assumption. rewrite Int.bits_shru by assumption. unfold shift32. rewrite <-(Z.opp_involutive z) at 1. rewrite shift_const_correct by assumption. rewrite Int.unsigned_repr by assumption. destruct (Coqlib.zlt _ _) as [Hiz|Hiz]. rewrite Int.testbit_repr by lia. reflexivity. rewrite toZ_mod, two_power_nat_equiv. apply Z.mod_pow2_bits_high. clear - Hiz. cbn in *. lia. Qed. Lemma rotate32_correct z (x : Word32) : Int.repr (toZ (|[rotate32 z]| x)) = SHA256.Rotr (-z) (Int.repr (toZ x)). Proof. unfold SHA256.Rotr. apply Int.same_bits_eq; intros i Hi. rewrite Int.bits_ror by assumption. rewrite Int.testbit_repr by assumption. rewrite Int.testbit_repr by (apply Z_mod_lt; constructor). unfold rotate32. rewrite <-(Z.opp_involutive z) at 1. rewrite rotate_const_correct_word by assumption. rewrite Int.unsigned_repr_eq, <- (Zplus_mod_idemp_r ((-z) mod Int.modulus))%Z, <- Znumtheory.Zmod_div_mod; try constructor. rewrite Zplus_mod_idemp_r. reflexivity. apply Znumtheory.Zmod_divide; auto with zarith. Qed. Lemma hashBlock_correct (h : Word256) (b : Word512) : to_hash256 (|[hashBlock]| (h, b)) = SHA256.hash_block (to_hash256 h) (repr_Block b) :> SHA256.registers. Proof. cbv beta delta [hashBlock]. do 7 clearLet. do 6 introLet. do 5 clearLet. do 6 introLet. simpl. change (|[O H &&& compression]| (h, b)) with (h, |[compression]| (h,b)). unfold SHA256.hash_block. replace (SHA256.Round (to_hash256 h) (SHA256.nthi (repr_Block b)) 63) with (hash256_reg (to_hash256 (|[compression]| (h,b)))). destruct (|[compression]| (h,b)) as [[[h'0 h'1][h'2 h'3]][[h'4 h'5][h'6 h'7]]]. destruct h as [[[h0 h1][h2 h3]][[h4 h5][h6 h7]]]. simpl. rewrite <- !add32_correct. reflexivity. clear collate. pose (ks' := k0::ks). pose (fr := fold_right (fun (k rec : Arrow (Word256 * Word512) (Word256 * Word512)) => rec >>> k) H (map (fun k => scribe32 k &&& H >>> step) (rev ks'))). replace (|[compression]| (h,b)) with (|[fr >>> O H]| (h, b)); revgoals. unfold fr, compression, ks'; clear fr compression ks'. clearbody ks. rewrite <- fold_symmetric by reflexivity. rewrite <- fold_left_rev_right, map_rev, rev_involutive. simpl fold_right at 1. set (fr0 := fold_right comp _ _);fold (Word256) in fr0. set (fr1 := fold_right _ _ _). unfold comp; simpl; fold Word32. match goal with |- _ = fr1 ?p => set (p0:=p) end. change (step _) with (step p0). generalize p0; clear p0. clear h b. induction ks;[reflexivity|]. intros p. unfold fr0. simpl fold_right at 1. unfold comp; simpl; rewrite IHks. destruct p as [k [h b]]. unfold fr1, comp; simpl; f_equal. unfold pair; simpl. unfold scribe32; rewrite !scribe_correct. reflexivity. cut (to_hash256 (fst (|[fr]| (h, b))) = SHA256.Round (to_hash256 h) (SHA256.nthi (repr_Block b)) 63 :> SHA256.registers /\ repr_Block (snd (|[fr]| (h, b))) = map (fun n => SHA256.W (SHA256.nthi (repr_Block b)) (Z.of_nat n)) (seq (Z.to_nat (63 + 1)) 16)). intros [<- _]. reflexivity. revert fr. rewrite <- (firstn_all ks'). change (length ks') with (Z.to_nat (63 + 1)). cut (63 < 64)%Z;[|lia]. apply SHA256.Round_ind. intros t Ht _ _ fr; unfold fr. replace (Z.to_nat _) with 0 by (destruct t as [|t|t];try discriminate;destruct t;reflexivity). split. reflexivity. cbn. repeat (rewrite SHA256.W_equation; cbn). destruct b as [[[[b0 b1][b2 b3]][[b4 b5][b6 b7]]] [[[b8 b9][ba bb]][[bc bd][be bf]]]]. reflexivity. intros t Ht Hzlt IH Ht0. assert (Ht1 : (t - 1 < 64)%Z) by lia. specialize (IH Ht1). rewrite Z.sub_add in IH. pose (kt := nth (Z.to_nat t) ks' 0%Z). assert (Ht2 : Z.to_nat t < length ks'). change (Z.to_nat t < Z.to_nat 64). rewrite <- Z2Nat.inj_lt; lia. replace (firstn (Z.to_nat (t + 1)) ks') with (firstn (Z.to_nat t) ks' ++ [kt]); revgoals. rewrite Z2Nat.inj_add by lia. unfold kt. rewrite sublist.firstn_1_skipn by auto. rewrite <- firstn_app_2, firstn_skipn, firstn_length_le by lia. reflexivity. rewrite rev_app_distr, map_app, fold_right_app. set (fr := fold_right _ H _) in *. replace (SHA256.nthi SHA256.K256 t) with (Int.repr kt) by (symmetry; apply map_nth). clearbody ks'; clear k0 ks compression. destruct IH as [IH0 IH1]. split. rewrite <- IH0. replace (SHA256.W (SHA256.nthi (repr_Block b)) t) with (hd Int.zero (repr_Block (snd (fr (h, b))))); revgoals. rewrite IH1. cbn. rewrite Z2Nat.id by lia. reflexivity. cbn -[round scribe32 kt]. unfold scribe32; rewrite scribe_correct. match goal with |- _ (to_hash256 (round (_, ?p))) = _ => destruct p as [[[[h0 h1][h2 h3]][[h4 h5][h6 h7]]] [[[[b0 b1][b2 b3]][[b4 b5][b6 b7]]] [[[b8 b9][ba bb]][[bc bd][be bf]]]]] end. cbn -[rotate32 xor3Word32 majWord32 chWord32 add32 toZ fromZ kt]. unfold SHA256.Sigma_0, SHA256.Sigma_1. assert (Hkt : Int.repr (toZ (fromZ kt : Word32)) = Int.repr kt). rewrite to_fromZ. symmetry. apply Int.eqm_samerepr. apply Zbits.eqmod_mod. reflexivity. repeat f_equal; rewrite !add32_correct, ?majWord32_Maj, chWord32_Ch, !xor3Word32_xor, !rotate32_correct, Hkt. rewrite Int.add_commut, Int.add_assoc; f_equal. rewrite Int.add_commut, <- Int.add_assoc; do 2 f_equal. rewrite Int.add_assoc; reflexivity. rewrite Int.add_commut; f_equal. rewrite Int.add_commut, <- Int.add_assoc; do 2 f_equal. rewrite Int.add_assoc; reflexivity. unfold iden; simpl. rewrite (Zplus_comm t 1), Z2Nat.inj_add by lia. clear -IH1 Ht. set (p := snd (fr (h, b))) in *. match goal with |- (Int.repr (toZ (O I H (fst (fst ?p0)))))::_ = _ => change p0 with p end. destruct p as [[[[b0 b1][b2 b3]][[b4 b5][b6 b7]]] [[[b8 b9][ba bb]][[bc bd][be bf]]]]. unfold drop, take, iden; simpl. injection IH1; repeat (intros ->); intros _. repeat f_equal. rewrite !Pos2Z.inj_succ, Zpos_P_of_succ_nat, Z2Nat.id by auto with zarith. replace (Z.succ _) with (16 + t)%Z by ring. rewrite SHA256.W_equation. destruct Coqlib.zlt;[lia|]. replace (16 + t - 2)%Z with (Z.of_nat 14 + t)%Z by ring. replace (16 + t - 7)%Z with (Z.of_nat 9 + t)%Z by ring. replace (16 + t - 15)%Z with (Z.of_nat 1 + t)%Z by ring. replace (16 + t - 16)%Z with (Z.of_nat 0 + t)%Z by ring. assert (HIH : forall i, i < 16 -> SHA256.W (SHA256.nthi (repr_Block b)) (Z.of_nat i + t) = nth i (map (fun n : nat => SHA256.W (SHA256.nthi (repr_Block b)) (Z.of_nat n)) (seq (Z.to_nat t) 16)) (SHA256.W (SHA256.nthi (repr_Block b)) (Z.of_nat 0))). intros i Hi. rewrite (map_nth (fun n => SHA256.W (SHA256.nthi (repr_Block b)) (Z.of_nat n))). rewrite seq_nth by auto. rewrite Nat.add_comm, Nat2Z.inj_add, Z2Nat.id by lia. reflexivity. rewrite <- IH1 in HIH. rewrite !HIH by lia. cbn -[shift32 rotate32 xor3Word32 add32 toZ]. rewrite !add32_correct, !xor3Word32_xor, !rotate32_correct, !shift32_correct by (cbn; lia). rewrite Int.add_commut; f_equal; apply Int.add_commut. Qed. Lemma scribe32_Parametric z {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {A} : R A _ (scribe32 z) (scribe32 z). Proof. unfold scribe32. auto with parametricity. Qed. #[export] Hint Immediate scribe32_Parametric : parametricity. Lemma add32_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ add32 add32. Proof. unfold add32. auto with parametricity. Qed. #[export] Hint Immediate add32_Parametric : parametricity. Lemma xor3Word32_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ xor3Word32 xor3Word32. Proof. unfold xor3Word32. repeat apply buildBitwiseTri_Parametric. auto with parametricity. Qed. #[export] Hint Immediate xor3Word32_Parametric : parametricity. Lemma chWord32_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ chWord32 chWord32. Proof. unfold chWord32. repeat apply buildBitwiseTri_Parametric. auto with parametricity. Qed. #[export] Hint Immediate chWord32_Parametric : parametricity. Lemma majWord32_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ majWord32 majWord32. Proof. unfold majWord32. repeat apply buildBitwiseTri_Parametric. auto with parametricity. Qed. #[export] Hint Immediate majWord32_Parametric : parametricity. Lemma shift32_Parametric z {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ (shift32 z) (shift32 z). Proof. unfold shift32. auto with parametricity. Qed. #[export] Hint Immediate shift32_Parametric : parametricity. Lemma rotate32_Parametric z {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ (rotate32 z) (rotate32 z). Proof. unfold rotate32. auto with parametricity. Qed. #[export] Hint Immediate rotate32_Parametric : parametricity. Lemma hashBlock_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ hashBlock hashBlock. Proof. unfold hashBlock. change Word512 with (Word256*Word256). change Word256 with ((Word64*Word64)*(Word64*Word64)). set (f0 := fun k => _). set (f1 := fun k => _). assert (Hfold : forall l e0 e1, R _ _ e0 e1 -> (forall k rec0 rec1, R _ _ rec0 rec1 -> R _ _ (f0 k rec0) (f1 k rec1)) -> R _ _ (fold_right f0 e0 l) (fold_right f1 e1 l)); [induction l;simpl|unfold f0, f1 in *; clear f0 f1]; solve [auto 30 with parametricity]. Qed. #[export] Hint Immediate hashBlock_Parametric : parametricity. Require Import Simplicity.MerkleRoot. Fact identityHash_hashBlock : map Byte.unsigned (hash256_to_bytelist (identityHash hashBlock)) = map Byte.unsigned (sha.functional_prog.hexstring_to_bytelist "609cc1459375db728f2172c962807e3161df4cced6592d2c4e594a7779ab3175"). Proof. vm_compute. reflexivity. Qed. ================================================ FILE: Coq/Simplicity/StaticAnalysis.v ================================================ Require Import NArith. Require Import Simplicity.Util.List. Require Import Simplicity.Alg. Require Import Simplicity.BitMachine. Require Import Simplicity.Translate. Require Import Simplicity.Ty. Set Implicit Arguments. Local Open Scope N_scope. Module StateShape. (* In this section we prove that executing Simplicity programs on the Bit * Machine starting from *any* state, preserves the shape of the state if it * doesn't crash or halt. * Although spec allows for starting from the Halted state, any program * starting from the Halted state must end in the Halted state, which will * violating the assumptions of spec that it doesn't end in the Halted state. * Hence this scenario vacuously sastifies the spec. *) Definition spec {A B : Ty} (p : Naive.Program_ty A B) := forall s0 (s1 : RunState), s0 >>- p ->> s1 -> stateShape s0 = stateShape s1. Lemma iden_spec {A : Ty} : spec (A:=A) iden. Proof. intros s0 s1. apply stateShape_copy. Qed. Lemma comp_spec {A B C : Ty} (s : Naive.Program_ty A B) (t : Naive.Program_ty B C) : spec s -> spec t -> spec (comp s t) . Proof. intros Hs Ht s0 s5 Hs05. simpl in Hs05. apply seq_complete in Hs05. destruct Hs05 as [s4 Hs04 Hs45]. apply seq_complete in Hs04. destruct Hs04 as [s3 Hs03 Hs34]. apply seq_complete in Hs03. destruct Hs03 as [s2 Hs02 Hs23]. apply seq_complete in Hs02. destruct Hs02 as [s1 Hs01 Hs12]. pose (inv := dropFrame_complete Hs45);inversion inv as [s4' s5' Hs45'|]; clear inv Hs45. subst s4; subst s5. apply Ht in Hs34. destruct s3 as [|s3];[discriminate|]. pose (inv := moveFrame_complete Hs23);inversion inv as [s2' s3' Hs23'|]; clear inv Hs23. subst s2; subst s3. apply Hs in Hs12. destruct s1 as [|s1];[discriminate|]. pose (inv := newFrame_complete Hs01);inversion inv as [s0' s1' Hs01'|]; clear inv Hs01. subst s0; subst s1. revert Hs12 Hs34. inversion_clear Hs01'. inversion_clear Hs23'. inversion_clear Hs45'. clear. unfold stateShape, runStateShape; cbn. do 2 inversion 1. reflexivity. Qed. Lemma unit_spec {A : Ty} : spec (A:=A) unit. Proof. intros x y Hxy. cbn in Hxy. apply nop_complete in Hxy. congruence. Qed. Lemma injl_spec {A B C : Ty} (t : Naive.Program_ty A B) : spec t -> spec (injl (C:=C) t). Proof. intros Ht s0 s3 Hs03. simpl in Hs03. apply seq_complete in Hs03. destruct Hs03 as [s2 Hs02 Hs23]. apply seq_complete in Hs02. destruct Hs02 as [s1 Hs01 Hs12]. rewrite (stateShape_write Hs01). rewrite (stateShape_skip Hs12). apply (Ht _ _ Hs23). Qed. Lemma injr_spec {A B C : Ty} (t : Naive.Program_ty A C) : spec t -> spec (injr (B:=B) t). Proof. intros Ht s0 s3 Hs03. simpl in Hs03. apply seq_complete in Hs03. destruct Hs03 as [s2 Hs02 Hs23]. apply seq_complete in Hs02. destruct Hs02 as [s1 Hs01 Hs12]. rewrite (stateShape_write Hs01). rewrite (stateShape_skip Hs12). apply (Ht _ _ Hs23). Qed. Lemma bump_spec {A B : Ty} (t : Naive.Program_ty A B) n (Ht : spec t) x (y : RunState) : x >>- bump n t ->> y -> stateShape x = stateShape y. Proof. unfold bump. intros Hxy. apply seq_complete in Hxy. destruct Hxy as [s2 Hxs2 Hs2y]. apply seq_complete in Hxs2. destruct Hxs2 as [s1 Hxs1 Hs1s2]. rewrite (stateShape_fwd Hxs1). destruct s2 as [|s2]. pose (inv := runHalt (trace Hs2y));inversion inv. rewrite (Ht _ _ Hs1s2). apply (stateShape_bwd Hs2y). Qed. Lemma case_spec {A B C D : Ty} (s : Naive.Program_ty (A * C) D) (t : Naive.Program_ty (B * C) D) : spec s -> spec t -> spec (case s t). Proof. intros Hs Ht x y Hxy. simpl in Hxy. remember (Running y) as y'. revert Heqy'; pattern x; pattern y; revert x y' Hxy. apply choice_complete;[intros x y' [|] Hb Hxy ->|discriminate]; eauto using bump_spec. Qed. Lemma pair_spec {A B C : Ty} (s : Naive.Program_ty A B) (t : Naive.Program_ty A C) : spec s -> spec t -> spec (pair s t). Proof. intros Hs Ht x z Hxz. simpl in Hxz. apply seq_complete in Hxz. destruct Hxz as [y Hxy Hyz]. destruct y as [|y]. pose (inv := runHalt (trace Hyz));inversion inv. rewrite (Hs _ _ Hxy). apply (Ht _ _ Hyz). Qed. Lemma take_spec {A B C : Ty} (t : Naive.Program_ty A C) : spec t -> spec (take (B:=B) t). Proof. auto. Qed. Lemma drop_spec {A B C : Ty} (t : Naive.Program_ty B C) : spec t -> spec (drop (A:=A) t). Proof. intros Ht x y; cbn. apply bump_spec. assumption. Qed. Lemma Core_spec {A B : Ty} (t : forall {alg : Core.Algebra}, alg A B) (Ht : Core.Parametric (@t)) : forall s0 (s1 : RunState), s0 >>- @t Naive.translate ->> s1 -> stateShape s0 = stateShape s1. Proof. refine (Ht _ _ (Core.Parametric.Pack (_ : Core.Parametric.class (fun A B x (_:Naive.Program_ty A B) => @spec A B x)))). constructor; intros. - apply iden_spec. - apply comp_spec; assumption. - apply unit_spec. - apply injl_spec; assumption. - apply injr_spec; assumption. - apply case_spec; assumption. - apply pair_spec; assumption. - apply take_spec; assumption. - apply drop_spec; assumption. Qed. Lemma StateSize A B (p : Naive.Program_ty A B) (Hp : spec p) s0 s1 : s0 >>- p ->> s1 -> stateSize s1 <= stateSize s0. Proof. intros H01. destruct s1 as [|s1];[apply N.le_0_l|]. unfold stateSize. rewrite (Hp _ _ H01). reflexivity. Qed. End StateShape. Module MaximumMemory. Definition bound_ty (A B : Ty) := N. Definition extraMemoryBound_class : Core.class bound_ty := {| Core.iden A := 0 ; Core.comp A B C s t := N.of_nat (bitSize B) + N.max s t ; Core.unit A := 0 ; Core.injl A B C t := t ; Core.injr A B C t := t ; Core.case A B C D s t := N.max s t ; Core.pair A B C s t := N.max s t ; Core.take A B C t := t ; Core.drop A B C t := t |}. Canonical Structure extraMemoryBound : Core.Algebra := Core.Pack bound_ty extraMemoryBound_class. Definition MemoryBound {A B : Ty} (t : bound_ty A B) x : N := stateSize x + t. Definition spec {A B : Ty} (p : Naive.Program_ty A B) (mt : bound_ty A B) := forall x y (tr : x >>- p ->> y), maximumMemoryResidence (trace tr) <= MemoryBound mt x. Lemma iden_spec {A : Ty} : spec iden (iden (A:=A)). Proof. intros x y tr. unfold MemoryBound. cbn in *. rewrite MMR_copy, N.add_0_r. reflexivity. Qed. Lemma comp_spec {A B C : Ty} (ps : Naive.Program_ty A B) (pt : Naive.Program_ty B C) ms mt: spec ps ms -> spec pt mt -> StateShape.spec ps -> StateShape.spec pt -> spec (comp ps pt) (comp ms mt). Proof. intros Hs Ht Ss St s0 s5 tr05. unfold MemoryBound. cbn in *. destruct (seq_complete tr05) as [s4 tr04 tr45]. rewrite (MMR_seq tr04 tr45 tr05). destruct (seq_complete tr04) as [s3 tr03 tr34]. rewrite (MMR_seq tr03 tr34 tr04). destruct (seq_complete tr03) as [s2 tr02 tr23]. rewrite (MMR_seq tr02 tr23 tr03). destruct (seq_complete tr02) as [s1 tr01 tr12]. rewrite (MMR_seq tr01 tr12 tr02). rewrite N.add_assoc. rewrite MMR_newFrame, MMR_moveFrame, MMR_dropFrame. transitivity (stateSize s1 + N.max ms mt). rewrite <- N.add_max_distr_l; do 2 rewrite <- N.max_assoc. apply N.max_le_compat. apply N.max_lub;[apply N.le_add_r|apply (Hs _ _ tr12)]. transitivity (stateSize s2 + mt). replace (stateSize s2) with (stateSize s3). transitivity (N.max (stateSize s3) (maximumMemoryResidence (trace tr34))). rewrite N.max_assoc. apply N.max_lub;[reflexivity|]. etransitivity;[apply (StateShape.StateSize St tr34)|apply N.le_max_l]. apply N.max_lub;[apply N.le_add_r|apply (Ht _ _ tr34)]. destruct (moveFrame_complete tr23) as [s2 s3 T23|];[|reflexivity]. inversion T23;cbn. rewrite fullWriteFrame_size. ring. apply N.add_le_mono_r. apply (StateShape.StateSize Ss tr12). apply N.add_le_mono_r. destruct (newFrame_complete tr01) as [s0 s1 T01|];[apply N.eq_le_incl|apply N.le_0_l]. inversion T01; cbn. ring. Qed. Lemma unit_spec {A : Ty} : spec unit (unit (A:=A)). Proof. intros x y tr. unfold MemoryBound. cbn in *. destruct (trace_subproof _); cbn. rewrite N.add_0_r. reflexivity. Qed. Lemma injl_spec {A B C : Ty} (pt : Naive.Program_ty A B) mt : spec pt mt -> spec (injl pt) (injl (C:=C) mt). Proof. intros Ht s0 s3 tr03. unfold MemoryBound. cbn in *. destruct (seq_complete tr03) as [s2 tr02 tr23]. rewrite (MMR_seq tr02 tr23 tr03). destruct (seq_complete tr02) as [s1 tr01 tr12]. rewrite (MMR_seq tr01 tr12 tr02). rewrite MMR_write, MMR_skip. unfold stateSize. rewrite (stateShape_write tr01), N.max_id, (stateShape_skip tr12). apply N.max_lub. apply N.le_add_r. apply Ht. Qed. Lemma injr_spec {A B C : Ty} (pt : Naive.Program_ty A C) mt : spec pt mt -> spec (injr pt) (injr (B:=B) mt). Proof. intros Ht s0 s3 tr03. unfold MemoryBound. cbn in *. destruct (seq_complete tr03) as [s2 tr02 tr23]. rewrite (MMR_seq tr02 tr23 tr03). destruct (seq_complete tr02) as [s1 tr01 tr12]. rewrite (MMR_seq tr01 tr12 tr02). rewrite MMR_write, MMR_skip. unfold stateSize. rewrite (stateShape_write tr01), N.max_id, (stateShape_skip tr12). apply N.max_lub. apply N.le_add_r. apply Ht. Qed. Lemma bump_spec {A B : Ty} (pt : Naive.Program_ty A B) mt (Ht : spec pt mt) x y n (tr : x >>- bump n pt ->> y) : maximumMemoryResidence (trace tr) <= MemoryBound mt x. Proof. unfold bump in tr. destruct (seq_complete tr) as [s2 tr02 tr23]. rewrite (MMR_seq tr02 tr23). destruct (seq_complete tr02) as [s1 tr01 tr12]. rewrite (MMR_seq tr01 tr12). rewrite MMR_bwd, MMR_fwd. unfold MemoryBound, stateSize. rewrite (stateShape_fwd tr01). rewrite (N.max_comm (stateShapeSize _)), <- N.max_assoc, N.max_l. apply Ht. apply MMR_bounds. Qed. Lemma case_spec {A B C D : Ty} (ps : Naive.Program_ty (A * C) D) (pt : Naive.Program_ty (B * C) D) ms mt : spec ps ms -> spec pt mt -> spec (case ps pt) (case ms mt). Proof. intros Hs Ht s0 s1 tr01. unfold MemoryBound. cbn in *. rewrite <- N.add_max_distr_l. generalize tr01. pattern s0; pattern s1. revert s0 s1 tr01. apply choice_complete. intros s0 s1 [|] Heq tr tr01. rewrite <- (trace_right tr tr01);[|assumption]. etransitivity;[apply bump_spec;apply Ht|apply N.le_max_r]. rewrite <- (trace_left tr tr01);[|assumption]. etransitivity;[apply bump_spec;apply Hs|apply N.le_max_l]. unfold runProgram, choice;cbn. intros tr01. destruct (trace_subproof _); cbn. apply N.le_0_l. Qed. Lemma pair_spec {A B C : Ty} (ps : Naive.Program_ty A B) (pt : Naive.Program_ty A C) ms mt : spec ps ms -> spec pt mt -> StateShape.spec ps -> spec (pair ps pt) (pair ms mt). Proof. intros Hs Ht Ss s0 s2 tr02. unfold MemoryBound. cbn in *. destruct (seq_complete tr02) as [s1 tr01 tr12]. rewrite (MMR_seq tr01 tr12 tr02). rewrite <- N.add_max_distr_l. apply N.max_le_compat. apply Hs. etransitivity;[apply Ht|]. apply N.add_le_mono_r. apply (StateShape.StateSize Ss tr01). Qed. Lemma take_spec {A B C : Ty} (pt : Naive.Program_ty A C) mt : spec pt mt -> spec (take pt) (take (B:=B) mt). Proof. auto. Qed. Lemma drop_spec {A B C : Ty} (pt : Naive.Program_ty B C) mt : spec pt mt -> spec (drop pt) (drop (A:=A) mt). Proof. intros Ht x n Hp;cbn. apply (bump_spec Ht Hp). Qed. Lemma Core_spec {A B : Ty} (t : forall {alg : Core.Algebra}, alg A B) (Ht : Core.Parametric (@t)) : spec t t. Proof. pose (R A B (x : Naive.Program_ty A B) y := StateShape.spec x /\ spec x y). cut (R A B (t _) (t _));[intros [spec1 spec2]; auto|]. refine (Ht _ _ (Core.Parametric.Pack (_ : Core.Parametric.class R))). constructor; unfold R; intros; split. - apply StateShape.iden_spec. - apply iden_spec. - apply StateShape.comp_spec; tauto. - apply comp_spec; tauto. - apply StateShape.unit_spec. - apply unit_spec. - apply StateShape.injl_spec; tauto. - apply injl_spec; tauto. - apply StateShape.injr_spec; tauto. - apply injr_spec; tauto. - apply StateShape.case_spec; tauto. - apply case_spec; tauto. - apply StateShape.pair_spec; tauto. - apply pair_spec; tauto. - apply StateShape.take_spec; tauto. - apply take_spec; tauto. - apply StateShape.drop_spec; tauto. - apply drop_spec; tauto. Qed. Definition CellBound {A B : Ty} (t : bound_ty A B) : N := N.of_nat (bitSize A) + N.of_nat (bitSize B) + t. Lemma CellBound_correct {A B : Ty} (t : forall {alg : Core.Algebra}, alg A B) (Ht : Core.Parametric (@t)) a y (tr : fillContext emptyCtx (Naive.LocalStateBegin t a) >>- @t Naive.translate ->> y) : maximumMemoryResidence (trace tr) <= CellBound t. Proof. etransitivity;[apply (Core_spec Ht tr)|]. unfold MemoryBound, CellBound, stateSize, stateShapeSize; cbn. rewrite app_nil_r, encode_length, N.add_0_r, <- plus_n_O. reflexivity. Qed. End MaximumMemory. ================================================ FILE: Coq/Simplicity/Translate.v ================================================ Require Import PeanoNat. Require Import Simplicity.Util.List. Require Import Simplicity.Util.Thrist. Require Import Simplicity.Alg. Require Import Simplicity.BitMachine. Require Import Simplicity.Ty. Set Implicit Arguments. Local Open Scope ty_scope. Local Open Scope mc_scope. Local Open Scope semantic_scope. Fixpoint bitSize (X : Ty) : nat := match X with | Unit => 0 | Sum A B => 1 + max (bitSize A) (bitSize B) | Prod A B => bitSize A + bitSize B end. (* We take advantage that x - y = 0 when x <= y for natural numbers. *) Definition padL (X Y : Ty) : nat := bitSize Y - bitSize X. Definition padR (X Y : Ty) : nat := bitSize X - bitSize Y. Lemma padL_bitSize (X Y : Ty) : (padL X Y + bitSize X = max (bitSize X) (bitSize Y))%nat. Proof. unfold padL. apply Nat.max_case_strong; intros HXY. - rewrite <- Nat.sub_0_le in HXY. rewrite HXY. reflexivity. - rewrite Nat.sub_add; auto. Qed. Lemma padR_bitSize (X Y : Ty) : (padR X Y + bitSize Y = max (bitSize X) (bitSize Y))%nat. Proof. unfold padR. apply Nat.max_case_strong; intros HXY. - rewrite Nat.sub_add; auto. - rewrite <- Nat.sub_0_le in HXY. rewrite HXY. reflexivity. Qed. Fixpoint encode {X : Ty} : X -> list Cell := match X with | Unit => fun _ => nil | Sum A B => fun ab => match ab with | inl a => Some false :: repeat None (padL A B) ++ encode a | inr b => Some true :: repeat None (padR A B) ++ encode b end | Prod A B => fun ab => let (a, b) := ab in encode a ++ encode b end. Lemma encode_length {X : Ty} : forall x : X, length (encode x) = bitSize X. Proof. induction X. - reflexivity. - intros [a|b]; cbn; rewrite app_length, repeat_length; [rewrite IHX1, padL_bitSize | rewrite IHX2, padR_bitSize]; reflexivity. - intros [a b]; cbn. rewrite app_length, IHX1, IHX2. reflexivity. Qed. Module Naive. Definition Program_ty (A B : Ty) := Program. Definition translate_class : Core.class Program_ty := {| Core.iden A := copy (bitSize A) ; Core.comp A B C ps pt := newFrame (bitSize B) ;;; ps ;;; moveFrame ;;; pt ;;; dropFrame ; Core.unit A := nop ; Core.injl A B C pt := write false ;;; skip (padL B C) ;;; pt ; Core.injr A B C pt := write true ;;; skip (padR B C) ;;; pt ; Core.case A B C D ps pt := bump (1 + padL A B) ps ||| bump (1 + padR A B) pt ; Core.pair A B C ps pt := ps ;;; pt ; Core.take A B C pt := pt ; Core.drop A B C pt := bump (bitSize A) pt |}. Canonical Structure translate : Core.Algebra := Core.Pack Program_ty translate_class. Definition LocalStateBegin {A B : Ty} (t : Arrow A B) (a : A) := {| readLocalState := encode a; writeLocalState := newWriteFrame (bitSize B) |}. Definition LocalStateEnd {A B : Ty} (t : Arrow A B) (a : A) := {| readLocalState := encode a; writeLocalState := fullWriteFrame (encode (t a)) |}. Definition spec {A B : Ty} (p : Program_ty A B) (t : Arrow A B) := forall a ctx, fillContext ctx (LocalStateBegin t a) >>- p ->> fillContext ctx (LocalStateEnd t a). Lemma iden_spec {A : Ty} : spec (A:=A) iden iden. Proof. intros a ctx; cbn. unfold LocalStateBegin, LocalStateEnd. rewrite <- (encode_length a). apply copy_correct. Qed. Lemma comp_spec {A B C : Ty} (s : Arrow A B) (t : Arrow B C) ps pt : spec ps s -> spec pt t -> spec (comp ps pt) (comp s t) . Proof. intros Hs Ht a ctx. unfold LocalStateBegin, LocalStateEnd. destruct ctx as [irf arf awf iwf]. repeat eapply seq_correct. - apply newFrame_correct. - cbn. pose (ctx0 := {| inactiveReadFrames := irf ; activeReadFrame := arf ; activeWriteFrame := newWriteFrame 0 ; inactiveWriteFrames := {| writeData := writeData awf ; writeEmpty := bitSize C + writeEmpty awf |} :: iwf |}). rewrite (plus_n_O (bitSize B)). apply (Hs a ctx0). - unfold fillContext; cbn. rewrite app_nil_r. apply moveFrame_correct. - cbn. pose (ctx0 := {| inactiveReadFrames := {| prevData := prevData arf; nextData := encode a ++ nextData arf |} :: irf ; activeReadFrame := setFrame nil ; activeWriteFrame := awf ; inactiveWriteFrames := iwf |}). rewrite <- (app_nil_r (encode (s a))). apply (Ht (s a) ctx0). - unfold fillContext; cbn. rewrite app_nil_r. apply dropFrame_correct. Qed. Lemma unit_spec {A : Ty} : spec (A:=A) unit unit. Proof. intros a ctx. apply nop_correct. Qed. Lemma injl_spec {A B C : Ty} (t : Arrow A B) pt : spec pt t -> spec (injl pt) (injl (C:=C) t). Proof. intros Ht a ctx. repeat eapply seq_correct. - pose (ls1 := {| readLocalState := encode a; writeLocalState := newWriteFrame (max (bitSize B) (bitSize C)) |}). pose (ls2 := {| readLocalState := nil; writeLocalState := newWriteFrame 1 |}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 ls2)) at 1. rewrite <- context_action. apply write_correct. - rewrite context_action. unfold appendLocalState; cbn. rewrite <- padL_bitSize. pose (ls1 := {| readLocalState := encode a; writeLocalState := {| writeData := Some false :: nil; writeEmpty := bitSize B |}|}). pose (ls2 := {| readLocalState := nil; writeLocalState := newWriteFrame (padL B C)|}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 ls2)) at 1. rewrite <- context_action. apply skip_correct. - rewrite context_action. unfold appendLocalState; cbn. rewrite <- (app_nil_r (encode a)), <- (Nat.add_0_r (bitSize B)). pose (ls1 := {| readLocalState := nil; writeLocalState := fullWriteFrame (Some false :: repeat None (padL B C))|}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateBegin t a))) at 1. unfold LocalStateEnd, fullWriteFrame; cbn. rewrite <- (app_nil_r (encode a)), rev_app_distr, <- app_assoc. change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateEnd t a))) at 2. do 2 rewrite <- context_action. apply Ht. Qed. Lemma injr_spec {A B C : Ty} (t : Arrow A C) pt : spec pt t -> spec (injr pt) (injr (B:=B) t). Proof. intros Ht a ctx. repeat eapply seq_correct. - pose (ls1 := {| readLocalState := encode a; writeLocalState := newWriteFrame (max (bitSize B) (bitSize C)) |}). pose (ls2 := {| readLocalState := nil; writeLocalState := newWriteFrame 1 |}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 ls2)) at 1. rewrite <- context_action. apply write_correct. - rewrite context_action. unfold appendLocalState; cbn. rewrite <- padR_bitSize. pose (ls1 := {| readLocalState := encode a; writeLocalState := {| writeData := Some true :: nil; writeEmpty := bitSize C |}|}). pose (ls2 := {| readLocalState := nil; writeLocalState := newWriteFrame (padR B C)|}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 ls2)) at 1. rewrite <- context_action. apply skip_correct. - rewrite context_action. unfold appendLocalState; cbn. rewrite <- (app_nil_r (encode a)), <- (Nat.add_0_r (bitSize C)). pose (ls1 := {| readLocalState := nil; writeLocalState := fullWriteFrame (Some true :: repeat None (padR B C))|}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateBegin t a))) at 1. unfold LocalStateEnd, fullWriteFrame; cbn. rewrite <- (app_nil_r (encode a)), rev_app_distr, <- app_assoc. change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateEnd t a))) at 2. do 2 rewrite <- context_action. apply Ht. Qed. Lemma caseL_spec {A B C D : Ty} (s : Arrow (A * C) D) (t : Arrow (B * C) D) ps pt : spec ps s -> forall (a : A) (c : C) ctx, fillContext ctx (LocalStateBegin (case s t) (inl a, c)) >>- bump (1 + padL A B) ps ||| bump (1 + padR A B) pt ->> fillContext ctx (LocalStateEnd (case s t) (inl a, c)). Proof. intros Hs a c ctx. apply choice_left_correct;[reflexivity|]. unfold LocalStateBegin, LocalStateEnd; cbn. rewrite <- app_assoc. rewrite <- (@repeat_length Cell None (padL A B)) at 1. set (prefix := Some false :: repeat None (padL A B)). pose (ls2 := {| readLocalState := prefix; writeLocalState := newWriteFrame 0 |}). change (fillContext _ _) with (fillContext ctx (appendLocalState (LocalStateBegin s (a,c)) ls2)) at 1. change (fillContext _ _) with (fillContext ctx (appendLocalState (LocalStateEnd s (a,c)) ls2)) at 2. repeat rewrite <- context_action. change (fillContext _ _) with (fillReadFrame (fillContext ctx (LocalStateBegin s (a,c))) {| prevData := nil; nextData := prefix |}) at 1. change (fillContext _ _) with (fillReadFrame (fillContext ctx (LocalStateEnd s (a,c))) {| prevData := nil; nextData := prefix |}) at 2. apply bump_correct. apply (Hs _ (fillReadFrame ctx {| prevData := rev (prefix); nextData := nil |})). Qed. Lemma caseR_spec {A B C D : Ty} (s : Arrow (A * C) D) (t : Arrow (B * C) D) ps pt : spec pt t -> forall (b : B) (c : C) ctx, fillContext ctx (LocalStateBegin (case s t) (inr b, c)) >>- bump (1 + padL A B) ps ||| bump (1 + padR A B) pt ->> fillContext ctx (LocalStateEnd (case s t) (inr b, c)). Proof. intros Ht b c ctx. apply choice_right_correct;[reflexivity|]. unfold LocalStateBegin, LocalStateEnd; cbn. rewrite <- app_assoc. rewrite <- (@repeat_length Cell None (padR A B)) at 1. set (prefix := Some true :: repeat None (padR A B)). pose (ls2 := {| readLocalState := prefix; writeLocalState := newWriteFrame 0 |}). change (fillContext _ _) with (fillContext ctx (appendLocalState (LocalStateBegin t (b,c)) ls2)) at 1. change (fillContext _ _) with (fillContext ctx (appendLocalState (LocalStateEnd t (b,c)) ls2)) at 2. repeat rewrite <- context_action. change (fillContext _ _) with (fillReadFrame (fillContext ctx (LocalStateBegin t (b,c))) {| prevData := nil; nextData := prefix |}) at 1. change (fillContext _ _) with (fillReadFrame (fillContext ctx (LocalStateEnd t (b,c))) {| prevData := nil; nextData := prefix |}) at 2. apply bump_correct. apply (Ht _ (fillReadFrame ctx {| prevData := rev (prefix); nextData := nil |})). Qed. Lemma case_spec {A B C D : Ty} (s : Arrow (A * C) D) (t : Arrow (B * C) D) ps pt : spec ps s -> spec pt t -> spec (case ps pt) (case s t). Proof. intros Hs Ht [[a|b] c] ctx. - apply caseL_spec; assumption. - apply caseR_spec; assumption. Qed. Lemma pair_spec {A B C : Ty} (s : Arrow A B) (t : Arrow A C) ps pt : spec ps s -> spec pt t -> spec (pair ps pt) (pair s t). Proof. intros Hs Ht a ctx. unfold LocalStateBegin, LocalStateEnd. eapply seq_correct. - rewrite <- (app_nil_r (encode a)) at 1. pose (ls1 := {| readLocalState := nil; writeLocalState := newWriteFrame (bitSize C) |}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateBegin s a))) at 1. rewrite <- context_action. apply Hs. - rewrite context_action. unfold appendLocalState, fullWriteFrame; cbn. rewrite (app_nil_r (rev _)), <- (Nat.add_0_r (bitSize C)), rev_app_distr. rewrite <- (app_nil_r (encode a)) at 2. pose (ls1 := {| readLocalState := nil; writeLocalState := fullWriteFrame (encode (s a)) |}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateBegin t a))) at 1. change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateEnd t a))) at 2. do 2 rewrite <- context_action. apply Ht. Qed. Lemma take_spec {A B C : Ty} (t : Arrow A C) pt : spec pt t -> spec (take pt) (take (B:=B) t). Proof. intros Ht [a b] ctx. unfold LocalStateBegin, LocalStateEnd, fullWriteFrame; cbn. rewrite <- (Nat.add_0_r (bitSize C)), <- (app_nil_r (rev _)). pose (ls1 := {| readLocalState := encode b; writeLocalState := newWriteFrame 0 |}). change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateBegin t a))) at 1. change (fillContext _ _) with (fillContext ctx (appendLocalState ls1 (LocalStateEnd t a))) at 2. do 2 rewrite <- context_action. apply Ht. Qed. Lemma drop_spec {A B C : Ty} (t : Arrow B C) pt : spec pt t -> spec (drop pt) (drop (A:=A) t). Proof. intros Ht [a b] ctx; cbn. pose (ls2 := {| readLocalState := encode a; writeLocalState := newWriteFrame 0 |}). change (fillContext _ _) with (fillContext ctx (appendLocalState (LocalStateBegin t b) ls2)) at 1. change (fillContext _ _) with (fillContext ctx (appendLocalState (LocalStateEnd t b) ls2)) at 2. repeat rewrite <- context_action. change (fillContext _ _) with (fillReadFrame (fillContext ctx (LocalStateBegin t b)) {| prevData := nil; nextData := encode a |}) at 1. change (fillContext _ _) with (fillReadFrame (fillContext ctx (LocalStateEnd t b)) {| prevData := nil; nextData := encode a |}) at 2. rewrite <- (encode_length a). apply bump_correct. apply (Ht _ (fillReadFrame ctx {| prevData := rev (encode a); nextData := nil |})). Qed. Theorem translate_correct {A B : Ty} (t : forall {alg : Core.Algebra}, alg A B) (Ht : Core.Parametric (@t)) : forall a ctx, fillContext ctx {| readLocalState := encode a; writeLocalState := newWriteFrame (bitSize B) |} >>- @t translate ->> fillContext ctx {| readLocalState := encode a; writeLocalState := fullWriteFrame (encode (|[ t ]| a)) |}. refine (Ht _ _ (Core.Parametric.Pack (_ : Core.Parametric.class (@spec)))). constructor; clear; intros. - apply iden_spec. - apply comp_spec; assumption. - apply unit_spec. - apply injl_spec; assumption. - apply injr_spec; assumption. - apply case_spec; assumption. - apply pair_spec; assumption. - apply take_spec; assumption. - apply drop_spec; assumption. Qed. End Naive. Canonical Structure Naive.translate. ================================================ FILE: Coq/Simplicity/Ty.v ================================================ Set Primitive Projections. Set Implicit Arguments. Declare Scope ty_scope. Inductive Ty : Set := | Unit : Ty | Sum : Ty -> Ty -> Ty | Prod : Ty -> Ty -> Ty. Bind Scope ty_scope with Ty. Fixpoint tySem (X : Ty) : Set := match X with | Unit => Datatypes.unit | Sum A B => tySem A + tySem B | Prod A B => tySem A * tySem B end. Notation "A + B" := (Sum A B) : ty_scope. Notation "A * B" := (Prod A B) : ty_scope. Coercion tySem : Ty >-> Sortclass. Definition Arrow (A B : Ty) := A -> B. Definition Kleisli (M : Type -> Type) (A B : Ty) := A -> M B. Record tyAlg (A : Set) : Set := { unitA : A ; sumA : A -> A -> A ; prodA : A -> A -> A }. Fixpoint tyCata A (alg : tyAlg A) (t : Ty) : A := match t with | Unit => unitA alg | Sum tl tr => sumA alg (tyCata alg tl) (tyCata alg tr) | Prod t1 t2 => prodA alg (tyCata alg t1) (tyCata alg t2) end. ================================================ FILE: Coq/Simplicity/Util/Arith.v ================================================ Require Import ZArith. Set Implicit Arguments. (* In order to compute, this needs to be transparent *) Definition natDiff : forall n m, {i | i + n = m} + {i | i + m = n}. Proof. assert (H0 : forall n, n + 0 = n). induction n. reflexivity. simpl; rewrite IHn; reflexivity. assert (HS : forall n m, n + S m = S (n + m)). induction n; intros m. reflexivity. simpl; rewrite IHn; reflexivity. induction n. intros m. left. exists m. apply H0. induction m. right. exists (S n). apply H0. case (IHn m); intros [i Hi]. left. exists i. rewrite <- Hi. apply HS. right. exists i. rewrite <- Hi. apply HS. Defined. Lemma Zmod_div (x y : Z) : (x mod y / y = 0)%Z. Proof. destruct (Z.eq_dec y 0) as [->|Hy]. - apply Zdiv_0_r. - auto using Z.mod_div. Qed. Lemma two_power_nat_le n m : n <= m -> (two_power_nat n <= two_power_nat m)%Z. Proof. repeat rewrite two_power_nat_equiv. auto using Z.pow_le_mono_r with zarith. Qed. Lemma two_power_nat_plus n m : (two_power_nat (n + m) = two_power_nat n * two_power_nat m)%Z. Proof. repeat rewrite two_power_nat_equiv. rewrite inj_plus, Z.pow_add_r; auto with zarith. Qed. ================================================ FILE: Coq/Simplicity/Util/List.v ================================================ Require Export Coq.Lists.List. Require Import ZArith. Lemma repeat_S_tail {A} : forall (a : A) n, repeat a n ++ (a :: nil) = repeat a (S n). Proof. intros a. induction n;[reflexivity|]. simpl. rewrite IHn. reflexivity. Qed. Lemma rev_repeat {A} : forall (a : A) n, rev (repeat a n) = repeat a n. Proof. intros a. induction n;[reflexivity|]. simpl. rewrite IHn, repeat_S_tail. reflexivity. Qed. Lemma firstn_app_3 {A} (l1 l2 : list A) : firstn (length l1) (l1 ++ l2) = l1. Proof. rewrite <- (Nat.add_0_r (length l1)), firstn_app_2; cbn. apply app_nil_r. Qed. Lemma skipn_all {A} (l : list A) : skipn (length l) l = nil. Proof. apply (app_inv_head (firstn (length l) l)). rewrite firstn_skipn, firstn_all, app_nil_r; auto. Qed. Lemma skipn_all2 {A} n (l : list A) : length l <= n -> skipn n l = nil. Proof. intros Hn. apply (app_inv_head (firstn n l)). rewrite firstn_skipn, firstn_all2, app_nil_r; auto. Qed. Lemma skipn_app {A} (n : nat) : forall (l1 l2 : list A), skipn n (l1 ++ l2) = skipn n l1 ++ skipn (n - length l1) l2. Proof. induction n. reflexivity. destruct l1. reflexivity. apply IHn. Qed. Lemma skipn_app_2 {A} (n : nat) : forall (l1 l2 : list A), skipn (length l1 + n) (l1 ++ l2) = skipn n l2. Proof. intros l1 l2. rewrite skipn_app, Nat.add_comm, Nat.add_sub, skipn_all2; auto with arith. Qed. Lemma skipn_app_3 {A} (l1 l2 : list A) : skipn (length l1) (l1 ++ l2) = l2. Proof. apply (app_inv_head l1). rewrite <- (firstn_app_3 l1 l2) at 1. apply firstn_skipn. Qed. Definition N_sum : list N -> N := fold_right N.add 0%N. Definition Z_sum : list Z -> Z := fold_right Z.add 0%Z. ================================================ FILE: Coq/Simplicity/Util/Monad/Reader.v ================================================ Require Import Logic.FunctionalExtensionality. Require Import Simplicity.Util.Monad. Local Open Scope monad_scope. Definition ReaderT E (M : Type -> Type) A := E -> M A. Section ReaderT_CIMonad. Variable E : Type. Variable M : CIMonad. Definition ReaderT_eta A (a : A) : ReaderT E M A := fun _ => eta a. Definition ReaderT_bind A B (f : A -> ReaderT E M B) (x : ReaderT E M A) : ReaderT E M B := fun e => bind (fun a => f a e) (x e). Definition ReaderT_CIMonad_class : CIMonad.class (ReaderT E M). exists ReaderT_eta ReaderT_bind. - abstract ( intros A B f0 f1 Hf a; extensionality e; unfold ReaderT_bind; rewrite !bind_def; apply f_equal; apply map_ext; intros a0; rewrite Hf; reflexivity). - abstract ( intros A x; extensionality e; unfold ReaderT_bind; rewrite bind_def, <- kleisli_comp_def; apply kleisli_compl). - abstract ( intros A B f a; extensionality e; unfold ReaderT_bind; rewrite bind_def; unfold ReaderT_eta; rewrite <- kleisli_comp_def, kleisli_compr; reflexivity). - abstract ( intros A B C g f x; extensionality e; unfold ReaderT_bind; rewrite !bind_def; rewrite <- (kleisli_comp_def (fun a : A => f a e)), <- kleisli_comp_def; rewrite <- kleisli_comp_assoc, !kleisli_comp_def; reflexivity). - abstract ( intros A B [x y]; extensionality e; unfold ReaderT_bind, ReaderT_eta; cbn; rewrite !bind_def; repeat (rewrite <- map_comp, <- (kleisli_comp_def eta), kleisli_compl); pose (f0 (p : A * M B) := bind (fun b => eta (fst p, b)) (snd p)); rewrite <- (map_comp f0 (fun p => (fst p, snd p e))); rewrite (map_comp (fun p => (fst p, snd p e)) ((fun a : A => (a, y)))); cbn; pose (f1 (p : M A * B) := bind (fun a => eta (a, snd p)) (fst p)); rewrite <- (map_comp f1 (fun p => (fst p e, snd p))); rewrite (map_comp (fun p => (fst p e, snd p)) (pair x)); cbn; rewrite (map_ext _ strength) by (intros [a y0]; unfold f0; rewrite bind_def; rewrite <- map_comp, <- (kleisli_comp_def eta), kleisli_compl; reflexivity); rewrite (map_ext _ strength') by (intros [a y0]; unfold f1; rewrite bind_def; rewrite <- map_comp, <- (kleisli_comp_def eta), kleisli_compl; reflexivity); rewrite <- !kleisli_comp_def; apply phi_phi'). - abstract ( intros A x; extensionality e; unfold ReaderT_bind, ReaderT_eta; cbn; rewrite !bind_def; repeat (rewrite <- map_comp, <- (kleisli_comp_def eta), kleisli_compl); pose (f0 (p : A * M A) := bind (fun b => eta (fst p, b)) (snd p)); rewrite <- (map_comp f0 (fun p => (fst p, snd p e))); rewrite (map_comp (fun p => (fst p, snd p e)) ((fun a : A => (a, x)))); cbn; rewrite (map_ext _ strength) by (intros [a y0]; unfold f0; rewrite bind_def; rewrite <- map_comp, <- (kleisli_comp_def eta), kleisli_compl; reflexivity); rewrite <- kleisli_comp_def; apply phi_diag). Defined. End ReaderT_CIMonad. Canonical Structure ReaderT_CIMonad E (M : CIMonad) := CIMonad.Pack (ReaderT E M) (ReaderT_CIMonad_class E M). Section ReaderT_CIMonadZero. Variable E : Type. Variable M : CIMonadZero. Definition ReaderT_mzero A : ReaderT E M A := fun _ => mzero. Definition ReaderT_MonadZero_mixin : MonadZero.mixin (ReaderT_CIMonad E M). exists ReaderT_mzero. - abstract ( intros A B f; extensionality e; change (map f mzero = mzero :> M B); apply mzero_natural). - abstract ( intros A B C f a; extensionality e; change ((kzero <-< (fun a => f a e)) a = kzero a :> M C); apply kleisli_comp_zerol). - abstract ( intros A B C f a; extensionality e; change (((fun b => f b e) <-< kzero) a = kzero a :> M C); apply kleisli_comp_zeror). Defined. End ReaderT_CIMonadZero. Canonical Structure ReaderT_CIMonadZero E (M : CIMonadZero) := MonadZero.Pack (ReaderT E M) (ReaderT_MonadZero_mixin E M). ================================================ FILE: Coq/Simplicity/Util/Monad.v ================================================ Require Import Simplicity.Util.PackedClass. Import Coq.Strings.String.StringSyntax. Set Implicit Arguments. Local Open Scope type_scope. Declare Scope monad_scope. (* Commutative and Idempotnent Monads *) Module CIMonad. (* Eventually we will need the functional extensionality axoim, but let's try * to delay that as long as possible. The alternative is to use Setoid / PERs * but that would seem to entail writing an entirely new standard library. *) Record class (M : Type -> Type) := Class { eta : forall {A}, A -> M A ; bind : forall {A B}, (A -> M B) -> M A -> M B ; map := (fun A B f => bind (fun a => eta (f a))) : forall {A B}, (A -> B) -> M A -> M B ; kleisliComp := (fun A B C g f a => bind g (f a)) : forall {A B C}, (B -> M C) -> (A -> M B) -> A -> M C ; strength := (fun A B p => map (pair (fst p)) (snd p)) : forall {A B}, A * M B -> M (A * B) ; strength' := (fun A B p => map (fun a => pair a (snd p)) (fst p)) : forall {A B}, M A * B -> M (A * B) ; _ : forall {A B} (f0 f1: A -> M B), (forall a, f0 a = f1 a) -> forall a, bind f0 a = bind f1 a ; _ : forall {A} (x : M A), bind eta x = x ; _ : forall {A B} (f : A -> M B) (a : A), bind f (eta a) = f a ; _ : forall {A B C} (g : B -> M C) (f : A -> M B) (x : M A), bind g (bind f x) = bind (fun a => bind g (f a)) x ; _ : forall {A B} (p : M A * M B), kleisliComp strength strength' p = kleisliComp strength' strength p ; _ : forall {A} (x : M A), kleisliComp strength strength' (pair x x) = map (fun a => pair a a) x }. Structure type := Pack { domain :> Type -> Type; class_of : class domain }. Arguments Pack : clear implicits. Module Theory. Section Context. Context {M : type}. Definition eta {A} (a : A) := eta (class_of M) a. Definition bind {A B} (f : A -> M B) := bind (class_of M) f. Definition map {A B} (f : A -> B) := map (class_of M) f. Definition kleisliComp {A B C} (g : B -> M C) (f : A -> M B) := kleisliComp (class_of M) g f. Definition strength {A B} (p : A * M B) := strength (class_of M) p. Definition strength' {A B} (p : M A * B) := strength' (class_of M) p. Definition mu {A} (x : M (M A)) : M A := bind (fun y => y) x. Infix "<-<" := kleisliComp (at level 40, left associativity). Definition phi {A B} (x : M A) (y : M B) : M (A * B) := (strength <-< strength') (pair x y). Definition phi' {A B} (x : M A) (y : M B) : M (A * B) := (strength' <-< strength) (pair x y). Lemma bind_def {A B} (f : A -> M B) (x : M A) : bind f x = mu (map f x). Proof. unfold mu, map. unfold bind, eta; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. rewrite bind_assoc. apply bind_ext; intros a. rewrite bind_right. reflexivity. Qed. Lemma kleisli_comp_def {A B C} (g : B -> M C) (f : A -> M B) (a : A) : (g <-< f) a = mu (map g (f a)). Proof. apply bind_def. Qed. Lemma kleisli_compl {A B} (f : A -> M B) (a : A) : (eta <-< f) a = f a. Proof. unfold kleisliComp. unfold bind, eta; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply bind_left. Qed. Lemma kleisli_compr {A B} (f : A -> M B) (a : A) : (f <-< eta) a = f a. Proof. unfold kleisliComp. unfold bind, eta; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply bind_right. Qed. Lemma kleisli_comp_assoc {A B C D} (h : C -> M D) (g : B -> M C) (f : A -> M B) (a : A) : ((h <-< g) <-< f) a = (h <-< (g <-< f)) a. Proof. unfold kleisliComp. unfold bind, eta; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. erewrite (bind_assoc _ _ _ h g);reflexivity. Qed. Lemma eta_natural {A B} (f : A -> B) (a : A) : map f (eta a) = eta (f a). Proof. unfold map, eta; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply bind_right. Qed. Lemma mu_natural {A B} (f : A -> B) (x : M (M A)) : map f (mu x) = mu (map (map f) x). Proof. unfold map, mu, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. repeat rewrite bind_assoc. apply bind_ext; intros y. rewrite bind_right. reflexivity. Qed. Lemma map_ext {A B} (f0 f1 : A -> B) (Hf : forall a, f0 a = f1 a) (x : M A) : map f0 x = map f1 x. Proof. unfold map, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply bind_ext. congruence. Qed. Lemma map_comp {A B C} (g : B -> C) (f : A -> B) (x : M A) : map g (map f x) = map (fun a => g (f a)) x. Proof. unfold map, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. rewrite bind_assoc. apply bind_ext. intros. apply bind_right. Qed. Lemma strength_eta {A B} (a : A) (b : B) : strength (a, eta b) = eta (a, b). Proof. unfold strength, eta, map, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply bind_right. Qed. Lemma strength'_eta {A B} (a : A) (b : B) : strength' (eta a, b) = eta (a, b). Proof. unfold strength', eta, map, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply bind_right. Qed. Lemma phi_eta {A B} (a : A) (b : B) : phi (eta a) (eta b) = eta (a, b). Proof. unfold phi. rewrite kleisli_comp_def, strength'_eta, <- kleisli_comp_def. rewrite kleisli_compr. apply strength_eta. Qed. Lemma phi_phi' {A B} (a : M A) (b : M B) : phi a b = phi' a b. Proof. unfold phi, phi', kleisliComp, strength, strength', eta, map, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply (comm _ _ (a,b)). Qed. Lemma phi_diag {A} (a : M A) : phi a a = map (fun x => (x,x)) a. Proof. unfold phi, kleisliComp, strength, strength', eta, map, bind; destruct (class_of M) as [eta0 bind0 map0 kleisliComp0 strength0 strength'0 bind_ext bind_left bind_right bind_assoc comm idem]; cbn. apply (idem _ a). Qed. End Context. End Theory. End CIMonad. Export CIMonad.Theory. Notation CIMonad := CIMonad.type. Coercion CIMonad.domain : CIMonad >-> Funclass. Infix "<-<" := kleisliComp (at level 40, left associativity) : monad_scope. Arguments kleisliComp {M A B C} g f : simpl never. Arguments map {M A B} f : simpl never. Local Open Scope monad_scope. Definition Identity (A : Type) : Type := A. Definition Identity_CIMonad_class : CIMonad.class Identity. exists (fun A a => a) (fun A B f => f); auto. Defined. Canonical Structure Identity_CIMonad := CIMonad.Pack Identity Identity_CIMonad_class. (* Monad with zero *) Module MonadZero. Record mixin (M : CIMonad) := Mixin { mzero : forall {A}, M A ; kzero := (fun A B a => mzero) : forall {A B}, A -> M B ; _ : forall {A B} (f : A -> B), map f mzero = mzero ; _ : forall {A B C} (f : A -> M B) (a : A), (kzero <-< f) a = kzero a :> M C ; _ : forall {A B C} (f : B -> M C) (a : A), (f <-< kzero) a = kzero a }. Record class (M : Type -> Type) := Class { base :> CIMonad.class M ; ext :> mixin (CIMonad.Pack M base) }. Structure type := _Pack { domain :> Type -> Type; class_of : class domain }. Definition packager F M0 (mz0 : mixin M0) := [find M | CIMonad.domain M ~ F | "is not a CIMonad" ] [find cM | CIMonad.class_of M0 ~ cM ] [find mz | mz ~ mz0 | "is not the right mixin" ] @_Pack F (@Class F cM mz). Notation Pack F mz := (@packager F _ mz _ id _ id _ id). Canonical Structure to_Monad (M : type) : CIMonad := CIMonad.Pack M (class_of M). Module Theory. Section Context. Context {M : type}. Definition mzero {A} := mzero (class_of M) : M A. Definition kzero {A B} := kzero (class_of M) : A -> M B. Lemma mzero_natural {A B} (f : A -> B) : map f mzero = mzero. Proof. unfold mzero; destruct M as [M0 [Monad_class0 [mzero0 kzero natural kzerol kzeror]]]; cbn. apply natural. Qed. Lemma kleisli_comp_zerol {A B C} (f : A -> M B) (a : A) : (kzero <-< f) a = kzero a :> M C. Proof. unfold kzero; destruct M as [M0 [Monad_class0 [mzero0 kzero natural kzerol kzeror]]]; cbn. apply kzerol. Qed. Lemma kleisli_comp_zeror {A B C} (f : B -> M C) (a : A) : (f <-< kzero) a = kzero a. Proof. unfold kzero; destruct M as [M0 [Monad_class0 [mzero0 kzero natural kzerol kzeror]]]; cbn. apply kzeror. Qed. Lemma mu_mzero {A} : mu mzero = mzero :> M A. Proof. cbn; change (@mzero (M A)) with (@kzero (M A) (M A) mzero). unfold mu. rewrite bind_def, <- kleisli_comp_def. rewrite kleisli_comp_zeror; reflexivity. Qed. Lemma mu_eta_mzero {A} : mu (eta mzero) = mzero :> M A. Proof. cbn; change (@mzero A) with (@kzero (M A) A mzero). unfold mu. rewrite bind_def, <- kleisli_comp_def. rewrite kleisli_compr; reflexivity. Qed. Lemma phi_mzeror {A B} (x : M B) : phi mzero x = mzero :> M (A * B). Proof. unfold phi. rewrite kleisli_comp_def. change (mu (map strength (map (fun a => pair a x) mzero)) = mzero :> M (A * B)). repeat rewrite mzero_natural. apply mu_mzero. Qed. Lemma phi_mzerol {A B} (x : M A) : phi x mzero = mzero :> M (A * B). Proof. unfold phi. rewrite kleisli_comp_def. change (mu (map strength (map (fun a => pair a mzero) x)) = mzero :> M (A * B)). rewrite map_comp. erewrite map_ext;[|intros; apply mzero_natural]. change x with ((fun y => y) x). rewrite <- kleisli_comp_def. apply kleisli_comp_zerol. Qed. End Context. End Theory. End MonadZero. Notation CIMonadZero := MonadZero.type. Canonical Structure MonadZero.to_Monad. Coercion MonadZero.to_Monad : CIMonadZero >-> CIMonad. Export MonadZero.Theory. ================================================ FILE: Coq/Simplicity/Util/Option.v ================================================ Require Import Simplicity.Util.Monad. Set Implicit Arguments. Local Open Scope monad_scope. Definition option_join {A} (x : option (option A)) : option A := match x with | None => None | Some x => x end. Definition option_bind {A B} (f : A -> option B) (x : option A) : option B := option_join (option_map f x). Lemma option_bind_ext {A B} (f1 f2 : A -> option B) : (forall a, f1 a = f2 a) -> forall x, option_bind f1 x = option_bind f2 x. Proof. intros H [|];[apply H|reflexivity]. Qed. Definition option_CIMonad_class : CIMonad.class option. exists @Some @option_bind; try abstract (intros; try destruct x; try reflexivity). - abstract (auto using option_bind_ext). - abstract (intros; destruct p as [[|] [|]]; reflexivity). Defined. Canonical Structure option_CIMonad := CIMonad.Pack option option_CIMonad_class. Definition option_MonadZero_mixin : MonadZero.mixin option_CIMonad. exists @None; try abstract (intros; try reflexivity). abstract (intros; unfold kleisliComp; cbn; destruct (f a); reflexivity). Defined. Canonical Structure option_Monad_Zero := MonadZero.Pack option option_MonadZero_mixin. Definition optionZero {M : CIMonadZero} {A} (x : option A) : M A := match x with | None => mzero | Some a => eta a end. Lemma optionZero_natural {M :CIMonadZero} {A B} (f : A -> B) x : map f (optionZero x) = optionZero (map f x) :> M B. Proof. destruct x; cbn. - apply eta_natural. - apply mzero_natural. Qed. Lemma optionZero_mu {M :CIMonadZero} {A} x : optionZero (mu x) = mu (map optionZero (optionZero x)) :> M A. Proof. destruct x as [x|]; cbn. - rewrite <- kleisli_comp_def, kleisli_compr. reflexivity. - rewrite mzero_natural. symmetry. apply mu_mzero. Qed. Lemma optionZero_phi {M :CIMonadZero} {A B} x y : optionZero (phi x y) = phi (optionZero x) (optionZero y) :> M (A * B)%type. Proof. destruct x as [a|]; destruct y as [b|]; cbn; try reflexivity; first [rewrite phi_eta|rewrite phi_mzerol|rewrite phi_mzeror]; reflexivity. Qed. (* TODO: move these into CIMonad when needed. Definition option_ap {A B} (f : option (A -> B)) : option A -> option B := option_bind (fun a => option_map (fun f => f a) f). Definition option_map2 {A B C} (f : A -> B -> C) (x : option A) : option B -> option C := option_ap (option_map f x). *) ================================================ FILE: Coq/Simplicity/Util/PackedClass.v ================================================ Require Import Coq.Strings.String. (* Assia Mahboubi, Enrico Tassi. Canonical Structures for the working Coq user. 2013. * https://hal.inria.fr/hal-00816703v1 *) Inductive phantom {T : Type} (t : T) : Type := Phantom. Definition unify {T1 T2} (t1 : T1) (t2 : T2) (s : option string) := phantom t1 -> phantom t2. Definition id {T} {t : T} (x : phantom t) := x. Notation "[find v | t1 ~ t2 ] p" := (fun v (_ : unify t1 t2 None) => p) (at level 50, v name, only parsing). Notation "[find v | t1 ~ t2 | msg ] p" := (fun v (_ : unify t1 t2 (Some msg)) => p) (at level 50, v name, only parsing). Notation "'Error : t : msg" := (unify _ t (Some msg)) (at level 50, format "''Error' : t : msg"). Open Scope string_scope. ================================================ FILE: Coq/Simplicity/Util/Thrist.v ================================================ Module Thrist. Declare Scope thrist_scope. Inductive T {A} (P : A -> A -> Type) (z:A) : A -> Type := | nil : T P z z | cons : forall x y, P x y -> T P z y -> T P z x. Fixpoint append {A : Type} {P : A -> A -> Type} {x y z} (thr1 : T P y x) : T P z y -> T P z x := match thr1 with | nil _ _ => fun thr2 => thr2 | cons _ _ _ _ hd tl => fun thr2 => cons _ _ _ _ hd (append tl thr2) end. End Thrist. Bind Scope thrist_scope with Thrist.T. Local Open Scope thrist_scope. Notation "'Thrst' P x y" := (Thrist.T P y x) (at level 0, P at level 0, x at level 0, y at level 0). Notation "x <| y" := (Thrist.cons _ _ _ _ x y) (at level 30) : thrist_scope. Notation "x |><| y" := (Thrist.append x y) (at level 30) : thrist_scope. Notation "[]" := (Thrist.nil _ _ ) : thrist_scope. Notation "x |> y" := (x |><| (y <| [])) (at level 30) : thrist_scope. Definition eq_nil {A : Type} {P : A -> A -> Type} {x y} (Hxy : x = y) : Thrst P x y := match Hxy with | eq_refl => [] end. Lemma thrist_app_nil {A : Type} {P : A -> A -> Type} {x y} (thr : Thrst P x y) : thr |><| [] = thr. Proof. induction thr. reflexivity. cbn. rewrite IHthr. reflexivity. Qed. ================================================ FILE: Coq/Simplicity/Word.v ================================================ Require Import Logic.Eqdep_dec. Require Import List. Require Import ZArith. Require Import Simplicity.Util.Arith. Require Import Lia. Require Coq.Vectors.Vector. Require compcert.lib.Integers. Require Import Simplicity.Ty. Require Import Simplicity.Alg. Require Import Simplicity.Bit. Require Import Simplicity.Digest. Set Implicit Arguments. Local Set Keyed Unification. Import ListNotations. Local Open Scope list_scope. Local Open Scope ty_scope. Local Open Scope term_scope. Local Open Scope semantic_scope. Fixpoint Vector X (n : nat) := match n with | 0 => X | S n => let rec := Vector X n in Prod rec rec end. Lemma VectorPromote {X n} : Vector X (S n) = Vector (X * X) n. Proof. induction n. - reflexivity. - cbn. rewrite <-!IHn. reflexivity. Defined. Definition Word := Vector Bit. Module ToZ. Record class T := Class { bitSize : nat ; toZ : T -> Z ; fromZ : Z -> T ; from_toZ : forall (v : T), fromZ (toZ v) = v ; to_fromZ : forall (z : Z), toZ (fromZ z) = Z.modulo z (two_power_nat bitSize) }. Structure type := Pack { obj :> Ty; class_of : class obj }. Arguments Pack : clear implicits. Module Theory. Section Context. Context {T : type}. Definition bitSize : nat := bitSize (class_of T). Definition toZ : obj T -> Z := toZ (class_of T). Definition fromZ : Z -> obj T := fromZ (class_of T). Lemma from_toZ (v : T) : fromZ (toZ v) = v. Proof. unfold fromZ, toZ. destruct (class_of T); auto. Qed. Lemma to_fromZ (z : Z) : toZ (fromZ z : T) = Z.modulo z (two_power_nat bitSize). Proof. unfold fromZ, toZ, bitSize. destruct (class_of T); auto. Qed. Lemma toZ_mod (v : T) : toZ v = Z.modulo (toZ v) (two_power_nat bitSize). Proof. rewrite <- from_toZ at 1. apply to_fromZ. Qed. Lemma galois (v : T) (z : Z) : v = fromZ z <-> eqm (two_power_nat bitSize) (toZ v) z. Proof. unfold eqm. split. - intros ->. rewrite to_fromZ. rewrite Z.mod_mod;[reflexivity|]. rewrite two_power_nat_equiv. auto using Z.pow_nonzero with zarith. - unfold eqm. rewrite <- 2!to_fromZ, from_toZ. rewrite <- from_toZ at 2. intros ->. rewrite from_toZ. reflexivity. Qed. End Context. Arguments bitSize : clear implicits. End Theory. End ToZ. Export ToZ.Theory. Coercion ToZ.obj : ToZ.type >-> Ty. Section BitToZ. Let BitToZ (v : Bit) : Z := match v with | Bit.zero => 0%Z | Bit.one => 1%Z end. Let BitFromZ (z : Z) : Bit := if Z.odd z then Bit.one else Bit.zero. Lemma Bit_from_toZ (v : Bit) : BitFromZ (BitToZ v) = v. Proof. destruct v as [[] | []]; reflexivity. Qed. Lemma Bit_to_fromZ (z : Z) : BitToZ (BitFromZ z) = Z.modulo z (two_power_nat 1). Proof. unfold BitFromZ. rewrite (Zmod_odd z). destruct (Z.odd z); reflexivity. Qed. Definition BitToZ_Class := ToZ.Class 1 BitToZ BitFromZ Bit_from_toZ Bit_to_fromZ. End BitToZ. Canonical Structure BitToZ : ToZ.type := ToZ.Pack Bit BitToZ_Class. Section PairToZ. Context {a b : ToZ.type}. Let PairBitSize : nat := bitSize a + bitSize b. Let PairToZ (v : a * b) : Z := let (va, vb) := v in toZ va * two_power_nat (bitSize b) + toZ vb. Let PairFromZ (z : Z) : a * b := ( fromZ (z / two_power_nat (bitSize b)) , fromZ z ). Lemma Pair_from_toZ (v : a * b) : PairFromZ (PairToZ v) = v. Proof. destruct v as [va vb]. cbn; unfold PairFromZ. assert (Hb : two_power_nat (bitSize b) <> 0%Z). rewrite two_power_nat_equiv. apply Z.pow_nonzero; auto with zarith. f_equal. - rewrite Z_div_plus_full_l by auto. rewrite <- (from_toZ vb), to_fromZ. rewrite Zmod_div, Z.add_0_r. apply from_toZ. - rewrite <- (from_toZ (fromZ _ )), to_fromZ. rewrite Zplus_comm, Z_mod_plus_full. rewrite <- toZ_mod. apply from_toZ. Qed. Lemma Pair_to_fromZ (z : Z) : PairToZ (PairFromZ z) = Z.modulo z (two_power_nat PairBitSize). Proof. assert (H2 : forall n, (0 < Zpower_nat 2 n)%Z). intros n. rewrite Zpower_nat_Z. auto using Z.pow_pos_nonneg with zarith. assert (H2' : forall n, (Zpower_nat 2 n <> 0)%Z). intros n. generalize (H2 n). lia. unfold PairBitSize. rewrite two_power_nat_correct, Zpower_nat_is_exp. rewrite Zmult_comm, Z.rem_mul_r by auto; cbn. rewrite 2!to_fromZ; rewrite !two_power_nat_correct. rewrite Zplus_comm, Zmult_comm; reflexivity. Qed. Definition PairToZ_Class := ToZ.Class PairBitSize PairToZ PairFromZ Pair_from_toZ Pair_to_fromZ. End PairToZ. Canonical Structure PairToZ (a b : ToZ.type) : ToZ.type := ToZ.Pack (a * b) PairToZ_Class. Lemma toZ_Pair {A B : ToZ.type} (a : A) (b : B) : @toZ (PairToZ A B) (a, b) = (toZ a * two_power_nat (bitSize B) + toZ b)%Z. Proof. destruct A; destruct B; reflexivity. Qed. Lemma bitSize_Pair (A B : ToZ.type) : bitSize (PairToZ A B) = (bitSize A + bitSize B)%nat. Proof. destruct A; destruct B; reflexivity. Qed. Fixpoint WordToZ_Class {n : nat} : ToZ.class (Word n) := match n with | 0 => BitToZ_Class | (S m) => @PairToZ_Class (ToZ.Pack _ WordToZ_Class) (ToZ.Pack _ WordToZ_Class) end. Canonical Structure WordToZ (n : nat) : ToZ.type := ToZ.Pack (Word n) WordToZ_Class. Notation Word8 := (Word 3). Notation Word16 := (Word 4). Notation Word32 := (Word 5). Notation Word64 := (Word 6). Notation Word256 := (Word 8). Notation Word512 := (Word 9). Lemma bitSize_Word n : Z.of_nat (bitSize (WordToZ n)) = two_power_nat n. Proof. induction n. reflexivity. cbn. rewrite Nat2Z.inj_add, IHn, two_power_nat_S. ring. Qed. Lemma testbitToZLo {n} (ahi alo : Word n) i (Hi : (i < two_power_nat n)%Z) : Z.testbit (toZ ((ahi, alo) : Word (S n))) i = Z.testbit (toZ alo) i. Proof. rewrite (toZ_Pair ahi alo), two_power_nat_equiv, <- (Z.mod_pow2_bits_low _ _ _ Hi), bitSize_Word, Zplus_comm, Z_mod_plus_full. auto using Z.mod_pow2_bits_low. Qed. Lemma testbitToZHi {n} (ahi alo : Word n) i (Hi : (two_power_nat n <= i)%Z) : Z.testbit (toZ ((ahi, alo) : Word (S n))) i = Z.testbit (toZ ahi) (i - two_power_nat n). Proof. rewrite <- bitSize_Word in *. replace i with (i - Z.of_nat (bitSize (WordToZ n)) + Z.of_nat (bitSize (WordToZ n)))%Z at 1 by ring. rewrite (toZ_Pair ahi alo), two_power_nat_equiv, <- Z.div_pow2_bits, Zplus_comm, Z_div_plus, (toZ_mod alo), two_power_nat_equiv, Zmod_div, Z.add_0_l; auto using Z.lt_gt, Z.pow_pos_nonneg with zarith. Qed. Definition to_hash256 (h : Word256) : hash256 := let '(((h0,h1),(h2,h3)),((h4,h5),(h6,h7))) := h in Hash256 (List.map (fun x : Word32 => Integers.Int.repr (toZ x)) [h0;h1;h2;h3;h4;h5;h6;h7]) refl_equal. Definition from_hash256 (l : hash256) : Word256 := match map (fun x => fromZ (Integers.Int.unsigned x) : Word32) (hash256_reg l) with | [h0;h1;h2;h3;h4;h5;h6;h7] => (((h0,h1),(h2,h3)),((h4,h5),(h6,h7))) | _ => fromZ 0%Z end. Lemma from_to_hash256 (h : Word256) : from_hash256 (to_hash256 h) = h. Proof. assert (H32 : forall x : Word32, (0 <= toZ x <= Integers.Int.max_unsigned)%Z). intros x. change Integers.Int.max_unsigned with (Z.pred Integers.Int.modulus). rewrite <- Z.lt_le_pred, toZ_mod. apply Z.mod_pos_bound. reflexivity. destruct h as [[[h0 h1][h2 h3]][[h4 h5][h6 h7]]]; cbn -[Word toZ fromZ]. repeat rewrite Integers.Int.unsigned_repr by auto. repeat rewrite from_toZ. reflexivity. Qed. Lemma to_from_hash256 (h : hash256) : to_hash256 (from_hash256 h) = h. Proof. destruct h as [[|h0 [|h1 [|h2 [|h3 [|h4 [|h5 [|h6 [|h7 [|h8 h]]]]]]]]] Hh]; try discriminate. simpl. rewrite !to_fromZ. change (two_power_nat (bitSize (WordToZ 5))) with Integers.Int.modulus. rewrite <- !Integers.Int.unsigned_repr_eq, !Integers.Int.repr_unsigned. elim Hh using K_dec_set;[decide equality|]. reflexivity. Qed. Section Definitions. Section Arith. Fixpoint zero {n : nat} {term : Core.Algebra} : term Unit (Word n) := match n with | 0 => false | S n => zero &&& zero end. Definition adderBit {term : Core.Algebra} : term (Bit * Bit) (Bit * Bit) := cond (iden &&& not iden) (false &&& iden). Definition fullAdderBit {term : Core.Algebra} : term (Bit * (Bit * Bit)) (Bit * Bit) := maj &&& xor3. Definition buildFullAdder {W} {term : Core.Algebra} (rec : term (Bit * (W * W)) (Bit * W)) : term (Bit * ((W * W) * (W * W))) (Bit * (W * W)) := drop (O O H &&& I O H) &&& (O H &&& drop (O I H &&& I I H) >>> rec) >>> I I H &&& (I O H &&& O H >>> rec) >>> I O H &&& (I I H &&& O H). Fixpoint fullAdder {n : nat} {term : Core.Algebra} : term (Bit * (Word n * Word n)) (Bit * Word n) := match n with | 0 => fullAdderBit | S n => buildFullAdder fullAdder end. Definition adder {n : nat} {term : Core.Algebra} : term (Word n * Word n) (Bit * Word n) := match n with | 0 => adderBit | S n => false &&& iden >>> fullAdder end. Definition fullMultiplierBit {term : Core.Algebra} : term ((Bit * Bit) * (Bit * Bit)) (Word 1) := take (cond iden false) &&& drop iden >>> fullAdderBit. Definition buildFullMultiplier {W} {term : Core.Algebra} (rec : term ((W * W) * (W * W)) (W * W)) : term (((W * W) * (W * W)) * ((W * W) * (W * W))) (((W * W) * (W * W))) := take (O O H &&& (I O H &&& O I H)) &&& ((take (O O H &&& I I H) &&& drop (O O H &&& I O H) >>> rec) &&& (take (O I H &&& I I H) &&& drop (O I H &&& I I H) >>> rec)) >>> take (O H &&& I O H) &&& (drop (O O H &&& I I H) &&& (O I H &&& drop (O I H &&& I O H) >>> rec)) >>> (O H &&& drop (I O H &&& O O H) >>> rec) &&& drop (I I H &&& O I H). Fixpoint fullMultiplier {n : nat} {term : Core.Algebra} : term ((Word n * Word n) * (Word n * Word n)) (Word (S n)) := match n with | 0 => fullMultiplierBit | S n => buildFullMultiplier fullMultiplier end. Definition multiplier {n : nat} {term : Core.Algebra} : term (Word n * Word n) (Word (S n)) := iden &&& (unit >>> zero &&& zero) >>> fullMultiplier. End Arith. Section Vector. Definition build_fill {C X} {term : Core.Algebra} (rec : term C X) : term C (X * X) := rec &&& rec. Fixpoint fill {C X n} {term : Core.Algebra} (t : term C X) : term C (Vector X n) := match n with | 0 => t | (S n) => build_fill (fill t) end. Definition buildBitwiseTri {W} {term : Core.Algebra} (rec : term (W * (W * W)) W) : term ((W * W) * ((W * W) * (W * W))) (W * W) := (O O H &&& (I O O H &&& I I O H) >>> rec) &&& (O I H &&& (I O I H &&& I I I H) >>> rec). Fixpoint bitwiseTri {X} {n : nat} {term : Core.Algebra} (op : term (X * (X * X)) X) : term (Vector X n * (Vector X n * Vector X n)) (Vector X n) := match n with | 0 => op | S n => buildBitwiseTri (bitwiseTri op) end. Definition build_leftmost {V X} {term : Core.Algebra} (rec : term V X) : term (V * V) X := take rec. Fixpoint leftmost {X n} {term : Core.Algebra} : term (Vector X n) X := match n with | 0 => iden | S n => build_leftmost leftmost end. Definition build_rightmost {V X} {term : Core.Algebra} (rec : term V X) : term (V * V) X := drop rec. Fixpoint rightmost {X n} {term : Core.Algebra} : term (Vector X n) X := match n with | 0 => iden | S n => build_rightmost rightmost end. Definition build_full_left_shift1 {X W} {term : Core.Algebra} (rec : term (W * X) (X * W)) : term ((W * W) * X) (X * (W * W)) := O O H &&& (O I H &&& I H >>> rec) >>> (O H &&& I O H >>> rec) &&& I I H >>> O O H &&& (O I H &&& I H). Fixpoint full_left_shift1 {X n} {term : Core.Algebra} : term (Vector X n * X) (X * Vector X n) := match n with | 0 => iden | S n => build_full_left_shift1 full_left_shift1 end. Definition build_full_right_shift1 {X W} {term : Core.Algebra} (rec : term (X * W) (W * X)) : term (X * (W * W)) ((W * W) * X) := (O H &&& I O H >>> rec) &&& I I H >>> O O H &&& (O I H &&& I H >>> rec) >>> (O H &&& I O H) &&& I I H. Fixpoint full_right_shift1 {X n} {term : Core.Algebra} : term (X * Vector X n) (Vector X n * X) := match n with | 0 => iden | S n => build_full_right_shift1 full_right_shift1 end. Definition left_shift1 {X n} {term : Core.Algebra} (t : term Unit X) : term (Vector X n) (Vector X n) := iden &&& (unit >>> t) >>> full_left_shift1 >>> I H. Fixpoint left_shift_const_by {X n} {term : Core.Algebra} (t : term Unit X) (p : positive) : term (Vector X n) (Vector X n) := if (Zpower_nat 2 n <=? Zpos p)%Z then unit >>> fill t else match n with | 0 => iden | (S n0) => match p with | xH => left_shift1 t | xO p0 => eq_rect _ (fun x => term x x) (left_shift_const_by (t &&& t) p0) _ (eq_sym VectorPromote) | xI p0 => left_shift1 t >>> eq_rect _ (fun x => term x x) (left_shift_const_by (t &&& t) p0) _ (eq_sym VectorPromote) end end. Definition right_shift1 {X n} {term : Core.Algebra} (t : term Unit X) : term (Vector X n) (Vector X n) := (unit >>> t) &&& iden >>> full_right_shift1 >>> O H. Fixpoint right_shift_const_by {X n} {term : Core.Algebra} (t : term Unit X) (p : positive) : term (Vector X n) (Vector X n) := if (Zpower_nat 2 n <=? Zpos p)%Z then unit >>> fill t else match n with | 0 => iden | (S n0) => match p with | xH => right_shift1 t | xO p0 => eq_rect _ (fun x => term x x) (right_shift_const_by (t &&& t) p0) _ (eq_sym VectorPromote) | xI p0 => right_shift1 t >>> eq_rect _ (fun x => term x x) (right_shift_const_by (t &&& t) p0) _ (eq_sym VectorPromote) end end. Definition shift_const_by {X n} {term : Core.Algebra} (t : term Unit X) (c : Z) : term (Vector X n) (Vector X n) := match c with | Z0 => iden | Zpos p => left_shift_const_by t p | Zneg p => right_shift_const_by t p end. Definition shift_const {n} {term : Core.Algebra} : Z -> term (Vector Bit n) (Vector Bit n) := shift_const_by false. Definition left_rotate1 {X n} {term : Core.Algebra} : term (Vector X n) (Vector X n) := iden &&& leftmost >>> full_left_shift1 >>> I H. Definition right_rotate1 {X n} {term : Core.Algebra} : term (Vector X n) (Vector X n) := rightmost &&& iden >>> full_right_shift1 >>> O H. Fixpoint rotate_const_list {X n} {term : Core.Algebra} (z : Z) : list (term (Vector X n) (Vector X n)) := match n with | 0 => [] | (S n0) => if Z.even z then eq_rect _ (fun x => list (term x x)) (rotate_const_list (Z.div z 2)%Z) _ (eq_sym VectorPromote) else if Z.even (Z.div z 2) then left_rotate1 :: eq_rect _ (fun x => list (term x x)) (rotate_const_list (Z.div z 2)%Z) _ (eq_sym VectorPromote) else right_rotate1 :: eq_rect _ (fun x => list (term x x)) (rotate_const_list (Z.div (z + 1) 2)%Z) _ (eq_sym VectorPromote) end. Fixpoint foldr_comp {X} {term : Core.Algebra} (l : list (term X X)) : term X X := match l with | [] => iden | i::[] => i | i::l => i >>> foldr_comp l end. Definition rotate_const {X n} {term : Core.Algebra} (z : Z) : term (Vector X n) (Vector X n) := foldr_comp (rotate_const_list z). End Vector. End Definitions. Section Specifications. Lemma zero_correct n : toZ (|[zero (n:=n)]| tt) = 0%Z. Proof. induction n; cbn;[|rewrite IHn];reflexivity. Qed. Lemma fullAdder_correct n : forall (a b : Word n) (c : Bit), (toZ (|[fullAdder]| (c, (a, b))) = toZ a + toZ b + toZ c)%Z. Proof. induction n. { intros [[] | []] [[] | []] [[] | []]; reflexivity. } intros [ahi alo] [bhi blo] c. fold Word in *. cbn -[toZ]; fold tySem; fold (tySem Bit). rewrite (toZ_Pair ahi alo), (toZ_Pair bhi blo). set (C := two_power_nat _). transitivity ((toZ ahi + toZ bhi) * C + (toZ alo + toZ blo + toZ c))%Z;[|ring]. rewrite <- IHn. destruct (|[fullAdder]| (c, (alo, blo))) as [c0 rlo]; clear alo blo c. cbn [fst snd]. rewrite (toZ_Pair c0 rlo). fold C. transitivity ((toZ ahi + toZ bhi + toZ c0) * C + toZ rlo)%Z;[|ring]. rewrite <- IHn. destruct (|[fullAdder]| (c0, (ahi, bhi))) as [c1 rhi]; clear ahi bhi c0. cbn [fst snd]. rewrite (toZ_Pair c1 rhi); fold C. rewrite (toZ_Pair c1 _). rewrite (bitSize_Pair (WordToZ n) (WordToZ n)). rewrite two_power_nat_correct, Zpower_nat_is_exp, <- two_power_nat_correct; fold C. rewrite (toZ_Pair rhi rlo); fold C. ring. Qed. Lemma adder_correct n : forall (a b : Word n), (toZ (|[adder]| (a, b)) = toZ a + toZ b)%Z. destruct n. { intros [[] | []] [[] | []]; reflexivity. } unfold adder. generalize (S n); clear n; intros n a b. cbn -[toZ]. rewrite fullAdder_correct. cbn. ring. Qed. Lemma fullMultiplier_correct n : forall (a b c d : Word n), (toZ (|[fullMultiplier]| ((a, b), (c, d))) = toZ a * toZ b + toZ c + toZ d)%Z. Proof. induction n. { intros [[] | []] [[] | []] [[] | []] [[] | []]; reflexivity. } intros [ahi alo] [bhi blo] [chi clo] [dhi dlo]. cbn -[toZ]; fold tySem; fold (tySem Bit). fold Word in *. rewrite (toZ_Pair ahi alo), (toZ_Pair bhi blo), (toZ_Pair chi clo), (toZ_Pair dhi dlo). set (C := two_power_nat _). transitivity ((toZ ahi * C + toZ alo) * toZ bhi * C + ((toZ ahi * toZ blo + toZ chi + toZ dhi) * C) + (toZ alo * toZ blo + toZ clo + toZ dlo))%Z; [|ring]. rewrite <- 2!IHn. destruct (|[fullMultiplier]| ((alo, blo), (clo, dlo))) as [c0 rOO]; clear clo dlo. destruct (|[fullMultiplier]| ((ahi, blo), (chi, dhi))) as [c1 c2]; clear chi dhi blo. cbn [fst snd]. fold Word in *. rewrite (toZ_Pair c1 c2), (toZ_Pair c0 rOO); fold C. transitivity ((toZ ahi * toZ bhi + toZ c1) * C * C + (toZ bhi * toZ alo + toZ c2 + toZ c0) * C + toZ rOO)%Z; [|ring]. rewrite <- IHn. destruct (|[fullMultiplier]| ((bhi, alo), (c2, c0))) as [c3 rOI]; clear c2 c0 alo. cbn [fst snd]. fold Word in *. rewrite (toZ_Pair c3 rOI); fold C. transitivity ((toZ ahi * toZ bhi + toZ c3 + toZ c1) * C * C + toZ rOI * C + toZ rOO)%Z; [|ring]. rewrite <- IHn. destruct (|[fullMultiplier]| ((ahi, bhi), (c3, c1))) as [rII rIO]; clear c3 c1 ahi bhi. rewrite (@toZ_Pair (WordToZ (S n)) (WordToZ (S n))), (toZ_Pair rOI rOO); fold C. rewrite (bitSize_Pair (WordToZ n) (WordToZ n)). rewrite two_power_nat_correct, Zpower_nat_is_exp, <- two_power_nat_correct; fold C. set (X := toZ _); ring. Qed. Lemma multiplier_correct n : forall (a b : Word n), (toZ (|[multiplier]| (a, b)) = toZ a * toZ b)%Z. Proof. intros a b. cbn -[toZ]. rewrite fullMultiplier_correct, zero_correct. ring. Qed. Import Coq.Vectors.Vector.VectorNotations. Fixpoint replicate {X} (x : X) n : Vector.t X n := match n return Vector.t X n with | 0 => [] | S m => (x :: replicate x m) end. Lemma replicate_append {X} (x : X) n m : replicate x n ++ replicate x m = replicate x (n + m). Proof. induction n. - reflexivity. - cbn. f_equal. assumption. Qed. Lemma nth_replicate {X n i} (x : X) (ix : i < n) : Vector.nth_order (replicate x n) ix = x. Proof. revert i ix. induction n;[|intros [|i] Hi]. - lia. - simpl. rewrite Vector.nth_order_hd. reflexivity. - assert (Hin : i < n) by lia. rewrite <- (Vector.nth_order_tl _ _ _ _ Hin). apply IHn. Qed. Lemma mul_2_r n : (2 * n = n + n)%nat. Proof. cbn. f_equal. induction n. - reflexivity. - cbn. f_equal. assumption. Defined. Fixpoint flatten {X n} : Vector X n -> Vector.t X (2^n) := match n return Vector X n -> Vector.t X (2^n) with | 0 => fun v => [v] | S n => fun v => eq_rect _ (Vector.t X) (flatten (fst v) ++ flatten (snd v)) _ (eq_sym (mul_2_r (2^n))) end. Lemma fill_correct {C X n} (t : Arrow C X) (c : C) : flatten (|[ fill t ]| c) = replicate (|[ t ]| c) (2^n). Proof. induction n. - reflexivity. - cbn. rewrite IHn. generalize ( (mul_2_r (2 ^ n))). cbn; intros ->; cbn. apply replicate_append. Qed. Definition TrinarySpec {n} (f : bool -> bool -> bool -> bool) (term : Arrow (Word n * (Word n * Word n)) (Word n)) := forall (x y z : Word n) i, (Z.testbit (toZ (term (x,(y,z)))) i = f (Z.testbit (toZ x) i) (Z.testbit (toZ y) i) (Z.testbit (toZ z) i))%Z. Lemma bitwiseTri_correct {n} (f : bool -> bool -> bool -> bool) (op : Arrow (Bit * (Bit * Bit)) Bit) (Hf : f Datatypes.false Datatypes.false Datatypes.false = Datatypes.false) (Hop : (forall (a b c : Bit), toBool (op (a,(b,c))) = f (toBool a) (toBool b) (toBool c))) : TrinarySpec (n:=n) f (bitwiseTri op). Proof. induction n. intros a b c i. simpl (bitwiseTri op). assert (to01 : (forall (b : Bit), Z.testbit (toZ b) i = if toBool b then Z.testbit 1 i else Z.testbit 0 i)%Z) by (intros [[] | []]; reflexivity). repeat rewrite to01. rewrite Hop; clear - Hf. destruct (toBool a); destruct (toBool b); destruct (toBool c); destruct i; cbn; try rewrite Hf; try reflexivity; destruct (f _ _ _) in |- *; reflexivity. intros [ahi alo] [bhi blo] [chi clo] i. destruct (Z_lt_le_dec i (two_power_nat n)) as [Hi|Hi]; cbn; [repeat rewrite (testbitToZLo _ _ Hi) |repeat rewrite (testbitToZHi _ _ Hi) ]; auto. Qed. Definition pow_succ n : (2^n = S (pred (2^n)))%nat. case_eq (2^n). - abstract (intros H;elim (Nat.pow_nonzero 2 n);lia). - reflexivity. Defined. Definition pow_hd {X n} (v : Vector.t X (2^n)) : X := Vector.hd (eq_rect _ (Vector.t X) v _ (pow_succ n)). Definition pow_last {X n} (v : Vector.t X (2^n)) : X := Vector.last (eq_rect _ (Vector.t X) v _ (pow_succ n)). Lemma hd_flatten {X n} (v0 v1 : Vector X n): pow_hd (@flatten X (S n) (v0,v1)) = pow_hd (@flatten X n v0). Proof. unfold pow_hd; cbn. generalize (mul_2_r (2 ^ n)) (pow_succ n) (pow_succ (S n)). change (2 * 2 ^ n)%nat with (2 ^ (S n))%nat. change (2 ^ n + (2 ^ n + 0))%nat with (2 ^ (S n))%nat. intros -> e0 e1; simpl. cut (forall a b (e0 : a = S (Init.Nat.pred a)) (e1 : (a + b)%nat = S (Init.Nat.pred (a + b))) (v : Vector.t X a) (w : Vector.t X b), Vector.hd (eq_rect (a + b)%nat (Vector.t X) (v ++ w) (S (Init.Nat.pred (a + b))) e1) = Vector.hd (eq_rect a (Vector.t X) v (S (Init.Nat.pred a)) e0)); [intros H0; apply H0|clear e0 e1]. intros a b -> e; simpl. elim e using K_dec_set;[apply Nat.eq_dec|simpl]. intros v. rewrite (Vector.eta v). reflexivity. Qed. Lemma leftmost_correct {X n v} : |[ leftmost ]| v = pow_hd (@flatten X n v). Proof. induction n. - reflexivity. - cbn. rewrite IHn; clear IHn. symmetry. apply hd_flatten. Qed. Lemma Vector_eta_shift {X n} (v : Vector.t X (S n)) : v = Vector.shiftin (Vector.last v) (Vector.shiftout v). Proof. elim v using Vector.rectS. - reflexivity. - simpl. intros a c w IH. f_equal. assumption. Qed. Lemma rightmost_correct {X n v} : |[ rightmost ]| v = pow_last (@flatten X n v). Proof. induction n. - reflexivity. - cbn. rewrite IHn; clear IHn. unfold pow_last. generalize (mul_2_r (2 ^ n)) (pow_succ n) (pow_succ (S n)). change (2 * 2 ^ n)%nat with (2 ^ (S n))%nat. change (2 ^ n + (2 ^ n + 0))%nat with (2 ^ (S n))%nat. intros -> e0 e1; simpl. cut (forall a b (e0 : b = S (Init.Nat.pred b)) (e1 : (a + b)%nat = S (Init.Nat.pred (a + b))) (v : Vector.t X a) (w : Vector.t X b), Vector.last (eq_rect b (Vector.t X) w (S (Init.Nat.pred b)) e0) = Vector.last (eq_rect (a + b)%nat (Vector.t X) (v ++ w) (S (Init.Nat.pred (a + b))) e1)); [intros H0; apply H0|clear v e0 e1]. intros a b ->; simpl. replace (Init.Nat.pred (a + S (Init.Nat.pred b))) with (a + Init.Nat.pred b)%nat by (rewrite Nat.add_succ_r; reflexivity). intros e v w. transitivity (Vector.last (Vector.shiftin (Vector.last w) (v ++ Vector.shiftout w))); [rewrite Vector.shiftin_last; reflexivity|]. f_equal. revert e w. generalize (pred b); clear b. (* This shiftin/app/shiftout lemma could perhaps be generalized *) induction v. + simpl. intros b e w. elim e using K_dec_set;[apply Nat.eq_dec|clear e]. simpl. symmetry. apply Vector_eta_shift. + simpl. intros b e w. assert (e0 : (n0 + S b)%nat = S (n0 + b)) by lia. rewrite (IHv b e0). generalize (v ++ w). revert e. rewrite e0. intros e. elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. Qed. Definition map_fst {A B C} (f : A -> B) (v : A * C) : B * C := (f (fst v), snd v). Definition map_snd {A B C} (f : B -> C) (v : A * B) : A * C := (fst v, f (snd v)). Lemma tail_shiftin {X n} x (v: Vector.t X (S n)) : Vector.tl (Vector.shiftin x v) = Vector.shiftin x (Vector.tl v). Proof. rewrite (Vector.eta v). reflexivity. Qed. Lemma shiftin_append {X n m} (e : (n + S m = S (n + m))%nat) x (v0 : Vector.t X n) (v1 : Vector.t X m) : Vector.shiftin x (v0 ++ v1) = eq_rect _ (Vector.t X) (v0 ++ (Vector.shiftin x v1)) _ e. Proof. revert e. induction v0. - cbn; intros e. elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. - intros e. assert (e0 : (n + S m)%nat = S (n + m)) by lia. cbn in *. rewrite (IHv0 e0). revert e. rewrite <- e0. cbn. intros e. elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. Qed. Lemma append_shiftin {X n m} (e : (n + S m = S (n + m))%nat) x (v0 : Vector.t X n) (v1 : Vector.t X m) : Vector.shiftin x v0 ++ v1 = eq_rect _ (Vector.t X) (v0 ++ x ::v1) _ e. Proof. revert e. induction v0. - cbn; intros e. elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. - intros e. assert (e0 : (n + S m)%nat = S (n + m)) by lia. cbn in *. rewrite (IHv0 e0). revert e. rewrite <- e0. cbn. intros e; elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. Qed. Lemma last_flatten {X n} v0 v1 : pow_last (@flatten X (S n) (v0,v1)) = pow_last (@flatten X n v1). Proof. fold tySem Vector in *. unfold pow_last; cbn. generalize (mul_2_r (2 ^ n)) (pow_succ n) (pow_succ (S n)). change (2 * 2 ^ n)%nat with (2 ^ (S n))%nat. change (2 ^ n + (2 ^ n + 0))%nat with (2 ^ (S n))%nat. intros -> e0 e1; simpl. cut (forall a b (e0 : b = S (Init.Nat.pred b)) (e1 : (a + b)%nat = S (Init.Nat.pred (a + b))) (v : Vector.t X a) (w : Vector.t X b), Vector.last (eq_rect (a + b)%nat (Vector.t X) (v ++ w) (S (Init.Nat.pred (a + b))) e1) = Vector.last (eq_rect b (Vector.t X) w (S (Init.Nat.pred b)) e0)); [intros H0; apply H0|clear e0 e1]. intros a b -> e v w; simpl. revert e. replace (Init.Nat.pred (a + S (Init.Nat.pred b))) with (a + (Init.Nat.pred b))%nat by lia. rewrite (Vector_eta_shift w). intros e. rewrite <- (shiftin_append e). rewrite !VectorSpec.shiftin_last. reflexivity. Qed. Lemma full_left_shift1_correct {X n v x} : map_snd flatten (|[ full_left_shift1 ]| (v, x)) = (pow_hd (@flatten X n v), Vector.tl (Vector.shiftin x (flatten v))). Proof. fold tySem in *. revert x. induction n. - reflexivity. - destruct v as [v0 v1]. simpl. unfold build_full_left_shift1. intros x. unfold map_snd. cbn. injection (IHn v1 x); intros -> ->. set (y := pow_hd (flatten v1)). injection (IHn v0 y); intros -> ->. clear IHn. f_equal. + symmetry. apply hd_flatten. + generalize (mul_2_r (2 ^ n)). cbn; intros ->; cbn. unfold y. generalize (flatten v0) (flatten v1). clear y v0 v1. unfold pow_hd. generalize (pow_succ n). set (Z := pred (2^n)). rewrite (pow_succ n). intros ->. unfold Z; clear Z. cbn. intros v0 v1. rewrite tail_shiftin. rewrite (append_shiftin (Nat.add_succ_r _ _)). replace (Vector.hd v1) with (Vector.hd (Vector.shiftin x v1)) by (rewrite (Vector.eta v1); reflexivity). rewrite <-Vector.eta. rewrite (shiftin_append (Nat.add_succ_r _ _) x v0 v1). set (e0 := (Nat.add_succ_r _ _)). set (e1 := (Nat.add_succ_r _ _)). clearbody e0 e1. cbn in *. revert e1. rewrite <- e0. intros e; elim e using K_dec_set;[apply Nat.eq_dec|]. cbn. rewrite (Vector.eta v0). reflexivity. Qed. Lemma left_shift1_correct {X n v t} : @flatten X n (|[ left_shift1 t ]| v) = Vector.tl (Vector.shiftin (|[ t ]| tt) (flatten v)). Proof. unfold left_shift1. cbn. change (flatten (snd _)) with (snd (map_snd flatten (|[full_left_shift1]| (v, t tt)))). rewrite full_left_shift1_correct. reflexivity. Qed. Lemma shiftout_append {X n m} (e : (n + S m = S (n + m))%nat) (v0 : Vector.t X n) (v1 : Vector.t X (S m)) : Vector.shiftout (eq_rect _ (Vector.t X) (v0 ++ v1) _ e) = v0 ++ (Vector.shiftout v1). Proof. revert e. induction v0. - cbn; intros e. elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. - intros e. assert (e0 : (n + S m)%nat = S (n + m)) by lia. cbn in *. rewrite <-(IHv0 e0). generalize (v0 ++ v1). revert e. rewrite e0. cbn. intros e. elim e using K_dec_set;[apply Nat.eq_dec|reflexivity]. Qed. Lemma full_right_shift1_correct {X n v x} : map_fst flatten (|[ full_right_shift1 ]| (x, v)) = (Vector.shiftout (x :: flatten v), pow_last (@flatten X n v)). Proof. fold tySem in *. revert x. induction n. - reflexivity. - destruct v as [v0 v1]. simpl (map_fst _ _). unfold build_full_right_shift1. intros x. unfold map_fst. etransitivity;[cbn|reflexivity]. unfold map_fst in IHn. replace (flatten (fst (|[full_right_shift1]| (x, v0)))) with (Vector.shiftout (x :: flatten v0)) by (injection (IHn v0 x); auto). replace (snd (|[full_right_shift1]| (x, v0))) with (pow_last (flatten v0)) by (injection (IHn v0 x); auto). set (y := pow_last (flatten v0)). replace (flatten (fst (|[full_right_shift1]| (y, v1)))) with (Vector.shiftout (y :: flatten v1)) by (injection (IHn v1 y); auto). replace (snd (|[full_right_shift1]| (y, v1))) with (pow_last (flatten v1)) by (injection (IHn v1 y); auto). clear IHn. f_equal. + simpl (@flatten X (S n) (v0, v1)). generalize (mul_2_r (2 ^ n)). simpl (2 * _)%nat; simpl (2 ^ (S n))%nat. intros ->. change (Vector.shiftout (x :: flatten v0) ++ Vector.shiftout (y :: flatten v1) = Vector.shiftout (x :: (flatten v0 ++ flatten v1))). unfold y. generalize (flatten v0) (flatten v1). clear y v0 v1. unfold pow_last. generalize (pow_succ n). set (Z := pred (2^n)). rewrite (pow_succ n). intros ->. unfold Z; clear Z. cbn. intros v0 v1. f_equal. change (eq_rect _ (Vector.t X) (Vector.shiftout v0 ++ Vector.last v0 :: Vector.shiftout v1) _ eq_refl = Vector.shiftout (v0 ++ v1)). rewrite <- (eq_trans_sym_inv_r (Nat.add_succ_r _ _)), eq_trans_rew_distr. rewrite <- append_shiftin. rewrite <- Vector_eta_shift. rewrite <- (shiftout_append (Nat.add_succ_r _ _)). generalize (v0 ++ v1). generalize (Nat.add_succ_r (S (Init.Nat.pred (2 ^ n))) (Init.Nat.pred (2 ^ n))). generalize (Nat.add_succ_r (Init.Nat.pred (2 ^ n)) (Init.Nat.pred (2 ^ n))). cbn; intros <-; cbn. intros e;elim e using K_dec_set;[apply Nat.eq_dec|]. reflexivity. + symmetry. apply last_flatten. Qed. Lemma right_shift1_correct {X n v t} : @flatten X n (|[ right_shift1 t ]| v) = Vector.shiftout (|[ t ]| tt :: flatten v). Proof. unfold right_shift1. etransitivity;[cbn|reflexivity]. change (flatten (fst _)) with (fst (map_fst flatten (|[full_right_shift1]| (t tt, v)))). rewrite full_right_shift1_correct. reflexivity. Qed. Lemma nth_order_shiftout {X n i} (v : Vector.t X (S n)) (ix1 : i < n) (ix2 : i < S n) : Vector.nth_order (Vector.shiftout v) ix1 = Vector.nth_order v ix2. Proof. revert i ix1 ix2. elim v using Vector.rectS. - lia. - intros h n0 t IHv i ix1 ix2. destruct i. + rewrite !Vector.nth_order_hd. reflexivity. + assert (ix1' : i < n0) by lia. assert (ix2' : i < S n0) by lia. rewrite <-(Vector.nth_order_tl _ _ _ _ ix1'). rewrite <-(Vector.nth_order_tl _ _ _ _ ix2'). change (VectorDef.nth_order (Vector.shiftout t) ix1' = VectorDef.nth_order t ix2'). apply IHv. Qed. Lemma nth_order_append_front {X n m i} (v : Vector.t X n) (w : Vector.t X m) (ix1 : i < n + m) (ix2 : i < n) : Vector.nth_order (v ++ w) ix1 = Vector.nth_order v ix2. Proof. revert i ix1 ix2. induction v;[lia|]. intros [|i] ix1 ix2;simpl. - rewrite !Vector.nth_order_hd. reflexivity. - assert (ix1' : i < n + m) by lia. assert (ix2' : i < n) by lia. rewrite <-(Vector.nth_order_tl _ _ _ _ ix1'), <-(Vector.nth_order_tl _ _ _ _ ix2'). simpl. apply IHv. Qed. Lemma nth_order_append_back {X n m i} (v : Vector.t X n) (w : Vector.t X m) (ix1 : n + i < n + m) (ix2 : i < m) : Vector.nth_order (v ++ w) ix1 = Vector.nth_order w ix2. Proof. revert i ix1 ix2. induction v; intros i ix1 ix2. - apply Vector.nth_order_ext. - simpl. assert (ix1' : n + i < n + m) by lia. rewrite <- (Vector.nth_order_tl _ _ _ _ ix1'). apply IHv. Qed. Lemma nth_order_flatten {X n i} (v : Vector (X * X) n) (ix :(i < 2^n)) (ix1 : 2*i < 2^(S n)) (ix2 : 2*i + 1 < 2^(S n)) : Vector.nth_order (flatten v) ix = (Vector.nth_order (flatten (eq_rect _ tySem v _ (eq_sym VectorPromote))) ix1, Vector.nth_order (flatten (eq_rect _ tySem v _ (eq_sym VectorPromote))) ix2). Proof. revert v i ix ix1 ix2. induction n; intros [v0 v1] i ix ix1 ix2. - simpl in *|-. destruct i;[|lia]. reflexivity. - simpl (@flatten _ (S n) _). simpl (2 ^ _)%nat in *. revert ix. generalize (mul_2_r (2 ^ n)); simpl (2 * 2 ^ n)%nat. intros -> ix. fold (2^n). simpl (eq_rect _ _ _ _ (eq_sym eq_refl)). replace (eq_rect (Vector (X * X) (S n)) tySem (v0, v1) (Vector X (S (S n))) (eq_sym VectorPromote)) with ((eq_rect (Vector (X * X) n) tySem v0 (Vector X (S n)) (eq_sym VectorPromote)), (eq_rect (Vector (X * X) n) tySem v1 (Vector X (S n)) (eq_sym VectorPromote))). 2:{ generalize (eq_sym (@VectorPromote X (S n))). revert v0 v1. generalize (eq_sym (@VectorPromote X n)). simpl. intros -> v0 v1 e. elim e using K_dec_set;[decide equality|]. reflexivity. } set (v0' := (eq_rect (Vector (X * X) n) _ _ _ _)). set (v1' := (eq_rect (Vector (X * X) n) _ _ _ _)). change (@flatten _ (S (S n)) (v0', v1')) with (eq_rect _ (Vector.t X) (flatten v0' ++ flatten v1') _ (eq_sym (mul_2_r (2 ^ (S n))))). revert ix1 ix2. generalize (mul_2_r (2 ^ S n)). simpl (2 * _)%nat. simpl (2 ^ _)%nat. intros -> ix1 ix2. change (Vector.nth_order (flatten v0 ++ flatten v1) ix = ( Vector.nth_order (flatten v0' ++ flatten v1') ix1 , Vector.nth_order (flatten v0' ++ flatten v1') ix2)). destruct (Nat.le_gt_cases (2^n) i) as [Hi|ix']. + pose (j:= i - 2^n). assert (ix' : j < 2 ^ n) by lia. assert (ix1' : 2 * j < 2 ^ S n) by (cbn; lia). assert (ix2' : 2 * j + 1 < 2 ^ S n) by (cbn; lia). revert ix. pattern i at 1 2. replace i with (2^n + j)%nat by lia. intros ix. fold (2*i)%nat in *. revert ix1. pattern (2*i)%nat at 1 2. replace (2*i)%nat with (2^(S n) + 2*j)%nat by (cbn;lia). intros ix1. revert ix2. replace (2*i + 1)%nat with (2^(S n) + (2*j + 1))%nat by (cbn;lia). intros ix2. rewrite (nth_order_append_back _ _ _ ix'), (nth_order_append_back _ _ _ ix1'), (nth_order_append_back _ _ _ ix2'). apply IHn. + assert (ix1' : 2 * i < 2 ^ S n) by (cbn; lia). assert (ix2' : 2 * i + 1 < 2 ^ S n) by (cbn; lia). rewrite (nth_order_append_front _ _ _ ix'), (nth_order_append_front _ _ _ ix1'), (nth_order_append_front _ _ _ ix2'). apply IHn. Qed. Lemma nth_order_flatten_if {X n i} (v : Vector (X * X) n) (ix : i < 2^(S n)) (ix_half : Nat.div2 i < 2^n) : Vector.nth_order (flatten (eq_rect _ tySem v _ (eq_sym VectorPromote))) ix = (if Nat.even i then fst else snd) (Vector.nth_order (flatten v) ix_half). Proof. assert (ix_half1 : 2 * Nat.div2 i < 2 ^ (S n)) by (cbn;lia). assert (ix_half2 : 2 * Nat.div2 i + 1 < 2 ^ (S n)) by (cbn;lia). rewrite (nth_order_flatten _ _ ix_half1 ix_half2). destruct (Nat.Even_Odd_dec i) as [Heven|Hodd]. - rewrite <- Nat.even_spec in Heven. rewrite Heven. rewrite Nat.even_spec in Heven. destruct Heven as [i' ->]. revert ix_half1 ix_half2. rewrite Nat.div2_double. intros; apply Vector.nth_order_ext. - rewrite <- Nat.odd_spec in Hodd. rewrite <- Nat.negb_odd, Hodd. rewrite Nat.odd_spec in Hodd. destruct Hodd as [i' ->]. revert ix ix_half1 ix_half2. replace (2 * i' + 1)%nat with (S (2 * i'))%nat by lia. rewrite Nat.div2_succ_double. replace (2 * i' + 1)%nat with (S (2 * i'))%nat by lia. intros; apply Vector.nth_order_ext. Qed. Lemma right_shift_const_by_correct {X n v t p i} (ix1 : i < 2^n) (ix2 : i - Pos.to_nat p < 2^n) : Vector.nth_order (@flatten X n (|[ right_shift_const_by t p ]| v)) ix1 = if i Vector.nth_order (flatten (( eq_rect (Vector (X * X) n) (fun x : Ty => Arrow x x) (right_shift_const_by (t &&& t) p0) (Vector X (S n)) (eq_sym VectorPromote)) (right_shift1 t v))) ix1 | (p0~0)%positive => Vector.nth_order (flatten ((eq_rect (Vector (X * X) n) (fun x : Ty => Arrow x x) (right_shift_const_by (t &&& t) p0) (Vector X (S n)) (eq_sym VectorPromote)) v)) ix1 | 1%positive => Vector.nth_order (flatten (right_shift1 t v)) ix1 end); [destruct p; reflexivity|]. assert (Hcast : forall (f : Arrow (Vector (X*X) n) (Vector (X*X) n)), (eq_rect _ (fun x : Ty => Arrow x x) f _ (eq_sym VectorPromote) = (fun w => eq_rect _ tySem (f (eq_rect _ tySem w _ VectorPromote)) _ (eq_sym VectorPromote)))). 1:{ generalize (@VectorPromote X n). intros <-. reflexivity. } assert (ix_half : Nat.div2 i < 2^n). 1:{ rewrite Nat.div2_div. apply Nat.Div0.div_lt_upper_bound. rewrite <- Nat.pow_succ_r'. assumption. } specialize (IHn (X*X) (t &&& t)). destruct p. + rewrite Hcast. set (w:= right_shift_const_by (t &&& t) p _). rewrite (nth_order_flatten_if _ _ ix_half). assert (ix_half2 : Nat.div2 i - Pos.to_nat p < 2 ^ n) by lia. rewrite (IHn _ _ _ ix_half ix_half2). elim Nat.ltb_spec; rewrite Nat.div2_div at 1. * intros Hip. elim Nat.ltb_spec. 2:{ rewrite (Pos2Nat.inj_xI p) at 1. intros Hpi. assert (Hpi0 : S (2 * Pos.to_nat p) / 2 <= i / 2) by (apply Nat.Div0.div_le_mono;lia). rewrite <- (Nat.div_unique _ _ (Pos.to_nat p) 1) in Hpi0; lia. } intros _. destruct (Nat.even i);reflexivity. * intros Hpi. assert (ix_half2a : 2*(Nat.div2 i - Pos.to_nat p) < 2 ^ (S n)) by (rewrite Nat.pow_succ_r';lia). assert (ix_half2b : 2*(Nat.div2 i - Pos.to_nat p) + 1 < 2 ^ (S n)) by (rewrite Nat.pow_succ_r';lia). erewrite (nth_order_flatten _ _ ix_half2a ix_half2b). rewrite <-eq_trans_rew_distr, eq_trans_sym_inv_r. cbn -[right_shift1 flatten Pos.to_nat Nat.ltb]. rewrite right_shift1_correct. elim Nat.ltb_spec. 1:{ rewrite (Pos2Nat.inj_xI p) at 1. intros Hip. assert (Hi : (i = 2*Pos.to_nat p)%nat). 1:{ apply Nat.le_antisymm;[lia|]. apply (Nat.mul_le_mono_l _ _ 2) in Hpi. assert (Hle := Nat.Div0.mul_div_le i 2). lia. } replace (Nat.even i) with (Nat.even (2 * Pos.to_nat p)%nat) by congruence. rewrite Nat.even_mul. change (Vector.nth_order (Vector.shiftout (t tt :: flatten v)) ix_half2a = t tt). revert ix_half2a. rewrite Hi, Nat.div2_double. replace (2 * (Pos.to_nat p - Pos.to_nat p))%nat with 0 by lia. intros ix_half2a. assert (ix_half2a' : 0 < S (2 ^ S n)) by lia. rewrite (nth_order_shiftout _ _ ix_half2a'). rewrite Vector.nth_order_hd. reflexivity. } assert (ix_half2a' : 2 * (Nat.div2 i - Pos.to_nat p) < S (2 ^ S n)) by lia. assert (ix_half2b' : 2 * (Nat.div2 i - Pos.to_nat p) + 1 < S (2 ^ S n)) by lia. rewrite (nth_order_shiftout _ _ ix_half2a'), (nth_order_shiftout _ _ ix_half2b'). intros Hp1i. transitivity (Vector.nth_order (Vector.tl (t tt :: flatten v)) ix2);[|reflexivity]. assert (ix2' : S (i - Pos.to_nat p~1) < S (2 ^ S n)) by lia. rewrite (VectorSpec.nth_order_tl _ _ _ _ _ ix2'). destruct (Nat.Even_Odd_dec i) as [Heven|Hodd]. 1:{ rewrite <- Nat.even_spec in Heven. rewrite Heven. rewrite Nat.even_spec in Heven. destruct Heven as [i' Hi']. revert ix2'. replace (S (i - Pos.to_nat p~1)) with (2 * (Nat.div2 i - Pos.to_nat p))%nat; [intros; apply Vector.nth_order_ext|]. rewrite Hi', Nat.div2_double. lia. } 1:{ rewrite <- Nat.odd_spec in Hodd. rewrite <- Nat.negb_odd, Hodd. rewrite Nat.odd_spec in Hodd. destruct Hodd as [i' Hi']. revert ix2'. replace (S (i - Pos.to_nat p~1)) with (2 * (Nat.div2 i - Pos.to_nat p) + 1)%nat; [intros; apply Vector.nth_order_ext|]. replace (2 * i' + 1)%nat with (S (2 * i')) in Hi' by lia. rewrite Hi', Nat.div2_succ_double. lia. } + rewrite Hcast. set (w:= right_shift_const_by (t &&& t) p _). rewrite (nth_order_flatten_if _ _ ix_half). assert (ix_half2 : Nat.div2 i - Pos.to_nat p < 2 ^ n) by lia. rewrite (IHn _ _ _ ix_half ix_half2). elim Nat.ltb_spec; rewrite Nat.div2_div at 1. * intros Hip. elim Nat.ltb_spec. 2:{ rewrite (Pos2Nat.inj_xO p) at 1. intros Hpi. assert (Hpi0 : (2 * Pos.to_nat p) / 2 <= i / 2) by (apply Nat.Div0.div_le_mono;lia). rewrite <- (Nat.div_unique _ _ (Pos.to_nat p) 0) in Hpi0; lia. } intros _. destruct (Nat.even i);reflexivity. * intros Hpi. elim Nat.ltb_spec. 1:{ rewrite (Pos2Nat.inj_xO p) at 1. assert (Hle := Nat.Div0.mul_div_le i 2). lia. } assert (ix_half2a : 2*(Nat.div2 i - Pos.to_nat p) < 2 ^ (S n)) by (rewrite Nat.pow_succ_r';lia). assert (ix_half2b : 2*(Nat.div2 i - Pos.to_nat p) + 1 < 2 ^ (S n)) by (rewrite Nat.pow_succ_r';lia). erewrite (nth_order_flatten _ _ ix_half2a ix_half2b). rewrite <-eq_trans_rew_distr, eq_trans_sym_inv_r. cbn -[right_shift1 flatten Pos.to_nat Nat.ltb]. intros Hp0i. destruct (Nat.Even_Odd_dec i) as [Heven|Hodd]. 1:{ rewrite <- Nat.even_spec in Heven. rewrite Heven. rewrite Nat.even_spec in Heven. destruct Heven as [i' Hi']. revert ix2. replace (i - Pos.to_nat p~0) with (2 * (Nat.div2 i - Pos.to_nat p))%nat; [intros; apply Vector.nth_order_ext|]. rewrite Hi', Nat.div2_double. lia. } 1:{ rewrite <- Nat.odd_spec in Hodd. rewrite <- Nat.negb_odd, Hodd. rewrite Nat.odd_spec in Hodd. destruct Hodd as [i' Hi']. revert ix2. replace (i - Pos.to_nat p~0) with (2 * (Nat.div2 i - Pos.to_nat p) + 1)%nat; [intros; apply Vector.nth_order_ext|]. replace (2 * i' + 1)%nat with (S (2 * i')) in Hi' by lia. rewrite Hi', Nat.div2_succ_double. lia. } + rewrite right_shift1_correct. assert (ix1' : i < S (2 ^ S n)) by lia. rewrite (nth_order_shiftout _ _ ix1'). elim Nat.ltb_spec; intros Hi. * destruct i;[|lia]. rewrite Vector.nth_order_hd. reflexivity. * destruct i;[lia|]. assert (ix1'S : i < 2 ^ S n) by lia. rewrite <- (Vector.nth_order_tl _ _ _ _ ix1'S). change (Vector.nth_order (flatten v) ix1'S = Vector.nth_order (flatten v) ix2). revert ix2. replace (S i - Pos.to_nat 1)%nat with i; [intros; apply Vector.nth_order_ext|lia]. Qed. Lemma shiftout_shiftin {X n} a (v : Vector.t X n) : (Vector.shiftout (Vector.shiftin a v)) = v. Proof. induction v. - reflexivity. - simpl. rewrite IHv. reflexivity. Qed. Lemma left_shift_const_by_correct {X n v t p i} (ix1 : i < 2^n) : Vector.nth_order (@flatten X n (|[ left_shift_const_by t p ]| v)) ix1 = match lt_dec (i + Pos.to_nat p) (2^n) with | left ix2 => Vector.nth_order (@flatten X n v) ix2 | right _ => |[ t ]| tt end. Proof. revert X t p v i ix1. induction n;intros X t p v i ix1. - simpl in *. destruct i;[|lia]. elim (Z.leb_spec);[intros _|lia]. destruct (lt_dec _ _);[lia|reflexivity]. - simpl (left_shift_const_by t p v). change (_ <=? _)%Z with (Zpower_nat 2 (S n) <=? Z.pos p)%Z. elim (Z.leb_spec). 1:{ rewrite Zpower_nat_Z. change 2%Z with (Z.of_nat 2%nat) at 1. rewrite <- Nat2Z.inj_pow. intros Hp. destruct (lt_dec _ _);[lia|]. change (Vector.nth_order (flatten (|[@fill _ X (S n) _ t]| tt)) ix1 = |[t]| tt). rewrite fill_correct. apply nth_replicate. } intros Hpn. transitivity (match p with | (p0~1)%positive => Vector.nth_order (flatten (( eq_rect (Vector (X * X) n) (fun x : Ty => Arrow x x) (left_shift_const_by (t &&& t) p0) (Vector X (S n)) (eq_sym VectorPromote)) (left_shift1 t v))) ix1 | (p0~0)%positive => Vector.nth_order (flatten ((eq_rect (Vector (X * X) n) (fun x : Ty => Arrow x x) (left_shift_const_by (t &&& t) p0) (Vector X (S n)) (eq_sym VectorPromote)) v)) ix1 | 1%positive => Vector.nth_order (flatten (left_shift1 t v)) ix1 end); [destruct p; reflexivity|]. assert (Hcast : forall (f : Arrow (Vector (X*X) n) (Vector (X*X) n)), (eq_rect _ (fun x : Ty => Arrow x x) f _ (eq_sym VectorPromote) = (fun w => eq_rect _ tySem (f (eq_rect _ tySem w _ VectorPromote)) _ (eq_sym VectorPromote)))). 1:{ generalize (@VectorPromote X n). intros <-. reflexivity. } assert (ix_half : Nat.div2 i < 2^n). 1:{ rewrite Nat.div2_div. apply Nat.Div0.div_lt_upper_bound. rewrite <- Nat.pow_succ_r'. assumption. } specialize (IHn (X*X) (t &&& t)). destruct p. + rewrite Hcast. set (w:= left_shift_const_by (t &&& t) p _). rewrite (nth_order_flatten_if _ _ ix_half). rewrite (IHn _ _ _ ix_half). elim lt_dec; rewrite Nat.div2_div. 2:{ intros Hip. elim lt_dec. 1:{ intros Hpi. exfalso. rewrite (Pos2Nat.inj_xI p) in Hpi. rewrite <- Nat.le_succ_l in Hpi. assert (Hpi0 : (i + (S (Pos.to_nat p)) * 2) / 2 <= 2 ^ (S n) / 2) by (apply Nat.Div0.div_le_mono;lia). rewrite Nat.div_add in Hpi0 by lia. change (2^(S n)) with (2*(2^n))%nat in Hpi0. rewrite Nat.mul_comm, Nat.div_mul in Hpi0 by lia. lia. } intros _. destruct (Nat.even i);reflexivity. } 1:{ intros ix_half2. assert (ix_half2a : 2 * (i / 2 + Pos.to_nat p) < 2 ^ (S n)) by (rewrite Nat.pow_succ_r';lia). assert (ix_half2b : 2 * (i / 2 + Pos.to_nat p) + 1 < 2 ^ (S n)) by (rewrite Nat.pow_succ_r';lia). erewrite (nth_order_flatten _ ix_half2 ix_half2a ix_half2b). rewrite <-eq_trans_rew_distr, eq_trans_sym_inv_r. cbn -[left_shift1 flatten Pos.to_nat Nat.ltb]. rewrite left_shift1_correct. elim lt_dec. 2:{ intros Hip. assert (Hi : (i = 2^(S n) - 2*(Pos.to_nat p) - 1)%nat). 1:{ apply Nat.le_antisymm;[|cbn;lia]. apply (Nat.mul_le_mono_l _ _ 2) in ix_half2. assert (Hlt := Nat.mul_succ_div_gt i 2). lia. } replace (Nat.even i) with (Nat.even (2^(S n) - 2*(Pos.to_nat p) - 1)) by congruence. rewrite !Nat.even_sub, Nat.even_pow, Nat.even_mul by lia. change (Vector.nth_order (Vector.tl (Vector.shiftin (t tt) (flatten v))) ix_half2b = t tt). revert ix_half2b. replace (2 * (i / 2 + Pos.to_nat p) + 1)%nat with (pred (2^(S n))). 2:{ rewrite Nat.mul_add_distr_l, Hi. change (2^ (S n)) with (2*(2^n))%nat. replace (2 * 2 ^ n - 2 * Pos.to_nat p - 1) with (((2 ^ n - Pos.to_nat p -1) * 2 + 1))%nat by lia. rewrite Nat.div_add_l by lia. change (1 / 2) with 0. lia. } intros ix_half2b. assert (ix_half2b' : S (Init.Nat.pred (2 ^ S n)) < S (2 ^ S n)) by lia. rewrite (VectorSpec.nth_order_tl _ _ _ _ _ ix_half2b'). revert ix_half2b'. rewrite <- pow_succ. intros ix_half2b'. rewrite Vector.nth_order_last, Vector.shiftin_last. reflexivity. } assert (ix_half2a' : S (2 * (i / 2 + Pos.to_nat p)) < S (2 ^ S n)) by lia. assert (ix_half2b' : S (2 * (i / 2 + Pos.to_nat p) + 1) < S (2 ^ S n)) by lia. rewrite (VectorSpec.nth_order_tl _ _ _ _ _ ix_half2a'), (VectorSpec.nth_order_tl _ _ _ _ _ ix_half2b'). intros ix2. transitivity (Vector.nth_order (Vector.shiftout (Vector.shiftin (t tt) (flatten v))) ix2); [|rewrite shiftout_shiftin;reflexivity]. assert (ix2' :i + Pos.to_nat p~1 < S (2 ^ n + (2 ^ n + 0))) by lia. rewrite (nth_order_shiftout _ _ ix2'). destruct (Nat.Even_Odd_dec i) as [Heven|Hodd]. 1:{ rewrite <- Nat.even_spec in Heven. rewrite Heven. rewrite Nat.even_spec in Heven. destruct Heven as [i' Hi']. revert ix2'. replace (i + Pos.to_nat p~1)%nat with (S (2 * (i / 2 + Pos.to_nat p)))%nat; [intros; apply Vector.nth_order_ext|]. rewrite Hi', (Nat.mul_comm _ i'), Nat.div_mul; lia. } 1:{ rewrite <- Nat.odd_spec in Hodd. rewrite <- Nat.negb_odd, Hodd. rewrite Nat.odd_spec in Hodd. destruct Hodd as [i' Hi']. revert ix2'. replace (i + Pos.to_nat p~1)%nat with (S (2 * (i / 2 + Pos.to_nat p) + 1))%nat; [intros; apply Vector.nth_order_ext|]. replace (2 * i' + 1)%nat with (S (2 * i')) in Hi' by lia. rewrite Hi', <- Nat.div2_div, Nat.div2_succ_double. lia. } } + rewrite Hcast. set (w:= left_shift_const_by (t &&& t) p _). rewrite (nth_order_flatten_if _ _ ix_half). rewrite (IHn _ _ _ ix_half). elim lt_dec; rewrite Nat.div2_div. 2:{ intros Hip. elim lt_dec. 1:{ intros Hpi. elim Hip. rewrite (Pos2Nat.inj_xO p) in Hpi. change (2^(S n)) with (2*(2^n))%nat in Hpi. assert (Hle := Nat.Div0.mul_div_le i 2). cut (i/2 <= 2^n - (Pos.to_nat p + 1));[lia|]. apply Nat.Div0.div_le_upper_bound;lia. } intros _. destruct (Nat.even i);reflexivity. } 1:{ intros ix_half2. elim lt_dec. 2:{ intros Hip. apply Nat.nlt_ge in Hip. rewrite (Pos2Nat.inj_xO p) in Hip. apply (Nat.Div0.div_le_mono _ _ 2) in Hip. change (2^(S n)) with (2*(2^n))%nat in Hip. rewrite Nat.mul_comm, Nat.div_mul in Hip by lia. rewrite Nat.mul_comm, Nat.div_add in Hip by lia. lia. } assert (ix_half2a : 2 * (i / 2 + Pos.to_nat p) < 2 ^ S n) by (rewrite Nat.pow_succ_r';lia). assert (ix_half2b : 2 * (i / 2 + Pos.to_nat p) + 1 < 2 ^ S n) by (rewrite Nat.pow_succ_r';lia). erewrite (nth_order_flatten _ _ ix_half2a ix_half2b). rewrite <-eq_trans_rew_distr, eq_trans_sym_inv_r. cbn -[flatten Pos.to_nat Nat.ltb]. intros ix2. destruct (Nat.Even_Odd_dec i) as [Heven|Hodd]. 1:{ rewrite <- Nat.even_spec in Heven. rewrite Heven. rewrite Nat.even_spec in Heven. destruct Heven as [i' Hi']. revert ix2. replace (i + Pos.to_nat p~0)%nat with (2 * (i / 2 + Pos.to_nat p))%nat; [intros; apply Vector.nth_order_ext|]. rewrite Hi', <- Nat.div2_div, Nat.div2_double. lia. } 1:{ rewrite <- Nat.odd_spec in Hodd. rewrite <- Nat.negb_odd, Hodd. rewrite Nat.odd_spec in Hodd. destruct Hodd as [i' Hi']. revert ix2. replace (i + Pos.to_nat p~0)%nat with (2 * (i / 2 + Pos.to_nat p) + 1)%nat; [intros; apply Vector.nth_order_ext|]. replace (2 * i' + 1)%nat with (S (2 * i')) in Hi' by lia. rewrite Hi', <- Nat.div2_div, Nat.div2_succ_double. lia. } } + rewrite left_shift1_correct. assert (ix1' : S i < S (2 ^ S n)) by lia. rewrite (Vector.nth_order_tl _ _ _ _ _ ix1'). elim lt_dec; intros Hi. * transitivity (VectorDef.nth_order (Vector.shiftout (Vector.shiftin (t tt) (flatten v))) Hi). 1:{ revert Hi. replace (i + Pos.to_nat 1)%nat with (S i) by lia. intros Hi. rewrite (nth_order_shiftout _ _ ix1'). reflexivity. } f_equal. apply shiftout_shiftin. * revert ix1'. replace (S i) with (2^S n) by lia. intros ix1'. rewrite Vector.nth_order_last. apply Vector.shiftin_last. Qed. Lemma nth_Word {n i} (x : Word n) (ix : i < 2^n) : toBool (Vector.nth_order (flatten x) ix) = Z.testbit (toZ x) (2^(Z.of_nat n) - 1 - Z.of_nat i). Proof. revert i x ix. induction n. - intros [|i];[|cbn;lia]. intros [[] | []];reflexivity. - intros i [x0 x1]. rewrite <- (Nat2Z.inj_pow 2) in *. simpl. generalize (mul_2_r (2 ^ n)); simpl. intros -> ix; simpl. destruct (lt_dec i (2^n)) as [ix'|Hi]. + rewrite (nth_order_append_front _ _ _ ix'), IHn, testbitToZHi; rewrite two_power_nat_equiv, <- (Nat2Z.inj_pow 2);[f_equal|];lia. + assert (ix' : i - 2^n < 2^n) by lia. revert ix. replace i with (2^n + (i - 2^n))%nat by lia. intros ix. rewrite (nth_order_append_back _ _ _ ix'), IHn, testbitToZLo;[f_equal;lia|]. rewrite two_power_nat_equiv, <- (Nat2Z.inj_pow 2). lia. Qed. Lemma shift_const_correct n z (x : Word n) i (Hi : (0 <= i < two_power_nat n)%Z) : Z.testbit (toZ (|[shift_const (-z)]| x : tySem (Word n))) i = Z.testbit (toZ x) (i + z)%Z. Proof. assert (Htwo : forall n, two_power_nat n = Z.of_nat (2 ^ n)). 1:{ intros. rewrite two_power_nat_equiv, <- (Nat2Z.inj_pow 2). reflexivity. } rewrite Htwo in *. assert (ix : 2^n - 1 - Z.to_nat i < 2^n) by lia. destruct z;cbn. - f_equal. lia. - replace i with (Z.of_nat (2 ^ n - 1 - (2 ^ n - 1 - Z.to_nat i))) at 1 by lia. rewrite Nat2Z.inj_sub, (Nat2Z.inj_sub _ 1), Nat2Z.inj_pow by lia. rewrite <- (nth_Word _ ix). assert (ix2 : (2 ^ n - 1 - Z.to_nat i) - Pos.to_nat p < 2 ^ n) by lia. rewrite (right_shift_const_by_correct _ ix2). elim Nat.ltb_spec; intros Hp. + rewrite toZ_mod. rewrite two_power_nat_equiv, Z.mod_pow2_bits_high;[reflexivity|]. rewrite bitSize_Word, two_power_nat_equiv, <- (Nat2Z.inj_pow 2). lia. + rewrite nth_Word. f_equal. rewrite <- (Nat2Z.inj_pow 2). lia. - replace i with (Z.of_nat (2 ^ n - 1 - (2 ^ n - 1 - Z.to_nat i))) at 1 by lia. rewrite Nat2Z.inj_sub, (Nat2Z.inj_sub _ 1), Nat2Z.inj_pow by lia. rewrite <- (nth_Word _ ix). rewrite left_shift_const_by_correct. elim lt_dec; intros Hp. + rewrite nth_Word. f_equal. rewrite <- (Nat2Z.inj_pow 2). lia. + rewrite Z.testbit_neg_r;[reflexivity|]. lia. Qed. Lemma left_rotate1_correct {X n v} : @flatten X n (|[ left_rotate1 ]| v) = Vector.tl (Vector.shiftin (pow_hd (flatten v)) (flatten v)). Proof. unfold left_rotate1. etransitivity;[cbn|reflexivity]. change (flatten (snd _)) with (snd (map_snd flatten (|[full_left_shift1]| (v, |[leftmost]| v)))). rewrite full_left_shift1_correct, leftmost_correct. reflexivity. Qed. Lemma right_rotate1_correct {X n v} : @flatten X n (|[ right_rotate1 ]| v) = Vector.shiftout (pow_last (flatten v) :: (flatten v)). Proof. unfold right_rotate1. etransitivity;[cbn|reflexivity]. change (flatten (fst _)) with (fst (map_fst flatten (|[full_right_shift1]| (|[rightmost]| v, v)))). rewrite full_right_shift1_correct, rightmost_correct. reflexivity. Qed. Lemma foldr_comp_correct {X} l v : |[foldr_comp l]| v = fold_right (@comp X X X CoreFunSem) |[iden]| l v. Proof. revert v. induction l;[reflexivity|]. destruct l as [|b l];[reflexivity|]. - intros v. change (foldr_comp (a :: b :: l) v) with (foldr_comp (b :: l) (a v)). apply IHl. Qed. Lemma rotate_const_correct {X n i j} z (v : Vector X n) (ix : i < 2^n) (jx : j < 2^n) : eqm (2^Z.of_nat n) (Z.of_nat j) (Z.of_nat i + z) -> Vector.nth_order (flatten (|[rotate_const z]| v)) ix = Vector.nth_order (flatten v) jx. Proof. rewrite <- (Nat2Z.inj_pow 2). unfold rotate_const. rewrite foldr_comp_correct. intros Hij. generalize jx. rewrite <-(Nat2Z.id j), <-(Z.mod_small (Z.of_nat j) (Z.of_nat (2^n))), Hij by lia. clear j jx Hij. intros jx. assert (ixmod : forall n a, Z.to_nat (a mod Z.of_nat (2 ^ n)) < 2 ^ n). 1:{ clear. intros n a. assert (Hmod := Z.mod_pos_bound a (Z.of_nat (2^n))). rewrite pow_succ in Hmod at 1. lia. } transitivity (Vector.nth_order (flatten v) (ixmod _ (Z.of_nat i + z)))%Z;[|apply Vector.nth_order_ext]. clear jx. revert X i z v ix. induction n; [intros X [|i] z;simpl;[generalize (ixmod 0 z);simpl;rewrite Z.mod_1_r;intros;apply Vector.nth_order_ext|lia] |]. intros X i z v ix. assert (Hcast : forall (l : list (Arrow (Vector (X*X) n) (Vector (X*X) n))) w, fold_right comp iden (eq_rect _ (fun x : Ty => list (Arrow x x)) l _ (eq_sym VectorPromote)) w = eq_rect _ tySem (fold_right comp iden l (eq_rect _ tySem w _ VectorPromote)) _ (eq_sym VectorPromote)). 1:{ generalize (@VectorPromote X n). intros <-. reflexivity. } assert (ix_half : Nat.div2 i < 2^n). 1:{ rewrite Nat.div2_div. apply Nat.Div0.div_lt_upper_bound. rewrite <- Nat.pow_succ_r'. assumption. } assert (Heven : forall a, Nat.even a = Z.even (Z.of_nat a)). 1:{ clear. intros a. induction a as [a IH] using lt_wf_ind. destruct a as [| [|a]]; try reflexivity. simpl (Nat.even _). rewrite IH;[|lia]. symmetry. etransitivity;[|apply Z.even_succ_succ]. f_equal. lia. } generalize (ixmod (S n) (Z.of_nat i + z)%Z). change (2^S n) with (2 * 2^n)%nat. rewrite Nat2Z.inj_mul. change (Z.of_nat 2) with 2%Z. intros jx. simpl (rotate_const_list z). case_eq (Z.even z);[|case_eq (Z.even (z/2))]. - rewrite Z.even_spec. intros [z' ->]. replace (2 * z' / 2)%Z with z' by (rewrite Z.mul_comm, Z_div_mult by lia;reflexivity). rewrite Hcast, (nth_order_flatten_if _ _ ix_half). rewrite (IHn _ _ _ _ ix_half). generalize (ixmod n (Z.of_nat (Nat.div2 i) + z')%Z). set (j := Z.to_nat ((Z.of_nat i + 2 * z') mod (2 * Z.of_nat (2 ^ n)))) in *. replace (Z.to_nat ((Z.of_nat (Nat.div2 i) + z') mod Z.of_nat (2 ^ n))) with (Nat.div2 j). 2:{ symmetry. rewrite !Nat.div2_div, Nat2Z.inj_div, <- Z_div_plus, <-Zaux.Zdiv_mod_mult, Z.mul_comm by lia. rewrite Z2Nat.inj_div by (assert (Hmod := Z.mod_pos_bound (Z.of_nat i + Z.of_nat 2 * z') (Z.of_nat 2 * Z.of_nat (2 ^ n)));lia). reflexivity. } intros jx_half. replace (Nat.even i) with (Nat.even j); [rewrite <-(nth_order_flatten_if _ jx jx_half), <-eq_trans_rew_distr, eq_trans_sym_inv_r; apply Vector.nth_order_ext|]. rewrite !Heven. symmetry. apply Bool.eqb_true_iff. rewrite <- Z.even_sub. symmetry. change ((Z.even 2 || Z.even z') = Z.even (Z.of_nat i - Z.of_nat j))%bool. apply Bool.eqb_true_iff. rewrite <- Z.even_mul, <- Z.even_add, Zeven_mod. apply Zeq_is_eq_bool. replace (_ + _)%Z with ((Z.of_nat i + 2 * z') - Z.of_nat j)%Z by lia. apply Z.mod_divide;[lia|]. etransitivity;[apply (Z.divide_factor_l 2 (Z.of_nat (2^n)))|]. apply Z.mod_divide;[lia|]. unfold j. rewrite Z2Nat.id by (assert (Hmod := Z.mod_pos_bound (Z.of_nat i + 2 * z') (2 * Z.of_nat (2^n)));lia). rewrite Zminus_mod_idemp_r, Z.sub_diag. reflexivity. - rewrite Z.even_spec, <-Z.negb_odd, Bool.negb_false_iff, Z.odd_spec. intros Hz' [z' ->]. replace ((2 * z' + 1) / 2)%Z with z' in * by (rewrite Z.mul_comm, Z.div_add_l, Z.add_0_r by lia;reflexivity). destruct Hz' as [z ->]. set (l := eq_rect _ _ _ _ _). change (fold_right comp H (_ :: l) v) with (fold_right comp H l (|[left_rotate1]| v)). rewrite Hcast, (nth_order_flatten_if _ _ ix_half), (IHn _ _ _ _ ix_half); clear l. generalize (ixmod n (Z.of_nat (Nat.div2 i) + 2 * z)%Z). rewrite Nat.div2_div, Nat2Z.inj_div, <- Z_div_plus, <-Zaux.Zdiv_mod_mult, Z.mul_comm by lia. change (Z.of_nat 2) with 2%Z. set (k:= (Z.of_nat i + 2 * (2 * z))%Z). assert (Hmod := Z.mod_pos_bound k (2 * Z.of_nat (2^n))). rewrite Z2Nat.inj_div by lia. rewrite <-Nat.div2_div. revert jx. rewrite Z.add_assoc. set (j := Z.to_nat (k mod (2 * Z.of_nat (2 ^ n)))). intros jx jx_half. assert (jx' : j < 2 ^ (S n)) by (cbn;lia). replace (Nat.even i) with (Nat.even j). * rewrite <-(nth_order_flatten_if _ jx'), <-eq_trans_rew_distr, eq_trans_sym_inv_r; simpl (eq_rect _ _ _ _ eq_refl). rewrite left_rotate1_correct. assert (jx'S : S j < S (2^S n)) by lia. rewrite (VectorSpec.nth_order_tl _ _ _ _ _ jx'S). elim (lt_dec (S j) (2 ^ S n)). + intros jx'S'. rewrite <- (nth_order_shiftout _ jx'S'), shiftout_shiftin. revert jx. fold k. rewrite <- Zplus_mod_idemp_l, Z.mod_small; [rewrite Z2Nat.inj_succ;[apply Vector.nth_order_ext|lia] |]. unfold j in jx'S'. rewrite <- Z2Nat.inj_succ in jx'S' by lia. change (2^S n) with (2 * 2^n)%nat in *. lia. + intros Hj. revert jx'S. replace (S j) with (2 ^ S n) by lia. intros jx'S. rewrite Vector.nth_order_last, Vector.shiftin_last. revert jx. rewrite <-Zplus_mod_idemp_l, <-(Z2Nat.id (k mod (2 * Z.of_nat (2 ^ n)))) by lia. fold (Z.succ (Z.of_nat (Z.to_nat (k mod (2 * Z.of_nat (2 ^ n)))))) j. rewrite <- Nat2Z.inj_succ. replace (S j) with (2 ^ S n) by lia. change (2^S n) with (2 * 2^n)%nat. rewrite Nat2Z.inj_mul, Z_mod_same_full. change (2 * 2^n)%nat with (2^S n). generalize (flatten v). unfold pow_hd. generalize (pow_succ (S n));intros -> w wx. symmetry. apply Vector.nth_order_hd. * rewrite !Heven, !Zeven_mod. change 2%Z with (2^1)%Z. unfold j. rewrite Z2Nat.id, Nat2Z.inj_pow, <- Z.pow_succ_r, <- !Z.land_ones, <- Z.land_assoc by lia. rewrite Z.land_ones, Z.ones_mod_pow2, !Z.land_ones, <-!Zeven_mod by lia. unfold k. rewrite Z.even_add, Z.even_mul. change (_ || _)%bool with (Z.even 0). rewrite <-Z.even_add. f_equal. lia. - rewrite <-!Z.negb_odd, !Bool.negb_false_iff, !Z.odd_spec. intros Hz' [z' ->]. replace ((2 * z' + 1) / 2)%Z with z' in * by (rewrite Z.mul_comm, Z.div_add_l, Z.add_0_r by lia;reflexivity). destruct Hz' as [z ->]. replace (2 * (2 * z + 1) + 1 + 1)%Z with ((2*(z + 1))*2)%Z by lia. rewrite Z_div_mult by lia. set (l := eq_rect _ _ _ _ _). change (fold_right comp H (_ :: l) v) with (fold_right comp H l (|[right_rotate1]| v)). rewrite Hcast, (nth_order_flatten_if _ _ ix_half), (IHn _ _ _ _ ix_half); clear l. generalize (ixmod n (Z.of_nat (Nat.div2 i) + 2 * (z + 1))%Z). rewrite Nat.div2_div, Nat2Z.inj_div, <- Z_div_plus, <-Zaux.Zdiv_mod_mult, Z.mul_comm by lia. change (Z.of_nat 2) with 2%Z. set (k:= (Z.of_nat i + 2 * (2 * (z + 1)))%Z). assert (Hmod := Z.mod_pos_bound k (2 * Z.of_nat (2^n))). rewrite Z2Nat.inj_div by lia. rewrite <-Nat.div2_div. revert jx. replace (Z.of_nat i + (2 * (2 * z + 1) + 1))%Z with (k - 1)%Z by lia. set (j := Z.to_nat (k mod (2 * Z.of_nat (2 ^ n)))). intros jx jx_half. assert (jx' : j < 2 ^ (S n)) by (cbn;lia). replace (Nat.even i) with (Nat.even j). * rewrite <-(nth_order_flatten_if _ jx'), <-eq_trans_rew_distr, eq_trans_sym_inv_r; simpl (eq_rect _ _ _ _ eq_refl). rewrite right_rotate1_correct. assert (jx'S : j < S (2^S n)) by lia. rewrite (nth_order_shiftout _ _ jx'S). elim (Nat.eq_dec j 0). + intros Hj. revert jx'S. rewrite Hj. intros jx'S. rewrite Vector.nth_order_hd. revert jx. rewrite <-Zplus_mod_idemp_l, <-(Z2Nat.id (k mod (2 * Z.of_nat (2 ^ n)))) by lia. fold j. rewrite Hj. simpl (Z.of_nat 0). rewrite <- (Z_mod_same_full (2 * Z.of_nat (2 ^ n))), Zplus_mod_idemp_l, Z.mod_small by lia. replace (_ * _)%Z with (Z.of_nat (2 * 2 ^ n)) by lia. change (2 * 2^n)%nat with (2^S n). generalize (flatten v). unfold pow_last. generalize (pow_succ (S n));intros -> w. replace (Z.to_nat _) with (Init.Nat.pred (2 ^ S n)) by lia. intros wx. symmetry. apply Vector.nth_order_last. + intros Hj. revert jx'S. replace j with (S (pred j)) by lia. intros jx'S. symmetry. change (flatten v) with (Vector.tl (pow_last (flatten v) :: flatten v)) at 1. revert jx. rewrite <-Zplus_mod_idemp_l, <-(Z2Nat.id (k mod (2 * Z.of_nat (2 ^ n)))) by lia. fold j. replace (Z.of_nat j + - (1))%Z with (Z.of_nat (pred j)) by lia. rewrite Z.mod_small, Nat2Z.id by lia. change (2 * 2^n)%nat with (2^S n). intros jx. apply Vector.nth_order_tl. * rewrite !Heven, !Zeven_mod. change 2%Z with (2^1)%Z. unfold j. rewrite Z2Nat.id, Nat2Z.inj_pow, <- Z.pow_succ_r, <- !Z.land_ones, <- Z.land_assoc by lia. rewrite Z.land_ones, Z.ones_mod_pow2, !Z.land_ones, <-!Zeven_mod by lia. unfold k. rewrite Z.even_add, Z.even_mul. change (_ || _)%bool with (Z.even 0). rewrite <-Z.even_add. f_equal. lia. Qed. Lemma rotate_const_correct_word n z (x : Word n) i (Hi : (0 <= i < two_power_nat n)%Z) : Z.testbit (toZ (|[rotate_const (-z)]| x : tySem (Word n))) i = Z.testbit (toZ x) (Z.modulo (i + z) (two_power_nat n))%Z. Proof. assert (Htwo : forall n, two_power_nat n = Z.of_nat (2 ^ n)). 1:{ intros. rewrite two_power_nat_equiv, <- (Nat2Z.inj_pow 2). reflexivity. } rewrite Htwo in *. set (i0 := Z.to_nat (Z.of_nat (2^n) - 1 - i)). assert (ix : i0 < 2^n) by lia. replace i with (Z.of_nat (2 ^ n) - 1 - Z.of_nat i0)%Z at 1 by lia. rewrite Nat2Z.inj_pow by lia. rewrite <- (nth_Word _ ix). set (j0 := Z.to_nat ((Z.of_nat (2^n) - 1 - i - z) mod (2^Z.of_nat n))). destruct (Z.mod_pos_bound (Z.of_nat (2 ^ n) - 1 - i - z) (2 ^ Z.of_nat n)) as [Hj0 Hj1];[lia|]. assert (jx : j0 < 2^n). 1:{ rewrite <- (Nat2Z.id (2^n)). rewrite Nat2Z.inj_pow by lia. apply Z2Nat.inj_lt;lia. } rewrite (rotate_const_correct _ _ _ jx). 2:{ unfold eqm, i0, j0. rewrite !Z2Nat.id, Zmod_mod by lia. reflexivity. } rewrite nth_Word. f_equal. rewrite <-(Z.mod_small (2 ^ Z.of_nat n - 1 - Z.of_nat j0)%Z (2 ^ Z.of_nat n)) by lia. unfold j0. rewrite Z2Nat.id, Nat2Z.inj_pow, Zminus_mod_idemp_r by lia. f_equal. lia. Qed. End Specifications. Lemma zero_Parametric {n} {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ (Word n) zero zero. Proof. induction n; cbn; auto with parametricity. Qed. #[export] Hint Immediate zero_Parametric : parametricity. Lemma adderBit_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ adderBit adderBit. Proof. unfold adderBit. auto with parametricity. Qed. #[export] Hint Immediate adderBit_Parametric : parametricity. Lemma fullAdderBit_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ fullAdderBit fullAdderBit. Proof. unfold fullAdderBit. auto 10 with parametricity. Qed. #[export] Hint Immediate fullAdderBit_Parametric : parametricity. Lemma buildFullAdder_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {W} t1 t2 : R _ (Bit * W) t1 t2 -> R _ _ (buildFullAdder t1) (buildFullAdder t2). Proof. unfold buildFullAdder. auto 10 with parametricity. Qed. #[export] Hint Resolve buildFullAdder_Parametric : parametricity. Lemma fullAdder_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {n} : R _ _ fullAdder (@fullAdder n _). Proof. induction n; cbn; auto with parametricity. Qed. #[export] Hint Immediate fullAdder_Parametric : parametricity. Lemma adder_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {n} : R _ _ adder (@adder n _). Proof. induction n; cbn; auto with parametricity. Qed. #[export] Hint Immediate adder_Parametric : parametricity. Lemma fullMultiplierBit_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R _ _ fullMultiplierBit fullMultiplierBit. Proof. unfold fullMultiplierBit. auto with parametricity. Qed. #[export] Hint Immediate fullMultiplierBit_Parametric : parametricity. Lemma buildFullMultiplier_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {W} t1 t2 : R _ (W * W) t1 t2 -> R _ _ (buildFullMultiplier t1) (buildFullMultiplier t2). Proof. unfold buildFullMultiplier. auto 15 with parametricity. Qed. #[export] Hint Resolve buildFullMultiplier_Parametric : parametricity. Lemma fullMultiplier_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {n} : R _ (Word n * Word n) fullMultiplier (@fullMultiplier n _). Proof. induction n; cbn; auto with parametricity. Qed. #[export] Hint Immediate fullMultiplier_Parametric : parametricity. Lemma multiplier_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {n} : R _ _ multiplier (@multiplier n _). Proof. unfold multiplier. cbn; auto with parametricity. Qed. #[export] Hint Immediate multiplier_Parametric : parametricity. Lemma build_fill_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {C X} t1 t2 : R C X t1 t2 -> R _ _ (build_fill t1) (build_fill t2). Proof. unfold build_fill. auto 10 with parametricity. Qed. #[export] Hint Resolve build_fill_Parametric : parametricity. Lemma fill_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {C X n} op1 op2 : R _ _ op1 op2 -> R _ _ (fill op1) (@fill C X n _ op2). Proof. induction n; simpl; auto with parametricity. Qed. #[export] Hint Resolve fill_Parametric : parametricity. Lemma buildBitwiseTri_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {W} t1 t2 : R _ W t1 t2 -> R _ _ (buildBitwiseTri t1) (buildBitwiseTri t2). Proof. unfold buildBitwiseTri. auto 10 with parametricity. Qed. #[export] Hint Resolve buildBitwiseTri_Parametric : parametricity. Lemma bitwiseTri_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} op1 op2 : R _ _ op1 op2 -> R _ _ (bitwiseTri op1) (@bitwiseTri X n _ op2). Proof. induction n; simpl; auto with parametricity. Qed. #[export] Hint Resolve bitwiseTri_Parametric : parametricity. Lemma build_leftmost_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {V X} t1 t2 : R V X t1 t2 -> R _ _ (build_leftmost t1) (build_leftmost t2). Proof. unfold build_leftmost. auto 10 with parametricity. Qed. #[export] Hint Resolve build_leftmost_Parametric : parametricity. Lemma leftmost_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} : R _ _ leftmost (@leftmost X n term2). Proof. induction n; simpl; auto with parametricity. Qed. #[export] Hint Resolve leftmost_Parametric : parametricity. Lemma build_rightmost_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {V X} t1 t2 : R V X t1 t2 -> R _ _ (build_rightmost t1) (build_rightmost t2). Proof. unfold build_rightmost. auto 10 with parametricity. Qed. #[export] Hint Resolve build_rightmost_Parametric : parametricity. Lemma rightmost_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} : R _ _ rightmost (@rightmost X n term2). Proof. induction n; simpl; auto with parametricity. Qed. #[export] Hint Resolve rightmost_Parametric : parametricity. Lemma build_full_left_shift1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X W} t1 t2 : R (W * X) (X * W) t1 t2 -> R _ _ (build_full_left_shift1 t1) (build_full_left_shift1 t2). Proof. unfold build_full_left_shift1. auto 10 with parametricity. Qed. #[export] Hint Resolve build_full_left_shift1_Parametric : parametricity. Lemma full_left_shift1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} : R _ _ full_left_shift1 (@full_left_shift1 X n term2). Proof. induction n; simpl; auto with parametricity. Qed. #[export] Hint Resolve full_left_shift1_Parametric : parametricity. Lemma build_full_right_shift1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X W} t1 t2 : R (W * X) (X * W) t1 t2 -> R _ _ (build_full_right_shift1 t1) (build_full_right_shift1 t2). Proof. unfold build_full_right_shift1. auto 10 with parametricity. Qed. #[export] Hint Resolve build_full_right_shift1_Parametric : parametricity. Lemma full_right_shift1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} : R _ _ full_right_shift1 (@full_right_shift1 X n term2). Proof. induction n; simpl; auto with parametricity. Qed. #[export] Hint Resolve full_right_shift1_Parametric : parametricity. Lemma left_shift1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} t1 t2 : R _ _ t1 t2 -> R _ _ (left_shift1 t1) (@left_shift1 X n term2 t2). Proof. unfold left_shift1. auto 10 with parametricity. Qed. #[export] Hint Resolve left_shift1_Parametric : parametricity. Lemma left_shift_const_by_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} t1 t2 p : R _ _ t1 t2 -> R _ _ (left_shift_const_by t1 p) (@left_shift_const_by X n term2 t2 p). Proof. revert X t1 t2 p. induction n; intros X t1 t2 p Ht; simpl; destruct (_ <=? _)%Z; auto with parametricity. change (Vector X n * Vector X n) with (Vector X (S n)). destruct p; try apply comp_Parametric;auto 10 with parametricity; destruct (@eq_sym Ty (Vector X (S n)) (Vector (X * X) n) (@VectorPromote X n)); apply IHn;auto 10 with parametricity. Qed. #[export] Hint Resolve left_shift_const_by_Parametric : parametricity. Lemma right_shift1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} t1 t2 : R _ _ t1 t2 -> R _ _ (right_shift1 t1) (@right_shift1 X n term2 t2). Proof. unfold right_shift1. auto 10 with parametricity. Qed. #[export] Hint Resolve right_shift1_Parametric : parametricity. Lemma right_shift_const_by_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} t1 t2 p : R _ _ t1 t2 -> R _ _ (right_shift_const_by t1 p) (@right_shift_const_by X n term2 t2 p). Proof. revert X t1 t2 p. induction n; intros X t1 t2 p Ht; simpl; destruct (_ <=? _)%Z; auto with parametricity. change (Vector X n * Vector X n) with (Vector X (S n)). destruct p; try apply comp_Parametric;auto 10 with parametricity; destruct (@eq_sym Ty (Vector X (S n)) (Vector (X * X) n) (@VectorPromote X n)); apply IHn;auto 10 with parametricity. Qed. #[export] Hint Resolve right_shift_const_by_Parametric : parametricity. Lemma shift_const_by_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} t1 t2 z : R _ _ t1 t2 -> R _ _ (shift_const_by t1 z) (@shift_const_by X n term2 t2 z). Proof. destruct z;simpl;auto 10 with parametricity. Qed. #[export] Hint Resolve shift_const_by_Parametric : parametricity. Lemma shift_const_Parametric {n} z {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R (Word n) (Word n) (shift_const z) (shift_const z). Proof. unfold shift_const. apply shift_const_by_Parametric. auto 10 with parametricity. Qed. #[export] Hint Immediate shift_const_Parametric : parametricity. Lemma left_rotate1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} : R _ _ left_rotate1 (@left_rotate1 X n term2). Proof. unfold left_rotate1. auto 10 with parametricity. Qed. #[export] Hint Resolve left_rotate1_Parametric : parametricity. Lemma right_rotate1_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} : R _ _ right_rotate1 (@right_rotate1 X n term2). Proof. unfold right_rotate1. auto 10 with parametricity. Qed. #[export] Hint Resolve right_rotate1_Parametric : parametricity. Lemma rotate_const_list_length {term1 term2 : Core.Algebra} {X n} z : length (@rotate_const_list X n term1 z) = length (@rotate_const_list X n term2 z). Proof. revert X z. induction n; intros X z; simpl. - reflexivity. - repeat destruct (Z.even _);simpl;change (Vector X n * Vector X n) with (Vector X (S n)); destruct (@eq_sym Ty (Vector X (S n)) (Vector (X * X) n) (@VectorPromote X n)); simpl; firstorder. Qed. Lemma rotate_const_list_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X n} z i : R _ _ (nth i (@rotate_const_list X n term1 z) iden) (nth i (@rotate_const_list X n term2 z) iden). Proof. revert X z i. induction n; intros X z i; simpl. - destruct i; auto with parametricity. - repeat destruct (Z.even _);[|destruct i|destruct i];simpl;change (Vector X n * Vector X n) with (Vector X (S n));auto 10 with parametricity; destruct (@eq_sym Ty (Vector X (S n)) (Vector (X * X) n) (@VectorPromote X n));apply IHn. Qed. Lemma foldr_comp_Parametric {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) {X} l1 l2 : length l1 = length l2 -> (forall i, R X X (nth i l1 iden) (nth i l2 iden)) -> R _ _ (foldr_comp l1) (foldr_comp l2). Proof. revert l2. induction l1; intros [|x l2]; simpl; try discriminate. - auto with parametricity. - intros H. inversion H. intros H0. assert (H00 := H0 0). destruct l1; destruct l2; try discriminate. + assumption. + apply comp_Parametric;[assumption|]. apply IHl1;[assumption|]. intros i. apply (H0 (S i)). Qed. Lemma rotate_const_Parametric {n} z {term1 term2 : Core.Algebra} (R : Core.Parametric.Rel term1 term2) : R (Word n) (Word n) (rotate_const z) (rotate_const z). Proof. unfold rotate_const. apply foldr_comp_Parametric. - apply rotate_const_list_length. - apply rotate_const_list_Parametric. Qed. #[export] Hint Immediate rotate_const_Parametric : parametricity. ================================================ FILE: Coq/_CoqProject ================================================ -Q Simplicity Simplicity -R C C Simplicity/StaticAnalysis.v Simplicity/MerkleRoot.v Simplicity/Core.v Simplicity/Digest.v Simplicity/BitMachine.v Simplicity/Alg.v Simplicity/Word.v Simplicity/Primitive.v Simplicity/Ty.v Simplicity/SHA256.v Simplicity/Bit.v Simplicity/Primitive/Bitcoin.v Simplicity/Translate.v Simplicity/Delegation.v Simplicity/Util/Monad.v Simplicity/Util/Thrist.v Simplicity/Util/List.v Simplicity/Util/Option.v Simplicity/Util/Arith.v Simplicity/Util/Monad/Reader.v Simplicity/Util/PackedClass.v C/jets_secp256k1.v C/extraMath.v C/progressC.v C/modinv.v C/divstep.v C/secp256k1/spec_int128.v C/secp256k1/spec_modinv64.v C/secp256k1/verif_int128_impl.v C/secp256k1/verif_modinv64_impl.v ================================================ FILE: Haskell/Bitcoin/Simplicity/Bitcoin/DataTypes.hs ================================================ -- | This module defines the data structures that make up the signed data in a Bitcoin transaction. module Simplicity.Bitcoin.DataTypes ( Script, Lock, Value , Outpoint(Outpoint), opHash, opIndex, putOutpointBE , SigTxInput(SigTxInput), sigTxiPreviousOutpoint, sigTxiTxo, sigTxiSequence, sigTxiAnnex, sigTxiScriptSig, sigTxiValue, sigTxiScript , TxOutput(TxOutput), txoValue, txoScript , SigTx(SigTx), sigTxVersion, sigTxIn, sigTxOut, sigTxLock , putNoWitnessTx, txid , TapEnv(..) , txTotalInputValue, txTotalOutputValue, txFee , txIsFinal, txiLockDistance, txiLockDuration , outputValuesHash, outputScriptsHash , outputsHash, outputHash , inputOutpointsHash, inputValuesHash, inputScriptsHash, inputUtxosHash , inputSequencesHash, inputAnnexesHash, inputScriptSigsHash, inputsHash, inputHash , txHash , tapleafHash, tappathHash, tapEnvHash , taptweak , module Simplicity.Bitcoin ) where import Control.Monad (guard) import qualified Data.ByteString as BS import qualified Data.ByteString.Lazy as BSL import Data.Semigroup (Max(Max,getMax), Sum(Sum,getSum)) import Data.Word (Word64, Word32, Word16, Word8) import Data.Serialize ( Serialize , Get, get, getWord8, getWord16le, getWord32le, getWord64le, getLazyByteString , Putter, put, putWord8, putWord16le, putWord32be, putWord32le, putWord64be, putWord64le, putLazyByteString, runPutLazy ) import Data.String (fromString) import Data.Vector (Vector) import qualified Data.Vector as V import Simplicity.Bitcoin import Simplicity.Digest import Simplicity.LibSecp256k1.Spec import Simplicity.LibSecp256k1.Schnorr {- getVarInteger :: Get Word64 getVarInteger = go =<< getWord8 where go 0xff = getWord64le go 0xfe = fromIntegral `fmap` getWord32le go 0xfd = fromIntegral `fmap` getWord16le go x = return (fromIntegral x) putVarInteger :: Word64 -> Put putVarInteger x | x < 0xfd = putWord8 (fromIntegral x) | x <= 0xffff = putWord8 0xfd >> putWord16le (fromIntegral x) | x <= 0xffffffff = putWord8 0xfe >> putWord32le (fromIntegral x) | otherwise = putWord8 0xff >> putWord64le (fromIntegral x) getVarByteString :: Get BSL.ByteString getVarByteString = do l <- getVarInteger let l' = fromIntegral l :: Word32 -- length must be strictly less than 2^32. -- This is how Bitcoin Core reads bytestrings. getLazyByteString (fromIntegral l') where putVarByteString :: BSL.ByteString -> Put putVarByteString s | len < 2^32 = putVarInteger len >> putLazyByteString s where len :: Word64 len = BSL.foldlChunks (\a c -> a + fromIntegral (BS.length c)) 0 s -} -- | Unparsed Bitcoin Script. -- Script in transactions outputs do not have to be parsable, so we encode this as a raw 'Data.ByteString.ByteString'. type Script = BSL.ByteString -- | Transaction locktime. -- This represents either a block height or a block time. -- It is encoded as a 32-bit value. type Lock = Word32 -- | A type for Bitcoin amounts measured in units of satoshi. type Value = Word64 -- bitcoin uses an Int64, but it doesn't really matter. moneyRange :: Value -> Bool moneyRange v = v <= 21000000 * 10^8 getValue :: Get Value getValue = do v <- getWord64le guard $ moneyRange v return v -- | An outpoint is an index into the TXO set. data Outpoint = Outpoint { opHash :: Hash256 , opIndex :: Word32 } deriving Show instance Serialize Outpoint where get = Outpoint <$> get <*> getWord32le put (Outpoint h i) = put h >> putWord32le i -- | Big endian serialization of an 'Outpoint' putOutpointBE :: Putter Outpoint putOutpointBE op = put (opHash op) >> putWord32be (opIndex op) -- | The data type for signed transaction inputs. -- Note that signed transaction inputs for BIP 143 include the value of the input, which doesn't appear in the serialized transaction input format. data SigTxInput = SigTxInput { sigTxiPreviousOutpoint :: Outpoint , sigTxiTxo :: TxOutput , sigTxiSequence :: Word32 , sigTxiAnnex :: Maybe BSL.ByteString , sigTxiScriptSig :: Script -- length must be strictly less than 2^32. } deriving Show -- | The value of the input being spent. sigTxiValue :: SigTxInput -> Value sigTxiValue = txoValue . sigTxiTxo -- | The value of the input being spent. sigTxiScript :: SigTxInput -> Script sigTxiScript = txoScript . sigTxiTxo {- instance Serialize SigTxInput where get = SigTxInput <$> get <*> getValue <*> getWord32le put (SigTxInput p v sq) = put p >> putWord64le v >> putWord32le sq -} -- | The data type for transaction outputs. -- The signed transactin output format is identical to the serialized transaction output format. data TxOutput = TxOutput { txoValue :: Value , txoScript :: Script -- length must be strictly less than 2^32. } deriving Show {- instance Serialize TxOutput where get = TxOutput <$> getValue <*> getVarByteString put (TxOutput v s) = putWord64le v >> putVarByteString s -} -- | The data type for transactions in the context of signatures. -- The data signed in a BIP 143 directly covers input values. data SigTx = SigTx { sigTxVersion :: Word32 , sigTxIn :: Vector SigTxInput , sigTxOut :: Vector TxOutput , sigTxLock :: Lock } deriving Show {- instance Serialize Tx where get = Tx <$> getWord32le <*> getList <*> getList <*> get put (Tx v is os t) = putWord32le v >> putList is >> putList os >> put t -} -- | Taproot specific environment data about the input being spent. data TapEnv = TapEnv { tapleafVersion :: Word8 , tapInternalKey :: PubKey , tappath :: [Hash256] , tapScriptCMR :: Hash256 } deriving Show txTotalInputValue :: SigTx -> Value txTotalInputValue tx = getSum . foldMap (Sum . sigTxiValue) $ sigTxIn tx txTotalOutputValue :: SigTx -> Value txTotalOutputValue tx = getSum . foldMap (Sum . txoValue) $ sigTxOut tx txFee :: SigTx -> Value txFee tx = txTotalInputValue tx - txTotalOutputValue tx txIsFinal :: SigTx -> Bool txIsFinal tx = all finalSequence (sigTxIn tx) where finalSequence sigin = sigTxiSequence sigin == maxBound txiLockDistance :: SigTxInput -> Word16 txiLockDistance sigin = case parseSequence (sigTxiSequence sigin) of Just (Left x) -> x _ -> 0 txiLockDuration :: SigTxInput -> Word16 txiLockDuration sigin = case parseSequence (sigTxiSequence sigin) of Just (Right x) -> x _ -> 0 -- | A hash of all 'txoValues's. outputValuesHash :: SigTx -> Hash256 outputValuesHash tx = bslHash . runPutLazy $ mapM_ (putWord64be . txoValue) (sigTxOut tx) -- | A hash of all 'txoScript' hashes. outputScriptsHash :: SigTx -> Hash256 outputScriptsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . txoScript) (sigTxOut tx) -- | A hash of -- -- * 'outputValuesHash' -- * 'outputScriptsHash' outputsHash :: SigTx -> Hash256 outputsHash tx = bslHash . runPutLazy $ do put $ outputValuesHash tx put $ outputScriptsHash tx -- | A hash of one output's -- -- * value -- * hash of its script outputHash :: TxOutput -> Hash256 outputHash txo = bslHash . runPutLazy $ do putWord64be $ txoValue txo put . bslHash $ txoScript txo -- | Serialize an input's previous output including whether the previous input is from an pegin or not, and which parent chain if it is a pegin. putOutpoint :: Putter SigTxInput putOutpoint txi = putOutpointBE (sigTxiPreviousOutpoint txi) -- | A hash of all 'sigTxiPreviousOutpoint's. inputOutpointsHash :: SigTx -> Hash256 inputOutpointsHash tx = bslHash . runPutLazy $ mapM_ putOutpoint (sigTxIn tx) -- | A hash of all 'utxoValue's. inputValuesHash :: SigTx -> Hash256 inputValuesHash tx = bslHash . runPutLazy $ mapM_ (putWord64be . sigTxiValue) (sigTxIn tx) -- | A hash of all 'utxoScript' hashes. inputScriptsHash :: SigTx -> Hash256 inputScriptsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . sigTxiScript) (sigTxIn tx) -- | A hash of -- -- * 'inputValuesHash' -- * 'inputScriptsHash' inputUtxosHash :: SigTx -> Hash256 inputUtxosHash tx = bslHash . runPutLazy $ do put $ inputValuesHash tx put $ inputScriptsHash tx -- | A hash of all 'sigTxiSequence's. inputSequencesHash :: SigTx -> Hash256 inputSequencesHash tx = bslHash . runPutLazy $ mapM_ (putWord32be . sigTxiSequence) (sigTxIn tx) putAnnex :: Putter (Maybe BSL.ByteString) putAnnex Nothing = putWord8 0x00 putAnnex (Just annex) = putWord8 0x01 >> put (bslHash annex) -- | A hash of all 'sigTxiAnnex' hashes. inputAnnexesHash :: SigTx -> Hash256 inputAnnexesHash tx = bslHash . runPutLazy $ mapM_ (putAnnex . sigTxiAnnex) (sigTxIn tx) -- | A hash of all 'sigTxiScriptSig' hashes. inputScriptSigsHash :: SigTx -> Hash256 inputScriptSigsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . sigTxiScriptSig) (sigTxIn tx) -- | A hash of -- -- * 'inputOutpointsHash' -- * 'inputSequencesHash' -- * 'inputAnnexesHash' -- -- Note that 'inputScriptSigsHash' is excluded. inputsHash :: SigTx -> Hash256 inputsHash tx = bslHash . runPutLazy $ do put $ inputOutpointsHash tx put $ inputSequencesHash tx put $ inputAnnexesHash tx -- | A hash of -- -- * The inputs's outpoint (including if and where the pegin came from) -- * The inputs's sequence number -- * Whether or not the input has an annex and the hash of that annex. inputHash :: SigTxInput -> Hash256 inputHash txi = bslHash . runPutLazy $ do putOutpoint txi putWord32be $ sigTxiSequence txi putAnnex $ sigTxiAnnex txi -- | A hash of -- -- * 'sigTxVersion' -- * 'sigTxLock' -- * 'inputsHash' -- * 'outputsHash' -- * 'inputUtxosHash' txHash :: SigTx -> Hash256 txHash tx = bslHash . runPutLazy $ do putWord32be $ sigTxVersion tx putWord32be $ sigTxLock tx put $ inputsHash tx put $ outputsHash tx put $ inputUtxosHash tx -- | Serialize transaction data without witness data. -- Mainly suitable for computing a 'txid'. putNoWitnessTx :: Putter SigTx putNoWitnessTx tx = do putWord32le $ sigTxVersion tx putVarInt (V.length (sigTxIn tx)) mapM_ putInput (sigTxIn tx) putVarInt (V.length (sigTxOut tx)) mapM_ putOutput (sigTxOut tx) putWord32le $ sigTxLock tx where putVarInt x | x < 0 = error "putVarInt: negative value" | x <= 0xFC = putWord8 (fromIntegral x) | x <= 0xFFFF = putWord8 0xFD >> putWord16le (fromIntegral x) | x <= 0xFFFFFFFF = putWord8 0xFE >> putWord32le (fromIntegral x) | x <= 0xFFFFFFFFFFFFFFFF = putWord8 0xFF >> putWord64le (fromIntegral x) putInput txi = do put (opHash (sigTxiPreviousOutpoint txi)) putWord32le (opIndex (sigTxiPreviousOutpoint txi)) putVarInt (BSL.length (sigTxiScriptSig txi)) putLazyByteString (sigTxiScriptSig txi) putWord32le (sigTxiSequence txi) putOutput txo = do putWord64le (txoValue txo) putVarInt (BSL.length (txoScript txo)) putLazyByteString (txoScript txo) -- | Return the txid of the transaction. txid :: SigTx -> Hash256 txid = bslDoubleHash . runPutLazy . putNoWitnessTx -- | A hash of -- -- * 'tapleafVersion' -- * 'tapScriptCMR' tapleafHash :: TapEnv -> Hash256 tapleafHash tapEnv = bslHash . runPutLazy $ do put tag put tag putWord8 $ tapleafVersion tapEnv putWord8 32 put $ tapScriptCMR tapEnv where tag = bsHash (fromString "TapLeaf") -- | A hash of 'tappath's. tappathHash :: TapEnv -> Hash256 tappathHash tapEnv = bslHash . runPutLazy $ mapM_ put (tappath tapEnv) -- | A hash of -- -- * 'tapleafHash' -- * 'tappathHash' -- * 'tapInternalKey' tapEnvHash :: TapEnv -> Hash256 tapEnvHash tapEnv = bslHash . runPutLazy $ do put $ tapleafHash tapEnv put $ tappathHash tapEnv put $ tapInternalKey tapEnv -- | Implementation of BIP-0341's taptweak function. taptweak :: PubKey -> Hash256 -> Maybe PubKey taptweak (PubKey internalKey) h = do guard $ toInteger internalKey < fieldOrder guard $ h0 < groupOrder a <- scale (scalar h0) g b <- decompress (Point False xkey) GE x y <- gej_normalize . snd $ gej_ge_add_ex a b return $ PubKey (fe_pack x) where xkey = fe (toInteger internalKey) h0 = integerHash256 . bslHash . runPutLazy $ do put tag put tag put (fe_pack xkey) put h tag = bsHash (fromString "TapTweak") ================================================ FILE: Haskell/Bitcoin/Simplicity/Bitcoin/Primitive.hs ================================================ {-# LANGUAGE GADTs, ScopedTypeVariables #-} -- | This module provides the Simplicity primitives specific for Bitcoin or Bitcoin-like applications. module Simplicity.Bitcoin.Primitive ( Prim(..), primPrefix, primName , PrimEnv(..), primEnv, primEnvHash , primSem -- * Re-exported Types , PubKey ) where import qualified Data.List as List import Data.Maybe (listToMaybe) import Data.Serialize (Get, getWord8, Putter, put, putWord8, putWord32be, putWord32le, putWord64le, runPutLazy) import qualified Data.Word import Data.Vector as Vector ((!?), length) import Simplicity.Digest import Simplicity.Bitcoin.DataTypes import qualified Simplicity.LibSecp256k1.Schnorr as Schnorr import Simplicity.Programs.LibSecp256k1 import Simplicity.Serialization import Simplicity.Ty import Simplicity.Ty.Word data Prim a b where Version :: Prim () Word32 LockTime :: Prim () Word32 CurrentIndex :: Prim () Word32 InputPrevOutpoint :: Prim Word32 (S (Word256,Word32)) InputValue :: Prim Word32 (S Word64) InputScriptHash :: Prim Word32 (S Word256) InputSequence :: Prim Word32 (S Word32) InputAnnexHash :: Prim Word32 (S (S Word256)) InputScriptSigHash :: Prim Word32 (S Word256) OutputValue :: Prim Word32 (S Word64) OutputScriptHash :: Prim Word32 (S Word256) TapleafVersion :: Prim () Word8 Tappath :: Prim Word8 (S Word256) InternalKey :: Prim () PubKey ScriptCMR :: Prim () Word256 TransactionId :: Prim () Word256 instance Eq (Prim a b) where Version == Version = True LockTime == LockTime = True CurrentIndex == CurrentIndex = True InputPrevOutpoint == InputPrevOutpoint = True InputValue == InputValue = True InputScriptHash == InputScriptHash = True InputSequence == InputSequence = True InputAnnexHash == InputAnnexHash = True InputScriptSigHash == InputScriptSigHash = True OutputValue == OutputValue = True OutputScriptHash == OutputScriptHash = True TapleafVersion == TapleafVersion = True Tappath == Tappath = True InternalKey == InternalKey = True ScriptCMR == ScriptCMR = True TransactionId == TransactionId = True _ == _ = False primPrefix :: String primPrefix = "Bitcoin" -- Consider deriving Show instead? primName :: Prim a b -> String primName Version = "version" primName LockTime = "lockTime" primName CurrentIndex = "currentIndex" primName InputPrevOutpoint = "inputPrevOutpoint" primName InputValue = "inputValue" primName InputScriptHash = "inputScriptHash" primName InputSequence = "inputSequence" primName InputAnnexHash = "inputAnnexHash" primName InputScriptSigHash = "inputScriptSigHash" primName OutputValue = "outputValue" primName OutputScriptHash = "outputScriptHash" primName TapleafVersion = "tapleafVersion" primName Tappath = "tappath" primName InternalKey = "internalKey" primName ScriptCMR = "scriptCMR" primName TransactionId = "transactionId" data PrimEnv = PrimEnv { envTx :: SigTx , envIx :: Data.Word.Word32 , envTap :: TapEnv } instance Show PrimEnv where showsPrec d env = showParen (d > 10) $ showString "primEnv " . showsPrec 11 (envTx env) . showString " " . showsPrec 11 (envIx env) . showString " " . showsPrec 11 (envTap env) primEnv :: SigTx -> Data.Word.Word32 -> TapEnv -> Maybe PrimEnv primEnv tx ix tap | cond = Just $ PrimEnv { envTx = tx , envIx = ix , envTap = tap } | otherwise = Nothing where cond = fromIntegral ix < Vector.length (sigTxIn tx) -- | A hash of -- -- * 'txHash' -- * 'tapEnvHash' -- * 'envIx' -- -- Note: this is the hash used for the "sig-all" hash. primEnvHash :: PrimEnv -> Hash256 primEnvHash env = bslHash . runPutLazy $ do put $ txHash (envTx env) put $ tapEnvHash (envTap env) putWord32be $ envIx env primSem :: Prim a b -> a -> PrimEnv -> Maybe b primSem p a env = interpret p a where tx = envTx env ix = envIx env lookupInput = (sigTxIn tx !?) . fromIntegral lookupOutput = (sigTxOut tx !?) . fromIntegral currentInput = lookupInput ix maxInput = fromIntegral $ Vector.length (sigTxIn tx) - 1 maxOutput = fromIntegral $ Vector.length (sigTxOut tx) - 1 cast :: Maybe a -> Either () a cast (Just x) = Right x cast Nothing = Left () element :: a -> () -> a element = const atInput :: (SigTxInput -> a) -> Word32 -> Either () a atInput f = cast . fmap f . lookupInput . fromInteger . fromWord32 atOutput :: (TxOutput -> a) -> Word32 -> Either () a atOutput f = cast . fmap f . lookupOutput . fromInteger . fromWord32 encodeHash = toWord256 . integerHash256 encodeOutpoint op = (toWord256 . integerHash256 $ opHash op, toWord32 . fromIntegral $ opIndex op) encodeKey (Schnorr.PubKey x) = toWord256 . toInteger $ x interpret Version = element . return . toWord32 . toInteger $ sigTxVersion tx interpret LockTime = element . return . toWord32 . toInteger $ sigTxLock tx interpret CurrentIndex = element . return . toWord32 . toInteger $ ix interpret InputPrevOutpoint = return . (atInput $ encodeOutpoint . sigTxiPreviousOutpoint) interpret InputValue = return . (atInput $ toWord64 . toInteger . sigTxiValue) interpret InputScriptHash = return . (atInput $ encodeHash . bslHash . sigTxiScript) interpret InputSequence = return . (atInput $ toWord32 . toInteger . sigTxiSequence) interpret InputAnnexHash = return . (atInput $ cast . fmap (encodeHash . bslHash) . sigTxiAnnex) interpret InputScriptSigHash = return . (atInput $ encodeHash . bslHash . sigTxiScriptSig) interpret OutputValue = return . (atOutput $ toWord64 . fromIntegral . txoValue) interpret OutputScriptHash = return . (atOutput $ encodeHash . bslHash . txoScript) interpret TapleafVersion = element . return . toWord8 . toInteger . tapleafVersion $ envTap env interpret Tappath = return . cast . fmap encodeHash . listToMaybe . flip drop (tappath (envTap env)) . fromInteger . fromWord8 interpret InternalKey = element . return . encodeKey . tapInternalKey $ envTap env interpret ScriptCMR = element . return . toWord256 . integerHash256 . tapScriptCMR $ envTap env interpret TransactionId = element . return . encodeHash . txid $ tx ================================================ FILE: Haskell/Core/Simplicity/BitMachine/Authentic.hs ================================================ {-# LANGUAGE FlexibleContexts #-} -- | This modules implements the Bit Machine according to its specification. -- -- This @Authentic@ module properly tracks undefined values in the Bit Machine's cells and will properly crash when, for example, reading from undefined cells. -- Other non-authentic implementations of the Bit Machine might invoke undefined behaviour when the Bit Machine crashes. module Simplicity.BitMachine.Authentic ( runMachine , Stats(..) , instrumentMachine ) where import Control.Monad ((>=>), guard, unless) import Control.Monad.Fail (MonadFail) import Control.Monad.Writer (MonadWriter, tell) import Data.Functor.Fixedpoint (cata) import Data.Monoid (Endo(..)) import Data.Vector ((//), (!?)) import qualified Data.Vector as V import qualified Data.Vector.Mutable as VM import Lens.Family2 ((^.), to) import Simplicity.BitMachine (Cell, MachineCodeF(..), MachineCode, Interpreter) -- For the Bit Machine a frame is an array of Cell's and a cursor pointing at a position within the array. data Frame = Frame { fData :: !(V.Vector Cell) , fOffset :: !Int } -- Create a frame from a list of cells with the cursor initialized to the start of the frame. fInit cells = Frame (V.fromList cells) 0 -- Create an empty frame of a given size with the cursor initialized to the start of the frame. fNew n | 0 <= n = Frame (V.replicate n Nothing) 0 -- Reset a frame by moving the cursor from the end of the frame to the beginning of the frame. -- This function fails if the input frame doesn't have its cursor at the end of the frame. fReset fm = unless (fOffset fm == length (fData fm)) (fail "fReset: offset not at end of frame") >> return (fm {fOffset = 0}) -- Return the value of the cell under the frame's cursor. -- This function fails if the cursor is at the end of the frame. fRead fr = maybe (fail "fRead: offset out of range") return (fData fr !? fOffset fr) -- Return an array of 'n' cells starting from the frame's cursor. -- The function fails if there are not enough cells in the frame. fSlice n = to go where go (Frame dt os) | os + n <= V.length dt = return $ V.slice os n dt | otherwise = fail "fSlice: slice too large" -- Write a Cell to a frame at the frame's cursor and advance the frame's cursor by 1. -- This function fails if the cursor is at the end of the frame. fWrite v (Frame dt os) | os < V.length dt = return $ Frame dt' os' | otherwise = fail "fWrite: data too large" where dt' = dt // [(os, v)] os' = os+1 -- Write a vector of Cells to a frame starting at the frame's cursor and advance the frame's cursor by the length of the written data. -- This function fails if there isn't sufficient room in the frame to write the data. fFill v (Frame dt os) | os + n <= V.length dt = return $ Frame dt' os' where n = V.length v dt' = V.modify go dt where go mv = V.copy (VM.slice os n mv) v os' = os + n -- Move a frame's cursor by 'n' cells. -- If 'n' is positive the cursor moves forward and if 'n' negative the cursor moves backward. -- This function fails if the cursors would end up past the end of the frame or past the beginning of the frame. fMove n (Frame dt os) | 0 <= os' && os' <= length dt = return $ Frame dt os' | otherwise = fail "fMove: index out of range" where os' = os+n -- Returns the number of cells in the frame. fSize (Frame dt _) = V.length dt -- The active frames are the frames at the top of the read frame stack and the write frame stack. data Active = Active { activeReadFrame :: !Frame , activeWriteFrame :: !Frame } -- Two lenses that access the active read and write frames. rf f x = (\y -> x { activeReadFrame = y }) <$> f (activeReadFrame x) wf f x = (\y -> x { activeWriteFrame = y }) <$> f (activeWriteFrame x) -- The state of the Bit Machine consists of the inactive read and write frames, and the active frames. data State = State { inactiveReadFrames :: [Frame] , activeFrames :: !Active , inactiveWriteFrames :: [Frame] } -- A lens that accesses the active frames of a state. act f x = (\y -> x { activeFrames = y }) <$> f (activeFrames x) -- A state transformation that turns one state into another with possible side effects (such as crashing). -- MachineCode instructions are interpreted as these State transformations. type StateTrans m = State -> m State -- Below are functions used in 'runMachineF' to implement the instructions for the Bit Machine. abort :: MonadFail m => StateTrans m abort _ = fail "explicit abort" copy :: MonadFail m => Int -> StateTrans m copy n st = do v <- st^.act.rf.fSlice n (act.wf) (fFill v) st newFrame :: MonadFail m => Int -> StateTrans m newFrame n (State irf (Active rf wf) iwf) = do unless (0 <= n) (fail "newFrame: negative size") return $ State irf (Active rf (fNew n)) (wf:iwf) moveFrame :: MonadFail m => StateTrans m moveFrame (State irf (Active rf wf) (iwf0:iwf)) = do nrf <- fReset wf return $ State (rf:irf) (Active nrf iwf0) iwf moveFrame _ = fail "moveFrame: empty write frame stack" dropFrame (State (irf0:irf) (Active _ wf) iwf) = return $ State irf (Active irf0 wf) iwf dropFrame _ = fail "dropFrame: empty read frame stack" -- 'runMachineF' is a MachineCode algebra that implements the bit machine. -- 'runMachine' calls this algebra to recursively evaluate 'MachineCode'. runMachineF :: MonadFail m => MachineCodeF (StateTrans m) -> StateTrans m runMachineF End = return runMachineF Abort = abort runMachineF (Write b k) = (act.wf) (fWrite (Just b)) >=> k runMachineF (Copy n k) | 0 <= n = copy n >=> k | otherwise = \_ -> fail "runMachineF Copy: negative index" runMachineF (Skip n k) | 0 <= n = (act.wf) (fMove n) >=> k | otherwise = \_ -> fail "runMachineF Skip: negative index" runMachineF (Fwd n k) | 0 <= n = (act.rf) (fMove n) >=> k | otherwise = \_ -> fail "runMachineF Fwd: negative index" runMachineF (Bwd n k) | 0 <= n = (act.rf) (fMove (-n)) >=> k | otherwise = \_ -> fail "runMachineF Bwd: negative index" runMachineF (NewFrame n k) = newFrame n >=> k runMachineF (MoveFrame k) = moveFrame >=> k runMachineF (DropFrame k) = dropFrame >=> k runMachineF (Read k0 k1) = \st -> do v <- fRead (st^.act.rf) b <- maybe (fail "runMachine Read: cell value undefined") return v if b then k1 st else k0 st -- Create an initial state from the initial data for the read frame and the size of the write frame. initialState :: [Cell] -> Int -> State initialState input outLength = State [] (Active (fInit input) (fNew outLength)) [] -- Extract the write frame's data which contains the output of the Bit Machine. finalState :: MonadFail m => State -> m [Cell] finalState (State [] (Active _ output) []) = return $ V.toList (fData output) finalState _ = fail "finalState: invalid final state" -- | The implementation of the authentic Bit Machine. -- -- Given 'MachineCode', creates an 'Interpreter'. -- The 'Interpreter' expects an initial state specified by the data for the initial read frame and the size of the initial write frame. -- The 'Interpreter' returns the final data on the write frame. runMachine :: MonadFail m => MachineCode -> Interpreter m runMachine code input outputSize = cata runMachineF code (initialState input outputSize) >>= finalState -- These functions are used to instrument the Bit Machine and calculate the computations resources used during execution. actReadFrameSize :: State -> Int actReadFrameSize st = fSize (st^.act.rf) actWriteFrameSize :: State -> Int actWriteFrameSize st = fSize (st^.act.wf) inactReadFrameSizes :: State -> [Int] inactReadFrameSizes st = fSize <$> inactiveReadFrames st inactWriteFrameSizes :: State -> [Int] inactWriteFrameSizes st = fSize <$> inactiveWriteFrames st -- | A collection of statistics about computation resources used during execution of the Bit Machine. data Stats = Stats { memSize :: !Int -- ^ Maximum total number of 'Cell's occurring during execution , stackSize :: !Int -- ^ Maximum total number of frames occurring during execution } deriving Show instance Semigroup Stats where a <> b = Stats { memSize = max (memSize a) (memSize b) , stackSize = max (stackSize a) (stackSize b) } -- The monoid instance for statistics combine intermediate execution profiles of the Bit Machine's state. instance Monoid Stats where mempty = Stats { memSize = 0 , stackSize = 0 } mappend = (<>) -- This function computes the memory statistics of a snapshot of the Bit Machine's state. profile :: State -> Stats profile st = Stats { memSize = sum readStackStats + sum writeStackStats + actReadFrameSize st + actWriteFrameSize st , stackSize = length readStackStats + length writeStackStats } where readStackStats = inactReadFrameSizes st writeStackStats = inactWriteFrameSizes st -- A state transformation that doesn't transform the state but results in a side effect that emits the statistics of the current state. instrument st = tell [profile st] >> return st -- | An instrumented version of the authentic Bit Machine. -- -- 'intrumentMachine' behaves as 'runMachine' but also profiles the execution returning 'Stats' about computation resources used during execution. instrumentMachine :: (MonadWriter [Stats] m, MonadFail m) => MachineCode -> Interpreter m instrumentMachine code input outputSize = interpreter (initialState input outputSize) >>= finalState where -- add an instrumentation step at the beginning of the runMachineF algebra. instrumentMachineF f = instrument >=> runMachineF f -- run the modified algebra and add a final instrumentation step to the result. interpreter = cata instrumentMachineF code >=> instrument ================================================ FILE: Haskell/Core/Simplicity/BitMachine/StaticAnalysis/Cost.hs ================================================ {-# LANGUAGE GADTs #-} module Simplicity.BitMachine.StaticAnalysis.Cost ( TermWeight(..) , overhead , milliWeigh -- * Reexports , Weight ) where import Simplicity.BitMachine.Ty import Simplicity.Term.Core import Simplicity.Weight -- | The CPU weight of a Simplicity expression. -- -- Note that serializing an expression could generalize the types of expressions and sub-expressions, lowering the weight. newtype TermWeight a b = TermWeight { weigh :: Weight } -- | Cost of a term in milli weight units milliWeigh :: TermWeight a b -> Integer milliWeigh = milliWeight . weigh instance Core TermWeight where iden = result where result = TermWeight $ overhead + milli (bitSizeR (reifyProxy result)) comp s0@(TermWeight s) (TermWeight t) = TermWeight $ overhead + milli (bitSizeR (reifyProxy s0)) + s + t unit = TermWeight overhead injl (TermWeight s) = TermWeight $ overhead + s injr (TermWeight s) = TermWeight $ overhead + s match (TermWeight s) (TermWeight t) = TermWeight $ overhead + max s t pair (TermWeight s) (TermWeight t) = TermWeight $ overhead + s + t take (TermWeight s) = TermWeight $ overhead + s drop (TermWeight s) = TermWeight $ overhead + s instance Assert TermWeight where assertl s _ = match s (TermWeight 0) assertr _ t = match (TermWeight 0) t fail _ = TermWeight 0 instance Witness TermWeight where witness _ = result where result = TermWeight $ overhead + milli (bitSizeR (reifyProxy result)) instance Delegate TermWeight where disconnect s0@(TermWeight s) t0@(TermWeight t) = TermWeight $ overhead + milli (2 * bitSizeR w256a + bitSizeR bc + bitSizeR b) + s + t where (w256a, bc@(ProdR b _c)) = reifyArrow s0 -- :TODO: This overhead is just estimated. It needs to be replaced with a measured value. -- :TODO: Perhaps fold this into a generic 'mkTermWeight' or 'withOverhead' constructor that adds in the overhead. -- | Helper value for creating 'TermWeight' instances. overhead :: Weight overhead = 0.1 ================================================ FILE: Haskell/Core/Simplicity/BitMachine/StaticAnalysis/TCO.hs ================================================ -- | This module has functions for computing static analysis of Bit Machine resources used during execution of tail call optimized translated Simplicity expressions. module Simplicity.BitMachine.StaticAnalysis.TCO ( ExtraCellsBnd, cellsBnd ) where import Simplicity.BitMachine.Ty import Simplicity.Delegator.Impl import Simplicity.Term.Core -- | @'ExtraCellsBnd' a b@ is the data type for the Simplicity algebra used for computing the bound on the maximum number of Cells used by the Bit Machine. data ExtraCellsBnd a b = ExtraCellsBnd Integer Integer -- @extraCellBnd r@ is the number of extra cells that will be allocated by the TCOon program when the active read frame as 'r' number of cells. -- The number of extra cells that will be allocated by TCOoff is (extraCellsBnd 0). extraCellsBnd r (ExtraCellsBnd n m) = max (n - r) m cellsBnd0 :: (TyC a, TyC b) => ExtraCellsBnd a b -> Integer cellsBnd0 t = bitSizeR a + bitSizeR b + extraCellsBnd 0 t where (a,b) = reifyArrow t -- | @'cellsBnd' t@ computes an upper bound on the maximum number of Cells used by the Bit Machine, including the cells used to hold the input and output, when executing TCO translated Simplicity expressions. -- -- Simplicity terms are represented in tagless-final style, so any Simplicity term can be instantiated as @'ExtraCellsBnd' a b@ and can be passed to the 'cellsBnd' function. cellsBnd :: (TyC a, TyC b) => Delegator ExtraCellsBnd a b -> Integer cellsBnd = cellsBnd0 . runDelegator -- Below is the Simplicity algebra that is used for computing 'cellsBnd' instance Core ExtraCellsBnd where iden = ExtraCellsBnd 0 0 comp arrS@(ExtraCellsBnd sn sm) (ExtraCellsBnd tn tm) = ExtraCellsBnd (maximum [s + sn, tn, s + tm]) (s + sm) where s = bitSizeR b b = reifyProxy arrS unit = ExtraCellsBnd 0 0 injl (ExtraCellsBnd tn tm) = ExtraCellsBnd tn tm injr (ExtraCellsBnd tn tm) = ExtraCellsBnd tn tm match (ExtraCellsBnd sn sm) (ExtraCellsBnd tn tm) = ExtraCellsBnd (max sn tn) (max sm tm) pair (ExtraCellsBnd sn sm) (ExtraCellsBnd tn tm) = ExtraCellsBnd tn (maximum [sn, sm, tm]) take (ExtraCellsBnd tn tm) = ExtraCellsBnd tn tm drop (ExtraCellsBnd tn tm) = ExtraCellsBnd tn tm instance Assert ExtraCellsBnd where assertl (ExtraCellsBnd sn sm) _ = ExtraCellsBnd sn sm assertr _ (ExtraCellsBnd tn tm) = ExtraCellsBnd tn tm fail _ = ExtraCellsBnd 0 0 ================================================ FILE: Haskell/Core/Simplicity/BitMachine/StaticAnalysis.hs ================================================ -- | This module has functions for computing static analysis of Bit Machine resources used during execution of naive translated Simplicity expressions. module Simplicity.BitMachine.StaticAnalysis ( ExtraCellsBnd, cellsBnd ) where import Simplicity.BitMachine.Ty import Simplicity.Delegator.Impl import Simplicity.Term.Core -- | @'ExtraCellsBnd' a b@ is the data type for the Simplicity algebra used for computing the bound on the maximum number of Cells used by the Bit Machine. newtype ExtraCellsBnd a b = ExtraCellsBnd { extraCellsBnd :: Integer } cellsBnd0 :: (TyC a, TyC b) => ExtraCellsBnd a b -> Integer cellsBnd0 t = bitSizeR a + bitSizeR b + extraCellsBnd t where (a,b) = reifyArrow t -- | @'cellsBnd' t@ computes an upper bound on the maximum number of Cells used by the Bit Machine, including the cells used to hold the input and output, when executing naive translated Simplicity expressions. -- -- Simplicity terms are represented in tagless-final style, so any Simplicity term can be instantiated as @'ExtraCellsBnd' a b@ and can be passed to the 'cellsBnd' function. cellsBnd :: (TyC a, TyC b) => Delegator ExtraCellsBnd a b -> Integer cellsBnd = cellsBnd0 . runDelegator -- Below is the Simplicity algebra that is used for computing 'cellsBnd' instance Core ExtraCellsBnd where iden = ExtraCellsBnd 0 comp arrS@(ExtraCellsBnd s) (ExtraCellsBnd t) = ExtraCellsBnd (bitSizeR b + max s t) where b = reifyProxy arrS unit = ExtraCellsBnd 0 injl (ExtraCellsBnd t) = ExtraCellsBnd t injr (ExtraCellsBnd t) = ExtraCellsBnd t match (ExtraCellsBnd s) (ExtraCellsBnd t) = ExtraCellsBnd (max s t) pair (ExtraCellsBnd s) (ExtraCellsBnd t) = ExtraCellsBnd (max s t) take (ExtraCellsBnd t) = ExtraCellsBnd t drop (ExtraCellsBnd t) = ExtraCellsBnd t instance Assert ExtraCellsBnd where assertl (ExtraCellsBnd s) _ = ExtraCellsBnd s assertr _ (ExtraCellsBnd t) = ExtraCellsBnd t fail _ = ExtraCellsBnd 0 ================================================ FILE: Haskell/Core/Simplicity/BitMachine/Translate/TCO.hs ================================================ -- | This module implements tail call optimized translation of Simplicity terms to Bit Machine 'MachineCode'. module Simplicity.BitMachine.Translate.TCO ( Translation, translate ) where import Data.Proxy (Proxy(..)) import Simplicity.BitMachine import Simplicity.BitMachine.Ty import Simplicity.Delegator.Impl import Simplicity.Term.Core -- | @'Translation' a b@ is the data type for the Simplicity algebra used for translating terms to 'MachineCode' data Translation a b = Translation { tcoOn :: MachineCodeK , tcoOff :: MachineCodeK } translate0 :: Translation a b -> MachineCode translate0 trans = tcoOff trans end -- | 'translate' converts a Simplicity term to the Bit Machine's 'MachineCode' with tail call optimization. -- -- Simplicity terms are represented in tagless-final style, so any Simplicity term can be instantiated as @'Translation' a b@ and can be passed to the 'translate' function. translate :: Delegator Translation a b -> MachineCode translate = translate0 . runDelegator -- Below is the Simplicity algebra that implements TCO translation to 'MachineCodeK'. -- Every term has two translations, one with TCO-on and one with TOC-off. -- The two translations are mutually recursive, which is why the are computed together in this Simplicity algebra. instance Core Translation where iden = result where a = reifyProxy result result = Translation { tcoOn = copy (bitSizeR a) . dropFrame , tcoOff = copy (bitSizeR a) } comp s t = Translation { tcoOn = newFrame (bitSizeR b) . tcoOn s . moveFrame . tcoOn t , tcoOff = newFrame (bitSizeR b) . tcoOff s . moveFrame . tcoOn t } where b = reifyProxy s unit = Translation { tcoOn = dropFrame , tcoOff = nop } injl t = result where proxyB :: arr a (Either b c) -> Proxy b proxyB _ = Proxy proxyC :: arr a (Either b c) -> Proxy c proxyC _ = Proxy pad = padLR (reifyProxy (proxyB result)) (reifyProxy (proxyC result)) result = Translation { tcoOn = write False . skip pad . tcoOn t , tcoOff = write False . skip pad . tcoOff t } injr t = result where proxyB :: arr a (Either b c) -> Proxy b proxyB _ = Proxy proxyC :: arr a (Either b c) -> Proxy c proxyC _ = Proxy pad = padRR (reifyProxy (proxyB result)) (reifyProxy (proxyC result)) result = Translation { tcoOn = write True . skip pad . tcoOn t , tcoOff = write True . skip pad . tcoOff t } match s t = result where result = Translation { tcoOn = (fwd padl . tcoOn s) ||| (fwd padr . tcoOn t) , tcoOff = bump padl (tcoOff s) ||| bump padr (tcoOff t) } proxy :: arr (Either a b, c) d -> (Proxy a, Proxy b) proxy _ = (Proxy, Proxy) a = reifyProxy . fst $ proxy result b = reifyProxy . snd $ proxy result padl = 1 + padLR a b padr = 1 + padRR a b pair s t = Translation { tcoOn = tcoOff s . tcoOn t , tcoOff = tcoOff s . tcoOff t } take t = Translation { tcoOn = tcoOn t , tcoOff = tcoOff t } drop t = result where proxyA :: arr (a, b) c -> Proxy a proxyA _ = Proxy bs = bitSizeR (reifyProxy (proxyA result)) result = Translation { tcoOn = fwd bs . tcoOn t , tcoOff = bump bs (tcoOff t) } instance Assert Translation where assertl s _ = result where result = Translation { tcoOn = (fwd padl . tcoOn s) ||| abort , tcoOff = bump padl (tcoOff s) ||| abort } proxy :: arr (Either a b, c) d -> (Proxy a, Proxy b) proxy _ = (Proxy, Proxy) a = reifyProxy . fst $ proxy result b = reifyProxy . snd $ proxy result padl = 1 + padLR a b assertr _ t = result where result = Translation { tcoOn = abort ||| (fwd padr . tcoOn t) , tcoOff = abort ||| bump padr (tcoOff t) } proxy :: arr (Either a b, c) d -> (Proxy a, Proxy b) proxy _ = (Proxy, Proxy) a = reifyProxy . fst $ proxy result b = reifyProxy . snd $ proxy result padr = 1 + padRR a b fail _ = Translation { tcoOn = abort, tcoOff = abort } ================================================ FILE: Haskell/Core/Simplicity/BitMachine/Translate.hs ================================================ -- | This module implements naive translation of Simplicity terms to Bit Machine 'MachineCode'. module Simplicity.BitMachine.Translate ( Translation, translate ) where import Data.Proxy (Proxy(..)) import Simplicity.BitMachine import Simplicity.BitMachine.Ty import Simplicity.Delegator.Impl import Simplicity.Term.Core -- | @'Translation' a b@ is the data type for the Simplicity algebra used for translating terms to 'MachineCode' newtype Translation a b = Translation MachineCodeK translate0 :: Translation a b -> MachineCode translate0 (Translation f) = f end -- | 'translate' converts a Simplicity term to the Bit Machine's 'MachineCode'. -- -- Simplicity terms are represented in tagless-final style, so any Simplicity term can be instantiated as @'Translation' a b@ and can be passed to the 'translate' function. translate :: Delegator Translation a b -> MachineCode translate = translate0 . runDelegator -- Below is the Simplicity algebra that implements naive translation to 'MachineCodeK'. instance Core Translation where iden = result where a = reifyProxy result result = Translation $ copy (bitSizeR a) comp arrS@(Translation s) (Translation t) = Translation $ newFrame (bitSizeR b) . s . moveFrame . t . dropFrame where b = reifyProxy arrS unit = Translation nop injl (Translation t) = result where proxyB :: arr a (Either b c) -> Proxy b proxyB _ = Proxy proxyC :: arr a (Either b c) -> Proxy c proxyC _ = Proxy pad = padLR (reifyProxy (proxyB result)) (reifyProxy (proxyC result)) result = Translation $ write False . skip pad . t injr (Translation t) = result where proxyB :: arr a (Either b c) -> Proxy b proxyB _ = Proxy proxyC :: arr a (Either b c) -> Proxy c proxyC _ = Proxy pad = padRR (reifyProxy (proxyB result)) (reifyProxy (proxyC result)) result = Translation $ write True . skip pad . t match (Translation s) (Translation t) = result where result = Translation $ bump padl s ||| bump padr t proxy :: arr (Either a b, c) d -> (Proxy a, Proxy b) proxy _ = (Proxy, Proxy) a = reifyProxy . fst $ proxy result b = reifyProxy . snd $ proxy result padl = 1 + padLR a b padr = 1 + padRR a b pair (Translation s) (Translation t) = Translation $ s . t take (Translation t) = Translation t drop (Translation t) = result where proxyA :: arr (a, b) c -> Proxy a proxyA _ = Proxy bs = bitSizeR (reifyProxy (proxyA result)) result = Translation $ bump bs t instance Assert Translation where assertl (Translation s) _ = result where result = Translation $ bump padl s ||| abort proxy :: arr (Either a b, c) d -> (Proxy a, Proxy b) proxy _ = (Proxy, Proxy) a = reifyProxy . fst $ proxy result b = reifyProxy . snd $ proxy result padl = 1 + padLR a b assertr _ (Translation t) = result where result = Translation $ abort ||| bump padr t proxy :: arr (Either a b, c) d -> (Proxy a, Proxy b) proxy _ = (Proxy, Proxy) a = reifyProxy . fst $ proxy result b = reifyProxy . snd $ proxy result padr = 1 + padRR a b fail _ = Translation $ abort ================================================ FILE: Haskell/Core/Simplicity/BitMachine/Ty.hs ================================================ -- | This module has some functions operating on Simplicity types that are used for evaluating Simplicity on the Bit Machine. module Simplicity.BitMachine.Ty ( bitSize, padL, padR , padLR, padRR, bitSizeR ) where import Data.Functor.Fixedpoint (cata) import Simplicity.Ty -- | Compute the number of cells needed to represent values of a Simplicity type. bitSize :: Integral i => Ty -> i bitSize = fromInteger . bitSizeMemo bitSizeMemo :: Ty -> Integer bitSizeMemo = cata bitSizeF where bitSizeF One = 0 bitSizeF (Sum a b) = 1 + max a b bitSizeF (Prod a b) = a + b -- | Compute the number of cells needed to represent values of a Simplicity type. -- -- @'bitsizeR' a = 'bitSize' ('unreflect' a)@ bitSizeR :: Integral i => TyReflect a -> i bitSizeR = bitSize . unreflect -- | @'padL' a b@ is the number of cells of padding used for σ^L tagged values of the Simplicity type @'sum' a b@. padL :: Integral i => Ty -> Ty -> i padL a b = max bsa bsb - bsa where bsa = bitSize a bsb = bitSize b -- | @'padLR' a b@ is the number of cells of padding used for σ^L tagged values of the Simplicity type @'SumR' a b@. -- -- @'padLR' a = 'padL' ('unreflect' a)@ padLR :: Integral i => TyReflect a -> TyReflect b -> i padLR a b = padL (unreflect a) (unreflect b) -- | @'padR' a b@ is the number of cells of padding used for σ^R tagged values of the Simplicity type @'sum' a b@. padR :: Integral i => Ty -> Ty -> i padR a b = max bsa bsb - bsb where bsa = bitSize a bsb = bitSize b -- | @'padRR' a b@ is the number of cells of padding used for σ^R tagged values of the Simplicity type @'SumR' a b@. -- -- @'padRR' a = 'padR' ('unreflect' a)@ padRR :: Integral i => TyReflect a -> TyReflect b -> i padRR a b = padR (unreflect a) (unreflect b) ================================================ FILE: Haskell/Core/Simplicity/BitMachine.hs ================================================ {-# LANGUAGE DeriveTraversable, GADTs #-} -- | This module defines encoding and decoding of values for the Bit Machine and the instructions for operating the Bit Machine. module Simplicity.BitMachine ( Cell , encode, decode , Interpreter, executeUsing -- * Bit Machine Code , MachineCode, MachineCodeF(..), MachineCodeK , end, abort, write, copy, skip, fwd, bwd, newFrame, moveFrame, dropFrame, (|||) , bump, nop ) where import Control.Monad (unless) import Control.Monad.Fail (MonadFail) import Data.Functor.Fixedpoint (Fix(..), cata) import Simplicity.Ty import Simplicity.BitMachine.Ty -- | The type representing Cell's for the Bit Machine. -- -- * @'Just' 'False'@ denotes a cell holding a @0@ value. -- * @'Just' 'True'@ denotes a cell holding a @1@ value. -- * 'Nothing' denotes a cell holding an unknown value @?@. type Cell = Maybe Bool safeSplitAt :: MonadFail m => Int -> [a] -> m ([a], [a]) safeSplitAt n l = do unless (0 <= n && n <= length l) (fail "safeSplitAt: index out of range") return (splitAt n l) -- | Encodes a value of a Simplicity type as a list of cells. -- -- @'length' ('encode' a) = 'bitSizeR' ('reifyProxy' ('Data.Functor.Identity.Identity' a))@ encode :: TyC a => a -> [Cell] encode x = encodeR reify x [] where encodeR :: TyReflect a -> a -> [Cell] -> [Cell] encodeR OneR () = id encodeR (SumR a b) (Left x) = ([Just False] ++) . (replicate (padLR a b) Nothing ++) . encodeR a x encodeR (SumR a b) (Right y) = ([Just True] ++) . (replicate (padRR a b) Nothing ++) . encodeR b y encodeR (ProdR a b) (x, y) = encodeR a x . encodeR b y -- | Decodes a value of a Simplicity type from a list of cells. -- -- 'decode' does strict checking of the padding used in sum types. -- The padding must be filled with unknown values (represented by 'Nothing'). -- -- @'decode' ('encode' a) = 'return' a@ decode :: (MonadFail m, TyC a) => [Cell] -> m a decode = decodeR reify where decodeR :: MonadFail m => TyReflect a -> [Cell] -> m a decodeR OneR [] = return () decodeR (SumR a b) (Just v:l) = do (l0, l1) <- safeSplitAt (pad a b) l unless (all (==Nothing) l0) (fail "decodeR SumR: bad padding") if v then Right <$> decodeR b l1 else Left <$> decodeR a l1 where pad = if v then padRR else padLR decodeR (ProdR a b) l = do (l0, l1) <- safeSplitAt (bitSizeR a) l (,) <$> decodeR a l0 <*> decodeR b l1 decodeR _ _ = fail "decode: invalid encoding" -- | @'Interpreter' m@ is a type capturing the form of Bit Machine execution functions. -- -- The Bit Machine expects an initial read frame and the size of the initial write frame. -- Execution of the Bit Machine returns the final write frame, which should be the same length as the initial size of the write frame. -- The 'm' parameter is a monad that captures side effects of execution such as failure, logging for aggregated signature, instrumentation of the Bit Machine for analysis, etc. type Interpreter m = [Cell] -> Int -> m [Cell] -- | Given a "compiler" that transforms any Simplicity program into a Bit Machine 'Interpreter', and a Simplicity program, execute it by encoding the input and decoding the output. -- -- This is largely a wrapper for handling encoding and decoding of values when executing Simplicity programs on an implementation of the Bit Machine. -- -- Typically this function is called as -- -- @'executeUsing' (runMachine . translator) program input@ -- -- where @translator@ converts a Simplicity term into a Bit Machine 'MachineCode', @runMachine@ executes 'MachineCode' and @program@ is a Simplicity term. executeUsing :: (MonadFail m, TyC a, TyC b) => (term a b -> Interpreter m) -> term a b -> a -> m b executeUsing interpreter program input = result where result = interpreter program (encode input) (bitSizeR (reifyProxy result)) >>= decode -- | 'MachineCode' is the type of (complete) BitMachine programs. -- -- It is a sequence of instructions with the exception of 'Read' which has two branches. -- The sequence is terminated by 'End' or 'Abort'. -- The semantics of Bit Machine program is defined by a model of execution found in 'Simplicity.BitMachine.Authentic'. -- -- This type is defined as the explicit fixedpoint of the 'MachineCodeF' functor. type MachineCode = Fix MachineCodeF -- | This is the functor used to define 'MachineCode'. data MachineCodeF a = End | Abort | Write Bool a | Copy Int a | Skip Int a | Fwd Int a | Bwd Int a | NewFrame Int a | MoveFrame a | DropFrame a | Read a a deriving (Functor, Show) -- | 'MachineCodeK' is a type used during construction of Bit Machine programs and can be viewed as a type holding incomplete programs. -- It is used in the same manner as difference lists (or 'StringS') and used a continuation expecting the rest of the program. -- -- The @p '.' q@ expression puts two 'MachineCodeK' values in sequence, and @p '|||' q@ is a 'MachineCodeK' value for a program that deterministically chooses between @p@ and @q@. type MachineCodeK = MachineCode -> MachineCode -- |'end' instructs the Bit Machine execution to terminate yielding success. end :: MachineCode end = Fix End -- | 'abort' instructs the Bit Machine execution to terminate by explicitly failing. abort :: MachineCodeK abort _ = Fix Abort -- | @'write' b@ instructs the Bit Machine to write the value 'b' to the active write frame and advance its cursor. write :: Bool -> MachineCodeK write b k = Fix (Write b k) -- | @'copy' n@ instructs the Bit Machine to copy 'n' values from the active read frame to the active write frame and advance the active write frame's cursor to the end of the written data. copy :: Int -> MachineCodeK copy i k = Fix (Copy i k) -- | @'skip' n@ instructs the Bit Machine to advance the active write frame's cursor by 'n' cells. skip :: Int -> MachineCodeK skip i k = Fix (Skip i k) -- | @'fwd' n@ instructs the Bit Machine to advance the active read frame's cursor by 'n' cells. fwd :: Int -> MachineCodeK fwd i k = Fix (Fwd i k) -- | @'bwd' n@ instructs the Bit Machine to move the active read frame's cursor backwards by 'n' cells. bwd :: Int -> MachineCodeK bwd i k = Fix (Bwd i k) -- | @'newFrame' n@ instructs the Bit Machine to push a new write frame of size 'n' onto the write frame stack. newFrame :: Int -> MachineCodeK newFrame i k = Fix (NewFrame i k) -- | 'moveFrame' instructs the Bit Machine to pop a frame off the write frame stack and push it onto the read frame stack while resetting that frame's cursor to the beginning of the frame. moveFrame :: MachineCodeK moveFrame k = Fix (MoveFrame k) -- | 'dropFrame' instructs the Bit Machine to pop a frame off the read frame stack. dropFrame :: MachineCodeK dropFrame k = Fix (DropFrame k) -- | @p '|||' q@ instructs the Bit Machine to deterministically choose between two programs by reading the value under the active read frame's cursor. -- If the value read is '0' then 'p' is executed. -- If the value read is '1' then 'q' is executed. (|||) :: MachineCodeK -> MachineCodeK -> MachineCodeK x ||| y = \k -> Fix (Read (x k) (y k)) -- | @'bump' i p@ temporarily advances the active read frame's cursor by @i@ cells and executes @p@ before moving the cursor back. -- -- It is intended that @p@ return the read frame stack back to its original configuration after execution; however, this is not enforced by 'bump'. -- -- @'bump' i p = 'fwd' i . p . 'bwd' i@ bump :: Int -> MachineCodeK -> MachineCodeK bump i p = fwd i . p . bwd i -- | 'nop' is the empty program that does nothing. nop :: MachineCodeK nop k = k ================================================ FILE: Haskell/Core/Simplicity/Bitcoin.hs ================================================ -- | This module defines utilities used in the processing of Bitcoin-like transaction data. module Simplicity.Bitcoin ( parseLock, parseSequence ) where import Data.Bits (testBit) import Data.Word (Word32, Word16) -- | Decodes a transaction's lock value into either @'Left' height@ or @'Right' time@. -- Note that an "unlocked" value is decoded as a height of @0@, which is semantically equivalent to being unlocked. parseLock :: Word32 -> Either Word32 Word32 parseLock v | v < 500000000 = Left v | otherwise = Right v -- | Decodes a transaction's input's sequence number into optionally either @'Just' ('Left' distance)@ or @'Just' ('Right' duration)@. -- If the sequence number's relative lock is disabled, 'Nothing' is returned -- Bits without relative lock time semantics are ignored. parseSequence :: Word32 -> Maybe (Either Word16 Word16) parseSequence v | testBit v 31 = Nothing | testBit v 22 = Just (Right (fromIntegral v)) | otherwise = Just (Left (fromIntegral v)) ================================================ FILE: Haskell/Core/Simplicity/CoreJets.hs ================================================ -- | This modules provides a GADT for a type of "core" Simplicity jets, i.e. those jets that don't use application specific primitives. -- -- While the 'CoreJet' data type could be made an instance of 'Simplicity.JetType.JetType', we instead generally expect it to be used as a substructure of all jets used in each specific Simplicity application. -- The other exports of this library aid in building an instance of 'Simplicity.JetType.JetType' for those that make use of 'CoreJet' as a substructure. {-# LANGUAGE RankNTypes, GADTs, StandaloneDeriving, ScopedTypeVariables, TypeFamilies #-} module Simplicity.CoreJets ( CoreJet(..), WordJet(..), ArithJet(..), HashJet(..), Secp256k1Jet(..), SignatureJet(..), BitcoinJet(..) , coreCatalogue , specification, coreJetMap, coreJetLookup , implementation , fastCoreEval , putJetBit, getJetBit , ConstWordContent(..), specificationConstWord, implementationConstWord, putConstWordBit, putConstWordValueBit , SomeConstWordContent(..), getConstWordBit , FastCoreEval ) where import qualified Prelude import Prelude hiding (fail, drop, take, negate, subtract, min, max, Word) import Control.Arrow ((+++), Kleisli(Kleisli), runKleisli) import Data.Bits ((.&.), (.|.), complement, rotate, shift, xor) import qualified Data.ByteString as BS import qualified Data.ByteString.Char8 as BSC import Data.Foldable (toList) import qualified Data.List as List import qualified Data.Map as Map import Data.Serialize (encode) import Data.Type.Equality ((:~:)(Refl)) import Data.Void (Void, vacuous) import Lens.Family2 ((^..), over, review) import Simplicity.Bitcoin import Simplicity.Digest import Simplicity.FFI.Jets as FFI import Simplicity.LibSecp256k1.Spec as LibSecp256k1 import Simplicity.MerkleRoot import Simplicity.Serialization import qualified Simplicity.Programs.Bit as Prog import qualified Simplicity.Programs.Arith as Prog import Simplicity.Programs.Generic as Prog import qualified Simplicity.Programs.CheckSig.Lib as CheckSig import qualified Simplicity.Programs.TimeLock as TimeLock import qualified Simplicity.Programs.LibSecp256k1.Lib as Secp256k1 import qualified Simplicity.Programs.Sha256.Lib as Sha256 import qualified Simplicity.Programs.Word as Prog import Simplicity.Term.Core import Simplicity.Tree import Simplicity.Ty.LibSecp256k1 import Simplicity.Ty.Word import Simplicity.Weight import qualified Simplicity.Word as W -- | A data type of (typed) tokens representing known "core" jets. -- -- A core jet is a jet that doesn't use primitives. data CoreJet a b where WordJet :: WordJet a b -> CoreJet a b ArithJet :: ArithJet a b -> CoreJet a b HashJet :: HashJet a b -> CoreJet a b Secp256k1Jet :: Secp256k1Jet a b -> CoreJet a b SignatureJet :: SignatureJet a b -> CoreJet a b BitcoinJet :: BitcoinJet a b -> CoreJet a b deriving instance Eq (CoreJet a b) deriving instance Show (CoreJet a b) data WordJet a b where Verify :: WordJet Bit () Low1 :: WordJet () Word1 Low8 :: WordJet () Word8 Low16 :: WordJet () Word16 Low32 :: WordJet () Word32 Low64 :: WordJet () Word64 High1 :: WordJet () Word1 High8 :: WordJet () Word8 High16 :: WordJet () Word16 High32 :: WordJet () Word32 High64 :: WordJet () Word64 Complement1 :: WordJet Word1 Word1 Complement8 :: WordJet Word8 Word8 Complement16 :: WordJet Word16 Word16 Complement32 :: WordJet Word32 Word32 Complement64 :: WordJet Word64 Word64 And1 :: WordJet (Word1, Word1) Word1 And8 :: WordJet (Word8, Word8) Word8 And16 :: WordJet (Word16, Word16) Word16 And32 :: WordJet (Word32, Word32) Word32 And64 :: WordJet (Word64, Word64) Word64 Or1 :: WordJet (Word1, Word1) Word1 Or8 :: WordJet (Word8, Word8) Word8 Or16 :: WordJet (Word16, Word16) Word16 Or32 :: WordJet (Word32, Word32) Word32 Or64 :: WordJet (Word64, Word64) Word64 Xor1 :: WordJet (Word1, Word1) Word1 Xor8 :: WordJet (Word8, Word8) Word8 Xor16 :: WordJet (Word16, Word16) Word16 Xor32 :: WordJet (Word32, Word32) Word32 Xor64 :: WordJet (Word64, Word64) Word64 Maj1 :: WordJet (Word1, (Word1, Word1)) Word1 Maj8 :: WordJet (Word8, (Word8, Word8)) Word8 Maj16 :: WordJet (Word16, (Word16, Word16)) Word16 Maj32 :: WordJet (Word32, (Word32, Word32)) Word32 Maj64 :: WordJet (Word64, (Word64, Word64)) Word64 XorXor1 :: WordJet (Word1, (Word1, Word1)) Word1 XorXor8 :: WordJet (Word8, (Word8, Word8)) Word8 XorXor16 :: WordJet (Word16, (Word16, Word16)) Word16 XorXor32 :: WordJet (Word32, (Word32, Word32)) Word32 XorXor64 :: WordJet (Word64, (Word64, Word64)) Word64 Ch1 :: WordJet (Word1, (Word1, Word1)) Word1 Ch8 :: WordJet (Word8, (Word8, Word8)) Word8 Ch16 :: WordJet (Word16, (Word16, Word16)) Word16 Ch32 :: WordJet (Word32, (Word32, Word32)) Word32 Ch64 :: WordJet (Word64, (Word64, Word64)) Word64 Some1 :: WordJet Word1 Bit Some8 :: WordJet Word8 Bit Some16 :: WordJet Word16 Bit Some32 :: WordJet Word32 Bit Some64 :: WordJet Word64 Bit All8 :: WordJet Word8 Bit All16 :: WordJet Word16 Bit All32 :: WordJet Word32 Bit All64 :: WordJet Word64 Bit Eq1 :: WordJet (Word1, Word1) Bit Eq8 :: WordJet (Word8, Word8) Bit Eq16 :: WordJet (Word16, Word16) Bit Eq32 :: WordJet (Word32, Word32) Bit Eq64 :: WordJet (Word64, Word64) Bit Eq256 :: WordJet (Word256, Word256) Bit FullLeftShift8_1 :: WordJet (Word8, Word1) (Word1, Word8) FullLeftShift8_2 :: WordJet (Word8, Word2) (Word2, Word8) FullLeftShift8_4 :: WordJet (Word8, Word4) (Word4, Word8) FullLeftShift16_1 :: WordJet (Word16, Word1) (Word1, Word16) FullLeftShift16_2 :: WordJet (Word16, Word2) (Word2, Word16) FullLeftShift16_4 :: WordJet (Word16, Word4) (Word4, Word16) FullLeftShift16_8 :: WordJet (Word16, Word8) (Word8, Word16) FullLeftShift32_1 :: WordJet (Word32, Word1) (Word1, Word32) FullLeftShift32_2 :: WordJet (Word32, Word2) (Word2, Word32) FullLeftShift32_4 :: WordJet (Word32, Word4) (Word4, Word32) FullLeftShift32_8 :: WordJet (Word32, Word8) (Word8, Word32) FullLeftShift32_16 :: WordJet (Word32, Word16) (Word16, Word32) FullLeftShift64_1 :: WordJet (Word64, Word1) (Word1, Word64) FullLeftShift64_2 :: WordJet (Word64, Word2) (Word2, Word64) FullLeftShift64_4 :: WordJet (Word64, Word4) (Word4, Word64) FullLeftShift64_8 :: WordJet (Word64, Word8) (Word8, Word64) FullLeftShift64_16 :: WordJet (Word64, Word16) (Word16, Word64) FullLeftShift64_32 :: WordJet (Word64, Word32) (Word32, Word64) FullRightShift8_1 :: WordJet (Word1, Word8) (Word8, Word1) FullRightShift8_2 :: WordJet (Word2, Word8) (Word8, Word2) FullRightShift8_4 :: WordJet (Word4, Word8) (Word8, Word4) FullRightShift16_1 :: WordJet (Word1, Word16) (Word16, Word1) FullRightShift16_2 :: WordJet (Word2, Word16) (Word16, Word2) FullRightShift16_4 :: WordJet (Word4, Word16) (Word16, Word4) FullRightShift16_8 :: WordJet (Word8, Word16) (Word16, Word8) FullRightShift32_1 :: WordJet (Word1, Word32) (Word32, Word1) FullRightShift32_2 :: WordJet (Word2, Word32) (Word32, Word2) FullRightShift32_4 :: WordJet (Word4, Word32) (Word32, Word4) FullRightShift32_8 :: WordJet (Word8, Word32) (Word32, Word8) FullRightShift32_16 :: WordJet (Word16, Word32) (Word32, Word16) FullRightShift64_1 :: WordJet (Word1, Word64) (Word64, Word1) FullRightShift64_2 :: WordJet (Word2, Word64) (Word64, Word2) FullRightShift64_4 :: WordJet (Word4, Word64) (Word64, Word4) FullRightShift64_8 :: WordJet (Word8, Word64) (Word64, Word8) FullRightShift64_16 :: WordJet (Word16, Word64) (Word64, Word16) FullRightShift64_32 :: WordJet (Word32, Word64) (Word64, Word32) Leftmost8_1 :: WordJet Word8 Word1 Leftmost8_2 :: WordJet Word8 Word2 Leftmost8_4 :: WordJet Word8 Word4 Leftmost16_1 :: WordJet Word16 Word1 Leftmost16_2 :: WordJet Word16 Word2 Leftmost16_4 :: WordJet Word16 Word4 Leftmost16_8 :: WordJet Word16 Word8 Leftmost32_1 :: WordJet Word32 Word1 Leftmost32_2 :: WordJet Word32 Word2 Leftmost32_4 :: WordJet Word32 Word4 Leftmost32_8 :: WordJet Word32 Word8 Leftmost32_16 :: WordJet Word32 Word16 Leftmost64_1 :: WordJet Word64 Word1 Leftmost64_2 :: WordJet Word64 Word2 Leftmost64_4 :: WordJet Word64 Word4 Leftmost64_8 :: WordJet Word64 Word8 Leftmost64_16 :: WordJet Word64 Word16 Leftmost64_32 :: WordJet Word64 Word32 Rightmost8_1 :: WordJet Word8 Word1 Rightmost8_2 :: WordJet Word8 Word2 Rightmost8_4 :: WordJet Word8 Word4 Rightmost16_1 :: WordJet Word16 Word1 Rightmost16_2 :: WordJet Word16 Word2 Rightmost16_4 :: WordJet Word16 Word4 Rightmost16_8 :: WordJet Word16 Word8 Rightmost32_1 :: WordJet Word32 Word1 Rightmost32_2 :: WordJet Word32 Word2 Rightmost32_4 :: WordJet Word32 Word4 Rightmost32_8 :: WordJet Word32 Word8 Rightmost32_16 :: WordJet Word32 Word16 Rightmost64_1 :: WordJet Word64 Word1 Rightmost64_2 :: WordJet Word64 Word2 Rightmost64_4 :: WordJet Word64 Word4 Rightmost64_8 :: WordJet Word64 Word8 Rightmost64_16 :: WordJet Word64 Word16 Rightmost64_32 :: WordJet Word64 Word32 LeftPadLow1_8 :: WordJet Word1 Word8 LeftPadLow1_16 :: WordJet Word1 Word16 LeftPadLow8_16 :: WordJet Word8 Word16 LeftPadLow1_32 :: WordJet Word1 Word32 LeftPadLow8_32 :: WordJet Word8 Word32 LeftPadLow16_32 :: WordJet Word16 Word32 LeftPadLow1_64 :: WordJet Word1 Word64 LeftPadLow8_64 :: WordJet Word8 Word64 LeftPadLow16_64 :: WordJet Word16 Word64 LeftPadLow32_64 :: WordJet Word32 Word64 LeftPadHigh1_8 :: WordJet Word1 Word8 LeftPadHigh1_16 :: WordJet Word1 Word16 LeftPadHigh8_16 :: WordJet Word8 Word16 LeftPadHigh1_32 :: WordJet Word1 Word32 LeftPadHigh8_32 :: WordJet Word8 Word32 LeftPadHigh16_32 :: WordJet Word16 Word32 LeftPadHigh1_64 :: WordJet Word1 Word64 LeftPadHigh8_64 :: WordJet Word8 Word64 LeftPadHigh16_64 :: WordJet Word16 Word64 LeftPadHigh32_64 :: WordJet Word32 Word64 LeftExtend1_8 :: WordJet Word1 Word8 LeftExtend1_16 :: WordJet Word1 Word16 LeftExtend8_16 :: WordJet Word8 Word16 LeftExtend1_32 :: WordJet Word1 Word32 LeftExtend8_32 :: WordJet Word8 Word32 LeftExtend16_32 :: WordJet Word16 Word32 LeftExtend1_64 :: WordJet Word1 Word64 LeftExtend8_64 :: WordJet Word8 Word64 LeftExtend16_64 :: WordJet Word16 Word64 LeftExtend32_64 :: WordJet Word32 Word64 RightPadLow1_8 :: WordJet Word1 Word8 RightPadLow1_16 :: WordJet Word1 Word16 RightPadLow8_16 :: WordJet Word8 Word16 RightPadLow1_32 :: WordJet Word1 Word32 RightPadLow8_32 :: WordJet Word8 Word32 RightPadLow16_32 :: WordJet Word16 Word32 RightPadLow1_64 :: WordJet Word1 Word64 RightPadLow8_64 :: WordJet Word8 Word64 RightPadLow16_64 :: WordJet Word16 Word64 RightPadLow32_64 :: WordJet Word32 Word64 RightPadHigh1_8 :: WordJet Word1 Word8 RightPadHigh1_16 :: WordJet Word1 Word16 RightPadHigh8_16 :: WordJet Word8 Word16 RightPadHigh1_32 :: WordJet Word1 Word32 RightPadHigh8_32 :: WordJet Word8 Word32 RightPadHigh16_32 :: WordJet Word16 Word32 RightPadHigh1_64 :: WordJet Word1 Word64 RightPadHigh8_64 :: WordJet Word8 Word64 RightPadHigh16_64 :: WordJet Word16 Word64 RightPadHigh32_64 :: WordJet Word32 Word64 RightExtend8_16 :: WordJet Word8 Word16 RightExtend8_32 :: WordJet Word8 Word32 RightExtend16_32 :: WordJet Word16 Word32 RightExtend8_64 :: WordJet Word8 Word64 RightExtend16_64 :: WordJet Word16 Word64 RightExtend32_64 :: WordJet Word32 Word64 LeftShiftWith8 :: WordJet (Bit, (Word4, Word8)) Word8 LeftShiftWith16 :: WordJet (Bit, (Word4, Word16)) Word16 LeftShiftWith32 :: WordJet (Bit, (Word8, Word32)) Word32 LeftShiftWith64 :: WordJet (Bit, (Word8, Word64)) Word64 LeftShift8 :: WordJet (Word4, Word8) Word8 LeftShift16 :: WordJet (Word4, Word16) Word16 LeftShift32 :: WordJet (Word8, Word32) Word32 LeftShift64 :: WordJet (Word8, Word64) Word64 RightShiftWith8 :: WordJet (Bit, (Word4, Word8)) Word8 RightShiftWith16 :: WordJet (Bit, (Word4, Word16)) Word16 RightShiftWith32 :: WordJet (Bit, (Word8, Word32)) Word32 RightShiftWith64 :: WordJet (Bit, (Word8, Word64)) Word64 RightShift8 :: WordJet (Word4, Word8) Word8 RightShift16 :: WordJet (Word4, Word16) Word16 RightShift32 :: WordJet (Word8, Word32) Word32 RightShift64 :: WordJet (Word8, Word64) Word64 LeftRotate8 :: WordJet (Word4, Word8) Word8 LeftRotate16 :: WordJet (Word4, Word16) Word16 LeftRotate32 :: WordJet (Word8, Word32) Word32 LeftRotate64 :: WordJet (Word8, Word64) Word64 RightRotate8 :: WordJet (Word4, Word8) Word8 RightRotate16 :: WordJet (Word4, Word16) Word16 RightRotate32 :: WordJet (Word8, Word32) Word32 RightRotate64 :: WordJet (Word8, Word64) Word64 deriving instance Eq (WordJet a b) deriving instance Show (WordJet a b) data ArithJet a b where One8 :: ArithJet () Word8 One16 :: ArithJet () Word16 One32 :: ArithJet () Word32 One64 :: ArithJet () Word64 Add8 :: ArithJet (Word8, Word8) (Bit, Word8) Add16 :: ArithJet (Word16, Word16) (Bit, Word16) Add32 :: ArithJet (Word32, Word32) (Bit, Word32) Add64 :: ArithJet (Word64, Word64) (Bit, Word64) FullAdd8 :: ArithJet (Bit, (Word8, Word8)) (Bit, Word8) FullAdd16 :: ArithJet (Bit, (Word16, Word16)) (Bit, Word16) FullAdd32 :: ArithJet (Bit, (Word32, Word32)) (Bit, Word32) FullAdd64 :: ArithJet (Bit, (Word64, Word64)) (Bit, Word64) FullIncrement8 :: ArithJet (Bit, Word8) (Bit, Word8) FullIncrement16 :: ArithJet (Bit, Word16) (Bit, Word16) FullIncrement32 :: ArithJet (Bit, Word32) (Bit, Word32) FullIncrement64 :: ArithJet (Bit, Word64) (Bit, Word64) Increment8 :: ArithJet Word8 (Bit, Word8) Increment16 :: ArithJet Word16 (Bit, Word16) Increment32 :: ArithJet Word32 (Bit, Word32) Increment64 :: ArithJet Word64 (Bit, Word64) Subtract8 :: ArithJet (Word8, Word8) (Bit, Word8) Subtract16 :: ArithJet (Word16, Word16) (Bit, Word16) Subtract32 :: ArithJet (Word32, Word32) (Bit, Word32) Subtract64 :: ArithJet (Word64, Word64) (Bit, Word64) FullSubtract8 :: ArithJet (Bit, (Word8, Word8)) (Bit, Word8) FullSubtract16 :: ArithJet (Bit, (Word16, Word16)) (Bit, Word16) FullSubtract32 :: ArithJet (Bit, (Word32, Word32)) (Bit, Word32) FullSubtract64 :: ArithJet (Bit, (Word64, Word64)) (Bit, Word64) Negate8 :: ArithJet Word8 (Bit, Word8) Negate16 :: ArithJet Word16 (Bit, Word16) Negate32 :: ArithJet Word32 (Bit, Word32) Negate64 :: ArithJet Word64 (Bit, Word64) FullDecrement8 :: ArithJet (Bit, Word8) (Bit, Word8) FullDecrement16 :: ArithJet (Bit, Word16) (Bit, Word16) FullDecrement32 :: ArithJet (Bit, Word32) (Bit, Word32) FullDecrement64 :: ArithJet (Bit, Word64) (Bit, Word64) Decrement8 :: ArithJet Word8 (Bit, Word8) Decrement16 :: ArithJet Word16 (Bit, Word16) Decrement32 :: ArithJet Word32 (Bit, Word32) Decrement64 :: ArithJet Word64 (Bit, Word64) Multiply8 :: ArithJet (Word8, Word8) Word16 Multiply16 :: ArithJet (Word16, Word16) Word32 Multiply32 :: ArithJet (Word32, Word32) Word64 Multiply64 :: ArithJet (Word64, Word64) Word128 FullMultiply8 :: ArithJet ((Word8, Word8), (Word8, Word8)) Word16 FullMultiply16 :: ArithJet ((Word16, Word16), (Word16, Word16)) Word32 FullMultiply32 :: ArithJet ((Word32, Word32), (Word32, Word32)) Word64 FullMultiply64 :: ArithJet ((Word64, Word64), (Word64, Word64)) Word128 IsZero8 :: ArithJet Word8 Bit IsZero16 :: ArithJet Word16 Bit IsZero32 :: ArithJet Word32 Bit IsZero64 :: ArithJet Word64 Bit IsOne8 :: ArithJet Word8 Bit IsOne16 :: ArithJet Word16 Bit IsOne32 :: ArithJet Word32 Bit IsOne64 :: ArithJet Word64 Bit Le8 :: ArithJet (Word8, Word8) Bit Le16 :: ArithJet (Word16, Word16) Bit Le32 :: ArithJet (Word32, Word32) Bit Le64 :: ArithJet (Word64, Word64) Bit Lt8 :: ArithJet (Word8, Word8) Bit Lt16 :: ArithJet (Word16, Word16) Bit Lt32 :: ArithJet (Word32, Word32) Bit Lt64 :: ArithJet (Word64, Word64) Bit Min8 :: ArithJet (Word8, Word8) Word8 Min16 :: ArithJet (Word16, Word16) Word16 Min32 :: ArithJet (Word32, Word32) Word32 Min64 :: ArithJet (Word64, Word64) Word64 Max8 :: ArithJet (Word8, Word8) Word8 Max16 :: ArithJet (Word16, Word16) Word16 Max32 :: ArithJet (Word32, Word32) Word32 Max64 :: ArithJet (Word64, Word64) Word64 Median8 :: ArithJet (Word8, (Word8, Word8)) Word8 Median16 :: ArithJet (Word16, (Word16, Word16)) Word16 Median32 :: ArithJet (Word32, (Word32, Word32)) Word32 Median64 :: ArithJet (Word64, (Word64, Word64)) Word64 DivMod8 :: ArithJet (Word8, Word8) (Word8, Word8) DivMod16 :: ArithJet (Word16, Word16) (Word16, Word16) DivMod32 :: ArithJet (Word32, Word32) (Word32, Word32) DivMod64 :: ArithJet (Word64, Word64) (Word64, Word64) Divide8 :: ArithJet (Word8, Word8) Word8 Divide16 :: ArithJet (Word16, Word16) Word16 Divide32 :: ArithJet (Word32, Word32) Word32 Divide64 :: ArithJet (Word64, Word64) Word64 Modulo8 :: ArithJet (Word8, Word8) Word8 Modulo16 :: ArithJet (Word16, Word16) Word16 Modulo32 :: ArithJet (Word32, Word32) Word32 Modulo64 :: ArithJet (Word64, Word64) Word64 Divides8 :: ArithJet (Word8, Word8) Bit Divides16 :: ArithJet (Word16, Word16) Bit Divides32 :: ArithJet (Word32, Word32) Bit Divides64 :: ArithJet (Word64, Word64) Bit DivMod128_64 :: ArithJet (Word128, Word64) (Word64, Word64) deriving instance Eq (ArithJet a b) deriving instance Show (ArithJet a b) data HashJet a b where Sha256Block :: HashJet (Sha256.Hash, Sha256.Block) Sha256.Hash Sha256Iv :: HashJet () Sha256.Hash Sha256Ctx8Init :: HashJet () Sha256.Ctx8 Sha256Ctx8Add1 :: HashJet (Sha256.Ctx8, Word8) Sha256.Ctx8 Sha256Ctx8Add2 :: HashJet (Sha256.Ctx8, Word16) Sha256.Ctx8 Sha256Ctx8Add4 :: HashJet (Sha256.Ctx8, Word32) Sha256.Ctx8 Sha256Ctx8Add8 :: HashJet (Sha256.Ctx8, Word64) Sha256.Ctx8 Sha256Ctx8Add16 :: HashJet (Sha256.Ctx8, Word128) Sha256.Ctx8 Sha256Ctx8Add32 :: HashJet (Sha256.Ctx8, Word256) Sha256.Ctx8 Sha256Ctx8Add64 :: HashJet (Sha256.Ctx8, Word512) Sha256.Ctx8 Sha256Ctx8Add128 :: HashJet (Sha256.Ctx8, Word1024) Sha256.Ctx8 Sha256Ctx8Add256 :: HashJet (Sha256.Ctx8, Word2048) Sha256.Ctx8 Sha256Ctx8Add512 :: HashJet (Sha256.Ctx8, Word4096) Sha256.Ctx8 Sha256Ctx8AddBuffer511 :: HashJet (Sha256.Ctx8, Buffer511 Word8) Sha256.Ctx8 Sha256Ctx8Finalize :: HashJet Sha256.Ctx8 Sha256.Hash deriving instance Eq (HashJet a b) deriving instance Show (HashJet a b) data Secp256k1Jet a b where FeNormalize :: Secp256k1Jet Secp256k1.FE Secp256k1.FE FeNegate :: Secp256k1Jet Secp256k1.FE Secp256k1.FE FeAdd :: Secp256k1Jet (Secp256k1.FE, Secp256k1.FE) Secp256k1.FE FeSquare :: Secp256k1Jet Secp256k1.FE Secp256k1.FE FeMultiply :: Secp256k1Jet (Secp256k1.FE, Secp256k1.FE) Secp256k1.FE FeMultiplyBeta :: Secp256k1Jet Secp256k1.FE Secp256k1.FE FeInvert :: Secp256k1Jet Secp256k1.FE Secp256k1.FE FeSquareRoot :: Secp256k1Jet Secp256k1.FE (Either () Secp256k1.FE) FeIsZero :: Secp256k1Jet Secp256k1.FE Bit FeIsOdd :: Secp256k1Jet Secp256k1.FE Bit ScalarNormalize :: Secp256k1Jet Secp256k1.Scalar Secp256k1.Scalar ScalarNegate :: Secp256k1Jet Secp256k1.Scalar Secp256k1.Scalar ScalarAdd :: Secp256k1Jet (Secp256k1.Scalar, Secp256k1.Scalar) Secp256k1.Scalar ScalarSquare :: Secp256k1Jet Secp256k1.Scalar Secp256k1.Scalar ScalarMultiply :: Secp256k1Jet (Secp256k1.Scalar, Secp256k1.Scalar) Secp256k1.Scalar ScalarMultiplyLambda :: Secp256k1Jet Secp256k1.Scalar Secp256k1.Scalar ScalarInvert :: Secp256k1Jet Secp256k1.Scalar Secp256k1.Scalar ScalarIsZero :: Secp256k1Jet Secp256k1.Scalar Bit GejInfinity :: Secp256k1Jet () Secp256k1.GEJ GejNormalize :: Secp256k1Jet Secp256k1.GEJ (Either () Secp256k1.GE) GejNegate :: Secp256k1Jet Secp256k1.GEJ Secp256k1.GEJ GeNegate :: Secp256k1Jet Secp256k1.GE Secp256k1.GE GejDouble :: Secp256k1Jet Secp256k1.GEJ Secp256k1.GEJ GejAdd :: Secp256k1Jet (Secp256k1.GEJ,Secp256k1.GEJ) Secp256k1.GEJ GejGeAddEx :: Secp256k1Jet (Secp256k1.GEJ,Secp256k1.GE) (Secp256k1.FE, Secp256k1.GEJ) GejGeAdd :: Secp256k1Jet (Secp256k1.GEJ,Secp256k1.GE) Secp256k1.GEJ GejRescale :: Secp256k1Jet (Secp256k1.GEJ,Secp256k1.FE) Secp256k1.GEJ GejIsInfinity :: Secp256k1Jet Secp256k1.GEJ Bit GejEquiv :: Secp256k1Jet (Secp256k1.GEJ, Secp256k1.GEJ) Bit GejGeEquiv :: Secp256k1Jet (Secp256k1.GEJ, Secp256k1.GE) Bit GejXEquiv :: Secp256k1Jet (Secp256k1.FE, Secp256k1.GEJ) Bit GejYIsOdd :: Secp256k1Jet Secp256k1.GEJ Bit GejIsOnCurve :: Secp256k1Jet Secp256k1.GEJ Bit GeIsOnCurve :: Secp256k1Jet Secp256k1.GE Bit Generate :: Secp256k1Jet Secp256k1.Scalar Secp256k1.GEJ Scale :: Secp256k1Jet (Secp256k1.Scalar,Secp256k1.GEJ) Secp256k1.GEJ LinearCombination1 :: Secp256k1Jet ((Secp256k1.Scalar,Secp256k1.GEJ),Secp256k1.Scalar) Secp256k1.GEJ LinearVerify1 :: Secp256k1Jet (((Secp256k1.Scalar,Secp256k1.GE),Secp256k1.Scalar),Secp256k1.GE) () PointVerify1 :: Secp256k1Jet (((Secp256k1.Scalar,Secp256k1.Point),Secp256k1.Scalar),Secp256k1.Point) () Decompress :: Secp256k1Jet Secp256k1.Point (Either () Secp256k1.GE) Swu :: Secp256k1Jet Secp256k1.FE Secp256k1.GE HashToCurve :: Secp256k1Jet Word256 Secp256k1.GE deriving instance Eq (Secp256k1Jet a b) deriving instance Show (Secp256k1Jet a b) data SignatureJet a b where CheckSigVerify :: SignatureJet ((Secp256k1.PubKey, Word512),Secp256k1.Sig) () Bip0340Verify :: SignatureJet ((Secp256k1.PubKey, Word256),Secp256k1.Sig) () deriving instance Eq (SignatureJet a b) deriving instance Show (SignatureJet a b) data BitcoinJet a b where ParseLock :: BitcoinJet Word32 (Either Word32 Word32) ParseSequence :: BitcoinJet Word32 (Either () (Either Word16 Word16)) TapdataInit :: BitcoinJet () Sha256.Ctx8 deriving instance Eq (BitcoinJet a b) deriving instance Show (BitcoinJet a b) -- | The specification of "core" jets. This can be used to help instantiate the 'Simplicity.JetType.specification' method. specification :: Assert term => CoreJet a b -> term a b specification (WordJet x) = specificationWord x specification (ArithJet x) = specificationArith x specification (HashJet x) = specificationHash x specification (Secp256k1Jet x) = specificationSecp256k1 x specification (SignatureJet x) = specificationSignature x specification (BitcoinJet x) = specificationBitcoin x specificationWord :: Assert term => WordJet a b -> term a b specificationWord Verify = Prog.verify specificationWord Low1 = Prog.zero word1 specificationWord Low8 = Prog.zero word8 specificationWord Low16 = Prog.zero word16 specificationWord Low32 = Prog.zero word32 specificationWord Low64 = Prog.zero word64 specificationWord High1 = Prog.high word1 specificationWord High8 = Prog.high word8 specificationWord High16 = Prog.high word16 specificationWord High32 = Prog.high word32 specificationWord High64 = Prog.high word64 specificationWord Complement1 = Prog.complement word1 specificationWord Complement8 = Prog.complement word8 specificationWord Complement16 = Prog.complement word16 specificationWord Complement32 = Prog.complement word32 specificationWord Complement64 = Prog.complement word64 specificationWord And1 = Prog.bitwise_and word1 specificationWord And8 = Prog.bitwise_and word8 specificationWord And16 = Prog.bitwise_and word16 specificationWord And32 = Prog.bitwise_and word32 specificationWord And64 = Prog.bitwise_and word64 specificationWord Or1 = Prog.bitwise_or word1 specificationWord Or8 = Prog.bitwise_or word8 specificationWord Or16 = Prog.bitwise_or word16 specificationWord Or32 = Prog.bitwise_or word32 specificationWord Or64 = Prog.bitwise_or word64 specificationWord Xor1 = Prog.bitwise_xor word1 specificationWord Xor8 = Prog.bitwise_xor word8 specificationWord Xor16 = Prog.bitwise_xor word16 specificationWord Xor32 = Prog.bitwise_xor word32 specificationWord Xor64 = Prog.bitwise_xor word64 specificationWord Maj1 = Prog.bitwise_maj word1 specificationWord Maj8 = Prog.bitwise_maj word8 specificationWord Maj16 = Prog.bitwise_maj word16 specificationWord Maj32 = Prog.bitwise_maj word32 specificationWord Maj64 = Prog.bitwise_maj word64 specificationWord XorXor1 = Prog.bitwise_xor_xor word1 specificationWord XorXor8 = Prog.bitwise_xor_xor word8 specificationWord XorXor16 = Prog.bitwise_xor_xor word16 specificationWord XorXor32 = Prog.bitwise_xor_xor word32 specificationWord XorXor64 = Prog.bitwise_xor_xor word64 specificationWord Ch1 = Prog.bitwise_ch word1 specificationWord Ch8 = Prog.bitwise_ch word8 specificationWord Ch16 = Prog.bitwise_ch word16 specificationWord Ch32 = Prog.bitwise_ch word32 specificationWord Ch64 = Prog.bitwise_ch word64 specificationWord Some1 = Prog.some word1 specificationWord Some8 = Prog.some word8 specificationWord Some16 = Prog.some word16 specificationWord Some32 = Prog.some word32 specificationWord Some64 = Prog.some word64 specificationWord All8 = Prog.all word8 specificationWord All16 = Prog.all word16 specificationWord All32 = Prog.all word32 specificationWord All64 = Prog.all word64 specificationWord Eq1 = eq specificationWord Eq8 = eq specificationWord Eq16 = eq specificationWord Eq32 = eq specificationWord Eq64 = eq specificationWord Eq256 = eq specificationWord FullLeftShift8_1 = Prog.full_shift word8 word1 specificationWord FullLeftShift8_2 = Prog.full_shift word8 word2 specificationWord FullLeftShift8_4 = Prog.full_shift word8 word4 specificationWord FullLeftShift16_1 = Prog.full_shift word16 word1 specificationWord FullLeftShift16_2 = Prog.full_shift word16 word2 specificationWord FullLeftShift16_4 = Prog.full_shift word16 word4 specificationWord FullLeftShift16_8 = Prog.full_shift word16 word8 specificationWord FullLeftShift32_1 = Prog.full_shift word32 word1 specificationWord FullLeftShift32_2 = Prog.full_shift word32 word2 specificationWord FullLeftShift32_4 = Prog.full_shift word32 word4 specificationWord FullLeftShift32_8 = Prog.full_shift word32 word8 specificationWord FullLeftShift32_16 = Prog.full_shift word32 word16 specificationWord FullLeftShift64_1 = Prog.full_shift word64 word1 specificationWord FullLeftShift64_2 = Prog.full_shift word64 word2 specificationWord FullLeftShift64_4 = Prog.full_shift word64 word4 specificationWord FullLeftShift64_8 = Prog.full_shift word64 word8 specificationWord FullLeftShift64_16 = Prog.full_shift word64 word16 specificationWord FullLeftShift64_32 = Prog.full_shift word64 word32 specificationWord FullRightShift8_1 = Prog.full_shift word1 word8 specificationWord FullRightShift8_2 = Prog.full_shift word2 word8 specificationWord FullRightShift8_4 = Prog.full_shift word4 word8 specificationWord FullRightShift16_1 = Prog.full_shift word1 word16 specificationWord FullRightShift16_2 = Prog.full_shift word2 word16 specificationWord FullRightShift16_4 = Prog.full_shift word4 word16 specificationWord FullRightShift16_8 = Prog.full_shift word8 word16 specificationWord FullRightShift32_1 = Prog.full_shift word1 word32 specificationWord FullRightShift32_2 = Prog.full_shift word2 word32 specificationWord FullRightShift32_4 = Prog.full_shift word4 word32 specificationWord FullRightShift32_8 = Prog.full_shift word8 word32 specificationWord FullRightShift32_16 = Prog.full_shift word16 word32 specificationWord FullRightShift64_1 = Prog.full_shift word1 word64 specificationWord FullRightShift64_2 = Prog.full_shift word2 word64 specificationWord FullRightShift64_4 = Prog.full_shift word4 word64 specificationWord FullRightShift64_8 = Prog.full_shift word8 word64 specificationWord FullRightShift64_16 = Prog.full_shift word16 word64 specificationWord FullRightShift64_32 = Prog.full_shift word32 word64 specificationWord Leftmost8_1 = Prog.leftmost vector8 specificationWord Leftmost8_2 = Prog.leftmost vector4 specificationWord Leftmost8_4 = Prog.leftmost vector2 specificationWord Leftmost16_1 = Prog.leftmost vector16 specificationWord Leftmost16_2 = Prog.leftmost vector8 specificationWord Leftmost16_4 = Prog.leftmost vector4 specificationWord Leftmost16_8 = Prog.leftmost vector2 specificationWord Leftmost32_1 = Prog.leftmost vector32 specificationWord Leftmost32_2 = Prog.leftmost vector16 specificationWord Leftmost32_4 = Prog.leftmost vector8 specificationWord Leftmost32_8 = Prog.leftmost vector4 specificationWord Leftmost32_16 = Prog.leftmost vector2 specificationWord Leftmost64_1 = Prog.leftmost vector64 specificationWord Leftmost64_2 = Prog.leftmost vector32 specificationWord Leftmost64_4 = Prog.leftmost vector16 specificationWord Leftmost64_8 = Prog.leftmost vector8 specificationWord Leftmost64_16 = Prog.leftmost vector4 specificationWord Leftmost64_32 = Prog.leftmost vector2 specificationWord Rightmost8_1 = Prog.rightmost vector8 specificationWord Rightmost8_2 = Prog.rightmost vector4 specificationWord Rightmost8_4 = Prog.rightmost vector2 specificationWord Rightmost16_1 = Prog.rightmost vector16 specificationWord Rightmost16_2 = Prog.rightmost vector8 specificationWord Rightmost16_4 = Prog.rightmost vector4 specificationWord Rightmost16_8 = Prog.rightmost vector2 specificationWord Rightmost32_1 = Prog.rightmost vector32 specificationWord Rightmost32_2 = Prog.rightmost vector16 specificationWord Rightmost32_4 = Prog.rightmost vector8 specificationWord Rightmost32_8 = Prog.rightmost vector4 specificationWord Rightmost32_16 = Prog.rightmost vector2 specificationWord Rightmost64_1 = Prog.rightmost vector64 specificationWord Rightmost64_2 = Prog.rightmost vector32 specificationWord Rightmost64_4 = Prog.rightmost vector16 specificationWord Rightmost64_8 = Prog.rightmost vector8 specificationWord Rightmost64_16 = Prog.rightmost vector4 specificationWord Rightmost64_32 = Prog.rightmost vector2 specificationWord LeftPadLow1_8 = Prog.left_pad_low word1 vector8 specificationWord LeftPadLow1_16 = Prog.left_pad_low word1 vector16 specificationWord LeftPadLow8_16 = Prog.left_pad_low word8 vector2 specificationWord LeftPadLow1_32 = Prog.left_pad_low word1 vector32 specificationWord LeftPadLow8_32 = Prog.left_pad_low word8 vector4 specificationWord LeftPadLow16_32 = Prog.left_pad_low word16 vector2 specificationWord LeftPadLow1_64 = Prog.left_pad_low word1 vector64 specificationWord LeftPadLow8_64 = Prog.left_pad_low word8 vector8 specificationWord LeftPadLow16_64 = Prog.left_pad_low word16 vector4 specificationWord LeftPadLow32_64 = Prog.left_pad_low word32 vector2 specificationWord LeftPadHigh1_8 = Prog.left_pad_high word1 vector8 specificationWord LeftPadHigh1_16 = Prog.left_pad_high word1 vector16 specificationWord LeftPadHigh8_16 = Prog.left_pad_high word8 vector2 specificationWord LeftPadHigh1_32 = Prog.left_pad_high word1 vector32 specificationWord LeftPadHigh8_32 = Prog.left_pad_high word8 vector4 specificationWord LeftPadHigh16_32 = Prog.left_pad_high word16 vector2 specificationWord LeftPadHigh1_64 = Prog.left_pad_high word1 vector64 specificationWord LeftPadHigh8_64 = Prog.left_pad_high word8 vector8 specificationWord LeftPadHigh16_64 = Prog.left_pad_high word16 vector4 specificationWord LeftPadHigh32_64 = Prog.left_pad_high word32 vector2 specificationWord LeftExtend1_8 = Prog.left_extend word1 vector8 specificationWord LeftExtend1_16 = Prog.left_extend word1 vector16 specificationWord LeftExtend8_16 = Prog.left_extend word8 vector2 specificationWord LeftExtend1_32 = Prog.left_extend word1 vector32 specificationWord LeftExtend8_32 = Prog.left_extend word8 vector4 specificationWord LeftExtend16_32 = Prog.left_extend word16 vector2 specificationWord LeftExtend1_64 = Prog.left_extend word1 vector64 specificationWord LeftExtend8_64 = Prog.left_extend word8 vector8 specificationWord LeftExtend16_64 = Prog.left_extend word16 vector4 specificationWord LeftExtend32_64 = Prog.left_extend word32 vector2 specificationWord RightPadLow1_8 = Prog.right_pad_low word1 vector8 specificationWord RightPadLow1_16 = Prog.right_pad_low word1 vector16 specificationWord RightPadLow8_16 = Prog.right_pad_low word8 vector2 specificationWord RightPadLow1_32 = Prog.right_pad_low word1 vector32 specificationWord RightPadLow8_32 = Prog.right_pad_low word8 vector4 specificationWord RightPadLow16_32 = Prog.right_pad_low word16 vector2 specificationWord RightPadLow1_64 = Prog.right_pad_low word1 vector64 specificationWord RightPadLow8_64 = Prog.right_pad_low word8 vector8 specificationWord RightPadLow16_64 = Prog.right_pad_low word16 vector4 specificationWord RightPadLow32_64 = Prog.right_pad_low word32 vector2 specificationWord RightPadHigh1_8 = Prog.right_pad_high word1 vector8 specificationWord RightPadHigh1_16 = Prog.right_pad_high word1 vector16 specificationWord RightPadHigh8_16 = Prog.right_pad_high word8 vector2 specificationWord RightPadHigh1_32 = Prog.right_pad_high word1 vector32 specificationWord RightPadHigh8_32 = Prog.right_pad_high word8 vector4 specificationWord RightPadHigh16_32 = Prog.right_pad_high word16 vector2 specificationWord RightPadHigh1_64 = Prog.right_pad_high word1 vector64 specificationWord RightPadHigh8_64 = Prog.right_pad_high word8 vector8 specificationWord RightPadHigh16_64 = Prog.right_pad_high word16 vector4 specificationWord RightPadHigh32_64 = Prog.right_pad_high word32 vector2 specificationWord RightExtend8_16 = Prog.right_extend word8 vector2 specificationWord RightExtend8_32 = Prog.right_extend word8 vector4 specificationWord RightExtend16_32 = Prog.right_extend word16 vector2 specificationWord RightExtend8_64 = Prog.right_extend word8 vector8 specificationWord RightExtend16_64 = Prog.right_extend word16 vector4 specificationWord RightExtend32_64 = Prog.right_extend word32 vector2 specificationWord LeftShiftWith8 = Prog.left_shift_with word4 word8 specificationWord LeftShiftWith16 = Prog.left_shift_with word4 word16 specificationWord LeftShiftWith32 = Prog.left_shift_with word8 word32 specificationWord LeftShiftWith64 = Prog.left_shift_with word8 word64 specificationWord LeftShift8 = Prog.left_shift word4 word8 specificationWord LeftShift16 = Prog.left_shift word4 word16 specificationWord LeftShift32 = Prog.left_shift word8 word32 specificationWord LeftShift64 = Prog.left_shift word8 word64 specificationWord RightShiftWith8 = Prog.right_shift_with word4 word8 specificationWord RightShiftWith16 = Prog.right_shift_with word4 word16 specificationWord RightShiftWith32 = Prog.right_shift_with word8 word32 specificationWord RightShiftWith64 = Prog.right_shift_with word8 word64 specificationWord RightShift8 = Prog.right_shift word4 word8 specificationWord RightShift16 = Prog.right_shift word4 word16 specificationWord RightShift32 = Prog.right_shift word8 word32 specificationWord RightShift64 = Prog.right_shift word8 word64 specificationWord LeftRotate8 = Prog.left_rotate word4 word8 specificationWord LeftRotate16 = Prog.left_rotate word4 word16 specificationWord LeftRotate32 = Prog.left_rotate word8 word32 specificationWord LeftRotate64 = Prog.left_rotate word8 word64 specificationWord RightRotate8 = Prog.right_rotate word4 word8 specificationWord RightRotate16 = Prog.right_rotate word4 word16 specificationWord RightRotate32 = Prog.right_rotate word8 word32 specificationWord RightRotate64 = Prog.right_rotate word8 word64 specificationArith :: Assert term => ArithJet a b -> term a b specificationArith One8 = Prog.one word8 specificationArith One16 = Prog.one word16 specificationArith One32 = Prog.one word32 specificationArith One64 = Prog.one word64 specificationArith Add8 = Prog.add word8 specificationArith Add16 = Prog.add word16 specificationArith Add32 = Prog.add word32 specificationArith Add64 = Prog.add word64 specificationArith FullAdd8 = Prog.full_add word8 specificationArith FullAdd16 = Prog.full_add word16 specificationArith FullAdd32 = Prog.full_add word32 specificationArith FullAdd64 = Prog.full_add word64 specificationArith FullIncrement8 = Prog.full_increment word8 specificationArith FullIncrement16 = Prog.full_increment word16 specificationArith FullIncrement32 = Prog.full_increment word32 specificationArith FullIncrement64 = Prog.full_increment word64 specificationArith Increment8 = Prog.increment word8 specificationArith Increment16 = Prog.increment word16 specificationArith Increment32 = Prog.increment word32 specificationArith Increment64 = Prog.increment word64 specificationArith Subtract8 = Prog.subtract word8 specificationArith Subtract16 = Prog.subtract word16 specificationArith Subtract32 = Prog.subtract word32 specificationArith Subtract64 = Prog.subtract word64 specificationArith FullSubtract8 = Prog.full_subtract word8 specificationArith FullSubtract16 = Prog.full_subtract word16 specificationArith FullSubtract32 = Prog.full_subtract word32 specificationArith FullSubtract64 = Prog.full_subtract word64 specificationArith Negate8 = Prog.negate word8 specificationArith Negate16 = Prog.negate word16 specificationArith Negate32 = Prog.negate word32 specificationArith Negate64 = Prog.negate word64 specificationArith FullDecrement8 = Prog.full_decrement word8 specificationArith FullDecrement16 = Prog.full_decrement word16 specificationArith FullDecrement32 = Prog.full_decrement word32 specificationArith FullDecrement64 = Prog.full_decrement word64 specificationArith Decrement8 = Prog.decrement word8 specificationArith Decrement16 = Prog.decrement word16 specificationArith Decrement32 = Prog.decrement word32 specificationArith Decrement64 = Prog.decrement word64 specificationArith Multiply8 = Prog.multiply word8 specificationArith Multiply16 = Prog.multiply word16 specificationArith Multiply32 = Prog.multiply word32 specificationArith Multiply64 = Prog.multiply word64 specificationArith FullMultiply8 = Prog.full_multiply word8 specificationArith FullMultiply16 = Prog.full_multiply word16 specificationArith FullMultiply32 = Prog.full_multiply word32 specificationArith FullMultiply64 = Prog.full_multiply word64 specificationArith IsZero8 = Prog.is_zero word8 specificationArith IsZero16 = Prog.is_zero word16 specificationArith IsZero32 = Prog.is_zero word32 specificationArith IsZero64 = Prog.is_zero word64 specificationArith IsOne8 = Prog.is_one word8 specificationArith IsOne16 = Prog.is_one word16 specificationArith IsOne32 = Prog.is_one word32 specificationArith IsOne64 = Prog.is_one word64 specificationArith Le8 = Prog.le word8 specificationArith Le16 = Prog.le word16 specificationArith Le32 = Prog.le word32 specificationArith Le64 = Prog.le word64 specificationArith Lt8 = Prog.lt word8 specificationArith Lt16 = Prog.lt word16 specificationArith Lt32 = Prog.lt word32 specificationArith Lt64 = Prog.lt word64 specificationArith Min8 = Prog.min word8 specificationArith Min16 = Prog.min word16 specificationArith Min32 = Prog.min word32 specificationArith Min64 = Prog.min word64 specificationArith Max8 = Prog.max word8 specificationArith Max16 = Prog.max word16 specificationArith Max32 = Prog.max word32 specificationArith Max64 = Prog.max word64 specificationArith Median8 = Prog.median word8 specificationArith Median16 = Prog.median word16 specificationArith Median32 = Prog.median word32 specificationArith Median64 = Prog.median word64 specificationArith DivMod8 = Prog.div_mod word8 specificationArith DivMod16 = Prog.div_mod word16 specificationArith DivMod32 = Prog.div_mod word32 specificationArith DivMod64 = Prog.div_mod word64 specificationArith Divide8 = Prog.divide word8 specificationArith Divide16 = Prog.divide word16 specificationArith Divide32 = Prog.divide word32 specificationArith Divide64 = Prog.divide word64 specificationArith Modulo8 = Prog.modulo word8 specificationArith Modulo16 = Prog.modulo word16 specificationArith Modulo32 = Prog.modulo word32 specificationArith Modulo64 = Prog.modulo word64 specificationArith Divides8 = Prog.divides word8 specificationArith Divides16 = Prog.divides word16 specificationArith Divides32 = Prog.divides word32 specificationArith Divides64 = Prog.divides word64 specificationArith DivMod128_64 = Prog.div2n1n word64 specificationHash :: Assert term => HashJet a b -> term a b specificationHash Sha256Block = Sha256.hashBlock specificationHash Sha256Iv = Sha256.iv specificationHash Sha256Ctx8Add1 = Sha256.ctx8Add1 specificationHash Sha256Ctx8Add2 = Sha256.ctx8Addn vector2 specificationHash Sha256Ctx8Add4 = Sha256.ctx8Addn vector4 specificationHash Sha256Ctx8Add8 = Sha256.ctx8Addn vector8 specificationHash Sha256Ctx8Add16 = Sha256.ctx8Addn vector16 specificationHash Sha256Ctx8Add32 = Sha256.ctx8Addn vector32 specificationHash Sha256Ctx8Add64 = Sha256.ctx8Addn vector64 specificationHash Sha256Ctx8Add128 = Sha256.ctx8Addn vector128 specificationHash Sha256Ctx8Add256 = Sha256.ctx8Addn vector256 specificationHash Sha256Ctx8Add512 = Sha256.ctx8Addn vector512 specificationHash Sha256Ctx8AddBuffer511 = Sha256.ctx8AddBuffer buffer511 specificationHash Sha256Ctx8Finalize = Sha256.ctx8Finalize specificationHash Sha256Ctx8Init = Sha256.ctx8Init specificationSecp256k1 :: Assert term => Secp256k1Jet a b -> term a b specificationSecp256k1 FeNormalize = Secp256k1.fe_normalize specificationSecp256k1 FeNegate = Secp256k1.fe_negate specificationSecp256k1 FeAdd = Secp256k1.fe_add specificationSecp256k1 FeSquare = Secp256k1.fe_square specificationSecp256k1 FeMultiply = Secp256k1.fe_multiply specificationSecp256k1 FeMultiplyBeta = Secp256k1.fe_multiply_beta specificationSecp256k1 FeInvert = Secp256k1.fe_invert specificationSecp256k1 FeSquareRoot = Secp256k1.fe_square_root specificationSecp256k1 FeIsZero = Secp256k1.fe_is_zero specificationSecp256k1 FeIsOdd = Secp256k1.fe_is_odd specificationSecp256k1 ScalarNormalize = Secp256k1.scalar_normalize specificationSecp256k1 ScalarNegate = Secp256k1.scalar_negate specificationSecp256k1 ScalarAdd = Secp256k1.scalar_add specificationSecp256k1 ScalarSquare = Secp256k1.scalar_square specificationSecp256k1 ScalarMultiply = Secp256k1.scalar_multiply specificationSecp256k1 ScalarMultiplyLambda = Secp256k1.scalar_multiply_lambda specificationSecp256k1 ScalarInvert = Secp256k1.scalar_invert specificationSecp256k1 ScalarIsZero = Secp256k1.scalar_is_zero specificationSecp256k1 GejInfinity = Secp256k1.gej_infinity specificationSecp256k1 GejNormalize = Secp256k1.gej_normalize specificationSecp256k1 GejNegate = Secp256k1.gej_negate specificationSecp256k1 GeNegate = Secp256k1.ge_negate specificationSecp256k1 GejDouble = Secp256k1.gej_double specificationSecp256k1 GejAdd = Secp256k1.gej_add specificationSecp256k1 GejGeAddEx = Secp256k1.gej_ge_add_ex specificationSecp256k1 GejGeAdd = Secp256k1.gej_ge_add specificationSecp256k1 GejRescale = Secp256k1.gej_rescale specificationSecp256k1 GejIsInfinity = Secp256k1.gej_is_infinity specificationSecp256k1 GejEquiv = Secp256k1.gej_equiv specificationSecp256k1 GejGeEquiv = Secp256k1.gej_ge_equiv specificationSecp256k1 GejXEquiv = Secp256k1.gej_x_equiv specificationSecp256k1 GejYIsOdd = Secp256k1.gej_y_is_odd specificationSecp256k1 GejIsOnCurve = Secp256k1.gej_is_on_curve specificationSecp256k1 GeIsOnCurve = Secp256k1.ge_is_on_curve specificationSecp256k1 Generate = Secp256k1.generate specificationSecp256k1 Scale = Secp256k1.scale specificationSecp256k1 LinearCombination1 = Secp256k1.linear_combination_1 specificationSecp256k1 LinearVerify1 = Secp256k1.linear_verify_1 specificationSecp256k1 PointVerify1 = Secp256k1.point_verify_1 specificationSecp256k1 Decompress = Secp256k1.decompress specificationSecp256k1 Swu = Secp256k1.swu specificationSecp256k1 HashToCurve = Secp256k1.hash_to_curve specificationSignature :: Assert term => SignatureJet a b -> term a b specificationSignature CheckSigVerify = CheckSig.checkSigVerify specificationSignature Bip0340Verify = Secp256k1.bip_0340_verify specificationBitcoin :: Assert term => BitcoinJet a b -> term a b specificationBitcoin ParseLock = TimeLock.parseLock specificationBitcoin ParseSequence = TimeLock.parseSequence specificationBitcoin TapdataInit = Sha256.tapdataInit -- | A jetted implementation for "core" jets. -- -- @ -- 'implementation' x === 'runKleisli' ('specification' x) -- @ implementation :: CoreJet a b -> a -> Maybe b implementation (WordJet x) = implementationWord x implementation (ArithJet x) = implementationArith x implementation (HashJet x) = implementationHash x implementation (Secp256k1Jet x) = implementationSecp256k1 x implementation (SignatureJet x) = implementationSignature x implementation (BitcoinJet x) = implementationBitcoin x implementationWord :: WordJet a b -> a -> Maybe b implementationWord Verify = either (const Nothing) Just implementationWord Low1 = const . return $ toWord1 0 implementationWord Low8 = const . return $ toWord8 0 implementationWord Low16 = const . return $ toWord16 0 implementationWord Low32 = const . return $ toWord32 0 implementationWord Low64 = const . return $ toWord64 0 implementationWord High1 = const . return $ toWord1 (-1) implementationWord High8 = const . return $ toWord8 (-1) implementationWord High16 = const . return $ toWord16 (-1) implementationWord High32 = const . return $ toWord32 (-1) implementationWord High64 = const . return $ toWord64 (-1) implementationWord Complement1 = \x -> return (toWord1 (complement (fromWord1 x))) implementationWord Complement8 = \x -> return (toWord8 (complement (fromWord8 x))) implementationWord Complement16 = \x -> return (toWord16 (complement (fromWord16 x))) implementationWord Complement32 = \x -> return (toWord32 (complement (fromWord32 x))) implementationWord Complement64 = \x -> return (toWord64 (complement (fromWord64 x))) implementationWord And1 = \(x, y) -> return (toWord1 (fromWord1 x .&. fromWord1 y)) implementationWord And8 = \(x, y) -> return (toWord8 (fromWord8 x .&. fromWord8 y)) implementationWord And16 = \(x, y) -> return (toWord16 (fromWord16 x .&. fromWord16 y)) implementationWord And32 = \(x, y) -> return (toWord32 (fromWord32 x .&. fromWord32 y)) implementationWord And64 = \(x, y) -> return (toWord64 (fromWord64 x .&. fromWord64 y)) implementationWord Or1 = \(x, y) -> return (toWord1 (fromWord1 x .|. fromWord1 y)) implementationWord Or8 = \(x, y) -> return (toWord8 (fromWord8 x .|. fromWord8 y)) implementationWord Or16 = \(x, y) -> return (toWord16 (fromWord16 x .|. fromWord16 y)) implementationWord Or32 = \(x, y) -> return (toWord32 (fromWord32 x .|. fromWord32 y)) implementationWord Or64 = \(x, y) -> return (toWord64 (fromWord64 x .|. fromWord64 y)) implementationWord Xor1 = \(x, y) -> return (toWord1 (fromWord1 x `xor` fromWord1 y)) implementationWord Xor8 = \(x, y) -> return (toWord8 (fromWord8 x `xor` fromWord8 y)) implementationWord Xor16 = \(x, y) -> return (toWord16 (fromWord16 x `xor` fromWord16 y)) implementationWord Xor32 = \(x, y) -> return (toWord32 (fromWord32 x `xor` fromWord32 y)) implementationWord Xor64 = \(x, y) -> return (toWord64 (fromWord64 x `xor` fromWord64 y)) implementationWord Maj1 = \(x, (y, z)) -> return (toWord1 (fromWord1 x .&. fromWord1 y .|. fromWord1 y .&. fromWord1 z .|. fromWord1 z .&. fromWord1 x)) implementationWord Maj8 = \(x, (y, z)) -> return (toWord8 (fromWord8 x .&. fromWord8 y .|. fromWord8 y .&. fromWord8 z .|. fromWord8 z .&. fromWord8 x)) implementationWord Maj16 = \(x, (y, z)) -> return (toWord16 (fromWord16 x .&. fromWord16 y .|. fromWord16 y .&. fromWord16 z .|. fromWord16 z .&. fromWord16 x)) implementationWord Maj32 = \(x, (y, z)) -> return (toWord32 (fromWord32 x .&. fromWord32 y .|. fromWord32 y .&. fromWord32 z .|. fromWord32 z .&. fromWord32 x)) implementationWord Maj64 = \(x, (y, z)) -> return (toWord64 (fromWord64 x .&. fromWord64 y .|. fromWord64 y .&. fromWord64 z .|. fromWord64 z .&. fromWord64 x)) implementationWord XorXor1 = \(x, (y, z)) -> return (toWord1 (fromWord1 x `xor` fromWord1 y `xor` fromWord1 z)) implementationWord XorXor8 = \(x, (y, z)) -> return (toWord8 (fromWord8 x `xor` fromWord8 y `xor` fromWord8 z)) implementationWord XorXor16 = \(x, (y, z)) -> return (toWord16 (fromWord16 x `xor` fromWord16 y `xor` fromWord16 z)) implementationWord XorXor32 = \(x, (y, z)) -> return (toWord32 (fromWord32 x `xor` fromWord32 y `xor` fromWord32 z)) implementationWord XorXor64 = \(x, (y, z)) -> return (toWord64 (fromWord64 x `xor` fromWord64 y `xor` fromWord64 z)) implementationWord Ch1 = \(x, (y, z)) -> return (toWord1 (fromWord1 x .&. fromWord1 y .|. complement (fromWord1 x) .&. fromWord1 z)) implementationWord Ch8 = \(x, (y, z)) -> return (toWord8 (fromWord8 x .&. fromWord8 y .|. complement (fromWord8 x) .&. fromWord8 z)) implementationWord Ch16 = \(x, (y, z)) -> return (toWord16 (fromWord16 x .&. fromWord16 y .|. complement (fromWord16 x) .&. fromWord16 z)) implementationWord Ch32 = \(x, (y, z)) -> return (toWord32 (fromWord32 x .&. fromWord32 y .|. complement (fromWord32 x) .&. fromWord32 z)) implementationWord Ch64 = \(x, (y, z)) -> return (toWord64 (fromWord64 x .&. fromWord64 y .|. complement (fromWord64 x) .&. fromWord64 z)) implementationWord Some1 = \x -> do let z = fromWord1 x /= 0 return (toBit z) implementationWord Some8 = \x -> do let z = fromWord8 x /= 0 return (toBit z) implementationWord Some16 = \x -> do let z = fromWord16 x /= 0 return (toBit z) implementationWord Some32 = \x -> do let z = fromWord32 x /= 0 return (toBit z) implementationWord Some64 = \x -> do let z = fromWord64 x /= 0 return (toBit z) implementationWord All8 = \x -> do let z = fromWord8 x == 2^8 - 1 return (toBit z) implementationWord All16 = \x -> do let z = fromWord16 x == 2^16 - 1 return (toBit z) implementationWord All32 = \x -> do let z = fromWord32 x == 2^32 - 1 return (toBit z) implementationWord All64 = \x -> do let z = fromWord64 x == 2^64 - 1 return (toBit z) implementationWord Eq1 = \(x, y) -> return (toBit (x == y)) implementationWord Eq8 = \(x, y) -> return (toBit (x == y)) implementationWord Eq16 = \(x, y) -> return (toBit (x == y)) implementationWord Eq32 = \(x, y) -> return (toBit (x == y)) implementationWord Eq64 = \(x, y) -> return (toBit (x == y)) implementationWord Eq256 = \(x, y) -> return (toBit (x == y)) implementationWord FullLeftShift8_1 = \(x, y) -> return (toWord1 $ fromWord8 x `shift` (1-8), toWord8 $ fromWord8 x `shift` 1 .|. fromWord1 y) implementationWord FullLeftShift8_2 = \(x, y) -> return (toWord2 $ fromWord8 x `shift` (2-8), toWord8 $ fromWord8 x `shift` 2 .|. fromWord2 y) implementationWord FullLeftShift8_4 = \(x, y) -> return (toWord4 $ fromWord8 x `shift` (4-8), toWord8 $ fromWord8 x `shift` 4 .|. fromWord4 y) implementationWord FullLeftShift16_1 = \(x, y) -> return (toWord1 $ fromWord16 x `shift` (1-16), toWord16 $ fromWord16 x `shift` 1 .|. fromWord1 y) implementationWord FullLeftShift16_2 = \(x, y) -> return (toWord2 $ fromWord16 x `shift` (2-16), toWord16 $ fromWord16 x `shift` 2 .|. fromWord2 y) implementationWord FullLeftShift16_4 = \(x, y) -> return (toWord4 $ fromWord16 x `shift` (4-16), toWord16 $ fromWord16 x `shift` 4 .|. fromWord4 y) implementationWord FullLeftShift16_8 = \(x, y) -> return (toWord8 $ fromWord16 x `shift` (8-16), toWord16 $ fromWord16 x `shift` 8 .|. fromWord8 y) implementationWord FullLeftShift32_1 = \(x, y) -> return (toWord1 $ fromWord32 x `shift` (1-32), toWord32 $ fromWord32 x `shift` 1 .|. fromWord1 y) implementationWord FullLeftShift32_2 = \(x, y) -> return (toWord2 $ fromWord32 x `shift` (2-32), toWord32 $ fromWord32 x `shift` 2 .|. fromWord2 y) implementationWord FullLeftShift32_4 = \(x, y) -> return (toWord4 $ fromWord32 x `shift` (4-32), toWord32 $ fromWord32 x `shift` 4 .|. fromWord4 y) implementationWord FullLeftShift32_8 = \(x, y) -> return (toWord8 $ fromWord32 x `shift` (8-32), toWord32 $ fromWord32 x `shift` 8 .|. fromWord8 y) implementationWord FullLeftShift32_16 = \(x, y) -> return (toWord16 $ fromWord32 x `shift` (16-32), toWord32 $ fromWord32 x `shift` 16 .|. fromWord16 y) implementationWord FullLeftShift64_1 = \(x, y) -> return (toWord1 $ fromWord64 x `shift` (1-64), toWord64 $ fromWord64 x `shift` 1 .|. fromWord1 y) implementationWord FullLeftShift64_2 = \(x, y) -> return (toWord2 $ fromWord64 x `shift` (2-64), toWord64 $ fromWord64 x `shift` 2 .|. fromWord2 y) implementationWord FullLeftShift64_4 = \(x, y) -> return (toWord4 $ fromWord64 x `shift` (4-64), toWord64 $ fromWord64 x `shift` 4 .|. fromWord4 y) implementationWord FullLeftShift64_8 = \(x, y) -> return (toWord8 $ fromWord64 x `shift` (8-64), toWord64 $ fromWord64 x `shift` 8 .|. fromWord8 y) implementationWord FullLeftShift64_16 = \(x, y) -> return (toWord16 $ fromWord64 x `shift` (16-64), toWord64 $ fromWord64 x `shift` 16 .|. fromWord16 y) implementationWord FullLeftShift64_32 = \(x, y) -> return (toWord32 $ fromWord64 x `shift` (32-64), toWord64 $ fromWord64 x `shift` 32 .|. fromWord32 y) implementationWord FullRightShift8_1 = \(x, y) -> return (toWord8 $ fromWord1 x `shift` (8-1) .|. fromWord8 y `shift` (-1), toWord1 $ fromWord8 y) implementationWord FullRightShift8_2 = \(x, y) -> return (toWord8 $ fromWord2 x `shift` (8-2) .|. fromWord8 y `shift` (-2), toWord2 $ fromWord8 y) implementationWord FullRightShift8_4 = \(x, y) -> return (toWord8 $ fromWord4 x `shift` (8-4) .|. fromWord8 y `shift` (-4), toWord4 $ fromWord8 y) implementationWord FullRightShift16_1 = \(x, y) -> return (toWord16 $ fromWord1 x `shift` (16-1) .|. fromWord16 y `shift` (-1), toWord1 $ fromWord16 y) implementationWord FullRightShift16_2 = \(x, y) -> return (toWord16 $ fromWord2 x `shift` (16-2) .|. fromWord16 y `shift` (-2), toWord2 $ fromWord16 y) implementationWord FullRightShift16_4 = \(x, y) -> return (toWord16 $ fromWord4 x `shift` (16-4) .|. fromWord16 y `shift` (-4), toWord4 $ fromWord16 y) implementationWord FullRightShift16_8 = \(x, y) -> return (toWord16 $ fromWord8 x `shift` (16-8) .|. fromWord16 y `shift` (-8), toWord8 $ fromWord16 y) implementationWord FullRightShift32_1 = \(x, y) -> return (toWord32 $ fromWord1 x `shift` (32-1) .|. fromWord32 y `shift` (-1), toWord1 $ fromWord32 y) implementationWord FullRightShift32_2 = \(x, y) -> return (toWord32 $ fromWord2 x `shift` (32-2) .|. fromWord32 y `shift` (-2), toWord2 $ fromWord32 y) implementationWord FullRightShift32_4 = \(x, y) -> return (toWord32 $ fromWord4 x `shift` (32-4) .|. fromWord32 y `shift` (-4), toWord4 $ fromWord32 y) implementationWord FullRightShift32_8 = \(x, y) -> return (toWord32 $ fromWord8 x `shift` (32-8) .|. fromWord32 y `shift` (-8), toWord8 $ fromWord32 y) implementationWord FullRightShift32_16 = \(x, y) -> return (toWord32 $ fromWord16 x `shift` (32-16) .|. fromWord32 y `shift` (-16), toWord16 $ fromWord32 y) implementationWord FullRightShift64_1 = \(x, y) -> return (toWord64 $ fromWord1 x `shift` (64-1) .|. fromWord64 y `shift` (-1), toWord1 $ fromWord64 y) implementationWord FullRightShift64_2 = \(x, y) -> return (toWord64 $ fromWord2 x `shift` (64-2) .|. fromWord64 y `shift` (-2), toWord2 $ fromWord64 y) implementationWord FullRightShift64_4 = \(x, y) -> return (toWord64 $ fromWord4 x `shift` (64-4) .|. fromWord64 y `shift` (-4), toWord4 $ fromWord64 y) implementationWord FullRightShift64_8 = \(x, y) -> return (toWord64 $ fromWord8 x `shift` (64-8) .|. fromWord64 y `shift` (-8), toWord8 $ fromWord64 y) implementationWord FullRightShift64_16 = \(x, y) -> return (toWord64 $ fromWord16 x `shift` (64-16) .|. fromWord64 y `shift` (-16), toWord16 $ fromWord64 y) implementationWord FullRightShift64_32 = \(x, y) -> return (toWord64 $ fromWord32 x `shift` (64-32) .|. fromWord64 y `shift` (-32), toWord32 $ fromWord64 y) implementationWord Leftmost8_1 = Just . fst . fst . fst implementationWord Leftmost8_2 = Just . fst . fst implementationWord Leftmost8_4 = Just . fst implementationWord Leftmost16_1 = Just . fst . fst . fst . fst implementationWord Leftmost16_2 = Just . fst . fst . fst implementationWord Leftmost16_4 = Just . fst . fst implementationWord Leftmost16_8 = Just . fst implementationWord Leftmost32_1 = Just . fst . fst . fst . fst . fst implementationWord Leftmost32_2 = Just . fst . fst . fst . fst implementationWord Leftmost32_4 = Just . fst . fst . fst implementationWord Leftmost32_8 = Just . fst . fst implementationWord Leftmost32_16 = Just . fst implementationWord Leftmost64_1 = Just . fst . fst . fst . fst . fst . fst implementationWord Leftmost64_2 = Just . fst . fst . fst . fst . fst implementationWord Leftmost64_4 = Just . fst . fst . fst . fst implementationWord Leftmost64_8 = Just . fst . fst . fst implementationWord Leftmost64_16 = Just . fst . fst implementationWord Leftmost64_32 = Just . fst implementationWord Rightmost8_1 = Just . snd . snd . snd implementationWord Rightmost8_2 = Just . snd . snd implementationWord Rightmost8_4 = Just . snd implementationWord Rightmost16_1 = Just . snd . snd . snd . snd implementationWord Rightmost16_2 = Just . snd . snd . snd implementationWord Rightmost16_4 = Just . snd . snd implementationWord Rightmost16_8 = Just . snd implementationWord Rightmost32_1 = Just . snd . snd . snd . snd . snd implementationWord Rightmost32_2 = Just . snd . snd . snd . snd implementationWord Rightmost32_4 = Just . snd . snd . snd implementationWord Rightmost32_8 = Just . snd . snd implementationWord Rightmost32_16 = Just . snd implementationWord Rightmost64_1 = Just . snd . snd . snd . snd . snd . snd implementationWord Rightmost64_2 = Just . snd . snd . snd . snd . snd implementationWord Rightmost64_4 = Just . snd . snd . snd . snd implementationWord Rightmost64_8 = Just . snd . snd . snd implementationWord Rightmost64_16 = Just . snd . snd implementationWord Rightmost64_32 = Just . snd implementationWord LeftPadLow1_8 = Just . toWord8 . fromWord1 implementationWord LeftPadLow1_16 = Just . toWord16 . fromWord1 implementationWord LeftPadLow8_16 = Just . toWord16 . fromWord8 implementationWord LeftPadLow1_32 = Just . toWord32 . fromWord1 implementationWord LeftPadLow8_32 = Just . toWord32 . fromWord8 implementationWord LeftPadLow16_32 = Just . toWord32 . fromWord16 implementationWord LeftPadLow1_64 = Just . toWord64 . fromWord1 implementationWord LeftPadLow8_64 = Just . toWord64 . fromWord8 implementationWord LeftPadLow16_64 = Just . toWord64 . fromWord16 implementationWord LeftPadLow32_64 = Just . toWord64 . fromWord32 implementationWord LeftPadHigh1_8 = \x -> Just . toWord8 $ ((-1) `shift` 1) .|. fromWord1 x implementationWord LeftPadHigh1_16 = \x -> Just . toWord16 $ ((-1) `shift` 1) .|. fromWord1 x implementationWord LeftPadHigh8_16 = \x -> Just . toWord16 $ ((-1) `shift` 8) .|. fromWord8 x implementationWord LeftPadHigh1_32 = \x -> Just . toWord32 $ ((-1) `shift` 1) .|. fromWord1 x implementationWord LeftPadHigh8_32 = \x -> Just . toWord32 $ ((-1) `shift` 8) .|. fromWord8 x implementationWord LeftPadHigh16_32 = \x -> Just . toWord32 $ ((-1) `shift` 16) .|. fromWord16 x implementationWord LeftPadHigh1_64 = \x -> Just . toWord64 $ ((-1) `shift` 1) .|. fromWord1 x implementationWord LeftPadHigh8_64 = \x -> Just . toWord64 $ ((-1) `shift` 8) .|. fromWord8 x implementationWord LeftPadHigh16_64 = \x -> Just . toWord64 $ ((-1) `shift` 16) .|. fromWord16 x implementationWord LeftPadHigh32_64 = \x -> Just . toWord64 $ ((-1) `shift` 32) .|. fromWord32 x implementationWord LeftExtend1_8 = Just . toWord8 . fromInt1 implementationWord LeftExtend1_16 = Just . toWord16 . fromInt1 implementationWord LeftExtend8_16 = Just . toWord16 . fromInt8 implementationWord LeftExtend1_32 = Just . toWord32 . fromInt1 implementationWord LeftExtend8_32 = Just . toWord32 . fromInt8 implementationWord LeftExtend16_32 = Just . toWord32 . fromInt16 implementationWord LeftExtend1_64 = Just . toWord64 . fromInt1 implementationWord LeftExtend8_64 = Just . toWord64 . fromInt8 implementationWord LeftExtend16_64 = Just . toWord64 . fromInt16 implementationWord LeftExtend32_64 = Just . toWord64 . fromInt32 implementationWord RightPadLow1_8 = \x -> Just . toWord8 $ fromWord1 x `shift` (8 - 1) implementationWord RightPadLow1_16 = \x -> Just . toWord16 $ fromWord1 x `shift` (16 - 1) implementationWord RightPadLow8_16 = \x -> Just . toWord16 $ fromWord8 x `shift` (16 - 8) implementationWord RightPadLow1_32 = \x -> Just . toWord32 $ fromWord1 x `shift` (32 - 1) implementationWord RightPadLow8_32 = \x -> Just . toWord32 $ fromWord8 x `shift` (32 - 8) implementationWord RightPadLow16_32 = \x -> Just . toWord32 $ fromWord16 x `shift` (32 - 16) implementationWord RightPadLow1_64 = \x -> Just . toWord64 $ fromWord1 x `shift` (64 - 1) implementationWord RightPadLow8_64 = \x -> Just . toWord64 $ fromWord8 x `shift` (64 - 8) implementationWord RightPadLow16_64 = \x -> Just . toWord64 $ fromWord16 x `shift` (64 - 16) implementationWord RightPadLow32_64 = \x -> Just . toWord64 $ fromWord32 x `shift` (64 - 32) implementationWord RightPadHigh1_8 = \x -> Just . toWord8 $ (fromWord1 x `shift` (8 - 1) .|. (2^(8 - 1) - 1)) implementationWord RightPadHigh1_16 = \x -> Just . toWord16 $ (fromWord1 x `shift` (16 - 1) .|. (2^(16 - 1) - 1)) implementationWord RightPadHigh8_16 = \x -> Just . toWord16 $ (fromWord8 x `shift` (16 - 8) .|. (2^(16 - 8) - 1)) implementationWord RightPadHigh1_32 = \x -> Just . toWord32 $ (fromWord1 x `shift` (32 - 1) .|. (2^(32 - 1) - 1)) implementationWord RightPadHigh8_32 = \x -> Just . toWord32 $ (fromWord8 x `shift` (32 - 8) .|. (2^(32 - 8) - 1)) implementationWord RightPadHigh16_32 = \x -> Just . toWord32 $ (fromWord16 x `shift` (32 - 16) .|. (2^(32 - 16) - 1)) implementationWord RightPadHigh1_64 = \x -> Just . toWord64 $ (fromWord1 x `shift` (64 - 1) .|. (2^(64 - 1) - 1)) implementationWord RightPadHigh8_64 = \x -> Just . toWord64 $ (fromWord8 x `shift` (64 - 8) .|. (2^(64 - 8) - 1)) implementationWord RightPadHigh16_64 = \x -> Just . toWord64 $ (fromWord16 x `shift` (64 - 16) .|. (2^(64 - 16) - 1)) implementationWord RightPadHigh32_64 = \x -> Just . toWord64 $ (fromWord32 x `shift` (64 - 32) .|. (2^(64 - 32) - 1)) implementationWord RightExtend8_16 = \x -> Just . toWord16 $ (fromWord8 x `shift` (16 - 8) .|. if odd (fromWord8 x) then (2^(16 - 8) - 1) else 0) implementationWord RightExtend8_32 = \x -> Just . toWord32 $ (fromWord8 x `shift` (32 - 8) .|. if odd (fromWord8 x) then (2^(32 - 8) - 1) else 0) implementationWord RightExtend16_32 = \x -> Just . toWord32 $ (fromWord16 x `shift` (32 - 16) .|. if odd (fromWord16 x) then (2^(32 - 16) - 1) else 0) implementationWord RightExtend8_64 = \x -> Just . toWord64 $ (fromWord8 x `shift` (64 - 8) .|. if odd (fromWord8 x) then (2^(64 - 8) - 1) else 0) implementationWord RightExtend16_64 = \x -> Just . toWord64 $ (fromWord16 x `shift` (64 - 16) .|. if odd (fromWord16 x) then (2^(64 - 16) - 1) else 0) implementationWord RightExtend32_64 = \x -> Just . toWord64 $ (fromWord32 x `shift` (64 - 32) .|. if odd (fromWord32 x) then (2^(64 - 32) - 1) else 0) implementationWord LeftShiftWith8 = \(w,(x,y)) -> Just . toWord8 $ (fromWord8 y `shift` fromInteger (fromWord4 x)) .|. if fromBit w then (2^(fromWord4 x) -1) else 0 implementationWord LeftShiftWith16 = \(w,(x,y)) -> Just . toWord16 $ (fromWord16 y `shift` fromInteger (fromWord4 x)) .|. if fromBit w then (2^(fromWord4 x) -1) else 0 implementationWord LeftShiftWith32 = \(w,(x,y)) -> Just . toWord32 $ (fromWord32 y `shift` fromInteger (fromWord8 x)) .|. if fromBit w then (2^(fromWord8 x) -1) else 0 implementationWord LeftShiftWith64 = \(w,(x,y)) -> Just . toWord64 $ (fromWord64 y `shift` fromInteger (fromWord8 x)) .|. if fromBit w then (2^(fromWord8 x) -1) else 0 implementationWord LeftShift8 = \(x,y) -> Just . toWord8 $ fromWord8 y `shift` fromInteger (fromWord4 x) implementationWord LeftShift16 = \(x,y) -> Just . toWord16 $ fromWord16 y `shift` fromInteger (fromWord4 x) implementationWord LeftShift32 = \(x,y) -> Just . toWord32 $ fromWord32 y `shift` fromInteger (fromWord8 x) implementationWord LeftShift64 = \(x,y) -> Just . toWord64 $ fromWord64 y `shift` fromInteger (fromWord8 x) implementationWord RightShiftWith8 = \(w,(x,y)) -> Just . toWord8 $ (fromWord8 y `shift` fromInteger (-fromWord4 x)) .|. if fromBit w then ((-1 :: Integer) `shift` fromInteger (8-fromWord4 x)) else 0 implementationWord RightShiftWith16 = \(w,(x,y)) -> Just . toWord16 $ (fromWord16 y `shift` fromInteger (-fromWord4 x)) .|. if fromBit w then ((-1 :: Integer) `shift` fromInteger (16-fromWord4 x)) else 0 implementationWord RightShiftWith32 = \(w,(x,y)) -> Just . toWord32 $ (fromWord32 y `shift` fromInteger (-fromWord8 x)) .|. if fromBit w then ((-1 :: Integer) `shift` fromInteger (32-fromWord8 x)) else 0 implementationWord RightShiftWith64 = \(w,(x,y)) -> Just . toWord64 $ (fromWord64 y `shift` fromInteger (-fromWord8 x)) .|. if fromBit w then ((-1 :: Integer) `shift` fromInteger (64-fromWord8 x)) else 0 implementationWord RightShift8 = \(x,y) -> Just . toWord8 $ fromWord8 y `shift` fromInteger (-fromWord4 x) implementationWord RightShift16 = \(x,y) -> Just . toWord16 $ fromWord16 y `shift` fromInteger (-fromWord4 x) implementationWord RightShift32 = \(x,y) -> Just . toWord32 $ fromWord32 y `shift` fromInteger (-fromWord8 x) implementationWord RightShift64 = \(x,y) -> Just . toWord64 $ fromWord64 y `shift` fromInteger (-fromWord8 x) implementationWord LeftRotate8 = \(x,y) -> Just . toWord8 . toInteger $ (fromInteger (fromWord8 y) :: W.Word8) `rotate` fromInteger (fromWord4 x) implementationWord LeftRotate16 = \(x,y) -> Just . toWord16 . toInteger $ (fromInteger (fromWord16 y) :: W.Word16) `rotate` fromInteger (fromWord4 x) implementationWord LeftRotate32 = \(x,y) -> Just . toWord32 . toInteger $ (fromInteger (fromWord32 y) :: W.Word32) `rotate` fromInteger (fromWord8 x) implementationWord LeftRotate64 = \(x,y) -> Just . toWord64 . toInteger $ (fromInteger (fromWord64 y) :: W.Word64) `rotate` fromInteger (fromWord8 x) implementationWord RightRotate8 = \(x,y) -> Just . toWord8 . toInteger $ (fromInteger (fromWord8 y) :: W.Word8) `rotate` fromInteger (-fromWord4 x) implementationWord RightRotate16 = \(x,y) -> Just . toWord16 . toInteger $ (fromInteger (fromWord16 y) :: W.Word16) `rotate` fromInteger (-fromWord4 x) implementationWord RightRotate32 = \(x,y) -> Just . toWord32 . toInteger $ (fromInteger (fromWord32 y) :: W.Word32) `rotate` fromInteger (-fromWord8 x) implementationWord RightRotate64 = \(x,y) -> Just . toWord64 . toInteger $ (fromInteger (fromWord64 y) :: W.Word64) `rotate` fromInteger (-fromWord8 x) implementationArith :: ArithJet a b -> a -> Maybe b implementationArith One8 = const . return $ toWord8 1 implementationArith One16 = const . return $ toWord16 1 implementationArith One32 = const . return $ toWord32 1 implementationArith One64 = const . return $ toWord64 1 implementationArith Add8 = \(x, y) -> do let z = fromWord8 x + fromWord8 y return (toBit (z >= 2 ^ 8), toWord8 z) implementationArith Add16 = \(x, y) -> do let z = fromWord16 x + fromWord16 y return (toBit (z >= 2 ^ 16), toWord16 z) implementationArith Add32 = \(x, y) -> do let z = fromWord32 x + fromWord32 y return (toBit (z >= 2 ^ 32), toWord32 z) implementationArith Add64 = \(x, y) -> do let z = fromWord64 x + fromWord64 y return (toBit (z >= 2 ^ 64), toWord64 z) implementationArith FullAdd8 = \(c, (x, y)) -> do let z = fromWord8 x + fromWord8 y + fromWord1 c return (toBit (z >= 2 ^ 8), toWord8 z) implementationArith FullAdd16 = \(c, (x, y)) -> do let z = fromWord16 x + fromWord16 y + fromWord1 c return (toBit (z >= 2 ^ 16), toWord16 z) implementationArith FullAdd32 = \(c, (x, y)) -> do let z = fromWord32 x + fromWord32 y + fromWord1 c return (toBit (z >= 2 ^ 32), toWord32 z) implementationArith FullAdd64 = \(c, (x, y)) -> do let z = fromWord64 x + fromWord64 y + fromWord1 c return (toBit (z >= 2 ^ 64), toWord64 z) implementationArith FullIncrement8 = \(b, x) -> do let z = fromWord8 x + fromWord1 b return (toBit (z >= 2 ^ 8), toWord8 z) implementationArith FullIncrement16 = \(b, x) -> do let z = fromWord16 x + fromWord1 b return (toBit (z >= 2 ^ 16), toWord16 z) implementationArith FullIncrement32 = \(b, x) -> do let z = fromWord32 x + fromWord1 b return (toBit (z >= 2 ^ 32), toWord32 z) implementationArith FullIncrement64 = \(b, x) -> do let z = fromWord64 x + fromWord1 b return (toBit (z >= 2 ^ 64), toWord64 z) implementationArith Increment8 = \x -> do let z = fromWord8 x + 1 return (toBit (z >= 2 ^ 8), toWord8 z) implementationArith Increment16 = \x -> do let z = fromWord16 x + 1 return (toBit (z >= 2 ^ 16), toWord16 z) implementationArith Increment32 = \x -> do let z = fromWord32 x + 1 return (toBit (z >= 2 ^ 32), toWord32 z) implementationArith Increment64 = \x -> do let z = fromWord64 x + 1 return (toBit (z >= 2 ^ 64), toWord64 z) implementationArith Subtract8 = \(x, y) -> do let z = fromWord8 x - fromWord8 y return (toBit (z < 0), toWord8 z) implementationArith Subtract16 = \(x, y) -> do let z = fromWord16 x - fromWord16 y return (toBit (z < 0), toWord16 z) implementationArith Subtract32 = \(x, y) -> do let z = fromWord32 x - fromWord32 y return (toBit (z < 0), toWord32 z) implementationArith Subtract64 = \(x, y) -> do let z = fromWord64 x - fromWord64 y return (toBit (z < 0), toWord64 z) implementationArith FullSubtract8 = \(b, (x, y)) -> do let z = fromWord8 x - fromWord8 y - fromWord1 b return (toBit (z < 0), toWord8 z) implementationArith FullSubtract16 = \(b, (x, y)) -> do let z = fromWord16 x - fromWord16 y - fromWord1 b return (toBit (z < 0), toWord16 z) implementationArith FullSubtract32 = \(b, (x, y)) -> do let z = fromWord32 x - fromWord32 y - fromWord1 b return (toBit (z < 0), toWord32 z) implementationArith FullSubtract64 = \(b, (x, y)) -> do let z = fromWord64 x - fromWord64 y - fromWord1 b return (toBit (z < 0), toWord64 z) implementationArith Negate8 = \x -> do let z = - fromWord8 x return (toBit (z < 0), toWord8 z) implementationArith Negate16 = \x -> do let z = - fromWord16 x return (toBit (z < 0), toWord16 z) implementationArith Negate32 = \x -> do let z = - fromWord32 x return (toBit (z < 0), toWord32 z) implementationArith Negate64 = \x -> do let z = - fromWord64 x return (toBit (z < 0), toWord64 z) implementationArith FullDecrement8 = \(b, x) -> do let z = fromWord8 x - fromWord1 b return (toBit (z < 0), toWord8 z) implementationArith FullDecrement16 = \(b, x) -> do let z = fromWord16 x - fromWord1 b return (toBit (z < 0), toWord16 z) implementationArith FullDecrement32 = \(b, x) -> do let z = fromWord32 x - fromWord1 b return (toBit (z < 0), toWord32 z) implementationArith FullDecrement64 = \(b, x) -> do let z = fromWord64 x - fromWord1 b return (toBit (z < 0), toWord64 z) implementationArith Decrement8 = \x -> do let z = fromWord8 x - 1 return (toBit (z < 0), toWord8 z) implementationArith Decrement16 = \x -> do let z = fromWord16 x - 1 return (toBit (z < 0), toWord16 z) implementationArith Decrement32 = \x -> do let z = fromWord32 x - 1 return (toBit (z < 0), toWord32 z) implementationArith Decrement64 = \x -> do let z = fromWord64 x - 1 return (toBit (z < 0), toWord64 z) implementationArith Multiply8 = \(x, y) -> do let z = fromWord8 x * fromWord8 y return (toWord16 z) implementationArith Multiply16 = \(x, y) -> do let z = fromWord16 x * fromWord16 y return (toWord32 z) implementationArith Multiply32 = \(x, y) -> do let z = fromWord32 x * fromWord32 y return (toWord64 z) implementationArith Multiply64 = \(x, y) -> do let z = fromWord64 x * fromWord64 y return (toWord128 z) implementationArith FullMultiply8 = \((x, y), (a, b)) -> do let z = fromWord8 x * fromWord8 y + fromWord8 a + fromWord8 b return (toWord16 z) implementationArith FullMultiply16 = \((x, y), (a, b)) -> do let z = fromWord16 x * fromWord16 y + fromWord16 a + fromWord16 b return (toWord32 z) implementationArith FullMultiply32 = \((x, y), (a, b)) -> do let z = fromWord32 x * fromWord32 y + fromWord32 a + fromWord32 b return (toWord64 z) implementationArith FullMultiply64 = \((x, y), (a, b)) -> do let z = fromWord64 x * fromWord64 y + fromWord64 a + fromWord64 b return (toWord128 z) implementationArith IsZero8 = \x -> do let z = fromWord8 x == 0 return (toBit z) implementationArith IsZero16 = \x -> do let z = fromWord16 x == 0 return (toBit z) implementationArith IsZero32 = \x -> do let z = fromWord32 x == 0 return (toBit z) implementationArith IsZero64 = \x -> do let z = fromWord64 x == 0 return (toBit z) implementationArith IsOne8 = \x -> do let z = fromWord8 x == 1 return (toBit z) implementationArith IsOne16 = \x -> do let z = fromWord16 x == 1 return (toBit z) implementationArith IsOne32 = \x -> do let z = fromWord32 x == 1 return (toBit z) implementationArith IsOne64 = \x -> do let z = fromWord64 x == 1 return (toBit z) implementationArith Le8 = \(x, y) -> do let z = fromWord8 x <= fromWord8 y return (toBit z) implementationArith Le16 = \(x, y) -> do let z = fromWord16 x <= fromWord16 y return (toBit z) implementationArith Le32 = \(x, y) -> do let z = fromWord32 x <= fromWord32 y return (toBit z) implementationArith Le64 = \(x, y) -> do let z = fromWord64 x <= fromWord64 y return (toBit z) implementationArith Lt8 = \(x, y) -> do let z = fromWord8 x < fromWord8 y return (toBit z) implementationArith Lt16 = \(x, y) -> do let z = fromWord16 x < fromWord16 y return (toBit z) implementationArith Lt32 = \(x, y) -> do let z = fromWord32 x < fromWord32 y return (toBit z) implementationArith Lt64 = \(x, y) -> do let z = fromWord64 x < fromWord64 y return (toBit z) implementationArith Min8 = \(x, y) -> do let z = Prelude.min (fromWord8 x) (fromWord8 y) return (toWord8 z) implementationArith Min16 = \(x, y) -> do let z = Prelude.min (fromWord16 x) (fromWord16 y) return (toWord16 z) implementationArith Min32 = \(x, y) -> do let z = Prelude.min (fromWord32 x) (fromWord32 y) return (toWord32 z) implementationArith Min64 = \(x, y) -> do let z = Prelude.min (fromWord64 x) (fromWord64 y) return (toWord64 z) implementationArith Max8 = \(x, y) -> do let z = Prelude.max (fromWord8 x) (fromWord8 y) return (toWord8 z) implementationArith Max16 = \(x, y) -> do let z = Prelude.max (fromWord16 x) (fromWord16 y) return (toWord16 z) implementationArith Max32 = \(x, y) -> do let z = Prelude.max (fromWord32 x) (fromWord32 y) return (toWord32 z) implementationArith Max64 = \(x, y) -> do let z = Prelude.max (fromWord64 x) (fromWord64 y) return (toWord64 z) implementationArith Median8 = \(x, (y, z)) -> do let r = median (fromWord8 x) (fromWord8 y) (fromWord8 z) return (toWord8 r) implementationArith Median16 = \(x, (y, z)) -> do let r = median (fromWord16 x) (fromWord16 y) (fromWord16 z) return (toWord16 r) implementationArith Median32 = \(x, (y, z)) -> do let r = median (fromWord32 x) (fromWord32 y) (fromWord32 z) return (toWord32 r) implementationArith Median64 = \(x, (y, z)) -> do let r = median (fromWord64 x) (fromWord64 y) (fromWord64 z) return (toWord64 r) implementationArith DivMod8 = \(x, y) -> do let (d,m) = Prelude.divMod (fromWord8 x) (fromWord8 y) return (if 0 == fromWord8 y then (y, x) else (toWord8 d, toWord8 m)) implementationArith DivMod16 = \(x, y) -> do let (d,m) = Prelude.divMod (fromWord16 x) (fromWord16 y) return (if 0 == fromWord16 y then (y, x) else (toWord16 d, toWord16 m)) implementationArith DivMod32 = \(x, y) -> do let (d,m) = Prelude.divMod (fromWord32 x) (fromWord32 y) return (if 0 == fromWord32 y then (y, x) else (toWord32 d, toWord32 m)) implementationArith DivMod64 = \(x, y) -> do let (d,m) = Prelude.divMod (fromWord64 x) (fromWord64 y) return (if 0 == fromWord64 y then (y, x) else (toWord64 d, toWord64 m)) implementationArith Divide8 = \(x, y) -> do let z = Prelude.div (fromWord8 x) (fromWord8 y) return (if 0 == fromWord8 y then y else toWord8 z) implementationArith Divide16 = \(x, y) -> do let z = Prelude.div (fromWord16 x) (fromWord16 y) return (if 0 == fromWord16 y then y else toWord16 z) implementationArith Divide32 = \(x, y) -> do let z = Prelude.div (fromWord32 x) (fromWord32 y) return (if 0 == fromWord32 y then y else toWord32 z) implementationArith Divide64 = \(x, y) -> do let z = Prelude.div (fromWord64 x) (fromWord64 y) return (if 0 == fromWord64 y then y else toWord64 z) implementationArith Modulo8 = \(x, y) -> do let z = Prelude.mod (fromWord8 x) (fromWord8 y) return (if 0 == fromWord8 y then x else toWord8 z) implementationArith Modulo16 = \(x, y) -> do let z = Prelude.mod (fromWord16 x) (fromWord16 y) return (if 0 == fromWord16 y then x else toWord16 z) implementationArith Modulo32 = \(x, y) -> do let z = Prelude.mod (fromWord32 x) (fromWord32 y) return (if 0 == fromWord32 y then x else toWord32 z) implementationArith Modulo64 = \(x, y) -> do let z = Prelude.mod (fromWord64 x) (fromWord64 y) return (if 0 == fromWord64 y then x else toWord64 z) implementationArith Divides8 = \(x, y) -> do let z = Prelude.mod (fromWord8 y) (fromWord8 x) return (toBit (0 == if 0 == fromWord8 x then fromWord8 y else z)) implementationArith Divides16 = \(x, y) -> do let z = Prelude.mod (fromWord16 y) (fromWord16 x) return (toBit (0 == if 0 == fromWord16 x then fromWord16 y else z)) implementationArith Divides32 = \(x, y) -> do let z = Prelude.mod (fromWord32 y) (fromWord32 x) return (toBit (0 == if 0 == fromWord32 x then fromWord32 y else z)) implementationArith Divides64 = \(x, y) -> do let z = Prelude.mod (fromWord64 y) (fromWord64 x) return (toBit (0 == if 0 == fromWord64 x then fromWord64 y else z)) implementationArith DivMod128_64 = \(x0, y0) -> do let x = fromWord128 x0 y = fromWord64 y0 (d,m) = Prelude.divMod x y return (if 2^63 <= y && x < y * 2^64 then (toWord64 d, toWord64 m) else (toWord64 (-1), toWord64 (-1))) implementationHash :: HashJet a b -> a -> Maybe b implementationHash = go where go :: HashJet a b -> a -> Maybe b go Sha256Block = \(h, (b1, b2)) -> Just . toWord256 . integerHash256 . ivHash $ compress (freeStart (fromHash h)) (fromHash b1, fromHash b2) go Sha256Iv = const (Just . toWord256 . integerHash256 . ivHash $ noTagIv) go Sha256Ctx8Add1 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack [fromInteger . fromWord8 $ v])) go Sha256Ctx8Add2 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector2))) go Sha256Ctx8Add4 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector4))) go Sha256Ctx8Add8 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector8))) go Sha256Ctx8Add16 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector16))) go Sha256Ctx8Add32 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector32))) go Sha256Ctx8Add64 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector64))) go Sha256Ctx8Add128 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector128))) go Sha256Ctx8Add256 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector256))) go Sha256Ctx8Add512 = \(ctx, v) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> v^..vector_ vector512))) go Sha256Ctx8AddBuffer511 = \(ctx, b) -> toCtx <$> (fromCtx ctx >>= flip ctxAdd (BS.pack (fromInteger . fromWord8 <$> b^..buffer_ buffer511))) go Sha256Ctx8Finalize = \ctx -> toWord256 . integerHash256 . ctxFinalize <$> fromCtx ctx go Sha256Ctx8Init = const (Just . toCtx $ ctxInit) fromHash = review (over be256) . fromIntegral . fromWord256 fromCtx (buffer, (count, midstate)) = ctxBuild (fromInteger . fromWord8 <$> buffer^..buffer_ buffer63) (fromWord64 count) (fromHash midstate) toCtx ctx = (buffer, (count, midstate)) where buffer = fst $ bufferFill buffer63 (toWord8 . fromIntegral <$> BS.unpack (ctxBuffer ctx)) count = toWord64 . fromIntegral $ ctxCounter ctx midstate = toWord256 . integerHash256 . ivHash $ ctxIV ctx implementationSecp256k1 :: Secp256k1Jet a b -> a -> Maybe b implementationSecp256k1 FeNormalize = FFI.fe_normalize implementationSecp256k1 FeNegate = FFI.fe_negate implementationSecp256k1 FeAdd = FFI.fe_add implementationSecp256k1 FeSquare = FFI.fe_square implementationSecp256k1 FeMultiply = FFI.fe_multiply implementationSecp256k1 FeMultiplyBeta = FFI.fe_multiply_beta implementationSecp256k1 FeInvert = FFI.fe_invert implementationSecp256k1 FeSquareRoot = FFI.fe_square_root implementationSecp256k1 FeIsZero = FFI.fe_is_zero implementationSecp256k1 FeIsOdd = FFI.fe_is_odd implementationSecp256k1 ScalarNormalize = FFI.scalar_normalize implementationSecp256k1 ScalarNegate = FFI.scalar_negate implementationSecp256k1 ScalarAdd = FFI.scalar_add implementationSecp256k1 ScalarSquare = FFI.scalar_square implementationSecp256k1 ScalarMultiply = FFI.scalar_multiply implementationSecp256k1 ScalarMultiplyLambda = FFI.scalar_multiply_lambda implementationSecp256k1 ScalarInvert = FFI.scalar_invert implementationSecp256k1 ScalarIsZero = FFI.scalar_is_zero implementationSecp256k1 GejInfinity = FFI.gej_infinity implementationSecp256k1 GejNormalize = FFI.gej_normalize implementationSecp256k1 GejNegate = FFI.gej_negate implementationSecp256k1 GeNegate = FFI.ge_negate implementationSecp256k1 GejDouble = FFI.gej_double implementationSecp256k1 GejAdd = FFI.gej_add implementationSecp256k1 GejGeAddEx = FFI.gej_ge_add_ex implementationSecp256k1 GejGeAdd = FFI.gej_ge_add implementationSecp256k1 GejRescale = FFI.gej_rescale implementationSecp256k1 GejIsInfinity = FFI.gej_is_infinity implementationSecp256k1 GejEquiv = \(a,b) -> return . toBit $ LibSecp256k1.gej_equiv (fromGEJ a) (fromGEJ b) implementationSecp256k1 GejGeEquiv = \(a,b) -> return . toBit $ LibSecp256k1.gej_ge_equiv (fromGEJ a) (fromGE b) implementationSecp256k1 GejXEquiv = FFI.gej_x_equiv implementationSecp256k1 GejYIsOdd = FFI.gej_y_is_odd implementationSecp256k1 GejIsOnCurve = FFI.gej_is_on_curve implementationSecp256k1 GeIsOnCurve = FFI.ge_is_on_curve implementationSecp256k1 Generate = FFI.generate implementationSecp256k1 Scale = FFI.scale implementationSecp256k1 LinearCombination1 = FFI.linear_combination_1 implementationSecp256k1 LinearVerify1 = FFI.linear_verify_1 implementationSecp256k1 PointVerify1 = FFI.point_verify_1 implementationSecp256k1 Decompress = FFI.decompress implementationSecp256k1 Swu = Just . toGE . LibSecp256k1.shallueVanDeWoestijne . fromFE where toGE (LibSecp256k1.GE x y) = (toWord256 (LibSecp256k1.fe_repr x), toWord256 (LibSecp256k1.fe_repr y)) fromFE = LibSecp256k1.fe . fromWord256 implementationSecp256k1 HashToCurve = fmap toGE . LibSecp256k1.hash_to_curve . fromW256 where toGE (LibSecp256k1.GE x y) = (toWord256 (LibSecp256k1.fe_repr x), toWord256 (LibSecp256k1.fe_repr y)) fromW256 = fromInteger . fromWord256 implementationSignature :: SignatureJet a b -> a -> Maybe b implementationSignature CheckSigVerify ((pk, (ir, h)), sig) = FFI.bip_0340_verify ((pk, msg), sig) where msg = toWord256 . integerHash256 $ sigHash (mkHash ir) (mkHash h) mkHash = review (over be256) . fromInteger . fromWord256 implementationSignature Bip0340Verify a = FFI.bip_0340_verify a implementationBitcoin :: BitcoinJet a b -> a -> Maybe b implementationBitcoin ParseLock v = Just . (toW32 +++ toW32) . parseLock $ fromW32 v where toW32 = toWord32 . fromIntegral fromW32 = fromInteger . fromWord32 implementationBitcoin ParseSequence v = Just . maybe (Left ()) (Right . (toW16 +++ toW16)) . parseSequence $ fromW32 v where toW16 = toWord16 . fromIntegral fromW32 = fromInteger . fromWord32 implementationBitcoin TapdataInit v = toCtx <$> ctxAdd ctxInit (tag<>tag) where tag = encode . bsHash . BSC.pack $ "TapData" toCtx ctx = (buffer, (count, midstate)) where buffer = fst $ bufferFill buffer63 (toWord8 . fromIntegral <$> BS.unpack (ctxBuffer ctx)) count = toWord64 . fromIntegral $ ctxCounter ctx midstate = toWord256 . integerHash256 . ivHash $ ctxIV ctx -- | A canonical deserialization operation for "core" jets. This can be used to help instantiate the 'Simplicity.JetType.getJetBit' method. getJetBit :: (Monad m) => m Void -> m Bool -> m (SomeArrow CoreJet) getJetBit = getCatalogue coreCatalogue -- | A 'Catalogue' of the core jets. The structure informs the canonical serialization format for the jets. coreCatalogue :: Catalogue (SomeArrow CoreJet) coreCatalogue = Shelf [ someArrowMap WordJet <$> wordBook , someArrowMap ArithJet <$> arithBook , someArrowMap HashJet <$> hashBook , someArrowMap Secp256k1Jet <$> secp256k1Book , someArrowMap SignatureJet <$> signatureBook , Missing , someArrowMap BitcoinJet <$> bitcoinBook ] wordBook = Shelf [ Item $ SomeArrow Verify , lowBook , highBook , complementBook , andBook , orBook , xorBook , majBook , xorXorBook , chBook , someBook , allBook , eqBook , fullLeftShiftBook , fullRightShiftBook , leftmostBook , rightmostBook , leftPadLowBook , leftPadHighBook , leftExtendBook , rightPadLowBook , rightPadHighBook , rightExtendBook , leftShiftWithBook , rightShiftWithBook , leftShiftBook , rightShiftBook , leftRotateBook , rightRotateBook ] lowBook = Shelf [ Item $ SomeArrow Low1 , Missing , Item $ SomeArrow Low8 , Item $ SomeArrow Low16 , Item $ SomeArrow Low32 , Item $ SomeArrow Low64 ] highBook = Shelf [ Item $ SomeArrow High1 , Missing , Item $ SomeArrow High8 , Item $ SomeArrow High16 , Item $ SomeArrow High32 , Item $ SomeArrow High64 ] complementBook = Shelf [ Item $ SomeArrow Complement1 , Missing , Item $ SomeArrow Complement8 , Item $ SomeArrow Complement16 , Item $ SomeArrow Complement32 , Item $ SomeArrow Complement64 ] andBook = Shelf [ Item $ SomeArrow And1 , Missing , Item $ SomeArrow And8 , Item $ SomeArrow And16 , Item $ SomeArrow And32 , Item $ SomeArrow And64 ] orBook = Shelf [ Item $ SomeArrow Or1 , Missing , Item $ SomeArrow Or8 , Item $ SomeArrow Or16 , Item $ SomeArrow Or32 , Item $ SomeArrow Or64 ] xorBook = Shelf [ Item $ SomeArrow Xor1 , Missing , Item $ SomeArrow Xor8 , Item $ SomeArrow Xor16 , Item $ SomeArrow Xor32 , Item $ SomeArrow Xor64 ] majBook = Shelf [ Item $ SomeArrow Maj1 , Missing , Item $ SomeArrow Maj8 , Item $ SomeArrow Maj16 , Item $ SomeArrow Maj32 , Item $ SomeArrow Maj64 ] xorXorBook = Shelf [ Item $ SomeArrow XorXor1 , Missing , Item $ SomeArrow XorXor8 , Item $ SomeArrow XorXor16 , Item $ SomeArrow XorXor32 , Item $ SomeArrow XorXor64 ] chBook = Shelf [ Item $ SomeArrow Ch1 , Missing , Item $ SomeArrow Ch8 , Item $ SomeArrow Ch16 , Item $ SomeArrow Ch32 , Item $ SomeArrow Ch64 ] someBook = Shelf [ Item $ SomeArrow Some1 , Missing , Item $ SomeArrow Some8 , Item $ SomeArrow Some16 , Item $ SomeArrow Some32 , Item $ SomeArrow Some64 ] allBook = Shelf [ Missing , Missing , Item $ SomeArrow All8 , Item $ SomeArrow All16 , Item $ SomeArrow All32 , Item $ SomeArrow All64 ] eqBook = Shelf [ Item $ SomeArrow Eq1 , Missing , Item $ SomeArrow Eq8 , Item $ SomeArrow Eq16 , Item $ SomeArrow Eq32 , Item $ SomeArrow Eq64 , Missing , Item $ SomeArrow Eq256 ] fullLeftShiftBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow FullLeftShift8_1 , Item $ SomeArrow FullLeftShift16_1 , Item $ SomeArrow FullLeftShift32_1 , Item $ SomeArrow FullLeftShift64_1 ] , Shelf [ Missing , Item $ SomeArrow FullLeftShift8_2 , Item $ SomeArrow FullLeftShift16_2 , Item $ SomeArrow FullLeftShift32_2 , Item $ SomeArrow FullLeftShift64_2 ] , Shelf [ Item $ SomeArrow FullLeftShift8_4 , Item $ SomeArrow FullLeftShift16_4 , Item $ SomeArrow FullLeftShift32_4 , Item $ SomeArrow FullLeftShift64_4 ] , Shelf [ Item $ SomeArrow FullLeftShift16_8 , Item $ SomeArrow FullLeftShift32_8 , Item $ SomeArrow FullLeftShift64_8 ] , Shelf [ Item $ SomeArrow FullLeftShift32_16 , Item $ SomeArrow FullLeftShift64_16 ] , Shelf [ Item $ SomeArrow FullLeftShift64_32 ] ] fullRightShiftBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow FullRightShift8_1 , Item $ SomeArrow FullRightShift16_1 , Item $ SomeArrow FullRightShift32_1 , Item $ SomeArrow FullRightShift64_1 ] , Shelf [ Missing , Item $ SomeArrow FullRightShift8_2 , Item $ SomeArrow FullRightShift16_2 , Item $ SomeArrow FullRightShift32_2 , Item $ SomeArrow FullRightShift64_2 ] , Shelf [ Item $ SomeArrow FullRightShift8_4 , Item $ SomeArrow FullRightShift16_4 , Item $ SomeArrow FullRightShift32_4 , Item $ SomeArrow FullRightShift64_4 ] , Shelf [ Item $ SomeArrow FullRightShift16_8 , Item $ SomeArrow FullRightShift32_8 , Item $ SomeArrow FullRightShift64_8 ] , Shelf [ Item $ SomeArrow FullRightShift32_16 , Item $ SomeArrow FullRightShift64_16 ] , Shelf [ Item $ SomeArrow FullRightShift64_32 ] ] leftmostBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow Leftmost8_1 , Item $ SomeArrow Leftmost16_1 , Item $ SomeArrow Leftmost32_1 , Item $ SomeArrow Leftmost64_1 ] , Shelf [ Missing , Item $ SomeArrow Leftmost8_2 , Item $ SomeArrow Leftmost16_2 , Item $ SomeArrow Leftmost32_2 , Item $ SomeArrow Leftmost64_2 ] , Shelf [ Item $ SomeArrow Leftmost8_4 , Item $ SomeArrow Leftmost16_4 , Item $ SomeArrow Leftmost32_4 , Item $ SomeArrow Leftmost64_4 ] , Shelf [ Item $ SomeArrow Leftmost16_8 , Item $ SomeArrow Leftmost32_8 , Item $ SomeArrow Leftmost64_8 ] , Shelf [ Item $ SomeArrow Leftmost32_16 , Item $ SomeArrow Leftmost64_16 ] , Shelf [ Item $ SomeArrow Leftmost64_32 ] ] rightmostBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow Rightmost8_1 , Item $ SomeArrow Rightmost16_1 , Item $ SomeArrow Rightmost32_1 , Item $ SomeArrow Rightmost64_1 ] , Shelf [ Missing , Item $ SomeArrow Rightmost8_2 , Item $ SomeArrow Rightmost16_2 , Item $ SomeArrow Rightmost32_2 , Item $ SomeArrow Rightmost64_2 ] , Shelf [ Item $ SomeArrow Rightmost8_4 , Item $ SomeArrow Rightmost16_4 , Item $ SomeArrow Rightmost32_4 , Item $ SomeArrow Rightmost64_4 ] , Shelf [ Item $ SomeArrow Rightmost16_8 , Item $ SomeArrow Rightmost32_8 , Item $ SomeArrow Rightmost64_8 ] , Shelf [ Item $ SomeArrow Rightmost32_16 , Item $ SomeArrow Rightmost64_16 ] , Shelf [ Item $ SomeArrow Rightmost64_32 ] ] leftPadLowBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow LeftPadLow1_8 , Item $ SomeArrow LeftPadLow1_16 , Item $ SomeArrow LeftPadLow1_32 , Item $ SomeArrow LeftPadLow1_64 ] , Missing , Missing , Shelf [ Item $ SomeArrow LeftPadLow8_16 , Item $ SomeArrow LeftPadLow8_32 , Item $ SomeArrow LeftPadLow8_64 ] , Shelf [ Item $ SomeArrow LeftPadLow16_32 , Item $ SomeArrow LeftPadLow16_64 ] , Shelf [ Item $ SomeArrow LeftPadLow32_64 ] ] leftPadHighBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow LeftPadHigh1_8 , Item $ SomeArrow LeftPadHigh1_16 , Item $ SomeArrow LeftPadHigh1_32 , Item $ SomeArrow LeftPadHigh1_64 ] , Missing , Missing , Shelf [ Item $ SomeArrow LeftPadHigh8_16 , Item $ SomeArrow LeftPadHigh8_32 , Item $ SomeArrow LeftPadHigh8_64 ] , Shelf [ Item $ SomeArrow LeftPadHigh16_32 , Item $ SomeArrow LeftPadHigh16_64 ] , Shelf [ Item $ SomeArrow LeftPadHigh32_64 ] ] leftExtendBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow LeftExtend1_8 , Item $ SomeArrow LeftExtend1_16 , Item $ SomeArrow LeftExtend1_32 , Item $ SomeArrow LeftExtend1_64 ] , Missing , Missing , Shelf [ Item $ SomeArrow LeftExtend8_16 , Item $ SomeArrow LeftExtend8_32 , Item $ SomeArrow LeftExtend8_64 ] , Shelf [ Item $ SomeArrow LeftExtend16_32 , Item $ SomeArrow LeftExtend16_64 ] , Shelf [ Item $ SomeArrow LeftExtend32_64 ] ] rightPadLowBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow RightPadLow1_8 , Item $ SomeArrow RightPadLow1_16 , Item $ SomeArrow RightPadLow1_32 , Item $ SomeArrow RightPadLow1_64 ] , Missing , Missing , Shelf [ Item $ SomeArrow RightPadLow8_16 , Item $ SomeArrow RightPadLow8_32 , Item $ SomeArrow RightPadLow8_64 ] , Shelf [ Item $ SomeArrow RightPadLow16_32 , Item $ SomeArrow RightPadLow16_64 ] , Shelf [ Item $ SomeArrow RightPadLow32_64 ] ] rightPadHighBook = Shelf [ Shelf [ Missing , Missing , Item $ SomeArrow RightPadHigh1_8 , Item $ SomeArrow RightPadHigh1_16 , Item $ SomeArrow RightPadHigh1_32 , Item $ SomeArrow RightPadHigh1_64 ] , Missing , Missing , Shelf [ Item $ SomeArrow RightPadHigh8_16 , Item $ SomeArrow RightPadHigh8_32 , Item $ SomeArrow RightPadHigh8_64 ] , Shelf [ Item $ SomeArrow RightPadHigh16_32 , Item $ SomeArrow RightPadHigh16_64 ] , Shelf [ Item $ SomeArrow RightPadHigh32_64 ] ] rightExtendBook = Shelf [ Missing , Missing , Missing , Shelf [ Item $ SomeArrow RightExtend8_16 , Item $ SomeArrow RightExtend8_32 , Item $ SomeArrow RightExtend8_64 ] , Shelf [ Item $ SomeArrow RightExtend16_32 , Item $ SomeArrow RightExtend16_64 ] , Shelf [ Item $ SomeArrow RightExtend32_64 ] ] leftShiftWithBook = Shelf [ Missing , Missing , Item $ SomeArrow LeftShiftWith8 , Item $ SomeArrow LeftShiftWith16 , Item $ SomeArrow LeftShiftWith32 , Item $ SomeArrow LeftShiftWith64 ] rightShiftWithBook = Shelf [ Missing , Missing , Item $ SomeArrow RightShiftWith8 , Item $ SomeArrow RightShiftWith16 , Item $ SomeArrow RightShiftWith32 , Item $ SomeArrow RightShiftWith64 ] leftShiftBook = Shelf [ Missing , Missing , Item $ SomeArrow LeftShift8 , Item $ SomeArrow LeftShift16 , Item $ SomeArrow LeftShift32 , Item $ SomeArrow LeftShift64 ] rightShiftBook = Shelf [ Missing , Missing , Item $ SomeArrow RightShift8 , Item $ SomeArrow RightShift16 , Item $ SomeArrow RightShift32 , Item $ SomeArrow RightShift64 ] leftRotateBook = Shelf [ Missing , Missing , Item $ SomeArrow LeftRotate8 , Item $ SomeArrow LeftRotate16 , Item $ SomeArrow LeftRotate32 , Item $ SomeArrow LeftRotate64 ] rightRotateBook = Shelf [ Missing , Missing , Item $ SomeArrow RightRotate8 , Item $ SomeArrow RightRotate16 , Item $ SomeArrow RightRotate32 , Item $ SomeArrow RightRotate64 ] arithBook = Shelf [ oneBook , fullAddBook , addBook , fullIncrementBook , incrementBook , Missing , fullSubtractBook , subtractBook , negateBook , fullDecrementBook , decrementBook , fullMultiplyBook , multiplyBook , isZeroBook , isOneBook , leBook , ltBook , minBook , maxBook , medianBook , div2n1nBook , divModBook , divideBook , moduloBook , dividesBook ] oneBook = Shelf [ Missing , Missing , Item $ SomeArrow One8 , Item $ SomeArrow One16 , Item $ SomeArrow One32 , Item $ SomeArrow One64 ] addBook = Shelf [ Missing , Missing , Item $ SomeArrow Add8 , Item $ SomeArrow Add16 , Item $ SomeArrow Add32 , Item $ SomeArrow Add64 ] fullAddBook = Shelf [ Missing , Missing , Item $ SomeArrow FullAdd8 , Item $ SomeArrow FullAdd16 , Item $ SomeArrow FullAdd32 , Item $ SomeArrow FullAdd64 ] fullIncrementBook = Shelf [ Missing , Missing , Item $ SomeArrow FullIncrement8 , Item $ SomeArrow FullIncrement16 , Item $ SomeArrow FullIncrement32 , Item $ SomeArrow FullIncrement64 ] incrementBook = Shelf [ Missing , Missing , Item $ SomeArrow Increment8 , Item $ SomeArrow Increment16 , Item $ SomeArrow Increment32 , Item $ SomeArrow Increment64 ] subtractBook = Shelf [ Missing , Missing , Item $ SomeArrow Subtract8 , Item $ SomeArrow Subtract16 , Item $ SomeArrow Subtract32 , Item $ SomeArrow Subtract64 ] fullSubtractBook = Shelf [ Missing , Missing , Item $ SomeArrow FullSubtract8 , Item $ SomeArrow FullSubtract16 , Item $ SomeArrow FullSubtract32 , Item $ SomeArrow FullSubtract64 ] negateBook = Shelf [ Missing , Missing , Item $ SomeArrow Negate8 , Item $ SomeArrow Negate16 , Item $ SomeArrow Negate32 , Item $ SomeArrow Negate64 ] fullDecrementBook = Shelf [ Missing , Missing , Item $ SomeArrow FullDecrement8 , Item $ SomeArrow FullDecrement16 , Item $ SomeArrow FullDecrement32 , Item $ SomeArrow FullDecrement64 ] decrementBook = Shelf [ Missing , Missing , Item $ SomeArrow Decrement8 , Item $ SomeArrow Decrement16 , Item $ SomeArrow Decrement32 , Item $ SomeArrow Decrement64 ] multiplyBook = Shelf [ Missing , Missing , Item $ SomeArrow Multiply8 , Item $ SomeArrow Multiply16 , Item $ SomeArrow Multiply32 , Item $ SomeArrow Multiply64 ] fullMultiplyBook = Shelf [ Missing , Missing , Item $ SomeArrow FullMultiply8 , Item $ SomeArrow FullMultiply16 , Item $ SomeArrow FullMultiply32 , Item $ SomeArrow FullMultiply64 ] isZeroBook = Shelf [ Missing , Missing , Item $ SomeArrow IsZero8 , Item $ SomeArrow IsZero16 , Item $ SomeArrow IsZero32 , Item $ SomeArrow IsZero64 ] isOneBook = Shelf [ Missing , Missing , Item $ SomeArrow IsOne8 , Item $ SomeArrow IsOne16 , Item $ SomeArrow IsOne32 , Item $ SomeArrow IsOne64 ] leBook = Shelf [ Missing , Missing , Item $ SomeArrow Le8 , Item $ SomeArrow Le16 , Item $ SomeArrow Le32 , Item $ SomeArrow Le64 ] ltBook = Shelf [ Missing , Missing , Item $ SomeArrow Lt8 , Item $ SomeArrow Lt16 , Item $ SomeArrow Lt32 , Item $ SomeArrow Lt64 ] minBook = Shelf [ Missing , Missing , Item $ SomeArrow Min8 , Item $ SomeArrow Min16 , Item $ SomeArrow Min32 , Item $ SomeArrow Min64 ] maxBook = Shelf [ Missing , Missing , Item $ SomeArrow Max8 , Item $ SomeArrow Max16 , Item $ SomeArrow Max32 , Item $ SomeArrow Max64 ] medianBook = Shelf [ Missing , Missing , Item $ SomeArrow Median8 , Item $ SomeArrow Median16 , Item $ SomeArrow Median32 , Item $ SomeArrow Median64 ] div2n1nBook = Shelf [ Missing , Missing , Missing , Missing , Missing , Item $ SomeArrow DivMod128_64 ] divModBook = Shelf [ Missing , Missing , Item $ SomeArrow DivMod8 , Item $ SomeArrow DivMod16 , Item $ SomeArrow DivMod32 , Item $ SomeArrow DivMod64 ] divideBook = Shelf [ Missing , Missing , Item $ SomeArrow Divide8 , Item $ SomeArrow Divide16 , Item $ SomeArrow Divide32 , Item $ SomeArrow Divide64 ] moduloBook = Shelf [ Missing , Missing , Item $ SomeArrow Modulo8 , Item $ SomeArrow Modulo16 , Item $ SomeArrow Modulo32 , Item $ SomeArrow Modulo64 ] dividesBook = Shelf [ Missing , Missing , Item $ SomeArrow Divides8 , Item $ SomeArrow Divides16 , Item $ SomeArrow Divides32 , Item $ SomeArrow Divides64 ] hashBook = Shelf [sha2Book] sha2Book = Shelf [ Item $ SomeArrow Sha256Block , Item $ SomeArrow Sha256Iv , sha2AddBook , Item $ SomeArrow Sha256Ctx8AddBuffer511 , Item $ SomeArrow Sha256Ctx8Finalize , Item $ SomeArrow Sha256Ctx8Init ] sha2AddBook = book [ SomeArrow Sha256Ctx8Add1 , SomeArrow Sha256Ctx8Add2 , SomeArrow Sha256Ctx8Add4 , SomeArrow Sha256Ctx8Add8 , SomeArrow Sha256Ctx8Add16 , SomeArrow Sha256Ctx8Add32 , SomeArrow Sha256Ctx8Add64 , SomeArrow Sha256Ctx8Add128 , SomeArrow Sha256Ctx8Add256 , SomeArrow Sha256Ctx8Add512 ] secp256k1Book = Shelf [ Shelf [Item $ SomeArrow PointVerify1] , Item $ SomeArrow Decompress , Shelf [Item $ SomeArrow LinearVerify1] , Shelf [Item $ SomeArrow LinearCombination1] , Item $ SomeArrow Scale , Item $ SomeArrow Generate , Item $ SomeArrow GejInfinity , Item $ SomeArrow GejNormalize , Item $ SomeArrow GejNegate , Item $ SomeArrow GeNegate , Item $ SomeArrow GejDouble , Item $ SomeArrow GejAdd , Item $ SomeArrow GejGeAddEx , Item $ SomeArrow GejGeAdd , Item $ SomeArrow GejRescale , Item $ SomeArrow GejIsInfinity , Item $ SomeArrow GejEquiv , Item $ SomeArrow GejGeEquiv , Item $ SomeArrow GejXEquiv , Item $ SomeArrow GejYIsOdd , Item $ SomeArrow GejIsOnCurve , Item $ SomeArrow GeIsOnCurve , Item $ SomeArrow ScalarNormalize , Item $ SomeArrow ScalarNegate , Item $ SomeArrow ScalarAdd , Item $ SomeArrow ScalarSquare , Item $ SomeArrow ScalarMultiply , Item $ SomeArrow ScalarMultiplyLambda , Item $ SomeArrow ScalarInvert , Item $ SomeArrow ScalarIsZero , Missing , Missing , Missing , Missing , Item $ SomeArrow FeNormalize , Item $ SomeArrow FeNegate , Item $ SomeArrow FeAdd , Item $ SomeArrow FeSquare , Item $ SomeArrow FeMultiply , Item $ SomeArrow FeMultiplyBeta , Item $ SomeArrow FeInvert , Item $ SomeArrow FeSquareRoot , Item $ SomeArrow FeIsZero , Item $ SomeArrow FeIsOdd , Missing , Item $ SomeArrow HashToCurve , Item $ SomeArrow Swu ] signatureBook = book [ SomeArrow CheckSigVerify , SomeArrow Bip0340Verify ] bitcoinBook = book [ SomeArrow ParseLock , SomeArrow ParseSequence , SomeArrow TapdataInit ] -- | A canonical serialization operation for "core" jets. This can be used to help instantiate the 'Simplicity.JetType.putJetBit' method. putJetBit :: CoreJet a b -> DList Bool putJetBit (WordJet x) = putPositive 1 . putJetBitWord x putJetBit (ArithJet x) = putPositive 2 . putJetBitArith x putJetBit (HashJet x) = putPositive 3 . putJetBitHash x putJetBit (Secp256k1Jet x) = putPositive 4 . putJetBitSecp256k1 x putJetBit (SignatureJet x) = putPositive 5 . putJetBitSignature x putJetBit (BitcoinJet x) = putPositive 7 . putJetBitBitcoin x putJetBitWord :: WordJet a b -> DList Bool putJetBitWord Verify = putPositive 1 putJetBitWord Low1 = putPositive 2 . putPositive 1 putJetBitWord Low8 = putPositive 2 . putPositive 3 putJetBitWord Low16 = putPositive 2 . putPositive 4 putJetBitWord Low32 = putPositive 2 . putPositive 5 putJetBitWord Low64 = putPositive 2 . putPositive 6 putJetBitWord High1 = putPositive 3 . putPositive 1 putJetBitWord High8 = putPositive 3 . putPositive 3 putJetBitWord High16 = putPositive 3 . putPositive 4 putJetBitWord High32 = putPositive 3 . putPositive 5 putJetBitWord High64 = putPositive 3 . putPositive 6 putJetBitWord Complement1 = putPositive 4 . putPositive 1 putJetBitWord Complement8 = putPositive 4 . putPositive 3 putJetBitWord Complement16 = putPositive 4 . putPositive 4 putJetBitWord Complement32 = putPositive 4 . putPositive 5 putJetBitWord Complement64 = putPositive 4 . putPositive 6 putJetBitWord And1 = putPositive 5 . putPositive 1 putJetBitWord And8 = putPositive 5 . putPositive 3 putJetBitWord And16 = putPositive 5 . putPositive 4 putJetBitWord And32 = putPositive 5 . putPositive 5 putJetBitWord And64 = putPositive 5 . putPositive 6 putJetBitWord Or1 = putPositive 6 . putPositive 1 putJetBitWord Or8 = putPositive 6 . putPositive 3 putJetBitWord Or16 = putPositive 6 . putPositive 4 putJetBitWord Or32 = putPositive 6 . putPositive 5 putJetBitWord Or64 = putPositive 6 . putPositive 6 putJetBitWord Xor1 = putPositive 7 . putPositive 1 putJetBitWord Xor8 = putPositive 7 . putPositive 3 putJetBitWord Xor16 = putPositive 7 . putPositive 4 putJetBitWord Xor32 = putPositive 7 . putPositive 5 putJetBitWord Xor64 = putPositive 7 . putPositive 6 putJetBitWord Maj1 = putPositive 8 . putPositive 1 putJetBitWord Maj8 = putPositive 8 . putPositive 3 putJetBitWord Maj16 = putPositive 8 . putPositive 4 putJetBitWord Maj32 = putPositive 8 . putPositive 5 putJetBitWord Maj64 = putPositive 8 . putPositive 6 putJetBitWord XorXor1 = putPositive 9 . putPositive 1 putJetBitWord XorXor8 = putPositive 9 . putPositive 3 putJetBitWord XorXor16 = putPositive 9 . putPositive 4 putJetBitWord XorXor32 = putPositive 9 . putPositive 5 putJetBitWord XorXor64 = putPositive 9 . putPositive 6 putJetBitWord Ch1 = putPositive 10 . putPositive 1 putJetBitWord Ch8 = putPositive 10 . putPositive 3 putJetBitWord Ch16 = putPositive 10 . putPositive 4 putJetBitWord Ch32 = putPositive 10 . putPositive 5 putJetBitWord Ch64 = putPositive 10 . putPositive 6 putJetBitWord Some1 = putPositive 11 . putPositive 1 putJetBitWord Some8 = putPositive 11 . putPositive 3 putJetBitWord Some16 = putPositive 11 . putPositive 4 putJetBitWord Some32 = putPositive 11 . putPositive 5 putJetBitWord Some64 = putPositive 11 . putPositive 6 putJetBitWord All8 = putPositive 12 . putPositive 3 putJetBitWord All16 = putPositive 12 . putPositive 4 putJetBitWord All32 = putPositive 12 . putPositive 5 putJetBitWord All64 = putPositive 12 . putPositive 6 putJetBitWord Eq1 = putPositive 13 . putPositive 1 putJetBitWord Eq8 = putPositive 13 . putPositive 3 putJetBitWord Eq16 = putPositive 13 . putPositive 4 putJetBitWord Eq32 = putPositive 13 . putPositive 5 putJetBitWord Eq64 = putPositive 13 . putPositive 6 putJetBitWord Eq256 = putPositive 13 . putPositive 8 putJetBitWord FullLeftShift8_1 = putPositive 14 . putPositive 1 . putPositive 3 putJetBitWord FullLeftShift8_2 = putPositive 14 . putPositive 2 . putPositive 2 putJetBitWord FullLeftShift8_4 = putPositive 14 . putPositive 3 . putPositive 1 putJetBitWord FullLeftShift16_1 = putPositive 14 . putPositive 1 . putPositive 4 putJetBitWord FullLeftShift16_2 = putPositive 14 . putPositive 2 . putPositive 3 putJetBitWord FullLeftShift16_4 = putPositive 14 . putPositive 3 . putPositive 2 putJetBitWord FullLeftShift16_8 = putPositive 14 . putPositive 4 . putPositive 1 putJetBitWord FullLeftShift32_1 = putPositive 14 . putPositive 1 . putPositive 5 putJetBitWord FullLeftShift32_2 = putPositive 14 . putPositive 2 . putPositive 4 putJetBitWord FullLeftShift32_4 = putPositive 14 . putPositive 3 . putPositive 3 putJetBitWord FullLeftShift32_8 = putPositive 14 . putPositive 4 . putPositive 2 putJetBitWord FullLeftShift32_16 = putPositive 14 . putPositive 5 . putPositive 1 putJetBitWord FullLeftShift64_1 = putPositive 14 . putPositive 1 . putPositive 6 putJetBitWord FullLeftShift64_2 = putPositive 14 . putPositive 2 . putPositive 5 putJetBitWord FullLeftShift64_4 = putPositive 14 . putPositive 3 . putPositive 4 putJetBitWord FullLeftShift64_8 = putPositive 14 . putPositive 4 . putPositive 3 putJetBitWord FullLeftShift64_16 = putPositive 14 . putPositive 5 . putPositive 2 putJetBitWord FullLeftShift64_32 = putPositive 14 . putPositive 6 . putPositive 1 putJetBitWord FullRightShift8_1 = putPositive 15 . putPositive 1 . putPositive 3 putJetBitWord FullRightShift8_2 = putPositive 15 . putPositive 2 . putPositive 2 putJetBitWord FullRightShift8_4 = putPositive 15 . putPositive 3 . putPositive 1 putJetBitWord FullRightShift16_1 = putPositive 15 . putPositive 1 . putPositive 4 putJetBitWord FullRightShift16_2 = putPositive 15 . putPositive 2 . putPositive 3 putJetBitWord FullRightShift16_4 = putPositive 15 . putPositive 3 . putPositive 2 putJetBitWord FullRightShift16_8 = putPositive 15 . putPositive 4 . putPositive 1 putJetBitWord FullRightShift32_1 = putPositive 15 . putPositive 1 . putPositive 5 putJetBitWord FullRightShift32_2 = putPositive 15 . putPositive 2 . putPositive 4 putJetBitWord FullRightShift32_4 = putPositive 15 . putPositive 3 . putPositive 3 putJetBitWord FullRightShift32_8 = putPositive 15 . putPositive 4 . putPositive 2 putJetBitWord FullRightShift32_16 = putPositive 15 . putPositive 5 . putPositive 1 putJetBitWord FullRightShift64_1 = putPositive 15 . putPositive 1 . putPositive 6 putJetBitWord FullRightShift64_2 = putPositive 15 . putPositive 2 . putPositive 5 putJetBitWord FullRightShift64_4 = putPositive 15 . putPositive 3 . putPositive 4 putJetBitWord FullRightShift64_8 = putPositive 15 . putPositive 4 . putPositive 3 putJetBitWord FullRightShift64_16 = putPositive 15 . putPositive 5 . putPositive 2 putJetBitWord FullRightShift64_32 = putPositive 15 . putPositive 6 . putPositive 1 putJetBitWord Leftmost8_1 = putPositive 16 . putPositive 1 . putPositive 3 putJetBitWord Leftmost8_2 = putPositive 16 . putPositive 2 . putPositive 2 putJetBitWord Leftmost8_4 = putPositive 16 . putPositive 3 . putPositive 1 putJetBitWord Leftmost16_1 = putPositive 16 . putPositive 1 . putPositive 4 putJetBitWord Leftmost16_2 = putPositive 16 . putPositive 2 . putPositive 3 putJetBitWord Leftmost16_4 = putPositive 16 . putPositive 3 . putPositive 2 putJetBitWord Leftmost16_8 = putPositive 16 . putPositive 4 . putPositive 1 putJetBitWord Leftmost32_1 = putPositive 16 . putPositive 1 . putPositive 5 putJetBitWord Leftmost32_2 = putPositive 16 . putPositive 2 . putPositive 4 putJetBitWord Leftmost32_4 = putPositive 16 . putPositive 3 . putPositive 3 putJetBitWord Leftmost32_8 = putPositive 16 . putPositive 4 . putPositive 2 putJetBitWord Leftmost32_16 = putPositive 16 . putPositive 5 . putPositive 1 putJetBitWord Leftmost64_1 = putPositive 16 . putPositive 1 . putPositive 6 putJetBitWord Leftmost64_2 = putPositive 16 . putPositive 2 . putPositive 5 putJetBitWord Leftmost64_4 = putPositive 16 . putPositive 3 . putPositive 4 putJetBitWord Leftmost64_8 = putPositive 16 . putPositive 4 . putPositive 3 putJetBitWord Leftmost64_16 = putPositive 16 . putPositive 5 . putPositive 2 putJetBitWord Leftmost64_32 = putPositive 16 . putPositive 6 . putPositive 1 putJetBitWord Rightmost8_1 = putPositive 17 . putPositive 1 . putPositive 3 putJetBitWord Rightmost8_2 = putPositive 17 . putPositive 2 . putPositive 2 putJetBitWord Rightmost8_4 = putPositive 17 . putPositive 3 . putPositive 1 putJetBitWord Rightmost16_1 = putPositive 17 . putPositive 1 . putPositive 4 putJetBitWord Rightmost16_2 = putPositive 17 . putPositive 2 . putPositive 3 putJetBitWord Rightmost16_4 = putPositive 17 . putPositive 3 . putPositive 2 putJetBitWord Rightmost16_8 = putPositive 17 . putPositive 4 . putPositive 1 putJetBitWord Rightmost32_1 = putPositive 17 . putPositive 1 . putPositive 5 putJetBitWord Rightmost32_2 = putPositive 17 . putPositive 2 . putPositive 4 putJetBitWord Rightmost32_4 = putPositive 17 . putPositive 3 . putPositive 3 putJetBitWord Rightmost32_8 = putPositive 17 . putPositive 4 . putPositive 2 putJetBitWord Rightmost32_16 = putPositive 17 . putPositive 5 . putPositive 1 putJetBitWord Rightmost64_1 = putPositive 17 . putPositive 1 . putPositive 6 putJetBitWord Rightmost64_2 = putPositive 17 . putPositive 2 . putPositive 5 putJetBitWord Rightmost64_4 = putPositive 17 . putPositive 3 . putPositive 4 putJetBitWord Rightmost64_8 = putPositive 17 . putPositive 4 . putPositive 3 putJetBitWord Rightmost64_16 = putPositive 17 . putPositive 5 . putPositive 2 putJetBitWord Rightmost64_32 = putPositive 17 . putPositive 6 . putPositive 1 putJetBitWord LeftPadLow1_8 = putPositive 18 . putPositive 1 . putPositive 3 putJetBitWord LeftPadLow1_16 = putPositive 18 . putPositive 1 . putPositive 4 putJetBitWord LeftPadLow8_16 = putPositive 18 . putPositive 4 . putPositive 1 putJetBitWord LeftPadLow1_32 = putPositive 18 . putPositive 1 . putPositive 5 putJetBitWord LeftPadLow8_32 = putPositive 18 . putPositive 4 . putPositive 2 putJetBitWord LeftPadLow16_32 = putPositive 18 . putPositive 5 . putPositive 1 putJetBitWord LeftPadLow1_64 = putPositive 18 . putPositive 1 . putPositive 6 putJetBitWord LeftPadLow8_64 = putPositive 18 . putPositive 4 . putPositive 3 putJetBitWord LeftPadLow16_64 = putPositive 18 . putPositive 5 . putPositive 2 putJetBitWord LeftPadLow32_64 = putPositive 18 . putPositive 6 . putPositive 1 putJetBitWord LeftPadHigh1_8 = putPositive 19 . putPositive 1 . putPositive 3 putJetBitWord LeftPadHigh1_16 = putPositive 19 . putPositive 1 . putPositive 4 putJetBitWord LeftPadHigh8_16 = putPositive 19 . putPositive 4 . putPositive 1 putJetBitWord LeftPadHigh1_32 = putPositive 19 . putPositive 1 . putPositive 5 putJetBitWord LeftPadHigh8_32 = putPositive 19 . putPositive 4 . putPositive 2 putJetBitWord LeftPadHigh16_32 = putPositive 19 . putPositive 5 . putPositive 1 putJetBitWord LeftPadHigh1_64 = putPositive 19 . putPositive 1 . putPositive 6 putJetBitWord LeftPadHigh8_64 = putPositive 19 . putPositive 4 . putPositive 3 putJetBitWord LeftPadHigh16_64 = putPositive 19 . putPositive 5 . putPositive 2 putJetBitWord LeftPadHigh32_64 = putPositive 19 . putPositive 6 . putPositive 1 putJetBitWord LeftExtend1_8 = putPositive 20 . putPositive 1 . putPositive 3 putJetBitWord LeftExtend1_16 = putPositive 20 . putPositive 1 . putPositive 4 putJetBitWord LeftExtend8_16 = putPositive 20 . putPositive 4 . putPositive 1 putJetBitWord LeftExtend1_32 = putPositive 20 . putPositive 1 . putPositive 5 putJetBitWord LeftExtend8_32 = putPositive 20 . putPositive 4 . putPositive 2 putJetBitWord LeftExtend16_32 = putPositive 20 . putPositive 5 . putPositive 1 putJetBitWord LeftExtend1_64 = putPositive 20 . putPositive 1 . putPositive 6 putJetBitWord LeftExtend8_64 = putPositive 20 . putPositive 4 . putPositive 3 putJetBitWord LeftExtend16_64 = putPositive 20 . putPositive 5 . putPositive 2 putJetBitWord LeftExtend32_64 = putPositive 20 . putPositive 6 . putPositive 1 putJetBitWord RightPadLow1_8 = putPositive 21 . putPositive 1 . putPositive 3 putJetBitWord RightPadLow1_16 = putPositive 21 . putPositive 1 . putPositive 4 putJetBitWord RightPadLow8_16 = putPositive 21 . putPositive 4 . putPositive 1 putJetBitWord RightPadLow1_32 = putPositive 21 . putPositive 1 . putPositive 5 putJetBitWord RightPadLow8_32 = putPositive 21 . putPositive 4 . putPositive 2 putJetBitWord RightPadLow16_32 = putPositive 21 . putPositive 5 . putPositive 1 putJetBitWord RightPadLow1_64 = putPositive 21 . putPositive 1 . putPositive 6 putJetBitWord RightPadLow8_64 = putPositive 21 . putPositive 4 . putPositive 3 putJetBitWord RightPadLow16_64 = putPositive 21 . putPositive 5 . putPositive 2 putJetBitWord RightPadLow32_64 = putPositive 21 . putPositive 6 . putPositive 1 putJetBitWord RightPadHigh1_8 = putPositive 22 . putPositive 1 . putPositive 3 putJetBitWord RightPadHigh1_16 = putPositive 22 . putPositive 1 . putPositive 4 putJetBitWord RightPadHigh8_16 = putPositive 22 . putPositive 4 . putPositive 1 putJetBitWord RightPadHigh1_32 = putPositive 22 . putPositive 1 . putPositive 5 putJetBitWord RightPadHigh8_32 = putPositive 22 . putPositive 4 . putPositive 2 putJetBitWord RightPadHigh16_32 = putPositive 22 . putPositive 5 . putPositive 1 putJetBitWord RightPadHigh1_64 = putPositive 22 . putPositive 1 . putPositive 6 putJetBitWord RightPadHigh8_64 = putPositive 22 . putPositive 4 . putPositive 3 putJetBitWord RightPadHigh16_64 = putPositive 22 . putPositive 5 . putPositive 2 putJetBitWord RightPadHigh32_64 = putPositive 22 . putPositive 6 . putPositive 1 putJetBitWord RightExtend8_16 = putPositive 23 . putPositive 4 . putPositive 1 putJetBitWord RightExtend8_32 = putPositive 23 . putPositive 4 . putPositive 2 putJetBitWord RightExtend16_32 = putPositive 23 . putPositive 5 . putPositive 1 putJetBitWord RightExtend8_64 = putPositive 23 . putPositive 4 . putPositive 3 putJetBitWord RightExtend16_64 = putPositive 23 . putPositive 5 . putPositive 2 putJetBitWord RightExtend32_64 = putPositive 23 . putPositive 6 . putPositive 1 putJetBitWord LeftShiftWith8 = putPositive 24 . putPositive 3 putJetBitWord LeftShiftWith16 = putPositive 24 . putPositive 4 putJetBitWord LeftShiftWith32 = putPositive 24 . putPositive 5 putJetBitWord LeftShiftWith64 = putPositive 24 . putPositive 6 putJetBitWord RightShiftWith8 = putPositive 25 . putPositive 3 putJetBitWord RightShiftWith16 = putPositive 25 . putPositive 4 putJetBitWord RightShiftWith32 = putPositive 25 . putPositive 5 putJetBitWord RightShiftWith64 = putPositive 25 . putPositive 6 putJetBitWord LeftShift8 = putPositive 26 . putPositive 3 putJetBitWord LeftShift16 = putPositive 26 . putPositive 4 putJetBitWord LeftShift32 = putPositive 26 . putPositive 5 putJetBitWord LeftShift64 = putPositive 26 . putPositive 6 putJetBitWord RightShift8 = putPositive 27 . putPositive 3 putJetBitWord RightShift16 = putPositive 27 . putPositive 4 putJetBitWord RightShift32 = putPositive 27 . putPositive 5 putJetBitWord RightShift64 = putPositive 27 . putPositive 6 putJetBitWord LeftRotate8 = putPositive 28 . putPositive 3 putJetBitWord LeftRotate16 = putPositive 28 . putPositive 4 putJetBitWord LeftRotate32 = putPositive 28 . putPositive 5 putJetBitWord LeftRotate64 = putPositive 28 . putPositive 6 putJetBitWord RightRotate8 = putPositive 29 . putPositive 3 putJetBitWord RightRotate16 = putPositive 29 . putPositive 4 putJetBitWord RightRotate32 = putPositive 29 . putPositive 5 putJetBitWord RightRotate64 = putPositive 29 . putPositive 6 putJetBitArith :: ArithJet a b -> DList Bool putJetBitArith One8 = putPositive 1 . putPositive 3 putJetBitArith One16 = putPositive 1 . putPositive 4 putJetBitArith One32 = putPositive 1 . putPositive 5 putJetBitArith One64 = putPositive 1 . putPositive 6 putJetBitArith FullAdd8 = putPositive 2 . putPositive 3 putJetBitArith FullAdd16 = putPositive 2 . putPositive 4 putJetBitArith FullAdd32 = putPositive 2 . putPositive 5 putJetBitArith FullAdd64 = putPositive 2 . putPositive 6 putJetBitArith Add8 = putPositive 3 . putPositive 3 putJetBitArith Add16 = putPositive 3 . putPositive 4 putJetBitArith Add32 = putPositive 3 . putPositive 5 putJetBitArith Add64 = putPositive 3 . putPositive 6 putJetBitArith FullIncrement8 = putPositive 4 . putPositive 3 putJetBitArith FullIncrement16 = putPositive 4 . putPositive 4 putJetBitArith FullIncrement32 = putPositive 4 . putPositive 5 putJetBitArith FullIncrement64 = putPositive 4 . putPositive 6 putJetBitArith Increment8 = putPositive 5 . putPositive 3 putJetBitArith Increment16 = putPositive 5 . putPositive 4 putJetBitArith Increment32 = putPositive 5 . putPositive 5 putJetBitArith Increment64 = putPositive 5 . putPositive 6 putJetBitArith FullSubtract8 = putPositive 7 . putPositive 3 putJetBitArith FullSubtract16 = putPositive 7 . putPositive 4 putJetBitArith FullSubtract32 = putPositive 7 . putPositive 5 putJetBitArith FullSubtract64 = putPositive 7 . putPositive 6 putJetBitArith Subtract8 = putPositive 8 . putPositive 3 putJetBitArith Subtract16 = putPositive 8 . putPositive 4 putJetBitArith Subtract32 = putPositive 8 . putPositive 5 putJetBitArith Subtract64 = putPositive 8 . putPositive 6 putJetBitArith Negate8 = putPositive 9 . putPositive 3 putJetBitArith Negate16 = putPositive 9 . putPositive 4 putJetBitArith Negate32 = putPositive 9 . putPositive 5 putJetBitArith Negate64 = putPositive 9 . putPositive 6 putJetBitArith FullDecrement8 = putPositive 10 . putPositive 3 putJetBitArith FullDecrement16 = putPositive 10 . putPositive 4 putJetBitArith FullDecrement32 = putPositive 10 . putPositive 5 putJetBitArith FullDecrement64 = putPositive 10 . putPositive 6 putJetBitArith Decrement8 = putPositive 11 . putPositive 3 putJetBitArith Decrement16 = putPositive 11 . putPositive 4 putJetBitArith Decrement32 = putPositive 11 . putPositive 5 putJetBitArith Decrement64 = putPositive 11 . putPositive 6 putJetBitArith FullMultiply8 = putPositive 12 . putPositive 3 putJetBitArith FullMultiply16 = putPositive 12 . putPositive 4 putJetBitArith FullMultiply32 = putPositive 12 . putPositive 5 putJetBitArith FullMultiply64 = putPositive 12 . putPositive 6 putJetBitArith Multiply8 = putPositive 13 . putPositive 3 putJetBitArith Multiply16 = putPositive 13 . putPositive 4 putJetBitArith Multiply32 = putPositive 13 . putPositive 5 putJetBitArith Multiply64 = putPositive 13 . putPositive 6 putJetBitArith IsZero8 = putPositive 14 . putPositive 3 putJetBitArith IsZero16 = putPositive 14 . putPositive 4 putJetBitArith IsZero32 = putPositive 14 . putPositive 5 putJetBitArith IsZero64 = putPositive 14 . putPositive 6 putJetBitArith IsOne8 = putPositive 15 . putPositive 3 putJetBitArith IsOne16 = putPositive 15 . putPositive 4 putJetBitArith IsOne32 = putPositive 15 . putPositive 5 putJetBitArith IsOne64 = putPositive 15 . putPositive 6 putJetBitArith Le8 = putPositive 16 . putPositive 3 putJetBitArith Le16 = putPositive 16 . putPositive 4 putJetBitArith Le32 = putPositive 16 . putPositive 5 putJetBitArith Le64 = putPositive 16 . putPositive 6 putJetBitArith Lt8 = putPositive 17 . putPositive 3 putJetBitArith Lt16 = putPositive 17 . putPositive 4 putJetBitArith Lt32 = putPositive 17 . putPositive 5 putJetBitArith Lt64 = putPositive 17 . putPositive 6 putJetBitArith Min8 = putPositive 18 . putPositive 3 putJetBitArith Min16 = putPositive 18 . putPositive 4 putJetBitArith Min32 = putPositive 18 . putPositive 5 putJetBitArith Min64 = putPositive 18 . putPositive 6 putJetBitArith Max8 = putPositive 19 . putPositive 3 putJetBitArith Max16 = putPositive 19 . putPositive 4 putJetBitArith Max32 = putPositive 19 . putPositive 5 putJetBitArith Max64 = putPositive 19 . putPositive 6 putJetBitArith Median8 = putPositive 20 . putPositive 3 putJetBitArith Median16 = putPositive 20 . putPositive 4 putJetBitArith Median32 = putPositive 20 . putPositive 5 putJetBitArith Median64 = putPositive 20 . putPositive 6 putJetBitArith DivMod128_64 = putPositive 21 . putPositive 6 putJetBitArith DivMod8 = putPositive 22 . putPositive 3 putJetBitArith DivMod16 = putPositive 22 . putPositive 4 putJetBitArith DivMod32 = putPositive 22 . putPositive 5 putJetBitArith DivMod64 = putPositive 22 . putPositive 6 putJetBitArith Divide8 = putPositive 23 . putPositive 3 putJetBitArith Divide16 = putPositive 23 . putPositive 4 putJetBitArith Divide32 = putPositive 23 . putPositive 5 putJetBitArith Divide64 = putPositive 23 . putPositive 6 putJetBitArith Modulo8 = putPositive 24 . putPositive 3 putJetBitArith Modulo16 = putPositive 24 . putPositive 4 putJetBitArith Modulo32 = putPositive 24 . putPositive 5 putJetBitArith Modulo64 = putPositive 24 . putPositive 6 putJetBitArith Divides8 = putPositive 25 . putPositive 3 putJetBitArith Divides16 = putPositive 25 . putPositive 4 putJetBitArith Divides32 = putPositive 25 . putPositive 5 putJetBitArith Divides64 = putPositive 25 . putPositive 6 putJetBitHash :: HashJet a b -> DList Bool putJetBitHash Sha256Block = putPositive 1 . putPositive 1 putJetBitHash Sha256Iv = putPositive 1 . putPositive 2 putJetBitHash Sha256Ctx8Add1 = putPositive 1 . putPositive 3 . putPositive 1 putJetBitHash Sha256Ctx8Add2 = putPositive 1 . putPositive 3 . putPositive 2 putJetBitHash Sha256Ctx8Add4 = putPositive 1 . putPositive 3 . putPositive 3 putJetBitHash Sha256Ctx8Add8 = putPositive 1 . putPositive 3 . putPositive 4 putJetBitHash Sha256Ctx8Add16 = putPositive 1 . putPositive 3 . putPositive 5 putJetBitHash Sha256Ctx8Add32 = putPositive 1 . putPositive 3 . putPositive 6 putJetBitHash Sha256Ctx8Add64 = putPositive 1 . putPositive 3 . putPositive 7 putJetBitHash Sha256Ctx8Add128 = putPositive 1 . putPositive 3 . putPositive 8 putJetBitHash Sha256Ctx8Add256 = putPositive 1 . putPositive 3 . putPositive 9 putJetBitHash Sha256Ctx8Add512 = putPositive 1 . putPositive 3 . putPositive 10 putJetBitHash Sha256Ctx8AddBuffer511 = putPositive 1 . putPositive 4 putJetBitHash Sha256Ctx8Finalize = putPositive 1 . putPositive 5 putJetBitHash Sha256Ctx8Init = putPositive 1 . putPositive 6 putJetBitSecp256k1 :: Secp256k1Jet a b -> DList Bool putJetBitSecp256k1 FeNormalize = putPositive 35 putJetBitSecp256k1 FeNegate = putPositive 36 putJetBitSecp256k1 FeAdd = putPositive 37 putJetBitSecp256k1 FeSquare = putPositive 38 putJetBitSecp256k1 FeMultiply = putPositive 39 putJetBitSecp256k1 FeMultiplyBeta = putPositive 40 putJetBitSecp256k1 FeInvert = putPositive 41 putJetBitSecp256k1 FeSquareRoot = putPositive 42 putJetBitSecp256k1 FeIsZero = putPositive 43 putJetBitSecp256k1 FeIsOdd = putPositive 44 putJetBitSecp256k1 ScalarNormalize = putPositive 23 putJetBitSecp256k1 ScalarNegate = putPositive 24 putJetBitSecp256k1 ScalarAdd = putPositive 25 putJetBitSecp256k1 ScalarSquare = putPositive 26 putJetBitSecp256k1 ScalarMultiply = putPositive 27 putJetBitSecp256k1 ScalarMultiplyLambda = putPositive 28 putJetBitSecp256k1 ScalarInvert = putPositive 29 putJetBitSecp256k1 ScalarIsZero = putPositive 30 putJetBitSecp256k1 GejInfinity = putPositive 7 putJetBitSecp256k1 GejNormalize = putPositive 8 putJetBitSecp256k1 GejNegate = putPositive 9 putJetBitSecp256k1 GeNegate = putPositive 10 putJetBitSecp256k1 GejDouble = putPositive 11 putJetBitSecp256k1 GejAdd = putPositive 12 putJetBitSecp256k1 GejGeAddEx = putPositive 13 putJetBitSecp256k1 GejGeAdd = putPositive 14 putJetBitSecp256k1 GejRescale = putPositive 15 putJetBitSecp256k1 GejIsInfinity = putPositive 16 putJetBitSecp256k1 GejEquiv = putPositive 17 putJetBitSecp256k1 GejGeEquiv = putPositive 18 putJetBitSecp256k1 GejXEquiv = putPositive 19 putJetBitSecp256k1 GejYIsOdd = putPositive 20 putJetBitSecp256k1 GejIsOnCurve = putPositive 21 putJetBitSecp256k1 GeIsOnCurve = putPositive 22 putJetBitSecp256k1 Generate = putPositive 6 putJetBitSecp256k1 Scale = putPositive 5 putJetBitSecp256k1 LinearCombination1 = putPositive 4 . putPositive 1 putJetBitSecp256k1 LinearVerify1 = putPositive 3 . putPositive 1 putJetBitSecp256k1 PointVerify1 = putPositive 1 . putPositive 1 putJetBitSecp256k1 Decompress = putPositive 2 putJetBitSecp256k1 HashToCurve = putPositive 46 putJetBitSecp256k1 Swu = putPositive 47 putJetBitSignature :: SignatureJet a b -> DList Bool putJetBitSignature CheckSigVerify = putPositive 1 putJetBitSignature Bip0340Verify = putPositive 2 putJetBitBitcoin :: BitcoinJet a b -> DList Bool putJetBitBitcoin ParseLock = putPositive 1 putJetBitBitcoin ParseSequence = putPositive 2 putJetBitBitcoin TapdataInit = putPositive 3 -- | A 'Map.Map' from the identity hashes of the "core" jet specification to their corresponding token. -- This can be used to help instantiate the 'Simplicity.JetType.matcher' method. coreJetMap :: Map.Map Hash256 (SomeArrow CoreJet) coreJetMap = Map.fromList . fmap mkAssoc $ toList coreCatalogue where mkAssoc :: SomeArrow CoreJet -> (Hash256, (SomeArrow CoreJet)) mkAssoc wrapped@(SomeArrow jt) = (identityHash (specification jt), wrapped) -- | Performs a lookup from `coreJetMap` from an `IdentityRoot`. -- This operation preserves the Simplicity types. coreJetLookup :: (TyC a, TyC b) => IdentityRoot a b -> Maybe (CoreJet a b) coreJetLookup ir = do SomeArrow jt <- Map.lookup (identityHash ir) coreJetMap let (ira, irb) = reifyArrow ir let (jta, jtb) = reifyArrow jt case (equalTyReflect ira jta, equalTyReflect irb jtb) of (Just Refl, Just Refl) -> return jt otherwise -> error "Simplicity.CoreJets.coreJetLookup: type match error" -- | The contents of the serialized content of a constant word jet. -- It consists of a "depth" indicating what word type the word jet produces, -- and a numeric value that the jet outputs. -- This numeric value fits with the size of the word type. data ConstWordContent b = ConstWordContent (Word b) Integer instance Eq (ConstWordContent b) where ConstWordContent _ x == ConstWordContent _ y = x == y instance Show (ConstWordContent b) where show (ConstWordContent w v) = show v ++ ": 2^" ++ show (wordSize w) -- | @Exists b. (Ty b) *> ConstWordContent b@ data SomeConstWordContent = forall b. (TyC b) => SomeConstWordContent (ConstWordContent b) instance Show SomeConstWordContent where show (SomeConstWordContent cwc) = show cwc -- | Returns the specification of a constant word jet corresponding to the contents of a given 'ConstWordContent'. specificationConstWord :: (Core term, TyC b) => ConstWordContent b -> term () b specificationConstWord (ConstWordContent w v) = scribe (toWord w v) -- | Returns an implementation of a constant word jet corresponding to the contents of a given 'ConstWordContent'. implementationConstWord :: ConstWordContent b -> () -> Maybe b implementationConstWord (ConstWordContent w v) _ = Just (toWord w v) -- | Parses the depth and value of a constant word jet and returns 'SomeConstWordContent'. getConstWordBit :: forall m. (Monad m) => m Void -> m Bool -> m SomeConstWordContent getConstWordBit abort next = do depth <- (\x -> x - 1) <$> getPositive next unDepth depth (fmap SomeConstWordContent . getValue) where unDepth :: Integer -> (forall b. TyC b => Word b -> o) -> o unDepth 0 k = k SingleV unDepth n k = unDepth (n-1) (k . DoubleV) getValue :: TyC b => Word b -> m (ConstWordContent b) getValue w@SingleV = do b <- next return $ ConstWordContent w (if b then 1 else 0) getValue ww@(DoubleV w) = do (ConstWordContent _ v1) <- getValue w (ConstWordContent _ v2) <- getValue w return (ConstWordContent ww (shift v1 (wordSize w) + v2)) -- | Given a 'ConstWordContent' of some type, output the serialization of that depth and value. putConstWordBit :: ConstWordContent b -> DList Bool putConstWordBit cwc@(ConstWordContent w v) = putPositive (1 + depth w) . (putConstWordValueBit cwc ++) where depth :: Word b -> Integer depth (SingleV) = 0 depth (DoubleV w) = 1 + depth w -- | Given a 'ConstWordContent' of some type, output the serialization of that value. putConstWordValueBit :: ConstWordContent b -> [Bool] putConstWordValueBit (ConstWordContent w v) | 0 <= v && v < 2^(wordSize w) = List.reverse . List.take (wordSize w) $ List.unfoldr (\i -> Just (odd i, i `div` 2)) v -- | An Assert instance for 'fastCoreEval'. data FastCoreEval a b = FastCoreEval { fastCoreEvalSem :: Kleisli Maybe a b , fastCoreEvalMatcher :: IdentityRoot a b } -- | 'fastCoreEval' optimizes Simplicity with assertions evaluation using jets. -- -- @ -- 'fastCoreEval' t === 'sem' t -- @ fastCoreEval = runKleisli . fastCoreEvalSem withJets :: (TyC a, TyC b) => FastCoreEval a b -> FastCoreEval a b withJets ~(FastCoreEval _ ir) | Just cj <- coreJetLookup ir = FastCoreEval { fastCoreEvalSem = Kleisli $ implementation cj , fastCoreEvalMatcher = ir } withJets fe | otherwise = fe mkLeaf sComb jmComb = withJets $ FastCoreEval { fastCoreEvalSem = sComb , fastCoreEvalMatcher = jmComb } mkUnary sComb jmComb t = withJets $ FastCoreEval { fastCoreEvalSem = sComb (fastCoreEvalSem t) , fastCoreEvalMatcher = jmComb (fastCoreEvalMatcher t) } mkBinary sComb jmComb s t = withJets $ FastCoreEval { fastCoreEvalSem = sComb (fastCoreEvalSem s) (fastCoreEvalSem t) , fastCoreEvalMatcher = jmComb (fastCoreEvalMatcher s) (fastCoreEvalMatcher t) } instance Core FastCoreEval where iden = mkLeaf iden iden comp = mkBinary comp comp unit = mkLeaf unit unit injl = mkUnary injl injl injr = mkUnary injr injr match = mkBinary match match pair = mkBinary pair pair take = mkUnary take take drop = mkUnary drop drop instance Assert FastCoreEval where assertl s h = mkUnary (flip assertl h) (flip assertl h) s assertr h t = mkUnary (assertr h) (assertr h) t fail b = mkLeaf (fail b) (fail b) median x y z = List.sort [x,y,z] !! 1 ================================================ FILE: Haskell/Core/Simplicity/Delegator/Impl.hs ================================================ -- | This internal module provides a Deleator instance that perform a semantic conversion of the 'disconnect' combinator. -- It should only be used for semantic operations, including BitMachine translation and static analysis. module Simplicity.Delegator.Impl ( Delegator(Delegator), runDelegator, delegatorRoot ) where import Prelude hiding (drop, take, fail) import Simplicity.Digest import Simplicity.MerkleRoot import Simplicity.Programs.Generic import Simplicity.Term.Core import Simplicity.Ty.Word -- Note: 'Delegator' differs from 'Simplicity.Tensor.Product CommitmentRoot' due to a different 'Delegate' instance. -- | @'Delegator' p@ is a helper data type for creating a 'Delegate' instance. -- @p@ is typically at least an instance of 'Core'. data Delegator p a b = Delegator { delegatorRoot :: CommitmentRoot a b , runDelegator :: p a b -- ^ Extract the @p a b@ arrow from the 'Delegator' } instance Core p => Core (Delegator p) where iden = Delegator iden iden comp ~(Delegator rs fs) ~(Delegator rt ft) = Delegator (comp rs rt) (comp fs ft) unit = Delegator unit unit injl ~(Delegator rt ft) = Delegator (injl rt) (injl ft) injr ~(Delegator rt ft) = Delegator (injr rt) (injr ft) match ~(Delegator rs fs) ~(Delegator rt ft) = Delegator (match rs rt) (match fs ft) pair ~(Delegator rs fs) ~(Delegator rt ft) = Delegator (pair rs rt) (pair fs ft) take ~(Delegator rt ft) = Delegator (take rt) (take ft) drop ~(Delegator rt ft) = Delegator (drop rt) (drop ft) instance Assert p => Assert (Delegator p) where assertl ~(Delegator rs fs) t = Delegator (assertl rs t) (assertl fs t) assertr s ~(Delegator rt ft) = Delegator (assertr s rt) (assertr s ft) fail b = Delegator (fail b) (fail b) instance Witness p => Witness (Delegator p) where witness b = Delegator (witness b) (witness b) instance Core p => Delegate (Delegator p) where disconnect ~(Delegator rs fs) ~(Delegator rt ft) = Delegator (disconnect rs rt) f where root256 = toWord256 . integerHash256 $ commitmentRoot rt f = scribe root256 &&& iden >>> fs >>> take iden &&& drop ft ================================================ FILE: Haskell/Core/Simplicity/Delegator.hs ================================================ -- | This module provides the functional semantics of Simplicity with 'Delegate'. module Simplicity.Delegator ( Delegator, runDelegatorCore, runDelegatorKleisli, delegatorRoot ) where import Control.Arrow (Kleisli, runKleisli) import Simplicity.Delegator.Impl -- | @ -- runDelegatorCore :: (forall term. (Core term, Delegate term, Witness term) => term a b) -> a -> b -- @ -- -- Returns the semantics of a Simplicity expression with 'Delegate'. runDelegatorCore :: Delegator (->) a b -> a -> b runDelegatorCore = runDelegator -- | @ -- runDelegatorKleisli :: Fail.MonadFail m => (forall term. (Assert term, Delegate term, Witness term) => term a b) -> a -> m b -- runDelegatorKleisli :: Monad m => (forall term. (Core term, Delegate term, Witness term) => term a b) -> a -> m b -- @ -- -- Returns the semantics of a Simplicity expression with 'Delegate' and 'Assert'. runDelegatorKleisli :: Delegator (Kleisli m) a b -> a -> m b runDelegatorKleisli = runKleisli . runDelegator ================================================ FILE: Haskell/Core/Simplicity/Digest/Pure/SHA.hs ================================================ {- This is a copy of Galoi's Data.Digets.Pure.SHA module. We copy it here in order to export some internal functions. This is needed to allow for "free-start" SHA-256, which violates normal SHA-256 encapsulation rules. This file is subject to their licence below. -} {- Copyright (c) 2008, Galois, Inc. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the Galois, Inc. nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -} {-# LANGUAGE BangPatterns, CPP, FlexibleInstances #-} -- |Pure implementations of the SHA suite of hash functions. The implementation -- is basically an unoptimized translation of FIPS 180-2 into Haskell. If you're -- looking for performance, you probably won't find it here. module Simplicity.Digest.Pure.SHA ( -- * 'Digest' and related functions Digest , SHA1State, SHA256State, SHA512State , showDigest , integerDigest , bytestringDigest -- * Calculating hashes , sha1 , sha224 , sha256 , sha384 , sha512 , sha1Incremental , completeSha1Incremental , sha224Incremental , completeSha224Incremental , sha256Incremental , completeSha256Incremental , sha384Incremental , completeSha384Incremental , sha512Incremental , completeSha512Incremental -- * Calculating message authentication codes (MACs) , hmacSha1 , hmacSha224 , hmacSha256 , hmacSha384 , hmacSha512 -- * Internal routines included for testing , toBigEndianSBS, fromBigEndianSBS , calc_k , padSHA1, padSHA512 , padSHA1Chunks, padSHA512Chunks -- * Internal routines included for freestart , runSHAIncremental, processSHA256Block ) where import Data.Binary import Data.Binary.Get import Data.Binary.Put import Data.Bits import Data.ByteString.Lazy(ByteString) import qualified Data.ByteString.Lazy as BS import qualified Data.ByteString as SBS import Data.Char (intToDigit) import Data.List (foldl') -- | An abstract datatype for digests. newtype Digest t = Digest ByteString deriving (Eq,Ord) instance Show (Digest t) where show = showDigest instance Binary (Digest SHA1State) where get = Digest `fmap` getLazyByteString 20 put (Digest bs) = putLazyByteString bs instance Binary (Digest SHA256State) where get = Digest `fmap` getLazyByteString 32 put (Digest bs) = putLazyByteString bs instance Binary (Digest SHA512State) where get = Digest `fmap` getLazyByteString 64 put (Digest bs) = putLazyByteString bs -- -------------------------------------------------------------------------- -- -- State Definitions and Initial States -- -- -------------------------------------------------------------------------- data SHA1State = SHA1S !Word32 !Word32 !Word32 !Word32 !Word32 initialSHA1State :: SHA1State initialSHA1State = SHA1S 0x67452301 0xefcdab89 0x98badcfe 0x10325476 0xc3d2e1f0 data SHA256State = SHA256S !Word32 !Word32 !Word32 !Word32 !Word32 !Word32 !Word32 !Word32 initialSHA224State :: SHA256State initialSHA224State = SHA256S 0xc1059ed8 0x367cd507 0x3070dd17 0xf70e5939 0xffc00b31 0x68581511 0x64f98fa7 0xbefa4fa4 initialSHA256State :: SHA256State initialSHA256State = SHA256S 0x6a09e667 0xbb67ae85 0x3c6ef372 0xa54ff53a 0x510e527f 0x9b05688c 0x1f83d9ab 0x5be0cd19 data SHA512State = SHA512S !Word64 !Word64 !Word64 !Word64 !Word64 !Word64 !Word64 !Word64 initialSHA384State :: SHA512State initialSHA384State = SHA512S 0xcbbb9d5dc1059ed8 0x629a292a367cd507 0x9159015a3070dd17 0x152fecd8f70e5939 0x67332667ffc00b31 0x8eb44a8768581511 0xdb0c2e0d64f98fa7 0x47b5481dbefa4fa4 initialSHA512State :: SHA512State initialSHA512State = SHA512S 0x6a09e667f3bcc908 0xbb67ae8584caa73b 0x3c6ef372fe94f82b 0xa54ff53a5f1d36f1 0x510e527fade682d1 0x9b05688c2b3e6c1f 0x1f83d9abfb41bd6b 0x5be0cd19137e2179 -- -------------------------------------------------------------------------- -- -- Synthesize of states to and from ByteStrings -- -- -------------------------------------------------------------------------- synthesizeSHA1 :: SHA1State -> Put synthesizeSHA1 (SHA1S a b c d e) = do putWord32be a putWord32be b putWord32be c putWord32be d putWord32be e getSHA1 :: Get SHA1State getSHA1 = do a <- getWord32be b <- getWord32be c <- getWord32be d <- getWord32be e <- getWord32be return $! SHA1S a b c d e synthesizeSHA224 :: SHA256State -> Put synthesizeSHA224 (SHA256S a b c d e f g _) = do putWord32be a putWord32be b putWord32be c putWord32be d putWord32be e putWord32be f putWord32be g synthesizeSHA256 :: SHA256State -> Put synthesizeSHA256 (SHA256S a b c d e f g h) = do putWord32be a putWord32be b putWord32be c putWord32be d putWord32be e putWord32be f putWord32be g putWord32be h getSHA256 :: Get SHA256State getSHA256 = do a <- getWord32be b <- getWord32be c <- getWord32be d <- getWord32be e <- getWord32be f <- getWord32be g <- getWord32be h <- getWord32be return $! SHA256S a b c d e f g h synthesizeSHA384 :: SHA512State -> Put synthesizeSHA384 (SHA512S a b c d e f _ _) = do putWord64be a putWord64be b putWord64be c putWord64be d putWord64be e putWord64be f synthesizeSHA512 :: SHA512State -> Put synthesizeSHA512 (SHA512S a b c d e f g h) = do putWord64be a putWord64be b putWord64be c putWord64be d putWord64be e putWord64be f putWord64be g putWord64be h getSHA512 :: Get SHA512State getSHA512 = do a <- getWord64be b <- getWord64be c <- getWord64be d <- getWord64be e <- getWord64be f <- getWord64be g <- getWord64be h <- getWord64be return $! SHA512S a b c d e f g h instance Binary SHA1State where put = synthesizeSHA1 get = getSHA1 instance Binary SHA256State where put = synthesizeSHA256 get = getSHA256 instance Binary SHA512State where put = synthesizeSHA512 get = getSHA512 -- -------------------------------------------------------------------------- -- -- Padding -- -- -------------------------------------------------------------------------- padSHA1 :: ByteString -> ByteString padSHA1 = generic_pad 448 512 64 padSHA1Chunks :: Int -> [SBS.ByteString] padSHA1Chunks = generic_pad_chunks 448 512 64 padSHA512 :: ByteString -> ByteString padSHA512 = generic_pad 896 1024 128 padSHA512Chunks :: Int -> [SBS.ByteString] padSHA512Chunks = generic_pad_chunks 896 1024 128 generic_pad :: Word64 -> Word64 -> Int -> ByteString -> ByteString generic_pad a b lSize bs = BS.fromChunks $! go 0 chunks where chunks = BS.toChunks bs -- Generates the padded ByteString at the same time it computes the length -- of input. If the length is computed before the computation of the hash, it -- will break the lazy evaluation of the input and no longer run in constant -- memory space. go !len [] = generic_pad_chunks a b lSize len go !len (c:cs) = c : go (len + SBS.length c) cs generic_pad_chunks :: Word64 -> Word64 -> Int -> Int -> [SBS.ByteString] generic_pad_chunks a b lSize len = let lenBits = fromIntegral $ len * 8 k = calc_k a b lenBits -- INVARIANT: k is necessarily > 0, and (k + 1) is a multiple of 8. kBytes = (k + 1) `div` 8 nZeroBytes = fromIntegral $! kBytes - 1 padLength = toBigEndianSBS lSize lenBits in [SBS.singleton 0x80, SBS.replicate nZeroBytes 0, padLength] -- Given a, b, and l, calculate the smallest k such that (l + 1 + k) mod b = a. calc_k :: Word64 -> Word64 -> Word64 -> Word64 calc_k a b l = if r <= -1 then fromIntegral r + b else fromIntegral r where r = toInteger a - toInteger l `mod` toInteger b - 1 toBigEndianSBS :: (Integral a, Bits a) => Int -> a -> SBS.ByteString toBigEndianSBS s val = SBS.pack $ map getBits [s - 8, s - 16 .. 0] where getBits x = fromIntegral $ (val `shiftR` x) .&. 0xFF fromBigEndianSBS :: (Integral a, Bits a) => SBS.ByteString -> a fromBigEndianSBS = SBS.foldl (\ acc x -> (acc `shiftL` 8) + fromIntegral x) 0 -- -------------------------------------------------------------------------- -- -- SHA Functions -- -- -------------------------------------------------------------------------- {-# SPECIALIZE ch :: Word32 -> Word32 -> Word32 -> Word32 #-} {-# SPECIALIZE ch :: Word64 -> Word64 -> Word64 -> Word64 #-} ch :: Bits a => a -> a -> a -> a ch x y z = (x .&. y) `xor` (complement x .&. z) {-# SPECIALIZE maj :: Word32 -> Word32 -> Word32 -> Word32 #-} {-# SPECIALIZE maj :: Word64 -> Word64 -> Word64 -> Word64 #-} maj :: Bits a => a -> a -> a -> a maj x y z = (x .&. (y .|. z)) .|. (y .&. z) -- note: -- the original functions is (x & y) ^ (x & z) ^ (y & z) -- if you fire off truth tables, this is equivalent to -- (x & y) | (x & z) | (y & z) -- which you can the use distribution on: -- (x & (y | z)) | (y & z) -- which saves us one operation. bsig256_0 :: Word32 -> Word32 bsig256_0 x = rotateR x 2 `xor` rotateR x 13 `xor` rotateR x 22 bsig256_1 :: Word32 -> Word32 bsig256_1 x = rotateR x 6 `xor` rotateR x 11 `xor` rotateR x 25 lsig256_0 :: Word32 -> Word32 lsig256_0 x = rotateR x 7 `xor` rotateR x 18 `xor` shiftR x 3 lsig256_1 :: Word32 -> Word32 lsig256_1 x = rotateR x 17 `xor` rotateR x 19 `xor` shiftR x 10 bsig512_0 :: Word64 -> Word64 bsig512_0 x = rotateR x 28 `xor` rotateR x 34 `xor` rotateR x 39 bsig512_1 :: Word64 -> Word64 bsig512_1 x = rotateR x 14 `xor` rotateR x 18 `xor` rotateR x 41 lsig512_0 :: Word64 -> Word64 lsig512_0 x = rotateR x 1 `xor` rotateR x 8 `xor` shiftR x 7 lsig512_1 :: Word64 -> Word64 lsig512_1 x = rotateR x 19 `xor` rotateR x 61 `xor` shiftR x 6 -- -------------------------------------------------------------------------- -- -- Message Schedules -- -- -------------------------------------------------------------------------- data SHA1Sched = SHA1Sched !Word32 !Word32 !Word32 !Word32 !Word32 -- 0 - 4 !Word32 !Word32 !Word32 !Word32 !Word32 -- 5 - 9 !Word32 !Word32 !Word32 !Word32 !Word32 -- 10 - 14 !Word32 !Word32 !Word32 !Word32 !Word32 -- 15 - 19 !Word32 !Word32 !Word32 !Word32 !Word32 -- 20 - 24 !Word32 !Word32 !Word32 !Word32 !Word32 -- 25 - 29 !Word32 !Word32 !Word32 !Word32 !Word32 -- 30 - 34 !Word32 !Word32 !Word32 !Word32 !Word32 -- 35 - 39 !Word32 !Word32 !Word32 !Word32 !Word32 -- 40 - 44 !Word32 !Word32 !Word32 !Word32 !Word32 -- 45 - 49 !Word32 !Word32 !Word32 !Word32 !Word32 -- 50 - 54 !Word32 !Word32 !Word32 !Word32 !Word32 -- 55 - 59 !Word32 !Word32 !Word32 !Word32 !Word32 -- 60 - 64 !Word32 !Word32 !Word32 !Word32 !Word32 -- 65 - 69 !Word32 !Word32 !Word32 !Word32 !Word32 -- 70 - 74 !Word32 !Word32 !Word32 !Word32 !Word32 -- 75 - 79 getSHA1Sched :: Get SHA1Sched getSHA1Sched = do w00 <- getWord32be w01 <- getWord32be w02 <- getWord32be w03 <- getWord32be w04 <- getWord32be w05 <- getWord32be w06 <- getWord32be w07 <- getWord32be w08 <- getWord32be w09 <- getWord32be w10 <- getWord32be w11 <- getWord32be w12 <- getWord32be w13 <- getWord32be w14 <- getWord32be w15 <- getWord32be let w16 = rotateL (w13 `xor` w08 `xor` w02 `xor` w00) 1 w17 = rotateL (w14 `xor` w09 `xor` w03 `xor` w01) 1 w18 = rotateL (w15 `xor` w10 `xor` w04 `xor` w02) 1 w19 = rotateL (w16 `xor` w11 `xor` w05 `xor` w03) 1 w20 = rotateL (w17 `xor` w12 `xor` w06 `xor` w04) 1 w21 = rotateL (w18 `xor` w13 `xor` w07 `xor` w05) 1 w22 = rotateL (w19 `xor` w14 `xor` w08 `xor` w06) 1 w23 = rotateL (w20 `xor` w15 `xor` w09 `xor` w07) 1 w24 = rotateL (w21 `xor` w16 `xor` w10 `xor` w08) 1 w25 = rotateL (w22 `xor` w17 `xor` w11 `xor` w09) 1 w26 = rotateL (w23 `xor` w18 `xor` w12 `xor` w10) 1 w27 = rotateL (w24 `xor` w19 `xor` w13 `xor` w11) 1 w28 = rotateL (w25 `xor` w20 `xor` w14 `xor` w12) 1 w29 = rotateL (w26 `xor` w21 `xor` w15 `xor` w13) 1 w30 = rotateL (w27 `xor` w22 `xor` w16 `xor` w14) 1 w31 = rotateL (w28 `xor` w23 `xor` w17 `xor` w15) 1 w32 = rotateL (w29 `xor` w24 `xor` w18 `xor` w16) 1 w33 = rotateL (w30 `xor` w25 `xor` w19 `xor` w17) 1 w34 = rotateL (w31 `xor` w26 `xor` w20 `xor` w18) 1 w35 = rotateL (w32 `xor` w27 `xor` w21 `xor` w19) 1 w36 = rotateL (w33 `xor` w28 `xor` w22 `xor` w20) 1 w37 = rotateL (w34 `xor` w29 `xor` w23 `xor` w21) 1 w38 = rotateL (w35 `xor` w30 `xor` w24 `xor` w22) 1 w39 = rotateL (w36 `xor` w31 `xor` w25 `xor` w23) 1 w40 = rotateL (w37 `xor` w32 `xor` w26 `xor` w24) 1 w41 = rotateL (w38 `xor` w33 `xor` w27 `xor` w25) 1 w42 = rotateL (w39 `xor` w34 `xor` w28 `xor` w26) 1 w43 = rotateL (w40 `xor` w35 `xor` w29 `xor` w27) 1 w44 = rotateL (w41 `xor` w36 `xor` w30 `xor` w28) 1 w45 = rotateL (w42 `xor` w37 `xor` w31 `xor` w29) 1 w46 = rotateL (w43 `xor` w38 `xor` w32 `xor` w30) 1 w47 = rotateL (w44 `xor` w39 `xor` w33 `xor` w31) 1 w48 = rotateL (w45 `xor` w40 `xor` w34 `xor` w32) 1 w49 = rotateL (w46 `xor` w41 `xor` w35 `xor` w33) 1 w50 = rotateL (w47 `xor` w42 `xor` w36 `xor` w34) 1 w51 = rotateL (w48 `xor` w43 `xor` w37 `xor` w35) 1 w52 = rotateL (w49 `xor` w44 `xor` w38 `xor` w36) 1 w53 = rotateL (w50 `xor` w45 `xor` w39 `xor` w37) 1 w54 = rotateL (w51 `xor` w46 `xor` w40 `xor` w38) 1 w55 = rotateL (w52 `xor` w47 `xor` w41 `xor` w39) 1 w56 = rotateL (w53 `xor` w48 `xor` w42 `xor` w40) 1 w57 = rotateL (w54 `xor` w49 `xor` w43 `xor` w41) 1 w58 = rotateL (w55 `xor` w50 `xor` w44 `xor` w42) 1 w59 = rotateL (w56 `xor` w51 `xor` w45 `xor` w43) 1 w60 = rotateL (w57 `xor` w52 `xor` w46 `xor` w44) 1 w61 = rotateL (w58 `xor` w53 `xor` w47 `xor` w45) 1 w62 = rotateL (w59 `xor` w54 `xor` w48 `xor` w46) 1 w63 = rotateL (w60 `xor` w55 `xor` w49 `xor` w47) 1 w64 = rotateL (w61 `xor` w56 `xor` w50 `xor` w48) 1 w65 = rotateL (w62 `xor` w57 `xor` w51 `xor` w49) 1 w66 = rotateL (w63 `xor` w58 `xor` w52 `xor` w50) 1 w67 = rotateL (w64 `xor` w59 `xor` w53 `xor` w51) 1 w68 = rotateL (w65 `xor` w60 `xor` w54 `xor` w52) 1 w69 = rotateL (w66 `xor` w61 `xor` w55 `xor` w53) 1 w70 = rotateL (w67 `xor` w62 `xor` w56 `xor` w54) 1 w71 = rotateL (w68 `xor` w63 `xor` w57 `xor` w55) 1 w72 = rotateL (w69 `xor` w64 `xor` w58 `xor` w56) 1 w73 = rotateL (w70 `xor` w65 `xor` w59 `xor` w57) 1 w74 = rotateL (w71 `xor` w66 `xor` w60 `xor` w58) 1 w75 = rotateL (w72 `xor` w67 `xor` w61 `xor` w59) 1 w76 = rotateL (w73 `xor` w68 `xor` w62 `xor` w60) 1 w77 = rotateL (w74 `xor` w69 `xor` w63 `xor` w61) 1 w78 = rotateL (w75 `xor` w70 `xor` w64 `xor` w62) 1 w79 = rotateL (w76 `xor` w71 `xor` w65 `xor` w63) 1 return $! SHA1Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59 w60 w61 w62 w63 w64 w65 w66 w67 w68 w69 w70 w71 w72 w73 w74 w75 w76 w77 w78 w79 data SHA256Sched = SHA256Sched !Word32 !Word32 !Word32 !Word32 !Word32 -- 00-04 !Word32 !Word32 !Word32 !Word32 !Word32 -- 05-09 !Word32 !Word32 !Word32 !Word32 !Word32 -- 10-04 !Word32 !Word32 !Word32 !Word32 !Word32 -- 15-09 !Word32 !Word32 !Word32 !Word32 !Word32 -- 20-04 !Word32 !Word32 !Word32 !Word32 !Word32 -- 25-09 !Word32 !Word32 !Word32 !Word32 !Word32 -- 30-04 !Word32 !Word32 !Word32 !Word32 !Word32 -- 35-09 !Word32 !Word32 !Word32 !Word32 !Word32 -- 40-04 !Word32 !Word32 !Word32 !Word32 !Word32 -- 45-09 !Word32 !Word32 !Word32 !Word32 !Word32 -- 50-04 !Word32 !Word32 !Word32 !Word32 !Word32 -- 55-09 !Word32 !Word32 !Word32 !Word32 -- 60-63 getSHA256Sched :: Get SHA256Sched getSHA256Sched = do w00 <- getWord32be w01 <- getWord32be w02 <- getWord32be w03 <- getWord32be w04 <- getWord32be w05 <- getWord32be w06 <- getWord32be w07 <- getWord32be w08 <- getWord32be w09 <- getWord32be w10 <- getWord32be w11 <- getWord32be w12 <- getWord32be w13 <- getWord32be w14 <- getWord32be w15 <- getWord32be let w16 = lsig256_1 w14 + w09 + lsig256_0 w01 + w00 w17 = lsig256_1 w15 + w10 + lsig256_0 w02 + w01 w18 = lsig256_1 w16 + w11 + lsig256_0 w03 + w02 w19 = lsig256_1 w17 + w12 + lsig256_0 w04 + w03 w20 = lsig256_1 w18 + w13 + lsig256_0 w05 + w04 w21 = lsig256_1 w19 + w14 + lsig256_0 w06 + w05 w22 = lsig256_1 w20 + w15 + lsig256_0 w07 + w06 w23 = lsig256_1 w21 + w16 + lsig256_0 w08 + w07 w24 = lsig256_1 w22 + w17 + lsig256_0 w09 + w08 w25 = lsig256_1 w23 + w18 + lsig256_0 w10 + w09 w26 = lsig256_1 w24 + w19 + lsig256_0 w11 + w10 w27 = lsig256_1 w25 + w20 + lsig256_0 w12 + w11 w28 = lsig256_1 w26 + w21 + lsig256_0 w13 + w12 w29 = lsig256_1 w27 + w22 + lsig256_0 w14 + w13 w30 = lsig256_1 w28 + w23 + lsig256_0 w15 + w14 w31 = lsig256_1 w29 + w24 + lsig256_0 w16 + w15 w32 = lsig256_1 w30 + w25 + lsig256_0 w17 + w16 w33 = lsig256_1 w31 + w26 + lsig256_0 w18 + w17 w34 = lsig256_1 w32 + w27 + lsig256_0 w19 + w18 w35 = lsig256_1 w33 + w28 + lsig256_0 w20 + w19 w36 = lsig256_1 w34 + w29 + lsig256_0 w21 + w20 w37 = lsig256_1 w35 + w30 + lsig256_0 w22 + w21 w38 = lsig256_1 w36 + w31 + lsig256_0 w23 + w22 w39 = lsig256_1 w37 + w32 + lsig256_0 w24 + w23 w40 = lsig256_1 w38 + w33 + lsig256_0 w25 + w24 w41 = lsig256_1 w39 + w34 + lsig256_0 w26 + w25 w42 = lsig256_1 w40 + w35 + lsig256_0 w27 + w26 w43 = lsig256_1 w41 + w36 + lsig256_0 w28 + w27 w44 = lsig256_1 w42 + w37 + lsig256_0 w29 + w28 w45 = lsig256_1 w43 + w38 + lsig256_0 w30 + w29 w46 = lsig256_1 w44 + w39 + lsig256_0 w31 + w30 w47 = lsig256_1 w45 + w40 + lsig256_0 w32 + w31 w48 = lsig256_1 w46 + w41 + lsig256_0 w33 + w32 w49 = lsig256_1 w47 + w42 + lsig256_0 w34 + w33 w50 = lsig256_1 w48 + w43 + lsig256_0 w35 + w34 w51 = lsig256_1 w49 + w44 + lsig256_0 w36 + w35 w52 = lsig256_1 w50 + w45 + lsig256_0 w37 + w36 w53 = lsig256_1 w51 + w46 + lsig256_0 w38 + w37 w54 = lsig256_1 w52 + w47 + lsig256_0 w39 + w38 w55 = lsig256_1 w53 + w48 + lsig256_0 w40 + w39 w56 = lsig256_1 w54 + w49 + lsig256_0 w41 + w40 w57 = lsig256_1 w55 + w50 + lsig256_0 w42 + w41 w58 = lsig256_1 w56 + w51 + lsig256_0 w43 + w42 w59 = lsig256_1 w57 + w52 + lsig256_0 w44 + w43 w60 = lsig256_1 w58 + w53 + lsig256_0 w45 + w44 w61 = lsig256_1 w59 + w54 + lsig256_0 w46 + w45 w62 = lsig256_1 w60 + w55 + lsig256_0 w47 + w46 w63 = lsig256_1 w61 + w56 + lsig256_0 w48 + w47 return $! SHA256Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59 w60 w61 w62 w63 data SHA512Sched = SHA512Sched !Word64 !Word64 !Word64 !Word64 !Word64 -- 0- 4 !Word64 !Word64 !Word64 !Word64 !Word64 -- 5- 9 !Word64 !Word64 !Word64 !Word64 !Word64 -- 10-14 !Word64 !Word64 !Word64 !Word64 !Word64 -- 15-19 !Word64 !Word64 !Word64 !Word64 !Word64 -- 20-24 !Word64 !Word64 !Word64 !Word64 !Word64 -- 25-29 !Word64 !Word64 !Word64 !Word64 !Word64 -- 30-34 !Word64 !Word64 !Word64 !Word64 !Word64 -- 35-39 !Word64 !Word64 !Word64 !Word64 !Word64 -- 40-44 !Word64 !Word64 !Word64 !Word64 !Word64 -- 45-49 !Word64 !Word64 !Word64 !Word64 !Word64 -- 50-54 !Word64 !Word64 !Word64 !Word64 !Word64 -- 55-59 !Word64 !Word64 !Word64 !Word64 !Word64 -- 60-64 !Word64 !Word64 !Word64 !Word64 !Word64 -- 65-69 !Word64 !Word64 !Word64 !Word64 !Word64 -- 70-74 !Word64 !Word64 !Word64 !Word64 !Word64 -- 75-79 getSHA512Sched :: Get SHA512Sched getSHA512Sched = do w00 <- getWord64be w01 <- getWord64be w02 <- getWord64be w03 <- getWord64be w04 <- getWord64be w05 <- getWord64be w06 <- getWord64be w07 <- getWord64be w08 <- getWord64be w09 <- getWord64be w10 <- getWord64be w11 <- getWord64be w12 <- getWord64be w13 <- getWord64be w14 <- getWord64be w15 <- getWord64be let w16 = lsig512_1 w14 + w09 + lsig512_0 w01 + w00 w17 = lsig512_1 w15 + w10 + lsig512_0 w02 + w01 w18 = lsig512_1 w16 + w11 + lsig512_0 w03 + w02 w19 = lsig512_1 w17 + w12 + lsig512_0 w04 + w03 w20 = lsig512_1 w18 + w13 + lsig512_0 w05 + w04 w21 = lsig512_1 w19 + w14 + lsig512_0 w06 + w05 w22 = lsig512_1 w20 + w15 + lsig512_0 w07 + w06 w23 = lsig512_1 w21 + w16 + lsig512_0 w08 + w07 w24 = lsig512_1 w22 + w17 + lsig512_0 w09 + w08 w25 = lsig512_1 w23 + w18 + lsig512_0 w10 + w09 w26 = lsig512_1 w24 + w19 + lsig512_0 w11 + w10 w27 = lsig512_1 w25 + w20 + lsig512_0 w12 + w11 w28 = lsig512_1 w26 + w21 + lsig512_0 w13 + w12 w29 = lsig512_1 w27 + w22 + lsig512_0 w14 + w13 w30 = lsig512_1 w28 + w23 + lsig512_0 w15 + w14 w31 = lsig512_1 w29 + w24 + lsig512_0 w16 + w15 w32 = lsig512_1 w30 + w25 + lsig512_0 w17 + w16 w33 = lsig512_1 w31 + w26 + lsig512_0 w18 + w17 w34 = lsig512_1 w32 + w27 + lsig512_0 w19 + w18 w35 = lsig512_1 w33 + w28 + lsig512_0 w20 + w19 w36 = lsig512_1 w34 + w29 + lsig512_0 w21 + w20 w37 = lsig512_1 w35 + w30 + lsig512_0 w22 + w21 w38 = lsig512_1 w36 + w31 + lsig512_0 w23 + w22 w39 = lsig512_1 w37 + w32 + lsig512_0 w24 + w23 w40 = lsig512_1 w38 + w33 + lsig512_0 w25 + w24 w41 = lsig512_1 w39 + w34 + lsig512_0 w26 + w25 w42 = lsig512_1 w40 + w35 + lsig512_0 w27 + w26 w43 = lsig512_1 w41 + w36 + lsig512_0 w28 + w27 w44 = lsig512_1 w42 + w37 + lsig512_0 w29 + w28 w45 = lsig512_1 w43 + w38 + lsig512_0 w30 + w29 w46 = lsig512_1 w44 + w39 + lsig512_0 w31 + w30 w47 = lsig512_1 w45 + w40 + lsig512_0 w32 + w31 w48 = lsig512_1 w46 + w41 + lsig512_0 w33 + w32 w49 = lsig512_1 w47 + w42 + lsig512_0 w34 + w33 w50 = lsig512_1 w48 + w43 + lsig512_0 w35 + w34 w51 = lsig512_1 w49 + w44 + lsig512_0 w36 + w35 w52 = lsig512_1 w50 + w45 + lsig512_0 w37 + w36 w53 = lsig512_1 w51 + w46 + lsig512_0 w38 + w37 w54 = lsig512_1 w52 + w47 + lsig512_0 w39 + w38 w55 = lsig512_1 w53 + w48 + lsig512_0 w40 + w39 w56 = lsig512_1 w54 + w49 + lsig512_0 w41 + w40 w57 = lsig512_1 w55 + w50 + lsig512_0 w42 + w41 w58 = lsig512_1 w56 + w51 + lsig512_0 w43 + w42 w59 = lsig512_1 w57 + w52 + lsig512_0 w44 + w43 w60 = lsig512_1 w58 + w53 + lsig512_0 w45 + w44 w61 = lsig512_1 w59 + w54 + lsig512_0 w46 + w45 w62 = lsig512_1 w60 + w55 + lsig512_0 w47 + w46 w63 = lsig512_1 w61 + w56 + lsig512_0 w48 + w47 w64 = lsig512_1 w62 + w57 + lsig512_0 w49 + w48 w65 = lsig512_1 w63 + w58 + lsig512_0 w50 + w49 w66 = lsig512_1 w64 + w59 + lsig512_0 w51 + w50 w67 = lsig512_1 w65 + w60 + lsig512_0 w52 + w51 w68 = lsig512_1 w66 + w61 + lsig512_0 w53 + w52 w69 = lsig512_1 w67 + w62 + lsig512_0 w54 + w53 w70 = lsig512_1 w68 + w63 + lsig512_0 w55 + w54 w71 = lsig512_1 w69 + w64 + lsig512_0 w56 + w55 w72 = lsig512_1 w70 + w65 + lsig512_0 w57 + w56 w73 = lsig512_1 w71 + w66 + lsig512_0 w58 + w57 w74 = lsig512_1 w72 + w67 + lsig512_0 w59 + w58 w75 = lsig512_1 w73 + w68 + lsig512_0 w60 + w59 w76 = lsig512_1 w74 + w69 + lsig512_0 w61 + w60 w77 = lsig512_1 w75 + w70 + lsig512_0 w62 + w61 w78 = lsig512_1 w76 + w71 + lsig512_0 w63 + w62 w79 = lsig512_1 w77 + w72 + lsig512_0 w64 + w63 return $! SHA512Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59 w60 w61 w62 w63 w64 w65 w66 w67 w68 w69 w70 w71 w72 w73 w74 w75 w76 w77 w78 w79 -- -------------------------------------------------------------------------- -- -- SHA Block Processors -- -- -------------------------------------------------------------------------- processSHA1Block :: SHA1State -> Get SHA1State processSHA1Block s00@(SHA1S a00 b00 c00 d00 e00) = do (SHA1Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59 w60 w61 w62 w63 w64 w65 w66 w67 w68 w69 w70 w71 w72 w73 w74 w75 w76 w77 w78 w79) <- getSHA1Sched let s01 = step1_ch s00 0x5a827999 w00 s02 = step1_ch s01 0x5a827999 w01 s03 = step1_ch s02 0x5a827999 w02 s04 = step1_ch s03 0x5a827999 w03 s05 = step1_ch s04 0x5a827999 w04 s06 = step1_ch s05 0x5a827999 w05 s07 = step1_ch s06 0x5a827999 w06 s08 = step1_ch s07 0x5a827999 w07 s09 = step1_ch s08 0x5a827999 w08 s10 = step1_ch s09 0x5a827999 w09 s11 = step1_ch s10 0x5a827999 w10 s12 = step1_ch s11 0x5a827999 w11 s13 = step1_ch s12 0x5a827999 w12 s14 = step1_ch s13 0x5a827999 w13 s15 = step1_ch s14 0x5a827999 w14 s16 = step1_ch s15 0x5a827999 w15 s17 = step1_ch s16 0x5a827999 w16 s18 = step1_ch s17 0x5a827999 w17 s19 = step1_ch s18 0x5a827999 w18 s20 = step1_ch s19 0x5a827999 w19 s21 = step1_par s20 0x6ed9eba1 w20 s22 = step1_par s21 0x6ed9eba1 w21 s23 = step1_par s22 0x6ed9eba1 w22 s24 = step1_par s23 0x6ed9eba1 w23 s25 = step1_par s24 0x6ed9eba1 w24 s26 = step1_par s25 0x6ed9eba1 w25 s27 = step1_par s26 0x6ed9eba1 w26 s28 = step1_par s27 0x6ed9eba1 w27 s29 = step1_par s28 0x6ed9eba1 w28 s30 = step1_par s29 0x6ed9eba1 w29 s31 = step1_par s30 0x6ed9eba1 w30 s32 = step1_par s31 0x6ed9eba1 w31 s33 = step1_par s32 0x6ed9eba1 w32 s34 = step1_par s33 0x6ed9eba1 w33 s35 = step1_par s34 0x6ed9eba1 w34 s36 = step1_par s35 0x6ed9eba1 w35 s37 = step1_par s36 0x6ed9eba1 w36 s38 = step1_par s37 0x6ed9eba1 w37 s39 = step1_par s38 0x6ed9eba1 w38 s40 = step1_par s39 0x6ed9eba1 w39 s41 = step1_maj s40 0x8f1bbcdc w40 s42 = step1_maj s41 0x8f1bbcdc w41 s43 = step1_maj s42 0x8f1bbcdc w42 s44 = step1_maj s43 0x8f1bbcdc w43 s45 = step1_maj s44 0x8f1bbcdc w44 s46 = step1_maj s45 0x8f1bbcdc w45 s47 = step1_maj s46 0x8f1bbcdc w46 s48 = step1_maj s47 0x8f1bbcdc w47 s49 = step1_maj s48 0x8f1bbcdc w48 s50 = step1_maj s49 0x8f1bbcdc w49 s51 = step1_maj s50 0x8f1bbcdc w50 s52 = step1_maj s51 0x8f1bbcdc w51 s53 = step1_maj s52 0x8f1bbcdc w52 s54 = step1_maj s53 0x8f1bbcdc w53 s55 = step1_maj s54 0x8f1bbcdc w54 s56 = step1_maj s55 0x8f1bbcdc w55 s57 = step1_maj s56 0x8f1bbcdc w56 s58 = step1_maj s57 0x8f1bbcdc w57 s59 = step1_maj s58 0x8f1bbcdc w58 s60 = step1_maj s59 0x8f1bbcdc w59 s61 = step1_par s60 0xca62c1d6 w60 s62 = step1_par s61 0xca62c1d6 w61 s63 = step1_par s62 0xca62c1d6 w62 s64 = step1_par s63 0xca62c1d6 w63 s65 = step1_par s64 0xca62c1d6 w64 s66 = step1_par s65 0xca62c1d6 w65 s67 = step1_par s66 0xca62c1d6 w66 s68 = step1_par s67 0xca62c1d6 w67 s69 = step1_par s68 0xca62c1d6 w68 s70 = step1_par s69 0xca62c1d6 w69 s71 = step1_par s70 0xca62c1d6 w70 s72 = step1_par s71 0xca62c1d6 w71 s73 = step1_par s72 0xca62c1d6 w72 s74 = step1_par s73 0xca62c1d6 w73 s75 = step1_par s74 0xca62c1d6 w74 s76 = step1_par s75 0xca62c1d6 w75 s77 = step1_par s76 0xca62c1d6 w76 s78 = step1_par s77 0xca62c1d6 w77 s79 = step1_par s78 0xca62c1d6 w78 s80 = step1_par s79 0xca62c1d6 w79 SHA1S a80 b80 c80 d80 e80 = s80 return $! SHA1S (a00 + a80) (b00 + b80) (c00 + c80) (d00 + d80) (e00 + e80) {-# INLINE step1_ch #-} step1_ch :: SHA1State -> Word32 -> Word32 -> SHA1State step1_ch !(SHA1S a b c d e) k w = SHA1S a' b' c' d' e' where a' = rotateL a 5 + ((b .&. c) `xor` (complement b .&. d)) + e + k + w b' = a c' = rotateL b 30 d' = c e' = d {-# INLINE step1_par #-} step1_par :: SHA1State -> Word32 -> Word32 -> SHA1State step1_par !(SHA1S a b c d e) k w = SHA1S a' b' c' d' e' where a' = rotateL a 5 + (b `xor` c `xor` d) + e + k + w b' = a c' = rotateL b 30 d' = c e' = d {-# INLINE step1_maj #-} step1_maj :: SHA1State -> Word32 -> Word32 -> SHA1State step1_maj !(SHA1S a b c d e) k w = SHA1S a' b' c' d' e' where a' = rotateL a 5 + ((b .&. (c .|. d)) .|. (c .&. d)) + e + k + w b' = a c' = rotateL b 30 d' = c e' = d -- See the note on maj, above processSHA256Block :: SHA256State -> Get SHA256State processSHA256Block !s00@(SHA256S a00 b00 c00 d00 e00 f00 g00 h00) = do (SHA256Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59 w60 w61 w62 w63) <- getSHA256Sched let s01 = step256 s00 0x428a2f98 w00 s02 = step256 s01 0x71374491 w01 s03 = step256 s02 0xb5c0fbcf w02 s04 = step256 s03 0xe9b5dba5 w03 s05 = step256 s04 0x3956c25b w04 s06 = step256 s05 0x59f111f1 w05 s07 = step256 s06 0x923f82a4 w06 s08 = step256 s07 0xab1c5ed5 w07 s09 = step256 s08 0xd807aa98 w08 s10 = step256 s09 0x12835b01 w09 s11 = step256 s10 0x243185be w10 s12 = step256 s11 0x550c7dc3 w11 s13 = step256 s12 0x72be5d74 w12 s14 = step256 s13 0x80deb1fe w13 s15 = step256 s14 0x9bdc06a7 w14 s16 = step256 s15 0xc19bf174 w15 s17 = step256 s16 0xe49b69c1 w16 s18 = step256 s17 0xefbe4786 w17 s19 = step256 s18 0x0fc19dc6 w18 s20 = step256 s19 0x240ca1cc w19 s21 = step256 s20 0x2de92c6f w20 s22 = step256 s21 0x4a7484aa w21 s23 = step256 s22 0x5cb0a9dc w22 s24 = step256 s23 0x76f988da w23 s25 = step256 s24 0x983e5152 w24 s26 = step256 s25 0xa831c66d w25 s27 = step256 s26 0xb00327c8 w26 s28 = step256 s27 0xbf597fc7 w27 s29 = step256 s28 0xc6e00bf3 w28 s30 = step256 s29 0xd5a79147 w29 s31 = step256 s30 0x06ca6351 w30 s32 = step256 s31 0x14292967 w31 s33 = step256 s32 0x27b70a85 w32 s34 = step256 s33 0x2e1b2138 w33 s35 = step256 s34 0x4d2c6dfc w34 s36 = step256 s35 0x53380d13 w35 s37 = step256 s36 0x650a7354 w36 s38 = step256 s37 0x766a0abb w37 s39 = step256 s38 0x81c2c92e w38 s40 = step256 s39 0x92722c85 w39 s41 = step256 s40 0xa2bfe8a1 w40 s42 = step256 s41 0xa81a664b w41 s43 = step256 s42 0xc24b8b70 w42 s44 = step256 s43 0xc76c51a3 w43 s45 = step256 s44 0xd192e819 w44 s46 = step256 s45 0xd6990624 w45 s47 = step256 s46 0xf40e3585 w46 s48 = step256 s47 0x106aa070 w47 s49 = step256 s48 0x19a4c116 w48 s50 = step256 s49 0x1e376c08 w49 s51 = step256 s50 0x2748774c w50 s52 = step256 s51 0x34b0bcb5 w51 s53 = step256 s52 0x391c0cb3 w52 s54 = step256 s53 0x4ed8aa4a w53 s55 = step256 s54 0x5b9cca4f w54 s56 = step256 s55 0x682e6ff3 w55 s57 = step256 s56 0x748f82ee w56 s58 = step256 s57 0x78a5636f w57 s59 = step256 s58 0x84c87814 w58 s60 = step256 s59 0x8cc70208 w59 s61 = step256 s60 0x90befffa w60 s62 = step256 s61 0xa4506ceb w61 s63 = step256 s62 0xbef9a3f7 w62 s64 = step256 s63 0xc67178f2 w63 SHA256S a64 b64 c64 d64 e64 f64 g64 h64 = s64 return $! SHA256S (a00 + a64) (b00 + b64) (c00 + c64) (d00 + d64) (e00 + e64) (f00 + f64) (g00 + g64) (h00 + h64) {-# INLINE step256 #-} step256 :: SHA256State -> Word32 -> Word32 -> SHA256State step256 !(SHA256S a b c d e f g h) k w = SHA256S a' b' c' d' e' f' g' h' where t1 = h + bsig256_1 e + ch e f g + k + w t2 = bsig256_0 a + maj a b c h' = g g' = f f' = e e' = d + t1 d' = c c' = b b' = a a' = t1 + t2 processSHA512Block :: SHA512State -> Get SHA512State processSHA512Block !s00@(SHA512S a00 b00 c00 d00 e00 f00 g00 h00) = do (SHA512Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59 w60 w61 w62 w63 w64 w65 w66 w67 w68 w69 w70 w71 w72 w73 w74 w75 w76 w77 w78 w79) <- getSHA512Sched let s01 = step512 s00 0x428a2f98d728ae22 w00 s02 = step512 s01 0x7137449123ef65cd w01 s03 = step512 s02 0xb5c0fbcfec4d3b2f w02 s04 = step512 s03 0xe9b5dba58189dbbc w03 s05 = step512 s04 0x3956c25bf348b538 w04 s06 = step512 s05 0x59f111f1b605d019 w05 s07 = step512 s06 0x923f82a4af194f9b w06 s08 = step512 s07 0xab1c5ed5da6d8118 w07 s09 = step512 s08 0xd807aa98a3030242 w08 s10 = step512 s09 0x12835b0145706fbe w09 s11 = step512 s10 0x243185be4ee4b28c w10 s12 = step512 s11 0x550c7dc3d5ffb4e2 w11 s13 = step512 s12 0x72be5d74f27b896f w12 s14 = step512 s13 0x80deb1fe3b1696b1 w13 s15 = step512 s14 0x9bdc06a725c71235 w14 s16 = step512 s15 0xc19bf174cf692694 w15 s17 = step512 s16 0xe49b69c19ef14ad2 w16 s18 = step512 s17 0xefbe4786384f25e3 w17 s19 = step512 s18 0x0fc19dc68b8cd5b5 w18 s20 = step512 s19 0x240ca1cc77ac9c65 w19 s21 = step512 s20 0x2de92c6f592b0275 w20 s22 = step512 s21 0x4a7484aa6ea6e483 w21 s23 = step512 s22 0x5cb0a9dcbd41fbd4 w22 s24 = step512 s23 0x76f988da831153b5 w23 s25 = step512 s24 0x983e5152ee66dfab w24 s26 = step512 s25 0xa831c66d2db43210 w25 s27 = step512 s26 0xb00327c898fb213f w26 s28 = step512 s27 0xbf597fc7beef0ee4 w27 s29 = step512 s28 0xc6e00bf33da88fc2 w28 s30 = step512 s29 0xd5a79147930aa725 w29 s31 = step512 s30 0x06ca6351e003826f w30 s32 = step512 s31 0x142929670a0e6e70 w31 s33 = step512 s32 0x27b70a8546d22ffc w32 s34 = step512 s33 0x2e1b21385c26c926 w33 s35 = step512 s34 0x4d2c6dfc5ac42aed w34 s36 = step512 s35 0x53380d139d95b3df w35 s37 = step512 s36 0x650a73548baf63de w36 s38 = step512 s37 0x766a0abb3c77b2a8 w37 s39 = step512 s38 0x81c2c92e47edaee6 w38 s40 = step512 s39 0x92722c851482353b w39 s41 = step512 s40 0xa2bfe8a14cf10364 w40 s42 = step512 s41 0xa81a664bbc423001 w41 s43 = step512 s42 0xc24b8b70d0f89791 w42 s44 = step512 s43 0xc76c51a30654be30 w43 s45 = step512 s44 0xd192e819d6ef5218 w44 s46 = step512 s45 0xd69906245565a910 w45 s47 = step512 s46 0xf40e35855771202a w46 s48 = step512 s47 0x106aa07032bbd1b8 w47 s49 = step512 s48 0x19a4c116b8d2d0c8 w48 s50 = step512 s49 0x1e376c085141ab53 w49 s51 = step512 s50 0x2748774cdf8eeb99 w50 s52 = step512 s51 0x34b0bcb5e19b48a8 w51 s53 = step512 s52 0x391c0cb3c5c95a63 w52 s54 = step512 s53 0x4ed8aa4ae3418acb w53 s55 = step512 s54 0x5b9cca4f7763e373 w54 s56 = step512 s55 0x682e6ff3d6b2b8a3 w55 s57 = step512 s56 0x748f82ee5defb2fc w56 s58 = step512 s57 0x78a5636f43172f60 w57 s59 = step512 s58 0x84c87814a1f0ab72 w58 s60 = step512 s59 0x8cc702081a6439ec w59 s61 = step512 s60 0x90befffa23631e28 w60 s62 = step512 s61 0xa4506cebde82bde9 w61 s63 = step512 s62 0xbef9a3f7b2c67915 w62 s64 = step512 s63 0xc67178f2e372532b w63 s65 = step512 s64 0xca273eceea26619c w64 s66 = step512 s65 0xd186b8c721c0c207 w65 s67 = step512 s66 0xeada7dd6cde0eb1e w66 s68 = step512 s67 0xf57d4f7fee6ed178 w67 s69 = step512 s68 0x06f067aa72176fba w68 s70 = step512 s69 0x0a637dc5a2c898a6 w69 s71 = step512 s70 0x113f9804bef90dae w70 s72 = step512 s71 0x1b710b35131c471b w71 s73 = step512 s72 0x28db77f523047d84 w72 s74 = step512 s73 0x32caab7b40c72493 w73 s75 = step512 s74 0x3c9ebe0a15c9bebc w74 s76 = step512 s75 0x431d67c49c100d4c w75 s77 = step512 s76 0x4cc5d4becb3e42b6 w76 s78 = step512 s77 0x597f299cfc657e2a w77 s79 = step512 s78 0x5fcb6fab3ad6faec w78 s80 = step512 s79 0x6c44198c4a475817 w79 SHA512S a80 b80 c80 d80 e80 f80 g80 h80 = s80 return $! SHA512S (a00 + a80) (b00 + b80) (c00 + c80) (d00 + d80) (e00 + e80) (f00 + f80) (g00 + g80) (h00 + h80) {-# INLINE step512 #-} step512 :: SHA512State -> Word64 -> Word64 -> SHA512State step512 !(SHA512S a b c d e f g h) k w = SHA512S a' b' c' d' e' f' g' h' where t1 = h + bsig512_1 e + ch e f g + k + w t2 = bsig512_0 a + maj a b c h' = g g' = f f' = e e' = d + t1 d' = c c' = b b' = a a' = t1 + t2 -- -------------------------------------------------------------------------- -- -- Run the routines -- -- -------------------------------------------------------------------------- runSHA :: a -> (a -> Get a) -> ByteString -> a runSHA s nextChunk input = runGet (getAll s) input where getAll s_in = do done <- isEmpty if done then return s_in else nextChunk s_in >>= getAll runSHAIncremental :: a -> (a -> Get a) -> Decoder a runSHAIncremental s nextChunk = runGetIncremental (getAll s) where getAll s_in = do done <- isEmpty if done then return s_in else nextChunk s_in >>= getAll generic_complete :: (t -> [SBS.ByteString]) -> (a -> Put) -> Decoder a -> t -> Digest a generic_complete pad synthesize decoder len = let decoder' = pushEndOfInput $ foldl' pushChunk decoder $ pad len in case decoder' of Fail _ _ _ -> error "Decoder is in Fail state." Partial _ -> error "Decoder is in Partial state." Done _ _ x -> Digest $ runPut $! synthesize x -- |Compute the SHA-1 hash of the given ByteString. The output is guaranteed -- to be exactly 160 bits, or 20 bytes, long. This is a good default for -- programs that need a good, but not necessarily hyper-secure, hash function. sha1 :: ByteString -> Digest SHA1State sha1 bs_in = Digest bs_out where bs_pad = padSHA1 bs_in fstate = runSHA initialSHA1State processSHA1Block bs_pad bs_out = runPut $! synthesizeSHA1 fstate -- |Similar to `sha1` but use an incremental interface. When the decoder has -- been completely fed, `completeSha1Incremental` must be used so it can -- finish successfully. sha1Incremental :: Decoder SHA1State sha1Incremental = runSHAIncremental initialSHA1State processSHA1Block completeSha1Incremental :: Decoder SHA1State -> Int -> Digest SHA1State completeSha1Incremental = generic_complete padSHA1Chunks synthesizeSHA1 -- |Compute the SHA-224 hash of the given ByteString. Note that SHA-224 and -- SHA-384 differ only slightly from SHA-256 and SHA-512, and use truncated -- versions of the resulting hashes. So using 224/384 may not, in fact, save -- you very much ... sha224 :: ByteString -> Digest SHA256State sha224 bs_in = Digest bs_out where bs_pad = padSHA1 bs_in fstate = runSHA initialSHA224State processSHA256Block bs_pad bs_out = runPut $! synthesizeSHA224 fstate -- |Similar to `sha224` but use an incremental interface. When the decoder has -- been completely fed, `completeSha224Incremental` must be used so it can -- finish successfully. sha224Incremental :: Decoder SHA256State sha224Incremental = runSHAIncremental initialSHA224State processSHA256Block completeSha224Incremental :: Decoder SHA256State -> Int -> Digest SHA256State completeSha224Incremental = generic_complete padSHA1Chunks synthesizeSHA224 -- |Compute the SHA-256 hash of the given ByteString. The output is guaranteed -- to be exactly 256 bits, or 32 bytes, long. If your security requirements -- are pretty serious, this is a good choice. For truly significant security -- concerns, however, you might try one of the bigger options. sha256 :: ByteString -> Digest SHA256State sha256 bs_in = Digest bs_out where bs_pad = padSHA1 bs_in fstate = runSHA initialSHA256State processSHA256Block bs_pad bs_out = runPut $! synthesizeSHA256 fstate -- |Similar to `sha256` but use an incremental interface. When the decoder has -- been completely fed, `completeSha256Incremental` must be used so it can -- finish successfully. sha256Incremental :: Decoder SHA256State sha256Incremental = runSHAIncremental initialSHA256State processSHA256Block completeSha256Incremental :: Decoder SHA256State -> Int -> Digest SHA256State completeSha256Incremental = generic_complete padSHA1Chunks synthesizeSHA256 -- |Compute the SHA-384 hash of the given ByteString. Yup, you guessed it, -- the output will be exactly 384 bits, or 48 bytes, long. sha384 :: ByteString -> Digest SHA512State sha384 bs_in = Digest bs_out where bs_pad = padSHA512 bs_in fstate = runSHA initialSHA384State processSHA512Block bs_pad bs_out = runPut $! synthesizeSHA384 fstate -- |Similar to `sha384` but use an incremental interface. When the decoder has -- been completely fed, `completeSha384Incremental` must be used so it can -- finish successfully. sha384Incremental :: Decoder SHA512State sha384Incremental = runSHAIncremental initialSHA384State processSHA512Block completeSha384Incremental :: Decoder SHA512State -> Int -> Digest SHA512State completeSha384Incremental = generic_complete padSHA512Chunks synthesizeSHA384 -- |For those for whom only the biggest hashes will do, this computes the -- SHA-512 hash of the given ByteString. The output will be 64 bytes, or -- 512 bits, long. sha512 :: ByteString -> Digest SHA512State sha512 bs_in = Digest bs_out where bs_pad = padSHA512 bs_in fstate = runSHA initialSHA512State processSHA512Block bs_pad bs_out = runPut $! synthesizeSHA512 fstate -- |Similar to `sha512` but use an incremental interface. When the decoder has -- been completely fed, `completeSha512Incremental` must be used so it can -- finish successfully. sha512Incremental :: Decoder SHA512State sha512Incremental = runSHAIncremental initialSHA512State processSHA512Block completeSha512Incremental :: Decoder SHA512State -> Int -> Digest SHA512State completeSha512Incremental = generic_complete padSHA512Chunks synthesizeSHA512 -- -------------------------------------------------------------------------- -- | Compute an HMAC using SHA-1. hmacSha1 :: ByteString -- ^ secret key -> ByteString -- ^ message -> Digest SHA1State -- ^ SHA-1 MAC hmacSha1 = hmac sha1 64 -- | Compute an HMAC using SHA-224. hmacSha224 :: ByteString -- ^ secret key -> ByteString -- ^ message -> Digest SHA256State -- ^ SHA-224 MAC hmacSha224 = hmac sha224 64 -- | Compute an HMAC using SHA-256. hmacSha256 :: ByteString -- ^ secret key -> ByteString -- ^ message -> Digest SHA256State -- ^ SHA-256 MAC hmacSha256 = hmac sha256 64 -- | Compute an HMAC using SHA-384. hmacSha384 :: ByteString -- ^ secret key -> ByteString -- ^ message -> Digest SHA512State -- ^ SHA-384 MAC hmacSha384 = hmac sha384 128 -- | Compute an HMAC using SHA-512. hmacSha512 :: ByteString -- ^ secret key -> ByteString -- ^ message -> Digest SHA512State -- ^ SHA-512 MAC hmacSha512 = hmac sha512 128 -- -------------------------------------------------------------------------- hmac :: (ByteString -> Digest t) -> Int -> ByteString -> ByteString -> Digest t hmac f bl k m = f (BS.append opad (bytestringDigest (f (BS.append ipad m)))) where opad = BS.map (xor ov) k' ipad = BS.map (xor iv) k' ov = 0x5c :: Word8 iv = 0x36 :: Word8 k' = BS.append kt pad where kt = if kn > bn then bytestringDigest (f k) else k pad = BS.replicate (bn - ktn) 0 kn = fromIntegral (BS.length k) ktn = fromIntegral (BS.length kt) bn = fromIntegral bl -- -------------------------------------------------------------------------- -- -- OTHER -- -- -------------------------------------------------------------------------- -- | Convert a digest to a string. -- The digest is rendered as fixed with hexadecimal number. showDigest :: Digest t -> String showDigest (Digest bs) = showDigestBS bs -- |Prints out a bytestring in hexadecimal. Just for convenience. showDigestBS :: ByteString -> String showDigestBS bs = foldr paddedShowHex [] (BS.unpack bs) where paddedShowHex x xs = intToDigit (fromIntegral (x `shiftR` 4)) : intToDigit (fromIntegral (x .&. 0xf)) : xs -- | Convert a digest to an Integer. integerDigest :: Digest t -> Integer integerDigest (Digest bs) = BS.foldl' addShift 0 bs where addShift n y = (n `shiftL` 8) .|. fromIntegral y -- | Convert a digest to a ByteString. bytestringDigest :: Digest t -> ByteString bytestringDigest (Digest bs) = bs ================================================ FILE: Haskell/Core/Simplicity/Digest.hs ================================================ -- | This modules wraps Data.Digest.Pure.SHA in order to simulate direct access to the SHA-256 compression function by providing access to SHA-256 midstates. {-# LANGUAGE BangPatterns #-} module Simplicity.Digest ( Hash256, be256, be256_, le256, le256_ , get256Bits, put256Bits , integerHash256, hash0 , IV, noTagIv, tagIv, ivHash, bslHash, bsHash, bslDoubleHash, taggedHash, bitStringHash , Block512, compress, compressHalf , freeStart , Ctx(..), ctxInit, ctxBuild, ctxAdd, ctxFinalize ) where import Control.Monad (replicateM) import Control.Monad.Trans.State (evalState, state) import Data.Binary.Get (Decoder(..), pushChunk, pushChunks, pushEndOfInput) import qualified Data.Binary as Binary import Data.Bits ((.|.), bit, shiftL, testBit, zeroBits) import qualified Data.ByteString as BS import qualified Data.ByteString.Char8 as BSC import qualified Data.ByteString.Short as BSS import qualified Data.ByteString.Lazy as BSL import Data.List (foldl') import Data.Serialize (Serialize, encode, get, getShortByteString, put, putShortByteString) import Lens.Family2 (Adapter', Lens', (^.), (^..), over, review, under) import Lens.Family2.Stock (bend, bend_) import Lens.Family2.Unchecked (adapter) import Numeric (showHex) import Simplicity.Digest.Pure.SHA import Simplicity.Word import Simplicity.Serialization -- | Represents a 256-bit hash value or midstate from SHA-256. newtype Hash256 = Hash256 { hash256 :: BSS.ShortByteString } deriving (Eq, Ord) instance Show Hash256 where show h = "0x" ++ showHex256 (h^.be256_) instance Serialize Hash256 where get = Hash256 <$> getShortByteString 32 put (Hash256 bs) = putShortByteString bs -- | A 'Lens' accessing a 'Word256' from a 'Hash256' using a big endian interpretation. be256_ :: Lens' Hash256 Word256 be256_ = under be256 -- | An adaptor converting a 'Hash256' to a 'Word256' using a big endian interpretation. be256 :: Adapter' Hash256 Word256 be256 = adapter to fro where fro w = Hash256 $ BSS.toShort (encode w) to h = foldl' go 0 . BSS.unpack $ hash256 h where go n w = (n `shiftL` 8) .|. fromIntegral w -- | A 'Lens' accessing a 'Word256' from a 'Hash256' using a little endian interpretation. le256_ :: Lens' Hash256 Word256 le256_ = under le256 -- | An adaptor converting a 'Hash256' to a 'Word256' using a little endian interpretation. le256 :: Adapter' Hash256 Word256 le256 = adapter rev rev . be256 where rev = Hash256 . BSS.toShort . BS.reverse . BSS.fromShort . hash256 -- | Deserializes a 256-bit hash value from a stream of 'Bool's. -- -- Note that the type @forall m. Monad m => m Bool -> m a@ is isomorphic to the free monad over the @X²@ functor. -- In other words, 'get256Bits' has the type of a binary branching tree with leaves containing 'Hash256' values. -- -- Due to the flat nature of 'Hash256' only the 'Applicative' interface happens to be used by 'get256Bits'. -- This is why the constraint is 'Applicative' instead of 'Monad'. get256Bits :: Applicative m => m Bool -> m Hash256 get256Bits = review (be256.bend) -- | Serializes a 256-bit hash value to a stream of 'Bool's. put256Bits :: Hash256 -> DList Bool put256Bits h k = (h^..be256_.bend_) ++ k -- | Extracts the 256 hash value as an integer. integerHash256 :: Hash256 -> Integer integerHash256 h = toInteger $ h^.be256_ -- | A hash value with all bits set to 0. -- -- @ integerHash256 hash0 = 0 @ hash0 :: Hash256 hash0 = review (over be256) 0 -- | Represents a SHA-256 midstate. This is either the SHA-256 initial value, -- or some SHA-256 midstate created from applying the SHA-256 'compress'ion -- function. newtype IV = IV (Decoder SHA256State) -- | The SHA-256 initial value. noTagIv :: IV noTagIv = IV sha256Incremental -- | Return the SHA-256 midstate after compression of a block of the SHA256 digest of the given tag name twice. -- This twice repeated SHA256 digest is the tagged hash format used by BIP-340 and BIP-341. tagIv :: String -> IV tagIv tag = compress noTagIv (tagDigest, tagDigest) where tagDigest = bsHash . BSC.pack $ tag -- | Realize a initial value as a concrete Hash. ivHash :: IV -> Hash256 ivHash (IV state) = case pushEndOfInput state of Done _ _ x -> Hash256 . BSS.toShort . BSL.toStrict . Binary.encode $ x _ -> error "getHash256 unexpected decoder state" -- | Restore an IV from an given midstate. -- -- WARNING: Use of 'freeStart' may violate the security assumptions about SHA-256. freeStart :: Hash256 -> IV freeStart midstate = IV $ runSHAIncremental midstateSHA256State processSHA256Block where midstateSHA256State = Binary.decode . BSL.fromStrict . encode $ midstate -- | Computes a SHA-256 hash from a lazy 'BSL.ByteString'. bslHash :: BSL.ByteString -> Hash256 bslHash = ivHash . IV . pushChunks sha256Incremental . padSHA1 -- | Computes a SHA-256 hash from a 'BS.ByteString'. bsHash :: BS.ByteString -> Hash256 bsHash = bslHash . BSL.fromStrict -- | Computes a Bitcoin-style double SHA-256 hash from a lazy 'BSL.ByteString'. bslDoubleHash :: BSL.ByteString -> Hash256 bslDoubleHash = bsHash . encode . bslHash -- | Computes a SHA-256 tagged hash. taggedHash :: String -- ^ tag -> BS.ByteString -- ^ message -> Hash256 taggedHash tag str = ivHash . IV . pushChunks state $ BSL.fromStrict str <> BSL.fromChunks (padSHA1Chunks (len + 64)) where IV state = tagIv tag len = BS.length str -- Prepare a bit string for SHA-256 hashing by adding the padding and grouping bits into blocks. padSha256 :: [Bool] -> [Block512] padSha256 l = go 0 (l ++ [True]) where go :: Word64 -> [Bool] -> [Block512] go !i l | 512 < lenPre + 64 = blockify pre : go (i + fromIntegral lenPre) post | otherwise = [blockify (pre ++ replicate (512 - 64 - lenPre) False ++ map (testBit (i + fromIntegral lenPre - 1)) [63, 62 .. 0])] where (pre, post) = splitAt 512 l lenPre = length pre blockify = evalState (twice (get256Bits (state prog))) where prog [] = (False, []) prog (b:bs) = (b, bs) twice m = (,) <$> m <*> m -- | Compues a SHA-256 hash from a bit-string. bitStringHash :: [Bool] -> Hash256 bitStringHash = ivHash . foldl' compress (IV sha256Incremental) . padSha256 -- | A SHA-256 block is 512 bits. For Simplicity's Merkle tree application, we -- will be building blocks containing hashes. type Block512 = (Hash256, Hash256) -- | Given an initial value and a block of data consisting of a pair of hashes, apply the SHA-256 compression function. compress :: IV -> Block512 -> IV compress (IV state) (h1, h2) = IV $ state `pushChunk` BSS.fromShort (hash256 h1) `pushChunk` BSS.fromShort (hash256 h2) -- | Given an initial value and a block of data consisting of a one hash preceded by 256-bits of zeros, apply the SHA-256 compression function. compressHalf :: IV -> Hash256 -> IV compressHalf iv h = compress iv (hash0, h) -- | A SHA-256 context for bytes. data Ctx = Ctx { ctxBuffer :: BS.ByteString , ctxCounter :: Integer , ctxIV :: IV } -- | Initialize an empty 'Ctx'. ctxInit :: Ctx ctxInit = Ctx { ctxBuffer = mempty, ctxCounter = 0, ctxIV = noTagIv } -- | Normalize the context's buffer to less than 64 bytes. -- -- This may fail if the SHA-256 counter overflows. ctxNormalize :: Ctx -> Maybe Ctx ctxNormalize ctx | 2^55 <= ctxCounter ctx = Nothing | BS.length (ctxBuffer ctx) < 64 = Just ctx | otherwise = ctxNormalize $ Ctx { ctxBuffer = BS.drop 64 (ctxBuffer ctx) , ctxCounter = 1 + ctxCounter ctx , ctxIV = let IV state = ctxIV ctx in IV (state `pushChunk` BS.take 64 (ctxBuffer ctx)) } -- | Append a bytestring to a context. -- -- This may fail if the SHA-256 counter overflows. ctxAdd :: Ctx -> BS.ByteString -> Maybe Ctx ctxAdd ctx bs = ctxNormalize $ ctx { ctxBuffer = ctxBuffer ctx <> bs } -- | Freely construct a SHA-256 'Ctx' from its components. -- -- This may fail if the SHA-256 counter overflows. -- -- WARNING: Use of 'ctxBuild' may violate the security assumptions about SHA-256. ctxBuild :: [Word8] -- ^ Buffer -> Integer -- ^ Compression count -> Hash256 -- ^ Midstate -> Maybe Ctx ctxBuild buffer counter midstate = ctxNormalize $ Ctx { ctxBuffer = BS.pack buffer , ctxCounter = counter , ctxIV = freeStart midstate } -- | Add the SHA-256 padding an produce the final hash output. ctxFinalize :: Ctx -> Hash256 ctxFinalize ctx | 8*size < 2^64 = Hash256 . BSS.toShort . BSL.toStrict . Binary.encode $ completeSha256Incremental (state `pushChunk` ctxBuffer ctx) (fromInteger size) where size = ctxCounter ctx * 64 + toInteger (BS.length (ctxBuffer ctx)) IV state = ctxIV ctx ================================================ FILE: Haskell/Core/Simplicity/FFI/Frame.hs ================================================ {-# LANGUAGE ForeignFunctionInterface, GADTs #-} module Simplicity.FFI.Frame ( unsafeCoreJet, unsafeLocalCoreJet , FrameItem ) where import Control.Arrow (Kleisli(Kleisli)) import Data.Functor.Compose (Compose(..)) import Foreign.C.Types (CSize(..), CBool(..)) import Foreign.Ptr (Ptr, plusPtr) import Foreign.Storable (Storable(..)) import Foreign.Marshal.Alloc (allocaBytes) import Foreign.Marshal.Unsafe (unsafeLocalState) import Foreign.Marshal.Utils (fillBytes) import System.IO.Unsafe (unsafePerformIO) import Simplicity.BitMachine.Ty (bitSizeR, padLR, padRR) import Simplicity.Ty -- Abstract types representing the C data types used in frame.c newtype UWORD = UWORD UWORD newtype FrameItem = FrameItem FrameItem foreign import ccall unsafe "&" c_sizeof_UWORD :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_frameItem :: Ptr CSize foreign import ccall unsafe "" c_readBit :: Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_writeBit :: Ptr FrameItem -> CBool -> IO () foreign import ccall unsafe "" c_forwardBits :: Ptr FrameItem -> CSize -> IO () foreign import ccall unsafe "" c_skipBits :: Ptr FrameItem -> CSize -> IO () foreign import ccall unsafe "" c_initReadFrame :: Ptr FrameItem -> CSize -> Ptr UWORD -> IO () foreign import ccall unsafe "" c_initWriteFrame :: Ptr FrameItem -> CSize -> Ptr UWORD -> IO () sizeof_UWORD :: Int sizeof_UWORD = fromIntegral . unsafeLocalState $ peek c_sizeof_UWORD sizeof_frameItem :: Int sizeof_frameItem = fromIntegral . unsafeLocalState $ peek c_sizeof_frameItem allocaFrameItem :: (Ptr FrameItem -> IO a) -> IO a allocaFrameItem = allocaBytes sizeof_frameItem readFrameItem :: TyC a => Ptr FrameItem -> IO a readFrameItem ptr = readFrameItemR reify ptr writeFrameItem :: TyC a => a -> Ptr FrameItem -> IO () writeFrameItem ptr = writeFrameItemR reify ptr readFrameItemR :: TyReflect a -> Ptr FrameItem -> IO a readFrameItemR OneR _ = return () readFrameItemR (SumR a b) frame = do bit <- c_readBit frame if 0 /= bit then c_forwardBits frame (fromIntegral (padRR a b)) >> Right <$> readFrameItemR b frame else c_forwardBits frame (fromIntegral (padLR a b)) >> Left <$> readFrameItemR a frame readFrameItemR (ProdR a b) frame = (,) <$> readFrameItemR a frame <*> readFrameItemR b frame writeFrameItemR :: TyReflect a -> a -> Ptr FrameItem -> IO () writeFrameItemR OneR _ _ = return () writeFrameItemR (SumR a b) (Left v) frame = do c_writeBit frame 0 c_skipBits frame (fromIntegral (padLR a b)) writeFrameItemR a v frame writeFrameItemR (SumR a b) (Right v) frame = do c_writeBit frame 1 c_skipBits frame (fromIntegral (padRR a b)) writeFrameItemR b v frame writeFrameItemR (ProdR a b) (va, vb) frame = writeFrameItemR a va frame >> writeFrameItemR b vb frame withReadFrame :: Int -> Ptr UWORD -> (Ptr FrameItem -> IO a) -> IO a withReadFrame n from k = allocaFrameItem $ \frame -> c_initReadFrame frame (fromIntegral n) from >> k frame withWriteFrame :: Int -> Ptr UWORD -> (Ptr FrameItem -> IO a) -> IO a withWriteFrame n from k = allocaFrameItem $ \frame -> c_initWriteFrame frame (fromIntegral n) from >> k frame runCoreJet :: (TyC a, TyC b) => (Ptr FrameItem -> Ptr FrameItem -> IO CBool) -> a -> IO (Maybe b) runCoreJet jet = go where (aR, bR) = reifyArrow . Kleisli $ Compose . go roundUWord n = -((-n) `div` (8 * sizeof_UWORD)) aSize = roundUWord (bitSizeR aR) * sizeof_UWORD bSize = roundUWord (bitSizeR bR) * sizeof_UWORD arrSize = aSize + bSize go a = allocaBytes arrSize $ \arr -> do fillBytes arr 0 arrSize withWriteFrame (bitSizeR aR) (arr `plusPtr` aSize) $ writeFrameItem a result <- withReadFrame (bitSizeR aR) arr $ \readFrame -> withWriteFrame (bitSizeR bR) (arr `plusPtr` arrSize) $ \writeFrame -> jet writeFrame readFrame if 0 /= result then Just <$> (withReadFrame (bitSizeR bR) (arr `plusPtr` aSize) $ readFrameItem) else return Nothing -- | This cannot be used with jets that access global variables. unsafeLocalCoreJet :: (TyC a, TyC b) => (Ptr FrameItem -> Ptr FrameItem -> IO CBool) -> a -> Maybe b unsafeLocalCoreJet jet = unsafeLocalState . runCoreJet jet unsafeCoreJet :: (TyC a, TyC b) => (Ptr FrameItem -> Ptr FrameItem -> IO CBool) -> a -> Maybe b unsafeCoreJet jet = unsafePerformIO . runCoreJet jet ================================================ FILE: Haskell/Core/Simplicity/FFI/Jets.hs ================================================ -- | This module binds the C implementation of jets for Simplicity for assertions. {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.FFI.Jets ( verify , low_1, low_8, low_16, low_32, low_64 , high_1, high_8, high_16, high_32, high_64 , complement_1, complement_8, complement_16, complement_32, complement_64 , and_1, and_8, and_16, and_32, and_64 , or_1, or_8, or_16, or_32, or_64 , xor_1, xor_8, xor_16, xor_32, xor_64 , maj_1, maj_8, maj_16, maj_32, maj_64 , xor_xor_1, xor_xor_8, xor_xor_16, xor_xor_32, xor_xor_64 , ch_1, ch_8, ch_16, ch_32, ch_64 , some_1, some_8, some_16, some_32, some_64 , all_8, all_16, all_32, all_64 , eq_1, eq_8, eq_16, eq_32, eq_64, eq_256 , full_left_shift_8_1, full_left_shift_8_2, full_left_shift_8_4 , full_left_shift_16_1, full_left_shift_16_2, full_left_shift_16_4, full_left_shift_16_8 , full_left_shift_32_1, full_left_shift_32_2, full_left_shift_32_4, full_left_shift_32_8, full_left_shift_32_16 , full_left_shift_64_1, full_left_shift_64_2, full_left_shift_64_4, full_left_shift_64_8, full_left_shift_64_16, full_left_shift_64_32 , full_right_shift_8_1, full_right_shift_8_2, full_right_shift_8_4 , full_right_shift_16_1, full_right_shift_16_2, full_right_shift_16_4, full_right_shift_16_8 , full_right_shift_32_1, full_right_shift_32_2, full_right_shift_32_4, full_right_shift_32_8, full_right_shift_32_16 , full_right_shift_64_1, full_right_shift_64_2, full_right_shift_64_4, full_right_shift_64_8, full_right_shift_64_16, full_right_shift_64_32 , leftmost_8_1, leftmost_8_2, leftmost_8_4 , leftmost_16_1, leftmost_16_2, leftmost_16_4, leftmost_16_8 , leftmost_32_1, leftmost_32_2, leftmost_32_4, leftmost_32_8, leftmost_32_16 , leftmost_64_1, leftmost_64_2, leftmost_64_4, leftmost_64_8, leftmost_64_16, leftmost_64_32 , rightmost_8_1, rightmost_8_2, rightmost_8_4 , rightmost_16_1, rightmost_16_2, rightmost_16_4, rightmost_16_8 , rightmost_32_1, rightmost_32_2, rightmost_32_4, rightmost_32_8, rightmost_32_16 , rightmost_64_1, rightmost_64_2, rightmost_64_4, rightmost_64_8, rightmost_64_16, rightmost_64_32 , left_pad_low_1_8 , left_pad_low_1_16, left_pad_low_8_16 , left_pad_low_1_32, left_pad_low_8_32, left_pad_low_16_32 , left_pad_low_1_64, left_pad_low_8_64, left_pad_low_16_64, left_pad_low_32_64 , left_pad_high_1_8 , left_pad_high_1_16, left_pad_high_8_16 , left_pad_high_1_32, left_pad_high_8_32, left_pad_high_16_32 , left_pad_high_1_64, left_pad_high_8_64, left_pad_high_16_64, left_pad_high_32_64 , left_extend_1_8 , left_extend_1_16, left_extend_8_16 , left_extend_1_32, left_extend_8_32, left_extend_16_32 , left_extend_1_64, left_extend_8_64, left_extend_16_64, left_extend_32_64 , right_pad_low_1_8 , right_pad_low_1_16, right_pad_low_8_16 , right_pad_low_1_32, right_pad_low_8_32, right_pad_low_16_32 , right_pad_low_1_64, right_pad_low_8_64, right_pad_low_16_64, right_pad_low_32_64 , right_pad_high_1_8 , right_pad_high_1_16, right_pad_high_8_16 , right_pad_high_1_32, right_pad_high_8_32, right_pad_high_16_32 , right_pad_high_1_64, right_pad_high_8_64, right_pad_high_16_64, right_pad_high_32_64 , right_extend_8_16 , right_extend_8_32, right_extend_16_32 , right_extend_8_64, right_extend_16_64, right_extend_32_64 , left_shift_with_8, left_shift_with_16, left_shift_with_32, left_shift_with_64 , left_shift_8, left_shift_16, left_shift_32, left_shift_64 , right_shift_with_8, right_shift_with_16, right_shift_with_32, right_shift_with_64 , right_shift_8, right_shift_16, right_shift_32, right_shift_64 , left_rotate_8, left_rotate_16, left_rotate_32, left_rotate_64 , right_rotate_8, right_rotate_16, right_rotate_32, right_rotate_64 , one_8, one_16, one_32, one_64 , add_8, add_16, add_32, add_64 , full_add_8, full_add_16, full_add_32, full_add_64 , full_increment_8, full_increment_16, full_increment_32, full_increment_64 , increment_8, increment_16, increment_32, increment_64 , subtract_8, subtract_16, subtract_32, subtract_64 , full_subtract_8, full_subtract_16, full_subtract_32, full_subtract_64 , negate_8, negate_16, negate_32, negate_64 , full_decrement_8, full_decrement_16, full_decrement_32, full_decrement_64 , decrement_8, decrement_16, decrement_32, decrement_64 , multiply_8, multiply_16, multiply_32, multiply_64 , full_multiply_8, full_multiply_16, full_multiply_32, full_multiply_64 , is_zero_8, is_zero_16, is_zero_32, is_zero_64 , is_one_8, is_one_16, is_one_32, is_one_64 , le_8, le_16, le_32, le_64 , lt_8, lt_16, lt_32, lt_64 , min_8, min_16, min_32, min_64 , max_8, max_16, max_32, max_64 , median_8, median_16, median_32, median_64 , div_mod_8, div_mod_16, div_mod_32, div_mod_64 , divide_8, divide_16, divide_32, divide_64 , modulo_8, modulo_16, modulo_32, modulo_64 , divides_8, divides_16, divides_32, divides_64 , div_mod_128_64 , sha_256_iv, sha_256_block , sha_256_ctx_8_init , sha_256_ctx_8_add_1 , sha_256_ctx_8_add_2 , sha_256_ctx_8_add_4 , sha_256_ctx_8_add_8 , sha_256_ctx_8_add_16 , sha_256_ctx_8_add_32 , sha_256_ctx_8_add_64 , sha_256_ctx_8_add_128 , sha_256_ctx_8_add_256 , sha_256_ctx_8_add_512 , sha_256_ctx_8_add_buffer_511 , sha_256_ctx_8_finalize , fe_normalize, fe_negate, fe_add, fe_square, fe_multiply, fe_multiply_beta, fe_invert, fe_square_root, fe_is_zero, fe_is_odd , scalar_normalize, scalar_negate, scalar_add, scalar_square, scalar_multiply, scalar_multiply_lambda, scalar_invert, scalar_is_zero , gej_infinity, gej_rescale, gej_normalize, gej_negate, ge_negate, gej_double, gej_add, gej_ge_add_ex, gej_ge_add, gej_is_infinity, gej_equiv, gej_ge_equiv, gej_x_equiv, gej_y_is_odd, gej_is_on_curve, ge_is_on_curve , scale, off_curve_scale, generate, linear_combination_1, linear_verify_1, off_curve_linear_combination_1 , decompress, point_verify_1 , check_sig_verify , bip_0340_verify , swu, hash_to_curve , parse_lock, parse_sequence , tapdata_init ) where import Foreign.Ptr (Ptr) import Foreign.C.Types (CBool(..)) import Simplicity.FFI.Frame import qualified Simplicity.Programs.Sha256.Lib as Sha256 import Simplicity.Programs.LibSecp256k1.Lib (FE, Scalar, GE, GEJ, Point, PubKey, Sig) import qualified Simplicity.Programs.LibSecp256k1.Lib as LibSecp256k1 import Simplicity.Ty.Word foreign import ccall unsafe "" c_verify :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_low_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_low_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_low_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_low_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_low_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_high_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_high_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_high_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_high_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_high_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_complement_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_complement_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_complement_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_complement_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_complement_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_and_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_and_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_and_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_and_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_and_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_or_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_or_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_or_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_or_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_or_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_maj_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_maj_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_maj_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_maj_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_maj_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_xor_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_xor_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_xor_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_xor_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_xor_xor_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ch_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ch_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ch_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ch_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ch_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_some_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_some_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_some_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_some_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_some_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_all_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_all_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_all_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_all_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_eq_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_eq_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_eq_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_eq_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_eq_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_eq_256 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_8_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_8_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_8_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_16_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_16_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_16_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_16_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_32_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_32_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_32_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_32_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_32_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_64_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_64_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_64_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_64_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_64_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_left_shift_64_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_8_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_8_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_8_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_16_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_16_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_16_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_16_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_32_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_32_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_32_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_32_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_32_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_64_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_64_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_64_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_64_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_64_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_right_shift_64_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_8_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_8_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_8_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_16_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_16_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_16_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_16_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_32_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_32_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_32_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_32_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_32_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_64_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_64_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_64_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_64_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_64_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_leftmost_64_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_8_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_8_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_8_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_16_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_16_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_16_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_16_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_32_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_32_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_32_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_32_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_32_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_64_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_64_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_64_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_64_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_64_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_rightmost_64_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_1_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_1_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_8_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_1_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_8_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_16_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_1_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_8_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_16_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_low_32_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_1_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_1_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_8_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_1_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_8_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_16_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_1_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_8_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_16_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_pad_high_32_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_1_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_1_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_8_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_1_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_8_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_16_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_1_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_8_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_16_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_extend_32_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_1_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_1_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_8_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_1_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_8_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_16_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_1_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_8_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_16_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_low_32_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_1_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_1_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_8_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_1_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_8_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_16_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_1_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_8_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_16_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_pad_high_32_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_extend_8_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_extend_8_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_extend_16_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_extend_8_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_extend_16_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_extend_32_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_with_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_with_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_with_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_with_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_shift_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_with_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_with_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_with_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_with_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_shift_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_rotate_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_rotate_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_rotate_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_left_rotate_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_rotate_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_rotate_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_rotate_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_right_rotate_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_one_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_one_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_one_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_one_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_add_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_add_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_add_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_add_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_add_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_add_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_add_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_add_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_increment_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_increment_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_increment_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_increment_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_increment_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_increment_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_increment_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_increment_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_subtract_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_subtract_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_subtract_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_subtract_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_subtract_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_subtract_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_subtract_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_subtract_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_negate_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_negate_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_negate_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_negate_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_decrement_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_decrement_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_decrement_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_decrement_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_decrement_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_decrement_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_decrement_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_decrement_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_multiply_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_multiply_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_multiply_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_multiply_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_multiply_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_multiply_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_multiply_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_full_multiply_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_zero_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_zero_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_zero_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_zero_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_one_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_one_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_one_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_is_one_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_le_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_le_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_le_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_le_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_lt_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_lt_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_lt_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_lt_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_min_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_min_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_min_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_min_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_max_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_max_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_max_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_max_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_median_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_median_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_median_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_median_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_div_mod_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_div_mod_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_div_mod_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_div_mod_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divide_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divide_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divide_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divide_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_modulo_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_modulo_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_modulo_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_modulo_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divides_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divides_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divides_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_divides_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_div_mod_128_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_iv :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_block :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_init :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_2 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_4 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_8 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_16 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_32 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_64 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_128 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_256 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_512 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_add_buffer_511 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_sha_256_ctx_8_finalize :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_normalize :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_negate :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_add :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_square :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_multiply :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_multiply_beta :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_invert :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_square_root :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_is_zero :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_fe_is_odd :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_normalize :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_negate :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_add :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_square :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_multiply :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_multiply_lambda :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_invert :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scalar_is_zero :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_infinity :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_rescale :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_normalize :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_negate :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ge_negate :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_double :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_add :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_ge_add_ex :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_ge_add :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_is_infinity :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_equiv :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_ge_equiv :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_x_equiv :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_y_is_odd :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_gej_is_on_curve :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_ge_is_on_curve :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_scale :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_off_curve_scale :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_generate :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_linear_combination_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_off_curve_linear_combination_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_linear_verify_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_decompress :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_point_verify_1 :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_check_sig_verify :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_bip_0340_verify :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_swu :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_hash_to_curve :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_parse_lock :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_parse_sequence :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_tapdata_init :: Ptr FrameItem -> Ptr FrameItem -> IO CBool verify :: Bit -> Maybe () verify = unsafeLocalCoreJet c_verify low_1 :: () -> Maybe Word1 low_1 = unsafeLocalCoreJet c_low_1 low_8 :: () -> Maybe Word8 low_8 = unsafeLocalCoreJet c_low_8 low_16 :: () -> Maybe Word16 low_16 = unsafeLocalCoreJet c_low_16 low_32 :: () -> Maybe Word32 low_32 = unsafeLocalCoreJet c_low_32 low_64 :: () -> Maybe Word64 low_64 = unsafeLocalCoreJet c_low_64 high_1 :: () -> Maybe Word1 high_1 = unsafeLocalCoreJet c_high_1 high_8 :: () -> Maybe Word8 high_8 = unsafeLocalCoreJet c_high_8 high_16 :: () -> Maybe Word16 high_16 = unsafeLocalCoreJet c_high_16 high_32 :: () -> Maybe Word32 high_32 = unsafeLocalCoreJet c_high_32 high_64 :: () -> Maybe Word64 high_64 = unsafeLocalCoreJet c_high_64 complement_1 :: Word1 -> Maybe Word1 complement_1 = unsafeLocalCoreJet c_complement_1 complement_8 :: Word8 -> Maybe Word8 complement_8 = unsafeLocalCoreJet c_complement_8 complement_16 :: Word16 -> Maybe Word16 complement_16 = unsafeLocalCoreJet c_complement_16 complement_32 :: Word32 -> Maybe Word32 complement_32 = unsafeLocalCoreJet c_complement_32 complement_64 :: Word64 -> Maybe Word64 complement_64 = unsafeLocalCoreJet c_complement_64 and_1 :: (Word1, Word1) -> Maybe Word1 and_1 = unsafeLocalCoreJet c_and_1 and_8 :: (Word8, Word8) -> Maybe Word8 and_8 = unsafeLocalCoreJet c_and_8 and_16 :: (Word16, Word16) -> Maybe Word16 and_16 = unsafeLocalCoreJet c_and_16 and_32 :: (Word32, Word32) -> Maybe Word32 and_32 = unsafeLocalCoreJet c_and_32 and_64 :: (Word64, Word64) -> Maybe Word64 and_64 = unsafeLocalCoreJet c_and_64 or_1 :: (Word1, Word1) -> Maybe Word1 or_1 = unsafeLocalCoreJet c_or_1 or_8 :: (Word8, Word8) -> Maybe Word8 or_8 = unsafeLocalCoreJet c_or_8 or_16 :: (Word16, Word16) -> Maybe Word16 or_16 = unsafeLocalCoreJet c_or_16 or_32 :: (Word32, Word32) -> Maybe Word32 or_32 = unsafeLocalCoreJet c_or_32 or_64 :: (Word64, Word64) -> Maybe Word64 or_64 = unsafeLocalCoreJet c_or_64 xor_1 :: (Word1, Word1) -> Maybe Word1 xor_1 = unsafeLocalCoreJet c_xor_1 xor_8 :: (Word8, Word8) -> Maybe Word8 xor_8 = unsafeLocalCoreJet c_xor_8 xor_16 :: (Word16, Word16) -> Maybe Word16 xor_16 = unsafeLocalCoreJet c_xor_16 xor_32 :: (Word32, Word32) -> Maybe Word32 xor_32 = unsafeLocalCoreJet c_xor_32 xor_64 :: (Word64, Word64) -> Maybe Word64 xor_64 = unsafeLocalCoreJet c_xor_64 maj_1 :: (Word1, (Word1, Word1)) -> Maybe Word1 maj_1 = unsafeLocalCoreJet c_maj_1 maj_8 :: (Word8, (Word8, Word8)) -> Maybe Word8 maj_8 = unsafeLocalCoreJet c_maj_8 maj_16 :: (Word16, (Word16, Word16)) -> Maybe Word16 maj_16 = unsafeLocalCoreJet c_maj_16 maj_32 :: (Word32, (Word32, Word32)) -> Maybe Word32 maj_32 = unsafeLocalCoreJet c_maj_32 maj_64 :: (Word64, (Word64, Word64)) -> Maybe Word64 maj_64 = unsafeLocalCoreJet c_maj_64 xor_xor_1 :: (Word1, (Word1, Word1)) -> Maybe Word1 xor_xor_1 = unsafeLocalCoreJet c_xor_xor_1 xor_xor_8 :: (Word8, (Word8, Word8)) -> Maybe Word8 xor_xor_8 = unsafeLocalCoreJet c_xor_xor_8 xor_xor_16 :: (Word16, (Word16, Word16)) -> Maybe Word16 xor_xor_16 = unsafeLocalCoreJet c_xor_xor_16 xor_xor_32 :: (Word32, (Word32, Word32)) -> Maybe Word32 xor_xor_32 = unsafeLocalCoreJet c_xor_xor_32 xor_xor_64 :: (Word64, (Word64, Word64)) -> Maybe Word64 xor_xor_64 = unsafeLocalCoreJet c_xor_xor_64 ch_1 :: (Word1, (Word1, Word1)) -> Maybe Word1 ch_1 = unsafeLocalCoreJet c_ch_1 ch_8 :: (Word8, (Word8, Word8)) -> Maybe Word8 ch_8 = unsafeLocalCoreJet c_ch_8 ch_16 :: (Word16, (Word16, Word16)) -> Maybe Word16 ch_16 = unsafeLocalCoreJet c_ch_16 ch_32 :: (Word32, (Word32, Word32)) -> Maybe Word32 ch_32 = unsafeLocalCoreJet c_ch_32 ch_64 :: (Word64, (Word64, Word64)) -> Maybe Word64 ch_64 = unsafeLocalCoreJet c_ch_64 some_1 :: Word1 -> Maybe Bit some_1 = unsafeLocalCoreJet c_some_1 some_8 :: Word8 -> Maybe Bit some_8 = unsafeLocalCoreJet c_some_8 some_16 :: Word16 -> Maybe Bit some_16 = unsafeLocalCoreJet c_some_16 some_32 :: Word32 -> Maybe Bit some_32 = unsafeLocalCoreJet c_some_32 some_64 :: Word64 -> Maybe Bit some_64 = unsafeLocalCoreJet c_some_64 all_8 :: Word8 -> Maybe Bit all_8 = unsafeLocalCoreJet c_all_8 all_16 :: Word16 -> Maybe Bit all_16 = unsafeLocalCoreJet c_all_16 all_32 :: Word32 -> Maybe Bit all_32 = unsafeLocalCoreJet c_all_32 all_64 :: Word64 -> Maybe Bit all_64 = unsafeLocalCoreJet c_all_64 eq_1 :: (Word1, Word1) -> Maybe Bit eq_1 = unsafeLocalCoreJet c_eq_1 eq_8 :: (Word8, Word8) -> Maybe Bit eq_8 = unsafeLocalCoreJet c_eq_8 eq_16 :: (Word16, Word16) -> Maybe Bit eq_16 = unsafeLocalCoreJet c_eq_16 eq_32 :: (Word32, Word32) -> Maybe Bit eq_32 = unsafeLocalCoreJet c_eq_32 eq_64 :: (Word64, Word64) -> Maybe Bit eq_64 = unsafeLocalCoreJet c_eq_64 eq_256 :: (Word256, Word256) -> Maybe Bit eq_256 = unsafeLocalCoreJet c_eq_256 full_left_shift_8_1 :: (Word8, Word1) -> Maybe (Word1, Word8) full_left_shift_8_1 = unsafeLocalCoreJet c_full_left_shift_8_1 full_left_shift_8_2 :: (Word8, Word2) -> Maybe (Word2, Word8) full_left_shift_8_2 = unsafeLocalCoreJet c_full_left_shift_8_2 full_left_shift_8_4 :: (Word8, Word4) -> Maybe (Word4, Word8) full_left_shift_8_4 = unsafeLocalCoreJet c_full_left_shift_8_4 full_left_shift_16_1 :: (Word16, Word1) -> Maybe (Word1, Word16) full_left_shift_16_1 = unsafeLocalCoreJet c_full_left_shift_16_1 full_left_shift_16_2 :: (Word16, Word2) -> Maybe (Word2, Word16) full_left_shift_16_2 = unsafeLocalCoreJet c_full_left_shift_16_2 full_left_shift_16_4 :: (Word16, Word4) -> Maybe (Word4, Word16) full_left_shift_16_4 = unsafeLocalCoreJet c_full_left_shift_16_4 full_left_shift_16_8 :: (Word16, Word8) -> Maybe (Word8, Word16) full_left_shift_16_8 = unsafeLocalCoreJet c_full_left_shift_16_8 full_left_shift_32_1 :: (Word32, Word1) -> Maybe (Word1, Word32) full_left_shift_32_1 = unsafeLocalCoreJet c_full_left_shift_32_1 full_left_shift_32_2 :: (Word32, Word2) -> Maybe (Word2, Word32) full_left_shift_32_2 = unsafeLocalCoreJet c_full_left_shift_32_2 full_left_shift_32_4 :: (Word32, Word4) -> Maybe (Word4, Word32) full_left_shift_32_4 = unsafeLocalCoreJet c_full_left_shift_32_4 full_left_shift_32_8 :: (Word32, Word8) -> Maybe (Word8, Word32) full_left_shift_32_8 = unsafeLocalCoreJet c_full_left_shift_32_8 full_left_shift_32_16 :: (Word32, Word16) -> Maybe (Word16, Word32) full_left_shift_32_16 = unsafeLocalCoreJet c_full_left_shift_32_16 full_left_shift_64_1 :: (Word64, Word1) -> Maybe (Word1, Word64) full_left_shift_64_1 = unsafeLocalCoreJet c_full_left_shift_64_1 full_left_shift_64_2 :: (Word64, Word2) -> Maybe (Word2, Word64) full_left_shift_64_2 = unsafeLocalCoreJet c_full_left_shift_64_2 full_left_shift_64_4 :: (Word64, Word4) -> Maybe (Word4, Word64) full_left_shift_64_4 = unsafeLocalCoreJet c_full_left_shift_64_4 full_left_shift_64_8 :: (Word64, Word8) -> Maybe (Word8, Word64) full_left_shift_64_8 = unsafeLocalCoreJet c_full_left_shift_64_8 full_left_shift_64_16 :: (Word64, Word16) -> Maybe (Word16, Word64) full_left_shift_64_16 = unsafeLocalCoreJet c_full_left_shift_64_16 full_left_shift_64_32 :: (Word64, Word32) -> Maybe (Word32, Word64) full_left_shift_64_32 = unsafeLocalCoreJet c_full_left_shift_64_32 full_right_shift_8_1 :: (Word1, Word8) -> Maybe (Word8, Word1) full_right_shift_8_1 = unsafeLocalCoreJet c_full_right_shift_8_1 full_right_shift_8_2 :: (Word2, Word8) -> Maybe (Word8, Word2) full_right_shift_8_2 = unsafeLocalCoreJet c_full_right_shift_8_2 full_right_shift_8_4 :: (Word4, Word8) -> Maybe (Word8, Word4) full_right_shift_8_4 = unsafeLocalCoreJet c_full_right_shift_8_4 full_right_shift_16_1 :: (Word1, Word16) -> Maybe (Word16, Word1) full_right_shift_16_1 = unsafeLocalCoreJet c_full_right_shift_16_1 full_right_shift_16_2 :: (Word2, Word16) -> Maybe (Word16, Word2) full_right_shift_16_2 = unsafeLocalCoreJet c_full_right_shift_16_2 full_right_shift_16_4 :: (Word4, Word16) -> Maybe (Word16, Word4) full_right_shift_16_4 = unsafeLocalCoreJet c_full_right_shift_16_4 full_right_shift_16_8 :: (Word8, Word16) -> Maybe (Word16, Word8) full_right_shift_16_8 = unsafeLocalCoreJet c_full_right_shift_16_8 full_right_shift_32_1 :: (Word1, Word32) -> Maybe (Word32, Word1) full_right_shift_32_1 = unsafeLocalCoreJet c_full_right_shift_32_1 full_right_shift_32_2 :: (Word2, Word32) -> Maybe (Word32, Word2) full_right_shift_32_2 = unsafeLocalCoreJet c_full_right_shift_32_2 full_right_shift_32_4 :: (Word4, Word32) -> Maybe (Word32, Word4) full_right_shift_32_4 = unsafeLocalCoreJet c_full_right_shift_32_4 full_right_shift_32_8 :: (Word8, Word32) -> Maybe (Word32, Word8) full_right_shift_32_8 = unsafeLocalCoreJet c_full_right_shift_32_8 full_right_shift_32_16 :: (Word16, Word32) -> Maybe (Word32, Word16) full_right_shift_32_16 = unsafeLocalCoreJet c_full_right_shift_32_16 full_right_shift_64_1 :: (Word1, Word64) -> Maybe (Word64, Word1) full_right_shift_64_1 = unsafeLocalCoreJet c_full_right_shift_64_1 full_right_shift_64_2 :: (Word2, Word64) -> Maybe (Word64, Word2) full_right_shift_64_2 = unsafeLocalCoreJet c_full_right_shift_64_2 full_right_shift_64_4 :: (Word4, Word64) -> Maybe (Word64, Word4) full_right_shift_64_4 = unsafeLocalCoreJet c_full_right_shift_64_4 full_right_shift_64_8 :: (Word8, Word64) -> Maybe (Word64, Word8) full_right_shift_64_8 = unsafeLocalCoreJet c_full_right_shift_64_8 full_right_shift_64_16 :: (Word16, Word64) -> Maybe (Word64, Word16) full_right_shift_64_16 = unsafeLocalCoreJet c_full_right_shift_64_16 full_right_shift_64_32 :: (Word32, Word64) -> Maybe (Word64, Word32) full_right_shift_64_32 = unsafeLocalCoreJet c_full_right_shift_64_32 leftmost_8_1 :: Word8 -> Maybe Word1 leftmost_8_1 = unsafeLocalCoreJet c_leftmost_8_1 leftmost_8_2 :: Word8 -> Maybe Word2 leftmost_8_2 = unsafeLocalCoreJet c_leftmost_8_2 leftmost_8_4 :: Word8 -> Maybe Word4 leftmost_8_4 = unsafeLocalCoreJet c_leftmost_8_4 leftmost_16_1 :: Word16 -> Maybe Word1 leftmost_16_1 = unsafeLocalCoreJet c_leftmost_16_1 leftmost_16_2 :: Word16 -> Maybe Word2 leftmost_16_2 = unsafeLocalCoreJet c_leftmost_16_2 leftmost_16_4 :: Word16 -> Maybe Word4 leftmost_16_4 = unsafeLocalCoreJet c_leftmost_16_4 leftmost_16_8 :: Word16 -> Maybe Word8 leftmost_16_8 = unsafeLocalCoreJet c_leftmost_16_8 leftmost_32_1 :: Word32 -> Maybe Word1 leftmost_32_1 = unsafeLocalCoreJet c_leftmost_32_1 leftmost_32_2 :: Word32 -> Maybe Word2 leftmost_32_2 = unsafeLocalCoreJet c_leftmost_32_2 leftmost_32_4 :: Word32 -> Maybe Word4 leftmost_32_4 = unsafeLocalCoreJet c_leftmost_32_4 leftmost_32_8 :: Word32 -> Maybe Word8 leftmost_32_8 = unsafeLocalCoreJet c_leftmost_32_8 leftmost_32_16 :: Word32 -> Maybe Word16 leftmost_32_16 = unsafeLocalCoreJet c_leftmost_32_16 leftmost_64_1 :: Word64 -> Maybe Word1 leftmost_64_1 = unsafeLocalCoreJet c_leftmost_64_1 leftmost_64_2 :: Word64 -> Maybe Word2 leftmost_64_2 = unsafeLocalCoreJet c_leftmost_64_2 leftmost_64_4 :: Word64 -> Maybe Word4 leftmost_64_4 = unsafeLocalCoreJet c_leftmost_64_4 leftmost_64_8 :: Word64 -> Maybe Word8 leftmost_64_8 = unsafeLocalCoreJet c_leftmost_64_8 leftmost_64_16 :: Word64 -> Maybe Word16 leftmost_64_16 = unsafeLocalCoreJet c_leftmost_64_16 leftmost_64_32 :: Word64 -> Maybe Word32 leftmost_64_32 = unsafeLocalCoreJet c_leftmost_64_32 rightmost_8_1 :: Word8 -> Maybe Word1 rightmost_8_1 = unsafeLocalCoreJet c_rightmost_8_1 rightmost_8_2 :: Word8 -> Maybe Word2 rightmost_8_2 = unsafeLocalCoreJet c_rightmost_8_2 rightmost_8_4 :: Word8 -> Maybe Word4 rightmost_8_4 = unsafeLocalCoreJet c_rightmost_8_4 rightmost_16_1 :: Word16 -> Maybe Word1 rightmost_16_1 = unsafeLocalCoreJet c_rightmost_16_1 rightmost_16_2 :: Word16 -> Maybe Word2 rightmost_16_2 = unsafeLocalCoreJet c_rightmost_16_2 rightmost_16_4 :: Word16 -> Maybe Word4 rightmost_16_4 = unsafeLocalCoreJet c_rightmost_16_4 rightmost_16_8 :: Word16 -> Maybe Word8 rightmost_16_8 = unsafeLocalCoreJet c_rightmost_16_8 rightmost_32_1 :: Word32 -> Maybe Word1 rightmost_32_1 = unsafeLocalCoreJet c_rightmost_32_1 rightmost_32_2 :: Word32 -> Maybe Word2 rightmost_32_2 = unsafeLocalCoreJet c_rightmost_32_2 rightmost_32_4 :: Word32 -> Maybe Word4 rightmost_32_4 = unsafeLocalCoreJet c_rightmost_32_4 rightmost_32_8 :: Word32 -> Maybe Word8 rightmost_32_8 = unsafeLocalCoreJet c_rightmost_32_8 rightmost_32_16 :: Word32 -> Maybe Word16 rightmost_32_16 = unsafeLocalCoreJet c_rightmost_32_16 rightmost_64_1 :: Word64 -> Maybe Word1 rightmost_64_1 = unsafeLocalCoreJet c_rightmost_64_1 rightmost_64_2 :: Word64 -> Maybe Word2 rightmost_64_2 = unsafeLocalCoreJet c_rightmost_64_2 rightmost_64_4 :: Word64 -> Maybe Word4 rightmost_64_4 = unsafeLocalCoreJet c_rightmost_64_4 rightmost_64_8 :: Word64 -> Maybe Word8 rightmost_64_8 = unsafeLocalCoreJet c_rightmost_64_8 rightmost_64_16 :: Word64 -> Maybe Word16 rightmost_64_16 = unsafeLocalCoreJet c_rightmost_64_16 rightmost_64_32 :: Word64 -> Maybe Word32 rightmost_64_32 = unsafeLocalCoreJet c_rightmost_64_32 left_pad_low_1_8 :: Word1 -> Maybe Word8 left_pad_low_1_8 = unsafeLocalCoreJet c_left_pad_low_1_8 left_pad_low_1_16 :: Word1 -> Maybe Word16 left_pad_low_1_16 = unsafeLocalCoreJet c_left_pad_low_1_16 left_pad_low_8_16 :: Word8 -> Maybe Word16 left_pad_low_8_16 = unsafeLocalCoreJet c_left_pad_low_8_16 left_pad_low_1_32 :: Word1 -> Maybe Word32 left_pad_low_1_32 = unsafeLocalCoreJet c_left_pad_low_1_32 left_pad_low_8_32 :: Word8 -> Maybe Word32 left_pad_low_8_32 = unsafeLocalCoreJet c_left_pad_low_8_32 left_pad_low_16_32 :: Word16 -> Maybe Word32 left_pad_low_16_32 = unsafeLocalCoreJet c_left_pad_low_16_32 left_pad_low_1_64 :: Word1 -> Maybe Word64 left_pad_low_1_64 = unsafeLocalCoreJet c_left_pad_low_1_64 left_pad_low_8_64 :: Word8 -> Maybe Word64 left_pad_low_8_64 = unsafeLocalCoreJet c_left_pad_low_8_64 left_pad_low_16_64 :: Word16 -> Maybe Word64 left_pad_low_16_64 = unsafeLocalCoreJet c_left_pad_low_16_64 left_pad_low_32_64 :: Word32 -> Maybe Word64 left_pad_low_32_64 = unsafeLocalCoreJet c_left_pad_low_32_64 left_pad_high_1_8 :: Word1 -> Maybe Word8 left_pad_high_1_8 = unsafeLocalCoreJet c_left_pad_high_1_8 left_pad_high_1_16 :: Word1 -> Maybe Word16 left_pad_high_1_16 = unsafeLocalCoreJet c_left_pad_high_1_16 left_pad_high_8_16 :: Word8 -> Maybe Word16 left_pad_high_8_16 = unsafeLocalCoreJet c_left_pad_high_8_16 left_pad_high_1_32 :: Word1 -> Maybe Word32 left_pad_high_1_32 = unsafeLocalCoreJet c_left_pad_high_1_32 left_pad_high_8_32 :: Word8 -> Maybe Word32 left_pad_high_8_32 = unsafeLocalCoreJet c_left_pad_high_8_32 left_pad_high_16_32 :: Word16 -> Maybe Word32 left_pad_high_16_32 = unsafeLocalCoreJet c_left_pad_high_16_32 left_pad_high_1_64 :: Word1 -> Maybe Word64 left_pad_high_1_64 = unsafeLocalCoreJet c_left_pad_high_1_64 left_pad_high_8_64 :: Word8 -> Maybe Word64 left_pad_high_8_64 = unsafeLocalCoreJet c_left_pad_high_8_64 left_pad_high_16_64 :: Word16 -> Maybe Word64 left_pad_high_16_64 = unsafeLocalCoreJet c_left_pad_high_16_64 left_pad_high_32_64 :: Word32 -> Maybe Word64 left_pad_high_32_64 = unsafeLocalCoreJet c_left_pad_high_32_64 left_extend_1_8 :: Word1 -> Maybe Word8 left_extend_1_8 = unsafeLocalCoreJet c_left_extend_1_8 left_extend_1_16 :: Word1 -> Maybe Word16 left_extend_1_16 = unsafeLocalCoreJet c_left_extend_1_16 left_extend_8_16 :: Word8 -> Maybe Word16 left_extend_8_16 = unsafeLocalCoreJet c_left_extend_8_16 left_extend_1_32 :: Word1 -> Maybe Word32 left_extend_1_32 = unsafeLocalCoreJet c_left_extend_1_32 left_extend_8_32 :: Word8 -> Maybe Word32 left_extend_8_32 = unsafeLocalCoreJet c_left_extend_8_32 left_extend_16_32 :: Word16 -> Maybe Word32 left_extend_16_32 = unsafeLocalCoreJet c_left_extend_16_32 left_extend_1_64 :: Word1 -> Maybe Word64 left_extend_1_64 = unsafeLocalCoreJet c_left_extend_1_64 left_extend_8_64 :: Word8 -> Maybe Word64 left_extend_8_64 = unsafeLocalCoreJet c_left_extend_8_64 left_extend_16_64 :: Word16 -> Maybe Word64 left_extend_16_64 = unsafeLocalCoreJet c_left_extend_16_64 left_extend_32_64 :: Word32 -> Maybe Word64 left_extend_32_64 = unsafeLocalCoreJet c_left_extend_32_64 right_pad_low_1_8 :: Word1 -> Maybe Word8 right_pad_low_1_8 = unsafeLocalCoreJet c_right_pad_low_1_8 right_pad_low_1_16 :: Word1 -> Maybe Word16 right_pad_low_1_16 = unsafeLocalCoreJet c_right_pad_low_1_16 right_pad_low_8_16 :: Word8 -> Maybe Word16 right_pad_low_8_16 = unsafeLocalCoreJet c_right_pad_low_8_16 right_pad_low_1_32 :: Word1 -> Maybe Word32 right_pad_low_1_32 = unsafeLocalCoreJet c_right_pad_low_1_32 right_pad_low_8_32 :: Word8 -> Maybe Word32 right_pad_low_8_32 = unsafeLocalCoreJet c_right_pad_low_8_32 right_pad_low_16_32 :: Word16 -> Maybe Word32 right_pad_low_16_32 = unsafeLocalCoreJet c_right_pad_low_16_32 right_pad_low_1_64 :: Word1 -> Maybe Word64 right_pad_low_1_64 = unsafeLocalCoreJet c_right_pad_low_1_64 right_pad_low_8_64 :: Word8 -> Maybe Word64 right_pad_low_8_64 = unsafeLocalCoreJet c_right_pad_low_8_64 right_pad_low_16_64 :: Word16 -> Maybe Word64 right_pad_low_16_64 = unsafeLocalCoreJet c_right_pad_low_16_64 right_pad_low_32_64 :: Word32 -> Maybe Word64 right_pad_low_32_64 = unsafeLocalCoreJet c_right_pad_low_32_64 right_pad_high_1_8 :: Word1 -> Maybe Word8 right_pad_high_1_8 = unsafeLocalCoreJet c_right_pad_high_1_8 right_pad_high_1_16 :: Word1 -> Maybe Word16 right_pad_high_1_16 = unsafeLocalCoreJet c_right_pad_high_1_16 right_pad_high_8_16 :: Word8 -> Maybe Word16 right_pad_high_8_16 = unsafeLocalCoreJet c_right_pad_high_8_16 right_pad_high_1_32 :: Word1 -> Maybe Word32 right_pad_high_1_32 = unsafeLocalCoreJet c_right_pad_high_1_32 right_pad_high_8_32 :: Word8 -> Maybe Word32 right_pad_high_8_32 = unsafeLocalCoreJet c_right_pad_high_8_32 right_pad_high_16_32 :: Word16 -> Maybe Word32 right_pad_high_16_32 = unsafeLocalCoreJet c_right_pad_high_16_32 right_pad_high_1_64 :: Word1 -> Maybe Word64 right_pad_high_1_64 = unsafeLocalCoreJet c_right_pad_high_1_64 right_pad_high_8_64 :: Word8 -> Maybe Word64 right_pad_high_8_64 = unsafeLocalCoreJet c_right_pad_high_8_64 right_pad_high_16_64 :: Word16 -> Maybe Word64 right_pad_high_16_64 = unsafeLocalCoreJet c_right_pad_high_16_64 right_pad_high_32_64 :: Word32 -> Maybe Word64 right_pad_high_32_64 = unsafeLocalCoreJet c_right_pad_high_32_64 right_extend_8_16 :: Word8 -> Maybe Word16 right_extend_8_16 = unsafeLocalCoreJet c_right_extend_8_16 right_extend_8_32 :: Word8 -> Maybe Word32 right_extend_8_32 = unsafeLocalCoreJet c_right_extend_8_32 right_extend_16_32 :: Word16 -> Maybe Word32 right_extend_16_32 = unsafeLocalCoreJet c_right_extend_16_32 right_extend_8_64 :: Word8 -> Maybe Word64 right_extend_8_64 = unsafeLocalCoreJet c_right_extend_8_64 right_extend_16_64 :: Word16 -> Maybe Word64 right_extend_16_64 = unsafeLocalCoreJet c_right_extend_16_64 right_extend_32_64 :: Word32 -> Maybe Word64 right_extend_32_64 = unsafeLocalCoreJet c_right_extend_32_64 left_shift_with_8 :: (Bit, (Word4, Word8)) -> Maybe Word8 left_shift_with_8 = unsafeLocalCoreJet c_left_shift_with_8 left_shift_with_16 :: (Bit, (Word4, Word16)) -> Maybe Word16 left_shift_with_16 = unsafeLocalCoreJet c_left_shift_with_16 left_shift_with_32 :: (Bit, (Word8, Word32)) -> Maybe Word32 left_shift_with_32 = unsafeLocalCoreJet c_left_shift_with_32 left_shift_with_64 :: (Bit, (Word8, Word64)) -> Maybe Word64 left_shift_with_64 = unsafeLocalCoreJet c_left_shift_with_64 left_shift_8 :: (Word4, Word8) -> Maybe Word8 left_shift_8 = unsafeLocalCoreJet c_left_shift_8 left_shift_16 :: (Word4, Word16) -> Maybe Word16 left_shift_16 = unsafeLocalCoreJet c_left_shift_16 left_shift_32 :: (Word8, Word32) -> Maybe Word32 left_shift_32 = unsafeLocalCoreJet c_left_shift_32 left_shift_64 :: (Word8, Word64) -> Maybe Word64 left_shift_64 = unsafeLocalCoreJet c_left_shift_64 right_shift_with_8 :: (Bit, (Word4, Word8)) -> Maybe Word8 right_shift_with_8 = unsafeLocalCoreJet c_right_shift_with_8 right_shift_with_16 :: (Bit, (Word4, Word16)) -> Maybe Word16 right_shift_with_16 = unsafeLocalCoreJet c_right_shift_with_16 right_shift_with_32 :: (Bit, (Word8, Word32)) -> Maybe Word32 right_shift_with_32 = unsafeLocalCoreJet c_right_shift_with_32 right_shift_with_64 :: (Bit, (Word8, Word64)) -> Maybe Word64 right_shift_with_64 = unsafeLocalCoreJet c_right_shift_with_64 right_shift_8 :: (Word4, Word8) -> Maybe Word8 right_shift_8 = unsafeLocalCoreJet c_right_shift_8 right_shift_16 :: (Word4, Word16) -> Maybe Word16 right_shift_16 = unsafeLocalCoreJet c_right_shift_16 right_shift_32 :: (Word8, Word32) -> Maybe Word32 right_shift_32 = unsafeLocalCoreJet c_right_shift_32 right_shift_64 :: (Word8, Word64) -> Maybe Word64 right_shift_64 = unsafeLocalCoreJet c_right_shift_64 left_rotate_8 :: (Word4, Word8) -> Maybe Word8 left_rotate_8 = unsafeLocalCoreJet c_left_rotate_8 left_rotate_16 :: (Word4, Word16) -> Maybe Word16 left_rotate_16 = unsafeLocalCoreJet c_left_rotate_16 left_rotate_32 :: (Word8, Word32) -> Maybe Word32 left_rotate_32 = unsafeLocalCoreJet c_left_rotate_32 left_rotate_64 :: (Word8, Word64) -> Maybe Word64 left_rotate_64 = unsafeLocalCoreJet c_left_rotate_64 right_rotate_8 :: (Word4, Word8) -> Maybe Word8 right_rotate_8 = unsafeLocalCoreJet c_right_rotate_8 right_rotate_16 :: (Word4, Word16) -> Maybe Word16 right_rotate_16 = unsafeLocalCoreJet c_right_rotate_16 right_rotate_32 :: (Word8, Word32) -> Maybe Word32 right_rotate_32 = unsafeLocalCoreJet c_right_rotate_32 right_rotate_64 :: (Word8, Word64) -> Maybe Word64 right_rotate_64 = unsafeLocalCoreJet c_right_rotate_64 one_8 :: () -> Maybe Word8 one_8 = unsafeLocalCoreJet c_one_8 one_16 :: () -> Maybe Word16 one_16 = unsafeLocalCoreJet c_one_16 one_32 :: () -> Maybe Word32 one_32 = unsafeLocalCoreJet c_one_32 one_64 :: () -> Maybe Word64 one_64 = unsafeLocalCoreJet c_one_64 add_8 :: (Word8, Word8) -> Maybe (Bit, Word8) add_8 = unsafeLocalCoreJet c_add_8 add_16 :: (Word16, Word16) -> Maybe (Bit, Word16) add_16 = unsafeLocalCoreJet c_add_16 add_32 :: (Word32, Word32) -> Maybe (Bit, Word32) add_32 = unsafeLocalCoreJet c_add_32 add_64 :: (Word64, Word64) -> Maybe (Bit, Word64) add_64 = unsafeLocalCoreJet c_add_64 full_add_8 :: (Bit, (Word8, Word8)) -> Maybe (Bit, Word8) full_add_8 = unsafeLocalCoreJet c_full_add_8 full_add_16 :: (Bit, (Word16, Word16)) -> Maybe (Bit, Word16) full_add_16 = unsafeLocalCoreJet c_full_add_16 full_add_32 :: (Bit, (Word32, Word32)) -> Maybe (Bit, Word32) full_add_32 = unsafeLocalCoreJet c_full_add_32 full_add_64 :: (Bit, (Word64, Word64)) -> Maybe (Bit, Word64) full_add_64 = unsafeLocalCoreJet c_full_add_64 full_increment_8 :: (Bit, Word8) -> Maybe (Bit, Word8) full_increment_8 = unsafeLocalCoreJet c_full_increment_8 full_increment_16 :: (Bit, Word16) -> Maybe (Bit, Word16) full_increment_16 = unsafeLocalCoreJet c_full_increment_16 full_increment_32 :: (Bit, Word32) -> Maybe (Bit, Word32) full_increment_32 = unsafeLocalCoreJet c_full_increment_32 full_increment_64 :: (Bit, Word64) -> Maybe (Bit, Word64) full_increment_64 = unsafeLocalCoreJet c_full_increment_64 increment_8 :: Word8 -> Maybe (Bit, Word8) increment_8 = unsafeLocalCoreJet c_increment_8 increment_16 :: Word16 -> Maybe (Bit, Word16) increment_16 = unsafeLocalCoreJet c_increment_16 increment_32 :: Word32 -> Maybe (Bit, Word32) increment_32 = unsafeLocalCoreJet c_increment_32 increment_64 :: Word64 -> Maybe (Bit, Word64) increment_64 = unsafeLocalCoreJet c_increment_64 subtract_8 :: (Word8, Word8) -> Maybe (Bit, Word8) subtract_8 = unsafeLocalCoreJet c_subtract_8 subtract_16 :: (Word16, Word16) -> Maybe (Bit, Word16) subtract_16 = unsafeLocalCoreJet c_subtract_16 subtract_32 :: (Word32, Word32) -> Maybe (Bit, Word32) subtract_32 = unsafeLocalCoreJet c_subtract_32 subtract_64 :: (Word64, Word64) -> Maybe (Bit, Word64) subtract_64 = unsafeLocalCoreJet c_subtract_64 full_subtract_8 :: (Bit, (Word8, Word8)) -> Maybe (Bit, Word8) full_subtract_8 = unsafeLocalCoreJet c_full_subtract_8 full_subtract_16 :: (Bit, (Word16, Word16)) -> Maybe (Bit, Word16) full_subtract_16 = unsafeLocalCoreJet c_full_subtract_16 full_subtract_32 :: (Bit, (Word32, Word32)) -> Maybe (Bit, Word32) full_subtract_32 = unsafeLocalCoreJet c_full_subtract_32 full_subtract_64 :: (Bit, (Word64, Word64)) -> Maybe (Bit, Word64) full_subtract_64 = unsafeLocalCoreJet c_full_subtract_64 negate_8 :: Word8 -> Maybe (Bit, Word8) negate_8 = unsafeLocalCoreJet c_negate_8 negate_16 :: Word16 -> Maybe (Bit, Word16) negate_16 = unsafeLocalCoreJet c_negate_16 negate_32 :: Word32 -> Maybe (Bit, Word32) negate_32 = unsafeLocalCoreJet c_negate_32 negate_64 :: Word64 -> Maybe (Bit, Word64) negate_64 = unsafeLocalCoreJet c_negate_64 full_decrement_8 :: (Bit, Word8) -> Maybe (Bit, Word8) full_decrement_8 = unsafeLocalCoreJet c_full_decrement_8 full_decrement_16 :: (Bit, Word16) -> Maybe (Bit, Word16) full_decrement_16 = unsafeLocalCoreJet c_full_decrement_16 full_decrement_32 :: (Bit, Word32) -> Maybe (Bit, Word32) full_decrement_32 = unsafeLocalCoreJet c_full_decrement_32 full_decrement_64 :: (Bit, Word64) -> Maybe (Bit, Word64) full_decrement_64 = unsafeLocalCoreJet c_full_decrement_64 decrement_8 :: Word8 -> Maybe (Bit, Word8) decrement_8 = unsafeLocalCoreJet c_decrement_8 decrement_16 :: Word16 -> Maybe (Bit, Word16) decrement_16 = unsafeLocalCoreJet c_decrement_16 decrement_32 :: Word32 -> Maybe (Bit, Word32) decrement_32 = unsafeLocalCoreJet c_decrement_32 decrement_64 :: Word64 -> Maybe (Bit, Word64) decrement_64 = unsafeLocalCoreJet c_decrement_64 multiply_8 :: (Word8, Word8) -> Maybe Word16 multiply_8 = unsafeLocalCoreJet c_multiply_8 multiply_16 :: (Word16, Word16) -> Maybe Word32 multiply_16 = unsafeLocalCoreJet c_multiply_16 multiply_32 :: (Word32, Word32) -> Maybe Word64 multiply_32 = unsafeLocalCoreJet c_multiply_32 multiply_64 :: (Word64, Word64) -> Maybe Word128 multiply_64 = unsafeLocalCoreJet c_multiply_64 full_multiply_8 :: ((Word8, Word8), (Word8, Word8)) -> Maybe Word16 full_multiply_8 = unsafeLocalCoreJet c_full_multiply_8 full_multiply_16 :: ((Word16, Word16), (Word16, Word16)) -> Maybe Word32 full_multiply_16 = unsafeLocalCoreJet c_full_multiply_16 full_multiply_32 :: ((Word32, Word32), (Word32, Word32)) -> Maybe Word64 full_multiply_32 = unsafeLocalCoreJet c_full_multiply_32 full_multiply_64 :: ((Word64, Word64), (Word64, Word64)) -> Maybe Word128 full_multiply_64 = unsafeLocalCoreJet c_full_multiply_64 is_zero_8 :: Word8 -> Maybe Bit is_zero_8 = unsafeLocalCoreJet c_is_zero_8 is_zero_16 :: Word16 -> Maybe Bit is_zero_16 = unsafeLocalCoreJet c_is_zero_16 is_zero_32 :: Word32 -> Maybe Bit is_zero_32 = unsafeLocalCoreJet c_is_zero_32 is_zero_64 :: Word64 -> Maybe Bit is_zero_64 = unsafeLocalCoreJet c_is_zero_64 is_one_8 :: Word8 -> Maybe Bit is_one_8 = unsafeLocalCoreJet c_is_one_8 is_one_16 :: Word16 -> Maybe Bit is_one_16 = unsafeLocalCoreJet c_is_one_16 is_one_32 :: Word32 -> Maybe Bit is_one_32 = unsafeLocalCoreJet c_is_one_32 is_one_64 :: Word64 -> Maybe Bit is_one_64 = unsafeLocalCoreJet c_is_one_64 le_8 :: (Word8, Word8) -> Maybe Bit le_8 = unsafeLocalCoreJet c_le_8 le_16 :: (Word16, Word16) -> Maybe Bit le_16 = unsafeLocalCoreJet c_le_16 le_32 :: (Word32, Word32) -> Maybe Bit le_32 = unsafeLocalCoreJet c_le_32 le_64 :: (Word64, Word64) -> Maybe Bit le_64 = unsafeLocalCoreJet c_le_64 lt_8 :: (Word8, Word8) -> Maybe Bit lt_8 = unsafeLocalCoreJet c_lt_8 lt_16 :: (Word16, Word16) -> Maybe Bit lt_16 = unsafeLocalCoreJet c_lt_16 lt_32 :: (Word32, Word32) -> Maybe Bit lt_32 = unsafeLocalCoreJet c_lt_32 lt_64 :: (Word64, Word64) -> Maybe Bit lt_64 = unsafeLocalCoreJet c_lt_64 min_8 :: (Word8, Word8) -> Maybe Word8 min_8 = unsafeLocalCoreJet c_min_8 min_16 :: (Word16, Word16) -> Maybe Word16 min_16 = unsafeLocalCoreJet c_min_16 min_32 :: (Word32, Word32) -> Maybe Word32 min_32 = unsafeLocalCoreJet c_min_32 min_64 :: (Word64, Word64) -> Maybe Word64 min_64 = unsafeLocalCoreJet c_min_64 max_8 :: (Word8, Word8) -> Maybe Word8 max_8 = unsafeLocalCoreJet c_max_8 max_16 :: (Word16, Word16) -> Maybe Word16 max_16 = unsafeLocalCoreJet c_max_16 max_32 :: (Word32, Word32) -> Maybe Word32 max_32 = unsafeLocalCoreJet c_max_32 max_64 :: (Word64, Word64) -> Maybe Word64 max_64 = unsafeLocalCoreJet c_max_64 median_8 :: (Word8, (Word8, Word8)) -> Maybe Word8 median_8 = unsafeLocalCoreJet c_median_8 median_16 :: (Word16, (Word16, Word16)) -> Maybe Word16 median_16 = unsafeLocalCoreJet c_median_16 median_32 :: (Word32, (Word32, Word32)) -> Maybe Word32 median_32 = unsafeLocalCoreJet c_median_32 median_64 :: (Word64, (Word64, Word64)) -> Maybe Word64 median_64 = unsafeLocalCoreJet c_median_64 div_mod_8 :: (Word8, Word8) -> Maybe (Word8, Word8) div_mod_8 = unsafeLocalCoreJet c_div_mod_8 div_mod_16 :: (Word16, Word16) -> Maybe (Word16, Word16) div_mod_16 = unsafeLocalCoreJet c_div_mod_16 div_mod_32 :: (Word32, Word32) -> Maybe (Word32, Word32) div_mod_32 = unsafeLocalCoreJet c_div_mod_32 div_mod_64 :: (Word64, Word64) -> Maybe (Word64, Word64) div_mod_64 = unsafeLocalCoreJet c_div_mod_64 divide_8 :: (Word8, Word8) -> Maybe Word8 divide_8 = unsafeLocalCoreJet c_divide_8 divide_16 :: (Word16, Word16) -> Maybe Word16 divide_16 = unsafeLocalCoreJet c_divide_16 divide_32 :: (Word32, Word32) -> Maybe Word32 divide_32 = unsafeLocalCoreJet c_divide_32 divide_64 :: (Word64, Word64) -> Maybe Word64 divide_64 = unsafeLocalCoreJet c_divide_64 modulo_8 :: (Word8, Word8) -> Maybe Word8 modulo_8 = unsafeLocalCoreJet c_modulo_8 modulo_16 :: (Word16, Word16) -> Maybe Word16 modulo_16 = unsafeLocalCoreJet c_modulo_16 modulo_32 :: (Word32, Word32) -> Maybe Word32 modulo_32 = unsafeLocalCoreJet c_modulo_32 modulo_64 :: (Word64, Word64) -> Maybe Word64 modulo_64 = unsafeLocalCoreJet c_modulo_64 divides_8 :: (Word8, Word8) -> Maybe Bit divides_8 = unsafeLocalCoreJet c_divides_8 divides_16 :: (Word16, Word16) -> Maybe Bit divides_16 = unsafeLocalCoreJet c_divides_16 divides_32 :: (Word32, Word32) -> Maybe Bit divides_32 = unsafeLocalCoreJet c_divides_32 divides_64 :: (Word64, Word64) -> Maybe Bit divides_64 = unsafeLocalCoreJet c_divides_64 div_mod_128_64 :: (Word128, Word64) -> Maybe (Word64, Word64) div_mod_128_64 = unsafeLocalCoreJet c_div_mod_128_64 sha_256_iv :: () -> Maybe Sha256.Hash sha_256_iv = unsafeLocalCoreJet c_sha_256_iv sha_256_block :: (Sha256.Hash, Sha256.Block) -> Maybe Sha256.Hash sha_256_block = unsafeLocalCoreJet c_sha_256_block sha_256_ctx_8_init :: () -> Maybe Sha256.Ctx8 sha_256_ctx_8_init = unsafeLocalCoreJet c_sha_256_ctx_8_init sha_256_ctx_8_add_1 :: (Sha256.Ctx8, Word8) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_1 = unsafeLocalCoreJet c_sha_256_ctx_8_add_1 sha_256_ctx_8_add_2 :: (Sha256.Ctx8, Word16) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_2 = unsafeLocalCoreJet c_sha_256_ctx_8_add_2 sha_256_ctx_8_add_4 :: (Sha256.Ctx8, Word32) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_4 = unsafeLocalCoreJet c_sha_256_ctx_8_add_4 sha_256_ctx_8_add_8 :: (Sha256.Ctx8, Word64) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_8 = unsafeLocalCoreJet c_sha_256_ctx_8_add_8 sha_256_ctx_8_add_16 :: (Sha256.Ctx8, Word128) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_16 = unsafeLocalCoreJet c_sha_256_ctx_8_add_16 sha_256_ctx_8_add_32 :: (Sha256.Ctx8, Word256) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_32 = unsafeLocalCoreJet c_sha_256_ctx_8_add_32 sha_256_ctx_8_add_64 :: (Sha256.Ctx8, Word512) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_64 = unsafeLocalCoreJet c_sha_256_ctx_8_add_64 sha_256_ctx_8_add_128 :: (Sha256.Ctx8, Word1024) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_128 = unsafeLocalCoreJet c_sha_256_ctx_8_add_128 sha_256_ctx_8_add_256 :: (Sha256.Ctx8, Word2048) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_256 = unsafeLocalCoreJet c_sha_256_ctx_8_add_256 sha_256_ctx_8_add_512 :: (Sha256.Ctx8, Word4096) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_512 = unsafeLocalCoreJet c_sha_256_ctx_8_add_512 sha_256_ctx_8_add_buffer_511 :: (Sha256.Ctx8, Buffer511 Word8) -> Maybe Sha256.Ctx8 sha_256_ctx_8_add_buffer_511 = unsafeLocalCoreJet c_sha_256_ctx_8_add_buffer_511 sha_256_ctx_8_finalize :: Sha256.Ctx8 -> Maybe Sha256.Hash sha_256_ctx_8_finalize = unsafeLocalCoreJet c_sha_256_ctx_8_finalize fe_normalize :: FE -> Maybe FE fe_normalize = unsafeLocalCoreJet c_fe_normalize fe_negate :: FE -> Maybe FE fe_negate = unsafeLocalCoreJet c_fe_negate fe_add :: (FE, FE) -> Maybe FE fe_add = unsafeLocalCoreJet c_fe_add fe_square :: FE -> Maybe FE fe_square = unsafeLocalCoreJet c_fe_square fe_multiply :: (FE, FE) -> Maybe FE fe_multiply = unsafeLocalCoreJet c_fe_multiply fe_multiply_beta :: FE -> Maybe FE fe_multiply_beta = unsafeLocalCoreJet c_fe_multiply_beta fe_invert :: FE -> Maybe FE fe_invert = unsafeLocalCoreJet c_fe_invert fe_square_root :: FE -> Maybe (Either () FE) fe_square_root = unsafeLocalCoreJet c_fe_square_root fe_is_zero :: FE -> Maybe Bit fe_is_zero = unsafeLocalCoreJet c_fe_is_zero fe_is_odd :: FE -> Maybe Bit fe_is_odd = unsafeLocalCoreJet c_fe_is_odd scalar_normalize :: Scalar -> Maybe Scalar scalar_normalize = unsafeLocalCoreJet c_scalar_normalize scalar_negate :: Scalar -> Maybe Scalar scalar_negate = unsafeLocalCoreJet c_scalar_negate scalar_add :: (Scalar, Scalar) -> Maybe Scalar scalar_add = unsafeLocalCoreJet c_scalar_add scalar_square :: Scalar -> Maybe Scalar scalar_square = unsafeLocalCoreJet c_scalar_square scalar_multiply :: (Scalar, Scalar) -> Maybe Scalar scalar_multiply = unsafeLocalCoreJet c_scalar_multiply scalar_multiply_lambda :: Scalar -> Maybe Scalar scalar_multiply_lambda = unsafeLocalCoreJet c_scalar_multiply_lambda scalar_invert :: Scalar -> Maybe Scalar scalar_invert = unsafeLocalCoreJet c_scalar_invert scalar_is_zero :: Scalar -> Maybe Bit scalar_is_zero = unsafeLocalCoreJet c_scalar_is_zero gej_infinity :: () -> Maybe GEJ gej_infinity = unsafeLocalCoreJet c_gej_infinity gej_rescale :: (GEJ, FE) -> Maybe GEJ gej_rescale = unsafeLocalCoreJet c_gej_rescale gej_normalize :: GEJ -> Maybe (Either () GE) gej_normalize = unsafeLocalCoreJet c_gej_normalize gej_negate :: GEJ -> Maybe GEJ gej_negate = unsafeLocalCoreJet c_gej_negate ge_negate :: GE -> Maybe GE ge_negate = unsafeLocalCoreJet c_ge_negate gej_double :: GEJ -> Maybe GEJ gej_double = unsafeLocalCoreJet c_gej_double gej_add :: (GEJ, GEJ) -> Maybe GEJ gej_add = unsafeLocalCoreJet c_gej_add gej_ge_add_ex :: (GEJ, GE) -> Maybe (FE, GEJ) gej_ge_add_ex = unsafeLocalCoreJet c_gej_ge_add_ex gej_ge_add :: (GEJ, GE) -> Maybe GEJ gej_ge_add = unsafeLocalCoreJet c_gej_ge_add gej_is_infinity :: GEJ -> Maybe Bit gej_is_infinity = unsafeLocalCoreJet c_gej_is_infinity gej_equiv :: (GEJ, GEJ) -> Maybe Bit gej_equiv = unsafeLocalCoreJet c_gej_equiv gej_ge_equiv :: (GEJ, GE) -> Maybe Bit gej_ge_equiv = unsafeLocalCoreJet c_gej_ge_equiv gej_x_equiv :: (FE, GEJ) -> Maybe Bit gej_x_equiv = unsafeLocalCoreJet c_gej_x_equiv gej_y_is_odd :: GEJ -> Maybe Bit gej_y_is_odd = unsafeLocalCoreJet c_gej_y_is_odd gej_is_on_curve :: GEJ -> Maybe Bit gej_is_on_curve = unsafeLocalCoreJet c_gej_is_on_curve ge_is_on_curve :: GE -> Maybe Bit ge_is_on_curve = unsafeLocalCoreJet c_ge_is_on_curve scale :: (Scalar, GEJ) -> Maybe GEJ scale = unsafeLocalCoreJet c_scale off_curve_scale :: (Scalar, GEJ) -> Maybe GEJ off_curve_scale = unsafeLocalCoreJet c_off_curve_scale generate :: Scalar -> Maybe GEJ generate = unsafeLocalCoreJet c_generate linear_combination_1 :: ((Scalar, GEJ), Scalar) -> Maybe GEJ linear_combination_1 = unsafeLocalCoreJet c_linear_combination_1 off_curve_linear_combination_1 :: ((Scalar, GEJ), Scalar) -> Maybe GEJ off_curve_linear_combination_1 = unsafeLocalCoreJet c_off_curve_linear_combination_1 linear_verify_1 :: (((Scalar, GE), Scalar), GE) -> Maybe () linear_verify_1 = unsafeLocalCoreJet c_linear_verify_1 decompress :: Point -> Maybe (Either () GE) decompress = unsafeLocalCoreJet c_decompress point_verify_1 :: (((Scalar, Point), Scalar), Point) -> Maybe () point_verify_1 = unsafeLocalCoreJet c_point_verify_1 check_sig_verify :: ((PubKey, Word512), Sig) -> Maybe () check_sig_verify = unsafeLocalCoreJet c_check_sig_verify bip_0340_verify :: ((PubKey, Word256), Sig) -> Maybe () bip_0340_verify = unsafeLocalCoreJet c_bip_0340_verify swu :: FE -> Maybe GE swu = unsafeLocalCoreJet c_swu hash_to_curve :: Word256 -> Maybe GE hash_to_curve = unsafeLocalCoreJet c_hash_to_curve parse_lock :: Word32 -> Maybe (Either Word32 Word32) parse_lock = unsafeLocalCoreJet c_parse_lock parse_sequence :: Word32 -> Maybe (Either () (Either Word16 Word16)) parse_sequence = unsafeLocalCoreJet c_parse_sequence tapdata_init :: () -> Maybe Sha256.Ctx8 tapdata_init = unsafeLocalCoreJet c_tapdata_init ================================================ FILE: Haskell/Core/Simplicity/Functor.hs ================================================ {-# LANGUAGE RankNTypes #-} -- | This module provides a product for computing multiple interpretations of Simplicity simultaneously. -- Other tensors can be added when they are needed. module Simplicity.Functor ( SimplicityFunctor(..) ) where import Simplicity.Ty class SimplicityFunctor h where sfmap :: (forall a b. (TyC a, TyC b) => f a b -> g a b) -> h f -> h g ================================================ FILE: Haskell/Core/Simplicity/LibSecp256k1/Schnorr.hs ================================================ -- | This module specifies the types to be used to interface with bindings to a real Schnorr signature module for Secp256k1. -- It largely acts as a placeholder at this point in time. module Simplicity.LibSecp256k1.Schnorr ( PubKey(..), Sig(..) ) where import Data.Serialize (Serialize, get, put) import Data.Serialize.Get (getWord8) import Data.Serialize.Put (putWord8) import Simplicity.Word -- | An (x-only) public key format to be used for Schnorr signatures. data PubKey = PubKey Word256 instance Show PubKey where showsPrec p (PubKey w) = showParen (p > 10) . showString $ "PubKey 0x" ++ showHex256 w instance Serialize PubKey where get = PubKey <$> get put (PubKey x) = put x -- | A Schnorr signature format. data Sig = Sig Word256 Word256 instance Serialize Sig where get = Sig <$> get <*> get put (Sig r s) = put r >> put s instance Show Sig where showsPrec p (Sig r s) = showParen (p > 10) . showString $ "Sig 0x" ++ showHex256 r ++ " 0x" ++ showHex256 s ================================================ FILE: Haskell/Core/Simplicity/LibSecp256k1/Spec.hs ================================================ module Simplicity.LibSecp256k1.Spec ( -- * Field operations. FE, fe, fe_repr, fe_pack, fe_unpack , fe_zero, fe_one , fe_is_zero, fe_is_odd , fe_negate, fe_add, fe_halve, fe_multiply, fe_square, fe_invert, fe_square_root , (.+.), (.-.), (.*.), (.^.) -- * Group operations. , GEJ(..), _gej, gej, _x, _y, _z, g , gej_equiv , gej_negate , gej_double, gej_add_ex , gej_x_equiv, gej_y_is_odd , gej_is_on_curve , GE(..) , ge_to_gej , gej_normalize, gej_rescale , gej_ge_add_ex, gej_ge_add_zinv , ge_negate, ge_scale_lambda , ge_is_on_curve , gej_ge_equiv , shallueVanDeWoestijne, hash_to_curve -- * Scalar operations , Scalar, scalar, scalar_repr, scalar_pack , scalar_zero, scalar_negate, scalar_add, scalar_square, scalar_multiply, scalar_invert, scalar_split_lambda, scalar_split_128 , wnaf, scale, off_curve_scale, off_curve_linear_combination, linear_combination_1, off_curve_linear_combination_1 , linear_check, linear_check_1 -- * Point operations , Point(..), decompress, point_check -- * Public key / Signature operations , PubKey(..), pubkey_unpack, pubkey_unpack_neg , Sig(..), signature_unpack , bip_0340_check -- * Some large integer constants for secp256k1. , fieldOrder, groupOrder, beta, lambda -- * points on other twists , ge_115792089237316195423570985008687907853508896131558604026424249738214906721757 , ge_115792089237316195423570985008687907853031073199722524052490918277602762621571 , ge_57896044618658097711785492504343953926299326406578432197819248705606044722122 , ge_38597363079105398474523661669562635951234135017402074565436668291433169282997 , ge_8270863516951156815969356072049136275281522608437447405948333614614684278506 , ge_199, ge_169, ge_39, ge_14, ge_13, ge_7, ge_6, ge_3 ) where import Control.Applicative ((<|>)) import Control.Monad (guard) import Control.Monad.Trans.RWS hiding (put) import Control.Monad.Trans.State (state, evalState) import Control.Monad.Trans.Tardis (Tardis, getFuture, getPast, getsPast, modifyBackwards, modifyForwards, runTardis, sendFuture) import Data.Bits ((.&.), (.|.), finiteBitSize) import Data.ByteString.Short (ShortByteString, pack) import qualified Data.ByteString.Char8 as BSC import Data.Ix (inRange) import Data.List (foldl', mapAccumL, mapAccumR, unfoldr) import Data.Maybe (isJust) import Data.Serialize (encode, put) import Data.Serialize.Put (putShortByteString, runPut) import qualified Data.Vector as V import Lens.Family2 ((^.), (^..), (&), (+~), (*~), (%~), allOf, over, review, under, zipWithOf) import Lens.Family2.Stock (_1, _2, lend_, some_) import Simplicity.Digest import Simplicity.LibSecp256k1.Schnorr import Simplicity.Word infixl 6 .+., .-. infixl 7 .*. infixr 8 .^. -- | The secp256k1 field is @GF[p]@ where p is this prime number. fieldOrder :: Integer fieldOrder = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f -- | The secp256k1 group has order @n@ where @n@ is this prime number. groupOrder :: Integer groupOrder = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 -- | The canonical primitive cube root of 1 in @GF[p]@. -- -- @ -- mod (beta ^ 2 + beta + 1) fieldOrder == 0 -- @ -- -- Note that @mod (beta ^ 2) fieldOrder@ is the other, non-canonical, cube root of 1. beta :: Integer beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee -- | The canonical primitive cube root of 1 in the scalar field @GF[n]@. -- -- @ -- mod (lambda ^ 2 + lambda + 1) groupOrder == 0 -- @ -- -- and -- -- @ -- 'gej_normalize' ('scalar_mulitply' ('scalar' 'lambda') p) == 'GE' ('fe' 'beta' .*. x) y -- where (x, y) = 'gej_normalize' p -- @ -- -- Note that @mod (lambda ^ 2) groupOrder@ is the other, non-canonical, cube root of 1. lambda :: Integer lambda = 0x5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72 -- | An element of secp256k1's field is represented as a normalized value. data FE = FE { fe_pack :: Word256 -- ^ Return the normalized representative of a field element as a 'Word256'. } deriving (Eq, Show) -- | Return the normalized integer representative of a field element. fe_repr :: FE -> Integer fe_repr = toInteger . fe_pack -- | Construct a field element from an integer. fe :: Integer -> FE fe n = FE . fromInteger $ n `mod` fieldOrder -- | The zero value of the field. fe_zero :: FE fe_zero = fe 0 -- | The one value of the field. fe_one :: FE fe_one = fe 1 -- | @'fe' 7@ fe_seven :: FE fe_seven = fe 7 -- | @'fe' 'beta'@ fe_beta :: FE fe_beta = fe beta -- | Decode a 256-bit word value as a field element, failing if the value is non-canonical. fe_unpack :: Word256 -> Maybe FE fe_unpack x0 = guard (x == fe_repr a) >> return a where x = toInteger x0 a = fe x -- | Checks if the field element's representative is odd. fe_is_odd :: FE -> Bool fe_is_odd = odd . fe_repr -- | Checks if the field element is 0. fe_is_zero :: FE -> Bool fe_is_zero = (0 ==) . fe_repr -- | Negate a field element. fe_negate :: FE -> FE fe_negate = fe . negate . fe_repr -- | Add two field elements. fe_add :: FE -> FE -> FE fe_add a b = fe (fe_repr a + fe_repr b) -- | Multiply two field elements. fe_multiply :: FE -> FE -> FE fe_multiply a b = fe (fe_repr a * fe_repr b) -- | Square a field element. fe_square :: FE -> FE fe_square a = fe_multiply a a -- | Halve a field element. fe_halve :: FE -> FE fe_halve a = fe ((x + if odd x then fieldOrder else 0) `div` 2) where x = fe_repr a -- | Multiply a field element by an integer. -- -- @ -- mulInt i a == fe i .*. a -- @ mulInt :: Integer -> FE -> FE mulInt i a = fe_multiply (fe i) a -- | Add two field elements. (.+.) = fe_add -- | Multiply two field elements. (.*.) = fe_multiply -- | Difference of two field elements. x .-. y = fe_add x (fe_negate y) -- | A field element raised to a given power. x .^. n = go x (n `mod` (fieldOrder - 1)) where go x 0 = fe_zero go x 1 = x go x n | even n = go (fe_square x) (n `div` 2) | odd n = fe_multiply x (go (fe_square x) (n `div` 2)) -- | The modulular inverse of a field element, with 'fe_zero' mapping to 'fe_zero'. fe_invert :: FE -> FE fe_invert a = a .^. (fieldOrder - 2) -- | A modular square root of a field element if it exists. -- If it exists it returns a value that is itself a square. fe_square_root :: FE -> Maybe FE fe_square_root a | 0 == (fieldOrder + 1) `mod` 4 = do let res = a .^. ((fieldOrder + 1) `div` 4) guard $ fe_is_zero (fe_square res .-. a) return res -- | Checks if a field element has a square root. isQuad :: FE -> Bool isQuad = isJust . fe_square_root -- | A "compressed" point on the secp256k1 curve. Infinity not included. data Point = Point Bool FE deriving Show -- | A point in Jacobian coordinates. -- A '_z' component of 'fe_zero' represents a point at infinity. -- -- A value @p :: 'GEJ'@ where @p^.'_z'@ is not 'fe_zero' represents a point with x-coordinate @p.^'_x' .*. ('fe_invert' p.^_z) .^. 2@ -- and with y-coordinate @p.^'_y' .*. ('fe_invert' p.^_z) .^. 3@. -- -- A canonical point has a z-component of 1, except for the point at infinity whose canonical value has all components 0. data GEJ = GEJ !FE !FE !FE deriving Show -- | A traversal of the 3 'GEJ' components. _gej :: Applicative f => (FE -> f FE) -> GEJ -> f GEJ _gej = under gej -- | A grid of the 3 'GEJ' components. gej :: (Functor g, Applicative f) => (g FE -> f FE) -> g GEJ -> f GEJ gej f a = GEJ <$> f ((^._x) <$> a) <*> f ((^._y) <$> a) <*> f ((^._z) <$> a) -- | A lens for the x-component of 'GEJ'. _x :: Functor f => (FE -> f FE) -> GEJ -> f GEJ _x f (GEJ x y z) = (\x -> GEJ x y z) <$> f x -- | A lens for the y-component of 'GEJ'. _y :: Functor f => (FE -> f FE) -> GEJ -> f GEJ _y f (GEJ x y z) = (\y -> GEJ x y z) <$> f y -- | A lens for the z-component of 'GEJ'. _z :: Functor f => (FE -> f FE) -> GEJ -> f GEJ _z f (GEJ x y z) = (\z -> GEJ x y z) <$> f z -- | Checks if the point is a representation of infinity. gej_is_infinity :: GEJ -> Bool gej_is_infinity a = fe_is_zero (a^._z) -- | Returns an equivalent point with the z-coefficent multiplied by the given constant. -- This will return infinity if the constant is zero. gej_rescale :: GEJ -> FE -> GEJ gej_rescale (GEJ x y z) c = GEJ (x .*. c .^. 2) (y .*. c .^. 3) (z .*. c) -- | Negates a 'GEJ'. gej_negate :: GEJ -> GEJ gej_negate (GEJ x y z) = GEJ x (fe_negate y) z -- | Compute the point doubling formula for a 'GEJ'. gej_double :: GEJ -> GEJ gej_double a@(GEJ x y z) | gej_is_infinity a = mempty | otherwise = GEJ x' y' z' where x' = fe_halve . fe_halve $ mulInt 9 (x .^. 4) .+. mulInt (-8) (x .*. y .^. 2) y' = fe_halve . fe_halve . fe_halve $ mulInt 36 (x .^. 3 .*. y .^. 2) .+. mulInt (-27) (x .^. 6) .+. mulInt (-8) (y .^. 4) z' = y .*. z -- | Compute the point addition formula for a 'GEJ'. -- This also returns the ratio between z-component of 'a' and z-component of the result. -- -- @ -- a^.'_z' .*. r = p^.'_z' -- @ -- -- where -- -- @ -- (r, p) = 'gej_add_ex' a b -- @ gej_add_ex :: GEJ -> GEJ -> (FE, GEJ) gej_add_ex a@(GEJ ax ay az) b@(GEJ bx by bz) | gej_is_infinity a = (fe_zero, GEJ bx by bz) | gej_is_infinity b = (fe_one, a) | isZeroH && isZeroI = (ay, gej_double a) | isZeroH = (fe_zero, mempty) | otherwise = (bz .*. h, GEJ x y z) where u1 = ax .*. bz .^. 2 u2 = bx .*. az .^. 2 s1 = ay .*. bz .^. 3 s2 = by .*. az .^. 3 h = u2 .-. u1 i = s1 .-. s2 isZeroH = fe_is_zero h isZeroI = fe_is_zero i z = az .*. bz .*. h t = fe_negate $ u1 .*. h .^. 2 x = i .^. 2 .+. mulInt 2 t .-. h .^. 3 y = (t .+. x) .*. i .-. h .^. 3 .*. s1 instance Semigroup GEJ where a <> b = snd $ gej_add_ex a b instance Monoid GEJ where mempty = GEJ fe_zero fe_zero fe_zero -- | Check if two points in jacobian coordinates are equivalent. gej_equiv :: GEJ -> GEJ -> Bool gej_equiv a b = gej_is_infinity $ gej_negate a <> b -- | Check if the x-coordinate of the point represented by a 'GEJ' has a given value. gej_x_equiv :: FE -> GEJ -> Bool gej_x_equiv x a | gej_is_infinity a = False | otherwise = fe_is_zero $ (fe_square (a^._z) .*. x) .-. (a^._x) -- | Check if the y-coordinate of the point represented by a 'GEJ' is odd. gej_y_is_odd :: GEJ -> Bool gej_y_is_odd a@(GEJ _ y z) | gej_is_infinity a = False | otherwise = fe_is_odd $ y .*. invz .^. 3 where invz = fe_invert z -- | Validates the secp256k1 curve equation: Y^2 = X^3 + 7Z^6 gej_is_on_curve :: GEJ -> Bool gej_is_on_curve (GEJ x y z) = fe_is_zero $ x.^.3 .+. fe_seven.*.z.^.6 .-. y.^.2 -- | An uncompressed point. Infinity not included data GE = GE !FE !FE -- Infinity not included. deriving Show -- | Convert an uncompressed point to Jacobian coordinates ge_to_gej (GE x y) = GEJ x y fe_one -- | Compute the point addition formula for a 'GEJ' and a 'GE'. -- This also returns the ratio between z-component of 'a' and z-component of the result. -- -- @ -- a^.'_z' .*. r = p^.'_z' -- @ -- -- where -- -- @ -- (r, p) = 'gej_add_ex' a b -- @ gej_ge_add_ex :: GEJ -> GE -> (FE, GEJ) gej_ge_add_ex a (GE bx by) = gej_add_ex a (GEJ bx by fe_one) -- | Compute a point addition formula for a 'GEJ' and another point with an inverted z coordinate. -- -- @ -- 'gej_is_infinity' $ ('gej_ge_add_zinv' a (GE bx by) bzinv) <> ('gej_negate' (a <> ('GEJ' bx by ('fe_invert' bzinf)))) -- @ -- -- where -- -- @ -- (r, p) = 'gej_add_ex' a b -- @ gej_ge_add_zinv :: GEJ -> GE -> FE -> GEJ gej_ge_add_zinv a (GE bx by) bzinv = snd $ gej_ge_add_ex a (GE (bx .*. bzinv .^. 2) (by .*. bzinv .^. 3)) -- | Convert a 'GEJ' to a 'GE'. -- If the input is infinity, returns Nothing. gej_normalize :: GEJ -> Maybe GE gej_normalize (GEJ x y z) | fe_is_zero z = Nothing | otherwise = Just $ GE (x .*. invz .^. 2) (y .*. invz .^. 3) where invz = fe_invert z -- | Negates a 'GE'. ge_negate :: GE -> GE ge_negate (GE x y) = GE x (fe_negate y) -- | Scale a 'GE' by 'lambda'. -- -- @ -- 'ge_scale_lambda' ('ge_normalze' p) == 'ge_normalize' ('scalar_multiply' 'scalar_lambda' p) -- @ ge_scale_lambda :: GE -> GE ge_scale_lambda (GE x y) = GE (x .*. fe_beta) y -- | Validates the secp256k1 curve equation: y^2 = x^3 + 7 ge_is_on_curve :: GE -> Bool ge_is_on_curve (GE x y) = gej_is_on_curve (GEJ x y fe_one) -- | Check if a point in jacobian coordinates is equivalent to one given in affine coordinates. gej_ge_equiv :: GEJ -> GE -> Bool gej_ge_equiv x y = gej_is_infinity . snd $ gej_ge_add_ex (gej_negate x) y -- | Algebraically distribute a field element to up to three candidate points on the secp256k1 curve. -- At least one point is guaranteed to be on curve. -- While the algebraic properties only hold for non-zero t, the code does return a valid point when t = 0. shallueVanDeWoestijne_internal :: FE -> (Maybe GE, Maybe GE, Maybe GE) shallueVanDeWoestijne_internal t = (GE x1 <$> y1, GE x2 <$> y2, GE x3 <$> y3) where Just c = fe_square_root (fe (-3)) d = fe_halve (c .-. fe_one) wn = c .*. t wd = (fe_one .+. fe_seven) .+. (t.^.2) invwd = fe_invert wd x1n = d .*. wd .-. t .*. wn x1 = x1n .*. invwd y1 = sign <$> fe_square_root (x1 .^. 3 .+. fe_seven) x2n = fe_negate (x1n .+. wd) x2 = x2n .*. invwd y2 = sign <$> fe_square_root (x2 .^. 3 .+. fe_seven) x3n = (wd.^.2) .+. c.^.2 .*. t.^.2 x3 = x3n .*. fe_invert (wn.^.2) y3 = sign <$> fe_square_root (x3 .^. 3 .+. fe_seven) sign | fe_is_odd t = fe_negate | otherwise = id -- | Algebraically distribute a field element over the secp256k1 curve as defined in -- "Indifferentiable Hashing to Barreto-Naehrig Curves" by Pierre-Alain Fouque, Mehdi Tibouchi -- -- -- While this by iteslf is not a cryptographic hash function, it can be used as a subrotuine -- in a 'hash_to_curve' function. However the distribution only approaches uniform when it is called twice. shallueVanDeWoestijne :: FE -> GE shallueVanDeWoestijne t = result where (p1, p2, p3) = shallueVanDeWoestijne_internal t Just result = p1 <|> p2 <|> p3 -- | An element of secp256k1's scalar field is represented as a normalized value. newtype Scalar = Scalar { scalar_pack :: Word256 -- ^ Return the normalized representative of a scalar element as a 'Word256'. } deriving (Eq, Show) instance Bounded Scalar where minBound = scalar 0 maxBound = scalar $ groupOrder - 1 -- | The zero value of the scalar field. scalar_zero :: Scalar scalar_zero = Scalar 0 -- | @'scalar' 'lambda'@ scalar_lambda :: Scalar scalar_lambda = scalar lambda -- | Construct a scalar element from an integer. scalar :: Integer -> Scalar scalar x = Scalar $ fromInteger (x `mod` groupOrder) -- | Return the normalized integer representative of a scalar element. scalar_repr :: Scalar -> Integer scalar_repr = toInteger . scalar_pack -- | Decode a 256-bit word value as a scalar element, failing if the value is non-canonical. scalar_unpack :: Word256 -> Maybe Scalar scalar_unpack x0 = guard (x == scalar_repr s) >> return s where x = toInteger x0 s = scalar x -- | Checks if the scalar element is 0. scalar_is_zero :: Scalar -> Bool scalar_is_zero a = scalar_repr a == 0 -- | Negate a scalar element. scalar_negate :: Scalar -> Scalar scalar_negate = scalar . negate . scalar_repr -- | Add two scalar elements. scalar_add :: Scalar -> Scalar -> Scalar scalar_add a b = scalar (scalar_repr a + scalar_repr b) -- | Multiply two scalar elements. scalar_multiply :: Scalar -> Scalar -> Scalar scalar_multiply a b = scalar (scalar_repr a * scalar_repr b) -- | Square a scalar element. scalar_square :: Scalar -> Scalar scalar_square a = scalar_multiply a a -- | The modulular inverse of a scalar element, with 'scalar_zero' mapping to 'scalar_zero'. scalar_invert :: Scalar -> Scalar scalar_invert a = a `scalar_power` (groupOrder - 2) where scalar_power x n = go x (n `mod` (groupOrder - 1)) where go x 0 = scalar_zero go x 1 = x go x n | even n = go (scalar_square x) (n `div` 2) | odd n = scalar_multiply x (go (scalar_square x) (n `div` 2)) -- | Scale a 'GEJ' by a scalar element. off_curve_scale :: Scalar -> GEJ -> GEJ off_curve_scale na a = off_curve_linear_combination_1 na a scalar_zero -- | Safe scale of a 'GEJ' by a scalar element. -- -- Returns 'Nothing' when the point @a@ is not 'gej_is_on_curve'. -- Otherwise, returns 'Just' the result of 'scale'. scale :: Scalar -> GEJ -> Maybe GEJ scale na a = linear_combination_1 na a scalar_zero -- | Decompose a scalar value in short components. -- -- @ -- 'scalar' (k1 + 'lambda' * k2) == a -- abs k1 < 2^128 && abs k2 < 2^128 -- @ -- -- where -- -- @ -- (k1, k2) = 'scalar_split_lambda' a -- @ scalar_split_lambda :: Scalar -> (Integer, Integer) scalar_split_lambda k0 = (k1, k2) where n = groupOrder n2 = n `div` 2 k = scalar_repr k0 g1 = 0x3086d221a7d46bcde86c90e49284eb153daa8a1471e8ca7fe893209a45dbb031 g2 = 0xe4437ed6010e88286f547fa90abfe4c4221208ac9df506c61571b4ae8ac47f71 b1 = -0xe4437ed6010e88286f547fa90abfe4c3 b2 = 0x3086d221a7d46bcde86c90e49284eb15 c1 = (k * g1 + 2^383) `div` (2^384) c2 = (k * g2 + 2^383) `div` (2^384) k2 = - c1*b1 - c2*b2 k1 = (k - k2 * lambda + n2) `mod` n - n2 -- | Decompose a scalar value in short components. -- -- @ -- 'scalar' (k1 + 2^128 * k2) == a -- 0 <= k1 < 2^128 && 0 <= k2 < 2^128 -- @ -- -- where -- -- @ -- (k1, k2) = 'scalar_split_128' a -- @ scalar_split_128 :: Scalar -> (Integer, Integer) scalar_split_128 k0 = (k1, k2) where k = scalar_repr k0 (k2, k1) = k `divMod` (2^128) -- | Fast computation of a linear combination of the secp256k1 curve generator and other points. -- -- @ -- 'gej_is_infinity' $ 'off_curve_linear_combination' [] ng <> 'gej_negate' ('scalar_multiply' ng 'g') -- @ -- -- @ -- 'gej_is_infinity' $ 'off_curve_linear_combination' ((na, a):tl) ng <> 'gej_negate' ('scalar_multiply' ng 'g' <> 'linear_combination' tl ng) -- @ off_curve_linear_combination :: [(Scalar, GEJ)] -> Scalar -> GEJ off_curve_linear_combination l ng = foldr f mempty zips & _z %~ (.*. globalZ) where wa = 5 (l', globalZ) = runTableM . sequence $ [(,) <$> pure na <*> scalarTable wa s | (na, s) <- l, not (gej_is_infinity s) && not (scalar_is_zero na)] (ng1, ng2) = scalar_split_128 ng split_l = do (na, table) <- l' let (na1, na2) = scalar_split_lambda na let table_lam = ge_scale_lambda <$> table [(na1, table), (na2, table_lam)] f (as, Nothing, Nothing) r0 = foldl' gej_ge_add (gej_double r0) as f (as, Just g1, Nothing) r0 = gej_ge_add_zinv (f (as, Nothing, Nothing) r0) (tableG ! g1) globalZ f (as, g1, Just g2) r0 = gej_ge_add_zinv (f (as, g1, Nothing) r0) (tableG128 ! g2) globalZ gej_ge_add p q = snd $ gej_ge_add_ex p q zip3Ex [] [] [] = [] zip3Ex [] bs cs = zip3Ex [[]] bs cs zip3Ex as [] cs = zip3Ex as [Nothing] cs zip3Ex as bs [] = zip3Ex as bs [Nothing] zip3Ex (a:as) (b:bs) (c:cs) = (a,b,c) : zip3Ex as bs cs zips = zip3Ex (transposeTables split_l) (wnaf wg ng1) (wnaf wg ng2) transposeTables [] = [] transposeTables ((na, ts):rest) = merge (wnaf wa na) ts (transposeTables rest) where merge [] _ tbls = tbls merge l t [] = [[t ! i | Just i <- [x]] | x <- l] merge (Just i : tl) t (htbls : ttbls) = ((t ! i) : htbls) : merge tl t ttbls merge (Nothing : tl) t (htbls : ttbls) = htbls : merge tl t ttbls -- | Fast computation of a linear combination of the secp256k1 curve generator and another point. -- -- @ -- 'gej_is_infinity' $ 'off_curve_linear_combination_1' na a ng <> 'gej_negate' ('scalar_multiply' na 'a' <> 'scalar_multiply' ng 'g') -- @ off_curve_linear_combination_1 :: Scalar -> GEJ -> Scalar -> GEJ off_curve_linear_combination_1 na a = off_curve_linear_combination [(na, a)] -- | Safe computation of a linear combination of the secp256k1 curve generator and another point. -- -- Returns 'Nothing' when the point @a@ is not 'gej_is_on_curve'. -- Otherwise, returns 'Just' the result of 'off_curve_linear_combination_1'. linear_combination_1 :: Scalar -> GEJ -> Scalar -> Maybe GEJ linear_combination_1 na a ng = do guard $ gej_is_on_curve a return $ off_curve_linear_combination_1 na a ng -- | Decompose an integer in windowed non-adjacent form wnafInteger :: Int -> Integer -> [Int] wnafInteger w | 0 < w && w <= finiteBitSize w = unfoldr f where f 0 = Nothing f i = Just (fromInteger x, (i - x) `div` 2) where x | odd i = ((i + 2^(w-1)) `mod` 2^w) - 2^(w-1) | otherwise = 0 -- | Decompose an integer in windowed non-adjacent form. -- Odd values have their least significant bit dropped. -- Zero values are returned as Nothing. wnaf :: Int -> Integer -> [Maybe Int] wnaf w s = post <$> wnafInteger w s where post 0 = Nothing post i | odd i = Just $ i `div` 2 | otherwise = error "Simplicity.LibSecp256k1.Spec: invalid result from wnafInteger" -- | A monad used to help construct scalar tables with a common z-coordinate. type TableM a = Tardis FE GEJ a -- | Execute a 'TableM' computation, also returning the combon z-coordinate value. runTableM :: TableM a -> (a, FE) runTableM tardis = (a, p^._z) where (a,(_,p)) = runTardis tardis (fe_one, GEJ fe_zero fe_zero fe_one) -- | Get the current table point, scalining it by the future z-factor. getTable :: TableM GE getTable = do a <- getPast zf <- getFuture return $ GE (a^._x .*. zf .^. 2) (a^._y .*. zf .^. 3) -- | Put a new table point into the 'TableM'. -- Requires the (true) z-ratio between the new point and the previous point. putTable :: FE -> GEJ -> TableM () putTable zr a = do modifyBackwards (.*. zr) sendFuture a -- | Precompute small odd multiplies of a 'GEJ' and give them a common z-coordinate. -- The point must not be at infinity. scalarTable :: Int -> GEJ -> TableM (V.Vector GE) scalarTable w a = do z0 <- getsPast (^._z) let a' = gej_rescale a z0 let d = gej_double a' let dz = d^._z let a'' = GEJ (a'^._x .*. dz .^. 2) (a'^._y .*. dz .^. 3) (a'^._z) putTable (a^._z .*. dz) a'' let tableNext = uncurry putTable =<< (gej_ge_add_ex <$> getPast <*> pure (GE (d^._x) (d^._y))) result <- V.cons <$> getTable <*> V.replicateM (len - 1) (tableNext >> getTable) modifyForwards $ _z %~ (.*. dz) return result where len = 2^(w-2) -- | The specified generator of the secp256k1 curve. g :: GEJ g = GEJ (fe 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798) (fe 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8) fe_one -- | A representation of 2^128 * 'g'. g128 :: GEJ g128 = iterate gej_double g !! 128 -- | The default window size for scalars multiplying by 'g'. wg = 15 -- | A precomputate table of odd multiples of 'g'. tableG = table wg g -- | A precomputate table of odd multiples of 'g128'. tableG128 = table wg g128 -- | Compute a table of odd multiple of a point and 'gej_normalize' all of them. table w p = t & traverse %~ norm where (t,z) = runTableM (scalarTable w p) zinv = fe_invert z norm (GE x y) = GE (x .*. zinv .^. 2) (y .*. zinv .^. 3) -- | An index into a precomputed odd multiple table of 'GE'. -- Negative indexes are accepted and automatically return the negation of the corresponding point. (!) :: V.Vector GE -> Int -> GE t ! i | i >= 0 = t V.! i | otherwise = ge_negate (t V.! (-i-1)) -- | Validates that all points are 'ge_is_on_curve' and that -- @'linear_check' l ng r@ implies -- -- @ -- 'gej_is_infinity' $ 'linear_combination' l ng <> 'ge_negate' r -- @ linear_check :: [(Scalar, GE)] -> Scalar -> GE -> Bool linear_check l ng r = isJust $ do guard $ ge_is_on_curve r guard $ allOf (traverse._2) ge_is_on_curve l guard $ gej_is_infinity (off_curve_linear_combination l' ng <> negR) where negR = toGEJ (ge_negate r) l' = l & (traverse._2) %~ toGEJ toGEJ (GE x y) = (GEJ x y fe_one) -- | Validates that all points are 'ge_is_on_curve' and that -- @'linear_check_1' na a ng r@ implies -- -- @ -- 'gej_is_infinity' $ 'linear_combination_1' na a ng <> 'ge_negate' r -- @ linear_check_1 :: Scalar -> GE -> Scalar -> GE -> Bool linear_check_1 na a = linear_check [(na, a)] -- | Convert a point from compressed coordinates to affine coordinates. -- Fails if the x-coordinate of the point is not on the secp256k1 curve. decompress :: Point -> Maybe GE decompress (Point yodd x) = do y <- fe_square_root (x .^. 3 .+. fe_seven) return (GE x (if fe_is_odd y == yodd then y else (fe_negate y))) -- | Given an (x-only) public key, check that the x-coordinate is normalized and returns a Point representing that pubkey. -- This does not check that the point is on-curve, which needed to be done by a subsequent call to `decompress`. pubkey_unpack :: PubKey -> Maybe Point pubkey_unpack (PubKey px) = Point False <$> fe_unpack px -- | Given an (x-only) public key, check that the x-coordinate is normalized and returns a Point representing the negation of that pubkey. -- This does not check that the point is on-curve, which needed to be done by a subsequent call to `decompress`. pubkey_unpack_neg :: PubKey -> Maybe Point pubkey_unpack_neg (PubKey px) = Point True <$> fe_unpack px -- | Given a bip0340 signature, unpack it r value as an 'FE', and its s value as a 'Scalar'. -- Fails if the signature components are out of range. signature_unpack :: Sig -> Maybe (FE, Scalar) signature_unpack (Sig r s) = (,) <$> fe_unpack r <*> scalar_unpack s -- | Validates that all points are 'decompress'able and that the 'linear_check' of the decompressed points is satisfied. point_check :: [(Scalar, Point)] -> Scalar -> Point -> Bool point_check l ng r = isJust $ do l' <- l & (traverse._2) decompress r' <- decompress r guard $ linear_check l' ng r' -- | Verify a bip0340 signature for a given public key on a given message. bip_0340_check :: PubKey -- ^ public key -> Hash256 -- ^ message -> Sig -- ^ signature -> Bool bip_0340_check pk m sg = isJust $ do negp <- pubkey_unpack_neg pk (rx, s) <- signature_unpack sg let tag = bsHash (BSC.pack "BIP0340/challenge") let h = bsHash . runPut $ put tag >> put tag >> put (fe_pack rx) >> put pk >> put m let e = scalar . integerHash256 $ h let r = Point False rx guard $ point_check [(e, negp)] s r -- | A cryptograph hash function that results in a point on the secp256k1 curve. -- -- It is cryptographically impossible for 'Nothing' to be returned. hash_to_curve :: Word256 -> Maybe GE hash_to_curve key = do p1 <- swu_limit hash1 p2 <- swu_limit hash2 gej_normalize . snd $ gej_ge_add_ex (ge_to_gej p1) p2 where hash1 = integerHash256 $ bsHash (BSC.pack "1st generation: " <> encode key) hash2 = integerHash256 $ bsHash (BSC.pack "2nd generation: " <> encode key) swu_limit x = shallueVanDeWoestijne <$> fe_unpack (fromInteger x) -- | Point of order 3 * 199 * 18979 * 5128356331187950431517 * 1992751017769525324118900703535975744264170999967 ge_115792089237316195423570985008687907853508896131558604026424249738214906721757 :: GE ge_115792089237316195423570985008687907853508896131558604026424249738214906721757 = GE fe_one (fe 47) -- | Point of order 109903 * 12977017 * 383229727 * 211853322379233867315890044223858703031485253961775684523 ge_115792089237316195423570985008687907853031073199722524052490918277602762621571 :: GE ge_115792089237316195423570985008687907853031073199722524052490918277602762621571 = GE fe_one (fe 2) -- | Point of order 2 * 3 * 20412485227 * 83380711482738671590122559 * 5669387787833452836421905244327672652059 ge_57896044618658097711785492504343953926299326406578432197819248705606044722122 :: GE ge_57896044618658097711785492504343953926299326406578432197819248705606044722122 = GE fe_one (fe 3) -- | Point of order 3 * 13^2 * 3319 * 22639 * 1013176677300131846900870239606035638738100997248092069256697437031 ge_38597363079105398474523661669562635951234135017402074565436668291433169282997 :: GE ge_38597363079105398474523661669562635951234135017402074565436668291433169282997 = GE fe_one (fe 4) -- | Point of order 2 * 7 * 10903 * 5290657 * 10833080827 * 22921299619447 * 41245443549316649091297836755593555342121 ge_8270863516951156815969356072049136275281522608437447405948333614614684278506 :: GE ge_8270863516951156815969356072049136275281522608437447405948333614614684278506 = GE fe_one (fe 9) -- | Point of order 199 ge_199 :: GE ge_199 = GE (fe 70687250180557772597302152869007174094074882915196773732325669623429152815718) (fe 33705998260714715075689047715894246886612372461530560867300550015040889896278) -- | Point of order 13^2 ge_169 :: GE ge_169 = GE (fe 76143429403124191739648005988712146536970826737586076805285435910939811650235) (fe 79206108477852635180125138589256689828047073885928765425620364817661860808444) -- | Point of order 3 * 13 ge_39 :: GE ge_39 = GE (fe 106383153246165320275512998590184975158094311190930717121540544272958714969874) (fe 60732340993648917667778372165513456197562368078430634464262139756474636012620) -- | Point of order 2 * 7 ge_14 :: GE ge_14 = GE (fe 23022798600391872912114696699513327158948857432264427056250729177241370144563) (fe 42638903475844439756199347045463393577799965344626237613274902440780224637754) -- | Point of order 13 ge_13 :: GE ge_13 = GE (fe 64527622301014718397267236002495618081577172385398418064146870396180094467254) (fe 64805533305984530191801092315596539809224403998577052480080063250771024326631) -- | Point of order 7 ge_7 :: GE ge_7 = GE (fe 114109980193979926462125731765358310155031959372310767812063216697230157494741) (fe 101398216421584366967138431919489099535284823381455250476556676772183350055487) -- | Point of order 2 * 3 ge_6 :: GE ge_6 = GE (fe 106586213356003376052770626926523423124273824193112332847656463919061591657353) (fe 26101920679609057376888884124959740524626979187904654689991505285331895977061) -- | Point of order 3 ge_3 :: GE ge_3 = GE (fe 93163632785783131583621179645788501141364174486796116157579303931124646196327) (fe 67800883132571304345368516576619608502750474897195575578939869419018063089619) ================================================ FILE: Haskell/Core/Simplicity/MerkleRoot/Impl.hs ================================================ -- | This module provides functions for computing commitment, identity and annotated Merkle roots of Simplicity expressions and Merkle roots of Simplicity types. -- It also provides some other functions for other hashing schemes that will avoid collisions with the aforementioned Merkle roots. -- -- This module is internal only. "Simplicity.MerkleRoot" is the public facing module. module Simplicity.MerkleRoot.Impl ( typeRoot, typeRootR , CommitmentRoot, commitmentRoot , IdentityRoot, identityHash , AnnotatedRoot, annotatedRoot , hiddenRoot , signatureTag, sigHash , cmrFail0 -- * Internal functions -- | These functions are use internally to define commitment, identity, and annotated Merkle root instances for -- Primitives and expressions that depend on Primitives. , primitiveCommitmentImpl, jetCommitmentImpl , primitiveIdentityImpl, jetIdentityImpl , primitiveAnnotatedImpl, jetAnnotatedImpl ) where import Data.List (intercalate) import Data.Proxy (Proxy(..)) import Data.Serialize (encode) import Lens.Family2 (over, review) import Simplicity.Digest import Simplicity.Tags import Simplicity.Term.Core import Simplicity.Ty.Word -- | This function hashes a hash such that it will not collide with any 'typeRoot' or 'identityRoot'. -- -- It is designed to be used as if it were a "identity hash" for hidden nodes. hiddenRoot :: Hash256 -> Hash256 hiddenRoot = ivHash . compressHalf hiddenTag -- | Computes a hash committing to a Simplicity type. -- This function is memoized. typeRoot :: Ty -> Hash256 typeRoot = memoCataTy typeRootF where typeRootF :: TyF Hash256 -> Hash256 typeRootF One = ivHash $ typeTag "unit" typeRootF (Sum a b) = ivHash $ compress (typeTag "sum") (a, b) typeRootF (Prod a b) = ivHash $ compress (typeTag "prod") (a, b) -- | A variant of 'typeRoot' for @'TyReflect' a@ values. -- -- @ -- typeRootR = typeRoot . unreflect -- @ typeRootR :: TyReflect a -> Hash256 typeRootR = typeRoot . unreflect newtype CommitmentRoot a b = CommitmentRoot { -- | A digest of a Simplicity expression that excludes 'witness' values and the 'disconnect'ed expressions. -- It also exclude typing information (with the exception of jets). commitmentRoot :: Hash256 } deriving (Eq, Show) commit = CommitmentRoot . ivHash -- | The commitment root of a @'fail' 'hash0' 'hash0'@ expression. -- -- This hash value can be used as a default value for assertions, but at the cost of not hiding the fact that it isn't a pruned alternative branch. cmrFail0 :: Hash256 cmrFail0 = commitmentRoot (fail0 :: CommitmentRoot () ()) instance Core CommitmentRoot where iden = commit $ commitmentTag "iden" comp (CommitmentRoot s) (CommitmentRoot t) = commit $ compress (commitmentTag "comp") (s, t) unit = commit $ commitmentTag "unit" injl (CommitmentRoot t) = commit $ compressHalf (commitmentTag "injl") t injr (CommitmentRoot t) = commit $ compressHalf (commitmentTag "injr") t match (CommitmentRoot s) (CommitmentRoot t) = commit $ compress (commitmentTag "case") (s, t) pair (CommitmentRoot s) (CommitmentRoot t) = commit $ compress (commitmentTag "pair") (s, t) take (CommitmentRoot t) = commit $ compressHalf (commitmentTag "take") t drop (CommitmentRoot t) = commit $ compressHalf (commitmentTag "drop") t instance Assert CommitmentRoot where assertl (CommitmentRoot s) t = commit $ compress (commitmentTag "case") (s, t) assertr s (CommitmentRoot t) = commit $ compress (commitmentTag "case") (s, t) fail b = commit $ compress (commitmentTag "fail") b instance Witness CommitmentRoot where witness _ = commit $ commitmentTag "witness" instance Delegate CommitmentRoot where disconnect (CommitmentRoot s) _ = commit $ compressHalf (commitmentTag "disconnect") s newtype IdentityRoot a b = IdentityRoot Hash256 -- | A hash of the identity Merkle root, which includes 'witness' values and 'disconnect'ed expressions, -- along with the type Merkle roots of the input and output types. identityHash :: (TyC a, TyC b) => IdentityRoot a b -> Hash256 identityHash ir@(IdentityRoot t) = ivHash $ compress (compressHalf identityHashTag t) (typeRootR ra, typeRootR rb) where (ra, rb) = reifyArrow ir identify = IdentityRoot . ivHash instance Core IdentityRoot where iden = identify $ commitmentTag "iden" comp (IdentityRoot s) (IdentityRoot t) = identify $ compress (commitmentTag "comp") (s, t) unit = identify $ commitmentTag "unit" injl (IdentityRoot t) = identify $ compressHalf (commitmentTag "injl") t injr (IdentityRoot t) = identify $ compressHalf (commitmentTag "injr") t match (IdentityRoot s) (IdentityRoot t) = identify $ compress (commitmentTag "case") (s, t) pair (IdentityRoot s) (IdentityRoot t) = identify $ compress (commitmentTag "pair") (s, t) take (IdentityRoot t) = identify $ compressHalf (commitmentTag "take") t drop (IdentityRoot t) = identify $ compressHalf (commitmentTag "drop") t instance Assert IdentityRoot where assertl (IdentityRoot s) t = identify $ compress (commitmentTag "case") (s, t) assertr s (IdentityRoot t) = identify $ compress (commitmentTag "case") (s, t) fail b = identify $ compress (commitmentTag "fail") b instance Witness IdentityRoot where witness v = result where result = identify $ compress (identityTag "witness") (bitStringHash (putValue v), typeRootR rb) rb = reifyProxy result instance Delegate IdentityRoot where disconnect (IdentityRoot s) (IdentityRoot t) = identify $ compress (identityTag "disconnect") (s, t) newtype AnnotatedRoot a b = AnnotatedRoot { -- | A digest of a Simplicity expression that also includes all typing annotations. annotatedRoot :: Hash256 } deriving (Eq, Show) observe = AnnotatedRoot . ivHash instance Core AnnotatedRoot where iden = result where result = observe $ compressHalf (annotatedTag "iden") (typeRootR (reifyProxy result)) comp ws@(AnnotatedRoot s) wt@(AnnotatedRoot t) = result where result = observe $ compress (compress (compressHalf (annotatedTag "comp") (typeRootR (reifyProxy proxyA))) (typeRootR (reifyProxy proxyB), (typeRootR (reifyProxy proxyC)))) (s, t) proxy :: proxy a b -> proxy b c -> (Proxy a, Proxy b, Proxy c) proxy _ _ = (Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC) = proxy ws wt unit = result where result = observe $ compressHalf (annotatedTag "unit") (typeRootR (fst (reifyArrow result))) injl (AnnotatedRoot t) = result where result = observe $ compress (compress (annotatedTag "injl") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), t) proxy :: proxy a (Either b c) -> (Proxy a, Proxy b, Proxy c) proxy _ = (Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC) = proxy result injr (AnnotatedRoot t) = result where result = observe $ compress (compress (annotatedTag "injr") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), t) proxy :: proxy a (Either b c) -> (Proxy a, Proxy b, Proxy c) proxy _ = (Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC) = proxy result match (AnnotatedRoot s) (AnnotatedRoot t) = result where result = observe $ compress (compress (compress (annotatedTag "case") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), typeRootR (reifyProxy proxyD))) (s, t) proxy :: proxy ((Either a b), c) d -> (Proxy a, Proxy b, Proxy c, Proxy d) proxy _ = (Proxy, Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC, proxyD) = proxy result pair (AnnotatedRoot s) (AnnotatedRoot t) = result where result = observe $ compress (compress (compressHalf (annotatedTag "pair") (typeRootR (reifyProxy proxyA))) (typeRootR (reifyProxy proxyB), (typeRootR (reifyProxy proxyC)))) (s, t) proxy :: proxy a (b,c) -> (Proxy a, Proxy b, Proxy c) proxy _ = (Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC) = proxy result take (AnnotatedRoot t) = result where result = observe $ compress (compress (annotatedTag "take") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), t) proxy :: proxy (a,b) c -> (Proxy a, Proxy b, Proxy c) proxy _ = (Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC) = proxy result drop (AnnotatedRoot t) = result where result = observe $ compress (compress (annotatedTag "drop") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), t) proxy :: proxy (a,b) c -> (Proxy a, Proxy b, Proxy c) proxy _ = (Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC) = proxy result instance Assert AnnotatedRoot where assertl (AnnotatedRoot s) t = result where result = observe $ compress (compress (compress (annotatedTag "assertl") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), typeRootR (reifyProxy proxyD))) (s, t) proxy :: proxy ((Either a b), c) d -> (Proxy a, Proxy b, Proxy c, Proxy d) proxy _ = (Proxy, Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC, proxyD) = proxy result assertr s (AnnotatedRoot t) = result where result = observe $ compress (compress (compress (annotatedTag "assertr") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), typeRootR (reifyProxy proxyD))) (s, t) proxy :: proxy ((Either a b), c) d -> (Proxy a, Proxy b, Proxy c, Proxy d) proxy _ = (Proxy, Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC, proxyD) = proxy result -- This should never be called in practice, but we add it for completeness. fail b = observe $ compress (annotatedTag "fail") b instance Witness AnnotatedRoot where witness v = result where result = observe $ compress (compressHalf (annotatedTag "witness") (typeRootR ra)) (typeRootR rb, bitStringHash (putValue v)) (ra, rb) = reifyArrow result instance Delegate AnnotatedRoot where disconnect ws@(AnnotatedRoot s) wt@(AnnotatedRoot t) = result where result = observe $ compress (compress (compress (annotatedTag "disconnect") (typeRootR (reifyProxy proxyA), typeRootR (reifyProxy proxyB))) (typeRootR (reifyProxy proxyC), typeRootR (reifyProxy proxyD))) (s, t) proxy :: proxy (w, a) (b, c) -> proxy c d -> (Proxy a, Proxy b, Proxy c, Proxy d) proxy _ _ = (Proxy, Proxy, Proxy, Proxy) (proxyA, proxyB, proxyC, proxyD) = proxy ws wt primitiveCommitmentImpl primPrefix primName = commit . primTag primPrefix . primName -- Jets commit to their types, so we use 'identityHash' here. jetCommitmentImpl ir milliweight = commit $ compress jetTag (review (over be256) milliweight, identityHash ir) primitiveIdentityImpl primPrefix primName = identify . primTag primPrefix . primName jetIdentityImpl ir milliweight = identify $ compress jetTag (review (over be256) milliweight, identityHash ir) primitiveAnnotatedImpl primPrefix primName = observe . primTag primPrefix . primName jetAnnotatedImpl ir milliweight = observe $ compress jetTag (review (over be256) milliweight, identityHash ir) ================================================ FILE: Haskell/Core/Simplicity/MerkleRoot.hs ================================================ -- | This module provides functions for computing commitment, identity and annotated Merkle roots of Simplicity expressions and Merkle roots of Simplicity types. -- It also provides some other functions for other hashing schemes that will avoid collisions with the aforementioned Merkle roots. module Simplicity.MerkleRoot ( typeRoot, typeRootR , CommitmentRoot, commitmentRoot , IdentityRoot, identityHash , AnnotatedRoot, annotatedRoot , hiddenRoot , signatureTag, sigHash , cmrFail0 ) where import Simplicity.MerkleRoot.Impl ================================================ FILE: Haskell/Core/Simplicity/Programs/Arith.hs ================================================ {-# LANGUAGE GADTs, ScopedTypeVariables, TypeOperators #-} -- | This module defines Simplicity expressions and combinators that operate on Words. module Simplicity.Programs.Arith ( module Simplicity.Ty.Word , zero , one , add, full_add, increment, full_increment , subtract, full_subtract, negate, decrement, full_decrement , multiply, full_multiply , div2n1n, div_mod, divide, modulo, divides , eea, bezout, cofactors, gcd, lcm , is_zero, is_one , le, lt , min, max, median , msb, lsb , absolute_value, sign ) where import Prelude hiding ( Word, drop, take, not, and, or, last , subtract, negate, min, max, gcd, lcm ) import Data.Type.Equality ((:~:)(Refl)) import Simplicity.Programs.Bit import Simplicity.Programs.Word import Simplicity.Term.Core hiding (one) import Simplicity.Ty.Word -- | Simplicity expression for the constant function that returns the representation of 0. -- -- @ -- 'fromWord' w ('zero' w _) == 0 -- @ zero :: Core term => Word a -> term () a zero = low -- | Simplicity expression for the constant function that returns the representation of 1. -- -- @ -- 'fromWord' w ('one' w _) == 1 -- @ one :: (Core term, TyC a) => Word a -> term () a one w = true >>> left_pad_low word1 w -- | Simplicity expression for computing the sum of two words and a carry input bit, including the carry output bit. -- -- @ -- 'fromWord1' cout * 2 ^ 'wordSize' w + 'fromWord' w z == 'fromWord' w x + 'fromWord' w y + 'fromWord1' cin -- where -- (cout, z) = 'full_add' w (cin, (x, y)) -- @ full_add :: Core term => Word a -> term (Bit, (a, a)) (Bit, a) full_add SingleV = maj &&& xor_xor full_add (DoubleV w) = drop (ooh &&& ioh) &&& (oh &&& drop (oih &&& iih) >>> rec) >>> iih &&& (ioh &&& oh >>> rec) >>> ioh &&& (iih &&& oh) where rec = full_add w -- | Simplicity expression for computing the sum of two words, including the carry bit. -- -- @ -- 'fromWord1' c * 2 ^ 'wordSize' w + 'fromWord' w z == 'fromWord' w x + 'fromWord' w y -- where -- (c, z) = 'add' w (x, y) -- @ add :: (Core term, TyC a) => Word a -> term (a, a) (Bit, a) add w = false &&& iden >>> full_add w -- | Simplicity expression for computing the sum a words and a bit, including the carry bit. -- -- @ -- 'fromWord1' c * 2 ^ 'wordSize' w + 'fromWord' w z == 'fromWord1' x + 'fromWord' w y -- where -- (c, z) = 'full_increment' w (x, y) -- @ full_increment :: (Core term, TyC a) => Word a -> term (Bit, a) (Bit, a) full_increment w = oh &&& (ih &&& (unit >>> zero w)) >>> full_add w -- | Simplicity expression for incrementing a word, including the carry bit. -- -- @ -- 'fromWord1' c * 2 ^ 'wordSize' w + 'fromWord' w y == 1 + 'fromWord' w x -- where -- (c, y) = 'increment' w x -- @ increment :: (Core term, TyC a) => Word a -> term a (Bit, a) increment w = true &&& iden >>> full_increment w -- | Simplicity expression for computing the difference of two words and a borrow input bit, also returning the borrow output bit. -- -- @ -- 'fromWord' w z == 'fromWord1' bout * 2 ^ 'wordSize' w + 'fromWord' w x - 'fromWord' w y - 'fromWord1' bin -- where -- (bout, z) = 'full_subtract' w (bin, (x, y)) -- @ full_subtract :: (Core term, TyC a) => Word a -> term (Bit, (a, a)) (Bit, a) full_subtract w = not oh &&& drop (oh &&& (ih >>> complement w)) >>> full_add w >>> not oh &&& ih -- | Simplicity expression for computing the difference of two words, also returning the borrow bit. -- -- @ -- 'fromWord' w z == 'fromWord1' b * 2 ^ 'wordSize' w + 'fromWord' w x - 'fromWord' w y -- where -- (b, z) = 'subtract' w (x, y) -- @ subtract :: (Core term, TyC a) => Word a -> term (a, a) (Bit, a) subtract w = false &&& iden >>> full_subtract w -- | Simplicity expression for negating a word, also returning the borrow bit. -- -- @ -- 'fromWord' w y == 'fromWord1' b * 2 ^ 'wordSize' w - 'fromWord' w x -- where -- (b, y) = 'negate' w x -- @ negate :: (Core term, TyC a) => Word a -> term a (Bit, a) negate w = (unit >>> zero w) &&& iden >>> subtract w -- | Simplicity expression for subtracting a bit from a word, also returning the borrow bit. -- -- @ -- 'fromWord' w z == 'fromWord1' b * 2 ^ 'wordSize' w + 'fromWord' w y - 'fromWord1' x -- where -- (b, z) = 'full_decrement' w (x, y) -- @ full_decrement :: (Core term, TyC a) => Word a -> term (Bit, a) (Bit, a) full_decrement w = oh &&& (ih &&& (unit >>> zero w)) >>> full_subtract w -- | Simplicity expression for decrementing a a word, also returning the borrow bit. -- -- @ -- 'fromWord' w y == 'fromWord1' b * 2 ^ 'wordSize' w + 'fromWord' w x - 1 -- where -- (b, y) = 'decrement' w x -- @ decrement :: (Core term, TyC a) => Word a -> term a (Bit, a) decrement w = true &&& iden >>> full_decrement w -- | A Simplicity expression that helps compute products of larger word sizes from smaller word sizes. -- -- @ -- 'fromWord' ('DoubleV' w) ('full_multiply' w ((a, b), (c, d))) == 'fromWord' w a * 'fromWord' w b + 'fromWord' w c + 'fromWord' w d -- @ full_multiply :: (Core term, TyC a) => Word a -> term ((a, a), (a, a)) (a, a) full_multiply SingleV = take (cond iden false) &&& ih >>> full_add SingleV full_multiply (DoubleV w) = take (ooh &&& (ioh &&& oih)) &&& ((take (ooh &&& iih) &&& drop (ooh &&& ioh) >>> rec) &&& (take (oih &&& iih) &&& drop (oih &&& iih) >>> rec)) >>> take (oh &&& ioh) &&& (drop (ooh &&& iih) &&& (oih &&& drop (oih &&& ioh) >>> rec)) >>> (oh &&& drop (ioh &&& ooh) >>> rec) &&& drop (iih &&& oih) where rec = full_multiply w -- | Simplicity expression for computing the product of two words, returning a doubled size word. -- -- @ -- 'fromWord' ('DoubleV' w) ('multiply' w (x, y)) == 'fromWord' w x * 'fromWord' w y -- @ multiply :: (Core term, TyC a) => Word a -> term (a, a) (a, a) multiply w = iden &&& (unit >>> zero (DoubleV w)) >>> full_multiply w -- | Test if a word is zero. -- -- @ -- 'fromBit' ('is_zero' w x) == ('fromWord' w x == 0) -- @ is_zero :: (Core term, TyC a) => Word a -> term a Bit is_zero w = not (some w) -- | Test if a word is one. -- -- @ -- 'fromBit' ('is_one' w x) == ('fromWord' w x == 1) -- @ is_one :: (Core term, TyC a) => Word a -> term a Bit is_one w = decrement w >>> drop (is_zero w) -- | Test if a word is less than another -- -- @ -- 'fromBit' ('lt' w (x, y)) == ('fromWord' w x < 'fromWord' w y) -- @ lt :: (Core term, TyC a) => Word a -> term (a,a) Bit lt w = subtract w >>> oh -- | Test if a word is less than or equal to another -- -- @ -- 'fromBit' ('le' w (x, y)) == ('fromWord' w x <= 'fromWord' w y) -- @ le :: (Core term, TyC a) => Word a -> term (a,a) Bit le w = not (ih &&& oh >>> lt w) -- | Compute the minimum of two words. -- -- @ -- 'fromWord' w ('min' w (x, y)) == 'Prelude.min' ('fromWord' w x) ('fromWord' w y) -- @ min :: (Core term, TyC a) => Word a -> term (a,a) a min w = le w &&& iden >>> cond oh ih -- | Compute the maximum of two words. -- -- @ -- 'fromWord' w ('max' w (x, y)) == 'Prelude.max' ('fromWord' w x) ('fromWord' w y) -- @ max :: (Core term, TyC a) => Word a -> term (a,a) a max w = le w &&& iden >>> cond ih oh -- | Compute the median of three words. -- -- @ -- 'fromWord' w ('median' w (x, (y, z))) == 'sort' ['fromWord' w x, 'fromWord' w y, 'fromWord' w z] !! 1 -- @ median :: (Core term, TyC a) => Word a -> term (a, (a, a)) a median w = ((oh &&& ioh >>> min w) &&& (oh &&& iih >>> min w) >>> max w) &&& drop (min w) >>> max w -- | Return the most significant bit of a word. -- -- @ -- 'fromBit' ('msb' w x) == (2 ^ ('wordSize' w - 1) <= 'fromWord' w x) -- @ msb :: (Core term, TyC a) => Word a -> term a Bit msb w = leftmost w -- | Return the least significant bit of a word. -- -- @ -- 'fromBit' ('lsb' w x) == odd ('fromWord' w x) -- @ lsb :: (Core term, TyC a) => Word a -> term a Bit lsb w = rightmost w -- div3n2n (((a1,a2),a3), (b1,b2)) -- precondition -- * [a1,a2,a3] < [b1,b2,0] -- * 1000... <= [b1,b2] -- postcondition: -- * div3n2n (((a1,a2),a3), (b1,b2)) = ([a1,a2,a3]/[b1,b2], [a1,a2,a3]%[b1,b2]) div3n2n :: (Core term, TyC a) => Word a -> term (((a, a), a), (a, a)) (a, (a, a)) div3n2n w = (ooh &&& ioh >>> approxDiv) &&& (oih &&& ih) >>> body where approxDiv = (ooh &&& ih >>> lt w) &&& iden >>> cond lt_case eq_case lt_case = false &&& div2n1n w eq_case = oih &&& ih >>> add w >>> oh &&& ((unit >>> high w) &&& ih) body = ooh &&& (((oiih &&& ioh) &&& (oioh &&& iiih >>> multiply w) >>> subtract (DoubleV w)) &&& (oioh &&& iih)) >>> cond overflow loop0 overflow = ioh &&& oih loop0 = ooh &&& (oih &&& ih) >>> cond loop1 (ioh &&& oh) loop1 = (oh &&& iih >>> add2w) &&& drop ((take (dec >>> ih)) &&& ih) >>> ooh &&& (oih &&& ih) >>> cond (ioh &&& oh) loop2 loop2 = drop (take (dec >>> ih)) &&& (oh &&& iih >>> add2w >>> ih) dec = decrement w add2w = add (DoubleV w) -- | A Simplicity expression that helps compute the division of words. -- -- @ -- When 'fromWord' ('DoubleV' w) a < 2^'wordSize' w * 'fromWord' w b -- and 2^('wordSize' w - 1) <= 'fromWord' w b -- then 'fromWord' w (fst ('div2n1n' w (a, b))) == div ('fromWord' ('DoubleV' w) a) ('fromWord' w b) -- and 'fromWord' w (snd ('div2n1n' w (a, b))) == mod ('fromWord' ('DoubleV' w) a) ('fromWord' w b) -- otherwise -- 'div2n1n' w (a, b) == 'Simplicity.Programs.Word.high' ('DoubleV' w) () -- @ div2n1n :: (Core term, TyC a) => Word a -> term ((a, a), a) (a, a) div2n1n SingleV = oih &&& or ooh (not ih) >>> or oh ih &&& ih div2n1n (DoubleV w) = conditions &&& iden >>> cond body (unit >>> high (DoubleV (DoubleV w))) where body = ((ooh &&& oioh) &&& ih >>> rec) &&& (oiih &&& ih) >>> ooh &&& ((oih &&& ioh) &&& iih >>> rec) >>> (oh &&& ioh) &&& iih rec = div3n2n w conditions = and (drop (msb (DoubleV w))) (ooh &&& ih >>> lt (DoubleV w)) -- Given a two words x and y, with x twice as wide as y, perform a left shift of both words by equal amounts until the msb of y becomes set. divPreShift :: (Core term, TyC a) => Word b -> Vector b a -> term ((a, a), a) ((a, a), a) divPreShift SingleV _ = iden divPreShift (DoubleV w) v = drop (leftmost v' >>> is_zero w) &&& iden >>> cond shift iden >>> divPreShift w v' where v' = vectorComp vector2 v shift = (oh &&& zv >>> full_shift (DoubleV (vectorComp w v')) w >>> ih) &&& (ih &&& zv >>> full_shift (vectorComp w v') w >>> ih) zv = unit >>> zero w -- Given a two words x and y, perform a right shift of the first word and a left shift of the second word by the same about until the msb of y becomes set. divPostShift :: (Core term, TyC a) => Word b -> Vector b a -> term (a, a) (a, a) divPostShift SingleV _ = iden divPostShift (DoubleV w) v = drop (leftmost v' >>> is_zero w) &&& iden >>> cond shift iden >>> divPostShift w v' where v' = vectorComp vector2 v shift = (zv &&& oh >>> full_shift w (vectorComp w v') >>> oh) &&& (ih &&& zv >>> full_shift (vectorComp w v') w >>> ih) zv = unit >>> zero w -- | Divide two words, also returning the remainder. -- -- @ -- 'fromWord' w (fst ('div_mod' w (x, 'zero' w))) == 0 -- && 'fromWord' w (snd ('div_mod' w (x, 'zero' w))) == 'fromWord' w x -- -- 'fromWord' w (fst ('div_mod' w (x, y))) == div ('fromWord' w x) ('fromWord' w y) -- && 'fromWord' w (snd ('div_mod' w (x, y))) == mod ('fromWord' w x) ('fromWord' w y) -- when -- 'fromWord' w y != 0 -- @ div_mod :: (Core term, TyC a) => Word a -> term (a, a) (a, a) div_mod w = (drop (is_zero w)) &&& iden >>> cond zero_case div_case where zero_case = ih &&& oh div_case = (((unit >>> zero w) &&& oh) &&& ih >>> divPreShift w SingleV >>> div2n1n w) &&& ih >>> ooh &&& (oih &&& ih >>> divPostShift w SingleV >>> oh) -- | Divide two words. -- -- @ -- 'fromWord' w ('divide' w (x, 'zero' w)) == 0 -- -- 'fromWord' w ('divide' w (x, y)) == div ('fromWord' w x) ('fromWord' w y) -- when -- 'fromWord' w y != 0 -- @ divide :: (Core term, TyC a) => Word a -> term (a, a) a divide w = div_mod w >>> oh -- | Compute the remainder after dividing two words. -- -- @ -- 'fromWord' w ('modulo' w (x, 'zero' w)) == 'fromWord' w x -- -- 'fromWord' w ('modulo' w (x, y)) == mod ('fromWord' w x) ('fromWord' w y) -- when -- 'fromWord' w y != 0 -- @ modulo :: (Core term, TyC a) => Word a -> term (a, a) a modulo w = div_mod w >>> ih -- | Check if one word divides another -- -- @ -- 'fromBit' ('divides' w ('zero' w, y)) == True -- -- 'fromBit' ('divides' w (x, y)) == (mod ('fromWord' w y) ('fromWord' w x) == 0) -- when -- 'fromWord' w x != 0 -- @ divides :: (Core term, TyC a) => Word a -> term (a, a) Bit divides w = ih &&& oh >>> modulo w >>> is_zero w -- A single step of the extended Euclidean algorithm. -- Given a matrix -- [ a -b | c ] -- [ -d e | f ] -- Then subtract either the largest possible multiple of the second row from the first such that c remains positive -- or the largest possible multiple of the first row from the second such that f remains positive. -- If either c of f is zero then this results in no change. eeaStep :: (Core term, TyC a) => Word a -> term (((a,a), a), ((a,a),a)) (((a,a), a), ((a,a),a)) eeaStep w = (iih &&& oih >>> lt w) &&& iden >>> cond (step &&& ih) (oh &&& (ih &&& oh >>> step)) where step = (oih &&& iih >>> div_mod w) &&& (ooh &&& ioh) >>> (((ooh &&& iioh) &&& (iooh &&& (unit >>> zero w)) >>> full_multiply w >>> ih) &&& ((ooh &&& iiih) &&& (ioih &&& (unit >>> zero w)) >>> full_multiply w >>> ih)) &&& oih -- Repeat eeaStep 2^wordsize (v :: Word b) many times.. eeaStep_iterate :: forall term a b. (Core term, TyC a) => Word a -> Word b -> term (((a,a), a), ((a,a),a)) (((a,a), a), ((a,a),a)) eeaStep_iterate w = go where go :: forall b. Word b -> term (((a,a), a), ((a,a),a)) (((a,a), a), ((a,a),a)) go SingleV = base >>> base where base = eeaStep w go (DoubleV d) = rec >>> rec where rec = go d -- | Compute the results of the extended euclidan algorithm. -- -- @ -- 'eea' (x, y) == (('bezout' (x, y), 'cofactors' (x, y)), 'gcd' (x, y)) -- @ eea :: (Core term, TyC a) => Word a -> term (a, a) ((Either (a, a) (a, a), (a, a)), a) eea w = pre >>> eeaStep_iterate w w >>> post where o = (unit >>> one w) z = (unit >>> zero w) pre = ((o &&& z) &&& oh) &&& ((z &&& o) &&& ih) post = drop (drop (is_zero w)) &&& iden >>> cond ((injl ooh &&& ioh) &&& oih) ((injr ioh &&& ooh) &&& iih) -- | Compute minimal bezout coeffecients of two words. -- -- @ -- 'fromWord' w cx * 'fromWord' w x - 'fromWord' w cy * 'fromWord' w y == Prelude.gcd ('fromWord' w x) ('fromWord' w y) -- when -- Left (cx, cy) = 'bezout' w (x, y) -- -- 'fromWord' w cy * 'fromWord' w y - 'fromWord' w cx * 'fromWord' w x == Prelude.gcd ('fromWord' w x) ('fromWord' w y) -- when -- Right (cx, cy) = 'bezout' w (x, y) -- @ bezout :: (Core term, TyC a) => Word a -> term (a, a) (Either (a, a) (a, a)) bezout w = eea w >>> ooh -- | Compute the cofactors of two words. -- -- @ -- 'fromWord' w cx * d == 'fromWord' w x -- && 'fromWord' w cy * d == 'fromWord' w y y -- where -- (cx, cy) = 'cofactors' w (x, y) -- d = Prelude.gcd ('fromWord' w x) ('fromWord' w y) -- @ cofactors :: (Core term, TyC a) => Word a -> term (a, a) (a, a) cofactors w = eea w >>> take (drop (ih &&& oh)) -- | Compute the greatest common divisor of two words. -- -- @ -- 'fromWord' w ('gcd' w (x, y)) == 'Prelude.gcd' ('fromWord' w x) ('fromWord' w y) -- @ gcd :: (Core term, TyC a) => Word a -> term (a, a) a gcd w = eea w >>> ih -- | Compute the least common multiple of two words. -- -- @ -- 'fromWord' (DoubleV w) ('lcm' w (x, y)) == 'Prelude.lcm' ('fromWord' w x) ('fromWord' w y) -- @ lcm :: (Core term, TyC a) => Word a -> term (a, a) (a,a) lcm w = (cofactors w >>> oh) &&& ih >>> multiply w -- | Compute the absolute value of a signed word. -- -- @ -- 'fromWord' w ('absolute_value' w x) == 'abs' ('fromInt' w x) -- @ absolute_value :: (Core term, TyC a) => Word a -> term a a absolute_value w = msb w &&& iden >>> cond (negate w >>> ih) iden -- | Compute the sign value of a signed word as a 2-bit value. -- -- @ -- 'fromInt2' ('sign' w x) == 'signum' ('fromInt' w x) -- @ sign :: (Core term, TyC a) => Word a -> term a Word2 sign w = msb w &&& some w ================================================ FILE: Haskell/Core/Simplicity/Programs/Bit.hs ================================================ -- | This module defines Simplicity combinators and expressions that operate on bits. module Simplicity.Programs.Bit ( module Simplicity.Ty.Bit , false, true , cond, ch, assert, verify , not, and, or, xor , xor_xor, maj ) where import Prelude hiding (drop, take, not, and, or) import Simplicity.MerkleRoot import Simplicity.Ty.Bit import Simplicity.Term.Core -- | Simplicity expression always returns the zero bit. -- -- @'false' = 'Simplicity.Programs.Generic.scribe' ('toBit' 'False')@ false :: (Core term, TyC a) => term a Bit false = injl unit -- | Simplicity expression always returns the one bit. -- -- @'true' = 'Simplicity.Programs.Generic.scribe' ('toBit' 'True')@ true :: (Core term, TyC a) => term a Bit true = injr unit -- | Simplicity's if-then-else combinator. -- -- @ -- 'cond' t _ ('toBit' 'True', a) = t a -- -- 'cond' _ e ('toBit' 'False', a) = e a -- @ cond :: (Core term, TyC a, TyC b) => term a b -> term a b -> term (Bit, a) b cond thn els = match (drop els) (drop thn) -- | Simplicity expression that chooses from a pair of values. -- -- @ -- 'ch' ('toBit' 'True', (a, _)) = a -- -- 'ch' ('toBit' 'False', (_, b)) = b -- @ ch :: (Core term, TyC a) => term (Bit, (a, a)) a ch = cond oh ih -- | Requires the value produced by @t@ to not be 'false' and fails otherwise. assert :: (Assert term, TyC a, TyC b) => term a (Either () b) -> term a b assert t = t &&& unit >>> assertr cmrFail0 oh -- | Requires the 'Right' value an fails if instead the value is 'Left'. -- -- When specialized, this asserts that the input bit is true and returns a unit value. verify :: (Assert term, TyC a) => term (Either () a) a verify = assert iden -- | Simplicity combinator that computes inverts the Bit result of an expression. not :: (Core term, TyC a) => term a Bit -> term a Bit not t = t &&& unit >>> cond false true -- | Simplicity combinator that computes the short-circut conjunction of the results of two expressions. and :: (Core term, TyC a) => term a Bit -> term a Bit -> term a Bit and s t = s &&& iden >>> cond t false -- | Simplicity combinator that computes the short-circut disjunction of the results of two expressions. or :: (Core term, TyC a) => term a Bit -> term a Bit -> term a Bit or s t = s &&& iden >>> cond true t -- | Simplicity expression that returns the three-way xor of three bits. xor :: (Core term, TyC a) => term a Bit -> term a Bit -> term a Bit xor s t = s &&& iden >>> cond (not t) t -- | Simplicity expression that returns the three-way xor of three bits. xor_xor :: Core term => term (Bit, (Bit, Bit)) Bit xor_xor = cond (cond iden (not iden)) (cond (not iden) iden) -- | Simplicity expression that returns the majority value of three bits. maj :: Core term => term (Bit, (Bit, Bit)) Bit maj = cond (cond true iden) (cond iden false) ================================================ FILE: Haskell/Core/Simplicity/Programs/Bitcoin/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Programs.Bitcoin.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Programs.Bitcoin.mkLib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Programs.Bitcoin.Lib ( buildTapleafSimplicity, buildTapbranch , outpointHash, annexHash , buildTaptweak , Bitcoin.Hash, Bitcoin.Ctx8 ) where import qualified Simplicity.Programs.Bitcoin as Bitcoin -- Maybe this ought to be Template Haskell. buildTapleafSimplicity = Bitcoin.buildTapleafSimplicity Bitcoin.lib buildTapbranch = Bitcoin.buildTapbranch Bitcoin.lib outpointHash = Bitcoin.outpointHash Bitcoin.libAssert annexHash = Bitcoin.annexHash Bitcoin.libAssert buildTaptweak = Bitcoin.buildTaptweak Bitcoin.libAssert ================================================ FILE: Haskell/Core/Simplicity/Programs/Bitcoin.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that implement pure calculations used by Bitcoin. module Simplicity.Programs.Bitcoin ( Lib(Lib), mkLib , buildTapleafSimplicity, buildTapbranch , LibAssert(LibAssert), mkLibAssert , outpointHash, annexHash , buildTaptweak -- * Example instances , lib, libAssert -- * Reexports , Hash, Ctx8 ) where import Prelude hiding (Word, drop, not, subtract, take) import Data.String (fromString) import Lens.Family2 (over, review) import Simplicity.Digest import Simplicity.Functor import Simplicity.LibSecp256k1.Spec (fieldOrder, groupOrder) import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Arith import Simplicity.Programs.Word import Simplicity.Term.Core hiding (one) import qualified Simplicity.Programs.LibSecp256k1 as LibSecp256k1 import Simplicity.Programs.LibSecp256k1 hiding (Lib(Lib), mkLib, lib) import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Programs.Sha256 hiding ( Lib(Lib), lib , LibAssert(LibAssert), mkLibAssert, libAssert) -- | A collection of core Simplicity expressions for Bitcoin calculations. -- Use 'mkLib' to construct an instance of this library. data Lib term = Lib { buildTapleafSimplicity :: term Hash Hash -- | Compute a tapbranch hash from two branches. , buildTapbranch :: term (Hash, Hash) Hash } -- | A collection of Simplicity with Assertions expressions for Bitcoin calculations. -- Use 'mkLibAssert' to construct an instance of this library. data LibAssert term = LibAssert { -- | A hash of an outpoint. outpointHash :: term (Ctx8, (Word256, Word32)) Ctx8 -- | A hash of an optional hash. , annexHash :: term (Ctx8, S Word256) Ctx8 -- | Compute a taptweak hash from a pubkey and a hash. , buildTaptweak :: term (PubKey, Hash) PubKey } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { buildTapleafSimplicity = m buildTapleafSimplicity , buildTapbranch = m buildTapbranch } instance SimplicityFunctor LibAssert where sfmap m LibAssert{..} = LibAssert { outpointHash = m outpointHash , annexHash = m annexHash , buildTaptweak = m buildTaptweak } -- | Build the Bitcoin 'Lib' library from its dependencies. mkLib :: forall term. Core term => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Lib term mkLib Sha256.Lib{..} = lib where lib@Lib{..} = Lib { buildTapleafSimplicity = (unit >>> tapleafPrefix) &&& ((unit >>> (simplicityVersion &&& scribe (toWord8 32))) &&& iden >>> full_shift word16 word256 >>> (oh &&& ((((ih &&& (unit >>> scribe (toWord16 0x8000))) &&& (unit >>> zero word32)) &&& (unit >>> zero word64)) &&& (unit >>> scribe (toWord128 (512+16+256)))))) >>> hashBlock , buildTapbranch = ((unit >>> tapbranchPrefix) &&& (lt word256 &&& iden >>> cond iden (ih &&& oh)) >>> hashBlock) &&& (unit >>> scribe (toWord512 $ 2^511 + 1024)) >>> hashBlock } where tapleafPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapLeaf" tapbranchPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapBranch" simplicityVersion = scribe . toWord8 $ 0xbe -- | An instance of the Bitcoin 'Lib' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. lib :: Core term => Lib term lib = mkLib Sha256.lib -- | Build the Bitcoin 'LibAssert' library. mkLibAssert :: forall term. Assert term => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Sha256.LibAssert term -- ^ "Simplicity.Programs.Sha256" -> LibSecp256k1.Lib term -- ^ "Simplicity.Programs.Libsecp256k1" -> LibAssert term mkLibAssert Sha256.Lib{..} Sha256.LibAssert{..} LibSecp256k1.Lib{..} = libAssert where libAssert@LibAssert{..} = LibAssert { outpointHash = (oh &&& ioh >>> ctx8Add32) &&& iih >>> ctx8Add4 , annexHash = ih &&& oh >>> match (ih &&& take (zero word8) >>> ctx8Add1) ((ih &&& (unit >>> scribe (toWord8 0x01)) >>> ctx8Add1) &&& oh >>> ctx8Add32) , buildTaptweak = assert ( (((assert (oh &&& (unit >>> scribe (toWord256 fieldOrder)) >>> lt256) >>> taptweakPrefix) &&& iden >>> hashBlock) &&& (unit >>> scribe (toWord512 $ 2^511 + 1024)) >>> hashBlock >>> (assert (iden &&& (unit >>> scribe (toWord256 groupOrder)) >>> lt256) &&& iden) >>> drop generate) &&& assert ((unit >>> false) &&& oh >>> decompress) >>> gej_ge_add >>> gej_normalize) >>> oh } where lt256 = lt word256 ctx8Add32 = ctx8Addn vector32 ctx8Add8 = ctx8Addn vector8 ctx8Add4 = ctx8Addn vector4 taptweakPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapTweak" -- | An instance of the Bitcoin 'LibAssert' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLibAssert' in order to share library dependencies. -- This instance is provided mostly for testing purposes. libAssert :: Assert term => LibAssert term libAssert = mkLibAssert Sha256.lib Sha256.libAssert LibSecp256k1.lib ================================================ FILE: Haskell/Core/Simplicity/Programs/CheckSig/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module instantiates the "Simplicity.Programs.CheckSig" module functions. -- Users should prefer to use "Simplicity.Programs.CheckSig" module in order to share library dependencies. module Simplicity.Programs.CheckSig.Lib ( sigHash' , checkSigVerify , checkSigVerify' -- * Types , CheckSig.Hash ) where import qualified Simplicity.Programs.CheckSig as CheckSig import qualified Simplicity.Programs.LibSecp256k1 as LibSecp256k1 import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Ty.Word sigHash' = CheckSig.sigHash' Sha256.lib checkSigVerify = CheckSig.checkSigVerify Sha256.lib LibSecp256k1.lib checkSigVerify' = CheckSig.checkSigVerify' Sha256.lib LibSecp256k1.lib ================================================ FILE: Haskell/Core/Simplicity/Programs/CheckSig.hs ================================================ {-# LANGUAGE RecordWildCards #-} -- | The module builds a Simplicity expression that mimics the behaviour of a @CHECKSIG@ operation for Bitcoin but with universal signature hash modes. -- This uses Schnorr signature verification specified in "Simplicity.Programs.LibSecp256k1". module Simplicity.Programs.CheckSig ( sigHash' , checkSigVerify, checkSigVerify' -- * Types , Hash ) where import Prelude hiding (drop, take) import Simplicity.Digest import Simplicity.Functor import qualified Simplicity.LibSecp256k1.Schnorr as Schnorr import Simplicity.MerkleRoot hiding (sigHash) import Simplicity.Programs.Generic import Simplicity.Programs.Sha256 hiding (Lib(Lib), lib) import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Programs.LibSecp256k1 hiding (Lib(Lib), lib, mkLib) import qualified Simplicity.Programs.LibSecp256k1 as LibSecp256k1 import Simplicity.Term.Core import Simplicity.Ty import Simplicity.Ty.Word -- | A Simplicity expression that computes a "standard" Simplicity tagged signature hash from the CMR of a sighash algorithm, and the output of that sighash. -- -- This expression should not be used directly. Instead use 'sigHash'' to ensure that inputs are properly constructed. sigHash :: (Core term) => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> term (Word256, Word256) Hash sigHash Sha256.Lib{..} = (scribe iv &&& iden >>> hb) &&& scribe (toWord512 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000400) >>> hb where iv = toWord256 . integerHash256 . ivHash $ signatureTag hb = hashBlock -- | Constructs a Simplicity expression for a "standard" Simplicity tagged signature hash using a given signature hash mode. -- -- The sighash mode is `disconnected` and thus doesn't affect this expression's CMR. sigHash' :: (Core term, Delegate term) => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> term () Hash -- ^ signature hash mode -> term () Hash sigHash' sha256 hashMode = disconnect iden hashMode >>> sigHash sha256 -- | A Simplicity expression that checks a "standard" Simplicity tagged signature hash given -- -- * A pubkey -- * A message that is intended to be the CMR of a sighash algorithm, and the output of that sighash. -- * A signature -- -- This expression should not be used directly. Instead use 'checkSigVerify'' to ensure that inputs are properly constructed. checkSigVerify :: (Assert term) => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> LibSecp256k1.Lib term -- ^ "Simplicity.Programs.LibSecp256k1" -> term ((Word256, (Word256, Word256)), Word512) () -- ^ signature hash mode checkSigVerify sha256 libsecp256k1 = take (oh &&& drop (sigHash sha256)) &&& ih >>> bip_0340_verify libsecp256k1 -- | Constructs a Simplicity program that validates a signature on a "standard" Simplicity tagged signature hash using -- -- * a given signature hash mode -- * a given public key -- * a given signature -- -- The sighash mode is `disconnected` and the signature is embedded inside a witness node. -- Thus these two inputs do not affect this expression's CMR. checkSigVerify' :: (Assert term, Delegate term, Witness term) => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> LibSecp256k1.Lib term -- ^ "Simplicity.Programs.LibSecp256k1" -> term () Hash -- ^ signature hash mode -> Schnorr.PubKey -> Schnorr.Sig -> term () () checkSigVerify' sha256 libsecp256k1 hashMode (Schnorr.PubKey x) ~(Schnorr.Sig r s) = (scribe (toWord256 . toInteger $ x) &&& disconnect iden hashMode) &&& (witness (toWord256 . toInteger $ r, toWord256 . toInteger $ s)) >>> checkSigVerify sha256 libsecp256k1 ================================================ FILE: Haskell/Core/Simplicity/Programs/Elements/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Programs.Elements.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Programs.Elements.mkLib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Programs.Elements.Lib ( Elements.Conf , calculateIssuanceEntropy, calculateAsset, calculateExplicitToken, calculateConfidentialToken , buildTapleafSimplicity, buildTapbranch , lbtcAsset , outpointHash, assetAmountHash, nonceHash, annexHash , buildTaptweak , Elements.Hash, Elements.Ctx8 ) where import qualified Simplicity.Programs.Elements as Elements -- Maybe this ought to be Template Haskell. calculateIssuanceEntropy = Elements.calculateIssuanceEntropy Elements.lib calculateAsset = Elements.calculateAsset Elements.lib calculateExplicitToken = Elements.calculateExplicitToken Elements.lib calculateConfidentialToken = Elements.calculateConfidentialToken Elements.lib buildTapleafSimplicity = Elements.buildTapleafSimplicity Elements.lib buildTapbranch = Elements.buildTapbranch Elements.lib lbtcAsset = Elements.lbtcAsset Elements.lib outpointHash = Elements.outpointHash Elements.libAssert assetAmountHash = Elements.assetAmountHash Elements.libAssert nonceHash = Elements.nonceHash Elements.libAssert annexHash = Elements.annexHash Elements.libAssert buildTaptweak = Elements.buildTaptweak Elements.libAssert ================================================ FILE: Haskell/Core/Simplicity/Programs/Elements.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that implement pure calculations used by Elements. module Simplicity.Programs.Elements ( Lib(Lib), mkLib , Conf , calculateIssuanceEntropy, calculateAsset, calculateExplicitToken, calculateConfidentialToken , buildTapleafSimplicity, buildTapbranch , lbtcAsset , LibAssert(LibAssert), mkLibAssert , outpointHash, assetAmountHash, nonceHash, annexHash , buildTaptweak -- * Example instances , lib, libAssert -- * Reexports , Hash, Ctx8 ) where import Prelude hiding (Word, drop, not, subtract, take) import Data.String (fromString) import Lens.Family2 (over, review) import Simplicity.Digest import Simplicity.Functor import Simplicity.LibSecp256k1.Spec (fieldOrder, groupOrder) import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Arith import Simplicity.Programs.Word import Simplicity.Term.Core hiding (one) import qualified Simplicity.Programs.LibSecp256k1 as LibSecp256k1 import Simplicity.Programs.LibSecp256k1 hiding (Lib(Lib), mkLib, lib) import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Programs.Sha256 hiding ( Lib(Lib), lib , LibAssert(LibAssert), mkLibAssert, libAssert) -- | A Simplicity type constructor for Elements confidential values. type Conf a = Either Point a -- | A collection of core Simplicity expressions for Elements calculations. -- Use 'mkLib' to construct an instance of this library. data Lib term = Lib { -- | An implementation of GenerateAssetEntropy from Element's @issuance.cpp@. calculateIssuanceEntropy :: term ((Hash, Word32), Hash) Hash -- | An implementation of CalculateAsset from Element's @issuance.cpp@. , calculateAsset :: term Hash Hash -- | An implementation of CalculateReissuanceToken for explicit values from Element's @issuance.cpp@. , calculateExplicitToken :: term Hash Hash -- | An implementation of CalculateReissuanceToken for confidential values from Element's @issuance.cpp@. , calculateConfidentialToken :: term Hash Hash -- | Compute a Simplicity tapleaf hash from a CMR. , buildTapleafSimplicity :: term Hash Hash -- | Compute a tapbranch hash from two branches. , buildTapbranch :: term (Hash, Hash) Hash -- | Return Liquid's (explicit) asset id for l-btc. , lbtcAsset :: term () Hash } -- | A collection of Simplicity with Assertions expressions for Elements calculations. -- Use 'mkLibAssert' to construct an instance of this library. data LibAssert term = LibAssert { -- | A hash of an optional parent genesis hash and an outpoint. outpointHash :: term (Ctx8, (S Word256, (Word256, Word32))) Ctx8 -- | A hash of a confidential asset and amount. , assetAmountHash :: term (Ctx8, (Conf Word256, Conf Word64)) Ctx8 -- | A hash of an optional nonce. , nonceHash :: term (Ctx8, S (Conf Word256)) Ctx8 -- | A hash of an optional hash. , annexHash :: term (Ctx8, S Word256) Ctx8 -- | Compute a taptweak hash from a pubkey and a hash. , buildTaptweak :: term (PubKey, Hash) PubKey } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { calculateIssuanceEntropy = m calculateIssuanceEntropy , calculateAsset = m calculateAsset , calculateExplicitToken = m calculateExplicitToken , calculateConfidentialToken = m calculateConfidentialToken , buildTapleafSimplicity = m buildTapleafSimplicity , buildTapbranch = m buildTapbranch , lbtcAsset = m lbtcAsset } instance SimplicityFunctor LibAssert where sfmap m LibAssert{..} = LibAssert { outpointHash = m outpointHash , assetAmountHash = m assetAmountHash , nonceHash = m nonceHash , annexHash = m annexHash , buildTaptweak = m buildTaptweak } -- | Build the Elements 'Lib' library from its dependencies. mkLib :: forall term. Core term => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Lib term mkLib Sha256.Lib{..} = lib where lib@Lib{..} = Lib { calculateIssuanceEntropy = (unit >>> iv) &&& (take opHash &&& ih) >>> hashBlock , calculateAsset = (unit >>> iv) &&& (iden &&& (unit >>> zero word256)) >>> hashBlock , calculateExplicitToken = (unit >>> iv) &&& (iden &&& (unit >>> scribe (toWord256 (2^248)))) >>> hashBlock , calculateConfidentialToken = (unit >>> iv) &&& (iden &&& (unit >>> scribe (toWord256 (2*2^248)))) >>> hashBlock , buildTapleafSimplicity = (unit >>> tapleafPrefix) &&& ((unit >>> (simplicityVersion &&& scribe (toWord8 32))) &&& iden >>> full_shift word16 word256 >>> (oh &&& ((((ih &&& (unit >>> scribe (toWord16 0x8000))) &&& (unit >>> zero word32)) &&& (unit >>> zero word64)) &&& (unit >>> scribe (toWord128 (512+16+256)))))) >>> hashBlock , buildTapbranch = ((unit >>> tapbranchPrefix) &&& (lt word256 &&& iden >>> cond iden (ih &&& oh)) >>> hashBlock) &&& (unit >>> scribe (toWord512 $ 2^511 + 1024)) >>> hashBlock , lbtcAsset = scribe (toWord256 (integerHash256 (review (over le256) 0x6f0279e9ed041c3d710a9f57d0c02928416460c4b722ae3457a11eec381c526d))) } where tapleafPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapLeaf/elements" tapbranchPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapBranch/elements" simplicityVersion = scribe . toWord8 $ 0xbe opHash :: term (Hash, Word32) Hash opHash = (unit >>> iv) &&& (((unit >>> iv) &&& (oh &&& (((drop (drop (ih &&& oh) &&& take (ih &&& oh)) &&& scribe (toWord32 (2^31))) &&& (unit >>> zero word64)) &&& (unit >>> scribe (toWord128 (256+32))))) >>> hashBlock) &&& (unit >>> scribe (toWord256 (2^255 + 256)))) >>> hashBlock -- | An instance of the Elements 'Lib' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. lib :: Core term => Lib term lib = mkLib Sha256.lib -- | Build the Elements 'LibAssert' library. mkLibAssert :: forall term. Assert term => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Sha256.LibAssert term -- ^ "Simplicity.Programs.Sha256" -> LibSecp256k1.Lib term -- ^ "Simplicity.Programs.Libsecp256k1" -> LibAssert term mkLibAssert Sha256.Lib{..} Sha256.LibAssert{..} LibSecp256k1.Lib{..} = libAssert where libAssert@LibAssert{..} = LibAssert { outpointHash = ((oh &&& ioh >>> annexHash) &&& iioh >>> ctx8Add32) &&& iiih >>> ctx8Add4 , assetAmountHash = (oh &&& ioh >>> assetHash) &&& iih >>> amountHash , nonceHash = ih &&& oh >>> match (ih &&& take (zero word8) >>> ctx8Add1) (ih &&& take (copair (take (copair (scribe (toWord8 0x02)) (scribe (toWord8 0x03))) &&& ih) ((unit >>> scribe (toWord8 0x01)) &&& iden)) >>> (oh &&& ioh >>> ctx8Add1) &&& iih >>> ctx8Add32) , annexHash = ih &&& oh >>> match (ih &&& take (zero word8) >>> ctx8Add1) ((ih &&& (unit >>> scribe (toWord8 0x01)) >>> ctx8Add1) &&& oh >>> ctx8Add32) , buildTaptweak = assert ( (((assert (oh &&& (unit >>> scribe (toWord256 fieldOrder)) >>> lt256) >>> taptweakPrefix) &&& iden >>> hashBlock) &&& (unit >>> scribe (toWord512 $ 2^511 + 1024)) >>> hashBlock >>> (assert (iden &&& (unit >>> scribe (toWord256 groupOrder)) >>> lt256) &&& iden) >>> drop generate) &&& assert ((unit >>> false) &&& oh >>> decompress) >>> gej_ge_add >>> gej_normalize) >>> oh } where lt256 = lt word256 ctx8Add32 = ctx8Addn vector32 ctx8Add8 = ctx8Addn vector8 ctx8Add4 = ctx8Addn vector4 assetHash = oh &&& drop (copair (take (copair (scribe (toWord8 0x0a)) (scribe (toWord8 0x0b))) &&& ih) ((unit >>> scribe (toWord8 0x01)) &&& iden)) >>> (oh &&& ioh >>> ctx8Add1) &&& iih >>> ctx8Add32 amountHash = ih &&& oh >>> match ((ih &&& take (take (copair (scribe (toWord8 0x08)) (scribe (toWord8 0x09)))) >>> ctx8Add1) &&& oih >>> ctx8Add32) ((ih &&& (unit >>> scribe (toWord8 0x01)) >>> ctx8Add1) &&& oh >>> ctx8Add8) taptweakPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapTweak/elements" -- | An instance of the Elements 'LibAssert' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLibAssert' in order to share library dependencies. -- This instance is provided mostly for testing purposes. libAssert :: Assert term => LibAssert term libAssert = mkLibAssert Sha256.lib Sha256.libAssert LibSecp256k1.lib ================================================ FILE: Haskell/Core/Simplicity/Programs/Generic.hs ================================================ {-# LANGUAGE GADTs #-} -- | This module is a collection of Simplicity expressions that are generic over a collection of Simplicity types. -- 'TyReflect'ion is used to analyse the Simplicity type of arguments and generate different Simplicity expressions based on the required types. module Simplicity.Programs.Generic ( scribe , eq ) where import Prelude hiding (drop, take) import Simplicity.Programs.Bit import Simplicity.Term.Core -- | For any Simplicity value, a Simplicity expression for a constant function returning that value. -- -- @'scribe' v _ = v@ scribe :: (Core term, TyC a, TyC b) => b -> term a b scribe = go reify where go :: (Core term, TyC a, TyC b) => TyReflect b -> b -> term a b go OneR () = unit go (SumR l _) (Left v) = injl (go l v) go (SumR _ r) (Right v) = injr (go r v) go (ProdR b1 b2) (v1, v2) = pair (go b1 v1) (go b2 v2) -- | Simplicity expression to compare a pair of inputs for equality. eq :: (Core term, TyC a) => term (a, a) Bit eq = go reify where go :: (TyC a, Core term) => TyReflect a -> term (a, a) Bit go OneR = true go (SumR l r) = match (swapP >>> match (go l) false) (swapP >>> match false (go r)) go (ProdR a1 a2) = pair (pair (take (take iden)) (drop (take iden)) >>> (go a1)) (pair (take (drop iden)) (drop (drop iden))) >>> cond (go a2) false ================================================ FILE: Haskell/Core/Simplicity/Programs/LibSecp256k1/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Programs.LibSecp256k1.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Programs.LibSecp256k1.mkLib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Programs.LibSecp256k1.Lib ( -- * Field operations LibSecp256k1.FE, fe_zero, fe_one, fe_is_zero , fe_normalize , fe_add, fe_negate, fe_halve, fe_square, fe_multiply, fe_multiply_beta, fe_invert, fe_square_root , fe_is_odd, fe_is_quad -- * Point operations , LibSecp256k1.Point, LibSecp256k1.GE, LibSecp256k1.GEJ, gej_is_on_curve , gej_infinity, gej_is_infinity , gej_rescale, gej_normalize, gej_negate, gej_scale_lambda , gej_double, gej_add_ex, gej_add, gej_ge_add_ex, gej_ge_add , ge_is_on_curve, ge_negate, ge_scale_lambda , gej_equiv, gej_ge_equiv, gej_x_equiv, gej_y_is_odd , decompress -- * Scalar operations , LibSecp256k1.Scalar, LibSecp256k1.Word129 , scalar_normalize, scalar_add, scalar_negate, scalar_square, scalar_multiply, scalar_multiply_lambda, scalar_invert , scalar_split_lambda, scalar_split_128 , scalar_is_zero -- * Elliptic curve multiplication related operations , LibSecp256k1.Vector129 , wnaf5, wnaf15 , generate, scale , linear_combination_1, linear_check_1, linear_verify_1 , point_check_1, point_verify_1 , off_curve_scale, off_curve_linear_combination_1 -- * Schnorr signature operations , LibSecp256k1.PubKey, pubkey_unpack, pubkey_unpack_neg , LibSecp256k1.Sig, signature_unpack , bip_0340_check, bip_0340_verify , swu, hash_to_curve ) where import qualified Simplicity.Programs.LibSecp256k1 as LibSecp256k1 -- Maybe this ought to be Template Haskell. fe_zero = LibSecp256k1.fe_zero LibSecp256k1.lib fe_one = LibSecp256k1.fe_one LibSecp256k1.lib fe_is_zero = LibSecp256k1.fe_is_zero LibSecp256k1.lib fe_normalize = LibSecp256k1.fe_normalize LibSecp256k1.lib fe_add = LibSecp256k1.fe_add LibSecp256k1.lib fe_negate = LibSecp256k1.fe_negate LibSecp256k1.lib fe_halve = LibSecp256k1.fe_halve LibSecp256k1.lib fe_square = LibSecp256k1.fe_square LibSecp256k1.lib fe_multiply = LibSecp256k1.fe_multiply LibSecp256k1.lib fe_multiply_beta = LibSecp256k1.fe_multiply_beta LibSecp256k1.lib fe_invert = LibSecp256k1.fe_invert LibSecp256k1.lib fe_square_root = LibSecp256k1.fe_square_root LibSecp256k1.lib fe_is_odd = LibSecp256k1.fe_is_odd LibSecp256k1.lib fe_is_quad = LibSecp256k1.fe_is_quad LibSecp256k1.lib gej_is_on_curve = LibSecp256k1.gej_is_on_curve LibSecp256k1.lib gej_infinity = LibSecp256k1.gej_infinity LibSecp256k1.lib gej_is_infinity = LibSecp256k1.gej_is_infinity LibSecp256k1.lib gej_rescale = LibSecp256k1.gej_rescale LibSecp256k1.lib gej_normalize = LibSecp256k1.gej_normalize LibSecp256k1.lib gej_negate = LibSecp256k1.gej_negate LibSecp256k1.lib gej_scale_lambda = LibSecp256k1.gej_scale_lambda LibSecp256k1.lib gej_double = LibSecp256k1.gej_double LibSecp256k1.lib gej_add_ex = LibSecp256k1.gej_add_ex LibSecp256k1.lib gej_add = LibSecp256k1.gej_add LibSecp256k1.lib gej_ge_add_ex = LibSecp256k1.gej_ge_add_ex LibSecp256k1.lib gej_ge_add = LibSecp256k1.gej_ge_add LibSecp256k1.lib ge_is_on_curve = LibSecp256k1.ge_is_on_curve LibSecp256k1.lib ge_negate = LibSecp256k1.ge_negate LibSecp256k1.lib ge_scale_lambda = LibSecp256k1.ge_scale_lambda LibSecp256k1.lib gej_equiv = LibSecp256k1.gej_equiv LibSecp256k1.lib gej_ge_equiv = LibSecp256k1.gej_ge_equiv LibSecp256k1.lib gej_x_equiv = LibSecp256k1.gej_x_equiv LibSecp256k1.lib gej_y_is_odd = LibSecp256k1.gej_y_is_odd LibSecp256k1.lib scalar_normalize = LibSecp256k1.scalar_normalize LibSecp256k1.lib scalar_add = LibSecp256k1.scalar_add LibSecp256k1.lib scalar_negate = LibSecp256k1.scalar_negate LibSecp256k1.lib scalar_square = LibSecp256k1.scalar_square LibSecp256k1.lib scalar_multiply = LibSecp256k1.scalar_multiply LibSecp256k1.lib scalar_multiply_lambda = LibSecp256k1.scalar_multiply_lambda LibSecp256k1.lib scalar_invert = LibSecp256k1.scalar_invert LibSecp256k1.lib scalar_split_lambda = LibSecp256k1.scalar_split_lambda LibSecp256k1.lib scalar_split_128 = LibSecp256k1.scalar_split_128 LibSecp256k1.lib scalar_is_zero = LibSecp256k1.scalar_is_zero LibSecp256k1.lib wnaf5 = LibSecp256k1.wnaf5 LibSecp256k1.lib wnaf15 = LibSecp256k1.wnaf15 LibSecp256k1.lib generate = LibSecp256k1.generate LibSecp256k1.lib scale = LibSecp256k1.scale LibSecp256k1.lib off_curve_scale = LibSecp256k1.off_curve_scale LibSecp256k1.lib linear_combination_1 = LibSecp256k1.linear_combination_1 LibSecp256k1.lib off_curve_linear_combination_1 = LibSecp256k1.off_curve_linear_combination_1 LibSecp256k1.lib linear_check_1 = LibSecp256k1.linear_check_1 LibSecp256k1.lib linear_verify_1 = LibSecp256k1.linear_verify_1 LibSecp256k1.lib decompress = LibSecp256k1.decompress LibSecp256k1.lib point_check_1 = LibSecp256k1.point_check_1 LibSecp256k1.lib point_verify_1 = LibSecp256k1.point_verify_1 LibSecp256k1.lib pubkey_unpack = LibSecp256k1.pubkey_unpack LibSecp256k1.lib pubkey_unpack_neg = LibSecp256k1.pubkey_unpack_neg LibSecp256k1.lib signature_unpack = LibSecp256k1.signature_unpack LibSecp256k1.lib bip_0340_check = LibSecp256k1.bip_0340_check LibSecp256k1.lib bip_0340_verify = LibSecp256k1.bip_0340_verify LibSecp256k1.lib swu = LibSecp256k1.swu LibSecp256k1.lib hash_to_curve = LibSecp256k1.hash_to_curve LibSecp256k1.lib ================================================ FILE: Haskell/Core/Simplicity/Programs/LibSecp256k1.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines a library of Simplicity expressions that replicate the functional behaviour of (a specific version of) libsecp256k1's elliptic curve operations . -- The functions defined here return precisely the same field and point representatives that the corresponding libsecp256k1's functions do, with a few exceptions with the way the point at infinity is handled. -- This makes these expressions suitable for being jetted by using libsecp256k1 functions. module Simplicity.Programs.LibSecp256k1 ( Lib(Lib), mkLib -- * Field operations , FE, fe_zero, fe_one, fe_is_zero , fe_normalize , fe_add, fe_negate, fe_halve, fe_square, fe_multiply, fe_multiply_beta, fe_invert, fe_square_root , fe_is_odd, fe_is_quad -- * Point operations , Point, GE, GEJ, gej_is_on_curve , gej_infinity, gej_is_infinity , gej_rescale, gej_normalize, gej_negate, gej_scale_lambda , gej_double, gej_add_ex, gej_add, gej_ge_add_ex, gej_ge_add , ge_is_on_curve, ge_negate, ge_scale_lambda , gej_equiv, gej_ge_equiv, gej_x_equiv, gej_y_is_odd , decompress -- * Scalar operations , Scalar, Word129 , scalar_normalize, scalar_add, scalar_negate, scalar_square, scalar_multiply, scalar_multiply_lambda, scalar_invert , scalar_split_lambda, scalar_split_128 , scalar_is_zero -- * Elliptic curve multiplication related operations , Vector129 , wnaf5, wnaf15 , generate, scale , linear_combination_1, linear_check_1, linear_verify_1 , point_check_1, point_verify_1 , off_curve_scale, off_curve_linear_combination_1 -- * Schnorr signature operations , PubKey, pubkey_unpack, pubkey_unpack_neg , Sig, signature_unpack , bip_0340_check, bip_0340_verify -- * Hash to curve , swu, hash_to_curve -- * Example instances , lib ) where import Prelude hiding (drop, take, and, or, not, Word) import Data.List (foldl') import Simplicity.Digest import Simplicity.Functor import qualified Simplicity.LibSecp256k1.Spec as LibSecp256k1 import Simplicity.MerkleRoot import qualified Simplicity.Programs.Arith as Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Word import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Programs.Sha256 hiding (Lib(Lib), lib) import Simplicity.Ty import Simplicity.Ty.LibSecp256k1 import Simplicity.Term.Core -- | 129 entry vector of values. type Vector129 x = (x, Vector128 x) -- | 129-bit signed word that is returned by 'scalar_split_lambda' and 'scalar_split_128'. type Word129 = Vector129 Bit -- | A collection of core Simplicity expressions for LibSecp256k1. -- Use 'mkLib' to construct an instance of this library. data Lib term = Lib { -- | Reduce the representation of a field element to its canonical representative. fe_normalize :: term Word256 FE -- | The normalized reprsentative for the field element 0. , fe_zero :: term () FE -- | The normalized reprsentative for the field element 1. , fe_one :: term () FE -- | Tests if the input value is a representative of the field element 0. , fe_is_zero :: term FE Bit -- | Adds two field elements. , fe_add :: term (FE, FE) FE -- | Negates a field element. , fe_negate :: term FE FE -- | Halves a field element. , fe_halve :: term FE FE -- | Multiplies two field elements. , fe_multiply :: term (FE, FE) FE -- | Multiplies a field element by the canonical primitive cube root of unity. , fe_multiply_beta :: term FE FE -- | Squares a field element. , fe_square :: term FE FE -- | Computes the modular inverse of a field element. , fe_invert :: term FE FE -- | Computes the modular square root of a field element if it exists. , fe_square_root :: term FE (Either () FE) -- | Tests if the canonical representative of the field element is odd. , fe_is_odd :: term FE Bit -- | Tests if the field element is a quadratic residue. , fe_is_quad :: term FE Bit -- | Returns the canonical representative of the point at infinity. , gej_infinity :: term () GEJ -- | Computes the negation of a point. , gej_negate :: term GEJ GEJ -- | Tests if the point is a representative of infinity. , gej_is_infinity :: term GEJ Bit -- | Doubles a point. -- If the result is the point at infinity, it is returned in canonical form. , gej_double :: term GEJ GEJ -- | Adds points 'a' and 'b'. -- Also returns the ratio of 'a''s z-coordinate and the result's z-coordinate. -- -- If the result is the point at infinity, it is returned in canonical form. , gej_add_ex :: term (GEJ, GEJ) (FE, GEJ) -- | Adds points 'a' and 'b'. , gej_add :: term (GEJ, GEJ) GEJ -- | Adds a point 'a' in Jacobian coordinates with a point 'b' in affine coordinates. -- Also returns the ratio of 'a''s z-coordinate and the result's z-coordinate. -- -- If the result is the point at infinity, it is returned in canonical form. , gej_ge_add_ex :: term (GEJ, GE) (FE, GEJ) -- | Adds a point in Jacobian coordinates with a point in affine coordinates. -- -- If the result is the point at infinity, it is returned in canonical form. , gej_ge_add :: term (GEJ, GE) GEJ -- | Multiply a point by the canonical cube root of unity. , gej_scale_lambda :: term GEJ GEJ -- | Negates a point in affine coordinates. , ge_negate :: term GE GE -- | Multiply a point in affine coordinates by the canonical cube root of unity. , ge_scale_lambda :: term GE GE -- | Changes representative of a point in Jacobian coordinates by multiplying the z-coefficent by a given value. , gej_rescale :: term (GEJ, FE) GEJ -- | Converts a point in Jacobian coordinates to the same point in affine coordinates, and normalizes the field representatives. -- Returns the point (0, 0) when given the point at infinity. , gej_normalize :: term GEJ (Either () GE) -- | Tests if two points in jacobian coordinates represent the same point. , gej_equiv :: term (GEJ, GEJ) Bit -- | Tests if a jacobian point and an affine point represent the same point. , gej_ge_equiv :: term (GEJ, GE) Bit -- | Given a field element and a point in Jacobian coordinates, test if the point represents one whose affine x-coordinate is equal to the given field element. , gej_x_equiv :: term (FE, GEJ) Bit -- | Given a point in Jacobian coordinates, test if the point represents one whose affine y-coordinate is odd. , gej_y_is_odd :: term GEJ Bit -- | Check if a given point in Jacobian coordinate satisfies the secp256k1 curve equation Y^2 = X^3 + 7Z^6. , gej_is_on_curve :: term GEJ Bit -- | Check if a given point in affine coordinate satisfies the secp256k1 curve equation Y^2 = X^3 + 7. , ge_is_on_curve :: term GE Bit -- | Reduce the representation of a scalar element to its canonical representative. , scalar_normalize :: term Word256 Scalar -- | Tests if the input value is a representative of the scalar element 0. , scalar_is_zero :: term Scalar Bit -- | Adds two scalar elements. , scalar_add :: term (Scalar, Scalar) Scalar -- | Negates a scalar element. , scalar_negate :: term Scalar Scalar -- | Multiplies two scalar elements. , scalar_square :: term Scalar Scalar -- | Multiplies two scalar elements. , scalar_multiply :: term (Scalar, Scalar) Scalar -- | Multiplies a scalar element by the canonical primitive cube root of unity. , scalar_multiply_lambda :: term Scalar Scalar -- | Computes the modular inverse of a scalar element. , scalar_invert :: term Scalar Scalar -- | Divide a scalar element into two short integers 'k1' and 'k2' such that @'k1' + 'k2' * 'Simplicity.LibSecp256k1.Spec.lambda'@ is the original scalar element. , scalar_split_lambda :: term Scalar (Word129, Word129) -- | Divide a scalar element into two short integers 'k1' and 'k2' such that @'k1' + 'k2' * 2^128@ is the original scalar element. , scalar_split_128 :: term Scalar (Word129, Word129) -- | Convert a scalar value to wnaf form, with a window of 5 bits. , wnaf5 :: term Word129 (Vector129 (Either () Word4)) -- | Convert a scalar value to wnaf form, with a window of 15 bits. , wnaf15 :: term Word129 (Vector129 (Either () Word16)) -- | Returns a multiple of the secp256k1's generator. , generate :: term Scalar GEJ -- | Multiply a point by a scalar element. , off_curve_scale :: term (Scalar, GEJ) GEJ -- | Given an elliptic curve point, @a@, and two scalar values @na@ and @ng@, return @na * a + ng * g@ where @g@ is secp256k1's generator. -- If the result is the point at infinity, it is returned in canonical form. , off_curve_linear_combination_1 :: term ((Scalar, GEJ), Scalar) GEJ -- | Verifies that all points are on the secp256k1 curve and checks if @na * a + ng * g == r@ on the input @(((na, a), ng), r)@ where @g@ is secp256k1's generator. , linear_check_1 :: term (((Scalar, GE), Scalar), GE) Bit -- | Decompress a compressed point into affine coordinates. Fails if the x-coordinate is no on the secp256k1, but it will succeed even if the x-coordinate is not normalized. , decompress :: term Point (Either () GE) -- | Decompresses and verifies that all points are on the secp256k1 curve as 'linear_check_1' does. -- This will fail if either point decompression fails or if the 'linear_check_1' would fail. , point_check_1 :: term (((Scalar, Point), Scalar), Point) Bit -- | This function unpacks a 'PubKey' as a elliptic curve point in compressed coordinates. -- -- If the x-coordinate isn't on the elliptice curve, the function returns @Left ()@. -- This does not check that the x-coordinate in on-curve. That would have to be performed by `decompress`. , pubkey_unpack :: term PubKey (Either () Point) -- | This function unpacks the negation of a 'PubKey' as a elliptic curve point in compressed coordinates. -- -- If the x-coordinate isn't on the elliptice curve, the function returns @Left ()@. -- This does not check that the x-coordinate in on-curve. That would have to be performed by `decompress`. , pubkey_unpack_neg :: term PubKey (Either () Point) -- | This function unpackes a 'Sig' as a pair of a field element and a scalar value. -- -- If the field element's value is greater than or equal to the field order, the function return @Left ()@. -- If the scalar element's value is greater than or equal to secp256k1's curve order, the function returns @Left ()@. , signature_unpack :: term Sig (Either () (FE, Scalar)) -- | This function is given a public key, a 256-bit message, and a signature, and checks if the signature is valid for the given message and public key. , bip_0340_check :: term ((PubKey, Word256), Sig) Bit -- | Algebraically distribute a field element over the secp256k1 curve as defined in -- "Indifferentiable Hashing to Barreto-Naehrig Curves" by Pierre-Alain Fouque, Mehdi Tibouchi -- -- -- While this by iteslf is not a cryptographic hash function, it can be used as a subrotuine -- in a 'hash_to_curve' function. However the distribution only approaches uniform when it is called twice. , swu :: term FE GE -- | A cryptograph hash function that results in a point on the secp256k1 curve. -- -- This matches the hash function used to map asset IDs to asset commitments. -- -- This version explicitly fails the the cryptographically impossible cases where sha-256 produces a value larger than the field size. -- See 'hash_to_curve' for the version that 'asserts' in this failure case. , hash_to_curve_core :: term Word256 (Either () GE) } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { fe_normalize = m fe_normalize , fe_zero = m fe_zero , fe_one = m fe_one , fe_is_zero = m fe_is_zero , fe_is_odd = m fe_is_odd , fe_add = m fe_add , fe_negate = m fe_negate , fe_halve = m fe_halve , fe_multiply = m fe_multiply , fe_multiply_beta = m fe_multiply_beta , fe_square = m fe_square , fe_invert = m fe_invert , fe_square_root = m fe_square_root , fe_is_quad = m fe_is_quad , gej_infinity = m gej_infinity , gej_negate = m gej_negate , gej_is_infinity = m gej_is_infinity , gej_double = m gej_double , gej_add_ex = m gej_add_ex , gej_add = m gej_add , gej_ge_add_ex = m gej_ge_add_ex , gej_ge_add = m gej_ge_add , gej_scale_lambda = m gej_scale_lambda , ge_negate = m ge_negate , ge_scale_lambda = m ge_scale_lambda , gej_rescale = m gej_rescale , gej_normalize = m gej_normalize , gej_equiv = m gej_equiv , gej_ge_equiv = m gej_ge_equiv , gej_x_equiv = m gej_x_equiv , gej_y_is_odd = m gej_y_is_odd , gej_is_on_curve = m gej_is_on_curve , ge_is_on_curve = m ge_is_on_curve , scalar_normalize = m scalar_normalize , scalar_is_zero = m scalar_is_zero , scalar_add = m scalar_add , scalar_negate = m scalar_negate , scalar_square = m scalar_square , scalar_multiply = m scalar_multiply , scalar_multiply_lambda = m scalar_multiply_lambda , scalar_invert = m scalar_invert , scalar_split_lambda = m scalar_split_lambda , scalar_split_128 = m scalar_split_128 , wnaf5 = m wnaf5 , wnaf15 = m wnaf15 , generate = m generate , off_curve_scale = m off_curve_scale , off_curve_linear_combination_1 = m off_curve_linear_combination_1 , linear_check_1 = m linear_check_1 , decompress = m decompress , point_check_1 = m point_check_1 , pubkey_unpack = m pubkey_unpack , pubkey_unpack_neg = m pubkey_unpack_neg , signature_unpack = m signature_unpack , bip_0340_check = m bip_0340_check , swu = m swu , hash_to_curve_core = m hash_to_curve_core } -- | Build the LibSecp256k1 'Lib' library from its dependencies. mkLib :: forall term. Core term => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Lib term mkLib Sha256.Lib{..} = lib where -- A constant expression for a 64-bit value. scribe64 :: TyC a => Integer -> term a Word64 scribe64 = scribe . toWord64 -- A constant expression for a 128-bit value. scribe128 :: TyC a => Integer -> term a Word128 scribe128 = scribe . toWord128 -- A constant expression for a 256-bit value. scribe256 :: TyC a => Integer -> term a Word256 scribe256 = scribe . toWord256 scribeFeOrder :: term () Word256 scribeFeOrder = scribe256 LibSecp256k1.fieldOrder scribeFeHalf :: term () Word256 scribeFeHalf = scribe256 ((LibSecp256k1.fieldOrder + 1) `div` 2) scribeGroupOrder :: term () Word256 scribeGroupOrder = scribe256 LibSecp256k1.groupOrder scribeGroupOrder512 :: term () Word512 scribeGroupOrder512 = zero256 &&& scribeGroupOrder fe_beta :: term () FE fe_beta = scribe256 LibSecp256k1.beta scalar_lambda :: term () Scalar scalar_lambda = scribe256 LibSecp256k1.lambda -- 256 bit addition. add256 :: term (Word256, Word256) (Bit, Word256) add256 = Arith.add word256 -- 256 bit subtraction. sub256 :: term (Word256, Word256) (Bit, Word256) sub256 = Arith.subtract word256 sub128 = Arith.subtract word128 -- Multiplication modulo 2^64. mul64 :: term (Word64, Word64) Word128 mul64 = Arith.multiply word64 mul128 = Arith.multiply word128 mul256 = Arith.multiply word256 -- 256 bit less-than lt256 = Arith.lt word256 -- 128 bit zero. zero128 = Arith.zero word128 -- 256 bit zero. zero256 = Arith.zero word256 -- 256 bit one. one256 = Arith.one word256 msb256 = Arith.msb word256 msb128 = Arith.msb word128 lsb256 = Arith.lsb word256 lsb128 = Arith.lsb word128 mod512 = Arith.modulo word512 -- | computes a 512 bit number modulo the field order. fe_normalize512 :: term Word512 FE fe_normalize512 = iden &&& (unit >>> zero256 &&& scribeFeOrder) >>> mod512 >>> ih -- | computes a 512 bit number modulo the group order. scalar_normalize512 :: term Word512 FE scalar_normalize512 = iden &&& (unit >>> zero256 &&& scribeGroupOrder) >>> mod512 >>> ih signResize4 = left_extend word4 (DoubleV . DoubleV . DoubleV . DoubleV . DoubleV $ SingleV) signResize16 = left_extend word16 (DoubleV . DoubleV . DoubleV $ SingleV) fullShift128 = full_shift word1 word128 >>> oh wnafsub128 :: term ((Bit, Word128), Word128) (Bit, Word128) wnafsub128 = xor ooh (drop msb128) &&& (oih &&& ih >>> sub128) >>> xor oh ioh &&& iih wnaf5step1 :: term (Bit, Word128) ((Bit, Word128), (Either () Word4)) wnaf5step1 = drop lsb128 &&& (oh &&& fullShift128) >>> cond body (iden &&& injl unit) where body = iden &&& (drop . drop . drop $ iiih) >>> (oh &&& drop signResize4 >>> wnafsub128) &&& injr ih wnaf15step1 :: term (Bit,Word128) ((Bit,Word128), (Either () Word16)) wnaf15step1 = drop lsb128 &&& iden >>> cond body ((oh &&& fullShift128) &&& injl unit) where mask = take (take (take (ih &&& ih) &&& ih) &&& ih) &&& ih body = iden &&& (drop iiih >>> mask) >>> ((ooh &&& take fullShift128) &&& drop (signResize16 >>> msb128 &&& iden >>> fullShift128) >>> wnafsub128) &&& injr ih wnafstepD :: (TyC s, TyC v) => term s (s, v) -> term s (s, (v, v)) wnafstepD rec = rec >>> take rec &&& ih >>> ooh &&& (oih &&& ih) wnaf5step16 = wnafstepD . wnafstepD . wnafstepD . wnafstepD $ wnaf5step1 wnaf5step128 = wnafstepD . wnafstepD . wnafstepD $ wnaf5step16 wnaf15step16 = wnafstepD . wnafstepD . wnafstepD . wnafstepD $ wnaf15step1 wnaf15step128 = wnafstepD . wnafstepD . wnafstepD $ wnaf15step16 wnafpre :: term Scalar Word256 wnafpre = msb256 &&& iden >>> cond (iden &&& (unit >>> scribeGroupOrder) >>> sub256 >>> ih) iden generate0 :: term () GE generate0 = scribe g where g = (toWord256 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, toWord256 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8) -- 2^128 * generate0 generate128 :: term () GE generate128 = scribe g128 where g128 = (toWord256 0x8f68b9d2f63b5f339239c1ad981f162ee88c5678723ea3351b7b444c9ec4c0da, toWord256 0x662a9f2dba063986de1d90c2b6be215dbbea2cfe95510bfdf23cbf79501fff82) scaleConstant :: term () GE -> Word a -> term (a, GEJ) GEJ scaleConstant base = go where go :: Word a -> term (a, GEJ) GEJ go SingleV = cond (gej_double &&& (unit >>> base) >>> gej_ge_add) gej_double go (DoubleV w) = oih &&& (ooh &&& ih >>> rec) >>> rec where rec = go w lib@Lib{..} = Lib { fe_normalize = (iden &&& (unit >>> scribeFeOrder) >>> sub256) &&& iden >>> ooh &&& (oih &&& ih) >>> cond ih oh , fe_zero = zero256 , fe_one = one256 , fe_is_zero = or (Arith.is_zero word256) ((unit >>> scribeFeOrder) &&& iden >>> eq) , fe_is_odd = fe_normalize >>> lsb256 , fe_add = add256 >>> cond ((unit >>> one256) &&& iden) ((unit >>> zero256) &&& iden) >>> fe_normalize512 , fe_negate = fe_multiplyInt (-1) , fe_multiply = mul256 >>> fe_normalize512 , fe_multiply_beta = (unit >>> fe_beta) &&& iden >>> fe_multiply , fe_square = iden &&& iden >>> fe_multiply , fe_halve = (false &&& iden) >>> full_shift word1 word256 >>> ih &&& oh >>> cond ((unit >>> scribeFeHalf) &&& iden >>> fe_add) iden , fe_invert = (unit >>> scribeFeOrder) &&& iden >>> Arith.bezout word256 >>> copair (drop fe_negate) ih , fe_square_root = iden &&& tower >>> oh &&& drop ((oh &&& drop fe_square >>> fe_multiply) >>> fe_square >>> fe_square) >>> (take fe_negate &&& drop fe_square >>> fe_add >>> fe_is_zero) &&& ih >>> cond (injr iden) (injl unit) , fe_is_quad = elimS fe_square_root false true , gej_infinity = let zero = fe_zero in (zero &&& zero) &&& zero , gej_negate = take ge_negate &&& drop fe_normalize , gej_is_infinity = drop fe_is_zero , gej_double = let body = (take (oh &&& (take fe_square >>> fe_multiplyInt 3 >>> fe_halve) &&& drop fe_square) -- (x, (3/2*x^2, y^2)) >>> ((iih &&& oh >>> fe_multiply >>> fe_negate) &&& ih) -- (-x*y^2, (3/2*x^2, y^2)) >>> (((take (fe_multiplyInt 2) &&& drop (take fe_square) >>> fe_add) &&& oh) &&& ih) -- ((9/4*x^4 - 2*x*y^2, x^2*y^4), (3/2*x^2, y^2)) >>> (ooh &&& ((ioh &&& (take fe_add) >>> fe_multiply) &&& drop (drop fe_square) >>> fe_add >>> fe_negate))) -- (9/4*x^4 - 2*x*y^2, -(3/2*x^2*(9/4*x^4 - 3*x*y^2) + y^4)) &&& (oih &&& ih >>> fe_multiply) -- y*z in gej_is_infinity &&& iden >>> cond (unit >>> gej_infinity) body , gej_add_ex = let body = ((oooh &&& (iih >>> fe_square) >>> fe_multiply) &&& (drop (take (take fe_negate)) &&& (oih >>> fe_square) >>> fe_multiply) >>> fe_add &&& oh) &&& ((ooih &&& (iih >>> fe_cube) >>> fe_multiply) &&& (drop (take (drop fe_negate)) &&& (oih >>> fe_cube) >>> fe_multiply) >>> fe_add &&& oh) &&& (oh &&& drop (drop fe_negate)) -- ((-h,u1),((-i,s1),(a,-bz)))) >>> take (take fe_is_zero) &&& iden >>> cond (drop zeroH) nonZeroH zeroH = take (take fe_is_zero) &&& ioh >>> cond (oih &&& gej_double) (unit >>> fe_zero &&& gej_infinity) nonZeroH = (ooh &&& ((ooh &&& drop ioih >>> fe_multiply) &&& iiih)) &&& ((take (take fe_square) &&& oih >>> fe_multiply) &&& ioh) -- ((-h,(-h*az,-bz)),(t,(i,s1))) >>> ((ooh &&& oiih >>> fe_multiply) &&& take (drop fe_multiply)) &&& (((ooh >>> fe_cube) &&& ioh) &&& iih) -- ((h*bz),z),((-h^3,t),(i,s1))) >>> ooh &&& drop ((((take (oh &&& drop (fe_multiplyInt (-2)) >>> fe_add) &&& drop (take fe_square) >>> fe_add) &&& oih) &&& (ioh &&& (ooh &&& iih >>> fe_multiply))) -- (h*bz,(((x,t),(i,(-h^3*s1))),z)) >>> ooh &&& (iih &&& (ioh &&& take (oh &&& drop fe_negate >>> fe_add) >>> fe_multiply) >>> fe_add)) -- ..,(x,y),... &&& oih in take gej_is_infinity &&& iden >>> cond ((unit >>> fe_zero) &&& (drop (take (take fe_normalize &&& drop fe_normalize) &&& (drop fe_normalize)))) (drop gej_is_infinity &&& iden >>> cond ((unit >>> fe_one) &&& (take (take (take fe_normalize &&& drop fe_normalize) &&& (drop fe_normalize)))) body) , gej_add = gej_add_ex >>> ih , gej_ge_add_ex = oh &&& (ih &&& (unit >>> fe_one)) >>> gej_add_ex , gej_ge_add = gej_ge_add_ex >>> ih , gej_scale_lambda = take ge_scale_lambda &&& drop fe_normalize , ge_negate = take fe_normalize &&& drop fe_negate , ge_scale_lambda = take fe_multiply_beta &&& drop fe_normalize , gej_rescale = (ooh &&& ih >>> zinv) &&& (oih &&& ih >>> fe_multiply) , gej_normalize = drop fe_is_zero &&& iden >>> cond (injl unit) (injr gej_norm) , gej_equiv = take (gej_negate) &&& ih >>> gej_add >>> gej_is_infinity , gej_ge_equiv = take (gej_negate) &&& ih >>> gej_ge_add >>> gej_is_infinity , gej_x_equiv = and (not (drop gej_is_infinity)) (drop (take (take fe_negate)) &&& (drop (drop fe_square) &&& oh >>> fe_multiply) >>> fe_add >>> fe_is_zero) , gej_y_is_odd = oih &&& (ih >>> fe_invert >>> fe_cube) >>> fe_multiply >>> fe_is_odd , gej_is_on_curve = ((unit >>> scribe256 7) &&& (ih >>> fe_cube >>> fe_square) >>> fe_multiply) &&& (take (take fe_cube &&& (drop fe_square >>> fe_negate)) >>> fe_add) >>> fe_add >>> fe_is_zero , ge_is_on_curve = iden &&& (unit >>> fe_one) >>> gej_is_on_curve , scalar_normalize = (iden &&& (unit >>> scribeGroupOrder) >>> sub256) &&& iden >>> ooh &&& (oih &&& ih) >>> cond ih oh , scalar_is_zero = or (Arith.is_zero word256) ((unit >>> scribeGroupOrder) &&& iden >>> eq) , scalar_add = add256 >>> cond ((unit >>> one256) &&& iden) ((unit >>> zero256) &&& iden) >>> scalar_normalize512 , scalar_negate = (unit >>> scribe256 ((-1) `mod` LibSecp256k1.groupOrder)) &&& iden >>> scalar_multiply , scalar_square = iden &&& iden >>> scalar_multiply , scalar_multiply = mul256 >>> scalar_normalize512 , scalar_multiply_lambda = (unit >>> scalar_lambda) &&& iden >>> scalar_multiply , scalar_invert = (unit >>> scribeGroupOrder) &&& iden >>> Arith.bezout word256 >>> copair (drop scalar_negate) ih , scalar_split_lambda = let g1 = scribe256 0x3086d221a7d46bcde86c90e49284eb153daa8a1471e8ca7fe893209a45dbb031 g2 = scribe256 0xe4437ed6010e88286f547fa90abfe4c4221208ac9df506c61571b4ae8ac47f71 negB1 = scribe128 0xe4437ed6010e88286f547fa90abfe4c3 b2 = scribe128 0x3086d221a7d46bcde86c90e49284eb15 roundDivTwo384 = take (drop (Arith.msb word128) &&& oh >>> Arith.full_increment word128) >>> ih c1 = ((iden &&& (unit >>> g1) >>> mul256) >>> roundDivTwo384) &&& (unit >>> negB1) >>> mul128 c2 = ((iden &&& (unit >>> g2) >>> mul256) >>> roundDivTwo384) &&& (unit >>> b2) >>> mul128 k1 = oh &&& drop (cond (((unit >>> high word128) &&& iden) &&& (unit >>> scribeGroupOrder) >>> add256 >>> ih) ((unit >>> zero128) &&& iden) &&& (unit >>> scalar_lambda) >>> scalar_multiply >>> scalar_negate) >>> scalar_add >>> msb256 &&& iden >>> cond (iden &&& (unit >>> scribeGroupOrder) >>> sub256 >>> injr unit &&& iih) (injl unit &&& ih) in scalar_normalize >>> iden &&& (c1 &&& c2 >>> sub256 >>> oh &&& iih) >>> k1 &&& ih , scalar_split_128 = scalar_normalize >>> (false &&& ih) &&& (false &&& oh) , wnaf5 = wnaf5step128 >>> (take wnaf5step1 >>> ih) &&& ih , wnaf15 = wnaf15step128 >>> (take wnaf15step1 >>> ih) &&& ih , generate = let step = iih &&& (ioh &&& take gej_double >>> match ih (ih &&& take generateSmall >>> gej_ge_add)) >>> match ih (ih &&& take generate128Small >>> gej_ge_add) step2 = (oh &&& (iooh &&& iioh) >>> step) &&& (ioih &&& iiih) >>> step step4 = (oh &&& (iooh &&& iioh) >>> step2) &&& (ioih &&& iiih) >>> step2 step8 = (oh &&& (iooh &&& iioh) >>> step4) &&& (ioih &&& iiih) >>> step4 step16 = (oh &&& (iooh &&& iioh) >>> step8) &&& (ioih &&& iiih) >>> step8 step32 = (oh &&& (iooh &&& iioh) >>> step16) &&& (ioih &&& iiih) >>> step16 step64 = (oh &&& (iooh &&& iioh) >>> step32) &&& (ioih &&& iiih) >>> step32 step128 = (oh &&& (iooh &&& iioh) >>> step64) &&& (ioih &&& iiih) >>> step64 step129 = (oh &&& (iooh &&& iioh) >>> step) &&& (ioih &&& iiih) >>> step128 in (unit >>> gej_infinity) &&& split128 >>> step129 , off_curve_linear_combination_1 = let splitLambda = scalar_split_lambda >>> take wnaf5 &&& drop wnaf5 body = (unit >>> gej_infinity) &&& (oih >>> scalarTable5) &&& (ooh >>> splitLambda) &&& (ih >>> split128) >>> iooh &&& step129 >>> ioh &&& (oh &&& iih >>> fe_multiply) step = drop iiih &&& (drop iioh &&& (drop ioih &&& (drop iooh &&& take gej_double &&& ioih >>> match ioh (ioh &&& (oh &&& iih >>> lookupTable5) >>> gej_ge_add)) &&& ioih >>> match ioh (ioh &&& (oh &&& iih >>> lookupTable5 >>> ge_scale_lambda) >>> gej_ge_add)) &&& iooh >>> match ioh (ioh &&& (take generateSmall &&& iih >>> zinv) >>> gej_ge_add)) &&& iooh >>> match ioh (ioh &&& (take generate128Small &&& iih >>> zinv) >>> gej_ge_add) step2 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step step4 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step2) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step2 step8 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step4) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step4 step16 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step8) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step8 step32 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step16) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step16 step64 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step32) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step32 step128 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step64) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step64 step129 = (oh &&& drop (oh &&& drop ((oooh &&& oioh) &&& (iooh &&& iioh))) >>> step) &&& drop (oh &&& drop ((ooih &&& oiih) &&& (ioih &&& iiih))) >>> step128 in -- In the case that the 'a' parameter is infinity or the 'na' parameter is 0, then scalarTable5 is not built. -- In particular the globalZ is set to 1 instead of whatever would have been generated by the table. or (take (drop gej_is_infinity)) (take (take scalar_is_zero)) &&& iden >>> cond (drop generate) body , linear_check_1 = and (drop ge_is_on_curve) (and (take (take (drop ge_is_on_curve))) ((take (take (oh &&& (ih &&& (unit >>> fe_one))) &&& ih >>> off_curve_linear_combination_1)) &&& drop ge_negate >>> gej_ge_add >>> gej_is_infinity)) , off_curve_scale = iden &&& (unit >>> zero256) >>> off_curve_linear_combination_1 , decompress = let k = drop (drop fe_normalize) &&& (xor (take fe_is_odd) ioh &&& oh >>> cond fe_negate iden) in drop y_from_x &&& iden >>> match (injl unit) (injr k) , point_check_1 = let k1 = drop (take (drop decompress)) &&& (drop (ooh &&& ih) &&& oh) >>> match false k2 k2 = ((iooh &&& oh) &&& ioih) &&& iih >>> linear_check_1 in drop decompress &&& oh >>> match false k1 , pubkey_unpack = pubkey_check >>> cond (injr ((unit >>> false) &&& iden)) (injl unit) , pubkey_unpack_neg = pubkey_check >>> cond (injr ((unit >>> true) &&& iden)) (injl unit) , signature_unpack = and (oh &&& scribe (toWord256 LibSecp256k1.fieldOrder) >>> lt256) (ih &&& scribe (toWord256 LibSecp256k1.groupOrder) >>> lt256) &&& iden >>> cond (injr iden) (injl unit) , bip_0340_check = let k1 = iih &&& (ioh &&& oh) >>> match false k2 k2 = (ih &&& oih) &&& ((unit >>> false) &&& ooh) >>> point_check_1 e = m >>> (iv &&& oh >>> hashBlock) &&& ih >>> hashBlock >>> scalar_normalize iv = scribe $ toWord256 . integerHash256 . ivHash . tagIv $ "BIP0340/challenge" m = (ioh &&& ooh) &&& (oih &&& (scribe (toWord256 0x8000000000000000000000000000000000000000000000000000000000000500))) in take (take pubkey_unpack_neg) &&& (e &&& drop signature_unpack) >>> match false k1 , swu = let Just c = LibSecp256k1.fe_square_root (LibSecp256k1.fe (-3)) d = LibSecp256k1.fe_halve (c LibSecp256k1..-. LibSecp256k1.fe_one) in fe_is_odd &&& (fe_square >>> (iden &&& scribe256 (LibSecp256k1.fe_repr (LibSecp256k1.fe_negate c)) >>> fe_multiply) &&& (iden &&& scribe256 8 >>> fe_add) &&& (iden &&& scribe256 3 >>> fe_multiply) >>> -- (-c*t^2, 8+t^2, -c^2*t^2) (iden &&& (drop fe_multiply >>> fe_invert)) >>> -- ((-c*t^2, 8+t^2, -c^2*t^2), -1/j) ((ooh &&& (oiih &&& ih >>> fe_multiply) >>> fe_multiply) &&& scribe256 (LibSecp256k1.fe_repr d) >>> fe_add) &&& -- x1 (((take (drop (take fe_cube))) &&& (drop fe_negate) >>> fe_multiply) &&& (unit >>> fe_one) >>> fe_add) >>> -- x3 (take y_from_x &&& iden) >>> flip match (ioh &&& oh) (drop ((oh &&& (unit >>> fe_one) >>> fe_add >>> fe_negate) &&& ih) >>> -- (x2, x3) (take y_from_x &&& iden) >>> flip match (ioh &&& oh) (drop (drop (y_from_x &&& iden) >>> flip match (ih &&& oh) (unit >>> fe_zero &&& fe_zero) )))) >>> cond ge_negate iden , hash_to_curve_core = let lt256 = Arith.lt word256 prefix1 = asW256 "1st generation: " prefix2 = asW256 "2nd generation: " asW256 str | 16 == length str = toWord128 $ foldl' (\n c -> n * 256 + toInteger (fromEnum c)) 0 str postfix = scribe . toWord128 $ 2^127 + 128 + 256 in ((unit >>> iv) &&& ((scribe prefix1 &&& oh) &&& (ih &&& postfix)) >>> hashBlock) &&& ((unit >>> iv) &&& ((scribe prefix2 &&& oh) &&& (ih &&& postfix)) >>> hashBlock) >>> (((oh &&& scribe (toWord256 LibSecp256k1.fieldOrder) >>> lt256) `and` (ih &&& scribe (toWord256 LibSecp256k1.fieldOrder) >>> lt256)) &&& iden) >>> cond ((take swu &&& (unit >>> fe_one)) &&& drop swu >>> gej_ge_add >>> gej_normalize) (injl unit) } where y_from_x = (unit >>> scribe256 7) &&& fe_cube >>> fe_add >>> fe_square_root fe_cube = iden &&& fe_square >>> fe_multiply fe_multiplyInt i = scribe256 (i `mod` LibSecp256k1.fieldOrder) &&& iden >>> fe_multiply -- Common code shared between 'fe_invert' and 'fe_square_root'. tower = iden &&& fe_cube >>> ih &&& (oh &&& drop fe_square >>> fe_multiply) >>> oh &&& ((ih &&& (oh &&& (drop (iden &&& (iden &&& (fe_square >>> fe_square >>> fe_square) >>> fe_multiply >>> fe_square >>> fe_square >>> fe_square) >>> fe_multiply) >>> fe_square >>> fe_square) >>> fe_multiply -- (x2,(x3,x11)) >>> iden &&& foldr1 (>>>) (replicate 11 fe_square) >>> fe_multiply)) -- (x2,(x3,x22)) >>> ih &&& (oh &&& drop (iden &&& foldr1 (>>>) (replicate 22 fe_square) >>> fe_multiply -- (x2,(x22,(x3,x44))) >>> (iden &&& (iden &&& foldr1 (>>>) (replicate 44 fe_square) >>> fe_multiply -- (x2,(x22,(x3,(x44,x88)))) >>> iden &&& foldr1 (>>>) (replicate 88 fe_square) >>> fe_multiply -- (x2,(x22,(x3,(x44,x176)))) >>> foldr1 (>>>) (replicate 44 fe_square)) >>> fe_multiply) -- (x2,(x22,(x3,x220))) >>> fe_square >>> fe_square >>> fe_square) >>> fe_multiply -- (x2,(x22,x223)) >>> foldr1 (>>>) (replicate 23 fe_square)) >>> fe_multiply -- (x2,t1) >>> foldr1 (>>>) (replicate 5 fe_square)) zinv = (ooh &&& drop fe_square >>> fe_multiply) &&& (oih &&& drop fe_cube >>> fe_multiply) gej_norm = oh &&& drop fe_invert >>> zinv -- Compute odd-multiples of a point for small (5-bit) multiples. -- The result is in Jacobian coordinates but the z-coordinate is identical for all outputs. scalarTable5 :: term GEJ (FE, Vector8 GE) scalarTable5 = iden &&& gej_double >>> iih &&& (((ooh &&& iih >>> zinv) &&& oih) &&& ioh -- (dz, (a', (dx,dy))) >>> pass1_8) >>> (oh &&& iih >>> fe_multiply) &&& drop (take pass2_8) where pass1_2 = iden &&& gej_ge_add_ex >>> (ioh &&& (oooh &&& iioh)) &&& (iih &&& oih) pass1_4 = pass1_2 >>> oh &&& drop (gej_ge_add_ex &&& ih >>> ooh &&& (oih &&& ih >>> pass1_2)) >>> (ioh &&& (oh &&& iioh)) &&& iiih pass1_8 = pass1_4 >>> oh &&& drop (gej_ge_add_ex &&& ih >>> ooh &&& (oih &&& ih >>> pass1_4)) >>> (ioh &&& (oh &&& iioh)) &&& drop (drop ioih) pass2_1 = oh &&& ih >>> zinv pass2_2 = (oioh &&& (ooh &&& ih >>> fe_multiply)) &&& (oiih &&& ih >>> pass2_1) >>> (take pass2_1 &&& ih) &&& oih pass2_4 = (ooh &&& oioh) &&& (oiih &&& ih >>> pass2_2) >>> (oih &&& (ooh &&& iih >>> fe_multiply) >>> pass2_2) &&& ioh >>> (ooh &&& ih) &&& oih pass2_8 = ( oh &&& ioh) &&& ( iih &&& (unit >>> fe_one) >>> pass2_4) >>> (oih &&& (ooh &&& iih >>> fe_multiply) >>> pass2_4) &&& ioh >>> ooh &&& ih -- Given an odd-multiples table of affinte points, extract the @i@th element of the table. -- If the index is negative @i@, then return the point negation of the @i@th element of the table. lookupTable5 :: term (Word4, Vector8 GE) GE lookupTable5 = oooh &&& ooih &&& oih &&& ih >>> cond neg pos where pos = ioih &&& (iooh &&& (oh &&& iih >>> cond ih oh) >>> cond ih oh) >>> cond ih oh neg = ioih &&& (iooh &&& (oh &&& iih >>> cond oh ih) >>> cond oh ih) >>> cond (take ge_negate) (drop ge_negate) split128 = scalar_split_128 >>> take wnaf15 &&& drop wnaf15 -- Returns a small, signed integer multiple of the secp256k1's generator as a normalized affine point. generateSigned :: Word a -> term a GEJ generateSigned SingleV = copair gej_infinity ((generate0 >>> ge_negate) &&& fe_one) generateSigned (DoubleV w) = ih &&& take rec >>> scaleConstant generate0 w where rec = generateSigned w generateSmall :: term Word16 GE generateSmall = generateSigned word16 >>> gej_norm generate128Signed :: Word a -> term a GEJ generate128Signed SingleV = copair gej_infinity ((generate128 >>> ge_negate) &&& fe_one) generate128Signed (DoubleV w) = ih &&& take rec >>> scaleConstant generate128 w where rec = generate128Signed w generate128Small :: term Word16 GE generate128Small = generate128Signed word16 >>> gej_norm pubkey_check = (iden &&& scribe (toWord256 LibSecp256k1.fieldOrder) >>> lt256) &&& iden -- | Same as 'off_curve_linear_combination_1' except it fails when the given point is off-curve. linear_combination_1 :: Assert term => Lib term -> term ((Scalar, GEJ), Scalar) GEJ linear_combination_1 m = take (drop (gej_is_on_curve m)) &&& (off_curve_linear_combination_1 m) >>> assertr cmrFail0 ih -- | Same as 'off_curve_scale' except it fails when the given point is off-curve. scale :: Assert term => Lib term -> term (Scalar, GEJ) GEJ scale m = drop (gej_is_on_curve m) &&& (off_curve_scale m) >>> assertr cmrFail0 ih linear_verify_1 :: Assert term => Lib term -> term (((Scalar, GE), Scalar), GE) () linear_verify_1 m = assert (linear_check_1 m) point_verify_1 :: Assert term => Lib term -> term (((Scalar, Point), Scalar), Point) () point_verify_1 m = assert (point_check_1 m) -- | This function is given a public key, a 256-bit message, and a signature, and asserts that the signature is valid for the given message and public key. bip_0340_verify :: Assert term => Lib term -> term ((PubKey, Word256), Sig) () bip_0340_verify m = assert (bip_0340_check m) -- | A cryptograph hash function that results in a point on the secp256k1 curve. -- -- This matches the hash function used to map asset IDs to asset commitments. hash_to_curve :: Assert term => Lib term -> term Word256 GE hash_to_curve m = assert (hash_to_curve_core m) -- | An instance of the Sha256 'Lib' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. lib :: Core term => Lib term lib = mkLib Sha256.lib ================================================ FILE: Haskell/Core/Simplicity/Programs/Loop.hs ================================================ {-# LANGUAGE ScopedTypeVariables #-} -- | This module is a stub for supporting looping behaviour in Simplicity via self-delegation. -- module Simplicity.Programs.Loop ( loop, loopDepth ) where import Prelude hiding (take) import Simplicity.Digest import Simplicity.MerkleRoot import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Term.Core import Simplicity.Tensor import Simplicity.Ty.Word loopTail :: (Assert term, Delegate term, TyC a, TyC b) => term (a, Word256) b -> term (a, Word256) b loopTail k = disconnect (assert (iih &&& oh >>> eq) &&& ih) k >>> ih loopBody :: (Assert term, Delegate term, TyC a, TyC b) => term a (Either a b) -> term (a, Word256) b -> term (a, Word256) b loopBody t k = take t &&& ih >>> match (loopTail k) oh loopEnd :: forall term a b. (Assert term, TyC a, TyC b) => term a (Either a b) -> term (a, Word256) b loopEnd t = take t &&& ih >>> assertr (commitmentRoot cmrTail) oh where cmrTail :: CommitmentRoot (a, Word256) b cmrTail = loopTail undefined -- | Builds an unbounded loop via a self-delegation construction. -- While loopBody is recursive, generating an infinite term, we anticipate a pruner will evaluate the term as far as needed to replace the 'match' with an 'assertr'. -- Thanks to Haskell's laziness, this is feasible. loop :: (Assert term, Delegate term, TyC a, TyC b) => Product CommitmentRoot term a (Either a b) -> term a b loop t = sndProduct $ iden &&& scribe cmr >>> lb where cmr = toWord256 . integerHash256 . commitmentRoot . fstProduct $ lb lb = loopBody t lb -- | Builds an loop via a self-delegation construction up to a given maximum depth. -- At the @n@th iteration, an assertion is uses. -- This is variant of 'loop' that has been pre-pruned at the given depth. -- Both @'loop' t@ and @'loopDepth' n t@ share the same 'commitmentRoot'. loopDepth n t | 1 <= n = sndProduct $ iden &&& scribe cmr >>> lb where cmr = toWord256 . integerHash256 . commitmentRoot . fstProduct $ lb lb = loopBodyDepth n loopBodyDepth 1 = loopEnd t loopBodyDepth n = loopBody t (loopBodyDepth (n-1)) ================================================ FILE: Haskell/Core/Simplicity/Programs/Sha256/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Programs.Sha256.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Programs.Sha256.lib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Programs.Sha256.Lib ( -- * Operations Sha256.Block, Sha256.Hash, Sha256.Ctx8 , iv, hashBlock , ctx8Init , tapdataInit , ctx8Add1 , ctx8Addn , ctx8AddBuffer , ctx8Add2 , ctx8Add4 , ctx8Add8 , ctx8Add16 , ctx8Add32 , ctx8Add64 , ctx8Add128 , ctx8Add256 , ctx8Add512 , ctx8AddBuffer511 , ctx8Finalize , hashLoop , ctx8InitTag ) where import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Ty.Word iv = Sha256.iv Sha256.lib hashBlock = Sha256.hashBlock Sha256.lib ctx8Init = Sha256.ctx8Init Sha256.lib tapdataInit = Sha256.tapdataInit Sha256.lib ctx8Add1 = Sha256.ctx8Add1 Sha256.libAssert ctx8Addn = Sha256.ctx8Addn Sha256.libAssert ctx8AddBuffer = Sha256.ctx8AddBuffer Sha256.libAssert ctx8Add2 = ctx8Addn vector2 ctx8Add4 = ctx8Addn vector4 ctx8Add8 = ctx8Addn vector8 ctx8Add16 = ctx8Addn vector16 ctx8Add32 = ctx8Addn vector32 ctx8Add64 = ctx8Addn vector64 ctx8Add128 = ctx8Addn vector128 ctx8Add256 = ctx8Addn vector256 ctx8Add512 = ctx8Addn vector512 ctx8AddBuffer511 = ctx8AddBuffer buffer511 ctx8Finalize = Sha256.ctx8Finalize Sha256.libAssert hashLoop = Sha256.hashLoop ctx8InitTag = Sha256.ctx8InitTag ================================================ FILE: Haskell/Core/Simplicity/Programs/Sha256.hs ================================================ {-# LANGUAGE GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expression and types that can be used for computing SHA-256 hashes. -- Be aware that SHA-256 padding isn't provided and messages should be manually padded. module Simplicity.Programs.Sha256 ( Lib(Lib), lib , LibAssert(LibAssert), mkLibAssert -- * Operations , Block, Hash, Ctx8 , iv, hashBlock , ctx8Init , ctx8Add1 , ctx8Addn , ctx8AddBuffer , ctx8Finalize , hashLoop , ctx8InitTag , tapdataInit -- * Example instances , libAssert ) where import Prelude hiding (Word, drop, not, take) import Data.String (fromString) import Simplicity.Digest import Simplicity.Functor import Simplicity.MerkleRoot import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Word import Simplicity.Term.Core hiding (one) -- | In SHA-256, each block of data passed to the compression function is a 512-bit 'Word'. type Block = Word512 -- | In SHA-256, the initial vector and hash value are 256-bit 'Word's. type Hash = Word256 -- | A SHA-256 context (for bytes) consists of a buffer of less than 94 bytes, a counter for the number of compression functions invoked, and a midstate. -- -- It is invalid for a context's counter to be greater than or equal to 2^55. type Ctx8 = (Buffer63 Word8, (Word64, Word256)) -- | A collection of core Simplicity expressions for SHA-256. -- Use 'lib' to construct an instance of this library. data Lib term = Lib { -- | Simplicity expression for the constant function that returns the SHA-256 initial vector. iv :: term () Hash -- | Simplicity expression for the SHA-256 compression function which takes a midstate (or initial vector) and a message block and outputs a hash value (which is used as a midstate if there are further message blocks). , hashBlock :: term (Hash, Block) Hash -- | Initialize an empty 'Ctx8'. , ctx8Init :: term () Ctx8 -- | Initialize a tapdata tagged sha256 context. , tapdataInit :: term () Ctx8 } data LibAssert term = LibAssert { -- | Append one byte to a 'Ctx8'. -- -- This operation fails if the input or output 'Ctx8' is or would be invalid. ctx8Add1 :: term (Ctx8, Word8) Ctx8 -- | Append a vector of bytes to a 'Ctx8'. -- -- This operation fails if the input or output 'Ctx8' is or would be invalid. , ctx8Addn :: forall v. TyC v => Vector Word8 v -> term (Ctx8, v) Ctx8 -- | Append a buffer of bytes to a 'Ctx8'. -- -- This operation fails if the input or output 'Ctx8' is or would be invalid. , ctx8AddBuffer :: forall v b. TyC b => Buffer Word8 v b -> term (Ctx8, b) Ctx8 -- | Append Sha-256 padding and finalize the hash -- -- This operation fails if the input 'Ctx8' is invalid. , ctx8Finalize :: term Ctx8 Hash } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { iv = m iv , hashBlock = m hashBlock , ctx8Init = m ctx8Init , tapdataInit = m tapdataInit } instance SimplicityFunctor LibAssert where sfmap m LibAssert{..} = LibAssert { ctx8Add1 = m ctx8Add1 , ctx8Addn = m . ctx8Addn , ctx8AddBuffer = m . ctx8AddBuffer , ctx8Finalize = m ctx8Finalize } -- | Build the Sha256 'Lib' library. lib :: Core term => Lib term lib = l where l@Lib{..} = Lib { iv = scribe . toWord256 $ 0x6a09e667bb67ae853c6ef372a54ff53a510e527f9b05688c1f83d9ab5be0cd19 , hashBlock = oh &&& compression >>> ((collate oooh &&& collate ooih) &&& (collate oioh &&& collate oiih)) &&& ((collate iooh &&& collate ioih) &&& (collate iioh &&& collate iiih)) , ctx8Init = buffer63Empty &&& (zero word64 &&& iv) , tapdataInit = buffer63Empty &&& (one word64 &&& tapdataPrefix) } where collate x = take x &&& drop x >>> add32 compression = scribe32 k0 &&& iden >>> foldr (\k rec -> scribe32 k &&& step >>> rec) round ks k0:ks = [0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5 ,0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174 ,0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da ,0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967 ,0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85 ,0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070 ,0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3 ,0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2] step = round &&& (drop (drop schedule)) scribe32 x = scribe (toWord32 x) round = part1 >>> part2 where part1 = ((t1 &&& io oooh) &&& io odiag) &&& io (bigDiag &&& idiag) part2 = ((t12 &&& ooih) &&& oih) &&& ((t1d &&& ioih) &&& iih) t1 = (oh &&& iio oooh >>> add32) &&& io (drop (iih &&& ((ooh >>> bigSigma1) &&& (ooh &&& diag >>> chWord32) >>> add32)) >>> add32) >>> add32 t12 = take ((oih &&& ih >>> majWord32) &&& (take (oh &&& (ih >>> bigSigma0)) >>> add32)) >>> add32 t1d = oooh &&& iooh >>> add32 bigSigma0 = rotateW32 (-2) &&& rotateW32 (-13) &&& rotateW32 (-22) >>> xor_xorWord32 bigSigma1 = rotateW32 (-6) &&& rotateW32 (-11) &&& rotateW32 (-25) >>> xor_xorWord32 chWord32 = bitwise_ch word32 majWord32 = bitwise_maj word32 schedule = (take part1 &&& (take idiag &&& (take iiih &&& drop oooh))) &&& (drop part1 &&& (drop idiag &&& (drop iiih &&& smallSigma))) where part1 = odiag &&& bigDiag smallSigma = (take (oo (oh &&& (ih >>> smallSigma0))) >>> add32) &&& (drop (ooih &&& (iioh >>> smallSigma1)) >>> add32) >>> add32 smallSigma0 = rotateW32 (-7) &&& rotateW32 (-18) &&& shiftW32 (-3) >>> xor_xorWord32 smallSigma1 = rotateW32 (-17) &&& rotateW32 (-19) &&& shiftW32 (-10) >>> xor_xorWord32 oo x = take (take x) io x = drop (take x) iio x = drop (io x) diag = oih &&& ioh odiag = take diag idiag = drop diag bigDiag = oiih &&& iooh add32 = add word32 >>> ih xor_xorWord32 = bitwise_xor_xor word32 rotateW32 = rotate_const word32 shiftW32 = shift_const_by false word32 buffer63Empty = bufferEmpty buffer63 tapdataPrefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ fromString "TapData" -- | Given an "array", which is a term that maps an index @w@ to a vector of bytes @v@, returning nothing if the index is out of bounds, -- hash all the bytes of the "array" in seqeuenced until the end of the array (i.e. up to the first index where the "array" term returns nothing). -- -- A context value of type "c" is available to be pass into the "array" term. hashLoop :: (Assert term, TyC c, TyC w, TyC v) => Vector Word8 v -> Word w -> term (c, w) (S v) -> term (c, Ctx8) Ctx8 hashLoop v = \w array -> let body = take array &&& ih >>> match (injl ih) (injr (ih &&& oh >>> ctx8Addv)) in forWhile w body >>> copair iden iden where ctx8Addv = ctx8Addn libAssert v ctx8InitTag :: Core term => String -> term () Ctx8 ctx8InitTag tag = buffer63Empty &&& (one word64 &&& prefix) where prefix = scribe . toWord256 . integerHash256 . ivHash . tagIv $ tag buffer63Empty = bufferEmpty buffer63 -- | Build the Sha256 'LibAssert' library. mkLibAssert :: Assert term => Lib term -> LibAssert term mkLibAssert Lib{..} = l where l@LibAssert{..} = LibAssert { ctx8Add1 = (ooh &&& ih >>> buffer63Snoc) &&& oih >>> match ((unit >>> buffer63Empty) &&& ((drop (take (increment word64) >>> assertl ih cmrFail0)) &&& (iih &&& oh >>> hashBlock))) iden >>> (verifyNumCompression &&& iden) >>> ih , ctx8Addn = \v -> case v of SingleV -> ctx8Add1 (DoubleV v) -> let rec = ctx8Addn v in (oh &&& ioh >>> rec) &&& iih >>> rec , ctx8AddBuffer = \b -> case b of SingleB -> ih &&& oh >>> match (drop (iden &&& verifyNumCompression >>> oh)) (ih &&& oh >>> ctx8Add1) (DoubleB b) -> (ioh &&& oh >>> match ih (ih &&& oh >>> ctx8Addn (bufferVector b))) &&& iih >>> ctx8AddBuffer b -- We clear the context's counter (after verifying it) because the counter is allowed to "overflow" during padding. , ctx8Finalize = ((oh &&& ((verifyNumCompression >>> zero word64) &&& iih)) &&& (unit >>> scribe (toWord64 (2^63))) >>> ctx8Add8 >>> (take pad063 &&& iih)) &&& ((take buffer63Size >>> left_pad_low word8 vector8) &&& drop (take (shift_const_by false word64 6)) >>> add64 >>> shift_const_by false word64 3) >>> oih &&& (oooh &&& (take oioh &&& (take (take iioh) &&& ih))) >>> hashBlock } where buffer63Empty = bufferEmpty buffer63 ctx8Add8 = ctx8Addn vector8 verifyNumCompression = assert (ioh &&& (unit >>> scribe (toWord64 (2^55))) >>> lt word64) add64 = add word64 >>> ih buffer63Snoc = bufferSnoc buffer63 buffer63Size = ((false &&& false) &&& (take (copair false true) &&& drop (take (copair false true)))) &&& drop (drop ((take (copair false true) &&& drop (take (copair false true))) &&& drop (drop (take (copair false true) &&& drop (copair false true))))) pad063 = oh &&& drop pad031 >>> match (ih &&& take (zero word256)) iden pad031 = oh &&& drop pad015 >>> match (ih &&& take (zero word128)) iden pad015 = oh &&& drop pad07 >>> match (ih &&& take (zero word64)) iden pad07 = oh &&& drop pad03 >>> match (ih &&& take (zero word32)) iden pad03 = oh &&& drop pad01 >>> match (ih &&& take (zero word16)) iden pad01 = copair (zero word16) (iden &&& (unit >>> zero word8)) -- | An instance of the Sha256 'LibAssert' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. libAssert :: Assert term => LibAssert term libAssert = mkLibAssert lib ================================================ FILE: Haskell/Core/Simplicity/Programs/TimeLock.hs ================================================ -- | This module defines Simplicity expressions that implement timelock functions from "Simplicity.Bitcoin". module Simplicity.Programs.TimeLock ( parseLock, parseSequence , Height, Time, Distance, Duration ) where import Prelude hiding (Word, drop, not, subtract, take) import Simplicity.Functor import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Arith import Simplicity.Programs.Word import Simplicity.Term.Core type Height = Word32 type Time = Word32 type Distance = Word16 type Duration = Word16 -- | Implements 'Simplicity.Bitcoin.parseLock'. parseLock :: Core term => term Word32 (Either Height Time) parseLock = (iden &&& scribe (toWord32 500000000) >>> subtract word32 >>> oh) &&& iden >>> cond (injl iden) (injr iden) -- | Implements 'Simplicity.Bitcoin.parseSequence'. parseSequence :: Core term => term Word32 (Either () (Either Distance Duration)) parseSequence = bit31 &&& (bit22 &&& ih) >>> cond (injl unit) (injr (cond (injr iden) (injl iden))) where bit31 = take (take oooh) bit22 = take (drop ooih) ================================================ FILE: Haskell/Core/Simplicity/Programs/Word.hs ================================================ {-# LANGUAGE RankNTypes, GADTs, ScopedTypeVariables, TypeOperators #-} -- | This module defines Simplicity expressions and combinators that operate on Words. module Simplicity.Programs.Word ( fill, low, high , complement , bitwise_bin, bitwise_tri , bitwise_and, bitwise_or, bitwise_xor , bitwise_maj, bitwise_xor_xor, bitwise_ch , some, all, eq , leftmost, left_pad_low, left_pad_high, left_extend , rightmost, right_pad_low, right_pad_high, right_extend , full_shift, shift_const_by, rotate_const , left_shift_with, left_shift , right_shift_with, right_shift , left_rotate, right_rotate , mapZV, transpose , bufferEmpty, bufferSnoc , forWhile, firstFail , ConstWord(..) , module Simplicity.Ty.Word ) where import Prelude hiding (Word, drop, take, not, or, and, last, all) import qualified Data.Bits as Bits import Data.Type.Equality ((:~:)(Refl)) import Simplicity.MerkleRoot import Simplicity.Programs.Generic (eq) import Simplicity.Programs.Bit import Simplicity.Term.Core import Simplicity.Ty.Word -- | 2^n-ary diagonal of a term. fill :: (Core term, TyC c) => term c a -> Vector a b -> term c b fill t SingleV = t fill t (DoubleV w) = rec &&& rec where rec = fill t w -- | Set all bits of a word to @0@. low :: Core term => Word a -> term () a low = fill false -- | Set all bits of a word to @1@. high :: Core term => Word a -> term () a high = fill true -- | Bitwise complement of a word. complement :: Core term => Word a -> term a a complement SingleV = not iden complement (DoubleV w) = take rec &&& drop rec where rec = complement w -- | Map a binary operation across a vecotor. bitwise_bin :: forall term a v. Core term => term (a, a) a -> Vector a v -> term (v, v) v bitwise_bin op = go where go :: forall v. Vector a v -> term (v, v) v go SingleV = op go (DoubleV w) = (ooh &&& ioh >>> rec) &&& (oih &&& iih >>> rec) where rec = go w -- | Map a trinary operation across a vecotor. bitwise_tri :: forall term a v. Core term => term (a, (a, a)) a -> Vector a v -> term (v, (v, v)) v bitwise_tri op = go where go :: forall v. Vector a v -> term (v, (v, v)) v go SingleV = op go (DoubleV w) = (ooh &&& (iooh &&& iioh) >>> rec) &&& (oih &&& (ioih &&& iiih) >>> rec) where rec = go w -- | Bitwise 'and' over a pair of words. bitwise_and :: Core term => Word a -> term (a, a) a bitwise_and = bitwise_bin (and oh ih) -- | Bitwise 'or' over a pair of words. bitwise_or :: Core term => Word a -> term (a, a) a bitwise_or = bitwise_bin (or oh ih) -- | Bitwise 'xor' over a pair of words. bitwise_xor :: Core term => Word a -> term (a, a) a bitwise_xor = bitwise_bin (xor oh ih) -- | Bitwise 'maj' over a triple of words. bitwise_maj :: Core term => Word a -> term (a, (a, a)) a bitwise_maj = bitwise_tri maj -- | Bitwise 'xor_xor' over a triple of words. bitwise_xor_xor :: Core term => Word a -> term (a, (a, a)) a bitwise_xor_xor = bitwise_tri xor_xor -- | Bitwise 'ch' over a triple of words. bitwise_ch :: Core term => Word a -> term (a, (a, a)) a bitwise_ch = bitwise_tri ch -- | Test if some bit of a word is non-zero. some :: Core term => Word a -> term a Bit some SingleV = iden some (DoubleV w) = or (take rec) (drop rec) where rec = some w -- | Test if all bits of a word are non-zero. all :: Core term => Word a -> term a Bit all SingleV = iden all (DoubleV w) = and (take rec) (drop rec) where rec = all w -- | Return the leftmost (a.k.a first) value from a vector. -- -- Will return the most significant bit, MSB, of a word. leftmost :: (Core term, TyC a, TyC b) => Vector a b -> term b a leftmost SingleV = iden leftmost (DoubleV v) = take (leftmost v) -- | Return the leftmost (a.k.a first) value from a vector. -- -- Will return the least significant bit, LSB, of a word. rightmost :: (Core term, TyC a, TyC b) => Vector a b -> term b a rightmost SingleV = iden rightmost (DoubleV v) = drop (rightmost v) -- | Given the last element of a vector, pad the rest of the elements with a value (derived from the input). left_pad_pad :: Core term => term a a -> Vector a b -> term a b left_pad_pad _ SingleV = iden left_pad_pad t (DoubleV v) = fill t v &&& left_pad_pad t v -- | Increase the size of a word by padding the left (MSB) bits with @0@s. left_pad_low :: (Core term, TyC a) => Word a -> Vector a b -> term a b left_pad_low w v = left_pad_pad (unit >>> low w) v -- | Increase the size of a word by padding the left (MSB) bits with @1@s. left_pad_high :: (Core term, TyC a) => Word a -> Vector a b -> term a b left_pad_high w v = left_pad_pad (unit >>> high w) v -- | Increase the size of a word by padding the left (MSB) bits with the MSB of the input. left_extend :: (Core term, TyC a, TyC b) => Word a -> Vector a b -> term a b left_extend w v = leftmost w &&& iden >>> cond (left_pad_high w v) (left_pad_low w v) -- | Given the first element of a vector, pad the rest of the elements with a value (derived from the input). right_pad_pad :: Core term => term a a -> Vector a b -> term a b right_pad_pad _ SingleV = iden right_pad_pad t (DoubleV v) = right_pad_pad t v &&& fill t v -- | Increase the size of a word by padding the right (LSB) bits with @0@s. right_pad_low :: (Core term, TyC a) => Word a -> Vector a b -> term a b right_pad_low w v = right_pad_pad (unit >>> low w) v -- | Increase the size of a word by padding the right (LSB) bits with @1@s. right_pad_high :: (Core term, TyC a) => Word a -> Vector a b -> term a b right_pad_high w v = right_pad_pad (unit >>> high w) v -- | Increase the size of a word by padding the right (LSB) bits with the LSB of the input. right_extend :: (Core term, TyC a, TyC b) => Word a -> Vector a b -> term a b right_extend w v = rightmost w &&& iden >>> cond (right_pad_high w v) (right_pad_low w v) -- | Left shift the values of a given vector, shifting in the provided value, and returning the value shifted out. full_left_shift1 :: Core term => Vector a va -> term (va, a) (a, va) full_left_shift1 SingleV = iden full_left_shift1 (DoubleV v) = ooh &&& (oih &&& ih >>> rec) >>> (oh &&& ioh >>> rec) &&& iih >>> ooh &&& (oih &&& ih) where rec = full_left_shift1 v -- | Right shift the values of a given vector, shifting in the provided value, and returning the value shifted out. full_right_shift1 :: Core term => Vector a va -> term (a, va) (va, a) full_right_shift1 SingleV = iden full_right_shift1 (DoubleV v) = (oh &&& ioh >>> rec) &&& iih >>> ooh &&& (oih &&& ih >>> rec) >>> (oh &&& ioh) &&& iih where rec = full_right_shift1 v -- | Given a pair of vectors, rebalance the tuple to return a pair of vectors with their sizes exchanged. -- -- This can be seen as a left shift of the vector @a@, shifting in the vector @b@ and returning the values shifted out. -- This can also be seen as a right shift of the vector @b@, shifting in the vector @a@ and returning the values shifted out. full_shift :: (Core term, TyC a, TyC b) => Vector x a -> Vector x b -> term (a, b) (b, a) full_shift wa wb = go (compareVectorSize wb wa) where go :: (Core term, TyC a, TyC b) => Either (Vector (a, a) b) (Either (b :~: a) (Vector (b, b) a)) -> term (a, b) (b, a) go (Left v) = full_right_shift1 (vectorComp vector2 v) go (Right (Left Refl)) = iden go (Right (Right v)) = full_left_shift1 (vectorComp vector2 v) -- | Left shift a vector by a constant number of places, shifting in copies the provided value. -- Shifting by a negative number of places will perform a right shift instead. shift_const_by :: (Core term, TyC a, TyC b) => term () a -> Vector a b -> Int -> term b b shift_const_by t v n | vectorSize v <= n = unit >>> fill t v | n < 0 = right_shift_const_by t v (-n) | otherwise = compose (go t v n) where compose [] = iden compose l = foldr1 (>>>) l go :: (Core term, TyC a, TyC b) => term () a -> Vector a b -> Int -> [term b b] go t SingleV 0 = [] go t v@(DoubleV v') n | even n = rec (n `div` 2) | otherwise = left_shift1 : rec ((n-1) `div` 2) where left_shift1 = iden &&& (unit >>> t) >>> full_left_shift1 v >>> ih rec = go (t &&& t) (vectorPromote v') -- | Right shift a vector by a constant number of places, shifting in copies the provided value. -- Shifting by a negative number of places will perform a left shift instead. right_shift_const_by :: (Core term, TyC a, TyC b) => term () a -> Vector a b -> Int -> term b b right_shift_const_by t v n | vectorSize v <= n = unit >>> fill t v | n < 0 = shift_const_by t v (-n) | otherwise = compose (go t v n) where compose [] = iden compose l = foldr1 (>>>) l go :: (Core term, TyC a, TyC b) => term () a -> Vector a b -> Int -> [term b b] go t SingleV 0 = [] go t v@(DoubleV v') n | even n = rec (n `div` 2) | otherwise = right_shift1 : rec ((n-1) `div` 2) where right_shift1 = (unit >>> t) &&& iden >>> full_right_shift1 v >>> oh rec = go (t &&& t) (vectorPromote v') -- | Return a list of expressions that projects out each item in the vector from left to right. itemsOf :: (Core term) => Vector a b -> [term b a] itemsOf SingleV = [iden] itemsOf (DoubleV v) = (take <$> rec) ++ (drop <$> rec) where rec = itemsOf v -- | Left shift a vector by a given amount, shifting in the value the value provided. left_shift_with :: (Core term, TyC a, TyC b, TyC c) => Word c -> Vector a b -> term (a, (c,b)) b left_shift_with c = go . reverse $ itemsOf c where go :: (Core term, TyC a, TyC b, TyC c) => [term c Bit] -> Vector a b -> term (a,(c,b)) b go [] v = iih go (control:controlBits) v = oh &&& (ioh &&& (drop (take control) &&& (iih &&& oh) >>> cond (full_left_shift1 v >>> ih) oh)) >>> case v of SingleV -> go controlBits v DoubleV v' -> (oh &&& oh) &&& ih >>> go controlBits (vectorPromote v') -- | Left shift a vector by a given amount, shifting in zero bits. left_shift :: (Core term, TyC b, TyC c) => Word c -> Word b -> term (c,b) b left_shift c b = false &&& iden >>> left_shift_with c b -- | Right shift a vector by a given amount, shifting in the value the value provided. right_shift_with :: (Core term, TyC a, TyC b, TyC c) => Word c -> Vector a b -> term (a, (c,b)) b right_shift_with c = go . reverse $ itemsOf c where go :: (Core term, TyC a, TyC b, TyC c) => [term c Bit] -> Vector a b -> term (a,(c,b)) b go [] v = iih go (control:controlBits) v = oh &&& (ioh &&& (drop (take control) &&& (oh &&& iih) >>> cond (full_right_shift1 v >>> oh) ih)) >>> case v of SingleV -> go controlBits v DoubleV v' -> (oh &&& oh) &&& ih >>> go controlBits (vectorPromote v') -- | Right shift a vector by a given amount, shifting in zero bits. right_shift :: (Core term, TyC b, TyC c) => Word c -> Word b -> term (c,b) b right_shift c b = false &&& iden >>> right_shift_with c b -- | Left shift a vector by shifting in the value that is shifted out. left_rotate1 :: (Core term, TyC a, TyC b) => Vector a b -> term b b left_rotate1 v = iden &&& leftmost v >>> full_left_shift1 v >>> ih -- | Right shift a vector by shifting in the value that is shifted out. right_rotate1 :: (Core term, TyC a, TyC b) => Vector a b -> term b b right_rotate1 v = rightmost v &&& iden >>> full_right_shift1 v >>> oh -- | Left rotate a vector by a constant number of places. -- Rotating by a negative number of places will perform a right rotate instead. rotate_const :: (Core term, TyC a, TyC b) => Vector a b -> Int -> term b b rotate_const v n = compose (go v n) where compose [] = iden compose l = foldr1 (>>>) l go :: (Core term, TyC a, TyC b) => Vector a b -> Int -> [term b b] go SingleV n = [] go v@(DoubleV v') n | even n = rec (n `div` 2) | 1 == n `mod` 4 = left_rotate1 v : rec ((n-1) `div` 2) | 3 == n `mod` 4 = right_rotate1 v : rec ((n+1) `div` 2) where rec = go (vectorPromote v') -- | Left rotate a vector by a given amount. left_rotate :: (Core term, TyC a, TyC b, TyC c) => Word c -> Vector a b -> term (c,b) b left_rotate c = go . reverse $ itemsOf c where go :: (Core term, TyC a, TyC b, TyC c) => [term c Bit] -> Vector a b -> term (c,b) b go [] v = ih go (control:controlBits) v = oh &&& (take control &&& ih >>> cond (left_rotate1 v) iden) >>> case v of SingleV -> ih DoubleV v' -> go controlBits (vectorPromote v') -- | Right rotate a vector by a given amount. right_rotate :: (Core term, TyC a, TyC b, TyC c) => Word c -> Vector a b -> term (c,b) b right_rotate c = go . reverse $ itemsOf c where go :: (Core term, TyC a, TyC b, TyC c) => [term c Bit] -> Vector a b -> term (c,b) b go [] v = ih go (control:controlBits) v = oh &&& (take control &&& ih >>> cond (right_rotate1 v) iden) >>> case v of SingleV -> ih DoubleV v' -> go controlBits (vectorPromote v') -- | Lift a provided term to map a vector of inputs to a vector of outputs of the same length. mapZV :: (Core term) => ZipVector x nx y ny -> term x y -> term nx ny mapZV SingleZV t = t mapZV (DoubleZV zv) t = take rec &&& drop rec where rec = mapZV zv t -- Polymorphic helper type isomorphic to @term a b@ via Yoneda embedding. data Yoneda term a b = Yoneda (forall d. TyC d => term b d -> term a d) runYoneda :: (Core term, TyC b) => Yoneda term a b -> term a b runYoneda (Yoneda k) = k iden -- An identity for the 'Yoneda' embedding. yId :: Yoneda term a a yId = Yoneda id -- Take the first value of a pair. Using the 'Yoneda' embedding avoids the 'comp' combinator. yoh :: (Core term, TyC a, TyC b, TyC c) => Yoneda term c (a, b) -> Yoneda term c a yoh (Yoneda k) = Yoneda (\t -> k (take t)) -- Take the second value of a pair. Using the 'Yoneda' embedding avoids the 'comp' combinator. yih :: (Core term, TyC a, TyC b, TyC c) => Yoneda term c (a, b) -> Yoneda term c b yih (Yoneda k) = Yoneda (\t -> k (drop t)) -- | Transpose a matrix (i.e a vector of vectors) of the specified dimensions. transpose :: (Core term, TyC mx, TyC nmx) => ZipVector x mx nx mnx -> ZipVector mx nmx x nx -> term nmx mnx transpose mzv nzv = go mzv nzv yId where go :: (Core term, TyC nm, TyC m) => ZipVector x kx nx knx -> ZipVector m nm x nx -> Yoneda term m kx -> term nm knx go SingleZV nzv t = mapZV nzv (runYoneda t) go (DoubleZV zv) nzv t = go zv nzv (yoh t) &&& go zv nzv (yih t) -- | Given a 'Buffer' @b@, return the empty buffer. bufferEmpty :: (Core term, TyC e) => Buffer x v b -> term e b bufferEmpty SingleB = injl unit bufferEmpty (DoubleB b) = injl unit &&& bufferEmpty b -- | Given a 'Buffer' @b@, append an 'x' value to the buffer. -- -- If the resulting buffer overflows, return a vector of all values from the input. bufferSnoc :: Core term => Buffer x v b -> term (b, x) (Either v b) bufferSnoc SingleB = match (injr (injr ih)) (injl iden) bufferSnoc (DoubleB b) = (oih &&& ih >>> bufferSnoc b) &&& ooh >>> match (ih &&& oh >>> match (injr (injr ih &&& bufferEmpty b)) (injl iden)) (injr (ih &&& oh)) -- | Given @body :: term ((c, w), a) (Either b a)@ where @c@ is a generic context type, @w@ is a counter value, and @a@ is a state value, -- then @loop body (c, a)@ repeatedly apply body with a fixed context @c@ and an initial state @a@ with an incrementing counter @w@ starting at zero -- with the state being updated by a result of @Right a@, until either @body@ returns @Left b@, in which case @Left b@ is immediately returned, or -- in case the counter reaches its maximum possible value, in which case @Right a@ is returned where @a@ is the final state value. forWhile :: (Core term, TyC c, TyC b, TyC a) => Word w -> term ((c, w), a) (Either b a) -> term (c, a) (Either b a) forWhile SingleV body = (((oh &&& false) &&& ih) >>> monobody) &&& oh >>> match (injl oh) (((ih &&& true) &&& oh) >>> monobody) where monobody = body forWhile (DoubleV n) body = forWhile n (forWhile n ((oooh &&& (ooih &&& oih)) &&& ih >>> body)) -- | Given op :: w |- a + b, find the first input where op returns Left. -- @'firstFail' w op@ will fail if op never returns Left. firstFail :: (Assert term, TyC w, TyC a, TyC b) => Word w -> term w (Either a b) -> term () w firstFail w op = (unit &&& unit) >>> forWhile w (take (drop (op &&& iden >>> match (injl ih) (injr unit)))) >>> iden &&& unit >>> assertl (take iden) cmrFail0 -- | Used to match Simplicity expressions to see of they are of the form scribe(v) : term () (Word b). data ConstWord a b where NotConstWord :: ConstWord a b EmptyConstWord :: ConstWord a () ConstWord :: Word b -> !Integer -> ConstWord () b constBit :: (TyC a, TyC b) => Bool -> ConstWord a b constBit bit = result where result = case reifyArrow result of (OneR, SumR OneR OneR) -> ConstWord word1 (if bit then 1 else 0) _ -> NotConstWord instance Core ConstWord where iden = NotConstWord comp _ t = NotConstWord unit = EmptyConstWord injl EmptyConstWord = constBit False injl _ = NotConstWord injr EmptyConstWord = constBit True injr _ = NotConstWord match _ _ = NotConstWord pair (ConstWord ws vs) (ConstWord wt vt) = case compareVectorSize ws wt of Right (Left Refl) -> ConstWord (DoubleV ws) (Bits.shift vs (wordSize ws) + vt) _ -> NotConstWord pair _ _ = NotConstWord take _ = NotConstWord drop _ = NotConstWord instance Assert ConstWord where assertl _ _ = NotConstWord assertr _ _ = NotConstWord fail _ = NotConstWord instance Witness ConstWord where witness _ = NotConstWord instance Delegate ConstWord where disconnect _ _ = NotConstWord ================================================ FILE: Haskell/Core/Simplicity/Serialization.hs ================================================ -- | This modules provides functionality to aid serializiang and deserializing to and from bit streams using difference lists and Van Laarhoven free monad representations. module Simplicity.Serialization ( DList, putBitString, putPositive , getBitString, getPositive, getPositiveUpTo , getItem , getCatalogue , evalStream, evalExactVector , evalStreamWithError , Error(..) , getEvalBitStream, treeEvalBitStream , putBitStream ) where import Prelude hiding (length) import Control.Monad (forM_, guard) import Control.Monad.Trans (lift) import Control.Monad.Trans.Cont (Cont, cont, runCont) import Control.Monad.Trans.State (StateT(..), evalStateT, get, put) import Data.Bits (setBit, testBit) import Data.List (foldl', genericLength, unfoldr) import Data.List.Split (chunksOf) import Data.Serialize.Get (Get, getWord8) import Data.Serialize.Put (Putter, putWord8) import Data.Vector.Unboxed (Vector, Unbox, indexM, length) import Data.Void (Void, vacuous) import Data.Word (Word8) import Simplicity.Tree -- | A type for difference lists: an efficient type for appending to lists. -- -- To convert a difference list, @l :: DList a@, to a list, apply it to the empty list, @l [] :: [a]@. -- To convert a list, @l :: [a]@, to a difference list, partially apply it to the append function, @(l++) :: DList a@. type DList a = [a] -> [a] -- | A self-delimiting encoding of variable length list of bits returned as a difference list. -- -- The empty list, @[]@, is encoded as the difference list representing @[False]@. -- A non-empty list, @l@, is encoded as the difference list representing @[True] ++ n ++ l@, -- where @n@ is the length of @l@ encoded by 'putPositive'. putBitString :: [Bool] -> DList Bool putBitString [] = (False :) putBitString l = (True :) . putPositive (genericLength l) . (l ++) -- | A self-delimiting encoding of arbitrary sized positive integers. -- -- A positive number is encoded by writing it base-2, choping off the leading '1', -- and encoding the remaining digits as a list of Booleans in big-endian using 'putBitString'. -- e.g. -- -- @putPositive 1 = putBitString []@ -- -- @putPositive 2 = putBitString [False]@ -- -- @putPositive 3 = putBitString [True]@ -- -- @putPositive 4 = putBitString [False,False]@ -- -- @putPositive 5 = putBitString [False,True]@ putPositive :: Integer -> DList Bool putPositive x | x <= 0 = error "Simplicity.Serialization.putPositive: non-positive value" | otherwise = putBitString . reverse $ unfoldr f x where f i | i <= 1 = Nothing | otherwise = Just (odd i, i `div` 2) -- | Decodes the self-delimiting encoding of a variable length list of bits. -- -- Note that the type @forall m. Monad m => m Bool -> m a@ is isomorphic to the free monad over the @X²@ functor. -- In other words, 'getBitString' has the type of a binary branching tree with leaves containing '[Bool]' values. -- -- @evalStream getBitString (putBitString l) == Just l@ getBitString :: Monad m => m Bool -> m [Bool] getBitString next = next >>= f where f False = return [] f True = getPositive next >>= loop loop i | i <= 0 = return [] | otherwise = (:) <$> next <*> loop (i-1) -- | Decodes the self-delimiting encoding of a positive integer. -- -- Note that the type @forall m. Monad m => m Bool -> m a@ is isomorphic to the free monad over the @X²@ functor. -- In other words, 'getPositive' has the type of a binary branching tree with leaves containing 'Integer' values. -- -- @evalStream getPositive (putPositive n) == Just n@ getPositive :: Monad m => m Bool -> m Integer getPositive = fmap (foldl' f 1) . getBitString where f i False = 2*i f i True = 2*i + 1 -- | Decodes the self-delimiting encoding of a positive integer that is less than or equal to a given bound. -- -- If the encoded value exceeds the bound, then nothing is returned. -- -- Note that the type @forall m. Monad m => m void -> m b -> m a@ is isomorphic to the free monad over the @X^b + 1@ functor at @a@. -- In other words, 'getPositiveUpTo' returns the type of a binary branching tree with leaves containing 'Integer' values or nothing. getPositiveUpTo :: Monad m => Integer -> m Void -> m Bool -> m Integer getPositiveUpTo bound abort | 0 < bound = getUpTo (putPositive bound []) (\abort_ -> getPositive) abort | otherwise = \next_ -> vacuous abort where getUpTo :: Monad m => [Bool] -> (StateT [Bool] m Void -> StateT [Bool] m Bool -> StateT [Bool] m a) -> m Void -> m Bool -> m a getUpTo bound prog abort next = evalStateT (prog (lift abort) (StateT boundNext)) bound where boundNext [] = vacuous abort boundNext (hd:tl) = next >>= k where k b | b <= hd = return (b, if b == hd then tl else repeat True) | otherwise = vacuous abort -- | Decodes the self-delimiting encoding of a positive integer that represents an item in a list. -- -- If the encoded value exceeds the length of the list, then nothing is returned. -- -- Note: Because only positive integers have an encoding, the indexing into the list is 1-based rather than the usual 0-based. -- -- Note that the type @forall m. Monad m => m void -> m b -> m a@ is isomorphic to the free monad over the @X^b + 1@ functor at @a@. -- In other words, 'getItem' returns the type of a binary branching tree with leaves containing 'a' values or nothing. getItem :: Monad m => [a] -> m Void -> m Bool -> m a getItem items abort next = select <$> getPositiveUpTo (genericLength items) abort next where select n = items !! fromInteger (n - 1) -- | Decodes the self-delimiting encoding of a sequence of positive integers that represents an item in a 'Catalogue'. -- Guided by the 'Catalogue' the 'getItem' decods a positive integer to select an item from a 'Shelf'. -- If that item is another 'Catalogue', then it recursively decodes another positive integer, otherwise it returns the 'Item' from the 'Shelf'. -- -- If an encoded value exceeds the length of any shelf list, then nothing is returned. -- -- If an encoded value references a 'Missing' item, then nothing is returned. -- -- Note: Because only positive integers have an encoding, the indexing into a 'Shelf' is 1-based rather than the usual 0-based. -- -- Note that the type @forall m. Monad m => m void -> m b -> m a@ is isomorphic to the free monad over the @X^b + 1@ functor at @a@. -- In other words, 'getCatalogue' returns the type of a binary branching tree with leaves containing 'a' values or nothing. getCatalogue :: Monad m => Catalogue a -> m Void -> m Bool -> m a getCatalogue Missing abort next = vacuous abort getCatalogue (Item a) abort next = return a getCatalogue (Shelf shelf) abort next = do item <- getItem shelf abort next getCatalogue item abort next -- | @evalStream :: (forall m. Monad m => m b -> m a) -> [b] -> Maybe a@ -- -- Interprets the free monad representation of a stream transformer as a function consuming lists. -- 'evalStream' returns 'Nothing' if the stream transforms consumes the entire input before returning a value. -- -- Note that the type @forall m. Monad m => m b -> m a@ is isomorphic to the free monad over the @X^b@ functor at @a@. -- In other words, 'evalStream' transforms a type of @b@-branching trees with leaves containing @a@ values -- into a function consuming a list of @b@s and returning a @Maybe a@. evalStream :: (StateT [b] Maybe b -> StateT [b] Maybe a) -> [b] -> Maybe a evalStream prog = evalStateT (prog (get >>= f)) where f [] = fail "Simplicity.Serialization.evalStream: End of Stream" f (hd:tl) = put tl >> return hd -- | @evalExactVector :: Unboxed b => (forall m. Monad m => m b -> m a) -> 'Vector' b -> Maybe a@ -- -- Interprets the free monad representation of a stream transformer as a function consuming unboxed 'Vector's. -- 'evalExactVector' returns 'Nothing' unless the input vector is entirely and exactly consumed. -- -- Note that the type @forall m. Monad m => m b -> m a@ is isomorphic to the free monad over the @X^b@ functor at @a@. -- In other words, 'evalExactVector' transforms a type of @b@-branching trees with leaves containing @a@ values -- into a function consuming a 'Vector' of @b@s and returning a @Maybe a@. evalExactVector :: Unbox b => (StateT Int Maybe b -> StateT Int Maybe a) -> Vector b -> Maybe a evalExactVector prog bs = evalStateT (prog next >>= assertEnd) 0 where n = length bs next = do i <- get guard (i < n) put (i + 1) indexM bs i assertEnd result = do i <- get guard (i == n) return result -- | The type of errors that can be produced by 'evalStreamWithError'. data Error = EndOfInput | ParseError deriving (Eq, Show) -- | @evalStreamWithError :: (forall m. Monad m => m void -> m b -> m a) -> [b] -> 'Either' 'Error' a@ -- -- Interprets the free monad representation of a partial stream transformer as a function consuming lists. -- 'evalStreamWithError' returns @'Left' 'EndOfInput'@ if the stream transforms consumes the entire input before returning a value and -- @'Left' 'ParseError'@ if the stream transforms aborts. -- -- Note that the type @forall m. Monad m => m void -> m b -> m a@ is isomorphic to the free monad over the @X^b + 1@ functor at @a@. -- In other words, 'evalStreamWithError' transforms a type of @b@-branching trees with leaves either containing @a@ values or no values -- into a function consuming a list of @b@s and returning an @'Either' 'Error' a@. evalStreamWithError :: (StateT [b] (Either Error) void -> StateT [b] (Either Error) b -> StateT [b] (Either Error) a) -> [b] -> Either Error a evalStreamWithError prog = evalStateT (prog abort (get >>= f)) where abort = lift (Left ParseError) f [] = lift (Left EndOfInput) f (hd:tl) = put tl >> return hd -- | @getEvalBitStream :: (forall m. Monad m => m void -> m Bool -> m a) -> Get a@ -- -- Interprets the free monad representation of a bit-stream transformer with failure in the 'Get' monad. -- This consumes bits from a 'ByteString' in big-endian order. -- Any unconsumed bits from the last byte processed are discarded. -- If the provided bit-stream transformer fails, then 'Control.Monad.fail' is called for the 'Get' monad. -- -- Note that the type @forall m. Monad m => m void -> m b -> m a@ is isomorphic to the free monad over the @X^b + 1@ functor at @a@. getEvalBitStream :: (StateT (Maybe (Word8, Int)) Get void -> StateT (Maybe (Word8, Int)) Get Bool -> StateT (Maybe (Word8, Int)) Get a) -> Get a getEvalBitStream prog = evalStateT (prog (fail "Simplicity.Serialization.getEvalBitStream: aborted") (StateT next)) Nothing where next Nothing = do w <- getWord8 return (testBit w 7, Just (w, 6)) next (Just (w, i)) | i < 0 = next Nothing | otherwise = return (testBit w i, Just (w, i-1)) -- Cont is a poor-man's Codensity Monad. -- | @treeEvalBitStream :: (forall m. Monad m => m void -> m Bool -> m a) -> BinTree a@ -- -- Reifies the free monad representation of a bit-stream transformer with failure as a 'BinTree'. -- -- Note that the type @forall m. Monad m => m void -> m Bool -> m a@ is isomorphic to the free monad over the @X^b + 1@ functor at @a@, -- which is the 'BinTree a' type. treeEvalBitStream :: (Cont (BinTree a) void -> Cont (BinTree a) Bool -> Cont (BinTree a) a) -> BinTree a treeEvalBitStream prog = runCont (prog abort next) Leaf where abort = cont $ const Dead next = cont $ \k -> branch (k False) (k True) -- | Packs and writes out a list of 'Bool's via the 'Data.Serialize.Put.Put' monad. -- It writes starting from MSB (most significant bit) to LSB (least significant bit) within a byte. putBitStream :: Putter [Bool] putBitStream l = forM_ (chunksOf 8 l) putChunk where putChunk bs = putWord8 $ foldr (flip setBit) 0 [i|(b, i) <- zip bs [7,6..0], b] ================================================ FILE: Haskell/Core/Simplicity/Tags.hs ================================================ module Simplicity.Tags ( typeTag , commitmentTag , identityHashTag, identityTag , annotatedTag , primTag , jetTag , hiddenTag , signatureTag, sigHash ) where import Data.List (intercalate) import Data.Serialize (encode) import Simplicity.Digest tag :: [String] -> IV tag = tagIv . intercalate "\US" prefix = ["Simplicity"] typePrefix = prefix ++ ["Type"] commitmentPrefix = prefix ++ ["Commitment"] identityPrefix = prefix ++ ["Identity"] annotatedPrefix = prefix ++ ["Annotated"] primitivePrefix primPrefix = prefix ++ ["Primitive", primPrefix] typeTag :: String -> IV typeTag x = tag $ typePrefix ++ [x] commitmentTag :: String -> IV commitmentTag x = tag $ commitmentPrefix ++ [x] identityHashTag :: IV identityHashTag = tag identityPrefix identityTag :: String -> IV identityTag x = tag $ identityPrefix ++ [x] annotatedTag :: String -> IV annotatedTag x = tag $ annotatedPrefix ++ [x] primTag :: String -> String -> IV primTag primPrefix x = tag $ primitivePrefix primPrefix ++ [x] jetTag :: IV jetTag = tag $ prefix ++ ["Jet"] hiddenTag :: IV hiddenTag = tag $ prefix ++ ["Hidden"] -- | The midstate after the "standard" Simplicity signed message tag. signatureTag :: IV signatureTag = tag $ prefix ++ ["Signature"] -- | Create a "standard" Simplicity signed message from an 'CommitmentRoot' of a sighash expression, and that expression's output. sigHash :: Hash256 -- ^ @'CommitmentRoot' () Word256@ -> Hash256 -- ^ Output if sighash -> Hash256 sigHash h1 h2 = taggedHash tag $ encode h1 <> encode h2 where tag = intercalate "\US" $ prefix ++ ["Signature"] ================================================ FILE: Haskell/Core/Simplicity/Tensor.hs ================================================ -- | This module provides a product for computing multiple interpretations of Simplicity simultaneously. -- Other tensors can be added when they are needed. module Simplicity.Tensor ( Product(..) , Unit(..) ) where data Product p q a b = Product { fstProduct :: p a b , sndProduct :: q a b } deriving Show data Unit a b = Unit deriving Show ================================================ FILE: Haskell/Core/Simplicity/Term/Core.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module defines the term language for 'Core' Simplicity using -- tagless-final style, plus a few extensions: 'Assert', 'Witness' and 'Delegate'. module Simplicity.Term.Core ( module Simplicity.Ty , Core(..) , elimS, copair , swapP, swapS -- * Notation for 'Core' terms , (>>>), (&&&) -- | The following expressions are for short sequences of 'take' and 'drop', with 'iden' that is used to access components of Simplicity inputs. -- -- * @o@ means 'take' -- * @i@ means 'drop' -- * @h@ means 'iden' -- -- For example, @'oih' = 'take' ('drop' 'iden')@. -- -- The string of @i@'s and @o@'s is meant to resemble a binary number that denotes an index to the leaves of a perfect binary tree. , oh, ih, ooh, oih, ioh, iih, oooh, ooih, oioh, oiih, iooh, ioih, iioh, iiih -- * Language extensions , Assert(..), fail0 , Witness(..) , Delegate(..) ) where import Prelude hiding (take, drop, fail) import Control.Arrow (Kleisli(..)) import Control.Monad ((>=>)) import qualified Control.Monad.Fail as Fail import Simplicity.Digest import Simplicity.Tensor import Simplicity.Ty import Simplicity.Ty.Word -- | Values of type @forall term. 'Core' term => term a b@ are well-typed terms of the core Simplicity language represented in tagless-final style. -- -- Functions that consume terms in this style are defined by creating instances of the 'Core' class. -- These instances are called /Simplicity Algebras/. class Core term where iden :: TyC a => term a a comp :: (TyC a, TyC b, TyC c) => term a b -> term b c -> term a c unit :: TyC a => term a () injl :: (TyC a, TyC b, TyC c) => term a b -> term a (Either b c) injr :: (TyC a, TyC b, TyC c) => term a c -> term a (Either b c) -- | Because @case@ is a reserved word in Haskell, we will be calling Simplicity's @case@ combinator 'match' instead. match :: (TyC a, TyC b, TyC c, TyC d) => term (a, c) d -> term (b, c) d -> term (Either a b, c) d pair :: (TyC a, TyC b, TyC c) => term a b -> term a c -> term a (b, c) take :: (TyC a, TyC b, TyC c) => term a c -> term (a, b) c drop :: (TyC a, TyC b, TyC c) => term b c -> term (a, b) c -- | Natural deduction style elimination rule for Sums. elimS :: (Core term, TyC a, TyC b, TyC c, TyC d) => term a (Either b c) -> term b d -> term c d -> term a d elimS r s t = r &&& unit >>> match (take s) (take t) -- | Categorical dual of 'pair' copair :: (Core term, TyC a, TyC b, TyC c) => term a c -> term b c -> term (Either a b) c copair = elimS iden -- | Term for swapping positions in products (Commutativity of Multiplication): A * B |- B * A swapP :: (Core term, TyC a, TyC b) => term (a, b) (b, a) swapP = pair (drop iden) (take iden) -- | Term for swapping positions in sums (Commutativity of Addition): A + B |- B + A swapS :: (Core term, TyC a, TyC b) => term (Either a b) (Either b a) swapS = copair (injr iden) (injl iden) -- same precedence as in Control.Category. infixr 1 >>> -- | @s '>>>' t = 'comp' s t@ (>>>) :: (Core term, TyC a, TyC b, TyC c) => term a b -> term b c -> term a c (>>>) = comp -- same precedence as in Control.Arrow. infixr 3 &&& -- | @s '&&&' t = 'pair' s t@ (&&&) :: (Core term, TyC a, TyC b, TyC c) => term a b -> term a c -> term a (b, c) (&&&) = pair oh :: (Core term, TyC x, TyC b) => term (x, b) x oh = take iden ih :: (Core term, TyC a, TyC x) => term (a, x) x ih = drop iden ooh :: (Core term, TyC x, TyC b, TyC c) => term ((x, b), c) x ooh = take oh oih :: (Core term, TyC a, TyC x, TyC c) => term ((a, x), c) x oih = take ih ioh :: (Core term, TyC a, TyC x, TyC c) => term (a, (x, c)) x ioh = drop oh iih :: (Core term, TyC a, TyC b, TyC x) => term (a, (b, x)) x iih = drop ih oooh :: (Core term, TyC x, TyC b, TyC c, TyC d) => term (((x, b), c), d) x oooh = take ooh ooih :: (Core term, TyC a, TyC x, TyC c, TyC d) => term (((a, x), c), d) x ooih = take oih oioh :: (Core term, TyC a, TyC x, TyC c, TyC d) => term ((a, (x, c)), d) x oioh = take ioh oiih :: (Core term, TyC a, TyC b, TyC x, TyC d) => term ((a, (b, x)), d) x oiih = take iih iooh :: (Core term, TyC a, TyC x, TyC c, TyC d) => term (a, ((x, c), d)) x iooh = drop ooh ioih :: (Core term, TyC a, TyC b, TyC x, TyC d) => term (a, ((b, x), d)) x ioih = drop oih iioh :: (Core term, TyC a, TyC b, TyC x, TyC d) => term (a, (b, (x, d))) x iioh = drop ioh iiih :: (Core term, TyC a, TyC b, TyC c, TyC x) => term (a, (b, (c, x))) x iiih = drop iih instance Core (->) where iden = id comp s t = t . s unit = const () injl t a = Left (t a) injr t a = Right (t a) match s _ (Left a, c) = s (a, c) match _ t (Right b, c) = t (b, c) pair s t a = (s a, t a) take t (a, _) = t a drop t (_, b) = t b -- | The Monad 'm' should be a commutative, idempotent monad. instance Monad m => Core (Kleisli m) where iden = Kleisli $ return comp (Kleisli s) (Kleisli t) = Kleisli $ s >=> t unit = Kleisli $ const (return ()) injl (Kleisli t) = Kleisli $ \a -> Left <$> t a injr (Kleisli t) = Kleisli $ \a -> Right <$> t a match (Kleisli s) (Kleisli t) = Kleisli $ go where go (Left a, c) = s (a, c) go (Right b, c) = t (b, c) pair (Kleisli s) (Kleisli t) = Kleisli $ \a -> (,) <$> s a <*> t a take (Kleisli t) = Kleisli $ \(a, _) -> t a drop (Kleisli t) = Kleisli $ \(_, b) -> t b -- | This class extends the 'Core' Simplicity language with two assertion expressions. -- These expressions are use for assertions and for pruning 'match' (case) expressions. -- This extension produces partial functions. class Core term => Assert term where assertl :: (TyC a, TyC b, TyC c, TyC d) => term (a, c) d -> Hash256 -> term (Either a b, c) d assertr :: (TyC a, TyC b, TyC c, TyC d) => Hash256 -> term (b, c) d -> term (Either a b, c) d fail :: (TyC a, TyC b) => Block512 -> term a b -- | A canonical version of the 'fail' combinator with the 'Block512' set to 0. fail0 :: (Assert term, TyC a, TyC b) => term a b fail0 = fail (hash0, hash0) -- | The Monad 'm' should be a commutative, idempotent monad with a zero that is both a left and right zero. instance Fail.MonadFail m => Assert (Kleisli m) where assertl (Kleisli s) _ = Kleisli $ go where go (Left a, c) = s (a, c) go (Right _, _) = Fail.fail "Simplicity.Term.Core: assertl failed" assertr _ (Kleisli t) = Kleisli $ go where go (Left _, _) = Fail.fail "Simplicity.Term.Core: assertr failed" go (Right b, c) = t (b, c) fail _ = Kleisli . const $ Fail.fail "Simplicity.Term.Core: fail" -- | This class adds 'witness' expressions to the Simplicity language. class Witness term where -- | The 'witness' expression denotes a constant function, however this value is not committed to the 'Simplicity.MerkleRoot.CommitmentRoot'. -- Compare this to 'Simplicity.Programs.Generic.scribe' which does commit to its value. -- -- @witness v _ = v@ witness :: (TyC a, TyC b) => b -> term a b instance Witness (->) where witness = const instance Monad m => Witness (Kleisli m) where witness = Kleisli . const . return -- | This class adds 'disconnect' expressions to the Simplicity language, which can be used for delegation. class Delegate term where disconnect :: (TyC a, TyC b, TyC c, TyC d) => term (Word256, a) (b, c) -> term c d -> term a (b, d) instance (Core p, Core q) => Core (Product p q) where iden = Product iden iden comp ~(Product rs fs) ~(Product rt ft) = Product (comp rs rt) (comp fs ft) unit = Product unit unit injl ~(Product rt ft) = Product (injl rt) (injl ft) injr ~(Product rt ft) = Product (injr rt) (injr ft) match ~(Product rs fs) ~(Product rt ft) = Product (match rs rt) (match fs ft) pair ~(Product rs fs) ~(Product rt ft) = Product (pair rs rt) (pair fs ft) take ~(Product rt ft) = Product (take rt) (take ft) drop ~(Product rt ft) = Product (drop rt) (drop ft) instance (Assert p, Assert q) => Assert (Product p q) where assertl ~(Product rs fs) t = Product (assertl rs t) (assertl fs t) assertr s ~(Product rt ft) = Product (assertr s rt) (assertr s ft) fail b = Product (fail b) (fail b) instance (Witness p, Witness q) => Witness (Product p q) where witness b = Product (witness b) (witness b) instance (Delegate p, Delegate q) => Delegate (Product p q) where disconnect ~(Product rs fs) ~(Product rt ft) = Product (disconnect rs rt) (disconnect fs ft) instance Core Unit where iden = Unit comp _ _ = Unit unit = Unit injl _ = Unit injr _ = Unit match _ _ = Unit pair _ _ = Unit take _ = Unit drop _ = Unit instance Assert Unit where assertl _ _ = Unit assertr _ _ = Unit fail _ = Unit instance Witness Unit where witness _ = Unit instance Delegate Unit where disconnect _ _ = Unit ================================================ FILE: Haskell/Core/Simplicity/Tree.hs ================================================ -- | This modules provides custom binary trees ('BinTree') and rose trees ('Catalogue') for use in Simplicity. module Simplicity.Tree ( BinTree(..), branch, traverseWithPath, foldMapWithPath , Catalogue(..), book ) where import Data.Functor.Const (Const(Const), getConst) import Data.Traversable (fmapDefault, foldMapDefault) import Data.Void (Void, vacuous) -- | A rose tree type. This type includes 'Missing' leaves that contain no value. data Catalogue a = Missing | Item a | Shelf [Catalogue a] instance Functor Catalogue where fmap = fmapDefault instance Foldable Catalogue where foldMap = foldMapDefault instance Traversable Catalogue where traverse f Missing = pure Missing traverse f (Item a) = Item <$> f a traverse f (Shelf l) = Shelf <$> traverse (traverse f) l instance Applicative Catalogue where pure = Item bf <*> bx = bf >>= \f -> bx >>= \x -> return (f x) instance Monad Catalogue where return = pure Missing >>= f = Missing (Item a) >>= f = f a (Shelf l) >>= f = Shelf $ map (>>= f) l -- | Builds a depth 1 'Catalog' from a list. book :: [a] -> Catalogue a book = Shelf . fmap Item -- | A binary tree type. This type includes 'Dead' leaves that contain no value. data BinTree a = Dead | Leaf a | Branch (BinTree a) (BinTree a) instance Functor BinTree where fmap = fmapDefault instance Foldable BinTree where foldMap = foldMapDefault instance Traversable BinTree where traverse f Dead = pure Dead traverse f (Leaf a) = Leaf <$> f a traverse f (Branch l r) = Branch <$> traverse f l <*> traverse f r instance Applicative BinTree where pure = Leaf bf <*> bx = bf >>= \f -> bx >>= \x -> return (f x) instance Monad BinTree where return = pure Dead >>= f = Dead (Leaf a) >>= f = f a (Branch l r) >>= f = Branch (l >>= f) (r >>= f) -- | An optimized 'Branch' that collapses 'Dead' leaves into one. branch :: BinTree a -> BinTree a -> BinTree a branch Dead Dead = Dead branch l r = Branch l r -- | Similar to 'traverse' but additionally provides the operation with the path from the root to the 'Leaf'. traverseWithPath :: Applicative f => ([Bool] -> a -> f b) -> BinTree a -> f (BinTree b) traverseWithPath f = go id where go ctx (Branch l r) = Branch <$> go (ctx . (False:)) l <*> go (ctx . (True:)) r go ctx (Leaf a) = Leaf <$> f (ctx []) a go ctx Dead = pure Dead -- | Similar to 'foldMap' but additionally provides the operation with the path from the root to the 'Leaf'. foldMapWithPath :: Monoid m => ([Bool] -> a -> m) -> BinTree a -> m foldMapWithPath f = getConst . traverseWithPath (\p -> Const . f p) ================================================ FILE: Haskell/Core/Simplicity/Ty/Bit.hs ================================================ -- | This module defines the 'Bit' type alais used in Simplicity. module Simplicity.Ty.Bit ( Bit, fromBit, toBit ) where -- | Simplicity types are composed from @()@, 'Either' and @(,)@. -- We cannot use Haskell's 'Bool' type directly in Simplicity. -- Instead we create use this isomorphic type in Simplicity to represent bits. type Bit = Either () () -- | Canonically convert a Simplicity 'Bit' type to the Haskell 'Bool' type. fromBit :: Bit -> Bool fromBit (Left ()) = False fromBit (Right ()) = True -- | Canonically convert a Hasekll 'Bool' type to the Simplicity 'Bit' type. toBit :: Bool -> Bit toBit False = Left () toBit True = Right () ================================================ FILE: Haskell/Core/Simplicity/Ty/LibSecp256k1.hs ================================================ module Simplicity.Ty.LibSecp256k1 ( FE, GE, GEJ, Scalar, Point , PubKey, Sig , fromFE, toFE , fromGE, toGE , fromGEJ, toGEJ ) where import qualified Simplicity.LibSecp256k1.Spec as Spec import Simplicity.Ty.Word -- | Simplicity's representation of field elements. type FE = Word256 -- | A point in compressed coordinates. -- The point at infinity isn't representable. type Point = (Bit, FE) -- | A point in affine coordinates. -- Usually expected to be on the elliptic curve. -- The point at infinity isn't representable. type GE = (FE, FE) -- | A point in Jacobian coordinates. -- Usually expected to be on the elliptic curve. -- The point at infinity's representatives are of the form @((a^2, a^3), 0)@, with @((0, 0), 0)@ being the canonical representative. type GEJ = (GE, FE) -- | Scalar values, those less than the order of secp256's elliptic curve, are represented by a 256-bit word type. type Scalar = Word256 -- | A format for (Schnorr) elliptic curve x-only public keys. -- The y-coordinate is implicitly the one on the curve that has an even y coordinate. -- The point at infinity isn't representable (nor is it a valid public key to begin with). type PubKey = Word256 -- | A format for Schnorr signatures. type Sig = (Word256, Word256) fromFE :: FE -> Spec.FE fromFE = Spec.fe . fromWord256 toFE :: Spec.FE -> FE toFE = toWord256 . toInteger . Spec.fe_pack fromGE :: GE -> Spec.GE fromGE (x,y) = Spec.GE (fromFE x) (fromFE y) toGE :: Spec.GE -> GE toGE (Spec.GE x y) = (toFE x, toFE y) fromGEJ :: GEJ -> Spec.GEJ fromGEJ ((x,y),z) = Spec.GEJ (fromFE x) (fromFE y) (fromFE z) toGEJ :: Spec.GEJ -> GEJ toGEJ (Spec.GEJ x y z) = ((toFE x, toFE y), toFE z) ================================================ FILE: Haskell/Core/Simplicity/Ty/Sha256.hs ================================================ -- | This modules provides some functions for mashalling data to and from Simplicity types that are used for some SHA-256 operations. module Simplicity.Ty.Sha256 ( fromHash , fromCtx8, toCtx8 , Ctx, Ctx8 ) where import qualified Data.ByteString as BS import Lens.Family2 ((^..), over, review) import Simplicity.Digest import Simplicity.Programs.Sha256 import Simplicity.Ty.Word fromHash :: Hash -> Hash256 fromHash = review (over be256) . fromIntegral . fromWord256 fromCtx8 :: Ctx8 -> Maybe Ctx fromCtx8 (buffer, (count, midstate)) = ctxBuild (fromInteger . fromWord8 <$> buffer^..buffer_ buffer63) (fromWord64 count) (fromHash midstate) toCtx8 :: Ctx -> Ctx8 toCtx8 ctx = (buffer, (count, midstate)) where buffer = fst $ bufferFill buffer63 (toWord8 . fromIntegral <$> BS.unpack (ctxBuffer ctx)) count = toWord64 . fromIntegral $ ctxCounter ctx midstate = toWord256 . integerHash256 . ivHash $ ctxIV ctx ================================================ FILE: Haskell/Core/Simplicity/Ty/Word.hs ================================================ {-# LANGUAGE GADTs, RankNTypes, TypeOperators #-} -- | This module defines 2^/n/ bit word Simplicity types. module Simplicity.Ty.Word ( Vector(..), vectorComp, vectorPromote, compareVectorSize , vectorSize, vector_ , Buffer(..), bufferFill, bufferVector, buffer_ , Word, wordSize, fromWord, toWord -- * Type aliases -- | Below are type aliases for Simplicity 'Word' types up to 4096-bit words. -- Note: This does not limit word sizes; arbitrarily large word sizes are allowed by making further pairs. , Word1, Word2, Word4, Word8, Word16, Word32, Word64, Word128, Word256, Word512, Word1024, Word2048, Word4096 , Vector1, Vector2, Vector4, Vector8, Vector16, Vector32, Vector64, Vector128, Vector256, Vector512, Vector1024, Vector2048, Vector4096 , vector1, vector2, vector4, vector8, vector16, vector32, vector64, vector128, vector256, vector512, vector1024, vector2048, vector4096 , Buffer1, Buffer3, Buffer7, Buffer15, Buffer31, Buffer63, Buffer127, Buffer255, Buffer511 , buffer1, buffer3, buffer7, buffer15, buffer31, buffer63, buffer127, buffer255, buffer511 -- * Specializations -- | The following are useful instances of 'Word' and specializations of 'fromWord' and 'toWord' for commonly used word sizes. -- Other word sizes can still be constructed using other 'Word' values. -- ** Word1 , word1, fromWord1, fromInt1, toWord1 -- ** Word2 , word2, fromWord2, fromInt2, toWord2 -- ** Word4 , word4, fromWord4, fromInt4, toWord4 -- ** Word8 , word8, fromWord8, fromInt8, toWord8 -- ** Word16 , word16, fromWord16, fromInt16, toWord16 -- ** Word32 , word32, fromWord32, fromInt32, toWord32 -- ** Word64 , word64, fromWord64, fromInt64, toWord64 -- ** Word128 , word128, fromWord128, fromInt128, toWord128 -- ** Word256 , word256, fromWord256, fromInt256, toWord256 -- ** Word512 , word512, fromWord512, fromInt512, toWord512 -- ** Word1024 , word1024, fromWord1024, fromInt1024, toWord1024 -- ** Word2048 , word2048, fromWord2048, fromInt2048, toWord2048 -- ** Word4096 , word4096, fromWord4096, fromInt4096, toWord4096 -- * Zip Vector , ZipVector(..) -- ** Bit , module Simplicity.Ty.Bit ) where import Prelude hiding (Word) import Control.Monad.Trans.State (State, evalState, get, put) import Data.Type.Equality ((:~:)(Refl)) import Lens.Family2.Stock (Traversal', rgt_) import Simplicity.Ty import Simplicity.Ty.Bit right_ f = rgt_ f type Vector1 x = x type Vector2 x = (x,x) type Vector4 x = Vector2 (Vector2 x) type Vector8 x = Vector2 (Vector4 x) type Vector16 x = Vector2 (Vector8 x) type Vector32 x = Vector2 (Vector16 x) type Vector64 x = Vector2 (Vector32 x) type Vector128 x = Vector2 (Vector64 x) type Vector256 x = Vector2 (Vector128 x) type Vector512 x = Vector2 (Vector256 x) type Vector1024 x = Vector2 (Vector512 x) type Vector2048 x = Vector2 (Vector1024 x) type Vector4096 x = Vector2 (Vector2048 x) vector1 :: TyC x => Vector x (Vector1 x) vector1 = SingleV vector2 :: TyC x => Vector x (Vector2 x) vector2 = DoubleV vector1 vector4 :: TyC x => Vector x (Vector4 x) vector4 = DoubleV vector2 vector8 :: TyC x => Vector x (Vector8 x) vector8 = DoubleV vector4 vector16 :: TyC x => Vector x (Vector16 x) vector16 = DoubleV vector8 vector32 :: TyC x => Vector x (Vector32 x) vector32 = DoubleV vector16 vector64 :: TyC x => Vector x (Vector64 x) vector64 = DoubleV vector32 vector128 :: TyC x => Vector x (Vector128 x) vector128 = DoubleV vector64 vector256 :: TyC x => Vector x (Vector256 x) vector256 = DoubleV vector128 vector512 :: TyC x => Vector x (Vector512 x) vector512 = DoubleV vector256 vector1024 :: TyC x => Vector x (Vector1024 x) vector1024 = DoubleV vector512 vector2048 :: TyC x => Vector x (Vector2048 x) vector2048 = DoubleV vector1024 vector4096 :: TyC x => Vector x (Vector4096 x) vector4096 = DoubleV vector2048 -- | @'Vector' x a@ specifies types, @a@, which are nested pairs of ... pairs of @x@'s. -- -- The type @a@ contain 2^/n/ @x@ values for some /n/. data Vector x a where SingleV :: TyC x => Vector x x DoubleV :: (TyC x, TyC a) => Vector x a -> Vector x (Vector2 a) -- | A proof that a 'Vector' of 'Vector's is itself a 'Vector'. vectorComp :: TyC a => Vector a b -> Vector b c -> Vector a c vectorComp v SingleV = v vectorComp v (DoubleV w) = DoubleV (vectorComp v w) -- | A proof that if @y@ is a 'Vector' of @x@'s then @(y, y)@ is a vector of @(x, x)@'s vectorPromote :: Vector x y -> Vector (x, x) (y, y) vectorPromote SingleV = SingleV vectorPromote (DoubleV v) = DoubleV (vectorPromote v) -- | Given @a@ and @b@ which are both 'Vector's of @z@'s, then decide which of the two 'Vector's is longer or prove that they are equal. compareVectorSize :: Vector z a -> Vector z b -> Either (Vector (b, b) a) (Either (a :~: b) (Vector (a, a) b)) compareVectorSize SingleV SingleV = Right (Left Refl) compareVectorSize (DoubleV n) SingleV = case compareVectorSize n SingleV of Left v -> Left (DoubleV v) Right (Left Refl) -> Left SingleV compareVectorSize SingleV (DoubleV m) = case compareVectorSize SingleV m of Right (Left Refl) -> Right (Right SingleV) Right (Right v) -> Right (Right (DoubleV v)) compareVectorSize (DoubleV n) (DoubleV m) = case compareVectorSize n m of Left v -> Left (vectorPromote v) Right (Left Refl) -> Right (Left Refl) Right (Right v) -> Right (Right (vectorPromote v)) -- | Given a 'Vector', @a@, fill it with values from a list, returning any unused elements. -- -- Fails if not enough elements are available. vectorFill :: Vector x a -> [x] -> Maybe (a, [x]) vectorFill SingleV [] = Nothing vectorFill SingleV (x:xs) = Just (x, xs) vectorFill (DoubleV vec) l = do (v1, l') <- vectorFill vec l (v2, l'') <- vectorFill vec l' return ((v1,v2),l'') -- | Computes the number of entries in a 'Vector'. vectorSize :: Vector x a -> Int vectorSize SingleV = 1 vectorSize (DoubleV w) = 2*(vectorSize w) -- | A (monomorphic) traversal of a 'Vector'. vector_ :: Vector x a -> Traversal' a x vector_ SingleV = ($) vector_ (DoubleV v) = \f (x,y) -> (,) <$> rec f x <*> rec f y where rec = vector_ v type Buffer1 x = S x type Buffer3 x = (S (Vector2 x), Buffer1 x) type Buffer7 x = (S (Vector4 x), Buffer3 x) type Buffer15 x = (S (Vector8 x), Buffer7 x) type Buffer31 x = (S (Vector16 x), Buffer15 x) type Buffer63 x = (S (Vector32 x), Buffer31 x) type Buffer127 x = (S (Vector64 x), Buffer63 x) type Buffer255 x = (S (Vector128 x), Buffer127 x) type Buffer511 x = (S (Vector256 x), Buffer255 x) -- | @'Buffer' x v b@ specifies a type @b@ which is of the form @('S' (x^(2^/n/)), ..., ('S' x^2, 'S' x)...)@ -- where @x^(2^/n/)@ is a 'Vector' of @x@. -- -- The type @b@ contains up to, but excluding, 2^/n/ @x@ values for some /n/. -- -- The type @b@ is isomorphic to @1 + x + x^2 + ... + x^(2^/n/-1)@. -- -- The type @v@ is a `Vector' of @x@'s which is used as a helper type (see 'bufferVector'). data Buffer x v b where SingleB :: TyC x => Buffer x (Vector2 x) (S x) DoubleB :: (TyC x, TyC v, TyC b) => Buffer x v b -> Buffer x (Vector2 v) (S v, b) buffer1 :: TyC x => Buffer x (Vector2 x) (Buffer1 x) buffer1 = SingleB buffer3 :: TyC x => Buffer x (Vector4 x) (Buffer3 x) buffer3 = DoubleB buffer1 buffer7 :: TyC x => Buffer x (Vector8 x) (Buffer7 x) buffer7 = DoubleB buffer3 buffer15 :: TyC x => Buffer x (Vector16 x) (Buffer15 x) buffer15 = DoubleB buffer7 buffer31 :: TyC x => Buffer x (Vector32 x) (Buffer31 x) buffer31 = DoubleB buffer15 buffer63 :: TyC x => Buffer x (Vector64 x) (Buffer63 x) buffer63 = DoubleB buffer31 buffer127 :: TyC x => Buffer x (Vector128 x) (Buffer127 x) buffer127 = DoubleB buffer63 buffer255 :: TyC x => Buffer x (Vector256 x) (Buffer255 x) buffer255 = DoubleB buffer127 buffer511 :: TyC x => Buffer x (Vector512 x) (Buffer511 x) buffer511 = DoubleB buffer255 -- | Given a 'Buffer', @b@, of up to 2^/n/ @x@'s, return a 'Vector' of 2^/n/ @x@'s. bufferVector :: Buffer x v b -> Vector x v bufferVector SingleB = vector2 bufferVector (DoubleB buf) = DoubleV (bufferVector buf) -- | Given a 'Buffer', @b@, return the empty buffer for it. bufferEmpty :: Buffer x v b -> b bufferEmpty SingleB = Left () bufferEmpty (DoubleB buf) = (Left (), bufferEmpty buf) -- | Given a 'Buffer', @b@, fill it with values from a list, returning any unused elements. bufferFill :: Buffer x v b -> [x] -> (b,[x]) bufferFill buf [] = (bufferEmpty buf, []) bufferFill SingleB (x:xs) = (Right x, xs) bufferFill (DoubleB buf) l = case vectorFill (bufferVector buf) l of Nothing -> let (rec,l'') = bufferFill buf l in ((Left (), rec), l'') Just (v, l') -> let (rec, l'') = bufferFill buf l' in ((Right v, rec), l'') -- | A (monomorphic) traversal of a 'Buffer'. buffer_ :: Buffer x v b -> Traversal' b x buffer_ SingleB = right_ buffer_ (DoubleB v) = \f (x,y) -> (,) <$> (right_.vector_ (bufferVector v)) f x <*> buffer_ v f y type Word1 = Vector1 Bit type Word2 = Vector2 Bit type Word4 = Vector4 Bit type Word8 = Vector8 Bit type Word16 = Vector16 Bit type Word32 = Vector32 Bit type Word64 = Vector64 Bit type Word128 = Vector128 Bit type Word256 = Vector256 Bit type Word512 = Vector512 Bit type Word1024 = Vector1024 Bit type Word2048 = Vector2048 Bit type Word4096 = Vector4096 Bit -- | @'Word' a@ specifies the types, @a@, which correspond to Simplicity word types. -- -- These are the types of 2^/n/ bit words and are made up of nested pairs of identically sized words down to the single-'Bit' type. type Word = Vector Bit word1 :: Word Word1 word1 = vector1 word2 :: Word Word2 word2 = vector2 word4 :: Word Word4 word4 = vector4 word8 :: Word Word8 word8 = vector8 word16 :: Word Word16 word16 = vector16 word32 :: Word Word32 word32 = vector32 word64 :: Word Word64 word64 = vector64 word128 :: Word Word128 word128 = vector128 word256 :: Word Word256 word256 = vector256 word512 :: Word Word512 word512 = vector512 word1024 :: Word Word1024 word1024 = vector1024 word2048 :: Word Word2048 word2048 = vector2048 word4096 :: Word Word4096 word4096 = vector4096 -- | Computes the number of entries in a 'Word'. -- -- @'wordSize' w = 'Simplicity.BitMachine.Ty.bitSizeR' ('reifyProxy' w)@ wordSize :: Word a -> Int wordSize = vectorSize -- | Convert a value of a Simplicity word type as a unsigned Haskell integer. -- -- @'toWord' w ('fromWord' w n) = n@ fromWord :: Word a -> a -> Integer fromWord = fromWordRec 0 fromWordRec :: Integer -> Word a -> a -> Integer fromWordRec i SingleV (Left ()) = 2 * i fromWordRec i SingleV (Right ()) = 2 * i + 1 fromWordRec i (DoubleV w) (hi, lo) = fromWordRec (fromWordRec i w hi) w lo -- | Convert a value of a Simplicity word type as a signed Haskell integer. -- -- @'toWord' w ('fromInt' w n) = n@ fromInt :: Word a -> a -> Integer fromInt SingleV (Left ()) = 0 fromInt SingleV (Right ()) = -1 fromInt (DoubleV w) (hi, lo) = fromWordRec (fromInt w hi) w lo -- | Convert a standard Haskell integer into a Simplicity word type. -- The value is take modulo 2^@('wordSize' w)@ where @w :: 'Word' a@ is the first argument. -- -- @'fromWord' w ('toWord' w n) = n \`mod\` 'wordSize' w@ toWord :: Word a -> Integer -> a toWord w i = evalState (go w) i where go :: Word a -> State Integer a go SingleV = do i <- get put (i `div` 2) return $ toBit (odd i) go (DoubleV w) = do b <- go w a <- go w return (a, b) fromWord1 :: Word1 -> Integer fromWord1 = fromWord word1 fromWord2 :: Word2 -> Integer fromWord2 = fromWord word2 fromWord4 :: Word4 -> Integer fromWord4 = fromWord word4 fromWord8 :: Word8 -> Integer fromWord8 = fromWord word8 fromWord16 :: Word16 -> Integer fromWord16 = fromWord word16 fromWord32 :: Word32 -> Integer fromWord32 = fromWord word32 fromWord64 :: Word64 -> Integer fromWord64 = fromWord word64 fromWord128 :: Word128 -> Integer fromWord128 = fromWord word128 fromWord256 :: Word256 -> Integer fromWord256 = fromWord word256 fromWord512 :: Word512 -> Integer fromWord512 = fromWord word512 fromWord1024 :: Word1024 -> Integer fromWord1024 = fromWord word1024 fromWord2048 :: Word2048 -> Integer fromWord2048 = fromWord word2048 fromWord4096 :: Word4096 -> Integer fromWord4096 = fromWord word4096 fromInt1 :: Word1 -> Integer fromInt1 = fromInt word1 fromInt2 :: Word2 -> Integer fromInt2 = fromInt word2 fromInt4 :: Word4 -> Integer fromInt4 = fromInt word4 fromInt8 :: Word8 -> Integer fromInt8 = fromInt word8 fromInt16 :: Word16 -> Integer fromInt16 = fromInt word16 fromInt32 :: Word32 -> Integer fromInt32 = fromInt word32 fromInt64 :: Word64 -> Integer fromInt64 = fromInt word64 fromInt128 :: Word128 -> Integer fromInt128 = fromInt word128 fromInt256 :: Word256 -> Integer fromInt256 = fromInt word256 fromInt512 :: Word512 -> Integer fromInt512 = fromInt word512 fromInt1024 :: Word1024 -> Integer fromInt1024 = fromInt word1024 fromInt2048 :: Word2048 -> Integer fromInt2048 = fromInt word2048 fromInt4096 :: Word4096 -> Integer fromInt4096 = fromInt word4096 toWord1 :: Integer -> Word1 toWord1 = toWord word1 toWord2 :: Integer -> Word2 toWord2 = toWord word2 toWord4 :: Integer -> Word4 toWord4 = toWord word4 toWord8 :: Integer -> Word8 toWord8 = toWord word8 toWord16 :: Integer -> Word16 toWord16 = toWord word16 toWord32 :: Integer -> Word32 toWord32 = toWord word32 toWord64 :: Integer -> Word64 toWord64 = toWord word64 toWord128 :: Integer -> Word128 toWord128 = toWord word128 toWord256 :: Integer -> Word256 toWord256 = toWord word256 toWord512 :: Integer -> Word512 toWord512 = toWord word512 toWord1024 :: Integer -> Word1024 toWord1024 = toWord word1024 toWord2048 :: Integer -> Word2048 toWord2048 = toWord word2048 toWord4096 :: Integer -> Word4096 toWord4096 = toWord word4096 -- | A pair of 'Vector's of the same length that have different contents. data ZipVector x a y b where SingleZV :: (TyC x, TyC y) => ZipVector x x y y DoubleZV :: (TyC x, TyC a, TyC y, TyC b) => ZipVector x a y b -> ZipVector x (Vector2 a) y (Vector2 b) ================================================ FILE: Haskell/Core/Simplicity/Ty.hs ================================================ {-# LANGUAGE UndecidableInstances, QuantifiedConstraints, RankNTypes, ExistentialQuantification, GADTs, TypeOperators, TypeFamilies, DeriveTraversable #-} -- | This module provides representations of Simplicity types in Haskell. -- -- The 'TyC' class captures those Haskell types that correspond to Simplicity types. -- The 'Ty' data type is a value-level representation of Simplicity types. -- The 'TyReflect' GADT links a value-level representation of Simplicity types with corresponding Haskell types. module Simplicity.Ty ( TyC , TyReflect(..) , reify, reifyProxy, reifyArrow , equalTyReflect , SomeArrow(..), someArrowR, someArrowMap , Ty, TyF(..) , one, sum, prod , unreflect , SomeTy(..), reflect , memoCataTy -- ** Serialization , putValue, putValueR, getValue, getValueR -- ** Untyped Simplicity Values , UntypedValue(..), untypedValue, untypedValueR, castUntypedValue, castUntypedValueR -- ** Synonyms , S ) where import Prelude hiding (sum, prod) import Control.Unification.Types (Unifiable, zipMatch) import Data.Functor.Fixedpoint (Fix(..)) import Data.Maybe (fromMaybe) import Data.MemoTrie (HasTrie(..), memo) import Data.Type.Equality ((:~:)(Refl)) import Lens.Family2 ((&), (%~)) import Lens.Family2.Stock (mapped, _1) -- | 'TyC' is a type class for those Haskell types that correspond to Simplicity types; -- specifically those composed from @()@, @'Either' a b@, and @(a, b)@. -- The 'ClosedClass_' superclass isn't exported preventing further instances of 'TyC'. class (ClosedClass_ a, Eq a, Ord a, Read a, Show a) => TyC a where -- This class isn't exported, so subclasses of it cannot be instantiated outside this module. class ClosedClass_ a where reify_ :: TyReflect a instance TyC () where instance ClosedClass_ () where reify_ = OneR instance (TyC a, TyC b) => TyC (Either a b) where instance (TyC a, TyC b) => ClosedClass_ (Either a b) where reify_ = SumR reify_ reify_ instance (TyC a, TyC b) => TyC (a, b) where instance (TyC a, TyC b) => ClosedClass_ (a, b) where reify_ = ProdR reify_ reify_ -- | The 'TyReflect' GADT provides a link between Haskell types correspondng to Simplicity types (i.e. members of the 'TyC' class) and values that can be manipulated by Haskell programs. -- -- There is a unique value of @'TyReflect' a@ for every @a@ that corresponds to a Simplicity type. -- This value can be decomposed by pattern matching to get the (unique) values of 'TyRefect' that correspond to the components of the Simplicity type. -- For example, the unique value of @'TyReflect' ('Either' () (), ())@ is @'ProdR' ('SumR' 'OneR' 'OneR') 'OneR'@. data TyReflect a where OneR :: TyReflect () SumR :: (TyC a, TyC b) => TyReflect a -> TyReflect b -> TyReflect (Either a b) ProdR :: (TyC a, TyC b) => TyReflect a -> TyReflect b -> TyReflect (a, b) -- | The unique 'TyReflect' value for any given 'TyC' type. reify :: TyC a => TyReflect a reify = reify_ -- | A helper function that use a proxy argument to help control the type inferred for 'reify'. reifyProxy :: TyC a => proxy a -> TyReflect a reifyProxy _ = reify -- | A helper function that use a proxy argument to help control the types inferred for 'reify'. reifyArrow :: (TyC a, TyC b) => proxy a b -> (TyReflect a, TyReflect b) reifyArrow _ = (reify, reify) -- | Decide if two 'TyReflect' values are equal or not, and if they are equal then unify their type variables. equalTyReflect :: TyReflect a -> TyReflect b -> Maybe (a :~: b) equalTyReflect OneR OneR = return Refl equalTyReflect (SumR a1 b1) (SumR a2 b2) = do Refl <- equalTyReflect a1 a2 Refl <- equalTyReflect b1 b2 return Refl equalTyReflect (ProdR a1 b1) (ProdR a2 b2) = do Refl <- equalTyReflect a1 a2 Refl <- equalTyReflect b1 b2 return Refl equalTyReflect _ _ = Nothing -- | @putValue@ produces a compact serialization of values of Simplicity types. -- The serialization format is simply a list of the tags of the sum types in canonical order. -- The type isn't serialized with the value in this format; -- you will need to know the original type in order to deserialize the value. putValue :: TyC a => a -> [Bool] putValue = putValueR reify -- | @putValueR@ produces a compact serialization of values of Simplicity types. -- The serialization format is simply a list of the tags of the sum types in canonical order. -- The type isn't serialized with the value in this format; -- you will need to know the original type in order to deserialize the value. -- -- @putValue = putValueR reify@ putValueR :: TyReflect a -> a -> [Bool] putValueR a x = go a x [] where go :: TyReflect a -> a -> [Bool] -> [Bool] go OneR () = id go (SumR a b) (Left x) = (False:) . go a x go (SumR a b) (Right y) = (True:) . go b y go (ProdR a b) (x, y) = go a x . go b y -- | Deserializes a Simplicity value of a given type from a stream of Bits -- -- Note that the type @forall m. Monad m => m Bool -> m a@ is isomorphic to the free monad over the @X²@ functor. -- In other words, 'getValue' has the type of a binary branching tree with leaves containing Simplicity values of a given . getValue :: (TyC a, Monad m) => m Bool -> m a getValue = getValueR reify -- | Deserializes a Simplicity value of a given type from a stream of Bits -- -- Note that the type @forall m. Monad m => m Bool -> m a@ is isomorphic to the free monad over the @X²@ functor. -- In other words, 'getValue' has the type of a binary branching tree with leaves containing Simplicity values of a given . -- -- @getValue = getValueR reify@ getValueR :: Monad m => TyReflect a -> m Bool -> m a getValueR OneR next = return () getValueR (SumR a b) next = next >>= f where f False = Left <$> getValueR a next f True = Right <$> getValueR b next getValueR (ProdR a b) next = (,) <$> getValueR a next <*> getValueR b next -- | @SomeArrow arr@ captures the existential type @exists a b. (Ty a, TyC b) *> arr a b@. data SomeArrow arr = forall a b. (TyC a, TyC b) => SomeArrow (arr a b) instance (forall a b. (TyC a, TyC b) => Eq (arr a b)) => Eq (SomeArrow arr) where (SomeArrow p0) == (SomeArrow p1) = fromMaybe False $ do Refl <- equalTyReflect ra0 ra1 Refl <- equalTyReflect rb0 rb1 return $ p0 == p1 where (ra0, rb0) = reifyArrow p0 (ra1, rb1) = reifyArrow p1 instance (forall a b. (TyC a, TyC b) => Show (arr a b)) => Show (SomeArrow arr) where showsPrec d (SomeArrow p) = showParen (d > 10) $ showString "SomeArrow " . showsPrec 11 p -- | A pseudo-constructor for 'SomeArrow' that provides proxy arguments to help specify the type parameters. someArrowR :: (TyC a, TyC b) => proxy a -> proxy b -> arr a b -> SomeArrow arr someArrowR _ _ x = SomeArrow x -- | The functor operation on 'SomeArrow'. someArrowMap :: (forall a b. (TyC a, TyC b) => arr0 a b -> arr1 a b) -> SomeArrow arr0 -> SomeArrow arr1 someArrowMap f (SomeArrow x) = SomeArrow (f x) -- | A Haskell data type for representing Simplicity types. -- It uses an explicit 'Fix'edpoint of the 'TyF' functor. type Ty = Fix TyF -- | The functor used to define 'Ty' type. data TyF a = One | Sum a a | Prod a a deriving (Eq, Functor, Foldable, Traversable, Show) instance Unifiable TyF where zipMatch One One = Just One zipMatch (Sum a1 b1) (Sum a2 b2) = Just (Sum (Right (a1, a2)) (Right (b1, b2))) zipMatch (Prod a1 b1) (Prod a2 b2) = Just (Prod (Right (a1, a2)) (Right (b1, b2))) zipMatch _ _ = Nothing -- | Construct the unit 'Ty' of Simplicity. one :: Ty one = Fix One -- | Construct the sum 'Ty' of two 'Ty's. sum :: Ty -> Ty -> Ty sum a b = Fix $ Sum a b -- | Construct the product 'Ty' of two 'Ty's. prod :: Ty -> Ty -> Ty prod a b = Fix $ Prod a b -- | Convert a 'TyReflect' value the corresponding 'Ty' value. unreflect :: TyReflect a -> Ty unreflect OneR = one unreflect (SumR a b) = sum (unreflect a) (unreflect b) unreflect (ProdR a b) = prod (unreflect a) (unreflect b) -- | SomeTy is isomorphic to Ty. data SomeTy = forall a. TyC a => SomeTy (TyReflect a) -- | Convert a Ty to SomeTy. reflect :: Ty -> SomeTy reflect (Fix One) = SomeTy OneR reflect (Fix (Sum a b)) = case (reflect a, reflect b) of (SomeTy ra, SomeTy rb) -> SomeTy $ SumR ra rb reflect (Fix (Prod a b)) = case (reflect a, reflect b) of (SomeTy ra, SomeTy rb) -> SomeTy $ ProdR ra rb -- | A union of all Simplicity values without type information. -- -- A single 'UntypedValue' could be successfully interpreted at multiple different Simplicity types. -- For example, @'LeftV' 'OneV'@ could be successfully interpreted as @'Either' () b@ for any Simplicity type @b@. data UntypedValue = OneV | LeftV UntypedValue | RightV UntypedValue | PairV UntypedValue UntypedValue deriving (Eq, Show) -- | Construct an 'UntypedValue' from a (typed) Simplicity value. untypedValue :: TyC a => a -> UntypedValue untypedValue = untypedValueR reify -- | Construct an 'UntypedValue' from a (typed) Simplicity value. untypedValueR :: TyReflect a -> a -> UntypedValue untypedValueR OneR _ = OneV untypedValueR (SumR a b) (Left x) = LeftV $ untypedValueR a x untypedValueR (SumR a b) (Right y) = RightV $ untypedValueR b y untypedValueR (ProdR a b) (x, y) = PairV (untypedValueR a x) (untypedValueR b y) -- | Attempt to interpret an UntypedValue at a given Simplicity type. -- -- Interpreting any 'UntypedValue' at the @()@ type is always successful, regardless of the UntypedValue. castUntypedValue :: TyC a => UntypedValue -> Maybe a castUntypedValue = castUntypedValueR reify -- | Attempt to interpret an UntypedValue at a given Simplicity type. -- -- Interpreting any 'UntypedValue' at the @()@ type is always successful, regardless of the UntypedValue. castUntypedValueR :: TyReflect a -> UntypedValue -> Maybe a castUntypedValueR OneR _ = Just () castUntypedValueR (SumR a b) (LeftV x) = Left <$> castUntypedValueR a x castUntypedValueR (SumR a b) (RightV y) = Right <$> castUntypedValueR b y castUntypedValueR (ProdR a b) (PairV x y) = (,) <$> castUntypedValueR a x <*> castUntypedValueR b y castUntypedValueR _ _ = Nothing -- memoTyF and dememoTyF hare non-exported helper functions for the -- HasTrie (TyF x) instance. memoTyF :: Maybe (Bool, x, x) -> TyF x memoTyF Nothing = One memoTyF (Just (False, a, b)) = Sum a b memoTyF (Just (True, a, b)) = Prod a b deMemoTyF :: TyF x -> Maybe (Bool, x, x) deMemoTyF One = Nothing deMemoTyF (Sum a b) = Just (False, a, b) deMemoTyF (Prod a b) = Just (True, a, b) instance HasTrie x => HasTrie (TyF x) where newtype TyF x :->: a = TyFTrie (Maybe (Bool, x, x) :->: a) trie f = TyFTrie (trie (f . memoTyF)) untrie (TyFTrie t) = untrie t . deMemoTyF enumerate (TyFTrie t) = enumerate t & mapped._1 %~ memoTyF -- MemoTy, memoTy and dememoTy hare non-exported helper types and functions for -- defining memoCataTy newtype MemoTy = MemoTy { unMemoTy :: Ty } memoTy :: TyF MemoTy -> MemoTy memoTy x = MemoTy (Fix (unMemoTy <$> x)) deMemoTy :: MemoTy -> TyF MemoTy deMemoTy (MemoTy (Fix v)) = MemoTy <$> v instance HasTrie MemoTy where newtype MemoTy :->: a = TyTrie (TyF MemoTy :->: a) trie f = TyTrie (trie (f . memoTy)) untrie (TyTrie t) = untrie t . deMemoTy enumerate (TyTrie t) = enumerate t & mapped._1 %~ memoTy -- | An implementation of 'Data.Functor.Fixedpoint.cata' for 'TyF' that is -- transparently memoized. -- -- @'memoCataTy' = 'Data.Functor.Fixedpoint.cata'@ memoCataTy :: (TyF a -> a) -> Ty -> a memoCataTy alg = f . MemoTy where f = memo (alg . fmap f . deMemoTy) -- | A 'Maybe' type for Simplicity type S a = Either () a ================================================ FILE: Haskell/Core/Simplicity/Weight.hs ================================================ module Simplicity.Weight ( Weight, milli, milliWeight ) where import Data.Fixed (Milli) -- | Simplicity CPU cost is measured in 'Weight' units, the same units as Bitcoin transaction size. -- Simplicity expressions are weighed to 3 decimal places of accuracy. type Weight = Milli -- | Construct a weight from a value in mulliWUs. milli :: Real a => a -> Weight milli n = realToFrac n / 1000 -- | Return a 'Weight' value as an integer in milliWUs. milliWeight :: Weight -> Integer milliWeight = round . (1000*) ================================================ FILE: Haskell/Core/Simplicity/Word.hs ================================================ module Simplicity.Word ( Word256, Word64, Word32, Word16, Word8 , showHex256 ) where import Data.Bits import Data.Ix import Data.Serialize import Data.Word (Word8, Word16, Word32, Word64) import Numeric (showHex) import Foreign.Ptr (castPtr) import Foreign.Storable import Lens.Family2 ((&), (%~)) import Lens.Family2.Stock (_1, both_, mapped) -- | 256-bit unsigned integer type data Word256 = Word256 !Word64 !Word64 !Word64 !Word64 deriving (Bounded, Eq, Ord) liftUnary op x = fromInteger (op (toInteger x)) liftBinary op x y = fromInteger (op (toInteger x) (toInteger y)) pointwiseUnary op (Word256 a3 a2 a1 a0) = Word256 (op a3) (op a2) (op a1) (op a0) pointwiseBinary op (Word256 a3 a2 a1 a0) (Word256 b3 b2 b1 b0) = Word256 (op a3 b3) (op a2 b2) (op a1 b1) (op a0 b0) instance Show Word256 where showsPrec p a = showsPrec p (toInteger a) instance Read Word256 where readsPrec p s = readsPrec p s & mapped._1 %~ fromInteger instance Num Word256 where (+) = liftBinary (+) (-) = liftBinary (-) (*) = liftBinary (*) negate = liftUnary negate abs = id signum = liftUnary signum fromInteger i = Word256 (fromInteger a3) (fromInteger a2) (fromInteger a1) (fromInteger i) where a1 = i `div` (2^64) a2 = a1 `div` (2^64) a3 = a2 `div` (2^64) instance Real Word256 where toRational a = toRational (toInteger a) instance Integral Word256 where quot = liftBinary quot rem = liftBinary rem div = liftBinary div mod = liftBinary mod quotRem a b = quotRem (toInteger a) (toInteger b) & both_ %~ fromInteger divMod a b = divMod (toInteger a) (toInteger b) & both_ %~ fromInteger toInteger (Word256 a3 a2 a1 a0) = toInteger a0 + 2^64*(toInteger a1 + 2^64*(toInteger a2 + 2^64*toInteger a3)) instance Enum Word256 where succ a | a == maxBound = error "Enum.succ{Word256}: tried to take `succ' of maxBound" | otherwise = liftUnary succ a pred a | a == minBound = error "Enum.pred{Word256}: tried to take `pred' of minBound" | otherwise = liftUnary pred a toEnum i = fromInteger (toEnum i) fromEnum a = fromEnum (toInteger a) enumFrom a = enumFromTo a maxBound enumFromThen a b | a <= b = enumFromThenTo a b maxBound | otherwise = enumFromThenTo a b minBound enumFromTo a b = fromInteger <$> enumFromTo (toInteger a) (toInteger b) enumFromThenTo a b c = fromInteger <$> enumFromThenTo (toInteger a) (toInteger b) (toInteger c) instance Ix Word256 where range (a,b) = enumFromTo a b index (a,b) c = index (toInteger a, toInteger b) (toInteger c) inRange (a,b) c = a <= c && c <= b rangeSize (a,b) = rangeSize (toInteger a, toInteger b) instance Bits Word256 where (.&.) = pointwiseBinary (.&.) (.|.) = pointwiseBinary (.|.) xor = pointwiseBinary xor complement = pointwiseUnary complement shift a i = liftUnary (flip shift i) a rotate a i = shiftL a i' .|. shiftR a (256-i') where i' = i `mod` 256 zeroBits = fromInteger 0 bit = bitDefault testBit a = testBit (toInteger a) bitSizeMaybe = Just . finiteBitSize bitSize = finiteBitSize isSigned _ = False popCount (Word256 a3 a2 a1 a0) = popCount a3 + popCount a2 + popCount a1 + popCount a0 instance FiniteBits Word256 where finiteBitSize _ = 4*64 countLeadingZeros (Word256 0 0 0 a0) = 3*64 + countLeadingZeros a0 countLeadingZeros (Word256 0 0 a1 _) = 2*64 + countLeadingZeros a1 countLeadingZeros (Word256 0 a2 _ _) = 64 + countLeadingZeros a2 countLeadingZeros (Word256 a3 _ _ _) = countLeadingZeros a3 countTrailingZeros (Word256 a3 0 0 0) = 3*64 + countTrailingZeros a3 countTrailingZeros (Word256 _ a2 0 0) = 2*64 + countTrailingZeros a2 countTrailingZeros (Word256 _ _ a1 0) = 64 + countTrailingZeros a1 countTrailingZeros (Word256 _ _ _ a0) = countTrailingZeros a0 instance Serialize Word256 where put (Word256 a3 a2 a1 a0) = put a3 >> put a2 >> put a1 >> put a0 get = Word256 <$> get <*> get <*> get <*> get -- | Show a Word256 value as a hex string padded with leading zeros. showHex256 :: Word256 -> String showHex256 w = replicate (64 - length hexStr) '0' ++ hexStr where hexStr = showHex w "" ================================================ FILE: Haskell/Elements/Simplicity/Elements/DataTypes.hs ================================================ {-# LANGUAGE DeriveTraversable, TupleSections #-} -- | This module defines the data structures that make up the signed data in a Bitcoin transaction. module Simplicity.Elements.DataTypes ( Point(..) , Script , TxNullDatumF(..), TxNullDatum, TxNullData, txNullData , Lock, Value, Entropy , Confidential(..), prf_ , AssetWith(..), AssetWithWitness, Asset, asset, clearAssetPrf, putAsset , AmountWith(..), AmountWithWitness, Amount, amount, clearAmountPrf, putAmount , TokenAmountWith, TokenAmountWithWitness, TokenAmount , Nonce(..) , putNonce, getNonce , putIssuance , NewIssuance(..) , Reissuance(..) , Issuance , Outpoint(Outpoint), opHash, opIndex, putOutpointBE , UTXO(UTXO), utxoAsset, utxoAmount, utxoScript , SigTxInput(SigTxInput), sigTxiPegin, sigTxiPreviousOutpoint, sigTxiTxo, sigTxiSequence, sigTxiIssuance, sigTxiAnnex, sigTxiScriptSig , sigTxiIssuanceEntropy, sigTxiIssuanceAsset, sigTxiIssuanceToken , TxOutput(TxOutput), txoAsset, txoAmount, txoNonce, txoScript , SigTx(SigTx), sigTxVersion, sigTxIn, sigTxOut, sigTxLock , putNoWitnessTx, txid , TapEnv(..) , txIsFinal, txLockBrokenDistance, txLockBrokenDuration , calculateIssuanceEntropy, calculateAsset, calculateToken , outputAmountsHash, outputNoncesHash, outputScriptsHash , outputRangeProofsHash, outputSurjectionProofsHash, outputsHash, outputHash , inputOutpointsHash, inputAmountsHash, inputScriptsHash, inputUtxosHash, inputUtxoHash , inputSequencesHash, inputAnnexesHash, inputScriptSigsHash, inputsHash, inputHash , issuanceAssetAmountsHash, issuanceTokenAmountsHash, issuanceRangeProofsHash, issuancesHash, issuanceHash, issuanceBlindingEntropyHash , txHash , tapleafHash, tappathHash, tapEnvHash , taptweak , outputFee, totalFee , lBtcAsset , module Simplicity.Bitcoin ) where import Control.Monad (guard, mzero) import Data.Bits ((.|.)) import qualified Data.ByteString as BS import qualified Data.ByteString.Lazy as BSL import Data.Foldable (toList) import qualified Data.Map as Map import Data.Maybe (catMaybes, isJust) import Data.Semigroup (Max(Max,getMax)) import Data.Serialize ( Serialize, encode , Get, get, runGetLazy, lookAhead, getWord8, getWord16le, getWord32le, getLazyByteString, isEmpty , Putter, put, putWord8, putWord64be, putWord64le, putWord32be, putWord32le, putWord16le, putLazyByteString, runPutLazy ) import Data.String (fromString) import Data.Vector (Vector) import qualified Data.Vector as V import Data.Word (Word64, Word32, Word16, Word8) import Lens.Family2 ((&), (.~), (^.), over, review, to, under, view) import Lens.Family2.Stock (some_) import Lens.Family2.Unchecked (Adapter, adapter, Traversal) import Simplicity.Bitcoin import Simplicity.Digest import Simplicity.LibSecp256k1.Spec import Simplicity.LibSecp256k1.Schnorr import Simplicity.Word just_ f = some_ f -- | Unparsed Bitcoin Script. -- Script in transactions outputs do not have to be parsable, so we encode this as a raw 'Data.ByteString.ByteString'. type Script = BSL.ByteString type SurjectionProof = BSL.ByteString type RangeProof = BSL.ByteString data TxNullDatumF a = Immediate a | PushData a | PushData2 a | PushData4 a | OP1Negate | OPReserved | OP1 | OP2 | OP3 | OP4 | OP5 | OP6 | OP7 | OP8 | OP9 | OP10 | OP11 | OP12 | OP13 | OP14 | OP15 | OP16 deriving (Functor, Foldable, Traversable, Show) type TxNullDatum = TxNullDatumF BSL.ByteString type TxNullData = [TxNullDatum] getTxNullDatum :: Get TxNullDatum getTxNullDatum = getWord8 >>= go where go 0x60 = return OP16 go 0x5f = return OP15 go 0x5e = return OP14 go 0x5d = return OP13 go 0x5c = return OP12 go 0x5b = return OP11 go 0x5a = return OP10 go 0x59 = return OP9 go 0x58 = return OP8 go 0x57 = return OP7 go 0x56 = return OP6 go 0x55 = return OP5 go 0x54 = return OP4 go 0x53 = return OP3 go 0x52 = return OP2 go 0x51 = return OP1 go 0x50 = return OPReserved go 0x4f = return OP1Negate go 0x4e = do n <- getWord32le PushData4 <$> getLazyByteString (fromIntegral n) go 0x4d = do n <- getWord16le PushData2 <$> getLazyByteString (fromIntegral n) go 0x4c = do n <- getWord8 PushData <$> getLazyByteString (fromIntegral n) go op | op < 0x4c = Immediate <$> getLazyByteString (fromIntegral op) | otherwise = fail $ "Serialize.get{getTxNullDatum}: " ++ show op ++ "is not a push-data opcode." txNullData :: Script -> Maybe TxNullData txNullData = either (const Nothing) Just . runGetLazy prog where prog = do 0x6a <- getWord8 go go = do emp <- isEmpty if emp then return [] else ((:) <$> getTxNullDatum <*> go) getFE :: Get FE getFE = fmap fe_unpack get >>= maybe mzero return putFE :: Putter FE putFE = put . fe_pack -- | Transaction locktime. -- This represents either a block height or a block time. -- It is encoded as a 32-bit value. type Lock = Word32 type Value = Word64 type Entropy = Hash256 data Confidential prf a = Explicit a | Confidential Point prf deriving Show prf_ :: Traversal (Confidential prfA a) (Confidential prfB a) prfA prfB prf_ f (Confidential pt prf) = Confidential pt <$> f prf prf_ f (Explicit x) = pure (Explicit x) newtype AssetWith prf = Asset (Confidential prf Hash256) deriving Show type Asset = AssetWith () type AssetWithWitness = AssetWith SurjectionProof asset :: Adapter (AssetWith prfA) (AssetWith prfB) (Confidential prfA Hash256) (Confidential prfB Hash256) asset = adapter to fro where to (Asset x) = x fro x = (Asset x) clearAssetPrf :: AssetWith prf -> Asset clearAssetPrf x = x & under asset . prf_ .~ () putAsset :: Putter Asset putAsset (Asset (Explicit h)) = putWord8 0x01 >> put h putAsset (Asset (Confidential (Point by x) _)) = putWord8 (if by then 0x0b else 0x0a) >> putFE x newtype AmountWith prf = Amount (Confidential prf Value) deriving Show type Amount = AmountWith () type AmountWithWitness = AmountWith RangeProof type TokenAmountWith prf = AmountWith prf type TokenAmount = Amount type TokenAmountWithWitness = AmountWithWitness amount :: Adapter (AmountWith prfA) (AmountWith prfB) (Confidential prfA Value) (Confidential prfB Value) amount = adapter to fro where to (Amount x) = x fro x = (Amount x) clearAmountPrf :: AmountWith prf -> Amount clearAmountPrf x = x & under amount . prf_ .~ () putAmount :: Putter Amount putAmount (Amount (Explicit v)) = putWord8 0x01 >> putWord64be v putAmount (Amount (Confidential (Point by x) _)) = putWord8 (if by then 0x09 else 0x08) >> putFE x newtype Nonce = Nonce { nonce :: Either (Bool, Word256) Hash256 } deriving Show instance Serialize Nonce where put (Nonce (Right h)) = putWord8 0x01 >> put h put (Nonce (Left (by, x))) = putWord8 (if by then 0x03 else 0x02) >> put x get = lookAhead getWord8 >>= go where go 0x01 = getWord8 *> (Nonce . Right <$> get) go 0x02 = Nonce . Left . (False,) <$> get go 0x03 = Nonce . Left . (True,) <$> get go _ = fail "Serialize.get{Simplicity.Primitive.Elements.DataTypes.Nonce}: bad prefix." putMaybeConfidential :: Putter a -> Putter (Maybe a) putMaybeConfidential _ Nothing = putWord8 0x00 putMaybeConfidential p (Just a) = p a getMaybeConfidential :: Get a -> Get (Maybe a) getMaybeConfidential g = lookAhead getWord8 >>= go where go 0x00 = getWord8 *> pure Nothing go _ = Just <$> g putNonce :: Putter (Maybe Nonce) putNonce = putMaybeConfidential put getNonce :: Get (Maybe Nonce) getNonce = getMaybeConfidential get data NewIssuance = NewIssuance { newIssuanceContractHash :: Hash256 , newIssuanceAmount :: AmountWithWitness , newIssuanceTokenAmount :: TokenAmountWithWitness } deriving Show data Reissuance = Reissuance { reissuanceBlindingNonce :: Hash256 , reissuanceEntropy :: Entropy , reissuanceAmount :: AmountWithWitness } deriving Show type Issuance = Either NewIssuance Reissuance putIssuance :: Putter (Maybe Issuance) putIssuance Nothing = putWord8 0x00 >> putWord8 0x00 putIssuance (Just x) = go x where maybeZero (Amount (Explicit 0)) = Nothing maybeZero x = Just x -- We serialize the range/surjection proofs separately. go (Left new) = putMaybeConfidential putAmount (maybeZero . clearAmountPrf $ newIssuanceAmount new) >> putMaybeConfidential putAmount (maybeZero . clearAmountPrf $ newIssuanceTokenAmount new) >> put (0 :: Word256) >> put (newIssuanceContractHash new) >> put (bslHash (newIssuanceAmount new ^. (under amount.prf_))) >> put (bslHash (newIssuanceTokenAmount new ^. (under amount.prf_))) go (Right re) = putAmount (clearAmountPrf $ reissuanceAmount re) >> putWord8 0x00 >> put (reissuanceBlindingNonce re) >> put (reissuanceEntropy re) >> put (bslHash (reissuanceAmount re ^. (under amount.prf_))) >> put (bslHash mempty) -- | An outpoint is an index into the TXO set. data Outpoint = Outpoint { opHash :: Hash256 , opIndex :: Word32 } deriving Show instance Serialize Outpoint where get = Outpoint <$> get <*> getWord32le put (Outpoint h i) = put h >> putWord32le i -- | Big endian serialization of an 'Outpoint' putOutpointBE :: Putter Outpoint putOutpointBE op = put (opHash op) >> putWord32be (opIndex op) -- | The data type for unspent transaction outputs. data UTXO = UTXO { utxoAsset :: Asset , utxoAmount :: Amount , utxoScript :: Script -- length must be strictly less than 2^32. } deriving Show -- | The data type for signed transaction inputs, including a copy of the TXO being spent. -- For pegins, the TXO data in 'sigTxiTxo' is synthesized. data SigTxInput = SigTxInput { sigTxiPegin :: Maybe Hash256 , sigTxiPreviousOutpoint :: Outpoint , sigTxiTxo :: UTXO , sigTxiSequence :: Word32 , sigTxiIssuance :: Maybe Issuance , sigTxiAnnex :: Maybe BSL.ByteString , sigTxiScriptSig :: Script -- length must be strictly less than 2^32. } deriving Show -- | The data type for transaction outputs. -- The signed transactin output format is identical to the serialized transaction output format. data TxOutput = TxOutput { txoAsset :: AssetWithWitness , txoAmount :: AmountWithWitness , txoNonce :: Maybe Nonce , txoScript :: Script -- length must be strictly less than 2^32. } deriving Show -- | The data type for transactions in the context of signatures. -- The data signed in a BIP 143 directly covers input values. data SigTx = SigTx { sigTxVersion :: Word32 , sigTxIn :: Vector SigTxInput , sigTxOut :: Vector TxOutput , sigTxLock :: Lock } deriving Show -- | Taproot specific environment data about the input being spent. data TapEnv = TapEnv { tapleafVersion :: Word8 , tapInternalKey :: PubKey , tappath :: [Hash256] , tapScriptCMR :: Hash256 } deriving Show txIsFinal :: SigTx -> Bool txIsFinal tx = all finalSequence (sigTxIn tx) where finalSequence sigin = sigTxiSequence sigin == maxBound -- | This function is used in a specification of broken relative timelock jets and should not be used other than for previous consensus reasons. txLockBrokenDistance :: SigTx -> Word16 txLockBrokenDistance tx | sigTxVersion tx < 2 = 0 | otherwise = getMax . foldMap distance $ sigTxIn tx where distance sigin = case parseSequence (sigTxiSequence sigin) of Just (Left x) -> Max x _ -> mempty -- | This function is used in a specification of broken relative timelock jets and should not be used other than for previous consensus reasons. txLockBrokenDuration :: SigTx -> Word16 txLockBrokenDuration tx | sigTxVersion tx < 2 = 0 | otherwise = getMax . foldMap duration $ sigTxIn tx where duration sigin = case parseSequence (sigTxiSequence sigin) of Just (Right x) -> Max x _ -> mempty -- | An implementation of GenerateIssuanceEntropy from Element's 'issuance.cpp'. calculateIssuanceEntropy :: Outpoint -> Hash256 -> Entropy calculateIssuanceEntropy op contract = ivHash $ compress noTagIv (bsHash (encode (bsHash (encode op))), contract) -- | An implementation of CalculateAsset from Element's 'issuance.cpp'. calculateAsset :: Entropy -> Hash256 calculateAsset entropy = ivHash $ compress noTagIv (entropy, review (over le256) 0) -- | An implementation of CalculateToken from Element's 'issuance.cpp'. calculateToken :: AmountWith prf -> Entropy -> Hash256 calculateToken amt entropy = ivHash $ compress noTagIv (entropy, review (over le256) tag) where tag | Amount (Explicit _) <- amt = 1 | Amount (Confidential _ _) <- amt = 2 -- | The entropy value of an issuance there is one, either given by a reissuance, or derived from a new issuance. sigTxiIssuanceEntropy :: SigTxInput -> Maybe Entropy sigTxiIssuanceEntropy txi = either mkEntropy reissuanceEntropy <$> sigTxiIssuance txi where mkEntropy = calculateIssuanceEntropy (sigTxiPreviousOutpoint txi) . newIssuanceContractHash -- | The issued asset ID if there is an issuance. sigTxiIssuanceAsset :: SigTxInput -> Maybe Hash256 sigTxiIssuanceAsset = fmap calculateAsset . sigTxiIssuanceEntropy -- | The issued token ID if there is an issuance. sigTxiIssuanceToken :: SigTxInput -> Maybe Hash256 sigTxiIssuanceToken txi = calculateToken <$> amount <*> entropy where amount = either newIssuanceAmount reissuanceAmount <$> sigTxiIssuance txi entropy = sigTxiIssuanceEntropy txi -- | A hash of all 'txoAsset's and 'txoAmount's. outputAmountsHash :: SigTx -> Hash256 outputAmountsHash tx = bslHash . runPutLazy $ mapM_ go (sigTxOut tx) where go txo = putAsset (clearAssetPrf $ txoAsset txo) >> putAmount (clearAmountPrf $ txoAmount txo) -- | A hash of all 'txoNonce's. outputNoncesHash :: SigTx -> Hash256 outputNoncesHash tx = bslHash . runPutLazy $ mapM_ (putNonce . txoNonce) (sigTxOut tx) -- | A hash of all 'txoScript' hashes. outputScriptsHash :: SigTx -> Hash256 outputScriptsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . txoScript) (sigTxOut tx) -- | A hash of all output range proof hashes. outputRangeProofsHash :: SigTx -> Hash256 outputRangeProofsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . view (to txoAmount.under amount.prf_)) (sigTxOut tx) -- | A hash of all output surjection proof hashes. outputSurjectionProofsHash :: SigTx -> Hash256 outputSurjectionProofsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . view (to txoAsset.under asset.prf_)) (sigTxOut tx) -- | A hash of -- -- * 'outputAmountsHash' -- * 'outputNoncesHash' -- * 'outputScriptsHash' -- * 'outputRangeProofsHash' -- -- Note that 'outputSurjectionProofsHash' is excluded. outputsHash :: SigTx -> Hash256 outputsHash tx = bslHash . runPutLazy $ do put $ outputAmountsHash tx put $ outputNoncesHash tx put $ outputScriptsHash tx put $ outputRangeProofsHash tx -- outputSurjectionProofsHash omitted -- | A hash of one output's -- -- * asset and amount -- * nonce -- * hash of its script -- * hash of its rangeproof. -- -- Note that surjection proof is excluded. outputHash :: TxOutput -> Hash256 outputHash txo = bslHash . runPutLazy $ do putAsset . clearAssetPrf $ txoAsset txo putAmount . clearAmountPrf $ txoAmount txo putNonce $ txoNonce txo put . bslHash $ txoScript txo put . bslHash $ view (to txoAmount.under amount.prf_) txo -- outputSurjectionProof omitted -- | Serialize an input's previous output including whether the previous input is from an pegin or not, and which parent chain if it is a pegin. putOutpoint :: Putter SigTxInput putOutpoint txi = maybePut put (sigTxiPegin txi) >> putOutpointBE (sigTxiPreviousOutpoint txi) where maybePut _ Nothing = putWord8 0x00 maybePut putter (Just x) = putWord8 0x01 >> putter x -- | A hash of all 'sigTxiPegin's and 'sigTxiPreviousOutpoint's. inputOutpointsHash :: SigTx -> Hash256 inputOutpointsHash tx = bslHash . runPutLazy $ mapM_ putOutpoint (sigTxIn tx) -- | A hash of all 'utxoAsset's and 'utxoAmount's. inputAmountsHash :: SigTx -> Hash256 inputAmountsHash tx = bslHash . runPutLazy $ mapM_ go (sigTxIn tx) where go txi = putAsset (clearAssetPrf . utxoAsset $ sigTxiTxo txi) >> putAmount (clearAmountPrf . utxoAmount $ sigTxiTxo txi) -- | A hash of all 'utxoScript' hashes. inputScriptsHash :: SigTx -> Hash256 inputScriptsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . utxoScript . sigTxiTxo) (sigTxIn tx) -- | A hash of -- -- * 'inputAmountsHash' -- * 'inputScriptsHash' inputUtxosHash :: SigTx -> Hash256 inputUtxosHash tx = bslHash . runPutLazy $ do put $ inputAmountsHash tx put $ inputScriptsHash tx -- | A hash of one utxo's -- -- * asset and amount -- * hash of its script inputUtxoHash :: UTXO -> Hash256 inputUtxoHash utxo = bslHash . runPutLazy $ do putAsset . clearAssetPrf $ utxoAsset utxo putAmount . clearAmountPrf $ utxoAmount utxo put . bslHash $ utxoScript utxo -- | A hash of all 'sigTxiSequence's. inputSequencesHash :: SigTx -> Hash256 inputSequencesHash tx = bslHash . runPutLazy $ mapM_ (putWord32be . sigTxiSequence) (sigTxIn tx) putAnnex :: Putter (Maybe BSL.ByteString) putAnnex Nothing = putWord8 0x00 putAnnex (Just annex) = putWord8 0x01 >> put (bslHash annex) -- | A hash of all 'sigTxiAnnex' hashes. inputAnnexesHash :: SigTx -> Hash256 inputAnnexesHash tx = bslHash . runPutLazy $ mapM_ (putAnnex . sigTxiAnnex) (sigTxIn tx) -- | A hash of all 'sigTxiScriptSig' hashes. inputScriptSigsHash :: SigTx -> Hash256 inputScriptSigsHash tx = bslHash . runPutLazy $ mapM_ (put . bslHash . sigTxiScriptSig) (sigTxIn tx) -- | A hash of -- -- * 'inputOutpointsHash' -- * 'inputSequencesHash' -- * 'inputAnnexesHash' -- -- Note that 'inputScriptSigsHash' is excluded. inputsHash :: SigTx -> Hash256 inputsHash tx = bslHash . runPutLazy $ do put $ inputOutpointsHash tx put $ inputSequencesHash tx put $ inputAnnexesHash tx -- | A hash of -- -- * The inputs's outpoint (including if and where the pegin came from) -- * The inputs's sequence number -- * Whether or not the input has an annex and the hash of that annex. inputHash :: SigTxInput -> Hash256 inputHash txi = bslHash . runPutLazy $ do putOutpoint txi putWord32be $ sigTxiSequence txi putAnnex $ sigTxiAnnex txi putIssuanceAssetAmount :: Putter SigTxInput putIssuanceAssetAmount txi = maybeConfPut putAsset (Asset . Explicit <$> sigTxiIssuanceAsset txi) >> maybeConfPut putAmount (clearAmountPrf . either newIssuanceAmount reissuanceAmount <$> sigTxiIssuance txi) where maybeConfPut _ Nothing = putWord8 0x00 maybeConfPut putter (Just x) = putter x -- | A hash of 'sigTxiIssuanceAsset' and either 'newIssuanceAmount' or 'reissuanceAmount' pairs as an asset-amount hash. -- -- Note that "null" amount is hashed as if it were an explicit zero. -- -- When an input has no issuance, a pair of zero bytes, @0x00 0x00@ are hashed. issuanceAssetAmountsHash :: SigTx -> Hash256 issuanceAssetAmountsHash tx = bslHash . runPutLazy $ mapM_ putIssuanceAssetAmount (sigTxIn tx) putIssuanceTokenAmount :: Putter SigTxInput putIssuanceTokenAmount txi = maybeConfPut putAsset (Asset . Explicit <$> sigTxiIssuanceToken txi) >> maybeConfPut putAmount (clearAmountPrf . either newIssuanceTokenAmount (const (Amount (Explicit 0))) <$> sigTxiIssuance txi) where maybeConfPut _ Nothing = putWord8 0x00 maybeConfPut putter (Just x) = putter x -- | A hash of 'sigTxiIssuanceToken' and 'newIssuanceTokenAmount' pairs as an asset-amount hash. -- -- Note that "null" amount is hashed as if it were an explicit zero. -- -- When an input has no issuance, a pair of zero bytes, @0x00 0x00@ are hashed. issuanceTokenAmountsHash :: SigTx -> Hash256 issuanceTokenAmountsHash tx = bslHash . runPutLazy $ mapM_ putIssuanceTokenAmount (sigTxIn tx) putIssuanceRangeProof :: Putter (Maybe Issuance) putIssuanceRangeProof issuance = put (bslHash . view (just_.under amount.prf_) $ either newIssuanceAmount reissuanceAmount <$> issuance) >> put (bslHash . view (just_.under amount.prf_) $ either newIssuanceTokenAmount (const (Amount (Explicit 0))) <$> issuance) -- | A hash of all issuance range proof hashes. issuanceRangeProofsHash :: SigTx -> Hash256 issuanceRangeProofsHash tx = bslHash . runPutLazy $ mapM_ (putIssuanceRangeProof . sigTxiIssuance) (sigTxIn tx) putIssuanceBlindingEntropy :: Putter (Maybe Issuance) putIssuanceBlindingEntropy Nothing = putWord8 0x00 putIssuanceBlindingEntropy (Just issuance) = do putWord8 0x01 put (either (const $ review (over be256) 0) reissuanceBlindingNonce $ issuance) put (either newIssuanceContractHash reissuanceEntropy $ issuance) -- | A hash of all 'reissuanceBlindingNonce' and either 'newIssuanceContractHash' or 'reissuanceEntropy' values. issuanceBlindingEntropyHash :: SigTx -> Hash256 issuanceBlindingEntropyHash tx = bslHash . runPutLazy $ mapM_ (putIssuanceBlindingEntropy . sigTxiIssuance) (sigTxIn tx) -- | A hash of -- -- * 'issuanceAssetAmountsHash' -- * 'issuanceTokenAmountsHash' -- * 'issuanceRangeProofsHash' -- * 'issuanceBlindingEntropyHash' issuancesHash :: SigTx -> Hash256 issuancesHash tx = bslHash . runPutLazy $ do put $ issuanceAssetAmountsHash tx put $ issuanceTokenAmountsHash tx put $ issuanceRangeProofsHash tx put $ issuanceBlindingEntropyHash tx -- | A hash of -- -- * If there is an issuance, the issued asset id and amount -- * If there is an issuance, the issued token id and amount -- * A hash of each of the rangeproofs -- * If there is an issuance, the contract hash and blinding/entropy fields issuanceHash :: SigTxInput -> Hash256 issuanceHash txi = bslHash . runPutLazy $ do putIssuanceAssetAmount txi putIssuanceTokenAmount txi putIssuanceRangeProof (sigTxiIssuance txi) putIssuanceBlindingEntropy (sigTxiIssuance txi) -- | A hash of -- -- * 'sigTxVersion' -- * 'sigTxLock' -- * 'inputsHash' -- * 'outputsHash' -- * 'issuancesHash' -- * 'outputSurjectionProofsHash' -- * 'inputUtxosHash' txHash :: SigTx -> Hash256 txHash tx = bslHash . runPutLazy $ do putWord32be $ sigTxVersion tx putWord32be $ sigTxLock tx put $ inputsHash tx put $ outputsHash tx put $ issuancesHash tx put $ outputSurjectionProofsHash tx put $ inputUtxosHash tx -- | Serialize transaction data without witness data. -- Mainly suitable for computing a 'txid'. putNoWitnessTx :: Putter SigTx putNoWitnessTx tx = do putWord32le $ sigTxVersion tx putWord8 0 putVarInt (V.length (sigTxIn tx)) mapM_ putInput (sigTxIn tx) putVarInt (V.length (sigTxOut tx)) mapM_ putOutput (sigTxOut tx) putWord32le $ sigTxLock tx where putVarInt x | x < 0 = error "putVarInt: negative value" | x <= 0xFC = putWord8 (fromIntegral x) | x <= 0xFFFF = putWord8 0xFD >> putWord16le (fromIntegral x) | x <= 0xFFFFFFFF = putWord8 0xFE >> putWord32le (fromIntegral x) | x <= 0xFFFFFFFFFFFFFFFF = putWord8 0xFF >> putWord64le (fromIntegral x) putInput txi = do put (opHash (sigTxiPreviousOutpoint txi)) putWord32le (flags .|. opIndex (sigTxiPreviousOutpoint txi)) putVarInt (BSL.length (sigTxiScriptSig txi)) putLazyByteString (sigTxiScriptSig txi) putWord32le (sigTxiSequence txi) putIssuance (sigTxiIssuance txi) where issuanceFlag | isJust (sigTxiIssuance txi) = 0x80000000 | otherwise = 0 peginFlag | isJust (sigTxiPegin txi) = 0x40000000 | otherwise = 0 flags = issuanceFlag .|. peginFlag putIssuance Nothing = return () putIssuance (Just (Left new)) = do put (0 :: Word256) put (newIssuanceContractHash new) putIssuanceAmount (clearAmountPrf (newIssuanceAmount new)) putIssuanceAmount (clearAmountPrf (newIssuanceTokenAmount new)) putIssuance (Just (Right re)) = do put (reissuanceBlindingNonce re) put (reissuanceEntropy re) putIssuanceAmount (clearAmountPrf (reissuanceAmount re)) putWord8 0 putIssuanceAmount (Amount (Explicit 0)) = putWord8 0 putIssuanceAmount amt = putAmount amt putOutput txo = do putAsset (clearAssetPrf (txoAsset txo)) putAmount (clearAmountPrf (txoAmount txo)) putNonce (txoNonce txo) putVarInt (BSL.length (txoScript txo)) putLazyByteString (txoScript txo) -- | Return the txid of the transaction. txid :: SigTx -> Hash256 txid = bslDoubleHash . runPutLazy . putNoWitnessTx -- | A hash of -- -- * 'tapleafVersion' -- * 'tapScriptCMR' tapleafHash :: TapEnv -> Hash256 tapleafHash tapEnv = bslHash . runPutLazy $ do put tag put tag putWord8 $ tapleafVersion tapEnv putWord8 32 put $ tapScriptCMR tapEnv where tag = bsHash (fromString "TapLeaf/elements") -- | A hash of 'tappath's. tappathHash :: TapEnv -> Hash256 tappathHash tapEnv = bslHash . runPutLazy $ mapM_ put (tappath tapEnv) -- | A hash of -- -- * 'tapleafHash' -- * 'tappathHash' -- * 'tapInternalKey' tapEnvHash :: TapEnv -> Hash256 tapEnvHash tapEnv = bslHash . runPutLazy $ do put $ tapleafHash tapEnv put $ tappathHash tapEnv put $ tapInternalKey tapEnv -- | Implementation of BIP-0341's taptweak function. taptweak :: PubKey -> Hash256 -> Maybe PubKey taptweak (PubKey internalKey) h = do guard $ toInteger internalKey < fieldOrder guard $ h0 < groupOrder a <- scale (scalar h0) g b <- decompress (Point False xkey) GE x y <- gej_normalize . snd $ gej_ge_add_ex a b return $ PubKey (fe_pack x) where xkey = fe (toInteger internalKey) h0 = integerHash256 . bslHash . runPutLazy $ do put tag put tag put (fe_pack xkey) put h tag = bsHash (fromString "TapTweak/elements") -- | Decides if an output is a fee output. -- If so, the (explicit) assetId and (explicit) value is returned. outputFee :: TxOutput -> Maybe (Hash256, Value) outputFee txo = do guard $ BSL.null (txoScript txo) Explicit assetId <- Just . view (under asset) $ txoAsset txo Explicit value <- Just . view (under amount) $ txoAmount txo return (assetId, value) -- | Adds up all 'outputFee's to build a map from (explicit) assetId to total value. totalFee :: SigTx -> Map.Map Hash256 Value totalFee tx = Map.fromListWith (+) . catMaybes . map outputFee . toList $ sigTxOut tx -- | The (explicit) asset ID for liquid BTC. -- Note that this asset is specific to the production liquid blockchain. lBtcAsset :: Hash256 lBtcAsset | result == review (over le256) 0x6f0279e9ed041c3d710a9f57d0c02928416460c4b722ae3457a11eec381c526d = result where result = calculateAsset $ calculateIssuanceEntropy (Outpoint commit 0) btcGenesisBlock bits = 0x1d00ffff extraNonce = 4 theTimes = fromString "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks" pubkey = runPutLazy $ do putWord8 4 put (review (over be256) 0x678AFDB0FE5548271967F1A67130B7105CD6A828E03909A67962E0EA1F61DEB6) put (review (over be256) 0x49F6BC3F4CEF38C4F35504E51EC112DE5C384DF7BA0B8D578A4C702B6BF11D5F) opChecksig = 0xac scriptsig = runPutLazy $ do putWord8 4 >> putWord32le bits putWord8 1 >> putWord8 extraNonce putWord8 (fromIntegral $ BSL.length theTimes) >> putLazyByteString theTimes scriptpubkey = runPutLazy $ do putWord8 (fromIntegral $ BSL.length pubkey) >> putLazyByteString pubkey putWord8 (opChecksig) genesisTxId = bslDoubleHash . runPutLazy $ do putWord32le 1 putWord8 1 put hash0 putWord32le (fromInteger (-1)) putWord8 (fromIntegral $ BSL.length scriptsig) putLazyByteString scriptsig putWord32le (fromInteger (-1)) putWord8 1 putWord64le (50 * 100000000) putWord8 (fromIntegral $ BSL.length scriptpubkey) putLazyByteString scriptpubkey putWord32le 0 btcGenesisBlock = bslDoubleHash . runPutLazy $ do putWord32le 1 put hash0 put genesisTxId putWord32le 0x495fab29 putWord32le bits putWord32le 0x7c2bac1d commit = bsHash $ networkId <> fedPegScript <> signBlockScript networkId = fromString "liquidv1" fedPegScript = fromString "745c87635b21020e0338c96a8870479f2396c373cc7696ba124e8635d41b0ea581112b678172612102675333a4e4b8fb51d9d4e22fa5a8eaced3fdac8a8cbf9be8c030f75712e6af992102896807d54bc55c24981f24a453c60ad3e8993d693732288068a23df3d9f50d4821029e51a5ef5db3137051de8323b001749932f2ff0d34c82e96a2c2461de96ae56c2102a4e1a9638d46923272c266631d94d36bdb03a64ee0e14c7518e49d2f29bc40102102f8a00b269f8c5e59c67d36db3cdc11b11b21f64b4bffb2815e9100d9aa8daf072103079e252e85abffd3c401a69b087e590a9b86f33f574f08129ccbd3521ecf516b2103111cf405b627e22135b3b3733a4a34aa5723fb0f58379a16d32861bf576b0ec2210318f331b3e5d38156da6633b31929c5b220349859cc9ca3d33fb4e68aa08401742103230dae6b4ac93480aeab26d000841298e3b8f6157028e47b0897c1e025165de121035abff4281ff00660f99ab27bb53e6b33689c2cd8dcd364bc3c90ca5aea0d71a62103bd45cddfacf2083b14310ae4a84e25de61e451637346325222747b157446614c2103cc297026b06c71cbfa52089149157b5ff23de027ac5ab781800a578192d175462103d3bde5d63bdb3a6379b461be64dad45eabff42f758543a9645afd42f6d4248282103ed1e8d5109c9ed66f7941bc53cc71137baa76d50d274bda8d5e8ffbd6e61fe9a5f6702c00fb275522103aab896d53a8e7d6433137bbba940f9c521e085dd07e60994579b64a6d992cf79210291b7d0b1b692f8f524516ed950872e5da10fb1b808b5a526dedc6fed1cf29807210386aa9372fbab374593466bc5451dc59954e90787f08060964d95c87ef34ca5bb5368ae" signBlockScript = fromString "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" ================================================ FILE: Haskell/Elements/Simplicity/Elements/Primitive.hs ================================================ {-# LANGUAGE GADTs, ScopedTypeVariables #-} -- | This module provides the Simplicity primitives specific for Elements sidechain applications. module Simplicity.Elements.Primitive ( Prim(..), primPrefix, primName , PrimEnv, primEnv, envTx, envIx, envTap, envGenesisBlock , primEnvHash , primSem -- * Re-exported Types , S, Conf, PubKey ) where import Control.Arrow ((***), (+++)) import Control.Monad ((<=<), guard) import qualified Data.ByteString.Lazy as BSL import qualified Data.List as List import Data.Maybe (fromMaybe, listToMaybe) import qualified Data.Monoid as Monoid import Data.Serialize (Get, getWord8, Putter, put, putWord8, putWord32be, putWord32le, putWord64le, runPutLazy) import qualified Data.Word import Data.Vector as Vector ((!?), length) import Lens.Family2 (to, view, under) import Lens.Family2.Stock (some_) import Simplicity.Digest import Simplicity.Elements.DataTypes import qualified Simplicity.LibSecp256k1.Schnorr as Schnorr import qualified Simplicity.LibSecp256k1.Spec as Schnorr import Simplicity.Programs.Elements import Simplicity.Programs.LibSecp256k1 import Simplicity.Serialization import Simplicity.Ty import Simplicity.Ty.Bit import Simplicity.Ty.Word just_ f = some_ f data Prim a b where Version :: Prim () Word32 LockTime :: Prim () Word32 InputPegin :: Prim Word32 (S (S Word256)) InputPrevOutpoint :: Prim Word32 (S (Word256,Word32)) InputAsset :: Prim Word32 (S (Conf Word256)) InputAmount :: Prim Word32 (S (Conf Word64)) InputScriptHash :: Prim Word32 (S Word256) InputSequence :: Prim Word32 (S Word32) InputAnnexHash :: Prim Word32 (S (S Word256)) InputScriptSigHash :: Prim Word32 (S Word256) ReissuanceBlinding :: Prim Word32 (S (S Word256)) NewIssuanceContract :: Prim Word32 (S (S Word256)) ReissuanceEntropy :: Prim Word32 (S (S Word256)) IssuanceAssetAmount :: Prim Word32 (S (S (Conf Word64))) IssuanceTokenAmount :: Prim Word32 (S (S (Conf Word64))) IssuanceAssetProof :: Prim Word32 (S Word256) IssuanceTokenProof :: Prim Word32 (S Word256) CurrentIndex :: Prim () Word32 TapleafVersion :: Prim () Word8 Tappath :: Prim Word8 (S Word256) InternalKey :: Prim () PubKey OutputAsset :: Prim Word32 (S (Conf Word256)) OutputAmount :: Prim Word32 (S (Conf Word64)) OutputNonce :: Prim Word32 (S (S (Conf Word256))) OutputScriptHash :: Prim Word32 (S Word256) OutputNullDatum :: Prim (Word32, Word32) (S (S (Either (Word2, Word256) (Either Bit Word4)))) OutputSurjectionProof :: Prim Word32 (S Word256) OutputRangeProof :: Prim Word32 (S Word256) GenesisBlockHash :: Prim () Word256 ScriptCMR :: Prim () Word256 TransactionId :: Prim () Word256 instance Eq (Prim a b) where Version == Version = True LockTime == LockTime = True InputPegin == InputPegin = True InputPrevOutpoint == InputPrevOutpoint = True InputAsset == InputAsset = True InputAmount == InputAmount = True InputScriptHash == InputScriptHash = True InputSequence == InputSequence = True InputAnnexHash == InputAnnexHash = True InputScriptSigHash == InputScriptSigHash = True ReissuanceBlinding == ReissuanceBlinding = True NewIssuanceContract == NewIssuanceContract = True ReissuanceEntropy == ReissuanceEntropy = True IssuanceAssetAmount == IssuanceAssetAmount = True IssuanceTokenAmount == IssuanceTokenAmount = True IssuanceAssetProof == IssuanceAssetProof = True IssuanceTokenProof == IssuanceTokenProof = True CurrentIndex == CurrentIndex = True TapleafVersion == TapleafVersion = True Tappath == Tappath = True InternalKey == InternalKey = True OutputAsset == OutputAsset = True OutputAmount == OutputAmount = True OutputNonce == OutputNonce = True OutputScriptHash == OutputScriptHash = True OutputNullDatum == OutputNullDatum = True OutputSurjectionProof == OutputSurjectionProof = True OutputRangeProof == OutputRangeProof = True GenesisBlockHash == GenesisBlockHash = True ScriptCMR == ScriptCMR = True TransactionId == TransactionId = True _ == _ = False primPrefix :: String primPrefix = "Elements" -- Consider deriving Show instead? primName :: Prim a b -> String primName Version = "version" primName LockTime = "lockTime" primName InputPegin = "inputPegin" primName InputPrevOutpoint = "inputPrevOutpoint" primName InputAsset = "inputAsset" primName InputAmount = "inputAmount" primName InputScriptHash = "inputScriptHash" primName InputSequence = "inputSequence" primName InputAnnexHash = "inputAnnexHash" primName InputScriptSigHash = "inputScriptSigHash" primName ReissuanceBlinding = "reissuanceBlinding" primName NewIssuanceContract = "newIssuanceContract" primName ReissuanceEntropy = "reissuanceEntropy" primName IssuanceAssetAmount = "issuanceAssetAmount" primName IssuanceTokenAmount = "issuanceTokenAmount" primName IssuanceAssetProof = "issuanceAssetProof" primName IssuanceTokenProof = "issuanceTokenProof" primName CurrentIndex = "currentIndex" primName TapleafVersion = "tapleafVersion" primName Tappath = "tappath" primName InternalKey = "internalKey" primName OutputAsset = "outputAsset" primName OutputAmount = "outputAmount" primName OutputNonce = "outputNonce" primName OutputScriptHash = "outputScriptHash" primName OutputNullDatum = "outputNullDatum" primName OutputSurjectionProof = "outputSurjectionProof" primName OutputRangeProof = "outputRangeProof" primName GenesisBlockHash = "genesisBlockHash" primName ScriptCMR = "scriptCMR" primName TransactionId = "transactionId" data PrimEnv = PrimEnv { envTx :: SigTx , envIx :: Data.Word.Word32 , envTap :: TapEnv , envGenesisBlock :: Hash256 } instance Show PrimEnv where showsPrec d env = showParen (d > 10) $ showString "primEnv " . showsPrec 11 (envTx env) . showString " " . showsPrec 11 (envIx env) . showString " " . showsPrec 11 (envTap env) primEnv :: SigTx -> Data.Word.Word32 -> TapEnv -> Hash256 -> Maybe PrimEnv primEnv tx ix tap gen | cond = Just $ PrimEnv { envTx = tx , envIx = ix , envTap = tap , envGenesisBlock = gen } | otherwise = Nothing where cond = fromIntegral ix < Vector.length (sigTxIn tx) -- | A hash of -- -- * 'envGenesisBlock' twice (this effictively makes a tagged hash). -- * 'txHash' -- * 'tapEnvHash' -- * 'envIx' -- -- Note: this is the hash used for the "sig-all" hash. primEnvHash :: PrimEnv -> Hash256 primEnvHash env = bslHash . runPutLazy $ do put $ envGenesisBlock env put $ envGenesisBlock env put $ txHash (envTx env) put $ tapEnvHash (envTap env) putWord32be $ envIx env primSem :: Prim a b -> a -> PrimEnv -> Maybe b primSem p a env = interpret p a where tx = envTx env ix = envIx env lookupInput = (sigTxIn tx !?) . fromIntegral lookupOutput = (sigTxOut tx !?) . fromIntegral cast :: Maybe a -> Either () a cast (Just x) = Right x cast Nothing = Left () element :: a -> () -> a element = const atInput :: (SigTxInput -> a) -> Word32 -> Either () a atInput f = cast . fmap f . lookupInput . fromInteger . fromWord32 atOutput :: (TxOutput -> a) -> Word32 -> Either () a atOutput f = cast . fmap f . lookupOutput . fromInteger . fromWord32 encodeHash = toWord256 . integerHash256 encodeConfidential enc (Explicit a) = Right (enc a) encodeConfidential enc (Confidential (Point by x) ()) = Left (toBit by, toWord256 . Schnorr.fe_repr $ x) encodeAsset = encodeConfidential encodeHash . view (under asset) encodeAmount = encodeConfidential (toWord64 . toInteger) . view (under amount) encodeNonce = cast . fmap (((toBit *** (toWord256 . toInteger)) +++ encodeHash) . nonce) encodeOutpoint op = (encodeHash $ opHash op, toWord32 . fromIntegral $ opIndex op) encodeKey (Schnorr.PubKey x) = toWord256 . toInteger $ x encodeNullDatum (Immediate h) = Left (toWord2 0, encodeHash h) encodeNullDatum (PushData h) = Left (toWord2 1, encodeHash h) encodeNullDatum (PushData2 h) = Left (toWord2 2, encodeHash h) encodeNullDatum (PushData4 h) = Left (toWord2 3, encodeHash h) encodeNullDatum OP1Negate = Right (Left (toBit False)) encodeNullDatum OPReserved = Right (Left (toBit True)) encodeNullDatum OP1 = Right (Right (toWord4 0x0)) encodeNullDatum OP2 = Right (Right (toWord4 0x1)) encodeNullDatum OP3 = Right (Right (toWord4 0x2)) encodeNullDatum OP4 = Right (Right (toWord4 0x3)) encodeNullDatum OP5 = Right (Right (toWord4 0x4)) encodeNullDatum OP6 = Right (Right (toWord4 0x5)) encodeNullDatum OP7 = Right (Right (toWord4 0x6)) encodeNullDatum OP8 = Right (Right (toWord4 0x7)) encodeNullDatum OP9 = Right (Right (toWord4 0x8)) encodeNullDatum OP10 = Right (Right (toWord4 0x9)) encodeNullDatum OP11 = Right (Right (toWord4 0xa)) encodeNullDatum OP12 = Right (Right (toWord4 0xb)) encodeNullDatum OP13 = Right (Right (toWord4 0xc)) encodeNullDatum OP14 = Right (Right (toWord4 0xd)) encodeNullDatum OP15 = Right (Right (toWord4 0xe)) encodeNullDatum OP16 = Right (Right (toWord4 0xf)) issuanceAmount = either newIssuanceAmount reissuanceAmount issuanceTokenAmount = either newIssuanceTokenAmount (const (Amount (Explicit 0))) interpret Version = element . return . toWord32 . toInteger $ sigTxVersion tx interpret LockTime = element . return . toWord32 . toInteger $ sigTxLock tx interpret InputPegin = return . (atInput $ cast . fmap encodeHash . sigTxiPegin) interpret InputPrevOutpoint = return . (atInput $ encodeOutpoint . sigTxiPreviousOutpoint) interpret InputAsset = return . (atInput $ encodeAsset . utxoAsset . sigTxiTxo) interpret InputAmount = return . (atInput $ encodeAmount . utxoAmount . sigTxiTxo) interpret InputScriptHash = return . (atInput $ encodeHash . bslHash . utxoScript . sigTxiTxo) interpret InputSequence = return . (atInput $ toWord32 . toInteger . sigTxiSequence) interpret InputAnnexHash = return . (atInput $ cast . fmap (encodeHash . bslHash) . sigTxiAnnex) interpret InputScriptSigHash = return . (atInput $ encodeHash . bslHash . sigTxiScriptSig) interpret ReissuanceBlinding = return . (atInput $ cast . fmap encodeHash . (either (const Nothing) (Just . reissuanceBlindingNonce) <=< sigTxiIssuance)) interpret NewIssuanceContract = return . (atInput $ cast . fmap encodeHash . (either (Just . newIssuanceContractHash) (const Nothing) <=< sigTxiIssuance)) interpret ReissuanceEntropy = return . (atInput $ cast . fmap encodeHash . (either (const Nothing) (Just . reissuanceEntropy) <=< sigTxiIssuance)) interpret IssuanceAssetAmount = return . (atInput $ cast . fmap (encodeAmount . clearAmountPrf . issuanceAmount) . sigTxiIssuance) interpret IssuanceTokenAmount = return . (atInput $ cast . fmap (encodeAmount . clearAmountPrf . issuanceTokenAmount) . sigTxiIssuance) interpret IssuanceAssetProof = return . (atInput $ encodeHash . bslHash . view (to sigTxiIssuance.just_.to issuanceAmount.under amount.prf_)) interpret IssuanceTokenProof = return . (atInput $ encodeHash . bslHash . view (to sigTxiIssuance.just_.to issuanceTokenAmount.under amount.prf_)) interpret CurrentIndex = element . return . toWord32 . toInteger $ ix interpret TapleafVersion = element . return . toWord8 . toInteger . tapleafVersion $ envTap env interpret Tappath = return . cast . fmap encodeHash . listToMaybe . flip drop (tappath (envTap env)) . fromInteger . fromWord8 interpret InternalKey = element . return . encodeKey . tapInternalKey $ envTap env interpret OutputAsset = return . (atOutput $ encodeAsset . clearAssetPrf . txoAsset) interpret OutputAmount = return . (atOutput $ encodeAmount . clearAmountPrf . txoAmount) interpret OutputNonce = return . (atOutput $ encodeNonce . txoNonce) interpret OutputScriptHash = return . (atOutput $ encodeHash . bslHash . txoScript) interpret OutputNullDatum = \(i, j) -> return . cast $ do txo <- lookupOutput . fromInteger $ fromWord32 i nullData <- txNullData $ txoScript txo return . cast . fmap (encodeNullDatum . fmap bslHash) . listToMaybe $ List.drop (fromInteger (fromWord32 j)) nullData interpret OutputSurjectionProof = return . (atOutput $ encodeHash . bslHash . view (to txoAsset.under asset.prf_)) interpret OutputRangeProof = return . (atOutput $ encodeHash . bslHash . view (to txoAmount.under amount.prf_)) interpret GenesisBlockHash = element . return . encodeHash $ envGenesisBlock env interpret ScriptCMR = element . return . encodeHash . tapScriptCMR $ envTap env interpret TransactionId = element . return . encodeHash . txid $ tx ================================================ FILE: Haskell/Indef/Simplicity/Dag.hs ================================================ {-# LANGUAGE ConstraintKinds, GADTs, RankNTypes, ScopedTypeVariables #-} -- | This module provides the 'sortDag' function for converting a Simplicity expression into an topologically sorted, DAG representation. module Simplicity.Dag ( jetDag, jetSubst , JetDag, NoJetDag , pruneSubst -- * Type annotated, open recursive Simplicity terms , TermF(..), SimplicityDag -- * Wrapped Simplicity , WrappedSimplicity, unwrap ) where import Prelude hiding (fail, drop, take) import Control.Arrow ((+++)) import Control.Applicative (empty) import Control.Monad.Trans.State (StateT(..), evalStateT) import Control.Monad.Trans.Writer (Writer, execWriter, tell) import Data.Either (isLeft) import Data.Foldable (toList) import Data.Map.Strict ((!)) import qualified Data.Map.Strict as Map import qualified Data.Set as Set import Data.Sequence (Seq) import Lens.Family2 ((&), (%~), (.~)) import Lens.Family2.State (use) import Lens.Family2.Stock (at, some_) import Simplicity.Digest import Simplicity.Delegator import Simplicity.Inference import Simplicity.JetType import Simplicity.MerkleRoot import Simplicity.Semantics import Simplicity.Tensor import Simplicity.Term -- A monad used in the implementation of linearizeDag. type LinearM j w a = StateT (Map.Map Hash256 Integer) (Writer (SimplicityDag [] () j w)) a execLinearM :: LinearM j w a -> SimplicityDag [] () j w execLinearM m = execWriter (evalStateT m Map.empty) -- Emit a new node and add insert it into the state's map. tellNode :: Hash256 -> TermF () j w Integer -> LinearM j w Integer tellNode h iterm = StateT go where go map = do tell $ [f <$> iterm] return (sz, Map.insert h sz map) where sz = toInteger (Map.size map) f i = sz - i -- transform indexes to offsets -- MapSet is a commutative, idempotent monoid. newtype MapSet a b = MapSet { getMapSet :: Map.Map a (Set.Set b) } singleton :: a -> b -> MapSet a b singleton a b = MapSet $ Map.singleton a (Set.singleton b) instance (Ord a, Ord b) => Semigroup (MapSet a b) where (MapSet ms1) <> (MapSet ms2) = MapSet $ Map.unionWith Set.union ms1 ms2 instance (Ord a, Ord b) => Monoid (MapSet a b) where mempty = MapSet Map.empty -- | A 'Simplicity' instance used with 'jetDag'. -- This instance merges identical typed Simplicity sub-expressions to create a DAG (directed acyclic graph) structure that represents the expression. -- -- A log of branches taken during evaluation is available to facilitate pruning. -- -- @'JetDag' jt@ is used to create DAGs containing jets of @'JetType' jt@ by finding subexpressions that match the jet specifications of @jt@. data JetDag jt a b = Dag { dagRoot :: IdentityRoot a b , dagMap :: Map.Map Hash256 (DagMapContents jt) -- During evaluation we log a map from the IMR of Case branches taken to the CMR of the untaken branch. -- A value of 'Right hash' is the CMR of the Right branch and it is logged when the Left branch is taken. -- A value of 'Left hash' is the CMR of the Left branch and it is logged when the Right branch is taken. , dagEval :: FastEvalLog (MapSet Hash256 (Either Hash256 Hash256)) jt a b } -- Each entry in the 'dagMap' contains an untyped term with references to the map index of its subexpressions, and the 'MatcherInfo' of some 'JetType'. data DagMapContents jt = DMC { dmcTerm :: UntypedTermF (SomeArrow jt) UntypedValue Hash256, dmcMatcher :: Maybe (SomeArrow (MatcherInfo jt)) } -- | A 'JetDag' instance that matches 'NoJets'. type NoJetDag a b = JetDag NoJets a b dmcTerm_ f dmc = (\x -> dmc {dmcTerm = x}) <$> f (dmcTerm dmc) rightCase_ f (Case a b c d l r) = Case a b c d l <$> f r rightCase_ f x = pure x leftCase_ f (Case a b c d l r) = (\x -> Case a b c d x r) <$> f l leftCase_ f x = pure x just_ f = some_ f pruneMap :: JetDag jt a b -> PrimEnv -> a -> Maybe (Map.Map Hash256 (DagMapContents jt)) pruneMap t env a = Map.foldrWithKey f (dagMap t) . getMapSet <$> fastEvalLog (dagEval t) env a where f key logs | Set.null rights = let [Left cmr] = Set.elems lefts hRoot = hiddenRoot cmr in Map.insert hRoot (DMC (uHidden cmr) Nothing) . ((at key.just_.dmcTerm_.leftCase_).~hRoot) | Set.null lefts = let [Right cmr] = Set.elems rights hRoot = hiddenRoot cmr in Map.insert hRoot (DMC (uHidden cmr) Nothing) . ((at key.just_.dmcTerm_.rightCase_).~hRoot) | otherwise = id where (lefts, rights) = Set.partition isLeft logs -- Topologically sort the 'Dag' into a list. -- Any jets found are condensed into 'uJet' nodes. linearizeDag :: (JetType jt, TyC a, TyC b) => IdentityRoot a b -> Map.Map Hash256 (DagMapContents jt) -> SimplicityDag [] () (SomeArrow jt) UntypedValue linearizeDag dagRoot dagMap = execLinearM . go . identityHash $ dagRoot where someArrowMatcher (SomeArrow jm) = SomeArrow <$> matcher jm go h = do mi <- use (at h) case mi of Just i -> return i Nothing -> case someArrowMatcher =<< dmcMatcher contents of Just jt -> tellNode h (uJet jt) Nothing -> traverse go (dmcTerm contents) >>= tellNode h where contents = dagMap ! h -- | A type isomorphic to @forall term. Simplicity term => term a b@ accessed by 'unwap'. -- Because the type @forall term. Simplicity term => term a b@ is polymorphic, it is very difficult to memoize computations that produce such a type. -- Internally `WrappedTerm` implements a co-yoneda transformation to provide a concrete hook for memoizing values. type WrappedSimplicity = WrappedTerm Simplicity data WrappedTerm simplicity a b where (:@:) :: (forall term. simplicity term => x -> term a b) -> x -> WrappedTerm simplicity a b -- | Transform a @WrappedTerm simplicity@ to a @forall term. simplicity term => term a b@. unwrap :: simplicity term => WrappedTerm simplicity a b -> term a b unwrap (f :@: x) = f x -- Not for export. -- Input DAG must be well typed. wrapWellTypedCheck :: (JetType jt, TyC a, TyC b) => SimplicityDag Seq Ty (SomeArrow jt) UntypedValue -> WrappedSimplicity a b wrapWellTypedCheck dag = k :@: dag where k x = case typeCheck x of Right pass -> pass Left e -> error $ "wrapWellTypedCheck: " ++ e -- | Find all the expressions in a term that can be replaced with jets of type @jt@. -- Because discounted jets are not transparent, this replacement will change the CMR of the term. -- In particular the CMR values passed to 'disconnect' may be different, and thus the result of -- evaluation could change in the presence of 'disconnect'. jetSubst :: forall k jt a b. (JetType jt, TyC a, TyC b) => JetDag jt a b -> WrappedSimplicity a b jetSubst t = wrapWellTypedCheck pass1 where -- The patterns should never fail as we are running type inference on terms that are already known to be well typed. -- A failure of a pattern match here suggests there is an error in the type inference engine. -- The first pass matches jets and wraps them in a uJet combinator to ensure their types are not simplified by the type inference pass, which could possibly destroy the structure of the jets. pass1 = case typeInference t (linearizeDag (dagRoot t) (dagMap t)) of Right pass -> pass Left e -> error $ "jetSubst.pass1: " ++ e -- | Performs 'jetSubst' and then evaluates the expression in the given environment and input to prune unused case branches, -- which transforms some case expressions into assertions. -- The resulting expression should always have the same CMR as the expression that 'jetSubst' would return. pruneSubst :: forall jt a b. (JetType jt, TyC a, TyC b) => JetDag jt a b -> PrimEnv -> a -> Maybe (WrappedSimplicity a b) pruneSubst t env a = wrapWellTypedCheck . pass2 <$> pruneMap pass1 env a where -- The first pass substutes jets so we can execute them using fastEval. pass1 :: JetDag jt a b pass1 = unwrap (jetSubst t) pass2 pMap = case typeInference t (linearizeDag (dagRoot pass1) pMap) of Right pass -> pass Left e -> error $ "jetDag.pass2: " ++ e -- | Given a Simplicity expression, return a type annotated 'SimplicityDag', with shared subexpressions and @'JetType' jt@ jets, that is suitable for serialization using "Simplicity.Serialization.BitString". -- -- Any discounted jets marked in the original expression are discarded and replaced with their specification. -- After the discounted jets are replaced, the Simplicity expression is scanned for jets matching the 'JetType' @jt@, which will introduce a new set of jets. -- If a different set of jets are introduced, then the 'CommitmentRoot' of the result might also not match the 'CommitmentRoot' of the input. -- This function invokes type inference to ensure that the type annotations are principle types (with type variables instantiated at unit types) -- in order to ensure maximum sharing of expressions with identical 'identityHash's. jetDag :: forall jt a b. (JetType jt, TyC a, TyC b) => JetDag jt a b -> SimplicityDag Seq Ty (SomeArrow jt) UntypedValue jetDag t = case typeInference t (linearizeDag (dagRoot pass1) (dagMap pass1)) of Right pass -> pass Left e -> error $ "jetDag.pass2: " ++ e where -- The first pass inferes principle types, so that witness values are properly truncated. pass1 :: JetDag jt a b pass1 = unwrap (jetSubst t) -- Add an entry mapping the identity root of a case combinator to the commitment root of either the left or right branch of that case expression. logRoot :: (TyC x, TyC a, TyC b, TyC c, TyC d) => (IdentityRoot (Either a b, c) d) -> (Either (CommitmentRoot (a, c) d) (CommitmentRoot (b, c) d)) -> JetDag jt (x, c) d -> JetDag jt (x, c) d logRoot ir cr ~(Dag dr dm de) = Dag dr dm (fastEvalTell (singleton (identityHash ir) (commitmentRoot +++ commitmentRoot $ cr)) de) -- These combinators are used in to assist making 'Dag' instances. mkLeaf idComb eComb uComb = Dag { dagRoot = root , dagMap = Map.singleton (identityHash root) (DMC uComb (SomeArrow <$> jm)) , dagEval = eval } where root = idComb eval = eComb jm = fastEvalMatcher eval mkUnary idComb eComb uComb t = Dag { dagRoot = root , dagMap = Map.insert (identityHash root) (DMC (uComb (identityHash (dagRoot t))) (SomeArrow <$> jm)) $ dagMap t , dagEval = eval } where root = idComb (dagRoot t) eval = eComb (dagEval t) jm = fastEvalMatcher eval mkBinary idComb eComb uComb s t = Dag { dagRoot = root , dagMap = Map.insert (identityHash root) (DMC (uComb (identityHash (dagRoot s)) (identityHash (dagRoot t))) (SomeArrow <$> jm)) $ union , dagEval = eval } where root = idComb (dagRoot s) (dagRoot t) eval = eComb (dagEval s) (dagEval t) jm = fastEvalMatcher eval union = Map.union (dagMap s) (dagMap t) -- 'Dag' instances for Simplicity expressions. instance JetType jt => Core (JetDag jt) where iden = mkLeaf iden iden uIden comp = mkBinary comp comp uComp unit = mkLeaf unit unit uUnit injl = mkUnary injl injl uInjl injr = mkUnary injr injr uInjr -- Log the branches taken by case during evaluation for pruning purposes. -- A value of 'Right hash' logs the CMR of the Right branch when the Left branch is taken. -- A value of 'Left hash' logs the CMR of the Left branch when the Right branch is taken. match s t = result where result = mkBinary match match uCase (logRoot (dagRoot result) (Right . delegatorRoot . fastEvalSem $ dagEval t) s) (logRoot (dagRoot result) (Left . delegatorRoot . fastEvalSem $ dagEval s) t) pair = mkBinary pair pair uPair take = mkUnary take take uTake drop = mkUnary drop drop uDrop instance JetType jt => Assert (JetDag jt) where assertl s h = Dag { dagRoot = root , dagMap = Map.insert (identityHash root) (DMC (uCase (identityHash (dagRoot s)) hRoot) (SomeArrow <$> jm)) . Map.insert hRoot (DMC (uHidden h) Nothing) $ dagMap s , dagEval = eval } where hRoot = hiddenRoot h root = assertl (dagRoot s) h eval = assertl (dagEval s) h jm = fastEvalMatcher eval assertr h t = Dag { dagRoot = root , dagMap = Map.insert (identityHash root) (DMC (uCase hRoot (identityHash (dagRoot t))) (SomeArrow <$> jm)) . Map.insert hRoot (DMC (uHidden h) Nothing) $ dagMap t , dagEval = eval } where hRoot = hiddenRoot h root = assertr h (dagRoot t) eval = assertr h (dagEval t) jm = fastEvalMatcher eval fail b = mkLeaf (fail b) (fail b) (uFail b) instance Witness (JetDag jt) where witness v = mkLeaf (witness v) (witness v) (uWitness (untypedValue v)) instance JetType jt => Delegate (JetDag jt) where disconnect = mkBinary disconnect disconnect uDisconnect instance JetType jt => Primitive (JetDag jt) where primitive p = mkLeaf (primitive p) (primitive p) (error "Primitives cannot be directly serialized. They can only be part of jet specifications.") -- Existing jets are discarded when converting to a dag. They are reconstructed using a jet matcher. instance JetType jt => Jet (JetDag jt) where jet w t = Dag { dagRoot = root -- We make this identityHash point to the same subexpression as the root of t. -- This lets the jet matcher match on nodes marked as jets, but otherwise the JetDag ignores marked jets. , dagMap = Map.insert (identityHash root) (DMC (dmcTerm (map ! identityHash (dagRoot dag))) (SomeArrow <$> jm)) $ map , dagEval = eval } where dag = t root = jet w t eval = jet w t jm = fastEvalMatcher eval map = dagMap dag instance JetType jt => Simplicity (JetDag jt) where ================================================ FILE: Haskell/Indef/Simplicity/Inference.hs ================================================ {-# LANGUAGE DeriveTraversable, FlexibleInstances, GADTs, MultiParamTypeClasses, RankNTypes, ScopedTypeVariables #-} -- | This module defines a type for Simplicity DAGs (directed acyclic graph) as well as a type checking function to convert such a DAG into a well-typed Simplicity expression. -- The expected progression is to first run 'typeInference' on an untyped Simplicity DAG. -- Then use the inferred type annotations to transform witness data into 'UntypedValue' using 'witnessData'. -- Finally use 'typeCheck' to create a Simplicity expression. module Simplicity.Inference ( -- * Type checking untyped Simplicity typeInference , typeCheck -- * Simplicity with type annotations , TermF(..) , UntypedTermF , SimplicityDag -- * optical (like) accessors for TermF data. , tyAnnotation, witnessData, jetData -- * Constructors for 'UntypedTermF'. , uIden, uUnit, uInjl, uInjr , uTake, uDrop, uComp, uCase, uPair, uDisconnect , uHidden, uWitness, uJet, uFail ) where import Prelude hiding (fail, take, drop) import Control.Arrow ((+++), left) import Control.Monad (foldM) import Control.Monad.Trans (lift) import Control.Monad.Trans.Except (ExceptT, catchE, runExceptT, throwE) import Control.Unification (Fallible(..), UTerm(..), (=:=), applyBindingsAll, freeVar, unfreeze) import Control.Unification.STVar (STBinding, STVar, runSTBinding) import Control.Unification.Types (UFailure) import Data.Functor.Compose (Compose(..)) import Data.Functor.Fixedpoint (Fix(..)) import Data.Sequence (Seq, (|>), (!?), empty, index, mapWithIndex, ViewR(..), viewr) import Data.Traversable (foldMapDefault, fmapDefault) import Data.Type.Equality ((:~:)(Refl)) import qualified Data.Vector.Unboxed as UV import Simplicity.Digest import Simplicity.JetType import Simplicity.MerkleRoot import Simplicity.Primitive import Simplicity.Term import Simplicity.Ty import Simplicity.Ty.Word -- (UTy a) is the type of Simplicity types augmented with unification variables, a. type UTy v = UTerm TyF v -- Convert a Simplicity type with unification variables into a regular Ty. -- Any remaining unification variables are turned into unit types, hence the name 'unital'. unital :: UTy v -> Ty unital (UVar _) = one unital (UTerm t) = Fix (unital <$> t) -- | An open recursive type for untyped Simplicity terms with type annotations. -- The 'ty' parameter holds the typing annotations, which can be, for example, 'Ty', or @()@ for untyped Simplicity terms without annotations. -- The 'j' parameter holds the data held by 'Jet' nodes. -- The 'w' parameter holds the data held by 'Witness' nodes. -- The 'a' parameter holds the (open) recursive subexpressions. data TermF ty j w a = Iden ty | Unit ty | Injl ty ty ty a | Injr ty ty ty a | Take ty ty ty a | Drop ty ty ty a | Comp ty ty ty a a | Case ty ty ty ty a a | Pair ty ty ty a a | Disconnect ty ty ty ty a a | Hidden Hash256 | Witness ty ty w | Jet j deriving (Functor, Foldable, Traversable) instance (Show ty, Show j, Show w, Show a) => Show (TermF ty j w a) where showsPrec p (Iden a) = showParen (10 < p) $ showString "Iden " . showsPrec 11 a showsPrec p (Unit a) = showParen (10 < p) $ showString "Unit " . showsPrec 11 a showsPrec p (Injl a b c t) = showParen (10 < p) $ showString "Injl " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 t showsPrec p (Injr a b c t) = showParen (10 < p) $ showString "Injr " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 t showsPrec p (Take a b c t) = showParen (10 < p) $ showString "Take " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 t showsPrec p (Drop a b c t) = showParen (10 < p) $ showString "Drop " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 t showsPrec p (Comp a b c s t) = showParen (10 < p) $ showString "Comp " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 s . showString " " . showsPrec 11 t showsPrec p (Case a b c d s t) = showParen (10 < p) $ showString "Case " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 d . showString " " . showsPrec 11 s . showString " " . showsPrec 11 t showsPrec p (Pair a b c s t) = showParen (10 < p) $ showString "Pair " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 s . showString " " . showsPrec 11 t showsPrec p (Disconnect a b c d s t) = showParen (10 < p) $ showString "Disconnect " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 c . showString " " . showsPrec 11 d . showString " " . showsPrec 11 s . showString " " . showsPrec 11 t showsPrec p (Hidden h) = showParen (10 < p) $ showString "Hidden " . showsPrec 11 h showsPrec p (Witness a b w) = showParen (10 < p) $ showString "Witness " . showsPrec 11 a . showString " " . showsPrec 11 b . showString " " . showsPrec 11 w showsPrec p (Jet j) = showParen (10 < p) $ showString "Jet " . showsPrec 11 j -- 'FocusTy j w a ty' is isomorphic to 'TermF ty j w a'. Its purpose is to provide functor instances to 'TermF's ty parameter. newtype FocusTy j w a ty = FocusTy { unFocusTy :: TermF ty j w a } instance Functor (FocusTy j w a) where fmap = fmapDefault instance Foldable (FocusTy j w a) where foldMap = foldMapDefault instance Traversable (FocusTy j w a) where traverse f (FocusTy (Iden a)) = FocusTy . Iden <$> f a traverse f (FocusTy (Unit a)) = FocusTy . Unit <$> f a traverse f (FocusTy (Injl a b c x)) = fmap FocusTy $ Injl <$> f a <*> f b <*> f c <*> pure x traverse f (FocusTy (Injr a b c x)) = fmap FocusTy $ Injr <$> f a <*> f b <*> f c <*> pure x traverse f (FocusTy (Take a b c x)) = fmap FocusTy $ Take <$> f a <*> f b <*> f c <*> pure x traverse f (FocusTy (Drop a b c x)) = fmap FocusTy $ Drop <$> f a <*> f b <*> f c <*> pure x traverse f (FocusTy (Comp a b c x y)) = fmap FocusTy $ Comp <$> f a <*> f b <*> f c <*> pure x <*> pure y traverse f (FocusTy (Case a b c d x y)) = fmap FocusTy $ Case <$> f a <*> f b <*> f c <*> f d <*> pure x <*> pure y traverse f (FocusTy (Pair a b c x y)) = fmap FocusTy $ Pair <$> f a <*> f b <*> f c <*> pure x <*> pure y traverse f (FocusTy (Disconnect a b c d x y)) = fmap FocusTy $ Disconnect <$> f a <*> f b <*> f c <*> f d <*> pure x <*> pure y traverse f (FocusTy (Hidden x)) = pure (FocusTy (Hidden x)) traverse f (FocusTy (Witness a b x)) = fmap FocusTy $ Witness <$> f a <*> f b <*> pure x traverse f (FocusTy (Jet j)) = pure (FocusTy (Jet j)) -- | A traversal of the type annotations of 'TermF'. tyAnnotation :: Applicative f => (ty0 -> f ty1) -> TermF ty0 j w a -> f (TermF ty1 j w a) tyAnnotation f = fmap unFocusTy . traverse f . FocusTy -- | A Traversal-like operation for 'TermF' that can be use to modify witness data in the context of witnesses type annotations. -- The 'witnessData' is to let you take @TermF Ty j (Vector Bool) a@ values and turn them into @TermF Ty j UntypedValue a@ values -- by parsing witness data stored as bit vector into Simplicity values after type inference. -- Alternatively, 'witnessData' can help build a @TermF Ty j () a -> m Bool -> m (TermF Ty j Untyped a)@ function that parses witness data -- after type inference from a 'Bool' stream accessible via a monadic effect. witnessData :: Applicative m => (ty -> w0 -> m w1) -> TermF ty j w0 a -> m (TermF ty j w1 a) witnessData f (Iden a) = pure $ Iden a witnessData f (Unit a) = pure $ Unit a witnessData f (Injl a b c x) = pure $ Injl a b c x witnessData f (Injr a b c x) = pure $ Injr a b c x witnessData f (Take a b c x) = pure $ Take a b c x witnessData f (Drop a b c x) = pure $ Drop a b c x witnessData f (Comp a b c x y) = pure $ Comp a b c x y witnessData f (Case a b c d x y) = pure $ Case a b c d x y witnessData f (Pair a b c x y) = pure $ Pair a b c x y witnessData f (Disconnect a b c d x y) = pure $ Disconnect a b c d x y witnessData f (Hidden x) = pure $ Hidden x witnessData f (Witness a b x) = Witness a b <$> f b x witnessData f (Jet p) = pure $ Jet p -- | An (affine) traversal for the 'Jet' values of a 'TermF'. jetData :: Applicative f => (j0 -> f j1) -> TermF ty j0 w a -> f (TermF ty j1 w a) jetData f (Iden a) = pure $ Iden a jetData f (Unit a) = pure $ Unit a jetData f (Injl a b c x) = pure $ Injl a b c x jetData f (Injr a b c x) = pure $ Injr a b c x jetData f (Take a b c x) = pure $ Take a b c x jetData f (Drop a b c x) = pure $ Drop a b c x jetData f (Comp a b c x y) = pure $ Comp a b c x y jetData f (Case a b c d x y) = pure $ Case a b c d x y jetData f (Pair a b c x y) = pure $ Pair a b c x y jetData f (Disconnect a b c d x y) = pure $ Disconnect a b c d x y jetData f (Hidden x) = pure $ Hidden x jetData f (Witness a b x) = pure $ Witness a b x jetData f (Jet j) = Jet <$> f j -- InferenceError holds the possible errors that can occur during the 'inference' step. data InferenceError s = UnificationFailure (UFailure TyF (STVar s TyF)) | IndexError Int Integer | HiddenError | Overflow deriving Show instance Fallible TyF (STVar s TyF) (InferenceError s) where occursFailure v t = UnificationFailure (occursFailure v t) mismatchFailure t1 t2 = UnificationFailure (mismatchFailure t1 t2) -- | A type synonym for Simplicity terms without type annotations. type UntypedTermF j w a = TermF () j w a -- Constructors for untyped 'TermF'. uIden :: UntypedTermF j w a uIden = Iden () uUnit :: UntypedTermF j w a uUnit = Unit () uInjl :: a -> UntypedTermF j w a uInjl = Injl () () () uInjr :: a -> UntypedTermF j w a uInjr = Injr () () () uTake :: a -> UntypedTermF j w a uTake = Take () () () uDrop :: a -> UntypedTermF j w a uDrop = Drop () () () uComp :: a -> a -> UntypedTermF j w a uComp = Comp () () () uCase :: a -> a -> UntypedTermF j w a uCase = Case () () () () uPair :: a -> a -> UntypedTermF j w a uPair = Pair () () () uDisconnect :: a -> a -> UntypedTermF j w a uDisconnect = Disconnect () () () () uHidden :: Hash256 -> UntypedTermF j w a uHidden = Hidden uWitness :: w -> UntypedTermF j w a uWitness = Witness () () uJet :: j -> UntypedTermF j w a uJet = Jet -- | :TODO: NOT YET IMPLEMENTED uFail :: Block512 -> UntypedTermF j w a uFail = error "uFail: :TODO: NOT YET IMPLEMENTED" -- Given a @'UTy' v@ annotated Simplicity 'TermF', return the implied input and output types given the annotations. termFArrow :: Monad m => TermF (UTy v) (SomeArrow j) w a -> ExceptT (InferenceError s) m (UTy v, UTy v) termFArrow (Iden a) = return (a, a) termFArrow (Unit a) = return (a, UTerm One) termFArrow (Injl a b c _) = return (a, UTerm (Sum b c)) termFArrow (Injr a b c _) = return (a, UTerm (Sum b c)) termFArrow (Take a b c _) = return (UTerm (Prod a b), c) termFArrow (Drop a b c _) = return (UTerm (Prod a b), c) termFArrow (Comp a b c _ _) = return (a, c) termFArrow (Case a b c d _ _) = return (UTerm (Prod (UTerm (Sum a b)) c), d) termFArrow (Pair a b c _ _) = return (a, UTerm (Prod b c)) termFArrow (Disconnect a b c d _ _) = return (a, UTerm (Prod b d)) termFArrow (Hidden _) = throwE HiddenError termFArrow (Witness a b _) = return (a, b) termFArrow (Jet (SomeArrow j)) = return (unfreeze (unreflect ra), unfreeze (unreflect rb)) where (ra, rb) = reifyArrow j -- | Simplicity terms with explicit sharing of subexpressions to form a topologically sorted DAG (directed acyclic graph). -- -- Every node in an Simplicity expression is an element of a finitary container with indices that reference the relative locations of their child subexpressions within that container. -- This reference is the difference in positions between referring node's position and the referred node's position. -- The number @1@ is a reference to the immediately preceding node. The number @0@ is not allowed as it would imply a node is referring to itself. -- -- The last element of the vector is the root of the Simplicity expression DAG. -- -- Invariant: -- -- @ -- 0 \<= /i/ && /i/ \< 'Foldable.length' /v/ ==> 'Foldable.all' (\\x -> 0 < x && x <= /i/) ('Foldable.toList' /v/ '!!' /i/) -- @ type SimplicityDag f ty j w = f (TermF ty j w Integer) -- 'inference' takes a 'SimplicityDag' and adds suitiable type annotations to the nodes in the DAG as well as unification constraints. -- This can cause unification failures, however the occurs check isn't performed in this step. -- This function also checks that the provided DAG is sorted in topological order. inference :: Foldable f => SimplicityDag f x (SomeArrow j) w -> ExceptT (InferenceError s) (STBinding s) (Seq (TermF (UTy (STVar s TyF)) (SomeArrow j) w Int)) inference = foldM loop empty where tyWord256 = unreflect (reify :: TyReflect Word256) loop :: Seq (TermF (UTy (STVar s TyF)) (SomeArrow j) w Int) -> TermF x (SomeArrow j) w Integer -> ExceptT (InferenceError s) (STBinding s) (Seq (TermF (UTy (STVar s TyF)) (SomeArrow j) w Int)) loop output node = (output |>) <$> go node where fresh :: ExceptT (InferenceError s) (STBinding s) (UTy (STVar s TyF)) fresh = UVar <$> lift freeVar lenOutput = length output lookup i | i <= toInteger (maxBound :: Int) = maybe (throwE (IndexError lenOutput i)) return (output !? (lenOutput - fromInteger i)) | otherwise = throwE Overflow go (Iden _) = Iden <$> fresh go (Unit _) = Unit <$> fresh go (Injl _ _ _ it) = do (a,b) <- termFArrow =<< lookup it c <- fresh return (Injl a b c (fromInteger it)) go (Injr _ _ _ it) = do (a,c) <- termFArrow =<< lookup it b <- fresh return (Injr a b c (fromInteger it)) go (Take _ _ _ it) = do (a,c) <- termFArrow =<< lookup it b <- fresh return (Take a b c (fromInteger it)) go (Drop _ _ _ it) = do (b,c) <- termFArrow =<< lookup it a <- fresh return (Drop a b c (fromInteger it)) go (Comp _ _ _ is it) = do (a,b0) <- termFArrow =<< lookup is (b1,c) <- termFArrow =<< lookup it b <- b0 =:= b1 return (Comp a b c (fromInteger is) (fromInteger it)) go (Case _ _ _ _ is it) = do a <- fresh b <- fresh c <- fresh d <- fresh ignoreHidden $ do (ac,d0) <- termFArrow =<< lookup is _ <- UTerm (Prod a c) =:= ac _ <- d =:= d0 return () ignoreHidden $ do (bc,d1) <- termFArrow =<< lookup it _ <- UTerm (Prod b c) =:= bc _ <- d =:= d1 return () return (Case a b c d (fromInteger is) (fromInteger it)) where ignoreHidden m = catchE m handler where handler HiddenError = return () handler e = throwE e go (Pair _ _ _ is it) = do (a0,b) <- termFArrow =<< lookup is (a1,c) <- termFArrow =<< lookup it a <- a0 =:= a1 return (Pair a b c (fromInteger is) (fromInteger it)) go (Disconnect _ _ _ _ is it) = do (aw,bc) <- termFArrow =<< lookup is (c,d) <- termFArrow =<< lookup it a <- fresh b <- fresh _ <- UTerm (Prod (unfreeze tyWord256) a) =:= aw _ <- UTerm (Prod b c) =:= bc return (Disconnect a b c d (fromInteger is) (fromInteger it)) go (Hidden h) = pure (Hidden h) go (Witness _ _ w) = Witness <$> fresh <*> fresh <*> pure w go (Jet j) = pure (Jet j) -- Given the output of 'inference', execute unification and return the container of type annotated Simplicity nodes. -- Any free type variables left over after unification are instantiated at the unit type. -- Errors, such as unification errors or occurs errors are returned as 'String's. runUnification :: Traversable t => (forall s. ExceptT (InferenceError s) (STBinding s) (t (TermF (UTy (STVar s TyF)) j w i))) -> Either String (t (TermF Ty j w i)) runUnification mv = runSTBinding $ left show <$> runExceptT (bindV mv) where bindV :: Traversable t => ExceptT (InferenceError s) (STBinding s) (t (TermF (UTy (STVar s TyF)) j w i)) -> ExceptT (InferenceError s) (STBinding s) (t (TermF Ty j w i)) bindV mv = do v <- mv bv <- applyBindingsAll (Compose (FocusTy <$> v)) return . fmap unFocusTy . getCompose $ unital <$> bv -- | Given a 'SimplicityDag', throw away the existing type annotations, if any, and run type inference to compute a new set of type annotations. -- The Simplicity types, @a@ and @b@, provides further constraints for the Simplicity expression for the 'SimplicityDag'. -- If type inference fails, such as a unification error or an occurs error, return an error message. typeInference :: forall proxy a b f x j w. (Foldable f, TyC a, TyC b) => proxy a b -> SimplicityDag f x (SomeArrow j) w -> Either String (SimplicityDag Seq Ty (SomeArrow j) w) typeInference p v = fmap (fmap toInteger) <$> runUnification inferenced where inferenced :: forall s. ExceptT (InferenceError s) (STBinding s) (Seq (TermF (UTy (STVar s TyF)) (SomeArrow j) w Int)) inferenced = do ev <- inference v _ <- case viewr ev of EmptyR -> return () _ :> end -> do (a1, b1) <- termFArrow end let (a0, b0) = reifyArrow p _ <- a1 =:= unfreeze (unreflect a0) _ <- b1 =:= unfreeze (unreflect b0) return () return ev -- Note: we could make a variant of this function taking a @SimplicityDag Seq Ty (SomeArrow JetSpec) UntypedValue@ argument if that is needed, where -- -- @ -- newtype JetSpec a b = JetSpec (forall term. (Assert term, Primitive term) => term a b) -- @ -- -- | Transform a well-typed-annotated 'SimplicityDag' into a Simplicity expression of a specified type. -- -- 'Jet' nodes must be contain @'SomeArrow' 'jt'@ value for a 'JetType'. -- 'Witness' nodes must contain 'UntypedValue's. -- -- If type checking fails, return an error message. -- -- Note: The one calling 'typeCheck' determines the input and output Simplicity types of the resulting Simplicity expression. -- They are __not__ inferered from the DAG input. -- Instead the types @a@ and @b@ are used as constraints during type inference. typeCheck :: forall term jt a b. (Simplicity term, JetType jt, TyC a, TyC b) => SimplicityDag Seq Ty (SomeArrow jt) UntypedValue -> Either String (term a b) typeCheck s = result where resultProxy = let Right x = result in undefined `asTypeOf` x result = case viewr typeCheckedDag of _ :> Right (SomeArrow t) -> maybe (error "Simplicity.Inference.typeCheck: unexpected mismatched type at end.") return $ do let (ra, rb) = reifyArrow t let (a0, b0) = reifyArrow resultProxy Refl <- equalTyReflect ra a0 Refl <- equalTyReflect rb b0 return t _ :> Left s -> Left s EmptyR -> Left "Simplicity.Inference.typeCheck: empty vector input." where assertEqualTyReflect a b = maybe err Right (equalTyReflect a b) where err = Left "Simplicity.Inference.typeCheck: unexpected mismatched type" typeCheckedDag = mapWithIndex (\i -> left (++ " at index " ++ show i ++ ".") . typeCheckTermIx i) s typeCheckTermIx :: Int -> TermF Ty (SomeArrow jt) UntypedValue Integer -> Either String (SomeArrow term) typeCheckTermIx i = typeCheckTerm . fmap fromInteger where lookup j = index typeCheckedDag (i - j) typeCheckTerm (Iden a) = case reflect a of SomeTy ra -> return (someArrowR ra ra iden) typeCheckTerm (Unit a) = case reflect a of SomeTy ra -> return (someArrowR ra OneR unit) typeCheckTerm (Injl a b c it) = case (reflect a, reflect b, reflect c) of (SomeTy ra, SomeTy rb, SomeTy rc) -> do SomeArrow t <- lookup it let (ra0, rb0) = reifyArrow t Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rb rb0 return (someArrowR ra (SumR rb rc) (injl t)) typeCheckTerm (Injr a b c it) = case (reflect a, reflect b, reflect c) of (SomeTy ra, SomeTy rb, SomeTy rc) -> do SomeArrow t <- lookup it let (ra0, rc0) = reifyArrow t Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rc rc0 return (someArrowR ra (SumR rb rc) (injr t)) typeCheckTerm (Take a b c it) = case (reflect a, reflect b, reflect c) of (SomeTy ra, SomeTy rb, SomeTy rc) -> do SomeArrow t <- lookup it let (ra0, rc0) = reifyArrow t Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rc rc0 return (someArrowR (ProdR ra rb) rc (take t)) typeCheckTerm (Drop a b c it) = case (reflect a, reflect b, reflect c) of (SomeTy ra, SomeTy rb, SomeTy rc) -> do SomeArrow t <- lookup it let (rb0, rc0) = reifyArrow t Refl <- assertEqualTyReflect rb rb0 Refl <- assertEqualTyReflect rc rc0 return (someArrowR (ProdR ra rb) rc (drop t)) typeCheckTerm (Comp a b c is it) = case (reflect a, reflect b, reflect c) of (SomeTy ra, SomeTy rb, SomeTy rc) -> do SomeArrow s <- lookup is SomeArrow t <- lookup it let (ra0, rb0) = reifyArrow s let (rb1, rc1) = reifyArrow t Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rb rb0 Refl <- assertEqualTyReflect rb rb1 Refl <- assertEqualTyReflect rc rc1 return (someArrowR ra rc (comp s t)) typeCheckTerm (Case a b c d is it) | Hidden hs <- index s (i - is) = case (reflect a, reflect b, reflect c, reflect d) of (SomeTy ra, SomeTy rb, SomeTy rc, SomeTy rd) -> do SomeArrow t <- lookup it let (rbc0, rd0) = reifyArrow t case rbc0 of ProdR rb0 rc0 -> do Refl <- assertEqualTyReflect rb rb0 Refl <- assertEqualTyReflect rc rc0 Refl <- assertEqualTyReflect rd rd0 return (someArrowR (ProdR (SumR ra rb) rc) rd (assertr hs t)) | Hidden ht <- index s (i - it) = case (reflect a, reflect b, reflect c, reflect d) of (SomeTy ra, SomeTy rb, SomeTy rc, SomeTy rd) -> do SomeArrow s <- lookup is let (rac0, rd0) = reifyArrow s case rac0 of ProdR ra0 rc0 -> do Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rc rc0 Refl <- assertEqualTyReflect rd rd0 return (someArrowR (ProdR (SumR ra rb) rc) rd (assertl s ht)) | otherwise = case (reflect a, reflect b, reflect c, reflect d) of (SomeTy ra, SomeTy rb, SomeTy rc, SomeTy rd) -> do SomeArrow s <- lookup is SomeArrow t <- lookup it let (rac0, rd0) = reifyArrow s let (rbc1, rd1) = reifyArrow t case (rac0, rbc1) of (ProdR ra0 rc0, ProdR rb1 rc1) -> do Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rb rb1 Refl <- assertEqualTyReflect rc rc0 Refl <- assertEqualTyReflect rc rc1 Refl <- assertEqualTyReflect rd rd0 Refl <- assertEqualTyReflect rd rd1 return (someArrowR (ProdR (SumR ra rb) rc0) rd0 (match s t)) typeCheckTerm (Pair a b c is it) = case (reflect a, reflect b, reflect c) of (SomeTy ra, SomeTy rb, SomeTy rc) -> do SomeArrow s <- lookup is SomeArrow t <- lookup it let (ra0, rb0) = reifyArrow s let (ra1, rc1) = reifyArrow t Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect ra ra1 Refl <- assertEqualTyReflect rb rb0 Refl <- assertEqualTyReflect rc rc1 return (someArrowR ra0 (ProdR rb rc) (pair s t)) typeCheckTerm (Disconnect a b c d is it) = case (reflect a, reflect b, reflect c, reflect d) of (SomeTy ra, SomeTy rb, SomeTy rc, SomeTy rd) -> do SomeArrow s <- lookup is SomeArrow t <- lookup it let (rc1, rd1) = reifyArrow t case reifyArrow s of ((ProdR rw0 ra0), (ProdR rb0 rc0)) -> do Refl <- assertEqualTyReflect (reify :: TyReflect Word256) rw0 Refl <- assertEqualTyReflect ra ra0 Refl <- assertEqualTyReflect rb rb0 Refl <- assertEqualTyReflect rc rc0 Refl <- assertEqualTyReflect rc rc1 Refl <- assertEqualTyReflect rd rd1 return (someArrowR ra (ProdR rb rd) (disconnect s t)) typeCheckTerm (Hidden _) = Left "Simplicity.Inference.typeCheck: encountered illegal use of Hidden node" typeCheckTerm (Witness a b w) = case (reflect a, reflect b) of (SomeTy ra, SomeTy rb) -> do vb <- maybe err return $ castUntypedValue w return (someArrowR ra rb (witness vb)) where err = Left "Simplicity.Inference.typeCheck: decode error in Witness value" typeCheckTerm (Jet (SomeArrow j)) = return . SomeArrow $ asJet j ================================================ FILE: Haskell/Indef/Simplicity/JetType.hs ================================================ {-# LANGUAGE EmptyCase, EmptyDataDecls, EmptyDataDeriving, FlexibleContexts, TypeFamilies #-} -- | This modules defines the 'JetType' class, and provides the trivial empty instance of this class, 'NoJets'. module Simplicity.JetType ( JetType(..) , asJet , NoJets(..) -- * Reexports , Weight ) where import Control.Arrow (runKleisli) import Control.Monad.Trans.Reader (runReaderT) import Data.Kind (Type) import Data.Void (Void, vacuous) import Simplicity.Primitive import Simplicity.Serialization import Simplicity.Tensor import Simplicity.Term import Simplicity.Weight -- | A 'JetType' is a data structure that represents a set of known jets. -- Every known jet has a 'specification' which is defined by some Simplicity expression (see 'Jet'). -- -- Each 'JetType' has an associated 'MatcherInfo' type that interprets Simplicity with jet expressions to -- summarise a set of data needed to determine what jet, if any, a particular expression is. -- Typically the 'MatcherInfo' consists of a 'Simplicity.MerkleRoot.IdentityRoot' value. -- The 'matcher' function uses this interpretation to decide which known jet, a given Simplicity expression is, if any. -- -- The 'implemenation' must match the 'specification' and is designed to be directly implemented using jets. -- -- 'putJetBit' and 'getJetBit' provide canonical serialization and deserialization methods for the 'JetType' -- (see "Simplicity.Serialization"). -- -- We require that given an expression @e :: forall term. ('Assert' term, 'Primitive' term) => term a b@, -- -- if -- -- @ -- 'matcher' e === Just j -- @ -- -- then -- -- @ -- 'Simplicity.Semantics.sem' ('specification' j) === 'Simplicity.Semantics.sem' e -- @ -- -- The jetted 'implementation' is required to match the specification. -- -- @ -- 'implementation' j === 'Simplicity.Semantics.sem' ('specification' j) -- @ -- -- We also require that serialized values can be deserialized: -- -- @ -- 'Simplicity.Serialization.evalStreamWithError' 'getJetBit' l === Right ('SomeArrow' j) -- @ -- -- if and only if -- -- @ -- 'putJetBit' j === (l ++) -- @ class (Assert (MatcherInfo jt), Primitive (MatcherInfo jt)) => JetType jt where type MatcherInfo jt :: Type -> Type -> Type specification :: (TyC a, TyC b, Assert term, Primitive term) => jt a b -> term a b implementation :: (TyC a, TyC b) => jt a b -> PrimEnv -> a -> Maybe b implementation jt = flip $ runReaderT . runKleisli (specification jt) matcher :: (TyC a, TyC b) => MatcherInfo jt a b -> Maybe (jt a b) getJetBit :: Monad m => m Void -> m Bool -> m (SomeArrow jt) putJetBit :: (TyC a, TyC b) => jt a b -> DList Bool jetCost :: (TyC a, TyC b) => jt a b -> Weight -- | Generate a 'Jet' using the 'jetCost' and 'specification' of a 'JetType'. asJet :: (JetType jt, Jet term, TyC a, TyC b) => jt a b -> term a b asJet jt = jet (jetCost jt) (specification jt) -- | 'NoJets' is an empty type that is an instance of 'JetType'. -- It allows one not to match any jets at all. data NoJets a b deriving (Eq, Show) instance JetType NoJets where type MatcherInfo NoJets = Unit specification noJets = case noJets of {} matcher _ = Nothing getJetBit abort next = vacuous abort putJetBit noJets = case noJets of {} jetCost noJets = case noJets of {} ================================================ FILE: Haskell/Indef/Simplicity/Primitive.hsig ================================================ signature Simplicity.Primitive where import Data.Serialize (Get, Putter) import Data.Word (Word8) import Simplicity.Serialization (DList) import Simplicity.Ty data Prim a b primPrefix :: String primName :: Prim a b -> String data PrimEnv primSem :: Prim a b -> a -> PrimEnv -> Maybe b ================================================ FILE: Haskell/Indef/Simplicity/Semantics.hs ================================================ -- | This module provides the functional semantics of the full 'Simplicity' language. -- The 'Semantics' arrow is an instance of the 'Simplicity' class and 'sem' evaluates terms of the full Simplicity language. -- The 'fastEval' implements the evaluation using the jets from the specified 'JetType'. module Simplicity.Semantics ( Semantics, sem , FastEval, fastEval , FastEvalLog(..), fastEvalLog, fastEvalTell , PrimEnv ) where import Prelude hiding (drop, take, fail) import Control.Arrow (Kleisli(..), first) import Control.Monad.Reader (ReaderT(..)) import Control.Monad.Trans.Class (lift) import Control.Monad.Trans.Writer (WriterT(..), tell) import Simplicity.Delegator.Impl import Simplicity.JetType import Simplicity.Primitive import Simplicity.Term -- | Adds logging to the 'Semantics' for Simplicity. -- -- The @log@ ought to be a commutative and idempontent monoid. -- -- Currently logging is used to implement pruning. type SemanticsLog log a b = Delegator (Kleisli (WriterT log (ReaderT PrimEnv Maybe))) a b -- | Execute the functional semantics of the full Simplicity language with delegation. -- If successful, return the log in addition to the output value. semLog :: SemanticsLog log a b -> PrimEnv -> a -> Maybe (b, log) semLog = flip . ((runReaderT . runWriterT) .) . runKleisli . runDelegator -- | Add data to the 'SemanticsLog' of a Simplicity expression. -- -- The @log@ ought to be a commutative and idempontent monoid. semTell :: Monoid log => log -> SemanticsLog log a b -> SemanticsLog log a b semTell msg ~(Delegator rs (Kleisli fs)) = Delegator rs (Kleisli $ \a -> tell msg >> fs a) -- | The functional semantics of the full Simplicity language consists of -- -- * Partial effect via the 'Maybe' effect. -- -- * Environment effects via the 'Control.Monad.Reader.Reader' effect for primitives to access the 'PrimEnv'. -- -- * Delegation via the 'Delegator' helper. type Semantics a b = SemanticsLog () a b -- | @ -- sem :: (forall term. Simplicity term => term a b) -> PrimEnv -> a -> Maybe b -- @ -- -- Execute the functional semantics of the full Simplicity language with delegation. sem :: SemanticsLog () a b -> PrimEnv -> a -> Maybe b sem = flip . ((runReaderT . fmap fst . runWriterT) .) . runKleisli . runDelegator instance Primitive p => Primitive (Delegator p) where primitive p = Delegator (primitive p) (primitive p) instance Jet p => Jet (Delegator p) where jet w t = Delegator (jet w t) (jet w t) instance (Jet p, Witness p) => Simplicity (Delegator p) where -- | A Simplicity instance for 'fastEval' type FastEval jt a b = FastEvalLog () jt a b -- | 'fastEval' optimizes Simplicity evaluation using jets. -- Unlike using 'Simplicity.Dag.jetSubst', 'fastEval' will not modify the commitment roots and therefore will always return the same -- result as 'sem' in the presence of 'disconnect'. -- -- @ -- 'fastEval' t === 'sem' t -- @ fastEval :: FastEval jt a b -> PrimEnv -> a -> Maybe b fastEval = sem . fastEvalSem -- | A Simplicity instance for 'fastEval' data FastEvalLog log jt a b = FastEvalLog { fastEvalSem :: SemanticsLog log a b , fastEvalMatcher :: Maybe (MatcherInfo jt a b) } -- | Add data to the 'FastEvalLog' of a Simplicity expression. -- -- The @log@ ought to be a commutative and idempontent monoid. fastEvalTell :: (Monoid log) => log -> FastEvalLog log jt a b -> FastEvalLog log jt a b fastEvalTell msg (FastEvalLog fs fm) = FastEvalLog (semTell msg fs) fm -- | If evaluation is successful, return the total of all 'fastEvalTell' data that was logged. fastEvalLog :: FastEvalLog log jt a b -> PrimEnv -> a -> Maybe log fastEvalLog prog env a = snd <$> semLog (fastEvalSem prog) env a proxyImplementation :: (JetType jt, TyC a, TyC b) => proxy jt a b -> jt a b -> PrimEnv -> a -> Maybe b proxyImplementation _proxy = implementation withJets :: (Monoid log, JetType jt, TyC a, TyC b) => FastEvalLog log jt a b -> FastEvalLog log jt a b withJets ~fe@(FastEvalLog ~(Delegator rs (Kleisli fs)) jm) = -- 'withJets' does not adjust the commitment root. FastEvalLog { fastEvalSem = Delegator rs (Kleisli optfs) , fastEvalMatcher = jm } where optfs a | Just jt <- matcher =<< jm = lift . ReaderT $ flip (proxyImplementation fe jt) a | otherwise = fs a mkLeaf sComb jmComb = withJets $ FastEvalLog { fastEvalSem = sComb , fastEvalMatcher = jmComb } mkUnary sComb jmComb t = withJets $ FastEvalLog { fastEvalSem = sComb (fastEvalSem t) , fastEvalMatcher = jmComb <*> fastEvalMatcher t } mkBinary sComb jmComb s t = withJets $ FastEvalLog { fastEvalSem = sComb (fastEvalSem s) (fastEvalSem t) , fastEvalMatcher = jmComb <*> fastEvalMatcher s <*> fastEvalMatcher t } instance (Monoid log, JetType jt) => Core (FastEvalLog log jt) where iden = mkLeaf iden (pure iden) comp = mkBinary comp (pure comp) unit = mkLeaf unit (pure unit) injl = mkUnary injl (pure injl) injr = mkUnary injr (pure injr) match = mkBinary match (pure match) pair = mkBinary pair (pure pair) take = mkUnary take (pure take) drop = mkUnary drop (pure drop) instance (Monoid log, JetType jt) => Assert (FastEvalLog log jt) where assertl s h = mkUnary (flip assertl h) (pure (flip assertl h)) s assertr h t = mkUnary (assertr h) (pure (assertr h)) t fail b = mkLeaf (fail b) (pure (fail b)) instance Monoid log => Witness (FastEvalLog log jt) where witness v = FastEvalLog { fastEvalSem = witness v , fastEvalMatcher = Nothing } instance (Monoid log, JetType jt) => Delegate (FastEvalLog log jt) where disconnect = mkBinary disconnect Nothing instance (Monoid log, JetType jt) => Primitive (FastEvalLog log jt) where primitive p = mkLeaf (primitive p) (pure (primitive p)) instance (Monoid log, JetType jt) => Jet (FastEvalLog log jt) where jet w t = result where result = FastEvalLog { fastEvalSem = Delegator (jet w t) fs , fastEvalMatcher = jm } FastEvalLog (Delegator _ fs) jm = t `asTypeOf` result instance (Monoid log, JetType jt) => Simplicity (FastEvalLog log jt) where ================================================ FILE: Haskell/Indef/Simplicity/Serialization/BitString.hs ================================================ {-# LANGUAGE ScopedTypeVariables #-} -- | This modules provides a bit-stream serialization and deserialization functions for 'SimplicityDag's and Simplicity expressions for both stop-code and length-code based formats. module Simplicity.Serialization.BitString ( getDagNoWitnessLengthCode , getWitnessData , getTermLengthCode , putDagNoWitnessLengthCode , putWitnessData , putTermLengthCode ) where import qualified Data.Vector as V import qualified Data.Vector.Unboxed as UV import Data.Void (Void, vacuous) import Lens.Family2 ((&), (%~)) import Simplicity.Dag import Simplicity.Digest import Simplicity.Inference import Simplicity.JetType import Simplicity.Primitive import Simplicity.Serialization import Simplicity.Term import Simplicity.Ty -- Decodes a single node and references for a 'UntypedSimplicityDag'. -- @abort@ is invoked if an invalid code is encountered. getNode :: (Monad m, JetType jt) => m Void -> m Bool -> m (TermF () (SomeArrow jt) () Integer) getNode abort next = (getBody >>= traverse (\_ -> getPositive next)) & (Jet <$> getJetBit abort next) where l & r = next >>= \b -> if b then r else l node = return getBody = (((node (uComp () ()) & node (uCase () ())) & (node (uPair () ()) & node (uDisconnect () ()))) & ((node (uInjl ()) & node (uInjr ())) & (node (uTake ()) & node (uDrop ())))) & (((node uIden & node uUnit) & vacuous abort) & ((uHidden <$> get256Bits next) & (node (uWitness ())))) -- | Decodes a length-code based self-delimiting bit-stream encoding of 'SimplicityDag' without witness data. -- -- @abort@ is invoked at the point an invalid prefix is encountered, meaning that the stream is not a valid code for a 'SimplicityDag'. -- -- Type annotations are not part of the encoding. After deserialization you will want to run type inference from "Simplicity.Inference". -- Type Inference needs to be completed before the witness data, which appears after the 'SimplicityDag' in the bit-stream, can be added to the DAG. -- -- Note that the type @forall m. Monad m => m Void -> m Bool -> m a@ is isomorphic to the free monad over the @X² + 1@ functor at @a@. -- In other words, 'getDagNoWitnessLengthCode' has the type of a binary branching tree with leaves either containing 'SimplicityDag' values or no value. -- See "Simplicity.Serialization" for functions to execute this free monad. getDagNoWitnessLengthCode :: (Monad m, JetType jt) => m Void -- ^ @abort@ -> m Bool -- ^ @next@ -> m (SimplicityDag V.Vector () (SomeArrow jt) ()) getDagNoWitnessLengthCode abort next = do len <- getPositive next V.replicateM (fromInteger len) $ do getNode abort next -- | Given a type-annotated 'SimplicityDag', decode a bit-stream encoding of the DAG's witness data as 'UntypedValue's. -- -- @abort@ is invoked if the encoded value of the witness length does not match the actual length of the witness data consumed by the DAG. -- -- Note that the type @forall m. Monad m => m Void -> m Bool -> m a@ is isomorphic to the free monad over the @X² + 1@ functor at @a@. -- In other words, @'getWitnessData' dag@ has the type of a binary branching tree with leaves either containing 'SimplicityDag' values or no value. -- See "Simplicity.Serialization" for functions to execute this free monad. getWitnessData :: (Traversable f, Monad m) => SimplicityDag f Ty jt w -> m Bool -- ^ @next@ -> m (SimplicityDag f Ty jt UntypedValue) getWitnessData dag next = do traverse (witnessData (witnessDecoder next)) dag where witnessDecoder next ty _ = case reflect ty of (SomeTy b) -> untypedValue <$> getValueR b next -- | Decodes a length-code based self-delimiting bit-stream encoding of a Simplicity expression. -- -- This function combines, 'getDagNoWitnessLengthCode', 'typeInference', 'getWitnessData', and 'typeCheck' to decode a Simplicity DAG and witness data and runs type inference. -- -- @abort@ is invoked if any decoding or type checking error occurs. -- -- The @proxy ('SomeArrow' jt)@ argument is used to specify the 'JetType' used for decoding known jets. -- -- Note: The one calling 'getTermLengthCode' determines the input and output Simplicity types of the resulting Simplicity expression. -- They are __not__ inferered from the DAG input. -- Instead the types @a@ and @b@ are used as constraints during type inference. -- -- Note that the type @forall m. Monad m => m Void -> m Bool -> m a@ is isomorphic to the free monad over the @X² + 1@ functor at @a@. -- In other words, 'getTermLengthCode' has the type of a binary branching tree with leaves either containing 'term a b' values or no value. -- See "Simplicity.Serialization" for functions to execute this free monad. getTermLengthCode :: forall proxy jt m term a b. (JetType jt, Monad m, Simplicity term, TyC a, TyC b) => proxy (SomeArrow jt) -> m Void -- ^ @abort@ -> m Bool -- ^ @next@ -> m (term a b) getTermLengthCode _ abort next = do dag <- getDagNoWitnessLengthCode abort next :: m (SimplicityDag V.Vector () (SomeArrow jt) ()) tyDag <- either (\err -> vacuous abort) return $ typeInference proxy dag wTyDag <- getWitnessData tyDag next either (\err -> vacuous abort) return $ typeCheck wTyDag where proxy :: term a b proxy = undefined -- Encodes a single node from as a self-delimiting bit-stream encoding as a difference list. -- Witness data is not encoded. putNode :: JetType jt => TermF Ty (SomeArrow jt) w Integer -> DList Bool putNode = go where go (Comp _ _ _ x y) = ([o,o,o,o,o]++) . putPositive x . putPositive y go (Case _ _ _ _ x y) = ([o,o,o,o,i]++) . putPositive x . putPositive y go (Pair _ _ _ x y) = ([o,o,o,i,o]++) . putPositive x . putPositive y go (Disconnect _ _ _ _ x y) = ([o,o,o,i,i]++) . putPositive x . putPositive y go (Injl _ _ _ x) = ([o,o,i,o,o]++) . putPositive x go (Injr _ _ _ x) = ([o,o,i,o,i]++) . putPositive x go (Take _ _ _ x) = ([o,o,i,i,o]++) . putPositive x go (Drop _ _ _ x) = ([o,o,i,i,i]++) . putPositive x go (Iden _) = ([o,i,o,o,o]++) go (Unit _) = ([o,i,o,o,i]++) go (Hidden h) = ([o,i,i,o]++) . put256Bits h go (Witness _ _ _) = ([o,i,i,i]++) go (Jet (SomeArrow j)) = ([i]++) . putJetBit j (o,i) = (False,True) -- Caution: Maybe [Bool] is a type that might cause space leaks. Investiagte alternatives. -- | Encodes an 'SimplicityDag' as a self-delimiting, length-code based bit-stream encoding, including witness data. -- -- Encoding of witness data requires that its type annotation be the value's principle type. -- This function may return 'Nothing' if witness data cannot be encoded using the witnesses' type annotation. putDagNoWitnessLengthCode :: (Foldable f, JetType jt) => SimplicityDag f Ty (SomeArrow jt) UntypedValue -> [Bool] putDagNoWitnessLengthCode v = putPositive len $ foldr putNode [] v where len = toInteger $ length v putWitnessData :: (Foldable f, JetType jt) => SimplicityDag f Ty (SomeArrow jt) UntypedValue -> Maybe [Bool] putWitnessData v = foldr (\x y -> encodeWitnessDatum x <*> y) (Just []) v where encodeWitnessDatum (Witness _ b w) = case reflect b of SomeTy rb -> ((++) . putValueR rb) <$> castUntypedValue w encodeWitnessDatum _ = Just id -- | Encodes a Simplicity expression as a self-delimiting, length-code based, bit-stream encoding. -- -- Subexpressions matching @'JetType' jt@ are replaced and encoded as jets. putTermLengthCode :: (JetType jt, TyC a, TyC b) => JetDag jt a b -> ([Bool],[Bool]) putTermLengthCode dag = (prog, witness) where jd = jetDag dag prog = putDagNoWitnessLengthCode jd {- jetDag ought not to ever produce a value where putDag fails. -} Just witness = putWitnessData jd ================================================ FILE: Haskell/Indef/Simplicity/Serialization/ByteString.hs ================================================ -- | This modules provides serialization and deserialization functions for 'SimplicityDag's via cereal's "Data.Serialize" library. module Simplicity.Serialization.ByteString ( getDag, putDag ) where import Control.Monad (unless) import Control.Monad.Trans (lift) import Control.Monad.Trans.State (StateT, runStateT) import qualified Control.Monad.Trans.State as MS import Data.Bits ((.|.), (.&.), testBit, setBit) import Data.ByteString.Short (ShortByteString) import Data.Foldable (toList) import Data.Serialize (Get, get, Putter, Put, put) import Data.Serialize.Get (getWord8, getWord16be, getShortByteString) import Data.Serialize.Put (putWord8, putWord16be, putShortByteString) import qualified Data.Vector as V import qualified Data.Vector.Unboxed as UV import qualified Data.Word as W import Lens.Family2.Stock (_1) import Simplicity.Digest import Simplicity.Inference import Simplicity.Primitive import Simplicity.Serialization import Simplicity.Ty -- Decodes a bit-string of given length from a byte-stream. getBoolVector :: Int -> Get (UV.Vector Bool) getBoolVector i = getEvalBitStream prog where prog _abort next = UV.replicateM i next putBoolVector :: Putter (UV.Vector Bool) putBoolVector = putBitStream . UV.toList {- Consider replacing @UV.Vector Bool@ with @Vector Bit@ from https://github.com/mokus0/bitvec when issues are resolved. see https://github.com/mokus0/bitvec/issues/3 & https://github.com/mokus0/bitvec/issues/4. -} -- Decodes a single node for a 'SimplicityDag'. -- The first byte is given as an argument, but if needed, more bytes may be consumed from the stream. decodeNode :: W.Word8 -> Get (TermF () j (UV.Vector Bool) Bool) decodeNode 0x20 = return uIden decodeNode 0x21 = return uUnit decodeNode 0x23 = uHidden <$> get decodeNode 0xff = do len <- fromIntegral <$> getWord16be unless (127 <= len) (fail "Simplicity.Serialization.ByteString.decodeNode: Badly coded long witness length.") uWitness <$> getBoolVector len decodeNode w | w .&. 0xf7 == 0x10 = return (uInjl (testBit w 3)) | w .&. 0xf7 == 0x11 = return (uInjr (testBit w 3)) | w .&. 0xf7 == 0x12 = return (uTake (testBit w 3)) | w .&. 0xf7 == 0x13 = return (uDrop (testBit w 3)) | w .&. 0xf3 == 0x00 = return (uComp (testBit w 3) (testBit w 2)) | w .&. 0xf3 == 0x01 = return (uCase (testBit w 3) (testBit w 2)) | w .&. 0xf3 == 0x02 = return (uPair (testBit w 3) (testBit w 2)) | w .&. 0xf3 == 0x03 = return (uDisconnect (testBit w 3) (testBit w 2)) | w .&. 0x80 == 0x80 = uWitness <$> getBoolVector (fromIntegral (w .&. 0x7f)) -- The 'DeserializeM' monad adds a counter to the 'Get' monad to count the number of nodes deserialized. -- This is used to compute the offsets of references. type DeserializeM a = StateT Integer Get a -- Decodes a node references (a.k.a. indices) for a 'SimplicityDag'. -- The input flag set to 'False' means to return the last index, which is offset 1. -- The input flag set to 'True' means to parse the reference from the stream. -- In this case we add 2 to the decoded value to get the relative offset since a relative offset of 1 is handled by the input flag set to 'False'. getIx :: Bool -> DeserializeM Integer getIx False = return 1 getIx True = do cnt <- MS.get ix <- lift (getSizedInteger (cnt - 2)) unless (ix <= cnt) (fail "getIx: index out of range") return (ix + 2) where getSizedInteger bound | bound <= 0 = return 0 | otherwise = do hi <- getSizedInteger (bound `div` 256) lo <- getWord8 return (hi * 256 + fromIntegral lo) -- Decodes a single node and references for a 'SimplicityDag'. -- 'Nothing' is returned when then end-of-stream code is encountered. getNode :: DeserializeM (Maybe (TermF () j (UV.Vector Bool) Integer)) getNode = do w <- lift getWord8 case w of 0x1f -> return Nothing _ -> do bNode <- lift (decodeNode w) Just <$> traverse getIx bNode -- | Decodes a self-delimiting byte-stream encoding of 'SimplicityDag'. -- -- Type annotations are not part of the encoding. After deserialization you will want to run type inference from "Simplicity.Inference". getDag :: Get (SimplicityDag V.Vector () j (UV.Vector Bool)) getDag = V.unfoldrM (fmap f . runStateT getNode) 0 where f (mnode, i) = do node <- mnode return (node, succ i) putIx bound i | bound <= 0 = return () | otherwise = putIx (bound `div` 256) (i `div` 256) >> putWord8 (fromIntegral i) -- Encode a Simplicity node that occurs at position 'bnd'. -- Caution: 'Maybe Put' might lead to space-leaks. Invesigate alternative formulations of this function. putNode :: Int -> TermF Ty j UntypedValue Integer -> Maybe Put putNode bnd = go where go (Comp _ _ _ x y) = Just $ putBinary x y 0x00 go (Case _ _ _ _ x y) = Just $ putBinary x y 0x01 go (Pair _ _ _ x y) = Just $ putBinary x y 0x02 go (Disconnect _ _ _ _ x y) = Just $ putBinary x y 0x03 go (Injl _ _ _ x) = Just $ putUnary x 0x10 go (Injr _ _ _ x) = Just $ putUnary x 0x11 go (Take _ _ _ x) = Just $ putUnary x 0x12 go (Drop _ _ _ x) = Just $ putUnary x 0x13 go (Iden _) = Just $ putWord8 0x20 go (Unit _) = Just $ putWord8 0x21 go (Hidden h) = Just $ putWord8 0x23 >> put h go (Witness _ b w) = case reflect b of SomeTy rb -> putWitness . UV.fromList . putValueR rb <$> castUntypedValue w go (Jet j) = error ":TODO: Implement bytestring serialization of discounted jets" putUnary 1 z = putWord8 z putUnary i z | 2 <= i = putWord8 (setBit z 3) >> putIx (bnd - 2) (i - 2) putBinary x 1 z = putUnary x z putBinary x i z | 2 <= i = putUnary x (setBit z 2) >> putIx (bnd - 2) (i - 2) putWitness w | len < 127 = putWord8 (0x80 .|. fromIntegral len) >> putBoolVector w | len <= fromIntegral (maxBound :: W.Word16) = putWord8 0xff >> putWord16be (fromIntegral len) >> putBoolVector w where len = UV.length w -- | Encodes a 'SimplicityDag' as a self-delimiting byte-stream code. -- -- Encoding of witness values require that its type annotation be the value's principle type. -- 'putDag' requires a type annotated 'SimplicityDag' in order to persuade the user to run 'typeInference' first. -- This function may return 'Nothing' if witness values cannot be encoded using the witnesses' type annotation. putDag :: Foldable f => SimplicityDag f Ty j UntypedValue -> Maybe Put putDag v = fmap sequence_ . sequence $ zipWith putNode [0..] (toList v) ++ [Just (putWord8 0x1f)] ================================================ FILE: Haskell/Indef/Simplicity/StaticAnalysis/Cost.hs ================================================ module Simplicity.StaticAnalysis.Cost ( module Cost ) where import Simplicity.BitMachine.StaticAnalysis.Cost as Cost import Simplicity.Term instance Jet TermWeight where jet w _t = TermWeight $ overhead + w instance Simplicity TermWeight where ================================================ FILE: Haskell/Indef/Simplicity/Term.hs ================================================ {-# LANGUAGE FlexibleContexts, UndecidableInstances, RankNTypes #-} -- | This module extends "Simplicity.Term.Core" to the full Simplicity languages by defining the remaining language extensions: 'Primitive' and 'Jet'. -- The 'Simplicity' class combines all the features of the full Simplicity language under one constraint. -- -- This is a separate module from "Simplicity.Term.Core" so that the core language need not depend on the "Simplicity.Primitive" module. module Simplicity.Term ( module Simplicity.Term.Core , Primitive(..) , Jet(..) , Simplicity(..) ) where import Control.Arrow (Kleisli(..)) import Control.Monad.Reader.Class (MonadReader(..)) import qualified Control.Monad.Fail as Fail import Simplicity.Digest import Simplicity.MerkleRoot.Impl import Simplicity.Primitive import Simplicity.Term.Core import Simplicity.Tensor import Simplicity.Ty import Simplicity.Programs.Word import Simplicity.Weight -- | This class embeds Blockchain 'Prim'itives into the Simplicity language. -- The semantics for these primitives is mediated by the 'Simplicity.Primitive' module. class Primitive term where primitive :: (TyC a, TyC b) => Prim a b -> term a b -- | The Monad 'm' should be a commutative monad. instance (MonadReader PrimEnv m, Fail.MonadFail m) => Primitive (Kleisli m) where primitive p = Kleisli $ \a -> do env <- ask let err = Fail.fail $ "Simplicity.Term.primitive in Primitive (Kleisli m) instance: " ++ primName p ++ " failed." maybe err return $ primSem p a env -- | This class creates expressions for discounted jets. -- A jet's specification is a Simplicity expression that isn't allowed to contain witness data, delegations or other jets. class Assert term => Jet term where jet :: (TyC a, TyC b) => Weight -> (forall term0. (Assert term0, Primitive term0) => term0 a b) -> term a b -- | The Monad 'm' should be a commutative monad. instance (MonadReader PrimEnv m, Fail.MonadFail m) => Jet (Kleisli m) where jet _w t = t -- | The class for the full Simplicity language with delegation. -- This includes 'Core', 'Assert', 'Primitive', 'Jet', 'Witness' and 'Delegate'. class (Jet term, Witness term, Delegate term) => Simplicity term where instance (Primitive p, Primitive q) => Primitive (Product p q) where primitive p = Product (primitive p) (primitive p) instance (Jet p, Jet q) => Jet (Product p q) where jet w t = Product (jet w t) (jet w t) instance (Simplicity p, Simplicity q) => Simplicity (Product p q) where instance Primitive Unit where primitive _ = Unit instance Jet Unit where jet _w _t = Unit instance Simplicity Unit where instance Primitive CommitmentRoot where primitive = primitiveCommitmentImpl primPrefix primName instance Jet CommitmentRoot where jet w t = jetCommitmentImpl t (fromInteger $ milliWeight w) instance Simplicity CommitmentRoot where instance Primitive IdentityRoot where primitive = primitiveIdentityImpl primPrefix primName instance Jet IdentityRoot where jet w t = jetIdentityImpl t (fromInteger $ milliWeight w) -- Idea for alternative IdentityRoot instance: -- jet t = t -- Transparent jet identities would mean we could define the jet class as -- jet :: (TyC a, TyC b) => (forall term0. (Assert term0, Primitive term0, Jet term0) => term0 a b) -> term a b -- And then jets could contain jets such that their Semantics, IdentityRoots, and hence CommitmentRoots would all be transparent to jet sub-experssions. -- Need to think carefully what this would mean for consensus, but I think it is okay. instance Simplicity IdentityRoot where instance Primitive AnnotatedRoot where primitive = primitiveAnnotatedImpl primPrefix primName instance Jet AnnotatedRoot where jet w t = jetAnnotatedImpl t (fromInteger $ milliWeight w) instance Simplicity AnnotatedRoot where instance Primitive ConstWord where primitive _ = NotConstWord ================================================ FILE: Haskell/Simplicity/Bitcoin/Benchmarks.hs ================================================ module Simplicity.Bitcoin.Benchmarks (cost) where import Simplicity.BitMachine.StaticAnalysis.Cost rawBenchmark :: String -> Double rawBenchmark "Add16" = 44.136682646740034 rawBenchmark "Add32" = 50.67335760329138 rawBenchmark "Add64" = 58.13732004794472 rawBenchmark "Add8" = 53.634532429883386 rawBenchmark "All16" = 33.39218872838866 rawBenchmark "All32" = 34.393968985341786 rawBenchmark "All64" = 34.80040636278102 rawBenchmark "All8" = 27.938330849119314 rawBenchmark "And1" = 42.58469301684835 rawBenchmark "And16" = 45.77680124552797 rawBenchmark "And32" = 42.754027977427256 rawBenchmark "And64" = 43.00176712484209 rawBenchmark "And8" = 53.8866889956115 rawBenchmark "AnnexHash" = 819.740625 rawBenchmark "Bip0340Verify" = 54331.05426506661 rawBenchmark "BuildTapbranch" = 1404.12 rawBenchmark "BuildTapleafSimplicity" = 1059.2866666666662 rawBenchmark "BuildTaptweak" = 42754.09 rawBenchmark "Ch1" = 27.603813636571267 rawBenchmark "Ch16" = 45.89850402102899 rawBenchmark "Ch32" = 38.31275682173218 rawBenchmark "Ch64" = 42.92425835586593 rawBenchmark "Ch8" = 47.33640905261615 rawBenchmark "CheckLockDistance" = 46.60555856358357 rawBenchmark "CheckLockDuration" = 43.16876427082058 rawBenchmark "CheckLockHeight" = 59.87833333333332 rawBenchmark "CheckLockTime" = 67.80111111111111 rawBenchmark "CheckSigVerify" = 54967.57662850159 rawBenchmark "Complement1" = 28.435070805108868 rawBenchmark "Complement16" = 47.500215918761754 rawBenchmark "Complement32" = 31.98797255311243 rawBenchmark "Complement64" = 35.28996457325325 rawBenchmark "Complement8" = 34.14730925832478 rawBenchmark "CurrentAnnexHash" = 40.81997764174008 rawBenchmark "CurrentIndex" = 36.67501589120791 rawBenchmark "CurrentPrevOutpoint" = 71.51737089421475 rawBenchmark "CurrentScriptHash" = 70.05882767381516 rawBenchmark "CurrentScriptSigHash" = 69.50572986703565 rawBenchmark "CurrentSequence" = 36.50762527293563 rawBenchmark "CurrentValue" = 47.03725600509109 rawBenchmark "Decompress" = 5768.97008230397 rawBenchmark "Decrement16" = 31.973438247351467 rawBenchmark "Decrement32" = 31.827141390753358 rawBenchmark "Decrement64" = 43.572228727724685 rawBenchmark "Decrement8" = 42.51247141156928 rawBenchmark "DivMod128_64" = 92.96107717827591 rawBenchmark "DivMod16" = 51.01793240325478 rawBenchmark "DivMod32" = 50.00632627123014 rawBenchmark "DivMod64" = 45.14217373859996 rawBenchmark "DivMod8" = 50.266833276757055 rawBenchmark "Divide16" = 47.101053943087365 rawBenchmark "Divide32" = 45.12027713560923 rawBenchmark "Divide64" = 45.024481801774456 rawBenchmark "Divide8" = 47.07658591767621 rawBenchmark "Divides16" = 46.59263826828251 rawBenchmark "Divides32" = 44.16401849008762 rawBenchmark "Divides64" = 37.30234275293551 rawBenchmark "Divides8" = 40.457774507513 rawBenchmark "Eq1" = 34.643806635068856 rawBenchmark "Eq16" = 37.772121907748854 rawBenchmark "Eq256" = 103.6766885315375 rawBenchmark "Eq32" = 41.04591615809853 rawBenchmark "Eq64" = 45.60855709671084 rawBenchmark "Eq8" = 41.792733559769715 rawBenchmark "FeAdd" = 427.4328308520785 rawBenchmark "FeInvert" = 1779.708904456149 rawBenchmark "FeIsOdd" = 172.57588971871166 rawBenchmark "FeIsZero" = 152.3799914138906 rawBenchmark "FeMultiply" = 447.0881850688682 rawBenchmark "FeMultiplyBeta" = 333.66342120570886 rawBenchmark "FeNegate" = 297.89941926884467 rawBenchmark "FeNormalize" = 360.7519695167116 rawBenchmark "FeSquare" = 313.8525825651813 rawBenchmark "FeSquareRoot" = 5586.354732640531 rawBenchmark "Fee" = 36.133896616156626 rawBenchmark "FullAdd16" = 58.729472246758526 rawBenchmark "FullAdd32" = 52.99493622545529 rawBenchmark "FullAdd64" = 51.13253677138998 rawBenchmark "FullAdd8" = 72.23485492171291 rawBenchmark "FullDecrement16" = 33.399900521956475 rawBenchmark "FullDecrement32" = 39.38785925372043 rawBenchmark "FullDecrement64" = 39.24945677947102 rawBenchmark "FullDecrement8" = 37.412092786253986 rawBenchmark "FullIncrement16" = 38.663856596153735 rawBenchmark "FullIncrement32" = 31.725758992573404 rawBenchmark "FullIncrement64" = 37.483004202661306 rawBenchmark "FullIncrement8" = 40.55732395910691 rawBenchmark "FullLeftShift16_1" = 42.054529131238006 rawBenchmark "FullLeftShift16_2" = 32.54646043040402 rawBenchmark "FullLeftShift16_4" = 37.57533508358536 rawBenchmark "FullLeftShift16_8" = 37.79145569730148 rawBenchmark "FullLeftShift32_1" = 32.089379606687615 rawBenchmark "FullLeftShift32_16" = 28.970989034936068 rawBenchmark "FullLeftShift32_2" = 40.28187645291576 rawBenchmark "FullLeftShift32_4" = 32.64900173735215 rawBenchmark "FullLeftShift32_8" = 33.2979641278353 rawBenchmark "FullLeftShift64_1" = 41.05324657358461 rawBenchmark "FullLeftShift64_16" = 38.18827279919049 rawBenchmark "FullLeftShift64_2" = 38.69904617685279 rawBenchmark "FullLeftShift64_32" = 40.206795616982305 rawBenchmark "FullLeftShift64_4" = 36.78811321017009 rawBenchmark "FullLeftShift64_8" = 37.83206326671019 rawBenchmark "FullLeftShift8_1" = 33.379700908291646 rawBenchmark "FullLeftShift8_2" = 35.64951681821717 rawBenchmark "FullLeftShift8_4" = 39.86048429071267 rawBenchmark "FullMultiply16" = 54.65862637714324 rawBenchmark "FullMultiply32" = 48.11422276214214 rawBenchmark "FullMultiply64" = 56.81191423066708 rawBenchmark "FullMultiply8" = 52.4218660338924 rawBenchmark "FullRightShift16_1" = 30.584441050887307 rawBenchmark "FullRightShift16_2" = 33.21876447294352 rawBenchmark "FullRightShift16_4" = 35.18370969327063 rawBenchmark "FullRightShift16_8" = 30.47185669900153 rawBenchmark "FullRightShift32_1" = 27.436660149075713 rawBenchmark "FullRightShift32_16" = 26.724590023675788 rawBenchmark "FullRightShift32_2" = 36.80213104058374 rawBenchmark "FullRightShift32_4" = 27.259552789409202 rawBenchmark "FullRightShift32_8" = 36.555094360956744 rawBenchmark "FullRightShift64_1" = 32.98877822633898 rawBenchmark "FullRightShift64_16" = 40.22696317634952 rawBenchmark "FullRightShift64_2" = 42.2504406313922 rawBenchmark "FullRightShift64_32" = 40.41141182230598 rawBenchmark "FullRightShift64_4" = 31.140853356406083 rawBenchmark "FullRightShift64_8" = 37.450653652486466 rawBenchmark "FullRightShift8_1" = 32.65477545853995 rawBenchmark "FullRightShift8_2" = 27.305918570286753 rawBenchmark "FullRightShift8_4" = 28.155447838248687 rawBenchmark "FullSubtract16" = 54.728904350750966 rawBenchmark "FullSubtract32" = 50.81650554076461 rawBenchmark "FullSubtract64" = 60.0317449293016 rawBenchmark "FullSubtract8" = 58.633081183275415 rawBenchmark "GeIsOnCurve" = 378.5419638083557 rawBenchmark "GeNegate" = 589.106037318137 rawBenchmark "GejAdd" = 1649.5102208129256 rawBenchmark "GejDouble" = 1023.76443975304 rawBenchmark "GejEquiv" = 1306.4752671692258 rawBenchmark "GejGeAdd" = 1434.336203430953 rawBenchmark "GejGeAddEx" = 1572.5375070989735 rawBenchmark "GejGeEquiv" = 1002.1525067123277 rawBenchmark "GejInfinity" = 420.6313287840956 rawBenchmark "GejIsInfinity" = 385.48142222438554 rawBenchmark "GejIsOnCurve" = 571.5188245928658 rawBenchmark "GejNegate" = 851.9540386494368 rawBenchmark "GejNormalize" = 2300.3299568675266 rawBenchmark "GejRescale" = 1105.939152104785 rawBenchmark "GejXEquiv" = 606.4526120785539 rawBenchmark "GejYIsOdd" = 2035.2240203735464 rawBenchmark "Generate" = 27402.027708000252 rawBenchmark "HashToCurve" = 38391.68265634641 rawBenchmark "High1" = 23.558953385170184 rawBenchmark "High16" = 27.62768113336012 rawBenchmark "High32" = 35.559286576856806 rawBenchmark "High64" = 28.814148698982258 rawBenchmark "High8" = 32.64377381019716 rawBenchmark "Increment16" = 30.957709970314895 rawBenchmark "Increment32" = 40.1796059898613 rawBenchmark "Increment64" = 35.418163558431324 rawBenchmark "Increment8" = 37.978203566684776 rawBenchmark "InputAnnexHash" = 42.70182967858256 rawBenchmark "InputAnnexesHash" = 68.35019717263717 rawBenchmark "InputHash" = 457.52660680735187 rawBenchmark "InputOutpointsHash" = 69.59081583677609 rawBenchmark "InputPrevOutpoint" = 77.25913319341868 rawBenchmark "InputScriptHash" = 78.91636262449325 rawBenchmark "InputScriptSigHash" = 75.71250391155941 rawBenchmark "InputScriptSigsHash" = 70.02210064106225 rawBenchmark "InputScriptsHash" = 71.31520028923777 rawBenchmark "InputSequence" = 43.377176188416094 rawBenchmark "InputSequencesHash" = 69.13203178900284 rawBenchmark "InputUtxoHash" = 453.33608745487885 rawBenchmark "InputUtxosHash" = 67.48494069291833 rawBenchmark "InputValue" = 44.687685815508615 rawBenchmark "InputValuesHash" = 69.29576042209113 rawBenchmark "InputsHash" = 67.35180070205234 rawBenchmark "InternalKey" = 68.33962864439388 rawBenchmark "IsOne16" = 35.465992740843575 rawBenchmark "IsOne32" = 35.650420317234165 rawBenchmark "IsOne64" = 36.53035640637033 rawBenchmark "IsOne8" = 26.213412673887795 rawBenchmark "IsZero16" = 28.906872512092153 rawBenchmark "IsZero32" = 32.26173309028192 rawBenchmark "IsZero64" = 37.66907585826825 rawBenchmark "IsZero8" = 32.81533812531282 rawBenchmark "Le16" = 45.648761967050916 rawBenchmark "Le32" = 54.84357743553501 rawBenchmark "Le64" = 43.787890397548175 rawBenchmark "Le8" = 51.66512564613219 rawBenchmark "LeftExtend16_32" = 40.12034744934846 rawBenchmark "LeftExtend16_64" = 38.394732425189424 rawBenchmark "LeftExtend1_16" = 27.525231328530527 rawBenchmark "LeftExtend1_32" = 26.56931256736324 rawBenchmark "LeftExtend1_64" = 27.097606190555393 rawBenchmark "LeftExtend1_8" = 25.320232305606424 rawBenchmark "LeftExtend32_64" = 38.18891728370718 rawBenchmark "LeftExtend8_16" = 32.278220418994046 rawBenchmark "LeftExtend8_32" = 47.58337299636622 rawBenchmark "LeftExtend8_64" = 54.11604704818987 rawBenchmark "LeftPadHigh16_32" = 39.50834765098096 rawBenchmark "LeftPadHigh16_64" = 45.218281108823284 rawBenchmark "LeftPadHigh1_16" = 58.27516690424025 rawBenchmark "LeftPadHigh1_32" = 121.39949621939901 rawBenchmark "LeftPadHigh1_64" = 166.27124660908493 rawBenchmark "LeftPadHigh1_8" = 40.22978177021594 rawBenchmark "LeftPadHigh32_64" = 38.02269928850963 rawBenchmark "LeftPadHigh8_16" = 35.82613973639665 rawBenchmark "LeftPadHigh8_32" = 58.0193548166602 rawBenchmark "LeftPadHigh8_64" = 62.35337553262941 rawBenchmark "LeftPadLow16_32" = 35.87033401657752 rawBenchmark "LeftPadLow16_64" = 37.635044597552366 rawBenchmark "LeftPadLow1_16" = 32.8600689080829 rawBenchmark "LeftPadLow1_32" = 26.339685979228115 rawBenchmark "LeftPadLow1_64" = 25.76808393390171 rawBenchmark "LeftPadLow1_8" = 26.38731781820569 rawBenchmark "LeftPadLow32_64" = 34.095306548305274 rawBenchmark "LeftPadLow8_16" = 31.15262809934076 rawBenchmark "LeftPadLow8_32" = 41.449761525764025 rawBenchmark "LeftPadLow8_64" = 63.90696863776934 rawBenchmark "LeftRotate16" = 48.43698053565599 rawBenchmark "LeftRotate32" = 34.223382583074084 rawBenchmark "LeftRotate64" = 37.863151911541166 rawBenchmark "LeftRotate8" = 36.750835333961355 rawBenchmark "LeftShift16" = 60.00168894665048 rawBenchmark "LeftShift32" = 43.73101788984439 rawBenchmark "LeftShift64" = 38.95747675143024 rawBenchmark "LeftShift8" = 40.0794370358082 rawBenchmark "LeftShiftWith16" = 39.84312352726623 rawBenchmark "LeftShiftWith32" = 48.04430200866582 rawBenchmark "LeftShiftWith64" = 53.492158105353546 rawBenchmark "LeftShiftWith8" = 57.58363622714932 rawBenchmark "Leftmost16_1" = 37.77996029994905 rawBenchmark "Leftmost16_2" = 32.07916609455383 rawBenchmark "Leftmost16_4" = 28.4904208330946 rawBenchmark "Leftmost16_8" = 34.271283448670985 rawBenchmark "Leftmost32_1" = 29.486816173861268 rawBenchmark "Leftmost32_16" = 35.0822646168527 rawBenchmark "Leftmost32_2" = 34.52857819040426 rawBenchmark "Leftmost32_4" = 34.04650601552063 rawBenchmark "Leftmost32_8" = 32.988290917801706 rawBenchmark "Leftmost64_1" = 35.899766384371475 rawBenchmark "Leftmost64_16" = 34.403331044052095 rawBenchmark "Leftmost64_2" = 33.92175587795361 rawBenchmark "Leftmost64_32" = 42.52310642557719 rawBenchmark "Leftmost64_4" = 44.19447608789629 rawBenchmark "Leftmost64_8" = 29.722452171944532 rawBenchmark "Leftmost8_1" = 29.68986985055512 rawBenchmark "Leftmost8_2" = 39.237095577098984 rawBenchmark "Leftmost8_4" = 35.924259137346226 rawBenchmark "LinearCombination1" = 47131.0603369374 rawBenchmark "LinearVerify1" = 47908.70714207623 rawBenchmark "LockTime" = 36.42503760383047 rawBenchmark "Low1" = 22.448243650192513 rawBenchmark "Low16" = 33.05884634647117 rawBenchmark "Low32" = 28.916591781217406 rawBenchmark "Low64" = 27.920588817108204 rawBenchmark "Low8" = 25.243161658299815 rawBenchmark "Lt16" = 45.781904249407944 rawBenchmark "Lt32" = 49.087861252970754 rawBenchmark "Lt64" = 39.062455921413196 rawBenchmark "Lt8" = 47.74682254263336 rawBenchmark "Maj1" = 29.826139878740626 rawBenchmark "Maj16" = 47.265903230578495 rawBenchmark "Maj32" = 40.55436366914694 rawBenchmark "Maj64" = 43.55950823865922 rawBenchmark "Maj8" = 35.657990855648016 rawBenchmark "Max16" = 44.47726396878382 rawBenchmark "Max32" = 38.950662288686694 rawBenchmark "Max64" = 41.38460759466962 rawBenchmark "Max8" = 43.57782075302293 rawBenchmark "Median16" = 44.107538380770755 rawBenchmark "Median32" = 42.45962357315993 rawBenchmark "Median64" = 49.25513808527035 rawBenchmark "Median8" = 42.484357807687246 rawBenchmark "Min16" = 46.070458872385544 rawBenchmark "Min32" = 53.2483761851601 rawBenchmark "Min64" = 45.573833255629424 rawBenchmark "Min8" = 43.41610607930553 rawBenchmark "Modulo16" = 47.128433018913505 rawBenchmark "Modulo32" = 45.02578963528636 rawBenchmark "Modulo64" = 39.51720104382203 rawBenchmark "Modulo8" = 47.0007907312594 rawBenchmark "Multiply16" = 43.92524295420403 rawBenchmark "Multiply32" = 43.28121274557034 rawBenchmark "Multiply64" = 39.86790833030251 rawBenchmark "Multiply8" = 43.645718125738156 rawBenchmark "Negate16" = 37.93471863105077 rawBenchmark "Negate32" = 30.974009687050092 rawBenchmark "Negate64" = 30.89293706480842 rawBenchmark "Negate8" = 38.193854929368385 rawBenchmark "NumInputs" = 40.73551435872619 rawBenchmark "NumOutputs" = 37.65318634370241 rawBenchmark "One16" = 24.932927514322092 rawBenchmark "One32" = 25.083366404018864 rawBenchmark "One64" = 24.856045418712885 rawBenchmark "One8" = 25.553521269415736 rawBenchmark "Or1" = 31.11339355232734 rawBenchmark "Or16" = 43.36559767625071 rawBenchmark "Or32" = 44.21394816407116 rawBenchmark "Or64" = 39.427267081807486 rawBenchmark "Or8" = 45.02021849512168 rawBenchmark "OutpointHash" = 983.317333333333 rawBenchmark "OutputHash" = 452.2184636591961 rawBenchmark "OutputScriptHash" = 74.41405907204627 rawBenchmark "OutputScriptsHash" = 68.05834717103335 rawBenchmark "OutputValue" = 45.60257162827426 rawBenchmark "OutputValuesHash" = 65.61832741446521 rawBenchmark "OutputsHash" = 64.64581382407765 rawBenchmark "ParseLock" = 45.35290512126786 rawBenchmark "ParseSequence" = 51.5230680067071 rawBenchmark "PointVerify1" = 45507.347775541704 rawBenchmark "RightExtend16_32" = 40.531291912436835 rawBenchmark "RightExtend16_64" = 38.52752760088984 rawBenchmark "RightExtend32_64" = 34.176187235896684 rawBenchmark "RightExtend8_16" = 35.061762680224525 rawBenchmark "RightExtend8_32" = 38.16726980102737 rawBenchmark "RightExtend8_64" = 77.5702996502455 rawBenchmark "RightPadHigh16_32" = 36.70784236730792 rawBenchmark "RightPadHigh16_64" = 44.705064610540965 rawBenchmark "RightPadHigh1_16" = 62.71840395843432 rawBenchmark "RightPadHigh1_32" = 120.97260212426238 rawBenchmark "RightPadHigh1_64" = 172.51836843296257 rawBenchmark "RightPadHigh1_8" = 40.38834290051296 rawBenchmark "RightPadHigh32_64" = 34.46051876907548 rawBenchmark "RightPadHigh8_16" = 41.43332863189036 rawBenchmark "RightPadHigh8_32" = 44.73635604381541 rawBenchmark "RightPadHigh8_64" = 65.15296456502712 rawBenchmark "RightPadLow16_32" = 34.40001143019563 rawBenchmark "RightPadLow16_64" = 54.23529169177612 rawBenchmark "RightPadLow1_16" = 33.503497630193564 rawBenchmark "RightPadLow1_32" = 26.381301641780443 rawBenchmark "RightPadLow1_64" = 31.65476539783318 rawBenchmark "RightPadLow1_8" = 26.41470163017274 rawBenchmark "RightPadLow32_64" = 40.71713700861584 rawBenchmark "RightPadLow8_16" = 34.4483583262288 rawBenchmark "RightPadLow8_32" = 38.27948995840353 rawBenchmark "RightPadLow8_64" = 54.368092647345414 rawBenchmark "RightRotate16" = 37.36033313598857 rawBenchmark "RightRotate32" = 42.615652394650354 rawBenchmark "RightRotate64" = 35.64158179151264 rawBenchmark "RightRotate8" = 40.03753763691489 rawBenchmark "RightShift16" = 33.35208821580021 rawBenchmark "RightShift32" = 38.161119277692045 rawBenchmark "RightShift64" = 37.614298057547266 rawBenchmark "RightShift8" = 34.69327959933897 rawBenchmark "RightShiftWith16" = 45.889906913538674 rawBenchmark "RightShiftWith32" = 43.310537219684626 rawBenchmark "RightShiftWith64" = 39.631329300288044 rawBenchmark "RightShiftWith8" = 39.24676071674883 rawBenchmark "Rightmost16_1" = 38.76071209405304 rawBenchmark "Rightmost16_2" = 35.77383871313445 rawBenchmark "Rightmost16_4" = 39.60458900221399 rawBenchmark "Rightmost16_8" = 38.294973627235066 rawBenchmark "Rightmost32_1" = 38.92331672791704 rawBenchmark "Rightmost32_16" = 31.196766658320886 rawBenchmark "Rightmost32_2" = 41.08958058573505 rawBenchmark "Rightmost32_4" = 31.547705560004022 rawBenchmark "Rightmost32_8" = 30.602950786324133 rawBenchmark "Rightmost64_1" = 33.706285004586555 rawBenchmark "Rightmost64_16" = 34.81784530720121 rawBenchmark "Rightmost64_2" = 35.74058201022178 rawBenchmark "Rightmost64_32" = 35.367078631048905 rawBenchmark "Rightmost64_4" = 31.40082244656152 rawBenchmark "Rightmost64_8" = 27.36940173406972 rawBenchmark "Rightmost8_1" = 35.975919335811774 rawBenchmark "Rightmost8_2" = 34.65406640633969 rawBenchmark "Rightmost8_4" = 31.214789131830344 rawBenchmark "ScalarAdd" = 428.04407963637175 rawBenchmark "ScalarInvert" = 1747.042635449764 rawBenchmark "ScalarIsZero" = 149.20494073681348 rawBenchmark "ScalarMultiply" = 436.16643391350664 rawBenchmark "ScalarMultiplyLambda" = 312.0130256538555 rawBenchmark "ScalarNegate" = 283.8402319918574 rawBenchmark "ScalarNormalize" = 275.12652301553385 rawBenchmark "ScalarSquare" = 314.3814893191518 rawBenchmark "Scale" = 40427.69365160943 rawBenchmark "ScriptCMR" = 67.37701384651857 rawBenchmark "Sha256Block" = 420.6376435133105 rawBenchmark "Sha256Ctx8Add1" = 365.3591701367009 rawBenchmark "Sha256Ctx8Add128" = 977.6641737286662 rawBenchmark "Sha256Ctx8Add16" = 429.68814728608913 rawBenchmark "Sha256Ctx8Add2" = 370.7077105998144 rawBenchmark "Sha256Ctx8Add256" = 1590.7879307821297 rawBenchmark "Sha256Ctx8Add32" = 510.60402668342346 rawBenchmark "Sha256Ctx8Add4" = 360.95418411462 rawBenchmark "Sha256Ctx8Add512" = 2836.901879638354 rawBenchmark "Sha256Ctx8Add64" = 670.9649367075863 rawBenchmark "Sha256Ctx8Add8" = 381.9619415429357 rawBenchmark "Sha256Ctx8AddBuffer511" = 2824.1862108666896 rawBenchmark "Sha256Ctx8Finalize" = 458.32459885061485 rawBenchmark "Sha256Ctx8Init" = 67.65996850191188 rawBenchmark "Sha256Iv" = 50.773287725834095 rawBenchmark "SigAllHash" = 66.11014015654936 rawBenchmark "Some1" = 33.07463363538328 rawBenchmark "Some16" = 28.91761255504874 rawBenchmark "Some32" = 27.049591600502875 rawBenchmark "Some64" = 34.19889043017354 rawBenchmark "Some8" = 31.407983723117024 rawBenchmark "Subtract16" = 51.66400326625853 rawBenchmark "Subtract32" = 48.21179847123583 rawBenchmark "Subtract64" = 69.23821934331896 rawBenchmark "Subtract8" = 52.95304343492633 rawBenchmark "Swu" = 18018.779203014277 rawBenchmark "TapEnvHash" = 66.0628594878007 rawBenchmark "TapdataInit" = 678.2566336758583 rawBenchmark "TapleafHash" = 64.18848496148071 rawBenchmark "TapleafVersion" = 36.5603078638849 rawBenchmark "Tappath" = 42.0390045311738 rawBenchmark "TappathHash" = 68.10222446255801 rawBenchmark "TotalInputValue" = 38.30265948379831 rawBenchmark "TotalOutputValue" = 39.341843676388926 rawBenchmark "TransactionId" = 67.41588797704385 rawBenchmark "TxHash" = 65.62540497960407 rawBenchmark "TxIsFinal" = 34.429668391912244 rawBenchmark "TxLockDistance" = 39.928584556301345 rawBenchmark "TxLockDuration" = 36.64653184689561 rawBenchmark "TxLockHeight" = 39.83812764696879 rawBenchmark "TxLockTime" = 40.08181000831813 rawBenchmark "Verify" = 24.4492730405965 rawBenchmark "Version" = 42.89777793306961 rawBenchmark "Xor1" = 33.15518794471267 rawBenchmark "Xor16" = 40.38906609022018 rawBenchmark "Xor32" = 42.40576279637569 rawBenchmark "Xor64" = 37.74657737058654 rawBenchmark "Xor8" = 44.027331427414154 rawBenchmark "XorXor1" = 27.746105883455872 rawBenchmark "XorXor16" = 45.11335992539446 rawBenchmark "XorXor32" = 45.174769386708675 rawBenchmark "XorXor64" = 44.17301856415719 rawBenchmark "XorXor8" = 47.53375204996623 -- benchmark adjusts the raw benchmark by giving a discount to batch verifiable jets. benchmark :: String -> Double benchmark jetName = rawBenchmark jetName * adjustment where batchable = ["LinearVerify1", "PointVerify1", "CheckSigVerify", "Bip0340Verify"] adjustment | jetName `elem` batchable = 0.5 | otherwise = 1 -- Normalized cost where cost "CheckSigVerify" = 50 Weight. cost :: String -> Weight cost jetName = realToFrac $ benchmark jetName * factor where factor = 50 / benchmark "CheckSigVerify" ================================================ FILE: Haskell/Simplicity/Bitcoin/FFI/Env.hs ================================================ -- | This module binds the C implementation of jets for Simplicity for assertions. {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.Bitcoin.FFI.Env ( CTransaction, CTapEnv, CTxEnv , marshallTransaction, marshallTapEnv , withEnv, withPrimEnv ) where import qualified Data.ByteString as BS import qualified Data.ByteString.Lazy as BSL import Data.Foldable (toList) import Data.Serialize (Serialize, encode, runPut) import Data.Vector (Vector) import Data.Word (Word32) import Foreign.C.Types (CSize(..), CChar(..), CUChar(..), CUInt(..), CULong(..)) import Foreign.ForeignPtr (ForeignPtr, newForeignPtr, withForeignPtr) import Foreign.Marshal.Alloc (allocaBytes) import Foreign.Marshal.Array (withArray, withArrayLen) import Foreign.Marshal.Unsafe (unsafeLocalState) import Foreign.Ptr (FunPtr, Ptr, nullPtr, plusPtr) import Foreign.Storable (Storable(..)) import Lens.Family2 ((^.), under) import Simplicity.Digest import Simplicity.Bitcoin.DataTypes import Simplicity.Bitcoin.Primitive -- Abstract representative for the C txEnv types. newtype RawBuffer = RawBuffer RawBuffer newtype RawOutput = RawOutput RawOutput newtype RawInput = RawInput RawInput newtype RawTransaction = RawTransaction RawTransaction newtype RawTapEnv = RawTapEnv RawTapEnv newtype CTransaction = CTransaction CTransaction newtype CTapEnv = CTapEnv CTapEnv newtype CTxEnv = CTxEnv CTxEnv foreign import ccall unsafe "&" c_sizeof_rawBitcoinBuffer :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawBitcoinOutput :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawBitcoinInput :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawBitcoinTransaction :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawBitcoinTapEnv :: Ptr CSize foreign import ccall unsafe "&" c_bitcoin_sizeof_txEnv :: Ptr CSize foreign import ccall unsafe "" c_set_rawBitcoinBuffer :: Ptr RawBuffer -> Ptr CChar -> CUInt -> IO () foreign import ccall unsafe "" c_set_rawBitcoinOutput :: Ptr RawOutput -> CULong -> Ptr RawBuffer -> IO () foreign import ccall unsafe "" c_set_rawBitcoinInput :: Ptr RawInput -> Ptr RawBuffer -> Ptr RawBuffer -> Ptr CChar -> CUInt -> CULong -> Ptr RawBuffer -> CUInt -> IO () foreign import ccall unsafe "" c_set_rawBitcoinTransaction :: Ptr RawTransaction -> Ptr CChar -> CUInt -> Ptr RawInput -> CUInt -> Ptr RawOutput -> CUInt -> CUInt -> IO () foreign import ccall unsafe "" c_set_rawBitcoinTapEnv :: Ptr RawTapEnv -> Ptr CChar -> CUChar -> Ptr CChar -> IO () foreign import ccall unsafe "" c_bitcoin_set_txEnv :: Ptr CTxEnv -> Ptr CTransaction -> Ptr CTapEnv -> CUInt -> IO () foreign import ccall unsafe "" simplicity_bitcoin_mallocTransaction :: Ptr RawTransaction -> IO (Ptr CTransaction) foreign import ccall unsafe "&" simplicity_bitcoin_freeTransaction :: FunPtr (Ptr CTransaction -> IO ()) foreign import ccall unsafe "" simplicity_bitcoin_mallocTapEnv :: Ptr RawTapEnv -> IO (Ptr CTapEnv) foreign import ccall unsafe "&" simplicity_bitcoin_freeTapEnv :: FunPtr (Ptr CTapEnv -> IO ()) sizeof_rawBuffer :: Int sizeof_rawBuffer = fromIntegral . unsafeLocalState $ peek c_sizeof_rawBitcoinBuffer sizeof_rawOutput :: Int sizeof_rawOutput = fromIntegral . unsafeLocalState $ peek c_sizeof_rawBitcoinOutput sizeof_rawInput :: Int sizeof_rawInput = fromIntegral . unsafeLocalState $ peek c_sizeof_rawBitcoinInput sizeof_rawTransaction :: Int sizeof_rawTransaction = fromIntegral . unsafeLocalState $ peek c_sizeof_rawBitcoinTransaction sizeof_rawTapEnv :: Int sizeof_rawTapEnv = fromIntegral . unsafeLocalState $ peek c_sizeof_rawBitcoinTapEnv sizeof_txEnv :: Int sizeof_txEnv = fromIntegral . unsafeLocalState $ peek c_bitcoin_sizeof_txEnv withRawBuffer :: BSL.ByteString -> (Ptr RawBuffer -> IO b) -> IO b withRawBuffer str k = allocaBytes sizeof_rawBuffer $ \pRawBuffer -> BS.useAsCStringLen (BSL.toStrict str) $ \(pCharStr, len) -> do c_set_rawBitcoinBuffer pRawBuffer pCharStr (fromIntegral len) k pRawBuffer withRawOutputs :: Vector TxOutput -> (Ptr RawOutput -> IO b) -> IO b withRawOutputs txos k = allocaBytes (len * sizeof_rawOutput) $ \pRawOutput -> foldr ($) (k pRawOutput) [pokeRawOutput txo (pRawOutput `plusPtr` (i*sizeof_rawOutput)) | (i, txo) <- zip [0..] (toList txos)] where len = fromIntegral $ length txos pokeRawOutput :: TxOutput -> Ptr RawOutput -> IO b -> IO b pokeRawOutput txo pRawOutput k = withRawBuffer (txoScript txo) $ \pScript -> do c_set_rawBitcoinOutput pRawOutput (fromIntegral $ txoValue txo) pScript k withRawInputs :: Vector SigTxInput -> (Ptr RawInput -> IO b) -> IO b withRawInputs txis k = allocaBytes (len * sizeof_rawInput) $ \pRawInput -> do foldr ($) (k pRawInput) [pokeRawInput txo (pRawInput `plusPtr` (i*sizeof_rawInput)) | (i, txo) <- zip [0..] (toList txis)] where len = fromIntegral $ length txis withMaybeRawBuffer Nothing = ($ nullPtr) withMaybeRawBuffer (Just buf) = withRawBuffer buf pokeRawInput :: SigTxInput -> Ptr RawInput -> IO b -> IO b pokeRawInput txi pRawInput k = withMaybeRawBuffer (sigTxiAnnex txi) $ \pAnnex -> withRawBuffer (sigTxiScriptSig txi) $ \pScriptSig -> BS.useAsCString (encode . opHash $ sigTxiPreviousOutpoint txi) $ \pPrevTxid -> withRawBuffer (txoScript $ sigTxiTxo txi) $ \pScript -> do c_set_rawBitcoinInput pRawInput pAnnex pScriptSig pPrevTxid (fromIntegral . opIndex . sigTxiPreviousOutpoint $ txi) (fromIntegral . txoValue $ sigTxiTxo txi) pScript (fromIntegral . sigTxiSequence $ txi) k withRawTransaction :: SigTx -> (Ptr RawTransaction -> IO b) -> IO b withRawTransaction tx k = allocaBytes sizeof_rawTransaction $ \pRawTransaction -> withRawInputs (sigTxIn tx) $ \pInput -> withRawOutputs (sigTxOut tx) $ \pOutput -> do BS.useAsCString (encode $ txid tx) $ \pTxid -> do c_set_rawBitcoinTransaction pRawTransaction pTxid version pInput numInputs pOutput numOutputs lockTime k pRawTransaction where version = fromIntegral (sigTxVersion tx) numInputs = fromIntegral $ length (sigTxIn tx) numOutputs = fromIntegral $ length (sigTxOut tx) lockTime = fromIntegral (sigTxLock tx) withRawTapEnv :: TapEnv -> (Ptr RawTapEnv -> IO b) -> IO b withRawTapEnv tapEnv k | length (tappath tapEnv) <= 128 = allocaBytes sizeof_rawTapEnv $ \pRawTapEnv -> BS.useAsCString encodePath $ \pControlBlock -> do BS.useAsCString (encode $ tapScriptCMR tapEnv) $ \pCmr -> do c_set_rawBitcoinTapEnv pRawTapEnv pControlBlock (fromIntegral . length $ tappath tapEnv) pCmr k pRawTapEnv where encodePath = BS.cons (tapleafVersion tapEnv) (BS.concat (encode (tapInternalKey tapEnv) : map encode (tappath tapEnv))) marshallTransaction :: SigTx -> IO (ForeignPtr CTransaction) marshallTransaction tx = withRawTransaction tx $ \pRawTransaction -> simplicity_bitcoin_mallocTransaction pRawTransaction >>= newForeignPtr simplicity_bitcoin_freeTransaction marshallTapEnv :: TapEnv -> IO (ForeignPtr CTapEnv) marshallTapEnv env = withRawTapEnv env $ \pRawTapEnv -> simplicity_bitcoin_mallocTapEnv pRawTapEnv >>= newForeignPtr simplicity_bitcoin_freeTapEnv withEnv :: ForeignPtr CTransaction -> Word32 -> ForeignPtr CTapEnv -> (Ptr CTxEnv -> IO b) -> IO b withEnv cTransaction ix cTapEnv k = allocaBytes sizeof_txEnv $ \pTxEnv -> withForeignPtr cTransaction $ \pTransaction -> withForeignPtr cTapEnv $ \pTapEnv -> do c_bitcoin_set_txEnv pTxEnv pTransaction pTapEnv (fromIntegral ix) k pTxEnv withPrimEnv :: PrimEnv -> (Ptr CTxEnv -> IO b) -> IO b withPrimEnv env k = do cTransaction <- marshallTransaction (envTx env) cTapEnv <- marshallTapEnv (envTap env) withEnv cTransaction (envIx env) cTapEnv k ================================================ FILE: Haskell/Simplicity/Bitcoin/FFI/Jets.hs ================================================ -- | This module binds the C implementation of jets for Simplicity for assertions. {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.Bitcoin.FFI.Jets ( version , lock_time , input_prev_outpoint , input_value , input_script_hash , input_sequence , input_annex_hash , input_script_sig_hash , output_value , output_script_hash , script_cmr , transaction_id , current_index , current_prev_outpoint , current_value , current_script_hash , current_sequence , current_annex_hash , current_script_sig_hash , tapleaf_version , tappath , internal_key , num_inputs , num_outputs , tx_is_final , tx_lock_height , tx_lock_time , tx_lock_distance , tx_lock_duration , check_lock_height , check_lock_time , check_lock_distance , check_lock_duration , outpoint_hash , annex_hash , build_tapleaf_simplicity , build_tapbranch , build_taptweak , output_values_hash , output_scripts_hash , outputs_hash , output_hash , total_output_value , input_outpoints_hash , input_values_hash , input_scripts_hash , input_utxos_hash , input_utxo_hash , input_sequences_hash , input_annexes_hash , input_script_sigs_hash , inputs_hash , input_hash , total_input_value , fee , tx_hash , tapleaf_hash , tappath_hash , tap_env_hash , sig_all_hash ) where import Foreign.Ptr (Ptr) import Foreign.C.Types (CBool(..)) import Simplicity.Bitcoin.FFI.Env import Simplicity.Bitcoin.Primitive import Simplicity.FFI.Frame import Simplicity.Programs.Elements import Simplicity.Programs.LibSecp256k1 import Simplicity.Ty import Simplicity.Ty.Word -- | This cannot be used with jets that access global variables. unsafeLocalJet :: (TyC a, TyC b) => (Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool) -> PrimEnv -> a -> Maybe b unsafeLocalJet jet env = unsafeLocalCoreJet (\dst src -> withPrimEnv env (jet dst src)) foreign import ccall unsafe "" c_bitcoin_version :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_lock_time :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_prev_outpoint :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_value :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_script_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_sequence :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_annex_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_script_sig_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_output_value :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_output_script_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_script_cmr :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_transaction_id :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_index :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_prev_outpoint :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_value :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_script_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_sequence :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_annex_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_current_script_sig_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tapleaf_version :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tappath :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_internal_key :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_num_inputs :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_num_outputs :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tx_is_final :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tx_lock_height :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tx_lock_time :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tx_lock_distance :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tx_lock_duration :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_check_lock_height :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_check_lock_time :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_check_lock_distance :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_check_lock_duration :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_outpoint_hash :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_bitcoin_annex_hash :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_bitcoin_build_tapleaf_simplicity :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_bitcoin_build_tapbranch :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_bitcoin_build_taptweak :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_bitcoin_output_values_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_output_nonces_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_output_scripts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_outputs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_output_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_total_output_value :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_outpoints_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_values_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_scripts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_utxos_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_utxo_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_sequences_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_annexes_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_script_sigs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_inputs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_input_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_total_input_value :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_fee :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tx_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tapleaf_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tappath_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_tap_env_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_bitcoin_sig_all_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool version :: PrimEnv -> () -> Maybe Word32 version = unsafeLocalJet c_bitcoin_version lock_time :: PrimEnv -> () -> Maybe Word32 lock_time = unsafeLocalJet c_bitcoin_lock_time num_inputs :: PrimEnv -> () -> Maybe Word32 num_inputs = unsafeLocalJet c_bitcoin_num_inputs input_prev_outpoint :: PrimEnv -> Word32 -> Maybe (S (Word256, Word32)) input_prev_outpoint = unsafeLocalJet c_bitcoin_input_prev_outpoint input_value :: PrimEnv -> Word32 -> Maybe (S Word64) input_value = unsafeLocalJet c_bitcoin_input_value input_script_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_script_hash = unsafeLocalJet c_bitcoin_input_script_hash input_sequence :: PrimEnv -> Word32 -> Maybe (S Word32) input_sequence = unsafeLocalJet c_bitcoin_input_sequence input_annex_hash :: PrimEnv -> Word32 -> Maybe (S (S Word256)) input_annex_hash = unsafeLocalJet c_bitcoin_input_annex_hash input_script_sig_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_script_sig_hash = unsafeLocalJet c_bitcoin_input_script_sig_hash current_index :: PrimEnv -> () -> Maybe Word32 current_index = unsafeLocalJet c_bitcoin_current_index current_prev_outpoint :: PrimEnv -> () -> Maybe (Word256, Word32) current_prev_outpoint = unsafeLocalJet c_bitcoin_current_prev_outpoint current_value :: PrimEnv -> () -> Maybe Word64 current_value = unsafeLocalJet c_bitcoin_current_value current_script_hash :: PrimEnv -> () -> Maybe Word256 current_script_hash = unsafeLocalJet c_bitcoin_current_script_hash current_sequence :: PrimEnv -> () -> Maybe Word32 current_sequence = unsafeLocalJet c_bitcoin_current_sequence current_annex_hash :: PrimEnv -> () -> Maybe (S Word256) current_annex_hash = unsafeLocalJet c_bitcoin_current_annex_hash current_script_sig_hash :: PrimEnv -> () -> Maybe Word256 current_script_sig_hash = unsafeLocalJet c_bitcoin_current_script_sig_hash tapleaf_version :: PrimEnv -> () -> Maybe Word8 tapleaf_version = unsafeLocalJet c_bitcoin_tapleaf_version tappath :: PrimEnv -> Word8 -> Maybe (S Word256) tappath = unsafeLocalJet c_bitcoin_tappath internal_key :: PrimEnv -> () -> Maybe PubKey internal_key = unsafeLocalJet c_bitcoin_internal_key num_outputs :: PrimEnv -> () -> Maybe Word32 num_outputs = unsafeLocalJet c_bitcoin_num_outputs output_value :: PrimEnv -> Word32 -> Maybe (S Word64) output_value = unsafeLocalJet c_bitcoin_output_value output_script_hash :: PrimEnv -> Word32 -> Maybe (S Word256) output_script_hash = unsafeLocalJet c_bitcoin_output_script_hash script_cmr :: PrimEnv -> () -> Maybe Word256 script_cmr = unsafeLocalJet c_bitcoin_script_cmr transaction_id :: PrimEnv -> () -> Maybe Word256 transaction_id = unsafeLocalJet c_bitcoin_transaction_id tx_is_final :: PrimEnv -> () -> Maybe Bit tx_is_final = unsafeLocalJet c_bitcoin_tx_is_final tx_lock_height :: PrimEnv -> () -> Maybe Word32 tx_lock_height = unsafeLocalJet c_bitcoin_tx_lock_height tx_lock_time :: PrimEnv -> () -> Maybe Word32 tx_lock_time = unsafeLocalJet c_bitcoin_tx_lock_time tx_lock_distance :: PrimEnv -> () -> Maybe Word16 tx_lock_distance = unsafeLocalJet c_bitcoin_tx_lock_distance tx_lock_duration :: PrimEnv -> () -> Maybe Word16 tx_lock_duration = unsafeLocalJet c_bitcoin_tx_lock_duration check_lock_height :: PrimEnv -> Word32 -> Maybe () check_lock_height = unsafeLocalJet c_bitcoin_check_lock_height check_lock_time :: PrimEnv -> Word32 -> Maybe () check_lock_time = unsafeLocalJet c_bitcoin_check_lock_time check_lock_distance :: PrimEnv -> Word16 -> Maybe () check_lock_distance = unsafeLocalJet c_bitcoin_check_lock_distance check_lock_duration :: PrimEnv -> Word16 -> Maybe () check_lock_duration = unsafeLocalJet c_bitcoin_check_lock_duration outpoint_hash :: (Ctx8, (Word256, Word32)) -> Maybe Ctx8 outpoint_hash = unsafeLocalCoreJet c_bitcoin_outpoint_hash annex_hash :: (Ctx8, S Word256) -> Maybe Ctx8 annex_hash = unsafeLocalCoreJet c_bitcoin_annex_hash build_tapleaf_simplicity :: Word256 -> Maybe Word256 build_tapleaf_simplicity = unsafeLocalCoreJet c_bitcoin_build_tapleaf_simplicity build_tapbranch :: (Word256, Word256) -> Maybe Word256 build_tapbranch = unsafeLocalCoreJet c_bitcoin_build_tapbranch build_taptweak :: (Word256, Word256) -> Maybe Word256 build_taptweak = unsafeLocalCoreJet c_bitcoin_build_taptweak output_values_hash :: PrimEnv -> () -> Maybe Word256 output_values_hash = unsafeLocalJet c_bitcoin_output_values_hash output_scripts_hash :: PrimEnv -> () -> Maybe Word256 output_scripts_hash = unsafeLocalJet c_bitcoin_output_scripts_hash outputs_hash :: PrimEnv -> () -> Maybe Word256 outputs_hash = unsafeLocalJet c_bitcoin_outputs_hash output_hash :: PrimEnv -> Word32 -> Maybe (S Word256) output_hash = unsafeLocalJet c_bitcoin_output_hash total_output_value :: PrimEnv -> () -> Maybe Word64 total_output_value = unsafeLocalJet c_bitcoin_total_output_value input_outpoints_hash :: PrimEnv -> () -> Maybe Word256 input_outpoints_hash = unsafeLocalJet c_bitcoin_input_outpoints_hash input_values_hash :: PrimEnv -> () -> Maybe Word256 input_values_hash = unsafeLocalJet c_bitcoin_input_values_hash input_scripts_hash :: PrimEnv -> () -> Maybe Word256 input_scripts_hash = unsafeLocalJet c_bitcoin_input_scripts_hash input_utxos_hash :: PrimEnv -> () -> Maybe Word256 input_utxos_hash = unsafeLocalJet c_bitcoin_input_utxos_hash input_utxo_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_utxo_hash = unsafeLocalJet c_bitcoin_input_utxo_hash input_sequences_hash :: PrimEnv -> () -> Maybe Word256 input_sequences_hash = unsafeLocalJet c_bitcoin_input_sequences_hash input_annexes_hash :: PrimEnv -> () -> Maybe Word256 input_annexes_hash = unsafeLocalJet c_bitcoin_input_annexes_hash input_script_sigs_hash :: PrimEnv -> () -> Maybe Word256 input_script_sigs_hash = unsafeLocalJet c_bitcoin_input_script_sigs_hash inputs_hash :: PrimEnv -> () -> Maybe Word256 inputs_hash = unsafeLocalJet c_bitcoin_inputs_hash input_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_hash = unsafeLocalJet c_bitcoin_input_hash total_input_value :: PrimEnv -> () -> Maybe Word64 total_input_value = unsafeLocalJet c_bitcoin_total_input_value fee :: PrimEnv -> () -> Maybe Word64 fee = unsafeLocalJet c_bitcoin_fee tx_hash :: PrimEnv -> () -> Maybe Word256 tx_hash = unsafeLocalJet c_bitcoin_tx_hash tapleaf_hash :: PrimEnv -> () -> Maybe Word256 tapleaf_hash = unsafeLocalJet c_bitcoin_tapleaf_hash tappath_hash :: PrimEnv -> () -> Maybe Word256 tappath_hash = unsafeLocalJet c_bitcoin_tappath_hash tap_env_hash :: PrimEnv -> () -> Maybe Word256 tap_env_hash = unsafeLocalJet c_bitcoin_tap_env_hash sig_all_hash :: PrimEnv -> () -> Maybe Word256 sig_all_hash = unsafeLocalJet c_bitcoin_sig_all_hash ================================================ FILE: Haskell/Simplicity/Bitcoin/Jets.hs ================================================ -- | This module provides a canonical set of known jets for Simplicity for Bitcoin. (At the moment this just consists of 'CoreJet's.) {-# LANGUAGE GADTs, StandaloneDeriving, TypeFamilies #-} module Simplicity.Bitcoin.Jets ( JetType(..), BitcoinJet(..), SigHashJet(..), TimeLockJet(..), TransactionJet(..) , bitcoinCatalogue , asJet , jetSubst, pruneSubst , getTermLengthCode, putTermLengthCode , fastEval , jetMap -- * Re-exports , WrappedSimplicity, unwrap , Simplicity.Bitcoin.JetType.specification, Simplicity.Bitcoin.JetType.implementation , Simplicity.Bitcoin.JetType.getJetBit, Simplicity.Bitcoin.JetType.putJetBit , Simplicity.Bitcoin.JetType.jetCost , Semantics.FastEval ) where import Prelude hiding (fail, drop, take) import Control.Applicative ((<|>)) import Control.Monad (guard) import Data.Foldable (toList) import qualified Data.Map as Map import Data.Proxy (Proxy(Proxy)) import Data.Type.Equality ((:~:)(Refl)) import Data.Serialize (runPut, put, putWord8) import Data.String (fromString) import Data.Vector ((!?)) import Data.Void (Void, vacuous) import Lens.Family2 ((^..), over, review) import Simplicity.Digest import Simplicity.CoreJets hiding (BitcoinJet) import qualified Simplicity.CoreJets as CoreJets import Simplicity.Bitcoin.Benchmarks import Simplicity.Bitcoin.Dag hiding (jetSubst, pruneSubst) import qualified Simplicity.Bitcoin.Dag as Dag import Simplicity.Bitcoin.Term import Simplicity.Bitcoin.DataTypes import qualified Simplicity.Bitcoin.JetType import Simplicity.Bitcoin.Primitive (PrimEnv, PubKey, primEnvHash, envTx, envIx, envTap) import qualified Simplicity.Bitcoin.Primitive as Prim import qualified Simplicity.Bitcoin.Serialization.BitString as BitString import qualified Simplicity.Bitcoin.Semantics as Semantics import qualified Simplicity.Bitcoin.Programs.SigHash.Lib as SigHash import qualified Simplicity.Bitcoin.Programs.TimeLock as TimeLock import qualified Simplicity.Bitcoin.Programs.Transaction.Lib as Prog import qualified Simplicity.LibSecp256k1.Schnorr as Schnorr import Simplicity.MerkleRoot import Simplicity.Programs.Sha256.Lib (Ctx8) import qualified Simplicity.Programs.Bitcoin.Lib as Prog import Simplicity.Programs.Word import Simplicity.Serialization import Simplicity.Tensor import Simplicity.Tree import Simplicity.Ty import Simplicity.Ty.Bit import Simplicity.Ty.Sha256 import Simplicity.Ty.Word import qualified Simplicity.Word as W import Simplicity.Weight -- | A type of tokens for the canonical set of known jets for Simplicity for Bitcoin. (At the moment this just consists of 'CoreJet's.) -- -- The tokens themselves are not exported. You are expected to use 'Simplicity.Dag.jetDag' to substitute known jets found in Simplicity expressions. data JetType a b where ConstWordJet :: ConstWordContent b -> JetType () b CoreJet :: CoreJet a b -> JetType a b BitcoinJet :: BitcoinJet a b -> JetType a b deriving instance Eq (JetType a b) deriving instance Show (JetType a b) data BitcoinJet a b where SigHashJet :: SigHashJet a b -> BitcoinJet a b TimeLockJet :: TimeLockJet a b -> BitcoinJet a b TransactionJet :: TransactionJet a b -> BitcoinJet a b deriving instance Eq (BitcoinJet a b) deriving instance Show (BitcoinJet a b) data SigHashJet a b where SigAllHash :: SigHashJet () Word256 TxHash :: SigHashJet () Word256 TapEnvHash :: SigHashJet () Word256 OutputsHash :: SigHashJet () Word256 InputsHash :: SigHashJet () Word256 InputUtxosHash :: SigHashJet () Word256 OutputHash :: SigHashJet Word32 (S Word256) OutputValuesHash :: SigHashJet () Word256 OutputScriptsHash :: SigHashJet () Word256 InputHash :: SigHashJet Word32 (S Word256) InputOutpointsHash :: SigHashJet () Word256 InputSequencesHash :: SigHashJet () Word256 InputAnnexesHash :: SigHashJet () Word256 InputScriptSigsHash :: SigHashJet () Word256 InputUtxoHash :: SigHashJet Word32 (S Word256) InputValuesHash :: SigHashJet () Word256 InputScriptsHash :: SigHashJet () Word256 TapleafHash :: SigHashJet () Word256 TappathHash :: SigHashJet () Word256 OutpointHash :: SigHashJet (Ctx8, (Word256, Word32)) Ctx8 AnnexHash :: SigHashJet (Ctx8, S Word256) Ctx8 BuildTapleafSimplicity :: SigHashJet Word256 Word256 BuildTapbranch :: SigHashJet (Word256, Word256) Word256 BuildTaptweak :: SigHashJet (PubKey, Word256) PubKey deriving instance Eq (SigHashJet a b) deriving instance Show (SigHashJet a b) data TimeLockJet a b where CheckLockHeight :: TimeLockJet TimeLock.Height () CheckLockTime :: TimeLockJet TimeLock.Time () CheckLockDistance :: TimeLockJet TimeLock.Distance () CheckLockDuration :: TimeLockJet TimeLock.Duration () TxLockHeight :: TimeLockJet () TimeLock.Height TxLockTime :: TimeLockJet () TimeLock.Time TxLockDistance :: TimeLockJet () TimeLock.Distance TxLockDuration :: TimeLockJet () TimeLock.Duration TxIsFinal :: TimeLockJet () TimeLock.Bit deriving instance Eq (TimeLockJet a b) deriving instance Show (TimeLockJet a b) data TransactionJet a b where ScriptCMR :: TransactionJet () Word256 InternalKey :: TransactionJet () PubKey CurrentIndex :: TransactionJet () Word32 NumInputs :: TransactionJet () Word32 NumOutputs :: TransactionJet () Word32 LockTime :: TransactionJet () Word32 Fee :: TransactionJet () Word64 OutputValue :: TransactionJet Word32 (Either () Word64) OutputScriptHash :: TransactionJet Word32 (Either () Word256) TotalOutputValue :: TransactionJet () Word64 CurrentPrevOutpoint :: TransactionJet () (Word256,Word32) CurrentValue :: TransactionJet () Word64 CurrentScriptHash :: TransactionJet () Word256 CurrentSequence :: TransactionJet () Word32 CurrentAnnexHash :: TransactionJet () (Either () Word256) CurrentScriptSigHash :: TransactionJet () Word256 InputPrevOutpoint :: TransactionJet Word32 (Either () (Word256,Word32)) InputValue :: TransactionJet Word32 (Either () Word64) InputScriptHash :: TransactionJet Word32 (S Word256) InputSequence :: TransactionJet Word32 (Either () Word32) InputAnnexHash :: TransactionJet Word32 (Either () (Either () Word256)) InputScriptSigHash :: TransactionJet Word32 (Either () Word256) TotalInputValue :: TransactionJet () Word64 TapleafVersion :: TransactionJet () Word8 Tappath :: TransactionJet Word8 (Either () Word256) Version :: TransactionJet () Word32 TransactionId :: TransactionJet () Word256 deriving instance Eq (TransactionJet a b) deriving instance Show (TransactionJet a b) specificationBitcoin :: (Assert term, Primitive term) => BitcoinJet a b -> term a b specificationBitcoin (SigHashJet x) = specificationSigHash x specificationBitcoin (TimeLockJet x) = specificationTimeLock x specificationBitcoin (TransactionJet x) = specificationTransaction x specificationSigHash :: (Assert term, Primitive term) => SigHashJet a b -> term a b specificationSigHash SigAllHash = SigHash.sigAllHash specificationSigHash TxHash = SigHash.txHash specificationSigHash TapEnvHash = SigHash.tapEnvHash specificationSigHash OutputsHash = SigHash.outputsHash specificationSigHash InputsHash = SigHash.inputsHash specificationSigHash InputUtxosHash = SigHash.inputUtxosHash specificationSigHash OutputHash = SigHash.outputHash specificationSigHash OutputValuesHash = SigHash.outputValuesHash specificationSigHash OutputScriptsHash = SigHash.outputScriptsHash specificationSigHash InputHash = SigHash.inputHash specificationSigHash InputOutpointsHash = SigHash.inputOutpointsHash specificationSigHash InputSequencesHash = SigHash.inputSequencesHash specificationSigHash InputAnnexesHash = SigHash.inputAnnexesHash specificationSigHash InputScriptSigsHash = SigHash.inputScriptSigsHash specificationSigHash InputUtxoHash = SigHash.inputUtxoHash specificationSigHash InputValuesHash = SigHash.inputValuesHash specificationSigHash InputScriptsHash = SigHash.inputScriptsHash specificationSigHash TapleafHash = SigHash.tapleafHash specificationSigHash TappathHash = SigHash.tappathHash specificationSigHash OutpointHash = Prog.outpointHash specificationSigHash AnnexHash = Prog.annexHash specificationSigHash BuildTapleafSimplicity = Prog.buildTapleafSimplicity specificationSigHash BuildTapbranch = Prog.buildTapbranch specificationSigHash BuildTaptweak = Prog.buildTaptweak specificationTimeLock :: (Assert term, Primitive term) => TimeLockJet a b -> term a b specificationTimeLock CheckLockHeight = TimeLock.checkLockHeight specificationTimeLock CheckLockTime = TimeLock.checkLockTime specificationTimeLock CheckLockDistance = TimeLock.checkLockDistance specificationTimeLock CheckLockDuration = TimeLock.checkLockDuration specificationTimeLock TxLockHeight = TimeLock.txLockHeight specificationTimeLock TxLockTime = TimeLock.txLockTime specificationTimeLock TxLockDistance = TimeLock.txLockDistance specificationTimeLock TxLockDuration = TimeLock.txLockDuration specificationTimeLock TxIsFinal = TimeLock.txIsFinal specificationTransaction :: (Assert term, Primitive term) => TransactionJet a b -> term a b specificationTransaction ScriptCMR = primitive Prim.ScriptCMR specificationTransaction InternalKey = primitive Prim.InternalKey specificationTransaction CurrentIndex = primitive Prim.CurrentIndex specificationTransaction NumInputs = Prog.numInputs specificationTransaction NumOutputs = Prog.numOutputs specificationTransaction LockTime = primitive Prim.LockTime specificationTransaction OutputValue = primitive Prim.OutputValue specificationTransaction OutputScriptHash = primitive Prim.OutputScriptHash specificationTransaction TotalOutputValue = Prog.totalOutputValue specificationTransaction CurrentPrevOutpoint = Prog.currentPrevOutpoint specificationTransaction CurrentValue = Prog.currentValue specificationTransaction CurrentScriptHash = Prog.currentScriptHash specificationTransaction CurrentSequence = Prog.currentSequence specificationTransaction CurrentAnnexHash = Prog.currentAnnexHash specificationTransaction CurrentScriptSigHash = Prog.currentScriptSigHash specificationTransaction InputPrevOutpoint = primitive Prim.InputPrevOutpoint specificationTransaction InputValue = primitive Prim.InputValue specificationTransaction InputScriptHash = primitive Prim.InputScriptHash specificationTransaction InputSequence = primitive Prim.InputSequence specificationTransaction InputAnnexHash = primitive Prim.InputAnnexHash specificationTransaction InputScriptSigHash = primitive Prim.InputScriptSigHash specificationTransaction TotalInputValue = Prog.totalInputValue specificationTransaction Fee = Prog.fee specificationTransaction TapleafVersion = primitive Prim.TapleafVersion specificationTransaction Tappath = primitive Prim.Tappath specificationTransaction Version = primitive Prim.Version specificationTransaction TransactionId = primitive Prim.TransactionId implementationBitcoin :: BitcoinJet a b -> PrimEnv -> a -> Maybe b implementationBitcoin (SigHashJet x) = implementationSigHash x implementationBitcoin (TimeLockJet x) = implementationTimeLock x implementationBitcoin (TransactionJet x) = implementationTransaction x implementationSigHash :: SigHashJet a b -> PrimEnv -> a -> Maybe b implementationSigHash SigAllHash env _ = Just . toWord256 . integerHash256 $ primEnvHash env implementationSigHash TxHash env _ = Just . toWord256 . integerHash256 $ txHash (envTx env) implementationSigHash TapEnvHash env _ = Just . toWord256 . integerHash256 $ tapEnvHash (envTap env) implementationSigHash OutputsHash env _ = Just . toWord256 . integerHash256 $ outputsHash (envTx env) implementationSigHash InputsHash env _ = Just . toWord256 . integerHash256 $ inputsHash (envTx env) implementationSigHash InputUtxosHash env _ = Just . toWord256 . integerHash256 $ inputUtxosHash (envTx env) implementationSigHash OutputHash env i = Just . fmap (toWord256 . integerHash256 . outputHash) . maybe (Left ()) Right $ sigTxOut (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash OutputValuesHash env _ = Just . toWord256 . integerHash256 $ outputValuesHash (envTx env) implementationSigHash OutputScriptsHash env _ = Just . toWord256 . integerHash256 $ outputScriptsHash (envTx env) implementationSigHash InputHash env i = Just . fmap (toWord256 . integerHash256 . inputHash) . maybe (Left ()) Right $ sigTxIn (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash InputOutpointsHash env _ = Just . toWord256 . integerHash256 $ inputOutpointsHash (envTx env) implementationSigHash InputSequencesHash env _ = Just . toWord256 . integerHash256 $ inputSequencesHash (envTx env) implementationSigHash InputAnnexesHash env _ = Just . toWord256 . integerHash256 $ inputAnnexesHash (envTx env) implementationSigHash InputScriptSigsHash env _ = Just . toWord256 . integerHash256 $ inputScriptSigsHash (envTx env) implementationSigHash InputUtxoHash env i = Just . fmap (toWord256 . integerHash256 . outputHash . sigTxiTxo) . maybe (Left ()) Right $ sigTxIn (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash InputValuesHash env _ = Just . toWord256 . integerHash256 $ inputValuesHash (envTx env) implementationSigHash InputScriptsHash env _ = Just . toWord256 . integerHash256 $ inputScriptsHash (envTx env) implementationSigHash TapleafHash env _ = Just . toWord256 . integerHash256 $ tapleafHash (envTap env) implementationSigHash TappathHash env _ = Just . toWord256 . integerHash256 $ tappathHash (envTap env) implementationSigHash OutpointHash _env (ctx, op) = toCtx8 <$> (flip ctxAdd (runPut (putOutpointBE (cast op))) =<< fromCtx8 ctx) where cast (h, i) = Outpoint (review (over be256) (fromW256 h)) (fromW32 i) fromW256 = fromIntegral . fromWord256 fromW32 = fromIntegral . fromWord32 implementationSigHash AnnexHash _env (ctx, mw256) = toCtx8 <$> (flip ctxAdd (runPut . putMW256 $ mw256) =<< fromCtx8 ctx) where putMW256 (Left _) = putWord8 0x00 putMW256 (Right w256) = putWord8 0x01 >> put (fromIntegral (fromWord256 w256) :: W.Word256) implementationSigHash BuildTapleafSimplicity _env cmr = Just . toWord256 . integerHash256 . bsHash . runPut $ put tag >> put tag >> putWord8 tapleafSimplicityVersion >> putWord8 32 >> put (fromW256 cmr) where tag = bsHash (fromString "TapLeaf") tapleafSimplicityVersion = 0xbe fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 implementationSigHash BuildTapbranch _env (wa,wb) = Just . toWord256 . integerHash256 . bsHash . runPut $ put tag >> put tag >> put min >> put max where a = fromW256 wa b = fromW256 wb min = if a < b then a else b max = if a < b then b else a tag = bsHash (fromString "TapBranch") fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 implementationSigHash BuildTaptweak _env (key,h) = cast <$> taptweak pk h0 where pk = Schnorr.PubKey (fromW256 key) h0 = review (over be256) (fromW256 h) cast (Schnorr.PubKey k) = toWord256 . toInteger $ k fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 implementationTimeLock :: TimeLockJet a b -> PrimEnv -> a -> Maybe b implementationTimeLock CheckLockHeight env x | txIsFinal (envTx env) = guard $ fromWord32 x <= 0 | Left l <- parseLock lock = guard $ fromWord32 x <= fromIntegral l | otherwise = guard $ fromWord32 x <= 0 where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock CheckLockTime env x | txIsFinal (envTx env) = guard $ fromWord32 x <= 0 | Right l <- parseLock lock = guard $ fromWord32 x <= fromIntegral l | otherwise = guard $ fromWord32 x <= 0 where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock CheckLockDistance env x | sigTxVersion (envTx env) < 2 = guard $ fromWord16 x <= 0 | Just (Left l) <- parseSequence =<< sequence = guard $ fromWord16 x <= fromIntegral l | otherwise = guard $ fromWord16 x <= 0 where sequence = sigTxiSequence <$> (sigTxIn (envTx env) !? (fromIntegral $ envIx env)) implementationTimeLock CheckLockDuration env x | sigTxVersion (envTx env) < 2 = guard $ fromWord16 x <= 0 | Just (Right l) <- parseSequence =<< sequence = guard $ fromWord16 x <= fromIntegral l | otherwise = guard $ fromWord16 x <= 0 where sequence = sigTxiSequence <$> (sigTxIn (envTx env) !? (fromIntegral $ envIx env)) implementationTimeLock TxLockHeight env () | txIsFinal (envTx env) = Just (toWord32 0) | Left l <- parseLock lock = Just . toWord32 $ fromIntegral l | otherwise = Just (toWord32 0) where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock TxLockTime env () | txIsFinal (envTx env) = Just (toWord32 0) | Right l <- parseLock lock = Just . toWord32 $ fromIntegral l | otherwise = Just (toWord32 0) where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock TxLockDistance env () | sigTxVersion (envTx env) < 2 = Just (toWord16 0) | Just (Left l) <- parseSequence =<< sequence = Just . toWord16 $ fromIntegral l | otherwise = Just (toWord16 0) where sequence = sigTxiSequence <$> (sigTxIn (envTx env) !? (fromIntegral $ envIx env)) implementationTimeLock TxLockDuration env () | sigTxVersion (envTx env) < 2 = Just (toWord16 0) | Just (Right l) <- parseSequence =<< sequence = Just . toWord16 $ fromIntegral l | otherwise = Just (toWord16 0) where sequence = sigTxiSequence <$> (sigTxIn (envTx env) !? (fromIntegral $ envIx env)) implementationTimeLock TxIsFinal env () = Just $ toBit (txIsFinal (envTx env)) implementationTransaction :: TransactionJet a b -> PrimEnv -> a -> Maybe b implementationTransaction TotalOutputValue env _ = Just . toWord64 . fromIntegral $ txTotalOutputValue (envTx env) implementationTransaction TotalInputValue env _ = Just . toWord64 . fromIntegral $ txTotalInputValue (envTx env) implementationTransaction Fee env _ = Just . toWord64 . fromIntegral $ txFee (envTx env) implementationTransaction x env i = Semantics.sem (specificationTransaction x) env i getJetBitBitcoin :: (Monad m) => m Void -> m Bool -> m (SomeArrow BitcoinJet) getJetBitBitcoin = getCatalogue bitcoinCatalogue bitcoinCatalogue :: Catalogue (SomeArrow BitcoinJet) bitcoinCatalogue = Shelf [ someArrowMap SigHashJet <$> sigHashCatalogue , someArrowMap TimeLockJet <$> timeLockCatalogue , someArrowMap TransactionJet <$> transactionCatalogue ] sigHashCatalogue = book [ SomeArrow SigAllHash , SomeArrow TxHash , SomeArrow TapEnvHash , SomeArrow OutputsHash , SomeArrow InputsHash , SomeArrow InputUtxosHash , SomeArrow OutputHash , SomeArrow OutputValuesHash , SomeArrow OutputScriptsHash , SomeArrow InputHash , SomeArrow InputOutpointsHash , SomeArrow InputSequencesHash , SomeArrow InputAnnexesHash , SomeArrow InputScriptSigsHash , SomeArrow InputUtxoHash , SomeArrow InputValuesHash , SomeArrow InputScriptsHash , SomeArrow TapleafHash , SomeArrow TappathHash , SomeArrow OutpointHash , SomeArrow AnnexHash , SomeArrow BuildTapleafSimplicity , SomeArrow BuildTapbranch , SomeArrow BuildTaptweak ] timeLockCatalogue = book [ SomeArrow CheckLockHeight , SomeArrow CheckLockTime , SomeArrow CheckLockDistance , SomeArrow CheckLockDuration , SomeArrow TxLockHeight , SomeArrow TxLockTime , SomeArrow TxLockDistance , SomeArrow TxLockDuration , SomeArrow TxIsFinal ] transactionCatalogue = book [ SomeArrow ScriptCMR , SomeArrow InternalKey , SomeArrow CurrentIndex , SomeArrow NumInputs , SomeArrow NumOutputs , SomeArrow LockTime , SomeArrow Fee , SomeArrow OutputValue , SomeArrow OutputScriptHash , SomeArrow TotalOutputValue , SomeArrow CurrentPrevOutpoint , SomeArrow CurrentValue , SomeArrow CurrentScriptHash , SomeArrow CurrentSequence , SomeArrow CurrentAnnexHash , SomeArrow CurrentScriptSigHash , SomeArrow InputPrevOutpoint , SomeArrow InputValue , SomeArrow InputScriptHash , SomeArrow InputSequence , SomeArrow InputAnnexHash , SomeArrow InputScriptSigHash , SomeArrow TotalInputValue , SomeArrow TapleafVersion , SomeArrow Tappath , SomeArrow Version , SomeArrow TransactionId ] putJetBitBitcoin :: BitcoinJet a b -> DList Bool putJetBitBitcoin (SigHashJet x) = putPositive 1 . putJetBitSigHash x putJetBitBitcoin (TimeLockJet x) = putPositive 2 . putJetBitTimeLock x putJetBitBitcoin (TransactionJet x) = putPositive 3 . putJetBitTransaction x putJetBitSigHash :: SigHashJet a b -> DList Bool putJetBitSigHash SigAllHash = putPositive 1 putJetBitSigHash TxHash = putPositive 2 putJetBitSigHash TapEnvHash = putPositive 3 putJetBitSigHash OutputsHash = putPositive 4 putJetBitSigHash InputsHash = putPositive 5 putJetBitSigHash InputUtxosHash = putPositive 6 putJetBitSigHash OutputHash = putPositive 7 putJetBitSigHash OutputValuesHash = putPositive 8 putJetBitSigHash OutputScriptsHash = putPositive 9 putJetBitSigHash InputHash = putPositive 10 putJetBitSigHash InputOutpointsHash = putPositive 11 putJetBitSigHash InputSequencesHash = putPositive 12 putJetBitSigHash InputAnnexesHash = putPositive 13 putJetBitSigHash InputScriptSigsHash = putPositive 14 putJetBitSigHash InputUtxoHash = putPositive 15 putJetBitSigHash InputValuesHash = putPositive 16 putJetBitSigHash InputScriptsHash = putPositive 17 putJetBitSigHash TapleafHash = putPositive 18 putJetBitSigHash TappathHash = putPositive 19 putJetBitSigHash OutpointHash = putPositive 20 putJetBitSigHash AnnexHash = putPositive 21 putJetBitSigHash BuildTapleafSimplicity = putPositive 22 putJetBitSigHash BuildTapbranch = putPositive 23 putJetBitSigHash BuildTaptweak = putPositive 24 putJetBitTimeLock :: TimeLockJet a b -> DList Bool putJetBitTimeLock CheckLockHeight = putPositive 1 putJetBitTimeLock CheckLockTime = putPositive 2 putJetBitTimeLock CheckLockDistance = putPositive 3 putJetBitTimeLock CheckLockDuration = putPositive 4 putJetBitTimeLock TxLockHeight = putPositive 5 putJetBitTimeLock TxLockTime = putPositive 6 putJetBitTimeLock TxLockDistance = putPositive 7 putJetBitTimeLock TxLockDuration = putPositive 8 putJetBitTimeLock TxIsFinal = putPositive 9 putJetBitTransaction :: TransactionJet a b -> DList Bool putJetBitTransaction ScriptCMR = putPositive 1 putJetBitTransaction InternalKey = putPositive 2 putJetBitTransaction CurrentIndex = putPositive 3 putJetBitTransaction NumInputs = putPositive 4 putJetBitTransaction NumOutputs = putPositive 5 putJetBitTransaction LockTime = putPositive 6 putJetBitTransaction Fee = putPositive 7 putJetBitTransaction OutputValue = putPositive 8 putJetBitTransaction OutputScriptHash = putPositive 9 putJetBitTransaction TotalOutputValue = putPositive 10 putJetBitTransaction CurrentPrevOutpoint = putPositive 11 putJetBitTransaction CurrentValue = putPositive 12 putJetBitTransaction CurrentScriptHash = putPositive 13 putJetBitTransaction CurrentSequence = putPositive 14 putJetBitTransaction CurrentAnnexHash = putPositive 15 putJetBitTransaction CurrentScriptSigHash = putPositive 16 putJetBitTransaction InputPrevOutpoint = putPositive 17 putJetBitTransaction InputValue = putPositive 18 putJetBitTransaction InputScriptHash = putPositive 19 putJetBitTransaction InputSequence = putPositive 20 putJetBitTransaction InputAnnexHash = putPositive 21 putJetBitTransaction InputScriptSigHash = putPositive 22 putJetBitTransaction TotalInputValue = putPositive 23 putJetBitTransaction TapleafVersion = putPositive 24 putJetBitTransaction Tappath = putPositive 25 putJetBitTransaction Version = putPositive 26 putJetBitTransaction TransactionId = putPositive 27 bitcoinJetMap :: Map.Map Hash256 (SomeArrow BitcoinJet) bitcoinJetMap = Map.fromList . fmap mkAssoc $ toList bitcoinCatalogue where mkAssoc :: SomeArrow BitcoinJet -> (Hash256, (SomeArrow BitcoinJet)) mkAssoc wrapped@(SomeArrow jt) = (identityHash (specificationBitcoin jt), wrapped) data MatcherInfo a b = MatcherInfo (Product ConstWord IdentityRoot a b) instance Simplicity.Bitcoin.JetType.JetType JetType where type MatcherInfo JetType = MatcherInfo specification (ConstWordJet cw) = CoreJets.specificationConstWord cw specification (CoreJet jt) = CoreJets.specification jt specification (BitcoinJet jt) = specificationBitcoin jt implementation (ConstWordJet cw) _env = CoreJets.implementationConstWord cw implementation (CoreJet jt) _env = CoreJets.implementation jt implementation (BitcoinJet jt) env = implementationBitcoin jt env matcher (MatcherInfo (Product cw ir)) = (do SomeArrow jt <- Map.lookup (identityHash ir) jetMap let (ira, irb) = reifyArrow ir let (jta, jtb) = reifyArrow jt -- If the error below is thrown it suggests there is some sort of type annotation mismatch in the map below case (equalTyReflect ira jta, equalTyReflect irb jtb) of (Just Refl, Just Refl) -> return jt otherwise -> error "mathcher{Simplicity.Bitcoin.Jets.JetType}: type match error" ) <|> case cw of (ConstWord w v) -> return (ConstWordJet (ConstWordContent w v)) otherwise -> Nothing getJetBit abort next = do b <- next if b then do c <- next if c then someArrowMap BitcoinJet <$> getJetBitBitcoin abort next else someArrowMap CoreJet <$> CoreJets.getJetBit abort next else mkConstWordJet <$> CoreJets.getConstWordBit abort next where mkConstWordJet (SomeConstWordContent cw) = SomeArrow (ConstWordJet cw) putJetBit = go where go (ConstWordJet cw) = ([o]++) . CoreJets.putConstWordBit cw go (CoreJet jt) = ([i,o]++) . CoreJets.putJetBit jt go (BitcoinJet jt) = ([i,i]++) . putJetBitBitcoin jt (o,i) = (False,True) jetCost (ConstWordJet cw) = jetCostConstWord cw jetCost (CoreJet jt) = jetCostCore jt jetCost (BitcoinJet jt) = jetCostBitcoin jt -- | Generate a 'Jet' using the 'Simplicity.Bitcoin.JetType.jetCost' and 'Simplicity.Bitcoin.JetType.specification' of a 'JetType'. asJet :: (Jet term, TyC a, TyC b) => JetType a b -> term a b asJet = Simplicity.Bitcoin.JetType.asJet -- This map is used in the 'matcher' method above. -- We have floated it out here to make sure the map is shared between invocations of the 'matcher' function. jetMap :: Map.Map Hash256 (SomeArrow JetType) jetMap = Map.union (someArrowMap CoreJet <$> coreJetMap) (someArrowMap BitcoinJet <$> bitcoinJetMap) -- | Find all the expressions in a term that can be replaced with Bitcoin jets. -- Because discounted jets are not transparent, this replacement will change the CMR of the term. -- In particular the CMR values passed to 'disconnect' may be different, and thus the result of -- evaluation could change in the presence of 'disconnect'. jetSubst :: (TyC a, TyC b) => JetDag JetType a b -> WrappedSimplicity a b jetSubst = Dag.jetSubst -- | Performs 'jetSubst' and then evaluates the program in the given environment to prune unused case branches, -- which transforms some case expressions into assertions. -- The resulting expression should always have the same CMR as the expression that 'jetSubst' would return. pruneSubst :: JetDag JetType () () -> PrimEnv -> Maybe (WrappedSimplicity () ()) pruneSubst prog env = Dag.pruneSubst prog env () -- | This is an instance of 'BitString.getTermLengthCode' that specifically decodes the canonical 'JetType' set of known jets. getTermLengthCode :: (Monad m, Simplicity term, TyC a, TyC b) => m Void -> m Bool -> m (term a b) getTermLengthCode = BitString.getTermLengthCode (Proxy :: Proxy (SomeArrow JetType)) -- | This is an instance of 'BitString.putTermLengthCode' that specifically encodes the canonical 'JetType' set of known jets. putTermLengthCode :: (TyC a, TyC b) => JetDag JetType a b -> ([Bool],[Bool]) putTermLengthCode = BitString.putTermLengthCode -- | 'fastEval' optimizes Simplicity evaluation using Bitcoin jets. -- Unlike using 'Simplicity.Dag.jetSubst', 'fastEval' will not modify the commitment roots and therefore will always return the same -- result as 'sem' in the presence of 'disconnect'. -- -- @ -- 'fastEval' t === 'sem' t -- @ fastEval :: Semantics.FastEval JetType a b -> Semantics.PrimEnv -> a -> Maybe b fastEval = Semantics.fastEval instance Core MatcherInfo where iden = MatcherInfo iden unit = MatcherInfo unit injl (MatcherInfo ir) = MatcherInfo (injl ir) injr (MatcherInfo ir) = MatcherInfo (injr ir) drop (MatcherInfo ir) = MatcherInfo (drop ir) take (MatcherInfo ir) = MatcherInfo (take ir) pair (MatcherInfo irl) (MatcherInfo irr) = MatcherInfo (pair irl irr) match (MatcherInfo irl) (MatcherInfo irr) = MatcherInfo (match irl irr) comp (MatcherInfo irl) (MatcherInfo irr) = MatcherInfo (comp irl irr) instance Assert MatcherInfo where assertl (MatcherInfo ir) h = MatcherInfo (assertl ir h) assertr h (MatcherInfo ir) = MatcherInfo (assertr h ir) fail b = MatcherInfo (fail b) instance Primitive MatcherInfo where primitive p = MatcherInfo (primitive p) -- | Returns the cost of a constant word jet corresponding to the contents of a given 'ConstWordContent'. jetCostConstWord :: ConstWordContent b -> Weight jetCostConstWord (ConstWordContent w _) = milli (wordSize w) -- | The costs of "core" jets. This can be used to help instantiate the 'Simplicity.JetType.jetCost' method. jetCostCore :: CoreJet a b -> Weight jetCostCore (WordJet x) = jetCostWord x jetCostCore (ArithJet x) = jetCostArith x jetCostCore (HashJet x) = jetCostHash x jetCostCore (Secp256k1Jet x) = jetCostSecp256k1 x jetCostCore (SignatureJet x) = jetCostSignature x jetCostCore (CoreJets.BitcoinJet x) = jetCostCoreBitcoin x jetCostWord :: WordJet a b -> Weight jetCostWord Verify = cost "Verify" jetCostWord Low1 = cost "Low1" jetCostWord Low8 = cost "Low8" jetCostWord Low16 = cost "Low16" jetCostWord Low32 = cost "Low32" jetCostWord Low64 = cost "Low64" jetCostWord High1 = cost "High1" jetCostWord High8 = cost "High8" jetCostWord High16 = cost "High16" jetCostWord High32 = cost "High32" jetCostWord High64 = cost "High64" jetCostWord Complement1 = cost "Complement1" jetCostWord Complement8 = cost "Complement8" jetCostWord Complement16 = cost "Complement16" jetCostWord Complement32 = cost "Complement32" jetCostWord Complement64 = cost "Complement64" jetCostWord And1 = cost "And1" jetCostWord And8 = cost "And8" jetCostWord And16 = cost "And16" jetCostWord And32 = cost "And32" jetCostWord And64 = cost "And64" jetCostWord Or1 = cost "Or1" jetCostWord Or8 = cost "Or8" jetCostWord Or16 = cost "Or16" jetCostWord Or32 = cost "Or32" jetCostWord Or64 = cost "Or64" jetCostWord Xor1 = cost "Xor1" jetCostWord Xor8 = cost "Xor8" jetCostWord Xor16 = cost "Xor16" jetCostWord Xor32 = cost "Xor32" jetCostWord Xor64 = cost "Xor64" jetCostWord Maj1 = cost "Maj1" jetCostWord Maj8 = cost "Maj8" jetCostWord Maj16 = cost "Maj16" jetCostWord Maj32 = cost "Maj32" jetCostWord Maj64 = cost "Maj64" jetCostWord XorXor1 = cost "XorXor1" jetCostWord XorXor8 = cost "XorXor8" jetCostWord XorXor16 = cost "XorXor16" jetCostWord XorXor32 = cost "XorXor32" jetCostWord XorXor64 = cost "XorXor64" jetCostWord Ch1 = cost "Ch1" jetCostWord Ch8 = cost "Ch8" jetCostWord Ch16 = cost "Ch16" jetCostWord Ch32 = cost "Ch32" jetCostWord Ch64 = cost "Ch64" jetCostWord Some1 = cost "Some1" jetCostWord Some8 = cost "Some8" jetCostWord Some16 = cost "Some16" jetCostWord Some32 = cost "Some32" jetCostWord Some64 = cost "Some64" jetCostWord All8 = cost "All8" jetCostWord All16 = cost "All16" jetCostWord All32 = cost "All32" jetCostWord All64 = cost "All64" jetCostWord Eq1 = cost "Eq1" jetCostWord Eq8 = cost "Eq8" jetCostWord Eq16 = cost "Eq16" jetCostWord Eq32 = cost "Eq32" jetCostWord Eq64 = cost "Eq64" jetCostWord Eq256 = cost "Eq256" jetCostWord FullLeftShift8_1 = cost "FullLeftShift8_1" jetCostWord FullLeftShift8_2 = cost "FullLeftShift8_2" jetCostWord FullLeftShift8_4 = cost "FullLeftShift8_4" jetCostWord FullLeftShift16_1 = cost "FullLeftShift16_1" jetCostWord FullLeftShift16_2 = cost "FullLeftShift16_2" jetCostWord FullLeftShift16_4 = cost "FullLeftShift16_4" jetCostWord FullLeftShift16_8 = cost "FullLeftShift16_8" jetCostWord FullLeftShift32_1 = cost "FullLeftShift32_1" jetCostWord FullLeftShift32_2 = cost "FullLeftShift32_2" jetCostWord FullLeftShift32_4 = cost "FullLeftShift32_4" jetCostWord FullLeftShift32_8 = cost "FullLeftShift32_8" jetCostWord FullLeftShift32_16 = cost "FullLeftShift32_16" jetCostWord FullLeftShift64_1 = cost "FullLeftShift64_1" jetCostWord FullLeftShift64_2 = cost "FullLeftShift64_2" jetCostWord FullLeftShift64_4 = cost "FullLeftShift64_4" jetCostWord FullLeftShift64_8 = cost "FullLeftShift64_8" jetCostWord FullLeftShift64_16 = cost "FullLeftShift64_16" jetCostWord FullLeftShift64_32 = cost "FullLeftShift64_32" jetCostWord FullRightShift8_1 = cost "FullRightShift8_1" jetCostWord FullRightShift8_2 = cost "FullRightShift8_2" jetCostWord FullRightShift8_4 = cost "FullRightShift8_4" jetCostWord FullRightShift16_1 = cost "FullRightShift16_1" jetCostWord FullRightShift16_2 = cost "FullRightShift16_2" jetCostWord FullRightShift16_4 = cost "FullRightShift16_4" jetCostWord FullRightShift16_8 = cost "FullRightShift16_8" jetCostWord FullRightShift32_1 = cost "FullRightShift32_1" jetCostWord FullRightShift32_2 = cost "FullRightShift32_2" jetCostWord FullRightShift32_4 = cost "FullRightShift32_4" jetCostWord FullRightShift32_8 = cost "FullRightShift32_8" jetCostWord FullRightShift32_16 = cost "FullRightShift32_16" jetCostWord FullRightShift64_1 = cost "FullRightShift64_1" jetCostWord FullRightShift64_2 = cost "FullRightShift64_2" jetCostWord FullRightShift64_4 = cost "FullRightShift64_4" jetCostWord FullRightShift64_8 = cost "FullRightShift64_8" jetCostWord FullRightShift64_16 = cost "FullRightShift64_16" jetCostWord FullRightShift64_32 = cost "FullRightShift64_32" jetCostWord Leftmost8_1 = cost "Leftmost8_1" jetCostWord Leftmost8_2 = cost "Leftmost8_2" jetCostWord Leftmost8_4 = cost "Leftmost8_4" jetCostWord Leftmost16_1 = cost "Leftmost16_1" jetCostWord Leftmost16_2 = cost "Leftmost16_2" jetCostWord Leftmost16_4 = cost "Leftmost16_4" jetCostWord Leftmost16_8 = cost "Leftmost16_8" jetCostWord Leftmost32_1 = cost "Leftmost32_1" jetCostWord Leftmost32_2 = cost "Leftmost32_2" jetCostWord Leftmost32_4 = cost "Leftmost32_4" jetCostWord Leftmost32_8 = cost "Leftmost32_8" jetCostWord Leftmost32_16 = cost "Leftmost32_16" jetCostWord Leftmost64_1 = cost "Leftmost64_1" jetCostWord Leftmost64_2 = cost "Leftmost64_2" jetCostWord Leftmost64_4 = cost "Leftmost64_4" jetCostWord Leftmost64_8 = cost "Leftmost64_8" jetCostWord Leftmost64_16 = cost "Leftmost64_16" jetCostWord Leftmost64_32 = cost "Leftmost64_32" jetCostWord Rightmost8_1 = cost "Rightmost8_1" jetCostWord Rightmost8_2 = cost "Rightmost8_2" jetCostWord Rightmost8_4 = cost "Rightmost8_4" jetCostWord Rightmost16_1 = cost "Rightmost16_1" jetCostWord Rightmost16_2 = cost "Rightmost16_2" jetCostWord Rightmost16_4 = cost "Rightmost16_4" jetCostWord Rightmost16_8 = cost "Rightmost16_8" jetCostWord Rightmost32_1 = cost "Rightmost32_1" jetCostWord Rightmost32_2 = cost "Rightmost32_2" jetCostWord Rightmost32_4 = cost "Rightmost32_4" jetCostWord Rightmost32_8 = cost "Rightmost32_8" jetCostWord Rightmost32_16 = cost "Rightmost32_16" jetCostWord Rightmost64_1 = cost "Rightmost64_1" jetCostWord Rightmost64_2 = cost "Rightmost64_2" jetCostWord Rightmost64_4 = cost "Rightmost64_4" jetCostWord Rightmost64_8 = cost "Rightmost64_8" jetCostWord Rightmost64_16 = cost "Rightmost64_16" jetCostWord Rightmost64_32 = cost "Rightmost64_32" jetCostWord LeftPadLow1_8 = cost "LeftPadLow1_8" jetCostWord LeftPadLow1_16 = cost "LeftPadLow1_16" jetCostWord LeftPadLow8_16 = cost "LeftPadLow8_16" jetCostWord LeftPadLow1_32 = cost "LeftPadLow1_32" jetCostWord LeftPadLow8_32 = cost "LeftPadLow8_32" jetCostWord LeftPadLow16_32 = cost "LeftPadLow16_32" jetCostWord LeftPadLow1_64 = cost "LeftPadLow1_64" jetCostWord LeftPadLow8_64 = cost "LeftPadLow8_64" jetCostWord LeftPadLow16_64 = cost "LeftPadLow16_64" jetCostWord LeftPadLow32_64 = cost "LeftPadLow32_64" jetCostWord LeftPadHigh1_8 = cost "LeftPadHigh1_8" jetCostWord LeftPadHigh1_16 = cost "LeftPadHigh1_16" jetCostWord LeftPadHigh8_16 = cost "LeftPadHigh8_16" jetCostWord LeftPadHigh1_32 = cost "LeftPadHigh1_32" jetCostWord LeftPadHigh8_32 = cost "LeftPadHigh8_32" jetCostWord LeftPadHigh16_32 = cost "LeftPadHigh16_32" jetCostWord LeftPadHigh1_64 = cost "LeftPadHigh1_64" jetCostWord LeftPadHigh8_64 = cost "LeftPadHigh8_64" jetCostWord LeftPadHigh16_64 = cost "LeftPadHigh16_64" jetCostWord LeftPadHigh32_64 = cost "LeftPadHigh32_64" jetCostWord LeftExtend1_8 = cost "LeftExtend1_8" jetCostWord LeftExtend1_16 = cost "LeftExtend1_16" jetCostWord LeftExtend8_16 = cost "LeftExtend8_16" jetCostWord LeftExtend1_32 = cost "LeftExtend1_32" jetCostWord LeftExtend8_32 = cost "LeftExtend8_32" jetCostWord LeftExtend16_32 = cost "LeftExtend16_32" jetCostWord LeftExtend1_64 = cost "LeftExtend1_64" jetCostWord LeftExtend8_64 = cost "LeftExtend8_64" jetCostWord LeftExtend16_64 = cost "LeftExtend16_64" jetCostWord LeftExtend32_64 = cost "LeftExtend32_64" jetCostWord RightPadLow1_8 = cost "RightPadLow1_8" jetCostWord RightPadLow1_16 = cost "RightPadLow1_16" jetCostWord RightPadLow8_16 = cost "RightPadLow8_16" jetCostWord RightPadLow1_32 = cost "RightPadLow1_32" jetCostWord RightPadLow8_32 = cost "RightPadLow8_32" jetCostWord RightPadLow16_32 = cost "RightPadLow16_32" jetCostWord RightPadLow1_64 = cost "RightPadLow1_64" jetCostWord RightPadLow8_64 = cost "RightPadLow8_64" jetCostWord RightPadLow16_64 = cost "RightPadLow16_64" jetCostWord RightPadLow32_64 = cost "RightPadLow32_64" jetCostWord RightPadHigh1_8 = cost "RightPadHigh1_8" jetCostWord RightPadHigh1_16 = cost "RightPadHigh1_16" jetCostWord RightPadHigh8_16 = cost "RightPadHigh8_16" jetCostWord RightPadHigh1_32 = cost "RightPadHigh1_32" jetCostWord RightPadHigh8_32 = cost "RightPadHigh8_32" jetCostWord RightPadHigh16_32 = cost "RightPadHigh16_32" jetCostWord RightPadHigh1_64 = cost "RightPadHigh1_64" jetCostWord RightPadHigh8_64 = cost "RightPadHigh8_64" jetCostWord RightPadHigh16_64 = cost "RightPadHigh16_64" jetCostWord RightPadHigh32_64 = cost "RightPadHigh32_64" jetCostWord RightExtend8_16 = cost "RightExtend8_16" jetCostWord RightExtend8_32 = cost "RightExtend8_32" jetCostWord RightExtend16_32 = cost "RightExtend16_32" jetCostWord RightExtend8_64 = cost "RightExtend8_64" jetCostWord RightExtend16_64 = cost "RightExtend16_64" jetCostWord RightExtend32_64 = cost "RightExtend32_64" jetCostWord LeftShiftWith8 = cost "LeftShiftWith8" jetCostWord LeftShiftWith16 = cost "LeftShiftWith16" jetCostWord LeftShiftWith32 = cost "LeftShiftWith32" jetCostWord LeftShiftWith64 = cost "LeftShiftWith64" jetCostWord LeftShift8 = cost "LeftShift8" jetCostWord LeftShift16 = cost "LeftShift16" jetCostWord LeftShift32 = cost "LeftShift32" jetCostWord LeftShift64 = cost "LeftShift64" jetCostWord RightShiftWith8 = cost "RightShiftWith8" jetCostWord RightShiftWith16 = cost "RightShiftWith16" jetCostWord RightShiftWith32 = cost "RightShiftWith32" jetCostWord RightShiftWith64 = cost "RightShiftWith64" jetCostWord RightShift8 = cost "RightShift8" jetCostWord RightShift16 = cost "RightShift16" jetCostWord RightShift32 = cost "RightShift32" jetCostWord RightShift64 = cost "RightShift64" jetCostWord LeftRotate8 = cost "LeftRotate8" jetCostWord LeftRotate16 = cost "LeftRotate16" jetCostWord LeftRotate32 = cost "LeftRotate32" jetCostWord LeftRotate64 = cost "LeftRotate64" jetCostWord RightRotate8 = cost "RightRotate8" jetCostWord RightRotate16 = cost "RightRotate16" jetCostWord RightRotate32 = cost "RightRotate32" jetCostWord RightRotate64 = cost "RightRotate64" jetCostArith :: ArithJet a b -> Weight jetCostArith One8 = cost "One8" jetCostArith One16 = cost "One16" jetCostArith One32 = cost "One32" jetCostArith One64 = cost "One64" jetCostArith FullAdd8 = cost "FullAdd8" jetCostArith FullAdd16 = cost "FullAdd16" jetCostArith FullAdd32 = cost "FullAdd32" jetCostArith FullAdd64 = cost "FullAdd64" jetCostArith Add8 = cost "Add8" jetCostArith Add16 = cost "Add16" jetCostArith Add32 = cost "Add32" jetCostArith Add64 = cost "Add64" jetCostArith FullIncrement8 = cost "FullIncrement8" jetCostArith FullIncrement16 = cost "FullIncrement16" jetCostArith FullIncrement32 = cost "FullIncrement32" jetCostArith FullIncrement64 = cost "FullIncrement64" jetCostArith Increment8 = cost "Increment8" jetCostArith Increment16 = cost "Increment16" jetCostArith Increment32 = cost "Increment32" jetCostArith Increment64 = cost "Increment64" jetCostArith FullSubtract8 = cost "FullSubtract8" jetCostArith FullSubtract16 = cost "FullSubtract16" jetCostArith FullSubtract32 = cost "FullSubtract32" jetCostArith FullSubtract64 = cost "FullSubtract64" jetCostArith Subtract8 = cost "Subtract8" jetCostArith Subtract16 = cost "Subtract16" jetCostArith Subtract32 = cost "Subtract32" jetCostArith Subtract64 = cost "Subtract64" jetCostArith Negate8 = cost "Negate8" jetCostArith Negate16 = cost "Negate16" jetCostArith Negate32 = cost "Negate32" jetCostArith Negate64 = cost "Negate64" jetCostArith FullDecrement8 = cost "FullDecrement8" jetCostArith FullDecrement16 = cost "FullDecrement16" jetCostArith FullDecrement32 = cost "FullDecrement32" jetCostArith FullDecrement64 = cost "FullDecrement64" jetCostArith Decrement8 = cost "Decrement8" jetCostArith Decrement16 = cost "Decrement16" jetCostArith Decrement32 = cost "Decrement32" jetCostArith Decrement64 = cost "Decrement64" jetCostArith Multiply8 = cost "Multiply8" jetCostArith Multiply16 = cost "Multiply16" jetCostArith Multiply32 = cost "Multiply32" jetCostArith Multiply64 = cost "Multiply64" jetCostArith FullMultiply8 = cost "FullMultiply8" jetCostArith FullMultiply16 = cost "FullMultiply16" jetCostArith FullMultiply32 = cost "FullMultiply32" jetCostArith FullMultiply64 = cost "FullMultiply64" jetCostArith IsZero8 = cost "IsZero8" jetCostArith IsZero16 = cost "IsZero16" jetCostArith IsZero32 = cost "IsZero32" jetCostArith IsZero64 = cost "IsZero64" jetCostArith IsOne8 = cost "IsOne8" jetCostArith IsOne16 = cost "IsOne16" jetCostArith IsOne32 = cost "IsOne32" jetCostArith IsOne64 = cost "IsOne64" jetCostArith Le8 = cost "Le8" jetCostArith Le16 = cost "Le16" jetCostArith Le32 = cost "Le32" jetCostArith Le64 = cost "Le64" jetCostArith Lt8 = cost "Lt8" jetCostArith Lt16 = cost "Lt16" jetCostArith Lt32 = cost "Lt32" jetCostArith Lt64 = cost "Lt64" jetCostArith Min8 = cost "Min8" jetCostArith Min16 = cost "Min16" jetCostArith Min32 = cost "Min32" jetCostArith Min64 = cost "Min64" jetCostArith Max8 = cost "Max8" jetCostArith Max16 = cost "Max16" jetCostArith Max32 = cost "Max32" jetCostArith Max64 = cost "Max64" jetCostArith Median8 = cost "Median8" jetCostArith Median16 = cost "Median16" jetCostArith Median32 = cost "Median32" jetCostArith Median64 = cost "Median64" jetCostArith DivMod128_64 = cost "DivMod128_64" jetCostArith DivMod8 = cost "DivMod8" jetCostArith DivMod16 = cost "DivMod16" jetCostArith DivMod32 = cost "DivMod32" jetCostArith DivMod64 = cost "DivMod64" jetCostArith Divide8 = cost "Divide8" jetCostArith Divide16 = cost "Divide16" jetCostArith Divide32 = cost "Divide32" jetCostArith Divide64 = cost "Divide64" jetCostArith Modulo8 = cost "Modulo8" jetCostArith Modulo16 = cost "Modulo16" jetCostArith Modulo32 = cost "Modulo32" jetCostArith Modulo64 = cost "Modulo64" jetCostArith Divides8 = cost "Divides8" jetCostArith Divides16 = cost "Divides16" jetCostArith Divides32 = cost "Divides32" jetCostArith Divides64 = cost "Divides64" jetCostHash :: HashJet a b -> Weight jetCostHash Sha256Block = cost "Sha256Block" jetCostHash Sha256Iv = cost "Sha256Iv" jetCostHash Sha256Ctx8Add1 = cost "Sha256Ctx8Add1" jetCostHash Sha256Ctx8Add2 = cost "Sha256Ctx8Add2" jetCostHash Sha256Ctx8Add4 = cost "Sha256Ctx8Add4" jetCostHash Sha256Ctx8Add8 = cost "Sha256Ctx8Add8" jetCostHash Sha256Ctx8Add16 = cost "Sha256Ctx8Add16" jetCostHash Sha256Ctx8Add32 = cost "Sha256Ctx8Add32" jetCostHash Sha256Ctx8Add64 = cost "Sha256Ctx8Add64" jetCostHash Sha256Ctx8Add128 = cost "Sha256Ctx8Add128" jetCostHash Sha256Ctx8Add256 = cost "Sha256Ctx8Add256" jetCostHash Sha256Ctx8Add512 = cost "Sha256Ctx8Add512" jetCostHash Sha256Ctx8AddBuffer511 = cost "Sha256Ctx8AddBuffer511" jetCostHash Sha256Ctx8Finalize = cost "Sha256Ctx8Finalize" jetCostHash Sha256Ctx8Init = cost "Sha256Ctx8Init" jetCostSecp256k1 :: Secp256k1Jet a b -> Weight jetCostSecp256k1 FeNormalize = cost "FeNormalize" jetCostSecp256k1 FeNegate = cost "FeNegate" jetCostSecp256k1 FeAdd = cost "FeAdd" jetCostSecp256k1 FeSquare = cost "FeSquare" jetCostSecp256k1 FeMultiply = cost "FeMultiply" jetCostSecp256k1 FeMultiplyBeta = cost "FeMultiplyBeta" jetCostSecp256k1 FeInvert = cost "FeInvert" jetCostSecp256k1 FeSquareRoot = cost "FeSquareRoot" jetCostSecp256k1 FeIsZero = cost "FeIsZero" jetCostSecp256k1 FeIsOdd = cost "FeIsOdd" jetCostSecp256k1 ScalarNormalize = cost "ScalarNormalize" jetCostSecp256k1 ScalarNegate = cost "ScalarNegate" jetCostSecp256k1 ScalarAdd = cost "ScalarAdd" jetCostSecp256k1 ScalarSquare = cost "ScalarSquare" jetCostSecp256k1 ScalarMultiply = cost "ScalarMultiply" jetCostSecp256k1 ScalarMultiplyLambda = cost "ScalarMultiplyLambda" jetCostSecp256k1 ScalarInvert = cost "ScalarInvert" jetCostSecp256k1 ScalarIsZero = cost "ScalarIsZero" jetCostSecp256k1 GejInfinity = cost "GejInfinity" jetCostSecp256k1 GejNormalize = cost "GejNormalize" jetCostSecp256k1 GejNegate = cost "GejNegate" jetCostSecp256k1 GeNegate = cost "GeNegate" jetCostSecp256k1 GejDouble = cost "GejDouble" jetCostSecp256k1 GejAdd = cost "GejAdd" jetCostSecp256k1 GejGeAddEx = cost "GejGeAddEx" jetCostSecp256k1 GejGeAdd = cost "GejGeAdd" jetCostSecp256k1 GejRescale = cost "GejRescale" jetCostSecp256k1 GejIsInfinity = cost "GejIsInfinity" jetCostSecp256k1 GejEquiv = cost "GejEquiv" jetCostSecp256k1 GejGeEquiv = cost "GejGeEquiv" jetCostSecp256k1 GejXEquiv = cost "GejXEquiv" jetCostSecp256k1 GejYIsOdd = cost "GejYIsOdd" jetCostSecp256k1 GejIsOnCurve = cost "GejIsOnCurve" jetCostSecp256k1 GeIsOnCurve = cost "GeIsOnCurve" jetCostSecp256k1 Generate = cost "Generate" jetCostSecp256k1 Scale = cost "Scale" jetCostSecp256k1 LinearCombination1 = cost "LinearCombination1" jetCostSecp256k1 LinearVerify1 = cost "LinearVerify1" jetCostSecp256k1 PointVerify1 = cost "PointVerify1" jetCostSecp256k1 Decompress = cost "Decompress" jetCostSecp256k1 Swu = cost "Swu" jetCostSecp256k1 HashToCurve = cost "HashToCurve" jetCostSignature :: SignatureJet a b -> Weight jetCostSignature CheckSigVerify = cost "CheckSigVerify" jetCostSignature Bip0340Verify = cost "Bip0340Verify" jetCostCoreBitcoin :: CoreJets.BitcoinJet a b -> Weight jetCostCoreBitcoin ParseLock = cost "ParseLock" jetCostCoreBitcoin ParseSequence = cost "ParseSequence" jetCostCoreBitcoin TapdataInit = cost "TapdataInit" jetCostBitcoin :: BitcoinJet a b -> Weight jetCostBitcoin (SigHashJet x) = jetCostSigHash x jetCostBitcoin (TimeLockJet x) = jetCostTimeLock x jetCostBitcoin (TransactionJet x) = jetCostTransaction x jetCostSigHash :: SigHashJet a b -> Weight jetCostSigHash SigAllHash = cost "SigAllHash" jetCostSigHash TxHash = cost "TxHash" jetCostSigHash TapEnvHash = cost "TapEnvHash" jetCostSigHash OutputsHash = cost "OutputsHash" jetCostSigHash InputsHash = cost "InputsHash" jetCostSigHash InputUtxosHash = cost "InputUtxosHash" jetCostSigHash OutputHash = cost "OutputHash" jetCostSigHash OutputValuesHash = cost "OutputValuesHash" jetCostSigHash OutputScriptsHash = cost "OutputScriptsHash" jetCostSigHash InputHash = cost "InputHash" jetCostSigHash InputOutpointsHash = cost "InputOutpointsHash" jetCostSigHash InputSequencesHash = cost "InputSequencesHash" jetCostSigHash InputAnnexesHash = cost "InputAnnexesHash" jetCostSigHash InputScriptSigsHash = cost "InputScriptSigsHash" jetCostSigHash InputUtxoHash = cost "InputUtxoHash" jetCostSigHash InputValuesHash = cost "InputValuesHash" jetCostSigHash InputScriptsHash = cost "InputScriptsHash" jetCostSigHash TapleafHash = cost "TapleafHash" jetCostSigHash TappathHash = cost "TappathHash" jetCostSigHash OutpointHash = cost "OutpointHash" jetCostSigHash AnnexHash = cost "AnnexHash" jetCostSigHash BuildTapleafSimplicity = cost "BuildTapleafSimplicity" jetCostSigHash BuildTapbranch = cost "BuildTapbranch" jetCostSigHash BuildTaptweak = cost "BuildTaptweak" jetCostTimeLock :: TimeLockJet a b -> Weight jetCostTimeLock CheckLockHeight = cost "CheckLockHeight" jetCostTimeLock CheckLockTime = cost "CheckLockTime" jetCostTimeLock CheckLockDistance = cost "CheckLockDistance" jetCostTimeLock CheckLockDuration = cost "CheckLockDuration" jetCostTimeLock TxLockHeight = cost "TxLockHeight" jetCostTimeLock TxLockTime = cost "TxLockTime" jetCostTimeLock TxLockDistance = cost "TxLockDistance" jetCostTimeLock TxLockDuration = cost "TxLockDuration" jetCostTimeLock TxIsFinal = cost "TxIsFinal" jetCostTransaction :: TransactionJet a b -> Weight jetCostTransaction ScriptCMR = cost "ScriptCMR" jetCostTransaction InternalKey = cost "InternalKey" jetCostTransaction CurrentIndex = cost "CurrentIndex" jetCostTransaction NumInputs = cost "NumInputs" jetCostTransaction NumOutputs = cost "NumOutputs" jetCostTransaction LockTime = cost "LockTime" jetCostTransaction Fee = cost "Fee" jetCostTransaction OutputValue = cost "OutputValue" jetCostTransaction OutputScriptHash = cost "OutputScriptHash" jetCostTransaction TotalOutputValue = cost "TotalOutputValue" jetCostTransaction CurrentPrevOutpoint = cost "CurrentPrevOutpoint" jetCostTransaction CurrentValue = cost "CurrentValue" jetCostTransaction CurrentScriptHash = cost "CurrentScriptHash" jetCostTransaction CurrentSequence = cost "CurrentSequence" jetCostTransaction CurrentAnnexHash = cost "CurrentAnnexHash" jetCostTransaction CurrentScriptSigHash = cost "CurrentScriptSigHash" jetCostTransaction InputPrevOutpoint = cost "InputPrevOutpoint" jetCostTransaction InputValue = cost "InputValue" jetCostTransaction InputScriptHash = cost "InputScriptHash" jetCostTransaction InputSequence = cost "InputSequence" jetCostTransaction InputAnnexHash = cost "InputAnnexHash" jetCostTransaction InputScriptSigHash = cost "InputScriptSigHash" jetCostTransaction TotalInputValue = cost "TotalInputValue" jetCostTransaction TapleafVersion = cost "TapleafVersion" jetCostTransaction Tappath = cost "Tappath" jetCostTransaction Version = cost "Version" jetCostTransaction TransactionId = cost "TransactionId" ================================================ FILE: Haskell/Simplicity/Bitcoin/Programs/SigHash/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Bitcoin.Programs.SigHash.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Bitcoin.Programs.SigHash.mkLib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Bitcoin.Programs.SigHash.Lib ( outputValuesHash, outputScriptsHash , outputsHash, outputHash , inputValuesHash, inputScriptsHash, inputUtxosHash, inputUtxoHash , inputOutpointsHash, inputSequencesHash, inputAnnexesHash, inputScriptSigsHash, inputsHash, inputHash , txHash , tapleafHash, tappathHash, tapEnvHash , sigAllHash ) where import qualified Simplicity.Bitcoin.Programs.SigHash as SigHash outputValuesHash = SigHash.outputValuesHash SigHash.lib outputScriptsHash = SigHash.outputScriptsHash SigHash.lib outputsHash = SigHash.outputsHash SigHash.lib outputHash = SigHash.outputHash SigHash.lib inputValuesHash = SigHash.inputValuesHash SigHash.lib inputScriptsHash = SigHash.inputScriptsHash SigHash.lib inputUtxosHash = SigHash.inputUtxosHash SigHash.lib inputUtxoHash = SigHash.inputUtxoHash SigHash.lib inputOutpointsHash = SigHash.inputOutpointsHash SigHash.lib inputSequencesHash = SigHash.inputSequencesHash SigHash.lib inputAnnexesHash = SigHash.inputAnnexesHash SigHash.lib inputsHash = SigHash.inputsHash SigHash.lib inputHash = SigHash.inputHash SigHash.lib inputScriptSigsHash = SigHash.inputScriptSigsHash SigHash.lib txHash = SigHash.txHash SigHash.lib tapleafHash = SigHash.tapleafHash SigHash.lib tappathHash = SigHash.tappathHash SigHash.lib tapEnvHash = SigHash.tapEnvHash SigHash.lib sigAllHash = SigHash.sigAllHash SigHash.lib ================================================ FILE: Haskell/Simplicity/Bitcoin/Programs/SigHash.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that implement timelock functions from "Simplicity.Bitcoin.DataTypes". module Simplicity.Bitcoin.Programs.SigHash ( Lib(Lib), mkLib , outputValuesHash, outputScriptsHash , outputsHash, outputHash , inputValuesHash, inputScriptsHash, inputUtxosHash, inputUtxoHash , inputOutpointsHash, inputSequencesHash, inputAnnexesHash, inputScriptSigsHash, inputsHash, inputHash , txHash , tapleafHash, tappathHash, tapEnvHash , sigAllHash -- * Example instances , lib ) where import Prelude hiding (Word, all, drop, max, not, take) import Data.String (fromString) import Simplicity.Digest import Simplicity.Bitcoin.Primitive import Simplicity.Bitcoin.Term hiding (one) import Simplicity.Functor import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Word import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Programs.Sha256 (Ctx8) import qualified Simplicity.Bitcoin.Programs.Transaction as Transaction import Simplicity.Programs.Bitcoin.Lib data Lib term = Lib { -- | A hash of all 'Transaction.outputValue's. outputValuesHash :: term () Word256 -- | A hash of all 'OutputScriptHash's. , outputScriptsHash :: term () Word256 -- | A hash of -- -- * 'outputValuesHash' -- * 'outputScriptsHash' , outputsHash :: term () Word256 -- | If the given output index exists, returns a hash of -- -- * The serialization of the output's value fields. -- * A hash of the output's scriptPubKey. , outputHash :: term Word32 (S Word256) -- | A hash of all 'Transaction.inputValue's. , inputValuesHash :: term () Word256 -- | A hash of all 'InputScriptHash's. , inputScriptsHash :: term () Word256 -- | A hash of -- -- * 'inputValuesHash' -- * 'inputScriptsHash' , inputUtxosHash :: term () Word256 -- | If the given input index exists, returns a hash of -- -- * The serialization of the input UTXO's value field. -- * A hash of the input UTXO's scriptPubKey. , inputUtxoHash :: term Word32 (S Word256) -- | A hash of all 'InputPrevOutpoint's. , inputOutpointsHash :: term () Word256 -- | A hash of all 'InputSequence's. , inputSequencesHash :: term () Word256 -- | A hash of all 'InputAnnexHash's. , inputAnnexesHash :: term () Word256 -- | A hash of all 'InputScriptSigHash's. , inputScriptSigsHash :: term () Word256 -- | A hash of -- -- * 'inputOutpointsHash' -- * 'inputSequencesHash' -- * 'inputAnnexesHash' -- -- Note that 'InputScriptSigHash' is excluded. , inputsHash :: term () Word256 -- | If the given input index exists, returns a hash of -- -- * The input's serialized previous transaction id. -- * The input's previous transaction index in big endian format. -- * The input's sequence number in big endian format. -- * If the input has no annex, or isn't a taproot spend, then the byte 0x00. -- * If the input has an annex, then the byte 0x01 followed by a SHA256 hash of the annex. , inputHash :: term Word32 (S Word256) -- | A hash of -- -- * 'Version' -- * 'LockTime' -- * 'inputsHash' -- * 'outputsHash' -- * 'inputUtxosHash' , txHash :: term () Word256 -- | A hash of -- -- * 'TapleafVersion' -- * 'ScriptCMR' , tapleafHash :: term () Word256 -- | A hash of all 'Tappath's. , tappathHash :: term () Word256 -- | A hash of -- -- * 'tapleafHash' -- * 'tappathHash' -- * 'InternalKey' , tapEnvHash :: term () Word256 -- | A hash of -- -- * 'txHash' -- * 'tapEnvHash' -- * 'CurrentIndex' , sigAllHash :: term () Word256 } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { outputValuesHash = m outputValuesHash , outputScriptsHash = m outputScriptsHash , outputsHash = m outputsHash , outputHash = m outputHash , inputValuesHash = m inputValuesHash , inputScriptsHash = m inputScriptsHash , inputUtxosHash = m inputUtxosHash , inputUtxoHash = m inputUtxoHash , inputOutpointsHash = m inputOutpointsHash , inputSequencesHash = m inputSequencesHash , inputAnnexesHash = m inputAnnexesHash , inputsHash = m inputsHash , inputHash = m inputHash , inputScriptSigsHash = m inputScriptSigsHash , txHash = m txHash , tapleafHash = m tapleafHash , tappathHash = m tappathHash , tapEnvHash = m tapEnvHash , sigAllHash = m sigAllHash } mkLib :: forall term. (Assert term, Primitive term) => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Sha256.LibAssert term -- ^ "Simplicity.Programs.Sha256" -> Transaction.Lib term -- ^ "Simplicity.Bitcoin.Programs.Transaction" -> Lib term mkLib Sha256.Lib{..} Sha256.LibAssert{..} Transaction.Lib{..} = lib where lib@Lib{..} = Lib { outputValuesHash = hashWord64s (drop (primitive OutputValue)) , outputScriptsHash = hashWord256s32 (drop (primitive OutputScriptHash)) , outputsHash = ctx8Init &&& (outputValuesHash &&& outputScriptsHash) >>> ctx8Add64 >>> ctx8Finalize , outputHash = (primitive OutputValue &&& primitive OutputScriptHash) >>> match (injl unit) (injr (((unit >>> ctx8Init) &&& oh >>> ctx8Add8) &&& (drop . assert $ iden) >>> ctx8Add32 >>> ctx8Finalize)) , inputValuesHash = hashWord64s (drop (primitive InputValue)) , inputScriptsHash = hashWord256s32 (drop (primitive InputScriptHash)) , inputUtxosHash = ctx8Init &&& (inputValuesHash &&& inputScriptsHash) >>> ctx8Addn vector64 >>> ctx8Finalize , inputUtxoHash = (primitive InputValue &&& primitive InputScriptHash) >>> match (injl unit) (injr (((unit >>> ctx8Init) &&& oh >>> ctx8Add8) &&& (drop . assert $ iden) >>> ctx8Add32 >>> ctx8Finalize)) , inputOutpointsHash = let finalize = ctx8Finalize body = (take (drop (primitive InputPrevOutpoint)) &&& ih) >>> match (injl ih) (injr (ih &&& oh >>> outpointHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , inputSequencesHash = hashWord32s (drop (primitive InputSequence)) , inputAnnexesHash = let finalize = ctx8Finalize body = take (drop (primitive InputAnnexHash)) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> annexHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , inputScriptSigsHash = hashWord256s32 (drop (primitive InputScriptSigHash)) , inputsHash = (ctx8Init &&& (inputOutpointsHash &&& inputSequencesHash) >>> ctx8Addn vector64) &&& inputAnnexesHash >>> ctx8Addn vector32 >>> ctx8Finalize , inputHash = (primitive InputPrevOutpoint &&& (primitive InputSequence &&& primitive InputAnnexHash)) >>> match (injl unit) (injr ((((unit >>> ctx8Init) &&& oh >>> outpointHash) &&& (drop . take . assert $ iden) >>> ctx8Add4) &&& (drop . drop . assert $ iden) >>> annexHash >>> ctx8Finalize)) , txHash = ((ctx8Init &&& (primitive Version &&& primitive LockTime) >>> ctx8Addn vector8) &&& (inputsHash &&& outputsHash) >>> ctx8Addn vector64) &&& inputUtxosHash >>> ctx8Addn vector32 >>> ctx8Finalize , tapleafHash = ((Sha256.ctx8InitTag "TapLeaf") &&& (primitive TapleafVersion &&& scribe (toWord8 32)) >>> ctx8Addn vector2) &&& (primitive ScriptCMR) >>> ctx8Addn vector32 >>> ctx8Finalize , tappathHash = hashWord256s8 (drop (primitive Tappath)) , tapEnvHash = (ctx8Init &&& tapleafHash >>> ctx8Addn vector32) &&& (tappathHash &&& primitive InternalKey) >>> ctx8Addn vector64 >>> ctx8Finalize , sigAllHash = (ctx8Init &&& (txHash &&& tapEnvHash) >>> ctx8Addn vector64) &&& primitive CurrentIndex >>> ctx8Addn vector4 >>> ctx8Finalize } hashLoop256 :: (TyC w, TyC c) => Word w -> term (c, w) (S Word256) -> term (c, Ctx8) Ctx8 hashLoop256 = Sha256.hashLoop vector32 hashWord256s :: (TyC w, TyC c) => Word w -> term (c, w) (S Word256) -> term c Word256 hashWord256s w array = iden &&& (unit >>> ctx8Init) >>> hashLoop256 w array >>> ctx8Finalize hashWord256s32 = hashWord256s word32 hashWord256s8 = hashWord256s word8 hashWord64s array = iden &&& (unit >>> ctx8Init) >>> Sha256.hashLoop vector8 word32 array >>> ctx8Finalize hashWord32s array = iden &&& (unit >>> ctx8Init) >>> Sha256.hashLoop vector4 word32 array >>> ctx8Finalize ctx8Add4 = ctx8Addn vector4 ctx8Add8 = ctx8Addn vector8 ctx8Add32 = ctx8Addn vector32 ctx8Add64 = ctx8Addn vector64 -- | An instance of the SigHash 'Lib' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. lib :: (Assert term, Primitive term) => Lib term lib = mkLib Sha256.lib Sha256.libAssert Transaction.lib ================================================ FILE: Haskell/Simplicity/Bitcoin/Programs/TimeLock.hs ================================================ -- | This module defines Simplicity expressions that implement timelock functions from "Simplicity.Bitcoin.DataTypes". module Simplicity.Bitcoin.Programs.TimeLock ( txIsFinal , txLockHeight, txLockTime , txLockDistance, txLockDuration , checkLockHeight, checkLockTime , checkLockDistance, checkLockDuration , module Simplicity.Programs.TimeLock , Bit ) where import Prelude hiding (Word, all, drop, max, not, take) import Simplicity.Bitcoin.Primitive import Simplicity.Bitcoin.Term import Simplicity.Bitcoin.Programs.Transaction.Lib import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.TimeLock import Simplicity.Programs.Word -- | Implements 'Simplicity.Bitcoin.DataTypes.txIsFinal'. txIsFinal :: (Core term, Primitive term) => term () Bit txIsFinal = (unit &&& unit) >>> forWhile word32 body >>> copair iden true where body = take (drop (primitive InputSequence)) >>> copair (injl true) (all word32 >>> copair (injl false) (injr unit)) -- | Returns the transaction's LockTime if it is a Height value, otherwise it returns 0. txLockHeight :: (Core term, Primitive term) => term () Height txLockHeight = txIsFinal &&& primitive LockTime >>> cond z (parseLock >>> (copair iden z)) where z = unit >>> zero word32 -- | Returns the transaction's LockTime if it is a Time value, otherwise it returns 0. txLockTime :: (Core term, Primitive term) => term () Time txLockTime = txIsFinal &&& primitive LockTime >>> cond z (parseLock >>> (copair z iden)) where z = unit >>> zero word32 bip68VersionCheck :: (Core term, Primitive term) => term () Bit bip68VersionCheck = scribe (toWord32 2) &&& primitive Version >>> le word32 -- | Computes the relative height timelock or 0 if there is no such timelock. txLockDistance :: (Assert term, Primitive term) => term () Distance txLockDistance = bip68VersionCheck &&& (currentSequence >>> parseSequence) >>> cond (copair (unit >>> z) (copair iden (unit >>> z))) (unit >>> z) where z = zero word16 -- | Computes the relative time timelock or 0 if there is no such timelock. txLockDuration :: (Assert term, Primitive term) => term () Distance txLockDuration = bip68VersionCheck &&& (currentSequence >>> parseSequence) >>> cond (copair (unit >>> z) (copair (unit >>> z) iden)) (unit >>> z) where z = zero word16 -- | Asserts that the input is less than or equal to the value returned by 'txLockHeight'. checkLockHeight :: (Assert term, Primitive term) => term Height () checkLockHeight = assert (iden &&& (unit >>> txLockHeight) >>> le word32) -- | Asserts that the input is less than or equal to the value returned by 'txLockTime'. checkLockTime :: (Assert term, Primitive term) => term Time () checkLockTime = assert (iden &&& (unit >>> txLockTime) >>> le word32) -- | Asserts that the input is less than or equal to the value returned by 'txLockDistance'. checkLockDistance :: (Assert term, Primitive term) => term Distance () checkLockDistance = assert (iden &&& (unit >>> txLockDistance) >>> le word16) -- | Asserts that the input is less than or equal to the value returned by 'txLockDuration'. checkLockDuration :: (Assert term, Primitive term) => term Duration () checkLockDuration = assert (iden &&& (unit >>> txLockDuration) >>> le word16) ================================================ FILE: Haskell/Simplicity/Bitcoin/Programs/Transaction/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Bitcoin.Programs.Transaction.lib' library instance into individual functions. module Simplicity.Bitcoin.Programs.Transaction.Lib ( numInputs , numOutputs , totalInputValue , totalOutputValue , fee , currentPrevOutpoint , currentValue , currentScriptHash , currentSequence , currentAnnexHash , currentScriptSigHash ) where import qualified Simplicity.Bitcoin.Programs.Transaction as Transaction numInputs = Transaction.numInputs Transaction.lib numOutputs = Transaction.numOutputs Transaction.lib totalInputValue = Transaction.totalInputValue Transaction.lib totalOutputValue = Transaction.totalOutputValue Transaction.lib fee = Transaction.fee Transaction.lib currentPrevOutpoint = Transaction.currentPrevOutpoint Transaction.lib currentValue = Transaction.currentValue Transaction.lib currentScriptHash = Transaction.currentScriptHash Transaction.lib currentSequence = Transaction.currentSequence Transaction.lib currentAnnexHash = Transaction.currentAnnexHash Transaction.lib currentScriptSigHash = Transaction.currentScriptSigHash Transaction.lib ================================================ FILE: Haskell/Simplicity/Bitcoin/Programs/Transaction.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that access transaction data. module Simplicity.Bitcoin.Programs.Transaction ( Lib(Lib), lib , numInputs , numOutputs , totalInputValue , totalOutputValue , fee , currentPrevOutpoint , currentValue , currentScriptHash , currentSequence , currentAnnexHash , currentScriptSigHash ) where import Prelude hiding (take, drop, subtract) import Simplicity.Digest import Simplicity.Bitcoin.Primitive import Simplicity.Bitcoin.Term hiding (one) import Simplicity.Functor import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Word import Simplicity.Ty.Word data Lib term = Lib { -- | Returns the number of inputs the transaction has. numInputs :: term () Word32 -- | Returns the number of outputs the transaction has. , numOutputs :: term () Word32 , totalInputValue :: term () Word64 , totalOutputValue :: term () Word64 , fee :: term () Word64 -- | Returns the `InputPrevOutpoint` of the `CurrentIndex`. , currentPrevOutpoint :: term () (Word256,Word32) -- | Returns the `InputValue` of the `CurrentIndex`. , currentValue :: term () Word64 -- | Returns the `InputScriptHash` of the `CurrentIndex`. , currentScriptHash :: term () Word256 -- | Returns the `InputSequence` of the `CurrentIndex`. , currentSequence :: term () Word32 -- | Returns the `InputAnnexHash` of the `CurrentIndex`. , currentAnnexHash :: term () (S Word256) -- | Returns the `InputScriptSigHash` of the `CurrentIndex`. , currentScriptSigHash :: term () Word256 } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { numInputs = m numInputs , numOutputs = m numOutputs , totalInputValue = m totalInputValue , totalOutputValue = m totalOutputValue , fee = m fee , currentPrevOutpoint = m currentPrevOutpoint , currentValue = m currentValue , currentScriptHash = m currentScriptHash , currentSequence = m currentSequence , currentAnnexHash = m currentAnnexHash , currentScriptSigHash = m currentScriptSigHash } -- | Build the Transaction 'Lib' library. lib :: forall term. (Assert term, Primitive term) => Lib term lib = l where l@Lib{..} = Lib { numInputs = firstFail word32 (primitive InputValue) , numOutputs = firstFail word32 (primitive OutputValue) , totalInputValue = let body = take (drop (primitive InputValue)) &&& ih >>> match (injl ih) (injr (add word64 >>> ih)) in (iden &&& zero word64) >>> forWhile word32 body >>> copair iden iden , totalOutputValue = let body = take (drop (primitive OutputValue)) &&& ih >>> match (injl ih) (injr (add word64 >>> ih)) in (iden &&& zero word64) >>> forWhile word32 body >>> copair iden iden , fee = totalInputValue &&& totalOutputValue >>> subtract word64 >>> ih , currentPrevOutpoint = primitive CurrentIndex >>> assert (primitive InputPrevOutpoint) , currentValue = primitive CurrentIndex >>> assert (primitive InputValue) , currentScriptHash = primitive CurrentIndex >>> assert (primitive InputScriptHash) , currentSequence = primitive CurrentIndex >>> assert (primitive InputSequence) , currentAnnexHash = primitive CurrentIndex >>> assert (primitive InputAnnexHash) , currentScriptSigHash = primitive CurrentIndex >>> assert (primitive InputScriptSigHash) } ================================================ FILE: Haskell/Simplicity/Elements/Benchmarks.hs ================================================ module Simplicity.Elements.Benchmarks (cost) where import Simplicity.BitMachine.StaticAnalysis.Cost rawBenchmark :: String -> Double rawBenchmark "Add16" = 60.085041109205505 rawBenchmark "Add32" = 65.00459118488351 rawBenchmark "Add64" = 60.770501535336855 rawBenchmark "Add8" = 62.62388142499319 rawBenchmark "All16" = 34.58413668932453 rawBenchmark "All32" = 36.12506541685401 rawBenchmark "All64" = 43.94474405869988 rawBenchmark "All8" = 42.298630039382395 rawBenchmark "And1" = 44.41796508997593 rawBenchmark "And16" = 49.190985826792 rawBenchmark "And32" = 52.330825534594354 rawBenchmark "And64" = 52.00679267933024 rawBenchmark "And8" = 50.9336818377678 rawBenchmark "AnnexHash" = 133.8975 rawBenchmark "AssetAmountHash" = 171.26 rawBenchmark "Bip0340Verify" = 54541.00304991227 rawBenchmark "BuildTapbranch" = 1424.2525 rawBenchmark "BuildTapleafSimplicity" = 1024.204285714286 rawBenchmark "BuildTaptweak" = 51562.63 rawBenchmark "CalculateAsset" = 448.8285714285716 rawBenchmark "CalculateConfidentialToken" = 392.9185714285713 rawBenchmark "CalculateExplicitToken" = 428.43571428571437 rawBenchmark "CalculateIssuanceEntropy" = 1163.9275 rawBenchmark "Ch1" = 43.38647329238317 rawBenchmark "Ch16" = 52.27708434095646 rawBenchmark "Ch32" = 50.75927210580458 rawBenchmark "Ch64" = 50.64224884783096 rawBenchmark "Ch8" = 43.247948521208684 rawBenchmark "CheckLockDistance" = 58.753725206887374 rawBenchmark "CheckLockDuration" = 57.030697303127475 rawBenchmark "CheckLockHeight" = 42.78170096368622 rawBenchmark "CheckLockTime" = 51.84407299762977 rawBenchmark "CheckSigVerify" = 55555.079016059564 rawBenchmark "Complement1" = 44.30963250954837 rawBenchmark "Complement16" = 41.853819540512724 rawBenchmark "Complement32" = 51.936600421665986 rawBenchmark "Complement64" = 49.44074859372622 rawBenchmark "Complement8" = 44.49004402013328 rawBenchmark "CurrentAmount" = 125.233683871098 rawBenchmark "CurrentAnnexHash" = 43.96303036926559 rawBenchmark "CurrentAsset" = 95.55358469768584 rawBenchmark "CurrentIndex" = 49.14822556250178 rawBenchmark "CurrentIssuanceAssetAmount" = 91.68812641475432 rawBenchmark "CurrentIssuanceAssetProof" = 78.32085006755332 rawBenchmark "CurrentIssuanceTokenAmount" = 104.56443464343835 rawBenchmark "CurrentIssuanceTokenProof" = 80.11480670010411 rawBenchmark "CurrentNewIssuanceContract" = 80.93662026502236 rawBenchmark "CurrentPegin" = 81.6814471387894 rawBenchmark "CurrentPrevOutpoint" = 87.01737208854547 rawBenchmark "CurrentReissuanceBlinding" = 52.34362964598284 rawBenchmark "CurrentReissuanceEntropy" = 47.41824644363429 rawBenchmark "CurrentScriptHash" = 74.54897385905238 rawBenchmark "CurrentScriptSigHash" = 77.29143987908452 rawBenchmark "CurrentSequence" = 49.55213254331629 rawBenchmark "Decompress" = 6034.0242131124305 rawBenchmark "Decrement16" = 47.619384690269044 rawBenchmark "Decrement32" = 50.70470833162736 rawBenchmark "Decrement64" = 49.91961044181172 rawBenchmark "Decrement8" = 44.41452963683716 rawBenchmark "DivMod128_64" = 115.77280158438838 rawBenchmark "DivMod16" = 65.69925000385433 rawBenchmark "DivMod32" = 64.04450140966351 rawBenchmark "DivMod64" = 48.188851905873335 rawBenchmark "DivMod8" = 71.3705571750924 rawBenchmark "Divide16" = 54.81267262645548 rawBenchmark "Divide32" = 55.81078135389193 rawBenchmark "Divide64" = 56.43166191465282 rawBenchmark "Divide8" = 60.07629081022806 rawBenchmark "Divides16" = 51.9870240819556 rawBenchmark "Divides32" = 48.77753656294132 rawBenchmark "Divides64" = 50.6929784746092 rawBenchmark "Divides8" = 54.766521462004285 rawBenchmark "Eq1" = 41.19704900879444 rawBenchmark "Eq16" = 46.96434429747661 rawBenchmark "Eq256" = 125.24267688284475 rawBenchmark "Eq32" = 49.127933441004416 rawBenchmark "Eq64" = 56.10776637742226 rawBenchmark "Eq8" = 53.09387335277708 rawBenchmark "FeAdd" = 419.4421553609743 rawBenchmark "FeInvert" = 1764.2095713900258 rawBenchmark "FeIsOdd" = 161.4908040889559 rawBenchmark "FeIsZero" = 148.9500015909772 rawBenchmark "FeMultiply" = 449.33346943264536 rawBenchmark "FeMultiplyBeta" = 321.936623495282 rawBenchmark "FeNegate" = 295.2583854628667 rawBenchmark "FeNormalize" = 289.8402224157142 rawBenchmark "FeSquare" = 309.0320861847194 rawBenchmark "FeSquareRoot" = 5708.658550943187 rawBenchmark "FullAdd16" = 67.58987477677238 rawBenchmark "FullAdd32" = 66.11773354771384 rawBenchmark "FullAdd64" = 67.48909817913685 rawBenchmark "FullAdd8" = 70.65903996899138 rawBenchmark "FullDecrement16" = 51.39362224910755 rawBenchmark "FullDecrement32" = 59.97907579303369 rawBenchmark "FullDecrement64" = 45.49679194449331 rawBenchmark "FullDecrement8" = 50.64117149094439 rawBenchmark "FullIncrement16" = 49.66797298374831 rawBenchmark "FullIncrement32" = 58.30643709946031 rawBenchmark "FullIncrement64" = 55.24105841134342 rawBenchmark "FullIncrement8" = 40.36810258706402 rawBenchmark "FullLeftShift16_1" = 46.18858118129996 rawBenchmark "FullLeftShift16_2" = 46.620891275146725 rawBenchmark "FullLeftShift16_4" = 49.483816401261585 rawBenchmark "FullLeftShift16_8" = 36.162357067674385 rawBenchmark "FullLeftShift32_1" = 46.939178133248234 rawBenchmark "FullLeftShift32_16" = 45.4571656643761 rawBenchmark "FullLeftShift32_2" = 37.55784335894769 rawBenchmark "FullLeftShift32_4" = 46.8616632714964 rawBenchmark "FullLeftShift32_8" = 50.89997070924756 rawBenchmark "FullLeftShift64_1" = 55.05773228244788 rawBenchmark "FullLeftShift64_16" = 50.35375142144335 rawBenchmark "FullLeftShift64_2" = 52.524422908169726 rawBenchmark "FullLeftShift64_32" = 48.19968554848869 rawBenchmark "FullLeftShift64_4" = 52.64511921564639 rawBenchmark "FullLeftShift64_8" = 47.92651978022118 rawBenchmark "FullLeftShift8_1" = 53.371611885499135 rawBenchmark "FullLeftShift8_2" = 53.40012672044502 rawBenchmark "FullLeftShift8_4" = 47.39442146733317 rawBenchmark "FullMultiply16" = 62.764043288900055 rawBenchmark "FullMultiply32" = 53.41609046991522 rawBenchmark "FullMultiply64" = 70.99465378729637 rawBenchmark "FullMultiply8" = 60.79100324703799 rawBenchmark "FullRightShift16_1" = 44.463801274297026 rawBenchmark "FullRightShift16_2" = 44.24484734954473 rawBenchmark "FullRightShift16_4" = 49.377415322695924 rawBenchmark "FullRightShift16_8" = 31.761769518909432 rawBenchmark "FullRightShift32_1" = 41.12634362378231 rawBenchmark "FullRightShift32_16" = 35.61914526793314 rawBenchmark "FullRightShift32_2" = 35.367670218288545 rawBenchmark "FullRightShift32_4" = 39.91820320167241 rawBenchmark "FullRightShift32_8" = 46.755300941717685 rawBenchmark "FullRightShift64_1" = 55.084156371380026 rawBenchmark "FullRightShift64_16" = 48.15200506212657 rawBenchmark "FullRightShift64_2" = 48.06952686812977 rawBenchmark "FullRightShift64_32" = 41.03987641674198 rawBenchmark "FullRightShift64_4" = 52.21526347861463 rawBenchmark "FullRightShift64_8" = 55.476007550145084 rawBenchmark "FullRightShift8_1" = 48.89242850292436 rawBenchmark "FullRightShift8_2" = 47.923842296151605 rawBenchmark "FullRightShift8_4" = 49.464558624033415 rawBenchmark "FullSubtract16" = 67.38341429479223 rawBenchmark "FullSubtract32" = 64.95233724051934 rawBenchmark "FullSubtract64" = 54.67370881511828 rawBenchmark "FullSubtract8" = 70.40320985209922 rawBenchmark "GeIsOnCurve" = 357.15050069150345 rawBenchmark "GeNegate" = 525.226102912438 rawBenchmark "GejAdd" = 1609.7141943875479 rawBenchmark "GejDouble" = 980.0399024548117 rawBenchmark "GejEquiv" = 1233.877894994496 rawBenchmark "GejGeAdd" = 1376.3073973202286 rawBenchmark "GejGeAddEx" = 1510.6965337240808 rawBenchmark "GejGeEquiv" = 980.6789399836443 rawBenchmark "GejInfinity" = 398.03834524479885 rawBenchmark "GejIsInfinity" = 370.3037942737992 rawBenchmark "GejIsOnCurve" = 564.8607923748427 rawBenchmark "GejNegate" = 767.335419690289 rawBenchmark "GejNormalize" = 2277.254498988017 rawBenchmark "GejRescale" = 1060.3680232144072 rawBenchmark "GejXEquiv" = 581.9587646807994 rawBenchmark "GejYIsOdd" = 2028.4000778806126 rawBenchmark "Generate" = 27817.092507074034 rawBenchmark "GenesisBlockHash" = 82.31162715271869 rawBenchmark "HashToCurve" = 37829.83541169991 rawBenchmark "High1" = 31.86779242260267 rawBenchmark "High16" = 36.868090596516424 rawBenchmark "High32" = 32.65996617035562 rawBenchmark "High64" = 37.93536469075943 rawBenchmark "High8" = 32.943473850377345 rawBenchmark "Increment16" = 38.392451852783076 rawBenchmark "Increment32" = 51.55474922519457 rawBenchmark "Increment64" = 48.75851943327705 rawBenchmark "Increment8" = 47.33246517826407 rawBenchmark "InputAmount" = 158.40519188620513 rawBenchmark "InputAmountsHash" = 78.18657902074679 rawBenchmark "InputAnnexHash" = 50.39975862268921 rawBenchmark "InputAnnexesHash" = 86.3866910419064 rawBenchmark "InputAsset" = 90.4780872924351 rawBenchmark "InputHash" = 536.5958475792895 rawBenchmark "InputOutpointsHash" = 79.08911806240489 rawBenchmark "InputPegin" = 83.98879360287582 rawBenchmark "InputPrevOutpoint" = 89.3872112500479 rawBenchmark "InputScriptHash" = 81.89252511817973 rawBenchmark "InputScriptSigHash" = 85.18974271907717 rawBenchmark "InputScriptSigsHash" = 76.77862968879907 rawBenchmark "InputScriptsHash" = 76.14052574532384 rawBenchmark "InputSequence" = 55.04705395962086 rawBenchmark "InputSequencesHash" = 79.43302880722794 rawBenchmark "InputUtxoHash" = 1109.0519630683661 rawBenchmark "InputUtxosHash" = 77.9855360566019 rawBenchmark "InputsHash" = 86.08549951543868 rawBenchmark "InternalKey" = 84.89379535345726 rawBenchmark "IsOne16" = 45.64683559591153 rawBenchmark "IsOne32" = 36.58111091935885 rawBenchmark "IsOne64" = 46.45643688595097 rawBenchmark "IsOne8" = 50.62634232797921 rawBenchmark "IsZero16" = 42.109412893391784 rawBenchmark "IsZero32" = 47.422659579472345 rawBenchmark "IsZero64" = 44.99474610179195 rawBenchmark "IsZero8" = 43.2557200624648 rawBenchmark "Issuance" = 50.74625704409637 rawBenchmark "IssuanceAsset" = 83.923133996747 rawBenchmark "IssuanceAssetAmount" = 90.39955141184957 rawBenchmark "IssuanceAssetAmountsHash" = 77.23792759162177 rawBenchmark "IssuanceAssetProof" = 83.58936713231286 rawBenchmark "IssuanceBlindingEntropyHash" = 71.8325573717658 rawBenchmark "IssuanceEntropy" = 85.07102143556246 rawBenchmark "IssuanceHash" = 2076.7943990862123 rawBenchmark "IssuanceRangeProofsHash" = 71.96306342619509 rawBenchmark "IssuanceToken" = 83.0717304440206 rawBenchmark "IssuanceTokenAmount" = 109.09867909211174 rawBenchmark "IssuanceTokenAmountsHash" = 76.77352744178933 rawBenchmark "IssuanceTokenProof" = 83.80024681603632 rawBenchmark "IssuancesHash" = 78.75424725524539 rawBenchmark "LbtcAsset" = 80.81176100612451 rawBenchmark "Le16" = 62.59866562816164 rawBenchmark "Le32" = 51.691597800360576 rawBenchmark "Le64" = 51.98614962560549 rawBenchmark "Le8" = 60.913133751779085 rawBenchmark "LeftExtend16_32" = 48.321737975265485 rawBenchmark "LeftExtend16_64" = 49.768255836158694 rawBenchmark "LeftExtend1_16" = 37.33174442804743 rawBenchmark "LeftExtend1_32" = 33.51980854843369 rawBenchmark "LeftExtend1_64" = 42.74855194501722 rawBenchmark "LeftExtend1_8" = 36.301294529908404 rawBenchmark "LeftExtend32_64" = 35.00507852860337 rawBenchmark "LeftExtend8_16" = 49.27356422938357 rawBenchmark "LeftExtend8_32" = 50.49729967016896 rawBenchmark "LeftExtend8_64" = 59.47812571540859 rawBenchmark "LeftPadHigh16_32" = 50.98338161795605 rawBenchmark "LeftPadHigh16_64" = 61.60346108788994 rawBenchmark "LeftPadHigh1_16" = 78.50508931127487 rawBenchmark "LeftPadHigh1_32" = 146.26121054697865 rawBenchmark "LeftPadHigh1_64" = 234.97787849061334 rawBenchmark "LeftPadHigh1_8" = 55.39324189082562 rawBenchmark "LeftPadHigh32_64" = 52.17097219985573 rawBenchmark "LeftPadHigh8_16" = 49.21564430401875 rawBenchmark "LeftPadHigh8_32" = 57.68232149971271 rawBenchmark "LeftPadHigh8_64" = 75.61993575310662 rawBenchmark "LeftPadLow16_32" = 38.49926754604619 rawBenchmark "LeftPadLow16_64" = 59.250342412456355 rawBenchmark "LeftPadLow1_16" = 36.36920559197807 rawBenchmark "LeftPadLow1_32" = 35.466251309723425 rawBenchmark "LeftPadLow1_64" = 33.98849564613479 rawBenchmark "LeftPadLow1_8" = 31.204669198216017 rawBenchmark "LeftPadLow32_64" = 50.99335457473273 rawBenchmark "LeftPadLow8_16" = 37.126983955984464 rawBenchmark "LeftPadLow8_32" = 34.00684198357385 rawBenchmark "LeftPadLow8_64" = 62.53255064489368 rawBenchmark "LeftRotate16" = 43.001392195690684 rawBenchmark "LeftRotate32" = 59.09903021360284 rawBenchmark "LeftRotate64" = 54.856167630986604 rawBenchmark "LeftRotate8" = 49.076586368944184 rawBenchmark "LeftShift16" = 40.235919376592726 rawBenchmark "LeftShift32" = 43.76932719716762 rawBenchmark "LeftShift64" = 45.73742443386188 rawBenchmark "LeftShift8" = 50.57937158222907 rawBenchmark "LeftShiftWith16" = 46.61700433558814 rawBenchmark "LeftShiftWith32" = 52.81674643546554 rawBenchmark "LeftShiftWith64" = 57.28743045790752 rawBenchmark "LeftShiftWith8" = 59.90532889097582 rawBenchmark "Leftmost16_1" = 51.70552021960683 rawBenchmark "Leftmost16_2" = 50.08994317254649 rawBenchmark "Leftmost16_4" = 41.80688946896769 rawBenchmark "Leftmost16_8" = 39.60132273936846 rawBenchmark "Leftmost32_1" = 43.30897199282181 rawBenchmark "Leftmost32_16" = 56.9016513351459 rawBenchmark "Leftmost32_2" = 37.2079258996741 rawBenchmark "Leftmost32_4" = 29.068274922258183 rawBenchmark "Leftmost32_8" = 57.77525039357289 rawBenchmark "Leftmost64_1" = 43.60916457293865 rawBenchmark "Leftmost64_16" = 48.96468216997573 rawBenchmark "Leftmost64_2" = 39.922903799137245 rawBenchmark "Leftmost64_32" = 50.08880572463181 rawBenchmark "Leftmost64_4" = 44.43246907916128 rawBenchmark "Leftmost64_8" = 47.83372489702833 rawBenchmark "Leftmost8_1" = 50.511534173537996 rawBenchmark "Leftmost8_2" = 50.40905212515953 rawBenchmark "Leftmost8_4" = 48.50341727771359 rawBenchmark "LinearCombination1" = 47040.93376314034 rawBenchmark "LinearVerify1" = 48182.42296619453 rawBenchmark "LockTime" = 47.70317349257734 rawBenchmark "Low1" = 21.364181571710727 rawBenchmark "Low16" = 38.49685288168574 rawBenchmark "Low32" = 34.91518106691244 rawBenchmark "Low64" = 26.186652606444063 rawBenchmark "Low8" = 26.29098053293153 rawBenchmark "Lt16" = 68.8706112088274 rawBenchmark "Lt32" = 59.53443050674163 rawBenchmark "Lt64" = 42.364172739029975 rawBenchmark "Lt8" = 59.93172194081304 rawBenchmark "Maj1" = 34.96061898351924 rawBenchmark "Maj16" = 44.94543138149138 rawBenchmark "Maj32" = 53.683025295042526 rawBenchmark "Maj64" = 51.72821494872019 rawBenchmark "Maj8" = 52.36812937443448 rawBenchmark "Max16" = 63.71134773209803 rawBenchmark "Max32" = 51.18820119510864 rawBenchmark "Max64" = 57.83190769189562 rawBenchmark "Max8" = 53.8515645366078 rawBenchmark "Median16" = 68.42782342281728 rawBenchmark "Median32" = 56.38805745851612 rawBenchmark "Median64" = 60.56301468794372 rawBenchmark "Median8" = 67.89381197782626 rawBenchmark "Min16" = 54.04518077046216 rawBenchmark "Min32" = 62.97525599888933 rawBenchmark "Min64" = 56.81753152966646 rawBenchmark "Min8" = 55.00456012337589 rawBenchmark "Modulo16" = 57.518560975532644 rawBenchmark "Modulo32" = 57.08875049862416 rawBenchmark "Modulo64" = 47.65027121643483 rawBenchmark "Modulo8" = 56.70553878631508 rawBenchmark "Multiply16" = 50.145505525636324 rawBenchmark "Multiply32" = 50.46424112527131 rawBenchmark "Multiply64" = 47.45018438748184 rawBenchmark "Multiply8" = 52.03683827069245 rawBenchmark "Negate16" = 38.90971489117882 rawBenchmark "Negate32" = 47.61426946368856 rawBenchmark "Negate64" = 52.41405985192276 rawBenchmark "Negate8" = 50.833505778893596 rawBenchmark "NewIssuanceContract" = 87.26032454930737 rawBenchmark "NonceHash" = 176.1925 rawBenchmark "NumInputs" = 48.16180127047511 rawBenchmark "NumOutputs" = 44.087257539344634 rawBenchmark "One16" = 33.60409513338236 rawBenchmark "One32" = 33.222841959359855 rawBenchmark "One64" = 33.2636748253045 rawBenchmark "One8" = 34.88577796465835 rawBenchmark "Or1" = 42.911584386668494 rawBenchmark "Or16" = 52.44067390159183 rawBenchmark "Or32" = 58.43280128473747 rawBenchmark "Or64" = 55.4909110467771 rawBenchmark "Or8" = 52.17171918086705 rawBenchmark "OutpointHash" = 177.4066666666666 rawBenchmark "OutputAmount" = 165.73152456360123 rawBenchmark "OutputAmountsHash" = 77.96882406434946 rawBenchmark "OutputAsset" = 94.686291527907 rawBenchmark "OutputHash" = 1582.7809306692625 rawBenchmark "OutputIsFee" = 51.60956472131248 rawBenchmark "OutputNonce" = 109.35522600953867 rawBenchmark "OutputNoncesHash" = 84.29265131406393 rawBenchmark "OutputNullDatum" = 48.47393556700054 rawBenchmark "OutputRangeProof" = 85.91729268925901 rawBenchmark "OutputRangeProofsHash" = 76.01487688752357 rawBenchmark "OutputScriptHash" = 84.3315823091484 rawBenchmark "OutputScriptsHash" = 79.43957403869098 rawBenchmark "OutputSurjectionProof" = 83.9027630832634 rawBenchmark "OutputSurjectionProofsHash" = 76.73829814634762 rawBenchmark "OutputsHash" = 75.43857791831756 rawBenchmark "ParseLock" = 54.40929208819059 rawBenchmark "ParseSequence" = 64.73080420529664 rawBenchmark "PointVerify1" = 46104.55214160499 rawBenchmark "ReissuanceBlinding" = 50.73337651212825 rawBenchmark "ReissuanceEntropy" = 51.84338682545885 rawBenchmark "RightExtend16_32" = 41.1152394906143 rawBenchmark "RightExtend16_64" = 45.58796842580513 rawBenchmark "RightExtend32_64" = 52.52115235015417 rawBenchmark "RightExtend8_16" = 42.62436355994448 rawBenchmark "RightExtend8_32" = 58.95339195029901 rawBenchmark "RightExtend8_64" = 69.32207026801537 rawBenchmark "RightPadHigh16_32" = 39.424436392837556 rawBenchmark "RightPadHigh16_64" = 49.248174058995446 rawBenchmark "RightPadHigh1_16" = 79.72621339569697 rawBenchmark "RightPadHigh1_32" = 124.40833120289545 rawBenchmark "RightPadHigh1_64" = 264.5187952944149 rawBenchmark "RightPadHigh1_8" = 59.84994335191323 rawBenchmark "RightPadHigh32_64" = 52.54942442499254 rawBenchmark "RightPadHigh8_16" = 49.67776118222926 rawBenchmark "RightPadHigh8_32" = 61.532852924980645 rawBenchmark "RightPadHigh8_64" = 59.83710387705546 rawBenchmark "RightPadLow16_32" = 39.87733699553977 rawBenchmark "RightPadLow16_64" = 53.36064826952089 rawBenchmark "RightPadLow1_16" = 45.07485014417921 rawBenchmark "RightPadLow1_32" = 41.676208784085105 rawBenchmark "RightPadLow1_64" = 41.090406238456374 rawBenchmark "RightPadLow1_8" = 37.92725470993486 rawBenchmark "RightPadLow32_64" = 44.8312134267434 rawBenchmark "RightPadLow8_16" = 41.75506302525163 rawBenchmark "RightPadLow8_32" = 43.22301100078246 rawBenchmark "RightPadLow8_64" = 46.0905871657453 rawBenchmark "RightRotate16" = 55.451707999091234 rawBenchmark "RightRotate32" = 51.33869960974644 rawBenchmark "RightRotate64" = 51.72067856450664 rawBenchmark "RightRotate8" = 41.88436010698827 rawBenchmark "RightShift16" = 47.19331997670199 rawBenchmark "RightShift32" = 49.25458525218545 rawBenchmark "RightShift64" = 50.88231418071366 rawBenchmark "RightShift8" = 49.252427103572366 rawBenchmark "RightShiftWith16" = 58.52512455955412 rawBenchmark "RightShiftWith32" = 51.447551882228765 rawBenchmark "RightShiftWith64" = 53.91540234901843 rawBenchmark "RightShiftWith8" = 57.29707045629772 rawBenchmark "Rightmost16_1" = 39.17928949934075 rawBenchmark "Rightmost16_2" = 45.91367784810004 rawBenchmark "Rightmost16_4" = 42.474022809253114 rawBenchmark "Rightmost16_8" = 38.446904909381345 rawBenchmark "Rightmost32_1" = 50.25654518416595 rawBenchmark "Rightmost32_16" = 35.92965867433983 rawBenchmark "Rightmost32_2" = 41.65904204963655 rawBenchmark "Rightmost32_4" = 51.37905781489622 rawBenchmark "Rightmost32_8" = 43.44904922808357 rawBenchmark "Rightmost64_1" = 43.0289803608958 rawBenchmark "Rightmost64_16" = 48.13330514376038 rawBenchmark "Rightmost64_2" = 41.49489356566985 rawBenchmark "Rightmost64_32" = 42.65585176023737 rawBenchmark "Rightmost64_4" = 39.403601089532856 rawBenchmark "Rightmost64_8" = 38.74161920301971 rawBenchmark "Rightmost8_1" = 44.41905969704213 rawBenchmark "Rightmost8_2" = 54.657570189798406 rawBenchmark "Rightmost8_4" = 54.51548104019699 rawBenchmark "ScalarAdd" = 410.7714457930927 rawBenchmark "ScalarInvert" = 1774.301764466127 rawBenchmark "ScalarIsZero" = 150.68813566357764 rawBenchmark "ScalarMultiply" = 430.52312683792223 rawBenchmark "ScalarMultiplyLambda" = 309.76081130635305 rawBenchmark "ScalarNegate" = 272.4586280769547 rawBenchmark "ScalarNormalize" = 262.222720853674 rawBenchmark "ScalarSquare" = 319.63744130697734 rawBenchmark "Scale" = 40374.728500765836 rawBenchmark "ScriptCMR" = 76.06354466217492 rawBenchmark "Sha256Block" = 428.73063753263835 rawBenchmark "Sha256Ctx8Add1" = 357.1469939873504 rawBenchmark "Sha256Ctx8Add128" = 988.6918403199944 rawBenchmark "Sha256Ctx8Add16" = 415.4784277283797 rawBenchmark "Sha256Ctx8Add2" = 367.61900312553604 rawBenchmark "Sha256Ctx8Add256" = 1618.063444006473 rawBenchmark "Sha256Ctx8Add32" = 498.1741652411793 rawBenchmark "Sha256Ctx8Add4" = 358.73790652714655 rawBenchmark "Sha256Ctx8Add512" = 2943.876504030598 rawBenchmark "Sha256Ctx8Add64" = 659.6032113473665 rawBenchmark "Sha256Ctx8Add8" = 374.68717127064343 rawBenchmark "Sha256Ctx8AddBuffer511" = 2811.1712632387207 rawBenchmark "Sha256Ctx8Finalize" = 464.13750087504866 rawBenchmark "Sha256Ctx8Init" = 65.72256048302079 rawBenchmark "Sha256Iv" = 51.86507201053729 rawBenchmark "SigAllHash" = 74.01780898147763 rawBenchmark "Some1" = 39.348504333222046 rawBenchmark "Some16" = 35.44393063743075 rawBenchmark "Some32" = 35.685777760954764 rawBenchmark "Some64" = 52.01425312522673 rawBenchmark "Some8" = 41.67994966835807 rawBenchmark "Subtract16" = 63.19727385093392 rawBenchmark "Subtract32" = 65.73711542469461 rawBenchmark "Subtract64" = 63.92384623761226 rawBenchmark "Subtract8" = 61.06034896812143 rawBenchmark "Swu" = 17844.670780310975 rawBenchmark "TapEnvHash" = 90.34785898924261 rawBenchmark "TapdataInit" = 654.8088901361084 rawBenchmark "TapleafHash" = 75.83151089538666 rawBenchmark "TapleafVersion" = 58.57378301922501 rawBenchmark "Tappath" = 46.60476841280421 rawBenchmark "TappathHash" = 79.52144445412839 rawBenchmark "TotalFee" = 128.3214285714286 rawBenchmark "TransactionId" = 77.57004212352764 rawBenchmark "TxHash" = 79.6895834815193 rawBenchmark "TxIsFinal" = 39.91991497511649 rawBenchmark "TxLockDistance" = 50.70260372831025 rawBenchmark "TxLockDuration" = 46.90895581164496 rawBenchmark "TxLockHeight" = 44.5346343811494 rawBenchmark "TxLockTime" = 44.50131256493571 rawBenchmark "Verify" = 32.09444427680617 rawBenchmark "Version" = 51.946730072789 rawBenchmark "Xor1" = 37.39423846227012 rawBenchmark "Xor16" = 46.3143332902559 rawBenchmark "Xor32" = 51.3678650882931 rawBenchmark "Xor64" = 53.19079568520052 rawBenchmark "Xor8" = 47.77399820413938 rawBenchmark "XorXor1" = 40.36662737601213 rawBenchmark "XorXor16" = 44.24820795601652 rawBenchmark "XorXor32" = 53.43665625904725 rawBenchmark "XorXor64" = 52.088775723655864 rawBenchmark "XorXor8" = 54.87228218084948 -- benchmark adjusts the raw benchmark by giving a discount to batch verifiable jets. benchmark :: String -> Double benchmark jetName = rawBenchmark jetName * adjustment where batchable = ["LinearVerify1", "PointVerify1", "CheckSigVerify", "Bip0340Verify"] adjustment | jetName `elem` batchable = 0.5 | otherwise = 1 -- Normalized cost where cost "CheckSigVerify" = 50 Weight. cost :: String -> Weight cost jetName = realToFrac $ benchmark jetName * factor where factor = 50 / benchmark "CheckSigVerify" ================================================ FILE: Haskell/Simplicity/Elements/FFI/Env.hs ================================================ -- | This module binds the C implementation of jets for Simplicity for assertions. {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.Elements.FFI.Env ( CTransaction, CTapEnv, CTxEnv , marshallTransaction, marshallTapEnv , withEnv, withPrimEnv ) where import qualified Data.ByteString as BS import qualified Data.ByteString.Lazy as BSL import Data.Foldable (toList) import Data.Serialize (Serialize, encode, runPut) import Data.Vector (Vector) import Data.Word (Word32) import Foreign.C.Types (CSize(..), CChar(..), CUChar(..), CUInt(..)) import Foreign.ForeignPtr (ForeignPtr, newForeignPtr, withForeignPtr) import Foreign.Marshal.Alloc (allocaBytes) import Foreign.Marshal.Array (withArray, withArrayLen) import Foreign.Marshal.Unsafe (unsafeLocalState) import Foreign.Ptr (FunPtr, Ptr, nullPtr, plusPtr) import Foreign.Storable (Storable(..)) import Lens.Family2 ((^.), under) import Simplicity.Digest import Simplicity.Elements.DataTypes import Simplicity.Elements.Primitive -- Abstract representative for the C txEnv types. newtype RawBuffer = RawBuffer RawBuffer newtype RawOutput = RawOutput RawOutput newtype RawInput = RawInput RawInput newtype RawTransaction = RawTransaction RawTransaction newtype RawTapEnv = RawTapEnv RawTapEnv newtype CTransaction = CTransaction CTransaction newtype CTapEnv = CTapEnv CTapEnv newtype CTxEnv = CTxEnv CTxEnv foreign import ccall unsafe "&" c_sizeof_rawElementsBuffer :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawElementsOutput :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawElementsInput :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawElementsTransaction :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_rawElementsTapEnv :: Ptr CSize foreign import ccall unsafe "&" c_sizeof_txEnv :: Ptr CSize foreign import ccall unsafe "" c_set_rawElementsBuffer :: Ptr RawBuffer -> Ptr CChar -> CUInt -> IO () foreign import ccall unsafe "" c_set_rawElementsOutput :: Ptr RawOutput -> Ptr CChar -> Ptr CChar -> Ptr CChar -> Ptr RawBuffer -> Ptr RawBuffer -> Ptr RawBuffer -> IO () foreign import ccall unsafe "" c_set_rawElementsInput :: Ptr RawInput -> Ptr RawBuffer -> Ptr CChar -> Ptr RawBuffer -> Ptr CChar -> CUInt -> Ptr CChar -> Ptr CChar -> Ptr RawBuffer -> CUInt -> Ptr CChar -> Ptr CChar -> Ptr CChar -> Ptr CChar -> Ptr RawBuffer -> Ptr RawBuffer -> IO () foreign import ccall unsafe "" c_set_rawElementsTransaction :: Ptr RawTransaction -> Ptr CChar -> CUInt -> Ptr RawInput -> CUInt -> Ptr RawOutput -> CUInt -> CUInt -> IO () foreign import ccall unsafe "" c_set_rawElementsTapEnv :: Ptr RawTapEnv -> Ptr CChar -> CUChar -> Ptr CChar -> IO () foreign import ccall unsafe "" c_set_txEnv :: Ptr CTxEnv -> Ptr CTransaction -> Ptr CTapEnv -> Ptr CChar -> CUInt -> IO () foreign import ccall unsafe "" simplicity_elements_mallocTransaction :: Ptr RawTransaction -> IO (Ptr CTransaction) foreign import ccall unsafe "&" simplicity_elements_freeTransaction :: FunPtr (Ptr CTransaction -> IO ()) foreign import ccall unsafe "" simplicity_elements_mallocTapEnv :: Ptr RawTapEnv -> IO (Ptr CTapEnv) foreign import ccall unsafe "&" simplicity_elements_freeTapEnv :: FunPtr (Ptr CTapEnv -> IO ()) sizeof_rawBuffer :: Int sizeof_rawBuffer = fromIntegral . unsafeLocalState $ peek c_sizeof_rawElementsBuffer sizeof_rawOutput :: Int sizeof_rawOutput = fromIntegral . unsafeLocalState $ peek c_sizeof_rawElementsOutput sizeof_rawInput :: Int sizeof_rawInput = fromIntegral . unsafeLocalState $ peek c_sizeof_rawElementsInput sizeof_rawTransaction :: Int sizeof_rawTransaction = fromIntegral . unsafeLocalState $ peek c_sizeof_rawElementsTransaction sizeof_rawTapEnv :: Int sizeof_rawTapEnv = fromIntegral . unsafeLocalState $ peek c_sizeof_rawElementsTapEnv sizeof_txEnv :: Int sizeof_txEnv = fromIntegral . unsafeLocalState $ peek c_sizeof_txEnv withRawBuffer :: BSL.ByteString -> (Ptr RawBuffer -> IO b) -> IO b withRawBuffer str k = allocaBytes sizeof_rawBuffer $ \pRawBuffer -> BS.useAsCStringLen (BSL.toStrict str) $ \(pCharStr, len) -> do c_set_rawElementsBuffer pRawBuffer pCharStr (fromIntegral len) k pRawBuffer withIssuance :: Maybe Issuance -> (Ptr CChar -> Ptr CChar -> Ptr CChar -> Ptr CChar -> Ptr RawBuffer -> Ptr RawBuffer -> IO b) -> IO b withIssuance Nothing k = withArray (replicate 32 0) $ \pZero -> withRawBuffer mempty $ \pEmpty -> k pZero pZero nullPtr nullPtr pEmpty pEmpty withIssuance (Just (Left newIssue)) k = withArray (replicate 32 0) $ \pZero -> BS.useAsCString (encode (newIssuanceContractHash newIssue)) $ \pContract -> maybeAmount issueAmount $ \pAmount -> maybeAmount tokenAmount $ \pToken -> withRawBuffer (issueAmount ^. (under amount.prf_)) $ \pAmountRangeProof -> withRawBuffer (tokenAmount ^. (under amount.prf_)) $ \pTokenRangeProof -> k pZero pContract pAmount pToken pAmountRangeProof pTokenRangeProof where issueAmount = newIssuanceAmount newIssue tokenAmount = newIssuanceTokenAmount newIssue maybeAmount (Amount (Explicit 0)) k = k nullPtr maybeAmount amt k = BS.useAsCString (runPut . putAmount $ clearAmountPrf amt) k withIssuance (Just (Right reIssue)) k = BS.useAsCString (encode (reissuanceBlindingNonce reIssue)) $ \pBlinding -> BS.useAsCString (encode (reissuanceEntropy reIssue)) $ \pEntropy -> BS.useAsCString (runPut . putAmount $ clearAmountPrf issueAmount) $ \pAmount -> withRawBuffer (issueAmount ^. (under amount.prf_)) $ \pAmountRangeProof -> withRawBuffer mempty $ \pEmpty -> k pBlinding pEntropy pAmount nullPtr pAmountRangeProof pEmpty where issueAmount = reissuanceAmount reIssue withRawOutputs :: Vector TxOutput -> (Ptr RawOutput -> IO b) -> IO b withRawOutputs txos k = allocaBytes (len * sizeof_rawOutput) $ \pRawOutput -> foldr ($) (k pRawOutput) [pokeRawOutput txo (pRawOutput `plusPtr` (i*sizeof_rawOutput)) | (i, txo) <- zip [0..] (toList txos)] where len = fromIntegral $ length txos pokeRawOutput :: TxOutput -> Ptr RawOutput -> IO b -> IO b pokeRawOutput txo pRawOutput k = BS.useAsCString (runPut . putAsset . clearAssetPrf $ txoAsset txo) $ \pAsset -> BS.useAsCString (runPut . putAmount . clearAmountPrf $ txoAmount txo) $ \pAmount -> withMaybe (txoNonce txo) $ \pNonce -> withRawBuffer (txoScript txo) $ \pScript -> withRawBuffer (txoAsset txo ^. (under asset.prf_)) $ \pSurjectionProof -> withRawBuffer (txoAmount txo ^. (under amount.prf_)) $ \pRangeProof -> do c_set_rawElementsOutput pRawOutput pAsset pAmount pNonce pScript pSurjectionProof pRangeProof k withMaybe Nothing = ($ nullPtr) withMaybe (Just x) = BS.useAsCString (encode x) withRawInputs :: Vector SigTxInput -> (Ptr RawInput -> IO b) -> IO b withRawInputs txis k = allocaBytes (len * sizeof_rawInput) $ \pRawInput -> do foldr ($) (k pRawInput) [pokeRawInput txo (pRawInput `plusPtr` (i*sizeof_rawInput)) | (i, txo) <- zip [0..] (toList txis)] where len = fromIntegral $ length txis withMaybe Nothing = ($ nullPtr) withMaybe (Just x) = BS.useAsCString (encode x) withMaybeRawBuffer Nothing = ($ nullPtr) withMaybeRawBuffer (Just buf) = withRawBuffer buf pokeRawInput :: SigTxInput -> Ptr RawInput -> IO b -> IO b pokeRawInput txi pRawInput k = withMaybeRawBuffer (sigTxiAnnex txi) $ \pAnnex -> withMaybe (sigTxiPegin txi) $ \pPegin -> withRawBuffer (sigTxiScriptSig txi) $ \pScriptSig -> BS.useAsCString (encode . opHash $ sigTxiPreviousOutpoint txi) $ \pPrevTxid -> BS.useAsCString (runPut . putAsset . utxoAsset $ sigTxiTxo txi) $ \pAsset -> BS.useAsCString (runPut . putAmount . utxoAmount $ sigTxiTxo txi) $ \pValue -> withRawBuffer (utxoScript $ sigTxiTxo txi) $ \pScript -> withIssuance (sigTxiIssuance txi) $ \pBlindingNonce pAssetEntropy pAmount pInflationKeys pAmountRangeProof pInflationKeysRangeProof -> do c_set_rawElementsInput pRawInput pAnnex pPegin pScriptSig pPrevTxid (fromIntegral . opIndex . sigTxiPreviousOutpoint $ txi) pAsset pValue pScript (fromIntegral . sigTxiSequence $ txi) pBlindingNonce pAssetEntropy pAmount pInflationKeys pAmountRangeProof pInflationKeysRangeProof k withRawTransaction :: SigTx -> (Ptr RawTransaction -> IO b) -> IO b withRawTransaction tx k = allocaBytes sizeof_rawTransaction $ \pRawTransaction -> withRawInputs (sigTxIn tx) $ \pInput -> withRawOutputs (sigTxOut tx) $ \pOutput -> do BS.useAsCString (encode $ txid tx) $ \pTxid -> do c_set_rawElementsTransaction pRawTransaction pTxid version pInput numInputs pOutput numOutputs lockTime k pRawTransaction where version = fromIntegral (sigTxVersion tx) numInputs = fromIntegral $ length (sigTxIn tx) numOutputs = fromIntegral $ length (sigTxOut tx) lockTime = fromIntegral (sigTxLock tx) withRawTapEnv :: TapEnv -> (Ptr RawTapEnv -> IO b) -> IO b withRawTapEnv tapEnv k | length (tappath tapEnv) <= 128 = allocaBytes sizeof_rawTapEnv $ \pRawTapEnv -> BS.useAsCString encodePath $ \pControlBlock -> do BS.useAsCString (encode $ tapScriptCMR tapEnv) $ \pCmr -> do c_set_rawElementsTapEnv pRawTapEnv pControlBlock (fromIntegral . length $ tappath tapEnv) pCmr k pRawTapEnv where encodePath = BS.cons (tapleafVersion tapEnv) (BS.concat (encode (tapInternalKey tapEnv) : map encode (tappath tapEnv))) marshallTransaction :: SigTx -> IO (ForeignPtr CTransaction) marshallTransaction tx = withRawTransaction tx $ \pRawTransaction -> simplicity_elements_mallocTransaction pRawTransaction >>= newForeignPtr simplicity_elements_freeTransaction marshallTapEnv :: TapEnv -> IO (ForeignPtr CTapEnv) marshallTapEnv env = withRawTapEnv env $ \pRawTapEnv -> simplicity_elements_mallocTapEnv pRawTapEnv >>= newForeignPtr simplicity_elements_freeTapEnv withEnv :: ForeignPtr CTransaction -> Word32 -> ForeignPtr CTapEnv -> Hash256 -> (Ptr CTxEnv -> IO b) -> IO b withEnv cTransaction ix cTapEnv genesisHash k = allocaBytes sizeof_txEnv $ \pTxEnv -> withForeignPtr cTransaction $ \pTransaction -> withForeignPtr cTapEnv $ \pTapEnv -> BS.useAsCString (encode genesisHash) $ \pGenesis -> do c_set_txEnv pTxEnv pTransaction pTapEnv pGenesis (fromIntegral ix) k pTxEnv withPrimEnv :: PrimEnv -> (Ptr CTxEnv -> IO b) -> IO b withPrimEnv env k = do cTransaction <- marshallTransaction (envTx env) cTapEnv <- marshallTapEnv (envTap env) withEnv cTransaction (envIx env) cTapEnv (envGenesisBlock env) k ================================================ FILE: Haskell/Simplicity/Elements/FFI/Jets.hs ================================================ -- | This module binds the C implementation of jets for Simplicity for assertions. {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.Elements.FFI.Jets ( version , lock_time , input_pegin , input_prev_outpoint , input_asset , input_amount , input_script_hash , input_sequence , input_annex_hash , input_script_sig_hash , reissuance_blinding , new_issuance_contract , reissuance_entropy , issuance_asset_amount , issuance_token_amount , issuance_asset_proof , issuance_token_proof , output_asset , output_amount , output_nonce , output_script_hash , output_null_datum , output_is_fee , output_surjection_proof , output_range_proof , total_fee , genesis_block_hash , script_cmr , transaction_id , current_index , current_pegin , current_prev_outpoint , current_asset , current_amount , current_script_hash , current_sequence , current_reissuance_blinding , current_new_issuance_contract , current_reissuance_entropy , current_issuance_asset_amount , current_issuance_token_amount , current_issuance_asset_proof , current_issuance_token_proof , current_annex_hash , current_script_sig_hash , tapleaf_version , tappath , internal_key , num_inputs , num_outputs , tx_is_final , tx_lock_height , tx_lock_time , broken_do_not_use_tx_lock_distance , broken_do_not_use_tx_lock_duration , check_lock_height , check_lock_time , broken_do_not_use_check_lock_distance , broken_do_not_use_check_lock_duration , calculate_issuance_entropy , calculate_asset , calculate_explicit_token , calculate_confidential_token , lbtc_asset , outpoint_hash , asset_amount_hash , nonce_hash , annex_hash , build_tapleaf_simplicity , build_tapbranch , build_taptweak , issuance , issuance_entropy , issuance_asset , issuance_token , output_amounts_hash , output_nonces_hash , output_scripts_hash , output_range_proofs_hash , output_surjection_proofs_hash , outputs_hash , output_hash , input_outpoints_hash , input_amounts_hash , input_scripts_hash , input_utxos_hash , input_utxo_hash , input_sequences_hash , input_annexes_hash , input_script_sigs_hash , inputs_hash , input_hash , issuance_asset_amounts_hash , issuance_token_amounts_hash , issuance_range_proofs_hash , issuance_blinding_entropy_hash , issuances_hash , issuance_hash , tx_hash , tapleaf_hash , tappath_hash , tap_env_hash , sig_all_hash ) where import Foreign.Ptr (Ptr) import Foreign.C.Types (CBool(..)) import Simplicity.Elements.FFI.Env import Simplicity.Elements.Primitive import Simplicity.FFI.Frame import Simplicity.Programs.Elements import Simplicity.Programs.LibSecp256k1 import Simplicity.Ty import Simplicity.Ty.Word -- | This cannot be used with jets that access global variables. unsafeLocalJet :: (TyC a, TyC b) => (Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool) -> PrimEnv -> a -> Maybe b unsafeLocalJet jet env = unsafeLocalCoreJet (\dst src -> withPrimEnv env (jet dst src)) foreign import ccall unsafe "" c_version :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_lock_time :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_pegin :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_prev_outpoint :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_asset :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_script_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_sequence :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_annex_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_script_sig_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_reissuance_blinding :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_new_issuance_contract :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_reissuance_entropy :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_asset_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_token_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_asset_proof :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_token_proof :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_asset :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_nonce :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_script_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_null_datum :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_is_fee :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_surjection_proof :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_range_proof :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_total_fee :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_genesis_block_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_script_cmr :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_transaction_id :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_index :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_pegin :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_prev_outpoint :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_asset :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_script_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_sequence :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_reissuance_blinding :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_new_issuance_contract :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_reissuance_entropy :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_issuance_asset_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_issuance_token_amount :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_issuance_asset_proof :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_issuance_token_proof :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_annex_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_current_script_sig_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tapleaf_version :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tappath :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_internal_key :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_num_inputs :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_num_outputs :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tx_is_final :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tx_lock_height :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tx_lock_time :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_broken_do_not_use_tx_lock_distance :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_broken_do_not_use_tx_lock_duration :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_check_lock_height :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_check_lock_time :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_broken_do_not_use_check_lock_distance :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_broken_do_not_use_check_lock_duration :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_calculate_issuance_entropy :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_calculate_asset :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_calculate_explicit_token :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_calculate_confidential_token :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_lbtc_asset :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_outpoint_hash :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_asset_amount_hash :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_nonce_hash :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_annex_hash :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_build_tapleaf_simplicity :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_build_tapbranch :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_build_taptweak :: Ptr FrameItem -> Ptr FrameItem -> IO CBool foreign import ccall unsafe "" c_issuance :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_entropy :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_asset :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_token :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_amounts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_nonces_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_scripts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_range_proofs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_surjection_proofs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_outputs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_output_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_outpoints_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_amounts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_scripts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_utxos_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_utxo_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_sequences_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_annexes_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_script_sigs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_inputs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_input_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_asset_amounts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_token_amounts_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_range_proofs_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_blinding_entropy_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuances_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_issuance_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tx_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tapleaf_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tappath_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_tap_env_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool foreign import ccall unsafe "" c_sig_all_hash :: Ptr FrameItem -> Ptr FrameItem -> Ptr CTxEnv -> IO CBool version :: PrimEnv -> () -> Maybe Word32 version = unsafeLocalJet c_version lock_time :: PrimEnv -> () -> Maybe Word32 lock_time = unsafeLocalJet c_lock_time num_inputs :: PrimEnv -> () -> Maybe Word32 num_inputs = unsafeLocalJet c_num_inputs input_pegin :: PrimEnv -> Word32 -> Maybe (S (S Word256)) input_pegin = unsafeLocalJet c_input_pegin input_prev_outpoint :: PrimEnv -> Word32 -> Maybe (S (Word256, Word32)) input_prev_outpoint = unsafeLocalJet c_input_prev_outpoint input_asset :: PrimEnv -> Word32 -> Maybe (S (Conf Word256)) input_asset = unsafeLocalJet c_input_asset input_amount :: PrimEnv -> Word32 -> Maybe (S (Conf Word256, Conf Word64)) input_amount = unsafeLocalJet c_input_amount input_script_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_script_hash = unsafeLocalJet c_input_script_hash input_sequence :: PrimEnv -> Word32 -> Maybe (S Word32) input_sequence = unsafeLocalJet c_input_sequence reissuance_blinding :: PrimEnv -> Word32 -> Maybe (S (S Word256)) reissuance_blinding = unsafeLocalJet c_reissuance_blinding new_issuance_contract :: PrimEnv -> Word32 -> Maybe (S (S Word256)) new_issuance_contract = unsafeLocalJet c_new_issuance_contract reissuance_entropy :: PrimEnv -> Word32 -> Maybe (S (S Word256)) reissuance_entropy = unsafeLocalJet c_reissuance_entropy issuance_asset_amount :: PrimEnv -> Word32 -> Maybe (S (S (Conf Word64))) issuance_asset_amount = unsafeLocalJet c_issuance_asset_amount issuance_token_amount :: PrimEnv -> Word32 -> Maybe (S (S (Conf Word64))) issuance_token_amount = unsafeLocalJet c_issuance_token_amount issuance_asset_proof :: PrimEnv -> Word32 -> Maybe (S Word256) issuance_asset_proof = unsafeLocalJet c_issuance_asset_proof issuance_token_proof :: PrimEnv -> Word32 -> Maybe (S Word256) issuance_token_proof = unsafeLocalJet c_issuance_token_proof input_annex_hash :: PrimEnv -> Word32 -> Maybe (S (S Word256)) input_annex_hash = unsafeLocalJet c_input_annex_hash input_script_sig_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_script_sig_hash = unsafeLocalJet c_input_script_sig_hash current_index :: PrimEnv -> () -> Maybe Word32 current_index = unsafeLocalJet c_current_index current_pegin :: PrimEnv -> () -> Maybe (S Word256) current_pegin = unsafeLocalJet c_current_pegin current_prev_outpoint :: PrimEnv -> () -> Maybe (Word256, Word32) current_prev_outpoint = unsafeLocalJet c_current_prev_outpoint current_asset :: PrimEnv -> () -> Maybe (Conf Word256) current_asset = unsafeLocalJet c_current_asset current_amount :: PrimEnv -> () -> Maybe (Conf Word256, Conf Word64) current_amount = unsafeLocalJet c_current_amount current_script_hash :: PrimEnv -> () -> Maybe Word256 current_script_hash = unsafeLocalJet c_current_script_hash current_sequence :: PrimEnv -> () -> Maybe Word32 current_sequence = unsafeLocalJet c_current_sequence current_reissuance_blinding :: PrimEnv -> () -> Maybe (S Word256) current_reissuance_blinding = unsafeLocalJet c_current_reissuance_blinding current_new_issuance_contract :: PrimEnv -> () -> Maybe (S Word256) current_new_issuance_contract = unsafeLocalJet c_current_new_issuance_contract current_reissuance_entropy :: PrimEnv -> () -> Maybe (S Word256) current_reissuance_entropy = unsafeLocalJet c_current_reissuance_entropy current_issuance_asset_amount :: PrimEnv -> () -> Maybe (S (Conf Word64)) current_issuance_asset_amount = unsafeLocalJet c_current_issuance_asset_amount current_issuance_token_amount :: PrimEnv -> () -> Maybe (S (Conf Word64)) current_issuance_token_amount = unsafeLocalJet c_current_issuance_token_amount current_issuance_asset_proof :: PrimEnv -> () -> Maybe Word256 current_issuance_asset_proof = unsafeLocalJet c_current_issuance_asset_proof current_issuance_token_proof :: PrimEnv -> () -> Maybe Word256 current_issuance_token_proof = unsafeLocalJet c_current_issuance_token_proof current_annex_hash :: PrimEnv -> () -> Maybe (S Word256) current_annex_hash = unsafeLocalJet c_current_annex_hash current_script_sig_hash :: PrimEnv -> () -> Maybe Word256 current_script_sig_hash = unsafeLocalJet c_current_script_sig_hash tapleaf_version :: PrimEnv -> () -> Maybe Word8 tapleaf_version = unsafeLocalJet c_tapleaf_version tappath :: PrimEnv -> Word8 -> Maybe (S Word256) tappath = unsafeLocalJet c_tappath internal_key :: PrimEnv -> () -> Maybe PubKey internal_key = unsafeLocalJet c_internal_key num_outputs :: PrimEnv -> () -> Maybe Word32 num_outputs = unsafeLocalJet c_num_outputs output_asset :: PrimEnv -> Word32 -> Maybe (S (Conf Word256)) output_asset = unsafeLocalJet c_output_asset output_amount :: PrimEnv -> Word32 -> Maybe (S (Conf Word256, Conf Word64)) output_amount = unsafeLocalJet c_output_amount output_nonce :: PrimEnv -> Word32 -> Maybe (S (S (Conf Word256))) output_nonce = unsafeLocalJet c_output_nonce output_script_hash :: PrimEnv -> Word32 -> Maybe (S Word256) output_script_hash = unsafeLocalJet c_output_script_hash output_null_datum :: PrimEnv -> (Word32,Word32) -> Maybe (S (S (Either (Word2, Word256) (Either Bit Word4)))) output_null_datum = unsafeLocalJet c_output_null_datum output_is_fee :: PrimEnv -> Word32 -> Maybe (S Bit) output_is_fee = unsafeLocalJet c_output_is_fee output_surjection_proof :: PrimEnv -> Word32 -> Maybe (S Word256) output_surjection_proof = unsafeLocalJet c_output_surjection_proof output_range_proof :: PrimEnv -> Word32 -> Maybe (S Word256) output_range_proof = unsafeLocalJet c_output_range_proof total_fee :: PrimEnv -> Word256 -> Maybe Word64 total_fee = unsafeLocalJet c_total_fee genesis_block_hash :: PrimEnv -> () -> Maybe Word256 genesis_block_hash = unsafeLocalJet c_genesis_block_hash script_cmr :: PrimEnv -> () -> Maybe Word256 script_cmr = unsafeLocalJet c_script_cmr transaction_id :: PrimEnv -> () -> Maybe Word256 transaction_id = unsafeLocalJet c_transaction_id tx_is_final :: PrimEnv -> () -> Maybe Bit tx_is_final = unsafeLocalJet c_tx_is_final tx_lock_height :: PrimEnv -> () -> Maybe Word32 tx_lock_height = unsafeLocalJet c_tx_lock_height tx_lock_time :: PrimEnv -> () -> Maybe Word32 tx_lock_time = unsafeLocalJet c_tx_lock_time broken_do_not_use_tx_lock_distance :: PrimEnv -> () -> Maybe Word16 broken_do_not_use_tx_lock_distance = unsafeLocalJet c_broken_do_not_use_tx_lock_distance broken_do_not_use_tx_lock_duration :: PrimEnv -> () -> Maybe Word16 broken_do_not_use_tx_lock_duration = unsafeLocalJet c_broken_do_not_use_tx_lock_duration check_lock_height :: PrimEnv -> Word32 -> Maybe () check_lock_height = unsafeLocalJet c_check_lock_height check_lock_time :: PrimEnv -> Word32 -> Maybe () check_lock_time = unsafeLocalJet c_check_lock_time broken_do_not_use_check_lock_distance :: PrimEnv -> Word16 -> Maybe () broken_do_not_use_check_lock_distance = unsafeLocalJet c_broken_do_not_use_check_lock_distance broken_do_not_use_check_lock_duration :: PrimEnv -> Word16 -> Maybe () broken_do_not_use_check_lock_duration = unsafeLocalJet c_broken_do_not_use_check_lock_duration calculate_issuance_entropy :: ((Word256, Word32), Word256) -> Maybe Word256 calculate_issuance_entropy = unsafeLocalCoreJet c_calculate_issuance_entropy calculate_asset :: Word256 -> Maybe Word256 calculate_asset = unsafeLocalCoreJet c_calculate_asset calculate_explicit_token :: Word256 -> Maybe Word256 calculate_explicit_token = unsafeLocalCoreJet c_calculate_explicit_token calculate_confidential_token :: Word256 -> Maybe Word256 calculate_confidential_token = unsafeLocalCoreJet c_calculate_confidential_token lbtc_asset :: () -> Maybe Word256 lbtc_asset = unsafeLocalCoreJet c_lbtc_asset outpoint_hash :: (Ctx8, (S Word256, (Word256, Word32))) -> Maybe Ctx8 outpoint_hash = unsafeLocalCoreJet c_outpoint_hash asset_amount_hash :: (Ctx8, (Conf Word256, Conf Word64)) -> Maybe Ctx8 asset_amount_hash = unsafeLocalCoreJet c_asset_amount_hash nonce_hash :: (Ctx8, S (Conf Word256)) -> Maybe Ctx8 nonce_hash = unsafeLocalCoreJet c_nonce_hash annex_hash :: (Ctx8, S Word256) -> Maybe Ctx8 annex_hash = unsafeLocalCoreJet c_annex_hash build_tapleaf_simplicity :: Word256 -> Maybe Word256 build_tapleaf_simplicity = unsafeLocalCoreJet c_build_tapleaf_simplicity build_tapbranch :: (Word256, Word256) -> Maybe Word256 build_tapbranch = unsafeLocalCoreJet c_build_tapbranch build_taptweak :: (Word256, Word256) -> Maybe Word256 build_taptweak = unsafeLocalCoreJet c_build_taptweak issuance :: PrimEnv -> Word32 -> Maybe (S (S Bit)) issuance = unsafeLocalJet c_issuance issuance_entropy :: PrimEnv -> Word32 -> Maybe (S (S Word256)) issuance_entropy = unsafeLocalJet c_issuance_entropy issuance_asset :: PrimEnv -> Word32 -> Maybe (S (S Word256)) issuance_asset = unsafeLocalJet c_issuance_asset issuance_token :: PrimEnv -> Word32 -> Maybe (S (S Word256)) issuance_token = unsafeLocalJet c_issuance_token output_amounts_hash :: PrimEnv -> () -> Maybe Word256 output_amounts_hash = unsafeLocalJet c_output_amounts_hash output_nonces_hash :: PrimEnv -> () -> Maybe Word256 output_nonces_hash = unsafeLocalJet c_output_nonces_hash output_scripts_hash :: PrimEnv -> () -> Maybe Word256 output_scripts_hash = unsafeLocalJet c_output_scripts_hash output_range_proofs_hash :: PrimEnv -> () -> Maybe Word256 output_range_proofs_hash = unsafeLocalJet c_output_range_proofs_hash output_surjection_proofs_hash :: PrimEnv -> () -> Maybe Word256 output_surjection_proofs_hash = unsafeLocalJet c_output_surjection_proofs_hash outputs_hash :: PrimEnv -> () -> Maybe Word256 outputs_hash = unsafeLocalJet c_outputs_hash output_hash :: PrimEnv -> Word32 -> Maybe (S Word256) output_hash = unsafeLocalJet c_output_hash input_outpoints_hash :: PrimEnv -> () -> Maybe Word256 input_outpoints_hash = unsafeLocalJet c_input_outpoints_hash input_amounts_hash :: PrimEnv -> () -> Maybe Word256 input_amounts_hash = unsafeLocalJet c_input_amounts_hash input_scripts_hash :: PrimEnv -> () -> Maybe Word256 input_scripts_hash = unsafeLocalJet c_input_scripts_hash input_utxos_hash :: PrimEnv -> () -> Maybe Word256 input_utxos_hash = unsafeLocalJet c_input_utxos_hash input_utxo_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_utxo_hash = unsafeLocalJet c_input_utxo_hash input_sequences_hash :: PrimEnv -> () -> Maybe Word256 input_sequences_hash = unsafeLocalJet c_input_sequences_hash input_annexes_hash :: PrimEnv -> () -> Maybe Word256 input_annexes_hash = unsafeLocalJet c_input_annexes_hash input_script_sigs_hash :: PrimEnv -> () -> Maybe Word256 input_script_sigs_hash = unsafeLocalJet c_input_script_sigs_hash inputs_hash :: PrimEnv -> () -> Maybe Word256 inputs_hash = unsafeLocalJet c_inputs_hash input_hash :: PrimEnv -> Word32 -> Maybe (S Word256) input_hash = unsafeLocalJet c_input_hash issuance_asset_amounts_hash :: PrimEnv -> () -> Maybe Word256 issuance_asset_amounts_hash = unsafeLocalJet c_issuance_asset_amounts_hash issuance_token_amounts_hash :: PrimEnv -> () -> Maybe Word256 issuance_token_amounts_hash = unsafeLocalJet c_issuance_token_amounts_hash issuance_range_proofs_hash :: PrimEnv -> () -> Maybe Word256 issuance_range_proofs_hash = unsafeLocalJet c_issuance_range_proofs_hash issuance_blinding_entropy_hash :: PrimEnv -> () -> Maybe Word256 issuance_blinding_entropy_hash = unsafeLocalJet c_issuance_blinding_entropy_hash issuances_hash :: PrimEnv -> () -> Maybe Word256 issuances_hash = unsafeLocalJet c_issuances_hash issuance_hash :: PrimEnv -> Word32 -> Maybe (S Word256) issuance_hash = unsafeLocalJet c_issuance_hash tx_hash :: PrimEnv -> () -> Maybe Word256 tx_hash = unsafeLocalJet c_tx_hash tapleaf_hash :: PrimEnv -> () -> Maybe Word256 tapleaf_hash = unsafeLocalJet c_tapleaf_hash tappath_hash :: PrimEnv -> () -> Maybe Word256 tappath_hash = unsafeLocalJet c_tappath_hash tap_env_hash :: PrimEnv -> () -> Maybe Word256 tap_env_hash = unsafeLocalJet c_tap_env_hash sig_all_hash :: PrimEnv -> () -> Maybe Word256 sig_all_hash = unsafeLocalJet c_sig_all_hash ================================================ FILE: Haskell/Simplicity/Elements/Jets.hs ================================================ -- | This module provides a canonical set of known jets for Simplicity for Elements. (At the moment this just consists of 'CoreJet's.) {-# LANGUAGE GADTs, StandaloneDeriving, TypeFamilies #-} module Simplicity.Elements.Jets ( JetType(..), ElementsJet(..), SigHashJet(..), TimeLockJet(..), IssuanceJet(..), TransactionJet(..) , elementsCatalogue , asJet , jetSubst, pruneSubst , getTermLengthCode, putTermLengthCode , fastEval , jetMap -- * Re-exports , WrappedSimplicity, unwrap , Simplicity.Elements.JetType.specification, Simplicity.Elements.JetType.implementation , Simplicity.Elements.JetType.getJetBit, Simplicity.Elements.JetType.putJetBit , Simplicity.Elements.JetType.jetCost , Semantics.FastEval ) where import Prelude hiding (fail, drop, take) import Control.Applicative ((<|>)) import Control.Arrow ((***), (+++)) import Control.Monad (guard) import Data.Either (isRight) import Data.Foldable (toList) import qualified Data.Map as Map import Data.Maybe (isJust) import Data.Proxy (Proxy(Proxy)) import Data.Serialize (runPut, put, putWord8) import Data.String (fromString) import Data.Type.Equality ((:~:)(Refl)) import Data.Vector ((!?)) import Data.Void (Void, vacuous) import Lens.Family2 ((^..), over, review) import Simplicity.Digest import Simplicity.CoreJets import qualified Simplicity.CoreJets as CoreJets import Simplicity.Elements.Benchmarks import Simplicity.Elements.Dag hiding (jetSubst, pruneSubst) import qualified Simplicity.Elements.Dag as Dag import Simplicity.Elements.Term import Simplicity.Elements.DataTypes import qualified Simplicity.Elements.JetType import Simplicity.Elements.Primitive (PrimEnv, S, Conf, PubKey, primEnvHash, envTx, envTap) import qualified Simplicity.Elements.Primitive as Prim import qualified Simplicity.Elements.Serialization.BitString as BitString import qualified Simplicity.Elements.Semantics as Semantics import qualified Simplicity.Elements.Programs.SigHash.Lib as SigHash import qualified Simplicity.Elements.Programs.Issuance.Lib as Issuance import qualified Simplicity.Elements.Programs.TimeLock as TimeLock import qualified Simplicity.Elements.Programs.Transaction.Lib as Prog import Simplicity.LibSecp256k1.Spec (fe) import qualified Simplicity.LibSecp256k1.Schnorr as Schnorr import Simplicity.MerkleRoot import Simplicity.Programs.Sha256.Lib (Ctx8) import qualified Simplicity.Programs.Elements.Lib as Prog import Simplicity.Programs.Word import Simplicity.Serialization import Simplicity.Tensor import Simplicity.Tree import Simplicity.Ty import Simplicity.Ty.Bit import Simplicity.Ty.Sha256 import Simplicity.Ty.Word import qualified Simplicity.Word as W import Simplicity.Weight -- | A type of tokens for the canonical set of known jets for Simplicity for Elements. (At the moment this just consists of 'CoreJet's.) -- -- The tokens themselves are not exported. You are expected to use 'Simplicity.Dag.jetDag' to substitute known jets found in Simplicity expressions. data JetType a b where ConstWordJet :: ConstWordContent b -> JetType () b CoreJet :: CoreJet a b -> JetType a b ElementsJet :: ElementsJet a b -> JetType a b deriving instance Eq (JetType a b) deriving instance Show (JetType a b) data ElementsJet a b where SigHashJet :: SigHashJet a b -> ElementsJet a b TimeLockJet :: TimeLockJet a b -> ElementsJet a b IssuanceJet :: IssuanceJet a b -> ElementsJet a b TransactionJet :: TransactionJet a b -> ElementsJet a b deriving instance Eq (ElementsJet a b) deriving instance Show (ElementsJet a b) data SigHashJet a b where SigAllHash :: SigHashJet () Word256 TxHash :: SigHashJet () Word256 TapEnvHash :: SigHashJet () Word256 OutputsHash :: SigHashJet () Word256 InputsHash :: SigHashJet () Word256 IssuancesHash :: SigHashJet () Word256 InputUtxosHash :: SigHashJet () Word256 OutputHash :: SigHashJet Word32 (S Word256) OutputAmountsHash :: SigHashJet () Word256 OutputScriptsHash :: SigHashJet () Word256 OutputNoncesHash :: SigHashJet () Word256 OutputRangeProofsHash :: SigHashJet () Word256 OutputSurjectionProofsHash :: SigHashJet () Word256 InputHash :: SigHashJet Word32 (S Word256) InputOutpointsHash :: SigHashJet () Word256 InputSequencesHash :: SigHashJet () Word256 InputAnnexesHash :: SigHashJet () Word256 InputScriptSigsHash :: SigHashJet () Word256 IssuanceHash :: SigHashJet Word32 (S Word256) IssuanceAssetAmountsHash :: SigHashJet () Word256 IssuanceTokenAmountsHash :: SigHashJet () Word256 IssuanceRangeProofsHash :: SigHashJet () Word256 IssuanceBlindingEntropyHash :: SigHashJet () Word256 InputUtxoHash :: SigHashJet Word32 (S Word256) InputAmountsHash :: SigHashJet () Word256 InputScriptsHash :: SigHashJet () Word256 TapleafHash :: SigHashJet () Word256 TappathHash :: SigHashJet () Word256 OutpointHash :: SigHashJet (Ctx8, (S Word256, (Word256, Word32))) Ctx8 AssetAmountHash :: SigHashJet (Ctx8, (Conf Word256, Conf Word64)) Ctx8 NonceHash :: SigHashJet (Ctx8, S (Conf Word256)) Ctx8 AnnexHash :: SigHashJet (Ctx8, S Word256) Ctx8 BuildTapleafSimplicity :: SigHashJet Word256 Word256 BuildTapbranch :: SigHashJet (Word256, Word256) Word256 BuildTaptweak :: SigHashJet (PubKey, Word256) PubKey deriving instance Eq (SigHashJet a b) deriving instance Show (SigHashJet a b) data TimeLockJet a b where CheckLockHeight :: TimeLockJet TimeLock.Height () CheckLockTime :: TimeLockJet TimeLock.Time () BrokenDoNotUseCheckLockDistance :: TimeLockJet TimeLock.Distance () BrokenDoNotUseCheckLockDuration :: TimeLockJet TimeLock.Duration () TxLockHeight :: TimeLockJet () TimeLock.Height TxLockTime :: TimeLockJet () TimeLock.Time BrokenDoNotUseTxLockDistance :: TimeLockJet () TimeLock.Distance BrokenDoNotUseTxLockDuration :: TimeLockJet () TimeLock.Duration TxIsFinal :: TimeLockJet () TimeLock.Bit deriving instance Eq (TimeLockJet a b) deriving instance Show (TimeLockJet a b) data IssuanceJet a b where Issuance :: IssuanceJet Word32 (S (S Bit)) IssuanceAsset :: IssuanceJet Word32 (S (S Word256)) IssuanceToken :: IssuanceJet Word32 (S (S Word256)) IssuanceEntropy :: IssuanceJet Word32 (S (S Word256)) CalculateIssuanceEntropy :: IssuanceJet ((Word256, Word32), Word256) Word256 CalculateAsset :: IssuanceJet Word256 Word256 CalculateExplicitToken :: IssuanceJet Word256 Word256 CalculateConfidentialToken :: IssuanceJet Word256 Word256 LbtcAsset :: IssuanceJet () Word256 deriving instance Eq (IssuanceJet a b) deriving instance Show (IssuanceJet a b) data TransactionJet a b where ScriptCMR :: TransactionJet () Word256 InternalKey :: TransactionJet () PubKey CurrentIndex :: TransactionJet () Word32 NumInputs :: TransactionJet () Word32 NumOutputs :: TransactionJet () Word32 LockTime :: TransactionJet () Word32 OutputAsset :: TransactionJet Word32 (S (Conf Word256)) OutputAmount :: TransactionJet Word32 (S (Conf Word256, Conf Word64)) OutputNonce :: TransactionJet Word32 (S (S (Conf Word256))) OutputScriptHash :: TransactionJet Word32 (S Word256) OutputNullDatum :: TransactionJet (Word32, Word32) (S (S (Either (Word2, Word256) (Either Bit Word4)))) OutputIsFee :: TransactionJet Word32 (S Bit) OutputSurjectionProof :: TransactionJet Word32 (S Word256) OutputRangeProof :: TransactionJet Word32 (S Word256) TotalFee :: TransactionJet Word256 Word64 CurrentPegin :: TransactionJet () (S Word256) CurrentPrevOutpoint :: TransactionJet () (Word256,Word32) CurrentAsset :: TransactionJet () (Conf Word256) CurrentAmount :: TransactionJet () (Conf Word256, Conf Word64) CurrentScriptHash :: TransactionJet () Word256 CurrentSequence :: TransactionJet () Word32 CurrentAnnexHash :: TransactionJet () (S Word256) CurrentScriptSigHash :: TransactionJet () Word256 CurrentReissuanceBlinding :: TransactionJet () (S Word256) CurrentNewIssuanceContract :: TransactionJet () (S Word256) CurrentReissuanceEntropy :: TransactionJet () (S Word256) CurrentIssuanceAssetAmount :: TransactionJet () (S (Conf Word64)) CurrentIssuanceTokenAmount :: TransactionJet () (S (Conf Word64)) CurrentIssuanceAssetProof :: TransactionJet () Word256 CurrentIssuanceTokenProof :: TransactionJet () Word256 InputPegin :: TransactionJet Word32 (S (S Word256)) InputPrevOutpoint :: TransactionJet Word32 (S (Word256,Word32)) InputAsset :: TransactionJet Word32 (S (Conf Word256)) InputAmount :: TransactionJet Word32 (S (Conf Word256, Conf Word64)) InputScriptHash :: TransactionJet Word32 (S Word256) InputSequence :: TransactionJet Word32 (S Word32) InputAnnexHash :: TransactionJet Word32 (S (S Word256)) InputScriptSigHash :: TransactionJet Word32 (S Word256) ReissuanceBlinding :: TransactionJet Word32 (S (S Word256)) NewIssuanceContract :: TransactionJet Word32 (S (S Word256)) ReissuanceEntropy :: TransactionJet Word32 (S (S Word256)) IssuanceAssetAmount :: TransactionJet Word32 (S (S (Conf Word64))) IssuanceTokenAmount :: TransactionJet Word32 (S (S (Conf Word64))) IssuanceAssetProof :: TransactionJet Word32 (S Word256) IssuanceTokenProof :: TransactionJet Word32 (S Word256) TapleafVersion :: TransactionJet () Word8 Tappath :: TransactionJet Word8 (S Word256) Version :: TransactionJet () Word32 GenesisBlockHash :: TransactionJet () Word256 TransactionId :: TransactionJet () Word256 deriving instance Eq (TransactionJet a b) deriving instance Show (TransactionJet a b) specificationElements :: (Assert term, Primitive term) => ElementsJet a b -> term a b specificationElements (SigHashJet x) = specificationSigHash x specificationElements (TimeLockJet x) = specificationTimeLock x specificationElements (IssuanceJet x) = specificationIssuance x specificationElements (TransactionJet x) = specificationTransaction x specificationSigHash :: (Assert term, Primitive term) => SigHashJet a b -> term a b specificationSigHash SigAllHash = SigHash.sigAllHash specificationSigHash TxHash = SigHash.txHash specificationSigHash TapEnvHash = SigHash.tapEnvHash specificationSigHash OutputsHash = SigHash.outputsHash specificationSigHash InputsHash = SigHash.inputsHash specificationSigHash IssuancesHash = SigHash.issuancesHash specificationSigHash InputUtxosHash = SigHash.inputUtxosHash specificationSigHash OutputHash = SigHash.outputHash specificationSigHash OutputAmountsHash = SigHash.outputAmountsHash specificationSigHash OutputScriptsHash = SigHash.outputScriptsHash specificationSigHash OutputNoncesHash = SigHash.outputNoncesHash specificationSigHash OutputRangeProofsHash = SigHash.outputRangeProofsHash specificationSigHash OutputSurjectionProofsHash = SigHash.outputSurjectionProofsHash specificationSigHash InputHash = SigHash.inputHash specificationSigHash InputOutpointsHash = SigHash.inputOutpointsHash specificationSigHash InputSequencesHash = SigHash.inputSequencesHash specificationSigHash InputAnnexesHash = SigHash.inputAnnexesHash specificationSigHash InputScriptSigsHash = SigHash.inputScriptSigsHash specificationSigHash IssuanceHash = SigHash.issuanceHash specificationSigHash IssuanceAssetAmountsHash = SigHash.issuanceAssetAmountsHash specificationSigHash IssuanceTokenAmountsHash = SigHash.issuanceTokenAmountsHash specificationSigHash IssuanceRangeProofsHash = SigHash.issuanceRangeProofsHash specificationSigHash IssuanceBlindingEntropyHash = SigHash.issuanceBlindingEntropyHash specificationSigHash InputUtxoHash = SigHash.inputUtxoHash specificationSigHash InputAmountsHash = SigHash.inputAmountsHash specificationSigHash InputScriptsHash = SigHash.inputScriptsHash specificationSigHash TapleafHash = SigHash.tapleafHash specificationSigHash TappathHash = SigHash.tappathHash specificationSigHash OutpointHash = Prog.outpointHash specificationSigHash AssetAmountHash = Prog.assetAmountHash specificationSigHash NonceHash = Prog.nonceHash specificationSigHash AnnexHash = Prog.annexHash specificationSigHash BuildTapleafSimplicity = Prog.buildTapleafSimplicity specificationSigHash BuildTapbranch = Prog.buildTapbranch specificationSigHash BuildTaptweak = Prog.buildTaptweak specificationTimeLock :: (Assert term, Primitive term) => TimeLockJet a b -> term a b specificationTimeLock CheckLockHeight = TimeLock.checkLockHeight specificationTimeLock CheckLockTime = TimeLock.checkLockTime specificationTimeLock BrokenDoNotUseCheckLockDistance = TimeLock.brokenCheckLockDistance specificationTimeLock BrokenDoNotUseCheckLockDuration = TimeLock.brokenCheckLockDuration specificationTimeLock TxLockHeight = TimeLock.txLockHeight specificationTimeLock TxLockTime = TimeLock.txLockTime specificationTimeLock BrokenDoNotUseTxLockDistance = TimeLock.brokenTxLockDistance specificationTimeLock BrokenDoNotUseTxLockDuration = TimeLock.brokenTxLockDuration specificationTimeLock TxIsFinal = TimeLock.txIsFinal specificationIssuance :: (Assert term, Primitive term) => IssuanceJet a b -> term a b specificationIssuance Issuance = Issuance.issuance specificationIssuance IssuanceAsset = Issuance.issuanceAsset specificationIssuance IssuanceToken = Issuance.issuanceToken specificationIssuance IssuanceEntropy = Issuance.issuanceEntropy specificationIssuance CalculateIssuanceEntropy = Prog.calculateIssuanceEntropy specificationIssuance CalculateAsset = Prog.calculateAsset specificationIssuance CalculateExplicitToken = Prog.calculateExplicitToken specificationIssuance CalculateConfidentialToken = Prog.calculateConfidentialToken specificationIssuance LbtcAsset = Prog.lbtcAsset specificationTransaction :: (Assert term, Primitive term) => TransactionJet a b -> term a b specificationTransaction ScriptCMR = primitive Prim.ScriptCMR specificationTransaction InternalKey = primitive Prim.InternalKey specificationTransaction CurrentIndex = primitive Prim.CurrentIndex specificationTransaction NumInputs = Prog.numInputs specificationTransaction NumOutputs = Prog.numOutputs specificationTransaction LockTime = primitive Prim.LockTime specificationTransaction OutputAsset = primitive Prim.OutputAsset specificationTransaction OutputAmount = Prog.outputAmount specificationTransaction OutputNonce = primitive Prim.OutputNonce specificationTransaction OutputScriptHash = primitive Prim.OutputScriptHash specificationTransaction OutputNullDatum = primitive Prim.OutputNullDatum specificationTransaction OutputIsFee = Prog.outputIsFee specificationTransaction OutputSurjectionProof = primitive Prim.OutputSurjectionProof specificationTransaction OutputRangeProof = primitive Prim.OutputRangeProof specificationTransaction TotalFee = Prog.totalFee specificationTransaction CurrentPegin = Prog.currentPegin specificationTransaction CurrentPrevOutpoint = Prog.currentPrevOutpoint specificationTransaction CurrentAsset = Prog.currentAsset specificationTransaction CurrentAmount = Prog.currentAmount specificationTransaction CurrentScriptHash = Prog.currentScriptHash specificationTransaction CurrentSequence = Prog.currentSequence specificationTransaction CurrentAnnexHash = Prog.currentAnnexHash specificationTransaction CurrentScriptSigHash = Prog.currentScriptSigHash specificationTransaction CurrentReissuanceBlinding = Prog.currentReissuanceBlinding specificationTransaction CurrentNewIssuanceContract = Prog.currentNewIssuanceContract specificationTransaction CurrentReissuanceEntropy = Prog.currentReissuanceEntropy specificationTransaction CurrentIssuanceAssetAmount = Prog.currentIssuanceAssetAmount specificationTransaction CurrentIssuanceTokenAmount = Prog.currentIssuanceTokenAmount specificationTransaction CurrentIssuanceAssetProof = Prog.currentIssuanceAssetProof specificationTransaction CurrentIssuanceTokenProof = Prog.currentIssuanceTokenProof specificationTransaction InputPegin = primitive Prim.InputPegin specificationTransaction InputPrevOutpoint = primitive Prim.InputPrevOutpoint specificationTransaction InputAsset = primitive Prim.InputAsset specificationTransaction InputAmount = Prog.inputAmount specificationTransaction InputScriptHash = primitive Prim.InputScriptHash specificationTransaction InputSequence = primitive Prim.InputSequence specificationTransaction InputAnnexHash = primitive Prim.InputAnnexHash specificationTransaction InputScriptSigHash = primitive Prim.InputScriptSigHash specificationTransaction ReissuanceBlinding = primitive Prim.ReissuanceBlinding specificationTransaction NewIssuanceContract = primitive Prim.NewIssuanceContract specificationTransaction ReissuanceEntropy = primitive Prim.ReissuanceEntropy specificationTransaction IssuanceAssetAmount = primitive Prim.IssuanceAssetAmount specificationTransaction IssuanceTokenAmount = primitive Prim.IssuanceTokenAmount specificationTransaction IssuanceAssetProof = primitive Prim.IssuanceAssetProof specificationTransaction IssuanceTokenProof = primitive Prim.IssuanceTokenProof specificationTransaction TapleafVersion = primitive Prim.TapleafVersion specificationTransaction Tappath = primitive Prim.Tappath specificationTransaction Version = primitive Prim.Version specificationTransaction GenesisBlockHash = primitive Prim.GenesisBlockHash specificationTransaction TransactionId = primitive Prim.TransactionId implementationElements :: ElementsJet a b -> PrimEnv -> a -> Maybe b implementationElements (SigHashJet x) = implementationSigHash x implementationElements (TimeLockJet x) = implementationTimeLock x implementationElements (IssuanceJet x) = implementationIssuance x implementationElements (TransactionJet x) = implementationTransaction x implementationSigHash :: SigHashJet a b -> PrimEnv -> a -> Maybe b implementationSigHash SigAllHash env _ = Just . toWord256 . integerHash256 $ primEnvHash env implementationSigHash TxHash env _ = Just . toWord256 . integerHash256 $ txHash (envTx env) implementationSigHash TapEnvHash env _ = Just . toWord256 . integerHash256 $ tapEnvHash (envTap env) implementationSigHash OutputsHash env _ = Just . toWord256 . integerHash256 $ outputsHash (envTx env) implementationSigHash InputsHash env _ = Just . toWord256 . integerHash256 $ inputsHash (envTx env) implementationSigHash IssuancesHash env _ = Just . toWord256 . integerHash256 $ issuancesHash (envTx env) implementationSigHash InputUtxosHash env _ = Just . toWord256 . integerHash256 $ inputUtxosHash (envTx env) implementationSigHash OutputHash env i = Just . fmap (toWord256 . integerHash256 . outputHash) . maybe (Left ()) Right $ sigTxOut (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash OutputAmountsHash env _ = Just . toWord256 . integerHash256 $ outputAmountsHash (envTx env) implementationSigHash OutputScriptsHash env _ = Just . toWord256 . integerHash256 $ outputScriptsHash (envTx env) implementationSigHash OutputNoncesHash env _ = Just . toWord256 . integerHash256 $ outputNoncesHash (envTx env) implementationSigHash OutputRangeProofsHash env _ = Just . toWord256 . integerHash256 $ outputRangeProofsHash (envTx env) implementationSigHash OutputSurjectionProofsHash env _ = Just . toWord256 . integerHash256 $ outputSurjectionProofsHash (envTx env) implementationSigHash InputHash env i = Just . fmap (toWord256 . integerHash256 . inputHash) . maybe (Left ()) Right $ sigTxIn (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash InputOutpointsHash env _ = Just . toWord256 . integerHash256 $ inputOutpointsHash (envTx env) implementationSigHash InputSequencesHash env _ = Just . toWord256 . integerHash256 $ inputSequencesHash (envTx env) implementationSigHash InputAnnexesHash env _ = Just . toWord256 . integerHash256 $ inputAnnexesHash (envTx env) implementationSigHash InputScriptSigsHash env _ = Just . toWord256 . integerHash256 $ inputScriptSigsHash (envTx env) implementationSigHash IssuanceHash env i = Just . fmap (toWord256 . integerHash256 . issuanceHash) . maybe (Left ()) Right $ sigTxIn (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash IssuanceAssetAmountsHash env _ = Just . toWord256 . integerHash256 $ issuanceAssetAmountsHash (envTx env) implementationSigHash IssuanceTokenAmountsHash env _ = Just . toWord256 . integerHash256 $ issuanceTokenAmountsHash (envTx env) implementationSigHash IssuanceRangeProofsHash env _ = Just . toWord256 . integerHash256 $ issuanceRangeProofsHash (envTx env) implementationSigHash IssuanceBlindingEntropyHash env _ = Just . toWord256 . integerHash256 $ issuanceBlindingEntropyHash (envTx env) implementationSigHash InputUtxoHash env i = Just . fmap (toWord256 . integerHash256 . inputUtxoHash . sigTxiTxo) . maybe (Left ()) Right $ sigTxIn (envTx env) !? (fromIntegral $ fromWord32 i) implementationSigHash InputAmountsHash env _ = Just . toWord256 . integerHash256 $ inputAmountsHash (envTx env) implementationSigHash InputScriptsHash env _ = Just . toWord256 . integerHash256 $ inputScriptsHash (envTx env) implementationSigHash TapleafHash env _ = Just . toWord256 . integerHash256 $ tapleafHash (envTap env) implementationSigHash TappathHash env _ = Just . toWord256 . integerHash256 $ tappathHash (envTap env) implementationSigHash OutpointHash _env (ctx, (mw256, op)) = toCtx8 <$> (flip ctxAdd (runPut (putMW256 mw256 >> putOutpointBE (cast op))) =<< fromCtx8 ctx) where putMW256 (Left _) = putWord8 0x00 putMW256 (Right w256) = putWord8 0x01 >> put (fromIntegral (fromWord256 w256) :: W.Word256) cast (h, i) = Outpoint (review (over be256) (fromW256 h)) (fromW32 i) fromW256 = fromIntegral . fromWord256 fromW32 = fromIntegral . fromWord32 implementationSigHash AssetAmountHash _env (ctx, (cw256, cw64)) = toCtx8 <$> (flip ctxAdd (runPut (put256 cw256 >> put64 cw64)) =<< fromCtx8 ctx) where put256 (Left (by, x)) = putWord8 (if fromBit by then 0xb else 0x0a) >> put (fromW256 x) put256 (Right w256) = putWord8 0x01 >> put (fromW256 w256) put64 (Left (by, x)) = putWord8 (if fromBit by then 0x9 else 0x08) >> put (fromW256 x) put64 (Right w64) = putWord8 0x01 >> put (fromW64 w64) fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 fromW64 :: Word64 -> W.Word64 fromW64 = fromIntegral . fromWord64 implementationSigHash NonceHash _env (ctx, mcw256) = toCtx8 <$> (flip ctxAdd (runPut . putNonce $ nonce) =<< fromCtx8 ctx) where nonce = either (const Nothing) (Just . Nonce . ((fromBit *** (fromIntegral . fromWord256)) +++ fromHash)) mcw256 implementationSigHash AnnexHash _env (ctx, mw256) = toCtx8 <$> (flip ctxAdd (runPut . putMW256 $ mw256) =<< fromCtx8 ctx) where putMW256 (Left _) = putWord8 0x00 putMW256 (Right w256) = putWord8 0x01 >> put (fromIntegral (fromWord256 w256) :: W.Word256) implementationSigHash BuildTapleafSimplicity _env cmr = Just . toWord256 . integerHash256 . bsHash . runPut $ put tag >> put tag >> putWord8 tapleafSimplicityVersion >> putWord8 32 >> put (fromW256 cmr) where tag = bsHash (fromString "TapLeaf/elements") tapleafSimplicityVersion = 0xbe fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 implementationSigHash BuildTapbranch _env (wa,wb) = Just . toWord256 . integerHash256 . bsHash . runPut $ put tag >> put tag >> put min >> put max where a = fromW256 wa b = fromW256 wb min = if a < b then a else b max = if a < b then b else a tag = bsHash (fromString "TapBranch/elements") fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 implementationSigHash BuildTaptweak _env (key,h) = cast <$> taptweak pk h0 where pk = Schnorr.PubKey (fromW256 key) h0 = review (over be256) (fromW256 h) cast (Schnorr.PubKey k) = toWord256 . toInteger $ k fromW256 :: Word256 -> W.Word256 fromW256 = fromIntegral . fromWord256 implementationTimeLock :: TimeLockJet a b -> PrimEnv -> a -> Maybe b implementationTimeLock CheckLockHeight env x | txIsFinal (envTx env) = guard $ fromWord32 x <= 0 | Left l <- parseLock lock = guard $ fromWord32 x <= fromIntegral l | otherwise = guard $ fromWord32 x <= 0 where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock CheckLockTime env x | txIsFinal (envTx env) = guard $ fromWord32 x <= 0 | Right l <- parseLock lock = guard $ fromWord32 x <= fromIntegral l | otherwise = guard $ fromWord32 x <= 0 where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock BrokenDoNotUseCheckLockDistance env x | fromWord16 x <= fromIntegral (txLockBrokenDistance (envTx env)) = Just () | otherwise = Nothing implementationTimeLock BrokenDoNotUseCheckLockDuration env x | fromWord16 x <= fromIntegral (txLockBrokenDuration (envTx env)) = Just () | otherwise = Nothing implementationTimeLock TxLockHeight env () | txIsFinal (envTx env) = Just (toWord32 0) | Left l <- parseLock lock = Just . toWord32 $ fromIntegral l | otherwise = Just (toWord32 0) where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock TxLockTime env () | txIsFinal (envTx env) = Just (toWord32 0) | Right l <- parseLock lock = Just . toWord32 $ fromIntegral l | otherwise = Just (toWord32 0) where lock = fromIntegral . sigTxLock . envTx $ env implementationTimeLock BrokenDoNotUseTxLockDistance env () = Just . toWord16 . fromIntegral $ txLockBrokenDistance (envTx env) implementationTimeLock BrokenDoNotUseTxLockDuration env () = Just . toWord16 . fromIntegral $ txLockBrokenDuration (envTx env) implementationTimeLock TxIsFinal env () = Just $ toBit (txIsFinal (envTx env)) implementationIssuance :: IssuanceJet a b -> PrimEnv -> a -> Maybe b implementationIssuance Issuance env i = fmap (cast . fmap (cast . fmap toBit)) body where cast = maybe (Left ()) Right body = return $ fmap isRight . sigTxiIssuance <$> sigTxIn (envTx env) !? (fromIntegral (fromWord32 i)) implementationIssuance IssuanceEntropy env i = fmap (cast . fmap (cast . fmap fromHash)) body where cast = maybe (Left ()) Right fromHash = toWord256 . integerHash256 body = return $ sigTxiIssuanceEntropy <$> sigTxIn (envTx env) !? (fromIntegral (fromWord32 i)) implementationIssuance IssuanceAsset env i = fmap (cast . fmap (cast . fmap fromHash)) body where cast = maybe (Left ()) Right fromHash = toWord256 . integerHash256 body = return $ sigTxiIssuanceAsset <$> sigTxIn (envTx env) !? (fromIntegral (fromWord32 i)) implementationIssuance IssuanceToken env i = fmap (cast . fmap (cast . fmap fromHash)) body where cast = maybe (Left ()) Right fromHash = toWord256 . integerHash256 body = return $ sigTxiIssuanceToken <$> sigTxIn (envTx env) !? (fromIntegral (fromWord32 i)) implementationIssuance CalculateIssuanceEntropy _ ((x,y), z) = Just (fromHash (calculateIssuanceEntropy op contract)) where fromHash = toWord256 . integerHash256 fromW256 = fromIntegral . fromWord256 fromW32 = fromIntegral . fromWord32 op = Outpoint (review (over be256) (fromW256 x)) (fromW32 y) contract = review (over be256) (fromW256 z) implementationIssuance CalculateAsset _ x = Just (fromHash (calculateAsset entropy)) where fromW256 = fromIntegral . fromWord256 fromHash = toWord256 . integerHash256 entropy = review (over be256) (fromW256 x) implementationIssuance CalculateExplicitToken _ x = Just (fromHash (calculateToken (Amount (Explicit undefined)) entropy)) where fromW256 = fromIntegral . fromWord256 fromHash = toWord256 . integerHash256 entropy = review (over be256) (fromW256 x) implementationIssuance CalculateConfidentialToken _ x = Just (fromHash (calculateToken (Amount (Confidential undefined undefined)) entropy)) where fromW256 = fromIntegral . fromWord256 fromHash = toWord256 . integerHash256 entropy = review (over be256) (fromW256 x) implementationIssuance LbtcAsset _ _ = Just (fromHash lBtcAsset) where fromHash = toWord256 . integerHash256 implementationTransaction :: TransactionJet a b -> PrimEnv -> a -> Maybe b implementationTransaction OutputIsFee env i = Just . cast $ toBit . isJust . outputFee <$> sigTxOut (envTx env) !? (fromIntegral (fromWord32 i)) where cast = maybe (Left ()) Right implementationTransaction TotalFee env x = Just . fromValue . Map.findWithDefault 0 assetId $ totalFee (envTx env) where fromValue = toWord64 . toInteger fromW256 = fromIntegral . fromWord256 assetId = review (over be256) (fromW256 x) implementationTransaction x env i = Semantics.sem (specificationTransaction x) env i getJetBitElements :: (Monad m) => m Void -> m Bool -> m (SomeArrow ElementsJet) getJetBitElements = getCatalogue elementsCatalogue elementsCatalogue :: Catalogue (SomeArrow ElementsJet) elementsCatalogue = Shelf [ someArrowMap SigHashJet <$> sigHashCatalogue , someArrowMap TimeLockJet <$> timeLockCatalogue , someArrowMap IssuanceJet <$> issuanceCatalogue , someArrowMap TransactionJet <$> transactionCatalogue ] sigHashCatalogue = book [ SomeArrow SigAllHash , SomeArrow TxHash , SomeArrow TapEnvHash , SomeArrow OutputsHash , SomeArrow InputsHash , SomeArrow IssuancesHash , SomeArrow InputUtxosHash , SomeArrow OutputHash , SomeArrow OutputAmountsHash , SomeArrow OutputScriptsHash , SomeArrow OutputNoncesHash , SomeArrow OutputRangeProofsHash , SomeArrow OutputSurjectionProofsHash , SomeArrow InputHash , SomeArrow InputOutpointsHash , SomeArrow InputSequencesHash , SomeArrow InputAnnexesHash , SomeArrow InputScriptSigsHash , SomeArrow IssuanceHash , SomeArrow IssuanceAssetAmountsHash , SomeArrow IssuanceTokenAmountsHash , SomeArrow IssuanceRangeProofsHash , SomeArrow IssuanceBlindingEntropyHash , SomeArrow InputUtxoHash , SomeArrow InputAmountsHash , SomeArrow InputScriptsHash , SomeArrow TapleafHash , SomeArrow TappathHash , SomeArrow OutpointHash , SomeArrow AssetAmountHash , SomeArrow NonceHash , SomeArrow AnnexHash , SomeArrow BuildTapleafSimplicity , SomeArrow BuildTapbranch , SomeArrow BuildTaptweak ] timeLockCatalogue = book [ SomeArrow CheckLockHeight , SomeArrow CheckLockTime , SomeArrow BrokenDoNotUseCheckLockDistance , SomeArrow BrokenDoNotUseCheckLockDuration , SomeArrow TxLockHeight , SomeArrow TxLockTime , SomeArrow BrokenDoNotUseTxLockDistance , SomeArrow BrokenDoNotUseTxLockDuration , SomeArrow TxIsFinal ] issuanceCatalogue = book [ SomeArrow Issuance , SomeArrow IssuanceAsset , SomeArrow IssuanceToken , SomeArrow IssuanceEntropy , SomeArrow CalculateIssuanceEntropy , SomeArrow CalculateAsset , SomeArrow CalculateExplicitToken , SomeArrow CalculateConfidentialToken , SomeArrow LbtcAsset ] transactionCatalogue = book [ SomeArrow ScriptCMR , SomeArrow InternalKey , SomeArrow CurrentIndex , SomeArrow NumInputs , SomeArrow NumOutputs , SomeArrow LockTime , SomeArrow OutputAsset , SomeArrow OutputAmount , SomeArrow OutputNonce , SomeArrow OutputScriptHash , SomeArrow OutputNullDatum , SomeArrow OutputIsFee , SomeArrow OutputSurjectionProof , SomeArrow OutputRangeProof , SomeArrow TotalFee , SomeArrow CurrentPegin , SomeArrow CurrentPrevOutpoint , SomeArrow CurrentAsset , SomeArrow CurrentAmount , SomeArrow CurrentScriptHash , SomeArrow CurrentSequence , SomeArrow CurrentAnnexHash , SomeArrow CurrentScriptSigHash , SomeArrow CurrentReissuanceBlinding , SomeArrow CurrentNewIssuanceContract , SomeArrow CurrentReissuanceEntropy , SomeArrow CurrentIssuanceAssetAmount , SomeArrow CurrentIssuanceTokenAmount , SomeArrow CurrentIssuanceAssetProof , SomeArrow CurrentIssuanceTokenProof , SomeArrow InputPegin , SomeArrow InputPrevOutpoint , SomeArrow InputAsset , SomeArrow InputAmount , SomeArrow InputScriptHash , SomeArrow InputSequence , SomeArrow InputAnnexHash , SomeArrow InputScriptSigHash , SomeArrow ReissuanceBlinding , SomeArrow NewIssuanceContract , SomeArrow ReissuanceEntropy , SomeArrow IssuanceAssetAmount , SomeArrow IssuanceTokenAmount , SomeArrow IssuanceAssetProof , SomeArrow IssuanceTokenProof , SomeArrow TapleafVersion , SomeArrow Tappath , SomeArrow Version , SomeArrow GenesisBlockHash , SomeArrow TransactionId ] putJetBitElements :: ElementsJet a b -> DList Bool putJetBitElements (SigHashJet x) = putPositive 1 . putJetBitSigHash x putJetBitElements (TimeLockJet x) = putPositive 2 . putJetBitTimeLock x putJetBitElements (IssuanceJet x) = putPositive 3 . putJetBitIssuance x putJetBitElements (TransactionJet x) = putPositive 4 . putJetBitTransaction x putJetBitSigHash :: SigHashJet a b -> DList Bool putJetBitSigHash SigAllHash = putPositive 1 putJetBitSigHash TxHash = putPositive 2 putJetBitSigHash TapEnvHash = putPositive 3 putJetBitSigHash OutputsHash = putPositive 4 putJetBitSigHash InputsHash = putPositive 5 putJetBitSigHash IssuancesHash = putPositive 6 putJetBitSigHash InputUtxosHash = putPositive 7 putJetBitSigHash OutputHash = putPositive 8 putJetBitSigHash OutputAmountsHash = putPositive 9 putJetBitSigHash OutputScriptsHash = putPositive 10 putJetBitSigHash OutputNoncesHash = putPositive 11 putJetBitSigHash OutputRangeProofsHash = putPositive 12 putJetBitSigHash OutputSurjectionProofsHash = putPositive 13 putJetBitSigHash InputHash = putPositive 14 putJetBitSigHash InputOutpointsHash = putPositive 15 putJetBitSigHash InputSequencesHash = putPositive 16 putJetBitSigHash InputAnnexesHash = putPositive 17 putJetBitSigHash InputScriptSigsHash = putPositive 18 putJetBitSigHash IssuanceHash = putPositive 19 putJetBitSigHash IssuanceAssetAmountsHash = putPositive 20 putJetBitSigHash IssuanceTokenAmountsHash = putPositive 21 putJetBitSigHash IssuanceRangeProofsHash = putPositive 22 putJetBitSigHash IssuanceBlindingEntropyHash = putPositive 23 putJetBitSigHash InputUtxoHash = putPositive 24 putJetBitSigHash InputAmountsHash = putPositive 25 putJetBitSigHash InputScriptsHash = putPositive 26 putJetBitSigHash TapleafHash = putPositive 27 putJetBitSigHash TappathHash = putPositive 28 putJetBitSigHash OutpointHash = putPositive 29 putJetBitSigHash AssetAmountHash = putPositive 30 putJetBitSigHash NonceHash = putPositive 31 putJetBitSigHash AnnexHash = putPositive 32 putJetBitSigHash BuildTapleafSimplicity = putPositive 33 putJetBitSigHash BuildTapbranch = putPositive 34 putJetBitSigHash BuildTaptweak = putPositive 35 putJetBitTimeLock :: TimeLockJet a b -> DList Bool putJetBitTimeLock CheckLockHeight = putPositive 1 putJetBitTimeLock CheckLockTime = putPositive 2 putJetBitTimeLock BrokenDoNotUseCheckLockDistance = putPositive 3 putJetBitTimeLock BrokenDoNotUseCheckLockDuration = putPositive 4 putJetBitTimeLock TxLockHeight = putPositive 5 putJetBitTimeLock TxLockTime = putPositive 6 putJetBitTimeLock BrokenDoNotUseTxLockDistance = putPositive 7 putJetBitTimeLock BrokenDoNotUseTxLockDuration = putPositive 8 putJetBitTimeLock TxIsFinal = putPositive 9 putJetBitIssuance :: IssuanceJet a b -> DList Bool putJetBitIssuance Issuance = putPositive 1 putJetBitIssuance IssuanceAsset = putPositive 2 putJetBitIssuance IssuanceToken = putPositive 3 putJetBitIssuance IssuanceEntropy = putPositive 4 putJetBitIssuance CalculateIssuanceEntropy = putPositive 5 putJetBitIssuance CalculateAsset = putPositive 6 putJetBitIssuance CalculateExplicitToken = putPositive 7 putJetBitIssuance CalculateConfidentialToken = putPositive 8 putJetBitIssuance LbtcAsset = putPositive 9 putJetBitTransaction :: TransactionJet a b -> DList Bool putJetBitTransaction ScriptCMR = putPositive 1 putJetBitTransaction InternalKey = putPositive 2 putJetBitTransaction CurrentIndex = putPositive 3 putJetBitTransaction NumInputs = putPositive 4 putJetBitTransaction NumOutputs = putPositive 5 putJetBitTransaction LockTime = putPositive 6 putJetBitTransaction OutputAsset = putPositive 7 putJetBitTransaction OutputAmount = putPositive 8 putJetBitTransaction OutputNonce = putPositive 9 putJetBitTransaction OutputScriptHash = putPositive 10 putJetBitTransaction OutputNullDatum = putPositive 11 putJetBitTransaction OutputIsFee = putPositive 12 putJetBitTransaction OutputSurjectionProof = putPositive 13 putJetBitTransaction OutputRangeProof = putPositive 14 putJetBitTransaction TotalFee = putPositive 15 putJetBitTransaction CurrentPegin = putPositive 16 putJetBitTransaction CurrentPrevOutpoint = putPositive 17 putJetBitTransaction CurrentAsset = putPositive 18 putJetBitTransaction CurrentAmount = putPositive 19 putJetBitTransaction CurrentScriptHash = putPositive 20 putJetBitTransaction CurrentSequence = putPositive 21 putJetBitTransaction CurrentAnnexHash = putPositive 22 putJetBitTransaction CurrentScriptSigHash = putPositive 23 putJetBitTransaction CurrentReissuanceBlinding = putPositive 24 putJetBitTransaction CurrentNewIssuanceContract = putPositive 25 putJetBitTransaction CurrentReissuanceEntropy = putPositive 26 putJetBitTransaction CurrentIssuanceAssetAmount = putPositive 27 putJetBitTransaction CurrentIssuanceTokenAmount = putPositive 28 putJetBitTransaction CurrentIssuanceAssetProof = putPositive 29 putJetBitTransaction CurrentIssuanceTokenProof = putPositive 30 putJetBitTransaction InputPegin = putPositive 31 putJetBitTransaction InputPrevOutpoint = putPositive 32 putJetBitTransaction InputAsset = putPositive 33 putJetBitTransaction InputAmount = putPositive 34 putJetBitTransaction InputScriptHash = putPositive 35 putJetBitTransaction InputSequence = putPositive 36 putJetBitTransaction InputAnnexHash = putPositive 37 putJetBitTransaction InputScriptSigHash = putPositive 38 putJetBitTransaction ReissuanceBlinding = putPositive 39 putJetBitTransaction NewIssuanceContract = putPositive 40 putJetBitTransaction ReissuanceEntropy = putPositive 41 putJetBitTransaction IssuanceAssetAmount = putPositive 42 putJetBitTransaction IssuanceTokenAmount = putPositive 43 putJetBitTransaction IssuanceAssetProof = putPositive 44 putJetBitTransaction IssuanceTokenProof = putPositive 45 putJetBitTransaction TapleafVersion = putPositive 46 putJetBitTransaction Tappath = putPositive 47 putJetBitTransaction Version = putPositive 48 putJetBitTransaction GenesisBlockHash = putPositive 49 putJetBitTransaction TransactionId = putPositive 50 elementsJetMap :: Map.Map Hash256 (SomeArrow ElementsJet) elementsJetMap = Map.fromList . fmap mkAssoc $ toList elementsCatalogue where mkAssoc :: SomeArrow ElementsJet -> (Hash256, (SomeArrow ElementsJet)) mkAssoc wrapped@(SomeArrow jt) = (identityHash (specificationElements jt), wrapped) data MatcherInfo a b = MatcherInfo (Product ConstWord IdentityRoot a b) instance Simplicity.Elements.JetType.JetType JetType where type MatcherInfo JetType = MatcherInfo specification (ConstWordJet cw) = CoreJets.specificationConstWord cw specification (CoreJet jt) = CoreJets.specification jt specification (ElementsJet jt) = specificationElements jt implementation (ConstWordJet cw) _env = CoreJets.implementationConstWord cw implementation (CoreJet jt) _env = CoreJets.implementation jt implementation (ElementsJet jt) env = implementationElements jt env matcher (MatcherInfo (Product cw ir)) = (do SomeArrow jt <- Map.lookup (identityHash ir) jetMap let (ira, irb) = reifyArrow ir let (jta, jtb) = reifyArrow jt -- If the error below is thrown it suggests there is some sort of type annotation mismatch in the map below case (equalTyReflect ira jta, equalTyReflect irb jtb) of (Just Refl, Just Refl) -> return jt otherwise -> error "mathcher{Simplicity.Elements.Jets.JetType}: type match error" ) <|> case cw of (ConstWord w v) -> return (ConstWordJet (ConstWordContent w v)) otherwise -> Nothing getJetBit abort next = do b <- next if b then do c <- next if c then someArrowMap ElementsJet <$> getJetBitElements abort next else someArrowMap CoreJet <$> CoreJets.getJetBit abort next else mkConstWordJet <$> CoreJets.getConstWordBit abort next where mkConstWordJet (SomeConstWordContent cw) = SomeArrow (ConstWordJet cw) putJetBit = go where go (ConstWordJet cw) = ([o]++) . CoreJets.putConstWordBit cw go (CoreJet jt) = ([i,o]++) . CoreJets.putJetBit jt go (ElementsJet jt) = ([i,i]++) . putJetBitElements jt (o,i) = (False,True) jetCost (ConstWordJet cw) = jetCostConstWord cw jetCost (CoreJet jt) = jetCostCore jt jetCost (ElementsJet jt) = jetCostElements jt -- | Generate a 'Jet' using the 'Simplicity.Elements.JetType.jetCost' and 'Simplicity.Elements.JetType.specification' of a 'JetType'. asJet :: (Jet term, TyC a, TyC b) => JetType a b -> term a b asJet = Simplicity.Elements.JetType.asJet -- This map is used in the 'matcher' method above. -- We have floated it out here to make sure the map is shared between invocations of the 'matcher' function. jetMap :: Map.Map Hash256 (SomeArrow JetType) jetMap = Map.union (someArrowMap CoreJet <$> coreJetMap) (someArrowMap ElementsJet <$> elementsJetMap) -- | Find all the expressions in a term that can be replaced with Elements jets. -- Because discounted jets are not transparent, this replacement will change the CMR of the term. -- In particular the CMR values passed to 'disconnect' may be different, and thus the result of -- evaluation could change in the presence of 'disconnect'. jetSubst :: (TyC a, TyC b) => JetDag JetType a b -> WrappedSimplicity a b jetSubst = Dag.jetSubst -- | Performs 'jetSubst' and then evaluates the program in the given environment to prune unused case branches, -- which transforms some case expressions into assertions. -- The resulting expression should always have the same CMR as the expression that 'jetSubst' would return. pruneSubst :: JetDag JetType () () -> PrimEnv -> Maybe (WrappedSimplicity () ()) pruneSubst prog env = Dag.pruneSubst prog env () -- | This is an instance of 'BitString.getTermLengthCode' that specifically decodes the canonical 'JetType' set of known jets. getTermLengthCode :: (Monad m, Simplicity term, TyC a, TyC b) => m Void -> m Bool -> m (term a b) getTermLengthCode = BitString.getTermLengthCode (Proxy :: Proxy (SomeArrow JetType)) -- | This is an instance of 'BitString.putTermLengthCode' that specifically encodes the canonical 'JetType' set of known jets. putTermLengthCode :: (TyC a, TyC b) => JetDag JetType a b -> ([Bool],[Bool]) putTermLengthCode = BitString.putTermLengthCode -- | 'fastEval' optimizes Simplicity evaluation using Elements jets. -- Unlike using 'Simplicity.Dag.jetSubst', 'fastEval' will not modify the commitment roots and therefore will always return the same -- result as 'sem' in the presence of 'disconnect'. -- -- @ -- 'fastEval' t === 'sem' t -- @ fastEval :: Semantics.FastEval JetType a b -> Semantics.PrimEnv -> a -> Maybe b fastEval = Semantics.fastEval instance Core MatcherInfo where iden = MatcherInfo iden unit = MatcherInfo unit injl (MatcherInfo ir) = MatcherInfo (injl ir) injr (MatcherInfo ir) = MatcherInfo (injr ir) drop (MatcherInfo ir) = MatcherInfo (drop ir) take (MatcherInfo ir) = MatcherInfo (take ir) pair (MatcherInfo irl) (MatcherInfo irr) = MatcherInfo (pair irl irr) match (MatcherInfo irl) (MatcherInfo irr) = MatcherInfo (match irl irr) comp (MatcherInfo irl) (MatcherInfo irr) = MatcherInfo (comp irl irr) instance Assert MatcherInfo where assertl (MatcherInfo ir) h = MatcherInfo (assertl ir h) assertr h (MatcherInfo ir) = MatcherInfo (assertr h ir) fail b = MatcherInfo (fail b) instance Primitive MatcherInfo where primitive p = MatcherInfo (primitive p) fromPoint (by, x) = Point (fromBit by) (fe (fromWord256 x)) -- | Returns the cost of a constant word jet corresponding to the contents of a given 'ConstWordContent'. jetCostConstWord :: ConstWordContent b -> Weight jetCostConstWord (ConstWordContent w _) = milli (wordSize w) -- | The costs of "core" jets. This can be used to help instantiate the 'Simplicity.JetType.jetCost' method. jetCostCore :: CoreJet a b -> Weight jetCostCore (WordJet x) = jetCostWord x jetCostCore (ArithJet x) = jetCostArith x jetCostCore (HashJet x) = jetCostHash x jetCostCore (Secp256k1Jet x) = jetCostSecp256k1 x jetCostCore (SignatureJet x) = jetCostSignature x jetCostCore (BitcoinJet x) = jetCostBitcoin x jetCostWord :: WordJet a b -> Weight jetCostWord Verify = cost "Verify" jetCostWord Low1 = cost "Low1" jetCostWord Low8 = cost "Low8" jetCostWord Low16 = cost "Low16" jetCostWord Low32 = cost "Low32" jetCostWord Low64 = cost "Low64" jetCostWord High1 = cost "High1" jetCostWord High8 = cost "High8" jetCostWord High16 = cost "High16" jetCostWord High32 = cost "High32" jetCostWord High64 = cost "High64" jetCostWord Complement1 = cost "Complement1" jetCostWord Complement8 = cost "Complement8" jetCostWord Complement16 = cost "Complement16" jetCostWord Complement32 = cost "Complement32" jetCostWord Complement64 = cost "Complement64" jetCostWord And1 = cost "And1" jetCostWord And8 = cost "And8" jetCostWord And16 = cost "And16" jetCostWord And32 = cost "And32" jetCostWord And64 = cost "And64" jetCostWord Or1 = cost "Or1" jetCostWord Or8 = cost "Or8" jetCostWord Or16 = cost "Or16" jetCostWord Or32 = cost "Or32" jetCostWord Or64 = cost "Or64" jetCostWord Xor1 = cost "Xor1" jetCostWord Xor8 = cost "Xor8" jetCostWord Xor16 = cost "Xor16" jetCostWord Xor32 = cost "Xor32" jetCostWord Xor64 = cost "Xor64" jetCostWord Maj1 = cost "Maj1" jetCostWord Maj8 = cost "Maj8" jetCostWord Maj16 = cost "Maj16" jetCostWord Maj32 = cost "Maj32" jetCostWord Maj64 = cost "Maj64" jetCostWord XorXor1 = cost "XorXor1" jetCostWord XorXor8 = cost "XorXor8" jetCostWord XorXor16 = cost "XorXor16" jetCostWord XorXor32 = cost "XorXor32" jetCostWord XorXor64 = cost "XorXor64" jetCostWord Ch1 = cost "Ch1" jetCostWord Ch8 = cost "Ch8" jetCostWord Ch16 = cost "Ch16" jetCostWord Ch32 = cost "Ch32" jetCostWord Ch64 = cost "Ch64" jetCostWord Some1 = cost "Some1" jetCostWord Some8 = cost "Some8" jetCostWord Some16 = cost "Some16" jetCostWord Some32 = cost "Some32" jetCostWord Some64 = cost "Some64" jetCostWord All8 = cost "All8" jetCostWord All16 = cost "All16" jetCostWord All32 = cost "All32" jetCostWord All64 = cost "All64" jetCostWord Eq1 = cost "Eq1" jetCostWord Eq8 = cost "Eq8" jetCostWord Eq16 = cost "Eq16" jetCostWord Eq32 = cost "Eq32" jetCostWord Eq64 = cost "Eq64" jetCostWord Eq256 = cost "Eq256" jetCostWord FullLeftShift8_1 = cost "FullLeftShift8_1" jetCostWord FullLeftShift8_2 = cost "FullLeftShift8_2" jetCostWord FullLeftShift8_4 = cost "FullLeftShift8_4" jetCostWord FullLeftShift16_1 = cost "FullLeftShift16_1" jetCostWord FullLeftShift16_2 = cost "FullLeftShift16_2" jetCostWord FullLeftShift16_4 = cost "FullLeftShift16_4" jetCostWord FullLeftShift16_8 = cost "FullLeftShift16_8" jetCostWord FullLeftShift32_1 = cost "FullLeftShift32_1" jetCostWord FullLeftShift32_2 = cost "FullLeftShift32_2" jetCostWord FullLeftShift32_4 = cost "FullLeftShift32_4" jetCostWord FullLeftShift32_8 = cost "FullLeftShift32_8" jetCostWord FullLeftShift32_16 = cost "FullLeftShift32_16" jetCostWord FullLeftShift64_1 = cost "FullLeftShift64_1" jetCostWord FullLeftShift64_2 = cost "FullLeftShift64_2" jetCostWord FullLeftShift64_4 = cost "FullLeftShift64_4" jetCostWord FullLeftShift64_8 = cost "FullLeftShift64_8" jetCostWord FullLeftShift64_16 = cost "FullLeftShift64_16" jetCostWord FullLeftShift64_32 = cost "FullLeftShift64_32" jetCostWord FullRightShift8_1 = cost "FullRightShift8_1" jetCostWord FullRightShift8_2 = cost "FullRightShift8_2" jetCostWord FullRightShift8_4 = cost "FullRightShift8_4" jetCostWord FullRightShift16_1 = cost "FullRightShift16_1" jetCostWord FullRightShift16_2 = cost "FullRightShift16_2" jetCostWord FullRightShift16_4 = cost "FullRightShift16_4" jetCostWord FullRightShift16_8 = cost "FullRightShift16_8" jetCostWord FullRightShift32_1 = cost "FullRightShift32_1" jetCostWord FullRightShift32_2 = cost "FullRightShift32_2" jetCostWord FullRightShift32_4 = cost "FullRightShift32_4" jetCostWord FullRightShift32_8 = cost "FullRightShift32_8" jetCostWord FullRightShift32_16 = cost "FullRightShift32_16" jetCostWord FullRightShift64_1 = cost "FullRightShift64_1" jetCostWord FullRightShift64_2 = cost "FullRightShift64_2" jetCostWord FullRightShift64_4 = cost "FullRightShift64_4" jetCostWord FullRightShift64_8 = cost "FullRightShift64_8" jetCostWord FullRightShift64_16 = cost "FullRightShift64_16" jetCostWord FullRightShift64_32 = cost "FullRightShift64_32" jetCostWord Leftmost8_1 = cost "Leftmost8_1" jetCostWord Leftmost8_2 = cost "Leftmost8_2" jetCostWord Leftmost8_4 = cost "Leftmost8_4" jetCostWord Leftmost16_1 = cost "Leftmost16_1" jetCostWord Leftmost16_2 = cost "Leftmost16_2" jetCostWord Leftmost16_4 = cost "Leftmost16_4" jetCostWord Leftmost16_8 = cost "Leftmost16_8" jetCostWord Leftmost32_1 = cost "Leftmost32_1" jetCostWord Leftmost32_2 = cost "Leftmost32_2" jetCostWord Leftmost32_4 = cost "Leftmost32_4" jetCostWord Leftmost32_8 = cost "Leftmost32_8" jetCostWord Leftmost32_16 = cost "Leftmost32_16" jetCostWord Leftmost64_1 = cost "Leftmost64_1" jetCostWord Leftmost64_2 = cost "Leftmost64_2" jetCostWord Leftmost64_4 = cost "Leftmost64_4" jetCostWord Leftmost64_8 = cost "Leftmost64_8" jetCostWord Leftmost64_16 = cost "Leftmost64_16" jetCostWord Leftmost64_32 = cost "Leftmost64_32" jetCostWord Rightmost8_1 = cost "Rightmost8_1" jetCostWord Rightmost8_2 = cost "Rightmost8_2" jetCostWord Rightmost8_4 = cost "Rightmost8_4" jetCostWord Rightmost16_1 = cost "Rightmost16_1" jetCostWord Rightmost16_2 = cost "Rightmost16_2" jetCostWord Rightmost16_4 = cost "Rightmost16_4" jetCostWord Rightmost16_8 = cost "Rightmost16_8" jetCostWord Rightmost32_1 = cost "Rightmost32_1" jetCostWord Rightmost32_2 = cost "Rightmost32_2" jetCostWord Rightmost32_4 = cost "Rightmost32_4" jetCostWord Rightmost32_8 = cost "Rightmost32_8" jetCostWord Rightmost32_16 = cost "Rightmost32_16" jetCostWord Rightmost64_1 = cost "Rightmost64_1" jetCostWord Rightmost64_2 = cost "Rightmost64_2" jetCostWord Rightmost64_4 = cost "Rightmost64_4" jetCostWord Rightmost64_8 = cost "Rightmost64_8" jetCostWord Rightmost64_16 = cost "Rightmost64_16" jetCostWord Rightmost64_32 = cost "Rightmost64_32" jetCostWord LeftPadLow1_8 = cost "LeftPadLow1_8" jetCostWord LeftPadLow1_16 = cost "LeftPadLow1_16" jetCostWord LeftPadLow8_16 = cost "LeftPadLow8_16" jetCostWord LeftPadLow1_32 = cost "LeftPadLow1_32" jetCostWord LeftPadLow8_32 = cost "LeftPadLow8_32" jetCostWord LeftPadLow16_32 = cost "LeftPadLow16_32" jetCostWord LeftPadLow1_64 = cost "LeftPadLow1_64" jetCostWord LeftPadLow8_64 = cost "LeftPadLow8_64" jetCostWord LeftPadLow16_64 = cost "LeftPadLow16_64" jetCostWord LeftPadLow32_64 = cost "LeftPadLow32_64" jetCostWord LeftPadHigh1_8 = cost "LeftPadHigh1_8" jetCostWord LeftPadHigh1_16 = cost "LeftPadHigh1_16" jetCostWord LeftPadHigh8_16 = cost "LeftPadHigh8_16" jetCostWord LeftPadHigh1_32 = cost "LeftPadHigh1_32" jetCostWord LeftPadHigh8_32 = cost "LeftPadHigh8_32" jetCostWord LeftPadHigh16_32 = cost "LeftPadHigh16_32" jetCostWord LeftPadHigh1_64 = cost "LeftPadHigh1_64" jetCostWord LeftPadHigh8_64 = cost "LeftPadHigh8_64" jetCostWord LeftPadHigh16_64 = cost "LeftPadHigh16_64" jetCostWord LeftPadHigh32_64 = cost "LeftPadHigh32_64" jetCostWord LeftExtend1_8 = cost "LeftExtend1_8" jetCostWord LeftExtend1_16 = cost "LeftExtend1_16" jetCostWord LeftExtend8_16 = cost "LeftExtend8_16" jetCostWord LeftExtend1_32 = cost "LeftExtend1_32" jetCostWord LeftExtend8_32 = cost "LeftExtend8_32" jetCostWord LeftExtend16_32 = cost "LeftExtend16_32" jetCostWord LeftExtend1_64 = cost "LeftExtend1_64" jetCostWord LeftExtend8_64 = cost "LeftExtend8_64" jetCostWord LeftExtend16_64 = cost "LeftExtend16_64" jetCostWord LeftExtend32_64 = cost "LeftExtend32_64" jetCostWord RightPadLow1_8 = cost "RightPadLow1_8" jetCostWord RightPadLow1_16 = cost "RightPadLow1_16" jetCostWord RightPadLow8_16 = cost "RightPadLow8_16" jetCostWord RightPadLow1_32 = cost "RightPadLow1_32" jetCostWord RightPadLow8_32 = cost "RightPadLow8_32" jetCostWord RightPadLow16_32 = cost "RightPadLow16_32" jetCostWord RightPadLow1_64 = cost "RightPadLow1_64" jetCostWord RightPadLow8_64 = cost "RightPadLow8_64" jetCostWord RightPadLow16_64 = cost "RightPadLow16_64" jetCostWord RightPadLow32_64 = cost "RightPadLow32_64" jetCostWord RightPadHigh1_8 = cost "RightPadHigh1_8" jetCostWord RightPadHigh1_16 = cost "RightPadHigh1_16" jetCostWord RightPadHigh8_16 = cost "RightPadHigh8_16" jetCostWord RightPadHigh1_32 = cost "RightPadHigh1_32" jetCostWord RightPadHigh8_32 = cost "RightPadHigh8_32" jetCostWord RightPadHigh16_32 = cost "RightPadHigh16_32" jetCostWord RightPadHigh1_64 = cost "RightPadHigh1_64" jetCostWord RightPadHigh8_64 = cost "RightPadHigh8_64" jetCostWord RightPadHigh16_64 = cost "RightPadHigh16_64" jetCostWord RightPadHigh32_64 = cost "RightPadHigh32_64" jetCostWord RightExtend8_16 = cost "RightExtend8_16" jetCostWord RightExtend8_32 = cost "RightExtend8_32" jetCostWord RightExtend16_32 = cost "RightExtend16_32" jetCostWord RightExtend8_64 = cost "RightExtend8_64" jetCostWord RightExtend16_64 = cost "RightExtend16_64" jetCostWord RightExtend32_64 = cost "RightExtend32_64" jetCostWord LeftShiftWith8 = cost "LeftShiftWith8" jetCostWord LeftShiftWith16 = cost "LeftShiftWith16" jetCostWord LeftShiftWith32 = cost "LeftShiftWith32" jetCostWord LeftShiftWith64 = cost "LeftShiftWith64" jetCostWord LeftShift8 = cost "LeftShift8" jetCostWord LeftShift16 = cost "LeftShift16" jetCostWord LeftShift32 = cost "LeftShift32" jetCostWord LeftShift64 = cost "LeftShift64" jetCostWord RightShiftWith8 = cost "RightShiftWith8" jetCostWord RightShiftWith16 = cost "RightShiftWith16" jetCostWord RightShiftWith32 = cost "RightShiftWith32" jetCostWord RightShiftWith64 = cost "RightShiftWith64" jetCostWord RightShift8 = cost "RightShift8" jetCostWord RightShift16 = cost "RightShift16" jetCostWord RightShift32 = cost "RightShift32" jetCostWord RightShift64 = cost "RightShift64" jetCostWord LeftRotate8 = cost "LeftRotate8" jetCostWord LeftRotate16 = cost "LeftRotate16" jetCostWord LeftRotate32 = cost "LeftRotate32" jetCostWord LeftRotate64 = cost "LeftRotate64" jetCostWord RightRotate8 = cost "RightRotate8" jetCostWord RightRotate16 = cost "RightRotate16" jetCostWord RightRotate32 = cost "RightRotate32" jetCostWord RightRotate64 = cost "RightRotate64" jetCostArith :: ArithJet a b -> Weight jetCostArith One8 = cost "One8" jetCostArith One16 = cost "One16" jetCostArith One32 = cost "One32" jetCostArith One64 = cost "One64" jetCostArith FullAdd8 = cost "FullAdd8" jetCostArith FullAdd16 = cost "FullAdd16" jetCostArith FullAdd32 = cost "FullAdd32" jetCostArith FullAdd64 = cost "FullAdd64" jetCostArith Add8 = cost "Add8" jetCostArith Add16 = cost "Add16" jetCostArith Add32 = cost "Add32" jetCostArith Add64 = cost "Add64" jetCostArith FullIncrement8 = cost "FullIncrement8" jetCostArith FullIncrement16 = cost "FullIncrement16" jetCostArith FullIncrement32 = cost "FullIncrement32" jetCostArith FullIncrement64 = cost "FullIncrement64" jetCostArith Increment8 = cost "Increment8" jetCostArith Increment16 = cost "Increment16" jetCostArith Increment32 = cost "Increment32" jetCostArith Increment64 = cost "Increment64" jetCostArith FullSubtract8 = cost "FullSubtract8" jetCostArith FullSubtract16 = cost "FullSubtract16" jetCostArith FullSubtract32 = cost "FullSubtract32" jetCostArith FullSubtract64 = cost "FullSubtract64" jetCostArith Subtract8 = cost "Subtract8" jetCostArith Subtract16 = cost "Subtract16" jetCostArith Subtract32 = cost "Subtract32" jetCostArith Subtract64 = cost "Subtract64" jetCostArith Negate8 = cost "Negate8" jetCostArith Negate16 = cost "Negate16" jetCostArith Negate32 = cost "Negate32" jetCostArith Negate64 = cost "Negate64" jetCostArith FullDecrement8 = cost "FullDecrement8" jetCostArith FullDecrement16 = cost "FullDecrement16" jetCostArith FullDecrement32 = cost "FullDecrement32" jetCostArith FullDecrement64 = cost "FullDecrement64" jetCostArith Decrement8 = cost "Decrement8" jetCostArith Decrement16 = cost "Decrement16" jetCostArith Decrement32 = cost "Decrement32" jetCostArith Decrement64 = cost "Decrement64" jetCostArith Multiply8 = cost "Multiply8" jetCostArith Multiply16 = cost "Multiply16" jetCostArith Multiply32 = cost "Multiply32" jetCostArith Multiply64 = cost "Multiply64" jetCostArith FullMultiply8 = cost "FullMultiply8" jetCostArith FullMultiply16 = cost "FullMultiply16" jetCostArith FullMultiply32 = cost "FullMultiply32" jetCostArith FullMultiply64 = cost "FullMultiply64" jetCostArith IsZero8 = cost "IsZero8" jetCostArith IsZero16 = cost "IsZero16" jetCostArith IsZero32 = cost "IsZero32" jetCostArith IsZero64 = cost "IsZero64" jetCostArith IsOne8 = cost "IsOne8" jetCostArith IsOne16 = cost "IsOne16" jetCostArith IsOne32 = cost "IsOne32" jetCostArith IsOne64 = cost "IsOne64" jetCostArith Le8 = cost "Le8" jetCostArith Le16 = cost "Le16" jetCostArith Le32 = cost "Le32" jetCostArith Le64 = cost "Le64" jetCostArith Lt8 = cost "Lt8" jetCostArith Lt16 = cost "Lt16" jetCostArith Lt32 = cost "Lt32" jetCostArith Lt64 = cost "Lt64" jetCostArith Min8 = cost "Min8" jetCostArith Min16 = cost "Min16" jetCostArith Min32 = cost "Min32" jetCostArith Min64 = cost "Min64" jetCostArith Max8 = cost "Max8" jetCostArith Max16 = cost "Max16" jetCostArith Max32 = cost "Max32" jetCostArith Max64 = cost "Max64" jetCostArith Median8 = cost "Median8" jetCostArith Median16 = cost "Median16" jetCostArith Median32 = cost "Median32" jetCostArith Median64 = cost "Median64" jetCostArith DivMod128_64 = cost "DivMod128_64" jetCostArith DivMod8 = cost "DivMod8" jetCostArith DivMod16 = cost "DivMod16" jetCostArith DivMod32 = cost "DivMod32" jetCostArith DivMod64 = cost "DivMod64" jetCostArith Divide8 = cost "Divide8" jetCostArith Divide16 = cost "Divide16" jetCostArith Divide32 = cost "Divide32" jetCostArith Divide64 = cost "Divide64" jetCostArith Modulo8 = cost "Modulo8" jetCostArith Modulo16 = cost "Modulo16" jetCostArith Modulo32 = cost "Modulo32" jetCostArith Modulo64 = cost "Modulo64" jetCostArith Divides8 = cost "Divides8" jetCostArith Divides16 = cost "Divides16" jetCostArith Divides32 = cost "Divides32" jetCostArith Divides64 = cost "Divides64" jetCostHash :: HashJet a b -> Weight jetCostHash Sha256Block = cost "Sha256Block" jetCostHash Sha256Iv = cost "Sha256Iv" jetCostHash Sha256Ctx8Add1 = cost "Sha256Ctx8Add1" jetCostHash Sha256Ctx8Add2 = cost "Sha256Ctx8Add2" jetCostHash Sha256Ctx8Add4 = cost "Sha256Ctx8Add4" jetCostHash Sha256Ctx8Add8 = cost "Sha256Ctx8Add8" jetCostHash Sha256Ctx8Add16 = cost "Sha256Ctx8Add16" jetCostHash Sha256Ctx8Add32 = cost "Sha256Ctx8Add32" jetCostHash Sha256Ctx8Add64 = cost "Sha256Ctx8Add64" jetCostHash Sha256Ctx8Add128 = cost "Sha256Ctx8Add128" jetCostHash Sha256Ctx8Add256 = cost "Sha256Ctx8Add256" jetCostHash Sha256Ctx8Add512 = cost "Sha256Ctx8Add512" jetCostHash Sha256Ctx8AddBuffer511 = cost "Sha256Ctx8AddBuffer511" jetCostHash Sha256Ctx8Finalize = cost "Sha256Ctx8Finalize" jetCostHash Sha256Ctx8Init = cost "Sha256Ctx8Init" jetCostSecp256k1 :: Secp256k1Jet a b -> Weight jetCostSecp256k1 FeNormalize = cost "FeNormalize" jetCostSecp256k1 FeNegate = cost "FeNegate" jetCostSecp256k1 FeAdd = cost "FeAdd" jetCostSecp256k1 FeSquare = cost "FeSquare" jetCostSecp256k1 FeMultiply = cost "FeMultiply" jetCostSecp256k1 FeMultiplyBeta = cost "FeMultiplyBeta" jetCostSecp256k1 FeInvert = cost "FeInvert" jetCostSecp256k1 FeSquareRoot = cost "FeSquareRoot" jetCostSecp256k1 FeIsZero = cost "FeIsZero" jetCostSecp256k1 FeIsOdd = cost "FeIsOdd" jetCostSecp256k1 ScalarNormalize = cost "ScalarNormalize" jetCostSecp256k1 ScalarNegate = cost "ScalarNegate" jetCostSecp256k1 ScalarAdd = cost "ScalarAdd" jetCostSecp256k1 ScalarSquare = cost "ScalarSquare" jetCostSecp256k1 ScalarMultiply = cost "ScalarMultiply" jetCostSecp256k1 ScalarMultiplyLambda = cost "ScalarMultiplyLambda" jetCostSecp256k1 ScalarInvert = cost "ScalarInvert" jetCostSecp256k1 ScalarIsZero = cost "ScalarIsZero" jetCostSecp256k1 GejInfinity = cost "GejInfinity" jetCostSecp256k1 GejNormalize = cost "GejNormalize" jetCostSecp256k1 GejNegate = cost "GejNegate" jetCostSecp256k1 GeNegate = cost "GeNegate" jetCostSecp256k1 GejDouble = cost "GejDouble" jetCostSecp256k1 GejAdd = cost "GejAdd" jetCostSecp256k1 GejGeAddEx = cost "GejGeAddEx" jetCostSecp256k1 GejGeAdd = cost "GejGeAdd" jetCostSecp256k1 GejRescale = cost "GejRescale" jetCostSecp256k1 GejIsInfinity = cost "GejIsInfinity" jetCostSecp256k1 GejEquiv = cost "GejEquiv" jetCostSecp256k1 GejGeEquiv = cost "GejGeEquiv" jetCostSecp256k1 GejXEquiv = cost "GejXEquiv" jetCostSecp256k1 GejYIsOdd = cost "GejYIsOdd" jetCostSecp256k1 GejIsOnCurve = cost "GejIsOnCurve" jetCostSecp256k1 GeIsOnCurve = cost "GeIsOnCurve" jetCostSecp256k1 Generate = cost "Generate" jetCostSecp256k1 Scale = cost "Scale" jetCostSecp256k1 LinearCombination1 = cost "LinearCombination1" jetCostSecp256k1 LinearVerify1 = cost "LinearVerify1" jetCostSecp256k1 PointVerify1 = cost "PointVerify1" jetCostSecp256k1 Decompress = cost "Decompress" jetCostSecp256k1 Swu = cost "Swu" jetCostSecp256k1 HashToCurve = cost "HashToCurve" jetCostSignature :: SignatureJet a b -> Weight jetCostSignature CheckSigVerify = cost "CheckSigVerify" jetCostSignature Bip0340Verify = cost "Bip0340Verify" jetCostBitcoin :: BitcoinJet a b -> Weight jetCostBitcoin ParseLock = cost "ParseLock" jetCostBitcoin ParseSequence = cost "ParseSequence" jetCostBitcoin TapdataInit = cost "TapdataInit" jetCostElements :: ElementsJet a b -> Weight jetCostElements (SigHashJet x) = jetCostSigHash x jetCostElements (TimeLockJet x) = jetCostTimeLock x jetCostElements (IssuanceJet x) = jetCostIssuance x jetCostElements (TransactionJet x) = jetCostTransaction x jetCostSigHash :: SigHashJet a b -> Weight jetCostSigHash SigAllHash = cost "SigAllHash" jetCostSigHash TxHash = cost "TxHash" jetCostSigHash TapEnvHash = cost "TapEnvHash" jetCostSigHash OutputsHash = cost "OutputsHash" jetCostSigHash InputsHash = cost "InputsHash" jetCostSigHash IssuancesHash = cost "IssuancesHash" jetCostSigHash InputUtxosHash = cost "InputUtxosHash" jetCostSigHash OutputHash = cost "OutputHash" jetCostSigHash OutputAmountsHash = cost "OutputAmountsHash" jetCostSigHash OutputScriptsHash = cost "OutputScriptsHash" jetCostSigHash OutputNoncesHash = cost "OutputNoncesHash" jetCostSigHash OutputRangeProofsHash = cost "OutputRangeProofsHash" jetCostSigHash OutputSurjectionProofsHash = cost "OutputSurjectionProofsHash" jetCostSigHash InputHash = cost "InputHash" jetCostSigHash InputOutpointsHash = cost "InputOutpointsHash" jetCostSigHash InputSequencesHash = cost "InputSequencesHash" jetCostSigHash InputAnnexesHash = cost "InputAnnexesHash" jetCostSigHash InputScriptSigsHash = cost "InputScriptSigsHash" jetCostSigHash IssuanceHash = cost "IssuanceHash" jetCostSigHash IssuanceAssetAmountsHash = cost "IssuanceAssetAmountsHash" jetCostSigHash IssuanceTokenAmountsHash = cost "IssuanceTokenAmountsHash" jetCostSigHash IssuanceRangeProofsHash = cost "IssuanceRangeProofsHash" jetCostSigHash IssuanceBlindingEntropyHash = cost "IssuanceBlindingEntropyHash" jetCostSigHash InputUtxoHash = cost "InputUtxoHash" jetCostSigHash InputAmountsHash = cost "InputAmountsHash" jetCostSigHash InputScriptsHash = cost "InputScriptsHash" jetCostSigHash TapleafHash = cost "TapleafHash" jetCostSigHash TappathHash = cost "TappathHash" jetCostSigHash OutpointHash = cost "OutpointHash" jetCostSigHash AssetAmountHash = cost "AssetAmountHash" jetCostSigHash NonceHash = cost "NonceHash" jetCostSigHash AnnexHash = cost "AnnexHash" jetCostSigHash BuildTapleafSimplicity = cost "BuildTapleafSimplicity" jetCostSigHash BuildTapbranch = cost "BuildTapbranch" jetCostSigHash BuildTaptweak = cost "BuildTaptweak" jetCostTimeLock :: TimeLockJet a b -> Weight jetCostTimeLock CheckLockHeight = cost "CheckLockHeight" jetCostTimeLock CheckLockTime = cost "CheckLockTime" jetCostTimeLock BrokenDoNotUseCheckLockDistance = cost "CheckLockDistance" jetCostTimeLock BrokenDoNotUseCheckLockDuration = cost "CheckLockDuration" jetCostTimeLock TxLockHeight = cost "TxLockHeight" jetCostTimeLock TxLockTime = cost "TxLockTime" jetCostTimeLock BrokenDoNotUseTxLockDistance = cost "TxLockDistance" jetCostTimeLock BrokenDoNotUseTxLockDuration = cost "TxLockDuration" jetCostTimeLock TxIsFinal = cost "TxIsFinal" jetCostIssuance :: IssuanceJet a b -> Weight jetCostIssuance Issuance = cost "Issuance" jetCostIssuance IssuanceAsset = cost "IssuanceAsset" jetCostIssuance IssuanceToken = cost "IssuanceToken" jetCostIssuance IssuanceEntropy = cost "IssuanceEntropy" jetCostIssuance CalculateIssuanceEntropy = cost "CalculateIssuanceEntropy" jetCostIssuance CalculateAsset = cost "CalculateAsset" jetCostIssuance CalculateExplicitToken = cost "CalculateExplicitToken" jetCostIssuance CalculateConfidentialToken = cost "CalculateConfidentialToken" jetCostIssuance LbtcAsset = cost "LbtcAsset" jetCostTransaction :: TransactionJet a b -> Weight jetCostTransaction ScriptCMR = cost "ScriptCMR" jetCostTransaction InternalKey = cost "InternalKey" jetCostTransaction CurrentIndex = cost "CurrentIndex" jetCostTransaction NumInputs = cost "NumInputs" jetCostTransaction NumOutputs = cost "NumOutputs" jetCostTransaction LockTime = cost "LockTime" jetCostTransaction OutputAsset = cost "OutputAsset" jetCostTransaction OutputAmount = cost "OutputAmount" jetCostTransaction OutputNonce = cost "OutputNonce" jetCostTransaction OutputScriptHash = cost "OutputScriptHash" jetCostTransaction OutputNullDatum = cost "OutputNullDatum" jetCostTransaction OutputIsFee = cost "OutputIsFee" jetCostTransaction OutputSurjectionProof = cost "OutputSurjectionProof" jetCostTransaction OutputRangeProof = cost "OutputRangeProof" jetCostTransaction TotalFee = cost "TotalFee" jetCostTransaction CurrentPegin = cost "CurrentPegin" jetCostTransaction CurrentPrevOutpoint = cost "CurrentPrevOutpoint" jetCostTransaction CurrentAsset = cost "CurrentAsset" jetCostTransaction CurrentAmount = cost "CurrentAmount" jetCostTransaction CurrentScriptHash = cost "CurrentScriptHash" jetCostTransaction CurrentSequence = cost "CurrentSequence" jetCostTransaction CurrentAnnexHash = cost "CurrentAnnexHash" jetCostTransaction CurrentScriptSigHash = cost "CurrentScriptSigHash" jetCostTransaction CurrentReissuanceBlinding = cost "CurrentReissuanceBlinding" jetCostTransaction CurrentNewIssuanceContract = cost "CurrentNewIssuanceContract" jetCostTransaction CurrentReissuanceEntropy = cost "CurrentReissuanceEntropy" jetCostTransaction CurrentIssuanceAssetAmount = cost "CurrentIssuanceAssetAmount" jetCostTransaction CurrentIssuanceTokenAmount = cost "CurrentIssuanceTokenAmount" jetCostTransaction CurrentIssuanceAssetProof = cost "CurrentIssuanceAssetProof" jetCostTransaction CurrentIssuanceTokenProof = cost "CurrentIssuanceTokenProof" jetCostTransaction InputPegin = cost "InputPegin" jetCostTransaction InputPrevOutpoint = cost "InputPrevOutpoint" jetCostTransaction InputAsset = cost "InputAsset" jetCostTransaction InputAmount = cost "InputAmount" jetCostTransaction InputScriptHash = cost "InputScriptHash" jetCostTransaction InputSequence = cost "InputSequence" jetCostTransaction InputAnnexHash = cost "InputAnnexHash" jetCostTransaction InputScriptSigHash = cost "InputScriptSigHash" jetCostTransaction ReissuanceBlinding = cost "ReissuanceBlinding" jetCostTransaction NewIssuanceContract = cost "NewIssuanceContract" jetCostTransaction ReissuanceEntropy = cost "ReissuanceEntropy" jetCostTransaction IssuanceAssetAmount = cost "IssuanceAssetAmount" jetCostTransaction IssuanceTokenAmount = cost "IssuanceTokenAmount" jetCostTransaction IssuanceAssetProof = cost "IssuanceAssetProof" jetCostTransaction IssuanceTokenProof = cost "IssuanceTokenProof" jetCostTransaction TapleafVersion = cost "TapleafVersion" jetCostTransaction Tappath = cost "Tappath" jetCostTransaction Version = cost "Version" jetCostTransaction GenesisBlockHash = cost "GenesisBlockHash" jetCostTransaction TransactionId = cost "TransactionId" ================================================ FILE: Haskell/Simplicity/Elements/Programs/Issuance/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Programs.Elements.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Programs.Elements.mkLib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Elements.Programs.Issuance.Lib ( issuance, issuanceEntropy, issuanceAsset, issuanceToken , Issuance.Bit, Issuance.Hash ) where import qualified Simplicity.Elements.Programs.Issuance as Issuance issuance = Issuance.issuance Issuance.lib issuanceEntropy = Issuance.issuanceEntropy Issuance.lib issuanceAsset = Issuance.issuanceAsset Issuance.lib issuanceToken = Issuance.issuanceToken Issuance.lib ================================================ FILE: Haskell/Simplicity/Elements/Programs/Issuance.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that implement Issuance functions from "Simplicity.Elements.DataTypes". module Simplicity.Elements.Programs.Issuance ( Lib(Lib), mkLib , issuance, issuanceEntropy, issuanceAsset, issuanceToken -- * Example instances , lib -- * Reexports , Bit, Hash ) where import Prelude hiding (Word, all, drop, max, not, take) import Simplicity.Functor import Simplicity.Elements.Primitive import Simplicity.Elements.Term hiding (one) import Simplicity.Programs.Arith import Simplicity.Programs.Bit import qualified Simplicity.Programs.Elements as Elements import Simplicity.Programs.Elements hiding (Lib(Lib), mkLib, lib) import Simplicity.Programs.Generic import Simplicity.Programs.Word -- | A collection of Simplicity expressions for Issuances. -- Use 'mkLib' to construct an instance of this library. data Lib term = Lib { -- | Returns a False value if the inputs issuance is a new issuance. -- Returns a True value if the input's issuance is a re-issuance. -- Returns a 'Just Nothing' value if the input has no issuance. -- Returns a Nothing value of the input index is out of range. issuance :: term Word32 (S (S Bit)) -- | Computes the entropy of a new issuance or returns the entropy of a reissuance. -- Returns a 'Just Nothing' value if the input has no issuance. -- Returns a Nothing value of the input index is out of range. , issuanceEntropy :: term Word32 (S (S Hash)) -- | Computes the asset ID of an issuance. -- Returns a 'Just Nothing' value if the input has no issuance. -- Returns a Nothing value of the input index is out of range. , issuanceAsset :: term Word32 (S (S Hash)) -- | Computes the reissuance token ID of an issuance. -- Returns a 'Just Nothing' value if the input has no issuance. -- Returns a Nothing value of the input index is out of range. , issuanceToken :: term Word32 (S (S Hash)) } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { issuance = m issuance , issuanceEntropy = m issuanceEntropy , issuanceAsset = m issuanceAsset , issuanceToken = m issuanceToken } -- | Build the Issuance 'Lib' library from its dependencies. mkLib :: forall term. (Core term, Primitive term) => Elements.Lib term -- ^ "Simplicity.Programs.Elements" -> Lib term mkLib Elements.Lib{..} = lib where lib@Lib{..} = Lib { issuance = primitive ReissuanceEntropy &&& primitive NewIssuanceContract >>> match (injl unit) (flip match (injr (injr true)) (drop (copair (injl unit) (copair (injr (injl unit)) (injr (injr false)))))) , issuanceEntropy = primitive ReissuanceEntropy &&& (primitive NewIssuanceContract &&& primitive InputPrevOutpoint) >>> match (injl unit) (flip match (take (injr (injr iden))) (drop (match (injl unit) (match (injr (injl unit)) (ih &&& oh >>> match (injl unit) (injr (injr calculateIssuanceEntropy))))))) , issuanceAsset = issuanceEntropy >>> copair (injl unit) (injr (copair (injl unit) (injr calculateAsset))) , issuanceToken = issuanceEntropy &&& primitive IssuanceAssetAmount >>> match (injl unit) (match (injr (injl unit)) (ih &&& oh >>> match (injl unit) (match (injl unit) (injr (injr (match (drop calculateConfidentialToken) (drop calculateExplicitToken))))))) } -- | An instance of the Issuance 'Lib' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. lib :: (Core term, Primitive term) => Lib term lib = mkLib Elements.lib ================================================ FILE: Haskell/Simplicity/Elements/Programs/SigHash/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Elements.Programs.SigHash.lib' library instance into individual functions. -- Users should prefer to use 'Simplicity.Elements.Programs.SigHash.mkLib' in order to share library dependencies. -- This module is provided mostly for testing purposes. module Simplicity.Elements.Programs.SigHash.Lib ( outputAmountsHash, outputNoncesHash, outputScriptsHash , outputRangeProofsHash, outputSurjectionProofsHash, outputsHash, outputHash , inputAmountsHash, inputScriptsHash, inputUtxosHash, inputUtxoHash , inputOutpointsHash, inputSequencesHash, inputAnnexesHash, inputScriptSigsHash, inputsHash, inputHash , issuanceAssetAmountsHash, issuanceTokenAmountsHash, issuanceRangeProofsHash, issuanceBlindingEntropyHash, issuancesHash, issuanceHash , txHash , tapleafHash, tappathHash, tapEnvHash , sigAllHash ) where import qualified Simplicity.Elements.Programs.SigHash as SigHash outputAmountsHash = SigHash.outputAmountsHash SigHash.lib outputNoncesHash = SigHash.outputNoncesHash SigHash.lib outputScriptsHash = SigHash.outputScriptsHash SigHash.lib outputRangeProofsHash = SigHash.outputRangeProofsHash SigHash.lib outputSurjectionProofsHash = SigHash.outputSurjectionProofsHash SigHash.lib outputsHash = SigHash.outputsHash SigHash.lib outputHash = SigHash.outputHash SigHash.lib inputAmountsHash = SigHash.inputAmountsHash SigHash.lib inputScriptsHash = SigHash.inputScriptsHash SigHash.lib inputUtxosHash = SigHash.inputUtxosHash SigHash.lib inputUtxoHash = SigHash.inputUtxoHash SigHash.lib inputOutpointsHash = SigHash.inputOutpointsHash SigHash.lib inputSequencesHash = SigHash.inputSequencesHash SigHash.lib inputAnnexesHash = SigHash.inputAnnexesHash SigHash.lib inputsHash = SigHash.inputsHash SigHash.lib inputHash = SigHash.inputHash SigHash.lib issuanceAssetAmountsHash = SigHash.issuanceAssetAmountsHash SigHash.lib issuanceTokenAmountsHash = SigHash.issuanceTokenAmountsHash SigHash.lib issuanceRangeProofsHash = SigHash.issuanceRangeProofsHash SigHash.lib issuanceBlindingEntropyHash = SigHash.issuanceBlindingEntropyHash SigHash.lib issuancesHash = SigHash.issuancesHash SigHash.lib issuanceHash = SigHash.issuanceHash SigHash.lib inputScriptSigsHash = SigHash.inputScriptSigsHash SigHash.lib txHash = SigHash.txHash SigHash.lib tapleafHash = SigHash.tapleafHash SigHash.lib tappathHash = SigHash.tappathHash SigHash.lib tapEnvHash = SigHash.tapEnvHash SigHash.lib sigAllHash = SigHash.sigAllHash SigHash.lib ================================================ FILE: Haskell/Simplicity/Elements/Programs/SigHash.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that implement timelock functions from "Simplicity.Elements.DataTypes". module Simplicity.Elements.Programs.SigHash ( Lib(Lib), mkLib , outputAmountsHash, outputNoncesHash, outputScriptsHash , outputRangeProofsHash, outputSurjectionProofsHash, outputsHash, outputHash , inputAmountsHash, inputScriptsHash, inputUtxosHash, inputUtxoHash , inputOutpointsHash, inputSequencesHash, inputAnnexesHash, inputScriptSigsHash, inputsHash, inputHash , issuanceAssetAmountsHash, issuanceTokenAmountsHash, issuanceRangeProofsHash, issuanceBlindingEntropyHash, issuancesHash, issuanceHash , txHash , tapleafHash, tappathHash, tapEnvHash , sigAllHash -- * Example instances , lib ) where import Prelude hiding (Word, all, drop, max, not, take) import Data.String (fromString) import Simplicity.Digest import Simplicity.Elements.Primitive import Simplicity.Elements.Term hiding (one) import Simplicity.Functor import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Word import qualified Simplicity.Programs.Sha256 as Sha256 import Simplicity.Programs.Sha256 (Ctx8) import Simplicity.Elements.Programs.Issuance.Lib import qualified Simplicity.Elements.Programs.Transaction as Transaction import Simplicity.Programs.Elements.Lib data Lib term = Lib { -- | A hash of all 'Transaction.outputAmount's. outputAmountsHash :: term () Word256 -- | A hash of all 'OutputNonce's. , outputNoncesHash :: term () Word256 -- | A hash of all 'OutputScriptHash's. , outputScriptsHash :: term () Word256 -- | A hash of all 'OutputRangeProofHash's. , outputRangeProofsHash :: term () Word256 -- | A hash of all 'OutputSurjectionProofHash's. , outputSurjectionProofsHash :: term () Word256 -- | A hash of -- -- * 'outputAmountsHash' -- * 'outputNoncesHash' -- * 'outputScriptsHash' -- * 'outputRangeProofsHash' -- -- Note that 'outputSurjectionProofsHash' is excluded. , outputsHash :: term () Word256 -- | If the given output index exists, returns a hash of -- -- * The serialization of the output's asset and amount fields. -- * The serialization of the output's nonce field. -- * A hash of the output's scriptPubKey. -- * A hash of the output's range proof. -- -- Note that output's surjection proof is excluded. , outputHash :: term Word32 (S Word256) -- | A hash of all 'Transaction.inputAmount's. , inputAmountsHash :: term () Word256 -- | A hash of all 'InputScriptHash's. , inputScriptsHash :: term () Word256 -- | A hash of -- -- * 'inputAmountsHash' -- * 'inputScriptsHash' , inputUtxosHash :: term () Word256 -- | If the given input index exists, returns a hash of -- -- * The serialization of the input UTXO's asset and amount fields. -- * A hash of the input UTXO's scriptPubKey. , inputUtxoHash :: term Word32 (S Word256) -- | A hash of all 'InputPegin' and 'InputPrevOutpoint' pairs. , inputOutpointsHash :: term () Word256 -- | A hash of all 'InputSequence's. , inputSequencesHash :: term () Word256 -- | A hash of all 'InputAnnexHash's. , inputAnnexesHash :: term () Word256 -- | A hash of all 'InputScriptSigHash's. , inputScriptSigsHash :: term () Word256 -- | A hash of -- -- * 'inputOutpointsHash' -- * 'inputSequencesHash' -- * 'inputAnnexesHash' -- -- Note that 'InputScriptSigHash' is excluded. , inputsHash :: term () Word256 -- | If the given input index exists, returns a hash of -- -- * If the input is not a pegin, then the byte 0x00. -- * If the input is a pegin, then the byte 0x01 followed by the parent chain's genesis hash. -- * The input's serialized previous transaction id. -- * The input's previous transaction index in big endian format. -- * The input's sequence number in big endian format. -- * If the input has no annex, or isn't a taproot spend, then the byte 0x00. -- * If the input has an annex, then the byte 0x01 followed by a SHA256 hash of the annex. , inputHash :: term Word32 (S Word256) -- | A hash of 'issuanceAsset' and 'IssuanceAssetAmount' pairs as an asset-amount hash. -- -- Note that "null" amount is hashed as if it were an explicit zero. -- -- When an input has no issuance, a pair of zero bytes, @0x00 0x00@ are hashed. , issuanceAssetAmountsHash :: term () Word256 -- | A hash of 'issuanceToken' and 'IssuanceAssetAmount' pairs as an asset-amount hash. -- -- Note that "null" amount is hashed as if it were an explicit zero. -- -- When an input has no issuance, a pair of zero bytes, @0x00 0x00@ are hashed. , issuanceTokenAmountsHash :: term () Word256 -- | A hash of all 'IssuanceAssetProof' and 'IssuanceTokenProof' pairs. , issuanceRangeProofsHash :: term () Word256 -- | A hash of all 'NewIssuanceContract', 'ReissuanceBlinding', 'ReissuanceBlinding' values. , issuanceBlindingEntropyHash :: term () Word256 -- | A hash of -- -- * 'issuanceAssetAmountsHash' -- * 'issuanceTokenAmountsHash' -- * 'issuanceRangeProofsHash' -- * 'issuanceBlindingEntropyHash' , issuancesHash :: term () Word256 -- | If the given input index exists, returns a hash of -- -- 1. The asset issuance: -- -- * If the input has no issuance then the two bytes 0x00 0x00. -- * If the input has a new issuance then the byte 0x01 followed by a serialization of the calculated issued asset id, -- followed by the serialization of the (possibly confidential) issued asset amount. -- * If the input has a reissuance then the byte 0x01 followed by a serialization of the issued asset id, -- followed by the serialization of the (possibly confidential) issued asset amount. -- -- 2. The token issuance: -- -- * If the input has no issuance then another two bytes 0x00 0x00. -- * If the input has a new issuance then the byte 0x01 followed by a serialization of the calculated issued token id, -- followed by the serialization of the (possibly confidential) issued token amount. -- * If the input has a re-issuance then the byte 0x01 followed by a serialization of the issued token id, -- followed by the serialization of the explicit 0 amount (i.e. 0x01 0x00 0x00 0x00 0x00 0x00 0x00 0x00 0x00 ) -- -- 3. The range proofs: -- -- * A hash of the range proof of the input's issuance asset amount. -- * A hash of the range proof of the input's issuance token amount. -- -- (Note: in the case of no issuese these will both be a hash of the empty proof) -- -- 4. The blinding entropy: -- -- * If the input has no issuance then another 0x00 byte. -- * If the input is a new issuance then the 0x01 byte followed by 32 0x00 bytes followed by the new issuance's contract hash field. -- * If the input is a reissuance then the 0x01 byte followed by the reissuance's blinding nonce field followed by the reissuance's entropy field. , issuanceHash :: term Word32 (S Word256) -- | A hash of -- -- * 'Version' -- * 'LockTime' -- * 'inputsHash' -- * 'outputsHash' -- * 'issuancesHash' -- * 'outputSurjectionProofsHash' -- * 'inputUtxosHash' , txHash :: term () Word256 -- | A hash of -- -- * 'TapleafVersion' -- * 'ScriptCMR' , tapleafHash :: term () Word256 -- | A hash of all 'Tappath's. , tappathHash :: term () Word256 -- | A hash of -- -- * 'tapleafHash' -- * 'tappathHash' -- * 'InternalKey' , tapEnvHash :: term () Word256 -- | A hash of -- -- * 'GenesisBlockHash' twice (This is effectively a tag.) -- * 'txHash' -- * 'tapEnvHash' -- * 'CurrentIndex' , sigAllHash :: term () Word256 } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { outputAmountsHash = m outputAmountsHash , outputNoncesHash = m outputNoncesHash , outputScriptsHash = m outputScriptsHash , outputRangeProofsHash = m outputRangeProofsHash , outputSurjectionProofsHash = m outputSurjectionProofsHash , outputsHash = m outputsHash , outputHash = m outputHash , inputAmountsHash = m inputAmountsHash , inputScriptsHash = m inputScriptsHash , inputUtxosHash = m inputUtxosHash , inputUtxoHash = m inputUtxoHash , inputOutpointsHash = m inputOutpointsHash , inputSequencesHash = m inputSequencesHash , inputAnnexesHash = m inputAnnexesHash , inputsHash = m inputsHash , inputHash = m inputHash , issuanceAssetAmountsHash = m issuanceAssetAmountsHash , issuanceTokenAmountsHash = m issuanceTokenAmountsHash , issuanceRangeProofsHash = m issuanceRangeProofsHash , issuanceBlindingEntropyHash = m issuanceBlindingEntropyHash , issuancesHash = m issuancesHash , issuanceHash = m issuanceHash , inputScriptSigsHash = m inputScriptSigsHash , txHash = m txHash , tapleafHash = m tapleafHash , tappathHash = m tappathHash , tapEnvHash = m tapEnvHash , sigAllHash = m sigAllHash } mkLib :: forall term. (Assert term, Primitive term) => Sha256.Lib term -- ^ "Simplicity.Programs.Sha256" -> Sha256.LibAssert term -- ^ "Simplicity.Programs.Sha256" -> Transaction.Lib term -- ^ "Simplicity.Elements.Programs.Transaction" -> Lib term mkLib Sha256.Lib{..} Sha256.LibAssert{..} Transaction.Lib{..} = lib where lib@Lib{..} = Lib { outputAmountsHash = let finalize = ctx8Finalize body = take (drop outputAmount) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> assetAmountHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , outputNoncesHash = let finalize = ctx8Finalize body = take (drop (primitive OutputNonce)) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> nonceHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , outputScriptsHash = hashWord256s32 (drop (primitive OutputScriptHash)) , outputRangeProofsHash = hashWord256s32 (drop (primitive OutputRangeProof)) , outputSurjectionProofsHash = hashWord256s32 (drop (primitive OutputSurjectionProof)) , outputsHash = ctx8Init &&& ((outputAmountsHash &&& outputNoncesHash) &&& (outputScriptsHash &&& outputRangeProofsHash)) >>> ctx8Addn vector128 >>> ctx8Finalize , outputHash = (outputAmount &&& (primitive OutputNonce &&& primitive OutputScriptHash &&& primitive OutputRangeProof)) >>> match (injl unit) (injr (((((unit >>> ctx8Init) &&& oh >>> assetAmountHash) &&& (drop . take . assert $ iden) >>> nonceHash) &&& (drop . drop . take . assert $ iden) >>> ctx8Add32) &&& (drop . drop . drop . assert $ iden) >>> ctx8Add32 >>> ctx8Finalize)) , inputAmountsHash = let finalize = ctx8Finalize body = take (drop inputAmount) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> assetAmountHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , inputScriptsHash = hashWord256s32 (drop (primitive InputScriptHash)) , inputUtxosHash = ctx8Init &&& (inputAmountsHash &&& inputScriptsHash) >>> ctx8Addn vector64 >>> ctx8Finalize , inputUtxoHash = (inputAmount &&& primitive InputScriptHash) >>> match (injl unit) (injr (((unit >>> ctx8Init) &&& oh >>> assetAmountHash) &&& (drop . assert $ iden) >>> ctx8Add32 >>> ctx8Finalize)) , inputOutpointsHash = let finalize = ctx8Finalize body = take (drop (primitive InputPegin)) &&& (take (drop (primitive InputPrevOutpoint)) &&& ih) >>> match (injl iih) (ioh &&& (oh &&& iih) >>> match (injl iih) (injr (iih &&& (ioh &&& oh) >>> outpointHash))) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , inputSequencesHash = hashWord32s (drop (primitive InputSequence)) , inputAnnexesHash = let finalize = ctx8Finalize body = take (drop (primitive InputAnnexHash)) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> annexHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , inputScriptSigsHash = hashWord256s32 (drop (primitive InputScriptSigHash)) , inputsHash = (ctx8Init &&& (inputOutpointsHash &&& inputSequencesHash) >>> ctx8Addn vector64) &&& inputAnnexesHash >>> ctx8Addn vector32 >>> ctx8Finalize , inputHash = (primitive InputPegin &&& (primitive InputPrevOutpoint &&& primitive InputSequence &&& primitive InputAnnexHash)) >>> match (injl unit) (injr ((((unit >>> ctx8Init) &&& (oh &&& (drop . take . assert $ iden)) >>> outpointHash) &&& (drop . drop . take . assert $ iden) >>> ctx8Add4) &&& (drop . drop . drop . assert $ iden) >>> annexHash >>> ctx8Finalize)) -- Note a "null" amount is serialized as an explicit value of 0. The asset id is still serialized in this case. -- Only when there is no issuance are two "null" values (i.e. 0x00 0x00) are serialized. , issuanceAssetAmountsHash = let finalize = ctx8Finalize body = take (drop issuanceAssetAmount) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> issuanceAssetAmountHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , issuanceTokenAmountsHash = let finalize = ctx8Finalize body = take (drop issuanceTokenAmount) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> issuanceAssetAmountHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , issuanceRangeProofsHash = let finalize = ctx8Finalize body = take (drop (primitive IssuanceAssetProof)) &&& (take (drop (primitive IssuanceTokenProof)) &&& ih) >>> match (injl iih) (ioh &&& (oh &&& iih) >>> match (injl iih) (injr (iih &&& (ioh &&& oh) >>> ctx8Addn vector64))) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , issuanceBlindingEntropyHash = let finalize = ctx8Finalize body = take (drop issuanceBlindingEntropy) &&& ih >>> match (injl ih) (injr (ih &&& oh >>> blindingEntropyHash)) in unit &&& ctx8Init >>> forWhile word32 body >>> copair finalize finalize , issuancesHash = (ctx8Init &&& ((issuanceAssetAmountsHash &&& issuanceTokenAmountsHash) &&& (issuanceRangeProofsHash &&& issuanceBlindingEntropyHash)) >>> ctx8Addn vector128) >>> ctx8Finalize , issuanceHash = issuanceAssetAmount &&& issuanceTokenAmount &&& (primitive IssuanceAssetProof &&& primitive IssuanceTokenProof) &&& issuanceBlindingEntropy >>> match (injl unit) (injr ((((((unit >>> ctx8Init) &&& oh >>> issuanceAssetAmountHash) &&& (drop . take . assert $ iden) >>> issuanceAssetAmountHash) &&& (drop . drop . take . take . assert $ iden) >>> ctx8Add32) &&& (drop . drop . take . drop . assert $ iden) >>> ctx8Add32) &&& (drop . drop . drop . assert $ iden) >>> blindingEntropyHash >>> ctx8Finalize)) , txHash = ((ctx8Init &&& (primitive Version &&& primitive LockTime) >>> ctx8Addn vector8) &&& ((inputsHash &&& outputsHash) &&& (issuancesHash &&& outputSurjectionProofsHash)) >>> ctx8Addn vector128) &&& inputUtxosHash >>> ctx8Addn vector32 >>> ctx8Finalize , tapleafHash = ((Sha256.ctx8InitTag "TapLeaf/elements") &&& (primitive TapleafVersion &&& scribe (toWord8 32)) >>> ctx8Addn vector2) &&& (primitive ScriptCMR) >>> ctx8Addn vector32 >>> ctx8Finalize , tappathHash = hashWord256s8 (drop (primitive Tappath)) , tapEnvHash = (ctx8Init &&& tapleafHash >>> ctx8Addn vector32) &&& (tappathHash &&& primitive InternalKey) >>> ctx8Addn vector64 >>> ctx8Finalize , sigAllHash = (ctx8Init &&& ((primitive GenesisBlockHash >>> iden &&& iden) &&& (txHash &&& tapEnvHash)) >>> ctx8Addn vector128) &&& primitive CurrentIndex >>> ctx8Addn vector4 >>> ctx8Finalize } hashLoop256 :: (TyC w, TyC c) => Word w -> term (c, w) (S Word256) -> term (c, Ctx8) Ctx8 hashLoop256 = Sha256.hashLoop vector32 hashWord256s :: (TyC w, TyC c) => Word w -> term (c, w) (S Word256) -> term c Word256 hashWord256s w array = iden &&& (unit >>> ctx8Init) >>> hashLoop256 w array >>> ctx8Finalize hashWord256s32 = hashWord256s word32 hashWord256s8 = hashWord256s word8 hashWord32s array = iden &&& (unit >>> ctx8Init) >>> Sha256.hashLoop vector4 word32 array >>> ctx8Finalize ctx8Add4 = ctx8Addn vector4 ctx8Add32 = ctx8Addn vector32 ctx8Add64 = ctx8Addn vector64 issuanceAssetAmount = issuanceAsset &&& primitive IssuanceAssetAmount >>> match (injl unit) (match (injr (injl unit)) (ih &&& oh >>> match (injl unit) (match (injl unit) (injr (injr (ih &&& oh)))))) issuanceTokenAmount = issuanceToken &&& primitive IssuanceTokenAmount >>> match (injl unit) (match (injr (injl unit)) (ih &&& oh >>> match (injl unit) (match (injl unit) (injr (injr (ih &&& oh)))))) issuanceAssetAmountHash = ih &&& oh >>> match (ih &&& (unit >>> zero word16) >>> ctx8Addn vector2) (ih &&& (injr ooh &&& oih) >>> assetAmountHash) issuanceBlindingEntropy = let issuanceEntropyBody = match (injl unit) (match (injr (injl unit)) ((ih &&& oh) >>> match (injl unit) (injr (match (injl unit) (injr (ih &&& oh)))))) in primitive NewIssuanceContract &&& primitive ReissuanceBlinding &&& primitive ReissuanceEntropy >>> match (injl unit) (match (drop issuanceEntropyBody) (injr (injr ((unit >>> zero word256) &&& oh)))) blindingEntropyHash = ih &&& oh >>> match (drop (iden &&& (unit >>> zero word8) >>> ctx8Add1)) (drop (iden &&& (unit >>> one word8) >>> ctx8Add1) &&& oh >>> ctx8Add64) -- | An instance of the SigHash 'Lib' library. -- This instance does not share its dependencies. -- Users should prefer to use 'mkLib' in order to share library dependencies. -- This instance is provided mostly for testing purposes. lib :: (Assert term, Primitive term) => Lib term lib = mkLib Sha256.lib Sha256.libAssert Transaction.lib ================================================ FILE: Haskell/Simplicity/Elements/Programs/TimeLock.hs ================================================ -- | This module defines Simplicity expressions that implement timelock functions from "Simplicity.Elements.DataTypes". module Simplicity.Elements.Programs.TimeLock ( txIsFinal , txLockHeight, txLockTime , brokenTxLockDistance, brokenTxLockDuration , checkLockHeight, checkLockTime , brokenCheckLockDistance, brokenCheckLockDuration , module Simplicity.Programs.TimeLock , Bit ) where import Prelude hiding (Word, all, drop, max, not, take) import Simplicity.Elements.Primitive import Simplicity.Elements.Term import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.TimeLock import Simplicity.Programs.Word -- | Implements 'Simplicity.Elements.DataTypes.txIsFinal'. txIsFinal :: (Core term, Primitive term) => term () Bit txIsFinal = (unit &&& unit) >>> forWhile word32 body >>> copair iden true where body = take (drop (primitive InputSequence)) >>> copair (injl true) (all word32 >>> copair (injl false) (injr unit)) -- | Returns the transaction's LockTime if it is a Height value, otherwise it returns 0. txLockHeight :: (Core term, Primitive term) => term () Height txLockHeight = txIsFinal &&& primitive LockTime >>> cond z (parseLock >>> (copair iden z)) where z = unit >>> zero word32 -- | Returns the transaction's LockTime if it is a Time value, otherwise it returns 0. txLockTime :: (Core term, Primitive term) => term () Time txLockTime = txIsFinal &&& primitive LockTime >>> cond z (parseLock >>> (copair z iden)) where z = unit >>> zero word32 bip68VersionCheck :: (Core term, Primitive term) => term () Bit bip68VersionCheck = scribe (toWord32 2) &&& primitive Version >>> le word32 -- | Implements 'Simplicity.Elements.DataTypes.txLockDistance'. brokenTxLockDistance :: (Core term, Primitive term) => term () Distance brokenTxLockDistance = bip68VersionCheck &&& zero word16 >>> match ih (forWhile word32 body >>> copair iden iden) where body = take (drop (primitive InputSequence)) &&& ih >>> match (injl ih) (injr (take parseSequence &&& ih >>> match ih (match (max word16) ih))) -- | Implements 'Simplicity.Elements.DataTypes.txLockDuration'. brokenTxLockDuration :: (Core term, Primitive term) => term () Duration brokenTxLockDuration = bip68VersionCheck &&& zero word16 >>> match ih (forWhile word32 body >>> copair iden iden) where body = take (drop (primitive InputSequence)) &&& ih >>> match (injl ih) (injr (take parseSequence &&& ih >>> match ih (match ih (max word16)))) -- | Asserts that the input is less than or equal to the value returned by 'txLockHeight'. checkLockHeight :: (Assert term, Primitive term) => term Height () checkLockHeight = assert (iden &&& (unit >>> txLockHeight) >>> le word32) -- | Asserts that the input is less than or equal to the value returned by 'txLockTime'. checkLockTime :: (Assert term, Primitive term) => term Time () checkLockTime = assert (iden &&& (unit >>> txLockTime) >>> le word32) -- | Asserts that the input is less than or equal to the value returned by 'txLockDistance'. brokenCheckLockDistance :: (Assert term, Primitive term) => term Distance () brokenCheckLockDistance = assert (iden &&& (unit >>> brokenTxLockDistance) >>> le word16) -- | Asserts that the input is less than or equal to the value returned by 'txLockDuration'. brokenCheckLockDuration :: (Assert term, Primitive term) => term Duration () brokenCheckLockDuration = assert (iden &&& (unit >>> brokenTxLockDuration) >>> le word16) ================================================ FILE: Haskell/Simplicity/Elements/Programs/Transaction/Lib.hs ================================================ {-# LANGUAGE NoMonomorphismRestriction #-} -- | This module unpacks the 'Simplicity.Elements.Programs.Transaction.lib' library instance into individual functions. module Simplicity.Elements.Programs.Transaction.Lib ( numInputs , numOutputs , outputAmount , outputIsFee , totalFee , inputAmount , currentPegin , currentPrevOutpoint , currentAsset , currentAmount , currentScriptHash , currentSequence , currentAnnexHash , currentScriptSigHash , currentReissuanceBlinding , currentNewIssuanceContract , currentReissuanceEntropy , currentIssuanceAssetAmount , currentIssuanceTokenAmount , currentIssuanceAssetProof , currentIssuanceTokenProof ) where import qualified Simplicity.Elements.Programs.Transaction as Transaction numInputs = Transaction.numInputs Transaction.lib numOutputs = Transaction.numOutputs Transaction.lib outputAmount = Transaction.outputAmount Transaction.lib outputIsFee = Transaction.outputIsFee Transaction.lib totalFee = Transaction.totalFee Transaction.lib inputAmount = Transaction.inputAmount Transaction.lib currentPegin = Transaction.currentPegin Transaction.lib currentPrevOutpoint = Transaction.currentPrevOutpoint Transaction.lib currentAsset = Transaction.currentAsset Transaction.lib currentAmount = Transaction.currentAmount Transaction.lib currentScriptHash = Transaction.currentScriptHash Transaction.lib currentSequence = Transaction.currentSequence Transaction.lib currentAnnexHash = Transaction.currentAnnexHash Transaction.lib currentScriptSigHash = Transaction.currentScriptSigHash Transaction.lib currentReissuanceBlinding = Transaction.currentReissuanceBlinding Transaction.lib currentNewIssuanceContract = Transaction.currentNewIssuanceContract Transaction.lib currentReissuanceEntropy = Transaction.currentReissuanceEntropy Transaction.lib currentIssuanceAssetAmount = Transaction.currentIssuanceAssetAmount Transaction.lib currentIssuanceTokenAmount = Transaction.currentIssuanceTokenAmount Transaction.lib currentIssuanceAssetProof = Transaction.currentIssuanceAssetProof Transaction.lib currentIssuanceTokenProof = Transaction.currentIssuanceTokenProof Transaction.lib ================================================ FILE: Haskell/Simplicity/Elements/Programs/Transaction.hs ================================================ {-# LANGUAGE ScopedTypeVariables, GADTs, RankNTypes, RecordWildCards #-} -- | This module defines Simplicity expressions that access transaction data. module Simplicity.Elements.Programs.Transaction ( Lib(Lib), lib , numInputs , numOutputs , outputAmount , outputIsFee , totalFee , inputAmount , currentPegin , currentPrevOutpoint , currentAsset , currentAmount , currentScriptHash , currentSequence , currentAnnexHash , currentScriptSigHash , currentReissuanceBlinding , currentNewIssuanceContract , currentReissuanceEntropy , currentIssuanceAssetAmount , currentIssuanceTokenAmount , currentIssuanceAssetProof , currentIssuanceTokenProof ) where import Prelude hiding (take, drop) import Simplicity.Digest import Simplicity.Elements.Primitive import Simplicity.Elements.Term hiding (one) import Simplicity.Functor import Simplicity.Programs.Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Word import Simplicity.Ty.Word data Lib term = Lib { -- | Returns the number of inputs the transaction has. numInputs :: term () Word32 -- | Returns the number of outputs the transaction has. , numOutputs :: term () Word32 -- | Returns a pair of asset and amounts for the given output index. -- Returns Nothing of the index is out of range. , outputAmount :: term Word32 (S (Conf Word256, Conf Word64)) -- | An output is a fee when its script is empty and the asset and amounts are explicit. -- Returns Nothing of the index is out of range. , outputIsFee :: term Word32 (S Bit) -- | Compute the total amount of fees paid to a given assetID. -- Returns 0 for any asset without fees. , totalFee :: term Word256 Word64 -- | Returns a pair of asset and amounts for the given input index. -- Returns Nothing of the index is out of range. , inputAmount :: term Word32 (S (Conf Word256, Conf Word64)) -- | Returns the `InputPegin` of the `CurrentIndex`. , currentPegin :: term () (S Word256) -- | Returns the `InputPrevOutpoint` of the `CurrentIndex`. , currentPrevOutpoint :: term () (Word256,Word32) -- | Returns the `InputAsset` of the `CurrentIndex`. , currentAsset :: term () (Conf Word256) -- | Returns the `inputAmount` of the `CurrentIndex`. , currentAmount :: term () (Conf Word256, Conf Word64) -- | Returns the `InputScriptHash` of the `CurrentIndex`. , currentScriptHash :: term () Word256 -- | Returns the `InputSequence` of the `CurrentIndex`. , currentSequence :: term () Word32 -- | Returns the `InputAnnexHash` of the `CurrentIndex`. , currentAnnexHash :: term () (S Word256) -- | Returns the `InputScriptSigHash` of the `CurrentIndex`. , currentScriptSigHash :: term () Word256 -- | Returns the `ReissuanceBlinding` of the `CurrentIndex`. , currentReissuanceBlinding :: term () (S Word256) -- | Returns the `NewIssuanceContract` of the `CurrentIndex`. , currentNewIssuanceContract :: term () (S Word256) -- | Returns the `ReissuanceEntropy` of the `CurrentIndex`. , currentReissuanceEntropy :: term () (S Word256) -- | Returns the `IssuanceAssetAmount` of the `CurrentIndex`. , currentIssuanceAssetAmount :: term () (S (Conf Word64)) -- | Returns the `IssuanceTokenAmount` of the `CurrentIndex`. , currentIssuanceTokenAmount :: term () (S (Conf Word64)) -- | Returns the `IssuanceAssetProof` of the `CurrentIndex`. , currentIssuanceAssetProof :: term () Word256 -- | Returns the `IssuanceTokenProof` of the `CurrentIndex`. , currentIssuanceTokenProof :: term () Word256 } instance SimplicityFunctor Lib where sfmap m Lib{..} = Lib { numInputs = m numInputs , numOutputs = m numOutputs , outputAmount = m outputAmount , outputIsFee = m outputIsFee , totalFee = m totalFee , inputAmount = m inputAmount , currentPegin = m currentPegin , currentPrevOutpoint = m currentPrevOutpoint , currentAsset = m currentAsset , currentAmount = m currentAmount , currentScriptHash = m currentScriptHash , currentSequence = m currentSequence , currentAnnexHash = m currentAnnexHash , currentScriptSigHash = m currentScriptSigHash , currentReissuanceBlinding = m currentReissuanceBlinding , currentNewIssuanceContract = m currentNewIssuanceContract , currentReissuanceEntropy = m currentReissuanceEntropy , currentIssuanceAssetAmount = m currentIssuanceAssetAmount , currentIssuanceTokenAmount = m currentIssuanceTokenAmount , currentIssuanceAssetProof = m currentIssuanceAssetProof , currentIssuanceTokenProof = m currentIssuanceTokenProof } -- | Build the Transaction 'Lib' library. lib :: forall term. (Assert term, Primitive term) => Lib term lib = l where l@Lib{..} = Lib { numInputs = firstFail word32 (primitive InputScriptHash) , numOutputs = firstFail word32 (primitive OutputScriptHash) , outputAmount = primitive OutputAmount &&& primitive OutputAsset >>> match (injl unit) (ih &&& oh >>> match (injl unit) (injr iden)) , outputIsFee = outputAmount &&& (primitive OutputScriptHash &&& scribe (Right emptyHash) >>> eq) >>> match (injl unit) (injr (oih &&& (ooh &&& ih) >>> match false (drop (match false ih)))) , totalFee = let body = take (drop outputIsFee) &&& (take (drop outputAmount) &&& (ooh &&& ih)) >>> match (injl iiih) -- reached last output (injr (match iiih -- not a fee. (drop (match iih -- reached last output (technically not possible at this point) ((ooh &&& (injr ioh) >>> eq) &&& (oih &&& iih) >>> (match iih -- assetid does not match (drop (match ih -- value is confidential (technically not possible at this point) (add word64 >>> ih) -- drop the carry bit )))))))) in (iden &&& (unit >>> zero word64)) >>> forWhile word32 body >>> copair iden iden , inputAmount = primitive InputAmount &&& primitive InputAsset >>> match (injl unit) (ih &&& oh >>> match (injl unit) (injr iden)) , currentPegin = primitive CurrentIndex >>> assert (primitive InputPegin) , currentPrevOutpoint = primitive CurrentIndex >>> assert (primitive InputPrevOutpoint) , currentAsset = primitive CurrentIndex >>> assert (primitive InputAsset) , currentAmount = primitive CurrentIndex >>> assert (inputAmount) , currentScriptHash = primitive CurrentIndex >>> assert (primitive InputScriptHash) , currentSequence = primitive CurrentIndex >>> assert (primitive InputSequence) , currentAnnexHash = primitive CurrentIndex >>> assert (primitive InputAnnexHash) , currentScriptSigHash = primitive CurrentIndex >>> assert (primitive InputScriptSigHash) , currentReissuanceBlinding = primitive CurrentIndex >>> assert (primitive ReissuanceBlinding) , currentNewIssuanceContract = primitive CurrentIndex >>> assert (primitive NewIssuanceContract) , currentReissuanceEntropy = primitive CurrentIndex >>> assert (primitive ReissuanceEntropy) , currentIssuanceAssetAmount = primitive CurrentIndex >>> assert (primitive IssuanceAssetAmount) , currentIssuanceTokenAmount = primitive CurrentIndex >>> assert (primitive IssuanceTokenAmount) , currentIssuanceAssetProof = primitive CurrentIndex >>> assert (primitive IssuanceAssetProof) , currentIssuanceTokenProof = primitive CurrentIndex >>> assert (primitive IssuanceTokenProof) } emptyHash = toWord256 . integerHash256 $ bsHash mempty ================================================ FILE: Haskell/Tests/Simplicity/Arbitrary.hs ================================================ module Simplicity.Arbitrary ( genBoundaryCases, genSignature ) where import Data.Serialize (encode) import Simplicity.CoreJets import Simplicity.Digest import Simplicity.LibSecp256k1.Schnorr import Simplicity.LibSecp256k1.Spec import Simplicity.Ty.Word import Test.Tasty.QuickCheck (Arbitrary(..), Gen, chooseBoundedIntegral, chooseInteger, growingElements, oneof) genBoundaryCases :: (Bounded w, Integral w) => w -> Gen w genBoundaryCases 0 = oneof [return 0, chooseBoundedIntegral (1, maxBound)] genBoundaryCases 1 = oneof [return 0, return 1, chooseBoundedIntegral (2, maxBound)] genBoundaryCases boundary = oneof [return 0, chooseBoundedIntegral (1, boundary-1), return boundary, chooseBoundedIntegral (boundary + 1, maxBound)] genSignature :: Hash256 -> Gen (PubKey, Sig) genSignature msg = do priv <- scalar <$> chooseInteger (1, scalar_repr maxBound) k <- scalar <$> chooseInteger (1, scalar_repr maxBound) let Just (GE px py) = gej_normalize $ off_curve_linear_combination [] priv let Just (GE rx ry) = gej_normalize $ off_curve_linear_combination [] k let pub = PubKey (fe_pack px) let msgBody = encode (fe_pack rx) <> encode pub <> encode msg let e = scalar . integerHash256 $ taggedHash "BIP0340/challenge" msgBody let s = (if fe_is_odd ry then scalar_negate k else k) `scalar_add` (scalar_multiply e (if fe_is_odd py then scalar_negate priv else priv)) return $ (pub, Sig (fe_pack rx) (scalar_pack s)) instance Arbitrary SomeConstWordContent where arbitrary = do n <- growingElements [0..10] v <- chooseInteger (0, 2^n - 1) return $ scwc v n where scwc v 0 = SomeConstWordContent (ConstWordContent SingleV v) scwc v n | 0 < n = case scwc v (n - 1) of SomeConstWordContent (ConstWordContent w _) -> SomeConstWordContent (ConstWordContent (DoubleV w) v) ================================================ FILE: Haskell/Tests/Simplicity/Bip0340.hs ================================================ module Simplicity.Bip0340 ( TestVector , bip0340TestPubKey, bip0340TestMessage, bip0340TestSig, bip0340TestResult , bip0340TestAsTy , bip0340Vectors ) where import Prelude import Simplicity.LibSecp256k1.Schnorr import Simplicity.Ty.Word (toBit, toWord256) import Simplicity.Word data TestVector = TestVector PubKey Word256 Sig Bool bip0340TestPubKey (TestVector p _ _ _) = p bip0340TestMessage (TestVector _ m _ _) = m bip0340TestSig (TestVector _ _ s _) = s bip0340TestResult (TestVector _ _ _ r) = r bip0340TestAsTy (TestVector (PubKey x) m (Sig r s) _) = ((conv x, conv m), (conv r, conv s)) where conv = toWord256 . fromIntegral bip0340Vectors = [ bip0340Vector0 , bip0340Vector1 , bip0340Vector2 , bip0340Vector3 , bip0340Vector4 , bip0340Vector5 , bip0340Vector6 , bip0340Vector7 , bip0340Vector8 , bip0340Vector9 , bip0340Vector10 , bip0340Vector11 , bip0340Vector12 , bip0340Vector13 , bip0340Vector14 ] bip0340Vector0 = TestVector pk m sig True where pk = PubKey 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9 m = 0 sig = Sig 0xE907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA8215 0x25F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0 bip0340Vector1 = TestVector pk m sig True where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 sig = Sig 0x6896BD60EEAE296DB48A229FF71DFE071BDE413E6D43F917DC8DCF8C78DE3341 0x8906D11AC976ABCCB20B091292BFF4EA897EFCB639EA871CFA95F6DE339E4B0A bip0340Vector2 = TestVector pk m sig True where pk = PubKey 0xDD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8 m = 0x7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x5831AAEED7B44BB74E5EAB94BA9D4294C49BCF2A60728D8B4C200F50DD313C1B 0xAB745879A5AD954A72C45A91C3A51D3C7ADEA98D82F8481E0E1E03674A6F3FB7 bip0340Vector3 = TestVector pk m sig True where pk = PubKey 0x25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517 m = -1 sig = Sig 0x7EB0509757E246F19449885651611CB965ECC1A187DD51B64FDA1EDC9637D5EC 0x97582B9CB13DB3933705B32BA982AF5AF25FD78881EBB32771FC5922EFC66EA3 bip0340Vector4 = TestVector pk m sig True where pk = PubKey 0xD69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9 m = 0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703 sig = Sig 0x00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C63 0x76AFB1548AF603B3EB45C9F8207DEE1060CB71C04E80F593060B07D28308D7F4 bip0340Vector5 = TestVector pk m sig False where pk = PubKey 0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34 m = 0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 sig = Sig 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769 0x69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340Vector6 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556 0x3CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2 bip0340Vector7 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x1FA62E331EDBC21C394792D2AB1100A7B432B013DF3F6FF4F99FCB33E0E1515F 0x28890B3EDB6E7189B630448B515CE4F8622A954CFE545735AAEA5134FCCDB2BD bip0340Vector8 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769 0x961764B3AA9B2FFCB6EF947B6887A226E8D7C93E00C5ED0C1834FF0D0C2E6DA6 bip0340Vector9 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x0000000000000000000000000000000000000000000000000000000000000000 0x123DDA8328AF9C23A94C1FEECFD123BA4FB73476F0D594DCB65C6425BD186051 bip0340Vector10 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x0000000000000000000000000000000000000000000000000000000000000001 0x7615FBAF5AE28864013C099742DEADB4DBA87F11AC6754F93780D5A1837CF197 bip0340Vector11 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D 0x69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340Vector12 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 0x69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340Vector13 = TestVector pk m sig False where pk = PubKey 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 bip0340Vector14 = TestVector pk m sig False where pk = PubKey 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30 m = 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = Sig 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769 0x69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B {- , testCase "vector 1" (assertBool "bip0340_check" $ , testCase "vector 2" (assertBool "bip0340_check" $ , testCase "vector 3" (assertBool "bip0340_check" $ , testCase "vector 4" (assertBool "bip0340_check" $ , testCase "vector 5" (assertBool "not bip0340_check" . not $ , testCase "vector 6" (assertBool "not bip0340_check" . not $ , testCase "vector 7" (assertBool "not bip0340_check" . not $ , testCase "vector 8" (assertBool "not bip0340_check" . not $ , testCase "vector 9" (assertBool "not bip0340_check" . not $ , testCase "vector 10" (assertBool "not bip0340_check" . not $ , testCase "vector 11" (assertBool "not bip0340_check" . not $ , testCase "vector 12" (assertBool "not bip0340_check" . not $ , testCase "vector 13" (assertBool "not bip0340_check" . not $ , testCase "vector 14" (assertBool "not bip0340_check" . not $ ] bip0340_0 = TestVector pk m sig where pk = PubKey 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9 m = 0 sig = Sig 0xE907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0 bip0340_1 :: Bool bip0340_1 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 sig = toWord512 0x6896BD60EEAE296DB48A229FF71DFE071BDE413E6D43F917DC8DCF8C78DE33418906D11AC976ABCCB20B091292BFF4EA897EFCB639EA871CFA95F6DE339E4B0A bip0340_2 :: Bool bip0340_2 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8 m = toWord256 0x7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x5831AAEED7B44BB74E5EAB94BA9D4294C49BCF2A60728D8B4C200F50DD313C1BAB745879A5AD954A72C45A91C3A51D3C7ADEA98D82F8481E0E1E03674A6F3FB7 bip0340_3 :: Bool bip0340_3 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0x25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517 m = toWord256 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF sig = toWord512 0x7EB0509757E246F19449885651611CB965ECC1A187DD51B64FDA1EDC9637D5EC97582B9CB13DB3933705B32BA982AF5AF25FD78881EBB32771FC5922EFC66EA3 bip0340_4 :: Bool bip0340_4 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xD69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9 m = toWord256 0x4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703 sig = toWord512 0x00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C6376AFB1548AF603B3EB45C9F8207DEE1060CB71C04E80F593060B07D28308D7F4 bip0340_5 :: Bool bip0340_5 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xEEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34 m = toWord256 0x243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89 sig = toWord512 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340_6 :: Bool bip0340_6 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2 bip0340_7 :: Bool bip0340_7 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x1FA62E331EDBC21C394792D2AB1100A7B432B013DF3F6FF4F99FCB33E0E1515F28890B3EDB6E7189B630448B515CE4F8622A954CFE545735AAEA5134FCCDB2BD bip0340_8 :: Bool bip0340_8 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769961764B3AA9B2FFCB6EF947B6887A226E8D7C93E00C5ED0C1834FF0D0C2E6DA6 bip0340_9 :: Bool bip0340_9 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x0000000000000000000000000000000000000000000000000000000000000000123DDA8328AF9C23A94C1FEECFD123BA4FB73476F0D594DCB65C6425BD186051 bip0340_10 :: Bool bip0340_10 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x00000000000000000000000000000000000000000000000000000000000000017615FBAF5AE28864013C099742DEADB4DBA87F11AC6754F93780D5A1837CF197 bip0340_11 :: Bool bip0340_11 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340_12 :: Bool bip0340_12 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340_13 :: Bool bip0340_13 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 bip0340_14 :: Bool bip0340_14 = fast_bip0340_check ((pk,m),sig) where pk = toWord256 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30 m = toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C sig = toWord512 0x6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B bip0340_tests :: Bool bip0340_tests = Prelude.and [bip0340_0, bip0340_1, bip0340_2, bip0340_3, bip0340_4] && Prelude.not (Prelude.or [bip0340_5, bip0340_6, bip0340_7, bip0340_8, bip0340_9, bip0340_10, bip0340_11, bip0340_12, bip0340_13, bip0340_14]) -} ================================================ FILE: Haskell/Tests/Simplicity/BitMachine/StaticAnalysis/Tests.hs ================================================ {-# LANGUAGE RankNTypes #-} -- This module tests the static analysis of computation resources used by the Bit Machine by comparing it with the results of dynamic execution by running the Bit Machine on arbitrary inputs. module Simplicity.BitMachine.StaticAnalysis.Tests (tests) where import Control.Monad.Trans.Maybe (runMaybeT) import Control.Monad.Trans.Writer (execWriter) import Data.List (foldl') import Simplicity.BitMachine import Simplicity.BitMachine.Authentic import Simplicity.BitMachine.StaticAnalysis as Analysis import Simplicity.BitMachine.StaticAnalysis.TCO as AnalysisTCO import Simplicity.BitMachine.Translate as Translate import Simplicity.BitMachine.Translate.TCO as TranslateTCO import Simplicity.Programs.Arith import Simplicity.Programs.Example import Simplicity.Programs.Sha256.Lib import Simplicity.Term.Core import qualified Simplicity.Word import Test.Tasty (TestTree, testGroup) import Test.Tasty.QuickCheck ( Gen, Property, Testable , arbitrary, arbitraryBoundedIntegral , property, testProperty , withMaxSuccess ) import Test.Tasty.HUnit (testCase, assert) -- Run the static analysis tests on a small set of Simplicity expressions. tests :: TestTree tests = testGroup "StaticAnalysis" [ testGroup "memSize" [ testSquare "full_add word8" (full_add word8) (arbitrary <×> gen16) , testSquare "add word8" (add word8) gen16 , testSquare "full_multiply word8" (full_multiply word8) gen32 , testSquare "multiply word8" (multiply word8) gen16 , testSquareAdj (withMaxSuccess 10) "hashBlock" hashBlock (gen256 <×> gen512) , testSquareAdj (withMaxSuccess 10) "fib" fib (arbitrary <×> gen32) ] ] where gen16 = (toWord16 . fromIntegral) <$> (arbitraryBoundedIntegral :: Gen Simplicity.Word.Word16) gen32 = (toWord32 . fromIntegral) <$> (arbitraryBoundedIntegral :: Gen Simplicity.Word.Word32) gen256 = (toWord256 . fromIntegral) <$> (arbitraryBoundedIntegral :: Gen Simplicity.Word.Word256) gen512 = gen256 <×> gen256 a <×> b = (,) <$> a <*> b -- For a given program we expect the static analysis of Cell use to bound the dynamic analysis of Cell use for both naive and TCO translation. -- We also expect TCO translation's static and dynamic analysis to be no greater than the same analysis of naive translation. -- Together these two pairs of tests for a square of comparisons that we expect to hold. testSquareAdj :: (TyC a, TyC b) => (forall prop. Testable prop => prop -> Property) -> String -> (forall term. (Delegate term, Assert term) => term a b) -> Gen a -> TestTree testSquareAdj adj name program gen = testProperty name (adj (assertion <$> gen)) where staticMem = Analysis.cellsBnd program staticMemTCO = AnalysisTCO.cellsBnd program dynamicMem i = fromIntegral . memSize . fold . execWriter . runMaybeT $ executeUsing (instrumentMachine . Translate.translate) program i dynamicMemTCO i = fromIntegral . memSize . fold . execWriter . runMaybeT $ executeUsing (instrumentMachine . TranslateTCO.translate) program i square a b c d = a <= b && a <= c && b <=d && c <= d assertion i = square (dynamicMemTCO i) (dynamicMem i) staticMemTCO staticMem fold l = foldl' mappend mempty l testSquare :: (TyC a, TyC b) => String -> (forall term. (Delegate term, Assert term) => term a b) -> Gen a -> TestTree testSquare = testSquareAdj property ================================================ FILE: Haskell/Tests/Simplicity/BitMachine/Tests.hs ================================================ {-# LANGUAGE RankNTypes #-} -- This module tests the Bit Machine evaluation by comparing its results with Simplicity's denotational semantics. module Simplicity.BitMachine.Tests (tests) where import Control.Arrow (runKleisli) import Simplicity.BitMachine import Simplicity.BitMachine.Authentic import Simplicity.BitMachine.Translate as Translate import Simplicity.BitMachine.Translate.TCO as TCO import Simplicity.Delegator import Simplicity.Programs.Sha256.Lib import Simplicity.Term.Core import Simplicity.Programs.Arith import Simplicity.Programs.Example import qualified Simplicity.Word import Test.Tasty (TestTree, testGroup) import Test.Tasty.QuickCheck (Gen, arbitrary, arbitraryBoundedIntegral, testProperty) -- Run tests comparing Bit Machine execution with Simplicity's denotational semantics using both naive and TCO translation. tests :: TestTree tests = testGroup "BitMachine" [ testCompiler "Translate" Translate.translate , testCompiler "TCO" TCO.translate ] -- Given a translator and a Simplicity expression, test that executing using the authentic Bit Machine is equivalent to denoational semantics of the Simplicity expression. testUsing :: (Delegate trans, Assert trans, TyC a, TyC b) => (trans a b -> MachineCode) -> (forall term. (Delegate term, Assert term) => term a b) -> a -> Bool testUsing translator program x = executeUsing (runMachine . translator) program x == (runDelegatorKleisli program x `asTypeOf` Nothing) -- Run the 'testUsing' test with a given translator on a small set of Simplicity expressions. testCompiler :: (Delegate trans, Assert trans) => String -> (forall a b. (TyC a, TyC b) => trans a b -> MachineCode) -> TestTree testCompiler name translator = testGroup name [ testProperty "full_add word8" (testUsing translator (full_add word8) <$> (arbitrary <×> gen16)) , testProperty "add word8" (testUsing translator (add word8) <$> gen16) , testProperty "full_multiply word8" (testUsing translator (full_multiply word8) <$> gen32) , testProperty "multiply word8" (testUsing translator (multiply word8) <$> gen16) , testProperty "hashBlock" (testUsing translator hashBlock <$> (gen256 <×> gen512)) , testProperty "fib" (testUsing translator fib <$> (arbitrary <×> gen32)) ] where gen16 = (toWord16 . fromIntegral) <$> (arbitraryBoundedIntegral :: Gen Simplicity.Word.Word16) gen32 = (toWord32 . fromIntegral) <$> (arbitraryBoundedIntegral :: Gen Simplicity.Word.Word32) gen256 = (toWord256 . fromIntegral) <$> (arbitraryBoundedIntegral :: Gen Simplicity.Word.Word256) gen512 = gen256 <×> gen256 a <×> b = (,) <$> a <*> b ================================================ FILE: Haskell/Tests/Simplicity/Bitcoin/Arbitrary.hs ================================================ -- This module tests the Simplicity programs on arbitrary inputs. module Simplicity.Bitcoin.Arbitrary ( arbitraryHash256, arbitraryLock , genPrimEnv, forallPrimEnv, forallInPrimEnv, forallOutPrimEnv ) where import Data.Bits ((.&.)) import qualified Data.ByteString.Lazy as BSL import Data.Vector (fromList) import Lens.Family2 (review, over) import Simplicity.Arbitrary import Simplicity.Digest import Simplicity.Bitcoin.DataTypes import Simplicity.Bitcoin.Primitive import Simplicity.LibSecp256k1.Spec import Simplicity.Ty.Arbitrary import Simplicity.Word import Test.Tasty.QuickCheck ( Arbitrary(..), Discard(Discard), Gen, Property, Testable , arbitraryBoundedIntegral, arbitrarySizedBoundedIntegral , choose, oneof, listOf, listOf1 , forAll, property ) arbitraryVersion :: Gen Word32 arbitraryVersion = genBoundaryCases 2 arbitraryLock :: Gen Lock arbitraryLock = genBoundaryCases 500000000 arbitraryHash256 :: Gen Hash256 arbitraryHash256 = review (over be256) <$> arbitraryBoundedIntegral arbitraryPoint :: Gen Point arbitraryPoint = pointAsSpec <$> arbitrary arbitraryBS :: Gen BSL.ByteString arbitraryBS = BSL.pack <$> listOf arbitrary instance Arbitrary TxOutput where arbitrary = TxOutput <$> arbitrarySizedBoundedIntegral <*> arbitraryBS instance Arbitrary Outpoint where arbitrary = Outpoint <$> arbitraryHash256 <*> arbitrarySizedBoundedIntegral instance Arbitrary SigTxInput where arbitrary = SigTxInput <$> arbitrary <*> arbitrary <*> oneof [return maxBound, arbitraryBoundedIntegral] <*> oneof [return Nothing, Just <$> arbitraryBS] <*> arbitraryBS instance Arbitrary SigTx where arbitrary = SigTx <$> arbitraryVersion <*> (fromList <$> listOf1 arbitrary) <*> (fromList <$> listOf1 arbitrary) <*> arbitraryLock instance Arbitrary TapEnv where arbitrary = TapEnv <$> ((0xfe .&.) <$> arbitraryBoundedIntegral) <*> (mkPubKey <$> arbitraryPoint) <*> listOf arbitraryHash256 <*> arbitraryHash256 where mkPubKey (Point _ x) = PubKey (fe_pack x) genPrimEnv :: Gen (Maybe PrimEnv) genPrimEnv = do tx <- arbitrary tapenv <- arbitrary ix <- fromIntegral <$> choose (0, length (sigTxIn tx) - 1) return $ primEnv tx ix tapenv forallPrimEnv :: Testable prop => (PrimEnv -> prop) -> Property forallPrimEnv p = forAll genPrimEnv go where go (Just env) = property $ p env go Nothing = property Discard forallInPrimEnv :: Testable prop => (PrimEnv -> Word32 -> prop) -> Property forallInPrimEnv p = forAll genPrimEnv go where go Nothing = property Discard go (Just env) = forAll genIx $ \i -> property $ p env i where genIx = fromIntegral <$> genBoundaryCases (length (sigTxIn (envTx env))) -- Generate out of bounds cases too. forallOutPrimEnv :: Testable prop => (PrimEnv -> Word32 -> prop) -> Property forallOutPrimEnv p = forAll genPrimEnv go where go Nothing = property Discard go (Just env) = forAll genIx $ \i -> property $ p env i where genIx = fromIntegral <$> genBoundaryCases (length (sigTxOut (envTx env))) -- Generate out of bounds cases too. ================================================ FILE: Haskell/Tests/Simplicity/Bitcoin/FFI/Primitive.hs ================================================ {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.Bitcoin.FFI.Primitive ( decodeJetCMR , ErrorCode(..) ) where import Foreign.C.Types (CInt(..)) import Foreign.Ptr (Ptr) import Foreign.Marshal.Unsafe (unsafeLocalState) import Simplicity.Digest import Simplicity.FFI.Bitstream import Simplicity.FFI.Dag data ErrorCode = BitstreamEof | DataOutOfRange deriving (Eq, Show) decodeError :: CInt -> Either ErrorCode () decodeError 0 = Right () decodeError (-2) = Left DataOutOfRange decodeError (-12) = Left BitstreamEof decodeError err = error $ "Simplicity.Bitcoin.FFI.Primitive.decodeError: Unexpected error code " ++ show err foreign import ccall unsafe "" simplicity_bitcoin_decodeJet :: Ptr DagNode -> Ptr Bitstream -> IO CInt decodeJetNode :: Ptr Bitstream -> (Either ErrorCode (Ptr DagNode) -> IO a) -> IO a decodeJetNode pstream k = withDagNode $ \pnode -> do error <- simplicity_bitcoin_decodeJet pnode pstream k (decodeError error >> return pnode) decodeJetCMR :: [Bool] -> Either ErrorCode Hash256 decodeJetCMR codeWord = unsafeLocalState $ initializeBitstream codeWord $ \pstream -> decodeJetNode pstream $ \result -> case result of Left err -> return $ Left err Right pnode -> Right <$> dagNodeGetCMR pnode ================================================ FILE: Haskell/Tests/Simplicity/Bitcoin/FFI/Tests.hs ================================================ module Simplicity.Bitcoin.FFI.Tests (tests) where import Control.Arrow ((***), (+++)) import qualified Data.Map as Map import Data.Maybe (fromMaybe, isJust) import Data.Vector ((!?)) import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit (Assertion, (@?=), testCase) import Test.Tasty.QuickCheck (NonNegative(..), Property, classify, forAll, testProperty) import Lens.Family2 (under, view) import Simplicity.Arbitrary import Simplicity.Digest import Simplicity.Bitcoin.Arbitrary import qualified Simplicity.Bitcoin.DataTypes as Prim import Simplicity.Bitcoin.FFI.Jets import Simplicity.Bitcoin.Jets import qualified Simplicity.Bitcoin.Primitive as Prim import Simplicity.Bitcoin.Semantics import Simplicity.Bitcoin.TestEval import Simplicity.FFI.Jets import qualified Simplicity.Programs.Bitcoin.Lib as Prog import Simplicity.TestCoreEval import Simplicity.Ty.Arbitrary import Simplicity.Ty.Word import qualified Simplicity.Word as Word toW32 :: Word.Word32 -> Word32 toW32 = toWord32 . fromIntegral toW8 :: Word.Word8 -> Word8 toW8 = toWord8 . fromIntegral tests :: TestTree tests = testGroup "Bitcoin" [ testGroup "Jets" [ testProperty "tx_is_final" prop_tx_is_final , testProperty "tx_lock_height" prop_tx_lock_height , testProperty "tx_lock_time" prop_tx_lock_time , testProperty "tx_lock_distance" prop_tx_lock_distance , testProperty "tx_lock_duration" prop_tx_lock_duration , testProperty "check_lock_height" prop_check_lock_height , testProperty "check_lock_time" prop_check_lock_time , testProperty "check_lock_distance" prop_check_lock_distance , testProperty "check_lock_duration" prop_check_lock_duration , testProperty "outpoint_hash" prop_outpoint_hash , testProperty "annex_hash" prop_annex_hash , testProperty "build_tapleaf_simplicity" prop_build_tapleaf_simplicity , testProperty "build_tapbranch" prop_build_tapbranch , testProperty "build_taptweak" prop_build_taptweak , testProperty "output_values_hash" prop_output_values_hash , testProperty "output_scripts_hash" prop_output_scripts_hash , testProperty "outputs_hash" prop_outputs_hash , testProperty "output_hash" prop_output_hash , testProperty "input_outpoints_hash" prop_input_outpoints_hash , testProperty "input_values_hash" prop_input_values_hash , testProperty "input_scripts_hash" prop_input_scripts_hash , testProperty "input_utxos_hash" prop_input_utxos_hash , testProperty "input_utxo_hash" prop_input_utxo_hash , testProperty "input_sequences_hash" prop_input_sequences_hash , testProperty "input_annexes_hash" prop_input_annexes_hash , testProperty "input_script_sigs_hash" prop_input_script_sigs_hash , testProperty "inputs_hash" prop_inputs_hash , testProperty "input_hash" prop_input_hash , testProperty "tx_hash" prop_tx_hash , testProperty "tapleaf_hash" prop_tapleaf_hash , testProperty "tappath_hash" prop_tappath_hash , testProperty "tap_env_hash" prop_tap_env_hash , testProperty "sig_all_hash" prop_sig_all_hash ] , testGroup "Transaction" [ testProperty "script_cmr" prop_script_cmr , testProperty "internal_key" prop_internal_key , testProperty "current_index" prop_current_index , testProperty "num_inputs" prop_num_inputs , testProperty "num_outputs" prop_num_outputs , testProperty "lock_time" prop_lock_time , testProperty "output_value" prop_output_value , testProperty "output_script_hash" prop_output_script_hash , testProperty "total_output_value" prop_total_output_value , testProperty "current_prev_outpoint" prop_current_prev_outpoint , testProperty "current_value" prop_current_value , testProperty "current_script_hash" prop_current_script_hash , testProperty "current_sequence" prop_current_sequence , testProperty "current_annex_hash" prop_current_annex_hash , testProperty "current_script_sig_hash" prop_current_script_sig_hash , testProperty "input_prev_outpoint" prop_input_prev_outpoint , testProperty "input_value" prop_input_value , testProperty "input_script_hash" prop_input_script_hash , testProperty "input_sequence" prop_input_sequence , testProperty "input_annex_hash" prop_input_annex_hash , testProperty "input_script_sig_hash" prop_input_script_sig_hash , testProperty "total_input_value" prop_total_input_value , testProperty "fee" prop_fee , testProperty "tapleaf_version" prop_tapleaf_version , testProperty "tappath" prop_tappath , testProperty "version" prop_version , testProperty "transaction_id" prop_transaction_id ] ] prop_tx_is_final :: Property prop_tx_is_final = forallPrimEnv $ \env -> fast_tx_is_final env () == tx_is_final env () where fast_tx_is_final = testEval (specification (BitcoinJet (TimeLockJet TxIsFinal))) prop_tx_lock_height :: Property prop_tx_lock_height = forallPrimEnv $ \env -> fast_tx_lock_height env () == tx_lock_height env () where fast_tx_lock_height = testEval (specification (BitcoinJet (TimeLockJet TxLockHeight))) prop_tx_lock_time :: Property prop_tx_lock_time = forallPrimEnv $ \env -> fast_tx_lock_time env () == tx_lock_time env () where fast_tx_lock_time = testEval (specification (BitcoinJet (TimeLockJet TxLockTime))) prop_tx_lock_distance :: Property prop_tx_lock_distance = forallPrimEnv $ \env -> fast_tx_lock_distance env () == tx_lock_distance env () where fast_tx_lock_distance = testEval (specification (BitcoinJet (TimeLockJet TxLockDistance))) prop_tx_lock_duration :: Property prop_tx_lock_duration = forallPrimEnv $ \env -> fast_tx_lock_duration env () == tx_lock_duration env () where fast_tx_lock_duration = testEval (specification (BitcoinJet (TimeLockJet TxLockDuration))) prop_check_lock_height :: Word32 -> Property prop_check_lock_height = \w -> forallPrimEnv $ \env -> fast_check_lock_height env w == check_lock_height env w where fast_check_lock_height = testEval (specification (BitcoinJet (TimeLockJet CheckLockHeight))) prop_check_lock_time :: Word32 -> Property prop_check_lock_time = \w -> forallPrimEnv $ \env -> fast_check_lock_time env w == check_lock_time env w where fast_check_lock_time = testEval (specification (BitcoinJet (TimeLockJet CheckLockTime))) prop_check_lock_distance :: Word16 -> Property prop_check_lock_distance = \w -> forallPrimEnv $ \env -> fast_check_lock_distance env w == check_lock_distance env w where fast_check_lock_distance = testEval (specification (BitcoinJet (TimeLockJet CheckLockDistance))) prop_check_lock_duration :: Word16 -> Property prop_check_lock_duration = \w -> forallPrimEnv $ \env -> fast_check_lock_duration env w == check_lock_duration env w where fast_check_lock_duration = testEval (specification (BitcoinJet (TimeLockJet CheckLockDuration))) prop_outpoint_hash :: Sha256CtxElement -> (Word256, Word32) -> Bool prop_outpoint_hash = \ctx op -> let input = (ctxAsTy ctx, op) in outpoint_hash input == fast_outpoint_hash input where fast_outpoint_hash = testCoreEval Prog.outpointHash prop_annex_hash :: Sha256CtxElement -> Maybe Word256 -> Bool prop_annex_hash = \ctx mw256 -> let input = (ctxAsTy ctx, cast mw256) in annex_hash input == fast_annex_hash input where fast_annex_hash = testCoreEval Prog.annexHash cast = maybe (Left ()) Right prop_build_tapleaf_simplicity :: Word256 -> Bool prop_build_tapleaf_simplicity = \w -> build_tapleaf_simplicity w == fast_build_tapleaf_simplicity w where fast_build_tapleaf_simplicity = testCoreEval Prog.buildTapleafSimplicity prop_build_tapbranch :: Word256 -> Word256 -> Bool prop_build_tapbranch = \a b -> build_tapbranch (a, b) == fast_build_tapbranch (a, b) where fast_build_tapbranch = testCoreEval Prog.buildTapbranch prop_build_taptweak :: FieldElement -> Word256 -> Bool prop_build_taptweak = \a b -> let input = (feAsTy a, b) in build_taptweak input == fast_build_taptweak input where fast_build_taptweak = testCoreEval Prog.buildTaptweak prop_output_values_hash :: Property prop_output_values_hash = forallPrimEnv $ \env -> fast_output_values_hash env () == output_values_hash env () where fast_output_values_hash = testEval (specification (BitcoinJet (SigHashJet OutputValuesHash))) prop_output_scripts_hash :: Property prop_output_scripts_hash = forallPrimEnv $ \env -> fast_output_scripts_hash env () == output_scripts_hash env () where fast_output_scripts_hash = testEval (specification (BitcoinJet (SigHashJet OutputScriptsHash))) prop_outputs_hash :: Property prop_outputs_hash = forallPrimEnv $ \env -> fast_outputs_hash env () == outputs_hash env () where fast_outputs_hash = testEval (specification (BitcoinJet (SigHashJet OutputsHash))) prop_output_hash :: Property prop_output_hash = forallOutPrimEnv $ \env i -> fast_output_hash env (toW32 i) == output_hash env (toW32 i) where fast_output_hash = testEval (specification (BitcoinJet (SigHashJet OutputHash))) prop_input_outpoints_hash :: Property prop_input_outpoints_hash = forallPrimEnv $ \env -> fast_input_outpoints_hash env () == input_outpoints_hash env () where fast_input_outpoints_hash = testEval (specification (BitcoinJet (SigHashJet InputOutpointsHash))) prop_input_values_hash :: Property prop_input_values_hash = forallPrimEnv $ \env -> fast_input_values_hash env () == input_values_hash env () where fast_input_values_hash = testEval (specification (BitcoinJet (SigHashJet InputValuesHash))) prop_input_scripts_hash :: Property prop_input_scripts_hash = forallPrimEnv $ \env -> fast_input_scripts_hash env () == input_scripts_hash env () where fast_input_scripts_hash = testEval (specification (BitcoinJet (SigHashJet InputScriptsHash))) prop_input_utxos_hash :: Property prop_input_utxos_hash = forallPrimEnv $ \env -> fast_input_utxos_hash env () == input_utxos_hash env () where fast_input_utxos_hash = testEval (specification (BitcoinJet (SigHashJet InputUtxosHash))) prop_input_utxo_hash :: Property prop_input_utxo_hash = forallInPrimEnv $ \env i -> fast_input_utxo_hash env (toW32 i) == input_utxo_hash env (toW32 i) where fast_input_utxo_hash = testEval (specification (BitcoinJet (SigHashJet InputUtxoHash))) prop_input_sequences_hash :: Property prop_input_sequences_hash = forallPrimEnv $ \env -> fast_input_sequences_hash env () == input_sequences_hash env () where fast_input_sequences_hash = testEval (specification (BitcoinJet (SigHashJet InputSequencesHash))) prop_input_annexes_hash :: Property prop_input_annexes_hash = forallPrimEnv $ \env -> fast_input_annexes_hash env () == input_annexes_hash env () where fast_input_annexes_hash = testEval (specification (BitcoinJet (SigHashJet InputAnnexesHash))) prop_input_script_sigs_hash :: Property prop_input_script_sigs_hash = forallPrimEnv $ \env -> fast_input_script_sigs_hash env () == input_script_sigs_hash env () where fast_input_script_sigs_hash = testEval (specification (BitcoinJet (SigHashJet InputScriptSigsHash))) prop_inputs_hash :: Property prop_inputs_hash = forallPrimEnv $ \env -> fast_inputs_hash env () == inputs_hash env () where fast_inputs_hash = testEval (specification (BitcoinJet (SigHashJet InputsHash))) prop_input_hash :: Property prop_input_hash = forallInPrimEnv $ \env i -> fast_input_hash env (toW32 i) == input_hash env (toW32 i) where fast_input_hash = testEval (specification (BitcoinJet (SigHashJet InputHash))) prop_tx_hash :: Property prop_tx_hash = forallPrimEnv $ \env -> fast_tx_hash env () == tx_hash env () where fast_tx_hash = testEval (specification (BitcoinJet (SigHashJet TxHash))) prop_tapleaf_hash :: Property prop_tapleaf_hash = forallPrimEnv $ \env -> fast_tapleaf_hash env () == tapleaf_hash env () where fast_tapleaf_hash = testEval (specification (BitcoinJet (SigHashJet TapleafHash))) prop_tappath_hash :: Property prop_tappath_hash = forallPrimEnv $ \env -> fast_tappath_hash env () == tappath_hash env () where fast_tappath_hash = testEval (specification (BitcoinJet (SigHashJet TappathHash))) prop_tap_env_hash :: Property prop_tap_env_hash = forallPrimEnv $ \env -> fast_tap_env_hash env () == tap_env_hash env () where fast_tap_env_hash = testEval (specification (BitcoinJet (SigHashJet TapEnvHash))) prop_sig_all_hash :: Property prop_sig_all_hash = forallPrimEnv $ \env -> fast_sig_all_hash env () == sig_all_hash env () where fast_sig_all_hash = testEval (specification (BitcoinJet (SigHashJet SigAllHash))) prop_script_cmr :: Property prop_script_cmr = forallPrimEnv $ \env -> fast_script_cmr env () == script_cmr env () where fast_script_cmr = testEval (specification (BitcoinJet (TransactionJet ScriptCMR))) prop_internal_key :: Property prop_internal_key = forallPrimEnv $ \env -> fast_internal_key env () == internal_key env () where fast_internal_key = testEval (specification (BitcoinJet (TransactionJet InternalKey))) prop_current_index :: Property prop_current_index = forallPrimEnv $ \env -> fast_current_index env () == current_index env () where fast_current_index = testEval (specification (BitcoinJet (TransactionJet CurrentIndex))) prop_num_inputs :: Property prop_num_inputs = forallPrimEnv $ \env -> fast_num_inputs env () == num_inputs env () where fast_num_inputs = testEval (specification (BitcoinJet (TransactionJet NumInputs))) prop_num_outputs :: Property prop_num_outputs = forallPrimEnv $ \env -> fast_num_outputs env () == num_outputs env () where fast_num_outputs = testEval (specification (BitcoinJet (TransactionJet NumOutputs))) prop_lock_time :: Property prop_lock_time = forallPrimEnv $ \env -> fast_lock_time env () == lock_time env () where fast_lock_time = testEval (specification (BitcoinJet (TransactionJet LockTime))) prop_output_value :: Property prop_output_value = forallOutPrimEnv $ \env i -> fast_output_value env (toW32 i) == output_value env (toW32 i) where fast_output_value = testEval (specification (BitcoinJet (TransactionJet OutputValue))) prop_output_script_hash :: Property prop_output_script_hash = forallOutPrimEnv $ \env i -> fast_output_script_hash env (toW32 i) == output_script_hash env (toW32 i) where fast_output_script_hash = testEval (specification (BitcoinJet (TransactionJet OutputScriptHash))) prop_total_output_value :: Property prop_total_output_value = forallPrimEnv $ \env -> fast_total_output_value env () == total_output_value env () where fast_total_output_value = testEval (specification (BitcoinJet (TransactionJet TotalOutputValue))) prop_current_prev_outpoint :: Property prop_current_prev_outpoint = forallPrimEnv $ \env -> fast_current_prev_outpoint env () == current_prev_outpoint env () where fast_current_prev_outpoint = testEval (specification (BitcoinJet (TransactionJet CurrentPrevOutpoint))) prop_current_value :: Property prop_current_value = forallPrimEnv $ \env -> fast_current_value env () == current_value env () where fast_current_value = testEval (specification (BitcoinJet (TransactionJet CurrentValue))) prop_current_script_hash :: Property prop_current_script_hash = forallPrimEnv $ \env -> fast_current_script_hash env () == current_script_hash env () where fast_current_script_hash = testEval (specification (BitcoinJet (TransactionJet CurrentScriptHash))) prop_current_sequence :: Property prop_current_sequence = forallPrimEnv $ \env -> fast_current_sequence env () == current_sequence env () where fast_current_sequence = testEval (specification (BitcoinJet (TransactionJet CurrentSequence))) prop_current_annex_hash :: Property prop_current_annex_hash = forallPrimEnv $ \env -> fast_current_annex_hash env () == current_annex_hash env () where fast_current_annex_hash = testEval (specification (BitcoinJet (TransactionJet CurrentAnnexHash))) prop_current_script_sig_hash :: Property prop_current_script_sig_hash = forallPrimEnv $ \env -> fast_current_script_sig_hash env () == current_script_sig_hash env () where fast_current_script_sig_hash = testEval (specification (BitcoinJet (TransactionJet CurrentScriptSigHash))) prop_input_prev_outpoint :: Property prop_input_prev_outpoint = forallInPrimEnv $ \env i -> fast_input_prev_outpoint env (toW32 i) == input_prev_outpoint env (toW32 i) where fast_input_prev_outpoint = testEval (specification (BitcoinJet (TransactionJet InputPrevOutpoint))) prop_input_value :: Property prop_input_value = forallInPrimEnv $ \env i -> fast_input_value env (toW32 i) == input_value env (toW32 i) where fast_input_value = testEval (specification (BitcoinJet (TransactionJet InputValue))) prop_input_script_hash :: Property prop_input_script_hash = forallInPrimEnv $ \env i -> fast_input_script_hash env (toW32 i) == input_script_hash env (toW32 i) where fast_input_script_hash = testEval (specification (BitcoinJet (TransactionJet InputScriptHash))) prop_input_sequence :: Property prop_input_sequence = forallInPrimEnv $ \env i -> fast_input_sequence env (toW32 i) == input_sequence env (toW32 i) where fast_input_sequence = testEval (specification (BitcoinJet (TransactionJet InputSequence))) prop_input_annex_hash :: Property prop_input_annex_hash = forallInPrimEnv $ \env i -> fast_input_annex_hash env (toW32 i) == input_annex_hash env (toW32 i) where fast_input_annex_hash = testEval (specification (BitcoinJet (TransactionJet InputAnnexHash))) prop_input_script_sig_hash :: Property prop_input_script_sig_hash = forallInPrimEnv $ \env i -> fast_input_script_sig_hash env (toW32 i) == input_script_sig_hash env (toW32 i) where fast_input_script_sig_hash = testEval (specification (BitcoinJet (TransactionJet InputScriptSigHash))) prop_total_input_value :: Property prop_total_input_value = forallPrimEnv $ \env -> fast_total_input_value env () == total_input_value env () where fast_total_input_value = testEval (specification (BitcoinJet (TransactionJet TotalInputValue))) prop_fee :: Property prop_fee = forallPrimEnv $ \env -> fast_fee env () == fee env () where fast_fee = testEval (specification (BitcoinJet (TransactionJet Fee))) prop_tapleaf_version :: Property prop_tapleaf_version = forallPrimEnv $ \env -> fast_tapleaf_version env () == tapleaf_version env () where fast_tapleaf_version = testEval (specification (BitcoinJet (TransactionJet TapleafVersion))) prop_tappath :: Property prop_tappath = forallPrimEnv $ \env -> forAll (genTappathIx env) $ \i -> fast_tappath env (toW8 i) == tappath env (toW8 i) where fast_tappath = testEval (specification (BitcoinJet (TransactionJet Tappath))) genTappathIx = genBoundaryCases . fromIntegral . length . Prim.tappath . Prim.envTap prop_version :: Property prop_version = forallPrimEnv $ \env -> fast_version env () == version env () where fast_version = testEval (specification (BitcoinJet (TransactionJet Version))) prop_transaction_id :: Property prop_transaction_id = forallPrimEnv $ \env -> fast_transaction_id env () == transaction_id env () where fast_transaction_id = testEval (specification (BitcoinJet (TransactionJet TransactionId))) ================================================ FILE: Haskell/Tests/Simplicity/Bitcoin/Serialization/Tests.hs ================================================ -- This module tests some serialization functionality. module Simplicity.Bitcoin.Serialization.Tests (tests) where import Control.Monad (mzero) import Data.Foldable (toList) import qualified Data.List as List import qualified Data.Vector.Unboxed as V import Simplicity.Arbitrary import Simplicity.CoreJets import Simplicity.Bitcoin.Jets as Bitcoin import Simplicity.Bitcoin.FFI.Primitive as Bitcoin import Simplicity.FFI.Dag import Simplicity.MerkleRoot import Simplicity.Serialization import Simplicity.Ty import Simplicity.Ty.Word import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit ((@=?), testCase) import Test.Tasty.QuickCheck (Property, arbitrary, forAll, chooseInt, testProperty, vectorOf) -- Run tests comparing Bit Machine execution with Simplicity's denotational semantics using both naive and TCO translation. tests :: TestTree tests = testGroup "Bitcoin Serialization" [ testGroup "Haskell" [ testDecodeBitcoinJet jt | SomeArrow jt@(Bitcoin.BitcoinJet _) <- toList Bitcoin.jetMap ] , testGroup "C" $ [ testDecodeBitcoinJetFFI jt | SomeArrow jt <- toList Bitcoin.jetMap ] ++ [ testProperty "prop_wordCMR" prop_wordCMR ] ] testDecodeBitcoinJet :: (TyC a, TyC b) => Bitcoin.JetType a b -> TestTree testDecodeBitcoinJet jt = testCase (show jt) (Just (SomeArrow jt) @=? decode) where vector = V.fromList $ Bitcoin.putJetBit jt [] decode = evalExactVector (Bitcoin.getJetBit mzero) vector testDecodeBitcoinJetFFI :: (TyC a, TyC b) => Bitcoin.JetType a b -> TestTree testDecodeBitcoinJetFFI jt = testCase (show jt) (Right cmr @=? Bitcoin.decodeJetCMR bitstream) where -- All jet encodings should begin with a 1 bit, which we consume. True:bitstream = Bitcoin.putJetBit jt [] cmr = commitmentRoot (asJet jt) prop_wordCMR :: SomeConstWordContent -> Property prop_wordCMR (SomeConstWordContent cwc) = forAll prefix prop where prefix = do n <- chooseInt (0, 7) vectorOf n arbitrary prop l = wordCMR == computeWordCMR (length l) (l ++ stream) where wordCMR = commitmentRoot $ asJet (ConstWordJet cwc) stream = putConstWordValueBit cwc ================================================ FILE: Haskell/Tests/Simplicity/Bitcoin/TestEval.hs ================================================ -- | This module builds a wrapper around 'Simplicity.Bitcoin.Semantics.fastEval' to define a 'testEval' variant. module Simplicity.Bitcoin.TestEval ( testEval, TestEval ) where import Prelude hiding (drop, take, fail) import Control.Arrow (Kleisli(..), first) import Control.Monad.Reader (ReaderT(..)) import qualified Simplicity.Bitcoin.Jets as Jets import Simplicity.Bitcoin.JetType import Simplicity.Bitcoin.Primitive import Simplicity.Bitcoin.Semantics import Simplicity.Bitcoin.Term -- | An Assert instance for 'testCoreEval'. data TestEval jt a b = TestEval { testEvalSem :: Kleisli (ReaderT PrimEnv Maybe) a b , testEvalFast :: FastEval jt a b } -- | 'testEval' optimizes Simplicity with assertions evaluation using jets, similar to 'fastEval', -- but excludes the expression itself from being substituted. -- This is used in for testing jets against their specifications under the assumption that jets for any subexpressions are correct. -- Delegation, witnesses, and jets are not supported since they are not allowed within jet definitions. testEval :: TestEval Jets.JetType a b -> PrimEnv -> a -> Maybe b testEval = flip . (runReaderT .) . runKleisli . testEvalSem testFastKleisli = Kleisli . (ReaderT .) . flip . fastEval . testEvalFast mkLeaf sComb fComb = TestEval sComb fComb mkUnary sComb fComb t = TestEval (sComb (testFastKleisli t)) (fComb (testEvalFast t)) mkBinary sComb fComb s t = TestEval (sComb (testFastKleisli s) (testFastKleisli t)) (fComb (testEvalFast s) (testEvalFast t)) instance JetType jt => Core (TestEval jt) where iden = mkLeaf iden iden comp = mkBinary comp comp unit = mkLeaf unit unit injl = mkUnary injl injl injr = mkUnary injr injr match = mkBinary match match pair = mkBinary pair pair take = mkUnary take take drop = mkUnary drop drop instance JetType jt => Assert (TestEval jt) where assertl s h = mkUnary (flip assertl h) (flip assertl h) s assertr h t = mkUnary (assertr h) (assertr h) t fail b = mkLeaf (fail b) (fail b) instance JetType jt => Primitive (TestEval jt) where primitive p = mkLeaf (primitive p) (primitive p) ================================================ FILE: Haskell/Tests/Simplicity/Bitcoin/Tests.hs ================================================ module Simplicity.Bitcoin.Tests (tests) where import Control.Arrow ((***), (+++)) import qualified Data.ByteString.Char8 as BSC import qualified Data.ByteString.Lazy as BSL import qualified Data.Map as Map import Data.Maybe (fromMaybe, fromJust, isJust) import Data.Serialize (encode, put, putWord8, putWord32be, runPutLazy) import Data.Vector ((!), (!?), fromList) import Lens.Family2 (review, over, under, view) import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit (Assertion, (@?=), assertBool, testCase) import Test.Tasty.QuickCheck (Property, NonNegative(..), arbitrary, classify, forAll, testProperty) import Simplicity.Arbitrary import Simplicity.Digest import Simplicity.Bitcoin.Arbitrary import Simplicity.Bitcoin.DataTypes import Simplicity.Bitcoin.Jets import Simplicity.Bitcoin.Term import Simplicity.Bitcoin.TestEval import Simplicity.Bitcoin.Primitive (primEnv, primEnvHash, envTx, envTap) import qualified Simplicity.Bitcoin.Programs.TimeLock as Prog import Simplicity.Bitcoin.Semantics import qualified Simplicity.LibSecp256k1.Spec as Schnorr import Simplicity.MerkleRoot import Simplicity.Programs.CheckSig.Lib import qualified Simplicity.Programs.Sha256 as Sha256 import qualified Simplicity.Programs.Bitcoin.Lib as Prog import qualified Simplicity.Bitcoin.Programs.SigHash.Lib as Prog import Simplicity.TestCoreEval import Simplicity.Ty.Arbitrary import Simplicity.Ty.Word import qualified Simplicity.Word as Word toW32 :: Word.Word32 -> Word32 toW32 = toWord32 . fromIntegral toW16 :: Word.Word16 -> Word16 toW16 = toWord16 . fromIntegral toW8 :: Word.Word8 -> Word8 toW8 = toWord8 . fromIntegral tests :: TestTree tests = testGroup "Bitcoin" [ -- Regression.tests testGroup "TimeLock" [ testProperty "tx_is_final" prop_tx_is_final , testProperty "tx_lock_height" prop_tx_lock_height , testProperty "tx_lock_time" prop_tx_lock_time , testProperty "tx_lock_distance" prop_tx_lock_distance , testProperty "tx_lock_duration" prop_tx_lock_duration , testProperty "check_lock_height" prop_check_lock_height , testProperty "check_lock_time" prop_check_lock_time , testProperty "check_lock_distance" prop_check_lock_distance , testProperty "check_lock_duration" prop_check_lock_duration ] , testGroup "Bitcoin Functions" [ testProperty "outpoint_hash" prop_outpoint_hash , testProperty "annex_hash" prop_annex_hash , testProperty "build_tapleaf_simplicity" prop_build_tapleaf_simplicity , testProperty "build_tapbranch" prop_build_tapbranch , testProperty "build_taptweak" prop_build_taptweak , testProperty "output_values_hash" prop_output_values_hash , testProperty "output_scripts_hash" prop_output_scripts_hash , testProperty "outputs_hash" prop_outputs_hash , testProperty "output_hash" prop_output_hash , testProperty "input_outpoints_hash" prop_input_outpoints_hash , testProperty "input_values_hash" prop_input_values_hash , testProperty "input_scripts_hash" prop_input_scripts_hash , testProperty "input_utxos_hash" prop_input_utxos_hash , testProperty "input_utxo_hash" prop_input_utxo_hash , testProperty "input_sequences_hash" prop_input_sequences_hash , testProperty "input_annexes_hash" prop_input_annexes_hash , testProperty "input_script_sigs_hash" prop_input_script_sigs_hash , testProperty "inputs_hash" prop_inputs_hash , testProperty "input_hash" prop_input_hash , testProperty "tx_hash" prop_tx_hash , testProperty "tap_env_hash" prop_tap_env_hash , testProperty "tappath_hash" prop_tappath_hash , testProperty "tapleaf_hash" prop_tapleaf_hash , testProperty "sig_all_hash" prop_sig_all_hash , testProperty "script_cmr" prop_script_cmr , testProperty "internal_key" prop_internal_key , testProperty "current_index" prop_current_index , testProperty "num_inputs" prop_num_inputs , testProperty "num_outputs" prop_num_outputs , testProperty "lock_time" prop_lock_time , testProperty "output_value" prop_output_value , testProperty "output_script_hash" prop_output_script_hash , testProperty "total_output_value" prop_total_output_value , testProperty "current_prev_outpoint" prop_current_prev_outpoint , testProperty "current_value" prop_current_value , testProperty "current_script_hash" prop_current_script_hash , testProperty "current_sequence" prop_current_sequence , testProperty "current_annex_hash" prop_current_annex_hash , testProperty "current_script_sig_hash" prop_current_script_sig_hash , testProperty "input_prev_outpoint" prop_input_prev_outpoint , testProperty "input_value" prop_input_value , testProperty "input_script_hash" prop_input_script_hash , testProperty "input_sequence" prop_input_sequence , testProperty "input_annex_hash" prop_input_annex_hash , testProperty "input_script_sig_hash" prop_input_script_sig_hash , testProperty "total_input_value" prop_total_input_value , testProperty "fee" prop_fee , testProperty "tapleaf_version" prop_tapleaf_version , testProperty "tappath" prop_tappath , testProperty "version" prop_version , testProperty "transaction_id" prop_transaction_id ] , testCase "sigHashAll" (assertBool "sigHashAll_matches" hunit_sigHashAll) ] -- We use continuations here because we need to ensure that 'fastSpec' is memoized outside of any lambda expressions. checkJet jet k = k (\env a -> fastSpec env a == implementation jet env a) where fastSpec = testEval (specification jet) prop_tx_is_final :: Property prop_tx_is_final = checkJet (BitcoinJet (TimeLockJet TxIsFinal)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_height :: Property prop_tx_lock_height = checkJet (BitcoinJet (TimeLockJet TxLockHeight)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_time :: Property prop_tx_lock_time = checkJet (BitcoinJet (TimeLockJet TxLockTime)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_distance :: Property prop_tx_lock_distance = checkJet (BitcoinJet (TimeLockJet TxLockDistance)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_duration :: Property prop_tx_lock_duration = checkJet (BitcoinJet (TimeLockJet TxLockDuration)) $ \check -> forallPrimEnv $ \env -> check env () prop_check_lock_height :: Property prop_check_lock_height = checkJet (BitcoinJet (TimeLockJet CheckLockHeight)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . sigTxLock $ envTx env) $ \w -> check env (toW32 w) prop_check_lock_time :: Property prop_check_lock_time = checkJet (BitcoinJet (TimeLockJet CheckLockTime)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . sigTxLock $ envTx env) $ \w -> check env (toW32 w) prop_check_lock_distance :: Property prop_check_lock_distance = checkJet (BitcoinJet (TimeLockJet CheckLockDistance)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . txLockDistance $ env) $ \w -> check env (toW16 w) where txLockDistance env = fromIntegral . fromWord16 . fromJust $ implementation (BitcoinJet (TimeLockJet TxLockDistance)) env () :: Word.Word16 prop_check_lock_duration :: Property prop_check_lock_duration = checkJet (BitcoinJet (TimeLockJet CheckLockDuration)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . txLockDuration $ env) $ \w -> check env (toW16 w) where txLockDuration env = fromIntegral . fromWord16 . fromJust $ implementation (BitcoinJet (TimeLockJet TxLockDuration)) env () :: Word.Word16 prop_build_tapleaf_simplicity :: HashElement -> Bool prop_build_tapleaf_simplicity = \cmr -> let input = heAsTy cmr in fast_build_tapleaf_simplicity input == implementation (BitcoinJet (SigHashJet BuildTapleafSimplicity)) undefined input where fast_build_tapleaf_simplicity = testCoreEval Prog.buildTapleafSimplicity prop_build_tapbranch :: HashElement -> HashElement -> Bool prop_build_tapbranch = \a b -> let input = (heAsTy a, heAsTy b) in fast_build_tapbranch input == implementation (BitcoinJet (SigHashJet BuildTapbranch)) undefined input where fast_build_tapbranch = testCoreEval Prog.buildTapbranch prop_build_taptweak :: FieldElement -> HashElement -> Bool prop_build_taptweak = \a b -> let input = (feAsTy a, heAsTy b) in fast_build_taptweak input == implementation (BitcoinJet (SigHashJet BuildTaptweak)) undefined input where fast_build_taptweak = testCoreEval Prog.buildTaptweak prop_outpoint_hash :: Sha256CtxElement -> (HashElement, Word.Word32) -> Bool prop_outpoint_hash = \ctx op -> let input = (ctxAsTy ctx, (heAsTy *** (toWord32 . fromIntegral) $ op)) in fast_outpoint_hash input == implementation (BitcoinJet (SigHashJet OutpointHash)) undefined input where fast_outpoint_hash = testCoreEval Prog.outpointHash prop_annex_hash :: Sha256CtxElement -> Maybe Word256 -> Bool prop_annex_hash = \ctx mw256 -> let input = (ctxAsTy ctx, cast mw256) in fast_annex_hash input == implementation (BitcoinJet (SigHashJet AnnexHash)) undefined input where fast_annex_hash = testCoreEval Prog.annexHash cast = maybe (Left ()) Right prop_output_values_hash :: Property prop_output_values_hash = checkJet (BitcoinJet (SigHashJet OutputValuesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_scripts_hash :: Property prop_output_scripts_hash = checkJet (BitcoinJet (SigHashJet OutputScriptsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_outputs_hash :: Property prop_outputs_hash = checkJet (BitcoinJet (SigHashJet OutputsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_hash :: Property prop_output_hash = checkJet (BitcoinJet (SigHashJet OutputHash)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_input_outpoints_hash :: Property prop_input_outpoints_hash = checkJet (BitcoinJet (SigHashJet InputOutpointsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_values_hash :: Property prop_input_values_hash = checkJet (BitcoinJet (SigHashJet InputValuesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_scripts_hash :: Property prop_input_scripts_hash = checkJet (BitcoinJet (SigHashJet InputScriptsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_utxos_hash :: Property prop_input_utxos_hash = checkJet (BitcoinJet (SigHashJet InputUtxosHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_utxo_hash :: Property prop_input_utxo_hash = checkJet (BitcoinJet (SigHashJet InputUtxoHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_sequences_hash :: Property prop_input_sequences_hash = checkJet (BitcoinJet (SigHashJet InputSequencesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_annexes_hash :: Property prop_input_annexes_hash = checkJet (BitcoinJet (SigHashJet InputAnnexesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_script_sigs_hash :: Property prop_input_script_sigs_hash = checkJet (BitcoinJet (SigHashJet InputScriptSigsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_inputs_hash :: Property prop_inputs_hash = checkJet (BitcoinJet (SigHashJet InputsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_hash :: Property prop_input_hash = checkJet (BitcoinJet (SigHashJet InputHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_tx_hash :: Property prop_tx_hash = checkJet (BitcoinJet (SigHashJet TxHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_tappath_hash :: Property prop_tappath_hash = checkJet (BitcoinJet (SigHashJet TappathHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_tapleaf_hash :: Property prop_tapleaf_hash = checkJet (BitcoinJet (SigHashJet TapleafHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_tap_env_hash :: Property prop_tap_env_hash = checkJet (BitcoinJet (SigHashJet TapEnvHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_sig_all_hash :: Property prop_sig_all_hash = checkJet (BitcoinJet (SigHashJet SigAllHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_script_cmr :: Property prop_script_cmr = checkJet (BitcoinJet (TransactionJet ScriptCMR)) $ \check -> forallPrimEnv $ \env -> check env () prop_internal_key :: Property prop_internal_key = checkJet (BitcoinJet (TransactionJet InternalKey)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_index :: Property prop_current_index = checkJet (BitcoinJet (TransactionJet CurrentIndex)) $ \check -> forallPrimEnv $ \env -> check env () prop_num_inputs :: Property prop_num_inputs = checkJet (BitcoinJet (TransactionJet NumInputs)) $ \check -> forallPrimEnv $ \env -> check env () prop_num_outputs :: Property prop_num_outputs = checkJet (BitcoinJet (TransactionJet NumOutputs)) $ \check -> forallPrimEnv $ \env -> check env () prop_lock_time :: Property prop_lock_time = checkJet (BitcoinJet (TransactionJet LockTime)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_value :: Property prop_output_value = checkJet (BitcoinJet (TransactionJet OutputValue)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_output_script_hash :: Property prop_output_script_hash = checkJet (BitcoinJet (TransactionJet OutputScriptHash)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_total_output_value :: Property prop_total_output_value = checkJet (BitcoinJet (TransactionJet TotalOutputValue)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_prev_outpoint :: Property prop_current_prev_outpoint = checkJet (BitcoinJet (TransactionJet CurrentPrevOutpoint)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_value :: Property prop_current_value = checkJet (BitcoinJet (TransactionJet CurrentValue)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_script_hash :: Property prop_current_script_hash = checkJet (BitcoinJet (TransactionJet CurrentScriptHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_sequence :: Property prop_current_sequence = checkJet (BitcoinJet (TransactionJet CurrentSequence)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_annex_hash :: Property prop_current_annex_hash = checkJet (BitcoinJet (TransactionJet CurrentAnnexHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_script_sig_hash :: Property prop_current_script_sig_hash = checkJet (BitcoinJet (TransactionJet CurrentScriptSigHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_prev_outpoint :: Property prop_input_prev_outpoint = checkJet (BitcoinJet (TransactionJet InputPrevOutpoint)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_value :: Property prop_input_value = checkJet (BitcoinJet (TransactionJet InputValue)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_script_hash :: Property prop_input_script_hash = checkJet (BitcoinJet (TransactionJet InputScriptHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_sequence :: Property prop_input_sequence = checkJet (BitcoinJet (TransactionJet InputSequence)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_annex_hash :: Property prop_input_annex_hash = checkJet (BitcoinJet (TransactionJet InputAnnexHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_script_sig_hash :: Property prop_input_script_sig_hash = checkJet (BitcoinJet (TransactionJet InputScriptSigHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_total_input_value :: Property prop_total_input_value = checkJet (BitcoinJet (TransactionJet TotalInputValue)) $ \check -> forallPrimEnv $ \env -> check env () prop_fee :: Property prop_fee = checkJet (BitcoinJet (TransactionJet Fee)) $ \check -> forallPrimEnv $ \env -> check env () prop_tapleaf_version :: Property prop_tapleaf_version = checkJet (BitcoinJet (TransactionJet TapleafVersion)) $ \check -> forallPrimEnv $ \env -> check env () prop_tappath :: Property prop_tappath = checkJet (BitcoinJet (TransactionJet Tappath)) $ \check -> forallPrimEnv $ \env -> forAll (genTappathIx env) $ \i -> check env (toW8 i) where genTappathIx = genBoundaryCases . fromIntegral . length . tappath . envTap prop_version :: Property prop_version = checkJet (BitcoinJet (TransactionJet Version)) $ \check -> forallPrimEnv $ \env -> check env () prop_transaction_id :: Property prop_transaction_id = checkJet (BitcoinJet (TransactionJet TransactionId)) $ \check -> forallPrimEnv $ \env -> check env () tapEnv :: TapEnv tapEnv = TapEnv { tapleafVersion = 0xbe , tapInternalKey = Schnorr.PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 , tappath = [] , tapScriptCMR = review (over be256) 0x896b16e4692350cb43c4807c8f9f63637f70f84a17b678ca9467109ff1e50f61 } tx1 :: SigTx tx1 = SigTx { sigTxVersion = 0x00000002 , sigTxIn = fromList [input0] , sigTxOut = fromList [output0] , sigTxLock = 0 } where input0 = SigTxInput { sigTxiPreviousOutpoint = Outpoint (review (over be256) 0xeb04b68e9a26d116046c76e8ff47332fb71dda90ff4bef5370f25226d3bc09fc) 0 , sigTxiTxo = TxOutput { txoValue = 10000000000 , txoScript = BSL.empty } , sigTxiSequence = 0xfffffffe , sigTxiAnnex = Nothing , sigTxiScriptSig = BSL.empty } output0 = TxOutput { txoValue = 9999996700 , txoScript = BSL.pack [ 0x19, 0x76, 0xa9, 0x14, 0x48, 0x63, 0x3e, 0x2c, 0x0e, 0xe9, 0x49, 0x5d, 0xd3, 0xf9, 0xc4, 0x37 , 0x32, 0xc4, 0x7f, 0x47, 0x02, 0xa3, 0x62, 0xc8, 0x88, 0xac] } hunit_sigHashAll :: Bool hunit_sigHashAll = Just (integerHash256 sigHashAll_spec) == (fromWord256 <$> (sem (sigHash' Prog.sigAllHash) txEnv ())) where ix = 0 txo = sigTxiTxo (sigTxIn tx1 ! (fromIntegral ix)) Just txEnv = primEnv tx1 ix tapEnv signatureTag = bsHash $ BSC.pack "Simplicity\USSignature" sigHashAll_spec = bslHash . runPutLazy $ put signatureTag >> put signatureTag >> put (commitmentRoot Prog.sigAllHash) >> put (primEnvHash txEnv) ================================================ FILE: Haskell/Tests/Simplicity/Elements/Arbitrary.hs ================================================ -- This module tests the Simplicity programs on arbitrary inputs. module Simplicity.Elements.Arbitrary ( arbitraryHash256, arbitraryLock , genPrimEnv, forallPrimEnv, forallInPrimEnv, forallOutPrimEnv ) where import Data.Bits ((.&.)) import qualified Data.ByteString.Char8 as BSC import qualified Data.ByteString.Lazy as BSL import Data.Serialize.Put (runPutLazy, putWord8, putWord16le, putWord32le, putLazyByteString) import Data.Vector (fromList) import Lens.Family2 (review, over) import Simplicity.Arbitrary import Simplicity.Digest import Simplicity.Elements.DataTypes import Simplicity.Elements.Primitive import Simplicity.LibSecp256k1.Schnorr import Simplicity.LibSecp256k1.Spec import Simplicity.Ty.Arbitrary import Simplicity.Word import Test.Tasty.QuickCheck ( Arbitrary(..), Discard(Discard), Gen, Property, Testable , arbitraryBoundedIntegral, arbitrarySizedBoundedIntegral , choose, elements, frequency, oneof, listOf, listOf1, suchThat , forAll, property ) nonZeroAmount :: AmountWith prf -> Bool nonZeroAmount (Amount (Explicit 0)) = False nonZeroAmount _ = True arbitraryVersion :: Gen Word32 arbitraryVersion = genBoundaryCases 2 arbitraryLock :: Gen Lock arbitraryLock = genBoundaryCases 500000000 arbitraryHash256 :: Gen Hash256 arbitraryHash256 = review (over be256) <$> arbitraryBoundedIntegral arbitraryPoint :: Gen Point arbitraryPoint = pointAsSpec <$> arbitrary arbitraryBS :: Gen BSL.ByteString arbitraryBS = BSL.pack <$> listOf arbitrary arbitraryNullData :: Gen BSL.ByteString arbitraryNullData = BSL.cons op_return . BSL.concat <$> listOf arbitraryDatum where op_return = 0x6a arbitraryDatum = oneof $ [immediate, push1, push2, push4] ++ (return . BSL.singleton <$> [0x4f .. 0x60]) immediate = do l <- listOf arbitraryBoundedIntegral `suchThat` ((<= 0x4b). length) return . runPutLazy $ putWord8 (fromIntegral (length l)) >> putLazyByteString (BSL.pack l) push1 = do l <- listOf arbitraryBoundedIntegral `suchThat` ((<= 0xff). length) return . runPutLazy $ putWord8 0x4c >> putWord8 (fromIntegral (length l)) >> putLazyByteString (BSL.pack l) push2 = do l <- listOf arbitraryBoundedIntegral `suchThat` ((<= 0xffff). length) return . runPutLazy $ putWord8 0x4d >> putWord16le (fromIntegral (length l)) >> putLazyByteString (BSL.pack l) push4 = do l <- listOf arbitraryBoundedIntegral `suchThat` ((<= 0xffffffff). length) return . runPutLazy $ putWord8 0x4e >> putWord32le (fromIntegral (length l)) >> putLazyByteString (BSL.pack l) arbitraryNonNullData :: Gen BSL.ByteString arbitraryNonNullData = do nulldata <- arbitraryNullData nondata <- arbitraryBS return $ BSL.append nulldata nondata arbitraryConfidential :: Gen prf -> Gen a -> Gen (Confidential prf a) arbitraryConfidential genPrf genA = oneof [conf, nonConf] where conf = Confidential <$> arbitraryPoint <*> genPrf nonConf = Explicit <$> genA arbitraryAsset :: Gen Asset arbitraryAsset = Asset <$> arbitraryConfidential (return ()) arbitraryHash256 arbitraryAssetWithWitness :: Gen AssetWithWitness arbitraryAssetWithWitness = Asset <$> arbitraryConfidential arbitraryBS arbitraryHash256 arbitraryAmount :: Gen Amount arbitraryAmount = Amount <$> arbitraryConfidential (return ()) arbitrarySizedBoundedIntegral arbitraryAmountWithWitness :: Gen AmountWithWitness arbitraryAmountWithWitness = Amount <$> arbitraryConfidential arbitraryBS arbitrarySizedBoundedIntegral arbitraryFee :: Gen TxOutput arbitraryFee = TxOutput <$> (Asset . Explicit <$> arbitraryExplicitAsset) <*> (Amount . Explicit <$> arbitrarySizedBoundedIntegral) <*> pure Nothing <*> pure BSL.empty where arbitraryExplicitAsset = bsHash . BSC.pack <$> elements ["Simplicity.Elements.Arbitrary.arbitraryFee.test0", "Simplicity.Elements.Arbitrary.arbitraryFee.test1"] arbitraryGenericOutput :: Gen TxOutput arbitraryGenericOutput = TxOutput <$> arbitraryAssetWithWitness <*> arbitraryAmountWithWitness <*> arbitrary <*> oneof [pure BSL.empty, arbitraryBS, arbitraryNullData, arbitraryNonNullData] instance Arbitrary Nonce where arbitrary = Nonce <$> oneof [Left <$> ((,) <$> arbitrary <*> (fromInteger <$> arbitrary)), Right <$> arbitraryHash256] instance Arbitrary TxOutput where arbitrary = oneof [arbitraryFee, arbitraryGenericOutput] instance Arbitrary UTXO where arbitrary = UTXO <$> arbitraryAsset <*> arbitraryAmount <*> arbitraryBS instance Arbitrary Outpoint where arbitrary = Outpoint <$> arbitraryHash256 <*> arbitrarySizedBoundedIntegral instance Arbitrary NewIssuance where arbitrary = (NewIssuance <$> arbitraryHash256 <*> oneof [return (Amount (Explicit 0)), arbitraryAmountWithWitness] <*> oneof [return (Amount (Explicit 0)), arbitraryAmountWithWitness] ) `suchThat` nonZeroIssuance where nonZeroIssuance x = nonZeroAmount (newIssuanceAmount x) || nonZeroAmount (newIssuanceTokenAmount x) instance Arbitrary Reissuance where arbitrary = Reissuance <$> arbitraryHash256 <*> arbitraryHash256 <*> (arbitraryAmountWithWitness `suchThat` nonZeroAmount) instance Arbitrary SigTxInput where arbitrary = SigTxInput <$> oneof [return Nothing, Just <$> arbitraryHash256] <*> arbitrary <*> arbitrary <*> oneof [return maxBound, arbitraryBoundedIntegral] <*> arbitrary <*> oneof [return Nothing, Just <$> arbitraryBS] <*> arbitraryBS instance Arbitrary SigTx where arbitrary = SigTx <$> arbitraryVersion <*> (fromList <$> listOf1 arbitrary) <*> (fromList <$> listOf1 arbitrary) <*> arbitraryLock instance Arbitrary TapEnv where arbitrary = TapEnv <$> ((0xfe .&.) <$> arbitraryBoundedIntegral) <*> (mkPubKey <$> arbitraryPoint) <*> listOf arbitraryHash256 <*> arbitraryHash256 where mkPubKey (Point _ x) = PubKey (fe_pack x) genPrimEnv :: Gen (Maybe PrimEnv) genPrimEnv = do tx <- arbitrary tapenv <- arbitrary gen <- arbitraryHash256 ix <- fromIntegral <$> choose (0, length (sigTxIn tx) - 1) return $ primEnv tx ix tapenv gen forallPrimEnv :: Testable prop => (PrimEnv -> prop) -> Property forallPrimEnv p = forAll genPrimEnv go where go (Just env) = property $ p env go Nothing = property Discard forallInPrimEnv :: Testable prop => (PrimEnv -> Word32 -> prop) -> Property forallInPrimEnv p = forAll genPrimEnv go where go Nothing = property Discard go (Just env) = forAll genIx $ \i -> property $ p env i where genIx = fromIntegral <$> genBoundaryCases (length (sigTxIn (envTx env))) -- Generate out of bounds cases too. forallOutPrimEnv :: Testable prop => (PrimEnv -> Word32 -> prop) -> Property forallOutPrimEnv p = forAll genPrimEnv go where go Nothing = property Discard go (Just env) = forAll genIx $ \i -> property $ p env i where genIx = fromIntegral <$> genBoundaryCases (length (sigTxOut (envTx env))) -- Generate out of bounds cases too. ================================================ FILE: Haskell/Tests/Simplicity/Elements/FFI/Primitive.hs ================================================ {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.Elements.FFI.Primitive ( decodeJetCMR , ErrorCode(..) ) where import Foreign.C.Types (CInt(..)) import Foreign.Ptr (Ptr) import Foreign.Marshal.Unsafe (unsafeLocalState) import Simplicity.Digest import Simplicity.FFI.Bitstream import Simplicity.FFI.Dag data ErrorCode = BitstreamEof | DataOutOfRange deriving (Eq, Show) decodeError :: CInt -> Either ErrorCode () decodeError 0 = Right () decodeError (-2) = Left DataOutOfRange decodeError (-12) = Left BitstreamEof decodeError err = error $ "Simplicity.Elements.FFI.Primitive.decodeError: Unexpected error code " ++ show err foreign import ccall unsafe "" simplicity_elements_decodeJet :: Ptr DagNode -> Ptr Bitstream -> IO CInt decodeJetNode :: Ptr Bitstream -> (Either ErrorCode (Ptr DagNode) -> IO a) -> IO a decodeJetNode pstream k = withDagNode $ \pnode -> do error <- simplicity_elements_decodeJet pnode pstream k (decodeError error >> return pnode) decodeJetCMR :: [Bool] -> Either ErrorCode Hash256 decodeJetCMR codeWord = unsafeLocalState $ initializeBitstream codeWord $ \pstream -> decodeJetNode pstream $ \result -> case result of Left err -> return $ Left err Right pnode -> Right <$> dagNodeGetCMR pnode ================================================ FILE: Haskell/Tests/Simplicity/Elements/FFI/Tests.hs ================================================ module Simplicity.Elements.FFI.Tests (tests) where import Control.Arrow ((***), (+++)) import qualified Data.Map as Map import Data.Maybe (fromMaybe, isJust) import Data.Vector ((!?)) import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit (Assertion, (@?=), testCase) import Test.Tasty.QuickCheck (NonNegative(..), Property, classify, forAll, testProperty) import Lens.Family2 (under, view) import Simplicity.Arbitrary import Simplicity.Digest import Simplicity.Elements.Arbitrary import qualified Simplicity.Elements.DataTypes as Prim import Simplicity.Elements.FFI.Jets import Simplicity.Elements.Jets import qualified Simplicity.Elements.Primitive as Prim import Simplicity.Elements.Semantics import Simplicity.Elements.TestEval import Simplicity.FFI.Jets import qualified Simplicity.Programs.Elements.Lib as Prog import Simplicity.TestCoreEval import Simplicity.Ty.Arbitrary import Simplicity.Ty.Word import qualified Simplicity.Word as Word toW32 :: Word.Word32 -> Word32 toW32 = toWord32 . fromIntegral toW8 :: Word.Word8 -> Word8 toW8 = toWord8 . fromIntegral tests :: TestTree tests = testGroup "Elements" [ testGroup "Jets" [ testProperty "tx_is_final" prop_tx_is_final , testProperty "tx_lock_height" prop_tx_lock_height , testProperty "tx_lock_time" prop_tx_lock_time , testProperty "tx_lock_distance" prop_tx_lock_distance , testProperty "tx_lock_duration" prop_tx_lock_duration , testProperty "check_lock_height" prop_check_lock_height , testProperty "check_lock_time" prop_check_lock_time , testProperty "check_lock_distance" prop_check_lock_distance , testProperty "check_lock_duration" prop_check_lock_duration , testProperty "calculate_issuance_entropy" prop_calculate_issuance_entropy , testProperty "calculate_asset" prop_calculate_asset , testProperty "calculate_explicit_token" prop_calculate_explicit_token , testProperty "calculate_confidential_token" prop_calculate_confidential_token , testProperty "outpoint_hash" prop_outpoint_hash , testProperty "asset_amount_hash" prop_asset_amount_hash , testProperty "nonce_hash" prop_nonce_hash , testProperty "annex_hash" prop_annex_hash , testProperty "build_tapleaf_simplicity" prop_build_tapleaf_simplicity , testProperty "build_tapbranch" prop_build_tapbranch , testProperty "build_taptweak" prop_build_taptweak , testProperty "issuance" prop_issuance , testProperty "issuance_asset" prop_issuance_asset , testProperty "issuance_token" prop_issuance_token , testProperty "issuance_entropy" prop_issuance_entropy , testProperty "output_amounts_hash" prop_output_amounts_hash , testProperty "output_nonces_hash" prop_output_nonces_hash , testProperty "output_scripts_hash" prop_output_scripts_hash , testProperty "output_range_proofs_hash" prop_output_range_proofs_hash , testProperty "output_surjection_proofs_hash" prop_output_surjection_proofs_hash , testProperty "outputs_hash" prop_outputs_hash , testProperty "output_hash" prop_output_hash , testProperty "input_outpoints_hash" prop_input_outpoints_hash , testProperty "input_amounts_hash" prop_input_amounts_hash , testProperty "input_scripts_hash" prop_input_scripts_hash , testProperty "input_utxos_hash" prop_input_utxos_hash , testProperty "input_utxo_hash" prop_input_utxo_hash , testProperty "input_sequences_hash" prop_input_sequences_hash , testProperty "input_annexes_hash" prop_input_annexes_hash , testProperty "input_script_sigs_hash" prop_input_script_sigs_hash , testProperty "inputs_hash" prop_inputs_hash , testProperty "input_hash" prop_input_hash , testProperty "issuance_asset_amounts_hash" prop_issuance_asset_amounts_hash , testProperty "issuance_token_amounts_hash" prop_issuance_token_amounts_hash , testProperty "issuance_range_proofs_hash" prop_issuance_range_proofs_hash , testProperty "issuance_blinding_entropy_hash" prop_issuance_blinding_entropy_hash , testProperty "issuances_hash" prop_issuances_hash , testProperty "issuance_hash" prop_issuance_hash , testProperty "tx_hash" prop_tx_hash , testProperty "tapleaf_hash" prop_tapleaf_hash , testProperty "tappath_hash" prop_tappath_hash , testProperty "tap_env_hash" prop_tap_env_hash , testProperty "sig_all_hash" prop_sig_all_hash , testCase "lbtc_asset" assert_lbtc_asset ] , testGroup "Transaction" [ testProperty "script_cmr" prop_script_cmr , testProperty "internal_key" prop_internal_key , testProperty "current_index" prop_current_index , testProperty "num_inputs" prop_num_inputs , testProperty "num_outputs" prop_num_outputs , testProperty "lock_time" prop_lock_time , testProperty "output_asset" prop_output_asset , testProperty "output_amount" prop_output_amount , testProperty "output_nonce" prop_output_nonce , testProperty "output_script_hash" prop_output_script_hash , testProperty "output_null_datum" prop_output_null_datum , testProperty "output_is_fee" prop_output_is_fee , testProperty "output_surjection_proof" prop_output_surjection_proof , testProperty "output_range_proof" prop_output_range_proof , testProperty "total_fee" prop_total_fee , testProperty "current_pegin" prop_current_pegin , testProperty "current_prev_outpoint" prop_current_prev_outpoint , testProperty "current_asset" prop_current_asset , testProperty "current_amount" prop_current_amount , testProperty "current_script_hash" prop_current_script_hash , testProperty "current_sequence" prop_current_sequence , testProperty "current_annex_hash" prop_current_annex_hash , testProperty "current_script_sig_hash" prop_current_script_sig_hash , testProperty "current_reissuance_blinding" prop_current_reissuance_blinding , testProperty "current_new_issuance_contract" prop_current_new_issuance_contract , testProperty "current_reissuance_entropy" prop_current_reissuance_entropy , testProperty "current_issuance_asset_amount" prop_current_issuance_asset_amount , testProperty "current_issuance_token_amount" prop_current_issuance_token_amount , testProperty "current_issuance_asset_proof" prop_current_issuance_asset_proof , testProperty "current_issuance_token_proof" prop_current_issuance_token_proof , testProperty "input_pegin" prop_input_pegin , testProperty "input_prev_outpoint" prop_input_prev_outpoint , testProperty "input_asset" prop_input_asset , testProperty "input_amount" prop_input_amount , testProperty "input_script_hash" prop_input_script_hash , testProperty "input_sequence" prop_input_sequence , testProperty "input_annex_hash" prop_input_annex_hash , testProperty "input_script_sig_hash" prop_input_script_sig_hash , testProperty "reissuance_blinding" prop_reissuance_blinding , testProperty "new_issuance_contract" prop_new_issuance_contract , testProperty "reissuance_entropy" prop_reissuance_entropy , testProperty "issuance_asset_amount" prop_issuance_asset_amount , testProperty "issuance_token_amount" prop_issuance_token_amount , testProperty "issuance_asset_proof" prop_issuance_asset_proof , testProperty "issuance_token_proof" prop_issuance_token_proof , testProperty "tapleaf_version" prop_tapleaf_version , testProperty "tappath" prop_tappath , testProperty "version" prop_version , testProperty "genesis_block_hash" prop_genesis_block_hash , testProperty "transaction_id" prop_transaction_id ] ] prop_tx_is_final :: Property prop_tx_is_final = forallPrimEnv $ \env -> fast_tx_is_final env () == tx_is_final env () where fast_tx_is_final = testEval (specification (ElementsJet (TimeLockJet TxIsFinal))) prop_tx_lock_height :: Property prop_tx_lock_height = forallPrimEnv $ \env -> fast_tx_lock_height env () == tx_lock_height env () where fast_tx_lock_height = testEval (specification (ElementsJet (TimeLockJet TxLockHeight))) prop_tx_lock_time :: Property prop_tx_lock_time = forallPrimEnv $ \env -> fast_tx_lock_time env () == tx_lock_time env () where fast_tx_lock_time = testEval (specification (ElementsJet (TimeLockJet TxLockTime))) prop_tx_lock_distance :: Property prop_tx_lock_distance = forallPrimEnv $ \env -> fast_tx_lock_distance env () == broken_do_not_use_tx_lock_distance env () where fast_tx_lock_distance = testEval (specification (ElementsJet (TimeLockJet BrokenDoNotUseTxLockDistance))) prop_tx_lock_duration :: Property prop_tx_lock_duration = forallPrimEnv $ \env -> fast_tx_lock_duration env () == broken_do_not_use_tx_lock_duration env () where fast_tx_lock_duration = testEval (specification (ElementsJet (TimeLockJet BrokenDoNotUseTxLockDuration))) prop_check_lock_height :: Word32 -> Property prop_check_lock_height = \w -> forallPrimEnv $ \env -> fast_check_lock_height env w == check_lock_height env w where fast_check_lock_height = testEval (specification (ElementsJet (TimeLockJet CheckLockHeight))) prop_check_lock_time :: Word32 -> Property prop_check_lock_time = \w -> forallPrimEnv $ \env -> fast_check_lock_time env w == check_lock_time env w where fast_check_lock_time = testEval (specification (ElementsJet (TimeLockJet CheckLockTime))) prop_check_lock_distance :: Word16 -> Property prop_check_lock_distance = \w -> forallPrimEnv $ \env -> fast_check_lock_distance env w == broken_do_not_use_check_lock_distance env w where fast_check_lock_distance = testEval (specification (ElementsJet (TimeLockJet BrokenDoNotUseCheckLockDistance))) prop_check_lock_duration :: Word16 -> Property prop_check_lock_duration = \w -> forallPrimEnv $ \env -> fast_check_lock_duration env w == broken_do_not_use_check_lock_duration env w where fast_check_lock_duration = testEval (specification (ElementsJet (TimeLockJet BrokenDoNotUseCheckLockDuration))) prop_calculate_issuance_entropy :: ((Word256, Word32), Word256) -> Bool prop_calculate_issuance_entropy = \input -> calculate_issuance_entropy input == fast_calculate_issuance_entropy input where fast_calculate_issuance_entropy = testCoreEval Prog.calculateIssuanceEntropy prop_calculate_asset :: Word256 -> Bool prop_calculate_asset = \input -> calculate_asset input == fast_calculate_asset input where fast_calculate_asset = testCoreEval Prog.calculateAsset prop_calculate_explicit_token :: Word256 -> Bool prop_calculate_explicit_token = \input -> calculate_explicit_token input == fast_calculate_explicit_token input where fast_calculate_explicit_token = testCoreEval Prog.calculateExplicitToken prop_calculate_confidential_token :: Word256 -> Bool prop_calculate_confidential_token = \input -> calculate_confidential_token input == fast_calculate_confidential_token input where fast_calculate_confidential_token = testCoreEval Prog.calculateConfidentialToken prop_outpoint_hash :: Sha256CtxElement -> (Either () Word256, (Word256, Word32)) -> Bool prop_outpoint_hash = \ctx op -> let input = (ctxAsTy ctx, op) in outpoint_hash input == fast_outpoint_hash input where fast_outpoint_hash = testCoreEval Prog.outpointHash prop_asset_amount_hash :: Sha256CtxElement -> Either PointElement Word256 -> Either PointElement Word64 -> Bool prop_asset_amount_hash = \ctx cw256 cw64 -> let input = (ctxAsTy ctx, (cast cw256, cast cw64)) in asset_amount_hash input == fast_asset_amount_hash input where fast_asset_amount_hash = testCoreEval Prog.assetAmountHash cast = either (Left . pointAsTy) Right prop_nonce_hash :: Sha256CtxElement -> Maybe Prim.Nonce -> Bool prop_nonce_hash = \ctx mnonce -> let input = (ctxAsTy ctx, cast mnonce) in nonce_hash input == fast_nonce_hash input where fast_nonce_hash = testCoreEval Prog.nonceHash cast = maybe (Left ()) (Right . ((toBit *** (toWord256 . fromIntegral)) +++ (toWord256 . integerHash256)) . Prim.nonce) prop_annex_hash :: Sha256CtxElement -> Maybe Word256 -> Bool prop_annex_hash = \ctx mw256 -> let input = (ctxAsTy ctx, cast mw256) in annex_hash input == fast_annex_hash input where fast_annex_hash = testCoreEval Prog.annexHash cast = maybe (Left ()) Right prop_build_tapleaf_simplicity :: Word256 -> Bool prop_build_tapleaf_simplicity = \w -> build_tapleaf_simplicity w == fast_build_tapleaf_simplicity w where fast_build_tapleaf_simplicity = testCoreEval Prog.buildTapleafSimplicity prop_build_tapbranch :: Word256 -> Word256 -> Bool prop_build_tapbranch = \a b -> build_tapbranch (a, b) == fast_build_tapbranch (a, b) where fast_build_tapbranch = testCoreEval Prog.buildTapbranch prop_build_taptweak :: FieldElement -> Word256 -> Bool prop_build_taptweak = \a b -> let input = (feAsTy a, b) in build_taptweak input == fast_build_taptweak input where fast_build_taptweak = testCoreEval Prog.buildTaptweak prop_issuance :: Property prop_issuance = forallInPrimEnv $ \env i -> fast_issuance env (toW32 i) == issuance env (toW32 i) where fast_issuance = testEval (specification (ElementsJet (IssuanceJet Issuance))) prop_issuance_asset :: Property prop_issuance_asset = forallInPrimEnv $ \env i -> fast_issuance_asset env (toW32 i) == issuance_asset env (toW32 i) where fast_issuance_asset = testEval (specification (ElementsJet (IssuanceJet IssuanceAsset))) prop_issuance_token :: Property prop_issuance_token = forallInPrimEnv $ \env i -> fast_issuance_token env (toW32 i) == issuance_token env (toW32 i) where fast_issuance_token = testEval (specification (ElementsJet (IssuanceJet IssuanceToken))) prop_issuance_entropy :: Property prop_issuance_entropy = forallInPrimEnv $ \env i -> fast_issuance_entropy env (toW32 i) == issuance_entropy env (toW32 i) where fast_issuance_entropy = testEval (specification (ElementsJet (IssuanceJet IssuanceEntropy))) prop_output_amounts_hash :: Property prop_output_amounts_hash = forallPrimEnv $ \env -> fast_output_amounts_hash env () == output_amounts_hash env () where fast_output_amounts_hash = testEval (specification (ElementsJet (SigHashJet OutputAmountsHash))) prop_output_nonces_hash :: Property prop_output_nonces_hash = forallPrimEnv $ \env -> fast_output_nonces_hash env () == output_nonces_hash env () where fast_output_nonces_hash = testEval (specification (ElementsJet (SigHashJet OutputNoncesHash))) prop_output_scripts_hash :: Property prop_output_scripts_hash = forallPrimEnv $ \env -> fast_output_scripts_hash env () == output_scripts_hash env () where fast_output_scripts_hash = testEval (specification (ElementsJet (SigHashJet OutputScriptsHash))) prop_output_range_proofs_hash :: Property prop_output_range_proofs_hash = forallPrimEnv $ \env -> fast_output_range_proofs_hash env () == output_range_proofs_hash env () where fast_output_range_proofs_hash = testEval (specification (ElementsJet (SigHashJet OutputRangeProofsHash))) prop_output_surjection_proofs_hash :: Property prop_output_surjection_proofs_hash = forallPrimEnv $ \env -> fast_output_surjection_proofs_hash env () == output_surjection_proofs_hash env () where fast_output_surjection_proofs_hash = testEval (specification (ElementsJet (SigHashJet OutputSurjectionProofsHash))) prop_outputs_hash :: Property prop_outputs_hash = forallPrimEnv $ \env -> fast_outputs_hash env () == outputs_hash env () where fast_outputs_hash = testEval (specification (ElementsJet (SigHashJet OutputsHash))) prop_output_hash :: Property prop_output_hash = forallOutPrimEnv $ \env i -> fast_output_hash env (toW32 i) == output_hash env (toW32 i) where fast_output_hash = testEval (specification (ElementsJet (SigHashJet OutputHash))) prop_input_outpoints_hash :: Property prop_input_outpoints_hash = forallPrimEnv $ \env -> fast_input_outpoints_hash env () == input_outpoints_hash env () where fast_input_outpoints_hash = testEval (specification (ElementsJet (SigHashJet InputOutpointsHash))) prop_input_amounts_hash :: Property prop_input_amounts_hash = forallPrimEnv $ \env -> fast_input_amounts_hash env () == input_amounts_hash env () where fast_input_amounts_hash = testEval (specification (ElementsJet (SigHashJet InputAmountsHash))) prop_input_scripts_hash :: Property prop_input_scripts_hash = forallPrimEnv $ \env -> fast_input_scripts_hash env () == input_scripts_hash env () where fast_input_scripts_hash = testEval (specification (ElementsJet (SigHashJet InputScriptsHash))) prop_input_utxos_hash :: Property prop_input_utxos_hash = forallPrimEnv $ \env -> fast_input_utxos_hash env () == input_utxos_hash env () where fast_input_utxos_hash = testEval (specification (ElementsJet (SigHashJet InputUtxosHash))) prop_input_utxo_hash :: Property prop_input_utxo_hash = forallInPrimEnv $ \env i -> fast_input_utxo_hash env (toW32 i) == input_utxo_hash env (toW32 i) where fast_input_utxo_hash = testEval (specification (ElementsJet (SigHashJet InputUtxoHash))) prop_input_sequences_hash :: Property prop_input_sequences_hash = forallPrimEnv $ \env -> fast_input_sequences_hash env () == input_sequences_hash env () where fast_input_sequences_hash = testEval (specification (ElementsJet (SigHashJet InputSequencesHash))) prop_input_annexes_hash :: Property prop_input_annexes_hash = forallPrimEnv $ \env -> fast_input_annexes_hash env () == input_annexes_hash env () where fast_input_annexes_hash = testEval (specification (ElementsJet (SigHashJet InputAnnexesHash))) prop_input_script_sigs_hash :: Property prop_input_script_sigs_hash = forallPrimEnv $ \env -> fast_input_script_sigs_hash env () == input_script_sigs_hash env () where fast_input_script_sigs_hash = testEval (specification (ElementsJet (SigHashJet InputScriptSigsHash))) prop_inputs_hash :: Property prop_inputs_hash = forallPrimEnv $ \env -> fast_inputs_hash env () == inputs_hash env () where fast_inputs_hash = testEval (specification (ElementsJet (SigHashJet InputsHash))) prop_input_hash :: Property prop_input_hash = forallInPrimEnv $ \env i -> fast_input_hash env (toW32 i) == input_hash env (toW32 i) where fast_input_hash = testEval (specification (ElementsJet (SigHashJet InputHash))) prop_issuance_asset_amounts_hash :: Property prop_issuance_asset_amounts_hash = forallPrimEnv $ \env -> fast_issuance_asset_amounts_hash env () == issuance_asset_amounts_hash env () where fast_issuance_asset_amounts_hash = testEval (specification (ElementsJet (SigHashJet IssuanceAssetAmountsHash))) prop_issuance_token_amounts_hash :: Property prop_issuance_token_amounts_hash = forallPrimEnv $ \env -> fast_issuance_token_amounts_hash env () == issuance_token_amounts_hash env () where fast_issuance_token_amounts_hash = testEval (specification (ElementsJet (SigHashJet IssuanceTokenAmountsHash))) prop_issuance_range_proofs_hash :: Property prop_issuance_range_proofs_hash = forallPrimEnv $ \env -> fast_issuance_range_proofs_hash env () == issuance_range_proofs_hash env () where fast_issuance_range_proofs_hash = testEval (specification (ElementsJet (SigHashJet IssuanceRangeProofsHash))) prop_issuance_blinding_entropy_hash :: Property prop_issuance_blinding_entropy_hash = forallPrimEnv $ \env -> fast_issuance_blinding_entropy_hash env () == issuance_blinding_entropy_hash env () where fast_issuance_blinding_entropy_hash = testEval (specification (ElementsJet (SigHashJet IssuanceBlindingEntropyHash))) prop_issuances_hash :: Property prop_issuances_hash = forallPrimEnv $ \env -> fast_issuances_hash env () == issuances_hash env () where fast_issuances_hash = testEval (specification (ElementsJet (SigHashJet IssuancesHash))) prop_issuance_hash :: Property prop_issuance_hash = forallInPrimEnv $ \env i -> fast_issuance_hash env (toW32 i) == issuance_hash env (toW32 i) where fast_issuance_hash = testEval (specification (ElementsJet (SigHashJet IssuanceHash))) prop_tx_hash :: Property prop_tx_hash = forallPrimEnv $ \env -> fast_tx_hash env () == tx_hash env () where fast_tx_hash = testEval (specification (ElementsJet (SigHashJet TxHash))) prop_tapleaf_hash :: Property prop_tapleaf_hash = forallPrimEnv $ \env -> fast_tapleaf_hash env () == tapleaf_hash env () where fast_tapleaf_hash = testEval (specification (ElementsJet (SigHashJet TapleafHash))) prop_tappath_hash :: Property prop_tappath_hash = forallPrimEnv $ \env -> fast_tappath_hash env () == tappath_hash env () where fast_tappath_hash = testEval (specification (ElementsJet (SigHashJet TappathHash))) prop_tap_env_hash :: Property prop_tap_env_hash = forallPrimEnv $ \env -> fast_tap_env_hash env () == tap_env_hash env () where fast_tap_env_hash = testEval (specification (ElementsJet (SigHashJet TapEnvHash))) prop_sig_all_hash :: Property prop_sig_all_hash = forallPrimEnv $ \env -> fast_sig_all_hash env () == sig_all_hash env () where fast_sig_all_hash = testEval (specification (ElementsJet (SigHashJet SigAllHash))) assert_lbtc_asset :: Assertion assert_lbtc_asset = lbtc_asset () @?= fast_lbtc_asset () where fast_lbtc_asset = testCoreEval Prog.lbtcAsset prop_script_cmr :: Property prop_script_cmr = forallPrimEnv $ \env -> fast_script_cmr env () == script_cmr env () where fast_script_cmr = testEval (specification (ElementsJet (TransactionJet ScriptCMR))) prop_internal_key :: Property prop_internal_key = forallPrimEnv $ \env -> fast_internal_key env () == internal_key env () where fast_internal_key = testEval (specification (ElementsJet (TransactionJet InternalKey))) prop_current_index :: Property prop_current_index = forallPrimEnv $ \env -> fast_current_index env () == current_index env () where fast_current_index = testEval (specification (ElementsJet (TransactionJet CurrentIndex))) prop_num_inputs :: Property prop_num_inputs = forallPrimEnv $ \env -> fast_num_inputs env () == num_inputs env () where fast_num_inputs = testEval (specification (ElementsJet (TransactionJet NumInputs))) prop_num_outputs :: Property prop_num_outputs = forallPrimEnv $ \env -> fast_num_outputs env () == num_outputs env () where fast_num_outputs = testEval (specification (ElementsJet (TransactionJet NumOutputs))) prop_lock_time :: Property prop_lock_time = forallPrimEnv $ \env -> fast_lock_time env () == lock_time env () where fast_lock_time = testEval (specification (ElementsJet (TransactionJet LockTime))) prop_output_asset :: Property prop_output_asset = forallOutPrimEnv $ \env i -> fast_output_asset env (toW32 i) == output_asset env (toW32 i) where fast_output_asset = testEval (specification (ElementsJet (TransactionJet OutputAsset))) prop_output_amount :: Property prop_output_amount = forallOutPrimEnv $ \env i -> fast_output_amount env (toW32 i) == output_amount env (toW32 i) where fast_output_amount = testEval (specification (ElementsJet (TransactionJet OutputAmount))) prop_output_nonce :: Property prop_output_nonce = forallOutPrimEnv $ \env i -> fast_output_nonce env (toW32 i) == output_nonce env (toW32 i) where fast_output_nonce = testEval (specification (ElementsJet (TransactionJet OutputNonce))) prop_output_script_hash :: Property prop_output_script_hash = forallOutPrimEnv $ \env i -> fast_output_script_hash env (toW32 i) == output_script_hash env (toW32 i) where fast_output_script_hash = testEval (specification (ElementsJet (TransactionJet OutputScriptHash))) prop_output_null_datum :: NonNegative Integer -> Property prop_output_null_datum = \(NonNegative j) -> forallOutPrimEnv $ \env i -> fast_output_null_datum env (toW32 i, toWord32 j) == output_null_datum env (toW32 i, toWord32 j) where fast_output_null_datum = testEval (specification (ElementsJet (TransactionJet OutputNullDatum))) prop_output_is_fee :: Property prop_output_is_fee = forallOutPrimEnv $ \env i -> classify (isJust $ Prim.sigTxOut (Prim.envTx env) !? (fromIntegral i) >>= Prim.outputFee) "is_fee" $ fast_output_is_fee env (toW32 i) == output_is_fee env (toW32 i) where fast_output_is_fee = testEval (specification (ElementsJet (TransactionJet OutputIsFee))) prop_output_surjection_proof :: Property prop_output_surjection_proof = forallOutPrimEnv $ \env i -> fast_output_surjection_proof env (toW32 i) == output_surjection_proof env (toW32 i) where fast_output_surjection_proof = testEval (specification (ElementsJet (TransactionJet OutputSurjectionProof))) prop_output_range_proof :: Property prop_output_range_proof = forallOutPrimEnv $ \env i -> fast_output_range_proof env (toW32 i) == output_range_proof env (toW32 i) where fast_output_range_proof = testEval (specification (ElementsJet (TransactionJet OutputRangeProof))) prop_total_fee :: Property prop_total_fee = forallOutPrimEnv $ \env i -> forAll arbitraryHash256 $ \hash -> let input = fromMaybe hash (getAssetId (Prim.sigTxOut (Prim.envTx env)) (fromIntegral i)) fee = Map.findWithDefault 0 input (Prim.totalFee (Prim.envTx env)) in classify (0 /= fee) "non-zero fee" $ fast_total_fee env (fromHash input) == total_fee env (fromHash input) where fast_total_fee = testEval (specification (ElementsJet (TransactionJet TotalFee))) getAssetId outputs ix = (outputs !? ix) >>= explicitId . view (under Prim.asset) . Prim.txoAsset explicitId (Prim.Explicit a) = Just a explicitId (Prim.Confidential _ _) = Nothing fromHash = toWord256 . integerHash256 prop_current_pegin :: Property prop_current_pegin = forallPrimEnv $ \env -> fast_current_pegin env () == current_pegin env () where fast_current_pegin = testEval (specification (ElementsJet (TransactionJet CurrentPegin))) prop_current_prev_outpoint :: Property prop_current_prev_outpoint = forallPrimEnv $ \env -> fast_current_prev_outpoint env () == current_prev_outpoint env () where fast_current_prev_outpoint = testEval (specification (ElementsJet (TransactionJet CurrentPrevOutpoint))) prop_current_asset :: Property prop_current_asset = forallPrimEnv $ \env -> fast_current_asset env () == current_asset env () where fast_current_asset = testEval (specification (ElementsJet (TransactionJet CurrentAsset))) prop_current_amount :: Property prop_current_amount = forallPrimEnv $ \env -> fast_current_amount env () == current_amount env () where fast_current_amount = testEval (specification (ElementsJet (TransactionJet CurrentAmount))) prop_current_script_hash :: Property prop_current_script_hash = forallPrimEnv $ \env -> fast_current_script_hash env () == current_script_hash env () where fast_current_script_hash = testEval (specification (ElementsJet (TransactionJet CurrentScriptHash))) prop_current_sequence :: Property prop_current_sequence = forallPrimEnv $ \env -> fast_current_sequence env () == current_sequence env () where fast_current_sequence = testEval (specification (ElementsJet (TransactionJet CurrentSequence))) prop_current_annex_hash :: Property prop_current_annex_hash = forallPrimEnv $ \env -> fast_current_annex_hash env () == current_annex_hash env () where fast_current_annex_hash = testEval (specification (ElementsJet (TransactionJet CurrentAnnexHash))) prop_current_script_sig_hash :: Property prop_current_script_sig_hash = forallPrimEnv $ \env -> fast_current_script_sig_hash env () == current_script_sig_hash env () where fast_current_script_sig_hash = testEval (specification (ElementsJet (TransactionJet CurrentScriptSigHash))) prop_current_reissuance_blinding :: Property prop_current_reissuance_blinding = forallPrimEnv $ \env -> fast_current_reissuance_blinding env () == current_reissuance_blinding env () where fast_current_reissuance_blinding = testEval (specification (ElementsJet (TransactionJet CurrentReissuanceBlinding))) prop_current_new_issuance_contract :: Property prop_current_new_issuance_contract = forallPrimEnv $ \env -> fast_current_new_issuance_contract env () == current_new_issuance_contract env () where fast_current_new_issuance_contract = testEval (specification (ElementsJet (TransactionJet CurrentNewIssuanceContract))) prop_current_reissuance_entropy :: Property prop_current_reissuance_entropy = forallPrimEnv $ \env -> fast_current_reissuance_entropy env () == current_reissuance_entropy env () where fast_current_reissuance_entropy = testEval (specification (ElementsJet (TransactionJet CurrentReissuanceEntropy))) prop_current_issuance_asset_amount :: Property prop_current_issuance_asset_amount = forallPrimEnv $ \env -> fast_current_issuance_asset_amount env () == current_issuance_asset_amount env () where fast_current_issuance_asset_amount = testEval (specification (ElementsJet (TransactionJet CurrentIssuanceAssetAmount))) prop_current_issuance_token_amount :: Property prop_current_issuance_token_amount = forallPrimEnv $ \env -> fast_current_issuance_token_amount env () == current_issuance_token_amount env () where fast_current_issuance_token_amount = testEval (specification (ElementsJet (TransactionJet CurrentIssuanceTokenAmount))) prop_current_issuance_asset_proof :: Property prop_current_issuance_asset_proof = forallPrimEnv $ \env -> fast_current_issuance_asset_proof env () == current_issuance_asset_proof env () where fast_current_issuance_asset_proof = testEval (specification (ElementsJet (TransactionJet CurrentIssuanceAssetProof))) prop_current_issuance_token_proof :: Property prop_current_issuance_token_proof = forallPrimEnv $ \env -> fast_current_issuance_token_proof env () == current_issuance_token_proof env () where fast_current_issuance_token_proof = testEval (specification (ElementsJet (TransactionJet CurrentIssuanceTokenProof))) prop_input_pegin :: Property prop_input_pegin = forallInPrimEnv $ \env i -> fast_input_pegin env (toW32 i) == input_pegin env (toW32 i) where fast_input_pegin = testEval (specification (ElementsJet (TransactionJet InputPegin))) prop_input_prev_outpoint :: Property prop_input_prev_outpoint = forallInPrimEnv $ \env i -> fast_input_prev_outpoint env (toW32 i) == input_prev_outpoint env (toW32 i) where fast_input_prev_outpoint = testEval (specification (ElementsJet (TransactionJet InputPrevOutpoint))) prop_input_asset :: Property prop_input_asset = forallInPrimEnv $ \env i -> fast_input_asset env (toW32 i) == input_asset env (toW32 i) where fast_input_asset = testEval (specification (ElementsJet (TransactionJet InputAsset))) prop_input_amount :: Property prop_input_amount = forallInPrimEnv $ \env i -> fast_input_amount env (toW32 i) == input_amount env (toW32 i) where fast_input_amount = testEval (specification (ElementsJet (TransactionJet InputAmount))) prop_input_script_hash :: Property prop_input_script_hash = forallInPrimEnv $ \env i -> fast_input_script_hash env (toW32 i) == input_script_hash env (toW32 i) where fast_input_script_hash = testEval (specification (ElementsJet (TransactionJet InputScriptHash))) prop_input_sequence :: Property prop_input_sequence = forallInPrimEnv $ \env i -> fast_input_sequence env (toW32 i) == input_sequence env (toW32 i) where fast_input_sequence = testEval (specification (ElementsJet (TransactionJet InputSequence))) prop_input_annex_hash :: Property prop_input_annex_hash = forallInPrimEnv $ \env i -> fast_input_annex_hash env (toW32 i) == input_annex_hash env (toW32 i) where fast_input_annex_hash = testEval (specification (ElementsJet (TransactionJet InputAnnexHash))) prop_input_script_sig_hash :: Property prop_input_script_sig_hash = forallInPrimEnv $ \env i -> fast_input_script_sig_hash env (toW32 i) == input_script_sig_hash env (toW32 i) where fast_input_script_sig_hash = testEval (specification (ElementsJet (TransactionJet InputScriptSigHash))) prop_reissuance_blinding :: Property prop_reissuance_blinding = forallInPrimEnv $ \env i -> fast_reissuance_blinding env (toW32 i) == reissuance_blinding env (toW32 i) where fast_reissuance_blinding = testEval (specification (ElementsJet (TransactionJet ReissuanceBlinding))) prop_new_issuance_contract :: Property prop_new_issuance_contract = forallInPrimEnv $ \env i -> fast_new_issuance_contract env (toW32 i) == new_issuance_contract env (toW32 i) where fast_new_issuance_contract = testEval (specification (ElementsJet (TransactionJet NewIssuanceContract))) prop_reissuance_entropy :: Property prop_reissuance_entropy = forallInPrimEnv $ \env i -> fast_reissuance_entropy env (toW32 i) == reissuance_entropy env (toW32 i) where fast_reissuance_entropy = testEval (specification (ElementsJet (TransactionJet ReissuanceEntropy))) prop_issuance_asset_amount :: Property prop_issuance_asset_amount = forallInPrimEnv $ \env i -> fast_issuance_asset_amount env (toW32 i) == issuance_asset_amount env (toW32 i) where fast_issuance_asset_amount = testEval (specification (ElementsJet (TransactionJet IssuanceAssetAmount))) prop_issuance_token_amount :: Property prop_issuance_token_amount = forallInPrimEnv $ \env i -> fast_issuance_token_amount env (toW32 i) == issuance_token_amount env (toW32 i) where fast_issuance_token_amount = testEval (specification (ElementsJet (TransactionJet IssuanceTokenAmount))) prop_issuance_asset_proof :: Property prop_issuance_asset_proof = forallInPrimEnv $ \env i -> fast_issuance_asset_proof env (toW32 i) == issuance_asset_proof env (toW32 i) where fast_issuance_asset_proof = testEval (specification (ElementsJet (TransactionJet IssuanceAssetProof))) prop_issuance_token_proof :: Property prop_issuance_token_proof = forallInPrimEnv $ \env i -> fast_issuance_token_proof env (toW32 i) == issuance_token_proof env (toW32 i) where fast_issuance_token_proof = testEval (specification (ElementsJet (TransactionJet IssuanceTokenProof))) prop_tapleaf_version :: Property prop_tapleaf_version = forallPrimEnv $ \env -> fast_tapleaf_version env () == tapleaf_version env () where fast_tapleaf_version = testEval (specification (ElementsJet (TransactionJet TapleafVersion))) prop_tappath :: Property prop_tappath = forallPrimEnv $ \env -> forAll (genTappathIx env) $ \i -> fast_tappath env (toW8 i) == tappath env (toW8 i) where fast_tappath = testEval (specification (ElementsJet (TransactionJet Tappath))) genTappathIx = genBoundaryCases . fromIntegral . length . Prim.tappath . Prim.envTap prop_version :: Property prop_version = forallPrimEnv $ \env -> fast_version env () == version env () where fast_version = testEval (specification (ElementsJet (TransactionJet Version))) prop_genesis_block_hash :: Property prop_genesis_block_hash = forallPrimEnv $ \env -> fast_genesis_block_hash env () == genesis_block_hash env () where fast_genesis_block_hash = testEval (specification (ElementsJet (TransactionJet GenesisBlockHash))) prop_transaction_id :: Property prop_transaction_id = forallPrimEnv $ \env -> fast_transaction_id env () == transaction_id env () where fast_transaction_id = testEval (specification (ElementsJet (TransactionJet TransactionId))) ================================================ FILE: Haskell/Tests/Simplicity/Elements/Regression.hs ================================================ {-# LANGUAGE GADTs, ScopedTypeVariables #-} -- | This module performs some regression testing to make sure that consensus critical items, just as jet CMR don't change. module Simplicity.Elements.Regression (tests) where import Data.Foldable (length, toList) import Lens.Family2 (review, over) import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit (Assertion, (@?=), assertBool, testCase) import Simplicity.CoreJets import Simplicity.Digest import Simplicity.Elements.Jets as Elements import Simplicity.MerkleRoot import Simplicity.Serialization import Simplicity.Tree import Simplicity.Ty import Simplicity.Ty.Word import qualified Simplicity.Word as Word tests :: TestTree tests = testGroup "Regression" [ testCase "jet count" assert_jet_count , assert_jet_cmrs ] wordJets :: BinTree (SomeArrow JetType) regularJets :: BinTree (SomeArrow JetType) (Branch wordJets regularJets) = treeEvalBitStream Elements.getJetBit assert_jet_count :: Assertion assert_jet_count = length regularJets @?= 471 assert_jet_cmr :: (TyC a, TyC b) => JetType a b -> Assertion assert_jet_cmr jt = commitmentRoot (asJet jt) @?= review (over be256) (expected_cmr jt) assert_jet_cmrs :: TestTree assert_jet_cmrs = testGroup "CMRs" [testCase (show jt) (assert_jet_cmr jt) | SomeArrow jt <- someWordJets ++ (toList regularJets)] where someWordJets = take 6 (toList wordJets) expected_cmr :: JetType a b -> Word.Word256 expected_cmr (CoreJet (WordJet Verify)) = 0x343e6dc16b3f52e83e3b4ccc99b8c6f96a074fe399327af364bc285e299745a2 expected_cmr (CoreJet (WordJet Low1)) = 0xf27b69bb091609f59e0033050d01a5bc77ff07d942707a79cf5ee410a998a043 expected_cmr (CoreJet (WordJet Low8)) = 0x217b5643956b4833aa5622f00f0688ba860d4adbf940cbdcd2b59f26d61593b1 expected_cmr (CoreJet (WordJet Low16)) = 0x977cbd1e7ffc05e716d9c1b49f7d517f853dbf3e98a4c748046eacf417f89c2f expected_cmr (CoreJet (WordJet Low32)) = 0xbe4169828f076778b60d5456f7886ed7f30b101d6ccbd9ea0c4db142eac66b12 expected_cmr (CoreJet (WordJet Low64)) = 0x019a66bfba1751688be71389ed7bf371b3014dfb329562ac3b3e9dfe9206a5bc expected_cmr (CoreJet (WordJet High1)) = 0xc32d877e670d6c037cb33533289e19a724c368aa7551daa6d2dacccd8c95f4d0 expected_cmr (CoreJet (WordJet High8)) = 0xcbd78d50af7799855adc4903dbbefc1345d51484f03d3c755caaa5caa97d4a14 expected_cmr (CoreJet (WordJet High16)) = 0x4164ab6e2ff8eef63c06c080f1dec6970b4c5c31c02305abccd8ed2c5e1c45ce expected_cmr (CoreJet (WordJet High32)) = 0xd3a7ce9cd5d5fb679a98ef57b86322770cb66fb6f0616e1634cfa84c8f6809c6 expected_cmr (CoreJet (WordJet High64)) = 0x4af91faf8e39f4da7c28a8796594a9228213d7323eea2ca630752ce4c57f16e1 expected_cmr (CoreJet (WordJet Complement1)) = 0xed74eeb83a00c713cc14f33efe553383cd0411cc3020fd89279316675d910e66 expected_cmr (CoreJet (WordJet Complement8)) = 0x6916b28fb574d9c908a3f33f74bf06f7ed937254247f9efc2603d7171dd497be expected_cmr (CoreJet (WordJet Complement16)) = 0x61fdd904a4aeb7eb7684af618e25aae907cd1db0f62d9703c5b854e1663cac9f expected_cmr (CoreJet (WordJet Complement32)) = 0xfeb02cc36e195b462ae504a912dadfe66ad47f23a0cb3baea21d31aaa0ce101d expected_cmr (CoreJet (WordJet Complement64)) = 0x45072d5aa0e5c37c9e521dcc92e8f39a5f75e7d928670acab79cd8c8b5b59e1a expected_cmr (CoreJet (WordJet And1)) = 0xb773cefa418957fea7dfb49c6c43b3dbfa35fa3d80de8cfd4d70c08d945f5fba expected_cmr (CoreJet (WordJet And8)) = 0xac828b724c5f5340b51e76e7b6e8b23aeab7533fd8c091ae2a515530ae7ab200 expected_cmr (CoreJet (WordJet And16)) = 0x57dd730b1c8ddff13cae2769562be0abc6ca3bc802da0abbb7fc138ca463da59 expected_cmr (CoreJet (WordJet And32)) = 0x753e332ddfa096f08399ffaa7ec4da4035bcbaa142e6e38d4cb607ce1f0b051d expected_cmr (CoreJet (WordJet And64)) = 0xf1ad5e6c63ee5c890b0f2e711561b905316487ac4044dd230cf6a736f81bd4f3 expected_cmr (CoreJet (WordJet Or1)) = 0x9bf59174410a809d3da2b58c7e0d05c55cec38bdaa5fcac382a311770ee0eb38 expected_cmr (CoreJet (WordJet Or8)) = 0x84b53689f21d4e697d0fe8988ce736ab72c9c86f847589daa9ae6a784630e620 expected_cmr (CoreJet (WordJet Or16)) = 0xdd9a3193d619d959fa0b6d8b47af7854f7e0467ba35901ce43d800fcaf730ff9 expected_cmr (CoreJet (WordJet Or32)) = 0x9a019f07df4996b33e647f4de7e56c1d8f03269cbfa3c7582cfe808e909870b7 expected_cmr (CoreJet (WordJet Or64)) = 0xc24f358005f803772b1c3e439cf1b709bd9f4d42527591303a36f6b1c3cf29cc expected_cmr (CoreJet (WordJet Xor1)) = 0x9dc9fe42f7eb34649f1c72d2e5dd167db21be5321372d5ca7f6a184f93e05ee3 expected_cmr (CoreJet (WordJet Xor8)) = 0xd8335f4890c1d8ed766c7135902e01a0094e3a9816f70c847cc3d7c000406efe expected_cmr (CoreJet (WordJet Xor16)) = 0x1fcaf40bdedd72e797b09fe78753b0ab27872c0bd12b034955fbfac23812ef26 expected_cmr (CoreJet (WordJet Xor32)) = 0x1d49fc94f22b5d31b7f9efb5378e5f8a42626aed4e92799348d6b788dfe86b1c expected_cmr (CoreJet (WordJet Xor64)) = 0x7a3f3f55204783653344311d1dc509d35b6639c0d8b967a207806cd87d31d6e6 expected_cmr (CoreJet (WordJet Maj1)) = 0xcb2d986d7f00107a3c25f6b2f14891d02e20ae16f0a1252c92d9b58ae73388aa expected_cmr (CoreJet (WordJet Maj8)) = 0x8930d1d0991b0a581d0b1d85ad72147d6649a35993283fc97214431f0b6a7aa8 expected_cmr (CoreJet (WordJet Maj16)) = 0x0af6d0c171fe33a2159bf98800f0412c2597e99784d074fdfa33d7fde597ddfd expected_cmr (CoreJet (WordJet Maj32)) = 0x3060838d48456f3392d5d69b5eec089276cd58bb67a12c642ec73aeb9adacbdd expected_cmr (CoreJet (WordJet Maj64)) = 0x8ebcc17457ea2b14231b0e901ea7b1d47b9b78986372a4416fe73f6763feb24b expected_cmr (CoreJet (WordJet XorXor1)) = 0x1e107b05ff941d31d7578b437328ba52f3ff20a068c0d2bdef08768093cc7c63 expected_cmr (CoreJet (WordJet XorXor8)) = 0xc2da6e9ca64d8a73c1772667b3d7a0938bcb8a6c43fd0473eec71b77494aad94 expected_cmr (CoreJet (WordJet XorXor16)) = 0xb776989da5095c4be94b1aef759466e11f639c1939471fa18e36e7e490c38961 expected_cmr (CoreJet (WordJet XorXor32)) = 0xd168fac1ac7fc48357be1b653375ec5e3f05823aae6ac985e9403eeab12bb9f8 expected_cmr (CoreJet (WordJet XorXor64)) = 0x361c57930ef97d49cbc679faef1e3bcffb787995b961e5537d2b1eebc9c9a6e8 expected_cmr (CoreJet (WordJet Ch1)) = 0xb841b857a4aa50eaca27a26f7442fcbfe954677ae6d455f605654989e35aeb13 expected_cmr (CoreJet (WordJet Ch8)) = 0x353f63b0f8cb54f5ae6575af8ca2242ceee9f27a84186eb80e620d5e2e8548ec expected_cmr (CoreJet (WordJet Ch16)) = 0x9cff11a09b6041e5f2639ae4c065a18fc675db2fbd985408e28f027a99110e11 expected_cmr (CoreJet (WordJet Ch32)) = 0x071cef8039c79f7131cd6a5fe493dc268f9db58f7b20a85555e297bdd216cf40 expected_cmr (CoreJet (WordJet Ch64)) = 0xd555d21963b0192fc97214b63dc1c3af758b291158f0e1a3bcfdea679c666da6 expected_cmr (CoreJet (WordJet Some1)) = 0xfbdad6b022a0c78ff35604aafacd27cc10f51ee0698c41f1ada90397618d526f expected_cmr (CoreJet (WordJet Some8)) = 0x2d8c8f71ee5e7582f0ed65f526c02605dcb93c0bddb9433aff3f25c228acda8a expected_cmr (CoreJet (WordJet Some16)) = 0x7e2ccdbfc24dd8d8a904b017dd4f57e7c87496348aca7d0458c9d16b68bcda1c expected_cmr (CoreJet (WordJet Some32)) = 0x4536aeb121c4273ffc2a48fed9eed0312ebd972dec5681f47ead0f62d954452a expected_cmr (CoreJet (WordJet Some64)) = 0x7f0bbd9d6631c1309f901c2f0d7a0d284a34416cf750db1fe2b9f3d6ed709409 expected_cmr (CoreJet (WordJet All8)) = 0x1d3ec7fb6a07847c92b8a998e1f6b478319d050a387642f4032d2f7d2e027fcd expected_cmr (CoreJet (WordJet All16)) = 0x16f0c9307eb8f4c1fdd1bafaef2879242958498e8f5b2e0d29f06553dc06a0bd expected_cmr (CoreJet (WordJet All32)) = 0x0eb8b40d29021747eec451d4e663586a436c2db0932675daf2166123bfe452a6 expected_cmr (CoreJet (WordJet All64)) = 0xa65c82d53d382ee29aa88b7718a97fbbce6475ec32c4b4cd6908fde45d81b624 expected_cmr (CoreJet (WordJet Eq1)) = 0x607f6b8f5d25b80e05a2bf79d62e870799522cc3e39ce96257455293f9b2b2ed expected_cmr (CoreJet (WordJet Eq8)) = 0x99787ba2672dd0eb4d7d2ea99449de8f798e7cb181a5e166e1a53f9802b62064 expected_cmr (CoreJet (WordJet Eq16)) = 0xc996e42b979abc530cc271636671e92054876a1ecaed1433fd619a25fe6d03ad expected_cmr (CoreJet (WordJet Eq32)) = 0x66d38903e73b1a1320c68a4a3970d71f94ba9e2b1516839943fb15e44ebf57fb expected_cmr (CoreJet (WordJet Eq64)) = 0xd6a666b4e0f9f575508dbf3b31ceea68393c7db2e98bc592fdd26fae837a0b87 expected_cmr (CoreJet (WordJet Eq256)) = 0x778d1506c735d2776b950facefc159b678dec03828cf0273eeea64a9da98c12c expected_cmr (CoreJet (WordJet FullLeftShift8_1)) = 0x733fed0847a2ffac9aabf50a2feb50598984f16d8b732468b3d315c01ea4299b expected_cmr (CoreJet (WordJet FullLeftShift16_1)) = 0x14dcc3466fa828a3f0740451b8037d7ad603eadc80aaeadc664434ac2ad7fd9c expected_cmr (CoreJet (WordJet FullLeftShift32_1)) = 0xce33b5d0c58d2d0b9b5a9944d3dabda023cd44647be67cf4082830bb205f8fbb expected_cmr (CoreJet (WordJet FullLeftShift64_1)) = 0xd463ccdc7fd14e5e894162b2ae714128a10dc92000b54c843b649ccb775626e5 expected_cmr (CoreJet (WordJet FullLeftShift8_2)) = 0xb4474d0ba1cf4fa2d64cd4fe67bdc92cb89efa70cb99af7791bf7ef6e909d2c7 expected_cmr (CoreJet (WordJet FullLeftShift16_2)) = 0xafb7e928b052c2287921662cd8ab122fe074efd251a5c9cfbcaa369d06337392 expected_cmr (CoreJet (WordJet FullLeftShift32_2)) = 0x3faea9b573fc069d8f430faca897b6871ea09573c715094b1f1be0818488a716 expected_cmr (CoreJet (WordJet FullLeftShift64_2)) = 0x48c89b191a51b6ab034c80eaff348238d93fb31c1e92e7f2ae49317e0e33f82d expected_cmr (CoreJet (WordJet FullLeftShift8_4)) = 0x8eb522b9970474adbb7ab0de37c4e7a056a1cb212e4103e4a8cbbbb63d975606 expected_cmr (CoreJet (WordJet FullLeftShift16_4)) = 0x166f348c59e26f89a83a991f67e5dbf710cfae3d6d96938282bb44c1afa7109b expected_cmr (CoreJet (WordJet FullLeftShift32_4)) = 0xcdbb0d23310590113c934fe66004d2a11da9cbf8873d00dee7f02296ff0a2f12 expected_cmr (CoreJet (WordJet FullLeftShift64_4)) = 0x293132eb15ddf41774b0005a3b5c50959fa8982b759e832827c74fa82850666c expected_cmr (CoreJet (WordJet FullLeftShift16_8)) = 0xc0cd015de8ac4fccd8db89f4e5142fde279755b542a24f57a2a3c7c1f50d1db5 expected_cmr (CoreJet (WordJet FullLeftShift32_8)) = 0xccd924e1a61849420ff62ed8b245a3aa18c98c41f9c5a3c0b885863c449b7d14 expected_cmr (CoreJet (WordJet FullLeftShift64_8)) = 0xe6abded8be585eb0b6d46e0c5eb28a745f4e5c56fd6521f8f396cb21a758f74c expected_cmr (CoreJet (WordJet FullLeftShift32_16)) = 0x1cb36e6f99308515d4b711909c574b2124c1ff422d8d7d9482e25d8788b3b957 expected_cmr (CoreJet (WordJet FullLeftShift64_16)) = 0x882dce212a0e61f8f94cb5e32e00a5287cf64f20c21fca84f1e3df7f4a6291cd expected_cmr (CoreJet (WordJet FullLeftShift64_32)) = 0x3975907333e127306255b7f88939e2857f42ae1bf0c66240a8224c8da38bb1be expected_cmr (CoreJet (WordJet FullRightShift8_1)) = 0xd9d4b16d37e4eb5cc5150426e3e86cf60abbdfa1d0ecb41582965e8000cbd291 expected_cmr (CoreJet (WordJet FullRightShift16_1)) = 0xb379e296e9a98fb3b5662b8ba04e3cc1a43c74429e931233fdd7fc8fe6b7a2e0 expected_cmr (CoreJet (WordJet FullRightShift32_1)) = 0xad0d5c75ea68437191770d7fdf804bbc9d573d5f10199823d809c9c46cd275ad expected_cmr (CoreJet (WordJet FullRightShift64_1)) = 0x03afb547c30913f16f3e370d7f9ca0290b615b4285051bb93c3c1a9b72ee8de4 expected_cmr (CoreJet (WordJet FullRightShift8_2)) = 0x079aa16617198ad5df2c98a63af76c1b3e120fd2106b225f63fd06ac571d04a4 expected_cmr (CoreJet (WordJet FullRightShift16_2)) = 0xaeb8c60806a479207758e39083b4a9a7a14da4ee9bc1097fc5cb4b75540d7578 expected_cmr (CoreJet (WordJet FullRightShift32_2)) = 0x44384b1506d443d2f8a2882b4563d7931a7ebce64acf0d02ee59ec69d3065239 expected_cmr (CoreJet (WordJet FullRightShift64_2)) = 0x0673bff21e375e5dbcaf3804664825dd674844d2fdb784a4fefbc925cf6b27ad expected_cmr (CoreJet (WordJet FullRightShift8_4)) = 0x9d9d3f638a846386a21e715f394616864a2ef7984a88cd95505566297be7e06c expected_cmr (CoreJet (WordJet FullRightShift16_4)) = 0x60b7f08475cc0cce64dca12d9f6a919c30618110eda14065929c004e7fc1b0fb expected_cmr (CoreJet (WordJet FullRightShift32_4)) = 0x2e9a8ab5a1817bd0b8a46626994917a0de1a745e99520ce6ebcc67d4636551b7 expected_cmr (CoreJet (WordJet FullRightShift64_4)) = 0x4c25f6011fd3d1ac18e11eb43061fad69f3ce39f7a99cede50cc85bf88bfba82 expected_cmr (CoreJet (WordJet FullRightShift16_8)) = 0xf79dba3e0af3d6a559a9e9dffea710af623fe6e6644b897995d71b8a4167ddb0 expected_cmr (CoreJet (WordJet FullRightShift32_8)) = 0xaf47d4f96e7d8026d44e6eca1b807f73344ce2eaf700b2c82b4bb00261a86f94 expected_cmr (CoreJet (WordJet FullRightShift64_8)) = 0xa51df9448602fa81001aa1b5b13be88d4b2f4d0f60740801cef991002fe37d6d expected_cmr (CoreJet (WordJet FullRightShift32_16)) = 0x455299fd6f42ab49dbb709e65a3b5366250bdc545d6229e8e236056ddd1977fd expected_cmr (CoreJet (WordJet FullRightShift64_16)) = 0x1fb056fcb690cee3cff72c7decda806d2146c492ae731a6b94b8bb4f1599b0cc expected_cmr (CoreJet (WordJet FullRightShift64_32)) = 0x356f7dd46ba33f84b06672fde9a2972e80f3ea965ae8bc0bff67aa2f69f10b56 expected_cmr (CoreJet (WordJet Leftmost8_1)) = 0x5a730b58e3abcb2f4de22159803023102cd66421911920ca21a2a05c9b211ce8 expected_cmr (CoreJet (WordJet Leftmost16_1)) = 0xde6a4c98337e680d6e6ee2bf36d3a0817d2a9a98325f87e5eceb8a6f1168f5ca expected_cmr (CoreJet (WordJet Leftmost32_1)) = 0x5fb8e6342ab74ee2c9225b872fa0c912046a69dbb719bcd6c8d79b7660c4ebca expected_cmr (CoreJet (WordJet Leftmost64_1)) = 0xb924d33b5efefc8e2042081925917cff239b31c8bdbdf4acae6bb8d9cd217b4f expected_cmr (CoreJet (WordJet Leftmost8_2)) = 0x25790856103dce6c7bbb3dd718b169109cae853799d12456c85d8349ec18dc53 expected_cmr (CoreJet (WordJet Leftmost16_2)) = 0x005809b8051a2a502833b22c2c17981eaf9dd1d3dbc8f8c894516c1d5f31146c expected_cmr (CoreJet (WordJet Leftmost32_2)) = 0x123068554595427e3c1de243bab66f3348368aaa44617d6a02479fb704bcfd1e expected_cmr (CoreJet (WordJet Leftmost64_2)) = 0xbcec97f43ba55cd40d85a1e76cbade7b0b1e9f139747793dcb3480bee1f751ca expected_cmr (CoreJet (WordJet Leftmost8_4)) = 0x73d9f018157a14784ee70b219ceb4042fa621d0ee6d545a0fdbab9444346e331 expected_cmr (CoreJet (WordJet Leftmost16_4)) = 0x9c50ee2284d857c47c0544471354105e98dfe02754d2e42de11d3234ed10b642 expected_cmr (CoreJet (WordJet Leftmost32_4)) = 0x55a87b66c339e363e03d4daac62290eba93c1a3a7382cbf61f20b34a505124ad expected_cmr (CoreJet (WordJet Leftmost64_4)) = 0xd2d6452092d6566f89a1f64e736596f9000e5e6f63e40017d0cb80f3f7adfd18 expected_cmr (CoreJet (WordJet Leftmost16_8)) = 0x5a1a72914e149c22b464c8f6a3d9cf41b07192bef0d8a1cc7cbe5704a9e8ea70 expected_cmr (CoreJet (WordJet Leftmost32_8)) = 0x9f345bee0b162d42a035718f8ca1adc8ac2f710dc40052a82566e6d807bef8b8 expected_cmr (CoreJet (WordJet Leftmost64_8)) = 0xf77b62bb01b90511b6d06ebf2e36c06565acb5aad1efc77c36a10a261de921da expected_cmr (CoreJet (WordJet Leftmost32_16)) = 0x54ae50b46b5b2e68f536c01c39617b0cee42e1c49a2cd1d26af8ea8715ac4d11 expected_cmr (CoreJet (WordJet Leftmost64_16)) = 0x12aa85e05c1e9622279c4c2ddcf897c95ddcc0113997283b6b3e0949bc8113cb expected_cmr (CoreJet (WordJet Leftmost64_32)) = 0x9c89693986e55733ab962a300b0579503d83de8ac19b179b417e1ca25385b38f expected_cmr (CoreJet (WordJet Rightmost8_1)) = 0x999b686e60b3d1ecd6c6d77fbca82cb2abbd4182c8211267475fa0c1901d89f9 expected_cmr (CoreJet (WordJet Rightmost16_1)) = 0x3f3c4346871742265e87f001b46de7d198751b34faa18018de60c8468d9b98a4 expected_cmr (CoreJet (WordJet Rightmost32_1)) = 0xcb0db569a36186a25605a9d2e4e10a20c111d50c34f17246520bc454d8682836 expected_cmr (CoreJet (WordJet Rightmost64_1)) = 0x5e8fb49face034481dc653618e2a8b65eaf0993f28844cc9b130cacce45e82de expected_cmr (CoreJet (WordJet Rightmost8_2)) = 0x5307ffbf516cd0eef3ff4387b9052c144a4dfa2329237c6b274992b2c8047b60 expected_cmr (CoreJet (WordJet Rightmost16_2)) = 0x78f171476a3b0ed1e3a5455a5fbbcc901981b3230fea1264204dacd081f94080 expected_cmr (CoreJet (WordJet Rightmost32_2)) = 0x00b8815ad7423dd58cb98be82cad26675c3bf54a0bedbade3464b4fe5a4e8ce6 expected_cmr (CoreJet (WordJet Rightmost64_2)) = 0x83d2da6f3420d779bcb8f60d0b696eed74c31db08addbebd1235a5df8f59c42f expected_cmr (CoreJet (WordJet Rightmost8_4)) = 0x7f52e645bbbbd79269c43ef02db982f8c63633c179e4069173933604cc635bca expected_cmr (CoreJet (WordJet Rightmost16_4)) = 0x75a1dfb6ae2c066b2d0e2093048adbc50d4650656fb2d3578b57d9de4c61c8b5 expected_cmr (CoreJet (WordJet Rightmost32_4)) = 0x3dfa7a20198e42d6a7948c8ed8e0d47ec7c0007b3d6866ca15e3da045b8563c7 expected_cmr (CoreJet (WordJet Rightmost64_4)) = 0x841bbd652742ddd3adeae43cfed6329f2fd62e6fecd0fd58e3c3fb8b5a0e4dd5 expected_cmr (CoreJet (WordJet Rightmost16_8)) = 0xee769c1cc8a3fdd1838fc9f0490ce70393fd91ba3cbd4abd08649fb9c44311bd expected_cmr (CoreJet (WordJet Rightmost32_8)) = 0x17b58d6e304b1c7e5dbf0c4df6fcc803c008944c7995555b94e1289b2549be99 expected_cmr (CoreJet (WordJet Rightmost64_8)) = 0xa0a61c7658a18623bf1d011a9792d518fbd024142a904400ecdeea92457a0a81 expected_cmr (CoreJet (WordJet Rightmost32_16)) = 0x06faa3be678cd6fdd7f3112ebf2c48627afa7875f7068d26a9cc045b2c8f11bc expected_cmr (CoreJet (WordJet Rightmost64_16)) = 0xc64ca9965536f237bc4d166e4aeca56eac2662e63accb98b6e542560f9e538da expected_cmr (CoreJet (WordJet Rightmost64_32)) = 0x7d2dff6e3dd504bb0e5703a033586d27d96644c048ab34a45bf535129d501167 expected_cmr (CoreJet (WordJet LeftPadLow1_8)) = 0xdc5a47f8d77765c994cbe86aae44a9c5ff2ebc3810d79cd83bd2c4098c762bf5 expected_cmr (CoreJet (WordJet LeftPadLow1_16)) = 0x4aa40520faed72e6e9be3be6930f1e32b0b182c4327ada94a71f006d149015f9 expected_cmr (CoreJet (WordJet LeftPadLow1_32)) = 0xcfb4753bb9ba3621ba0937825fade643098e385ed68efb16ff58ecf365d7e5e2 expected_cmr (CoreJet (WordJet LeftPadLow1_64)) = 0xe6f1c09b5fe126d0ea86e7bfc0b28e849f8f7efd31064ea4fd1cca071b45db93 expected_cmr (CoreJet (WordJet LeftPadLow8_16)) = 0xac1a4c9783e4dbed2700eb2952e3062a5a72712f82159861b08e67ef4a71f5f2 expected_cmr (CoreJet (WordJet LeftPadLow8_32)) = 0x3da5f1a8c97819ae7e10b9364ff84996d0d73e698a49da691f69a273254201cd expected_cmr (CoreJet (WordJet LeftPadLow8_64)) = 0x25bc18d49f934072277d3f613bf16c118df197bc92872d2affe417adeaaf1a85 expected_cmr (CoreJet (WordJet LeftPadLow16_32)) = 0x21537f7d8f97f2203cccb035ef1d46289ee8aa50f0236077d0d0b210700440a1 expected_cmr (CoreJet (WordJet LeftPadLow16_64)) = 0x6b2ea9630c5dde037aab2bf733219b99c7edc2ecedb9a03adfd169430b08bb9c expected_cmr (CoreJet (WordJet LeftPadLow32_64)) = 0x2d88e4d01e0108c0d6880f3ce8482bb0951f2b3fc5df4b1adb184a1bfd1f6465 expected_cmr (CoreJet (WordJet LeftPadHigh1_8)) = 0x6c277c4cd053dd3502dbe0bbc14eb0b36a201abef3b174b0ebfe052018b67e67 expected_cmr (CoreJet (WordJet LeftPadHigh1_16)) = 0x93aed6f68750774b2dbf8314cadebe5a415243fbdf7c2eea8b223df3261e3bdb expected_cmr (CoreJet (WordJet LeftPadHigh1_32)) = 0x008298f82fb6cf37e9dc703ea4f949565c2965a7c7f4fa22f55456423408a3ab expected_cmr (CoreJet (WordJet LeftPadHigh1_64)) = 0x2b454ebd791ec7dacedcb86c69d026794a5dc3725261e7dc1650cc888117fc4f expected_cmr (CoreJet (WordJet LeftPadHigh8_16)) = 0x2178dc76c04c79d91815d38c967f34213ffcc6c5f243c9562973f090ca5caefa expected_cmr (CoreJet (WordJet LeftPadHigh8_32)) = 0xa4e86b53e5d00faf0b3e9d53202af7738dcb8887a18dfee5be34c497698ca6b7 expected_cmr (CoreJet (WordJet LeftPadHigh8_64)) = 0xc843a72c41170f403433c436a39b05cf193c27d8be3530f9b94e42d763003d54 expected_cmr (CoreJet (WordJet LeftPadHigh16_32)) = 0x888c7e0ab0031475c514f9b37c81f45a47314984e5027508ddc5eb8d8d10beb9 expected_cmr (CoreJet (WordJet LeftPadHigh16_64)) = 0x526b3505450136d681a50b4bde4fa612da9d69bd08170ea32d0a2651115072eb expected_cmr (CoreJet (WordJet LeftPadHigh32_64)) = 0x5d41221cf6158297b06c1957112c0d12f3eb917a2f509a539d5c9b7910219b65 expected_cmr (CoreJet (WordJet LeftExtend1_8)) = 0x5a831ca99621517a2b354e5cac38bc3a30c4001f20d25d7797addcac5da86106 expected_cmr (CoreJet (WordJet LeftExtend1_16)) = 0x9a48a4778e7c3c285ab65329d1ccc4999d2d194e005bd7946949533d8cba806c expected_cmr (CoreJet (WordJet LeftExtend1_32)) = 0xdab6a533cbcbe8362cf1d5a16ea37cbc7edc7fc8a9428571e171ec6ee44d0800 expected_cmr (CoreJet (WordJet LeftExtend1_64)) = 0x110e5c1ef0b469a7638570da944d232e0f28c46151a225357de3e90457a88ea2 expected_cmr (CoreJet (WordJet LeftExtend8_16)) = 0xfea1f25a82fdf6f8669cc40fbb8e54a92658bfab94eb082f717ba265b5d844b4 expected_cmr (CoreJet (WordJet LeftExtend8_32)) = 0x09d703ca46f75d051a93d0e8a2af0501a38e848683ef109c1fb4b5be20e6315d expected_cmr (CoreJet (WordJet LeftExtend8_64)) = 0xd3dafcbdab69a2bb320f8d230cefd09c27a154c51e7e5cd5334eafed19e20df4 expected_cmr (CoreJet (WordJet LeftExtend16_32)) = 0xdcf42b6542f6d41cb7b50e7c772f3c7f6e432232f2ba2079b386a05d7b466add expected_cmr (CoreJet (WordJet LeftExtend16_64)) = 0x2eee48a92237947c1a517df995f44f1dfef20ddb4e9b530b22d18a0a7fd628aa expected_cmr (CoreJet (WordJet LeftExtend32_64)) = 0x84fcc69ba1db50dbd5363cf2777957601de2568adf07af4161debb1e5e37310a expected_cmr (CoreJet (WordJet RightPadLow1_8)) = 0x59d72270ef0e8f770c8d11f31773f9b6e90a4aeceb5bfb3dfe968c4e9dac5fe8 expected_cmr (CoreJet (WordJet RightPadLow1_16)) = 0x7914c8f22247c2c34b9c84e92d1444aec2e17a0ef586bab2788ee6ef68840d98 expected_cmr (CoreJet (WordJet RightPadLow1_32)) = 0x31b6ce26e559f76cf366f4806985ecc299550f15d4c3a6729e29d70e39895652 expected_cmr (CoreJet (WordJet RightPadLow1_64)) = 0xc5524ae6548acd63082d94893e18f9edbb9231e76bb4e11bbff6a7bd16f4b029 expected_cmr (CoreJet (WordJet RightPadLow8_16)) = 0xaba47a536e1227e122baacf19cfd2823b9b78d79cc06d34c348b14a1a15abd64 expected_cmr (CoreJet (WordJet RightPadLow8_32)) = 0x8f80a6c274716b6722041134ea1c68aabf0213298f4e18f8f492dc53808a3174 expected_cmr (CoreJet (WordJet RightPadLow8_64)) = 0xd69c85e7b2d7e949436cb1295e4aa70557d75e7cbdec02cca85fbfb13308b210 expected_cmr (CoreJet (WordJet RightPadLow16_32)) = 0x7731d560d37592d1a31f7362967ab2e47592aca6e92ab858823792dae5d2db52 expected_cmr (CoreJet (WordJet RightPadLow16_64)) = 0x0fe1c0db9d4a2d63e2ba4a33117aadba64514a2b87a7a4e793faacfe6b363447 expected_cmr (CoreJet (WordJet RightPadLow32_64)) = 0xd4227d066f18b911d6f5d9bfb9d9f46e9aeadbbefa34d474432a1e789e4886ff expected_cmr (CoreJet (WordJet RightPadHigh1_8)) = 0x7103c0fe00f522a2216c4a6be5f7e0eb4d703ca78f9c598f6b3dfde437d80c84 expected_cmr (CoreJet (WordJet RightPadHigh1_16)) = 0xff1297d878e26e1959bcc7e8aef97ac0b65adc39923ec6505e50f98305733b6c expected_cmr (CoreJet (WordJet RightPadHigh1_32)) = 0x283f8afb41382d2be18f8a77c314ba1776cb80c8ec36ca12aa67b32bb64ed843 expected_cmr (CoreJet (WordJet RightPadHigh1_64)) = 0xa342352860a3350d79c3e9fc7a4ab3789b8b0297856fd169ca4d7de25f7d7cc4 expected_cmr (CoreJet (WordJet RightPadHigh8_16)) = 0xc0e2fd46f7883b1285a6f1a1db96d93c2548040fcd3f5c23fbb20b5e83037c96 expected_cmr (CoreJet (WordJet RightPadHigh8_32)) = 0x291e627708520c2ca6aece32a877b77849c4a7a213cb89e1bda7c5c5fe755f73 expected_cmr (CoreJet (WordJet RightPadHigh8_64)) = 0x6b6fa2372ed25e4a34d4ae172342adbb259be8987600db192ecb8da434b9d88f expected_cmr (CoreJet (WordJet RightPadHigh16_32)) = 0x3e4e5e9e71e137a2686343e05ac56316acfc58991cb38db1b3234413f730a142 expected_cmr (CoreJet (WordJet RightPadHigh16_64)) = 0xde09df9d43ddad2d691204986cf0819d6b8045bca414d80af2162892a9257ead expected_cmr (CoreJet (WordJet RightPadHigh32_64)) = 0x5dc9107d4534958ce4422767563a031a380f60d3837148ab3c8cc9c4c7d996a2 expected_cmr (CoreJet (WordJet RightExtend8_16)) = 0xbcb2683a8cb8b8c235faa896a9c069e1b55bb0558e739e70e28914211e3275c8 expected_cmr (CoreJet (WordJet RightExtend8_32)) = 0x6ddb5548fd583cd2d3586e6b8bf995246b61934f4976446777dd5740b319e462 expected_cmr (CoreJet (WordJet RightExtend8_64)) = 0xda4f9c21455126820758a2e4b53fceb4523e6e7a2923a1a161fc37892ac8da2a expected_cmr (CoreJet (WordJet RightExtend16_32)) = 0x780716d3e8291a51e45ada50558efe411c475c085eec5a28ad9791c312fee2bc expected_cmr (CoreJet (WordJet RightExtend16_64)) = 0xc770497e452308ebf52e51b0585e9151e0ffc35086ab772d7241532a1be15e07 expected_cmr (CoreJet (WordJet RightExtend32_64)) = 0x42b43adc74b5266c91d73df491dcae59738804eb440b23da327530487486b7e8 expected_cmr (CoreJet (WordJet LeftShiftWith8)) = 0xdd9cc1cea74909481ff58f876ff66e0f5d52bf89b0258fa95b320002c32a7915 expected_cmr (CoreJet (WordJet LeftShiftWith16)) = 0xe29107885550450eb727d0cf14e104ae12f83a24e2e2aca3cce433de2f35d7b3 expected_cmr (CoreJet (WordJet LeftShiftWith32)) = 0xf39250c45a1310cc638c788deec5c365b4d176d10efbf4c601cf5eebe0a573e9 expected_cmr (CoreJet (WordJet LeftShiftWith64)) = 0xad8794cfaef2b7f774fa68d309bbc98dfee58c40400b2eb578a212f438bd07ab expected_cmr (CoreJet (WordJet RightShiftWith8)) = 0xfcb5be6507f0ca44be2be1cc3c3cfe3994404b8083bd7602b2102cb1fcfa2c61 expected_cmr (CoreJet (WordJet RightShiftWith16)) = 0xfd977030e3a25a32e775b8d5e87174a7a9e8731ec36cf1326420ad91502e6e98 expected_cmr (CoreJet (WordJet RightShiftWith32)) = 0x2829ba021f54077affb66ac6b6dfd3fef38bc41491845a41ce9dd370586c2d04 expected_cmr (CoreJet (WordJet RightShiftWith64)) = 0x006fa3c54579754786fc64dc32e19a225cc152c94deeb3c6ab2967ddbfc64653 expected_cmr (CoreJet (WordJet LeftShift8)) = 0xab9d3e9ac39038ad88b103f072254c0ec6e27475e275c245e88cce0d072e6446 expected_cmr (CoreJet (WordJet LeftShift16)) = 0xb05360184d0602b581405e32960b31c05219358de89efdf49464723dd625617a expected_cmr (CoreJet (WordJet LeftShift32)) = 0x34bf54f594c2621007f8c78b30fad39672009bb366aace1e5e41ee4d9cc541a8 expected_cmr (CoreJet (WordJet LeftShift64)) = 0x5de953f04deaed9047567647a1eb7abe665feccbe7ed10cb7dbe691273c094b0 expected_cmr (CoreJet (WordJet RightShift8)) = 0xa4c3546ff27e56d64e918ab2fa6d00fc2704585b25bde0049d6d8f48d8cf1cd0 expected_cmr (CoreJet (WordJet RightShift16)) = 0x8b5e0feb958130f0508332159e54c2df98af83521acab3084fd4f7c3a2ccea77 expected_cmr (CoreJet (WordJet RightShift32)) = 0x4b1f2580e0850d38e2a1157338052f1c379f9d8157f62d33890af24fd9a7f73e expected_cmr (CoreJet (WordJet RightShift64)) = 0x91a297d7b58a393bf59025947747c86dd487659cc56fb5a6f6439955129a9563 expected_cmr (CoreJet (WordJet LeftRotate8)) = 0x9e966e880c6b0c483c90beeed7c5737ca5f3facf85aab3d531ad34bd7b1a9b68 expected_cmr (CoreJet (WordJet LeftRotate16)) = 0x88c12337cd754f8380986d86fe3a89e262746653e1badd9cc9b47645fe57195a expected_cmr (CoreJet (WordJet LeftRotate32)) = 0x39816ccd9e9cf1191f065d2eb7a7fb83828d91ec7d9977a1fc70be9b31a468b9 expected_cmr (CoreJet (WordJet LeftRotate64)) = 0x8b2355c31e3b614bd4b41c3ecf277424d026766b37bc6c105621f4f6a16f9bdf expected_cmr (CoreJet (WordJet RightRotate8)) = 0x00c7c26d95a50b5af9349ffe47e1d43f3d761f17a7453c984791e87dc6a311c8 expected_cmr (CoreJet (WordJet RightRotate16)) = 0xe510708247f91b4f0a8a22a446b8137d0d42bee74c8c1edd6d446edb2013b598 expected_cmr (CoreJet (WordJet RightRotate32)) = 0x98915731412922dbc516a7373afc4de64809f83b264bcfca6ae74883dbe104d6 expected_cmr (CoreJet (WordJet RightRotate64)) = 0x9e2fb98adf1029339dbe45a22a54a390ca0986edcea32eacb82ebcc894a2711a expected_cmr (CoreJet (ArithJet One8)) = 0xff594e22bfd75813c056e0a234ed12fa8287d1d5316f23902bf079dbcc4f4ea8 expected_cmr (CoreJet (ArithJet One16)) = 0x3f9f8dd14c46ee02471557929ac2bb6c1aca00521d8afaf0dcd9f2ca7f31e604 expected_cmr (CoreJet (ArithJet One32)) = 0x478dc39dc3995e2edb7ec674656cae798f52e572926174a668cc97bca448d1cc expected_cmr (CoreJet (ArithJet One64)) = 0xa392cefc0da53c65aee612f5c6816ca892fc156d43714876b3a00568e1ba3eba expected_cmr (CoreJet (ArithJet FullAdd8)) = 0xed3ba5b79ea45b187a2d43e8ed802de1ed4426596cbe32e757c8511915ffa5cf expected_cmr (CoreJet (ArithJet FullAdd16)) = 0xfc9e5df83bfdb9028c87d139f8583903cb2a07042a73e53481deb52ff1f1f884 expected_cmr (CoreJet (ArithJet FullAdd32)) = 0xa7d98d50d045cb906b195e6511879495c851095949a9c01e6039a84b2a5ec909 expected_cmr (CoreJet (ArithJet FullAdd64)) = 0x7aecc8c9053bb2fb170c1c972fd4002564e152a06d9f458075e38c7a0698a7f4 expected_cmr (CoreJet (ArithJet Add8)) = 0xd7328c0914ee999efa0a6cb26eb40912c215c062e58a981ae6b2e4a80474a1da expected_cmr (CoreJet (ArithJet Add16)) = 0x26ae0994ce8b771af7ad2851b83b49a5950536589f67bd855947046029751c0d expected_cmr (CoreJet (ArithJet Add32)) = 0x3d7674466ed69e1dbedcd48057a9e6288c222532fbc5048049928cfb77f829d9 expected_cmr (CoreJet (ArithJet Add64)) = 0x9b56e61eefe2805ca87396bdfb03f5e1b1385f7ac4bff7684026a07cf97fb6f6 expected_cmr (CoreJet (ArithJet FullIncrement8)) = 0xd304ea28a95d496d14b4f2fb5c860372ecf247befde3ea3b2ad67bce99039dbc expected_cmr (CoreJet (ArithJet FullIncrement16)) = 0x81380adaa3a547f1bc4bbb646bda9d9fb7bd4dc1b3a9f3dd220b56a47c2798fb expected_cmr (CoreJet (ArithJet FullIncrement32)) = 0xa760a8449a2ab5dedb4ee51bf5c25a8f06af0666df7fc419b498b90976d698cb expected_cmr (CoreJet (ArithJet FullIncrement64)) = 0xc6af30dd286d6e21c38860ed1e2f212a21b2fd1edeadb5e0fce2e3fd75b7f3c2 expected_cmr (CoreJet (ArithJet Increment8)) = 0x0c717e84df67823f5741b3d55dbeb4729c2bd62f5d1def3cabccdd6cb8dcb56c expected_cmr (CoreJet (ArithJet Increment16)) = 0xdf274888ce4cebdd5708b38dc3dbb19cc2f0364b2463e99cf5aab4f8a23ea58a expected_cmr (CoreJet (ArithJet Increment32)) = 0x54f757aea76bc7a39fc43d19b8dd563a6807df0277a56fcb501089ce7d06774c expected_cmr (CoreJet (ArithJet Increment64)) = 0x79ed5f7799fb09da510429a20128bed091d8587647071285cdec3a0c95709e5b expected_cmr (CoreJet (ArithJet FullSubtract8)) = 0x6885e141ae234c1e2a7e4f235298939036969c950f2cefd459b498ac3dd89220 expected_cmr (CoreJet (ArithJet FullSubtract16)) = 0x1fc88e2329f4aaf12b30513f7a21cf5d8de24b600a19a21741281b4d61aac633 expected_cmr (CoreJet (ArithJet FullSubtract32)) = 0x782705fb42e36a7ef831200c617738d31e13b1d0e7ceed693f13338835b30acb expected_cmr (CoreJet (ArithJet FullSubtract64)) = 0xb2856a9180231bee3cb89230f75c292af3e75239dbeb396548441e6b5a27e813 expected_cmr (CoreJet (ArithJet Subtract8)) = 0x40950b86f6f1f99355dee11f77daf279a0cb6c6d156ae44b7d5d257164b267c5 expected_cmr (CoreJet (ArithJet Subtract16)) = 0x569e6c6b39e7d812659b67aac08ad15099eead798fd1d42da17ee3f0d4d4492a expected_cmr (CoreJet (ArithJet Subtract32)) = 0x19d35e0af1e16514a6dfc29a914187133964c480f660e7eb924ee16dbaa249cb expected_cmr (CoreJet (ArithJet Subtract64)) = 0x523e118628bf3ac1a6be5a72bdb1141b89e0e001e402adda8258790003f88ad8 expected_cmr (CoreJet (ArithJet Negate8)) = 0xd871c542473f4dd902d31fe3fc9ac0f3319e42e80cae2181ffc85e6c60fb0988 expected_cmr (CoreJet (ArithJet Negate16)) = 0xf642173b85ef21969d8d9048807e3d4facf3f5f9e59aa5cf0c60f87422ed7c8f expected_cmr (CoreJet (ArithJet Negate32)) = 0x549b65ce97c6b334b8ae9456960e365bb284d76d4005e921f489bc3626171b06 expected_cmr (CoreJet (ArithJet Negate64)) = 0x35acca27ce658579ef1c55ad1abea0050d9366d12209ad13052549c3436491d0 expected_cmr (CoreJet (ArithJet FullDecrement8)) = 0x7c5e94a9980281821737b1ce73bfda4c79ef649b3d05cc1c00c4a8b64b949bbe expected_cmr (CoreJet (ArithJet FullDecrement16)) = 0xd4c2edda872c05506f792cf546a89d4d7cffcb1e17f5da6103100e7e73a7737d expected_cmr (CoreJet (ArithJet FullDecrement32)) = 0x7cc2304d174312102e9b736345c77f771d1f6a9c9e1d1cd8db8cb4613980c8c2 expected_cmr (CoreJet (ArithJet FullDecrement64)) = 0x15c163454bcd754430da5579bbcaad26e57e95c772224b7b83c705f7deb64aa6 expected_cmr (CoreJet (ArithJet Decrement8)) = 0x2892ceb3b6ec5325d0c1b9f520425e4b05c2e1f437e0b3f581f41b9d0f7dff4d expected_cmr (CoreJet (ArithJet Decrement16)) = 0xe34db11879272b327a3bd034c0f61ef60a2be96fdfe0b2d57ffe39ce714c78fb expected_cmr (CoreJet (ArithJet Decrement32)) = 0x019ead5a7305606dc950fb55476d09c17d66f570dab510b90d2a27e2266599cf expected_cmr (CoreJet (ArithJet Decrement64)) = 0x34752cf4e1d0a431f017a68bebfab741bbc88affb57cc0b3025ccfdd67622f35 expected_cmr (CoreJet (ArithJet FullMultiply8)) = 0xd3d24554c466dd603754524736a71eb235def9b506965e32d56826e19fbad6c1 expected_cmr (CoreJet (ArithJet FullMultiply16)) = 0x88470cbf9b4dec37ea05d7b630f2f112547567d34f33d96e5f611bd9da97abb5 expected_cmr (CoreJet (ArithJet FullMultiply32)) = 0x28040600a66e1a0c52258520488b94c820c6cf86ca27ae39034dddcab904d1d5 expected_cmr (CoreJet (ArithJet FullMultiply64)) = 0x53014f35a8df2091af3ef9b8d16b38b9bc9661bfdbc957333fba2a948c1e8c25 expected_cmr (CoreJet (ArithJet Multiply8)) = 0x29da13374f7cb308405fe230f899485c500e6e9520c15e8a76e53a92e7ac64d6 expected_cmr (CoreJet (ArithJet Multiply16)) = 0x46e62abf8e30a7746de0e929f7beeddbde8b269bab08f76e9547108b1c360174 expected_cmr (CoreJet (ArithJet Multiply32)) = 0x2decdc5b0c6ff63d11f53852e0deed114481355bb6c6ce1546ae9f815bee7750 expected_cmr (CoreJet (ArithJet Multiply64)) = 0xbfa8626dbf10001de390d997f2ee7b190c24a78cfecb91f5d7c10c3f9ddbb1e6 expected_cmr (CoreJet (ArithJet IsZero8)) = 0xb4baa50938108426740d82cf1211e0ed126de3b76b8d259c50ad4b8fcab10ab6 expected_cmr (CoreJet (ArithJet IsZero16)) = 0xa25abd9cd2a4070c742ef8deb068292246032b96a517223b128cfc12d215c5ba expected_cmr (CoreJet (ArithJet IsZero32)) = 0x612a480ced6a79da6119546e056b8df9fa95d1124b96d601e1d3ea918cc56069 expected_cmr (CoreJet (ArithJet IsZero64)) = 0x18e8e1776ba080ccd3e1d60cb753414536bf70df185f72c9e070796f4c63cc71 expected_cmr (CoreJet (ArithJet IsOne8)) = 0x0aba9e576e64d2804c8ac4682bbba5390ebc31a6e3e2650f9219235df4a6ecbb expected_cmr (CoreJet (ArithJet IsOne16)) = 0x8435879ccb8644198dcb9a0cd73546d701fdd5a4c44323f563971599c37d16fb expected_cmr (CoreJet (ArithJet IsOne32)) = 0xddfbd9f0a2e67c07dedb89e896b6c4f7d45c5147eed0614e4ce7d08769aff82d expected_cmr (CoreJet (ArithJet IsOne64)) = 0x35c525548e48eea0f77b3bf97ab67a1ffe8fb094ede3325e4064b1659c6d0765 expected_cmr (CoreJet (ArithJet Le8)) = 0x0fb72d9f8ee2370aba55663a4899162e40ca5514713efb25e4a89e2a104b34db expected_cmr (CoreJet (ArithJet Le16)) = 0x63da727ccb4c6a9d4e000964e763bff934eaafd044287e1268d07ecdfde207e1 expected_cmr (CoreJet (ArithJet Le32)) = 0xdee29a91656d7ae73df4956fd8a2c6b627aab51c1129f9fe7f6ed3e34792c762 expected_cmr (CoreJet (ArithJet Le64)) = 0x01c55df7d4465966659ddfc94b36d033242c2ec593cee1212244077566ed015f expected_cmr (CoreJet (ArithJet Lt8)) = 0x73d0044655c0df45c271a1713ff9b9a43dde56e674d1754e76edb16f949c4fab expected_cmr (CoreJet (ArithJet Lt16)) = 0x56a20d55edb44388180544c3ed404145a3b66fd2c4113842f64eaeafbad4bb06 expected_cmr (CoreJet (ArithJet Lt32)) = 0xcab0dc5b0ecbf6d24816fc2010fc31193663c306968d9cee3b004c0bc184b478 expected_cmr (CoreJet (ArithJet Lt64)) = 0x47d67e52b27ba78edd075aa270ded007a7a9a68499344f2862f5069049a0cefe expected_cmr (CoreJet (ArithJet Min8)) = 0x6b012ca3185dc005e8942cfbc9f238dcedaf0c0043526447e3ec31cefa6e4064 expected_cmr (CoreJet (ArithJet Min16)) = 0xf158f40a860993b4107fb271fb4c8f955ba4542ad1821cd2f13c880ca4bee2e2 expected_cmr (CoreJet (ArithJet Min32)) = 0xe5e413dc5de5e22d66f32d8dbf50053ed278e175c0d4b344ebd461beb108e55e expected_cmr (CoreJet (ArithJet Min64)) = 0x43d82f6c6128aa01a997bb17e5e7f501e7be7db9589e566de97a32eae7e7b339 expected_cmr (CoreJet (ArithJet Max8)) = 0x6bc10370f3e7a7b92acb1423bbdf0b3d7e3cd0d2dbc705a34d8dc99c910422fb expected_cmr (CoreJet (ArithJet Max16)) = 0xe0114717691ac1a739288fc6ffa1c6507c43e6f1d4c18770ffa166ae839dd533 expected_cmr (CoreJet (ArithJet Max32)) = 0x1d723cb389942219ec103485317fa5d87ee15c24b2080f5046650d80308b189d expected_cmr (CoreJet (ArithJet Max64)) = 0x0073ac3c6ea939dcc7eee4ea63dcfd752037355b484f6e7016b300e2d28c07c3 expected_cmr (CoreJet (ArithJet Median8)) = 0xa4a0b6310ff0ed4a4c3e03ebc7a91306ef660424bc95a0d3f2fdb71fb6afd8b7 expected_cmr (CoreJet (ArithJet Median16)) = 0x2414e3c439659d8aa9d087e1ade77266673d1c8bd4e7501b22ac46a3ff39975d expected_cmr (CoreJet (ArithJet Median32)) = 0x0792356b610b57d0ec199e98535ea9bccce843a5df5dd2408c414886dfd6bd1e expected_cmr (CoreJet (ArithJet Median64)) = 0x0766d89b430ffdf038691b18439cd6fc4929172ea884fdaf166936b38b15fd0c expected_cmr (CoreJet (ArithJet DivMod128_64)) = 0x2296b70f600e8a214ad070b2194a677d3051bc1c490183975f2a1d3e0cade378 expected_cmr (CoreJet (ArithJet DivMod8)) = 0x48cd501bb2aa2acae014fe208bb9941d07a9bffe1ad6cd3d36fc6b0860f6eba7 expected_cmr (CoreJet (ArithJet DivMod16)) = 0x648fab864374846abf4f9d9defe275614d33f4829c36a47ecb53d7bfb605485f expected_cmr (CoreJet (ArithJet DivMod32)) = 0xbd3d4d552d7b347bd8a44e3ee224c846be230ff6e2044ddb97f48e27d20c4225 expected_cmr (CoreJet (ArithJet DivMod64)) = 0xfa6bad6a95e2aba4305bfe91cc47acc3d99b92e675e69d3b37bb09133d390d0f expected_cmr (CoreJet (ArithJet Divide8)) = 0x2ccfbc7c02bf4d530493bb22867a951d8ae913126687597284e9bbb3e1e7e349 expected_cmr (CoreJet (ArithJet Divide16)) = 0x470b01a57c4f9d8f997fcde006191611dda4c98ba2a5f1da134ae4c22d52e920 expected_cmr (CoreJet (ArithJet Divide32)) = 0xab03acd893610c3c6582e7f7fbe5e7562574a7b26646f1c2fdc6e76e445a77a1 expected_cmr (CoreJet (ArithJet Divide64)) = 0xebfc56fbb8a47e73ffabb7ea228ac78437be820eddfa47814ccebd261bd8cfff expected_cmr (CoreJet (ArithJet Modulo8)) = 0x5c63c77a1608e2f6a3748c110fbb9a1c569fb4d540f3dd2e4f80e90dd5ea9982 expected_cmr (CoreJet (ArithJet Modulo16)) = 0x62c179ac84c5750b425f9a1b8f81edaa7f5cf22c19d86b0dcf96dea6bad99b3b expected_cmr (CoreJet (ArithJet Modulo32)) = 0xa1f01c106fc36a764e99b23398e21e7c267f889fccebd1487d3de1cc67c32bd9 expected_cmr (CoreJet (ArithJet Modulo64)) = 0x50c82fd03109c98b7237e91674041964381e6c2ebbe25bf3e0d37a9f060f1502 expected_cmr (CoreJet (ArithJet Divides8)) = 0x0b5502ac4f21f230a09ccfaffaac77a7c41b2bf30b1468481e4dfb98b6187a0d expected_cmr (CoreJet (ArithJet Divides16)) = 0x5fc3ac384d5f45404156971a768d93bc064bc17c15a37c27019ddeef17046dd4 expected_cmr (CoreJet (ArithJet Divides32)) = 0xcc45b405246438f765740b4fb0a34dc81b34780198863b0fb186446adfbb09de expected_cmr (CoreJet (ArithJet Divides64)) = 0xdc473bfdec30ab98d48cd08884ef4fffef3d4b16ad5c37112a2035b99bb77458 expected_cmr (CoreJet (HashJet Sha256Block)) = 0x0c97a008ade87bb1e0ac06b7d0313023362858ef90ec14ec9cb95f0da964e008 expected_cmr (CoreJet (HashJet Sha256Iv)) = 0x7389f0025305dce828d4a1fe83743046a367c923f18abf365e391e5b04af1a47 expected_cmr (CoreJet (HashJet Sha256Ctx8Add1)) = 0x37066c67ad95249d4ba6e18144ca0a415d9c832aa6b60628e97c967eb1793383 expected_cmr (CoreJet (HashJet Sha256Ctx8Add2)) = 0x8bae3e7e1ed4dcba6e645aa14341bbae0dbb3ae21bb63dc030ca0e447a857ec2 expected_cmr (CoreJet (HashJet Sha256Ctx8Add4)) = 0xd7d745614b37a7e07dce22f64e7b1edfe23beda851f1e76f1a6b028fcc5e9fc0 expected_cmr (CoreJet (HashJet Sha256Ctx8Add8)) = 0x9c988330799a680bfe73d7caa3689fe4e483da4ee6d818587927c7f43392def7 expected_cmr (CoreJet (HashJet Sha256Ctx8Add16)) = 0x8299252040cb39e326a248d5c788f9516d15a2ff4145bb64ad6577ae1a3ef727 expected_cmr (CoreJet (HashJet Sha256Ctx8Add32)) = 0x39239a43a84bac6f2969bfa95bfe6a04fcba8092895939f12a1ce0e26321ec10 expected_cmr (CoreJet (HashJet Sha256Ctx8Add64)) = 0xfdc434ce83dbdce0782aa36d418def7f99af8293afb29e839fe4948f6234f77f expected_cmr (CoreJet (HashJet Sha256Ctx8Add128)) = 0x2dcf484c257f67940ca375ba98e83ce0e2a71e16da5051d1bb19fb5f346f154f expected_cmr (CoreJet (HashJet Sha256Ctx8Add256)) = 0x44b717e1970999b66b693d8c9d1d3b0605c2b7a6213e6ba56c69af8d7fae1686 expected_cmr (CoreJet (HashJet Sha256Ctx8Add512)) = 0xbe368032d86ebcf213ca45ba6ecab54cb1f2661d403da05906300bc51137aab5 expected_cmr (CoreJet (HashJet Sha256Ctx8AddBuffer511)) = 0xc027e1062996ae94ac3971a2c4fae54997ebf09b9f7da575639be617167f02e3 expected_cmr (CoreJet (HashJet Sha256Ctx8Finalize)) = 0xcbba1f1d8a97ab4d1fa9686e7aeef066fb5bf290716eae10e70b619996c59594 expected_cmr (CoreJet (HashJet Sha256Ctx8Init)) = 0xa53c7679e3ae0347d4d79126a7c7e49ac0dec90cdf935799cddb58da8f4496e4 expected_cmr (CoreJet (Secp256k1Jet PointVerify1)) = 0x90a3d669b00da795efb2bed8c370c9e3ea0f19c41c7cf23e492e33171a47f5ff expected_cmr (CoreJet (Secp256k1Jet Decompress)) = 0x13973317d587418ef3063631a6edb0acfa1cbe4983d7574b1b305f9661c048cb expected_cmr (CoreJet (Secp256k1Jet LinearVerify1)) = 0x278313d7ce4ad58911de24ee540d19ecebb62f4ab4a71e2aadd4512b2e4bc2e2 expected_cmr (CoreJet (Secp256k1Jet LinearCombination1)) = 0x6d9f4a870fbf740c220efff307b5ed91a58c5e51a8adfc3b159030f512d39941 expected_cmr (CoreJet (Secp256k1Jet Scale)) = 0xc04543dc85ef11374a930f4a948eb735a6500a1a7158d573123f07217175f318 expected_cmr (CoreJet (Secp256k1Jet Generate)) = 0xdf44e17d2a559dd0a7034954ab33377778b151f1cd1e4f9fd31b361d34a8d973 expected_cmr (CoreJet (Secp256k1Jet GejInfinity)) = 0x88a952db3816e94259a67537fa8fca1a35a907a86f51ede451fd32ec253d9c62 expected_cmr (CoreJet (Secp256k1Jet GejNormalize)) = 0x5de0976ae7f38b36f0022814966db2baed5c476714944d741a8979c4bcf8be25 expected_cmr (CoreJet (Secp256k1Jet GejNegate)) = 0xb32c74cab2c7500b73f8ec0560fe23fc4c21aa66596d7f2acf4967886b76d856 expected_cmr (CoreJet (Secp256k1Jet GeNegate)) = 0x1ed0ced8dd2558e3485f6fc32d69a2405ecaee312dc4dc65e0fd347773f5983d expected_cmr (CoreJet (Secp256k1Jet GejDouble)) = 0x1edd0582e2fcad99b12d506d29b50a63017f676928be511369006e07cb80d982 expected_cmr (CoreJet (Secp256k1Jet GejAdd)) = 0x5a1c310349e8ff5c5a61ac3e10123f74e87faba14c78bc83f9e3413687ecf28b expected_cmr (CoreJet (Secp256k1Jet GejGeAddEx)) = 0x78f0871b8173abde718711263b3ac1d922337ed5ed138d294962d65ce559bd92 expected_cmr (CoreJet (Secp256k1Jet GejGeAdd)) = 0x1ea710d56eafee325d2607ddb45ff0170adec2e0ee9bcc68e4b93e1de6ad3568 expected_cmr (CoreJet (Secp256k1Jet GejRescale)) = 0xdcfc72a768d5be770f8db278aeafd18e27704c64f8b40fa6fe54ca94727a076e expected_cmr (CoreJet (Secp256k1Jet GejIsInfinity)) = 0x2980a735414e4321afeffefa8837edb0a3309a337d59b7bdea921c13056b0428 expected_cmr (CoreJet (Secp256k1Jet GejEquiv)) = 0x027471059487a12ca207f0940594d6cd87fc930a8b5b31434a16a2d67f1d8dd4 expected_cmr (CoreJet (Secp256k1Jet GejGeEquiv)) = 0xba899a006216d1c93bd5ecbe0080d9078a500a729bbd396a004af51d4ff7d93a expected_cmr (CoreJet (Secp256k1Jet GejXEquiv)) = 0x52cc214709c0d9fca9db1d09cc807c75cf5a6313ca540a772d4ea9921f37e624 expected_cmr (CoreJet (Secp256k1Jet GejYIsOdd)) = 0xfe0106afb9d9e24fd4dbe54511fe272f4dcb307a0ea56d591ceb93ab4bf88745 expected_cmr (CoreJet (Secp256k1Jet GejIsOnCurve)) = 0x0187e1e5ef7634a5f016124d4feb5a93dde6aa78176cda48b165a9aa8e0449f2 expected_cmr (CoreJet (Secp256k1Jet GeIsOnCurve)) = 0x69f0e7a0c5fff87084ed6925f8db762e419e057b96834dce9699b0b009423059 expected_cmr (CoreJet (Secp256k1Jet ScalarNormalize)) = 0xa061e19d75c325a26d565aad7e3f9ae26b222f25e802174f6bacd511277aeaa5 expected_cmr (CoreJet (Secp256k1Jet ScalarNegate)) = 0x0705acdfb86640000e3d3bad509a14a78c171f61edc08423b042b94748439cf8 expected_cmr (CoreJet (Secp256k1Jet ScalarAdd)) = 0x34baa40b2e0aa8cb7e97c73e3ed3b365a15b7c3f7661fb19715ec605c1149d11 expected_cmr (CoreJet (Secp256k1Jet ScalarSquare)) = 0x49f734a2659ca0ab7c9e67fcfc3c0d72af0f917c9edcb9929d177a0f0de89d59 expected_cmr (CoreJet (Secp256k1Jet ScalarMultiply)) = 0xb2bcc390d637b9e03fbfc42fff71d22e7200f69329cef7169e68a8c71a7f0a4b expected_cmr (CoreJet (Secp256k1Jet ScalarMultiplyLambda)) = 0x89d5855c5f85c0035d27b0c09e20330b001c684b5986abced8360cd39b08c4e1 expected_cmr (CoreJet (Secp256k1Jet ScalarInvert)) = 0x6231bdab73ca34ea7e837daad692ede5babfae09b5756d2ab36c5a36475a6589 expected_cmr (CoreJet (Secp256k1Jet ScalarIsZero)) = 0xf75eda06ce6af09fae37db4e6225e6a8ac86a23637627d626409190ff3b39d90 expected_cmr (CoreJet (Secp256k1Jet FeNormalize)) = 0xc51beffa215e9cde8e933bb94680bae012c4daab3d04b6cbf0733fd735733538 expected_cmr (CoreJet (Secp256k1Jet FeNegate)) = 0x3b0d7b5c2e6c3aeb5e00085b9d30585aff054e325a998361113bfd2328c008f6 expected_cmr (CoreJet (Secp256k1Jet FeAdd)) = 0xb0593e187ee7333c47a05467df66d5820a6f5bef914a4b76e5d163314b5ef20e expected_cmr (CoreJet (Secp256k1Jet FeSquare)) = 0x5a6e7b2eac73f4e44dfa28fb86bb117b65606f2874d565c9799c63e0fe692b1a expected_cmr (CoreJet (Secp256k1Jet FeMultiply)) = 0x5669929b5f31fa3d02c5839dd06354cd171635f3a0727f322abfc994ba6290de expected_cmr (CoreJet (Secp256k1Jet FeMultiplyBeta)) = 0x7a7813450d82e935690f433e65df707a4dd17534a00ddd40dd85e3e3f78402c3 expected_cmr (CoreJet (Secp256k1Jet FeInvert)) = 0x343e9c90f128506056b548d2ed5e223c81f5b06a1ed86b7cd9354057aa595102 expected_cmr (CoreJet (Secp256k1Jet FeSquareRoot)) = 0xe00142ea03094a304ac82bc1e2d2dc71fb064ed082856735b14ff2c7faf036f0 expected_cmr (CoreJet (Secp256k1Jet FeIsZero)) = 0x28ff41699a881aafb7a976c0c576353f7fe54463b6aa754cf2c6329af2650e3b expected_cmr (CoreJet (Secp256k1Jet FeIsOdd)) = 0xdcf0375d20818a99f723f8123cbd051a3878a42824b3740f6821a5fa123f14c7 expected_cmr (CoreJet (Secp256k1Jet HashToCurve)) = 0x76f7ca1db944ee315ed362fee0673c5894f8853b446070901b857901f9499d9b expected_cmr (CoreJet (Secp256k1Jet Swu)) = 0xabf70be00b30f577f987cb50488996ba3596dbf9c1e844a8b1b8b710853b65eb expected_cmr (CoreJet (SignatureJet CheckSigVerify)) = 0xb58015546d2852665dd21bf11266267020fa5e275001dd4618fa415625952e68 expected_cmr (CoreJet (SignatureJet Bip0340Verify)) = 0xc9c45a8aec8659143bfe2af6ead48d4e0542453acae84b9bbb97656b670bdfdd expected_cmr (CoreJet (BitcoinJet ParseLock)) = 0x3d3836fd3085c1fbac6cd5fa0dbf4a3fb255459317a266d6d6f7382bb05f07ad expected_cmr (CoreJet (BitcoinJet ParseSequence)) = 0x74f35c019ef514b70ab008bf2a126de7e00f6e3ccd285d51dbd3ac71bea9c88d expected_cmr (CoreJet (BitcoinJet TapdataInit)) = 0x6c67e5c10735305ee7deb59a6c6ac2effcab4ff7bb479ea70081606e60484ca7 expected_cmr (ElementsJet (SigHashJet SigAllHash)) = 0x6ac53d3f93b8caf3ea8534ae612abd32325d2b0fec17de36af0f71aa978f7cde expected_cmr (ElementsJet (SigHashJet TxHash)) = 0xc36102aeda8bcf62a85e714b18e4c50cd417ffbf86d73734e02cbfcb5313fccf expected_cmr (ElementsJet (SigHashJet TapEnvHash)) = 0x7227077193ec17418ebf7877afdc7097bd5eed57e826df6605c648691d003403 expected_cmr (ElementsJet (SigHashJet OutputsHash)) = 0x95b3511aea00d043a4e028b25a171c742ec2ff7ad3a7df2f1f6edad08bad2b69 expected_cmr (ElementsJet (SigHashJet InputsHash)) = 0x523cd71c5789882f8375a5a54560def8463d1c51e56b7e112693e77b844f4740 expected_cmr (ElementsJet (SigHashJet IssuancesHash)) = 0x58659f3f7e0130c4fc916f49bc32eaa0883acb9022fcad5e7805839a99e50cf9 expected_cmr (ElementsJet (SigHashJet InputUtxosHash)) = 0x9c48ab31c050ed065aed516866c16c1b96c195ea8e18b024bfc0b8175849f04e expected_cmr (ElementsJet (SigHashJet OutputHash)) = 0x7cb17f8fc7a1ae4efce30a1454e52f8585213cd0f367a127ac27bb9766ea9eee expected_cmr (ElementsJet (SigHashJet OutputAmountsHash)) = 0x40236963e10ef8ad9cb6e0a7c79ac8660d2fc1a57feff88515a7852791b186cb expected_cmr (ElementsJet (SigHashJet OutputScriptsHash)) = 0x21333ac958a4ebfd5eab7956db73ed03269426af8d7d2498de57eef68704fb0a expected_cmr (ElementsJet (SigHashJet OutputNoncesHash)) = 0x50f18766de9828db0a8c41d7beb840f77bc6e121ff123d5496f1ea0d6a78b83a expected_cmr (ElementsJet (SigHashJet OutputRangeProofsHash)) = 0x0d7d8ac97af9539abba64d8104d17e970854677c27461d25df21a7f6b662081e expected_cmr (ElementsJet (SigHashJet OutputSurjectionProofsHash)) = 0x3630b5208302641bf19c4bf5ca047ac3eb7af54d5d3f5bf8f1d41312499d6384 expected_cmr (ElementsJet (SigHashJet InputHash)) = 0x3309bb46b3158d23124f8cedaaa1ed3b09a8aefe81212e11335523b6b207c544 expected_cmr (ElementsJet (SigHashJet InputOutpointsHash)) = 0x140a2baead083baac806128ab649e52bbd3c6456700cbcfc6dbb2959173a4df2 expected_cmr (ElementsJet (SigHashJet InputSequencesHash)) = 0xc888c873302b92b00f206852c9eaef000b40109a53dd686a53f11db5074d9937 expected_cmr (ElementsJet (SigHashJet InputAnnexesHash)) = 0xded1522efa5a2b376173e440de227ad0c92be2edce7c23b51480e50a77fc564b expected_cmr (ElementsJet (SigHashJet InputScriptSigsHash)) = 0x6c7481420124b6645d32ff9b454a1c92c67186410e23cf609915df9072120fc6 expected_cmr (ElementsJet (SigHashJet IssuanceHash)) = 0x6e9f8ae8c45bfb7e4e0cf2d00f66832b479de7582cdbc851d0b3230fdfbbb78d expected_cmr (ElementsJet (SigHashJet IssuanceAssetAmountsHash)) = 0x70f11c3b3b5d1657d3b7c7eeec850c30a32ea96aa36426fa30ebf5499851a880 expected_cmr (ElementsJet (SigHashJet IssuanceTokenAmountsHash)) = 0x94b5a4595b674dbfc49c4e8ea1a9abc93ed2f7707c4212a32b5b86ac1318c9de expected_cmr (ElementsJet (SigHashJet IssuanceRangeProofsHash)) = 0x7e97f519534831c77acf73a20fd53cb31d1d156c9acbbf873d1492d60d1367d8 expected_cmr (ElementsJet (SigHashJet IssuanceBlindingEntropyHash)) = 0xbfb6a93444e2a0b3fb7c13d1589a787b66e84b69b6274cea20ad9999eb8ca67c expected_cmr (ElementsJet (SigHashJet InputUtxoHash)) = 0x8503d0526ba95a8fba8ca1351c7991c2a386b72fa81431eadbab62cc1f5dc518 expected_cmr (ElementsJet (SigHashJet InputAmountsHash)) = 0x2b4df47e758ffe88e9cd5d396df3d7f9ec2fbd5a5395a6d8c1ab704400c64f70 expected_cmr (ElementsJet (SigHashJet InputScriptsHash)) = 0xdc13519e753e58753c70988541ad8a0bb5888d0846e35e4d4273f65685322ae9 expected_cmr (ElementsJet (SigHashJet TapleafHash)) = 0xd45a661fc9100e2ea9df789ca2346da842717ef6a8c824184f2da8c7fb016203 expected_cmr (ElementsJet (SigHashJet TappathHash)) = 0x9da906e3ec086065be144136b51620b66ddf4d713857354eba3b97c77585f443 expected_cmr (ElementsJet (SigHashJet OutpointHash)) = 0x8d2a5aa06e98c41b30fd0703e5e54c86b42bee33bc89cb6093cdb09405a72d9d expected_cmr (ElementsJet (SigHashJet AssetAmountHash)) = 0xa864d1f1f83950b63196fe88baec2e4228953230be45c88c4e0b99178b338f07 expected_cmr (ElementsJet (SigHashJet NonceHash)) = 0xfb1e0344dcdaf9db91b987e8f96610679f05deb206b401057502a484aa87f8bf expected_cmr (ElementsJet (SigHashJet AnnexHash)) = 0xeba1b7fb2ea8d57af3b6273e5182fb99db1708b2d0afb9c6ad0358cc3f647dc8 expected_cmr (ElementsJet (SigHashJet BuildTapleafSimplicity)) = 0x736e9fcefb5b873e09f2681e74e49f5a1056f90af52ab3ec5b197727d39834be expected_cmr (ElementsJet (SigHashJet BuildTapbranch)) = 0xcbecf9bce172c50f585951dff0e0523db109e57025ec37de2c3a74d4a673f225 expected_cmr (ElementsJet (SigHashJet BuildTaptweak)) = 0x38741f80a2bf10f8f8723077c6741cbeae2dcac857901b813725806f21898ee3 expected_cmr (ElementsJet (TimeLockJet CheckLockHeight)) = 0x9e7898d037627134d2bd70c7fca9cba45eaf267d4d09ad50a9ef717a8f2749db expected_cmr (ElementsJet (TimeLockJet CheckLockTime)) = 0x68673d12e2732faa1d39e2136b1406afa098a84c96e8d60502a2dd61c59570bb expected_cmr (ElementsJet (TimeLockJet BrokenDoNotUseCheckLockDistance)) = 0x7f78c7a77a25ada223267d239a5922f764b8ac0c2fcef68eb93c0d92da4af515 expected_cmr (ElementsJet (TimeLockJet BrokenDoNotUseCheckLockDuration)) = 0x73dac8e25d87eaf382c2a77206ad38b9384361e7d0dc87c0fa7af7ea524597b7 expected_cmr (ElementsJet (TimeLockJet TxLockHeight)) = 0xc20257f8e76ecd0ae7ad634f5dfa68ae9a5eded0e2eebe4ee52cb47acfb0264c expected_cmr (ElementsJet (TimeLockJet TxLockTime)) = 0x3ee1900542d01efd4e9a01d4efb1f9dd992ced35b7a752f83da593381538dea4 expected_cmr (ElementsJet (TimeLockJet BrokenDoNotUseTxLockDistance)) = 0x4c7773b818cb7ee5f54f925aad015677a043a72f316a187cc28c696cfcb90807 expected_cmr (ElementsJet (TimeLockJet BrokenDoNotUseTxLockDuration)) = 0xcc9c64c8b6eb4bf09694af5a35d957a405e66c1b35224ed675878918452440b2 expected_cmr (ElementsJet (TimeLockJet TxIsFinal)) = 0x8b3145722470a07de90a28ba89f3f8864261009654ce866cd8eaf76c5d8626eb expected_cmr (ElementsJet (IssuanceJet Issuance)) = 0x5c646312c169c68027979e1bc326c5dc95e5c5168d00d98e9d504a7cde21d768 expected_cmr (ElementsJet (IssuanceJet IssuanceAsset)) = 0x690bf918e1527756cfbbf51c831362143756d52d04e1294f1264950c6267e5c9 expected_cmr (ElementsJet (IssuanceJet IssuanceToken)) = 0xbc2cb7e964b2a2aed79b75c5f4408fe84a6dc9b9e8cd2c694d57c5f9b61205b9 expected_cmr (ElementsJet (IssuanceJet IssuanceEntropy)) = 0x6ddf99f28c70198d65417a836074f1b9b610f21f5119fd550f60b6f8e995bbf3 expected_cmr (ElementsJet (IssuanceJet CalculateIssuanceEntropy)) = 0xa6e7c434aee5a7330c1fc246f71dcf051ce54bdee7b8e63957be18c2d751c653 expected_cmr (ElementsJet (IssuanceJet CalculateAsset)) = 0x676f988e547251e7a09eede1920a9c5d35e75759e6d8d49b580ceb3e146bcf7e expected_cmr (ElementsJet (IssuanceJet CalculateExplicitToken)) = 0x875228020b456c998aad3ac5c4836f719445dcbe6bd274e8ca145d82797e1b92 expected_cmr (ElementsJet (IssuanceJet CalculateConfidentialToken)) = 0x8e4029056074339840c0e7009b66f382bb98d7dde719dd2c9f2fd3acd9325ac6 expected_cmr (ElementsJet (IssuanceJet LbtcAsset)) = 0x2af7f73ae3fbbfa2d23a8774e6e3ca093254da2fd2a9f397a6ae0a30bb48f0d7 expected_cmr (ElementsJet (TransactionJet ScriptCMR)) = 0xec15f59c524d941469811954654f635830ecd7de517662b25ca4e8d05c2cce89 expected_cmr (ElementsJet (TransactionJet InternalKey)) = 0x9b742e471b0e591a972b0d4421f9c9659397f5daba2c14dac62c4a339cc3e7ec expected_cmr (ElementsJet (TransactionJet CurrentIndex)) = 0x15e1051ff23f851c19131f0de6edc4882376a25790dbd9102824aa22a889ae84 expected_cmr (ElementsJet (TransactionJet NumInputs)) = 0xb2288ebaadcbcfce1c631964c86b127d6f91dc657c59a7fb453e9111d87481f5 expected_cmr (ElementsJet (TransactionJet NumOutputs)) = 0x267d41654493903e0257751ae6d42d9ce1bb92246d0ef767c337b0c32b1972fd expected_cmr (ElementsJet (TransactionJet LockTime)) = 0xa16897c5db4927c6cb07b165bd2cc38b36a602686c74a19034aa3787ac582a0b expected_cmr (ElementsJet (TransactionJet OutputAsset)) = 0x575a49bab21ffee8e5bd00edce32406104a05ddef5fc31a1a645b129548c8f3e expected_cmr (ElementsJet (TransactionJet OutputAmount)) = 0x55e413992169408e338e11a8d7be602b3ec9511e7eb691df32d9797a6395a1a1 expected_cmr (ElementsJet (TransactionJet OutputNonce)) = 0x7175fd99a2baa1c3afaaf7fabdaa67c2c827483bc8a0b97650cb7942ea295a18 expected_cmr (ElementsJet (TransactionJet OutputScriptHash)) = 0x2f5139266f143a33e1668e594f43e8d1394407e3a9b8b802b39a5e1edc54e851 expected_cmr (ElementsJet (TransactionJet OutputNullDatum)) = 0x38a5a7e861b3b36cce683a772db0c8628b7fd3b4cf8e7bce70758fa6f6f147bf expected_cmr (ElementsJet (TransactionJet OutputIsFee)) = 0x9fbbe8aebdedd577ae466280a99b67b7343287ef340692534a00980315e51772 expected_cmr (ElementsJet (TransactionJet OutputSurjectionProof)) = 0x091660081d52c33f17a956bddac62aa2d2ed928f8cffef4cf8dbb697b153aa65 expected_cmr (ElementsJet (TransactionJet OutputRangeProof)) = 0x6ff9ef3dac504310dfbc60561d2addeb44932f777e7f13adf0774eb6b14df966 expected_cmr (ElementsJet (TransactionJet TotalFee)) = 0x4eba3f22bac0a465e4d08a9ac40518ef972c2e8612090a51e3203fcbd2f4edbe expected_cmr (ElementsJet (TransactionJet CurrentPegin)) = 0x369ad5f6d760481cb353a9bacf900ff162b76040c07ad0a83e52fccef1295790 expected_cmr (ElementsJet (TransactionJet CurrentPrevOutpoint)) = 0xa1ec909c81e508e86e1361ba82e5fb47a2c76bffba7321a6fc13cb12af7f697c expected_cmr (ElementsJet (TransactionJet CurrentAsset)) = 0x03c84459a5ecdfdb46e3d38ecb79ff22243fdcf70d80da1ba45699e7008eecfe expected_cmr (ElementsJet (TransactionJet CurrentAmount)) = 0x9e7bc96d06c1f4a4d2bd4333d55643cba6863d3a338e31dc0d1795584156ea69 expected_cmr (ElementsJet (TransactionJet CurrentScriptHash)) = 0xbfaf858443cec8337e37839dc41135027184580c892157ce730418c08d5ed838 expected_cmr (ElementsJet (TransactionJet CurrentSequence)) = 0x0f4224f9aa8644f5c0f7910f1739041aec8e7af77b5f38cfdca0fdf48267a6c3 expected_cmr (ElementsJet (TransactionJet CurrentAnnexHash)) = 0x5f68bdafd417febb10dee16b1d47c21fa97efc919157c7f7bc54a61dc4f9f7d6 expected_cmr (ElementsJet (TransactionJet CurrentScriptSigHash)) = 0x8baa9df854fe33eeea66195c97ce18ed701e107eea7e02fb2603b2c121575066 expected_cmr (ElementsJet (TransactionJet CurrentReissuanceBlinding)) = 0xb71550c8f62e7aacff13e8d3c0ae054ef036409d76c06579c026ad68a1b561f8 expected_cmr (ElementsJet (TransactionJet CurrentNewIssuanceContract)) = 0x237815675e9e9cf4d8548560c761e3ba7f64dcf25c99521be9d857e4ea41d868 expected_cmr (ElementsJet (TransactionJet CurrentReissuanceEntropy)) = 0x8b2715327a0ac6b0d18a2e51fbda46c4b118ee0637d114ae3e58a23b45d67ff8 expected_cmr (ElementsJet (TransactionJet CurrentIssuanceAssetAmount)) = 0xdc410ec69946f08b9c4a40cf38819cbb014e98fce0a9b196514557477fe1c2a7 expected_cmr (ElementsJet (TransactionJet CurrentIssuanceTokenAmount)) = 0xe3ea9c6170955f27b01b120cd63a360850cc700f4725193bdff88e01dfb04ead expected_cmr (ElementsJet (TransactionJet CurrentIssuanceAssetProof)) = 0xe5c1c6f7ea0296148e76f8b179d415198273dcc8e1fd891f83ef2bdfb0692936 expected_cmr (ElementsJet (TransactionJet CurrentIssuanceTokenProof)) = 0x92e7d9ddbf756e3e622a44d4d00e84236bcce42f16f3200e8b89c03c441e458a expected_cmr (ElementsJet (TransactionJet InputPegin)) = 0xdb376f4ae84ec051a494d7668039727b53353be5ae045be76c4b04dabd5bbfbb expected_cmr (ElementsJet (TransactionJet InputPrevOutpoint)) = 0x91f4d6ec484f60cae9297858cac47dad50db07dc1f937ac6144c9cb4a9ef79d2 expected_cmr (ElementsJet (TransactionJet InputAsset)) = 0x872b3653d65ae7f9166cbf70d4fd31404798884d611b647fb9f4a307c48011b8 expected_cmr (ElementsJet (TransactionJet InputAmount)) = 0xdd65ac32c87d996b407200feefc479a9119c1f28caa488b0aac3acf59378d6ba expected_cmr (ElementsJet (TransactionJet InputScriptHash)) = 0xc316df21778e624105ca59904b9208e2d423228b3eb1cf68b8eca47bbc7b2ff3 expected_cmr (ElementsJet (TransactionJet InputSequence)) = 0x3c6e4a3c21ced524736c545c20e4e2def7678f084cd12bcd6506a5200b5c1738 expected_cmr (ElementsJet (TransactionJet InputAnnexHash)) = 0x0fd9e4c6316b37286e8854430e7d741821dc89544a3a59f03dfa40e532b8107f expected_cmr (ElementsJet (TransactionJet InputScriptSigHash)) = 0x941f2b4f3b7f2097d6ea00e97c1e2ba01cb26487c5d2f4723738b37c732c05c4 expected_cmr (ElementsJet (TransactionJet ReissuanceBlinding)) = 0xeb6e581e20ba0babe904c8da71a81f7c88b9cf4f42d78b540c1b398c3f105ccc expected_cmr (ElementsJet (TransactionJet NewIssuanceContract)) = 0xdb64808c3ff44880d72bc295d9ac0643e51404de5398ad9e931bd3d2adbca6c4 expected_cmr (ElementsJet (TransactionJet ReissuanceEntropy)) = 0xd1d22c497f129c6d6fdbe491364a3513bcd66e15618cbbe2e50739bd834db7f8 expected_cmr (ElementsJet (TransactionJet IssuanceAssetAmount)) = 0x83605146ff26a49ca16f1c4a6e0ce0b7c214df12c377f522523deb6d5d0ee44d expected_cmr (ElementsJet (TransactionJet IssuanceTokenAmount)) = 0x7e106464a13b6764ce74d3fe6ba1cbd5f4aeb86bbbdf5888ddf9901dd8b619aa expected_cmr (ElementsJet (TransactionJet IssuanceAssetProof)) = 0x0b061f9f670c05dc39f438313c1379d9bf63f44f9876b956693b41b7f94c6c9d expected_cmr (ElementsJet (TransactionJet IssuanceTokenProof)) = 0x46ed5275f55ab341f57c3519ffedf4e37f3f59c97ce9b8e17fffae16c6cc1c0e expected_cmr (ElementsJet (TransactionJet TapleafVersion)) = 0xddb0edd6ce1e07983d1a6226f00b125189af13bd5cd068123ad43f48201b006f expected_cmr (ElementsJet (TransactionJet Tappath)) = 0x42c0c1f2ef0e28ae7defa15e84a06f35fbf6fc897b29f683fe1a24e30dc58baf expected_cmr (ElementsJet (TransactionJet Version)) = 0x087fc95c41003348759fd840372c6f912d9be4e61eee3c6a7a40dc13c9c1bc70 expected_cmr (ElementsJet (TransactionJet GenesisBlockHash)) = 0x0060b60d02b1336072846acff44dd0f4346c74a35e7b56423f9519c442d15daf expected_cmr (ElementsJet (TransactionJet TransactionId)) = 0x08b8eb3c2d2d958458e163e94334950c0bb914a0b9d214fc5e9de8f70a17a0d4 expected_cmr (ConstWordJet (ConstWordContent SingleV 0)) = 0xa51cfd799d0bc368f48208032fc3881953f35aa7fd2b985cb237cbad143e30d2 expected_cmr (ConstWordJet (ConstWordContent SingleV 1)) = 0xfd49252606a2febe2ad17de13b0a738b1b023bad8f7307e6bb7b65a8b83153cb expected_cmr (ConstWordJet (ConstWordContent (DoubleV SingleV) 0)) = 0xe93b30864811cc800369118d7573ab400d872e2338e406b051de69fb76cd57d4 expected_cmr (ConstWordJet (ConstWordContent (DoubleV SingleV) 1)) = 0x31a87b65445c9893c575df925d5472858483a465c59d3ccbd74f609ca8a77d23 expected_cmr (ConstWordJet (ConstWordContent (DoubleV SingleV) 2)) = 0x7e83d146509bc020c64683fe5158c5826046a69050eb0336e743d173e05647f0 expected_cmr (ConstWordJet (ConstWordContent (DoubleV SingleV) 3)) = 0x0a4f2b4f2f4b0f5d83f565060f3634e35d1e0d0d4309363c58fb6c571d2d42b2 ================================================ FILE: Haskell/Tests/Simplicity/Elements/Serialization/Tests.hs ================================================ -- This module tests some serialization functionality. module Simplicity.Elements.Serialization.Tests (tests) where import Control.Monad (mzero) import Data.Foldable (toList) import qualified Data.List as List import qualified Data.Vector.Unboxed as V import Simplicity.Arbitrary import Simplicity.CoreJets import Simplicity.Elements.Jets as Elements import Simplicity.Elements.FFI.Primitive as Elements import Simplicity.FFI.Dag import Simplicity.MerkleRoot import Simplicity.Serialization import Simplicity.Ty import Simplicity.Ty.Word import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit ((@=?), testCase) import Test.Tasty.QuickCheck (Property, arbitrary, forAll, chooseInt, testProperty, vectorOf) -- Run tests comparing Bit Machine execution with Simplicity's denotational semantics using both naive and TCO translation. tests :: TestTree tests = testGroup "Elements Serialization" [ testGroup "Haskell" [ testDecodeElementsJet jt | SomeArrow jt@(ElementsJet _) <- toList Elements.jetMap ] , testGroup "C" $ [ testDecodeElementsJetFFI jt | SomeArrow jt <- toList Elements.jetMap ] ++ [ testProperty "prop_wordCMR" prop_wordCMR ] ] testDecodeElementsJet :: (TyC a, TyC b) => Elements.JetType a b -> TestTree testDecodeElementsJet jt = testCase (show jt) (Just (SomeArrow jt) @=? decode) where vector = V.fromList $ Elements.putJetBit jt [] decode = evalExactVector (Elements.getJetBit mzero) vector testDecodeElementsJetFFI :: (TyC a, TyC b) => Elements.JetType a b -> TestTree testDecodeElementsJetFFI jt = testCase (show jt) (Right cmr @=? Elements.decodeJetCMR bitstream) where -- All jet encodings should begin with a 1 bit, which we consume. True:bitstream = Elements.putJetBit jt [] cmr = commitmentRoot (asJet jt) prop_wordCMR :: SomeConstWordContent -> Property prop_wordCMR (SomeConstWordContent cwc) = forAll prefix prop where prefix = do n <- chooseInt (0, 7) vectorOf n arbitrary prop l = wordCMR == computeWordCMR (length l) (l ++ stream) where wordCMR = commitmentRoot $ asJet (ConstWordJet cwc) stream = putConstWordValueBit cwc ================================================ FILE: Haskell/Tests/Simplicity/Elements/TestEval.hs ================================================ -- | This module builds a wrapper around 'Simplicity.Elements.Semantics.fastEval' to define a 'testEval' variant. module Simplicity.Elements.TestEval ( testEval, TestEval ) where import Prelude hiding (drop, take, fail) import Control.Arrow (Kleisli(..), first) import Control.Monad.Reader (ReaderT(..)) import qualified Simplicity.Elements.Jets as Jets import Simplicity.Elements.JetType import Simplicity.Elements.Primitive import Simplicity.Elements.Semantics import Simplicity.Elements.Term -- | An Assert instance for 'testCoreEval'. data TestEval jt a b = TestEval { testEvalSem :: Kleisli (ReaderT PrimEnv Maybe) a b , testEvalFast :: FastEval jt a b } -- | 'testEval' optimizes Simplicity with assertions evaluation using jets, similar to 'fastEval', -- but excludes the expression itself from being substituted. -- This is used in for testing jets against their specifications under the assumption that jets for any subexpressions are correct. -- Delegation, witnesses, and jets are not supported since they are not allowed within jet definitions. testEval :: TestEval Jets.JetType a b -> PrimEnv -> a -> Maybe b testEval = flip . (runReaderT .) . runKleisli . testEvalSem testFastKleisli = Kleisli . (ReaderT .) . flip . fastEval . testEvalFast mkLeaf sComb fComb = TestEval sComb fComb mkUnary sComb fComb t = TestEval (sComb (testFastKleisli t)) (fComb (testEvalFast t)) mkBinary sComb fComb s t = TestEval (sComb (testFastKleisli s) (testFastKleisli t)) (fComb (testEvalFast s) (testEvalFast t)) instance JetType jt => Core (TestEval jt) where iden = mkLeaf iden iden comp = mkBinary comp comp unit = mkLeaf unit unit injl = mkUnary injl injl injr = mkUnary injr injr match = mkBinary match match pair = mkBinary pair pair take = mkUnary take take drop = mkUnary drop drop instance JetType jt => Assert (TestEval jt) where assertl s h = mkUnary (flip assertl h) (flip assertl h) s assertr h t = mkUnary (assertr h) (assertr h) t fail b = mkLeaf (fail b) (fail b) instance JetType jt => Primitive (TestEval jt) where primitive p = mkLeaf (primitive p) (primitive p) ================================================ FILE: Haskell/Tests/Simplicity/Elements/Tests.hs ================================================ module Simplicity.Elements.Tests (tests) where import Control.Arrow ((***), (+++)) import qualified Data.ByteString.Char8 as BSC import qualified Data.ByteString.Lazy as BSL import qualified Data.Map as Map import Data.Maybe (fromMaybe, isJust) import Data.Serialize (encode, put, putWord8, putWord32be, runPutLazy) import Data.Vector ((!), (!?), fromList) import Lens.Family2 (review, over, under, view) import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit (Assertion, (@?=), assertBool, testCase) import Test.Tasty.QuickCheck (Property, NonNegative(..), arbitrary, classify, forAll, testProperty) import Simplicity.Arbitrary import Simplicity.Digest import Simplicity.Elements.Arbitrary import Simplicity.Elements.DataTypes import Simplicity.Elements.Jets import Simplicity.Elements.Term import Simplicity.Elements.TestEval import qualified Simplicity.Elements.Regression as Regression import Simplicity.Elements.Primitive (primEnv, primEnvHash, envTx, envTap) import qualified Simplicity.Elements.Programs.TimeLock as Prog import Simplicity.Elements.Semantics import qualified Simplicity.LibSecp256k1.Spec as Schnorr import Simplicity.MerkleRoot import Simplicity.Programs.CheckSig.Lib import qualified Simplicity.Programs.Sha256 as Sha256 import qualified Simplicity.Programs.Elements.Lib as Prog import qualified Simplicity.Elements.Programs.Issuance.Lib as Prog import qualified Simplicity.Elements.Programs.SigHash.Lib as Prog import Simplicity.TestCoreEval import Simplicity.Ty.Arbitrary import Simplicity.Ty.Word import qualified Simplicity.Word as Word toW32 :: Word.Word32 -> Word32 toW32 = toWord32 . fromIntegral toW16 :: Word.Word16 -> Word16 toW16 = toWord16 . fromIntegral toW8 :: Word.Word8 -> Word8 toW8 = toWord8 . fromIntegral tests :: TestTree tests = testGroup "Elements" [ Regression.tests , testGroup "TimeLock" [ testProperty "tx_is_final" prop_tx_is_final , testProperty "tx_lock_height" prop_tx_lock_height , testProperty "tx_lock_time" prop_tx_lock_time , testProperty "tx_lock_distance" prop_tx_lock_distance , testProperty "tx_lock_duration" prop_tx_lock_duration , testProperty "check_lock_height" prop_check_lock_height , testProperty "check_lock_time" prop_check_lock_time , testProperty "check_lock_distance" prop_check_lock_distance , testProperty "check_lock_duration" prop_check_lock_duration ] , testGroup "Elements Functions" [ testProperty "calculate_issuance_entropy" prop_calculate_issuance_entropy , testProperty "calculate_asset" prop_calculate_asset , testProperty "calculate_explicit_token" prop_calculate_explicit_token , testProperty "calculate_confidential_token" prop_calculate_confidential_token , testProperty "outpoint_hash" prop_outpoint_hash , testProperty "asset_amount_hash" prop_asset_amount_hash , testProperty "nonce_hash" prop_nonce_hash , testProperty "annex_hash" prop_annex_hash , testProperty "build_tapleaf_simplicity" prop_build_tapleaf_simplicity , testProperty "build_tapbranch" prop_build_tapbranch , testProperty "build_taptweak" prop_build_taptweak , testProperty "input_issuance" prop_input_issuance , testProperty "input_issuance_asset" prop_input_issuance_asset , testProperty "input_issuance_token" prop_input_issuance_token , testProperty "input_issuance_entropy" prop_input_issuance_entropy , testProperty "output_amounts_hash" prop_output_amounts_hash , testProperty "output_nonces_hash" prop_output_nonces_hash , testProperty "output_scripts_hash" prop_output_scripts_hash , testProperty "output_range_proofs_hash" prop_output_range_proofs_hash , testProperty "output_surjection_proofs_hash" prop_output_surjection_proofs_hash , testProperty "outputs_hash" prop_outputs_hash , testProperty "output_hash" prop_output_hash , testProperty "input_outpoints_hash" prop_input_outpoints_hash , testProperty "input_amounts_hash" prop_input_amounts_hash , testProperty "input_scripts_hash" prop_input_scripts_hash , testProperty "input_utxos_hash" prop_input_utxos_hash , testProperty "input_utxo_hash" prop_input_utxo_hash , testProperty "input_sequences_hash" prop_input_sequences_hash , testProperty "input_annexes_hash" prop_input_annexes_hash , testProperty "input_script_sigs_hash" prop_input_script_sigs_hash , testProperty "inputs_hash" prop_inputs_hash , testProperty "input_hash" prop_input_hash , testProperty "issuance_asset_amounts_hash" prop_issuance_asset_amounts_hash , testProperty "issuance_token_amounts_hash" prop_issuance_token_amounts_hash , testProperty "issuance_range_proofs_hash" prop_issuance_range_proofs_hash , testProperty "issuance_blinding_entropy_hash" prop_issuance_blinding_entropy_hash , testProperty "issuances_hash" prop_issuances_hash , testProperty "issuance_hash" prop_issuance_hash , testProperty "tx_hash" prop_tx_hash , testProperty "tap_env_hash" prop_tap_env_hash , testProperty "tappath_hash" prop_tappath_hash , testProperty "tapleaf_hash" prop_tapleaf_hash , testProperty "sig_all_hash" prop_sig_all_hash , testProperty "script_cmr" prop_script_cmr , testProperty "internal_key" prop_internal_key , testProperty "current_index" prop_current_index , testProperty "num_inputs" prop_num_inputs , testProperty "num_outputs" prop_num_outputs , testProperty "lock_time" prop_lock_time , testProperty "output_asset" prop_output_asset , testProperty "output_amount" prop_output_amount , testProperty "output_nonce" prop_output_nonce , testProperty "output_script_hash" prop_output_script_hash , testProperty "output_null_datum" prop_output_null_datum , testProperty "output_is_fee" prop_output_is_fee , testProperty "output_surjection_proof" prop_output_surjection_proof , testProperty "output_range_proof" prop_output_range_proof , testProperty "total_fee" prop_total_fee , testProperty "current_pegin" prop_current_pegin , testProperty "current_prev_outpoint" prop_current_prev_outpoint , testProperty "current_asset" prop_current_asset , testProperty "current_amount" prop_current_amount , testProperty "current_script_hash" prop_current_script_hash , testProperty "current_sequence" prop_current_sequence , testProperty "current_annex_hash" prop_current_annex_hash , testProperty "current_script_sig_hash" prop_current_script_sig_hash , testProperty "current_reissuance_blinding" prop_current_reissuance_blinding , testProperty "current_new_issuance_contract" prop_current_new_issuance_contract , testProperty "current_reissuance_entropy" prop_current_reissuance_entropy , testProperty "current_issuance_asset_amount" prop_current_issuance_asset_amount , testProperty "current_issuance_token_amount" prop_current_issuance_token_amount , testProperty "current_issuance_asset_proof" prop_current_issuance_asset_proof , testProperty "current_issuance_token_proof" prop_current_issuance_token_proof , testProperty "input_pegin" prop_input_pegin , testProperty "input_prev_outpoint" prop_input_prev_outpoint , testProperty "input_asset" prop_input_asset , testProperty "input_amount" prop_input_amount , testProperty "input_script_hash" prop_input_script_hash , testProperty "input_sequence" prop_input_sequence , testProperty "input_annex_hash" prop_input_annex_hash , testProperty "input_script_sig_hash" prop_input_script_sig_hash , testProperty "reissuance_blinding" prop_reissuance_blinding , testProperty "new_issuance_contract" prop_new_issuance_contract , testProperty "reissuance_entropy" prop_reissuance_entropy , testProperty "issuance_asset_amount" prop_issuance_asset_amount , testProperty "issuance_token_amount" prop_issuance_token_amount , testProperty "issuance_asset_proof" prop_issuance_asset_proof , testProperty "issuance_token_proof" prop_issuance_token_proof , testProperty "tapleaf_version" prop_tapleaf_version , testProperty "tappath" prop_tappath , testProperty "version" prop_version , testProperty "genesis_block_hash" prop_genesis_block_hash , testProperty "transaction_id" prop_transaction_id , testCase "lbtc_asset" assert_lbtc_asset , testCase "issuance_entropy_1" assert_issuance_entropy_1 , testCase "calculate_asset_1" assert_calculate_asset_1 , testCase "calculcate_token_1" assert_calculcate_token_1 , testCase "issuance_entropy_2" assert_issuance_entropy_2 , testCase "calculate_asset_2" assert_calculate_asset_2 , testCase "calculcate_token_2" assert_calculcate_token_2 , testCase "issuance_entropy_3" assert_issuance_entropy_3 , testCase "calculate_asset_3" assert_calculate_asset_3 , testCase "calculcate_token_3" assert_calculcate_token_3 , testCase "issuance_entropy_4" assert_issuance_entropy_4 , testCase "calculate_asset_4" assert_calculate_asset_4 , testCase "calculcate_token_4" assert_calculcate_token_4 ] , testCase "sigHashAll" (assertBool "sigHashAll_matches" hunit_sigHashAll) ] -- We use continuations here because we need to ensure that 'fastSpec' is memoized outside of any lambda expressions. checkJet jet k = k (\env a -> fastSpec env a == implementation jet env a) where fastSpec = testEval (specification jet) prop_tx_is_final :: Property prop_tx_is_final = checkJet (ElementsJet (TimeLockJet TxIsFinal)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_height :: Property prop_tx_lock_height = checkJet (ElementsJet (TimeLockJet TxLockHeight)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_time :: Property prop_tx_lock_time = checkJet (ElementsJet (TimeLockJet TxLockTime)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_distance :: Property prop_tx_lock_distance = checkJet (ElementsJet (TimeLockJet BrokenDoNotUseTxLockDistance)) $ \check -> forallPrimEnv $ \env -> check env () prop_tx_lock_duration :: Property prop_tx_lock_duration = checkJet (ElementsJet (TimeLockJet BrokenDoNotUseTxLockDuration)) $ \check -> forallPrimEnv $ \env -> check env () prop_check_lock_height :: Property prop_check_lock_height = checkJet (ElementsJet (TimeLockJet CheckLockHeight)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . sigTxLock $ envTx env) $ \w -> check env (toW32 w) prop_check_lock_time :: Property prop_check_lock_time = checkJet (ElementsJet (TimeLockJet CheckLockTime)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . sigTxLock $ envTx env) $ \w -> check env (toW32 w) prop_check_lock_distance :: Property prop_check_lock_distance = checkJet (ElementsJet (TimeLockJet BrokenDoNotUseCheckLockDistance)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . txLockBrokenDistance $ envTx env) $ \w -> check env (toW16 w) prop_check_lock_duration :: Property prop_check_lock_duration = checkJet (ElementsJet (TimeLockJet BrokenDoNotUseCheckLockDuration)) $ \check -> forallPrimEnv $ \env -> forAll (genBoundaryCases . txLockBrokenDuration $ envTx env) $ \w -> check env (toW16 w) prop_calculate_issuance_entropy :: Outpoint -> HashElement -> Bool prop_calculate_issuance_entropy = \op contract -> let input = ((fromHash (opHash op), fromIndex (opIndex op)), heAsTy contract) in fast_calculate_issuance_entropy input == implementation (ElementsJet (IssuanceJet CalculateIssuanceEntropy)) undefined input where fromHash = toWord256 . integerHash256 fromIndex = toWord32 . fromIntegral fast_calculate_issuance_entropy = testCoreEval Prog.calculateIssuanceEntropy prop_calculate_asset :: HashElement -> Bool prop_calculate_asset = \entropy -> let input = heAsTy entropy in fast_calculate_asset input == implementation (ElementsJet (IssuanceJet CalculateAsset)) undefined input where fast_calculate_asset = testCoreEval Prog.calculateAsset prop_calculate_explicit_token :: HashElement -> Bool prop_calculate_explicit_token = \entropy -> let input = heAsTy entropy in fast_calculate_explicit_token input == implementation (ElementsJet (IssuanceJet CalculateExplicitToken)) undefined input where fast_calculate_explicit_token = testCoreEval Prog.calculateExplicitToken prop_calculate_confidential_token :: HashElement -> Bool prop_calculate_confidential_token = \entropy -> let input = heAsTy entropy in fast_calculate_confidential_token input == implementation (ElementsJet (IssuanceJet CalculateConfidentialToken)) undefined input where fast_calculate_confidential_token = testCoreEval Prog.calculateConfidentialToken prop_build_tapleaf_simplicity :: HashElement -> Bool prop_build_tapleaf_simplicity = \cmr -> let input = heAsTy cmr in fast_build_tapleaf_simplicity input == implementation (ElementsJet (SigHashJet BuildTapleafSimplicity)) undefined input where fast_build_tapleaf_simplicity = testCoreEval Prog.buildTapleafSimplicity prop_build_tapbranch :: HashElement -> HashElement -> Bool prop_build_tapbranch = \a b -> let input = (heAsTy a, heAsTy b) in fast_build_tapbranch input == implementation (ElementsJet (SigHashJet BuildTapbranch)) undefined input where fast_build_tapbranch = testCoreEval Prog.buildTapbranch prop_build_taptweak :: FieldElement -> HashElement -> Bool prop_build_taptweak = \a b -> let input = (feAsTy a, heAsTy b) in fast_build_taptweak input == implementation (ElementsJet (SigHashJet BuildTaptweak)) undefined input where fast_build_taptweak = testCoreEval Prog.buildTaptweak prop_outpoint_hash :: Sha256CtxElement -> Maybe HashElement -> (HashElement, Word.Word32) -> Bool prop_outpoint_hash = \ctx pegin op -> let input = (ctxAsTy ctx, (maybe (Left ()) (Right . heAsTy) pegin, (heAsTy *** (toWord32 . fromIntegral) $ op))) in fast_outpoint_hash input == implementation (ElementsJet (SigHashJet OutpointHash)) undefined input where fast_outpoint_hash = testCoreEval Prog.outpointHash prop_asset_amount_hash :: Sha256CtxElement -> Either PointElement Word256 -> Either PointElement Word64 -> Bool prop_asset_amount_hash = \ctx cw256 cw64 -> let input = (ctxAsTy ctx, (cast cw256, cast cw64)) in fast_asset_amount_hash input == implementation (ElementsJet (SigHashJet AssetAmountHash)) undefined input where fast_asset_amount_hash = testCoreEval Prog.assetAmountHash cast = either (Left . pointAsTy) Right prop_nonce_hash :: Sha256CtxElement -> Maybe Nonce -> Bool prop_nonce_hash = \ctx mnonce -> let input = (ctxAsTy ctx, cast mnonce) in fast_nonce_hash input == implementation (ElementsJet (SigHashJet NonceHash)) undefined input where fast_nonce_hash = testCoreEval Prog.nonceHash cast = maybe (Left ()) (Right . ((toBit *** (toWord256 . fromIntegral)) +++ (toWord256 . integerHash256)) . nonce) prop_annex_hash :: Sha256CtxElement -> Maybe Word256 -> Bool prop_annex_hash = \ctx mw256 -> let input = (ctxAsTy ctx, cast mw256) in fast_annex_hash input == implementation (ElementsJet (SigHashJet AnnexHash)) undefined input where fast_annex_hash = testCoreEval Prog.annexHash cast = maybe (Left ()) Right prop_input_issuance :: Property prop_input_issuance = checkJet (ElementsJet (IssuanceJet Issuance)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_issuance_asset :: Property prop_input_issuance_asset = checkJet (ElementsJet (IssuanceJet IssuanceAsset)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_issuance_token :: Property prop_input_issuance_token = checkJet (ElementsJet (IssuanceJet IssuanceToken)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_issuance_entropy :: Property prop_input_issuance_entropy = checkJet (ElementsJet (IssuanceJet IssuanceEntropy)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_output_amounts_hash :: Property prop_output_amounts_hash = checkJet (ElementsJet (SigHashJet OutputAmountsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_nonces_hash :: Property prop_output_nonces_hash = checkJet (ElementsJet (SigHashJet OutputNoncesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_scripts_hash :: Property prop_output_scripts_hash = checkJet (ElementsJet (SigHashJet OutputScriptsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_range_proofs_hash :: Property prop_output_range_proofs_hash = checkJet (ElementsJet (SigHashJet OutputRangeProofsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_surjection_proofs_hash :: Property prop_output_surjection_proofs_hash = checkJet (ElementsJet (SigHashJet OutputSurjectionProofsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_outputs_hash :: Property prop_outputs_hash = checkJet (ElementsJet (SigHashJet OutputsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_hash :: Property prop_output_hash = checkJet (ElementsJet (SigHashJet OutputHash)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_input_outpoints_hash :: Property prop_input_outpoints_hash = checkJet (ElementsJet (SigHashJet InputOutpointsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_amounts_hash :: Property prop_input_amounts_hash = checkJet (ElementsJet (SigHashJet InputAmountsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_scripts_hash :: Property prop_input_scripts_hash = checkJet (ElementsJet (SigHashJet InputScriptsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_utxos_hash :: Property prop_input_utxos_hash = checkJet (ElementsJet (SigHashJet InputUtxosHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_utxo_hash :: Property prop_input_utxo_hash = checkJet (ElementsJet (SigHashJet InputUtxoHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_sequences_hash :: Property prop_input_sequences_hash = checkJet (ElementsJet (SigHashJet InputSequencesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_annexes_hash :: Property prop_input_annexes_hash = checkJet (ElementsJet (SigHashJet InputAnnexesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_script_sigs_hash :: Property prop_input_script_sigs_hash = checkJet (ElementsJet (SigHashJet InputScriptSigsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_inputs_hash :: Property prop_inputs_hash = checkJet (ElementsJet (SigHashJet InputsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_hash :: Property prop_input_hash = checkJet (ElementsJet (SigHashJet InputHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_issuance_asset_amounts_hash :: Property prop_issuance_asset_amounts_hash = checkJet (ElementsJet (SigHashJet IssuanceAssetAmountsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_issuance_token_amounts_hash :: Property prop_issuance_token_amounts_hash = checkJet (ElementsJet (SigHashJet IssuanceTokenAmountsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_issuance_range_proofs_hash :: Property prop_issuance_range_proofs_hash = checkJet (ElementsJet (SigHashJet IssuanceRangeProofsHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_issuance_blinding_entropy_hash :: Property prop_issuance_blinding_entropy_hash = checkJet (ElementsJet (SigHashJet IssuanceBlindingEntropyHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_issuances_hash :: Property prop_issuances_hash = checkJet (ElementsJet (SigHashJet IssuancesHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_issuance_hash :: Property prop_issuance_hash = checkJet (ElementsJet (SigHashJet IssuanceHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_tx_hash :: Property prop_tx_hash = checkJet (ElementsJet (SigHashJet TxHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_tappath_hash :: Property prop_tappath_hash = checkJet (ElementsJet (SigHashJet TappathHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_tapleaf_hash :: Property prop_tapleaf_hash = checkJet (ElementsJet (SigHashJet TapleafHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_tap_env_hash :: Property prop_tap_env_hash = checkJet (ElementsJet (SigHashJet TapEnvHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_sig_all_hash :: Property prop_sig_all_hash = checkJet (ElementsJet (SigHashJet SigAllHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_script_cmr :: Property prop_script_cmr = checkJet (ElementsJet (TransactionJet ScriptCMR)) $ \check -> forallPrimEnv $ \env -> check env () prop_internal_key :: Property prop_internal_key = checkJet (ElementsJet (TransactionJet InternalKey)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_index :: Property prop_current_index = checkJet (ElementsJet (TransactionJet CurrentIndex)) $ \check -> forallPrimEnv $ \env -> check env () prop_num_inputs :: Property prop_num_inputs = checkJet (ElementsJet (TransactionJet NumInputs)) $ \check -> forallPrimEnv $ \env -> check env () prop_num_outputs :: Property prop_num_outputs = checkJet (ElementsJet (TransactionJet NumOutputs)) $ \check -> forallPrimEnv $ \env -> check env () prop_lock_time :: Property prop_lock_time = checkJet (ElementsJet (TransactionJet LockTime)) $ \check -> forallPrimEnv $ \env -> check env () prop_output_asset :: Property prop_output_asset = checkJet (ElementsJet (TransactionJet OutputAsset)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_output_amount :: Property prop_output_amount = checkJet (ElementsJet (TransactionJet OutputAmount)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_output_nonce :: Property prop_output_nonce = checkJet (ElementsJet (TransactionJet OutputNonce)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_output_script_hash :: Property prop_output_script_hash = checkJet (ElementsJet (TransactionJet OutputScriptHash)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_output_null_datum :: Property prop_output_null_datum = checkJet (ElementsJet (TransactionJet OutputNullDatum)) $ \check -> forallOutPrimEnv $ \env i -> forAll arbitrary $ \(NonNegative j) -> check env (toW32 i, toWord32 j) prop_output_is_fee :: Property prop_output_is_fee = checkJet (ElementsJet (TransactionJet OutputIsFee)) $ \check -> forallOutPrimEnv $ \env i -> classify (isJust $ sigTxOut (envTx env) !? (fromIntegral i) >>= outputFee) "is_fee" (check env (toW32 i)) prop_output_surjection_proof :: Property prop_output_surjection_proof = checkJet (ElementsJet (TransactionJet OutputSurjectionProof)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_output_range_proof :: Property prop_output_range_proof = checkJet (ElementsJet (TransactionJet OutputRangeProof)) $ \check -> forallOutPrimEnv $ \env i -> check env (toW32 i) prop_total_fee :: Property prop_total_fee = checkJet (ElementsJet (TransactionJet TotalFee)) $ \check -> forallOutPrimEnv $ \env i -> forAll arbitraryHash256 $ \hash -> let input = fromMaybe hash (getAssetId (sigTxOut (envTx env)) (fromIntegral i)) fee = Map.findWithDefault 0 input (totalFee (envTx env)) in classify (0 /= fee) "non-zero fee" $ check env (fromHash input) where getAssetId outputs ix = (outputs !? ix) >>= explicitId . view (under asset) . txoAsset explicitId (Explicit a) = Just a explicitId (Confidential _ _) = Nothing fromHash = toWord256 . integerHash256 prop_current_pegin :: Property prop_current_pegin = checkJet (ElementsJet (TransactionJet CurrentPegin)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_prev_outpoint :: Property prop_current_prev_outpoint = checkJet (ElementsJet (TransactionJet CurrentPrevOutpoint)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_asset :: Property prop_current_asset = checkJet (ElementsJet (TransactionJet CurrentAsset)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_amount :: Property prop_current_amount = checkJet (ElementsJet (TransactionJet CurrentAmount)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_script_hash :: Property prop_current_script_hash = checkJet (ElementsJet (TransactionJet CurrentScriptHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_sequence :: Property prop_current_sequence = checkJet (ElementsJet (TransactionJet CurrentSequence)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_annex_hash :: Property prop_current_annex_hash = checkJet (ElementsJet (TransactionJet CurrentAnnexHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_script_sig_hash :: Property prop_current_script_sig_hash = checkJet (ElementsJet (TransactionJet CurrentScriptSigHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_reissuance_blinding :: Property prop_current_reissuance_blinding = checkJet (ElementsJet (TransactionJet CurrentReissuanceBlinding)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_new_issuance_contract :: Property prop_current_new_issuance_contract = checkJet (ElementsJet (TransactionJet CurrentNewIssuanceContract)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_reissuance_entropy :: Property prop_current_reissuance_entropy = checkJet (ElementsJet (TransactionJet CurrentReissuanceEntropy)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_issuance_asset_amount :: Property prop_current_issuance_asset_amount = checkJet (ElementsJet (TransactionJet CurrentIssuanceAssetAmount)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_issuance_token_amount :: Property prop_current_issuance_token_amount = checkJet (ElementsJet (TransactionJet CurrentIssuanceTokenAmount)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_issuance_asset_proof :: Property prop_current_issuance_asset_proof = checkJet (ElementsJet (TransactionJet CurrentIssuanceAssetProof)) $ \check -> forallPrimEnv $ \env -> check env () prop_current_issuance_token_proof :: Property prop_current_issuance_token_proof = checkJet (ElementsJet (TransactionJet CurrentIssuanceTokenProof)) $ \check -> forallPrimEnv $ \env -> check env () prop_input_pegin :: Property prop_input_pegin = checkJet (ElementsJet (TransactionJet InputPegin)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_prev_outpoint :: Property prop_input_prev_outpoint = checkJet (ElementsJet (TransactionJet InputPrevOutpoint)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_asset :: Property prop_input_asset = checkJet (ElementsJet (TransactionJet InputAsset)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_amount :: Property prop_input_amount = checkJet (ElementsJet (TransactionJet InputAmount)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_script_hash :: Property prop_input_script_hash = checkJet (ElementsJet (TransactionJet InputScriptHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_sequence :: Property prop_input_sequence = checkJet (ElementsJet (TransactionJet InputSequence)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_annex_hash :: Property prop_input_annex_hash = checkJet (ElementsJet (TransactionJet InputAnnexHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_input_script_sig_hash :: Property prop_input_script_sig_hash = checkJet (ElementsJet (TransactionJet InputScriptSigHash)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_reissuance_blinding :: Property prop_reissuance_blinding = checkJet (ElementsJet (TransactionJet ReissuanceBlinding)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_new_issuance_contract :: Property prop_new_issuance_contract = checkJet (ElementsJet (TransactionJet NewIssuanceContract)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_reissuance_entropy :: Property prop_reissuance_entropy = checkJet (ElementsJet (TransactionJet ReissuanceEntropy)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_issuance_asset_amount :: Property prop_issuance_asset_amount = checkJet (ElementsJet (TransactionJet IssuanceAssetAmount)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_issuance_token_amount :: Property prop_issuance_token_amount = checkJet (ElementsJet (TransactionJet IssuanceTokenAmount)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_issuance_asset_proof :: Property prop_issuance_asset_proof = checkJet (ElementsJet (TransactionJet IssuanceAssetProof)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_issuance_token_proof :: Property prop_issuance_token_proof = checkJet (ElementsJet (TransactionJet IssuanceTokenProof)) $ \check -> forallInPrimEnv $ \env i -> check env (toW32 i) prop_tapleaf_version :: Property prop_tapleaf_version = checkJet (ElementsJet (TransactionJet TapleafVersion)) $ \check -> forallPrimEnv $ \env -> check env () prop_tappath :: Property prop_tappath = checkJet (ElementsJet (TransactionJet Tappath)) $ \check -> forallPrimEnv $ \env -> forAll (genTappathIx env) $ \i -> check env (toW8 i) where genTappathIx = genBoundaryCases . fromIntegral . length . tappath . envTap prop_version :: Property prop_version = checkJet (ElementsJet (TransactionJet Version)) $ \check -> forallPrimEnv $ \env -> check env () prop_genesis_block_hash :: Property prop_genesis_block_hash = checkJet (ElementsJet (TransactionJet GenesisBlockHash)) $ \check -> forallPrimEnv $ \env -> check env () prop_transaction_id :: Property prop_transaction_id = checkJet (ElementsJet (TransactionJet TransactionId)) $ \check -> forallPrimEnv $ \env -> check env () assert_lbtc_asset :: Assertion assert_lbtc_asset = testEval (specification jet) env () @?= implementation jet env () where jet = ElementsJet (IssuanceJet LbtcAsset) env = undefined -- example test data from Elements Core 0.17 (assert_issuance_entropy_1, assert_calculate_asset_1, assert_calculcate_token_1) = ( calculateIssuanceEntropy outpoint contractHash @?= entropy , calculateAsset entropy @?= assetID , calculateToken (Amount (Explicit undefined)) entropy @?= tokenID ) where contractHash = review (over le256) 0 outpoint = Outpoint (review (over le256) 0x05a047c98e82a848dee94efcf32462b065198bebf2404d201ba2e06db30b28f4) 0 entropy = review (over le256) 0x746f447f691323502cad2ef646f932613d37a83aeaa2133185b316648df4b70a assetID = review (over le256) 0xdcd60818d863b5c026c40b2bc3ba6fdaf5018bcc8606c18adf7db4da0bcd8533 tokenID = review (over le256) 0xc1adb114f4f87d33bf9ce90dd4f9ca523dd414d6cd010a7917903e2009689530 -- example test data from Elements Core 0.21 with prevout vout = 1 (assert_issuance_entropy_2, assert_calculate_asset_2, assert_calculcate_token_2) = ( calculateIssuanceEntropy outpoint contractHash @?= entropy , calculateAsset entropy @?= assetID , calculateToken (Amount (Confidential undefined undefined)) entropy @?= tokenID ) where contractHash = review (over le256) 0 outpoint = Outpoint (review (over le256) 0xc76664aa4be760056dcc39b59637eeea8f3c3c3b2aeefb9f23a7b99945a2931e) 1 entropy = review (over le256) 0xbc67a13736341d8ad19e558433483a38cae48a44a5a8b5598ca0b01b5f9f9f41 assetID = review (over le256) 0x2ec6c1a06e895b06fffb8dc36084255f890467fb906565b0c048d4c807b4a129 tokenID = review (over le256) 0xd09d205ff7c626ca98c91fed24787ff747fec62194ed1b7e6ef6cc775a1a1fdc -- example test data from Elements Core 0.21 with a given contract hash and non-blinded issuance (assert_issuance_entropy_3, assert_calculate_asset_3, assert_calculcate_token_3) = ( calculateIssuanceEntropy outpoint contractHash @?= entropy , calculateAsset entropy @?= assetID , calculateToken (Amount (Explicit undefined)) entropy @?= tokenID ) where contractHash = review (over le256) 0xe06e6d4933e76afd7b9cc6a013e0855aa60bbe6d2fca1c27ec6951ff5f1a20c9 outpoint = Outpoint (review (over le256) 0xee45365ddb62e8822182fbdd132fb156b4991e0b7411cff4aab576fd964f2edb) 0 entropy = review (over le256) 0x1922da340705eef526640b49d28b08928630d1ad52db0f945f3c389267e292c9 assetID = review (over le256) 0x8eebf6109bca0331fe559f0cbd1ef846a2bbb6812f3ae3d8b0b610170cc21a4e tokenID = review (over le256) 0xeb02cbc591c9ede071625c129f0a1fab386202cb27a894a45be0d564e961d6bc -- example test data from Elements Core 0.21 with confidential re-issuance (assert_issuance_entropy_4, assert_calculate_asset_4, assert_calculcate_token_4) = ( calculateIssuanceEntropy outpoint contractHash @?= entropy , calculateAsset entropy @?= assetID , calculateToken (Amount (Confidential undefined undefined)) entropy @?= tokenID ) where contractHash = review (over le256) 0 outpoint = Outpoint (review (over le256) 0x8903ee739b52859877fbfedc58194c2d59d0f5a4ea3c2774dc3cba3031cec757) 0 entropy = review (over le256) 0xb9789de8589dc1b664e4f2bda4d04af9d4d2180394a8c47b1f889acfb5e0acc4 assetID = review (over le256) 0xbdab916e8cda17781bcdb84505452e44d0ab2f080e9e5dd7765ffd5ce0c07cd9 tokenID = review (over le256) 0xf144868169dfc7afc024c4d8f55607ac8dfe925e67688650a9cdc54c3cfa5b1c tapEnv :: TapEnv tapEnv = TapEnv { tapleafVersion = 0xbe , tapInternalKey = Schnorr.PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 , tappath = [] , tapScriptCMR = review (over be256) 0x896b16e4692350cb43c4807c8f9f63637f70f84a17b678ca9467109ff1e50f61 } tx1 :: SigTx tx1 = SigTx { sigTxVersion = 0x00000002 , sigTxIn = fromList [input0] , sigTxOut = fromList [output0, output1] , sigTxLock = 0 } where assetId = Asset . Explicit $ review (over be256) 0x230f4f5d4b7c6fa845806ee4f67713459e1b69e8e60fcee2e4940c7a0d5de1b2 input0 = SigTxInput { sigTxiPegin = Nothing , sigTxiPreviousOutpoint = Outpoint (review (over be256) 0xeb04b68e9a26d116046c76e8ff47332fb71dda90ff4bef5370f25226d3bc09fc) 0 , sigTxiTxo = UTXO { utxoAsset = assetId , utxoAmount = Amount . Explicit $ 10000000000 , utxoScript = BSL.empty } , sigTxiSequence = 0xfffffffe , sigTxiIssuance = Nothing , sigTxiAnnex = Nothing , sigTxiScriptSig = BSL.empty } output0 = TxOutput { txoAsset = assetId , txoAmount = Amount . Explicit $ 9999996700 , txoNonce = Nothing , txoScript = BSL.pack [ 0x19, 0x76, 0xa9, 0x14, 0x48, 0x63, 0x3e, 0x2c, 0x0e, 0xe9, 0x49, 0x5d, 0xd3, 0xf9, 0xc4, 0x37 , 0x32, 0xc4, 0x7f, 0x47, 0x02, 0xa3, 0x62, 0xc8, 0x88, 0xac] } output1 = TxOutput { txoAsset = assetId , txoAmount = Amount . Explicit $ 3300 , txoNonce = Nothing , txoScript = BSL.empty } hunit_sigHashAll :: Bool hunit_sigHashAll = Just (integerHash256 sigHashAll_spec) == (fromWord256 <$> (sem (sigHash' Prog.sigAllHash) txEnv ())) where ix = 0 genesis = review (over be256) 0x0f9188f13cb7b2c71f2a335e3a4fc328bf5beb436012afca590b1a11466e2206 txo = sigTxiTxo (sigTxIn tx1 ! (fromIntegral ix)) Just txEnv = primEnv tx1 ix tapEnv genesis signatureTag = bsHash $ BSC.pack "Simplicity\USSignature" sigHashAll_spec = bslHash . runPutLazy $ put signatureTag >> put signatureTag >> put (commitmentRoot Prog.sigAllHash) >> put (primEnvHash txEnv) ================================================ FILE: Haskell/Tests/Simplicity/FFI/Bitstream.hs ================================================ {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.FFI.Bitstream ( Bitstream , initializeBitstream ) where import qualified Data.ByteString as BS import Data.Serialize (decode) import Data.Serialize.Put (runPut) import Foreign.C.Types (CSize(..), CChar(..)) import Foreign.Ptr (Ptr) import Foreign.Marshal.Alloc (allocaBytes) import Foreign.Marshal.Unsafe (unsafeLocalState) import Foreign.Storable (Storable(..)) import Simplicity.Serialization -- Abstract representative for our C structures. newtype Bitstream = Bitstream Bitstream foreign import ccall unsafe "&" c_sizeof_bitstream :: Ptr CSize foreign import ccall unsafe "" c_initializeBitstream :: Ptr Bitstream -> Ptr CChar -> CSize -> IO () sizeof_bitstream :: Int sizeof_bitstream = fromIntegral . unsafeLocalState $ peek c_sizeof_bitstream initializeBitstream :: [Bool] -> (Ptr Bitstream -> IO a) -> IO a initializeBitstream stream k = allocaBytes sizeof_bitstream $ \pstream -> BS.useAsCString bs $ \pbs -> do c_initializeBitstream pstream pbs (fromIntegral len) k pstream where bs = runPut $ putBitStream stream len = length stream ================================================ FILE: Haskell/Tests/Simplicity/FFI/Dag.hs ================================================ {-# LANGUAGE ForeignFunctionInterface #-} module Simplicity.FFI.Dag ( DagNode , dagNodeGetCMR , withDagNode , computeWordCMR ) where import qualified Data.ByteString as BS import Data.Serialize (decode) import Data.Serialize.Put (runPut) import Foreign.C.Types (CSize(..), CChar(..)) import Foreign.Ptr (Ptr) import Foreign.Marshal.Alloc (allocaBytes) import Foreign.Marshal.Array (allocaArray) import Foreign.Marshal.Unsafe (unsafeLocalState) import Foreign.Storable (Storable(..)) import Simplicity.Digest import Simplicity.FFI.Bitstream -- Abstract representative for our C structures. newtype DagNode = DagNode DagNode foreign import ccall unsafe "&" c_sizeof_dag_node :: Ptr CSize foreign import ccall unsafe "" c_dag_node_get_cmr :: Ptr CChar -> Ptr DagNode -> IO () foreign import ccall unsafe "" c_compute_word_cmr :: Ptr CChar -> Ptr Bitstream -> CSize -> CSize -> IO () sizeof_dag_node :: Int sizeof_dag_node = fromIntegral . unsafeLocalState $ peek c_sizeof_dag_node withDagNode :: (Ptr DagNode -> IO a) -> IO a withDagNode = allocaBytes sizeof_dag_node dagNodeGetCMR :: Ptr DagNode -> IO Hash256 dagNodeGetCMR pnode = allocaArray 32 $ \buf -> do c_dag_node_get_cmr buf pnode Right hash <- decode <$> BS.packCStringLen (buf, 32) return hash computeWordCMR :: Int -> [Bool] -> Hash256 computeWordCMR offset stream = case log2Of (length stream - offset) of Nothing -> error $ "Simplicity.FFI.Dag.computeWordCMR: Bad stream length " ++ show (length stream - offset) Just n -> unsafeLocalState $ initializeBitstream stream $ \pstream -> allocaArray 32 $ \buf -> do c_compute_word_cmr buf pstream (fromIntegral offset) (fromIntegral n) Right hash <- decode <$> BS.packCStringLen (buf, 32) return hash log2Of :: Int -> Maybe Int log2Of 1 = Just 0 log2Of n | n <= 0 = Nothing | odd n = Nothing | otherwise = (+ 1) <$> log2Of (n `div` 2) ================================================ FILE: Haskell/Tests/Simplicity/FFI/Tests.hs ================================================ module Simplicity.FFI.Tests ( tests , main , prop_div_mod_128_64 ) where import Control.Arrow ((***)) import Data.Bits ((.|.)) import Lens.Family2 ((^.), (^..), over, allOf, review, zipWithOf) import Test.Tasty (TestTree, defaultMain, testGroup) import Test.Tasty.QuickCheck ( Arbitrary(..), Gen, Property, arbitraryBoundedIntegral, arbitrarySizedBoundedIntegral, shrinkIntegral , choose, forAll, property, Discard(Discard), testProperty, vectorOf, withMaxSuccess , label ) import Test.Tasty.HUnit (Assertion, (@=?), assertBool, testCase) import Simplicity.Arbitrary import Simplicity.CoreJets import Simplicity.Digest import Simplicity.Elements.Arbitrary import qualified Simplicity.FFI.Jets as C import Simplicity.Programs.LibSecp256k1.Lib as Prog import Simplicity.LibSecp256k1.Spec as Spec import Simplicity.MerkleRoot import Simplicity.TestCoreEval import Simplicity.Ty.Arbitrary import Simplicity.Ty.LibSecp256k1 import Simplicity.Ty.Word import Simplicity.Bip0340 import Simplicity.Word as W main = defaultMain tests tests :: TestTree tests = testGroup "C / SPEC" [ testGroup "word" $ [ testCase "verify" assert_verify , testCase "low_1" assert_low_1 , testCase "low_8" assert_low_8 , testCase "low_16" assert_low_16 , testCase "low_32" assert_low_32 , testCase "low_64" assert_low_64 , testCase "high_1" assert_high_1 , testCase "high_8" assert_high_8 , testCase "high_16" assert_high_16 , testCase "high_32" assert_high_32 , testCase "high_64" assert_high_64 , testProperty "complement_1" prop_complement_1 , testProperty "complement_8" prop_complement_8 , testProperty "complement_16" prop_complement_16 , testProperty "complement_32" prop_complement_32 , testProperty "complement_64" prop_complement_64 , testProperty "and_1" prop_and_1 , testProperty "and_8" prop_and_8 , testProperty "and_16" prop_and_16 , testProperty "and_32" prop_and_32 , testProperty "and_64" prop_and_64 , testProperty "or_1" prop_or_1 , testProperty "or_8" prop_or_8 , testProperty "or_16" prop_or_16 , testProperty "or_32" prop_or_32 , testProperty "or_64" prop_or_64 , testProperty "xor_1" prop_xor_1 , testProperty "xor_8" prop_xor_8 , testProperty "xor_16" prop_xor_16 , testProperty "xor_32" prop_xor_32 , testProperty "xor_64" prop_xor_64 , testProperty "maj_1" prop_maj_1 , testProperty "maj_8" prop_maj_8 , testProperty "maj_16" prop_maj_16 , testProperty "maj_32" prop_maj_32 , testProperty "maj_64" prop_maj_64 , testProperty "xor_xor_1" prop_xor_xor_1 , testProperty "xor_xor_8" prop_xor_xor_8 , testProperty "xor_xor_16" prop_xor_xor_16 , testProperty "xor_xor_32" prop_xor_xor_32 , testProperty "xor_xor_64" prop_xor_xor_64 , testProperty "ch_1" prop_ch_1 , testProperty "ch_8" prop_ch_8 , testProperty "ch_16" prop_ch_16 , testProperty "ch_32" prop_ch_32 , testProperty "ch_64" prop_ch_64 , testProperty "some_1" prop_some_1 , testProperty "some_8" prop_some_8 , testProperty "some_16" prop_some_16 , testProperty "some_32" prop_some_32 , testProperty "some_64" prop_some_64 , testProperty "all_8" prop_all_8 , testProperty "all_16" prop_all_16 , testProperty "all_32" prop_all_32 , testProperty "all_64" prop_all_64 , testProperty "eq_1" prop_eq_1 , testProperty "eq_8" prop_eq_8 , testProperty "eq_16" prop_eq_16 , testProperty "eq_32" prop_eq_32 , testProperty "eq_64" prop_eq_64 , testProperty "eq_256" prop_eq_256 , testProperty "eq_diag_8" prop_eq_diag_8 , testProperty "eq_diag_16" prop_eq_diag_16 , testProperty "eq_diag_32" prop_eq_diag_32 , testProperty "eq_diag_64" prop_eq_diag_64 , testProperty "eq_diag_256" prop_eq_diag_256 , testProperty "full_left_shift_8_1" prop_full_left_shift_8_1 , testProperty "full_left_shift_8_2" prop_full_left_shift_8_2 , testProperty "full_left_shift_8_4" prop_full_left_shift_8_4 , testProperty "full_left_shift_16_1" prop_full_left_shift_16_1 , testProperty "full_left_shift_16_2" prop_full_left_shift_16_2 , testProperty "full_left_shift_16_4" prop_full_left_shift_16_4 , testProperty "full_left_shift_16_8" prop_full_left_shift_16_8 , testProperty "full_left_shift_32_1" prop_full_left_shift_32_1 , testProperty "full_left_shift_32_2" prop_full_left_shift_32_2 , testProperty "full_left_shift_32_4" prop_full_left_shift_32_4 , testProperty "full_left_shift_32_8" prop_full_left_shift_32_8 , testProperty "full_left_shift_32_16" prop_full_left_shift_32_16 , testProperty "full_left_shift_64_1" prop_full_left_shift_64_1 , testProperty "full_left_shift_64_2" prop_full_left_shift_64_2 , testProperty "full_left_shift_64_4" prop_full_left_shift_64_4 , testProperty "full_left_shift_64_8" prop_full_left_shift_64_8 , testProperty "full_left_shift_64_16" prop_full_left_shift_64_16 , testProperty "full_left_shift_64_32" prop_full_left_shift_64_32 , testProperty "full_right_shift_8_1" prop_full_right_shift_8_1 , testProperty "full_right_shift_8_2" prop_full_right_shift_8_2 , testProperty "full_right_shift_8_4" prop_full_right_shift_8_4 , testProperty "full_right_shift_16_1" prop_full_right_shift_16_1 , testProperty "full_right_shift_16_2" prop_full_right_shift_16_2 , testProperty "full_right_shift_16_4" prop_full_right_shift_16_4 , testProperty "full_right_shift_16_8" prop_full_right_shift_16_8 , testProperty "full_right_shift_32_1" prop_full_right_shift_32_1 , testProperty "full_right_shift_32_2" prop_full_right_shift_32_2 , testProperty "full_right_shift_32_4" prop_full_right_shift_32_4 , testProperty "full_right_shift_32_8" prop_full_right_shift_32_8 , testProperty "full_right_shift_32_16" prop_full_right_shift_32_16 , testProperty "full_right_shift_64_1" prop_full_right_shift_64_1 , testProperty "full_right_shift_64_2" prop_full_right_shift_64_2 , testProperty "full_right_shift_64_4" prop_full_right_shift_64_4 , testProperty "full_right_shift_64_8" prop_full_right_shift_64_8 , testProperty "full_right_shift_64_16" prop_full_right_shift_64_16 , testProperty "full_right_shift_64_32" prop_full_right_shift_64_32 , testProperty "leftmost_8_1" prop_leftmost_8_1 , testProperty "leftmost_8_2" prop_leftmost_8_2 , testProperty "leftmost_8_4" prop_leftmost_8_4 , testProperty "leftmost_16_1" prop_leftmost_16_1 , testProperty "leftmost_16_2" prop_leftmost_16_2 , testProperty "leftmost_16_4" prop_leftmost_16_4 , testProperty "leftmost_16_8" prop_leftmost_16_8 , testProperty "leftmost_32_1" prop_leftmost_32_1 , testProperty "leftmost_32_2" prop_leftmost_32_2 , testProperty "leftmost_32_4" prop_leftmost_32_4 , testProperty "leftmost_32_8" prop_leftmost_32_8 , testProperty "leftmost_32_16" prop_leftmost_32_16 , testProperty "leftmost_64_1" prop_leftmost_64_1 , testProperty "leftmost_64_2" prop_leftmost_64_2 , testProperty "leftmost_64_4" prop_leftmost_64_4 , testProperty "leftmost_64_8" prop_leftmost_64_8 , testProperty "leftmost_64_16" prop_leftmost_64_16 , testProperty "leftmost_64_32" prop_leftmost_64_32 , testProperty "rightmost_8_1" prop_rightmost_8_1 , testProperty "rightmost_8_2" prop_rightmost_8_2 , testProperty "rightmost_8_4" prop_rightmost_8_4 , testProperty "rightmost_16_1" prop_rightmost_16_1 , testProperty "rightmost_16_2" prop_rightmost_16_2 , testProperty "rightmost_16_4" prop_rightmost_16_4 , testProperty "rightmost_16_8" prop_rightmost_16_8 , testProperty "rightmost_32_1" prop_rightmost_32_1 , testProperty "rightmost_32_2" prop_rightmost_32_2 , testProperty "rightmost_32_4" prop_rightmost_32_4 , testProperty "rightmost_32_8" prop_rightmost_32_8 , testProperty "rightmost_32_16" prop_rightmost_32_16 , testProperty "rightmost_64_1" prop_rightmost_64_1 , testProperty "rightmost_64_2" prop_rightmost_64_2 , testProperty "rightmost_64_4" prop_rightmost_64_4 , testProperty "rightmost_64_8" prop_rightmost_64_8 , testProperty "rightmost_64_16" prop_rightmost_64_16 , testProperty "rightmost_64_32" prop_rightmost_64_32 , testProperty "left_pad_low_1_8" prop_left_pad_low_1_8 , testProperty "left_pad_low_1_16" prop_left_pad_low_1_16 , testProperty "left_pad_low_8_16" prop_left_pad_low_8_16 , testProperty "left_pad_low_1_32" prop_left_pad_low_1_32 , testProperty "left_pad_low_8_32" prop_left_pad_low_8_32 , testProperty "left_pad_low_16_32" prop_left_pad_low_16_32 , testProperty "left_pad_low_1_64" prop_left_pad_low_1_64 , testProperty "left_pad_low_8_64" prop_left_pad_low_8_64 , testProperty "left_pad_low_16_64" prop_left_pad_low_16_64 , testProperty "left_pad_low_32_64" prop_left_pad_low_32_64 , testProperty "left_pad_high_1_8" prop_left_pad_high_1_8 , testProperty "left_pad_high_1_16" prop_left_pad_high_1_16 , testProperty "left_pad_high_8_16" prop_left_pad_high_8_16 , testProperty "left_pad_high_1_32" prop_left_pad_high_1_32 , testProperty "left_pad_high_8_32" prop_left_pad_high_8_32 , testProperty "left_pad_high_16_32" prop_left_pad_high_16_32 , testProperty "left_pad_high_1_64" prop_left_pad_high_1_64 , testProperty "left_pad_high_8_64" prop_left_pad_high_8_64 , testProperty "left_pad_high_16_64" prop_left_pad_high_16_64 , testProperty "left_pad_high_32_64" prop_left_pad_high_32_64 , testProperty "left_extend_1_8" prop_left_extend_1_8 , testProperty "left_extend_1_16" prop_left_extend_1_16 , testProperty "left_extend_8_16" prop_left_extend_8_16 , testProperty "left_extend_1_32" prop_left_extend_1_32 , testProperty "left_extend_8_32" prop_left_extend_8_32 , testProperty "left_extend_16_32" prop_left_extend_16_32 , testProperty "left_extend_1_64" prop_left_extend_1_64 , testProperty "left_extend_8_64" prop_left_extend_8_64 , testProperty "left_extend_16_64" prop_left_extend_16_64 , testProperty "left_extend_32_64" prop_left_extend_32_64 , testProperty "right_pad_low_1_8" prop_right_pad_low_1_8 , testProperty "right_pad_low_1_16" prop_right_pad_low_1_16 , testProperty "right_pad_low_8_16" prop_right_pad_low_8_16 , testProperty "right_pad_low_1_32" prop_right_pad_low_1_32 , testProperty "right_pad_low_8_32" prop_right_pad_low_8_32 , testProperty "right_pad_low_16_32" prop_right_pad_low_16_32 , testProperty "right_pad_low_1_64" prop_right_pad_low_1_64 , testProperty "right_pad_low_8_64" prop_right_pad_low_8_64 , testProperty "right_pad_low_16_64" prop_right_pad_low_16_64 , testProperty "right_pad_low_32_64" prop_right_pad_low_32_64 , testProperty "right_pad_high_1_8" prop_right_pad_high_1_8 , testProperty "right_pad_high_1_16" prop_right_pad_high_1_16 , testProperty "right_pad_high_8_16" prop_right_pad_high_8_16 , testProperty "right_pad_high_1_32" prop_right_pad_high_1_32 , testProperty "right_pad_high_8_32" prop_right_pad_high_8_32 , testProperty "right_pad_high_16_32" prop_right_pad_high_16_32 , testProperty "right_pad_high_1_64" prop_right_pad_high_1_64 , testProperty "right_pad_high_8_64" prop_right_pad_high_8_64 , testProperty "right_pad_high_16_64" prop_right_pad_high_16_64 , testProperty "right_pad_high_32_64" prop_right_pad_high_32_64 , testProperty "right_extend_8_16" prop_right_extend_8_16 , testProperty "right_extend_8_32" prop_right_extend_8_32 , testProperty "right_extend_16_32" prop_right_extend_16_32 , testProperty "right_extend_8_64" prop_right_extend_8_64 , testProperty "right_extend_16_64" prop_right_extend_16_64 , testProperty "right_extend_32_64" prop_right_extend_32_64 , testProperty "left_shift_with_8" prop_left_shift_with_8 , testProperty "left_shift_with_16" prop_left_shift_with_16 , testProperty "left_shift_with_32" prop_left_shift_with_32 , testProperty "left_shift_with_64" prop_left_shift_with_64 , testProperty "left_shift_8" prop_left_shift_8 , testProperty "left_shift_16" prop_left_shift_16 , testProperty "left_shift_32" prop_left_shift_32 , testProperty "left_shift_64" prop_left_shift_64 , testProperty "right_shift_with_8" prop_right_shift_with_8 , testProperty "right_shift_with_16" prop_right_shift_with_16 , testProperty "right_shift_with_32" prop_right_shift_with_32 , testProperty "right_shift_with_64" prop_right_shift_with_64 , testProperty "right_shift_8" prop_right_shift_8 , testProperty "right_shift_16" prop_right_shift_16 , testProperty "right_shift_32" prop_right_shift_32 , testProperty "right_shift_64" prop_right_shift_64 , testProperty "left_rotate_8" prop_left_rotate_8 , testProperty "left_rotate_16" prop_left_rotate_16 , testProperty "left_rotate_32" prop_left_rotate_32 , testProperty "left_rotate_64" prop_left_rotate_64 , testProperty "right_rotate_8" prop_right_rotate_8 , testProperty "right_rotate_16" prop_right_rotate_16 , testProperty "right_rotate_32" prop_right_rotate_32 , testProperty "right_rotate_64" prop_right_rotate_64 ] , testGroup "arith" $ [ testCase "one_8" assert_one_8 , testCase "one_16" assert_one_16 , testCase "one_32" assert_one_32 , testCase "one_64" assert_one_64 , testProperty "add_8" prop_add_8 , testProperty "add_16" prop_add_16 , testProperty "add_32" prop_add_32 , testProperty "add_64" prop_add_64 , testProperty "full_add_8" prop_full_add_8 , testProperty "full_add_16" prop_full_add_16 , testProperty "full_add_32" prop_full_add_32 , testProperty "full_add_64" prop_full_add_64 , testProperty "full_increment_8" prop_full_increment_8 , testProperty "full_increment_16" prop_full_increment_16 , testProperty "full_increment_32" prop_full_increment_32 , testProperty "full_increment_64" prop_full_increment_64 , testCase "full_increment_max_8" assert_full_increment_max_8 , testCase "full_increment_max_16" assert_full_increment_max_16 , testCase "full_increment_max_32" assert_full_increment_max_32 , testCase "full_increment_max_64" assert_full_increment_max_64 , testProperty "increment_8" prop_increment_8 , testProperty "increment_16" prop_increment_16 , testProperty "increment_32" prop_increment_32 , testProperty "increment_64" prop_increment_64 , testCase "increment_max_8" assert_increment_max_8 , testCase "increment_max_16" assert_increment_max_16 , testCase "increment_max_32" assert_increment_max_32 , testCase "increment_max_64" assert_increment_max_64 , testProperty "subtract_8" prop_subtract_8 , testProperty "subtract_16" prop_subtract_16 , testProperty "subtract_32" prop_subtract_32 , testProperty "subtract_64" prop_subtract_64 , testProperty "full_subtract_8" prop_full_subtract_8 , testProperty "full_subtract_16" prop_full_subtract_16 , testProperty "full_subtract_32" prop_full_subtract_32 , testProperty "full_subtract_64" prop_full_subtract_64 , testProperty "negate_8" prop_negate_8 , testProperty "negate_16" prop_negate_16 , testProperty "negate_32" prop_negate_32 , testProperty "negate_64" prop_negate_64 , testProperty "full_decrement_8" prop_full_decrement_8 , testProperty "full_decrement_16" prop_full_decrement_16 , testProperty "full_decrement_32" prop_full_decrement_32 , testProperty "full_decrement_64" prop_full_decrement_64 , testCase "full_decrement_zero_8" assert_full_decrement_zero_8 , testCase "full_decrement_zero_16" assert_full_decrement_zero_16 , testCase "full_decrement_zero_32" assert_full_decrement_zero_32 , testCase "full_decrement_zero_64" assert_full_decrement_zero_64 , testProperty "decrement_8" prop_decrement_8 , testProperty "decrement_16" prop_decrement_16 , testProperty "decrement_32" prop_decrement_32 , testProperty "decrement_64" prop_decrement_64 , testCase "decrement_zero_8" assert_decrement_zero_8 , testCase "decrement_zero_16" assert_decrement_zero_16 , testCase "decrement_zero_32" assert_decrement_zero_32 , testCase "decrement_zero_64" assert_decrement_zero_64 , testProperty "multiply_8" prop_multiply_8 , testProperty "multiply_16" prop_multiply_16 , testProperty "multiply_32" prop_multiply_32 , testProperty "multiply_64" prop_multiply_64 , testProperty "full_multiply_8" prop_full_multiply_8 , testProperty "full_multiply_16" prop_full_multiply_16 , testProperty "full_multiply_32" prop_full_multiply_32 , testProperty "full_multiply_64" prop_full_multiply_64 , testProperty "is_zero_8" prop_is_zero_8 , testProperty "is_zero_16" prop_is_zero_16 , testProperty "is_zero_32" prop_is_zero_32 , testProperty "is_zero_64" prop_is_zero_64 , testCase "zero_is_zero_8" assert_zero_is_zero_8 , testCase "zero_is_zero_16" assert_zero_is_zero_16 , testCase "zero_is_zero_32" assert_zero_is_zero_32 , testCase "zero_is_zero_64" assert_zero_is_zero_64 , testProperty "is_one_8" prop_is_one_8 , testProperty "is_one_16" prop_is_one_16 , testProperty "is_one_32" prop_is_one_32 , testProperty "is_one_64" prop_is_one_64 , testCase "one_is_one_8" assert_one_is_one_8 , testCase "one_is_one_16" assert_one_is_one_16 , testCase "one_is_one_32" assert_one_is_one_32 , testCase "one_is_one_64" assert_one_is_one_64 , testProperty "le_8" prop_le_8 , testProperty "le_16" prop_le_16 , testProperty "le_32" prop_le_32 , testProperty "le_64" prop_le_64 , testProperty "le_diag_8" prop_le_diag_8 , testProperty "le_diag_16" prop_le_diag_16 , testProperty "le_diag_32" prop_le_diag_32 , testProperty "le_diag_64" prop_le_diag_64 , testProperty "lt_8" prop_lt_8 , testProperty "lt_16" prop_lt_16 , testProperty "lt_32" prop_lt_32 , testProperty "lt_64" prop_lt_64 , testProperty "lt_diag_8" prop_lt_diag_8 , testProperty "lt_diag_16" prop_lt_diag_16 , testProperty "lt_diag_32" prop_lt_diag_32 , testProperty "lt_diag_64" prop_lt_diag_64 , testProperty "min_8" prop_min_8 , testProperty "min_16" prop_min_16 , testProperty "min_32" prop_min_32 , testProperty "min_64" prop_min_64 , testProperty "max_8" prop_max_8 , testProperty "max_16" prop_max_16 , testProperty "max_32" prop_max_32 , testProperty "max_64" prop_max_64 , testProperty "median_8" prop_median_8 , testProperty "median_16" prop_median_16 , testProperty "median_32" prop_median_32 , testProperty "median_64" prop_median_64 , testProperty "div_mod_8" prop_div_mod_8 , testProperty "div_mod_16" prop_div_mod_16 , testProperty "div_mod_32" prop_div_mod_32 , testProperty "div_mod_64" prop_div_mod_64 , testProperty "divide_8" prop_divide_8 , testProperty "divide_16" prop_divide_16 , testProperty "divide_32" prop_divide_32 , testProperty "divide_64" prop_divide_64 , testProperty "modulo_8" prop_modulo_8 , testProperty "modulo_16" prop_modulo_16 , testProperty "modulo_32" prop_modulo_32 , testProperty "modulo_64" prop_modulo_64 , testProperty "divides_8" prop_divides_8 , testProperty "divides_16" prop_divides_16 , testProperty "divides_32" prop_divides_32 , testProperty "divides_64" prop_divides_64 , testProperty "div_mod_zero_8" prop_div_mod_zero_8 , testProperty "div_mod_zero_16" prop_div_mod_zero_16 , testProperty "div_mod_zero_32" prop_div_mod_zero_32 , testProperty "div_mod_zero_64" prop_div_mod_zero_64 , testProperty "divide_zero_8" prop_divide_zero_8 , testProperty "divide_zero_16" prop_divide_zero_16 , testProperty "divide_zero_32" prop_divide_zero_32 , testProperty "divide_zero_64" prop_divide_zero_64 , testProperty "modulo_zero_8" prop_modulo_zero_8 , testProperty "modulo_zero_16" prop_modulo_zero_16 , testProperty "modulo_zero_32" prop_modulo_zero_32 , testProperty "modulo_zero_64" prop_modulo_zero_64 , testProperty "divides_zero_8" prop_divides_zero_8 , testProperty "divides_zero_16" prop_divides_zero_16 , testProperty "divides_zero_32" prop_divides_zero_32 , testProperty "divides_zero_64" prop_divides_zero_64 , testProperty "div_mod_128_64" prop_div_mod_128_64 , testProperty "div_mod_128_64_low_y" prop_div_mod_128_64_low_y , testProperty "div_mod_128_64_high_x" prop_div_mod_128_64_high_x ] , testGroup "sha256" $ [ testCase "sha_256_iv" assert_sha_256_iv , testProperty "sha_256_block" prop_sha_256_block , testCase "sha_256_ctx_8_init" assert_sha_256_ctx_8_init , testProperty "sha_256_ctx_8_add_1" prop_sha_256_ctx_8_add_1 , testProperty "sha_256_ctx_8_add_2" prop_sha_256_ctx_8_add_2 , testProperty "sha_256_ctx_8_add_4" prop_sha_256_ctx_8_add_4 , testProperty "sha_256_ctx_8_add_8" prop_sha_256_ctx_8_add_8 , testProperty "sha_256_ctx_8_add_16" prop_sha_256_ctx_8_add_16 , testProperty "sha_256_ctx_8_add_32" prop_sha_256_ctx_8_add_32 , testProperty "sha_256_ctx_8_add_64" prop_sha_256_ctx_8_add_64 , testProperty "sha_256_ctx_8_add_128" prop_sha_256_ctx_8_add_128 , testProperty "sha_256_ctx_8_add_256" prop_sha_256_ctx_8_add_256 , testProperty "sha_256_ctx_8_add_512" prop_sha_256_ctx_8_add_512 , testProperty "sha_256_ctx_8_add_buffer_511" prop_sha_256_ctx_8_add_buffer_511 , testProperty "sha_256_ctx_8_finalize" prop_sha_256_ctx_8_finalize ] , testGroup "bitcoin" $ [ testProperty "parse_lock" prop_parse_lock , testProperty "parse_sequence" prop_parse_sequence , testCase "tapdata_init" assert_tapdata_init ] , testGroup "field" [ testProperty "fe_normlaize" prop_fe_normalize , testProperty "fe_negate" prop_fe_negate , testProperty "fe_add" prop_fe_add , testProperty "fe_square" prop_fe_square , testProperty "fe_multiply" prop_fe_multiply , testProperty "fe_multiply_beta" prop_fe_multiply_beta , testProperty "fe_invert" (withMaxSuccess 10 prop_fe_invert) , testProperty "fe_square_root" prop_fe_square_root , testProperty "fe_is_zero" prop_fe_is_zero , testProperty "fe_is_odd" prop_fe_is_odd ] , testGroup "scalar" [ testProperty "scalar_normalize" prop_scalar_normalize , testProperty "scalar_negate" prop_scalar_negate , testProperty "scalar_add" prop_scalar_add , testProperty "scalar_square" prop_scalar_square , testProperty "scalar_multiply" prop_scalar_multiply , testProperty "scalar_multiply_lambda" prop_scalar_multiply_lambda , testProperty "scalar_invert" (withMaxSuccess 10 prop_scalar_invert) , testProperty "scalar_is_zero" prop_scalar_is_zero ] , testGroup "group" [ testCase "gej_infinity" assert_gej_infinity , testProperty "gej_rescale" prop_gej_rescale , testProperty "gej_rescale_inf" prop_gej_rescale_inf , testProperty "gej_normalize" prop_gej_normalize , testProperty "gej_normalize_inf" prop_gej_normalize_inf , testProperty "gej_negate" prop_gej_negate , testProperty "gej_negate_inf" prop_gej_negate_inf , testProperty "ge_negate" prop_ge_negate , testProperty "gej_double" prop_gej_double , testProperty "gej_double_inf" prop_gej_double_inf , testProperty "gej_double_zero" prop_gej_double_zero , testProperty "gej_add" prop_gej_add , testProperty "gej_add_double" prop_gej_add_double , testProperty "gej_add_opp" prop_gej_add_opp , testProperty "gej_add_infl" prop_gej_add_infl , testProperty "gej_add_infr" prop_gej_add_infr , testProperty "gej_ge_add_ex_double" prop_gej_ge_add_ex_double , testProperty "gej_ge_add_ex_opp" prop_gej_ge_add_ex_opp , testProperty "gej_ge_add_ex_inf" prop_gej_ge_add_ex_inf , testProperty "gej_ge_add" prop_gej_ge_add , testProperty "gej_is_infinity" prop_gej_is_infinity , testProperty "gej_equiv" prop_gej_equiv , testProperty "gej_equiv_infl" prop_gej_equiv_infl , testProperty "gej_equiv_infr" prop_gej_equiv_infr , testProperty "gej_equiv_inf" prop_gej_equiv_inf , testProperty "gej_equiv_true" prop_gej_equiv_true , testProperty "gej_ge_equiv" prop_gej_ge_equiv , testProperty "gej_ge_equiv_inf" prop_gej_ge_equiv_inf , testProperty "gej_ge_equiv_true" prop_gej_ge_equiv_true , testProperty "gej_x_equiv" prop_gej_x_equiv , testProperty "gej_x_equiv_inf" prop_gej_x_equiv_inf , testProperty "gej_x_equiv_true" prop_gej_x_equiv_true , testProperty "gej_x_equiv_inf_zero" prop_gej_x_equiv_inf_zero , testProperty "gej_y_is_odd" prop_gej_y_is_odd , testProperty "gej_is_on_curve" prop_gej_is_on_curve , testProperty "gej_is_on_curve_inf" prop_gej_is_on_curve_inf , testProperty "gej_is_on_curve_half" prop_gej_is_on_curve_half , testProperty "gej_is_on_curve_inf_half" prop_gej_is_on_curve_inf_half , testProperty "ge_is_on_curve" prop_ge_is_on_curve , testProperty "ge_is_on_curve_half" prop_ge_is_on_curve_half ] , testGroup "ecMult" [ testCase "off_curve_linear_combination_1_order_6" assert_off_curve_linear_combination_1_order_6 , testProperty "off_curve_linear_combination_1_inf" prop_off_curve_linear_combination_1_inf , testProperty "off_curve_linear_combination_1_0" prop_off_curve_linear_combination_1_0 , testProperty "off_curve_linear_combination_1" prop_off_curve_linear_combination_1 , testProperty "linear_combination_1_half" prop_linear_combination_1_half , testProperty "linear_combination_1_half_inf" prop_linear_combination_1_half_inf , testProperty "linear_combination_1_half_0" prop_linear_combination_1_half_0 , testProperty "linear_combination_1_inf" prop_linear_combination_1_inf , testProperty "linear_combination_1_0" prop_linear_combination_1_0 , testProperty "linear_combination_1" prop_linear_combination_1 , testProperty "generate" prop_generate , testProperty "off_curve_scale" prop_off_curve_scale , testProperty "off_curve_scale_0" prop_off_curve_scale_0 , testProperty "off_curve_scale_inf" prop_off_curve_scale_inf , testProperty "scale_half" prop_scale_half , testProperty "scale_half_inf" prop_scale_half_inf , testProperty "scale_half_0" prop_scale_half_0 , testProperty "scale_inf" prop_scale_inf , testProperty "scale_0" prop_scale_0 , testProperty "scale" prop_scale , testProperty "linear_verify_1_true_half" prop_linear_verify_1_true_half , testProperty "linear_verify_1_0" prop_linear_verify_1_0 , testProperty "linear_verify_1" prop_linear_verify_1 ] , testGroup "point" [ testProperty "point_verify_1" prop_point_verify_1 , testProperty "point_verify_1_true" prop_point_verify_1 , testProperty "decompress" prop_decompress ] , testGroup "bip0340" $ [ testProperty "bip_0340_verify" prop_bip_0340_verify ] ++ zipWith case_bip_0340_verify_vector [0..] bip0340Vectors ++ [ testProperty "check_sig_verify" prop_check_sig_verify , testProperty "check_sig_verify_true" prop_check_sig_verify_true ] , testGroup "generator" [ testProperty "swu" prop_swu , testProperty "hash_to_curve" prop_hash_to_curve ] ] assert_verify :: Assertion assert_verify = (fastF (toBit False), fastF (toBit True)) @=? (C.verify (toBit False), C.verify (toBit True)) where fastF = testCoreEval (specification (WordJet Verify)) assert_low_1 :: Assertion assert_low_1 = fastF () @=? C.low_1 () where fastF = testCoreEval (specification (WordJet Low1)) assert_low_8 :: Assertion assert_low_8 = fastF () @=? C.low_8 () where fastF = testCoreEval (specification (WordJet Low8)) assert_low_16 :: Assertion assert_low_16 = fastF () @=? C.low_16 () where fastF = testCoreEval (specification (WordJet Low16)) assert_low_32 :: Assertion assert_low_32 = fastF () @=? C.low_32 () where fastF = testCoreEval (specification (WordJet Low32)) assert_low_64 :: Assertion assert_low_64 = fastF () @=? C.low_64 () where fastF = testCoreEval (specification (WordJet Low64)) assert_high_1 :: Assertion assert_high_1 = fastF () @=? C.high_1 () where fastF = testCoreEval (specification (WordJet High1)) assert_high_8 :: Assertion assert_high_8 = fastF () @=? C.high_8 () where fastF = testCoreEval (specification (WordJet High8)) assert_high_16 :: Assertion assert_high_16 = fastF () @=? C.high_16 () where fastF = testCoreEval (specification (WordJet High16)) assert_high_32 :: Assertion assert_high_32 = fastF () @=? C.high_32 () where fastF = testCoreEval (specification (WordJet High32)) assert_high_64 :: Assertion assert_high_64 = fastF () @=? C.high_64 () where fastF = testCoreEval (specification (WordJet High64)) prop_complement_1 :: Bool -> Bool prop_complement_1 = \x -> let input = toBit x in fastF input == C.complement_1 input where fastF = testCoreEval (specification (WordJet Complement1)) prop_complement_8 :: W.Word8 -> Bool prop_complement_8 = \x -> let input = toW8 x in fastF input == C.complement_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Complement8)) prop_complement_16 :: W.Word16 -> Bool prop_complement_16 = \x -> let input = toW16 x in fastF input == C.complement_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Complement16)) prop_complement_32 :: W.Word32 -> Bool prop_complement_32 = \x -> let input = toW32 x in fastF input == C.complement_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Complement32)) prop_complement_64 :: W.Word64 -> Bool prop_complement_64 = \x -> let input = toW64 x in fastF input == C.complement_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Complement64)) prop_and_1 :: Bool -> Bool -> Bool prop_and_1 = \x y -> let input = (toBit x, toBit y) in fastF input == C.and_1 input where fastF = testCoreEval (specification (WordJet And1)) prop_and_8 :: W.Word8 -> W.Word8 -> Bool prop_and_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.and_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet And8)) prop_and_16 :: W.Word16 -> W.Word16 -> Bool prop_and_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.and_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet And16)) prop_and_32 :: W.Word32 -> W.Word32 -> Bool prop_and_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.and_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet And32)) prop_and_64 :: W.Word64 -> W.Word64 -> Bool prop_and_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.and_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet And64)) prop_or_1 :: Bool -> Bool -> Bool prop_or_1 = \x y -> let input = (toBit x, toBit y) in fastF input == C.or_1 input where fastF = testCoreEval (specification (WordJet Or1)) prop_or_8 :: W.Word8 -> W.Word8 -> Bool prop_or_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.or_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Or8)) prop_or_16 :: W.Word16 -> W.Word16 -> Bool prop_or_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.or_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Or16)) prop_or_32 :: W.Word32 -> W.Word32 -> Bool prop_or_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.or_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Or32)) prop_or_64 :: W.Word64 -> W.Word64 -> Bool prop_or_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.or_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Or64)) prop_xor_1 :: Bool -> Bool -> Bool prop_xor_1 = \x y -> let input = (toBit x, toBit y) in fastF input == C.xor_1 input where fastF = testCoreEval (specification (WordJet Xor1)) prop_xor_8 :: W.Word8 -> W.Word8 -> Bool prop_xor_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.xor_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Xor8)) prop_xor_16 :: W.Word16 -> W.Word16 -> Bool prop_xor_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.xor_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Xor16)) prop_xor_32 :: W.Word32 -> W.Word32 -> Bool prop_xor_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.xor_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Xor32)) prop_xor_64 :: W.Word64 -> W.Word64 -> Bool prop_xor_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.xor_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Xor64)) prop_maj_1 :: Bool -> Bool -> Bool -> Bool prop_maj_1 = \x y z -> let input = (toBit x, (toBit y, toBit z)) in fastF input == C.maj_1 input where fastF = testCoreEval (specification (WordJet Maj1)) prop_maj_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_maj_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == C.maj_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Maj8)) prop_maj_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_maj_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == C.maj_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Maj16)) prop_maj_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_maj_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == C.maj_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Maj32)) prop_maj_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_maj_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == C.maj_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Maj64)) prop_xor_xor_1 :: Bool -> Bool -> Bool -> Bool prop_xor_xor_1 = \x y z -> let input = (toBit x, (toBit y, toBit z)) in fastF input == C.xor_xor_1 input where fastF = testCoreEval (specification (WordJet XorXor1)) prop_xor_xor_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_xor_xor_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == C.xor_xor_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor8)) prop_xor_xor_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_xor_xor_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == C.xor_xor_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor16)) prop_xor_xor_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_xor_xor_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == C.xor_xor_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor32)) prop_xor_xor_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_xor_xor_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == C.xor_xor_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor64)) prop_ch_1 :: Bool -> Bool -> Bool -> Bool prop_ch_1 = \x y z -> let input = (toBit x, (toBit y, toBit z)) in fastF input == C.ch_1 input where fastF = testCoreEval (specification (WordJet Ch1)) prop_ch_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_ch_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == C.ch_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Ch8)) prop_ch_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_ch_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == C.ch_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Ch16)) prop_ch_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_ch_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == C.ch_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Ch32)) prop_ch_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_ch_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == C.ch_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Ch64)) prop_some_1 :: Bool -> Bool prop_some_1 = \x -> let input = toBit x in fastF input == C.some_1 input where fastF = testCoreEval (specification (WordJet Some1)) prop_some_8 :: W.Word8 -> Bool prop_some_8 = \x -> let input = toW8 x in fastF input == C.some_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Some8)) prop_some_16 :: W.Word16 -> Bool prop_some_16 = \x -> let input = toW16 x in fastF input == C.some_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Some16)) prop_some_32 :: W.Word32 -> Bool prop_some_32 = \x -> let input = toW32 x in fastF input == C.some_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Some32)) prop_some_64 :: W.Word64 -> Bool prop_some_64 = \x -> let input = toW64 x in fastF input == C.some_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Some64)) prop_all_8 :: W.Word8 -> Bool prop_all_8 = \x -> let input = toW8 x in fastF input == C.all_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet All8)) prop_all_16 :: W.Word16 -> Bool prop_all_16 = \x -> let input = toW16 x in fastF input == C.all_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet All16)) prop_all_32 :: W.Word32 -> Bool prop_all_32 = \x -> let input = toW32 x in fastF input == C.all_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet All32)) prop_all_64 :: W.Word64 -> Bool prop_all_64 = \x -> let input = toW64 x in fastF input == C.all_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet All64)) prop_eq_1 :: Bool -> Bool -> Bool prop_eq_1 = \x y -> let input = (toBit x, toBit y) in fastF input == C.eq_1 input where fastF = testCoreEval (specification (WordJet Eq1)) prop_eq_8 :: W.Word8 -> W.Word8 -> Bool prop_eq_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.eq_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Eq8)) prop_eq_16 :: W.Word16 -> W.Word16 -> Bool prop_eq_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.eq_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Eq16)) prop_eq_32 :: W.Word32 -> W.Word32 -> Bool prop_eq_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.eq_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Eq32)) prop_eq_64 :: W.Word64 -> W.Word64 -> Bool prop_eq_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.eq_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Eq64)) prop_eq_256 :: W.Word256 -> W.Word256 -> Bool prop_eq_256 = \x y -> let input = (toW256 x, toW256 y) in fastF input == C.eq_256 input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (WordJet Eq256)) prop_eq_diag_8 :: W.Word8 -> Bool prop_eq_diag_8 = \x -> let input = (toW8 x, toW8 x) in fastF input == C.eq_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Eq8)) prop_eq_diag_16 :: W.Word16 -> Bool prop_eq_diag_16 = \x -> let input = (toW16 x, toW16 x) in fastF input == C.eq_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Eq16)) prop_eq_diag_32 :: W.Word32 -> Bool prop_eq_diag_32 = \x -> let input = (toW32 x, toW32 x) in fastF input == C.eq_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Eq32)) prop_eq_diag_64 :: W.Word64 -> Bool prop_eq_diag_64 = \x -> let input = (toW64 x, toW64 x) in fastF input == C.eq_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Eq64)) prop_eq_diag_256 :: W.Word256 -> Bool prop_eq_diag_256 = \x -> let input = (toW256 x, toW256 x) in fastF input == C.eq_256 input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (WordJet Eq256)) prop_full_left_shift_8_1 :: W.Word8 -> Bool -> Bool prop_full_left_shift_8_1 = \x y -> let input = (toW8 x, toBit y) in fastF input == C.full_left_shift_8_1 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift8_1)) prop_full_left_shift_8_2 :: W.Word8 -> W.Word8 -> Bool prop_full_left_shift_8_2 = \x y -> let input = (toW8 x, toW2 y) in fastF input == C.full_left_shift_8_2 input where toW8 = toWord8 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift8_2)) prop_full_left_shift_8_4 :: W.Word8 -> W.Word8 -> Bool prop_full_left_shift_8_4 = \x y -> let input = (toW8 x, toW4 y) in fastF input == C.full_left_shift_8_4 input where toW8 = toWord8 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift8_4)) prop_full_left_shift_16_1 :: W.Word16 -> Bool -> Bool prop_full_left_shift_16_1 = \x y -> let input = (toW16 x, toBit y) in fastF input == C.full_left_shift_16_1 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_1)) prop_full_left_shift_16_2 :: W.Word16 -> W.Word8 -> Bool prop_full_left_shift_16_2 = \x y -> let input = (toW16 x, toW2 y) in fastF input == C.full_left_shift_16_2 input where toW16 = toWord16 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_2)) prop_full_left_shift_16_4 :: W.Word16 -> W.Word8 -> Bool prop_full_left_shift_16_4 = \x y -> let input = (toW16 x, toW4 y) in fastF input == C.full_left_shift_16_4 input where toW16 = toWord16 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_4)) prop_full_left_shift_16_8 :: W.Word16 -> W.Word8 -> Bool prop_full_left_shift_16_8 = \x y -> let input = (toW16 x, toW8 y) in fastF input == C.full_left_shift_16_8 input where toW16 = toWord16 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_8)) prop_full_left_shift_32_1 :: W.Word32 -> Bool -> Bool prop_full_left_shift_32_1 = \x y -> let input = (toW32 x, toBit y) in fastF input == C.full_left_shift_32_1 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_1)) prop_full_left_shift_32_2 :: W.Word32 -> W.Word8 -> Bool prop_full_left_shift_32_2 = \x y -> let input = (toW32 x, toW2 y) in fastF input == C.full_left_shift_32_2 input where toW32 = toWord32 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_2)) prop_full_left_shift_32_4 :: W.Word32 -> W.Word8 -> Bool prop_full_left_shift_32_4 = \x y -> let input = (toW32 x, toW4 y) in fastF input == C.full_left_shift_32_4 input where toW32 = toWord32 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_4)) prop_full_left_shift_32_8 :: W.Word32 -> W.Word8 -> Bool prop_full_left_shift_32_8 = \x y -> let input = (toW32 x, toW8 y) in fastF input == C.full_left_shift_32_8 input where toW32 = toWord32 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_8)) prop_full_left_shift_32_16 :: W.Word32 -> W.Word16 -> Bool prop_full_left_shift_32_16 = \x y -> let input = (toW32 x, toW16 y) in fastF input == C.full_left_shift_32_16 input where toW32 = toWord32 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_16)) prop_full_left_shift_64_1 :: W.Word64 -> Bool -> Bool prop_full_left_shift_64_1 = \x y -> let input = (toW64 x, toBit y) in fastF input == C.full_left_shift_64_1 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_1)) prop_full_left_shift_64_2 :: W.Word64 -> W.Word8 -> Bool prop_full_left_shift_64_2 = \x y -> let input = (toW64 x, toW2 y) in fastF input == C.full_left_shift_64_2 input where toW64 = toWord64 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_2)) prop_full_left_shift_64_4 :: W.Word64 -> W.Word8 -> Bool prop_full_left_shift_64_4 = \x y -> let input = (toW64 x, toW4 y) in fastF input == C.full_left_shift_64_4 input where toW64 = toWord64 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_4)) prop_full_left_shift_64_8 :: W.Word64 -> W.Word8 -> Bool prop_full_left_shift_64_8 = \x y -> let input = (toW64 x, toW8 y) in fastF input == C.full_left_shift_64_8 input where toW64 = toWord64 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_8)) prop_full_left_shift_64_16 :: W.Word64 -> W.Word16 -> Bool prop_full_left_shift_64_16 = \x y -> let input = (toW64 x, toW16 y) in fastF input == C.full_left_shift_64_16 input where toW64 = toWord64 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_16)) prop_full_left_shift_64_32 :: W.Word64 -> W.Word32 -> Bool prop_full_left_shift_64_32 = \x y -> let input = (toW64 x, toW32 y) in fastF input == C.full_left_shift_64_32 input where toW64 = toWord64 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_32)) prop_full_right_shift_8_1 :: W.Word8 -> Bool -> Bool prop_full_right_shift_8_1 = \x y -> let input = (toBit y, toW8 x) in fastF input == C.full_right_shift_8_1 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift8_1)) prop_full_right_shift_8_2 :: W.Word8 -> W.Word8 -> Bool prop_full_right_shift_8_2 = \x y -> let input = (toW2 y, toW8 x) in fastF input == C.full_right_shift_8_2 input where toW8 = toWord8 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift8_2)) prop_full_right_shift_8_4 :: W.Word8 -> W.Word8 -> Bool prop_full_right_shift_8_4 = \x y -> let input = (toW4 y, toW8 x) in fastF input == C.full_right_shift_8_4 input where toW8 = toWord8 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift8_4)) prop_full_right_shift_16_1 :: W.Word16 -> Bool -> Bool prop_full_right_shift_16_1 = \x y -> let input = (toBit y, toW16 x) in fastF input == C.full_right_shift_16_1 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_1)) prop_full_right_shift_16_2 :: W.Word16 -> W.Word8 -> Bool prop_full_right_shift_16_2 = \x y -> let input = (toW2 y, toW16 x) in fastF input == C.full_right_shift_16_2 input where toW16 = toWord16 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_2)) prop_full_right_shift_16_4 :: W.Word16 -> W.Word8 -> Bool prop_full_right_shift_16_4 = \x y -> let input = (toW4 y, toW16 x) in fastF input == C.full_right_shift_16_4 input where toW16 = toWord16 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_4)) prop_full_right_shift_16_8 :: W.Word16 -> W.Word8 -> Bool prop_full_right_shift_16_8 = \x y -> let input = (toW8 y, toW16 x) in fastF input == C.full_right_shift_16_8 input where toW16 = toWord16 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_8)) prop_full_right_shift_32_1 :: W.Word32 -> Bool -> Bool prop_full_right_shift_32_1 = \x y -> let input = (toBit y, toW32 x) in fastF input == C.full_right_shift_32_1 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_1)) prop_full_right_shift_32_2 :: W.Word32 -> W.Word8 -> Bool prop_full_right_shift_32_2 = \x y -> let input = (toW2 y, toW32 x) in fastF input == C.full_right_shift_32_2 input where toW32 = toWord32 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_2)) prop_full_right_shift_32_4 :: W.Word32 -> W.Word8 -> Bool prop_full_right_shift_32_4 = \x y -> let input = (toW4 y, toW32 x) in fastF input == C.full_right_shift_32_4 input where toW32 = toWord32 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_4)) prop_full_right_shift_32_8 :: W.Word32 -> W.Word8 -> Bool prop_full_right_shift_32_8 = \x y -> let input = (toW8 y, toW32 x) in fastF input == C.full_right_shift_32_8 input where toW32 = toWord32 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_8)) prop_full_right_shift_32_16 :: W.Word32 -> W.Word16 -> Bool prop_full_right_shift_32_16 = \x y -> let input = (toW16 y, toW32 x) in fastF input == C.full_right_shift_32_16 input where toW32 = toWord32 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_16)) prop_full_right_shift_64_1 :: W.Word64 -> Bool -> Bool prop_full_right_shift_64_1 = \x y -> let input = (toBit y, toW64 x) in fastF input == C.full_right_shift_64_1 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_1)) prop_full_right_shift_64_2 :: W.Word64 -> W.Word8 -> Bool prop_full_right_shift_64_2 = \x y -> let input = (toW2 y, toW64 x) in fastF input == C.full_right_shift_64_2 input where toW64 = toWord64 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_2)) prop_full_right_shift_64_4 :: W.Word64 -> W.Word8 -> Bool prop_full_right_shift_64_4 = \x y -> let input = (toW4 y, toW64 x) in fastF input == C.full_right_shift_64_4 input where toW64 = toWord64 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_4)) prop_full_right_shift_64_8 :: W.Word64 -> W.Word8 -> Bool prop_full_right_shift_64_8 = \x y -> let input = (toW8 y, toW64 x) in fastF input == C.full_right_shift_64_8 input where toW64 = toWord64 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_8)) prop_full_right_shift_64_16 :: W.Word64 -> W.Word16 -> Bool prop_full_right_shift_64_16 = \x y -> let input = (toW16 y, toW64 x) in fastF input == C.full_right_shift_64_16 input where toW64 = toWord64 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_16)) prop_full_right_shift_64_32 :: W.Word64 -> W.Word32 -> Bool prop_full_right_shift_64_32 = \x y -> let input = (toW32 y, toW64 x) in fastF input == C.full_right_shift_64_32 input where toW64 = toWord64 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_32)) prop_leftmost_8_1 :: W.Word8 -> Bool prop_leftmost_8_1 = \x -> let input = toW8 x in fastF input == C.leftmost_8_1 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost8_1)) prop_leftmost_8_2 :: W.Word8 -> Bool prop_leftmost_8_2 = \x -> let input = toW8 x in fastF input == C.leftmost_8_2 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost8_2)) prop_leftmost_8_4 :: W.Word8 -> Bool prop_leftmost_8_4 = \x -> let input = toW8 x in fastF input == C.leftmost_8_4 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost8_4)) prop_leftmost_16_1 :: W.Word16 -> Bool prop_leftmost_16_1 = \x -> let input = toW16 x in fastF input == C.leftmost_16_1 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_1)) prop_leftmost_16_2 :: W.Word16 -> Bool prop_leftmost_16_2 = \x -> let input = toW16 x in fastF input == C.leftmost_16_2 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_2)) prop_leftmost_16_4 :: W.Word16 -> Bool prop_leftmost_16_4 = \x -> let input = toW16 x in fastF input == C.leftmost_16_4 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_4)) prop_leftmost_16_8 :: W.Word16 -> Bool prop_leftmost_16_8 = \x -> let input = toW16 x in fastF input == C.leftmost_16_8 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_8)) prop_leftmost_32_1 :: W.Word32 -> Bool prop_leftmost_32_1 = \x -> let input = toW32 x in fastF input == C.leftmost_32_1 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_1)) prop_leftmost_32_2 :: W.Word32 -> Bool prop_leftmost_32_2 = \x -> let input = toW32 x in fastF input == C.leftmost_32_2 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_2)) prop_leftmost_32_4 :: W.Word32 -> Bool prop_leftmost_32_4 = \x -> let input = toW32 x in fastF input == C.leftmost_32_4 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_4)) prop_leftmost_32_8 :: W.Word32 -> Bool prop_leftmost_32_8 = \x -> let input = toW32 x in fastF input == C.leftmost_32_8 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_8)) prop_leftmost_32_16 :: W.Word32 -> Bool prop_leftmost_32_16 = \x -> let input = toW32 x in fastF input == C.leftmost_32_16 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_16)) prop_leftmost_64_1 :: W.Word64 -> Bool prop_leftmost_64_1 = \x -> let input = toW64 x in fastF input == C.leftmost_64_1 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_1)) prop_leftmost_64_2 :: W.Word64 -> Bool prop_leftmost_64_2 = \x -> let input = toW64 x in fastF input == C.leftmost_64_2 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_2)) prop_leftmost_64_4 :: W.Word64 -> Bool prop_leftmost_64_4 = \x -> let input = toW64 x in fastF input == C.leftmost_64_4 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_4)) prop_leftmost_64_8 :: W.Word64 -> Bool prop_leftmost_64_8 = \x -> let input = toW64 x in fastF input == C.leftmost_64_8 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_8)) prop_leftmost_64_16 :: W.Word64 -> Bool prop_leftmost_64_16 = \x -> let input = toW64 x in fastF input == C.leftmost_64_16 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_16)) prop_leftmost_64_32 :: W.Word64 -> Bool prop_leftmost_64_32 = \x -> let input = toW64 x in fastF input == C.leftmost_64_32 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_32)) prop_rightmost_8_1 :: W.Word8 -> Bool prop_rightmost_8_1 = \x -> let input = toW8 x in fastF input == C.rightmost_8_1 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost8_1)) prop_rightmost_8_2 :: W.Word8 -> Bool prop_rightmost_8_2 = \x -> let input = toW8 x in fastF input == C.rightmost_8_2 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost8_2)) prop_rightmost_8_4 :: W.Word8 -> Bool prop_rightmost_8_4 = \x -> let input = toW8 x in fastF input == C.rightmost_8_4 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost8_4)) prop_rightmost_16_1 :: W.Word16 -> Bool prop_rightmost_16_1 = \x -> let input = toW16 x in fastF input == C.rightmost_16_1 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_1)) prop_rightmost_16_2 :: W.Word16 -> Bool prop_rightmost_16_2 = \x -> let input = toW16 x in fastF input == C.rightmost_16_2 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_2)) prop_rightmost_16_4 :: W.Word16 -> Bool prop_rightmost_16_4 = \x -> let input = toW16 x in fastF input == C.rightmost_16_4 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_4)) prop_rightmost_16_8 :: W.Word16 -> Bool prop_rightmost_16_8 = \x -> let input = toW16 x in fastF input == C.rightmost_16_8 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_8)) prop_rightmost_32_1 :: W.Word32 -> Bool prop_rightmost_32_1 = \x -> let input = toW32 x in fastF input == C.rightmost_32_1 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_1)) prop_rightmost_32_2 :: W.Word32 -> Bool prop_rightmost_32_2 = \x -> let input = toW32 x in fastF input == C.rightmost_32_2 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_2)) prop_rightmost_32_4 :: W.Word32 -> Bool prop_rightmost_32_4 = \x -> let input = toW32 x in fastF input == C.rightmost_32_4 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_4)) prop_rightmost_32_8 :: W.Word32 -> Bool prop_rightmost_32_8 = \x -> let input = toW32 x in fastF input == C.rightmost_32_8 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_8)) prop_rightmost_32_16 :: W.Word32 -> Bool prop_rightmost_32_16 = \x -> let input = toW32 x in fastF input == C.rightmost_32_16 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_16)) prop_rightmost_64_1 :: W.Word64 -> Bool prop_rightmost_64_1 = \x -> let input = toW64 x in fastF input == C.rightmost_64_1 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_1)) prop_rightmost_64_2 :: W.Word64 -> Bool prop_rightmost_64_2 = \x -> let input = toW64 x in fastF input == C.rightmost_64_2 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_2)) prop_rightmost_64_4 :: W.Word64 -> Bool prop_rightmost_64_4 = \x -> let input = toW64 x in fastF input == C.rightmost_64_4 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_4)) prop_rightmost_64_8 :: W.Word64 -> Bool prop_rightmost_64_8 = \x -> let input = toW64 x in fastF input == C.rightmost_64_8 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_8)) prop_rightmost_64_16 :: W.Word64 -> Bool prop_rightmost_64_16 = \x -> let input = toW64 x in fastF input == C.rightmost_64_16 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_16)) prop_rightmost_64_32 :: W.Word64 -> Bool prop_rightmost_64_32 = \x -> let input = toW64 x in fastF input == C.rightmost_64_32 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_32)) prop_left_pad_low_1_8 :: Bool -> Bool prop_left_pad_low_1_8 = \x -> let input = toBit x in fastF input == C.left_pad_low_1_8 input where fastF = testCoreEval (specification (WordJet LeftPadLow1_8)) prop_left_pad_low_1_16 :: Bool -> Bool prop_left_pad_low_1_16 = \x -> let input = toBit x in fastF input == C.left_pad_low_1_16 input where fastF = testCoreEval (specification (WordJet LeftPadLow1_16)) prop_left_pad_low_8_16 :: W.Word8 -> Bool prop_left_pad_low_8_16 = \x -> let input = toW8 x in fastF input == C.left_pad_low_8_16 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow8_16)) prop_left_pad_low_1_32 :: Bool -> Bool prop_left_pad_low_1_32 = \x -> let input = toBit x in fastF input == C.left_pad_low_1_32 input where fastF = testCoreEval (specification (WordJet LeftPadLow1_32)) prop_left_pad_low_8_32 :: W.Word8 -> Bool prop_left_pad_low_8_32 = \x -> let input = toW8 x in fastF input == C.left_pad_low_8_32 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow8_32)) prop_left_pad_low_16_32 :: W.Word16 -> Bool prop_left_pad_low_16_32 = \x -> let input = toW16 x in fastF input == C.left_pad_low_16_32 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow16_32)) prop_left_pad_low_1_64 :: Bool -> Bool prop_left_pad_low_1_64 = \x -> let input = toBit x in fastF input == C.left_pad_low_1_64 input where fastF = testCoreEval (specification (WordJet LeftPadLow1_64)) prop_left_pad_low_8_64 :: W.Word8 -> Bool prop_left_pad_low_8_64 = \x -> let input = toW8 x in fastF input == C.left_pad_low_8_64 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow8_64)) prop_left_pad_low_16_64 :: W.Word16 -> Bool prop_left_pad_low_16_64 = \x -> let input = toW16 x in fastF input == C.left_pad_low_16_64 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow16_64)) prop_left_pad_low_32_64 :: W.Word32 -> Bool prop_left_pad_low_32_64 = \x -> let input = toW32 x in fastF input == C.left_pad_low_32_64 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow32_64)) prop_left_pad_high_1_8 :: Bool -> Bool prop_left_pad_high_1_8 = \x -> let input = toBit x in fastF input == C.left_pad_high_1_8 input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_8)) prop_left_pad_high_1_16 :: Bool -> Bool prop_left_pad_high_1_16 = \x -> let input = toBit x in fastF input == C.left_pad_high_1_16 input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_16)) prop_left_pad_high_8_16 :: W.Word8 -> Bool prop_left_pad_high_8_16 = \x -> let input = toW8 x in fastF input == C.left_pad_high_8_16 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh8_16)) prop_left_pad_high_1_32 :: Bool -> Bool prop_left_pad_high_1_32 = \x -> let input = toBit x in fastF input == C.left_pad_high_1_32 input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_32)) prop_left_pad_high_8_32 :: W.Word8 -> Bool prop_left_pad_high_8_32 = \x -> let input = toW8 x in fastF input == C.left_pad_high_8_32 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh8_32)) prop_left_pad_high_16_32 :: W.Word16 -> Bool prop_left_pad_high_16_32 = \x -> let input = toW16 x in fastF input == C.left_pad_high_16_32 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh16_32)) prop_left_pad_high_1_64 :: Bool -> Bool prop_left_pad_high_1_64 = \x -> let input = toBit x in fastF input == C.left_pad_high_1_64 input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_64)) prop_left_pad_high_8_64 :: W.Word8 -> Bool prop_left_pad_high_8_64 = \x -> let input = toW8 x in fastF input == C.left_pad_high_8_64 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh8_64)) prop_left_pad_high_16_64 :: W.Word16 -> Bool prop_left_pad_high_16_64 = \x -> let input = toW16 x in fastF input == C.left_pad_high_16_64 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh16_64)) prop_left_pad_high_32_64 :: W.Word32 -> Bool prop_left_pad_high_32_64 = \x -> let input = toW32 x in fastF input == C.left_pad_high_32_64 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh32_64)) prop_left_extend_1_8 :: Bool -> Bool prop_left_extend_1_8 = \x -> let input = toBit x in fastF input == C.left_extend_1_8 input where fastF = testCoreEval (specification (WordJet LeftExtend1_8)) prop_left_extend_1_16 :: Bool -> Bool prop_left_extend_1_16 = \x -> let input = toBit x in fastF input == C.left_extend_1_16 input where fastF = testCoreEval (specification (WordJet LeftExtend1_16)) prop_left_extend_8_16 :: W.Word8 -> Bool prop_left_extend_8_16 = \x -> let input = toW8 x in fastF input == C.left_extend_8_16 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend8_16)) prop_left_extend_1_32 :: Bool -> Bool prop_left_extend_1_32 = \x -> let input = toBit x in fastF input == C.left_extend_1_32 input where fastF = testCoreEval (specification (WordJet LeftExtend1_32)) prop_left_extend_8_32 :: W.Word8 -> Bool prop_left_extend_8_32 = \x -> let input = toW8 x in fastF input == C.left_extend_8_32 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend8_32)) prop_left_extend_16_32 :: W.Word16 -> Bool prop_left_extend_16_32 = \x -> let input = toW16 x in fastF input == C.left_extend_16_32 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend16_32)) prop_left_extend_1_64 :: Bool -> Bool prop_left_extend_1_64 = \x -> let input = toBit x in fastF input == C.left_extend_1_64 input where fastF = testCoreEval (specification (WordJet LeftExtend1_64)) prop_left_extend_8_64 :: W.Word8 -> Bool prop_left_extend_8_64 = \x -> let input = toW8 x in fastF input == C.left_extend_8_64 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend8_64)) prop_left_extend_16_64 :: W.Word16 -> Bool prop_left_extend_16_64 = \x -> let input = toW16 x in fastF input == C.left_extend_16_64 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend16_64)) prop_left_extend_32_64 :: W.Word32 -> Bool prop_left_extend_32_64 = \x -> let input = toW32 x in fastF input == C.left_extend_32_64 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend32_64)) prop_right_pad_low_1_8 :: Bool -> Bool prop_right_pad_low_1_8 = \x -> let input = toBit x in fastF input == C.right_pad_low_1_8 input where fastF = testCoreEval (specification (WordJet RightPadLow1_8)) prop_right_pad_low_1_16 :: Bool -> Bool prop_right_pad_low_1_16 = \x -> let input = toBit x in fastF input == C.right_pad_low_1_16 input where fastF = testCoreEval (specification (WordJet RightPadLow1_16)) prop_right_pad_low_8_16 :: W.Word8 -> Bool prop_right_pad_low_8_16 = \x -> let input = toW8 x in fastF input == C.right_pad_low_8_16 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow8_16)) prop_right_pad_low_1_32 :: Bool -> Bool prop_right_pad_low_1_32 = \x -> let input = toBit x in fastF input == C.right_pad_low_1_32 input where fastF = testCoreEval (specification (WordJet RightPadLow1_32)) prop_right_pad_low_8_32 :: W.Word8 -> Bool prop_right_pad_low_8_32 = \x -> let input = toW8 x in fastF input == C.right_pad_low_8_32 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow8_32)) prop_right_pad_low_16_32 :: W.Word16 -> Bool prop_right_pad_low_16_32 = \x -> let input = toW16 x in fastF input == C.right_pad_low_16_32 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow16_32)) prop_right_pad_low_1_64 :: Bool -> Bool prop_right_pad_low_1_64 = \x -> let input = toBit x in fastF input == C.right_pad_low_1_64 input where fastF = testCoreEval (specification (WordJet RightPadLow1_64)) prop_right_pad_low_8_64 :: W.Word8 -> Bool prop_right_pad_low_8_64 = \x -> let input = toW8 x in fastF input == C.right_pad_low_8_64 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow8_64)) prop_right_pad_low_16_64 :: W.Word16 -> Bool prop_right_pad_low_16_64 = \x -> let input = toW16 x in fastF input == C.right_pad_low_16_64 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow16_64)) prop_right_pad_low_32_64 :: W.Word32 -> Bool prop_right_pad_low_32_64 = \x -> let input = toW32 x in fastF input == C.right_pad_low_32_64 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow32_64)) prop_right_pad_high_1_8 :: Bool -> Bool prop_right_pad_high_1_8 = \x -> let input = toBit x in fastF input == C.right_pad_high_1_8 input where fastF = testCoreEval (specification (WordJet RightPadHigh1_8)) prop_right_pad_high_1_16 :: Bool -> Bool prop_right_pad_high_1_16 = \x -> let input = toBit x in fastF input == C.right_pad_high_1_16 input where fastF = testCoreEval (specification (WordJet RightPadHigh1_16)) prop_right_pad_high_8_16 :: W.Word8 -> Bool prop_right_pad_high_8_16 = \x -> let input = toW8 x in fastF input == C.right_pad_high_8_16 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh8_16)) prop_right_pad_high_1_32 :: Bool -> Bool prop_right_pad_high_1_32 = \x -> let input = toBit x in fastF input == C.right_pad_high_1_32 input where fastF = testCoreEval (specification (WordJet RightPadHigh1_32)) prop_right_pad_high_8_32 :: W.Word8 -> Bool prop_right_pad_high_8_32 = \x -> let input = toW8 x in fastF input == C.right_pad_high_8_32 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh8_32)) prop_right_pad_high_16_32 :: W.Word16 -> Bool prop_right_pad_high_16_32 = \x -> let input = toW16 x in fastF input == C.right_pad_high_16_32 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh16_32)) prop_right_pad_high_1_64 :: Bool -> Bool prop_right_pad_high_1_64 = \x -> let input = toBit x in fastF input == C.right_pad_high_1_64 input where fastF = testCoreEval (specification (WordJet RightPadHigh1_64)) prop_right_pad_high_8_64 :: W.Word8 -> Bool prop_right_pad_high_8_64 = \x -> let input = toW8 x in fastF input == C.right_pad_high_8_64 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh8_64)) prop_right_pad_high_16_64 :: W.Word16 -> Bool prop_right_pad_high_16_64 = \x -> let input = toW16 x in fastF input == C.right_pad_high_16_64 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh16_64)) prop_right_pad_high_32_64 :: W.Word32 -> Bool prop_right_pad_high_32_64 = \x -> let input = toW32 x in fastF input == C.right_pad_high_32_64 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh32_64)) prop_right_extend_8_16 :: W.Word8 -> Bool prop_right_extend_8_16 = \x -> let input = toW8 x in fastF input == C.right_extend_8_16 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend8_16)) prop_right_extend_8_32 :: W.Word8 -> Bool prop_right_extend_8_32 = \x -> let input = toW8 x in fastF input == C.right_extend_8_32 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend8_32)) prop_right_extend_16_32 :: W.Word16 -> Bool prop_right_extend_16_32 = \x -> let input = toW16 x in fastF input == C.right_extend_16_32 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend16_32)) prop_right_extend_8_64 :: W.Word8 -> Bool prop_right_extend_8_64 = \x -> let input = toW8 x in fastF input == C.right_extend_8_64 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend8_64)) prop_right_extend_16_64 :: W.Word16 -> Bool prop_right_extend_16_64 = \x -> let input = toW16 x in fastF input == C.right_extend_16_64 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend16_64)) prop_right_extend_32_64 :: W.Word32 -> Bool prop_right_extend_32_64 = \x -> let input = toW32 x in fastF input == C.right_extend_32_64 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend32_64)) prop_left_shift_with_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_left_shift_with_8 = \w x y -> let input = (toBit w, (toW4 x, toW8 y)) in fastF input == C.left_shift_with_8 input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith8)) prop_left_shift_with_16 :: Bool -> W.Word8 -> W.Word16 -> Bool prop_left_shift_with_16 = \w x y -> let input = (toBit w, (toW4 x, toW16 y)) in fastF input == C.left_shift_with_16 input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith16)) prop_left_shift_with_32 :: Bool -> W.Word8 -> W.Word32 -> Bool prop_left_shift_with_32 = \w x y -> let input = (toBit w, (toW8 x, toW32 y)) in fastF input == C.left_shift_with_32 input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith32)) prop_left_shift_with_64 :: Bool -> W.Word8 -> W.Word64 -> Bool prop_left_shift_with_64 = \w x y -> let input = (toBit w, (toW8 x, toW64 y)) in fastF input == C.left_shift_with_64 input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith64)) prop_left_shift_8 :: W.Word8 -> W.Word8 -> Bool prop_left_shift_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == C.left_shift_8 input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift8)) prop_left_shift_16 :: W.Word8 -> W.Word16 -> Bool prop_left_shift_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == C.left_shift_16 input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift16)) prop_left_shift_32 :: W.Word8 -> W.Word32 -> Bool prop_left_shift_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == C.left_shift_32 input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift32)) prop_left_shift_64 :: W.Word8 -> W.Word64 -> Bool prop_left_shift_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == C.left_shift_64 input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift64)) prop_right_shift_with_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_right_shift_with_8 = \w x y -> let input = (toBit w, (toW4 x, toW8 y)) in fastF input == C.right_shift_with_8 input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith8)) prop_right_shift_with_16 :: Bool -> W.Word8 -> W.Word16 -> Bool prop_right_shift_with_16 = \w x y -> let input = (toBit w, (toW4 x, toW16 y)) in fastF input == C.right_shift_with_16 input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith16)) prop_right_shift_with_32 :: Bool -> W.Word8 -> W.Word32 -> Bool prop_right_shift_with_32 = \w x y -> let input = (toBit w, (toW8 x, toW32 y)) in fastF input == C.right_shift_with_32 input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith32)) prop_right_shift_with_64 :: Bool -> W.Word8 -> W.Word64 -> Bool prop_right_shift_with_64 = \w x y -> let input = (toBit w, (toW8 x, toW64 y)) in fastF input == C.right_shift_with_64 input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith64)) prop_right_shift_8 :: W.Word8 -> W.Word8 -> Bool prop_right_shift_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == C.right_shift_8 input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift8)) prop_right_shift_16 :: W.Word8 -> W.Word16 -> Bool prop_right_shift_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == C.right_shift_16 input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift16)) prop_right_shift_32 :: W.Word8 -> W.Word32 -> Bool prop_right_shift_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == C.right_shift_32 input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift32)) prop_right_shift_64 :: W.Word8 -> W.Word64 -> Bool prop_right_shift_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == C.right_shift_64 input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift64)) prop_left_rotate_8 :: W.Word8 -> W.Word8 -> Bool prop_left_rotate_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == C.left_rotate_8 input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate8)) prop_left_rotate_16 :: W.Word8 -> W.Word16 -> Bool prop_left_rotate_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == C.left_rotate_16 input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate16)) prop_left_rotate_32 :: W.Word8 -> W.Word32 -> Bool prop_left_rotate_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == C.left_rotate_32 input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate32)) prop_left_rotate_64 :: W.Word8 -> W.Word64 -> Bool prop_left_rotate_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == C.left_rotate_64 input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate64)) prop_right_rotate_8 :: W.Word8 -> W.Word8 -> Bool prop_right_rotate_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == C.right_rotate_8 input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate8)) prop_right_rotate_16 :: W.Word8 -> W.Word16 -> Bool prop_right_rotate_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == C.right_rotate_16 input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate16)) prop_right_rotate_32 :: W.Word8 -> W.Word32 -> Bool prop_right_rotate_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == C.right_rotate_32 input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate32)) prop_right_rotate_64 :: W.Word8 -> W.Word64 -> Bool prop_right_rotate_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == C.right_rotate_64 input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate64)) assert_one_8 :: Assertion assert_one_8 = fastF () @=? C.one_8 () where fastF = testCoreEval (specification (ArithJet One8)) assert_one_16 :: Assertion assert_one_16 = fastF () @=? C.one_16 () where fastF = testCoreEval (specification (ArithJet One16)) assert_one_32 :: Assertion assert_one_32 = fastF () @=? C.one_32 () where fastF = testCoreEval (specification (ArithJet One32)) assert_one_64 :: Assertion assert_one_64 = fastF () @=? C.one_64 () where fastF = testCoreEval (specification (ArithJet One64)) prop_add_8 :: W.Word8 -> W.Word8 -> Bool prop_add_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.add_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Add8)) prop_add_16 :: W.Word16 -> W.Word16 -> Bool prop_add_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.add_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Add16)) prop_add_32 :: W.Word32 -> W.Word32 -> Bool prop_add_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.add_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Add32)) prop_add_64 :: W.Word64 -> W.Word64 -> Bool prop_add_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.add_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Add64)) prop_full_add_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_full_add_8 = \c x y -> let input = (toBit c, (toW8 x, toW8 y)) in fastF input == C.full_add_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd8)) prop_full_add_16 :: Bool -> W.Word16 -> W.Word16 -> Bool prop_full_add_16 = \c x y -> let input = (toBit c, (toW16 x, toW16 y)) in fastF input == C.full_add_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd16)) prop_full_add_32 :: Bool -> W.Word32 -> W.Word32 -> Bool prop_full_add_32 = \c x y -> let input = (toBit c, (toW32 x, toW32 y)) in fastF input == C.full_add_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd32)) prop_full_add_64 :: Bool -> W.Word64 -> W.Word64 -> Bool prop_full_add_64 = \c x y -> let input = (toBit c, (toW64 x, toW64 y)) in fastF input == C.full_add_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd64)) prop_full_increment_8 :: Bool -> W.Word8 -> Bool prop_full_increment_8 = \b x -> let input = (toBit b, toW8 x) in fastF input == C.full_increment_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement8)) prop_full_increment_16 :: Bool -> W.Word16 -> Bool prop_full_increment_16 = \b x -> let input = (toBit b, toW16 x) in fastF input == C.full_increment_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement16)) prop_full_increment_32 :: Bool -> W.Word32 -> Bool prop_full_increment_32 = \b x -> let input = (toBit b, toW32 x) in fastF input == C.full_increment_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement32)) prop_full_increment_64 :: Bool -> W.Word64 -> Bool prop_full_increment_64 = \b x -> let input = (toBit b, toW64 x) in fastF input == C.full_increment_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement64)) assert_full_increment_max_8 :: Assertion assert_full_increment_max_8 = fastF input @=? C.full_increment_8 input where input = (toBit True, toWord8 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement8)) assert_full_increment_max_16 :: Assertion assert_full_increment_max_16 = fastF input @=? C.full_increment_16 input where input = (toBit True, toWord16 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement16)) assert_full_increment_max_32 :: Assertion assert_full_increment_max_32 = fastF input @=? C.full_increment_32 input where input = (toBit True, toWord32 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement32)) assert_full_increment_max_64 :: Assertion assert_full_increment_max_64 = fastF input @=? C.full_increment_64 input where input = (toBit True, toWord64 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement64)) prop_increment_8 :: W.Word8 -> Bool prop_increment_8 = \x -> let input = toW8 x in fastF input == C.increment_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment8)) prop_increment_16 :: W.Word16 -> Bool prop_increment_16 = \x -> let input = toW16 x in fastF input == C.increment_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment16)) prop_increment_32 :: W.Word32 -> Bool prop_increment_32 = \x -> let input = toW32 x in fastF input == C.increment_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment32)) prop_increment_64 :: W.Word64 -> Bool prop_increment_64 = \x -> let input = toW64 x in fastF input == C.increment_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment64)) assert_increment_max_8 :: Assertion assert_increment_max_8 = fastF input @=? C.increment_8 input where input = toWord8 (-1) fastF = testCoreEval (specification (ArithJet Increment8)) assert_increment_max_16 :: Assertion assert_increment_max_16 = fastF input @=? C.increment_16 input where input = toWord16 (-1) fastF = testCoreEval (specification (ArithJet Increment16)) assert_increment_max_32 :: Assertion assert_increment_max_32 = fastF input @=? C.increment_32 input where input = toWord32 (-1) fastF = testCoreEval (specification (ArithJet Increment32)) assert_increment_max_64 :: Assertion assert_increment_max_64 = fastF input @=? C.increment_64 input where input = toWord64 (-1) fastF = testCoreEval (specification (ArithJet Increment64)) prop_subtract_8 :: W.Word8 -> W.Word8 -> Bool prop_subtract_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.subtract_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract8)) prop_subtract_16 :: W.Word16 -> W.Word16 -> Bool prop_subtract_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.subtract_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract16)) prop_subtract_32 :: W.Word32 -> W.Word32 -> Bool prop_subtract_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.subtract_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract32)) prop_subtract_64 :: W.Word64 -> W.Word64 -> Bool prop_subtract_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.subtract_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract64)) prop_full_subtract_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_full_subtract_8 = \c x y -> let input = (toBit c, (toW8 x, toW8 y)) in fastF input == C.full_subtract_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract8)) prop_full_subtract_16 :: Bool -> W.Word16 -> W.Word16 -> Bool prop_full_subtract_16 = \c x y -> let input = (toBit c, (toW16 x, toW16 y)) in fastF input == C.full_subtract_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract16)) prop_full_subtract_32 :: Bool -> W.Word32 -> W.Word32 -> Bool prop_full_subtract_32 = \c x y -> let input = (toBit c, (toW32 x, toW32 y)) in fastF input == C.full_subtract_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract32)) prop_full_subtract_64 :: Bool -> W.Word64 -> W.Word64 -> Bool prop_full_subtract_64 = \c x y -> let input = (toBit c, (toW64 x, toW64 y)) in fastF input == C.full_subtract_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract64)) prop_full_decrement_8 :: Bool -> W.Word8 -> Bool prop_full_decrement_8 = \b x -> let input = (toBit b, toW8 x) in fastF input == C.full_decrement_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement8)) prop_full_decrement_16 :: Bool -> W.Word16 -> Bool prop_full_decrement_16 = \b x -> let input = (toBit b, toW16 x) in fastF input == C.full_decrement_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement16)) prop_full_decrement_32 :: Bool -> W.Word32 -> Bool prop_full_decrement_32 = \b x -> let input = (toBit b, toW32 x) in fastF input == C.full_decrement_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement32)) prop_full_decrement_64 :: Bool -> W.Word64 -> Bool prop_full_decrement_64 = \b x -> let input = (toBit b, toW64 x) in fastF input == C.full_decrement_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement64)) assert_full_decrement_zero_8 :: Assertion assert_full_decrement_zero_8 = fastF input @=? C.full_decrement_8 input where input = (toBit True, toWord8 0) fastF = testCoreEval (specification (ArithJet FullDecrement8)) assert_full_decrement_zero_16 :: Assertion assert_full_decrement_zero_16 = fastF input @=? C.full_decrement_16 input where input = (toBit True, toWord16 0) fastF = testCoreEval (specification (ArithJet FullDecrement16)) assert_full_decrement_zero_32 :: Assertion assert_full_decrement_zero_32 = fastF input @=? C.full_decrement_32 input where input = (toBit True, toWord32 0) fastF = testCoreEval (specification (ArithJet FullDecrement32)) assert_full_decrement_zero_64 :: Assertion assert_full_decrement_zero_64 = fastF input @=? C.full_decrement_64 input where input = (toBit True, toWord64 0) fastF = testCoreEval (specification (ArithJet FullDecrement64)) prop_decrement_8 :: W.Word8 -> Bool prop_decrement_8 = \x -> let input = toW8 x in fastF input == C.decrement_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement8)) prop_decrement_16 :: W.Word16 -> Bool prop_decrement_16 = \x -> let input = toW16 x in fastF input == C.decrement_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement16)) prop_decrement_32 :: W.Word32 -> Bool prop_decrement_32 = \x -> let input = toW32 x in fastF input == C.decrement_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement32)) prop_decrement_64 :: W.Word64 -> Bool prop_decrement_64 = \x -> let input = toW64 x in fastF input == C.decrement_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement64)) assert_decrement_zero_8 :: Assertion assert_decrement_zero_8 = fastF input @=? C.decrement_8 input where input = toWord8 0 fastF = testCoreEval (specification (ArithJet Decrement8)) assert_decrement_zero_16 :: Assertion assert_decrement_zero_16 = fastF input @=? C.decrement_16 input where input = toWord16 0 fastF = testCoreEval (specification (ArithJet Decrement16)) assert_decrement_zero_32 :: Assertion assert_decrement_zero_32 = fastF input @=? C.decrement_32 input where input = toWord32 0 fastF = testCoreEval (specification (ArithJet Decrement32)) assert_decrement_zero_64 :: Assertion assert_decrement_zero_64 = fastF input @=? C.decrement_64 input where input = toWord64 0 fastF = testCoreEval (specification (ArithJet Decrement64)) prop_negate_8 :: W.Word8 -> Bool prop_negate_8 = \x -> let input = toW8 x in fastF input == C.negate_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate8)) prop_negate_16 :: W.Word16 -> Bool prop_negate_16 = \x -> let input = toW16 x in fastF input == C.negate_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate16)) prop_negate_32 :: W.Word32 -> Bool prop_negate_32 = \x -> let input = toW32 x in fastF input == C.negate_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate32)) prop_negate_64 :: W.Word64 -> Bool prop_negate_64 = \x -> let input = toW64 x in fastF input == C.negate_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate64)) prop_multiply_8 :: W.Word8 -> W.Word8 -> Bool prop_multiply_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.multiply_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply8)) prop_multiply_16 :: W.Word16 -> W.Word16 -> Bool prop_multiply_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.multiply_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply16)) prop_multiply_32 :: W.Word32 -> W.Word32 -> Bool prop_multiply_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.multiply_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply32)) prop_multiply_64 :: W.Word64 -> W.Word64 -> Bool prop_multiply_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.multiply_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply64)) prop_full_multiply_8 :: W.Word8 -> W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_full_multiply_8 = \x y z w -> let input = ((toW8 x, toW8 y), (toW8 z, toW8 w)) in fastF input == C.full_multiply_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply8)) prop_full_multiply_16 :: W.Word16 -> W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_full_multiply_16 = \x y z w -> let input = ((toW16 x, toW16 y), (toW16 z, toW16 w)) in fastF input == C.full_multiply_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply16)) prop_full_multiply_32 :: W.Word32 -> W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_full_multiply_32 = \x y z w -> let input = ((toW32 x, toW32 y), (toW32 z, toW32 w)) in fastF input == C.full_multiply_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply32)) prop_full_multiply_64 :: W.Word64 -> W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_full_multiply_64 = \x y z w -> let input = ((toW64 x, toW64 y), (toW64 z, toW64 w)) in fastF input == C.full_multiply_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply64)) prop_is_zero_8 :: W.Word8 -> Bool prop_is_zero_8 = \x -> let input = toW8 x in fastF input == C.is_zero_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero8)) prop_is_zero_16 :: W.Word16 -> Bool prop_is_zero_16 = \x -> let input = toW16 x in fastF input == C.is_zero_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero16)) prop_is_zero_32 :: W.Word32 -> Bool prop_is_zero_32 = \x -> let input = toW32 x in fastF input == C.is_zero_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero32)) prop_is_zero_64 :: W.Word64 -> Bool prop_is_zero_64 = \x -> let input = toW64 x in fastF input == C.is_zero_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero64)) assert_zero_is_zero_8 :: Assertion assert_zero_is_zero_8 = fastF input @=? C.is_zero_8 input where input = toWord8 0 fastF = testCoreEval (specification (ArithJet IsZero8)) assert_zero_is_zero_16 :: Assertion assert_zero_is_zero_16 = fastF input @=? C.is_zero_16 input where input = toWord16 0 fastF = testCoreEval (specification (ArithJet IsZero16)) assert_zero_is_zero_32 :: Assertion assert_zero_is_zero_32 = fastF input @=? C.is_zero_32 input where input = toWord32 0 fastF = testCoreEval (specification (ArithJet IsZero32)) assert_zero_is_zero_64 :: Assertion assert_zero_is_zero_64 = fastF input @=? C.is_zero_64 input where input = toWord64 0 fastF = testCoreEval (specification (ArithJet IsZero64)) prop_is_one_8 :: W.Word8 -> Bool prop_is_one_8 = \x -> let input = toW8 x in fastF input == C.is_one_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne8)) prop_is_one_16 :: W.Word16 -> Bool prop_is_one_16 = \x -> let input = toW16 x in fastF input == C.is_one_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne16)) prop_is_one_32 :: W.Word32 -> Bool prop_is_one_32 = \x -> let input = toW32 x in fastF input == C.is_one_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne32)) prop_is_one_64 :: W.Word64 -> Bool prop_is_one_64 = \x -> let input = toW64 x in fastF input == C.is_one_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne64)) assert_one_is_one_8 :: Assertion assert_one_is_one_8 = fastF input @=? C.is_one_8 input where input = toWord8 1 fastF = testCoreEval (specification (ArithJet IsOne8)) assert_one_is_one_16 :: Assertion assert_one_is_one_16 = fastF input @=? C.is_one_16 input where input = toWord16 1 fastF = testCoreEval (specification (ArithJet IsOne16)) assert_one_is_one_32 :: Assertion assert_one_is_one_32 = fastF input @=? C.is_one_32 input where input = toWord32 1 fastF = testCoreEval (specification (ArithJet IsOne32)) assert_one_is_one_64 :: Assertion assert_one_is_one_64 = fastF input @=? C.is_one_64 input where input = toWord64 1 fastF = testCoreEval (specification (ArithJet IsOne64)) prop_le_8 :: W.Word8 -> W.Word8 -> Bool prop_le_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.le_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Le8)) prop_le_16 :: W.Word16 -> W.Word16 -> Bool prop_le_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.le_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Le16)) prop_le_32 :: W.Word32 -> W.Word32 -> Bool prop_le_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.le_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Le32)) prop_le_64 :: W.Word64 -> W.Word64 -> Bool prop_le_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.le_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Le64)) prop_le_diag_8 :: W.Word8 -> Bool prop_le_diag_8 = \x -> let input = (toW8 x, toW8 x) in fastF input == C.le_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Le8)) prop_le_diag_16 :: W.Word16 -> Bool prop_le_diag_16 = \x -> let input = (toW16 x, toW16 x) in fastF input == C.le_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Le16)) prop_le_diag_32 :: W.Word32 -> Bool prop_le_diag_32 = \x -> let input = (toW32 x, toW32 x) in fastF input == C.le_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Le32)) prop_le_diag_64 :: W.Word64 -> Bool prop_le_diag_64 = \x -> let input = (toW64 x, toW64 x) in fastF input == C.le_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Le64)) prop_lt_8 :: W.Word8 -> W.Word8 -> Bool prop_lt_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.lt_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt8)) prop_lt_16 :: W.Word16 -> W.Word16 -> Bool prop_lt_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.lt_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt16)) prop_lt_32 :: W.Word32 -> W.Word32 -> Bool prop_lt_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.lt_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt32)) prop_lt_64 :: W.Word64 -> W.Word64 -> Bool prop_lt_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.lt_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt64)) prop_lt_diag_8 :: W.Word8 -> Bool prop_lt_diag_8 = \x -> let input = (toW8 x, toW8 x) in fastF input == C.lt_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt8)) prop_lt_diag_16 :: W.Word16 -> Bool prop_lt_diag_16 = \x -> let input = (toW16 x, toW16 x) in fastF input == C.lt_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt16)) prop_lt_diag_32 :: W.Word32 -> Bool prop_lt_diag_32 = \x -> let input = (toW32 x, toW32 x) in fastF input == C.lt_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt32)) prop_lt_diag_64 :: W.Word64 -> Bool prop_lt_diag_64 = \x -> let input = (toW64 x, toW64 x) in fastF input == C.lt_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt64)) prop_min_8 :: W.Word8 -> W.Word8 -> Bool prop_min_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.min_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Min8)) prop_min_16 :: W.Word16 -> W.Word16 -> Bool prop_min_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.min_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Min16)) prop_min_32 :: W.Word32 -> W.Word32 -> Bool prop_min_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.min_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Min32)) prop_min_64 :: W.Word64 -> W.Word64 -> Bool prop_min_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.min_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Min64)) prop_max_8 :: W.Word8 -> W.Word8 -> Bool prop_max_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.max_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Max8)) prop_max_16 :: W.Word16 -> W.Word16 -> Bool prop_max_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.max_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Max16)) prop_max_32 :: W.Word32 -> W.Word32 -> Bool prop_max_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.max_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Max32)) prop_max_64 :: W.Word64 -> W.Word64 -> Bool prop_max_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.max_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Max64)) prop_median_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_median_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == C.median_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Median8)) prop_median_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_median_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == C.median_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Median16)) prop_median_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_median_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == C.median_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Median32)) prop_median_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_median_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == C.median_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Median64)) prop_div_mod_8 :: W.Word8 -> W.Word8 -> Bool prop_div_mod_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.div_mod_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod8)) prop_div_mod_16 :: W.Word16 -> W.Word16 -> Bool prop_div_mod_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.div_mod_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod16)) prop_div_mod_32 :: W.Word32 -> W.Word32 -> Bool prop_div_mod_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.div_mod_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod32)) prop_div_mod_64 :: W.Word64 -> W.Word64 -> Bool prop_div_mod_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.div_mod_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod64)) prop_divide_8 :: W.Word8 -> W.Word8 -> Bool prop_divide_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.divide_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide8)) prop_divide_16 :: W.Word16 -> W.Word16 -> Bool prop_divide_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.divide_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide16)) prop_divide_32 :: W.Word32 -> W.Word32 -> Bool prop_divide_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.divide_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide32)) prop_divide_64 :: W.Word64 -> W.Word64 -> Bool prop_divide_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.divide_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide64)) prop_modulo_8 :: W.Word8 -> W.Word8 -> Bool prop_modulo_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.modulo_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo8)) prop_modulo_16 :: W.Word16 -> W.Word16 -> Bool prop_modulo_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.modulo_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo16)) prop_modulo_32 :: W.Word32 -> W.Word32 -> Bool prop_modulo_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.modulo_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo32)) prop_modulo_64 :: W.Word64 -> W.Word64 -> Bool prop_modulo_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.modulo_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo64)) prop_divides_8 :: W.Word8 -> W.Word8 -> Bool prop_divides_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == C.divides_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides8)) prop_divides_16 :: W.Word16 -> W.Word16 -> Bool prop_divides_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == C.divides_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides16)) prop_divides_32 :: W.Word32 -> W.Word32 -> Bool prop_divides_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == C.divides_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides32)) prop_divides_64 :: W.Word64 -> W.Word64 -> Bool prop_divides_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == C.divides_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides64)) prop_div_mod_zero_8 :: W.Word8 -> Bool prop_div_mod_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == C.div_mod_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod8)) prop_div_mod_zero_16 :: W.Word16 -> Bool prop_div_mod_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == C.div_mod_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod16)) prop_div_mod_zero_32 :: W.Word32 -> Bool prop_div_mod_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == C.div_mod_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod32)) prop_div_mod_zero_64 :: W.Word64 -> Bool prop_div_mod_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == C.div_mod_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod64)) prop_divide_zero_8 :: W.Word8 -> Bool prop_divide_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == C.divide_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide8)) prop_divide_zero_16 :: W.Word16 -> Bool prop_divide_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == C.divide_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide16)) prop_divide_zero_32 :: W.Word32 -> Bool prop_divide_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == C.divide_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide32)) prop_divide_zero_64 :: W.Word64 -> Bool prop_divide_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == C.divide_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide64)) prop_modulo_zero_8 :: W.Word8 -> Bool prop_modulo_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == C.modulo_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo8)) prop_modulo_zero_16 :: W.Word16 -> Bool prop_modulo_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == C.modulo_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo16)) prop_modulo_zero_32 :: W.Word32 -> Bool prop_modulo_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == C.modulo_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo32)) prop_modulo_zero_64 :: W.Word64 -> Bool prop_modulo_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == C.modulo_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo64)) prop_divides_zero_8 :: W.Word8 -> Bool prop_divides_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == C.divides_8 input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides8)) prop_divides_zero_16 :: W.Word16 -> Bool prop_divides_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == C.divides_16 input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides16)) prop_divides_zero_32 :: W.Word32 -> Bool prop_divides_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == C.divides_32 input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides32)) prop_divides_zero_64 :: W.Word64 -> Bool prop_divides_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == C.divides_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides64)) prop_div_mod_128_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Property prop_div_mod_128_64 = \xh0 xl0 y0 -> let y = y0 .|. 2^63 xh = y - 1 - xh0 `mod` y xl = - xl0 input = ((toW64 xh, toW64 xl), toW64 y) x = toInteger xh * 2^64 + toInteger xl qh = (x `div` 2^32) `div` toInteger y approxQh = toInteger xh `div` (toInteger y `div` 2^32) annotate | 2^32 <= approxQh = label "high approxQh" | otherwise = label ("deltaQh: " ++ show (approxQh -qh)) in annotate $ fastF input == C.div_mod_128_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod128_64)) prop_div_mod_128_64_low_y :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_div_mod_128_64_low_y = \xh0 xl0 y0 -> let y = y0 `mod` 2^63 xh = y - xh0 `mod` (y + 1) xl = - xl0 input = ((toW64 xh, toW64 xl), toW64 y) in fastF input == C.div_mod_128_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod128_64)) prop_div_mod_128_64_high_x :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_div_mod_128_64_high_x = \xh0 xl0 y0 -> let y = y0 xh = - xh0 xl = - xl0 input = ((toW64 xh, toW64 xl), toW64 y) in fastF input == C.div_mod_128_64 input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod128_64)) assert_sha_256_iv :: Assertion assert_sha_256_iv = fastF () @=? C.sha_256_iv () where fastF = testCoreEval (specification (HashJet Sha256Iv)) prop_sha_256_block :: HashElement -> HashElement -> HashElement -> Bool prop_sha_256_block = \h b1 b2 -> fastF (heAsTy h, (heAsTy b1, heAsTy b2)) == C.sha_256_block (heAsTy h, (heAsTy b1, heAsTy b2)) where fastF = testCoreEval (specification (HashJet Sha256Block)) assert_sha_256_ctx_8_init :: Assertion assert_sha_256_ctx_8_init = fastF () @=? C.sha_256_ctx_8_init () where fastF = testCoreEval (specification (HashJet Sha256Ctx8Init)) prop_sha_256_ctx_8_add_1 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_1 = \ctx -> forAll arbitraryW8 $ \w8 -> let input = (ctxAsTy ctx, toW8 w8) in fastF input == C.sha_256_ctx_8_add_1 input where arbitraryW8 :: Gen W.Word8 arbitraryW8 = arbitraryBoundedIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add1)) prop_sha_256_ctx_8_add_2 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_2 = \ctx -> forAll arbitraryW16 $ \w16 -> let input = (ctxAsTy ctx, toW16 w16) in fastF input == C.sha_256_ctx_8_add_2 input where arbitraryW16 :: Gen W.Word16 arbitraryW16 = arbitraryBoundedIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add2)) prop_sha_256_ctx_8_add_4 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_4 = \ctx -> forAll arbitraryW32 $ \w32 -> let input = (ctxAsTy ctx, toW32 w32) in fastF input == C.sha_256_ctx_8_add_4 input where arbitraryW32 :: Gen W.Word32 arbitraryW32 = arbitraryBoundedIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add4)) prop_sha_256_ctx_8_add_8 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_8 = \ctx -> forAll arbitraryW64 $ \w64 -> let input = (ctxAsTy ctx, toW64 w64) in fastF input == C.sha_256_ctx_8_add_8 input where arbitraryW64 :: Gen W.Word64 arbitraryW64 = arbitraryBoundedIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add8)) prop_sha_256_ctx_8_add_16 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_16 = \ctx -> forAll arbitraryW64 $ \w64a -> forAll arbitraryW64 $ \w64b -> let input = (ctxAsTy ctx, (toW64 w64a, toW64 w64b)) in fastF input == C.sha_256_ctx_8_add_16 input where arbitraryW64 :: Gen W.Word64 arbitraryW64 = arbitraryBoundedIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add16)) prop_sha_256_ctx_8_add_32 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_32 = \ctx -> forAll arbitraryW256 $ \w256 -> let input = (ctxAsTy ctx, toW256 w256) in fastF input == C.sha_256_ctx_8_add_32 input where arbitraryW256 :: Gen W.Word256 arbitraryW256 = arbitraryBoundedIntegral toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add32)) prop_sha_256_ctx_8_add_64 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_64 = \ctx -> forAll arbitraryW256 $ \w256a -> forAll arbitraryW256 $ \w256b -> let input = (ctxAsTy ctx, (toW256 w256a, toW256 w256b)) in fastF input == C.sha_256_ctx_8_add_64 input where arbitraryW256 :: Gen W.Word256 arbitraryW256 = arbitraryBoundedIntegral toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add64)) prop_sha_256_ctx_8_add_128 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_128 = \ctx -> forAll arbitraryW256 $ \w256a -> forAll arbitraryW256 $ \w256b -> forAll arbitraryW256 $ \w256c -> forAll arbitraryW256 $ \w256d -> let input = (ctxAsTy ctx, ((toW256 w256a, toW256 w256b), (toW256 w256c, toW256 w256d))) in fastF input == C.sha_256_ctx_8_add_128 input where arbitraryW256 :: Gen W.Word256 arbitraryW256 = arbitraryBoundedIntegral toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add128)) prop_sha_256_ctx_8_add_256 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_256 = \ctx -> forAll arbitraryW256 $ \w256a -> forAll arbitraryW256 $ \w256b -> forAll arbitraryW256 $ \w256c -> forAll arbitraryW256 $ \w256d -> forAll arbitraryW256 $ \w256e -> forAll arbitraryW256 $ \w256f -> forAll arbitraryW256 $ \w256g -> forAll arbitraryW256 $ \w256h -> let input = (ctxAsTy ctx, (((toW256 w256a, toW256 w256b), (toW256 w256c, toW256 w256d)), ((toW256 w256e, toW256 w256f), (toW256 w256g, toW256 w256h)))) in fastF input == C.sha_256_ctx_8_add_256 input where arbitraryW256 :: Gen W.Word256 arbitraryW256 = arbitraryBoundedIntegral toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add256)) prop_sha_256_ctx_8_add_512 :: Sha256CtxElement -> Property prop_sha_256_ctx_8_add_512 = \ctx -> forAll arbitraryW256 $ \w256a -> forAll arbitraryW256 $ \w256b -> forAll arbitraryW256 $ \w256c -> forAll arbitraryW256 $ \w256d -> forAll arbitraryW256 $ \w256e -> forAll arbitraryW256 $ \w256f -> forAll arbitraryW256 $ \w256g -> forAll arbitraryW256 $ \w256h -> forAll arbitraryW256 $ \w256i -> forAll arbitraryW256 $ \w256j -> forAll arbitraryW256 $ \w256k -> forAll arbitraryW256 $ \w256l -> forAll arbitraryW256 $ \w256m -> forAll arbitraryW256 $ \w256n -> forAll arbitraryW256 $ \w256o -> forAll arbitraryW256 $ \w256p -> let input = (ctxAsTy ctx, ((((toW256 w256a, toW256 w256b), (toW256 w256c, toW256 w256d)), ((toW256 w256e, toW256 w256f), (toW256 w256g, toW256 w256h))), (((toW256 w256i, toW256 w256j), (toW256 w256k, toW256 w256l)), ((toW256 w256m, toW256 w256n), (toW256 w256o, toW256 w256p))))) in fastF input == C.sha_256_ctx_8_add_512 input where arbitraryW256 :: Gen W.Word256 arbitraryW256 = arbitraryBoundedIntegral toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add512)) prop_sha_256_ctx_8_add_buffer_511 :: Sha256CtxElement -> Int -> Property prop_sha_256_ctx_8_add_buffer_511 = \ctx preLen -> forAll (vectorOf (preLen `mod` 512) arbitraryW8) $ \w8s -> let input = (ctxAsTy ctx, fst $ bufferFill buffer511 (toW8 <$> w8s)) in fastF input == C.sha_256_ctx_8_add_buffer_511 input where arbitraryW8 :: Gen W.Word8 arbitraryW8 = arbitraryBoundedIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8AddBuffer511)) prop_sha_256_ctx_8_finalize :: Sha256CtxElement -> Bool prop_sha_256_ctx_8_finalize = \ctx -> fastF (ctxAsTy ctx) == C.sha_256_ctx_8_finalize (ctxAsTy ctx) where fastF = testCoreEval (specification (HashJet Sha256Ctx8Finalize)) prop_parse_lock = forAll arbitraryLock $ \a -> fastF (toWord32 (fromIntegral a)) == C.parse_lock (toWord32 (fromIntegral a)) where fastF = testCoreEval (specification (BitcoinJet ParseLock)) prop_parse_sequence = forAll arbitraryLock $ \a -> fastF (toWord32 (fromIntegral a)) == C.parse_sequence (toWord32 (fromIntegral a)) where fastF = testCoreEval (specification (BitcoinJet ParseSequence)) assert_tapdata_init :: Assertion assert_tapdata_init = fastF () @=? C.tapdata_init () where fastF = testCoreEval (specification (BitcoinJet TapdataInit)) fe_unary_prop f g = \a -> fastF (feAsTy a) == g (feAsTy a) where fastF = testCoreEval f fe_binary_prop f g = \a b -> fastF (feAsTy a, feAsTy b) == g (feAsTy a, feAsTy b) where fastF = testCoreEval f prop_fe_normalize :: FieldElement -> Bool prop_fe_normalize = fe_unary_prop Prog.fe_normalize C.fe_normalize prop_fe_negate :: FieldElement -> Bool prop_fe_negate = fe_unary_prop Prog.fe_negate C.fe_negate prop_fe_add :: FieldElement -> FieldElement -> Bool prop_fe_add = fe_binary_prop Prog.fe_add C.fe_add prop_fe_square :: FieldElement -> Bool prop_fe_square = fe_unary_prop Prog.fe_square C.fe_square prop_fe_multiply :: FieldElement -> FieldElement -> Bool prop_fe_multiply = fe_binary_prop Prog.fe_multiply C.fe_multiply prop_fe_multiply_beta :: FieldElement -> Bool prop_fe_multiply_beta = fe_unary_prop Prog.fe_multiply_beta C.fe_multiply_beta prop_fe_invert :: FieldElement -> Bool prop_fe_invert = fe_unary_prop Prog.fe_invert C.fe_invert prop_fe_square_root :: FieldElement -> Bool prop_fe_square_root = fe_unary_prop Prog.fe_square_root C.fe_square_root prop_fe_is_zero :: FieldElement -> Bool prop_fe_is_zero = fe_unary_prop Prog.fe_is_zero C.fe_is_zero prop_fe_is_odd :: FieldElement -> Bool prop_fe_is_odd = fe_unary_prop Prog.fe_is_odd C.fe_is_odd scalar_unary_prop f g = \a -> fastF (scalarAsTy a) == g (scalarAsTy a) where fastF = testCoreEval f scalar_binary_prop f g = \a b -> fastF (scalarAsTy a, scalarAsTy b) == g (scalarAsTy a, scalarAsTy b) where fastF = testCoreEval f prop_scalar_normalize :: ScalarElement -> Bool prop_scalar_normalize = scalar_unary_prop Prog.scalar_normalize C.scalar_normalize prop_scalar_negate :: ScalarElement -> Bool prop_scalar_negate = scalar_unary_prop Prog.scalar_negate C.scalar_negate prop_scalar_add :: ScalarElement -> ScalarElement -> Bool prop_scalar_add = scalar_binary_prop Prog.scalar_add C.scalar_add prop_scalar_square :: ScalarElement -> Bool prop_scalar_square = scalar_unary_prop Prog.scalar_square C.scalar_square prop_scalar_multiply :: ScalarElement -> ScalarElement -> Bool prop_scalar_multiply = scalar_binary_prop Prog.scalar_multiply C.scalar_multiply prop_scalar_multiply_lambda :: ScalarElement -> Bool prop_scalar_multiply_lambda = scalar_unary_prop Prog.scalar_multiply_lambda C.scalar_multiply_lambda prop_scalar_invert :: ScalarElement -> Bool prop_scalar_invert = scalar_unary_prop Prog.scalar_invert C.scalar_invert prop_scalar_is_zero :: ScalarElement -> Bool prop_scalar_is_zero = scalar_unary_prop Prog.scalar_is_zero C.scalar_is_zero assert_gej_infinity :: Assertion assert_gej_infinity = fast_gej_infinity () @=? C.gej_infinity () where fast_gej_infinity = testCoreEval Prog.gej_infinity prop_gej_rescale :: GroupElementJacobian -> FieldElement -> Bool prop_gej_rescale = \a c -> fast_gej_rescale (gejAsTy a, feAsTy c) == C.gej_rescale (gejAsTy a, feAsTy c) where fast_gej_rescale = testCoreEval Prog.gej_rescale prop_gej_rescale_inf :: FieldElement -> Property prop_gej_rescale_inf c = forAll gen_inf $ flip prop_gej_rescale c prop_gej_normalize :: GroupElementJacobian -> Bool prop_gej_normalize = \a -> fast_gej_normalize (gejAsTy a) == C.gej_normalize (gejAsTy a) where fast_gej_normalize = testCoreEval Prog.gej_normalize prop_gej_normalize_inf :: Property prop_gej_normalize_inf = forAll gen_inf $ prop_gej_normalize prop_gej_negate :: GroupElementJacobian -> Bool prop_gej_negate = \a -> fast_gej_negate (gejAsTy a) == C.gej_negate (gejAsTy a) where fast_gej_negate = testCoreEval Prog.gej_negate prop_gej_negate_inf :: Property prop_gej_negate_inf = forAll gen_inf $ prop_gej_negate prop_ge_negate :: GroupElement -> Bool prop_ge_negate = \a -> fast_ge_negate (geAsTy a) == C.ge_negate (geAsTy a) where fast_ge_negate = testCoreEval Prog.ge_negate prop_gej_double :: GroupElementJacobian -> Bool prop_gej_double = \a -> fast_gej_double (gejAsTy a) == C.gej_double (gejAsTy a) where fast_gej_double = testCoreEval Prog.gej_double prop_gej_double_inf :: Property prop_gej_double_inf = forAll gen_inf $ prop_gej_double prop_gej_double_zero :: FieldElement -> FieldElement -> Bool prop_gej_double_zero x z = prop_gej_double a where x' = feAsSpec x z' = feAsSpec z a = GroupElementJacobian (FieldElement . Spec.fe_pack $ x') (FieldElement . Spec.fe_pack $ Spec.fe_zero) (FieldElement . Spec.fe_pack $ z') prop_gej_add :: GroupElementJacobian -> GroupElementJacobian -> Bool prop_gej_add = \a b -> fast_gej_add (gejAsTy a, gejAsTy b) == C.gej_add (gejAsTy a, gejAsTy b) where fast_gej_add = testCoreEval Prog.gej_add prop_gej_add_double :: FieldElement -> GroupElementJacobian -> Bool prop_gej_add_double z b@(GroupElementJacobian bx by bz) = prop_gej_add a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by bz' = feAsSpec bz a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack $ by' .*. z' .^. 3) (FieldElement . Spec.fe_pack $ bz' .*. z') prop_gej_add_opp :: FieldElement -> GroupElementJacobian -> Bool prop_gej_add_opp z b@(GroupElementJacobian bx by bz) = prop_gej_add a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by bz' = feAsSpec bz a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack . Spec.fe_negate $ by' .*. z' .^. 3) (FieldElement . Spec.fe_pack $ bz' .*. z') prop_gej_add_infl b = forAll gen_inf $ \a -> prop_gej_add a b prop_gej_add_infr a = forAll gen_inf $ \b -> prop_gej_add a b prop_gej_ge_add_ex :: GroupElementJacobian -> GroupElement -> Bool prop_gej_ge_add_ex = \a b -> fast_gej_ge_add_ex (gejAsTy a, geAsTy b) == C.gej_ge_add_ex (gejAsTy a, geAsTy b) where fast_gej_ge_add_ex = testCoreEval Prog.gej_ge_add_ex prop_gej_ge_add_ex_double z b@(GroupElement bx by) = prop_gej_ge_add_ex a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack $ by' .*. z' .^. 3) z prop_gej_ge_add_ex_opp z b@(GroupElement bx by) = prop_gej_ge_add_ex a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack . Spec.fe_negate $ by' .*. z' .^. 3) z prop_gej_ge_add_ex_inf b = forAll gen_inf $ \a -> prop_gej_ge_add_ex a b prop_gej_ge_add :: GroupElementJacobian -> GroupElement -> Bool prop_gej_ge_add = \a b -> fast_gej_ge_add (gejAsTy a, geAsTy b) == C.gej_ge_add (gejAsTy a, geAsTy b) where fast_gej_ge_add = testCoreEval Prog.gej_ge_add prop_gej_is_infinity :: GroupElementJacobian -> Bool prop_gej_is_infinity = \a -> fast_gej_is_infinity (gejAsTy a) == C.gej_is_infinity (gejAsTy a) where fast_gej_is_infinity = testCoreEval Prog.gej_is_infinity prop_gej_equiv :: GroupElementJacobian -> GroupElementJacobian -> Bool prop_gej_equiv = \a b -> fast_gej_equiv (gejAsTy a, gejAsTy b) == C.gej_equiv (gejAsTy a, gejAsTy b) where fast_gej_equiv = testCoreEval Prog.gej_equiv prop_gej_equiv_infl b = forAll gen_inf $ \a -> prop_gej_equiv a b prop_gej_equiv_infr a = forAll gen_inf $ \b -> prop_gej_equiv a b prop_gej_equiv_inf = forAll gen_inf $ \a -> forAll gen_inf $ \b -> prop_gej_equiv a b prop_gej_equiv_true = \a c -> let b = toGEJ $ Spec.gej_rescale (gejAsSpec a) (feAsSpec c) in fast_gej_equiv (gejAsTy a, b) == C.gej_equiv (gejAsTy a, b) where fast_gej_equiv = testCoreEval Prog.gej_equiv prop_gej_ge_equiv :: GroupElementJacobian -> GroupElement -> Bool prop_gej_ge_equiv = \a b -> fast_gej_ge_equiv (gejAsTy a, geAsTy b) == C.gej_ge_equiv (gejAsTy a, geAsTy b) where fast_gej_ge_equiv = testCoreEval Prog.gej_ge_equiv prop_gej_ge_equiv_inf b = forAll gen_inf $ \a -> prop_gej_ge_equiv a b prop_gej_ge_equiv_true = \a -> maybe (property Discard) (\b -> property $ fast_gej_ge_equiv (gejAsTy a, b) == C.gej_ge_equiv (gejAsTy a, b)) (toGE <$> Spec.gej_normalize (gejAsSpec a)) where fast_gej_ge_equiv = testCoreEval Prog.gej_ge_equiv prop_gej_x_equiv :: FieldElement -> GroupElementJacobian -> Bool prop_gej_x_equiv = \a b -> fast_gej_x_equiv (feAsTy a, gejAsTy b) == C.gej_x_equiv (feAsTy a, gejAsTy b) where fast_gej_x_equiv = testCoreEval Prog.gej_x_equiv prop_gej_x_equiv_inf x0 = forAll gen_inf $ prop_gej_x_equiv x0 prop_gej_x_equiv_true y z x0 = prop_gej_x_equiv x0 a where z' = feAsSpec z x0' = feAsSpec x0 a = GroupElementJacobian (FieldElement . Spec.fe_pack $ x0' .*. z' .^. 2) y z prop_gej_x_equiv_inf_zero = prop_gej_x_equiv_inf (FieldElement 0) prop_gej_y_is_odd :: GroupElementJacobian -> Bool prop_gej_y_is_odd = \a -> fast_gej_y_is_odd (gejAsTy a) == C.gej_y_is_odd (gejAsTy a) where fast_gej_y_is_odd = testCoreEval Prog.gej_y_is_odd prop_gej_is_on_curve :: GroupElementJacobian -> Bool prop_gej_is_on_curve = \a -> fast_gej_is_on_curve (gejAsTy a) == C.gej_is_on_curve (gejAsTy a) where fast_gej_is_on_curve = testCoreEval Prog.gej_is_on_curve prop_ge_is_on_curve :: GroupElement -> Bool prop_gej_is_on_curve_inf = forAll gen_inf prop_gej_is_on_curve prop_gej_is_on_curve_inf_half = forAll gen_half_curve_inf prop_gej_is_on_curve prop_gej_is_on_curve_half = forAll gen_half_curve_jacobian prop_gej_is_on_curve prop_ge_is_on_curve = \a -> fast_ge_is_on_curve (geAsTy a) == C.ge_is_on_curve (geAsTy a) where fast_ge_is_on_curve = testCoreEval Prog.ge_is_on_curve prop_ge_is_on_curve_half = forAll gen_half_curve prop_ge_is_on_curve prop_generate = \ng -> fast_generate (scalarAsTy ng) == C.generate (scalarAsTy ng) where fast_generate = testCoreEval Prog.generate prop_off_curve_scale = \na a -> fast_off_curve_scale (scalarAsTy na, gejAsTy a) == C.off_curve_scale (scalarAsTy na, gejAsTy a) where fast_off_curve_scale = testCoreEval Prog.off_curve_scale prop_off_curve_scale_0 a = prop_off_curve_scale na a where na = ScalarElement 0 prop_off_curve_scale_inf na = forAll gen_inf $ \a -> prop_off_curve_scale na a prop_scale :: ScalarElement -> GroupElementJacobian -> Bool prop_scale = \na a -> safe_fast_scale (scalarAsTy na, gejAsTy a) == C.scale (scalarAsTy na, gejAsTy a) where safe_fast_scale = testCoreEval Prog.scale prop_scale_0 a = prop_scale na a where na = ScalarElement 0 prop_scale_inf na = forAll gen_inf $ \a -> prop_scale na a prop_scale_half na = forAll gen_half_curve_jacobian $ \a -> prop_scale na a prop_scale_half_inf na = forAll gen_half_curve_inf $ \a -> prop_scale na a prop_scale_half_0 = forAll gen_half_curve_inf $ \a -> prop_scale na a where na = ScalarElement 0 prop_off_curve_linear_combination_1 :: ScalarElement -> GroupElementJacobian -> ScalarElement -> Bool prop_off_curve_linear_combination_1 = \na a ng -> fast_off_curve_linear_combination_1 ((scalarAsTy na, gejAsTy a), scalarAsTy ng) == C.off_curve_linear_combination_1 ((scalarAsTy na, gejAsTy a), scalarAsTy ng) where fast_off_curve_linear_combination_1 = testCoreEval Prog.off_curve_linear_combination_1 prop_off_curve_linear_combination_1_0 a ng = prop_off_curve_linear_combination_1 na a ng where na = ScalarElement 0 prop_off_curve_linear_combination_1_inf na ng = forAll gen_inf $ \a -> prop_off_curve_linear_combination_1 na a ng -- :TODO: expand test coverage on low-order (off-curve) points. -- This particular test case will fail if the gej_double_var function in the C implementation isn't "fixed" to handle -- setting the infinity flag for off-curve points of order 2. assert_off_curve_linear_combination_1_order_6 :: Assertion assert_off_curve_linear_combination_1_order_6 = True @=? prop_off_curve_linear_combination_1 na a ng where na = ScalarElement 6 a = GroupElementJacobian (FieldElement 106586213356003376052770626926523423124273824193112332847656463919061591657353) (FieldElement 26101920679609057376888884124959740524626979187904654689991505285331895977061) (FieldElement 1) ng = ScalarElement 1 prop_linear_combination_1 :: ScalarElement -> GroupElementJacobian -> ScalarElement -> Bool prop_linear_combination_1 = \na a ng -> safe_fast_linear_combination_1 ((scalarAsTy na, gejAsTy a), scalarAsTy ng) == C.linear_combination_1 ((scalarAsTy na, gejAsTy a), scalarAsTy ng) where safe_fast_linear_combination_1 = testCoreEval Prog.linear_combination_1 prop_linear_combination_1_0 a ng = prop_linear_combination_1 na a ng where na = ScalarElement 0 prop_linear_combination_1_inf na ng = forAll gen_inf $ \a -> prop_linear_combination_1 na a ng prop_linear_combination_1_half na ng = forAll gen_half_curve_jacobian $ \a -> prop_linear_combination_1 na a ng prop_linear_combination_1_half_inf na ng = forAll gen_half_curve_inf $ \a -> prop_linear_combination_1 na a ng prop_linear_combination_1_half_0 ng = forAll gen_half_curve_inf $ \a -> prop_linear_combination_1 na a ng where na = ScalarElement 0 prop_linear_verify_1 = \na a ng r -> fast_linear_verify_1 (((scalarAsTy na, geAsTy a), scalarAsTy ng), geAsTy r) == C.linear_verify_1 (((scalarAsTy na, geAsTy a), scalarAsTy ng), geAsTy r) where fast_linear_verify_1 = testCoreEval Prog.linear_verify_1 prop_linear_verify_1_0 a ng = prop_linear_verify_1 na a ng where na = ScalarElement 0 prop_linear_verify_1_true_half na ng = forAll gen_half_curve $ \a -> prop_linear_verify_1_true na a ng where prop_linear_verify_1_true na a ng | Just (GE rx' ry') <- r' = property $ prop_linear_verify_1 na a ng (mkGE rx' ry') | otherwise = property Discard where na' = scalarAsSpec na a' = geAsSpec a ng' = scalarAsSpec ng toGEJ (GE x y) = (GEJ x y Spec.fe_one) r' = Spec.gej_normalize $ Spec.off_curve_linear_combination [(na', toGEJ a')] ng' mkGE rx' ry' = GroupElement (FieldElement (Spec.fe_pack rx')) (FieldElement (Spec.fe_pack ry')) prop_point_verify_1 = \na a ng r -> fast_point_verify_1 (((scalarAsTy na, pointAsTy a), scalarAsTy ng), pointAsTy r) == C.point_verify_1 (((scalarAsTy na, pointAsTy a), scalarAsTy ng), pointAsTy r) where fast_point_verify_1 = testCoreEval Prog.point_verify_1 prop_point_verify_1_true na p ng | Just a' <- Spec.decompress p' = property $ prop a' | otherwise = property Discard where na' = scalarAsSpec na ng' = scalarAsSpec ng p' = pointAsSpec p prop a' = prop_point_verify_1 na p ng r where toGEJ (GE x y) = (GEJ x y Spec.fe_one) Just (GE rx' ry') = Spec.gej_normalize $ Spec.off_curve_linear_combination [(na', toGEJ a')] ng' r = PointElement (Spec.fe_is_odd ry') (FieldElement (Spec.fe_pack rx')) prop_decompress = \a -> fast_decompress (pointAsTy a) == C.decompress (pointAsTy a) where fast_decompress = testCoreEval Prog.decompress prop_bip_0340_verify = \pk m sig -> fast_bip_0340_verify ((pk, m), sig) == C.bip_0340_verify ((pk, m), sig) where fast_bip_0340_verify = testCoreEval Prog.bip_0340_verify assert_bip_0340_verify_vector tv = True @=? prop_bip_0340_verify pk m sig where ((pk, m), sig) = (bip0340TestAsTy tv) case_bip_0340_verify_vector n tv = testCase name (assert_bip_0340_verify_vector tv) where name = "bip_0340_vector_" ++ show n prop_check_sig_verify :: FieldElement -> HashElement -> HashElement -> FieldElement -> ScalarElement -> Bool prop_check_sig_verify = \pk m1 m2 r s -> let input = ((feAsTy pk, (heAsTy m1, heAsTy m2)), (feAsTy r, scalarAsTy s)) in fast_check_sig_verify input == C.check_sig_verify input where fast_check_sig_verify = testCoreEval (specification (SignatureJet CheckSigVerify)) prop_check_sig_verify_true :: HashElement -> HashElement -> Property prop_check_sig_verify_true = \m1 m2 -> let msg = sigHash (heAsSpec m1) (heAsSpec m2) in forAll (genSignature msg) $ \(PubKey pk, Sig r s) -> let input = ((toW256 pk, (heAsTy m1, heAsTy m2)), (toW256 r, toW256 s)) in Just () == C.check_sig_verify input && Just () == fast_check_sig_verify input where toW256 = toWord256 . fromIntegral fast_check_sig_verify = testCoreEval (specification (SignatureJet CheckSigVerify)) prop_swu :: FieldElement -> Bool prop_swu = \a -> let input = feAsTy a in fastF input == C.swu input where fastF = testCoreEval (specification (Secp256k1Jet Swu)) prop_hash_to_curve :: HashElement -> Bool prop_hash_to_curve = \a -> let input = heAsTy a in fastF input == C.hash_to_curve input where fastF = testCoreEval (specification (Secp256k1Jet HashToCurve)) ================================================ FILE: Haskell/Tests/Simplicity/Programs/Example.hs ================================================ -- A set of example Simplicity programs that can be used for tests, but otherwise are not expected to be useful. module Simplicity.Programs.Example ( fib ) where import Prelude hiding (drop) import Simplicity.Programs.Arith as Arith import Simplicity.Programs.Bit import Simplicity.Programs.Generic import Simplicity.Programs.Loop import Simplicity.Term.Core -- | An example program that uses disconnect via the 'loop' construction. -- @'fib' (3,(1,0))@ will compute the 2^4, or 16th Fibonacci number fib :: (Delegate term, Assert term) => term (Word2, (Word16, Word16)) Word16 fib = loopDepth 4 (((unit >>> Arith.zero word2) &&& oh >>> eq) &&& ((oh &&& (unit >>> Arith.one word2) >>> Arith.subtract word2 >>> ih) &&& drop (iden &&& iden >>> step)) >>> cond (injr ioh) (injl iden)) where add = Arith.add word16 >>> ih; mul = Arith.multiply word16 >>> ih; step = ((ooh &&& ioh >>> mul) &&& (ooh &&& iih >>> mul)) &&& ((oih &&& ioh >>> mul) &&& (oih &&& iih >>> mul)) >>> (ooh &&& (ioh &&& oih >>> add) >>> add) &&& (ooh &&& iih >>> add) ================================================ FILE: Haskell/Tests/Simplicity/Programs/Tests.hs ================================================ -- This module tests the Simplicity programs on arbitrary inputs. module Simplicity.Programs.Tests (tests) where import Prelude hiding (sqrt, all) import Control.Arrow ((***), right) import Data.Bits ((.|.)) import qualified Data.Bits as W import Data.ByteString (pack) import Data.ByteString.Short (toShort) import qualified Data.List as L import Lens.Family2 ((^..), allOf, over, zipWithOf) import Lens.Family2.Stock (backwards, both_) import Simplicity.Arbitrary import Simplicity.Bip0340 import Simplicity.CoreJets import Simplicity.Digest import Simplicity.Elements.Arbitrary (arbitraryLock) import Simplicity.LibSecp256k1.Schnorr import Simplicity.LibSecp256k1.Spec ((.+.), (.*.), (.^.)) import qualified Simplicity.LibSecp256k1.Spec as Spec import Simplicity.MerkleRoot import qualified Simplicity.Programs.Arith as Arith import Simplicity.Programs.Bit import Simplicity.Programs.LibSecp256k1.Lib import Simplicity.Programs.Sha256.Lib import Simplicity.Programs.Word import Simplicity.Term.Core import Simplicity.TestCoreEval import Simplicity.Ty.Arbitrary import Simplicity.Ty.Word as Ty import qualified Simplicity.Word as W import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit ((@=?), Assertion, testCase) import Test.Tasty.QuickCheck (Arbitrary(..), Discard(Discard), Gen, Property , arbitraryBoundedIntegral, choose, elements, forAll, resize, sized, vectorOf , property , testProperty, withMaxSuccess , label ) toW256 :: W.Word256 -> Word256 toW256 = toWord256 . fromIntegral toW32 :: W.Word32 -> Word32 toW32 = toWord32 . fromIntegral toW16 :: W.Word16 -> Word16 toW16 = toWord16 . fromIntegral -- This collects the tests for the various Simplicity programs. tests :: TestTree tests = testGroup "Programs" [ testGroup "Word" [ testCase "verify" assert_verify , testCase "low_1" assert_low_1 , testCase "low_8" assert_low_8 , testCase "low_16" assert_low_16 , testCase "low_32" assert_low_32 , testCase "low_64" assert_low_64 , testCase "high_1" assert_high_1 , testCase "high_8" assert_high_8 , testCase "high_16" assert_high_16 , testCase "high_32" assert_high_32 , testCase "high_64" assert_high_64 , testProperty "complement_1" prop_complement_1 , testProperty "complement_8" prop_complement_8 , testProperty "complement_16" prop_complement_16 , testProperty "complement_32" prop_complement_32 , testProperty "complement_64" prop_complement_64 , testProperty "and_1" prop_and_1 , testProperty "and_8" prop_and_8 , testProperty "and_16" prop_and_16 , testProperty "and_32" prop_and_32 , testProperty "and_64" prop_and_64 , testProperty "or_1" prop_or_1 , testProperty "or_8" prop_or_8 , testProperty "or_16" prop_or_16 , testProperty "or_32" prop_or_32 , testProperty "or_64" prop_or_64 , testProperty "xor_1" prop_xor_1 , testProperty "xor_8" prop_xor_8 , testProperty "xor_16" prop_xor_16 , testProperty "xor_32" prop_xor_32 , testProperty "xor_64" prop_xor_64 , testProperty "maj_1" prop_maj_1 , testProperty "maj_8" prop_maj_8 , testProperty "maj_16" prop_maj_16 , testProperty "maj_32" prop_maj_32 , testProperty "maj_64" prop_maj_64 , testProperty "xor_xor_1" prop_xor_xor_1 , testProperty "xor_xor_8" prop_xor_xor_8 , testProperty "xor_xor_16" prop_xor_xor_16 , testProperty "xor_xor_32" prop_xor_xor_32 , testProperty "xor_xor_64" prop_xor_xor_64 , testProperty "ch_1" prop_ch_1 , testProperty "ch_8" prop_ch_8 , testProperty "ch_16" prop_ch_16 , testProperty "ch_32" prop_ch_32 , testProperty "ch_64" prop_ch_64 , testProperty "some_1" prop_some_1 , testProperty "some_8" prop_some_8 , testProperty "some_16" prop_some_16 , testProperty "some_32" prop_some_32 , testProperty "some_64" prop_some_64 , testProperty "all_8" prop_all_8 , testProperty "all_16" prop_all_16 , testProperty "all_32" prop_all_32 , testProperty "all_64" prop_all_64 , testProperty "eq_8" prop_eq_8 , testProperty "eq_16" prop_eq_16 , testProperty "eq_32" prop_eq_32 , testProperty "eq_64" prop_eq_64 , testProperty "eq_256" prop_eq_256 , testProperty "eq_diag_8" prop_eq_diag_8 , testProperty "eq_diag_16" prop_eq_diag_16 , testProperty "eq_diag_32" prop_eq_diag_32 , testProperty "eq_diag_64" prop_eq_diag_64 , testProperty "eq_diag_256" prop_eq_diag_256 , testProperty "full_left_shift_8_1" prop_full_left_shift_8_1 , testProperty "full_left_shift_8_2" prop_full_left_shift_8_2 , testProperty "full_left_shift_8_4" prop_full_left_shift_8_4 , testProperty "full_left_shift_16_1" prop_full_left_shift_16_1 , testProperty "full_left_shift_16_2" prop_full_left_shift_16_2 , testProperty "full_left_shift_16_4" prop_full_left_shift_16_4 , testProperty "full_left_shift_16_8" prop_full_left_shift_16_8 , testProperty "full_left_shift_32_1" prop_full_left_shift_32_1 , testProperty "full_left_shift_32_2" prop_full_left_shift_32_2 , testProperty "full_left_shift_32_4" prop_full_left_shift_32_4 , testProperty "full_left_shift_32_8" prop_full_left_shift_32_8 , testProperty "full_left_shift_32_16" prop_full_left_shift_32_16 , testProperty "full_left_shift_64_1" prop_full_left_shift_64_1 , testProperty "full_left_shift_64_2" prop_full_left_shift_64_2 , testProperty "full_left_shift_64_4" prop_full_left_shift_64_4 , testProperty "full_left_shift_64_8" prop_full_left_shift_64_8 , testProperty "full_left_shift_64_16" prop_full_left_shift_64_16 , testProperty "full_left_shift_64_32" prop_full_left_shift_64_32 , testProperty "full_right_shift_8_1" prop_full_right_shift_8_1 , testProperty "full_right_shift_8_2" prop_full_right_shift_8_2 , testProperty "full_right_shift_8_4" prop_full_right_shift_8_4 , testProperty "full_right_shift_16_1" prop_full_right_shift_16_1 , testProperty "full_right_shift_16_2" prop_full_right_shift_16_2 , testProperty "full_right_shift_16_4" prop_full_right_shift_16_4 , testProperty "full_right_shift_16_8" prop_full_right_shift_16_8 , testProperty "full_right_shift_32_1" prop_full_right_shift_32_1 , testProperty "full_right_shift_32_2" prop_full_right_shift_32_2 , testProperty "full_right_shift_32_4" prop_full_right_shift_32_4 , testProperty "full_right_shift_32_8" prop_full_right_shift_32_8 , testProperty "full_right_shift_32_16" prop_full_right_shift_32_16 , testProperty "full_right_shift_64_1" prop_full_right_shift_64_1 , testProperty "full_right_shift_64_2" prop_full_right_shift_64_2 , testProperty "full_right_shift_64_4" prop_full_right_shift_64_4 , testProperty "full_right_shift_64_8" prop_full_right_shift_64_8 , testProperty "full_right_shift_64_16" prop_full_right_shift_64_16 , testProperty "full_right_shift_64_32" prop_full_right_shift_64_32 , testProperty "leftmost_8_1" prop_leftmost_8_1 , testProperty "leftmost_8_2" prop_leftmost_8_2 , testProperty "leftmost_8_4" prop_leftmost_8_4 , testProperty "leftmost_16_1" prop_leftmost_16_1 , testProperty "leftmost_16_2" prop_leftmost_16_2 , testProperty "leftmost_16_4" prop_leftmost_16_4 , testProperty "leftmost_16_8" prop_leftmost_16_8 , testProperty "leftmost_32_1" prop_leftmost_32_1 , testProperty "leftmost_32_2" prop_leftmost_32_2 , testProperty "leftmost_32_4" prop_leftmost_32_4 , testProperty "leftmost_32_8" prop_leftmost_32_8 , testProperty "leftmost_32_16" prop_leftmost_32_16 , testProperty "leftmost_64_1" prop_leftmost_64_1 , testProperty "leftmost_64_2" prop_leftmost_64_2 , testProperty "leftmost_64_4" prop_leftmost_64_4 , testProperty "leftmost_64_8" prop_leftmost_64_8 , testProperty "leftmost_64_16" prop_leftmost_64_16 , testProperty "leftmost_64_32" prop_leftmost_64_32 , testProperty "rightmost_8_1" prop_rightmost_8_1 , testProperty "rightmost_8_2" prop_rightmost_8_2 , testProperty "rightmost_8_4" prop_rightmost_8_4 , testProperty "rightmost_16_1" prop_rightmost_16_1 , testProperty "rightmost_16_2" prop_rightmost_16_2 , testProperty "rightmost_16_4" prop_rightmost_16_4 , testProperty "rightmost_16_8" prop_rightmost_16_8 , testProperty "rightmost_32_1" prop_rightmost_32_1 , testProperty "rightmost_32_2" prop_rightmost_32_2 , testProperty "rightmost_32_4" prop_rightmost_32_4 , testProperty "rightmost_32_8" prop_rightmost_32_8 , testProperty "rightmost_32_16" prop_rightmost_32_16 , testProperty "rightmost_64_1" prop_rightmost_64_1 , testProperty "rightmost_64_2" prop_rightmost_64_2 , testProperty "rightmost_64_4" prop_rightmost_64_4 , testProperty "rightmost_64_8" prop_rightmost_64_8 , testProperty "rightmost_64_16" prop_rightmost_64_16 , testProperty "rightmost_64_32" prop_rightmost_64_32 , testProperty "left_pad_low_1_8" prop_left_pad_low_1_8 , testProperty "left_pad_low_1_16" prop_left_pad_low_1_16 , testProperty "left_pad_low_8_16" prop_left_pad_low_8_16 , testProperty "left_pad_low_1_32" prop_left_pad_low_1_32 , testProperty "left_pad_low_8_32" prop_left_pad_low_8_32 , testProperty "left_pad_low_16_32" prop_left_pad_low_16_32 , testProperty "left_pad_low_1_64" prop_left_pad_low_1_64 , testProperty "left_pad_low_8_64" prop_left_pad_low_8_64 , testProperty "left_pad_low_16_64" prop_left_pad_low_16_64 , testProperty "left_pad_low_32_64" prop_left_pad_low_32_64 , testProperty "left_pad_high_1_8" prop_left_pad_high_1_8 , testProperty "left_pad_high_1_16" prop_left_pad_high_1_16 , testProperty "left_pad_high_8_16" prop_left_pad_high_8_16 , testProperty "left_pad_high_1_32" prop_left_pad_high_1_32 , testProperty "left_pad_high_8_32" prop_left_pad_high_8_32 , testProperty "left_pad_high_16_32" prop_left_pad_high_16_32 , testProperty "left_pad_high_1_64" prop_left_pad_high_1_64 , testProperty "left_pad_high_8_64" prop_left_pad_high_8_64 , testProperty "left_pad_high_16_64" prop_left_pad_high_16_64 , testProperty "left_pad_high_32_64" prop_left_pad_high_32_64 , testProperty "left_extend_1_8" prop_left_extend_1_8 , testProperty "left_extend_1_16" prop_left_extend_1_16 , testProperty "left_extend_8_16" prop_left_extend_8_16 , testProperty "left_extend_1_32" prop_left_extend_1_32 , testProperty "left_extend_8_32" prop_left_extend_8_32 , testProperty "left_extend_16_32" prop_left_extend_16_32 , testProperty "left_extend_1_64" prop_left_extend_1_64 , testProperty "left_extend_8_64" prop_left_extend_8_64 , testProperty "left_extend_16_64" prop_left_extend_16_64 , testProperty "left_extend_32_64" prop_left_extend_32_64 , testProperty "right_pad_low_1_8" prop_right_pad_low_1_8 , testProperty "right_pad_low_1_16" prop_right_pad_low_1_16 , testProperty "right_pad_low_8_16" prop_right_pad_low_8_16 , testProperty "right_pad_low_1_32" prop_right_pad_low_1_32 , testProperty "right_pad_low_8_32" prop_right_pad_low_8_32 , testProperty "right_pad_low_16_32" prop_right_pad_low_16_32 , testProperty "right_pad_low_1_64" prop_right_pad_low_1_64 , testProperty "right_pad_low_8_64" prop_right_pad_low_8_64 , testProperty "right_pad_low_16_64" prop_right_pad_low_16_64 , testProperty "right_pad_low_32_64" prop_right_pad_low_32_64 , testProperty "right_pad_high_1_8" prop_right_pad_high_1_8 , testProperty "right_pad_high_1_16" prop_right_pad_high_1_16 , testProperty "right_pad_high_8_16" prop_right_pad_high_8_16 , testProperty "right_pad_high_1_32" prop_right_pad_high_1_32 , testProperty "right_pad_high_8_32" prop_right_pad_high_8_32 , testProperty "right_pad_high_16_32" prop_right_pad_high_16_32 , testProperty "right_pad_high_1_64" prop_right_pad_high_1_64 , testProperty "right_pad_high_8_64" prop_right_pad_high_8_64 , testProperty "right_pad_high_16_64" prop_right_pad_high_16_64 , testProperty "right_pad_high_32_64" prop_right_pad_high_32_64 , testProperty "right_extend_8_16" prop_right_extend_8_16 , testProperty "right_extend_8_32" prop_right_extend_8_32 , testProperty "right_extend_16_32" prop_right_extend_16_32 , testProperty "right_extend_8_64" prop_right_extend_8_64 , testProperty "right_extend_16_64" prop_right_extend_16_64 , testProperty "right_extend_32_64" prop_right_extend_32_64 , testProperty "left_shift_with_8" prop_left_shift_with_8 , testProperty "left_shift_with_16" prop_left_shift_with_16 , testProperty "left_shift_with_32" prop_left_shift_with_32 , testProperty "left_shift_with_64" prop_left_shift_with_64 , testProperty "left_shift_8" prop_left_shift_8 , testProperty "left_shift_16" prop_left_shift_16 , testProperty "left_shift_32" prop_left_shift_32 , testProperty "left_shift_64" prop_left_shift_64 , testProperty "right_shift_with_8" prop_right_shift_with_8 , testProperty "right_shift_with_16" prop_right_shift_with_16 , testProperty "right_shift_with_32" prop_right_shift_with_32 , testProperty "right_shift_with_64" prop_right_shift_with_64 , testProperty "right_shift_8" prop_right_shift_8 , testProperty "right_shift_16" prop_right_shift_16 , testProperty "right_shift_32" prop_right_shift_32 , testProperty "right_shift_64" prop_right_shift_64 , testProperty "left_rotate_8" prop_left_rotate_8 , testProperty "left_rotate_16" prop_left_rotate_16 , testProperty "left_rotate_32" prop_left_rotate_32 , testProperty "left_rotate_64" prop_left_rotate_64 , testProperty "right_rotate_8" prop_right_rotate_8 , testProperty "right_rotate_16" prop_right_rotate_16 , testProperty "right_rotate_32" prop_right_rotate_32 , testProperty "right_rotate_64" prop_right_rotate_64 , testProperty "shift_const_by false word8" prop_shift_const_by_false8 , testProperty "rotate_const word8" prop_rotate_const8 , testProperty "transpose zv2 zv8" prop_transpose_2x8 , testProperty "transpose zv8 zv8" prop_transpose_8x8 ] , testGroup "Arith" [ testProperty "lsb word8" prop_lsb8 , testProperty "msb word8" prop_msb8 , testProperty "bezout word8" prop_bezout8 , testProperty "cofactors word8" prop_cofactors8 , testProperty "gcd word8" prop_gcd8 , testProperty "lcm word8" prop_lcm8 , testProperty "absolute_value word4" prop_absolute_value4 , testProperty "sign word4" prop_sign4 , testCase "one_8" assert_one_8 , testCase "one_16" assert_one_16 , testCase "one_32" assert_one_32 , testCase "one_64" assert_one_64 , testProperty "add_8" prop_add_8 , testProperty "add_16" prop_add_16 , testProperty "add_32" prop_add_32 , testProperty "add_64" prop_add_64 , testProperty "full_add_8" prop_full_add_8 , testProperty "full_add_16" prop_full_add_16 , testProperty "full_add_32" prop_full_add_32 , testProperty "full_add_64" prop_full_add_64 , testProperty "full_increment_8" prop_full_increment_8 , testProperty "full_increment_16" prop_full_increment_16 , testProperty "full_increment_32" prop_full_increment_32 , testProperty "full_increment_64" prop_full_increment_64 , testCase "full_increment_max_8" assert_full_increment_max_8 , testCase "full_increment_max_16" assert_full_increment_max_16 , testCase "full_increment_max_32" assert_full_increment_max_32 , testCase "full_increment_max_64" assert_full_increment_max_64 , testProperty "increment_8" prop_increment_8 , testProperty "increment_16" prop_increment_16 , testProperty "increment_32" prop_increment_32 , testProperty "increment_64" prop_increment_64 , testCase "increment_max_8" assert_increment_max_8 , testCase "increment_max_16" assert_increment_max_16 , testCase "increment_max_32" assert_increment_max_32 , testCase "increment_max_64" assert_increment_max_64 , testProperty "subtract_8" prop_subtract_8 , testProperty "subtract_16" prop_subtract_16 , testProperty "subtract_32" prop_subtract_32 , testProperty "subtract_64" prop_subtract_64 , testProperty "full_subtract_8" prop_full_subtract_8 , testProperty "full_subtract_16" prop_full_subtract_16 , testProperty "full_subtract_32" prop_full_subtract_32 , testProperty "full_subtract_64" prop_full_subtract_64 , testProperty "negate_8" prop_negate_8 , testProperty "negate_16" prop_negate_16 , testProperty "negate_32" prop_negate_32 , testProperty "negate_64" prop_negate_64 , testProperty "full_decrement_8" prop_full_decrement_8 , testProperty "full_decrement_16" prop_full_decrement_16 , testProperty "full_decrement_32" prop_full_decrement_32 , testProperty "full_decrement_64" prop_full_decrement_64 , testCase "full_decrement_zero_8" assert_full_decrement_zero_8 , testCase "full_decrement_zero_16" assert_full_decrement_zero_16 , testCase "full_decrement_zero_32" assert_full_decrement_zero_32 , testCase "full_decrement_zero_64" assert_full_decrement_zero_64 , testProperty "decrement_8" prop_decrement_8 , testProperty "decrement_16" prop_decrement_16 , testProperty "decrement_32" prop_decrement_32 , testProperty "decrement_64" prop_decrement_64 , testCase "decrement_zero_8" assert_decrement_zero_8 , testCase "decrement_zero_16" assert_decrement_zero_16 , testCase "decrement_zero_32" assert_decrement_zero_32 , testCase "decrement_zero_64" assert_decrement_zero_64 , testProperty "multiply_8" prop_multiply_8 , testProperty "multiply_16" prop_multiply_16 , testProperty "multiply_32" prop_multiply_32 , testProperty "multiply_64" prop_multiply_64 , testProperty "full_multiply_8" prop_full_multiply_8 , testProperty "full_multiply_16" prop_full_multiply_16 , testProperty "full_multiply_32" prop_full_multiply_32 , testProperty "full_multiply_64" prop_full_multiply_64 , testProperty "is_zero_8" prop_is_zero_8 , testProperty "is_zero_16" prop_is_zero_16 , testProperty "is_zero_32" prop_is_zero_32 , testProperty "is_zero_64" prop_is_zero_64 , testCase "zero_is_zero_8" assert_zero_is_zero_8 , testCase "zero_is_zero_16" assert_zero_is_zero_16 , testCase "zero_is_zero_32" assert_zero_is_zero_32 , testCase "zero_is_zero_64" assert_zero_is_zero_64 , testProperty "is_one_8" prop_is_one_8 , testProperty "is_one_16" prop_is_one_16 , testProperty "is_one_32" prop_is_one_32 , testProperty "is_one_64" prop_is_one_64 , testCase "one_is_one_8" assert_one_is_one_8 , testCase "one_is_one_16" assert_one_is_one_16 , testCase "one_is_one_32" assert_one_is_one_32 , testCase "one_is_one_64" assert_one_is_one_64 , testProperty "le_8" prop_le_8 , testProperty "le_16" prop_le_16 , testProperty "le_32" prop_le_32 , testProperty "le_64" prop_le_64 , testProperty "le_diag_8" prop_le_diag_8 , testProperty "le_diag_16" prop_le_diag_16 , testProperty "le_diag_32" prop_le_diag_32 , testProperty "le_diag_64" prop_le_diag_64 , testProperty "lt_8" prop_lt_8 , testProperty "lt_16" prop_lt_16 , testProperty "lt_32" prop_lt_32 , testProperty "lt_64" prop_lt_64 , testProperty "lt_diag_8" prop_lt_diag_8 , testProperty "lt_diag_16" prop_lt_diag_16 , testProperty "lt_diag_32" prop_lt_diag_32 , testProperty "lt_diag_64" prop_lt_diag_64 , testProperty "min_8" prop_min_8 , testProperty "min_16" prop_min_16 , testProperty "min_32" prop_min_32 , testProperty "min_64" prop_min_64 , testProperty "max_8" prop_max_8 , testProperty "max_16" prop_max_16 , testProperty "max_32" prop_max_32 , testProperty "max_64" prop_max_64 , testProperty "median_8" prop_median_8 , testProperty "median_16" prop_median_16 , testProperty "median_32" prop_median_32 , testProperty "median_64" prop_median_64 , testProperty "div_mod_8" prop_div_mod_8 , testProperty "div_mod_16" prop_div_mod_16 , testProperty "div_mod_32" prop_div_mod_32 , testProperty "div_mod_64" prop_div_mod_64 , testProperty "divide_8" prop_divide_8 , testProperty "divide_16" prop_divide_16 , testProperty "divide_32" prop_divide_32 , testProperty "divide_64" prop_divide_64 , testProperty "modulo_8" prop_modulo_8 , testProperty "modulo_16" prop_modulo_16 , testProperty "modulo_32" prop_modulo_32 , testProperty "modulo_64" prop_modulo_64 , testProperty "divides_8" prop_divides_8 , testProperty "divides_16" prop_divides_16 , testProperty "divides_32" prop_divides_32 , testProperty "divides_64" prop_divides_64 , testProperty "div_mod_zero_8" prop_div_mod_zero_8 , testProperty "div_mod_zero_16" prop_div_mod_zero_16 , testProperty "div_mod_zero_32" prop_div_mod_zero_32 , testProperty "div_mod_zero_64" prop_div_mod_zero_64 , testProperty "divide_zero_8" prop_divide_zero_8 , testProperty "divide_zero_16" prop_divide_zero_16 , testProperty "divide_zero_32" prop_divide_zero_32 , testProperty "divide_zero_64" prop_divide_zero_64 , testProperty "modulo_zero_8" prop_modulo_zero_8 , testProperty "modulo_zero_16" prop_modulo_zero_16 , testProperty "modulo_zero_32" prop_modulo_zero_32 , testProperty "modulo_zero_64" prop_modulo_zero_64 , testProperty "divides_zero_8" prop_divides_zero_8 , testProperty "divides_zero_16" prop_divides_zero_16 , testProperty "divides_zero_32" prop_divides_zero_32 , testProperty "divides_zero_64" prop_divides_zero_64 , testProperty "div_mod_128_64" prop_div_mod_128_64 , testProperty "div_mod_128_64_low_y" prop_div_mod_128_64_low_y , testProperty "div_mod_128_64_high_x" prop_div_mod_128_64_high_x ] , testGroup "Hash" [ testCase "sha_256_iv" assert_sha_256_iv , testProperty "sha_256_block" prop_sha_256_block , testCase "sha_256_ctx_8_init" assert_sha_256_ctx_8_init , testProperty "sha_256_ctx_8_add_1" prop_sha_256_ctx_8_add_1 , testProperty "sha_256_ctx_8_add_2" prop_sha_256_ctx_8_add_2 , testProperty "sha_256_ctx_8_add_4" prop_sha_256_ctx_8_add_4 , testProperty "sha_256_ctx_8_add_8" prop_sha_256_ctx_8_add_8 , testProperty "sha_256_ctx_8_add_16" prop_sha_256_ctx_8_add_16 , testProperty "sha_256_ctx_8_add_32" prop_sha_256_ctx_8_add_32 , testProperty "sha_256_ctx_8_add_64" prop_sha_256_ctx_8_add_64 , testProperty "sha_256_ctx_8_add_128" prop_sha_256_ctx_8_add_128 , testProperty "sha_256_ctx_8_add_256" prop_sha_256_ctx_8_add_256 , testProperty "sha_256_ctx_8_add_512" prop_sha_256_ctx_8_add_512 , testProperty "sha_256_ctx_8_add_buffer_511" prop_sha_256_ctx_8_add_buffer_511 , testProperty "sha_256_ctx_8_finalize" prop_sha_256_ctx_8_finalize ] , testGroup "ellipticCurve" [ testProperty "fe_normalize" prop_fe_normalize , testProperty "fe_add" prop_fe_add , testProperty "fe_multiply" prop_fe_multiply , testProperty "fe_square" prop_fe_square , testProperty "fe_negate" prop_fe_negate , testProperty "fe_halve" prop_fe_halve , testProperty "fe_invert" (withMaxSuccess 10 prop_fe_invert) , testProperty "fe_square_root" (withMaxSuccess 10 prop_fe_square_root) , testProperty "gej_rescale" prop_gej_rescale , testProperty "gej_rescale_inf" prop_gej_rescale_inf , testProperty "gej_double" prop_gej_double , testProperty "gej_double_inf" prop_gej_double_inf , testProperty "gej_add_ex" prop_gej_add_ex , testProperty "gej_add_ex_double" prop_gej_add_ex_double , testProperty "gej_add_ex_opp" prop_gej_add_ex_opp , testProperty "gej_add_ex_infl" prop_gej_add_ex_infl , testProperty "gej_add_ex_infr" prop_gej_add_ex_infr , testProperty "gej_add" prop_gej_add , testProperty "gej_add_double" prop_gej_add_double , testProperty "gej_add_opp" prop_gej_add_opp , testProperty "gej_add_infl" prop_gej_add_infl , testProperty "gej_add_infr" prop_gej_add_infr , testProperty "gej_ge_add_ex" prop_gej_ge_add_ex , testProperty "gej_ge_add_ex_double" prop_gej_ge_add_ex_double , testProperty "gej_ge_add_ex_opp" prop_gej_ge_add_ex_opp , testProperty "gej_ge_add_ex_inf" prop_gej_ge_add_ex_inf , testProperty "gej_equiv" prop_gej_equiv , testProperty "gej_equiv_infl" prop_gej_equiv_infl , testProperty "gej_equiv_infr" prop_gej_equiv_infr , testProperty "gej_equiv_inf" prop_gej_equiv_inf , testProperty "gej_equiv_true" prop_gej_equiv_true , testProperty "gej_ge_equiv" prop_gej_ge_equiv , testProperty "gej_ge_equiv_inf" prop_gej_ge_equiv_inf , testProperty "gej_ge_equiv_true" prop_gej_ge_equiv_true , testProperty "gej_x_equiv" prop_gej_x_equiv , testProperty "gej_x_equiv_inf" prop_gej_x_equiv_inf , testProperty "gej_x_equiv_true" prop_gej_x_equiv_true , testProperty "gej_x_equiv_inf_zero" prop_gej_x_equiv_inf_zero , testProperty "gej_is_on_curve" prop_gej_is_on_curve , testProperty "gej_is_on_curve_half" prop_gej_is_on_curve_half , testProperty "gej_is_on_curve_inf" prop_gej_is_on_curve_inf , testProperty "gej_is_on_curve_inf_half" prop_gej_is_on_curve_inf_half , testProperty "ge_is_on_curve" prop_ge_is_on_curve , testProperty "ge_is_on_curve_half" prop_ge_is_on_curve_half , testProperty "scalar_normalize" prop_scalar_normalize , testProperty "scalar_add" prop_scalar_add , testProperty "scalar_square" prop_scalar_square , testProperty "scalar_multiply" prop_scalar_multiply , testProperty "scalar_negate" prop_scalar_negate , testProperty "scalar_invert" (withMaxSuccess 10 prop_scalar_invert) , testProperty "scalar_split_lambda" prop_scalar_split_lambda , testProperty "wnaf5" prop_wnaf5 , testProperty "wnaf15" prop_wnaf15 , testProperty "decompress" prop_decompress , testProperty "off_curve_scale" prop_off_curve_scale , testProperty "off_curve_scale_0" prop_off_curve_scale_0 , testProperty "off_curve_scale_inf" prop_off_curve_scale_inf , testProperty "scale" prop_scale , testProperty "scale_0" prop_scale_0 , testProperty "scale_inf" prop_scale_inf , testProperty "scale_half" prop_scale_half , testProperty "scale_half_0" prop_scale_half_0 , testProperty "scale_half_inf" prop_scale_half_inf , testProperty "off_curve_linear_combination_1" prop_off_curve_linear_combination_1 , testProperty "off_curve_linear_combination_1_0" prop_off_curve_linear_combination_1_0 , testProperty "off_curve_linear_combination_1_inf" prop_off_curve_linear_combination_1_inf , testProperty "linear_combination_1" prop_linear_combination_1 , testProperty "linear_combination_1_0" prop_linear_combination_1_0 , testProperty "linear_combination_1_inf" prop_linear_combination_1_inf , testProperty "linear_combination_1_half" prop_linear_combination_1_half , testProperty "linear_combination_1_half_0" prop_linear_combination_1_half_0 , testProperty "linear_combination_1_half_inf" prop_linear_combination_1_half_inf , testProperty "linear_check_1" prop_linear_check_1 , testProperty "point_check_1" prop_point_check_1 , testProperty "swu" prop_swu , testProperty "hash_to_curve" prop_hash_to_curve ] , testGroup "bip0340" [ testProperty "pubkey_unpack" prop_pubkey_unpack , testProperty "pubkey_unpack_neg" prop_pubkey_unpack_neg , testProperty "signature_unpack" prop_signature_unpack , testProperty "check_sig_verify" prop_check_sig_verify , testProperty "check_sig_verify_true" prop_check_sig_verify_true ] , group_bip_0340_check , testGroup "bitcoin" [ testProperty "parse_lock" prop_parse_lock , testProperty "parse_sequence" prop_parse_sequence , testCase "tapdata_init" assert_tapdata_init ] ] assert_verify :: Assertion assert_verify = (fastF (toBit False), fastF (toBit True)) @=? (implF (toBit False), implF (toBit True)) where fastF = testCoreEval (specification (WordJet Verify)) implF = implementation (WordJet Verify) prop_shift_const_by_false8 :: Word8 -> Property prop_shift_const_by_false8 x = forAll (choose (-8,16)) $ \c -> W.shift (conv x) c == conv (shift_const_by false word8 c x) where conv :: Word8 -> W.Word8 conv = fromInteger . fromWord8 prop_rotate_const8 :: Word8 -> Property prop_rotate_const8 x = forAll (choose (-8,16)) $ \c -> W.rotate (conv x) c == conv (rotate_const word8 c x) where conv :: Word8 -> W.Word8 conv = fromInteger . fromWord8 prop_transpose_2x8 :: Word16 -> Bool prop_transpose_2x8 x = L.transpose (map (^..both_) (x^..both_.both_.both_)) == map (^..both_.both_.both_) (transpose zv2 zv8 x^..both_) where zv2 = DoubleZV SingleZV zv8 = DoubleZV . DoubleZV . DoubleZV $ SingleZV prop_transpose_8x8 :: Word64 -> Bool prop_transpose_8x8 x = L.transpose (map (^..both_.both_.both_) (x^..both_.both_.both_)) == map (^..both_.both_.both_) (transpose zv8 zv8' x^..both_.both_.both_) where zv8 = DoubleZV . DoubleZV . DoubleZV $ SingleZV zv8' = DoubleZV . DoubleZV . DoubleZV $ SingleZV -- monomorhpism restriction prop_lsb8 :: Word8 -> Bool prop_lsb8 x = W.testBit (fromWord8 x) 0 == fromBit (Arith.lsb word8 x) prop_msb8 :: Word8 -> Bool prop_msb8 x = W.testBit (fromWord8 x) 7 == fromBit (Arith.msb word8 x) prop_bezout8 :: Word8 -> Word8 -> Bool prop_bezout8 x y = a * x' + b * y' == d && if x' == y' then (a == 1 && b == 0) else if y' == 0 then (a == 1 && b == 0) else if x' == 0 then (a == 0 && b == 1) else (if d == y' then a == 0 else abs a * 2 * d <= y') && (if d == x' then b == 0 else abs b * 2 * d <= x') where x' = fromWord8 x y' = fromWord8 y d = x' `gcd` y' (a, b) = either f g $ Arith.bezout word8 (x, y) f (a, b) = (fromWord8 a, - fromWord8 b) g (a, b) = (- fromWord8 a, fromWord8 b) prop_cofactors8 :: Word8 -> Word8 -> Bool prop_cofactors8 x y = fromWord8 x == d * fromWord8 a && fromWord8 y == d * fromWord8 b where d = fromWord8 x `gcd` fromWord8 y (a, b) = Arith.cofactors word8 (x, y) prop_gcd8 :: Word8 -> Word8 -> Bool prop_gcd8 x y = (fromWord8 x `gcd` fromWord8 y) == fromWord8 (Arith.gcd word8 (x,y)) prop_lcm8 :: Word8 -> Word8 -> Bool prop_lcm8 x y = (fromWord8 x `lcm` fromWord8 y) == fromWord16 (Arith.lcm word8 (x,y)) prop_absolute_value4 :: Word4 -> Bool prop_absolute_value4 x = abs (fromInt4 x) == fromWord4 (Arith.absolute_value word4 x) where fromInt4 x = if 2^3 <= w4 then w4 - 2^4 else w4 where w4 = fromWord4 x prop_sign4 :: Word4 -> Bool prop_sign4 x = signum (fromInt4 x) == fromInt2 (Arith.sign word4 x) where fromInt4 x = if 2^3 <= w4 then w4 - 2^4 else w4 where w4 = fromWord4 x fromInt2 x = if 2^1 <= w2 then w2 - 2^2 else w2 where w2 = fromWord2 x assert_low_1 :: Assertion assert_low_1 = fastF () @=? implementation (WordJet Low1) () where fastF = testCoreEval (specification (WordJet Low1)) assert_low_8 :: Assertion assert_low_8 = fastF () @=? implementation (WordJet Low8) () where fastF = testCoreEval (specification (WordJet Low8)) assert_low_16 :: Assertion assert_low_16 = fastF () @=? implementation (WordJet Low16) () where fastF = testCoreEval (specification (WordJet Low16)) assert_low_32 :: Assertion assert_low_32 = fastF () @=? implementation (WordJet Low32) () where fastF = testCoreEval (specification (WordJet Low32)) assert_low_64 :: Assertion assert_low_64 = fastF () @=? implementation (WordJet Low64) () where fastF = testCoreEval (specification (WordJet Low64)) assert_high_1 :: Assertion assert_high_1 = fastF () @=? implementation (WordJet High1) () where fastF = testCoreEval (specification (WordJet High1)) assert_high_8 :: Assertion assert_high_8 = fastF () @=? implementation (WordJet High8) () where fastF = testCoreEval (specification (WordJet High8)) assert_high_16 :: Assertion assert_high_16 = fastF () @=? implementation (WordJet High16) () where fastF = testCoreEval (specification (WordJet High16)) assert_high_32 :: Assertion assert_high_32 = fastF () @=? implementation (WordJet High32) () where fastF = testCoreEval (specification (WordJet High32)) assert_high_64 :: Assertion assert_high_64 = fastF () @=? implementation (WordJet High64) () where fastF = testCoreEval (specification (WordJet High64)) prop_complement_1 :: Bool -> Bool prop_complement_1 = \x -> let input = toBit x in fastF input == implementation (WordJet Complement1) input where fastF = testCoreEval (specification (WordJet Complement1)) prop_complement_8 :: W.Word8 -> Bool prop_complement_8 = \x -> let input = toW8 x in fastF input == implementation (WordJet Complement8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Complement8)) prop_complement_16 :: W.Word16 -> Bool prop_complement_16 = \x -> let input = toW16 x in fastF input == implementation (WordJet Complement16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Complement16)) prop_complement_32 :: W.Word32 -> Bool prop_complement_32 = \x -> let input = toW32 x in fastF input == implementation (WordJet Complement32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Complement32)) prop_complement_64 :: W.Word64 -> Bool prop_complement_64 = \x -> let input = toW64 x in fastF input == implementation (WordJet Complement64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Complement64)) prop_and_1 :: Bool -> Bool -> Bool prop_and_1 = \x y -> let input = (toBit x, toBit y) in fastF input == implementation (WordJet And1) input where fastF = testCoreEval (specification (WordJet And1)) prop_and_8 :: W.Word8 -> W.Word8 -> Bool prop_and_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (WordJet And8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet And8)) prop_and_16 :: W.Word16 -> W.Word16 -> Bool prop_and_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (WordJet And16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet And16)) prop_and_32 :: W.Word32 -> W.Word32 -> Bool prop_and_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (WordJet And32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet And32)) prop_and_64 :: W.Word64 -> W.Word64 -> Bool prop_and_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (WordJet And64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet And64)) prop_or_1 :: Bool -> Bool -> Bool prop_or_1 = \x y -> let input = (toBit x, toBit y) in fastF input == implementation (WordJet Or1) input where fastF = testCoreEval (specification (WordJet Or1)) prop_or_8 :: W.Word8 -> W.Word8 -> Bool prop_or_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (WordJet Or8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Or8)) prop_or_16 :: W.Word16 -> W.Word16 -> Bool prop_or_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (WordJet Or16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Or16)) prop_or_32 :: W.Word32 -> W.Word32 -> Bool prop_or_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (WordJet Or32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Or32)) prop_or_64 :: W.Word64 -> W.Word64 -> Bool prop_or_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (WordJet Or64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Or64)) prop_xor_1 :: Bool -> Bool -> Bool prop_xor_1 = \x y -> let input = (toBit x, toBit y) in fastF input == implementation (WordJet Xor1) input where fastF = testCoreEval (specification (WordJet Xor1)) prop_xor_8 :: W.Word8 -> W.Word8 -> Bool prop_xor_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (WordJet Xor8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Xor8)) prop_xor_16 :: W.Word16 -> W.Word16 -> Bool prop_xor_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (WordJet Xor16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Xor16)) prop_xor_32 :: W.Word32 -> W.Word32 -> Bool prop_xor_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (WordJet Xor32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Xor32)) prop_xor_64 :: W.Word64 -> W.Word64 -> Bool prop_xor_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (WordJet Xor64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Xor64)) prop_maj_1 :: Bool -> Bool -> Bool -> Bool prop_maj_1 = \x y z -> let input = (toBit x, (toBit y, toBit z)) in fastF input == implementation (WordJet Maj1) input where fastF = testCoreEval (specification (WordJet Maj1)) prop_maj_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_maj_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == implementation (WordJet Maj8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Maj8)) prop_maj_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_maj_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == implementation (WordJet Maj16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Maj16)) prop_maj_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_maj_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == implementation (WordJet Maj32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Maj32)) prop_maj_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_maj_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == implementation (WordJet Maj64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Maj64)) prop_xor_xor_1 :: Bool -> Bool -> Bool -> Bool prop_xor_xor_1 = \x y z -> let input = (toBit x, (toBit y, toBit z)) in fastF input == implementation (WordJet XorXor1) input where fastF = testCoreEval (specification (WordJet XorXor1)) prop_xor_xor_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_xor_xor_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == implementation (WordJet XorXor8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor8)) prop_xor_xor_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_xor_xor_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == implementation (WordJet XorXor16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor16)) prop_xor_xor_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_xor_xor_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == implementation (WordJet XorXor32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor32)) prop_xor_xor_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_xor_xor_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == implementation (WordJet XorXor64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet XorXor64)) prop_ch_1 :: Bool -> Bool -> Bool -> Bool prop_ch_1 = \x y z -> let input = (toBit x, (toBit y, toBit z)) in fastF input == implementation (WordJet Ch1) input where fastF = testCoreEval (specification (WordJet Ch1)) prop_ch_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_ch_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == implementation (WordJet Ch8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Ch8)) prop_ch_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_ch_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == implementation (WordJet Ch16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Ch16)) prop_ch_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_ch_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == implementation (WordJet Ch32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Ch32)) prop_ch_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_ch_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == implementation (WordJet Ch64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Ch64)) prop_some_1 :: Bool -> Bool prop_some_1 = \x -> let input = toBit x in fastF input == implementation (WordJet Some1) input where fastF = testCoreEval (specification (WordJet Some1)) prop_some_8 :: W.Word8 -> Bool prop_some_8 = \x -> let input = toW8 x in fastF input == implementation (WordJet Some8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Some8)) prop_some_16 :: W.Word16 -> Bool prop_some_16 = \x -> let input = toW16 x in fastF input == implementation (WordJet Some16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Some16)) prop_some_32 :: W.Word32 -> Bool prop_some_32 = \x -> let input = toW32 x in fastF input == implementation (WordJet Some32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Some32)) prop_some_64 :: W.Word64 -> Bool prop_some_64 = \x -> let input = toW64 x in fastF input == implementation (WordJet Some64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Some64)) prop_all_8 :: W.Word8 -> Bool prop_all_8 = \x -> let input = toW8 x in fastF input == implementation (WordJet All8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet All8)) prop_all_16 :: W.Word16 -> Bool prop_all_16 = \x -> let input = toW16 x in fastF input == implementation (WordJet All16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet All16)) prop_all_32 :: W.Word32 -> Bool prop_all_32 = \x -> let input = toW32 x in fastF input == implementation (WordJet All32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet All32)) prop_all_64 :: W.Word64 -> Bool prop_all_64 = \x -> let input = toW64 x in fastF input == implementation (WordJet All64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet All64)) prop_eq_8 :: W.Word8 -> W.Word8 -> Bool prop_eq_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (WordJet Eq8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Eq8)) prop_eq_16 :: W.Word16 -> W.Word16 -> Bool prop_eq_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (WordJet Eq16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Eq16)) prop_eq_32 :: W.Word32 -> W.Word32 -> Bool prop_eq_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (WordJet Eq32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Eq32)) prop_eq_64 :: W.Word64 -> W.Word64 -> Bool prop_eq_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (WordJet Eq64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Eq64)) prop_eq_256 :: W.Word256 -> W.Word256 -> Bool prop_eq_256 = \x y -> let input = (toW256 x, toW256 y) in fastF input == implementation (WordJet Eq256) input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (WordJet Eq256)) prop_eq_diag_8 :: W.Word8 -> Bool prop_eq_diag_8 = \x -> let input = (toW8 x, toW8 x) in fastF input == implementation (WordJet Eq8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Eq8)) prop_eq_diag_16 :: W.Word16 -> Bool prop_eq_diag_16 = \x -> let input = (toW16 x, toW16 x) in fastF input == implementation (WordJet Eq16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Eq16)) prop_eq_diag_32 :: W.Word32 -> Bool prop_eq_diag_32 = \x -> let input = (toW32 x, toW32 x) in fastF input == implementation (WordJet Eq32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Eq32)) prop_eq_diag_64 :: W.Word64 -> Bool prop_eq_diag_64 = \x -> let input = (toW64 x, toW64 x) in fastF input == implementation (WordJet Eq64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Eq64)) prop_eq_diag_256 :: W.Word256 -> Bool prop_eq_diag_256 = \x -> let input = (toW256 x, toW256 x) in fastF input == implementation (WordJet Eq256) input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (WordJet Eq256)) prop_full_left_shift_8_1 :: W.Word8 -> Bool -> Bool prop_full_left_shift_8_1 = \x y -> let input = (toW8 x, toBit y) in fastF input == implementation (WordJet FullLeftShift8_1) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift8_1)) prop_full_left_shift_8_2 :: W.Word8 -> W.Word8 -> Bool prop_full_left_shift_8_2 = \x y -> let input = (toW8 x, toW2 y) in fastF input == implementation (WordJet FullLeftShift8_2) input where toW8 = toWord8 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift8_2)) prop_full_left_shift_8_4 :: W.Word8 -> W.Word8 -> Bool prop_full_left_shift_8_4 = \x y -> let input = (toW8 x, toW4 y) in fastF input == implementation (WordJet FullLeftShift8_4) input where toW8 = toWord8 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift8_4)) prop_full_left_shift_16_1 :: W.Word16 -> Bool -> Bool prop_full_left_shift_16_1 = \x y -> let input = (toW16 x, toBit y) in fastF input == implementation (WordJet FullLeftShift16_1) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_1)) prop_full_left_shift_16_2 :: W.Word16 -> W.Word8 -> Bool prop_full_left_shift_16_2 = \x y -> let input = (toW16 x, toW2 y) in fastF input == implementation (WordJet FullLeftShift16_2) input where toW16 = toWord16 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_2)) prop_full_left_shift_16_4 :: W.Word16 -> W.Word8 -> Bool prop_full_left_shift_16_4 = \x y -> let input = (toW16 x, toW4 y) in fastF input == implementation (WordJet FullLeftShift16_4) input where toW16 = toWord16 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_4)) prop_full_left_shift_16_8 :: W.Word16 -> W.Word8 -> Bool prop_full_left_shift_16_8 = \x y -> let input = (toW16 x, toW8 y) in fastF input == implementation (WordJet FullLeftShift16_8) input where toW16 = toWord16 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift16_8)) prop_full_left_shift_32_1 :: W.Word32 -> Bool -> Bool prop_full_left_shift_32_1 = \x y -> let input = (toW32 x, toBit y) in fastF input == implementation (WordJet FullLeftShift32_1) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_1)) prop_full_left_shift_32_2 :: W.Word32 -> W.Word8 -> Bool prop_full_left_shift_32_2 = \x y -> let input = (toW32 x, toW2 y) in fastF input == implementation (WordJet FullLeftShift32_2) input where toW32 = toWord32 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_2)) prop_full_left_shift_32_4 :: W.Word32 -> W.Word8 -> Bool prop_full_left_shift_32_4 = \x y -> let input = (toW32 x, toW4 y) in fastF input == implementation (WordJet FullLeftShift32_4) input where toW32 = toWord32 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_4)) prop_full_left_shift_32_8 :: W.Word32 -> W.Word8 -> Bool prop_full_left_shift_32_8 = \x y -> let input = (toW32 x, toW8 y) in fastF input == implementation (WordJet FullLeftShift32_8) input where toW32 = toWord32 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_8)) prop_full_left_shift_32_16 :: W.Word32 -> W.Word16 -> Bool prop_full_left_shift_32_16 = \x y -> let input = (toW32 x, toW16 y) in fastF input == implementation (WordJet FullLeftShift32_16) input where toW32 = toWord32 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift32_16)) prop_full_left_shift_64_1 :: W.Word64 -> Bool -> Bool prop_full_left_shift_64_1 = \x y -> let input = (toW64 x, toBit y) in fastF input == implementation (WordJet FullLeftShift64_1) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_1)) prop_full_left_shift_64_2 :: W.Word64 -> W.Word8 -> Bool prop_full_left_shift_64_2 = \x y -> let input = (toW64 x, toW2 y) in fastF input == implementation (WordJet FullLeftShift64_2) input where toW64 = toWord64 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_2)) prop_full_left_shift_64_4 :: W.Word64 -> W.Word8 -> Bool prop_full_left_shift_64_4 = \x y -> let input = (toW64 x, toW4 y) in fastF input == implementation (WordJet FullLeftShift64_4) input where toW64 = toWord64 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_4)) prop_full_left_shift_64_8 :: W.Word64 -> W.Word8 -> Bool prop_full_left_shift_64_8 = \x y -> let input = (toW64 x, toW8 y) in fastF input == implementation (WordJet FullLeftShift64_8) input where toW64 = toWord64 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_8)) prop_full_left_shift_64_16 :: W.Word64 -> W.Word16 -> Bool prop_full_left_shift_64_16 = \x y -> let input = (toW64 x, toW16 y) in fastF input == implementation (WordJet FullLeftShift64_16) input where toW64 = toWord64 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_16)) prop_full_left_shift_64_32 :: W.Word64 -> W.Word32 -> Bool prop_full_left_shift_64_32 = \x y -> let input = (toW64 x, toW32 y) in fastF input == implementation (WordJet FullLeftShift64_32) input where toW64 = toWord64 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullLeftShift64_32)) prop_full_right_shift_8_1 :: W.Word8 -> Bool -> Bool prop_full_right_shift_8_1 = \x y -> let input = (toBit y, toW8 x) in fastF input == implementation (WordJet FullRightShift8_1) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift8_1)) prop_full_right_shift_8_2 :: W.Word8 -> W.Word8 -> Bool prop_full_right_shift_8_2 = \x y -> let input = (toW2 y, toW8 x) in fastF input == implementation (WordJet FullRightShift8_2) input where toW8 = toWord8 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift8_2)) prop_full_right_shift_8_4 :: W.Word8 -> W.Word8 -> Bool prop_full_right_shift_8_4 = \x y -> let input = (toW4 y, toW8 x) in fastF input == implementation (WordJet FullRightShift8_4) input where toW8 = toWord8 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift8_4)) prop_full_right_shift_16_1 :: W.Word16 -> Bool -> Bool prop_full_right_shift_16_1 = \x y -> let input = (toBit y, toW16 x) in fastF input == implementation (WordJet FullRightShift16_1) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_1)) prop_full_right_shift_16_2 :: W.Word16 -> W.Word8 -> Bool prop_full_right_shift_16_2 = \x y -> let input = (toW2 y, toW16 x) in fastF input == implementation (WordJet FullRightShift16_2) input where toW16 = toWord16 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_2)) prop_full_right_shift_16_4 :: W.Word16 -> W.Word8 -> Bool prop_full_right_shift_16_4 = \x y -> let input = (toW4 y, toW16 x) in fastF input == implementation (WordJet FullRightShift16_4) input where toW16 = toWord16 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_4)) prop_full_right_shift_16_8 :: W.Word16 -> W.Word8 -> Bool prop_full_right_shift_16_8 = \x y -> let input = (toW8 y, toW16 x) in fastF input == implementation (WordJet FullRightShift16_8) input where toW16 = toWord16 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift16_8)) prop_full_right_shift_32_1 :: W.Word32 -> Bool -> Bool prop_full_right_shift_32_1 = \x y -> let input = (toBit y, toW32 x) in fastF input == implementation (WordJet FullRightShift32_1) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_1)) prop_full_right_shift_32_2 :: W.Word32 -> W.Word8 -> Bool prop_full_right_shift_32_2 = \x y -> let input = (toW2 y, toW32 x) in fastF input == implementation (WordJet FullRightShift32_2) input where toW32 = toWord32 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_2)) prop_full_right_shift_32_4 :: W.Word32 -> W.Word8 -> Bool prop_full_right_shift_32_4 = \x y -> let input = (toW4 y, toW32 x) in fastF input == implementation (WordJet FullRightShift32_4) input where toW32 = toWord32 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_4)) prop_full_right_shift_32_8 :: W.Word32 -> W.Word8 -> Bool prop_full_right_shift_32_8 = \x y -> let input = (toW8 y, toW32 x) in fastF input == implementation (WordJet FullRightShift32_8) input where toW32 = toWord32 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_8)) prop_full_right_shift_32_16 :: W.Word32 -> W.Word16 -> Bool prop_full_right_shift_32_16 = \x y -> let input = (toW16 y, toW32 x) in fastF input == implementation (WordJet FullRightShift32_16) input where toW32 = toWord32 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift32_16)) prop_full_right_shift_64_1 :: W.Word64 -> Bool -> Bool prop_full_right_shift_64_1 = \x y -> let input = (toBit y, toW64 x) in fastF input == implementation (WordJet FullRightShift64_1) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_1)) prop_full_right_shift_64_2 :: W.Word64 -> W.Word8 -> Bool prop_full_right_shift_64_2 = \x y -> let input = (toW2 y, toW64 x) in fastF input == implementation (WordJet FullRightShift64_2) input where toW64 = toWord64 . fromIntegral toW2 = toWord2 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_2)) prop_full_right_shift_64_4 :: W.Word64 -> W.Word8 -> Bool prop_full_right_shift_64_4 = \x y -> let input = (toW4 y, toW64 x) in fastF input == implementation (WordJet FullRightShift64_4) input where toW64 = toWord64 . fromIntegral toW4 = toWord4 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_4)) prop_full_right_shift_64_8 :: W.Word64 -> W.Word8 -> Bool prop_full_right_shift_64_8 = \x y -> let input = (toW8 y, toW64 x) in fastF input == implementation (WordJet FullRightShift64_8) input where toW64 = toWord64 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_8)) prop_full_right_shift_64_16 :: W.Word64 -> W.Word16 -> Bool prop_full_right_shift_64_16 = \x y -> let input = (toW16 y, toW64 x) in fastF input == implementation (WordJet FullRightShift64_16) input where toW64 = toWord64 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_16)) prop_full_right_shift_64_32 :: W.Word64 -> W.Word32 -> Bool prop_full_right_shift_64_32 = \x y -> let input = (toW32 y, toW64 x) in fastF input == implementation (WordJet FullRightShift64_32) input where toW64 = toWord64 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet FullRightShift64_32)) prop_leftmost_8_1 :: W.Word8 -> Bool prop_leftmost_8_1 = \x -> let input = toW8 x in fastF input == implementation (WordJet Leftmost8_1) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost8_1)) prop_leftmost_8_2 :: W.Word8 -> Bool prop_leftmost_8_2 = \x -> let input = toW8 x in fastF input == implementation (WordJet Leftmost8_2) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost8_2)) prop_leftmost_8_4 :: W.Word8 -> Bool prop_leftmost_8_4 = \x -> let input = toW8 x in fastF input == implementation (WordJet Leftmost8_4) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost8_4)) prop_leftmost_16_1 :: W.Word16 -> Bool prop_leftmost_16_1 = \x -> let input = toW16 x in fastF input == implementation (WordJet Leftmost16_1) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_1)) prop_leftmost_16_2 :: W.Word16 -> Bool prop_leftmost_16_2 = \x -> let input = toW16 x in fastF input == implementation (WordJet Leftmost16_2) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_2)) prop_leftmost_16_4 :: W.Word16 -> Bool prop_leftmost_16_4 = \x -> let input = toW16 x in fastF input == implementation (WordJet Leftmost16_4) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_4)) prop_leftmost_16_8 :: W.Word16 -> Bool prop_leftmost_16_8 = \x -> let input = toW16 x in fastF input == implementation (WordJet Leftmost16_8) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost16_8)) prop_leftmost_32_1 :: W.Word32 -> Bool prop_leftmost_32_1 = \x -> let input = toW32 x in fastF input == implementation (WordJet Leftmost32_1) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_1)) prop_leftmost_32_2 :: W.Word32 -> Bool prop_leftmost_32_2 = \x -> let input = toW32 x in fastF input == implementation (WordJet Leftmost32_2) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_2)) prop_leftmost_32_4 :: W.Word32 -> Bool prop_leftmost_32_4 = \x -> let input = toW32 x in fastF input == implementation (WordJet Leftmost32_4) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_4)) prop_leftmost_32_8 :: W.Word32 -> Bool prop_leftmost_32_8 = \x -> let input = toW32 x in fastF input == implementation (WordJet Leftmost32_8) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_8)) prop_leftmost_32_16 :: W.Word32 -> Bool prop_leftmost_32_16 = \x -> let input = toW32 x in fastF input == implementation (WordJet Leftmost32_16) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost32_16)) prop_leftmost_64_1 :: W.Word64 -> Bool prop_leftmost_64_1 = \x -> let input = toW64 x in fastF input == implementation (WordJet Leftmost64_1) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_1)) prop_leftmost_64_2 :: W.Word64 -> Bool prop_leftmost_64_2 = \x -> let input = toW64 x in fastF input == implementation (WordJet Leftmost64_2) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_2)) prop_leftmost_64_4 :: W.Word64 -> Bool prop_leftmost_64_4 = \x -> let input = toW64 x in fastF input == implementation (WordJet Leftmost64_4) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_4)) prop_leftmost_64_8 :: W.Word64 -> Bool prop_leftmost_64_8 = \x -> let input = toW64 x in fastF input == implementation (WordJet Leftmost64_8) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_8)) prop_leftmost_64_16 :: W.Word64 -> Bool prop_leftmost_64_16 = \x -> let input = toW64 x in fastF input == implementation (WordJet Leftmost64_16) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_16)) prop_leftmost_64_32 :: W.Word64 -> Bool prop_leftmost_64_32 = \x -> let input = toW64 x in fastF input == implementation (WordJet Leftmost64_32) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Leftmost64_32)) prop_rightmost_8_1 :: W.Word8 -> Bool prop_rightmost_8_1 = \x -> let input = toW8 x in fastF input == implementation (WordJet Rightmost8_1) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost8_1)) prop_rightmost_8_2 :: W.Word8 -> Bool prop_rightmost_8_2 = \x -> let input = toW8 x in fastF input == implementation (WordJet Rightmost8_2) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost8_2)) prop_rightmost_8_4 :: W.Word8 -> Bool prop_rightmost_8_4 = \x -> let input = toW8 x in fastF input == implementation (WordJet Rightmost8_4) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost8_4)) prop_rightmost_16_1 :: W.Word16 -> Bool prop_rightmost_16_1 = \x -> let input = toW16 x in fastF input == implementation (WordJet Rightmost16_1) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_1)) prop_rightmost_16_2 :: W.Word16 -> Bool prop_rightmost_16_2 = \x -> let input = toW16 x in fastF input == implementation (WordJet Rightmost16_2) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_2)) prop_rightmost_16_4 :: W.Word16 -> Bool prop_rightmost_16_4 = \x -> let input = toW16 x in fastF input == implementation (WordJet Rightmost16_4) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_4)) prop_rightmost_16_8 :: W.Word16 -> Bool prop_rightmost_16_8 = \x -> let input = toW16 x in fastF input == implementation (WordJet Rightmost16_8) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost16_8)) prop_rightmost_32_1 :: W.Word32 -> Bool prop_rightmost_32_1 = \x -> let input = toW32 x in fastF input == implementation (WordJet Rightmost32_1) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_1)) prop_rightmost_32_2 :: W.Word32 -> Bool prop_rightmost_32_2 = \x -> let input = toW32 x in fastF input == implementation (WordJet Rightmost32_2) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_2)) prop_rightmost_32_4 :: W.Word32 -> Bool prop_rightmost_32_4 = \x -> let input = toW32 x in fastF input == implementation (WordJet Rightmost32_4) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_4)) prop_rightmost_32_8 :: W.Word32 -> Bool prop_rightmost_32_8 = \x -> let input = toW32 x in fastF input == implementation (WordJet Rightmost32_8) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_8)) prop_rightmost_32_16 :: W.Word32 -> Bool prop_rightmost_32_16 = \x -> let input = toW32 x in fastF input == implementation (WordJet Rightmost32_16) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost32_16)) prop_rightmost_64_1 :: W.Word64 -> Bool prop_rightmost_64_1 = \x -> let input = toW64 x in fastF input == implementation (WordJet Rightmost64_1) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_1)) prop_rightmost_64_2 :: W.Word64 -> Bool prop_rightmost_64_2 = \x -> let input = toW64 x in fastF input == implementation (WordJet Rightmost64_2) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_2)) prop_rightmost_64_4 :: W.Word64 -> Bool prop_rightmost_64_4 = \x -> let input = toW64 x in fastF input == implementation (WordJet Rightmost64_4) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_4)) prop_rightmost_64_8 :: W.Word64 -> Bool prop_rightmost_64_8 = \x -> let input = toW64 x in fastF input == implementation (WordJet Rightmost64_8) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_8)) prop_rightmost_64_16 :: W.Word64 -> Bool prop_rightmost_64_16 = \x -> let input = toW64 x in fastF input == implementation (WordJet Rightmost64_16) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_16)) prop_rightmost_64_32 :: W.Word64 -> Bool prop_rightmost_64_32 = \x -> let input = toW64 x in fastF input == implementation (WordJet Rightmost64_32) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet Rightmost64_32)) prop_left_pad_low_1_8 :: Bool -> Bool prop_left_pad_low_1_8 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadLow1_8) input where fastF = testCoreEval (specification (WordJet LeftPadLow1_8)) prop_left_pad_low_1_16 :: Bool -> Bool prop_left_pad_low_1_16 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadLow1_16) input where fastF = testCoreEval (specification (WordJet LeftPadLow1_16)) prop_left_pad_low_8_16 :: W.Word8 -> Bool prop_left_pad_low_8_16 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftPadLow8_16) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow8_16)) prop_left_pad_low_1_32 :: Bool -> Bool prop_left_pad_low_1_32 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadLow1_32) input where fastF = testCoreEval (specification (WordJet LeftPadLow1_32)) prop_left_pad_low_8_32 :: W.Word8 -> Bool prop_left_pad_low_8_32 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftPadLow8_32) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow8_32)) prop_left_pad_low_16_32 :: W.Word16 -> Bool prop_left_pad_low_16_32 = \x -> let input = toW16 x in fastF input == implementation (WordJet LeftPadLow16_32) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow16_32)) prop_left_pad_low_1_64 :: Bool -> Bool prop_left_pad_low_1_64 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadLow1_64) input where fastF = testCoreEval (specification (WordJet LeftPadLow1_64)) prop_left_pad_low_8_64 :: W.Word8 -> Bool prop_left_pad_low_8_64 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftPadLow8_64) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow8_64)) prop_left_pad_low_16_64 :: W.Word16 -> Bool prop_left_pad_low_16_64 = \x -> let input = toW16 x in fastF input == implementation (WordJet LeftPadLow16_64) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow16_64)) prop_left_pad_low_32_64 :: W.Word32 -> Bool prop_left_pad_low_32_64 = \x -> let input = toW32 x in fastF input == implementation (WordJet LeftPadLow32_64) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadLow32_64)) prop_left_pad_high_1_8 :: Bool -> Bool prop_left_pad_high_1_8 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadHigh1_8) input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_8)) prop_left_pad_high_1_16 :: Bool -> Bool prop_left_pad_high_1_16 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadHigh1_16) input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_16)) prop_left_pad_high_8_16 :: W.Word8 -> Bool prop_left_pad_high_8_16 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftPadHigh8_16) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh8_16)) prop_left_pad_high_1_32 :: Bool -> Bool prop_left_pad_high_1_32 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadHigh1_32) input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_32)) prop_left_pad_high_8_32 :: W.Word8 -> Bool prop_left_pad_high_8_32 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftPadHigh8_32) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh8_32)) prop_left_pad_high_16_32 :: W.Word16 -> Bool prop_left_pad_high_16_32 = \x -> let input = toW16 x in fastF input == implementation (WordJet LeftPadHigh16_32) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh16_32)) prop_left_pad_high_1_64 :: Bool -> Bool prop_left_pad_high_1_64 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftPadHigh1_64) input where fastF = testCoreEval (specification (WordJet LeftPadHigh1_64)) prop_left_pad_high_8_64 :: W.Word8 -> Bool prop_left_pad_high_8_64 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftPadHigh8_64) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh8_64)) prop_left_pad_high_16_64 :: W.Word16 -> Bool prop_left_pad_high_16_64 = \x -> let input = toW16 x in fastF input == implementation (WordJet LeftPadHigh16_64) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh16_64)) prop_left_pad_high_32_64 :: W.Word32 -> Bool prop_left_pad_high_32_64 = \x -> let input = toW32 x in fastF input == implementation (WordJet LeftPadHigh32_64) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftPadHigh32_64)) prop_left_extend_1_8 :: Bool -> Bool prop_left_extend_1_8 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftExtend1_8) input where fastF = testCoreEval (specification (WordJet LeftExtend1_8)) prop_left_extend_1_16 :: Bool -> Bool prop_left_extend_1_16 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftExtend1_16) input where fastF = testCoreEval (specification (WordJet LeftExtend1_16)) prop_left_extend_8_16 :: W.Word8 -> Bool prop_left_extend_8_16 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftExtend8_16) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend8_16)) prop_left_extend_1_32 :: Bool -> Bool prop_left_extend_1_32 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftExtend1_32) input where fastF = testCoreEval (specification (WordJet LeftExtend1_32)) prop_left_extend_8_32 :: W.Word8 -> Bool prop_left_extend_8_32 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftExtend8_32) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend8_32)) prop_left_extend_16_32 :: W.Word16 -> Bool prop_left_extend_16_32 = \x -> let input = toW16 x in fastF input == implementation (WordJet LeftExtend16_32) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend16_32)) prop_left_extend_1_64 :: Bool -> Bool prop_left_extend_1_64 = \x -> let input = toBit x in fastF input == implementation (WordJet LeftExtend1_64) input where fastF = testCoreEval (specification (WordJet LeftExtend1_64)) prop_left_extend_8_64 :: W.Word8 -> Bool prop_left_extend_8_64 = \x -> let input = toW8 x in fastF input == implementation (WordJet LeftExtend8_64) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend8_64)) prop_left_extend_16_64 :: W.Word16 -> Bool prop_left_extend_16_64 = \x -> let input = toW16 x in fastF input == implementation (WordJet LeftExtend16_64) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend16_64)) prop_left_extend_32_64 :: W.Word32 -> Bool prop_left_extend_32_64 = \x -> let input = toW32 x in fastF input == implementation (WordJet LeftExtend32_64) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftExtend32_64)) prop_right_pad_low_1_8 :: Bool -> Bool prop_right_pad_low_1_8 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadLow1_8) input where fastF = testCoreEval (specification (WordJet RightPadLow1_8)) prop_right_pad_low_1_16 :: Bool -> Bool prop_right_pad_low_1_16 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadLow1_16) input where fastF = testCoreEval (specification (WordJet RightPadLow1_16)) prop_right_pad_low_8_16 :: W.Word8 -> Bool prop_right_pad_low_8_16 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightPadLow8_16) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow8_16)) prop_right_pad_low_1_32 :: Bool -> Bool prop_right_pad_low_1_32 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadLow1_32) input where fastF = testCoreEval (specification (WordJet RightPadLow1_32)) prop_right_pad_low_8_32 :: W.Word8 -> Bool prop_right_pad_low_8_32 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightPadLow8_32) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow8_32)) prop_right_pad_low_16_32 :: W.Word16 -> Bool prop_right_pad_low_16_32 = \x -> let input = toW16 x in fastF input == implementation (WordJet RightPadLow16_32) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow16_32)) prop_right_pad_low_1_64 :: Bool -> Bool prop_right_pad_low_1_64 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadLow1_64) input where fastF = testCoreEval (specification (WordJet RightPadLow1_64)) prop_right_pad_low_8_64 :: W.Word8 -> Bool prop_right_pad_low_8_64 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightPadLow8_64) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow8_64)) prop_right_pad_low_16_64 :: W.Word16 -> Bool prop_right_pad_low_16_64 = \x -> let input = toW16 x in fastF input == implementation (WordJet RightPadLow16_64) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow16_64)) prop_right_pad_low_32_64 :: W.Word32 -> Bool prop_right_pad_low_32_64 = \x -> let input = toW32 x in fastF input == implementation (WordJet RightPadLow32_64) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadLow32_64)) prop_right_pad_high_1_8 :: Bool -> Bool prop_right_pad_high_1_8 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadHigh1_8) input where fastF = testCoreEval (specification (WordJet RightPadHigh1_8)) prop_right_pad_high_1_16 :: Bool -> Bool prop_right_pad_high_1_16 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadHigh1_16) input where fastF = testCoreEval (specification (WordJet RightPadHigh1_16)) prop_right_pad_high_8_16 :: W.Word8 -> Bool prop_right_pad_high_8_16 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightPadHigh8_16) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh8_16)) prop_right_pad_high_1_32 :: Bool -> Bool prop_right_pad_high_1_32 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadHigh1_32) input where fastF = testCoreEval (specification (WordJet RightPadHigh1_32)) prop_right_pad_high_8_32 :: W.Word8 -> Bool prop_right_pad_high_8_32 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightPadHigh8_32) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh8_32)) prop_right_pad_high_16_32 :: W.Word16 -> Bool prop_right_pad_high_16_32 = \x -> let input = toW16 x in fastF input == implementation (WordJet RightPadHigh16_32) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh16_32)) prop_right_pad_high_1_64 :: Bool -> Bool prop_right_pad_high_1_64 = \x -> let input = toBit x in fastF input == implementation (WordJet RightPadHigh1_64) input where fastF = testCoreEval (specification (WordJet RightPadHigh1_64)) prop_right_pad_high_8_64 :: W.Word8 -> Bool prop_right_pad_high_8_64 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightPadHigh8_64) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh8_64)) prop_right_pad_high_16_64 :: W.Word16 -> Bool prop_right_pad_high_16_64 = \x -> let input = toW16 x in fastF input == implementation (WordJet RightPadHigh16_64) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh16_64)) prop_right_pad_high_32_64 :: W.Word32 -> Bool prop_right_pad_high_32_64 = \x -> let input = toW32 x in fastF input == implementation (WordJet RightPadHigh32_64) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightPadHigh32_64)) prop_right_extend_8_16 :: W.Word8 -> Bool prop_right_extend_8_16 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightExtend8_16) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend8_16)) prop_right_extend_8_32 :: W.Word8 -> Bool prop_right_extend_8_32 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightExtend8_32) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend8_32)) prop_right_extend_16_32 :: W.Word16 -> Bool prop_right_extend_16_32 = \x -> let input = toW16 x in fastF input == implementation (WordJet RightExtend16_32) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend16_32)) prop_right_extend_8_64 :: W.Word8 -> Bool prop_right_extend_8_64 = \x -> let input = toW8 x in fastF input == implementation (WordJet RightExtend8_64) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend8_64)) prop_right_extend_16_64 :: W.Word16 -> Bool prop_right_extend_16_64 = \x -> let input = toW16 x in fastF input == implementation (WordJet RightExtend16_64) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend16_64)) prop_right_extend_32_64 :: W.Word32 -> Bool prop_right_extend_32_64 = \x -> let input = toW32 x in fastF input == implementation (WordJet RightExtend32_64) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightExtend32_64)) prop_left_shift_with_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_left_shift_with_8 = \w x y -> let input = (toBit w, (toW4 x, toW8 y)) in fastF input == implementation (WordJet LeftShiftWith8) input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith8)) prop_left_shift_with_16 :: Bool -> W.Word8 -> W.Word16 -> Bool prop_left_shift_with_16 = \w x y -> let input = (toBit w, (toW4 x, toW16 y)) in fastF input == implementation (WordJet LeftShiftWith16) input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith16)) prop_left_shift_with_32 :: Bool -> W.Word8 -> W.Word32 -> Bool prop_left_shift_with_32 = \w x y -> let input = (toBit w, (toW8 x, toW32 y)) in fastF input == implementation (WordJet LeftShiftWith32) input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith32)) prop_left_shift_with_64 :: Bool -> W.Word8 -> W.Word64 -> Bool prop_left_shift_with_64 = \w x y -> let input = (toBit w, (toW8 x, toW64 y)) in fastF input == implementation (WordJet LeftShiftWith64) input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShiftWith64)) prop_left_shift_8 :: W.Word8 -> W.Word8 -> Bool prop_left_shift_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == implementation (WordJet LeftShift8) input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift8)) prop_left_shift_16 :: W.Word8 -> W.Word16 -> Bool prop_left_shift_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == implementation (WordJet LeftShift16) input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift16)) prop_left_shift_32 :: W.Word8 -> W.Word32 -> Bool prop_left_shift_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == implementation (WordJet LeftShift32) input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift32)) prop_left_shift_64 :: W.Word8 -> W.Word64 -> Bool prop_left_shift_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == implementation (WordJet LeftShift64) input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet LeftShift64)) prop_right_shift_with_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_right_shift_with_8 = \w x y -> let input = (toBit w, (toW4 x, toW8 y)) in fastF input == implementation (WordJet RightShiftWith8) input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith8)) prop_right_shift_with_16 :: Bool -> W.Word8 -> W.Word16 -> Bool prop_right_shift_with_16 = \w x y -> let input = (toBit w, (toW4 x, toW16 y)) in fastF input == implementation (WordJet RightShiftWith16) input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith16)) prop_right_shift_with_32 :: Bool -> W.Word8 -> W.Word32 -> Bool prop_right_shift_with_32 = \w x y -> let input = (toBit w, (toW8 x, toW32 y)) in fastF input == implementation (WordJet RightShiftWith32) input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith32)) prop_right_shift_with_64 :: Bool -> W.Word8 -> W.Word64 -> Bool prop_right_shift_with_64 = \w x y -> let input = (toBit w, (toW8 x, toW64 y)) in fastF input == implementation (WordJet RightShiftWith64) input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet RightShiftWith64)) prop_right_shift_8 :: W.Word8 -> W.Word8 -> Bool prop_right_shift_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == implementation (WordJet RightShift8) input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift8)) prop_right_shift_16 :: W.Word8 -> W.Word16 -> Bool prop_right_shift_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == implementation (WordJet RightShift16) input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift16)) prop_right_shift_32 :: W.Word8 -> W.Word32 -> Bool prop_right_shift_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == implementation (WordJet RightShift32) input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift32)) prop_right_shift_64 :: W.Word8 -> W.Word64 -> Bool prop_right_shift_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == implementation (WordJet RightShift64) input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet RightShift64)) prop_left_rotate_8 :: W.Word8 -> W.Word8 -> Bool prop_left_rotate_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == implementation (WordJet LeftRotate8) input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate8)) prop_left_rotate_16 :: W.Word8 -> W.Word16 -> Bool prop_left_rotate_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == implementation (WordJet LeftRotate16) input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate16)) prop_left_rotate_32 :: W.Word8 -> W.Word32 -> Bool prop_left_rotate_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == implementation (WordJet LeftRotate32) input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate32)) prop_left_rotate_64 :: W.Word8 -> W.Word64 -> Bool prop_left_rotate_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == implementation (WordJet LeftRotate64) input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet LeftRotate64)) prop_right_rotate_8 :: W.Word8 -> W.Word8 -> Bool prop_right_rotate_8 = \x y -> let input = (toW4 x, toW8 y) in fastF input == implementation (WordJet RightRotate8) input where toW4 = toWord4 . fromIntegral toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate8)) prop_right_rotate_16 :: W.Word8 -> W.Word16 -> Bool prop_right_rotate_16 = \x y -> let input = (toW4 x, toW16 y) in fastF input == implementation (WordJet RightRotate16) input where toW4 = toWord4 . fromIntegral toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate16)) prop_right_rotate_32 :: W.Word8 -> W.Word32 -> Bool prop_right_rotate_32 = \x y -> let input = (toW8 x, toW32 y) in fastF input == implementation (WordJet RightRotate32) input where toW8 = toWord8 . fromIntegral toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate32)) prop_right_rotate_64 :: W.Word8 -> W.Word64 -> Bool prop_right_rotate_64 = \x y -> let input = (toW8 x, toW64 y) in fastF input == implementation (WordJet RightRotate64) input where toW8 = toWord8 . fromIntegral toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (WordJet RightRotate64)) assert_one_8 :: Assertion assert_one_8 = fastF () @=? implementation (ArithJet One8) () where fastF = testCoreEval (specification (ArithJet One8)) assert_one_16 :: Assertion assert_one_16 = fastF () @=? implementation (ArithJet One16) () where fastF = testCoreEval (specification (ArithJet One16)) assert_one_32 :: Assertion assert_one_32 = fastF () @=? implementation (ArithJet One32) () where fastF = testCoreEval (specification (ArithJet One32)) assert_one_64 :: Assertion assert_one_64 = fastF () @=? implementation (ArithJet One64) () where fastF = testCoreEval (specification (ArithJet One64)) prop_add_8 :: W.Word8 -> W.Word8 -> Bool prop_add_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Add8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Add8)) prop_add_16 :: W.Word16 -> W.Word16 -> Bool prop_add_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Add16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Add16)) prop_add_32 :: W.Word32 -> W.Word32 -> Bool prop_add_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Add32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Add32)) prop_add_64 :: W.Word64 -> W.Word64 -> Bool prop_add_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Add64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Add64)) prop_full_add_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_full_add_8 = \c x y -> let input = (toBit c, (toW8 x, toW8 y)) in fastF input == implementation (ArithJet FullAdd8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd8)) prop_full_add_16 :: Bool -> W.Word16 -> W.Word16 -> Bool prop_full_add_16 = \c x y -> let input = (toBit c, (toW16 x, toW16 y)) in fastF input == implementation (ArithJet FullAdd16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd16)) prop_full_add_32 :: Bool -> W.Word32 -> W.Word32 -> Bool prop_full_add_32 = \c x y -> let input = (toBit c, (toW32 x, toW32 y)) in fastF input == implementation (ArithJet FullAdd32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd32)) prop_full_add_64 :: Bool -> W.Word64 -> W.Word64 -> Bool prop_full_add_64 = \c x y -> let input = (toBit c, (toW64 x, toW64 y)) in fastF input == implementation (ArithJet FullAdd64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullAdd64)) prop_full_increment_8 :: Bool -> W.Word8 -> Bool prop_full_increment_8 = \b x -> let input = (toBit b, toW8 x) in fastF input == implementation (ArithJet FullIncrement8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement8)) prop_full_increment_16 :: Bool -> W.Word16 -> Bool prop_full_increment_16 = \b x -> let input = (toBit b, toW16 x) in fastF input == implementation (ArithJet FullIncrement16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement16)) prop_full_increment_32 :: Bool -> W.Word32 -> Bool prop_full_increment_32 = \b x -> let input = (toBit b, toW32 x) in fastF input == implementation (ArithJet FullIncrement32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement32)) prop_full_increment_64 :: Bool -> W.Word64 -> Bool prop_full_increment_64 = \b x -> let input = (toBit b, toW64 x) in fastF input == implementation (ArithJet FullIncrement64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullIncrement64)) assert_full_increment_max_8 :: Assertion assert_full_increment_max_8 = fastF input @=? implementation (ArithJet FullIncrement8) input where input = (toBit True, toWord8 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement8)) assert_full_increment_max_16 :: Assertion assert_full_increment_max_16 = fastF input @=? implementation (ArithJet FullIncrement16) input where input = (toBit True, toWord16 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement16)) assert_full_increment_max_32 :: Assertion assert_full_increment_max_32 = fastF input @=? implementation (ArithJet FullIncrement32) input where input = (toBit True, toWord32 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement32)) assert_full_increment_max_64 :: Assertion assert_full_increment_max_64 = fastF input @=? implementation (ArithJet FullIncrement64) input where input = (toBit True, toWord64 (-1)) fastF = testCoreEval (specification (ArithJet FullIncrement64)) prop_increment_8 :: W.Word8 -> Bool prop_increment_8 = \x -> let input = toW8 x in fastF input == implementation (ArithJet Increment8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment8)) prop_increment_16 :: W.Word16 -> Bool prop_increment_16 = \x -> let input = toW16 x in fastF input == implementation (ArithJet Increment16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment16)) prop_increment_32 :: W.Word32 -> Bool prop_increment_32 = \x -> let input = toW32 x in fastF input == implementation (ArithJet Increment32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment32)) prop_increment_64 :: W.Word64 -> Bool prop_increment_64 = \x -> let input = toW64 x in fastF input == implementation (ArithJet Increment64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Increment64)) assert_increment_max_8 :: Assertion assert_increment_max_8 = fastF input @=? implementation (ArithJet Increment8) input where input = toWord8 (-1) fastF = testCoreEval (specification (ArithJet Increment8)) assert_increment_max_16 :: Assertion assert_increment_max_16 = fastF input @=? implementation (ArithJet Increment16) input where input = toWord16 (-1) fastF = testCoreEval (specification (ArithJet Increment16)) assert_increment_max_32 :: Assertion assert_increment_max_32 = fastF input @=? implementation (ArithJet Increment32) input where input = toWord32 (-1) fastF = testCoreEval (specification (ArithJet Increment32)) assert_increment_max_64 :: Assertion assert_increment_max_64 = fastF input @=? implementation (ArithJet Increment64) input where input = toWord64 (-1) fastF = testCoreEval (specification (ArithJet Increment64)) prop_subtract_8 :: W.Word8 -> W.Word8 -> Bool prop_subtract_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Subtract8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract8)) prop_subtract_16 :: W.Word16 -> W.Word16 -> Bool prop_subtract_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Subtract16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract16)) prop_subtract_32 :: W.Word32 -> W.Word32 -> Bool prop_subtract_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Subtract32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract32)) prop_subtract_64 :: W.Word64 -> W.Word64 -> Bool prop_subtract_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Subtract64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Subtract64)) prop_full_subtract_8 :: Bool -> W.Word8 -> W.Word8 -> Bool prop_full_subtract_8 = \c x y -> let input = (toBit c, (toW8 x, toW8 y)) in fastF input == implementation (ArithJet FullSubtract8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract8)) prop_full_subtract_16 :: Bool -> W.Word16 -> W.Word16 -> Bool prop_full_subtract_16 = \c x y -> let input = (toBit c, (toW16 x, toW16 y)) in fastF input == implementation (ArithJet FullSubtract16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract16)) prop_full_subtract_32 :: Bool -> W.Word32 -> W.Word32 -> Bool prop_full_subtract_32 = \c x y -> let input = (toBit c, (toW32 x, toW32 y)) in fastF input == implementation (ArithJet FullSubtract32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract32)) prop_full_subtract_64 :: Bool -> W.Word64 -> W.Word64 -> Bool prop_full_subtract_64 = \c x y -> let input = (toBit c, (toW64 x, toW64 y)) in fastF input == implementation (ArithJet FullSubtract64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullSubtract64)) prop_full_decrement_8 :: Bool -> W.Word8 -> Bool prop_full_decrement_8 = \b x -> let input = (toBit b, toW8 x) in fastF input == implementation (ArithJet FullDecrement8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement8)) prop_full_decrement_16 :: Bool -> W.Word16 -> Bool prop_full_decrement_16 = \b x -> let input = (toBit b, toW16 x) in fastF input == implementation (ArithJet FullDecrement16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement16)) prop_full_decrement_32 :: Bool -> W.Word32 -> Bool prop_full_decrement_32 = \b x -> let input = (toBit b, toW32 x) in fastF input == implementation (ArithJet FullDecrement32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement32)) prop_full_decrement_64 :: Bool -> W.Word64 -> Bool prop_full_decrement_64 = \b x -> let input = (toBit b, toW64 x) in fastF input == implementation (ArithJet FullDecrement64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullDecrement64)) assert_full_decrement_zero_8 :: Assertion assert_full_decrement_zero_8 = fastF input @=? implementation (ArithJet FullDecrement8) input where input = (toBit True, toWord8 0) fastF = testCoreEval (specification (ArithJet FullDecrement8)) assert_full_decrement_zero_16 :: Assertion assert_full_decrement_zero_16 = fastF input @=? implementation (ArithJet FullDecrement16) input where input = (toBit True, toWord16 0) fastF = testCoreEval (specification (ArithJet FullDecrement16)) assert_full_decrement_zero_32 :: Assertion assert_full_decrement_zero_32 = fastF input @=? implementation (ArithJet FullDecrement32) input where input = (toBit True, toWord32 0) fastF = testCoreEval (specification (ArithJet FullDecrement32)) assert_full_decrement_zero_64 :: Assertion assert_full_decrement_zero_64 = fastF input @=? implementation (ArithJet FullDecrement64) input where input = (toBit True, toWord64 0) fastF = testCoreEval (specification (ArithJet FullDecrement64)) prop_decrement_8 :: W.Word8 -> Bool prop_decrement_8 = \x -> let input = toW8 x in fastF input == implementation (ArithJet Decrement8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement8)) prop_decrement_16 :: W.Word16 -> Bool prop_decrement_16 = \x -> let input = toW16 x in fastF input == implementation (ArithJet Decrement16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement16)) prop_decrement_32 :: W.Word32 -> Bool prop_decrement_32 = \x -> let input = toW32 x in fastF input == implementation (ArithJet Decrement32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement32)) prop_decrement_64 :: W.Word64 -> Bool prop_decrement_64 = \x -> let input = toW64 x in fastF input == implementation (ArithJet Decrement64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Decrement64)) assert_decrement_zero_8 :: Assertion assert_decrement_zero_8 = fastF input @=? implementation (ArithJet Decrement8) input where input = toWord8 0 fastF = testCoreEval (specification (ArithJet Decrement8)) assert_decrement_zero_16 :: Assertion assert_decrement_zero_16 = fastF input @=? implementation (ArithJet Decrement16) input where input = toWord16 0 fastF = testCoreEval (specification (ArithJet Decrement16)) assert_decrement_zero_32 :: Assertion assert_decrement_zero_32 = fastF input @=? implementation (ArithJet Decrement32) input where input = toWord32 0 fastF = testCoreEval (specification (ArithJet Decrement32)) assert_decrement_zero_64 :: Assertion assert_decrement_zero_64 = fastF input @=? implementation (ArithJet Decrement64) input where input = toWord64 0 fastF = testCoreEval (specification (ArithJet Decrement64)) prop_negate_8 :: W.Word8 -> Bool prop_negate_8 = \x -> let input = toW8 x in fastF input == implementation (ArithJet Negate8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate8)) prop_negate_16 :: W.Word16 -> Bool prop_negate_16 = \x -> let input = toW16 x in fastF input == implementation (ArithJet Negate16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate16)) prop_negate_32 :: W.Word32 -> Bool prop_negate_32 = \x -> let input = toW32 x in fastF input == implementation (ArithJet Negate32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate32)) prop_negate_64 :: W.Word64 -> Bool prop_negate_64 = \x -> let input = toW64 x in fastF input == implementation (ArithJet Negate64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Negate64)) prop_multiply_8 :: W.Word8 -> W.Word8 -> Bool prop_multiply_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Multiply8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply8)) prop_multiply_16 :: W.Word16 -> W.Word16 -> Bool prop_multiply_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Multiply16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply16)) prop_multiply_32 :: W.Word32 -> W.Word32 -> Bool prop_multiply_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Multiply32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply32)) prop_multiply_64 :: W.Word64 -> W.Word64 -> Bool prop_multiply_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Multiply64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Multiply64)) prop_full_multiply_8 :: W.Word8 -> W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_full_multiply_8 = \x y z w -> let input = ((toW8 x, toW8 y), (toW8 z, toW8 w)) in fastF input == implementation (ArithJet FullMultiply8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply8)) prop_full_multiply_16 :: W.Word16 -> W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_full_multiply_16 = \x y z w -> let input = ((toW16 x, toW16 y), (toW16 z, toW16 w)) in fastF input == implementation (ArithJet FullMultiply16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply16)) prop_full_multiply_32 :: W.Word32 -> W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_full_multiply_32 = \x y z w -> let input = ((toW32 x, toW32 y), (toW32 z, toW32 w)) in fastF input == implementation (ArithJet FullMultiply32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply32)) prop_full_multiply_64 :: W.Word64 -> W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_full_multiply_64 = \x y z w -> let input = ((toW64 x, toW64 y), (toW64 z, toW64 w)) in fastF input == implementation (ArithJet FullMultiply64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet FullMultiply64)) prop_is_zero_8 :: W.Word8 -> Bool prop_is_zero_8 = \x -> let input = toW8 x in fastF input == implementation (ArithJet IsZero8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero8)) prop_is_zero_16 :: W.Word16 -> Bool prop_is_zero_16 = \x -> let input = toW16 x in fastF input == implementation (ArithJet IsZero16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero16)) prop_is_zero_32 :: W.Word32 -> Bool prop_is_zero_32 = \x -> let input = toW32 x in fastF input == implementation (ArithJet IsZero32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero32)) prop_is_zero_64 :: W.Word64 -> Bool prop_is_zero_64 = \x -> let input = toW64 x in fastF input == implementation (ArithJet IsZero64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet IsZero64)) assert_zero_is_zero_8 :: Assertion assert_zero_is_zero_8 = fastF input @=? implementation (ArithJet IsZero8) input where input = toWord8 0 fastF = testCoreEval (specification (ArithJet IsZero8)) assert_zero_is_zero_16 :: Assertion assert_zero_is_zero_16 = fastF input @=? implementation (ArithJet IsZero16) input where input = toWord16 0 fastF = testCoreEval (specification (ArithJet IsZero16)) assert_zero_is_zero_32 :: Assertion assert_zero_is_zero_32 = fastF input @=? implementation (ArithJet IsZero32) input where input = toWord32 0 fastF = testCoreEval (specification (ArithJet IsZero32)) assert_zero_is_zero_64 :: Assertion assert_zero_is_zero_64 = fastF input @=? implementation (ArithJet IsZero64) input where input = toWord64 0 fastF = testCoreEval (specification (ArithJet IsZero64)) prop_is_one_8 :: W.Word8 -> Bool prop_is_one_8 = \x -> let input = toW8 x in fastF input == implementation (ArithJet IsOne8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne8)) prop_is_one_16 :: W.Word16 -> Bool prop_is_one_16 = \x -> let input = toW16 x in fastF input == implementation (ArithJet IsOne16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne16)) prop_is_one_32 :: W.Word32 -> Bool prop_is_one_32 = \x -> let input = toW32 x in fastF input == implementation (ArithJet IsOne32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne32)) prop_is_one_64 :: W.Word64 -> Bool prop_is_one_64 = \x -> let input = toW64 x in fastF input == implementation (ArithJet IsOne64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet IsOne64)) assert_one_is_one_8 :: Assertion assert_one_is_one_8 = fastF input @=? implementation (ArithJet IsOne8) input where input = toWord8 1 fastF = testCoreEval (specification (ArithJet IsOne8)) assert_one_is_one_16 :: Assertion assert_one_is_one_16 = fastF input @=? implementation (ArithJet IsOne16) input where input = toWord16 1 fastF = testCoreEval (specification (ArithJet IsOne16)) assert_one_is_one_32 :: Assertion assert_one_is_one_32 = fastF input @=? implementation (ArithJet IsOne32) input where input = toWord32 1 fastF = testCoreEval (specification (ArithJet IsOne32)) assert_one_is_one_64 :: Assertion assert_one_is_one_64 = fastF input @=? implementation (ArithJet IsOne64) input where input = toWord64 1 fastF = testCoreEval (specification (ArithJet IsOne64)) prop_le_8 :: W.Word8 -> W.Word8 -> Bool prop_le_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Le8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Le8)) prop_le_16 :: W.Word16 -> W.Word16 -> Bool prop_le_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Le16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Le16)) prop_le_32 :: W.Word32 -> W.Word32 -> Bool prop_le_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Le32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Le32)) prop_le_64 :: W.Word64 -> W.Word64 -> Bool prop_le_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Le64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Le64)) prop_le_diag_8 :: W.Word8 -> Bool prop_le_diag_8 = \x -> let input = (toW8 x, toW8 x) in fastF input == implementation (ArithJet Le8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Le8)) prop_le_diag_16 :: W.Word16 -> Bool prop_le_diag_16 = \x -> let input = (toW16 x, toW16 x) in fastF input == implementation (ArithJet Le16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Le16)) prop_le_diag_32 :: W.Word32 -> Bool prop_le_diag_32 = \x -> let input = (toW32 x, toW32 x) in fastF input == implementation (ArithJet Le32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Le32)) prop_le_diag_64 :: W.Word64 -> Bool prop_le_diag_64 = \x -> let input = (toW64 x, toW64 x) in fastF input == implementation (ArithJet Le64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Le64)) prop_lt_8 :: W.Word8 -> W.Word8 -> Bool prop_lt_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Lt8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt8)) prop_lt_16 :: W.Word16 -> W.Word16 -> Bool prop_lt_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Lt16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt16)) prop_lt_32 :: W.Word32 -> W.Word32 -> Bool prop_lt_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Lt32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt32)) prop_lt_64 :: W.Word64 -> W.Word64 -> Bool prop_lt_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Lt64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt64)) prop_lt_diag_8 :: W.Word8 -> Bool prop_lt_diag_8 = \x -> let input = (toW8 x, toW8 x) in fastF input == implementation (ArithJet Lt8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt8)) prop_lt_diag_16 :: W.Word16 -> Bool prop_lt_diag_16 = \x -> let input = (toW16 x, toW16 x) in fastF input == implementation (ArithJet Lt16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt16)) prop_lt_diag_32 :: W.Word32 -> Bool prop_lt_diag_32 = \x -> let input = (toW32 x, toW32 x) in fastF input == implementation (ArithJet Lt32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt32)) prop_lt_diag_64 :: W.Word64 -> Bool prop_lt_diag_64 = \x -> let input = (toW64 x, toW64 x) in fastF input == implementation (ArithJet Lt64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Lt64)) prop_min_8 :: W.Word8 -> W.Word8 -> Bool prop_min_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Min8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Min8)) prop_min_16 :: W.Word16 -> W.Word16 -> Bool prop_min_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Min16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Min16)) prop_min_32 :: W.Word32 -> W.Word32 -> Bool prop_min_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Min32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Min32)) prop_min_64 :: W.Word64 -> W.Word64 -> Bool prop_min_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Min64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Min64)) prop_max_8 :: W.Word8 -> W.Word8 -> Bool prop_max_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Max8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Max8)) prop_max_16 :: W.Word16 -> W.Word16 -> Bool prop_max_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Max16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Max16)) prop_max_32 :: W.Word32 -> W.Word32 -> Bool prop_max_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Max32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Max32)) prop_max_64 :: W.Word64 -> W.Word64 -> Bool prop_max_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Max64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Max64)) prop_median_8 :: W.Word8 -> W.Word8 -> W.Word8 -> Bool prop_median_8 = \x y z -> let input = (toW8 x, (toW8 y, toW8 z)) in fastF input == implementation (ArithJet Median8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Median8)) prop_median_16 :: W.Word16 -> W.Word16 -> W.Word16 -> Bool prop_median_16 = \x y z -> let input = (toW16 x, (toW16 y, toW16 z)) in fastF input == implementation (ArithJet Median16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Median16)) prop_median_32 :: W.Word32 -> W.Word32 -> W.Word32 -> Bool prop_median_32 = \x y z -> let input = (toW32 x, (toW32 y, toW32 z)) in fastF input == implementation (ArithJet Median32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Median32)) prop_median_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_median_64 = \x y z -> let input = (toW64 x, (toW64 y, toW64 z)) in fastF input == implementation (ArithJet Median64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Median64)) prop_div_mod_8 :: W.Word8 -> W.Word8 -> Bool prop_div_mod_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet DivMod8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod8)) prop_div_mod_16 :: W.Word16 -> W.Word16 -> Bool prop_div_mod_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet DivMod16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod16)) prop_div_mod_32 :: W.Word32 -> W.Word32 -> Bool prop_div_mod_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet DivMod32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod32)) prop_div_mod_64 :: W.Word64 -> W.Word64 -> Bool prop_div_mod_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet DivMod64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod64)) prop_divide_8 :: W.Word8 -> W.Word8 -> Bool prop_divide_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Divide8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide8)) prop_divide_16 :: W.Word16 -> W.Word16 -> Bool prop_divide_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Divide16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide16)) prop_divide_32 :: W.Word32 -> W.Word32 -> Bool prop_divide_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Divide32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide32)) prop_divide_64 :: W.Word64 -> W.Word64 -> Bool prop_divide_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Divide64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide64)) prop_modulo_8 :: W.Word8 -> W.Word8 -> Bool prop_modulo_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Modulo8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo8)) prop_modulo_16 :: W.Word16 -> W.Word16 -> Bool prop_modulo_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Modulo16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo16)) prop_modulo_32 :: W.Word32 -> W.Word32 -> Bool prop_modulo_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Modulo32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo32)) prop_modulo_64 :: W.Word64 -> W.Word64 -> Bool prop_modulo_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Modulo64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo64)) prop_divides_8 :: W.Word8 -> W.Word8 -> Bool prop_divides_8 = \x y -> let input = (toW8 x, toW8 y) in fastF input == implementation (ArithJet Divides8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides8)) prop_divides_16 :: W.Word16 -> W.Word16 -> Bool prop_divides_16 = \x y -> let input = (toW16 x, toW16 y) in fastF input == implementation (ArithJet Divides16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides16)) prop_divides_32 :: W.Word32 -> W.Word32 -> Bool prop_divides_32 = \x y -> let input = (toW32 x, toW32 y) in fastF input == implementation (ArithJet Divides32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides32)) prop_divides_64 :: W.Word64 -> W.Word64 -> Bool prop_divides_64 = \x y -> let input = (toW64 x, toW64 y) in fastF input == implementation (ArithJet Divides64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides64)) prop_div_mod_zero_8 :: W.Word8 -> Bool prop_div_mod_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == implementation (ArithJet DivMod8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod8)) prop_div_mod_zero_16 :: W.Word16 -> Bool prop_div_mod_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == implementation (ArithJet DivMod16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod16)) prop_div_mod_zero_32 :: W.Word32 -> Bool prop_div_mod_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == implementation (ArithJet DivMod32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod32)) prop_div_mod_zero_64 :: W.Word64 -> Bool prop_div_mod_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == implementation (ArithJet DivMod64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod64)) prop_divide_zero_8 :: W.Word8 -> Bool prop_divide_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == implementation (ArithJet Divide8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide8)) prop_divide_zero_16 :: W.Word16 -> Bool prop_divide_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == implementation (ArithJet Divide16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide16)) prop_divide_zero_32 :: W.Word32 -> Bool prop_divide_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == implementation (ArithJet Divide32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide32)) prop_divide_zero_64 :: W.Word64 -> Bool prop_divide_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == implementation (ArithJet Divide64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divide64)) prop_modulo_zero_8 :: W.Word8 -> Bool prop_modulo_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == implementation (ArithJet Modulo8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo8)) prop_modulo_zero_16 :: W.Word16 -> Bool prop_modulo_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == implementation (ArithJet Modulo16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo16)) prop_modulo_zero_32 :: W.Word32 -> Bool prop_modulo_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == implementation (ArithJet Modulo32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo32)) prop_modulo_zero_64 :: W.Word64 -> Bool prop_modulo_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == implementation (ArithJet Modulo64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Modulo64)) prop_divides_zero_8 :: W.Word8 -> Bool prop_divides_zero_8 = \x -> let input = (toW8 x, toW8 0) in fastF input == implementation (ArithJet Divides8) input where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides8)) prop_divides_zero_16 :: W.Word16 -> Bool prop_divides_zero_16 = \x -> let input = (toW16 x, toW16 0) in fastF input == implementation (ArithJet Divides16) input where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides16)) prop_divides_zero_32 :: W.Word32 -> Bool prop_divides_zero_32 = \x -> let input = (toW32 x, toW32 0) in fastF input == implementation (ArithJet Divides32) input where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides32)) prop_divides_zero_64 :: W.Word64 -> Bool prop_divides_zero_64 = \x -> let input = (toW64 x, toW64 0) in fastF input == implementation (ArithJet Divides64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet Divides64)) prop_div_mod_128_64 :: W.Word64 -> W.Word64 -> W.Word64 -> Property prop_div_mod_128_64 = \xh0 xl0 y0 -> let y = y0 .|. 2^63 xh = y - 1 - xh0 `mod` y xl = - xl0 input = ((toW64 xh, toW64 xl), toW64 y) x = toInteger xh * 2^64 + toInteger xl qh = (x `div` 2^32) `div` toInteger y approxQh = toInteger xh `div` (toInteger y `div` 2^32) annotate | 2^32 <= approxQh = label "high approxQh" | otherwise = label ("deltaQh: " ++ show (approxQh -qh)) in annotate $ fastF input == implementation (ArithJet DivMod128_64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod128_64)) prop_div_mod_128_64_low_y :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_div_mod_128_64_low_y = \xh0 xl0 y0 -> let y = y0 `mod` 2^63 xh = y - xh0 `mod` (y + 1) xl = - xl0 input = ((toW64 xh, toW64 xl), toW64 y) in fastF input == implementation (ArithJet DivMod128_64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod128_64)) prop_div_mod_128_64_high_x :: W.Word64 -> W.Word64 -> W.Word64 -> Bool prop_div_mod_128_64_high_x = \xh0 xl0 y0 -> let y = y0 xh = - xh0 xl = - xl0 input = ((toW64 xh, toW64 xl), toW64 y) in fastF input == implementation (ArithJet DivMod128_64) input where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (ArithJet DivMod128_64)) assert_sha_256_iv :: Assertion assert_sha_256_iv = fastF () @=? implementation (HashJet Sha256Iv) () where fastF = testCoreEval (specification (HashJet Sha256Iv)) prop_sha_256_block :: HashElement -> HashElement -> HashElement -> Bool prop_sha_256_block = \h b1 b2 -> let input = (heAsTy h, (heAsTy b1, heAsTy b2)) in implementation (HashJet Sha256Block) input == fastF input where fastF = testCoreEval (specification (HashJet Sha256Block)) assert_sha_256_ctx_8_init :: Assertion assert_sha_256_ctx_8_init = fastF () @=? implementation (HashJet Sha256Ctx8Init) () where fastF = testCoreEval (specification (HashJet Sha256Ctx8Init)) prop_sha_256_ctx_8_add_1 :: Sha256CtxElement -> W.Word8 -> Bool prop_sha_256_ctx_8_add_1 = \ce w -> fastF (ctxAsTy ce, toW8 w) == implementation (HashJet Sha256Ctx8Add1) (ctxAsTy ce, toW8 w) where toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add1)) prop_sha_256_ctx_8_add_2 :: Sha256CtxElement -> W.Word16 -> Bool prop_sha_256_ctx_8_add_2 = \ce w -> fastF (ctxAsTy ce, toW16 w) == implementation (HashJet Sha256Ctx8Add2) (ctxAsTy ce, toW16 w) where toW16 = toWord16 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add2)) prop_sha_256_ctx_8_add_4 :: Sha256CtxElement -> W.Word32 -> Bool prop_sha_256_ctx_8_add_4 = \ce w -> fastF (ctxAsTy ce, toW32 w) == implementation (HashJet Sha256Ctx8Add4) (ctxAsTy ce, toW32 w) where toW32 = toWord32 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add4)) prop_sha_256_ctx_8_add_8 :: Sha256CtxElement -> W.Word64 -> Bool prop_sha_256_ctx_8_add_8 = \ce w -> fastF (ctxAsTy ce, toW64 w) == implementation (HashJet Sha256Ctx8Add8) (ctxAsTy ce, toW64 w) where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add8)) prop_sha_256_ctx_8_add_16 :: Sha256CtxElement -> (W.Word64, W.Word64) -> Bool prop_sha_256_ctx_8_add_16 = \ce (w1, w2) -> fastF (ctxAsTy ce, (toW64 w1, toW64 w2)) == implementation (HashJet Sha256Ctx8Add16) (ctxAsTy ce, (toW64 w1, toW64 w2)) where toW64 = toWord64 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add16)) prop_sha_256_ctx_8_add_32 :: Sha256CtxElement -> W.Word256 -> Bool prop_sha_256_ctx_8_add_32 = \ce w -> fastF (ctxAsTy ce, toW256 w) == implementation (HashJet Sha256Ctx8Add32) (ctxAsTy ce, toW256 w) where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add32)) prop_sha_256_ctx_8_add_64 :: Sha256CtxElement -> (W.Word256, W.Word256) -> Bool prop_sha_256_ctx_8_add_64 = \ce (w1, w2) -> fastF (ctxAsTy ce, (toW256 w1, toW256 w2)) == implementation (HashJet Sha256Ctx8Add64) (ctxAsTy ce, (toW256 w1, toW256 w2)) where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add64)) prop_sha_256_ctx_8_add_128 :: Sha256CtxElement -> ((W.Word256, W.Word256), (W.Word256, W.Word256)) -> Bool prop_sha_256_ctx_8_add_128 = \ce ws -> let input = (ctxAsTy ce, over (both_.both_) toW256 ws) in fastF input == implementation (HashJet Sha256Ctx8Add128) input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add128)) prop_sha_256_ctx_8_add_256 :: Sha256CtxElement -> (((W.Word256, W.Word256), (W.Word256, W.Word256)), ((W.Word256, W.Word256), (W.Word256, W.Word256))) -> Bool prop_sha_256_ctx_8_add_256 = \ce ws -> let input = (ctxAsTy ce, over (both_.both_.both_) toW256 ws) in fastF input == implementation (HashJet Sha256Ctx8Add256) input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add256)) prop_sha_256_ctx_8_add_512 :: Sha256CtxElement -> ((((W.Word256, W.Word256), (W.Word256, W.Word256)), ((W.Word256, W.Word256), (W.Word256, W.Word256))), (((W.Word256, W.Word256), (W.Word256, W.Word256)), ((W.Word256, W.Word256), (W.Word256, W.Word256)))) -> Bool prop_sha_256_ctx_8_add_512 = \ce ws -> let input = (ctxAsTy ce, over (both_.both_.both_.both_) toW256 ws) in fastF input == implementation (HashJet Sha256Ctx8Add512) input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8Add512)) prop_sha_256_ctx_8_add_buffer_511 :: Int -> Sha256CtxElement -> Property prop_sha_256_ctx_8_add_buffer_511 = \preLen ce -> forAll (vectorOf (preLen `mod` 512) arbitraryBoundedIntegral) $ \ws -> let input = (ctxAsTy ce, fst $ bufferFill buffer511 (toW8 <$> ws)) in fastF input == implementation (HashJet Sha256Ctx8AddBuffer511) input where toW8 :: W.Word8 -> Word8 toW8 = toWord8 . fromIntegral fastF = testCoreEval (specification (HashJet Sha256Ctx8AddBuffer511)) prop_sha_256_ctx_8_finalize :: Sha256CtxElement -> Bool prop_sha_256_ctx_8_finalize = \ce -> fastF (ctxAsTy ce) == implementation (HashJet Sha256Ctx8Finalize) (ctxAsTy ce) where fastF = testCoreEval (specification (HashJet Sha256Ctx8Finalize)) prop_fe_normalize :: FieldElement -> Bool prop_fe_normalize a = fe_normalize (feAsTy a) == toFE (feAsSpec a) fe_unary_prop f g = \a -> fastF (feAsTy a) == Just (toFE (g (feAsSpec a))) where fastF = testCoreEval f fe_binary_prop f g = \a b -> fastF (feAsTy a, feAsTy b) == Just (toFE (g (feAsSpec a) (feAsSpec b))) where fastF = testCoreEval f prop_fe_add :: FieldElement -> FieldElement -> Bool prop_fe_add = fe_binary_prop fe_add Spec.fe_add prop_fe_multiply :: FieldElement -> FieldElement -> Bool prop_fe_multiply = fe_binary_prop fe_multiply Spec.fe_multiply prop_fe_square :: FieldElement -> Bool prop_fe_square = fe_unary_prop fe_square Spec.fe_square prop_fe_negate :: FieldElement -> Bool prop_fe_negate = fe_unary_prop fe_negate Spec.fe_negate prop_fe_halve :: FieldElement -> Bool prop_fe_halve = fe_unary_prop fe_halve Spec.fe_halve prop_fe_invert :: FieldElement -> Bool prop_fe_invert = fe_unary_prop fe_invert Spec.fe_invert prop_fe_square_root :: FieldElement -> Bool prop_fe_square_root = \a -> fastSqrt (feAsTy a) == Just ((fmap toFE . maybeToTy) (Spec.fe_square_root (feAsSpec a))) where fastSqrt = testCoreEval fe_square_root prop_gej_rescale :: GroupElementJacobian -> FieldElement -> Bool prop_gej_rescale = \a c -> fast_gej_rescale (gejAsTy a, feAsTy c) == Just (toGEJ (Spec.gej_rescale (gejAsSpec a) (feAsSpec c))) where fast_gej_rescale = testCoreEval gej_rescale prop_gej_rescale_inf :: FieldElement -> Property prop_gej_rescale_inf c = forAll gen_inf $ flip prop_gej_rescale c prop_gej_double :: GroupElementJacobian -> Bool prop_gej_double = \a -> fast_gej_double (gejAsTy a) == Just (toGEJ (Spec.gej_double (gejAsSpec a))) where fast_gej_double = testCoreEval gej_double prop_gej_double_inf :: Property prop_gej_double_inf = forAll gen_inf $ prop_gej_double prop_gej_add_ex :: GroupElementJacobian -> GroupElementJacobian -> Bool prop_gej_add_ex = \a b -> let rzc = fast_gej_add_ex (gejAsTy a, gejAsTy b) (rz', c') = Spec.gej_add_ex (gejAsSpec a) (gejAsSpec b) in (fst <$> rzc) == Just (toFE rz') && (snd <$> rzc) == Just (toGEJ c') where fast_gej_add_ex = testCoreEval gej_add_ex prop_gej_add_ex_double :: FieldElement -> GroupElementJacobian -> Bool prop_gej_add_ex_double z b@(GroupElementJacobian bx by bz) = prop_gej_add_ex a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by bz' = feAsSpec bz a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack $ by' .*. z' .^. 3) (FieldElement . Spec.fe_pack $ bz' .*. z') prop_gej_add_ex_opp :: FieldElement -> GroupElementJacobian -> Bool prop_gej_add_ex_opp z b@(GroupElementJacobian bx by bz) = prop_gej_add_ex a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by bz' = feAsSpec bz a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack . Spec.fe_negate $ by' .*. z' .^. 3) (FieldElement . Spec.fe_pack $ bz' .*. z') prop_gej_add_ex_infl b = forAll gen_inf $ \a -> prop_gej_add_ex a b prop_gej_add_ex_infr a = forAll gen_inf $ \b -> prop_gej_add_ex a b prop_gej_add :: GroupElementJacobian -> GroupElementJacobian -> Bool prop_gej_add = \a b -> fast_gej_add (gejAsTy a, gejAsTy b) == Just (toGEJ (gejAsSpec a <> gejAsSpec b)) where fast_gej_add = testCoreEval gej_add prop_gej_add_double :: FieldElement -> GroupElementJacobian -> Bool prop_gej_add_double z b@(GroupElementJacobian bx by bz) = prop_gej_add a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by bz' = feAsSpec bz a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack $ by' .*. z' .^. 3) (FieldElement . Spec.fe_pack $ bz' .*. z') prop_gej_add_opp :: FieldElement -> GroupElementJacobian -> Bool prop_gej_add_opp z b@(GroupElementJacobian bx by bz) = prop_gej_add a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by bz' = feAsSpec bz a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack . Spec.fe_negate $ by' .*. z' .^. 3) (FieldElement . Spec.fe_pack $ bz' .*. z') prop_gej_add_infl b = forAll gen_inf $ \a -> prop_gej_add a b prop_gej_add_infr a = forAll gen_inf $ \b -> prop_gej_add a b prop_gej_ge_add_ex :: GroupElementJacobian -> GroupElement -> Bool prop_gej_ge_add_ex = \a b -> let rzc = fast_gej_ge_add_ex (gejAsTy a, geAsTy b) (rz', c') = Spec.gej_ge_add_ex (gejAsSpec a) (geAsSpec b) in (fst <$> rzc) == Just (toFE rz') && (snd <$> rzc) == Just (toGEJ c') where fast_gej_ge_add_ex = testCoreEval gej_ge_add_ex prop_gej_ge_add_ex_double :: FieldElement -> GroupElement -> Bool prop_gej_ge_add_ex_double z b@(GroupElement bx by) = prop_gej_ge_add_ex a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack $ by' .*. z' .^. 3) z prop_gej_ge_add_ex_opp :: FieldElement -> GroupElement -> Bool prop_gej_ge_add_ex_opp z b@(GroupElement bx by) = prop_gej_ge_add_ex a b where z' = feAsSpec z bx' = feAsSpec bx by' = feAsSpec by a = GroupElementJacobian (FieldElement . Spec.fe_pack $ bx' .*. z' .^. 2) (FieldElement . Spec.fe_pack . Spec.fe_negate $ by' .*. z' .^. 3) z prop_gej_ge_add_ex_inf b = forAll gen_inf $ \a -> prop_gej_ge_add_ex a b prop_gej_equiv :: GroupElementJacobian -> GroupElementJacobian -> Bool prop_gej_equiv = \a b -> fast_gej_equiv (gejAsTy a, gejAsTy b) == Just (toBit (Spec.gej_equiv (gejAsSpec a) (gejAsSpec b))) where fast_gej_equiv = testCoreEval gej_equiv prop_gej_equiv_infl b = forAll gen_inf $ \a -> prop_gej_equiv a b prop_gej_equiv_infr a = forAll gen_inf $ \b -> prop_gej_equiv a b prop_gej_equiv_inf = forAll gen_inf $ \a -> forAll gen_inf $ \b -> prop_gej_equiv a b prop_gej_equiv_true = \a c -> let b = Spec.gej_rescale (gejAsSpec a) (feAsSpec c) in fast_gej_equiv (gejAsTy a, toGEJ b) == Just (toBit (Spec.gej_equiv (gejAsSpec a) b)) where fast_gej_equiv = testCoreEval gej_equiv prop_gej_ge_equiv :: GroupElementJacobian -> GroupElement -> Bool prop_gej_ge_equiv = \a b -> fast_gej_ge_equiv (gejAsTy a, geAsTy b) == Just (toBit (Spec.gej_ge_equiv (gejAsSpec a) (geAsSpec b))) where fast_gej_ge_equiv = testCoreEval gej_ge_equiv prop_gej_x_equiv :: FieldElement -> GroupElementJacobian -> Bool -- gej_x_equiv will essentially always be false on random inputs. prop_gej_x_equiv = \x0 a -> fast_gej_x_equiv (feAsTy x0, gejAsTy a) == Just (toBit (Spec.gej_x_equiv (feAsSpec x0) (gejAsSpec a) )) where fast_gej_x_equiv = testCoreEval gej_x_equiv prop_gej_x_equiv_inf x0 = forAll gen_inf $ prop_gej_x_equiv x0 prop_gej_x_equiv_true y z x0 = prop_gej_x_equiv x0 a where z' = feAsSpec z x0' = feAsSpec x0 a = GroupElementJacobian (FieldElement . Spec.fe_pack $ x0' .*. z' .^. 2) y z prop_gej_ge_equiv_inf b = forAll gen_inf $ \a -> prop_gej_ge_equiv a b prop_gej_ge_equiv_true = \a -> maybe (property Discard) (\b -> property $ fast_gej_ge_equiv (gejAsTy a, toGE b) == Just (toBit (Spec.gej_ge_equiv (gejAsSpec a) b))) (Spec.gej_normalize (gejAsSpec a)) where fast_gej_ge_equiv = testCoreEval gej_ge_equiv prop_gej_x_equiv_inf_zero = prop_gej_x_equiv_inf (FieldElement 0) prop_ge_is_on_curve :: GroupElement -> Bool prop_ge_is_on_curve = \a -> fast_ge_is_on_curve (geAsTy a) == Just (toBit (Spec.ge_is_on_curve (geAsSpec a))) where fast_ge_is_on_curve = testCoreEval ge_is_on_curve prop_ge_is_on_curve_half = forAll gen_half_curve prop_ge_is_on_curve prop_gej_is_on_curve :: GroupElementJacobian -> Bool prop_gej_is_on_curve = \a -> fast_gej_is_on_curve (gejAsTy a) == Just (toBit (Spec.gej_is_on_curve (gejAsSpec a))) where fast_gej_is_on_curve = testCoreEval gej_is_on_curve prop_gej_is_on_curve_inf = forAll gen_inf prop_gej_is_on_curve prop_gej_is_on_curve_inf_half = forAll gen_half_curve_inf prop_gej_is_on_curve prop_gej_is_on_curve_half = forAll gen_half_curve_jacobian prop_gej_is_on_curve scalar_unary_prop f g = \a -> fastF (scalarAsTy a) == Just (toScalar (g (scalarAsSpec a))) where fastF = testCoreEval f scalar_binary_prop f g = \a b -> fastF (scalarAsTy a, scalarAsTy b) == Just (toScalar (g (scalarAsSpec a) (scalarAsSpec b))) where fastF = testCoreEval f prop_scalar_normalize :: ScalarElement -> Bool prop_scalar_normalize a@(ScalarElement w) = scalar_normalize (scalarAsTy a) == toScalar (Spec.scalar (toInteger w)) prop_scalar_add :: ScalarElement -> ScalarElement -> Bool prop_scalar_add = scalar_binary_prop scalar_add Spec.scalar_add prop_scalar_square :: ScalarElement -> Bool prop_scalar_square = scalar_unary_prop scalar_square Spec.scalar_square prop_scalar_multiply :: ScalarElement -> ScalarElement -> Bool prop_scalar_multiply = scalar_binary_prop scalar_multiply Spec.scalar_multiply prop_scalar_negate :: ScalarElement -> Bool prop_scalar_negate = scalar_unary_prop scalar_negate Spec.scalar_negate prop_scalar_invert :: ScalarElement -> Bool prop_scalar_invert = scalar_unary_prop scalar_invert Spec.scalar_invert prop_scalar_split_lambda :: ScalarElement -> Bool prop_scalar_split_lambda = \a -> ((interp *** interp) <$> fast_scalar_split_lambda (scalarAsTy a)) == Just (Spec.scalar_split_lambda (scalarAsSpec a)) where interp (b,x) = fromWord128 x - if fromBit b then 2^128 else 0 fast_scalar_split_lambda = testCoreEval scalar_split_lambda prop_wnaf5 :: WnafElement -> Bool prop_wnaf5 n = L.and $ zipWith (==) lhs (fmap (maybeToTy . fmap (unsign . toInteger)) (Spec.wnaf 5 (wnafAsSpec n) ++ repeat Nothing)) where lhs = fmap fromWord4 <$> wnaf5 (wnafAsTy n)^..(backwards traverseWnaf) unsign x | x < 0 = 2^4 + x | otherwise = x prop_wnaf15 :: WnafElement -> Bool prop_wnaf15 n = L.and $ zipWith (==) lhs (fmap (maybeToTy . fmap (unsign . toInteger)) (Spec.wnaf 15 (wnafAsSpec n) ++ repeat Nothing)) where lhs = fmap (fromWord16) <$> wnaf15 (wnafAsTy n)^..(backwards traverseWnaf) unsign x | x < 0 = 2^16 + 2*x+1 | otherwise = 2*x+1 prop_off_curve_scale :: ScalarElement -> GroupElementJacobian -> Bool prop_off_curve_scale = \na a -> fast_off_curve_scale (scalarAsTy na, gejAsTy a) == Just (toGEJ (Spec.off_curve_scale (scalarAsSpec na) (gejAsSpec a))) where fast_off_curve_scale = testCoreEval off_curve_scale prop_off_curve_scale_0 :: GroupElementJacobian -> Bool prop_off_curve_scale_0 a = prop_off_curve_scale na a where na = ScalarElement 0 prop_off_curve_scale_inf :: ScalarElement -> Property prop_off_curve_scale_inf na = forAll gen_inf $ \a -> prop_off_curve_scale na a prop_scale :: ScalarElement -> GroupElementJacobian -> Bool prop_scale = \na a -> fast_scale (scalarAsTy na, gejAsTy a) == (toGEJ <$> Spec.scale (scalarAsSpec na) (gejAsSpec a)) where fast_scale = testCoreEval scale prop_scale_0 :: GroupElementJacobian -> Bool prop_scale_0 a = prop_scale na a where na = ScalarElement 0 prop_scale_inf :: ScalarElement -> Property prop_scale_inf na = forAll gen_inf $ \a -> prop_scale na a prop_scale_half :: ScalarElement -> Property prop_scale_half na = forAll gen_half_curve_jacobian $ \a -> prop_scale na a prop_scale_half_inf :: ScalarElement -> Property prop_scale_half_inf na = forAll gen_half_curve_inf $ \a -> prop_scale na a prop_scale_half_0 :: Property prop_scale_half_0 = forAll gen_half_curve_inf $ \a -> prop_scale na a where na = ScalarElement 0 prop_off_curve_linear_combination_1 :: ScalarElement -> GroupElementJacobian -> ScalarElement -> Bool prop_off_curve_linear_combination_1 = \na a ng -> fast_off_curve_linear_combination_1 ((scalarAsTy na, gejAsTy a), scalarAsTy ng) == Just (toGEJ (Spec.off_curve_linear_combination_1 (scalarAsSpec na) (gejAsSpec a) (scalarAsSpec ng))) where fast_off_curve_linear_combination_1 = testCoreEval off_curve_linear_combination_1 prop_off_curve_linear_combination_1_0 :: GroupElementJacobian -> ScalarElement -> Bool prop_off_curve_linear_combination_1_0 a ng = prop_off_curve_linear_combination_1 na a ng where na = ScalarElement 0 prop_off_curve_linear_combination_1_inf :: ScalarElement -> ScalarElement -> Property prop_off_curve_linear_combination_1_inf na ng = forAll gen_inf $ \a -> prop_off_curve_linear_combination_1 na a ng prop_linear_combination_1 :: ScalarElement -> GroupElementJacobian -> ScalarElement -> Bool prop_linear_combination_1 = \na a ng -> fast_linear_combination_1 ((scalarAsTy na, gejAsTy a), scalarAsTy ng) == (toGEJ <$> Spec.linear_combination_1 (scalarAsSpec na) (gejAsSpec a) (scalarAsSpec ng)) where fast_linear_combination_1 = testCoreEval linear_combination_1 prop_linear_combination_1_0 :: GroupElementJacobian -> ScalarElement -> Bool prop_linear_combination_1_0 a ng = prop_linear_combination_1 na a ng where na = ScalarElement 0 prop_linear_combination_1_inf :: ScalarElement -> ScalarElement -> Property prop_linear_combination_1_inf na ng = forAll gen_inf $ \a -> prop_linear_combination_1 na a ng prop_linear_combination_1_half :: ScalarElement -> ScalarElement -> Property prop_linear_combination_1_half na ng = forAll gen_half_curve_jacobian $ \a -> prop_linear_combination_1 na a ng prop_linear_combination_1_half_inf :: ScalarElement -> ScalarElement -> Property prop_linear_combination_1_half_inf na ng = forAll gen_half_curve_inf $ \a -> prop_linear_combination_1 na a ng prop_linear_combination_1_half_0 :: ScalarElement -> Property prop_linear_combination_1_half_0 ng = forAll gen_half_curve_inf $ \a -> prop_linear_combination_1 na a ng where na = ScalarElement 0 prop_linear_check_1 :: ScalarElement -> GroupElement -> ScalarElement -> GroupElement -> Bool prop_linear_check_1 = \na a ng r -> fast_linear_check_1 (((scalarAsTy na, geAsTy a), scalarAsTy ng), geAsTy r) == Just (toBit (Spec.linear_check [(scalarAsSpec na, geAsSpec a)] (scalarAsSpec ng) (geAsSpec r))) where fast_linear_check_1 = testCoreEval linear_check_1 prop_decompress :: PointElement -> Bool prop_decompress = \a -> fast_decompress (pointAsTy a) == Just ((fmap toGE . maybeToTy) (Spec.decompress (pointAsSpec a))) where fast_decompress = testCoreEval decompress prop_point_check_1 :: ScalarElement -> PointElement -> ScalarElement -> PointElement -> Bool prop_point_check_1 = \na a ng r -> fast_point_check_1 (((scalarAsTy na, pointAsTy a), scalarAsTy ng), pointAsTy r) == Just (toBit (Spec.point_check [(scalarAsSpec na, pointAsSpec a)] (scalarAsSpec ng) (pointAsSpec r))) where fast_point_check_1 = testCoreEval point_check_1 prop_swu :: FieldElement -> Bool prop_swu = \a -> let input = feAsTy a in fastF input == implementation (Secp256k1Jet Swu) input where fastF = testCoreEval (specification (Secp256k1Jet Swu)) prop_hash_to_curve :: W.Word256 -> Bool prop_hash_to_curve = \a -> let input = toW256 a in fastF input == implementation (Secp256k1Jet HashToCurve) input where toW256 = toWord256 . fromIntegral fastF = testCoreEval (specification (Secp256k1Jet HashToCurve)) prop_pubkey_unpack :: FieldElement -> Bool prop_pubkey_unpack a@(FieldElement w) = fast_pubkey_unpack (feAsTy a) == Just ((fmap toPoint . maybeToTy) (Spec.pubkey_unpack (Spec.PubKey w))) where fast_pubkey_unpack = testCoreEval pubkey_unpack prop_pubkey_unpack_neg :: FieldElement -> Bool prop_pubkey_unpack_neg a@(FieldElement w) = fast_pubkey_unpack_neg (feAsTy a) == Just ((fmap toPoint . maybeToTy) (Spec.pubkey_unpack_neg (Spec.PubKey w))) where fast_pubkey_unpack_neg = testCoreEval pubkey_unpack_neg prop_signature_unpack :: FieldElement -> ScalarElement -> Bool prop_signature_unpack r@(FieldElement wr) s@(ScalarElement ws) = fast_signature_unpack (feAsTy r, scalarAsTy s) == Just ((fmap (toFE *** toScalar) . maybeToTy) (Spec.signature_unpack (Spec.Sig wr ws))) where fast_signature_unpack = testCoreEval signature_unpack fast_bip_0340_check = fromJust . testCoreEval bip_0340_check where fromJust (Just a) = fromBit a fromJust Nothing = False group_bip_0340_check = testGroup "bip_0340_check" (zipWith case_bip_0340_check_vector [0..] bip0340Vectors) where assert_bip_0340_check_vector tv = bip0340TestResult tv @=? fast_bip_0340_check (bip0340TestAsTy tv) case_bip_0340_check_vector n tv = testCase name (assert_bip_0340_check_vector tv) where name = "bip_0340_vector_" ++ show n prop_check_sig_verify :: FieldElement -> HashElement -> HashElement -> FieldElement -> ScalarElement -> Bool prop_check_sig_verify = \pk m1 m2 r s -> let input = ((feAsTy pk, (heAsTy m1, heAsTy m2)), (feAsTy r, scalarAsTy s)) in fast_check_sig_verify input == implementation (SignatureJet CheckSigVerify) input where fast_check_sig_verify = testCoreEval (specification (SignatureJet CheckSigVerify)) prop_check_sig_verify_true :: HashElement -> HashElement -> Property prop_check_sig_verify_true = \m1 m2 -> let msg = sigHash (heAsSpec m1) (heAsSpec m2) in forAll (genSignature msg) $ \(PubKey pk, Sig r s) -> let input = ((toW256 pk, (heAsTy m1, heAsTy m2)), (toW256 r, toW256 s)) in Just () == implementation (SignatureJet CheckSigVerify) input && Just () == fast_check_sig_verify input where toW256 = toWord256 . fromIntegral fast_check_sig_verify = testCoreEval (specification (SignatureJet CheckSigVerify)) prop_parse_lock = forAll arbitraryLock $ \a -> fastF (toW32 a) == implementation (BitcoinJet ParseLock) (toW32 a) where fastF = testCoreEval (specification (BitcoinJet ParseLock)) prop_parse_sequence a = fastF (toW32 a) == implementation (BitcoinJet ParseSequence) (toW32 a) where fastF = testCoreEval (specification (BitcoinJet ParseSequence)) assert_tapdata_init :: Assertion assert_tapdata_init = fastF () @=? implementation (BitcoinJet TapdataInit) () where fastF = testCoreEval (specification (BitcoinJet TapdataInit)) ================================================ FILE: Haskell/Tests/Simplicity/Serialization/Tests.hs ================================================ {-# LANGUAGE RankNTypes, ScopedTypeVariables #-} -- This module tests some serialization functionality. module Simplicity.Serialization.Tests (tests) where import Control.Arrow ((|||)) import Control.Monad (mzero) import Data.Either (lefts) import Data.Foldable (toList) import Data.Maybe (fromMaybe) import Data.Serialize (Get, Putter, runGetState, runPut) import qualified Data.Vector as V import qualified Data.Vector.Unboxed as UV import Lens.Family2 (Traversal, (&), (.~)) import Simplicity.Bitcoin.Dag import Simplicity.Bitcoin.Inference import Simplicity.MerkleRoot import Simplicity.Bitcoin.Primitive import Simplicity.Bitcoin.JetType import Simplicity.Bitcoin.Serialization.BitString as BitString import Simplicity.Bitcoin.Serialization.ByteString as ByteString import Simplicity.Bitcoin.Term import Simplicity.CoreJets as Core import Simplicity.Digest import qualified Simplicity.Programs.Arith as Arith import Simplicity.Programs.Sha256.Lib import Simplicity.Serialization import Simplicity.Ty.Tests hiding (tests) import Simplicity.Ty.Word import Test.Tasty (TestTree, testGroup) import Test.Tasty.HUnit ((@=?), testCase) import Test.Tasty.QuickCheck ( Testable, testProperty, Positive(Positive) , Gen, Property, arbitrary, choose, elements, forAll, listOf1, oneof) import Test.QuickCheck.Property (Result, failed, succeeded, reason) -- This collects the tests for the various serialization/deserialization pairs. tests :: TestTree tests = testGroup "Serialization" [ testProperty "get-put bit-string" prop_getPutBitString , testProperty "get-put positive" prop_getPutPositive , testProperty "get-put BitString DAG" prop_getPutBitStringDag , testProperty "get-put ByteString DAG" prop_getPutByteStringDag -- This collection tests type inference on a few sample programs. , testGroup "Inference" [ testInference "full_add word8" (Arith.full_add word8) , testInference "add word8" (Arith.add word8) , testInference "full_multiply word8" (Arith.full_multiply word8) , testInference "multiply word8" (Arith.multiply word8) , testInference "hashBlock" hashBlock ] , testGroup "Hasekll Core Jets" (testDecodeCoreJet <$> toList coreJetMap) ] -- Check that deserialization of serialization of bit-strings returns the original input. prop_getPutBitString :: [Bool] -> Bool prop_getPutBitString l = evalExactVector getBitString (UV.fromList (putBitString l [])) == Just l -- Check that deserialization of serialization of positive numbers returns the original input. prop_getPutPositive :: Positive Integer -> Bool prop_getPutPositive (Positive n) = evalExactVector getPositive (UV.fromList (putPositive n [])) == Just n -- Test a 'SimplicityDag' predicate over suitable Arbitrary inputs. forallSimplicityDag :: Testable prop => (SimplicityDag [] Ty (SomeArrow NoJets) UntypedValue -> prop) -> Property forallSimplicityDag = forAll gen_UntypedTermF_list where gen_UntypedTermF_list = do l <- traverse f =<< (zip [1..] <$> listOf1 gen_UntypedTermF) case l of [] -> return [] nl -> (:nl) <$> elements [Iden one, Unit one] where f (i, term) = traverse (const (choose (1,i))) term -- We are subverting putDag's type annotation requirement. It is for purpose of testing the 'putDag' function, so maybe it is okay to do. -- :TODO: replace this with a proper generator for well-typed Simplicity terms. gen_UntypedTermF :: Gen (TermF Ty j UntypedValue ()) gen_UntypedTermF = oneof [ pure $ Iden one , pure $ Unit one , pure $ Injl one one one () , pure $ Injr one one one () , pure $ Take one one one () , pure $ Drop one one one () , pure $ Comp one one one () () , pure $ Case one one one one () () , pure $ Pair one one one () () , pure $ Disconnect one one one one () () , Hidden <$> get256Bits arbitrary , wit ] where -- Here we are careful to place a correct type annotation for witness values. wit = do b <- arbTy v <- case reflect b of SomeTy rb -> untypedValue <$> arbValueR rb return (Witness one b v) -- Compare 'SimplicityDag' disregarding most type annotations. -- Witness nodes are compared using the 'compareWitness' function which may or may not consider type annotations. compareDag :: (Eq a, Eq j) => (ty0 -> w0 -> ty1 -> w1 -> Bool) -> [TermF ty0 j w0 a] -> [TermF ty1 j w1 a] -> Bool compareDag compareWitness v1 v2 = (and $ zipWith compareNode v1 v2) && (length v1 == length v2) where compareNode (Iden _) (Iden _) = True compareNode (Unit _) (Unit _) = True compareNode (Injl _ _ _ x0) (Injl _ _ _ x1) = x0 == x1 compareNode (Injr _ _ _ x0) (Injr _ _ _ x1) = x0 == x1 compareNode (Take _ _ _ x0) (Take _ _ _ x1) = x0 == x1 compareNode (Drop _ _ _ x0) (Drop _ _ _ x1) = x0 == x1 compareNode (Comp _ _ _ x0 y0) (Comp _ _ _ x1 y1) = [x0,y0] == [x1,y1] compareNode (Case _ _ _ _ x0 y0) (Case _ _ _ _ x1 y1) = [x0,y0] == [x1,y1] compareNode (Pair _ _ _ x0 y0) (Pair _ _ _ x1 y1) = [x0,y0] == [x1,y1] compareNode (Disconnect _ _ _ _ x0 y0) (Disconnect _ _ _ _ x1 y1) = [x0,y0] == [x1,y1] compareNode (Hidden h0) (Hidden h1) = h0 == h1 compareNode (Witness _ b0 w0) (Witness _ b1 w1) = compareWitness b0 w0 b1 w1 compareNode (Jet j0) (Jet j1) = j0 == j1 compareNode _ _ = False -- Check that 'BitString.putDag's serialization of 'SimplicityDag's works can be deserialized by a combination of 'BitString.getDagNoWitness' and 'BitString.getWitnessData'. -- Note: Because we do not yet have a generator for arbitrary well-typed Simplicity expressions we cannot easily test 'BitString.putTerm' with 'BitString.getTerm'. -- Instead we perform an awkward combinator of 'BitString.getDagNoWitness' and 'BitString.getWitnessData' on mostly untyped Simplicity DAGs for now. prop_getPutBitStringDag :: Property prop_getPutBitStringDag = forallSimplicityDag prop where compareWitness _ w0 _ w1 = w0 == w1 prop :: SimplicityDag [] Ty (SomeArrow NoJets) UntypedValue -> Result prop v = case eval of Left msg -> failed { reason = show msg } Right (pdag, wdag) | not (compareDag (\_ _ _ _ -> True) v (toList pdag)) -> failed { reason = "Bitstring.getDagNoWiness returned bad value" } | not (compareDag compareWitness v (toList wdag)) -> failed { reason = "Bitstring.getWitnessData returned bad value" } | otherwise -> succeeded where pbs = BitString.putDagNoWitnessLengthCode v Just wbs = BitString.putWitnessData v -- generation is designed to create terms that always succeed at serializaiton. evalPDag = flip evalStreamWithError pbs $ \abort next -> do BitString.getDagNoWitnessLengthCode abort next evalWDag = flip evalStreamWithError wbs $ \abort next -> do BitString.getWitnessData vStripped next eval = (,) <$> evalPDag <*> evalWDag vStripped = v & traverse . witness_ .~ () where witness_ :: Traversal (TermF ty j w0 a) (TermF ty j w1 a) w0 w1 witness_ = witnessData . const -- Check that deserialization of serialization of 'SimplicityDag's works for the byte-string serialization. prop_getPutByteStringDag :: Property prop_getPutByteStringDag = forallSimplicityDag prop where compareWitness b w0 _ w1 = case reflect b of SomeTy rb -> fromMaybe False $ (==) <$> castUntypedValueR rb w0 <*> evalExactVector (getValueR rb) w1 prop v = case runGetState (toList <$> ByteString.getDag) bs 0 of Left _ -> False Right (v', rest) -> rest == mempty && compareDag compareWitness v (v' :: SimplicityDag [] () (SomeArrow NoJets) (UV.Vector Bool)) where Just bs = runPut <$> ByteString.putDag v -- generation is designed to create terms that always succeed at serializaiton. -- Check that type inference on Simplicity expressions produce correct terms by testing their Merkle roots. testInference :: forall a b. (TyC a, TyC b) => String -> (forall term. (Core term) => term a b) -> TestTree testInference name program = testGroup name [testProperty "CommitmentRoot" assertion1, testProperty "AnnotatedRoot" assertion2] where dag :: NoJetDag a b dag = program -- type inference on first pass is not necessarily equal to the original program because the Haskell type of internal nodes in the original program might not have the term's principle type. pass1 :: forall term. Simplicity term => Either String (term a b) pass1 = typeCheck =<< typeInference dag (jetDag dag) -- Type inference on the second pass ought to always be equal to the first pass. pass2 :: forall term. Simplicity term => Either String (term a b) pass2 = typeCheck =<< (typeInference dag . jetDag) =<< (pass1 :: Either String (NoJetDag a b)) assertion1 = pass1 == Right (program :: CommitmentRoot a b) assertion2 = pass2 == (pass1 :: Either String (AnnotatedRoot a b)) testDecodeCoreJet :: SomeArrow CoreJet -> TestTree testDecodeCoreJet (SomeArrow jt) = testCase (show jt) (Just (SomeArrow jt) @=? decode) where vector = UV.fromList $ Core.putJetBit jt [] decode = evalExactVector (Core.getJetBit mzero) vector ================================================ FILE: Haskell/Tests/Simplicity/TestCoreEval.hs ================================================ -- | This module builds a wrapper around 'Simplicity.CoreJets.fastCoreEval' to define a 'testCoreEval' variant. module Simplicity.TestCoreEval ( TestCoreEval, testCoreEval ) where import Prelude hiding (drop, fail, take) import Control.Arrow (Kleisli(Kleisli), runKleisli) import Simplicity.CoreJets import Simplicity.Digest import Simplicity.MerkleRoot import Simplicity.Term.Core -- | An Assert instance for 'testCoreEval'. data TestCoreEval a b = TestCoreEval { testCoreEvalSem :: Kleisli Maybe a b , testCoreEvalFast :: FastCoreEval a b } -- | 'testCoreEval' optimizes Simplicity with assertions evaluation using jets, similar to 'fastCoreEval', -- but excludes the expression itself from being substituted. -- This is used in for testing jets against their specifications under the assumption that jets for any subexpressions are correct. testCoreEval = runKleisli . testCoreEvalSem testFastKleisli = Kleisli . fastCoreEval . testCoreEvalFast mkLeaf sComb fComb = TestCoreEval sComb fComb mkUnary sComb fComb t = TestCoreEval (sComb (testFastKleisli t)) (fComb (testCoreEvalFast t)) mkBinary sComb fComb s t = TestCoreEval (sComb (testFastKleisli s) (testFastKleisli t)) (fComb (testCoreEvalFast s) (testCoreEvalFast t)) instance Core TestCoreEval where iden = mkLeaf iden iden comp = mkBinary comp comp unit = mkLeaf unit unit injl = mkUnary injl injl injr = mkUnary injr injr match = mkBinary match match pair = mkBinary pair pair take = mkUnary take take drop = mkUnary drop drop instance Assert TestCoreEval where assertl s h = mkUnary (flip assertl h) (flip assertl h) s assertr h t = mkUnary (assertr h) (assertr h) t fail b = mkLeaf (fail b) (fail b) ================================================ FILE: Haskell/Tests/Simplicity/Ty/Arbitrary.hs ================================================ -- This module tests the Simplicity programs on arbitrary inputs. module Simplicity.Ty.Arbitrary ( maybeToTy , HashElement(..), heAsTy, heAsSpec, toHE , FieldElement(..), feAsTy, feAsSpec, toFE , GroupElement(..), geAsTy, geAsSpec, toGE , PointElement(..), pointAsTy, pointAsSpec, toPoint , GroupElementJacobian(..), gejAsTy, gejAsSpec, toGEJ , gen_inf, gen_half_curve, gen_half_curve_jacobian, gen_half_curve_inf , ScalarElement(..), scalarAsTy, scalarAsSpec, toScalar , WnafElement(..), wnafAsTy, traverseWnaf , Sha256CtxElement(..), ctxAsTy, ctxAsSpec, toCtx ) where import qualified Data.ByteString as BS import Lens.Family2 (review, over) import Lens.Family2.Stock (both_) import Simplicity.Digest import Simplicity.LibSecp256k1.Spec ((.+.), (.*.), (.^.)) import qualified Simplicity.LibSecp256k1.Spec as Spec import Simplicity.Programs.LibSecp256k1.Lib import Simplicity.Ty.LibSecp256k1 import Simplicity.Ty.Word import qualified Simplicity.Word as W import Test.Tasty.QuickCheck (Arbitrary(..), Gen , arbitraryBoundedIntegral, arbitrarySizedBoundedIntegral , choose, elements, frequency, resize, sized, oneof, vectorOf , shrinkIntegral ) maybeToTy :: Maybe a -> Either () a maybeToTy Nothing = Left () maybeToTy (Just x) = Right x toW8 :: W.Word8 -> Word8 toW8 = toWord8 . fromIntegral toW64 :: W.Word64 -> Word64 toW64 = toWord64 . fromIntegral instance Arbitrary W.Word256 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral data HashElement = HashElement W.Word256 deriving Show instance Arbitrary HashElement where arbitrary = do b <- arbitrary i <- arbitrarySizedBoundedIntegral return . HashElement $ if b then i else -i shrink (HashElement h) = HashElement <$> takeWhile ( Word256 toHE = toWord256 .integerHash256 genModularWord256 :: W.Word256 -> Gen W.Word256 genModularWord256 w = do b <- arbitrary i <- arbitrary return $ fromInteger i + if b then w else 0 data FieldElement = FieldElement W.Word256 deriving Show instance Arbitrary FieldElement where arbitrary = FieldElement <$> genModularWord256 (fromInteger Spec.fieldOrder) shrink (FieldElement fe) = FieldElement <$> takeWhile ( [Spec.ge_3, Spec.ge_6, Spec.ge_7, Spec.ge_13, Spec.ge_14]) where mkGE (Spec.GE x y) = GroupElement (FieldElement (Spec.fe_pack x)) (FieldElement (Spec.fe_pack y)) instance Arbitrary GroupElement where arbitrary = sized $ \n -> frequency [(1, lowOrderGE), (n `div` 10, GroupElement <$> arbitrary <*> arbitrary)] shrink (GroupElement x y) = [GroupElement x' y' | (x', y') <- shrink (x, y)] geAsTy (GroupElement x y) = (feAsTy x, feAsTy y) geAsSpec (GroupElement x y) = Spec.GE (feAsSpec x) (feAsSpec y) data PointElement = PointElement Bool FieldElement deriving Show instance Arbitrary PointElement where arbitrary = PointElement <$> arbitrary <*> arbitrary shrink (PointElement x y) = [PointElement x' y' | (x', y') <- shrink (x, y)] pointAsTy (PointElement x y) = (toBit x, feAsTy y) pointAsSpec (PointElement x y) = Spec.Point x (feAsSpec y) toPoint :: Spec.Point -> Point toPoint (Spec.Point b x) = (toBit b, toFE x) data GroupElementJacobian = GroupElementJacobian FieldElement FieldElement FieldElement deriving Show lowOrderGEJ :: Gen GroupElementJacobian lowOrderGEJ = do Spec.GE x y <- geAsSpec <$> lowOrderGE z <- arbitrary let Spec.GEJ x' y' z' = Spec.gej_rescale (Spec.GEJ x y Spec.fe_one) (feAsSpec z) return $ GroupElementJacobian (FieldElement (Spec.fe_pack x')) (FieldElement (Spec.fe_pack y')) (FieldElement (Spec.fe_pack z')) instance Arbitrary GroupElementJacobian where arbitrary = sized $ \n -> frequency [(1, lowOrderGEJ), (n `div` 10, GroupElementJacobian <$> arbitrary <*> arbitrary <*> arbitrary)] shrink (GroupElementJacobian x y z) = [GroupElementJacobian x' y' z' | (x', y', z') <- shrink (x, y, z)] gejAsTy (GroupElementJacobian x y z) = ((feAsTy x, feAsTy y), feAsTy z) gejAsSpec (GroupElementJacobian x y z) = Spec.GEJ (feAsSpec x) (feAsSpec y) (feAsSpec z) gen_inf :: Gen GroupElementJacobian gen_inf = GroupElementJacobian <$> arbitrary <*> arbitrary <*> pure (FieldElement 0) gen_half_curve :: Gen GroupElement gen_half_curve = half_curve <$> arbitrary where half_curve x = GroupElement x (FieldElement . Spec.fe_pack $ y') where x' = feAsSpec x y' = (x' .^. 3 .+. (Spec.fe 7)) .^. ((Spec.fieldOrder + 1) `div` 4) gen_half_curve_jacobian :: Gen GroupElementJacobian gen_half_curve_jacobian = half_curve_jacobian <$> gen_half_curve <*> arbitrary where half_curve_jacobian (GroupElement x y) z = GroupElementJacobian (FieldElement . Spec.fe_pack $ x' .*. z' .^. 2) (FieldElement . Spec.fe_pack $ y' .*. z' .^. 3) z where x' = feAsSpec x y' = feAsSpec y z' = feAsSpec z gen_half_curve_inf :: Gen GroupElementJacobian gen_half_curve_inf = half_curve_inf <$> arbitrary where half_curve_inf :: FieldElement -> GroupElementJacobian half_curve_inf x = GroupElementJacobian x (FieldElement . Spec.fe_pack $ y') (FieldElement 0) where x' = feAsSpec x y' = x' .^. (3 * ((Spec.fieldOrder + 1) `div` 4)) data ScalarElement = ScalarElement W.Word256 deriving Show instance Arbitrary ScalarElement where arbitrary = sized $ \n -> if n == 0 then return case1 else resize (n-1) $ do i <- arbitrary j <- arbitrary e <- elements [0, 2^255, Spec.groupOrder, halforder] return . ScalarElement . fromInteger $ i + (j * Spec.lambda `mod` Spec.groupOrder) + e where -- This denormailzed scalar would produce a different result on split-lambda than the canonical scalar due to -- the approximate division used in the implementation. case1 = ScalarElement $ fromInteger Spec.groupOrder + c where c = 0x8f8da4d57dc094c4ecdd5448564d85f6 -- 2^383 `div` g2 + 1 halforder = Spec.groupOrder `div` 2 shrink (ScalarElement se) = ScalarElement <$> filter ( Scalar toScalar = toWord256 . Spec.scalar_repr data WnafElement = WnafElement { wnafAsSpec :: Integer } deriving Show instance Arbitrary WnafElement where arbitrary = WnafElement <$> choose (-2^128, 2^128-1) shrink (WnafElement we) = WnafElement <$> shrink we wnafAsTy :: WnafElement -> (Bit, Word128) wnafAsTy (WnafElement we) = (toBit (we < 0), toWord128 we) traverseWnaf f (x,y) = (,) <$> f x <*> (both_.both_.both_.both_.both_.both_.both_) f y data Sha256CtxElement = Sha256CtxElement [W.Word8] W.Word64 HashElement deriving Show instance Arbitrary Sha256CtxElement where arbitrary = do preLen <- arbitrary count <- oneof [pure id, pure (2^55 +)] <*> ((`div` 256) <$> arbitrary) Sha256CtxElement <$> (vectorOf (preLen `mod` 64) arbitraryBoundedIntegral) <*> pure (fromInteger count) <*> arbitrary shrink (Sha256CtxElement l w h) = [Sha256CtxElement l w h | (l,w,h) <- shrink (l, w, h)] ctxAsTy (Sha256CtxElement l w h) = (fst (bufferFill buffer63 (toW8 <$> l)), (toW64 w, heAsTy h)) ctxAsSpec (Sha256CtxElement l w h) = ctxBuild l (fromIntegral w) (heAsSpec h) toCtx ctx = (buffer, (count, midstate)) where buffer = fst $ bufferFill buffer63 (toWord8 . fromIntegral <$> BS.unpack (ctxBuffer ctx)) count = toWord64 . fromIntegral $ ctxCounter ctx midstate = toHE . ivHash $ ctxIV ctx ================================================ FILE: Haskell/Tests/Simplicity/Ty/Tests.hs ================================================ {-# LANGUAGE GADTs #-} -- This modules tests for some operations for Simplicity types. module Simplicity.Ty.Tests (arbTy, arbValue, arbValueR, tests) where import Prelude hiding (sum, prod) import Data.Functor.Compose (Compose(..)) import Data.Vector.Unboxed (fromList) import Simplicity.Serialization import Simplicity.Ty import Test.Tasty (TestTree, testGroup) import Test.Tasty.QuickCheck (Arbitrary(..), Gen, Property, forAll, choose, elements, oneof, sized, testProperty) -- Choose an arbitrary Simplicity type of a given size. arbSizeTy :: Int -> Gen Ty arbSizeTy 0 = return one arbSizeTy n = do i <- choose (0, n-1) elements [sum, prod] <*> arbSizeTy i <*> arbSizeTy (n-1-i) arbTy :: Gen Ty arbTy = sized arbSizeTy -- Choose an arbitrary value of a given Simplicity type. arbValueR :: TyReflect a -> Gen a arbValueR ra = case ra of OneR -> arbitrary SumR rl rr -> oneof [Left <$> arbValueR rl, Right <$> arbValueR rr] ProdR r1 r2 -> (,) <$> arbValueR r1 <*> arbValueR r2 arbValue :: TyC a => Gen a arbValue = arbValueR reify tests :: TestTree tests = testGroup "Ty" [ testProperty "get-put value of Simplicity type" prop_getPutValue ] -- Verify that the serialization of arbitrary values of arbitrary Simplicity types can be deserialized. prop_getPutValue :: Property prop_getPutValue = forAll arbTy go where go a = case reflect a of SomeTy ra -> forAll (arbValueR ra) (\v -> evalExactVector (getValueR ra) (fromList (putValueR ra v)) == Just v) ================================================ FILE: Haskell/Tests/Tests.hs ================================================ -- The main test module that gathers and runs the tests in the Simplicity Haskell project. module Main (main) where import Test.Tasty import qualified Simplicity.BitMachine.Tests as BitMachine import qualified Simplicity.BitMachine.StaticAnalysis.Tests as StaticAnalysis import qualified Simplicity.FFI.Tests as FFI import qualified Simplicity.Programs.Tests as Programs import qualified Simplicity.Bitcoin.Tests as Bitcoin import qualified Simplicity.Bitcoin.FFI.Tests as BitcoinFFI import qualified Simplicity.Bitcoin.Serialization.Tests as BitcoinSerialization import qualified Simplicity.Elements.Tests as Elements import qualified Simplicity.Elements.FFI.Tests as ElementsFFI import qualified Simplicity.Elements.Serialization.Tests as ElementsSerialization import qualified Simplicity.Serialization.Tests as Serialization import qualified Simplicity.Ty.Tests as Ty main :: IO () main = defaultMain tests tests :: TestTree tests = testGroup "Tests" [ Programs.tests , FFI.tests , BitMachine.tests , StaticAnalysis.tests , Bitcoin.tests , BitcoinFFI.tests , BitcoinSerialization.tests , Ty.tests , Elements.tests , ElementsFFI.tests , ElementsSerialization.tests , Serialization.tests ] ================================================ FILE: Haskell/cbits/bitcoin/env.c ================================================ #include "simplicity_alloc.h" #include "simplicity/bitcoin/env.h" #include "bitcoin/txEnv.h" const size_t c_sizeof_rawBitcoinBuffer = sizeof(rawBitcoinBuffer); const size_t c_sizeof_rawBitcoinOutput = sizeof(rawBitcoinOutput); const size_t c_sizeof_rawBitcoinInput = sizeof(rawBitcoinInput); const size_t c_sizeof_rawBitcoinTransaction = sizeof(rawBitcoinTransaction); const size_t c_sizeof_rawBitcoinTapEnv = sizeof(rawBitcoinTapEnv); const size_t c_bitcoin_sizeof_txEnv = sizeof(txEnv); void c_set_rawBitcoinBuffer(rawBitcoinBuffer* result, const char* buf, unsigned int len) { *result = (rawBitcoinBuffer){ .buf = buf, .len = len }; } void c_set_rawBitcoinOutput(rawBitcoinOutput* result, unsigned long value, const rawBitcoinBuffer* scriptPubKey) { *result = (rawBitcoinOutput){ .value = value , .scriptPubKey = *scriptPubKey }; } void c_set_rawBitcoinInput(rawBitcoinInput* result, const rawBitcoinBuffer* annex, const rawBitcoinBuffer* scriptSig, const char* prevTxid, unsigned int prevIx, unsigned long value, const rawBitcoinBuffer* scriptPubKey, unsigned int sequence) { *result = (rawBitcoinInput){ .annex = annex , .scriptSig = *scriptSig , .prevTxid = prevTxid , .txo = {.value = value, .scriptPubKey = *scriptPubKey} , .prevIx = prevIx , .sequence = sequence }; } void c_set_rawBitcoinTransaction(rawBitcoinTransaction* result, const unsigned char* txid, unsigned int version, const rawBitcoinInput* input, unsigned int numInputs, const rawBitcoinOutput* output, unsigned int numOutputs, unsigned int lockTime) { *result = (rawBitcoinTransaction){ .txid = txid , .version = version , .input = input, .numInputs = numInputs , .output = output, .numOutputs = numOutputs , .lockTime = lockTime, }; } void c_set_rawBitcoinTapEnv(rawBitcoinTapEnv* result, const char* controlBlock, unsigned char pathLen, const char* scriptCMR) { *result = (rawBitcoinTapEnv){ .controlBlock = controlBlock, .pathLen = pathLen, .scriptCMR = scriptCMR }; } void c_bitcoin_set_txEnv(txEnv* result, const bitcoinTransaction* tx, const bitcoinTapEnv* taproot, unsigned int ix) { *result = simplicity_bitcoin_build_txEnv(tx, taproot, ix); } ================================================ FILE: Haskell/cbits/bitcoin/jets.c ================================================ #include "bitcoin/bitcoinJets.h" #include "../wrappers.h" WRAP_(bitcoin_version) WRAP_(bitcoin_lock_time) WRAP_(bitcoin_input_prev_outpoint) WRAP_(bitcoin_input_value) WRAP_(bitcoin_input_script_hash) WRAP_(bitcoin_input_sequence) WRAP_(bitcoin_input_annex_hash) WRAP_(bitcoin_input_script_sig_hash) WRAP_(bitcoin_output_value) WRAP_(bitcoin_output_script_hash) WRAP_(bitcoin_fee) WRAP_(bitcoin_total_input_value) WRAP_(bitcoin_total_output_value) WRAP_(bitcoin_script_cmr) WRAP_(bitcoin_transaction_id) WRAP_(bitcoin_current_index) WRAP_(bitcoin_current_prev_outpoint) WRAP_(bitcoin_current_value) WRAP_(bitcoin_current_script_hash) WRAP_(bitcoin_current_sequence) WRAP_(bitcoin_current_annex_hash) WRAP_(bitcoin_current_script_sig_hash) WRAP_(bitcoin_tapleaf_version) WRAP_(bitcoin_tappath) WRAP_(bitcoin_internal_key) WRAP_(bitcoin_num_inputs) WRAP_(bitcoin_num_outputs) WRAP_(bitcoin_tx_is_final) WRAP_(bitcoin_tx_lock_height) WRAP_(bitcoin_tx_lock_time) WRAP_(bitcoin_tx_lock_distance) WRAP_(bitcoin_tx_lock_duration) WRAP_(bitcoin_check_lock_height) WRAP_(bitcoin_check_lock_time) WRAP_(bitcoin_check_lock_distance) WRAP_(bitcoin_check_lock_duration) COREWRAP_(bitcoin_outpoint_hash) COREWRAP_(bitcoin_annex_hash) COREWRAP_(bitcoin_build_tapleaf_simplicity) COREWRAP_(bitcoin_build_tapbranch) COREWRAP_(bitcoin_build_taptweak) WRAP_(bitcoin_output_values_hash) WRAP_(bitcoin_output_scripts_hash) WRAP_(bitcoin_outputs_hash) WRAP_(bitcoin_output_hash) WRAP_(bitcoin_input_outpoints_hash) WRAP_(bitcoin_input_values_hash) WRAP_(bitcoin_input_scripts_hash) WRAP_(bitcoin_input_utxos_hash) WRAP_(bitcoin_input_utxo_hash) WRAP_(bitcoin_input_sequences_hash) WRAP_(bitcoin_input_annexes_hash) WRAP_(bitcoin_input_script_sigs_hash) WRAP_(bitcoin_inputs_hash) WRAP_(bitcoin_input_hash) WRAP_(bitcoin_tx_hash) WRAP_(bitcoin_tapleaf_hash) WRAP_(bitcoin_tappath_hash) WRAP_(bitcoin_tap_env_hash) WRAP_(bitcoin_sig_all_hash) ================================================ FILE: Haskell/cbits/bitstream.c ================================================ #include "bitstream.h" const size_t c_sizeof_bitstream = sizeof(bitstream); void c_initializeBitstream(bitstream *result, const unsigned char* arr, size_t len) { *result = initializeBitstream(arr, len); } ================================================ FILE: Haskell/cbits/coreJets.c ================================================ #include "jets.h" #include "wrappers.h" COREWRAP_(verify) COREWRAP_(low_1) COREWRAP_(low_8) COREWRAP_(low_16) COREWRAP_(low_32) COREWRAP_(low_64) COREWRAP_(high_1) COREWRAP_(high_8) COREWRAP_(high_16) COREWRAP_(high_32) COREWRAP_(high_64) COREWRAP_(complement_1) COREWRAP_(complement_8) COREWRAP_(complement_16) COREWRAP_(complement_32) COREWRAP_(complement_64) COREWRAP_(and_1) COREWRAP_(and_8) COREWRAP_(and_16) COREWRAP_(and_32) COREWRAP_(and_64) COREWRAP_(or_1) COREWRAP_(or_8) COREWRAP_(or_16) COREWRAP_(or_32) COREWRAP_(or_64) COREWRAP_(xor_1) COREWRAP_(xor_8) COREWRAP_(xor_16) COREWRAP_(xor_32) COREWRAP_(xor_64) COREWRAP_(maj_1) COREWRAP_(maj_8) COREWRAP_(maj_16) COREWRAP_(maj_32) COREWRAP_(maj_64) COREWRAP_(xor_xor_1) COREWRAP_(xor_xor_8) COREWRAP_(xor_xor_16) COREWRAP_(xor_xor_32) COREWRAP_(xor_xor_64) COREWRAP_(ch_1) COREWRAP_(ch_8) COREWRAP_(ch_16) COREWRAP_(ch_32) COREWRAP_(ch_64) COREWRAP_(some_1) COREWRAP_(some_8) COREWRAP_(some_16) COREWRAP_(some_32) COREWRAP_(some_64) COREWRAP_(all_8) COREWRAP_(all_16) COREWRAP_(all_32) COREWRAP_(all_64) COREWRAP_(eq_1) COREWRAP_(eq_8) COREWRAP_(eq_16) COREWRAP_(eq_32) COREWRAP_(eq_64) COREWRAP_(eq_256) COREWRAP_(full_left_shift_8_1) COREWRAP_(full_left_shift_8_2) COREWRAP_(full_left_shift_8_4) COREWRAP_(full_left_shift_16_1) COREWRAP_(full_left_shift_16_2) COREWRAP_(full_left_shift_16_4) COREWRAP_(full_left_shift_16_8) COREWRAP_(full_left_shift_32_1) COREWRAP_(full_left_shift_32_2) COREWRAP_(full_left_shift_32_4) COREWRAP_(full_left_shift_32_8) COREWRAP_(full_left_shift_32_16) COREWRAP_(full_left_shift_64_1) COREWRAP_(full_left_shift_64_2) COREWRAP_(full_left_shift_64_4) COREWRAP_(full_left_shift_64_8) COREWRAP_(full_left_shift_64_16) COREWRAP_(full_left_shift_64_32) COREWRAP_(full_right_shift_8_1) COREWRAP_(full_right_shift_8_2) COREWRAP_(full_right_shift_8_4) COREWRAP_(full_right_shift_16_1) COREWRAP_(full_right_shift_16_2) COREWRAP_(full_right_shift_16_4) COREWRAP_(full_right_shift_16_8) COREWRAP_(full_right_shift_32_1) COREWRAP_(full_right_shift_32_2) COREWRAP_(full_right_shift_32_4) COREWRAP_(full_right_shift_32_8) COREWRAP_(full_right_shift_32_16) COREWRAP_(full_right_shift_64_1) COREWRAP_(full_right_shift_64_2) COREWRAP_(full_right_shift_64_4) COREWRAP_(full_right_shift_64_8) COREWRAP_(full_right_shift_64_16) COREWRAP_(full_right_shift_64_32) COREWRAP_(leftmost_8_1) COREWRAP_(leftmost_8_2) COREWRAP_(leftmost_8_4) COREWRAP_(leftmost_16_1) COREWRAP_(leftmost_16_2) COREWRAP_(leftmost_16_4) COREWRAP_(leftmost_16_8) COREWRAP_(leftmost_32_1) COREWRAP_(leftmost_32_2) COREWRAP_(leftmost_32_4) COREWRAP_(leftmost_32_8) COREWRAP_(leftmost_32_16) COREWRAP_(leftmost_64_1) COREWRAP_(leftmost_64_2) COREWRAP_(leftmost_64_4) COREWRAP_(leftmost_64_8) COREWRAP_(leftmost_64_16) COREWRAP_(leftmost_64_32) COREWRAP_(rightmost_8_1) COREWRAP_(rightmost_8_2) COREWRAP_(rightmost_8_4) COREWRAP_(rightmost_16_1) COREWRAP_(rightmost_16_2) COREWRAP_(rightmost_16_4) COREWRAP_(rightmost_16_8) COREWRAP_(rightmost_32_1) COREWRAP_(rightmost_32_2) COREWRAP_(rightmost_32_4) COREWRAP_(rightmost_32_8) COREWRAP_(rightmost_32_16) COREWRAP_(rightmost_64_1) COREWRAP_(rightmost_64_2) COREWRAP_(rightmost_64_4) COREWRAP_(rightmost_64_8) COREWRAP_(rightmost_64_16) COREWRAP_(rightmost_64_32) COREWRAP_(left_pad_low_1_8) COREWRAP_(left_pad_low_1_16) COREWRAP_(left_pad_low_8_16) COREWRAP_(left_pad_low_1_32) COREWRAP_(left_pad_low_8_32) COREWRAP_(left_pad_low_16_32) COREWRAP_(left_pad_low_1_64) COREWRAP_(left_pad_low_8_64) COREWRAP_(left_pad_low_16_64) COREWRAP_(left_pad_low_32_64) COREWRAP_(left_pad_high_1_8) COREWRAP_(left_pad_high_1_16) COREWRAP_(left_pad_high_8_16) COREWRAP_(left_pad_high_1_32) COREWRAP_(left_pad_high_8_32) COREWRAP_(left_pad_high_16_32) COREWRAP_(left_pad_high_1_64) COREWRAP_(left_pad_high_8_64) COREWRAP_(left_pad_high_16_64) COREWRAP_(left_pad_high_32_64) COREWRAP_(left_extend_1_8) COREWRAP_(left_extend_1_16) COREWRAP_(left_extend_8_16) COREWRAP_(left_extend_1_32) COREWRAP_(left_extend_8_32) COREWRAP_(left_extend_16_32) COREWRAP_(left_extend_1_64) COREWRAP_(left_extend_8_64) COREWRAP_(left_extend_16_64) COREWRAP_(left_extend_32_64) COREWRAP_(right_pad_low_1_8) COREWRAP_(right_pad_low_1_16) COREWRAP_(right_pad_low_8_16) COREWRAP_(right_pad_low_1_32) COREWRAP_(right_pad_low_8_32) COREWRAP_(right_pad_low_16_32) COREWRAP_(right_pad_low_1_64) COREWRAP_(right_pad_low_8_64) COREWRAP_(right_pad_low_16_64) COREWRAP_(right_pad_low_32_64) COREWRAP_(right_pad_high_1_8) COREWRAP_(right_pad_high_1_16) COREWRAP_(right_pad_high_8_16) COREWRAP_(right_pad_high_1_32) COREWRAP_(right_pad_high_8_32) COREWRAP_(right_pad_high_16_32) COREWRAP_(right_pad_high_1_64) COREWRAP_(right_pad_high_8_64) COREWRAP_(right_pad_high_16_64) COREWRAP_(right_pad_high_32_64) COREWRAP_(right_extend_8_16) COREWRAP_(right_extend_8_32) COREWRAP_(right_extend_16_32) COREWRAP_(right_extend_8_64) COREWRAP_(right_extend_16_64) COREWRAP_(right_extend_32_64) COREWRAP_(left_shift_with_8) COREWRAP_(left_shift_with_16) COREWRAP_(left_shift_with_32) COREWRAP_(left_shift_with_64) COREWRAP_(left_shift_8) COREWRAP_(left_shift_16) COREWRAP_(left_shift_32) COREWRAP_(left_shift_64) COREWRAP_(right_shift_with_8) COREWRAP_(right_shift_with_16) COREWRAP_(right_shift_with_32) COREWRAP_(right_shift_with_64) COREWRAP_(right_shift_8) COREWRAP_(right_shift_16) COREWRAP_(right_shift_32) COREWRAP_(right_shift_64) COREWRAP_(left_rotate_8) COREWRAP_(left_rotate_16) COREWRAP_(left_rotate_32) COREWRAP_(left_rotate_64) COREWRAP_(right_rotate_8) COREWRAP_(right_rotate_16) COREWRAP_(right_rotate_32) COREWRAP_(right_rotate_64) COREWRAP_(one_8) COREWRAP_(one_16) COREWRAP_(one_32) COREWRAP_(one_64) COREWRAP_(add_8) COREWRAP_(add_16) COREWRAP_(add_32) COREWRAP_(add_64) COREWRAP_(full_add_8) COREWRAP_(full_add_16) COREWRAP_(full_add_32) COREWRAP_(full_add_64) COREWRAP_(full_increment_8) COREWRAP_(full_increment_16) COREWRAP_(full_increment_32) COREWRAP_(full_increment_64) COREWRAP_(increment_8) COREWRAP_(increment_16) COREWRAP_(increment_32) COREWRAP_(increment_64) COREWRAP_(subtract_8) COREWRAP_(subtract_16) COREWRAP_(subtract_32) COREWRAP_(subtract_64) COREWRAP_(full_decrement_8) COREWRAP_(full_decrement_16) COREWRAP_(full_decrement_32) COREWRAP_(full_decrement_64) COREWRAP_(decrement_8) COREWRAP_(decrement_16) COREWRAP_(decrement_32) COREWRAP_(decrement_64) COREWRAP_(negate_8) COREWRAP_(negate_16) COREWRAP_(negate_32) COREWRAP_(negate_64) COREWRAP_(full_subtract_8) COREWRAP_(full_subtract_16) COREWRAP_(full_subtract_32) COREWRAP_(full_subtract_64) COREWRAP_(multiply_8) COREWRAP_(multiply_16) COREWRAP_(multiply_32) COREWRAP_(multiply_64) COREWRAP_(full_multiply_8) COREWRAP_(full_multiply_16) COREWRAP_(full_multiply_32) COREWRAP_(full_multiply_64) COREWRAP_(is_zero_8) COREWRAP_(is_zero_16) COREWRAP_(is_zero_32) COREWRAP_(is_zero_64) COREWRAP_(is_one_8) COREWRAP_(is_one_16) COREWRAP_(is_one_32) COREWRAP_(is_one_64) COREWRAP_(le_8) COREWRAP_(le_16) COREWRAP_(le_32) COREWRAP_(le_64) COREWRAP_(lt_8) COREWRAP_(lt_16) COREWRAP_(lt_32) COREWRAP_(lt_64) COREWRAP_(min_8) COREWRAP_(min_16) COREWRAP_(min_32) COREWRAP_(min_64) COREWRAP_(max_8) COREWRAP_(max_16) COREWRAP_(max_32) COREWRAP_(max_64) COREWRAP_(median_8) COREWRAP_(median_16) COREWRAP_(median_32) COREWRAP_(median_64) COREWRAP_(div_mod_8) COREWRAP_(div_mod_16) COREWRAP_(div_mod_32) COREWRAP_(div_mod_64) COREWRAP_(divide_8) COREWRAP_(divide_16) COREWRAP_(divide_32) COREWRAP_(divide_64) COREWRAP_(modulo_8) COREWRAP_(modulo_16) COREWRAP_(modulo_32) COREWRAP_(modulo_64) COREWRAP_(divides_8) COREWRAP_(divides_16) COREWRAP_(divides_32) COREWRAP_(divides_64) COREWRAP_(div_mod_128_64) COREWRAP_(sha_256_iv) COREWRAP_(sha_256_block) COREWRAP_(sha_256_ctx_8_init) COREWRAP_(sha_256_ctx_8_add_1) COREWRAP_(sha_256_ctx_8_add_2) COREWRAP_(sha_256_ctx_8_add_4) COREWRAP_(sha_256_ctx_8_add_8) COREWRAP_(sha_256_ctx_8_add_16) COREWRAP_(sha_256_ctx_8_add_32) COREWRAP_(sha_256_ctx_8_add_64) COREWRAP_(sha_256_ctx_8_add_128) COREWRAP_(sha_256_ctx_8_add_256) COREWRAP_(sha_256_ctx_8_add_512) COREWRAP_(sha_256_ctx_8_add_buffer_511) COREWRAP_(sha_256_ctx_8_finalize) COREWRAP_(fe_normalize) COREWRAP_(fe_negate) COREWRAP_(fe_add) COREWRAP_(fe_square) COREWRAP_(fe_multiply) COREWRAP_(fe_multiply_beta) COREWRAP_(fe_invert) COREWRAP_(fe_square_root) COREWRAP_(fe_is_zero) COREWRAP_(fe_is_odd) COREWRAP_(scalar_normalize) COREWRAP_(scalar_negate) COREWRAP_(scalar_add) COREWRAP_(scalar_square) COREWRAP_(scalar_multiply) COREWRAP_(scalar_multiply_lambda) COREWRAP_(scalar_invert) COREWRAP_(scalar_is_zero) COREWRAP_(gej_infinity) COREWRAP_(gej_rescale) COREWRAP_(gej_normalize) COREWRAP_(gej_negate) COREWRAP_(ge_negate) COREWRAP_(gej_double) COREWRAP_(gej_add) COREWRAP_(gej_ge_add_ex) COREWRAP_(gej_ge_add) COREWRAP_(gej_is_infinity) COREWRAP_(gej_equiv) COREWRAP_(gej_ge_equiv) COREWRAP_(gej_x_equiv) COREWRAP_(gej_y_is_odd) COREWRAP_(gej_is_on_curve) COREWRAP_(ge_is_on_curve) COREWRAP_(scale) COREWRAP_(off_curve_scale) COREWRAP_(generate) COREWRAP_(linear_combination_1) COREWRAP_(off_curve_linear_combination_1) COREWRAP_(linear_verify_1) COREWRAP_(decompress) COREWRAP_(point_verify_1) COREWRAP_(check_sig_verify) COREWRAP_(bip_0340_verify) COREWRAP_(swu) COREWRAP_(hash_to_curve) COREWRAP_(parse_lock) COREWRAP_(parse_sequence) COREWRAP_(tapdata_init) ================================================ FILE: Haskell/cbits/dag.c ================================================ #include "dag.h" #include "bitstream.h" #include "bitstring.h" const size_t c_sizeof_dag_node = sizeof(dag_node); void c_compute_word_cmr(unsigned char *cmr, bitstream* stream, size_t offset, size_t n) { sha256_midstate result; bitstring value; simplicity_readBitstring(&value, offset, stream); /* skip offset many bits. */ simplicity_readBitstring(&value, (size_t)1 << n, stream); result = simplicity_computeWordCMR(&value, n); sha256_fromMidstate(cmr, result.s); } void c_dag_node_get_cmr(unsigned char *cmr, const dag_node* node) { sha256_fromMidstate(cmr, node->cmr.s); } ================================================ FILE: Haskell/cbits/elements/env.c ================================================ #include "simplicity_alloc.h" #include "simplicity/elements/env.h" #include "elements/txEnv.h" const size_t c_sizeof_rawElementsBuffer = sizeof(rawElementsBuffer); const size_t c_sizeof_rawElementsOutput = sizeof(rawElementsOutput); const size_t c_sizeof_rawElementsInput = sizeof(rawElementsInput); const size_t c_sizeof_rawElementsTransaction = sizeof(rawElementsTransaction); const size_t c_sizeof_rawElementsTapEnv = sizeof(rawElementsTapEnv); const size_t c_sizeof_txEnv = sizeof(txEnv); void c_set_rawElementsBuffer(rawElementsBuffer* result, const char* buf, unsigned int len) { *result = (rawElementsBuffer){ .buf = buf, .len = len }; } void c_set_rawElementsOutput(rawElementsOutput* result, const char* asset, const char* value, const char* nonce, const rawElementsBuffer* scriptPubKey, const rawElementsBuffer* surjectionProof, const rawElementsBuffer* rangeProof) { *result = (rawElementsOutput){ .asset = asset , .value = value , .nonce = nonce , .scriptPubKey = *scriptPubKey , .surjectionProof = *surjectionProof , .rangeProof = *rangeProof }; } void c_set_rawElementsInput(rawElementsInput* result, const rawElementsBuffer* annex, const char* pegin, const rawElementsBuffer* scriptSig, const char* prevTxid, unsigned int prevIx, const char* asset, const char* value, const rawElementsBuffer* scriptPubKey, unsigned int sequence, const char* blindingNonce, const char* assetEntropy, const char* amount, const char* inflationKeys, const rawElementsBuffer* amountRangePrf, const rawElementsBuffer* inflationKeysRangePrf) { *result = (rawElementsInput){ .annex = annex , .scriptSig = *scriptSig , .prevTxid = prevTxid , .pegin = pegin , .issuance = { .blindingNonce = blindingNonce , .assetEntropy = assetEntropy , .amount = amount , .inflationKeys = inflationKeys , .amountRangePrf = *amountRangePrf , .inflationKeysRangePrf = *inflationKeysRangePrf } , .txo = {.asset = asset, .value = value, .scriptPubKey = *scriptPubKey} , .prevIx = prevIx , .sequence = sequence }; } void c_set_rawElementsTransaction(rawElementsTransaction* result, const unsigned char* txid, unsigned int version, const rawElementsInput* input, unsigned int numInputs, const rawElementsOutput* output, unsigned int numOutputs, unsigned int lockTime) { *result = (rawElementsTransaction){ .txid = txid , .version = version , .input = input, .numInputs = numInputs , .output = output, .numOutputs = numOutputs , .lockTime = lockTime, }; } void c_set_rawElementsTapEnv(rawElementsTapEnv* result, const char* controlBlock, unsigned char pathLen, const char* scriptCMR) { *result = (rawElementsTapEnv){ .controlBlock = controlBlock, .pathLen = pathLen, .scriptCMR = scriptCMR }; } void c_set_txEnv(txEnv* result, const elementsTransaction* tx, const elementsTapEnv* taproot, const char* genesisHash, unsigned int ix) { sha256_midstate genesis; sha256_toMidstate(genesis.s, genesisHash); *result = simplicity_elements_build_txEnv(tx, taproot, &genesis, ix); } ================================================ FILE: Haskell/cbits/elements/jets.c ================================================ #include "elements/elementsJets.h" #include "../wrappers.h" WRAP_(version) WRAP_(lock_time) WRAP_(input_pegin) WRAP_(input_prev_outpoint) WRAP_(input_asset) WRAP_(input_amount) WRAP_(input_script_hash) WRAP_(input_sequence) WRAP_(input_annex_hash) WRAP_(input_script_sig_hash) WRAP_(reissuance_blinding) WRAP_(new_issuance_contract) WRAP_(reissuance_entropy) WRAP_(issuance_asset_amount) WRAP_(issuance_token_amount) WRAP_(issuance_asset_proof) WRAP_(issuance_token_proof) WRAP_(output_asset) WRAP_(output_amount) WRAP_(output_nonce) WRAP_(output_script_hash) WRAP_(output_null_datum) WRAP_(output_is_fee) WRAP_(output_surjection_proof) WRAP_(output_range_proof) WRAP_(total_fee) WRAP_(genesis_block_hash) WRAP_(script_cmr) WRAP_(transaction_id) WRAP_(current_index) WRAP_(current_pegin) WRAP_(current_prev_outpoint) WRAP_(current_asset) WRAP_(current_amount) WRAP_(current_script_hash) WRAP_(current_sequence) WRAP_(current_reissuance_blinding) WRAP_(current_new_issuance_contract) WRAP_(current_reissuance_entropy) WRAP_(current_issuance_asset_amount) WRAP_(current_issuance_token_amount) WRAP_(current_issuance_asset_proof) WRAP_(current_issuance_token_proof) WRAP_(current_annex_hash) WRAP_(current_script_sig_hash) WRAP_(tapleaf_version) WRAP_(tappath) WRAP_(internal_key) WRAP_(num_inputs) WRAP_(num_outputs) WRAP_(tx_is_final) WRAP_(tx_lock_height) WRAP_(tx_lock_time) WRAP_(broken_do_not_use_tx_lock_distance) WRAP_(broken_do_not_use_tx_lock_duration) WRAP_(check_lock_height) WRAP_(check_lock_time) WRAP_(broken_do_not_use_check_lock_distance) WRAP_(broken_do_not_use_check_lock_duration) COREWRAP_(calculate_issuance_entropy) COREWRAP_(calculate_asset) COREWRAP_(calculate_explicit_token) COREWRAP_(calculate_confidential_token) COREWRAP_(lbtc_asset) COREWRAP_(outpoint_hash) COREWRAP_(asset_amount_hash) COREWRAP_(nonce_hash) COREWRAP_(annex_hash) COREWRAP_(build_tapleaf_simplicity) COREWRAP_(build_tapbranch) COREWRAP_(build_taptweak) WRAP_(issuance) WRAP_(issuance_entropy) WRAP_(issuance_asset) WRAP_(issuance_token) WRAP_(output_amounts_hash) WRAP_(output_nonces_hash) WRAP_(output_scripts_hash) WRAP_(output_range_proofs_hash) WRAP_(output_surjection_proofs_hash) WRAP_(outputs_hash) WRAP_(output_hash) WRAP_(input_outpoints_hash) WRAP_(input_amounts_hash) WRAP_(input_scripts_hash) WRAP_(input_utxos_hash) WRAP_(input_utxo_hash) WRAP_(input_sequences_hash) WRAP_(input_annexes_hash) WRAP_(input_script_sigs_hash) WRAP_(inputs_hash) WRAP_(input_hash) WRAP_(issuance_asset_amounts_hash) WRAP_(issuance_token_amounts_hash) WRAP_(issuance_range_proofs_hash) WRAP_(issuance_blinding_entropy_hash) WRAP_(issuances_hash) WRAP_(issuance_hash) WRAP_(tx_hash) WRAP_(tapleaf_hash) WRAP_(tappath_hash) WRAP_(tap_env_hash) WRAP_(sig_all_hash) ================================================ FILE: Haskell/cbits/frame.c ================================================ #include "frame.h" const size_t c_sizeof_UWORD = sizeof(UWORD); const size_t c_sizeof_frameItem = sizeof(frameItem); void c_initReadFrame(frameItem* frame, size_t n, UWORD* from) { *frame = initReadFrame(n, from); } void c_initWriteFrame(frameItem* frame, size_t n, UWORD* from) { *frame = initWriteFrame(n, from); } bool c_readBit(frameItem* frame) { return readBit(frame); } void c_writeBit(frameItem* frame, bool bit) { writeBit(frame, bit); } void c_forwardBits(frameItem* frame, size_t n) { forwardBits(frame, n); } void c_skipBits(frameItem* frame, size_t n) { skipBits(frame, n); } ================================================ FILE: Haskell/cbits/wrappers.h ================================================ #ifndef WRAPPERS_H #define WRAPPERS_H #define COREWRAP_(jet) \ bool c_##jet(frameItem* dst, const frameItem* src) { \ bool result = simplicity_##jet(dst, *src, NULL); \ assert (!result || 0 == dst->offset); \ return result; \ } #define WRAP_(jet) \ bool c_##jet(frameItem* dst, const frameItem* src, const txEnv* env) { \ bool result = simplicity_##jet(dst, *src, env); \ assert (!result || 0 == dst->offset); \ return result; \ } #endif ================================================ FILE: Haskell-Examples/TestnetTransaction.hs ================================================ -- | A little program that can be used to make a test network transactions on liquid testnet or other regtest networks. -- See for a walkthrogh on how to use it. module TestnetTransaction where import Control.Monad (guard) import qualified Data.Array as Arr import Data.Bits (Bits, testBit, unsafeShiftL, unsafeShiftR, xor, (.&.), (.|.)) import qualified Data.ByteString as BS import qualified Data.ByteString.Lazy as BSL import qualified Data.ByteString.Char8 as BSC import Data.Char (toLower, toUpper) import Data.Foldable (foldl') import Data.Functor.Identity (Identity, runIdentity) import Data.Ix (Ix (..)) import Data.Word (Word8) import Data.List (intercalate) import Data.String (fromString) import Data.Serialize (decode, encode, runPut) import Data.Vector (fromList) import Numeric (readHex, showHex) import Lens.Family2 ((^.), review, over) import System.IO (BufferMode(NoBuffering), hSetBuffering, stdin, stdout) import System.Entropy (getEntropy) import Simplicity.Digest (Hash256, le256, be256, bsHash, integerHash256) import Simplicity.LibSecp256k1.Spec ( PubKey(PubKey), GE(GE), Point(Point), Sig(Sig) , g, gej_normalize, gej_ge_add_ex, scale, scalar , pubkey_unpack, decompress, groupOrder, fe_pack, fe_is_odd , linear_combination_1, ge_to_gej ) import Simplicity.Word (Word256) import Simplicity.MerkleRoot (CommitmentRoot, commitmentRoot) import Simplicity.Programs.Generic (scribe) import Simplicity.Programs.CheckSig.Lib (checkSigVerify') import Simplicity.Serialization (putBitStream) import Simplicity.Elements.Jets (jetSubst, pruneSubst, fastEval, unwrap, putTermLengthCode) import Simplicity.Elements.Programs.SigHash.Lib (sigAllHash) import Simplicity.Elements.DataTypes ( Asset, asset, Amount, amount, clearAssetPrf , Nonce(Nonce), Confidential(Explicit), Outpoint(Outpoint) , UTXO(..), SigTxInput(..), TxOutput(..), SigTx(..) , TapEnv(..) ) import Simplicity.Elements.Primitive (primEnv) import qualified Simplicity.Ty.Word import Data.List (sort) -- # Bech 32 -- Adapted from https://github.com/sipa/bech32/blob/842b49701067c585762a7b6550439d2d5f4918ad/ref/haskell/src/Codec/Binary/Bech32.hs -- Copyright (c) 2017 Marko Bencun -- -- Permission is hereby granted, free of charge, to any person obtaining a copy -- of this software and associated documentation files (the "Software"), to deal -- in the Software without restriction, including without limitation the rights -- to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -- copies of the Software, and to permit persons to whom the Software is -- furnished to do so, subject to the following conditions: -- -- The above copyright notice and this permission notice shall be included in -- all copies or substantial portions of the Software. -- -- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -- AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -- OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN -- THE SOFTWARE. type HRP = BS.ByteString type Data = [Word8] (.>>.), (.<<.) :: Bits a => a -> Int -> a (.>>.) = unsafeShiftR (.<<.) = unsafeShiftL newtype Word5 = UnsafeWord5 Word8 deriving (Eq, Ord, Show) instance Ix Word5 where range (UnsafeWord5 m, UnsafeWord5 n) = map UnsafeWord5 $ range (m, n) index (UnsafeWord5 m, UnsafeWord5 n) (UnsafeWord5 i) = index (m, n) i inRange (m,n) i = m <= i && i <= n word5 :: Integral a => a -> Word5 word5 x = UnsafeWord5 ((fromIntegral x) .&. 31) {-# INLINE word5 #-} {-# SPECIALIZE INLINE word5 :: Word8 -> Word5 #-} fromWord5 :: Num a => Word5 -> a fromWord5 (UnsafeWord5 x) = fromIntegral x {-# INLINE fromWord5 #-} {-# SPECIALIZE INLINE fromWord5 :: Word5 -> Word8 #-} charset :: Arr.Array Word5 Char charset = Arr.listArray (UnsafeWord5 0, UnsafeWord5 31) "qpzry9x8gf2tvdw0s3jn54khce6mua7l" charsetMap :: Char -> Maybe Word5 charsetMap c | inRange (Arr.bounds inv) upperC = inv Arr.! upperC | otherwise = Nothing where upperC = toUpper c inv = Arr.listArray ('0', 'Z') (repeat Nothing) Arr.// (map swap (Arr.assocs charset)) swap (a, b) = (toUpper b, Just a) bech32Polymod :: [Word5] -> Word bech32Polymod values = foldl' go 1 values .&. 0x3fffffff where go chk value = foldl' xor chk' [g | (g, i) <- zip generator [25..], testBit chk i] where generator = [0x3b6a57b2, 0x26508e6d, 0x1ea119fa, 0x3d4233dd, 0x2a1462b3] chk' = chk .<<. 5 `xor` (fromWord5 value) bech32HRPExpand :: HRP -> [Word5] bech32HRPExpand hrp = map (UnsafeWord5 . (.>>. 5)) (BS.unpack hrp) ++ [UnsafeWord5 0] ++ map word5 (BS.unpack hrp) bech32CreateChecksum :: Word -> HRP -> [Word5] -> [Word5] bech32CreateChecksum spec hrp dat = [word5 (polymod .>>. i) | i <- [25,20..0]] where values = bech32HRPExpand hrp ++ dat polymod = bech32Polymod (values ++ map UnsafeWord5 [0, 0, 0, 0, 0, 0]) `xor` spec bech32VerifyChecksum :: HRP -> [Word5] -> Word bech32VerifyChecksum hrp dat = bech32Polymod (bech32HRPExpand hrp ++ dat) data EncodeError = ResultStringLengthExceeded | InvalidHumanReadablePart deriving (Show, Eq) bech32Encode :: Word -> HRP -> [Word5] -> Either EncodeError BS.ByteString bech32Encode spec hrp dat = do verify InvalidHumanReadablePart $ validHRP hrp let dat' = dat ++ bech32CreateChecksum spec hrp dat rest = map (charset Arr.!) dat' result = BSC.concat [BSC.map toLower hrp, BSC.pack "1", BSC.pack rest] verify ResultStringLengthExceeded $ BS.length result <= 90 return result validHRP :: BS.ByteString -> Bool validHRP hrp = not (BS.null hrp) && BS.all (\char -> char >= 33 && char <= 126) hrp data DecodeError = Bech32StringLengthExceeded | CaseInconsistency | TooShortDataPart | InvalidHRP | ChecksumVerificationFail | InvalidCharsetMap deriving (Show, Eq) bech32Decode :: BS.ByteString -> Either DecodeError (Word, HRP, [Word5]) bech32Decode bech32 = do verify Bech32StringLengthExceeded $ BS.length bech32 <= 90 verify CaseInconsistency $ validCase bech32 let (hrp, dat) = BSC.breakEnd (== '1') $ BSC.map toLower bech32 verify TooShortDataPart $ BS.length dat >= 6 hrp' <- maybeToRight InvalidHRP $ BSC.stripSuffix (BSC.pack "1") hrp verify InvalidHRP $ validHRP hrp' dat' <- maybeToRight InvalidCharsetMap . mapM charsetMap $ BSC.unpack dat let spec = bech32VerifyChecksum hrp' dat' return (spec, hrp', take (BS.length dat - 6) dat') where validCase :: BS.ByteString -> Bool validCase b32 = BSC.map toUpper b32 == b32 || BSC.map toLower b32 == b32 type Pad f = Int -> Int -> Word -> [[Word]] -> f [[Word]] yesPadding :: Pad Identity yesPadding _ 0 _ result = return result yesPadding _ _ padValue result = return $ [padValue] : result {-# INLINE yesPadding #-} noPadding :: Pad Maybe noPadding frombits bits padValue result = do guard $ bits < frombits && padValue == 0 return result {-# INLINE noPadding #-} -- Big endian conversion of a bytestring from base 2^frombits to base 2^tobits. -- frombits and twobits must be positive and 2^frombits and 2^tobits must be smaller than the size of Word. -- Every value in dat must be strictly smaller than 2^frombits. convertBits :: Functor f => [Word] -> Int -> Int -> Pad f -> f [Word] convertBits dat frombits tobits pad = fmap (concat . reverse) $ go dat 0 0 [] where go [] acc bits result = let padValue = (acc .<<. (tobits - bits)) .&. maxv in pad frombits bits padValue result go (value:dat') acc bits result = go dat' acc' (bits' `rem` tobits) (result':result) where acc' = (acc .<<. frombits) .|. fromIntegral value bits' = bits + frombits result' = [(acc' .>>. b) .&. maxv | b <- [bits'-tobits,bits'-2*tobits..0]] maxv = (1 .<<. tobits) - 1 {-# INLINE convertBits #-} toBase32 :: [Word8] -> [Word5] toBase32 dat = map word5 $ runIdentity $ convertBits (map fromIntegral dat) 8 5 yesPadding toBase256 :: [Word5] -> Maybe [Word8] toBase256 dat = fmap (map fromIntegral) $ convertBits (map fromWord5 dat) 5 8 noPadding segwitCheck :: Word8 -> Data -> Maybe Word segwitCheck witver witprog = do guard $ witver <= 16 if witver == 0 then guard (length witprog == 20 || length witprog == 32) >> return 1 else guard (length witprog >= 2 && length witprog <= 40) >> return bech32mConst where bech32mConst = 0x2bc830a3 segwitDecode :: HRP -> BS.ByteString -> Maybe (Word8, Data) segwitDecode hrp addr = do (spec', hrp', dat) <- rightToMaybe $ bech32Decode addr guard $ (hrp == hrp') && not (null dat) let (UnsafeWord5 witver : datBase32) = dat decoded <- toBase256 datBase32 spec <- segwitCheck witver decoded guard $ spec == spec' return (witver, decoded) segwitEncode :: HRP -> Word8 -> Data -> Maybe BS.ByteString segwitEncode hrp witver witprog = do spec <- segwitCheck witver witprog rightToMaybe $ bech32Encode spec hrp $ UnsafeWord5 witver : toBase32 witprog rightToMaybe :: Either l r -> Maybe r rightToMaybe = either (const Nothing) Just maybeToRight :: l -> Maybe r -> Either l r maybeToRight l = maybe (Left l) Right verify :: a -> Bool -> Either a () verify _ True = Right () verify v False = Left v -- Construct an Elements regtest non-blinded address for a segwit program texScriptPubKey :: Word8 -> Data -> BSL.ByteString texScriptPubKey segver prog | 2 <= len && len <= 40 = BSL.singleton encver <> BSL.singleton len <> (BSL.pack prog) where len = fromIntegral (length prog) encver | segver == 0 = 0 | segver <= 16 = 80 + segver -- # Taproot constructions -- Construct a tapleaf hash for a given "script" for a given leaf version. tapleafHash :: Word8 -> BS.ByteString -> Hash256 tapleafHash leafver script | even leafver = bsHash $ encode tag <> encode tag <> BS.singleton leafver <> compactSize script <> script where tag = bsHash (fromString "TapLeaf/elements") compactSize str | size < 0xfd = BS.singleton (fromIntegral size) where size = BS.length str -- TapPath contains the data relevant for a taproot address supporting a single tapleaf program. -- It contains the taproot output key, the control block connecting to the leaf, and the script at that leaf data TapPath = TapPath { outputKey :: PubKey , controlBlock :: BS.ByteString , script :: BS.ByteString } -- Create a TapPath for a taproot program. tapPath :: Word8 -> BS.ByteString -> [Hash256] -> PubKey -> Maybe TapPath tapPath leafver script path internalKey | even leafver = do pt <- pubkey_unpack internalKey p <- decompress pt guard (tweak < groupOrder) let Just ge = (do s <- scale (scalar tweak) g gej_normalize (snd (gej_ge_add_ex s p))) let Point b x = compress ge let cb = BS.singleton (leafver .|. if b then 1 else 0) <> encode internalKey <> foldMap encode path return $ TapPath { outputKey = PubKey (fe_pack x), controlBlock = cb, script = script } where leafHash = tapleafHash leafver script branch h1 h2 = bsHash $ encode branchtag <> encode branchtag <> encode a <> encode b where branchtag = bsHash (fromString "TapBranch/elements") [a,b] = sort [h1, h2] rootHash = foldl branch leafHash path tag = bsHash (fromString "TapTweak/elements") tweak = integerHash256 . bsHash $ encode tag <> encode tag <> encode internalKey <> encode rootHash compress (GE x y) = Point (fe_is_odd y) x -- # Misc. hexString :: BS.ByteString -> String hexString str = (\s -> replicate (2-length s) '0' ++ s) . flip showHex "" =<< BS.unpack str getHexLine :: (Show a, Integral a) => String -> Int -> Maybe a -> IO a getHexLine prompt digits mdef = do putStr (showString prompt . maybe id (\def -> showString " " . showParen True (showHex def)) mdef $ "? ") str <- getLine case (str, mdef) of ("", Just x) -> return x otherwise -> do guard $ digits == length str let [(x,"")] = readHex str return x getIntLine :: (Read a, Integral a) => String -> IO a getIntLine prompt = do putStr $ prompt ++ "? " readLn getStrLine :: String -> String -> IO String getStrLine prompt def = do putStr $ prompt ++ " (" ++ def ++ ")? " str <- getLine return $ if null str then def else str -- This is an standard unspendable public key with no known private key as defined in BIP-0341. unspendablePubKey tweak = PubKey (fe_pack x) where Just unspendable = pubkey_unpack (PubKey 0x50929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0) >>= decompress Just (GE x _) = linear_combination_1 (scalar 1) (ge_to_gej unspendable) tweak >>= gej_normalize -- This is an example Pubkey. It has a well know private key. DO NOT USE for anything but testing. insecurePubKey = PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 -- DO NOT USE! -- This is for testing purposes only. -- Do not even copy this function and try to "fix it" to make it work. -- It is insecure. It uses an insecure nonce; it signs only for insecurePubKey. -- DO NOT USE! -- For production purposes you need to use proper bindings to . insecureSign :: Hash256 -> Sig insecureSign msg = Sig 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 (fromInteger ((k * (1 + e)) `mod` order)) where order = groupOrder k = 1 + fromInteger order `div` 2 tag = encode . Simplicity.Digest.bsHash $ Data.String.fromString "BIP0340/challenge" e = integerHash256 . bsHash $ tag <> tag <> encode insecurePubKey <> encode insecurePubKey <> encode msg main :: IO () main = do hSetBuffering stdin NoBuffering hSetBuffering stdout NoBuffering -- Randomize the taproot internal key for privacy. Right randomTweak <- decode <$> getEntropy 32 tweak <- scalar <$> getHexLine "Random privacy tweak" 64 (Just (toInteger (randomTweak :: Word256))) let internalKey = unspendablePubKey tweak putStr "Internal " >> print internalKey -- A generic checksig program written in Simplicity, optimized with jets. -- Works on an arbitrary sighash function. Requires a public key and a signature. -- This program is the standard single key Simpliciy program. let optCheckSig sighash sig pubkey = jetSubst $ checkSigVerify' sighash pubkey sig -- Compute the commitment Merkle root (CMR) of this standard program. -- We need to fill in a dummy sighash an a dummy signature, -- but the CMR only depends on the pubkey. let standardCMR pubkey = let { dummySig = Sig 0 0 ; dummySigHash = scribe (Simplicity.Ty.Word.toWord256 0) } in commitmentRoot . unwrap $ optCheckSig dummySigHash dummySig pubkey let path = review (over be256) <$> [{-path goes here-}] -- Compute a taproot for this standard program. -- 0xbe is the tapleaf version we have chosen for Simplicity. let standardTR pubkey = tapPath 0xbe (encode (standardCMR pubkey)) path internalKey -- In our example we will be using "insecurePubKey" as our public key. let p = insecurePubKey putStr "Simplicity " >> print p -- Compute the CMR of the standard program for our chosen key. let cmrP = standardCMR p -- Compute the taproot for the standard program for our chosen key. let Just trP = standardTR p -- compute the address for our standard program for our chosen key. let Just simplicityAddress = segwitEncode (fromString "tex") 0x01 (BS.unpack . encode $ outputKey trP) putStr "Example simplicity address: " >> BSC.putStrLn simplicityAddress putStrLn "Press ⏎ to continue." getLine -- When funds are send to this address we will want to spend this. -- In this spending example the entire funds in a UTXO are send to another address, less fees. -- We could sign with the taproot key path; that does not require the use of Simplicity. -- However, in this example we will show how to use the Simplicity spending path to redeem funds. -- To spend funds we need to choose a sighash algorithm. -- Unlike Bitcoin script there is no fixed choice; we can program any sighash function we want. -- In this example we will be using Simplicity's version similar to sigAllHash. -- Optimize the sigAllHash program with jets. let optSigAllHash = jetSubst sigAllHash -- By default use Liquid testnet's genesis hash genesisHash <- review (over le256) <$> getHexLine "Chain's Genesis Hash" 64 (Just 0xa771da8e52ee6ad581ed1e9a99825e5b3b7992225534eaa2ae23244fe26ab1c1) -- To spend funds we need the UTXO data, including the txid, vout, asset id and amount. inputTxid <- getHexLine "Input's TXID" 64 Nothing inputVout <- getIntLine "Input's vout" -- By default use Liquid testnet's tl-btc asset assetId <- review (over asset) . Explicit . review (over le256) <$> getHexLine "Input's asset ID" 64 (Just 0x144c654344aa716d6f3abcc1ca90e5641e4e2a7f633bc09fe3baf64585819a49) inputAmount <- getIntLine "Input's value in sats" let inputUtxo = UTXO { utxoAsset = clearAssetPrf assetId , utxoAmount = review (over amount) . Explicit $ inputAmount , utxoScript = texScriptPubKey 1 (BS.unpack . encode $ outputKey trP) } -- By default use Liquid testnet's faucet as the (unblinded) output address outputAddress <- getStrLine "Output's address" "tex1qyh6tyhspd9w8jhqee8a2uzvyk9lnwp2n8ssur0" let Just outputScript = uncurry texScriptPubKey <$> segwitDecode (fromString "tex") (fromString outputAddress) fee <- getIntLine "fee in sats" let outputAmount = inputAmount-fee guard (0 < outputAmount) -- Construct the output script from the given address. -- Construct the transaction data, including inputs and outputs, including the explicit fee required by Elements. -- We assume a standard sequence number. let inputSequence = 0xfffffffe let input0 = SigTxInput { sigTxiAnnex = Nothing , sigTxiPegin = Nothing , sigTxiPreviousOutpoint = Outpoint (review (over le256) inputTxid) inputVout , sigTxiTxo = inputUtxo , sigTxiSequence = inputSequence , sigTxiIssuance = Nothing , sigTxiScriptSig = mempty } let output0 = TxOutput { txoAsset = assetId , txoAmount = review (over amount) . Explicit $ outputAmount , txoNonce = Nothing , txoScript = outputScript } let output1 = TxOutput { txoAsset = assetId , txoAmount = review (over amount) . Explicit $ fee , txoNonce = Nothing , txoScript = mempty } let tx = SigTx { sigTxVersion = 0x00000002 , sigTxIn = fromList [input0] , sigTxOut = fromList [output0, output1] , sigTxLock = 0 } -- Define our taproot environment. let tapEnv = TapEnv { tapleafVersion = 0xbe , tapInternalKey = internalKey , tappath = path , tapScriptCMR = cmrP } -- The signing environment includes the transaction data and which input we are signing for. let ix = 0 let Just env = primEnv tx ix tapEnv genesisHash -- Run our optimized sigAllHash function in this environment to compute the transaction hash we are going to be signing. let Just txSigAllHash = fromInteger . Simplicity.Ty.Word.fromWord256 <$> fastEval (unwrap optSigAllHash) env () :: Maybe Word256 -- Our message is a tagged hash that covers both the CMR of our chosen sighash algorithm, and the output of that algorithm. let msg = let tag = bsHash (fromString "Simplicity\USSignature") in bsHash $ encode tag <> encode tag <> encode (commitmentRoot . unwrap $ optSigAllHash) <> encode (txSigAllHash :: Word256) -- Create a BIP-0340 signature for our insecure pubkey using an insecure signing algorithm. -- This is for demonstration purposes only. DO NOT USE! let sig = insecureSign msg -- Create our optimized checkSig simplicity program with our chosen hash algorithm and the signature we computed. -- Encode this program in Simplicity's binary format. let Just (bin,wit) = putTermLengthCode . unwrap <$> pruneSubst (checkSigVerify' (unwrap optSigAllHash) p sig) env let binary = runPut . putBitStream $ bin let witness = runPut . putBitStream $ wit -- The witness stack consists of (1) the binary program (2) the CMR of our program, and (3) the taproot control block. putStrLn $ "--final-script-witness " ++ intercalate "," (hexString <$> [witness, binary, script trP, controlBlock trP]) ================================================ FILE: Haskell-Generate/GenDecodeJet.hs ================================================ {-# LANGUAGE OverloadedStrings, QuantifiedConstraints, RankNTypes, ScopedTypeVariables #-} module GenDecodeJet where import Data.Maybe (catMaybes) import Prettyprinter ( Doc, (<+>), braces, colon, line, nest, pretty, semi, vsep , SimpleDocStream, LayoutOptions(..), PageWidth(..), defaultLayoutOptions, layoutPretty ) import Prettyprinter.Render.Text (renderIO) import System.IO (IOMode(WriteMode), withFile) import NameWrangler import Simplicity.Bitcoin.Jets (bitcoinCatalogue) import Simplicity.CoreJets (coreCatalogue) import Simplicity.Elements.Jets (elementsCatalogue) import Simplicity.Ty import Simplicity.Tree x <-> y = x <> line <> y nestBraces x = braces (nest 2 (line <> x) <> line) labelCase ix = "case" <+> pretty ix <> colon decodeCatalogue :: Catalogue String -> Doc a decodeCatalogue Missing = mempty decodeCatalogue (Item name) = "*result =" <+> pretty (upperSnakeCase name) <> semi <+> "return SIMPLICITY_NO_ERROR" <> semi decodeCatalogue (Shelf l) = vsep [ "code = simplicity_decodeUptoMaxInt(stream)" <> semi , "if (code < 0) return (simplicity_err)code" <> semi , "switch (code)" <+> nestBraces (vsep cases) ] where cases = catMaybes $ zipWith f [(1::Int)..] l f _ Missing = Nothing f ix cat@(Item _) = Just . nest 2 $ labelCase ix <+> decodeCatalogue cat f ix cat@(Shelf _) = Just . nest 2 $ labelCase ix <-> decodeCatalogue cat <-> "break" <> semi renderFile name doc = withFile name WriteMode (\h -> renderIO h (layoutPretty layoutOptions (header <-> doc))) where header = "/* This file has been automatically generated. */\n" main = do renderFile "decodeCoreJets.inc" (wrap (decodeCatalogue (mkName <$> coreCatalogue))) renderFile "decodeElementsJets.inc" (wrap (decodeCatalogue (mkName <$> elementsCatalogue))) renderFile "decodeBitcoinJets.inc" (wrap (decodeCatalogue (mkName <$> bitcoinCatalogue))) where wrap doc = nestBraces ("int32_t code;" <-> doc) layoutOptions = LayoutOptions { layoutPageWidth = AvailablePerLine 100 1 } ================================================ FILE: Haskell-Generate/GenPrecomputed.hs ================================================ {-# LANGUAGE OverloadedStrings #-} module GenPrecomputed where import Prelude hiding (sum) import Data.List.Split (chunksOf) import Numeric (showHex) import Prettyprinter ( Doc, (<+>), encloseSep, flatAlt, fillSep, group, line, nest, pretty, vsep , SimpleDocStream, LayoutOptions(..), PageWidth(..), defaultLayoutOptions, layoutPretty , lbrace, rbrace, semi ) import Prettyprinter.Render.Text (renderIO) import System.IO (IOMode(WriteMode), withFile) import Simplicity.Digest import Simplicity.MerkleRoot import Simplicity.Programs.Generic import Simplicity.Tags import Simplicity.Ty import Simplicity.Ty.Word x <-> y = x <> line <> y class Enumerable a where allValues :: [a] instance Enumerable () where allValues = [()] instance (Enumerable a, Enumerable b) => Enumerable (Either a b) where allValues = (Left <$> allValues) ++ (Right <$> allValues) instance (Enumerable a, Enumerable b) => Enumerable (a, b) where allValues = pair <$> allValues <*> allValues where pair x y = (x, y) single = (:[]) bracket = group . encloseSep (flatAlt "{ " "{") (flatAlt " }" "}") ", " prettyCHash :: Hash256 -> Doc a prettyCHash h = bracket (format <$> chunksOf 8 str_h) where format x = "0x" <> pretty x <> "u" str_h = padding ++ text where padding = replicate (64 - length text) '0' text = showHex (integerHash256 h) "" declIV :: String -> IV -> Doc a declIV name iv = nest 2 $ (pretty $ "static const sha256_midstate "++name++"IV =") <-> (bracket . single . prettyCHash $ ivHash iv) <> semi declareSignatureIV :: Doc a declareSignatureIV = vsep [ "/* Initial values for Simplicity's standard tagged message digest. */" , declIV "signature" signatureTag ] declareTyIVs :: Doc a declareTyIVs = vsep $ "/* Initial values for all the 'typeName's. */":(declTy <$> ["unit", "sum", "prod"]) where declTy name = declIV name (typeTag name) declareMRIVs :: Doc a declareMRIVs = vsep $ ["/* Initial values for all the tags for 'CMR's, 'AMR's and 'IMR's. */"] ++ (declCMR <$> names) ++ (declAMR <$> ["assertl", "assertr"] ++ names) ++ (declIMR <$> ["disconnect", "witness"]) ++ [declIV "identity" identityHashTag, declIV "hidden" hiddenTag, declIV "jet" jetTag] where declCMR name = declIV ("cmr_" ++ name) (commitmentTag name) declAMR name = declIV ("amr_" ++ name) (annotatedTag name) declIMR name = declIV ("imr_" ++ name) (identityTag name) names = ["comp", "case", "pair", "disconnect", "injl", "injr", "take", "drop", "iden", "unit", "witness"] declareWordCMRs :: Doc a declareWordCMRs = vsep [ "/* This array contains the cmr of all canonical expressions of type X |- TWO through X |- TWO^8 that output distinct values." , " * word_cmr[0..1] contain the cmrs for scribe(0) .. scribe(1) : X | - TWO" , " * word_cmr[2..5] contain the cmrs for scribe(0) .. scribe(3) : X | - TWO^2" , " * word_cmr[6..21] contain the cmrs for scribe(0) .. scribe(15) : X | - TWO^4" , " * word_cmr[22..277] contain the cmrs for scribe(0) .. scribe(255) : X | - TWO^8" , " */" ] <> line <> nest 2 (vsep [ "static const sha256_midstate word_cmr[] =" , bracket (concat [word1s, word2s, word4s, word8s]) <> semi ]) where word1s = [bracket . single . prettyCHash . commitmentRoot $ (scribe x :: CommitmentRoot () Word1) | x <- allValues] word2s = [bracket . single . prettyCHash . commitmentRoot $ (scribe x :: CommitmentRoot () Word2) | x <- allValues] word4s = [bracket . single . prettyCHash . commitmentRoot $ (scribe x :: CommitmentRoot () Word4) | x <- allValues] word8s = [bracket . single . prettyCHash . commitmentRoot $ (scribe x :: CommitmentRoot () Word8) | x <- allValues] allWordRoots :: [Hash256] allWordRoots = typeRoot one : iterate diag bit where bit = typeRoot (sum one one) diag x = ivHash $ compress (typeTag "prod") (x,x) declareWordTypeRoots :: Doc a declareWordTypeRoots = vsep [ "/* word_type_root[0] contains the type root of the ONE type." , " * word_type_root[1] contains the type root of the TWO type." , " * word_type_root[2] contains the type root of the TWO^2 type." , " * word_type_root[3] contains the type root of the TWO^4 type." , " * ..." , " * word_type_root[32] contains the type root of the TWO^(2^31) type." , " */" ] <> line <> nest 2 (vsep [ "static const sha256_midstate word_type_root[] =" , bracket [bracket . single . prettyCHash $ x | x <- take 33 allWordRoots] <> semi ]) header = vsep $ [ "/* This file has been automatically generated by GenPecomputed.hs */" , "#ifndef SIMPLICITY_PRECOMPUTED_H" , "#define SIMPLICITY_PRECOMPUTED_H" , "" , "#include \"sha256.h\"" ] footer = vsep $ [ "#endif" ] precomputed_h :: SimpleDocStream a precomputed_h = layoutPretty layoutOptions $ vsep (map (<> line) [ header , declareSignatureIV , declareTyIVs , declareMRIVs , declareWordCMRs , declareWordTypeRoots , footer ]) where layoutOptions = LayoutOptions { layoutPageWidth = AvailablePerLine 132 1 } renderFile name doc = withFile name WriteMode (\h -> renderIO h doc) main = do renderFile "precomputed.h" precomputed_h ================================================ FILE: Haskell-Generate/GenPrimitive.hs ================================================ module GenPrimitives where import Prelude hiding (sum) import Control.Monad.Cont (Cont, cont, runCont) import Data.Function (on) import Data.Functor.Fixedpoint (Fix(..), cata) import Data.List (intercalate, sortBy) import Data.List.Split (chunksOf) import Data.Maybe (isJust) import qualified Data.Map as Map import Numeric (showHex) import System.Environment (getArgs) import System.Exit (exitFailure) import NameWrangler import Simplicity.Digest import qualified Simplicity.Bitcoin.Jets as Bitcoin import qualified Simplicity.Elements.Jets as Elements import Simplicity.MerkleRoot import Simplicity.Serialization import Simplicity.Ty import Simplicity.Weight data JetInfo = JetInfo { name :: String , cmr :: Hash256 , mw :: Integer , sourceType :: Ty , targetType :: Ty , moduleName :: String } data CompactTy = CTyOne | CTyWord Int | CTyMaybe CompactTy | CTySum CompactTy CompactTy | CTyProd CompactTy CompactTy deriving (Eq, Ord) showCHash h = intercalate ", " (format <$> chunksOf 8 str_h) where format x = "0x" ++ x ++ "u" str_h = padding ++ text where padding = replicate (64 - length text) '0' text = showHex (integerHash256 h) "" compactTy :: Ty -> CompactTy compactTy = cata go -- memoCataTy go where go One = CTyOne go (Sum CTyOne CTyOne) = CTyWord 1 go (Sum CTyOne y) = CTyMaybe y go (Sum x y) = CTySum x y go (Prod (CTyWord wx) (CTyWord wy)) | wx == wy = CTyWord (wx + wy) go (Prod x y) = CTyProd x y compactCName :: CompactTy -> ShowS compactCName s = showString "ty_" . go s where go CTyOne = showString "u" go (CTyWord 1) = showString "b" go (CTyWord n) | n < 2^10 = showString "w" . shows n | n < 2^20 = showString "w" . shows (n `div` (2^10)) . showString "Ki" | n < 2^30 = showString "w" . shows (n `div` (2^20)) . showString "Mi" | otherwise = showString "w" . shows (n `div` (2^30)) . showString "Gi" go (CTyMaybe x) = showString "m" . go x go (CTySum x y) = showString "s" . go x . go y go (CTyProd x y) = showString "p" . go x . go y cInitializeTy :: CompactTy -> String cInitializeTy ty = showString "(*bound_var)[" . compactCName ty . showString "] = (unification_var){ .isBound = true, .bound = " . cBoundTy ty . showString "};" $ "" where cBoundTy CTyOne = showString "{ .kind = ONE }" cBoundTy (CTyWord 1) = cBoundTy (CTySum CTyOne CTyOne) cBoundTy (CTyWord n) = cBoundTy (CTyProd rec rec) where rec = CTyWord (n `div` 2) cBoundTy (CTyMaybe x) = cBoundTy (CTySum CTyOne x) cBoundTy (CTySum x y) = showString "{ .kind = SUM, .arg = { &(*bound_var)[" . compactCName x . showString "], &(*bound_var)[" . compactCName y . showString "] } }" cBoundTy (CTyProd x y) = showString "{ .kind = PRODUCT, .arg = { &(*bound_var)[" . compactCName x . showString "], &(*bound_var)[" . compactCName y . showString "] } }" cJetNode :: JetInfo -> String cJetNode ji = unlines [ "[" ++ upperSnakeCase (name ji) ++ "] =" , "{ .tag = JET" , ", .jet = simplicity_" ++ moduleName ji ++ lowerSnakeCase (name ji) , ", .cmr = {{" ++ showCHash (cmr ji) ++ "}}" , ", .sourceIx = " ++ compactCName (compactTy (sourceType ji)) "" , ", .targetIx = " ++ compactCName (compactTy (targetType ji)) "" , ", .cost = " ++ show (mw ji) ++ " /* milli weight units */" , "}" ] mkTyList :: [JetInfo] -> [CompactTy] mkTyList jetList = Map.keys . foldr combine wordMap $ (tys =<< jetList) where wordMap = Map.fromList [(CTyWord n, ty) | (n, ty) <- Prelude.take 32 words] where words = (1, sum one one) : [(2*n, prod ty ty) | (n, ty) <- words] tys ji = [sourceType ji, targetType ji] combine ty map | isJust (Map.lookup cTy map) = map | otherwise = Map.insert cTy ty (foldr combine map (children ty)) where cTy = compactTy ty children (Fix One) = [] children (Fix (Sum x y)) = [x,y] children (Fix (Prod x y)) = [x,y] cEnumTyFile :: [CompactTy] -> String cEnumTyFile tyList = unlines . fmap item $ tyList where item ty@CTyOne = compactCName ty " = 0," item ty@(CTyWord n) = compactCName ty " = " ++ show (1 + ln n) ++ "," item ty = compactCName ty "," ln n = length . Prelude.drop 1 . takeWhile (0 <) $ iterate (`div` 2) n cInitializeTyFile :: [CompactTy] -> String cInitializeTyFile tyList = unlines $ cInitializeTy <$> tyList cEnumJetFile :: [JetInfo] -> String cEnumJetFile jetList = unlines $ map f jetList where f ji = (upperSnakeCase (name ji)) ++ "," cJetNodeFile :: [JetInfo] -> String cJetNodeFile jetList = intercalate "," $ map cJetNode jetList writeIncludeFile :: FilePath -> String -> IO () writeIncludeFile name content = writeFile name (header ++ content) where header = "/* This file has been automatically generated. */\n" mkJetList :: (a -> JetInfo) -> [a] -> [JetInfo] mkJetList f l = sortBy (compare `on` name) . map f $ l writeFiles list = do writeIncludeFile ("primitiveEnumTy.inc") (cEnumTyFile tyList) writeIncludeFile ("primitiveInitTy.inc") (cInitializeTyFile tyList) writeIncludeFile ("primitiveEnumJet.inc") (cEnumJetFile list) writeIncludeFile ("primitiveJetNode.inc") (cJetNodeFile list) where tyList = mkTyList list data Option = OptElements | OptBitcoin parseOptions :: [String] -> Maybe Option parseOptions [] = Just OptElements parseOptions ["--elements"] = Just OptElements parseOptions ["--bitcoin"] = Just OptBitcoin parseOptions _ = Nothing main = do mopt <- parseOptions <$> getArgs case mopt of Nothing -> putStrLn "Invalid Arguments" >> exitFailure Just OptElements -> writeFiles elementsJetList Just OptBitcoin -> writeFiles bitcoinJetList where elementsJetList = mkJetList fromElements $ Map.elems Elements.jetMap fromElements :: SomeArrow Elements.JetType -> JetInfo fromElements (SomeArrow jt) = JetInfo { name = mkName jt , cmr = commitmentRoot (Elements.asJet jt) , mw = milliWeight (Elements.jetCost jt) , sourceType = unreflect tyx , targetType = unreflect tyy , moduleName = "" } where (tyx, tyy) = reifyArrow jt bitcoinJetList = mkJetList fromBitcoin $ Map.elems Bitcoin.jetMap fromBitcoin :: SomeArrow Bitcoin.JetType -> JetInfo fromBitcoin (SomeArrow jt) = JetInfo { name = mkName jt , cmr = commitmentRoot (Bitcoin.asJet jt) , mw = milliWeight (Bitcoin.jetCost jt) , sourceType = unreflect tyx , targetType = unreflect tyy , moduleName = jetModule } where jetModule | Bitcoin.CoreJet _ <- jt = "" | otherwise = "bitcoin_" (tyx, tyy) = reifyArrow jt ================================================ FILE: Haskell-Generate/GenRustJets.hs ================================================ {-# LANGUAGE OverloadedStrings #-} module GenRustJets where import Data.Char (toLower) import Data.Foldable (toList) import Data.Function (on) import Data.Functor.Fixedpoint (Fix(..)) import Data.List (sortBy) import Data.List.Split (chunksOf) import Data.Maybe (fromMaybe) import qualified Data.Map as Map import Numeric (showHex) import Prettyprinter ( Doc, (<+>), braces, comma, dquotes, fillSep, line, nest, parens, pretty, punctuate, semi, tupled, vsep , SimpleDocStream, LayoutOptions(..), PageWidth(..), defaultLayoutOptions, layoutPretty ) import Prettyprinter.Render.Text (renderIO) import System.IO (IOMode(WriteMode), withFile) import NameWrangler import qualified Simplicity.Bitcoin.Jets as Bitcoin import qualified Simplicity.Bitcoin.Term as Bitcoin import qualified Simplicity.CoreJets as Core import Simplicity.CoreJets (CoreJet) import Simplicity.Digest import qualified Simplicity.Elements.Jets as Elements import qualified Simplicity.Elements.Term as Elements import Simplicity.MerkleRoot import Simplicity.Serialization import Simplicity.Tree import Simplicity.Ty import Simplicity.Weight x <-> y = x <> line <> y nestBraces x = braces (nest 4 (line <> x) <> line) data JetModule = CoreModule | BitcoinModule | ElementsModule deriving Eq data JetData x y = JetData { jetName :: String , jetCMR :: CommitmentRoot x y , jetModule :: JetModule , jetCost :: Weight } sortJetName = sortBy (compare `on` name) where name (SomeArrow j) = jetName j cJetName = lowerSnakeCase . jetName coreJetData :: (TyC x, TyC y) => CoreJet x y -> JetData x y coreJetData jet = JetData { jetName = mkName jet , jetCMR = cmr , jetModule = CoreModule , jetCost = cost } where cmr = Bitcoin.asJet (Bitcoin.CoreJet jet) cost = Bitcoin.jetCost (Bitcoin.CoreJet jet) elementsJetData :: (TyC x, TyC y) => Elements.JetType x y -> JetData x y elementsJetData jet = JetData { jetName = mkName jet , jetCMR = Elements.asJet jet , jetModule = jetModule , jetCost = Elements.jetCost jet } where jetModule | Elements.CoreJet _ <- jet = CoreModule | otherwise = ElementsModule bitcoinJetData :: (TyC x, TyC y) => Bitcoin.JetType x y -> JetData x y bitcoinJetData jet = JetData { jetName = mkName jet , jetCMR = Bitcoin.asJet jet , jetModule = jetModule , jetCost = Bitcoin.jetCost jet } where jetModule | Bitcoin.CoreJet _ <- jet = CoreModule | otherwise = BitcoinModule data Module = Module { moduleName :: Maybe String , moduleCodes :: BinTree (SomeArrow JetData) } moduleJets :: Module -> [SomeArrow JetData] moduleJets = sortJetName . toList . moduleCodes rustModuleName = fromMaybe "Core" . moduleName lowerRustModuleName = map toLower . rustModuleName coreModule :: Module coreModule = Module Nothing (someArrowMap coreJetData <$> (treeEvalBitStream Core.getJetBit)) -- Take Right is used to drop the (infinite) branch of constant word jets. takeRight (Branch _ r) = r elementsModule :: Module elementsModule = Module (Just "Elements") (someArrowMap elementsJetData <$> takeRight (treeEvalBitStream Elements.getJetBit)) bitcoinModule :: Module bitcoinModule = Module (Just "Bitcoin") (someArrowMap bitcoinJetData <$> takeRight (treeEvalBitStream Bitcoin.getJetBit)) data CompactTy = CTyOne | CTyWord Int | CTyMaybe CompactTy | CTySum CompactTy CompactTy | CTyProd CompactTy CompactTy deriving (Eq, Ord) compactTy :: Ty -> CompactTy compactTy = memoCataTy go where go One = CTyOne go (Sum CTyOne CTyOne) = CTyWord 1 go (Sum CTyOne y) = CTyMaybe y go (Sum x y) = CTySum x y go (Prod (CTyWord wx) (CTyWord wy)) | wx == wy = CTyWord (wx + wy) go (Prod x y) = CTyProd x y compactRustName :: CompactTy -> ShowS compactRustName s = showString "b\"" . go s . showString "\"" where go CTyOne = showString "1" go (CTyWord 1) = showString "2" go (CTyWord 32) = showString "i" go (CTyWord 64) = showString "l" go (CTyWord 256) = showString "h" go (CTyWord n) | even n = let rec = go (CTyWord (n `div` 2)) in showString "*" . rec . rec go (CTyMaybe x) = showString "+1" . go x go (CTySum x y) = showString "+" . go x . go y go (CTyProd x y) = showString "*" . go x . go y showRustHash :: Hash256 -> Doc a showRustHash h = fillSep $ ((<> comma) . format <$> chunksOf 2 str_h) where format x = pretty $ "0x" ++ x str_h = padding ++ text where padding = replicate (64 - length text) '0' text = showHex (integerHash256 h) "" rustJetCmr :: Module -> Doc a rustJetCmr mod = vsep $ [ nest 4 (vsep ("fn cmr(&self) -> Cmr {" : -- Temporary if statement until Bitcoin Jets have weight costs assigned to them -- See Haskell/Simplicity/Bitcoin/Jets.hs: jetCost (BitcoinJet jt) = error "Simplicity.Bitcoin.Jets.jetCost: :TODO: Implement jets for Bitcoin and benchmark them." if Just "Bitcoin" == moduleName mod then ["unimplemented!(\"Bitcoin jet CMRs weights have not yet been implemented.\")"] else [ nest 4 (vsep ("let bytes = match self {" : map (<>comma) [ nest 4 (vsep [ pretty modname <> "::" <> pretty (jetName jet) <+> "=> [" , showRustHash (commitmentRoot (jetCMR jet)) ]) <-> "]" | (SomeArrow jet) <- moduleJets mod ])) , "};" , mempty , "Cmr(Midstate(bytes))" ])) , "}" ] where modname = rustModuleName mod rustJetTy fname getTy mod = vsep $ [ nest 4 (vsep (pretty ("fn "++fname++"(&self) -> TypeName {") : [ nest 4 (vsep ("let name: &'static [u8] = match self {" : map (<>comma) [ pretty modname <> "::" <> pretty (jetName jet) <+> "=>" <+> pretty (compactRustName (compactTy (getTy j)) "") | j@(SomeArrow jet) <- moduleJets mod ])) , "};" , mempty , "TypeName(name)" ])) , "}" ] where modname = rustModuleName mod rustJetSourceTy :: Module -> Doc a rustJetSourceTy = rustJetTy "source_ty" (\(SomeArrow jet) -> unreflect (fst (reifyArrow jet))) rustJetTargetTy :: Module -> Doc a rustJetTargetTy = rustJetTy "target_ty" (\(SomeArrow jet) -> unreflect (snd (reifyArrow jet))) rustJetCJetPtr :: Module -> Doc a rustJetCJetPtr mod = vsep $ [ nest 4 (vsep [ pretty ("pub(crate) fn c_jet_ptr(jet: &" ++ modname ++ ") -> fn(&mut CFrameItem, CFrameItem, &" ++ cJetEnvType ++ ") -> bool {") , if modname == "Bitcoin" then " unimplemented!(\"Bitcoin jets have not yet been implemented.\")" else vsep [ nest 4 (vsep ("match jet {" : map (<>comma) [ pretty modname <> "::" <> pretty (jetName jet) <+> "=>" <+> pretty ("simplicity_sys::c_jets::jets_wrapper::"++cJetName jet) | SomeArrow jet <- moduleJets mod ])) , "}" ] ]) , "}" ] where modname = rustModuleName mod cJetEnvType | Just "Elements" == moduleName mod = "CElementsTxEnv" :: String | otherwise = "()" rustJetEncode :: Module -> Doc a rustJetEncode mod = "fn encode(&self, w: &mut BitWriter<&mut dyn Write>) -> std::io::Result" <+> nestBraces ("let (n, len) = match self" <+> nestBraces (vsep (foldMapWithPath item (moduleCodes mod))) <> semi <-> line <> "w.write_bits_be(n, len)") where item path (SomeArrow jet) = [pretty (rustModuleName mod ++ "::" ++ jetName jet) <+> "=>" <+> tupled [pretty (code path 0 :: Int), pretty (length path)] <> comma] code [] n = n code (b : l) n = code l (2*n + if b then 1 else 0) rustJetDecode :: Module -> Doc a rustJetDecode mod = "fn decode>(bits: &mut BitIter) -> Result where Self: Sized" <+> nestBraces ("decode_bits!(bits," <+> braces (docTree (moduleCodes mod)) <> ")") where docTree Dead = mempty docTree (Leaf (SomeArrow jet)) = pretty (rustModuleName mod ++ "::" ++ jetName jet) docTree (Branch l r) = nest 4 ( line <> ("0" <+> "=>" <+> braces (docTree l)) <> comma <-> ("1" <+> "=>" <+> braces (docTree r)) ) <> line rustJetCost :: Module -> Doc a rustJetCost mod = vsep $ [ nest 4 (vsep ("fn cost(&self) -> Cost {" : if modname == "Bitcoin" then ["unimplemented!(\"Unspecified cost of Bitcoin jets\")"] else [ nest 4 (vsep ("match self {" : map (<>comma) [ pretty modname <> "::" <> pretty (jetName jet) <+> "=>" <+> "Cost::from_milliweight(" <> (pretty . milliWeight $ jetCost jet) <> ")" | SomeArrow jet <- moduleJets mod ])) , "}" ])) , "}" ] where modname = rustModuleName mod rustJetParse :: Doc a rustJetParse = "fn parse(s: &str) -> Result where Self: Sized" <+> nestBraces "str::FromStr::from_str(s)" rustJetImpl :: Module -> Doc a rustJetImpl mod = vsep $ [ nest 4 (vsep $ punctuate line ["impl Jet for" <+> pretty modname <+> "{" , rustJetCmr mod , rustJetSourceTy mod , rustJetTargetTy mod , rustJetEncode mod , rustJetDecode mod , rustJetCost mod , rustJetParse ]) , "}" ] where modname = rustModuleName mod rustJetEnum :: Module -> Doc a rustJetEnum mod = vsep [ "/// The" <+> pretty (rustModuleName mod) <+> "jet family." , "#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Debug, Hash)]" , nest 4 $ vsep $ ("pub enum" <+> pretty (rustModuleName mod) <+> "{") : [ pretty (jetName jet) <> comma | (SomeArrow jet) <- moduleJets mod ] , "}" , "" , nest 4 $ vsep $ ("impl" <+> pretty (rustModuleName mod) <+> "{") : ("/// Array of all" <+> pretty (rustModuleName mod) <+> "jets.") : [ nest 4 $ vsep $ ("pub const ALL: [Self;" <+> pretty (length $ moduleJets mod) <> "] = [") : [ "Self::" <> (pretty $ jetName jet) <> comma | (SomeArrow jet) <- moduleJets mod ] , "];" ] , "}" ] rustJetDisplay :: Module -> Doc a rustJetDisplay mod = "impl fmt::Display for" <+> pretty modname <+> nestBraces ("fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result" <+> nestBraces ("match self" <+> nestBraces (vsep ( map (<>comma) [ pretty modname <> "::" <> pretty (jetName jet) <+> "=> f.write_str" <> (parens . dquotes . pretty $ cJetName jet) | SomeArrow jet <- moduleJets mod ])) ) ) where modname = rustModuleName mod rustJetFromStr :: Module -> Doc a rustJetFromStr mod = "impl str::FromStr for" <+> pretty modname <+> nestBraces (vsep [ "type Err = crate::Error;" , mempty , ("fn from_str(s: &str) -> Result" <+> nestBraces ("match s" <+> nestBraces (vsep ( map (<> comma) ([ dquotes (pretty (cJetName jet)) <+> "=> Ok" <> parens (pretty modname <> "::" <> pretty (jetName jet)) | SomeArrow jet <- moduleJets mod ] ++ [ "x => Err(crate::Error::InvalidJetName(x.to_owned()))" ] ))) )) ]) where modname = rustModuleName mod rustHeader :: Doc a rustHeader = "/* This file has been automatically generated. */" rustImports :: Module -> Doc a rustImports mod = vsep (map (<> semi) ([ "use crate::jet::type_name::TypeName" , "use crate::jet::Jet" , "use crate::merkle::cmr::Cmr" , "use crate::decode_bits" , "use crate::{decode, BitIter, BitWriter}" , "use crate::analysis::Cost" , "use hashes::sha256::Midstate" , "use simplicity_sys::CFrameItem" , "use std::io::Write" , "use std::{fmt, str}" ] ++ envImports)) where envImports | Just "Elements" == moduleName mod = ["use simplicity_sys::CElementsTxEnv"] | otherwise = [] rustJetDoc :: Module -> SimpleDocStream a rustJetDoc mod = layoutPretty layoutOptions $ vsep (map (<> line) [ rustHeader , rustImports mod , rustJetEnum mod , rustJetImpl mod , rustJetDisplay mod , rustJetFromStr mod , rustJetCJetPtr mod ]) rustFFIImports :: Doc a rustFFIImports = vsep (map (<> semi) [ "use crate::ffi::c_void" , "use crate::{CElementsTxEnv, CFrameItem}" ]) rustFFISigs :: Module -> Doc a rustFFISigs mod = vsep [ nest 4 $ vsep $ "extern \"C\" {" : (declaration <$> moduleJets mod) , "}" ] where declaration (SomeArrow jet) = (<> semi) . vsep $ pretty <$> [ linkName , signature ] where linkName = "#[link_name = \"c_"++cJetName jet++"\"]" signature = "pub fn "++cJetName jet++"(dst: *mut CFrameItem, src: *const CFrameItem, env: *const "++envType++") -> bool" envType | CoreModule <- jetModule jet = "c_void" | ElementsModule <- jetModule jet = "CElementsTxEnv" rustFFIDoc :: Module -> SimpleDocStream a rustFFIDoc mod = layoutPretty layoutOptions $ vsep (map (<> line) [ rustHeader , rustFFIImports , rustFFISigs mod ]) rustWrapperImports :: Doc a rustWrapperImports = vsep (map (<> semi) [ "use crate::{CElementsTxEnv, CFrameItem}" , "use super::elements_ffi" ]) rustWrappers :: Module -> Doc a rustWrappers mod = vsep ((<> line) . wrapper <$> moduleJets mod) where wrapper (SomeArrow jet) = vsep [ nest 4 $ vsep [ pretty $ "pub fn "++cJetName jet++templateParam++"(dst: &mut CFrameItem, src: CFrameItem, "++envParam++") -> bool {" , pretty $ "unsafe { "++lowerRustModuleName mod++"_ffi::"++cJetName jet++"(dst, &src, "++envArg++") }" ] , "}" ] where templateParam | CoreModule <- jetModule jet = "" | otherwise = "" envParam | CoreModule <- jetModule jet = "_env: &T" | ElementsModule <- jetModule jet = "env: &CElementsTxEnv" envArg | CoreModule <- jetModule jet = "std::ptr::null()" | ElementsModule <- jetModule jet = "env" rustWrapperDoc :: Module -> SimpleDocStream a rustWrapperDoc mod = layoutPretty layoutOptions $ vsep (map (<> line) [ rustHeader , rustWrapperImports , rustWrappers mod ]) cWrapperImports :: Doc a cWrapperImports = vsep [ "#include \"simplicity/elements/elementsJets.h\"" , "#include \"simplicity/simplicity_assert.h\"" , "#include \"wrapper.h\"" ] cWrappers :: Module -> Doc a cWrappers mod = vsep (map wrapper $ moduleJets mod) where wrapper (SomeArrow jet) = pretty $ "WRAP_("++cJetName jet++")" cWrapperDoc :: Module -> SimpleDocStream a cWrapperDoc mod = layoutPretty layoutOptions $ vsep (map (<> line) [ rustHeader -- also works for C , cWrapperImports , cWrappers mod ]) renderFile name doc = withFile name WriteMode (\h -> renderIO h doc) main = do renderFile "core.rs" (rustJetDoc coreModule) renderFile "elements.rs" (rustJetDoc elementsModule) renderFile "bitcoin.rs" (rustJetDoc bitcoinModule) renderFile "jets_ffi.rs" (rustFFIDoc elementsModule) renderFile "jets_wrapper.rs" (rustWrapperDoc elementsModule) renderFile "jets_wrapper.c" (cWrapperDoc elementsModule) layoutOptions = LayoutOptions { layoutPageWidth = AvailablePerLine 100 1 } ================================================ FILE: Haskell-Generate/GenTests.hs ================================================ {-# LANGUAGE KindSignatures, ScopedTypeVariables #-} module GenTests where import Prelude hiding (drop, take) import qualified Data.ByteString as BS import qualified Data.ByteString.Char8 as BSC import qualified Data.ByteString.Lazy as BSL import Data.Char (toUpper) import Data.Functor.Identity (runIdentity) import Data.Maybe (fromJust) import Data.Kind (Type) import Data.List (intercalate) import Data.List.Split (chunksOf) import Data.Serialize (encode, runPut) import Data.Vector (fromList) import Numeric (showHex) import System.IO (hPutStrLn, stderr) import Lens.Family2 ((^.), (&), (.~), over, review, to, Getter') import Lens.Family2.Stock (mapped) import Simplicity.Digest import qualified Simplicity.Elements.JetType import qualified Simplicity.Elements.Dag import Simplicity.Elements.DataTypes import Simplicity.Elements.Dag (SimplicityDag) import Simplicity.Elements.Inference import Simplicity.Elements.Primitive import Simplicity.Elements.Jets (JetType, WrappedSimplicity, fastEval, jetSubst, pruneSubst, unwrap) import Simplicity.Elements.Serialization.BitString import Simplicity.Elements.StaticAnalysis.Cost import qualified Simplicity.Elements.Programs.SigHash.Lib import Simplicity.Elements.Term import qualified Simplicity.LibSecp256k1.Spec import Simplicity.MerkleRoot import Simplicity.Programs.Generic import qualified Simplicity.Programs.Arith as Arith import Simplicity.Programs.Bit import qualified Simplicity.Programs.Sha256 import Simplicity.Programs.Sha256.Lib import qualified Simplicity.Programs.LibSecp256k1.Lib import qualified Simplicity.Programs.CheckSig.Lib import Simplicity.Serialization import Simplicity.Ty import Simplicity.Word data Example (jt :: Type -> Type -> Type) a b = Example { _name :: String , _path :: [String] , _text :: [String] , _withJets :: Bool , _prog :: WrappedSimplicity a b } type ExampleNoJets a b = Example Simplicity.Elements.JetType.NoJets a b type ExampleProg = Example JetType () () name f (Example n pa t wj pr) = (\n -> Example n pa t wj pr) <$> f n path f (Example n pa t wj pr) = (\pa -> Example n pa t wj pr) <$> f pa text f (Example n pa t wj pr) = (\t -> Example n pa t wj pr) <$> f t withJets f (Example n pa t wj pr) = (\wj -> Example n pa t wj pr) <$> f wj prog f (Example n pa t wj pr) = (\pr -> Example n pa t wj pr) <$> f pr fullname = to proj where proj x | null (x^.path) = x^.name | otherwise = last (x^.path) ++ capital (x^.name) capital [] = [] capital (a:b) = toUpper a : b showComment wj txt = unlines $ ["/* A length-prefixed encoding of the following Simplicity program:"] ++ body ++ [" * with jets." | wj] ++ [" */"] where body = map (" * "++) $ txt showBinary name bin = unlines $ start ++ [intercalate ",\n" chunks] ++ finish where start = ["const unsigned char "++name++"[] = " ++ open] open | null bin = "\"\";" | otherwise = "{" finish = close ++ ["", "const size_t sizeof_"++name++" = "++sizeof++";"] close | null bin = [] | otherwise = ["};"] sizeof | null bin = "0" | otherwise = "sizeof("++name++")" chunks = (" "++) . intercalate ", " <$> chunksOf 20 (showByte <$> bin) showByte b = "0x" ++ padding ++ t where padding = replicate (2 - length t) '0' t = showHex b "" showHash name h = unlines $ ["const uint32_t "++name++"[] = {", body, "};"] where str_h = padding ++ text where padding = replicate (64 - length text) '0' text = Numeric.showHex (integerHash256 h) "" body = " " ++ intercalate ", " (format <$> chunksOf 8 str_h) where format x = "0x" ++ x ++ "u" fileC :: forall jt a b. (Simplicity.Elements.JetType.JetType jt, TyC a, TyC b) => Example jt a b -> String fileC example = "#include \""++example^.name++".h\"\n" ++ "\n" ++ showComment (example^.withJets) (example^.text) ++ showBinary (example^.fullname) binP ++ showBinary (example^.fullname++"_witness") binW ++ "\n" ++ "/* The commitment Merkle root of the above "++example^.fullname++" Simplicity expression. */\n" ++ showHash (example^.fullname++"_cmr") cmr ++ "\n" ++ "/* The identity hash of the root of the above "++example^.fullname++" Simplicity expression. */\n" ++ showHash (example^.fullname++"_ihr") ihr ++ "\n" ++ "/* The annotated Merkle root of the above "++example^.fullname++" Simplicity expression. */\n" ++ showHash (example^.fullname++"_amr") amr ++ "\n" ++ "/* The cost of the above "++example^.fullname++" Simplicity expression in milli weight units. */\n" ++ "const ubounded "++example^.fullname++"_cost = "++ (if cost < 2^32 then show cost else "UBOUNDED_MAX") ++";\n" where (program,witness) = putTermLengthCode (unwrap (example^.prog) :: Simplicity.Elements.Dag.JetDag jt a b) binP = BS.unpack . runPut $ putBitStream program binW = BS.unpack . runPut $ putBitStream witness cmr = commitmentRoot . unwrap $ example^.prog ihr = identityHash . unwrap $ example^.prog amr = annotatedRoot . unwrap $ example^.prog cost = milliWeigh . unwrap $ example^.prog fileH example = "#ifndef "++headerDef++"\n" ++ "#define "++headerDef++"\n" ++ "\n" ++ "#include \n" ++ "#include \n" ++ "#include \""++concat (replicate (length (example^.path)) "../")++"bounded.h\"\n" ++ "\n" ++ showComment (example^.withJets) (example^.text) ++ "extern const unsigned char "++example^.fullname++"[];\n" ++ "extern const size_t sizeof_"++example^.fullname++";\n" ++ "extern const unsigned char "++example^.fullname++"_witness[];\n" ++ "extern const size_t sizeof_"++example^.fullname++"_witness;\n" ++ "\n" ++ "/* The commitment Merkle root of the above "++example^.fullname++" Simplicity expression. */\n" ++ "extern const uint32_t "++example^.fullname++"_cmr[];\n" ++ "\n" ++ "/* The identity hash of the root of the above "++example^.fullname++" Simplicity expression. */\n" ++ "extern const uint32_t "++example^.fullname++"_ihr[];\n" ++ "\n" ++ "/* The annotated Merkle root of the above "++example^.fullname++" Simplicity expression. */\n" ++ "extern const uint32_t "++example^.fullname++"_amr[];\n" ++ "\n" ++ "/* The cost of the above "++example^.fullname++" Simplicity expression in milli weight units. */\n" ++ "extern const ubounded "++example^.fullname++"_cost;\n" ++ "\n" ++ "#endif\n" where headerDef = "SIMPLICITY_" ++ (toUpper <$> intercalate "_" (example^.path ++ [example^.name])) ++ "_H" writeFiles example = do hPutStrLn stderr $ "Writing "++example^.name writeFile (example^.name++".h") (fileH example) writeFile (example^.name++".c") (fileC example) main = do writeFiles example_hashBlock writeFiles ctx8Unpruned writeFiles ctx8Pruned writeFiles schnorr0 writeFiles schnorr6 writeFiles checkSigHashAllTx1 writeRegression4 writeFiles typeSkipTest noJetSubst :: (TyC a, TyC b) => Simplicity.Elements.Dag.NoJetDag a b -> WrappedSimplicity a b noJetSubst = Simplicity.Elements.Dag.jetSubst noJetPrune :: (TyC a, TyC b) => PrimEnv -> a -> Simplicity.Elements.Dag.NoJetDag a b -> Maybe (WrappedSimplicity a b) noJetPrune env a prog = Simplicity.Elements.Dag.pruneSubst prog env a example_hashBlock :: ExampleNoJets (Hash, Block) Hash example_hashBlock = Example { _name = "hashBlock" , _path = [] , _text = [ "hashBlock" ] , _withJets = False , _prog = noJetSubst hashBlock } ctx8Unpruned :: ExampleNoJets () () ctx8Unpruned = Example { _name = "ctx8Unpruned" , _path = [] , _text = [ "(scribe (toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&&" , " (ctx8Init &&& scribe (toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn vector16 >>> ctx8Finalize) >>>" , "eq >>> verify" ] , _withJets = False , _prog = noJetSubst $ (scribe (Arith.toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&& ((ctx8Init &&& scribe (Arith.toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn Arith.vector16 >>> ctx8Finalize)) >>> eq >>> verify } ctx8Pruned :: ExampleNoJets () () ctx8Pruned = Example { _name = "ctx8Pruned" , _path = [] , _text = [ "(scribe (toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&&" , " (ctx8Init &&& scribe (toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn vector16 >>> ctx8Finalize) >>>" , "eq >>> verify" ] , _withJets = False , _prog = prog } where Just prog = noJetPrune undefined () $ (scribe (Arith.toWord256 0x067C531269735CA7F541FDACA8F0DC76305D3CADA140F89372A410FE5EFF6E4D) &&& ((ctx8Init &&& scribe (Arith.toWord128 0xDE188941A3375D3A8A061E67576E926D)) >>> ctx8Addn Arith.vector16 >>> ctx8Finalize)) >>> eq >>> verify schnorr0 :: ExampleProg schnorr0 = Example { _name = "schnorr0" , _path = [] , _text = [ "(scribe (toWord256 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9) &&&" , " zero word256) &&&" , " witness (toWord512 0xE907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0) >>>" , "Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify" ] , _withJets = True , _prog = jetSubst $ (scribe (Arith.toWord256 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9) &&& Arith.zero Arith.word256) &&& witness (Arith.toWord512 0xE907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0) >>> Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify } schnorr6 :: ExampleProg schnorr6 = Example { _name = "schnorr6" , _path = [] , _text = [ "(scribe (toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659) &&&" , " scribe (toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)) &&&" , " witness (toWord512 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2) >>>" , "Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify" ] , _withJets = True , _prog = jetSubst $ (scribe (Arith.toWord256 0xDFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659) &&& scribe (Arith.toWord256 0x5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C)) &&& witness (Arith.toWord512 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2) >>> Simplicity.Programs.LibSecp256k1.Lib.bip_0340_verify } checkSigHashAllTx1 :: ExampleProg checkSigHashAllTx1 = Example { _name = "checkSigHashAllTx1" , _path = ["elements"] , _text = [ "Simplicity.Programs.CheckSig.Lib.checkSigVerify' Simplicity.Elements.Programs.SigHash.Lib.sigAllHash" , "(Simplicity.LibSecp256k1.Spec.PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63)" , "(Simplicity.LibSecp256k1.Spec.Sig 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63" , " 0x" ++ sh s ++ ")" ] , _withJets = True , _prog = prunedProg $ (Simplicity.LibSecp256k1.Spec.Sig 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 s) } where pk = Simplicity.LibSecp256k1.Spec.PubKey 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 program sig = jetSubst $ Simplicity.Programs.CheckSig.Lib.checkSigVerify' (unwrap hashMode) pk sig prunedProg sig = fromJust $ pruneSubst (Simplicity.Programs.CheckSig.Lib.checkSigVerify' (unwrap hashMode) pk sig) env sh v = replicate (64 - length s) '0' ++ s where s = Numeric.showHex v "" s = insecureSig . fromIntegral . Arith.fromWord256 $ msg Just msg = fastEval (Simplicity.Programs.CheckSig.Lib.sigHash' (unwrap hashMode)) env () hashMode = jetSubst $ Simplicity.Elements.Programs.SigHash.Lib.sigAllHash genesis = review (over be256) 0x0f9188f13cb7b2c71f2a335e3a4fc328bf5beb436012afca590b1a11466e2206 Just env = primEnv tx1 0 tapEnv genesis cmr = commitmentRoot . unwrap $ program (Simplicity.LibSecp256k1.Spec.Sig 0 0) tapEnv = TapEnv { tapleafVersion = 0xbe , tapInternalKey = pk , tappath = [] , tapScriptCMR = cmr } tx1 = SigTx { sigTxVersion = 0x00000002 , sigTxIn = fromList [input0] , sigTxOut = fromList [output0, output1] , sigTxLock = 0 } where assetId = Asset . Explicit $ review (over be256) 0x230f4f5d4b7c6fa845806ee4f67713459e1b69e8e60fcee2e4940c7a0d5de1b2 input0 = SigTxInput { sigTxiPegin = Nothing , sigTxiPreviousOutpoint = Outpoint (review (over be256) 0xeb04b68e9a26d116046c76e8ff47332fb71dda90ff4bef5370f25226d3bc09fc) 0 , sigTxiTxo = UTXO { utxoAsset = assetId , utxoAmount = Amount . Explicit $ 10000000000 , utxoScript = BSL.empty } , sigTxiSequence = 0xfffffffe , sigTxiIssuance = Nothing , sigTxiAnnex = Nothing , sigTxiScriptSig = BSL.empty } output0 = TxOutput { txoAsset = assetId , txoAmount = Amount . Explicit $ 9999996700 , txoNonce = Nothing , txoScript = BSL.pack [ 0x19, 0x76, 0xa9, 0x14, 0x48, 0x63, 0x3e, 0x2c, 0x0e, 0xe9, 0x49, 0x5d, 0xd3, 0xf9, 0xc4, 0x37 , 0x32, 0xc4, 0x7f, 0x47, 0x02, 0xa3, 0x62, 0xc8, 0x88, 0xac] } output1 = TxOutput { txoAsset = assetId , txoAmount = Amount . Explicit $ 3300 , txoNonce = Nothing , txoScript = BSL.empty } insecureSig :: Word256 -> Word256 insecureSig msg = fromInteger ((toInteger k * (1 + e)) `mod` order) where order = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 k :: Word256 k = 1 + fromInteger order `div` 2 px :: Word256 px = 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 e = integerHash256 . bsHash $ schnorrTag <> schnorrTag <> encode px <> encode px <> encode msg schnorrTag = encode . bsHash $ BSC.pack "BIP0340/challenge" writeRegression4 = do hPutStrLn stderr $ "Writing regression4" writeFile "regression4.h" regression4H writeFile "regression4.c" regression4C where regression4Bin = BS.unpack . runPut . Simplicity.Serialization.putBitStream . putDagNoWitnessLengthCode $ code where -- We bypass the requirement for type annotations since they are expensive to compute and are not actually need for serialization. -- I promise the term we are generating is in fact well typed (with very large types that GHC doesn't particularly like to process). code :: SimplicityDag [] Ty (SomeArrow Simplicity.Elements.JetType.NoJets) UntypedValue code = (uWitness OneV : f 15 ++ [uComp (3*2^16) 1]) & (mapped.tyAnnotation) .~ bypassTyping where f 0 = [uIden, uTake 1, uIden, uDrop 1, uComp 3 1] f n = rec ++ rec ++ [uComp (3*2^n) 1] where rec = f (n-1) bypassTyping = undefined regression4Src = [ "uWitness OneV : f 15 ++ [uComp (3*2^16) 1]", " where", " f 0 = [uIden, uTake 1, uIden, uDrop 1, uComp 3 1]", " f n = rec ++ rec ++ [uComp (3*2^n) 1]", " where", " rec = f (n-1)"] regression4C = "#include \"regression4.h\"\n" ++ "\n" ++ showComment False regression4Src ++ showBinary "regression4" regression4Bin regression4H = "#ifndef "++headerDef++"\n" ++ "#define "++headerDef++"\n" ++ "\n" ++ "#include \n" ++ "#include \n" ++ "#include \"bounded.h\"\n" ++ "\n" ++ showComment False regression4Src ++ "extern const unsigned char "++"regression4"++"[];\n" ++ "extern const size_t sizeof_"++"regression4"++";\n" ++ "\n" ++ "#endif\n" where headerDef = "SIMPLICITY_" ++ (toUpper <$> "regression4") ++ "_H" typeSkipTest :: ExampleNoJets () () typeSkipTest = Example { _name = "typeSkipTest" , _path = [] , _text = [ "witness (runIdentity (getValue (return True))) >>> mn >>> unit" , " where" , " l1 = take l0 &&& drop l0" , " l2 = take l1 &&& drop l1" , " l3 = take l2 &&& drop l2" , " ltop = l3" , " m1 = copair l3 l3" , " m2 = take l1 &&& drop m1" , " m3 = take m2 &&& drop l2" , " m4 = take l3 &&& drop m3" , " m5 = copair (injl m4) (injr ltop)" , " m6 = take l1 &&& drop m5" , " m7 = take m6 &&& drop l2" , " m8 = take l3 &&& drop m7" , " n1 = copair l3 l3" , " n2 = take n1 &&& drop l1" , " n3 = take l2 &&& drop n2" , " n4 = take n3 &&& drop l3" , " n5 = copair (injl ltop) (injr n4)" , " n6 = take n5 &&& drop l0" , " n7 = take l1 &&& drop n6" , " n8 = take n7 &&& drop l2" , " mn = copair (injl m8) (injr n8)" ] , _withJets = False , _prog = prog } where l0 = iden :: (Core term) => term () () l1 = take l0 &&& drop l0 l2 = take l1 &&& drop l1 l3 = take l2 &&& drop l2 ltop = l3 m1 = copair l3 l3 m2 = take l1 &&& drop m1 m3 = take m2 &&& drop l2 m4 = take l3 &&& drop m3 m5 = copair (injl m4) (injr ltop) m6 = take m5 &&& drop l0 m7 = take l1 &&& drop m6 m8 = take m7 &&& drop l2 n1 = copair l3 l3 n2 = take n1 &&& drop l1 n3 = take l2 &&& drop n2 n4 = take n3 &&& drop l3 n5 = copair (injl ltop) (injr n4) n6 = take l0 &&& drop n5 n7 = take n6 &&& drop l1 n8 = take l2 &&& drop n7 mn = copair (injl m8) (injr n8) Just prog = noJetPrune undefined () $ witness (runIdentity (getValue (return True))) >>> mn >>> unit ================================================ FILE: Haskell-Generate/NameWrangler.hs ================================================ module NameWrangler ( upperSnakeCase , lowerSnakeCase , mkName ) where import Data.Char (isAlpha, isDigit, isUpper, toLower, toUpper) import Data.List (groupBy, intercalate) import Data.List.Split (condense, dropInitBlank, keepDelimsL, split, splitOn, whenElt) snakeCase :: String -> String snakeCase str = intercalate "_" . groupSingles $ (split . keepDelimsL . dropInitBlank . whenElt) isUpper =<< splitDigit =<< splitOn "_" str where splitDigit = (split . condense . whenElt) isDigit groupSingles = map concat . groupBy singles where singles [x] [y] = isAlpha x && isAlpha y singles _ _ = False upperSnakeCase :: String -> String upperSnakeCase = map toUpper . snakeCase lowerSnakeCase :: String -> String lowerSnakeCase = map toLower . snakeCase mkName :: Show a => a -> String mkName = filter (`notElem` "()") . last . words . show ================================================ FILE: LICENSE ================================================ MIT License Copyright (c) 2018 Blockstream Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ================================================ FILE: README.md ================================================ # Simplicity Simplicity is a blockchain programming language designed as an alternative to Bitcoin script. The language and implementation is still under development. ## Contents This project contains * A C implementation of a minimal, consensus-critical Simplicity runtime for full nodes. * A Haskell implementation of Simplicity's language semantics, type inference engine, serialization functions, and some example Simplicity code. * A Haskell code generator that exports Simplicity constants to C and Rust. * A Coq implementation of Simplicity's formal denotational and operational semantics. ## Build Use [Nix](https://nixos.org) for the easiest build. Alternatively, use GNU Autotools. ### C project #### Nix Change into the root directory of this repository. Build the nix package. ```bash nix-build -A c ``` Enter a nix shell to develop the project manually (see below). ```bash nix-shell --arg coq false --arg haskell false ``` Use arguments to enable / disable the other projects. #### Manual Change into the C directory of this repository. Build the project using make. ```bash make -j$(nproc) ``` To install the project, run make. ``` make install # use "out=/path/to/dir" for local install ``` To run the tests, run make. ```bash make check ``` ### Haskell project #### Nix Change into the root directory of this repository. Build the nix package. ```bash nix-build -A haskell ``` Enter a nix shell to develop the project manually (see below). ```bash nix-shell --arg c false --arg coq false ``` Use arguments to enable / disable the other projects. #### Manual Install the [Glasgow Haskell Compiler](https://www.haskell.org/ghc/) and [Cabal](https://www.haskell.org/cabal/). Change into the root directory of this repository. Build the project using cabal. ```bash cabal build ``` To run tests, run cabal. ```bash cabal test # use --test-options="+RTS -N -RTS" for parallel jobs ``` To enter an interactive GHCi prompt with the project loaded, run cabal. ```bash cabal repl Simplicity ``` ### Coq project #### Nix Change into the root directory of this repository. Build the nix package. ```bash nix-build -A coq ``` Enter a nix shell to develop the project manually (see below). The shell provides Coq, CompCert and VST. ```bash nix-shell --arg c false --arg haskell false ``` Use arguments to enable / disable the other projects. #### Manual Install the [opam package manager](https://opam.ocaml.org/). Enter the opam environment in your shell. ```bash opam init eval $(opam env) ``` Install the [Coq theorem prover](https://coq.inria.fr/). ```bash opam pin -j$(nproc) add coq 8.17.1 ``` Install the [CompCert certified C compiler](https://compcert.org/). ```bash opam repo add coq-released https://coq.inria.fr/opam/released opam install -j$(nproc) coq-compcert.3.13.1 ``` Install a custom version of the [Verified Software Toolchain](https://vst.cs.princeton.edu/). **You cannot use opam for this step!** ``` wget -O - https://github.com/PrincetonUniversity/VST/archive/v2.13.tar.gz | tar -xvzf - cd VST-2.13 make -j$(nproc) default_target sha make install install -d $(coqc -where)/user-contrib/sha install -m 0644 -t $(coqc -where)/user-contrib/sha sha/*.v sha/*.vo ``` Enter the Coq directory of this repository. Build the project using make. ```bash coq_makefile -f _CoqProject -o CoqMakefile make -f CoqMakefile -j$(nproc) ``` To install the project, run make. ```bash make -f CoqMakefile install ``` ## Documentation Detailed documentation can be found in the `Simplicity-TR.tm` TeXmacs file. A recent PDF version can be found in the [pdf](https://github.com/ElementsProject/simplicity/blob/pdf/Simplicity-TR.pdf) branch. ## Further Resources * Our [paper that originally introduced Simplicity](https://arxiv.org/abs/1711.03028). Some of the finer details are out of date, but it is still a good introduction. * [BPASE 2018 presentation](https://youtu.be/VOeUq3oR2fk) of the above paper. * [Scale by the Bay 2018 presentation](https://youtu.be/M4XnDrRIKx8) that illustrates formal verification of Simplicity in Agda ([slides](https://lists.ozlabs.org/pipermail/simplicity/2018/000011.html)). * Our library [rust-simplicity](https://github.com/BlockstreamResearch/rust-simplicity) that implements Simplicity in Rust. ## Contact Interested parties are welcome to join the [Simplicity mailing list](https://lists.ozlabs.org/listinfo/simplicity). Issues and pull-requests can be made through GitHub's interface. ================================================ FILE: Setup.hs ================================================ import Distribution.Simple main = defaultMain ================================================ FILE: Simplicity-Primitive.html ================================================ Simplicity.Primitive (signature)

Simplicity-0.0.0

Safe HaskellSafe
LanguageHaskell2010

Simplicity.Primitive (signature[?])

Documentation

data Prim a b #

primPrefix :: String #

primName :: Prim a b -> String #

getPrimBit :: Monad m => m Bool -> m (SomeArrow Prim) #

getPrimByte :: Word8 -> Get (Maybe (SomeArrow Prim)) #

putPrimBit :: Prim a b -> DList Bool #

putPrimByte :: Putter (Prim a b) #

data PrimEnv #

primSem :: Prim a b -> a -> PrimEnv -> Maybe b #

================================================ FILE: Simplicity-TR.tm ================================================ > <\body> <\doc-data|<\doc-title> Simplicity ||<\author-affiliation> Blockstream |>>||>> \; <\table-of-contents|toc> Introduction> |.>>>>|> 1.1Bitcoin Script |.>>>>|> 1.2Simplicity's Design Goals |.>>>>|> Static Analysis |.>>>>|> > Pruning and Sharing |.>>>>|> > Formal Semantics |.>>>>|> > Type Theory Preliminaries> |.>>>>|> 2.1Algebraic Types |.>>>>|> Records |.>>>>|> > 2.2Functors |.>>>>|> Option Functor |.>>>>|> > List Functors |.>>>>|> > Buffers |.>>>>|> > 2.3Monads |.>>>>|> Kleisli Morphisms |.>>>>|> > Cartesian Strength |.>>>>|> > Identity Monad |.>>>>|> > Monad Zero |.>>>>|> > Option Monad |.>>>>|> > 2.4Multi-bit Words |.>>>>|> Byte Strings |.>>>>|> > Bit Strings |.>>>>|> > Core Simplicity> |.>>>>|> 3.1Types |.>>>>|> Abstract Syntax |.>>>>|> > Formal Syntax |.>>>>|> > Formal Semantics |.>>>>|> > 3.2Terms |.>>>>|> Identity |.>>>>|> > Composition |.>>>>|> > Constant Unit |.>>>>|> > Left Injection |.>>>>|> > Right Injection |.>>>>|> > Case |.>>>>|> > Pair |.>>>>|> > Take |.>>>>|> > Drop |.>>>>|> > Formal Syntax |.>>>>|> > Formal Semantics |.>>>>|> > 3.3Example Simplicity |.>>>>|> Bit Operations |.>>>>|> > Simplicity Notation |.>>>>|> > Generic Equality |.>>>>|> > Arithmetic |.>>>>|> > Bitwise Operations |.>>>>|> > SHA-256 |.>>>>|> > Tagged Hashes |.>>>>|> > Elliptic Curve Operations on secp256k1 |.>>>>|> > libsecp256k1 |.>>>>|> > libsecp256k1 in Simplicity |.>>>>|> > Schnorr Signature Validation |.>>>>|> > 3.4Completeness Theorem |.>>>>|> 3.5Operational Semantics |.>>>>|> Representing Values as Cell Arrays |.>>>>|> > Bit Machine |.>>>>|> > Frame Instructions |.>>>>|> > Active Write Frame Instructions |.>>>>|> > Active Read Frame Instructions |.>>>>|> > Abort Instruction |.>>>>|> > Bit Machine Programs |.>>>>|> > Crashing the Bit Machine |.>>>>|> > Executing Simplicity |.>>>>|> > Tail Composition Optimisation (TCO) |.>>>>|> > 3.6Static Analysis |.>>>>|> Space Resources |.>>>>|> > Maximum Cell Count Bound |.>>>>|> > Maximum Frame Count Bound |.>>>>|> > Time Resources |.>>>>|> > 3.7Commitment Merkle Root |.>>>>|> 3.8Type Merkle Root |.>>>>|> Simplicity Extensions> |.>>>>|> 4.1Monadic Semantics |.>>>>|> 4.2Witness |.>>>>|> Elided Computation |.>>>>|> > Type Inference with Witness |.>>>>|> > 4.3Assertions and Failure |.>>>>|> Denotational Semantics |.>>>>|> > Merkle Roots |.>>>>|> > Pruning Unused Branches |.>>>>|> > Salted Expressions |.>>>>|> > 4.4Blockchain Primitives |.>>>>|> Bitcoin Transactions |.>>>>|> > Denotational Semantics |.>>>>|> > Merkle Roots |.>>>>|> > 4.5Simplicity Programs |.>>>>|> Example: >> |.>>>>|> > 4.6Schnorr Signature Aggregation |.>>>>|> 4.7Malleability |.>>>>|> Transaction Weight |.>>>>|> > Jets> |.>>>>|> Delegation> |.>>>>|> 6.1Implementing on the Bit Machine |.>>>>|> Static Analysis of |.>>>>|> > Space Resources |.>>>>|> > 6.2Unbounded Loops |.>>>>|> Adding a primitive to Simplicity? |.>>>>|> > 6.3Universal Signature Hash Modes |.>>>>|> Side-Effects and Delegation |.>>>>|> > Type Inference and Serialization> |.>>>>|> 7.1Explicit Simplicity DAGs |.>>>>|> Type Inference |.>>>>|> > Reconstructing Simplicity Expressions |.>>>>|> > syncase |.>>>>|> > inflate |.>>>>|> > 7.2Serialization |.>>>>|> Serialization of Bit Strings and Positive Numbers |.>>>>|> > Serialization of Simplicity |.>>>>|> > Serialization of Word Jets |.>>>>|> > Identity Merkle Root |.>>>>|> > Coq Library Guide> |.>>>>|> 8.1Simplicity Types |.>>>>|> 8.2Simplicity Terms |.>>>>|> The \PInitial\Q Representation of Terms |.>>>>|> > The \PFinal\Q Representation of Terms |.>>>>|> > Simplicity Algebras |.>>>>|> > The \PFinal\Q Representation |.>>>>|> > Constructing \PFinal\Q Terms |.>>>>|> > Why two representations of Terms? |.>>>>|> > 8.3Example Simplicity Expressions |.>>>>|> Bits |.>>>>|> > Arithmetic |.>>>>|> > SHA256 |.>>>>|> > 8.4The Hierarchy of Simplicity Language Extensions |.>>>>|> Witness |.>>>>|> > Assertion |.>>>>|> > Delegation |.>>>>|> > Primitives |.>>>>|> > Bitcoin |.>>>>|> > Jets |.>>>>|> > Full Simplicity |.>>>>|> > 8.5Merkle Roots |.>>>>|> 8.6The Bit Machine |.>>>>|> Bit Machine Code |.>>>>|> > Bit Machine Programs |.>>>>|> > Translating Simplicity to the Bit Machine |.>>>>|> > Static Analysis |.>>>>|> > Haskell Library Guide> |.>>>>|> 9.1 library |.>>>>|> Simplicity Types |.>>>>|> > Simplicity Terms |.>>>>|> > Merkle Roots |.>>>>|> > Tensors |.>>>>|> > Example Simplicity Expressions |.>>>>|> > Generic |.>>>>|> > Bits |.>>>>|> > Multi-bit Words |.>>>>|> > Arithmetic |.>>>>|> > Loop |.>>>>|> > Libraries of Simplicity Expressions |.>>>>|> > SHA-256 |.>>>>|> > LibSecp256k1 |.>>>>|> > CheckSigHash |.>>>>|> > The Bit Machine |.>>>>|> > Translating Simplicity to the Bit Machine |.>>>>|> > Static Analysis |.>>>>|> > Fast Evaluation with FFI |.>>>>|> > 9.2 library |.>>>>|> Primitive Signature |.>>>>|> > Primitive Terms |.>>>>|> > class |.>>>>|> > Denotational Semantics of Full Simplicity |.>>>>|> > Type Inference |.>>>>|> > Serialization |.>>>>|> > Free Monadic Deserializaiton |.>>>>|> > Serialization of Simplicity DAGs |.>>>>|> > Jet Substitution |.>>>>|> > 9.3 Library |.>>>>|> 9.4 Library |.>>>>|> CheckSigHashAll |.>>>>|> > Known Discounted Jets |.>>>>|> > 9.5Simplicity |.>>>>|> C Library Guide> |.>>>>|> Elements Application> |.>>>>|> A.1Denotational Semantics |.>>>>|> Null Data |.>>>>|> > Merkle Roots |.>>>>|> > Catelogue of Jets> |.>>>>|> B.1Core Jets |.>>>>|> Jets for multi-bit logic |.>>>>|> > verify |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Jets for arithmetic |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (unsigned) |.>>>>|> > (signed input/unsigned output) |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > (unsigned denominator) |.>>>>|> > (unsigned denominator) |.>>>>|> > (signed denominator) |.>>>>|> > (signed denominator) |.>>>>|> > Jets for hash functions |.>>>>|> > Jets for SHA-2 |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Jets for SHA-3 |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Jets for RIPEMD |.>>>>|> > Jets for SHA-1 (RESERVED) |.>>>>|> > Jets for elliptic curve functions |.>>>>|> > Jets for secp256k1 |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Jets for digital signatures |.>>>>|> > Jets for secp256k1 based digital signatures |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Jets for Simplicity |.>>>>|> > Jets for tagged hash IVs |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Jets for Bitcoin (without primitives) |.>>>>|> > |.>>>>|> > |.>>>>|> > B.2Bitcoin Jets |.>>>>|> Signature Hash Modes |.>>>>|> > Time Locks |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Transaction |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > B.3Elements Jets |.>>>>|> Signature Hash Modes |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Time Locks |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Issuance |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Transaction |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > |.>>>>|> > Alternative Serialization of Simplicity DAGs> |.>>>>|> |.>>>>|> |.>>>>|> Bitcoin was the first protocol that used a blockchain to build a distributed ledger that allows anyone to transact a cryptographic currency with minimal risk of their transaction being reversed or undone, and without relying on a trusted third party or central authority. Typically access to funds are controlled by a cryptographic private key. References to one or more of these funds, which may or may not have the same private keys, are assembled into a data structure, called a , along with a set of one or more outputs which specify which cryptographic public keys that will control each output. This transaction data is signed with each private key for each input and added to the transaction as . More precisely, the outputs are not necessarily controlled by a simple single cryptographic key, rather each output is controlled by a small program written in a language called . Bitcoin Script is a stack-based language with conditionals operations for control flow and no loops. Bitcoin has stack manipulation operations, Boolean logic operations, and very simple arithmetic operations (without even multiplication). It also has some cryptographic operations that include cryptographic hash functions, and digital signature verification operations. The operation does an ECDSA digital signature verification of transaction data. A basic example of a Bitcoin Script program pushes an ECDSA public key onto the stack, followed by a operation. This Script is part of the output data within a transaction. In order to spend the funds held by such an output, one builds a transaction with an input referencing this output and adds a ECDSA signature to the transaction's witness data for the input (called a ScriptSig). The witness data describes which part of the transaction data is being signed (typically everything other than the witness data itself) and has the signature. To validate an input, the witness data is pushed onto the stack, and the the program in the referenced output is executed. In our example above, the program pushes a specific ECDSA public key onto the stack and then executes . The operation pops the public key and the signature data off the stack. Then it cryptographically hashes the transaction data as specified by the signature data, including which input is being signed, and verifies that the digital signature for that public key is valid for that hashed data. Only if successful is the value pushed back onto the stack. In order for a transaction to be valid, all inputs are checked in this fashion, by pushing its associated witness data onto the stack and then executing the program found in the referenced output and requiring a non-zero value be left on the stack. From this example, we see that there are three parts that go into checking if a transaction's input is authorized to be spent: <\itemize-dot> A Bitcoin Script, which is contained in a transaction output. Witness data, for each transactions input. The rest of the transaction data, which includes things like output amounts, version numbers, etc. All the data needed to validate a transaction is part of (or cryptographically committed within) the transaction data. This means the inputs can be validated independently of the state of the rest of the blockchain, as far as Bitcoin Script is concerned. In the above example, the Bitcoin Script is included into a transaction's output, at what I call . The signature and transaction data is specified later at what I call . That said, the Bitcoin Script does not have to be entirely presented at commitment time; it is acceptable to just commit to the Bitcoin Script's cryptographic hash. Then, at redemption time, the script is revealed together with the witness data and the rest of the transaction. In this case the program's hash is verified to be equal to the hash committed in the output, and then the witness data, and revealed Bitcoin Script are validated as before. Bitcoin's (a.k.a. ) follows this modified procedure which makes it easy for users to specify complex Bitcoin Scripts with to control funds while only needing to provide a single hash value to their counterparty when they are first receiving their funds. More complex scripts can be devised to do multi-signature, escrow, hashed-timelock contracts, etc. However, because of the the limited expressiveness of Bitcoin Script (e.g. no multiplication operation), only so much can be programmed. Therefore, we want to design an alternative to Bitcoin Script that will be more expressive, without sacrificing the good properties of Bitcoin Script. We call this new language . Our goals for Simplicity include the following: <\itemize-dot> Create an expressive language that lets users build novel programs and smart contracts. Enable useful static analysis to bound computational resource usage of programs. Minimize bandwidth and storage requirements by allowing sharing of expressions and pruning of unused expressions. Capture the computational environment entirely within a unit of transaction. Provide formal semantics for reasoning with off-the-shelf proof-assistant software. In Bitcoin Script, static analysis lets us count how many operations there are and, in particular, bound the maximum number of expensive operations, such as signature validation, that could be performed. We can do this because Bitcoin Script has no looping operations. In a transaction, if Bitcoin Script is deemed to be potentially too expensive from this analysis, the program is rejected at redemption time. We want to support this same sort of static analysis in Simplicity. It lets users determine, at commitment time, the worst case cost for redeeming the program, for any possible witness inputs. At redemption time it allows, as part of the consensus rules, to bound the cost of running programs prior to execution. This serves as one method of avoiding denial of service attacks in a blockchain protocol like Bitcoin. As we saw before at commitment time we only need to specify a cryptographic commitment to the program, and the program can be revealed at redemption time. For more complex programs with multiple alternative branches, only those branches that are actually going to be executed need to be revealed, and the remainder of the program that is not executed for this particular transaction can be excluded. Using a technique called a.k.a. , we can commit to a Merkle root of a program's abstract syntax tree. At redemption time, we can prune unused sub-expressions. Instead only the Merkle root of the pruned branches need to be revealed in order to verify that the program's Merkle root matches the root specified at commitment time. Because two identical subexpressions necessarily have the same Merkle root, this procedure also lets us reduce program size by sharing these identical subexpressions. In principle, this sharing could extend as wide as between different program in different transactions. Once a program has been committed to, it cannot be changed or updated later. If a program has errors or security vulnerabilities, it can no longer be fixed. Therefore, it is essential to get these program correct. Fortunately these programs tend to be relatively small, and hence amenable to formal analysis. We use the Coq proof assistant to specify formal semantics of Simplicity. This allows us to both reason about programs written in Simplicity, and also lets us reason about our static analysis and Simplicity interpreters and prove that they are correct. While we specifically use the Coq proof assistant, the formal semantics of Simplicity is designed to be easy enough to define in any proof assistant, especially others based on dependent type theory. >>>,>>>>>>,>>>>>>|,|\>,>>>>>>>>>>>>In this document we endeavour to be precise about the semantics surrounding the definition of the Simplicity language. To this end we use formal language composed from a mix of mathematics, category theory, simple type theory, and functional programming. While most all our notation is standard in some community, readers may not be familiar with all of it. To that end, and to ensure completeness of our semantics, we give detailed definitions below of the common notation used throughout this document. Our formal language is phrased in terms of simple type theory and readers familiar with mathematics should not have too much trouble following it since mathematics notation already borrows heavily from simple type theory. To begin with we will assume that we have a notation of a type of natural numbers, >, with \>, \>, and so forth for all other numbers. Given natural numbers \> and \>, we take it for granted that we have <\itemize> notions of arithmetic including , , and >; comparison operations including m>, m>, m>, and m>; when m> then the difference is a natural number. We will partake in several notational conveniences. We will generally elide parentheses when the value they surround already has has its own brackets. For example, <\itemize> we will write |x,y|\>> instead of |x,y|\>|)>>; we will write > instead of |)>>; we will write |n|\>> instead of |n|\>|]>>. As you will see, we have a lot of notation with type annotations that are used to fully disambiguate them. Often these type annotations can be completely inferred from the surrounding context and accordingly we will usually omit these annotations to reduce notational clutter and reserve the annotated versions for cases where the annotations are ambiguous or where we want to draw specific attention to them. We write the primitive unit type as >. The unique value of the unit type is ||\>\>. Given types and , then , B>, and B> are the sum type (also known as disjoint union type), the (Cartesian) product type, and the function type respectively. Given A> and B> we denote values of the sum and product types as <\eqnarray*> >>||A+B>|>>||>||a,b|\>>||B>>>> We will usually omit the annotations, writing >>, >>, and |a,b|\>>. We write an expression of type B> using lambda notation: <\equation*> \x:A\e\A\B where is an expression with A> as a bound variable (that may occur or zero or more times in ). Given A\B> and A>, then ordinary function application retrieves a value of type : <\equation*> f\B The type operator > is right associative: <\equation*> A\B\C=A\C|)> \; We define the identity function \A\A> as <\equation*> id\\a:A\a and given A\B> and B\C> we define their composition f\A\C> as <\equation*> g\f\\a:A\g|)> \; We may also write function definitions in \Papplication\Q style where we implicitly define a function in terms of function application. In this style we would write the above definitions of the identity function and function composition as <\eqnarray*> >|>|>|f|)>>|>||)>>>>> To access components of sum and product types we define functions using pattern matching in application style. For example given A> and B>, we define the first and second projection functions as <\eqnarray*> |a,b|\>>|>|>||a,b|\>>|>|>>> and given A\C> and B\C>, we define their copair \A+B\C> by the pair of equations <\eqnarray*> >|)>>|>|>>|>|)>>|>|>>>> \; When we take a product type with itself, we form a square and denote it by exponential notation accordingly: <\eqnarray*> >|>|A>>>> When we take repeated squares, we denote this by exponential notation with successively larger powers of two: <\eqnarray*> >|>|>|>|>|\A>>|>|>|\A>>||>|>|>>|>|>\A>>>||>|>>> We define the diagonal function returning a square type, \A\A>: <\equation*> \\|a,a|\> We define <2> as the Boolean type (or Bit type): <\equation*> <2>\<1>+<1> We name the two values of this type, >\<2>> and >\<2>>. <\eqnarray*> >>|>|||||\>>>>|>>|>|||||\>>>>>> Record types are essentially the same as product types, but with fancy syntax. We write a record type enclosed by curly braces. <\equation*> |\A>>|\A>>|>>|\A>>>>>|}> If is the above record type and R>, then we denote access the component of the record as follows. <\eqnarray*> ||]>\A>|>|||]>\A>|>||>|>|||]>\A>|>>> To construct a record value given values \A,\,a\A>, we again use a curly brace notation. <\equation*> |\a>>|\a>>|>>|\a>>>>>|}>:|\A>>|\A>>|>>|\A>>>>>|}> A functor > is a type parameterized by a free type variable, such that whenever is a type then > is a type. Given a function A\B>, is it often possible to define a new function f\\A\\B> such that for all A\B> and B\C> we have <\eqnarray*> id>||A>>>|g|)>>||f\\g>>>> When this happens we call such a functor a . In this document all our functors will be covariant functors, and we will simply call them s. By way of a useful example, we define to be the option functor, also known as the maybe functor, <\eqnarray*> A>|>|+A>>|f|A|||\>>|)>>|>||B|||\>>>>|f|A|>|)>>|>||B||)>>>>>> where A\B>. We define special notation for values of \Poptional\Q types A>, <\eqnarray*> >>|>||A|||\>>\A>>|>|>||A|>\A>>>> where A>. This notation is designed to coincide with the monadic notation that we will define in Section. Given a type , we recursively define the list functor >> and the non-empty list functor >, \; <\eqnarray*> >>|>|A>>|>|>|A>>>|>>>|)>>|>|>>>>|>>>|)>>|>|>>|)>>>||a,l|\>>|>||f,f>|\>>>>> where A\B>. We leave implicit the fact that these are inductive types and recursive definitions over them need to be checked that they are well-founded. Suffice to say that the definitions in this section are all well-defined. Given a list A>> or a non-empty list A>, we define \\> to be its length. <\eqnarray*> >>|\|>>|>|>|>>|\|>>|>|>>||a,l|\>|\|>>|>|>>>> \; To retrieve an element we define lookup functions for lists and non-empty lists. Given a natural number \> and either list A>> or a non-empty list A>, in both cases we define \A> to lookup the th value in . <\eqnarray*> >>|)>>|>|>>>|>>|)>>|>|>>||a,l|\>>|>|>>>||a,l|\>>|>|>>>> Naturally, the lookup returns > when the index goes beyond the end of the list. <\lemma> For all \> and A>> or A>, =\> if and only if \n>. Given a list A>> (or a non-empty list A>), we define \\A|)>>> (and \\A|)>> respectively) as a list of elements paired with its index, <\equation*> indexed\indexedRec where <\eqnarray*> >>|)>>|>|>\A|)>>>>|>>|)>>|>|>\A|)>>|)>>>||a,l|\>|)>>|>|||i,a|\>,indexedRec|\>>>>> <\lemma> For all \> and A>> or A>>, =a.|i,a|\>|)>|)>>. The fold operation on a list is a most general way of consuming a list. Given a type with a monoid |\,e|\>> over that type, we define |\,e|\>>> for both lists A>> and non-empty lists A>. <\eqnarray*> |\,e|\>>>>|)>>|>|>||\,e|\>>>>|)>>|>||\,e|\>>>>||\,e|\>>|a,l|\>>|>|fold|\,e|\>>>>>> Often we will write |\,e|\>>> as simply >> since usually both the type and the unit for a monoid is can be inferred from just its binary operation. For lists, we provide special notations for its two effective constructors called , \A>>, and , l\A>> <\eqnarray*> >|>|>>>>|l>|>|>>|a,l|\>>>>> where A> and A>>. As a consequence the following equations hold. <\eqnarray*> |\,e|\>>|)>>||>||\,e|\>>\a\\\a\\|)>>||\a\\\a>>>> For example, given two lists ,l\A>>, we define the append operation \l:A>> using nil and cons <\eqnarray*> \l>|>|>|l|)>\l|>|\l|)>>>>> The append operation together with nil, |\,\|\>>, forms a monoid over >>. This allows us to define the concatenation function >\A\>\A>> <\equation*> \>\fold>>|\,\|\>> Now it is only natural to define a function that generates a list with one element, >\A\A>>. <\equation*> \>\a\\ We write replication of a list, A>> as exponentiation: <\eqnarray*> >|>|>>|>|>|l>>>> We also define quantifier notation for elements of lists. Given a list A>>, and a predicate over , we define <\eqnarray*> a\l\P>|>|>>|)>>>|a\l\P>|>|>>|)>>>>> and similarly for a non-empty list A>: <\eqnarray*> a\l\P>|>|>|)>>>|a\l\P>|>|>|)>>>>> A buffer is defined as a bounded list. \ We recursively define a buffer up to (but excluding) > as <\eqnarray*> 2>>|>|A>>|4>>|>||)>\A2>>>||>|>|2>>|>|>|)>\A2>>>||>|>>> Notice that the type for buffers is isomorphic to a finite geometric series of tuples: <\equation*> ||2>\1+A+A|)>+A\A|)>+\+>|\*\A|)>|\>>>||-1 times>>>>>\ A monad, >, is a functor that comes with two functions <\eqnarray*> >>||\*A>>|>>||*\*A\\*A>>>> that are both natural transformations, meaning for all A\B>, <\eqnarray*> *f\\>>||>\f>>|*f\\>>||>\\*\*f>>>> The >> and >> functions are required to satisfy certain coherence laws. These monad laws are best presented using Kleisli composition. Functions from to that produce side-effects can often be represented by Kleisli morphisms, which are (pure) functions \*B>, where > is a monad that captures the particular side-effects of the function in the result. A function A\\*B> is called a from to . For Kleisli morphisms A\\*B> and B\\*C> we define the of them as |>>f\A\\*C> where <\equation*> g|>>f\\>\\*g\f We will usually omit the annotation. The monad laws can be presented in terms of Kleisli composition. For all A\\*B>, B\\*C>, and C\\*D>, we require that Kleisli composition satisfy the laws of composition with >> as its identity: <\eqnarray*> \>>||>|>\f>||>|g|)>\f>||f|)>>>>> In addition to Kleisli composition we define a series of helper functions for manipulating products. \; ||||>>>|\*B\\B|)>>>>|>|a,b|\>>>|\x\|a,x|\>|)>>>>>>>> \; \; |||||\>>>>|*A\B\\B|)>>>>||\>>|a,b|\>>>|\x\|x,b|\>|)>>>>>>>> \; \; ||||>>>|*A\\*B\\B|)>>>>|>>>|\>\|\>>>>>>>>> \; \; |||||\>>>>|*A\\*B\\B|)>>>>||\>>>>||\>>\\>>>>>>>> \; The operations >> and |\>>> are similar, but differ in the order that effects are applied in. Roughly speaking, >> applies the effects of the first component first, while |\>>> applies the effects of the second component first. For some monads, the order of the effects is immaterial and >=|\>>>. We call such monads . It is always the case that <\equation*> \>\\*A>=|\>>\\*A>\\*A\\|)> holds, even for non-commutative monads. In this case, the effect specified by the input is duplicated. Compare this with *\\\*A\\|)>> where the contents of type are duplicated, but not the effect itself. When we have *\=\>\\*A>> *\=|\>>\\*A>>|)>, we say that > is an .<\footnote> Beware that we are using the definition of idempotent monad from King and Wadler, as opposed to the traditional categorical definition of an idempotent monad. For idempotent monads, the same effect is occurring two or more times in a row is equivalent to it occurring once. The most trivial monad is the identity monad, , where A\A> and f\f>. The natural transformations > and > are both the identity function. The identity monad captures no side-effects and it is commutative and idempotent. Some monads have a universal value <\equation*> \>\\*A where for all A\B>, <\equation*> \f>|)>=\> This zero value denotes a side-effect that captures the notion of a failed or aborted computation or some kind of empty result. The laws for these monads with zero are, again, best expressed using Kleisli morphisms. At the risk of some notational confusion, we define >\A\\*B> as a . <\equation*> \>\\> Zero morphisms are required to be an absorbing element for Kleisli composition. For all A\\*B> and B\\*C> we require that <\eqnarray*> >\>>||>>>|>>f>||>>>>> (Note: In Haskell, the value typically is only required to satisfy the first equation; however, we require monads with zero to satisfy both laws.) The functor > forms a monad with the following operations: <\eqnarray*> >>|>|>>>|||\>>|)>>|>|||\>>>>|>|)>>|>|>>> The option monad is commutative and idempotent. The option monad has a zero: <\equation*> \>\||\>> There is a natural transformation from the option monad into any monad with zero, >,A>\A\\*A>: <\eqnarray*> >,A>>|)>>|>|>>>|>,A>>|)>>|>|>>>>> <\lemma> For all B>, \; <\equation*> \>,B>\f=\*f\\>,A> Also <\equation*> \>,A>\\>=\>\\>,\*A>\\>,A> >\\*\>,A>\\>,A>|)> By repeatedly taking products of the bit type we can build the types >> which denote >-bit words. We choose to represent values in big endian format, meaning that given a pair representing the low and high bits of a value, the most significant bits are stored in the first half. Given a value <2>>, where is a power of two, we recursively define |a|\>\\> to be the number that represents: <\eqnarray*> |>|\>>|>|>||>|\>>|>|>|||a,b|\>|\>>|>||a|\>*2+|b|\>>>>> We also make use of the following variation of this value interpretation function. <\equation*> ||a,b|\>|\>\|a|\>*2+|b|\> These value interpretation functions are all injective (one-to-one) and we can choose a left inverse. Given \>, we implicitly define |m|\>\<2>> such that ||m|\>|\>\m |)>>. We have chosen |m|\>> so that it represents modulo >. We can equip the type > with addition and multiplication operations, so that |\|\>> becomes a semiring homomorphism. Given <2>> and <2>>, we define |+|\>b\<2>> and |\|\>b\<2>> such that <\eqnarray*> |m|\>|+|\>|m|\>>|||m+m|\>>>||m|\>|\|\>|m|\>>|||m*m|\>>>>> \; We write >,>,\,>> to denote the 16 values of > that represent their respective hexadecimal values. Similarly, we write >,>,\,>> to denote the 256 values of >, and so forth. It is worth observing that for hexadecimal digits >> and >>, we have >>=|>>,>>|\>>. The type |)>>> is known as byte strings. We will write byte string values as sequences of hexadecimal digits surrounded by square brackets, e.g. >> denotes >\>\\>> (whereas >> denotes |>,>|\>>). For all these values, we may omit the subscript when the interpretation is clear from the context. Words larger than a byte are commonly encoded as byte strings in either big endian or little endian order. We define \<2>\|)>>> and \<2>\|)>>> as big endian and little endian encodings of words respectively for 8>. <\eqnarray*> >|>|>>>||a,a|\>>|>||)>\LE|)>(when n>)>>>|>|>|>>>||a,a|\>>|>||)>\BE|)>(when n>)>>>>> The type >> is known as bit strings. We will write bit string values as sequences of binary digits surrounded by square brackets, e.g. >> denotes >\>\>\>\\>>. Again, we may omit the subscript when the interpretation is clear from context. Simplicity is a typed functional programming language based on Gentzen's sequent calculus. The core language consists of nine combinators for forming expressions. These nine combinators capture the computational power of Simplicity. In later chapters other combinators will extend this core language and provide other effects to handle input and access the transaction that provides context for the Simplicity program. This section introduces the abstract syntax and semantics types available in Simplicity. Simplicity uses a particular subset of the simple type theory we developed in Chapter. Simplicity has only three kinds of types: <\itemize-minus> The unit type, . The sum of two Simplicity types, . The product of two Simplicity types, B>. \; Simplicity has neither function types nor recursive types. Every type in Simplicity can only contain a finite number of values. For example, the type <2>, which is +>, has exactly two values, namely ||||\>> and ||||\>>. The type +|)>\+|)>> has exactly four values. As you can see, the number of values that a type contains can be easily calculated by interpreting the type as an arithmetic expression. Be aware that types are not arithmetic expressions. For example, the types +|)>++|)>> and +|)>\+|)>> are distinct and not interchangeable. Formally we define the abstract syntax of types as an inductive type in Coq: <\render-code> <\verbatim> Ty : Set := \| Unit : Ty \| Sum \ : Ty -\ Ty -\ Ty \| Prod : Ty -\ Ty -\ Ty. Formally we define the denotational semantics of Simplicity types as a function from syntax to Coq types: \; <\verbatim> Fixpoint tySem (X : Ty) : Set := match X with \| Unit =\ Datatypes.unit \| Sum A B =\ tySem A + tySem B \| Prod A B =\ tySem A * tySem B end. Simplicity programs are composed of terms that denote functions between types. Every Simplicity term is associated with an input type and an output type and we write a type annotated term as A\B> where is the term, is the input type and is the output type. We write |t|\>\A\B> for the function that the term denotes. Core Simplicity has nine combinators for forming well-typed terms. <\with|par-mode|center> |\A\A>>>>>> <\equation*> ||\>\\a\a For every Simplicity type , we have an identity term that denotes the identity function for that type. We can also write the semantics in application style as <\equation*> ||\>\a which is just a different way of writing the same definition. However, please note that the argument is an argument of the function denoted by > and is not an argument to the Simplicity term itself. <\with|par-mode|center> |||||||A\B>>|B\C>>>>>>>>| s t\A\C>>>>>> <\equation*> | s t|\>\|t|\>\|s|\> The composition combinator functionally composes its two arguments, and , when the output type of matches the input type of . <\with|par-mode|center> |\A\>>>>>> <\equation*> ||\>\\a\||\> The unit term denotes the constant function that always returns ||\>>, the unique value of the unit type. The function's argument is ignored and we have a constant unit term for every type of input. We can also write semantics in application style as <\equation*> ||\>\||\> We will use application style when writing the definition of the remaining combinators, trusting that the reader will be mindful of the distinction between arguments of the combinators versus the argument of the function that the Simplicity term denotes. <\with|par-mode|center> |||A\B>>>| t\A\B+C>>>>>> <\equation*> | t|\>\|t|\>|)>> The left injection combinator composes a left-tag with its argument . <\with|par-mode|center> |||A\C>>>| t\A\B+C>>>>>> <\equation*> | t|\>\|t|\>|)>> The right injection combinator composes a right-tag with its argument . <\with|par-mode|center> |||||||A\C\D>>|B\C\D>>>>>>>>| s t\\C\D>>>>>> <\eqnarray*> | s t|\>|>,c|\>>|>||s|\>|a,c|\>>>|| s t|\>|>,c|\>>|>||t|\>|b,c|\>>>>> The case combinator is Simplicity's only branching operation. Given a pair of values with the first component being a sum type, this combinator evaluates either its or argument, depending on which tag the first component has, on the pair of inputs. \; <\with|par-mode|center> |||||||A\B>>|A\C>>>>>>>>| s t\A\B\C>>>>>> <\equation*> | s t|\>\||s|\>,|t|\>|\> The pair combinator evaluates both its arguments, and , on the same input and returns the pair of the two results. <\with|par-mode|center> |||A\C>>>| t\A\B\C>>>>>> <\equation*> | t|\>|a,b|\>\|t|\> The take combinator denotes a function on pairs that passes its first component to and ignores its second component. <\with|par-mode|center> |||B\C>>>| t\A\B\C>>>>>> <\equation*> | t|\>|a,b|\>\|t|\> The drop combinator denotes a function on pairs that passes its second component to and ignores its first component. We define the formal syntax of well-typed core Simplicity terms as an inductive family in Coq: <\render-code> <\verbatim> Term : Ty -\ Ty -\ Set := \| iden : forall {A}, Term A A \| comp : forall {A B C}, Term A B -\ Term B C -\ Term A C \| unit : forall {A}, Term A Unit \| injl : forall {A B C}, Term A B -\ Term A (Sum B C) \| injr : forall {A B C}, Term A C -\ Term A (Sum B C) \| case : forall {A B C D}, \ \ \ \ Term (Prod A C) D -\ Term (Prod B C) D -\ Term (Prod (Sum A B) C) D \| pair : forall {A B C}, Term A B -\ Term A C -\ Term A (Prod B C) \| take : forall {A B C}, Term A C -\ Term (Prod A B) C \| drop : forall {A B C}, Term B C -\ Term (Prod A B) C. The formal semantics for core Simplicity in Coq recursively interprets each term as a function between the formal semantics of its associated types: \; <\verbatim> Fixpoint eval {A B} (x : Term A B) : tySem A -\ tySem B := match x in Term A B return tySem A -\ tySem B with \| iden =\ fun a =\ a \| comp s t =\ fun a =\ eval t (eval s a) \| unit =\ fun _ =\ tt \| injl t =\ fun a =\ inl (eval t a) \| injr t =\ fun a =\ inr (eval t a) \| case s t =\ fun p =\ let (ab, c) := p in \ \ \ \ match ab with \ \ \ \ \| inl a =\ eval s (a, c) \ \ \ \ \| inr b =\ eval t (b, c) \ \ \ \ end \| pair s t =\ fun a =\ (eval s a, eval t a) \| take t =\ fun ab =\ eval t (fst ab) \| drop t =\ fun ab =\ eval t (snd ab) end. Simplicity is not meant to be a language to directly write programs in. It is intended to be a backend language that some other language (or languages) is complied or translated to. However, one can program directly in Simplicity just as one can write programs directly in an assembly language. Because the core Simplicity language may seem meager, it is worthwhile to see how one can build up sophisticated functions in it. For the bit type, <2>, we can define core Simplicity terms that represent the two constant functions that return this type: <\eqnarray*> >|>|,> \A\<2>>>|>|>|,> \A\<2>>>>> From these definitions, we can prove that > and > have the following semantics. <\eqnarray*> ||\>>||>>>|||\>>||>>>>> Next, we define a condition combinator to branch based on the value of a bit using > and . The first argument is the \Pthen\Q clause and the second argument is the \Pelse\Q clause. \; <\with|par-mode|center> |||||||A\B>>|A\B>>>>>>>>| s t\,,A,B> t|)> s|)>\<2>\A\B>>>>>> \; We can prove that > has the following semantics. <\eqnarray*> | s t|\>|>,a|\>>|||s|\>>>|| s t|\>|>,a|\>>|||t|\>>>>> With these fundamental operations for bits in hand, we can define standard Boolean connectives: <\with|par-mode|center> ||||||A\<2>>>>>>>>>| t\\,<2>> t |)> |)>\A\<2>>>>>>> \; \; <\with|par-mode|center> |||||||A\<2>>>|A\<2>>>>>>>>>| s t\\A,<2>> s |)> t |)>\A\<2>>>>>>> \; \; <\with|par-mode|center> |||||||A\<2>>>|<2>>>>>>>>>| s t\\A,<2>> s |)> t|)>\A\<2>>>>>>> \; We use combinators to define and in order to give them short-circuit evaluation behaviour. Short-circuit evaluation useful because if we know the second branch does not need to be evaluated, the source code for it can be pruned at redemption time (see Section). If instead we directly defined the Boolean functions with types :<2>\<2>\<2>> and :<2>\<2>\<2>>, then the two arguments to and would both be fully evaluated under strict semantics (see Section). For the combinator, this is less of an issue, but we define it in combinator form to be consistent. In the previous section, we were relatively detailed with the annotations given to the definitions. Going forward we will be a bit more lax in the presentation. We will also begin using some notation to abbreviate terms. <\eqnarray*> t>|>| s t>>||>| s t>>>> with the > operator having higher precedence than the ; operator. Composition of sequences of and with is a very common way of picking data from a nested tuple input. To make this more concise we will use the following notation. <\eqnarray*> >|>|>>|s>|>| s>>|s>|>| s>>>> where is a string of 's and 's that ends with . With our notion of a bit in hand, we can build Simplicity predicates of type <2>>. For example, for any Simplicity type we can build a Simplicity predicate \A\A\<2>>, that decides if two values of the same type are equal or not. <\eqnarray*> >>|>|>>|>|>| \ ; |)> \ ; |)>>>|B>>|>| \ ;|)> \ \ |)>; >>>> <\theorem> Given any Simplicity type A, for values ,a\A>, <\equation*> ||\>|a,a|\>=>a=a. Using techniques familiar from digital logic, we can build an adders and full adders from our Boolean operations defined in Section. We begin with definitions of the single bit full adder. \; <\render-code> \<2>\\<2>|)>\<2>> |>>|| \ >>>>>>>>>>>> where <\render-code> \<2>\\<2>|)>\<2>> |>>|| |)> |)>>>>>>>>>>>> and <\render-code> \<2>\\<2>|)>\<2>> |>>|| |)>|)> |)> |)>>>>>>>>>>>> The full adder meets the following specification. <\eqnarray*> |||\>|c,|a,b|\>|\>|\>>|||a|\>+|b|\>+|c|\>>>>> It is easy to exhaustively check the above equations because there are only eight inputs to consider. We will illustrate this for a single case where >>, >>, and >>. <\eqnarray*> |||\>|>,|>,>|\>|\>|\>>|||| \ >|\>|>,|>,>|\>|\>|\>>>||||||>>|\>|>,|>,>|\>|\>,|>|\>|>,|>,>|\>|\>>|\>|\>>>|||||| |)> |)>>|\>|>,|>,>|\>|\>,|>|\>|>,|>,>|\>|\>>|\>|\>>>|||||| >>|\>|>,>|\>,|>|\>|>,|>,>|\>|\>>|\>|\>>>||||||>>|\>>|)>,|>|\>|>,|>,>|\>|\>>|\>|\>>>|||||>,|>|\>|>,|>,>|\>|\>>|\>|\>>>|||||>,| |)>|)> |)> |)>>>|\>|>,|>,>|\>|\>>|\>|\>>>|||||>,| |)>>>|\>|>,>|\>>|\>|\>>>|||||>,|>>|\>>|)>>|\>|\>>>|||||>,>>|\>|\>>>||||>|\>\2+|>|\>>>|||2+0>>|||>|||>||||>|\>+|>|\>+|>|\>>>>> The calculations for the other cases are similar. Next, we recursively build full adders for any word size. <\render-code> \<2>\\<2>|)>\<2>\<2>> |>>|| \ |)> \ \ \ |)> ;|)>>>>||| \ \ ;|)>>>>||| \ \ |)>>>>>>>>>>>> We generalize the specification of the single bit full adder to the multi-bit full adders. <\eqnarray*> |||\>|c,|a,b|\>|\>|\>>|||a|\>+|b|\>+|c|\>>>>> <\theorem> For all which is a power of 2, and for all >, >, and >, we have that |||\>|c,|a,b|\>|\>|\>=|a|\>+|b|\>+|c|\>>. <\proof> We prove > meets its specification by induction on . As mentioned before, the > case is easily checked by verifying all eight possible inputs. Next, we prove that > meets its specification under the assumption that > does. Specifically we need to show that <\equation> |||\>|c,||a,a|\>,|b,b|\>|\>|\>|\>=||a,a|\>|\>+||b,b|\>|\>+|c|\> Let us first consider the right hand side of equation . By the definition of our value function we have that <\eqnarray*> ||a,a|\>|\>+||b,b|\>|\>+|c|\>>|||a|\>\2+|a|\>+|b|\>\2+|b|\>+|c|\>>>||||a|\>+|b|\>|)>\2+|a|\>+|b|\>+|c|\>>>>> By our inductive hypothesis, we have that <\equation*> |||\>|c,|a,b|\>|\>|\>=|a|\>+|b|\>+|c|\> so we know that <\equation*> ||a,a|\>|\>+||b,b|\>|\>+|c|\>=|a|\>+|b|\>|)>\2+|||\>|c,|a,b|\>|\>|\> Let us define > and > such that |c,r|\>\||\>|c,|a,b|\>|\>>. Thus we have that <\eqnarray*> ||a,a|\>|\>+||b,b|\>|\>+|c|\>>|||a|\>+|b|\>|)>\2+||c,r|\>|\>>>||||a|\>+|b|\>|)>\2+|c|\>\2+|r|\>>>||||a|\>+|b|\>+|c|\>|)>\2+|r|\>>>>> Again, by our inductive hypothesis, we have that <\equation*> |||\>|c,|a,b|\>|\>|\>=|a|\>+|b|\>+|c|\> therefore we have that <\equation*> ||a,a|\>|\>+||b,b|\>|\>+|c|\>=|||\>|c,|a,b|\>|\>|\>\2+|r|\> Let us define > and > such that |c,r|\>\||\>||a,b|\>,c|\>>. Thus we have that <\eqnarray*> ||a,a|\>|\>+||b,b|\>|\>+|c|\>>||||c,r|\>|\>\2+|r|\>>>||||c|\>\2+|r|\>|)>\2+|r|\>>>||||c|\>\2+|r|\>\2+|r|\>>>>> Now let us consider the left hand side of equation . By the definition and semantics of > we have that <\eqnarray*> |||\>|c,||a,a|\>,|b,b|\>|\>|\>>||| \ \ |)>|\>>>||>|| \ \ ;|)>|\>>>||>|| \ |)> \ \ \ |)>;|)>|\>>>||||c,||a,a|\>,|b,b|\>|\>|\>>>|||| \ \ |)>|\>>>||>|| \ \ ;|)>|\>>>|||||a,b|\>,||\>|c,|a,b|\>|\>|\>>>|||| \ \ |)>|\>>>||>|| \ \ ;|)>|\>>>|||||a,b|\>,|c,r|\>|\>>>|||| \ \ |)>|\>>>||||r,||\>|c,|a,b|\>|\>|\>>>|||| \ \ |)>|\>>>||||r,|c,r|\>|\>>>||||c,|r,r|\>|\>>>>> Therefore we have that <\eqnarray*> ||||\>|c,||a,a|\>,|b,b|\>|\>|\>|\>>||||c,|r,r|\>|\>|\>>>||||c|\>\2+||r,r|\>|\>>>||||c|\>\2+|r|\>\2+|r|\>>>>> Together equations and show that the right hand side and left hand side of equation are equal, as required. Computer verified versions of these proofs can be found in the Coq library (see Section). With a full adder we can recursively build full multipliers. <\render-code> \\<2>|)>\\<2>|)>\<2>> |>>|| |)> \ ;>>>>>>>>>>> <\render-code> \\<2>|)>\\<2>|)>\<2>> |>>|| \ \ |)>|)>>>>||>>| \ |)> \ \ |)>;|)>>>>||>>| \ |)> \ \ |)>;|)>>)>>||| \ |)>>>>||>>| \ |)> \ \ \ |)>;|)>|)>>>>||| \ \ |)>;|)> \ \ |)>>>>>>>>>>>> \; We can prove that the full multipliers meet the following specifications. <\eqnarray*> |||\>||a,b|\>,|c,d|\>|\>|\>>|||a|\>\|b|\>+|c|\>+|d|\>>>>> \; The official standard for the SHA-2 family, which includes SHA-256, can be found in the . We define the SHA-256 function, >\<2>>\<2>>, as a function from bit strings to a 256-bit word. Technically, SHA-256 is restricted to inputs <2>>> where \2>. The SHA-256 hash function is composed from two components, a padding function \<2>>\|)>>, which appends padding and length data to produce a (non-empty) sequence of blocks of 512 bits, and the Merkle\UDamgrd construction \<2>\|)>>\<2>>. <\equation*> SHA256>=SHA256|SHA256,\|)>|\> where \<2>> is the SHA-256 initial value and >\A\A>> formally converts a non-empty list to a regular list. The > function is a left fold using the SHA-256 block compression function \<2>\<2>\<2>>. <\eqnarray*> |h,\|\>>|>|>||h,b\l|\>>|>||SHA256|h,b|\>,l|\>>>>> The block compression function \<2>\<2>\<2>> is a function whose type fits in Simplicity's framework. We can create a core Simplicity term \<2>\<2>\<2>> that implements this function <\equation*> ||\>=SHA256 We can also define SHA-256's initial value \\<2>>. <\equation*> ||\>||\>=SHA256 Beyond defining the block compression function in the Simplicity language, we will also be using the SHA-256 hash function elsewhere in this specification. In practice, SHA-256 is applied to byte strings rather than bit strings. To this end, we define the variant >\|)>>\<2>>. <\equation*> SHA256>\SHA256>\\>\>>>|)>> where >>>\<2>\<2>>> formally converts a byte to a bit string (in big endian format). <\equation*> \>>>|||b,b|\>,|b,b|\>|\>,||b,b|\>,|b,b|\>|\>|\>\b\b\b\b\b\b\b\b\\ Since the >> variant is so commonly used, we will write it unadorned as simply . BIP-340, BIP-341 used a \Ptagged-hash\Q format to help avoid message collisions between different message variants. We adopt the same format here to avoid message collisions within a Simplicity application and we hope to avoid message collision across various applications. The tagged hash format begins every message with one block prefix which indicate the variant, or type of digest data being hashed. This first block consists of the SHA-256 digest of a string repeated twice. \ Given a byte string |)>>>, we can defined the tagged hash of bit strings, >\<2>>\<2>>, and byte strings, \ >\|)>>\<2>>. <\eqnarray*> >>|>|>>>>>|)>>p|)>|)>\x|)>>>|>>|>|>p\x|)>>>|||BE>|)>>>>> \ We can compute the SHA-256 midstate after compressing this first block containing the prefix tag. <\equation*> SHA256\SHA256|SHA256,\>|)>|\> \; The Standards for Efficient Cryptography (SEC) documents have recommend modular elliptic curve parameters including the secp256k1 curve, which is used by Bitcoin's EC-DSA signature scheme and the proposed EC-Schnorr scheme. Most points on an elliptic curve, such as secp256k1, consist of a pair of coordinates from a specified finite field. In the case of secp256k1, the finite field is the prime field > where 2-4294968273>. The elliptic curve for secp256k1 consists of the points |x,y|\>> satisfying the equation \x+7 >, plus an additional \Ppoint at infinity\Q, which we will write as >. It turns out that elliptic curves can be given a group structure via \Pgeometry\Q, where any three points on the curve that are co-linear sum to 0 under this group structure, and where > is the group's identity element. We have to be careful to count lines \Ptangent\Q to the curve as passing through the same point twice, and count vertical lines as passing through >. This group structure is Abelian, and therefore can also be viewed as a >-module<\footnote> Mathematically, we actually have a 1-dimensional vector space; however determining the linear dependence between two vectors is presumed to be infeasible. Indeed, the security properties of the elliptic curve depends on this being infeasible. For this reason, it is more useful to think of this structure as a module rather than as a vector space. where 2-432420386565659656852420866394968145599> is the order of this elliptic curve. This >-module structure allows us to talk about \Padding\Q two points of the elliptic curve, and scaling a point by a factor from >. Because the order of the elliptic curve, , is a prime number, every non-> element generates the entire curve (through scalar multiplication). The specification for secp256k1 comes with a reference generator, >, which is defined as the following point. <\eqnarray*> >|>||55066263022277343669578718895168534326250603453777594175500187360389116729240,32670510020758816978083085130507043184471273380659243275938904335757337482424|\>>>>> The libsecp256k1 library is a C implementation of optimized functions on this elliptic curve. This library has two variants for the representation of elliptic curve point values. The affine coordinate representation consists of a pair of field elements, and a flag to indicate the value > (in which case the coordinate values are ignored). The Jacobian coordinate representation consists of a triple of field elements, and a flag to indicate the value > (in which case the coordinates are ignored). A point in Jacobian coordinates, |x,y,z|\>> is defined to be on the elliptic curve when <\equation*> y\x+7z and two points in Jacobian coordinates are equivalent, |x,y,z|\>\|x,y,z|\>>, when <\equation*> x*z\x*z y*z\y*z A point in Jacobian coordinates, |x,y,z|\>> represents the curve point |x*z,y*z|\>> in affine coordinates when 0>. In particular, the point |x,y,1|\>> in Jacobian coordinates represents the point |x,y|\>> in affine coordinates. The same point has multiple representations in Jacobian coordinates, however, even the affine coordinate representation is redundant because the underlying field representation is itself redundant. Normally the point at infinity would be represented by |a,a,0|\>> in Jacobian coordinates for any \>; however this is not done in libsecp256k1. Instead a flag is used to represent the point at infinity (and the coordinates are ignored when this flag is set). Testing if a field element is equivalent to 0 is a non-trivial operation, so using a flag like this may be sensible. The various group and >-module operations are implemented efficiently, again subject to various specific preconditions on their inputs. In particular, the operation for forming linear combinations of the form <\equation*> n>*\+n>*\ is supported using an algorithm known as Shamir's trick, where >\\>, >\\>, and > are points on the elliptic curve. The primary application for Simplicity is to implement computation for public validation. In implementing cryptographic operations in Simplicity, we have no need to worry about constant-time implementations, nor securing private key material because Simplicity's application only processes public data. When it comes to implementing elliptic curve operations in Simplicity, we do face one problem. In order for elliptic curve operations to be fast, we need a representation of field elements and curve points that have redundant representations, but then the choice of which specific representative returned by Simplicity expressions becomes consensus critical. We see three possible ways of addressing this problem: <\enumerate-numeric> We can define minimal Simplicity types that can represent field elements and elliptic curve points and return values in normal form after every elliptic curve operation. We can define Simplicity types that can represent field elements and elliptic curve points with redundant representations and specify precisely which representative is the result of each elliptic curve operation. We can extend Simplicity with abstract data types for field elements and elliptic curve points and enforce data abstraction in the elliptic curve operations. Option 1 would make it easy for developers to implement elliptic curve jets (see Section>>) that short-cut the interpretation of Simplicity's elliptic curve operations by running native code instead. The native code for these jets can be implemented by any reasonable algorithm, and the results normalized. The problem with this option is that computing the normal form of elliptic curve points is an expensive operation. In particular, normalizing a point in Jacobian coordinates requires computing a modular inverse, which is a very expensive operation compared to the other field operations. Option 2 means we must ensure that the native code for jets returns exactly the same representative that the Simplicity expression it replaces would have produced. Even libsecp256k1 does not guarantee that different versions of the library will return the same representatives for its basic elliptic curve operations, so Simplicity jets would not be able to keep up with libsecp256k1 updates. Option 3 would let us change the underlying representations of elliptic curve values, allowing us to use any version of any secp256k1 library. However, it would extend the scope of Simplicity beyond what we are willing to do. We have chosen to go with option 2. We have reimplemented the exact same algorithms for field and elliptic curve operations that the most recent release of libsecp256k1 uses as of the time of this writing, including computing of linear combinations of the form <\equation*> n>*\+n>*\ which is used for Schnorr signature validation. Our jets will be tied to this specific version of libsecp256k1, and the commitment Merkle root (see Section) captures the formal specification of the functional behaviour of our jets. The libsecp256k1 is already reasonably mature, so we are not expecting to lose out too much by missing future advances. When there are major improvements, new versions of Simplicity jets could be substituted in by using a versioning mechanism for Simplicity. In Simplicity, we represent a field element by the type <\equation*> FE\<2> and a value FE> represents the field element <\equation*> |a|\>\|a|\> We represent non-> points on the secp256k1 elliptic curve in affine coordinates by the type <\equation*> GE\FE\FE and a value |x,y|\>\GE> represents the point <\equation*> ||x,y|\>|\>\||x|\>,|y|\>|\> We also represent points on the secp256k1 elliptic curve in Jacobian coordinates by the type <\equation*> GEJ\GE\FE and a value ||x,y|\>,z|\>> represents the point <\eqnarray*> |||x,y|\>,z|\>|\>>|>|||x|\>\|z|\> ,|y|\>\|z|\> |\>|z|\> \0 >>>>||||x,y|\>,z|\>|\>>|>||z|\>\0 > and >|y|\>\|x|\> >>>> The translation between libsecp256k1's affine coordinate representation of elliptic curve points and Simplicity's is straightforward except that Simplicity's type has no flag and cannot represent the > point. The translation between libsecp256k1's Jacobian coordinate representation of elliptic curve points and Simplicity's type is mostly straight forward, however the type represents the > point using a z-coordinate representing 0, while libsecp256k1 uses a flag to represent the > point. The Simplicity implementation of libsecp256k1 is designed so that libsecp256k1 can be used as jets for these Simplicity expressions. As such, the Simplicity expressions are designed to mimic the exact behaviour of a specific version of libsecp256k1's elliptic curve functions. For inputs of particular representations of point in Jacobian coordinates, the Simplicity expression returns the exact same representative for its result as libsecp256k1. If an off-curve point is passed to a libsecp256k1 function, the Simplicity code again computes the same result that the libsecp256k1 function does. The only subtle point with using libsecp256k1 for jets lies in the different representation of >. The inputs and outputs of operations need to be suitable translated between the two representations. However, this can be done as part of the marshalling code for the jets, and the Simplicity expressions are written with this in mind. With elliptic curve operations defined, we are able to implement Schnorr signature validation in accordance with the BIP-0340 specification. We define Simplicity types for the formats of x-only public keys, ; messages, ; and Schnorr signatures, , below. <\eqnarray*> |>|>>||>|>>||>|>>>> The type is an x-coordinate of a point whose y-coordinate's least significant bit is even. A value represents the byte-string > for a Schnorr signature's message, and a value represents the byte-string > for a Schnorr signature. We have implemented a core Simplicity expression to check a Schnorr signature for a public key on a given message: <\equation*> \Msg|)>\Sig\<2> The semantics are such that ||\>||p,m|\>,s|\>=>> only when the values that the inputs represents satisfy the verification conditions of the BIP-0340 specification. General purpose programming languages are famously incomplete because there are functions that are uncomputable, the halting problem being the most famous of these. Core Simplicity is even more limited that these general purpose programming languages because its denotational semantics are limited to functions from finite types to finite types. However, we can ask the question, is every function from a finite type to a finite type expressible in core Simplicity? This question is answered by the following completeness theorem. <\theorem> Core Simplicity Completeness Theorem. For any Simplicity types and and any function B>, there exists some core Simplicity term such that for all , <\equation*> |t|\>=f This result is possible because these functions are all finitary and can be, in principle, expressed as a large lookup table. It is possible to encode these lookup tables with Simplicity expressions. The formal proof of this theorem can be found in the Coq library (see Section). It is worth emphasizing that this result is a purely theoretical result that shows that core Simplicity is fully expressive for its domain; it is completely impractical to generate Simplicity expressions this way as many expressions would be astronomical in size. Thus we can view Simplicity programming as an exercise in compression: how can we take advantage of the structure within computations to express our functions succinctly. One practical variant of the core Simplicity completeness theorem is that for any value of a Simplicity type B>, the constant function _\b\A\B> can be realized by a Simplicity expression. We call the function that constructs this term, \A\B>. <\eqnarray*> >||\>>|>|>>|>|)>>|>| |)>>>|>|)>>|>| |)>>>|C>|b,c|\>>|>| \ >>>> <\theorem> For all Simplicity types and , and for all values A> and B>, <\equation*> ||\>=b The denotational semantics of Simplicity determine the functional behaviour of expressions. However, they are not suitable for determining the computation resources needed to evaluate expressions. For this reason we define an operational semantics for Simplicity via an abstract machine we call the . ]>>>>>>\>>>>Values in the Bit Machine are represented by arrays of cells where each cell contains one of three values: a value, a value, or a value which we call an undefined value. We write an array of cells by enclosing a sequence of cells with square brackets (e.g. ). We denote the length of an array using |\|>>. For example, |\|>=3>. The concatenation of two arrays, and is denoted by b>, and replication of an array times is denoted by exponentiation, >. Sometimes we will omit the dot when performing concatenation. For any given type, we define the number of cells needed to hold values of that type using the following function. <\eqnarray*> |)>>|>|>|>|>|,bitSize|)>>>|B|)>>|>|+bitSize>>>> We define a representation of values of Simplicity types as arrays of cells as follows. <\eqnarray*> ||\>|>>|>|>>|>|A+B>>|>|\>\>>|>|A+B>>|>|\>\>>||a,b|\>|A\B>>|>|\>>>> The representation of values of a sum type are padded with undefined cells so that the representation has the proper length. <\eqnarray*> >|>|,bitSize|)>-bitSize>>|>|>|,bitSize|)>-bitSize>>>> <\theorem> Given any value of some Simplicity type, A>, we have |\|>=bitSize>. A frame is a, possibly empty, cell array with a cursor referencing a cell in the array, which we denote using an underscore. <\equation*> ?10> The cursor may also reference the end of the array, which we denote by marking the end of the array with an underscore. <\equation*> Frames can be concatenated with cell arrays either on the left or on the right without moving the cursor. Note that when concatenating a non-empty cell array onto the right hand side of a frame whose cursor is at the end of the frame, the cursor ends up pointing to the first cell of the added cell array. <\equation*> =>11??> >>>We will sometimes denote the empty frame, >, with a small cursor, . The state of the Bit Machine consists of two non-empty stacks of frames: a read-frame stack and a write-frame stack. The top elements of the two stacks are called the and the respectively. The other frames are called inactive read-frames and inactive write-frames. ||||>|1??110101000>>|>>|000>>|?>>>|>|>|0>>|>>>>|Example state of the Bit Machine.> >>>Notationally we will write a stack of read frames as \\\r\r>, with > as the active read frame. We will write a stack of write frames in the opposite order, as \w\\\w> with > as the active write frame. We write a state of the Bit Machine as \r\|w\\|]>> where > is the (possibly empty) inactive read frame stack, > is the (possibly empty) inactive write frame stack, > is the active read frame, and > is the active write frame.<\footnote> The notation for the Bit Machine's state is intended to mimic the gap buffer used in our C implementation of the Bit Machine (see ). There is one additional state of the Bit Machine called the state, which we denote by . The Bit Machine has nine basic instructions that, when executed, transform the Bit Machine's state. We denote these basic instructions as S\S>, where is the instructions's name, > is a state of the Bit Machine before executing the instruction, and > is the state of the machine after the successful execution of the instructions. Our first three basic instructions, create, move, and delete active frames. <\eqnarray*> >||\r\|w\\|]>\\r\|\w\\|]>>>|||\r\|*\*c>\w\\|]>\\r\|\>\*c>\|w\\|]>>>|||\r\r\|\|]>\\r\|\|]>>>>> Executing a > instruction pushes a new frame of length onto the write frame stack. This new frame has its cursor at the beginning of the frame and the entire frame is filled with undefined values. It is legal for the new frame to have length 0. Executing the instruction moves the top frame of the write frame stack to the read frame stack. This instruction is only legal to execute when the cursor of the active write frame is at the end of the frame. The cursor is reset to the beginning of the frame when it is placed onto the read frame stack. Executing the instruction removes the top frame of the read frame stack. Our next three instructions operate on the active write frame. <\eqnarray*> >||\r\|w\>>\\|]>\\r\|w\\\|]>>>|>||\r\|w\>>\\|]>\\r\|w\\\|]>>>|>||\r\|w\\|]>\\r\|w\\\|]>>>|>||\r\|\>\*c>\r\|w\\|]>\\r\|\>\*c>\r\|w\*\*c>\\|]>>>>> Executing a > instruction writes a 0 or 1 to the active write frame and advances its cursor. Writing an undefined value using this instruction is not allowed. The cursor cannot be at the end of the frame. Executing a > instruction advances the active write frame's cursor without writing any data. There must be sufficient number of cells after the cursor. The trivial instruction > is legal and executing it is effectively a no-op. Executing a > instruction copies the values of the cells after the active read frame's cursor into the active write frame, advancing the write frame's cursor. The must be a sufficient number of cells after both the active read frame and active write frame's cursors. Note that undefined cell values are legal to copy. The trivial instruction > is legal and executing it is effectively a no-op. The next two instructions are used to manipulate the active read frame's cursor. <\equation*> fwd\\r\|\>\*c>\r\|w\\|]>\\r\*\*c>\r\|w\\|]> <\equation*> bwd\\r\*\*c>\r\|w\\|]>\\r\|\>\*c>\r\|w\\|]> Executing a > instructions moves the cursor on the active read frame forward, and executing a > instruction moves the cursor backwards. In both cases there must be sufficient number of cells before or after the cursor. The trivial instructions > and > are legal and executing them are effectively no-ops. The final instruction of for the Bit Machine moves from any non-halted state into the halted state. <\equation*> abort\\r\|w\\|]>\ This is the only way to enter the halted state, and once in the halted state no further instructions can be executed. >\>>>The basic instructions of the Bit Machine are combined to produce programs that take the Bit Machine through a sequence of states. We write |k|S> for a program, , that, when executed, successfully transforms an initial state > to the final state >. \; <\with|par-mode|center> |||>>>>> We write for the trivial program with no instructions. The initial and final states are identical in this case. <\with|par-mode|center> |||\S>>>||i|S>>>>>> For every basic instruction there is a single instruction program whose initial and final states match those of the basic instruction. \; <\with|par-mode|center> ||||||||k|S>>||k|S>>>>>>>>||k;k|S>>>>>> \; We write ;k> for a sequence of two programs, > and >. The Bit Machine executes the two programs in turn, concatenating the sequence of states of the two programs. \; <\with|par-mode|center> |||\r\>>\r\|w\\|]>|k|S>>>|\r\>>\r\|w\\|]>|k\|\|k|S>>>>>> \; \; <\with|par-mode|center> |||\r\>>\r\|w\\|]>|k|S>>>|\r\>>\r\|w\\|]>|k\|\|k|S>>>>>> We define \|\|k> as a deterministic choice between two programs, > and >. When executing a deterministic choice, the value under the active read frame's cursor decides which one of the two programs are executed. When encountering a deterministic choice, the active read frame's cursor must not be at the end of its array and the cell under the cursor must not be an undefined value. \; <\with|par-mode|center> ||||k|>>>>>> Lastly, we stipulate that every program when executed from the halted state ignores all instructions and perform a no-op instead. Take care to note this difference between instructions and programs containing one instruction. A single instruction cannot be executed starting from the halted state, while a program that consists of a single instruction can be run starting from the halted state (however, it does nothing from this state). <\equation*> n\k\fwd;k;bwd The k> notation (called \Pbump\Q) is for a program that temporarily advances the active read frame's cursor when executing . <\theorem> \; <\with|par-mode|center> |||\r\\c>\r\|w\\|]>|k|\r\\c>\r\|w\\|]>>>>|\r\|\>\c>\r\|w\\|]>|n\k|\r\|\>\c>\r\|w\\|]>>>>>>> \; Bit Machine programs are deterministic. Given a program and an initial state > there exists at most one state > such that |k|S>. However it is possible that there is no state > such that |k|S> given an initial state for a program. This happens when the Bit Machine is trying to execute a single instruction program, , from a non-halted state where that instruction cannot legally execute from. This can also happen when a deterministic choice operation is encountered starting from a state where the active read frame's cursor is at the end of the frame, or is referencing and undefined value. When a program cannot execute to completion from a given initial state, we say that the Bit Machine crashes, or we say that the program crashes the Bit Machine. Crashing is distinct from halting. We will have a number of theorems that prove that a Bit Machine interpreting a Simplicity expression from a suitable initial state never crashes the Bit Machine; however in some of these cases the program may cause the Bit Machine to legitimately enter the halted state. We recursively translate a core Simplicity program, A\B>, into a program for the Bit Machine, |t|\>>, called the naive translation: <\eqnarray*> |||\>>|>||)>>>|| s t|\>>|>||)>>>||||s|\>>>|||>||||t|\>>>|||>|||\>>|>|>|| t|\>>|>|;skip|)>;|t|\>>>|| t|\>>|>|;skip|)>;|t|\>>>|| s t|\>>|>||)>\|s|\>>>||||)>\|t|\>>>|| s t|\>>|>||s|\>;|t|\>>>|| t|\>>|>||t|\>>>|| t|\>>|>|\|t|\>>>>> <\theorem> Given a well-typed core Simplicity program B> and an input , then <\equation*> \r\r\|w+m>\\|]>||t|\>|\r\r\|w\|t|\>|>\\|]>> for any cell arrays >, >, >, any stacks >, >, and any natural number . In particular, for a well-typed core Simplicity program B>, we have <\equation*> \|>|]>||t|\>|\||t|\>|>|]>> which means we if we start the Bit Machine with only the input represented on the read stack, and enough space for the output on the write stack, the Bit Machine will compute the representation of the value |t|\>> without crashing. ||\>>>>||\>>>>Traditional imperative language implementations often make use of tail call optimization that occurs when the last command of a procedure is a call to a second procedure. Normally the first procedure's stack frame would be free after the second procedure returns. The tail call optimization instead frees the first procedure's stack frame prior to the call to the second procedure instead. This can reduce the overall memory use of the program. The composition combinator, >, in Simplicity plays a role similar to a procedure call. We can perform a tail composition optimization that moves the instruction earlier to reduce the overall memory requirements needed to evaluate Simplicity programs. We define an alternate translation of Simplicity programs to Bit Machine programs via two mutually recursively defined functions, >> and >: \; <\eqnarray*> ||>>|>||)>>>| s t>>|>||)>>>|||>>|||>|||>>|>>|>|>| t>>|>|;skip|)>;>>| t>>|>|;skip|)>;>>| s t>>|>||)>\>>||||)>\>>| s t>>|>|;>>| t>>|>|>>| t>>|>|\>>|||>|>>|>||)>>>|||>| s t>>|>||)>>>|||>>|||>|||>>|>>|>|>| t>>|>|;skip|)>;>>| t>>|>|;skip|)>;>>| s t>>|>||)>;>>||||)>;>>| s t>>|>|;>>| t>>|>|>>| t>>|>||)>;>>>> The definition of the >> translation is very similar to the naive one, except the instruction at the end of the translation of the composition combinator is replaced by having a recursive call to >> instead. The definition of >> puts the instruction in the translations of > and >. The instructions are removed from the translations of > and >. Lastly notice that the first recursive call in the translation of > is to >. <\theorem> Given a well-typed core Simplicity program B> and an input , then <\equation*> \r\r\|w+m>\\|]>||\r\r\|w\|t|\>|>\\|]>> and <\equation*> \r\r\r\|w+m>\\|]>||\r\|w\|t|\>|>\\|]>> for any cell arrays >, >, >, any frame >, any stacks >, >, and any natural number . In particular, for a well-typed core Simplicity program B>, we have <\equation*> \|>|]>||\||t|\>|>|]>> Static analysis lets us quickly compute properties of expressions, without the need for exhaustively executing expressions on all possible inputs. We use static analysis in Simplicity to bound the computation costs in terms of time and space of Simplicity expressions for all their inputs. The analysis we do are linear in the size of the DAG representing the Simplicity expression, and typically the analysis runs much faster than the cost of evaluating an expression on a single input. We can do this because the intermediate results of static analysis can be shared where there are shared sub-expressions. The primary source of memory resources used by the Bit Machine is the cells used by all the frames that make of the state of Bit Machine. A secondary source of memory resources used comes from the overhead of the frames themselves, which need to store their boundaries or sizes, and the position of their cursors. In our analysis we will make a simplifying assumption that these boundaries / sizes / positions values are all of constant size. This assumption holds when the Bit Machine is implemented on real hardware which has an upper bound on its addressable memory and there is a limit on the number of Cells that can be held anyways. To bound these resources we perform a static analysis to compute an upper bound on the maximum number of cells needed when executing a Simplicity program on the Bit Machine for any input, and we compute an upper bound on the maximum number of frames needed as well. We define the cell count of a frame to be the length of its underlying cell array and the cell count of a Bit Machine state to be the sum of the cell counts of all its frames. <\eqnarray*> *\|\>\*c>|)>>|>|>|\\\r\|w\\\w|]>|)>>|>|cellCount|)>+cellCount|)>>>||)>>|>|>>> We define the cells required by a program |p|S> as the maximum cell count over every intermediate state. <\with|par-mode|center> ||||)>\cellCount>>>>>> \; <\with|par-mode|center> |||\S>>>||i|S>|)>\max|)>,cellCount|)>|)>>>>>>> \; \; <\with|par-mode|center> ||||||||||k|S>>||k|S>>>>>>>>||k;k|S>|)>\max|k|S>|)>,cellsReq|k|S>|)>|)>>>>>>> \; \; <\with|par-mode|center> |||\r\>>\r\|w\\|]>|k|S>>>|\r\>>\r\|w\\|]>|k*k|S>|)>\cellsReq\r\>>\r\|w\\|]>|k|S>|)>>>>>>> \; \; <\with|par-mode|center> |||\r\>>\r\|w\\|]>|k|S>>>|\r\>>\r\|w\\|]>|k*k|S>|)>\cellsReq\r\>>\r\|w\\|]>|k|S>|)>>>>>>> \; \; <\with|par-mode|center> ||||k|>|)>\0>>>>>> \; Note that when executing a Simplicity expression on the Bit Machine, the size of the state prior and after execution is identical. For naive translation of Simplicity to the Bit Machine, we can write a simple recursive function that bounds the number of additional Cells needed to evaluate a Simplicity expression beyond the size of the initial and final state. <\eqnarray*> |||)>>|>|>| s t|)>>|>|+max,extraCellsBound|)>>>||)>>|>|>| t|)>>|>|>>| t|)>>|>|>>| s t|)>>|>|,extraCellsBound|)>>>| s t|)>>|>|,extraCellsBound|)>>>| t|)>>|>|>>| t|)>>|>|>>>> <\lemma> For any core Simplicity expression B>, such that <\equation*> \r\|w\\|]>||t|\>|\r\|w\\|]>> we have that <\enumerate> \r\|w\\|]>|)>=cellCount\r\|w\\|]>|)>> \r\|w\\|]>||t|\>|\r\|w\\|]>>|)>\cellCount\r\|w\\|]>|)>+extraCellsBound>. In particular for and <\equation*> \|>|]>||t|\>|>\||t|\>|>|]> we have that \|>|]>||t|\>|>\||t|\>|>|]>|)>\bitSize+bitSize+extraCellsBound>. We can compute a tighter bound for TCO translation, but the calculation is a bit more complicated. The number of extra cells needed depends on whether TCO is in the \Pon\Q state, and what the size of the active read frame is. <\eqnarray*> |||)>>|>|>| s t|)>*>|>|+max,extraCellsBound|)>-r|)>>>||)>>|>|>| t|)>>|>|>>| t|)>>|>|>>| s t|)>>|>|,extraCellsBound|)>>>| s t|)>>|>|>,extraCellsBound|)>>>| t|)>>|>|>>| t|)>>|>|>>>> <\lemma> For any core Simplicity expression B>, such that <\equation*> \r\|w\\|]>||\r\|w\\|]>>> and <\equation*> \r\|w\\|]>|>|\r\|w\\|]>> we have that <\enumerate> \r\|w\\|]>|)>=cellCount|)>+cellCount\r\|w\\|]>|)>> and\r\|w\\|]>|)>=cellCount\r\|w\\|]>|)>> \r\|w\\|]>||\r\|w\\|]>>|)>\cellCount\r\|w\\|]>|)>+extraCellsBound|)>|)>> and\r\|w\\|]>|>|\r\|w\\|]>>|)>\cellCount\r\|w\\|]>|)>+extraCellsBound>. In particular for and <\equation*> \|>|]>||\||t|\>|>|]>> we have that \|>|]>||\||t|\>|>|]>>|)>\bitSize+bitSize+extraCellsBound>. The problem with > is that it is effectively a dynamic analysis because its result is a function. We cannot directly use this definition to perform a static analysis because we cannot cache and reuse results on shared sub-expressions. Fortunately, we can characterize the set of possible functions returned by > by a pair of parameters. <\equation*> interp|n,m|\>\max We can write a static analysis to compute the pair of parameters that characterize the results of >. <\eqnarray*> ||||||||||||||||||||)>>|>||0,0|\>>>| s t|)>>|>||max+n,n,r+m|)>,r+m|\>>>||||n,m|\>\extraCellsBound>>||||n,m|\>\extraCellsBound>>|||\bitSize>>||)>>|>||0,0|\>>>| t|)>>|>|>>| t|)>>|>|>>| s t|)>>|>||max,n|)>,max,m|)>|\>>>||||n,m|\>\extraCellsBound>>||||n,m|\>\extraCellsBound>>| s t|)>>|>||n,max,m,m|)>|\>>>||||n,m|\>\extraCellsBound>>||||n,m|\>\extraCellsBound>>| t|)>>|>|>>| t|)>>|>|>>>> When computing > resulting values for shared sub-expressions can be shared, making > a static analysis. We can use > and > to compute > for our bound on cell count. <\lemma> =interp|)>>. <\corollary> For any core Simplicity expression B> and such that <\equation*> \|>|]>||\||t|\>|>|]>> we have that \|>|]>||\||t|\>|>|]>>|)>\bitSize+bitSize+max> where |n,m|\>\extraCellsBound>. In modern Bitcoin, users who use P2SH (pay to script hash) do not commit funds directly to Bitcoin Script, rather they commit to a hash of their Bitcoin Script. Only when they wish to redeem their funds do they reveal their Bitcoin Script for execution. Bitcoin's consensus protocol enforces that the Bitcoin Script presented during redemption has a hash that matches the committed hash. |)>>>>|)>>>>>|)>>>>Simplicity is designed to work in the same way. However, instead of a linear hash of a serialized Simplicity program (Section) we follow the tree structure of a Simplicity expression and compute a commitment Merkle root of its syntax tree. Below we define both the commitment Merkle root of a Simplicity expression A\B> as \<2>> as well as a value \<2>> that will later be used to define a varianted for identity Merkle Roots (Section). \ Below \> and hence for core Simplicity expression , =>, but they will no longer be equal when we consider some extensions to core Simplicity. <\eqnarray*> ||>>|>|>>>>|| s t>>|>||SHA256>>>\ ||s>,|t>|\>|\>>>||>>|>|>>>>|| t>>|>||SHA256>>\ ||0|\>,|t>|\>|\>>>|| t>>|>||SHA256>>\ ||0|\>,|t>|\>|\>>>|| s t>>|>||SHA256>>\ ||s>,|t>|\>|\>>>|| s t>>|>||SHA256>>\ ||s>,|t>|\>|\>>>|| t>>|>||SHA256>>\ ||0|\>,|t>|\>|\>>>|| t>>|>||SHA256>>\ ||0|\>,|t>|\>|\>>>>> Here we are directly using SHA-256's compression function, |i,b|\>>, which takes two arguments. The first argument, , is a 256-bit tagged initial value. The second value, , is a 512-bit block of data. Above we divide a block into two 256-bit values, |b,b|\>>, and recursively pass Merkle roots into the compression function. Like static analysis, the time needed to computing the commitment Merkle root is linear in the size of the DAG representing the term because the intermediate results on sub-expressions can be shared. We define unique tags > for every combinator. <\eqnarray*> >>|>|1f436f6d6d69746d656e741f6964656e]>>>>|>>|>|1f436f6d6d69746d656e741f636f6d70]>>>>|>>|>|1f436f6d6d69746d656e741f756e6974]>>>>|>>|>|1f436f6d6d69746d656e741f696e6a6c]>>>|>>|>|1f436f6d6d69746d656e741f696e6a72]>>>|>>|>|1f436f6d6d69746d656e741f63617365]>>>|>>|>|1f436f6d6d69746d656e741f70616972]>>>|>>|>|1f436f6d6d69746d656e741f74616b65]>>>|>>|>|1f436f6d6d69746d656e741f64726f70]>>>>> Notice that the type annotations for expressions are not included in the commitment Merkle root. We will rely on type inference to derive principle type annotations (see Section>). Later, we will make use of this flexibility when pruning unused branches from expressions (see Section). |)>>>>We also define a Merkle root that follows the tree structure of types in the same way that we defined the commitment Merkle Root. <\eqnarray*> |>>|>|>>>>|>|>||SHA256>>>\ |,|\>|\>>>|B>>|>||SHA256>>>\ |,|\>|\>>>>> We define unique tags > for every sort of type. <\eqnarray*> >>|>|1f547970651f756e6974]>>>>|>>|>|1f547970651f73756d]>>>>|>>|>|1f547970651f70726f64]>>>>>> The core Simplicity completeness theorem (Theorem) proves that the core Simplicity language is already computationally complete for Simplicity types. Our primary method of extending Simplicity is by adding expressions with side-effects. We will use monads to formally specify these new effects. \; We define a new interpretation of Simplicity expressions, A\B>, whose denotations are Kleisli morphisms, |t|\>>\A\\*B>. <\eqnarray*> ||\>>>|>|>>>|| s t|\>>>|>||t|\>>>|s|\>>|)>>>|||\>>>|>|>||\>>>|| t|\>>>|>||t|\>>|)>>>>|| t|\>>>|>||t|\>>|)>>>>|| s t|\>>|>,c|\>>|>||s|\>>|a,c|\>>>|| s t|\>>|>,c|\>>|>||t|\>>|b,c|\>>>|| s t|\>>>|>|>||s|\>>,|t|\>>|\>>>|| t|\>>|a,b|\>>|>||t|\>>>>|| t|\>>|a,b|\>>|>||t|\>>>>>> The above interpretation for Kleisli morphisms is nearly uniquely defined (under the requirement of parametericity). Many well-typed variations of the definition above end up being equivalent due to the monad laws. The main choice we have is between using >> or |\>>> in the definition of | s t|\>>>. The only other definitions amount to duplicating the effects of sub-expressions. To ensure that all these possible choices are immaterial, we demand that > be a commutative, idempotent monad when interpreting Simplicity expressions. This lets us ignore the order of effects, and duplication of effects, which simplifies reasoning about Simplicity programs. It also provides an opportunity for a Simplicity optimizer to, for example, reorder pairs without worrying about changing the denotational semantics. <\theorem> For any core Simplicity expression, A\B>, we have |t|\>>\\>\|t|\>>. <\corollary> For any core Simplicity expression, A\B>, we have |t|\>\|t|\>>. Notice that our monadic semantics are strict in their side-effects in the sense that the definition of | s t|\>>> implies that the side-effects of |s|\>>> and |t|\>>> are both realized even if it ends up that one (or both) of the values returned by and end up never used. Our first extension to core Simplicity is the witness expression. The language that uses this extension is called . \; <\with|par-mode|center> |B>>>| b\A\B>>>>>> \; The denotational semantics of the witness expression is simply a constant function that returns its parameter. \; <\equation*> | b|\>>\\> As far as semantics goes, this extension does not provide any new expressivity. A constant function for any value can already be expressed in core Simplicity using >. The difference between and expressions lies in their commitment Merkle root. <\eqnarray*> || b>>|>|>>>>>> where >> value is a unique value. <\eqnarray*> >>|>|1f436f6d6d69746d656e741f7769746e657373]>>>>>> Notice that a b> expression does not commit to its parameter in the commitment root. This means that at redemption time a expression's parameter, called a , could be set to any value. This differs from the identity root (Section) which will include a commitment to its parameter. Witness values play the same role as Bitcoin Script's input stack in its or Segwit's . They act as inputs to Simplicity programs. Rather than accepting arguments as inputs and passing them down to where they are needed, expressions lets input data appear right where it is needed. Like other expressions, a expression does not commit to its type in its commitment Merkle root. Type inference is used to compute the minimal type needed for each witness expression (see Section) This helps ensures that third parties cannot perform witness malleation to add unused data on transactions during transit. Our first side-effect will be aborting a computation. New assertion and expressions make use of this effect. The language that uses this extension is called . \; <\with|par-mode|center> |||||||A\C\D>>|<2>>>>>>>>>| s h\\C\D>>>>>> \; \; <\with|par-mode|center> |||||||<2>>>|B\C\D>>>>>>>>| h t\\C\D>>>>>> \; \; <\with|par-mode|center> |<2>>>>| h\A\B>>>>>> \; Assertions serve a dual purpose. One purpose is to replicate the behaviour of Bitcoin Script's and similar operations that are used to validate checks on programmable conditions, such as verifying that a digital signature verification passes or causing the program to abort otherwise. The second purpose is to support pruning of unused branches during redemption. The 256-bit value is used in the commitment Merkle root computation to hold Merkle root of the pruned branches. This will be covered in Section. Because we are extending Simplicity's semantics to support an abort effect, there is no harm in adding a generic expression. The parameter to the expression is used to support salted expressions (see Section). We will see that expressions never manifest themselves within a blockchain's consensus protocol. Given an commutative, idempotent monad with zero, >, we extend the monadic semantics for Simplicity expressions, |t|\>>>, to include assertion expressions: <\eqnarray*> | s h|\>>|>,c|\>>|>||s|\>>|a,c|\>>>|| s h|\>>|>,c|\>>|>|>>>|| h t|\>>|>,c|\>>|>|>>>|| h t|\>>|>,c|\>>|>||t|\>>|b,c|\>>>|| h|\>>>|>|>>>>> Notice that the parameters are ignored in the semantics. They will be used instead for the Merkle root definitions in Section. A term in the language of core Simplicity extended with witnesses and assertions, A\B>, can be interpreted as a function returning an optional result: |t|\>>\A\B>, using the option monad (see Section). <\theorem> For any core Simplicity expression with assertions, A\B>, and any commutative idempotent monad with zero >, we have |t|\>>\\>,B>\|t|\>>>. We extend the definition of commitment Merkle root and identity Merkle root to support the new assertion and expressions \; <\eqnarray*> ||| s h>>|>||SHA256>>\ ||s>,h|\>|\>>>|| h t>>|>||SHA256>>\ |h,|t>|\>|\>>>|| h>>|>||SHA256>>,h|\>>>>> where >> value is a unique value. <\eqnarray*> >>|>|1f436f6d6d69746d656e741f6661696c]>>>>>> It is important to notice that we are reusing >> when tagging assertions in their commitment Merkle root. Also notice that the value, which was ignored in the semantics, is used in the commitment Merkle root. Together this allows an assertion expression to substitute for a case expression at redemption time while maintaining the same commitment Merkle root. This enables a feature of Simplicity called pruning. \; Branches> The commitment Merkle roots of the assertion expression reuses >> in the compression function. This means that the following identities hold. <\equation*> s >= s t>= t> In particular, it means that when a > expression is used at commitment time, it can be replaced by an assertion expression. If we substitute a with an assertion expression and that assertion fails during evaluation, then the whole transaction will be deemed invalid and rejected. On the other hand if the assertion does not fail, then we are guaranteed to end up with the same result as before (which ultimately could still be failure due to a later assertion failure). Therefore, assuming the transaction is valid, a substitution of assertions will not change the semantics. We can take advantage of this by performing this substitution at redemption time. We can effectively replace any unused branch in a case expression with its commitment Merkle root. In fact, we will require this replacement to occur during redemption (see Section>>). For those cases where we want to use an assertion at commitment time, for example when performing something similar to Bitcoin Script's , we use the following derived combinator, \; <\with|par-mode|center> ||||||A\<2>>>>>>>>>| t\t \ ; |0|\>> \A\<1>>>>>>> \; where |0|\>> is used as a canonical parameter for . Naturally, the |0|\> parameter can be replaced with any value. This can be used as a method of salting expression, which is the subject of the next section. <\theorem> For any core Simplicity expression A\<2>>, <\equation*> | t|\>=|t|\> During pruning, unused branches are replaced by its commitment Merkle root. Since hashes are one way functions, one might believe that third parties will be unable to recover the pruned branch from just its commitment Merkle root. However, this argument is not so straightforward. Whether or not the expression can be recovered from just its commitment Merkle root depends on how much entropy the pruned expression contains. Third parties can grind, testing many different expressions, until they find one whose commitment Merkle root matches the one occurring in the assertion. If the entropy of the pruned expression is low, then this grinding is feasible. Some expressions naturally have high entropy. For example, any branch that contains a commitment to a public key will have at least the entropy of the public key space. However, this only holds so long as that public key is not reused nor will ever be reused elsewhere. For expressions that reuse public keys, or otherwise naturally having low entropy, one can add salt, which is random data, to increase its entropy. There are several possible ways to incorporate random data into a Simplicity expression without altering the program's semantics. One way is to incorporate the expression which lets us directly incorporate random into is commitment Merkle root. Given a block of random data, >, and a Simplicity expression A\B>, we can define two salted variants of : <\eqnarray*> h t>|>| > \ ; t|)> h>:A\B>>| h t>|>| >> \ ; h> t|)>:A\B>>>> The h t> expression will have high entropy so long as the random data has high entropy. By randomly choosing between these two variants, this method of salting obscures the fact that the expression is salted at all. Without knowing , it is impractical to determine if h|)>> is the commitment Merkle root of a expression, or if it is a some other, high-entropy, alternate expression that the redeemer has simply chosen not to execute. By explicitly using the expression here, one has the option prove that these alternative branches are unexecutable by revealing the value . If the Simplicity expression is part of a multi-party smart contract, it maybe required to reveal (or prove in a deniable way that such an exists) to all party members so everyone can vet the security properties of the overall smart contract. Of course, lots of variations of this expression are possible. We extend Simplicity with primitive expressions that provide blockchain specific features. Naturally the specifics of these primitive expressions depends on the specific blockchain application, but generally speaking the primitives allow reading data from the context that a Simplicity program is being executed within. This is usually the data of the encompassing transaction including details about the inputs and outputs of the transaction, and which specific input is being evaluated. A blockchain application needs to provide a set of typed primitive expressions and a monad to capture the side-effects for these primitives. This monad should be a commutative, idempotent monad with zero in order to interpret Simplicity and its extensions. All primitive expressions must be monomorphic and have no parameters (i.e. they are not themselves combinators). In the next section we will be detailing the primitives used for Bitcoin, or a Bitcoin-like application. In Appendix we describe the primitives used for the Elements sidechain. For the Bitcoin application, Simplicity's primitives will be primarily focuses on accessing the , which is the data that is hashed and signed in Bitcoin. We define a record type that captures this environment, called . <\eqnarray*> |>|>>||>|>>||>|\<2>>>||>|Outpoint>>|Value>>>|<2>>>||)>>|)> >> prefix|)>>>>||)>>>>>>>|}>>>||>|Value>>||)>>>>>>>|}>>>||>|<2>>>|SigInput>>|SigOutput>>|Lock>>>>>|}>>>||>|<2>>>|PubKey>>||)>>>>>>>|}>>>||>|SigTx>>|<2>>>|TapEnv>>|<2>>>>>>|}>>>>> The type contains the signed transaction data. Following a design similar to BIP 143, this signed transaction data excludes transaction inputs' ScriptSigs and includes inputs' Bitcoin values. The field is input index whose redemption is being processed by this Simplicity program. The field holds the commitment Merkle root of the Simplicity program being executed. The type given above allows for an unbounded number of inputs and outputs. However, there are limits imposed by the Bitcoin protocol. The number of inputs and outputs are limited to less than or equal to > by Bitcoin's deserialization implementation. Similarly, the length of 's is limited to less than or equal to > bytes. We assume all transactions to adhere to these limits when reasoning about Bitcoin transactions. Furthermore, we assume that for every BCEnv> that |e|\>\|\|>> so that \Pcurrent\Q index being validated is, in fact, an input of the transaction. \ We also assume that the annex length, when it exists, is strictly less than > (because it excludes the 0x50 prefix), |e|\>> is even, and |\|>\128> in accordance with Taproot limitations. Bitcoin's money supply is capped below 000000\10> satoshi, therefore it is safe to assume that all monetary values are within this bound. In particular, we assume that for every BCEnv> that the following inequalities hold. <\equation*> 0\fold|+,0|\>>>o\|o|\>|)>|)>|)>\fold|+,0|\>>>i\|i|\>|)>|)>|)>\21000000\10 \; >The monad we use for the Bitcoin application provides an environment effect (also known as a reader effect) that allows read-access to the value defining the Simplicity program's evaluation context. We call this monad . <\eqnarray*> A>|>|A>>|f>|>|e\BCEnv\f|)>>>>> \; is a commutative, idempotent monad with zero: <\eqnarray*> >>|>|e\BCEnv\\>>>|>>|>|e\BCEnv\\>f\f|)>|)>|)>>>|>>|>|e\BCEnv\\>>>>> \; We define several new primitive expressions for reading data from a value. The language that uses this extension is called . \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\\Lock>>>>>> \; <\with|par-mode|center> |\\Value>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\\Value>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\\PubKey>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> We extend the formal semantics of these new expressions as follows. <\eqnarray*> ||\>>||\>>|>|e\BCEnv\\>|)>>>|||\>>||\>>|>|e\BCEnv\\>|)>>>||>|\>>||\>>|>|e\BCEnv\\>|+|\>>l\l|)>|)>|)>|)>>>||>|\>>||\>>|>|e\BCEnv\\>|)>>>||>|\>>>|>|e\BCEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>>|>|e\BCEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>>|>|e\BCEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>>|>|e\BCEnv\\>l\|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\BCEnv\\>l\SHA256|)>|)>|i|\>|)>|)>>>||>|\>>||\>>|>|e\BCEnv\\>|+|\>>l\l|)>|)>|)>|)>>>||>|\>>>|>|e\BCEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>>|>|e\BCEnv\\>l\SHA256|)>|)>|i|\>|)>|)>>>||>|\>>||\>>|>|e\BCEnv\\>|)>>>||>|\>>>|>|e\BCEnv\\>|i|\>|)>>>||>|\>>||\>>|>|e\BCEnv\\>|)>>>||>|\>>||\>>|>|e\BCEnv\\>|)>>>>> \; The sums computed for |>|\>>||\>> and |>|\>>||\>> never \Poverflow\Q their 64-bit values due to our assumptions about Bitcoin's money supply. We extend the definition of the commitment Merkle root and identity Merkle root to support the new expressions by using the initial value of with tags of new unique byte strings. <\eqnarray*> |>>|>|>>>||>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|]>>>>||>>>|>|>>>||>>>|>|>>>||>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|>>>||>>>|>|>>>>> where <\equation*> BCprefix\1f5072696d69746976651f426974636f696e1f]> Ultimately, we only are interested in the side-effects of Simplicity expressions; we only care that a particular expression does not fail when executed within the context of a given transaction. We do not care about the output value of a Simplicity expression, nor do we provide explicit inputs to Simplicity expressions, which are handled by expressions instead. To this end, we define a to be a Simplicity expression of type \<1>>. A core Simplicity expression of this type is useless. However, a Simplicity program with witnesses, assertions, and Bitcoin, <1>\<1>>, has semantics of |t|\>>||\>\BCEnv \ <2>>, which is the type of predicates over . This is exactly what we want to use a Blockchain program for: to decide if a given set of witness data authorizes the redemption of funds for a specific input of a specific transaction. A particular input authorizes the transaction in the context BCEnv> only when |t|\>>||\>=>>, and all inputs must authorize the transaction for the transaction to be valid. Let us look at a basic example of a Simplicity program that requires a single Schnorr signature. > Using Simplicity with witnesses, assertions and Bitcoin, we are able to build an expression that use Schnorr signatures to authorize spending of funds. Using the assertion extension we are able to define a variant of > called >: <\equation*> \ \Msg|)>\Sig\<1> such that <\eqnarray*> ||\>>||p,m|\>,s|\>=\>||\>>|>|||\>||p,m|\>,s|\>=>>>>> Next, we use the Bitcoin transaction extension to build a > expression that computes a SHA-256 hash that commits to all of the current transaction data from the environment and which input is being signed for. <\render-code> \<1>\<2>> |||>>||1f53696748617368]>>|)>>>>||>>|> \ >>|)>>>|||)>>||>>| \ \ |)>|)> |\>|\>>>>||>>|| | \ |2|\>|)>|)> \ |0|\>|)>|)>|)> \ |1184|\>|)>|)>>>>|||>>>>>>>>>>> The expression derives a total of 672 bits of data from the environment. The initial adds one 512-bit block constant prefix to this, which totals 1184 bits of data. While it is not strictly necessary, we choose to explicitly append the SHA-256 padding for this length of data. Next we pair the commitment Merkle root of with its output. This commitment Merkle root plays the role of the signature hash flag that is covered by the signature in Bitcoin script. It is a specification of which parts of the transaction data is being signed, and exactly how those parts are combined to form the digest being signed. <\render-code> \<1>\<2>> ||>||1f5369676e6174757265]>>|)>>|>||>>|>>|)>>|)>>|>|||)>|2+1024|\>|)>>|>|||>|>>>>>>>>>> The pair of the commitment Merkle root and the digest itself is 512 bits. \ The initial adds one 512-bit block constant prefix to this, which totals 1024 bits of data. While it is not strictly necessary, we choose to explicitly append the SHA-256 padding for this length of data. Finally, given a Schnorr public key PubKey> and a Schnorr signature Sig> we can create a Simplicity program that checks the signature against the public key and above message digest. <\render-code> |p,s|\>\<1>\<1>> ||p,s|\>>||\>>>|)> \ >>|||>>>>>>>>>>> The combinator ensures that the program's commitment Merkle root |p,s|\>>> is independent of the value of the signature . This allows us to commit to this program without committing to the signature, and only providing the signature at redemption time. As with normal Bitcoin transactions, the signature is only valid in the context, BCEnv>, of a particular input on a particular transaction during redemption because our program only executes successfully, i.e. ||p,s|\>|\>>||\>=\>||\>>, when provided a witness that is a valid signature on the transaction data and index number. s.> Our last Simplicity extension is the combinator. This extension allows for delegation but using it loses some nice properties of Simplicity. The language that uses this extension is called . The language that uses this and all other extensions is called . \; <\with|par-mode|center> |||||||<2>\A\B\C>>|C\D>>>>>>>>| s t\A\B\D>>>>>> \; Semantically, the combinator behaves similar to the composition combinator, but where the commitment Merkle root of the expression is passed as an argument to the expression . We extend our formal semantics to the combinator by defining it in terms of core Simplicity as follows. <\equation*> | s t|\>>\|>|)>\ >;s; \ t|\>> We can simplify the semantics as follows. <\equation*> | s t|\>>=| \ t|\>>>\|s|\>>|)>|,a|\>> Like a expression, the real significance comes from the form of its commitment Merkle root. We extend the definition of the commitment Merkle root as follows. <\eqnarray*> || s t>>|>||SHA256>>\ ||0|\>,|\>|\>>>>> where the >> value is a unique value. <\small> <\eqnarray*> >>|>|1f436f6d6d69746d656e741f646973636f6e6e656374]>>>>>> The commitment Merkle root only commits to the first argument, , of a s t> expression. During redemption the second argument, , can be freely set to any Simplicity expression. This differs from the identity root (Section) which will include a commitment to both arguments. In order to place restrictions on what is allowed, the commitment Merkle root of is passed to as an input. This way is allowed to dynamically decide if is an acceptable expression to be used here. The primary purpose of is for delegation. In this scenario, , validates that the commitment Merkle root > is signed by a fixed public key. This lets a user postpone defining until redemption time, while still maintaining full control, because any redemption requires their signature on . For example, a user can require that |t|\>>> returns a public key. After commitment, but before redemption, the user can delegate authorization to redeem these funds to a third party by signing the that party's key in this fashion. The combinator comes with some significant caveats. Because the whole program is not committed to at commitment time, it is no longer possible to statically analyze the maximum resource costs for redemption before commitment. During redemption |t|\>>> could, a priori, perform arbitrary amounts computation. Indeed we can use to commit to what are effectively unbounded loops in Simplicity (see Section). Contrast this with the expression, where type inference limits the size of the witness data, so bounds are still possible to compute. Of course, depending on the specifics of the policy enforced by , it may be possible to bound the maximum resource costs for redemption in specific cases. However, that depends on the details of and there is no practical, universal algorithm that will work for any Simplicity expression. Using risks creating program that ends up impractical to redeem due to costs. This danger is why is not part of full Simplicity and it is instead considered an extension to be used with caution. However, it is also important to note that static analysis can be performed at redemption time. At that point time the expression has been provided and usual static analysis can proceed. Static analysis can still be part of the consensus protocol, even when the expression is used. on the Bit Machine> The semantics of the combinator can tell us how to implement it on the Bit Machine. \ We simply define the translation of the combinator to be the translation of its semantics. <\eqnarray*> |||| s t|\>>>|>||>|)>\ >; \ t|)>|\>>>| s t>>>|>|>|)>\ >; \ t|)>>>>| s t>>>|>|>|)>\ >; \ t|)>>>>>> We can expand out each of these definitions in turn to see their definition in terms of Bit Machine operations: <\eqnarray*> ||||||||||| s t|\>>|||)>>>|||>|)>;copy|)>>>|||>|||+bitSize|)>>>||||s|\>>>|||>||||)>;bitSize\|t|\>>>|||>|||>>> <\eqnarray*> |||||| s t>>>|||)>>>|||>|)>;copy|)>>>|||>|||+bitSize|)>>>|||>>|||>||||)>;fwd|)>;>>>> <\eqnarray*> |||||| s t>>>|||)>>>|||>|)>;copy|)>>>|||>|||>|||+bitSize|)>>>|||>>|||>||||)>;fwd|)>;>>>> where <\eqnarray*> |||||||||>>|)>>|>|;skip;nop>>|>>|)>>|>|;skip;nop>>|>|a,b|\>|)>>|>|>;write>>>>> Of course, in an optimized implementation of we would discard the > and operations from the definition of >>. .> Because the Bit Machine instructions are directly derived from the semantics of the correctness theorems for the Bit Machine still hold. <\theorem> Given a well-typed Simplicity program with delegation B> and an input , then <\equation*> \r\r\|w+m>\\|]>||t|\>|\r\r\|w\|t|\>|>\\|]>> for any cell arrays >, >, >, any stacks >, >, and any natural number . In particular, for a well-typed Simplicity program with delegation B>, we have <\equation*> \|>|]>||t|\>|\||t|\>|>|]>> <\theorem> Given a well-typed Simplicity program with delegation B> and an input , then <\equation*> \r\r\|w+m>\\|]>||\r\r\|w\|t|\>|>\\|]>> and <\equation*> \r\r\r\|w+m>\\|]>||\r\|w\|t|\>|>\\|]>> for any cell arrays >, >, >, any frame >, any stacks >, >, and any natural number . In particular, for a well-typed Simplicity program with delegation B>, we have <\equation*> \|>|]>||\||t|\>|>|]>> > Because the Bit Machine implementation of the combinator is derived from its semantics in core Simplicity, we can derive the static analysis of the space resources used by the Bit Machine implementation of the combintor from its defining Simplicity expression. <\eqnarray*> ||| s t|)>>|>|>|)>\ >; \ t|)>|)>>>| s t|)>>|>|>|)>\ >; \ t|)>|)>>>| s t|)>>|>|>|)>\ >; \ t|)>|)>>>>> We can expand out each of these definitions in turn: \; <\eqnarray*> ||||| s t|)>>||>>|||+bitSize>>|||,extraCellsBound|)>>>>> \; <\eqnarray*> ||||||||||||||| s t|)>>||, max|)>+r,extraCellsBound|)>|)>+r-r|)>>>|||\256+bitSize>>|||\bitSize+bitSize>>>> \; <\eqnarray*> ||||||||||||||||||| s t|)>>|||max,r+max,m,r+m|)>|)>,r|\>>>||||n,m|\>\extraCellsBound>>||||n,m|\>\extraCellsBound>>|||\256+bitSize>>|||\bitSize+bitSize>>>> The correctness theorems about these analyses still holds: <\lemma> For any Simplicity expression with delegation B>, such that <\equation*> \r\|w\\|]>||t|\>|\r\|w\\|]>> we have that <\enumerate> \r\|w\\|]>|)>=cellCount\r\|w\\|]>|)>> \r\|w\\|]>||t|\>|\r\|w\\|]>>|)>\cellCount\r\|w\\|]>|)>+extraCellsBound>. In particular for and <\equation*> \|>|]>||t|\>|>\||t|\>|>|]> we have that \|>|]>||t|\>|>\||t|\>|>|]>|)>\bitSize+bitSize+extraCellsBound>. <\lemma> For any Simplicity expression with delegation B>, such that <\equation*> \r\|w\\|]>||\r\|w\\|]>>> and <\equation*> \r\|w\\|]>|>|\r\|w\\|]>> we have that <\enumerate> \r\|w\\|]>|)>=cellCount|)>+cellCount\r\|w\\|]>|)>> and\r\|w\\|]>|)>=cellCount\r\|w\\|]>|)>> \r\|w\\|]>||\r\|w\\|]>>|)>\cellCount\r\|w\\|]>|)>+extraCellsBound|)>|)>> and\r\|w\\|]>|>|\r\|w\\|]>>|)>\cellCount\r\|w\\|]>|)>+extraCellsBound>. In particular for and <\equation*> \|>|]>||\||t|\>|>|]>> we have that \|>|]>||\||t|\>|>|]>>|)>\bitSize+bitSize+extraCellsBound>. <\lemma> For any Simplicity expression with delegation B>, <\equation*> =interp|)>> <\corollary> For any Simplicity expression with delegation B> and such that <\equation*> \|>|]>||\||t|\>|>|]>> we have that \|>|]>||\||t|\>|>|]>>|)>\bitSize+bitSize+max> where |n,m|\>\extraCellsBound>. While the primary purpose of is for delegation, the construct can be used to create what is effectively an unbounded loop in Simplicity. Given a Simplicity expression, A\A+B>, we can build a commitment Merkle root to an expression that will repeatedly recursively evaluate |t|\>:A \A+B> on an input until a value is returned. Consider a Simplicity expression A\A+B>, and a continuation A\<2>\B>. We define t k>: <\render-code> t k\A\<2>\B> | t k>>|| t \ >>>||| \ ;>|)> \ |)> k; >|)>> >>>>>>>>>>> \; Let us consider the semantics | t k|\>>>. Given inputs \A> and <2>>, then in the first clause in the definition of we have <\equation*> | t \ |\>>|a,h|\>=\>||t|\>>|)>,\>|\>\\\<2>|)> It evaluates |t|\>>|)>> and pairs that with . For those contexts in which |t|\>>|)>> doesn't fail, it results in either an |)>\A+B> for some \A>, or \A+B> from some B>. Let us consider the easy case, >>, first. The remainder of continues as follows. <\eqnarray*> ||| \ ;>|)> \ |)> k; >|)>> >|\>>|>,h|\>>>||||>|\>>|b,h|\>>>|||>>>>> Whenever |t|\>>|)>>, \Preturns\Q a > value, that value is the \Presult\Q of | t k|\>>, and is ignored. Now let us consider the case when |t|\>>|)>> results in an |)>> value. In this case the remainder of continues as follows. <\eqnarray*> ||| \ ;>|)> \ |)> k; >|)>> >|\>>||)>>,h|\>>>||| \ ;>|)> \ |)> k; >>|\>>|a,h|\>>>||||>|\>>\| \ ;>|)> \ |)> k>|\>>|)>|a,h|\>>>||||>|\>>\| \ k|\>>\| \ ;>|)> \ |\>>|)>|,|a,h|\>|\>>>|||| \ k;|\>>\| \ ;>|)> \ |\>>|)>|,|a,h|\>|\>>>|||| k|\>>\| \ ;>|)> \ |\>>|)>|,|a,h|\>|\>>>>> For the first part we have <\eqnarray*> ||| \ ;>|)> \ |\>>|,|a,h|\>|\>>>|||>>| \ ;>|)> \ |\>>|,|a,h|\>|\>|)>>>|||>>>|| \ ;>|)>|\>>|,|a,h|\>|\>,\|a,h|\>|\>|)>>>|||>>>|| \ ;>|\>|,|a,h|\>|\>,\|a,h|\>|\>|)>>>|||>>>||>|\>|h,|\>,\|a,h|\>|\>|)>>>>> We know that |>|\>|h,|\>=>=\||\>> if and only if > and that |>|\>|h,|\>=>=\> if and only if >. When >, then <\equation*> | \ ;>|)> \ |\>>||a,h|\>,|\>=\> and the whole expression fails with a >> result. However, when > we have that <\equation*> | \ ;>|)> \ |\>>||a,h|\>,|\>=\>|||\>,|a,h|\>|\> and we can continue with <\eqnarray*> | k|\>>|||\>,|a,h|\>|\>>|||k|\>>|a,h|\>>>>> and the result is that <\equation*> | \ ;>|)> \ |)> k; >|)>> >|\>>||)>>,h|\>=|k|\>>|a,h|\> \; Recapping, when |t|\>>|)>> results in an |)>>, then | t k|\>>|a,h|\>> evaluates the continuation |k|\>>|a,h|\>> under the condition that the value matches the commitment Merkle root of , i.e. >, and fails when >. Now let us consider 's commitment Merkle root, t k>>. Because of the use of , this commitment Merkle root is independent of the expression . <\lemma> For all A\A+B> and A\<2>\B>, t k>=loopBodyCMR> where <\eqnarray*> >|>||SHA256>>\ | t \ >,SHA256|SHA256>>\ |loopTail,>|\>|\>|\>|\>>>>> and <\eqnarray*> |>||SHA256>>\ |SHA256|>>>\ ||0|\>, \ ;>|)> \ >|\>|\>,>|\>|\>>>>> While the commitment Merkle root of t k> does not restrict what the continuation is, the second component of the input to the expression does, since > is required for evaluation to be successful. We can build a new expression that forces the continuation to be t k> itself: <\render-code> t k\A\B> | t k>>|| \ scribe|)>; t k>>>>>>>>>>> Again, 's commitment Merkle root is independent of the continuation : <\lemma> For all A\A+B> and A\<2>\B>, t k>=loopCMR> where <\eqnarray*> >|>||SHA256>>\ | \ scribe|)>>,loopBodyCMR|\>|\>>>>> By design, | t k|\>>|)>> passes > as the value to t k>, and the result can only be successful when =loopBodyCMR= t k>> for some further continuation \A\<2>\B>. Furthermore, the same value, is passed again into |k|\>>|a,h|\>=| t k|\>>|a,h|\>>, and that result can only be successful when >= t k>> for some yet further continuation \A\<2>\B>. This process looks endless, making it impossible to redeem any loopCMR commitment. However we can end this chain by using <\render-code> t\A\<2>\B> | t>>|| t \ >>>||| >>>>>>>>>>> The t> expression replaces the combinator in t> with an assertion that |t|\>>|)>> results in a >>. By construction t>=loopBodyCMR>, so that it can be used as a final continuation to terminate our chain of expressions in t k>. Tying everything together, we have a commitment Merkle root, >, that makes a commitment to a subexpression that can be redeemed by a subexpression of the form <\equation*> t t t t t|)>|)>|)>|)>|)> where is repeated the number of times necessary for |t|\>>|)>> to result in a >> value in the particular redemption context. Note that while it appears that is duplicated times, the subexpression will be shared in a DAG representation of this expression, avoiding a large of a blow up in program size. We have repeated the same expression in during redemption in the above example; however, if the expression contains subexpressions, those witness values could be different for each instance of shown above. Thus, more generally, the commitment can be redeemed by <\equation*> t t t t t|)>|)>|)>|)>|)> when >=> for all . For example, this construction would let you build a Simplicity expression that takes an arbitrarily long stream of SHA-256's 512 bit data blocks and computes the SHA-256 compression function composed over this stream of blocks by putting each data block into a expression within the different >'s. primitive to Simplicity?> The purpose of the above derivation of the construction is to understand the theoretical expressiveness that Simplicity's delegation extension adds to the language. The construction proves that the delegation extension brings Simplicity's expressiveness beyond what is possible with full Simplicity without delegation. While it is, in principle, possible to use the construction in Simplicity applications (that support the delegation extension), the construction is subject to all the same problems that using delegation entails: One cannot bound the computation costs of redemption at commitment time using general purpose static analysis. One might be able to perform an ad-hoc analysis on a particular program in order to bound the computation costs, but there are programs you can write in Simplicity with delegation where no upper bound on redemption costs exists. As with , using risks creating program that ends up impractical to redeem due to costs. Therefore we strongly recommend against using in practice. If, contrary to our expectations, the construction ends up very popular, we could amend the specification of Simplicity to add native t k> and t> combinators to Simplicity such that their commitment Merkle roots that depends only on , and with rules that require the continuation be one of the two constructors (with the same parameter). This would somewhat reduce the overhead of using unbounded loops. In Section we defined a Simplicity Program for a single signature check with over fixed transaction digest message. However, in Bitcoin Script, the user can select among a set of multiple different signature hash modes. Moreover, this choice is made at redeption time rather than at commitment time. We could replicate this behaviour by writing a Simplicity program that, given a signature hash flag value defined by a node, selects amongst a small variety of transaction digest expressions to use. However by using , we can provide the user with an unlimited choice of signature hash modes. Below we define t> where <1>\<2>> is a Simplicity expression that defines some signature hash mode. <\render-code> t\<1>\<2>> ||| t>||1f5369676e6174757265]>>|)>>>||>>| t>>|||)>|2+1024|\>|)>>>|||>>>>>>>>>>> This expression can be composed with pubkey key and signature values to form a Simplicity program that supports universal signature hash modes. <\render-code> t|)>|p,s|\>\<1>\<1>> | t|)>>|p,s|\>>||\> t|)> \ >>|||>>>>>>>>>>> The t> expression is similar to the definition of from Section. \ The difference is that we have replaced the >>|)>>|)>> subexpression with t>. \ When is , these two expressions have identical semantics: <\eqnarray*> ||| |\>>||\>>>||||>|)>\ >;; \ |\>>|)>||\>>>|||| \ |\>>\\\|>|)>\ >|\>>|)>||\>>>|||| \ |\>>\|>|)>\ >|\>>|)>||\>>>|||| \ |\>>\\\|>|)>\ >|\>|)>||\>>>|||| \ |\>>\|>|)>\ >|\>|)>||\>>>|||| \ |\>>||>|)>|\>||\>,||\>|\>>>||||\|>|)>|\>|)>||\>,| |\>>||\>|\>>>|||||>|)>|\>>||\>,| |\>>||\>|\>>>||=||>|)>>|\>>||\>>>>> The difference between the two expressions is that the subexpression > does not commit to using the > transaction digest. \ During redemption any alternative expression \ <1>\<2>> for creating a digest can be used instead. \ Because > is covered by the digital signature proveded to t>, the signature fixes the digest expression and it cannot be altered by a third party while still satisfying the >, with the exception of any values or ed expressions within . This allows users not only to simulate any of Script's signature hash flags, but to create and use any novel signtature hash mode that they desire. While the primary purpose of the <1>\<2>> parameter in t> is to use the Bitcoin primitives (or more generally the primitives for the specific blockchain application being used) to construct a cryptographic digest, the parameter can additionally include assertion side-effects. \ For example, one could include a condition that an absolute or relative timelock meets some specific threshold, without the signature covering any specific timelock value in the digest. Another possibility is to have the expression return a trivial value (e.g. |0|\>>) and have itself contain its own t|)>|p,s|\>> program for a different public key and its own digest expression >. \ The side-effect of the > within this inner expression essures that the whole Simplicity expression is only successful if the signature > is valid for the public key > and for the transaction digest >. This process lets you delegate control to another public key by creating a signature with the original public key that covers such a delegaton mode for a specific public key, >. \ Further conditions can be added as to such a delegation such as checks to limit the amount of funds being spent while ensuring the change is send back to a fixed address. \ Such delegation can be recursively applied, but could also be restricted by delegating to |)>|p,s|\>> or to some other fixed set of signature hash modes instead. Using t|)>|p,s|\>> as a standard Simplicity expression gives users maximal control over how they are able to later redeem their funds. In this chapter we will define a representation of Simplicity expressions as an untyped Simplicity DAG where subexpressions have explicit sharing. We will define how to perform type inference and reconstruct a Simplicity expression from this Simplicity DAG and we will define a binary serialization format for these Simplicity DAGs. In this section, we will introduce an DAG representation for (untyped) Simplicity expressions with explicit sharing of subexpressions. A Simplicity DAG is a topologically sorted list of Simplicity nodes. Each Simplicity node is a combinator name with a payload of references to earlier nodes in the list, or a payload of witness data, etc. First we enumerate the possible values for Simplicity nodes. \; <\with|par-mode|center> |||\Node>>>>>> \; <\with|par-mode|center> |||\Node>>>>>> \; <\with|par-mode|center> ||||||\>>>>>>>>| i\Node>>>>>> \; \; <\with|par-mode|center> ||||||\>>>>>>>>| i\Node>>>>>> \; \; <\with|par-mode|center> ||||||\>>>>>>>>| i\Node>>>>>> \; \; <\with|par-mode|center> ||||||\>>>>>>>>| i\Node>>>>>> \; \; <\with|par-mode|center> |||||||\>>|\>>>>>>>>| i j\Node>>>>>> \; \; <\with|par-mode|center> |||||||\>>|\>>>>>>>>| i j\Node>>>>>> \; \; <\with|par-mode|center> |||||||\>>|\>>>>>>>>| i j\Node>>>>>> \; \; <\with|par-mode|center> |||||||\>>|\>>>>>>>>| i j\Node>>>>>> \; \; <\with|par-mode|center> ||||||<2>>>>>>>>>>| v\Node>>>>>> \; \; <\with|par-mode|center> ||||||<2>>>>>>>>>| b\Node>>>>>> \; \; <\with|par-mode|center> ||||||<2>>>>>>>>>| h\Node>>>>>> \; In addition to the above, every primitive name is a Node. This set of primitives is application specific. For Simplicity with Bitcoin, we have \Node>, \Node>, etc. The single quotes around the Node names is there to distinguish them from their corresponding Simplicity combinator. Notice that there is not a perfect 1-to-1 relationship between Node names and Simplicity combinators. In particular, there are no Node names for the and combinators. Instead we have one Node name that will be used in conjunction with to represent assertions. A Simplicity DAG is represented as a topologically sorted, (non-empty) list of Nodes. (You may wish to review Section to recall our notation for list related operators.) <\equation*> DAG\Node Each node has between 0 and 2 references to nodes found earlier in the list represented by a relative offset. <\eqnarray*> |)>>|>|>>||)>>|>|>>| i|)>>|>|\>>| i|)>>|>|\>>| i|)>>|>|\>>| i|)>>|>|\>>| i j|)>>|>|j\\>>| i j|)>>|>|j\\>>| i j|)>>|>|j\\>>| i j|)>>|>|j\\>>| v|)>>|>|>>| b|)>>|>|>>| h|)>>|>|>>||)>>|>|>>||)>>|>|>>|>||>>>> In order for a list to be well-formed, it must satisfy two conditions. Firstly, we require that references only have offsets that refer to nodes occurring strictly earlier in the list: <\equation*> \|k,a|\>\indexed\\i\ref\0\i\k Secondly, when > a node is a child, the parent must be a > node, which in turn can only have at most one > child node. <\equation*> \|k,a|\>\indexed\\i\ref\ \h.l=\ h|)>\ \ j j. a= j j and <\equation*> \|k, i j|\>\indexed\\hh.l\\ h|)>\l\\ h|)> <\theorem> If a list is well-formed, and :DAG> is a prefix of (i.e. there exists an > such that |)>\l=\>) then > is also well-formed. Note that technically the root of a well-formed DAG, -1|]>>, can be a > node. Simplicity DAGs, as described above, do not have type information associated with them. Before we can interpret a Simplicity DAG as a Simplicity expression we must first perform type inference. Type inference can be done by solving unification equations of typing constraints to compute a most general unifier. A unification equation is written as T> were and are Simplicity type expressions with unification variables, where unification variables are denoted by Greek letters >, >, >, etc. Given a well-formed , we associate with each index in the list, k\>, a pair of fresh unification variables ,\> that are to be instantiated at the inferred source and target types of the expression for the node at index . Each different node occurring at an index in the DAG implies a set of unification equations over these type variables, possibly requiring further fresh unification variables. <\eqnarray*> |k,|\>>|>|\\|}>>>||k,|\>>|>|\<1>|}>>>||k, i|\>>|>|\\,\\\+\|}>*where \ is fresh>>||k, i|\>>|>|\\,\\\+\|}>*where \ is fresh>>||k,`take'> i|\>>|>|\\\\,\\\|}>*where \ is fresh>>||k, i|\>>|>|\\\\,\\\|}>*where \ is fresh>>||k, i j|\>>|>|\\,\\\,\\\|}>>>||k, i j|\>>|>|\+\|)>\\|}>\\\\\,\\\\|\h.l\\ h|)>|}>\\\\\,\\\\|\h.l\\ h|)>|}>where \,\,\ are fresh>>||k, i j|\>>|>|\\\\,\\\\\|}>>>||k, i j|\>>|>|\\\<2>,\\\\\,\\\\\|}>*where \ is fresh>>||k, v|\>>|>|>>||k, b|\>>|>|>>||k, h|\>>|>|>>||k,|\>>|>|\<1>,\\<2>|}>>>||k,|\>>|>|\<1>,\\Lock|}>>>|>||>>>> The rest of the constraints for the other Bitcoin primitive names follows the same pattern of adding constraints for the > and > variables to be equal to the input and output types of the corresponding primitives, all of which are required to be concrete types. Notice that the unification variables for nodes are unused. When nodes occur as children, their parent must be a node and the constraints for nodes specifically excludes references to their children's unification variables. Thus when a node represents an assertion, the only type constraints needed for an assertion are added. Using the > function, we can collect all the constraints that need to be solved for a well-formed (untyped) Simplicity DAG, , to be well-typed: <\equation*> con\fold>>|)>|)> Depending on the application there may be further constraints imposed on the root of the DAG. For example, if the DAG is supposed to represent a Simplicity program, which has type \<1>>, we would also add the constraints -1>\<1>,\-1>\<1>|}>>. A > is a function from unification variables to Simplicity type expressions with unification variables. A substitution, >, is a if for every unification variable >, the Simplicity type |)>> has no unification variables. A substitution, >, applied to Simplicity type expression , is a new Simplicity type expression >> with each unification variable > replaced by |)>>: <\eqnarray*> \|>>|>||)>>>|\|>>|>|>>|\|>>|>|>+T>>>|T|)>\|>>|>|>\T>>>>> A substitution > can also be applied to other substitutions yielding a composite substitution: <\equation*> \\|>|)>\\|)>\|> A substitution > is an instance of another substitution > whenever there exists a substitution > such that =\\|>>. If > and > are both instances of each other then they are >-equivalent. A unifier for a set of constraints is a substitution > such that for every constraint T|)>\C> we have >= T|\|>>>. The most general unifier for a set of constraints is a unifier > for those constraints such that every other unifier > for those constraints is an instance of >. The most general unifier is unique up to >-equivalence. Once all the constraints have be gathered we can perform first-order unification to solve for the most general unifier >. The most general unifier, >, may still contain free variables. To eliminate these free variables, we define an instance of > that sets all remaining free variable to the unit type <1>. We call the resulting ground substitution >>: <\equation*> \>\\\|\.<1>> Notice that if > and > are >-equivalent then >=\>>. In particular, this means that the ground substitution >> is independent of which choice of > we compute as the most general unifier. It is possible that there is no unifier for the given collection of constraints. In such a case the Simplicity DAG is ill-typed, (or does not meet the type constraints imposed by the application) and does not represent a well-typed Simplicity expression. First-order unification can be performed time linear in the size of the constraints, although in practice quasi-linear time algorithms using the union-find algorithm are simpler and may perform better on the size of problems one is likely to encounter. Our set of constraints is linear in the size of the DAG thus we can compute the most general unifier in linear (or quasi-linear) time. It is important to note that these (quasi-)linear time computations rely on having sharing of (type) subexpressions in the representation of the substitution. If you flatten out the representation of the substitution, for example by printing out all the types, the result can be exponential in the size of the input DAG. Fortunately, all of the computation required for Simplicity's consensus operations, can operate without flattening the representation of the inferred types. Also notice that our set of constraints imply we are doing monomorphic type inference, meaning that any shared subexpressions are assigned the same type. Sometimes we will require multiple instances of the same sub-DAG within a DAG so that different types can be inferred for the subexpressions corresponding to those sub-DAG. As a trivial example, a DAG will often have multiple nodes, one for each type that the combinator is be used for. A DAG should never have sub-DAGs that end up with the same pair of inferred types and will be disallowed by anti-malleability rules (see Section>>). \ We could remove duplicate sub-DAGs entirely by using polymorphic type inference instead. Polymorphic type inference is DEXPTIME-complete. However, because removing duplicated sub-DAGs can produce exponentially smaller terms it might be the case that polymorphic type inference is linear in the size of the DAG with duplicated sub-DAGs that are needed for monomorphic type inference. If this is the case, we could switch to polymorphic type inference without opening up DoS attacks. Whether this is possible or not is currently open question for me. Given a well-formed Simplicity DAG, , that does have a substitution > yielding the most general unifier for >, we can attempt to synthesize the Simplicity expression that the DAG represents by recursively interpreting the DAG as \\>-1>|)>\\>-1>|)>> where <\equation*> syn\syn-1,l-1|]>|)> and where <\eqnarray*> >|)>>|>|>>|>|)>|)>>|>|>|)>>>>|>|)>|)>>|>|>|)>>>>|> i|)>|)>>|>|>|)>,B,C> syn|)>*where B+C=\>|)>>>|> i|)>|)>>|>|>|)>,B,C> syn|)>*where B+C=\>|)>>>|> i|)>|)>>|>|>|)>> syn|)>*where A\B=\>|)>>>|> i|)>|)>>|>|>|)>> syn|)>*where A\B=\>|)>>>|> i j|)>|)>>|>|>|)>,\>|)>,\>|)>> syn|)> syn|)>>>|> i j|)>|)>>|>|,k-j,l|)>>>|> i j|)>|)>>|>|>|)>,\>|)>,\>|)>> syn|)> syn|)>>>|> i j|)>|)>>|>|>|)>,B,C,\>|)>> syn|)> syn|)>where B\C=\>|)>>>|> v|)>|)>>|>|>|)>,\>|)>> inflate>|)>,v|)>>>|> b|)>|)>>|>|>|)>,\>|)>> b>>|> h|)>|)>>|>|>>|>|)>|)>>|>|>>|>|)>|)>>|>|>>|>||>>>> The and clauses require special consideration which we define below. The syn function never encounters a > node when is well-formed except when h.l-1|]>=\> h|)>>, in which case the entire expression itself is hidden. These > nodes are only used by the syncase function. The syncase function constructs expressions as well as and expressions. Assertion expressions are produced when hidden nodes are passed as parameters. However both branches of a case expression cannot be hidden when is well-formed. <\eqnarray*> ,k,\> h|)>,k,\> h|)>|)>>|>|>>|,k,n,k,\> h|)>|)>>|>|>>|)>> syn,n|)> hwhere \>>|)>=\C and when \h\n\\> h|)>>>|,k,\> h|)>,k,n|)>>|>|>>|)>> h syn,n|)>where \>>|)>=\C and when \h\n\\> h|)>>>|,k,n,k,n|)>>|>|>>|)>> syn,n|)> syn,n|)>where \>>|)>=\C and when \h,h\n\\> h|)>\n\\> h|)>>>>> A node does not hold a Simplicity value, like the combinator requires. Instead it has a bit string that encodes a Simplicity value. The inflate function performs a type-directed decoding of this bit string to reconstruct the witness value. The inflate function is defined recursively via the inflation function. These two functions are defined below. <\eqnarray*> ,v|)>>|>||||\>,v|\>>>|>\v|)>>|>||,v|\>*where |a,v|\>=inflation>>|>\v|)>>|>||,v|\>*where |b,v|\>=inflation>>||)>>|>|>>|B,v|)>>|>|||a,b|\>,v|\>*where |a,v|\>=inflationand |b,v|\>=inflation|)>>>>> \; <\eqnarray*> >|>|when |a,\|\>=inflation>>|>|>|otherwise>>>> As part of DoS protections and malleability protection, we want to prevent witness data from being inflated with unused bits. Notice that that in the definition of v|)>>, the inflate function is passed the inferred type >|)>>. Using the inferred type ensures that the witness data only contains data that is nominally useful by the surrounding Simplicity program. Furthermore, the inflate function fails unless it consumes exactly all of its bit string argument. This prevents data from being padded with extra, unused bits. In this section, we define a binary prefix code for serializing Simplicity DAGs. Because prefix codes are self-delimiting, they provide a convenient framework for creating serialization formats. Compound structures can be serialized by concatenation of prefix codes of its substructures. Our serialization of Simplicity DAGs can be used as part of a network protocol or for writing data to a file. The program size metric (see Section>>) computed for terms can be used to bound to the length of this binary encoding. However, specific binary encodings, such of this one, do not form a consensus critical aspect of Simplicity's design and can be substituted with other encodings that have similar suitable bounds. Appendix describes an alternative, byte-based, binary encoding. In this section we present a recursive Elias prefix code for bit strings and positive natural numbers. Our code for positive natural numbers it has properties similar to the Elias omega coding, but is a has a simple recursive functional definition and some other nice properties. First, for any > with n>, we define |n|\>>>> to be a bit string for , written in binary, with the leading >> chopped off. <\eqnarray*> |1|\>>>>|>|>>>>||2*n|\>>>>|>||n|\>>>\>>>>||2*n+1|\>>>>|>||n|\>>>\>>>>>> For example, <\eqnarray*> |1|\>>>>||>>>>||2|\>>>>||>>>>||3|\>>>>||>>>>||4|\>>>>||>>>>|>||>>||7|\>>>>||>>>>|>||>>>> This binary code is not a prefix code. To make a prefix code we define mutually recursive function on bit strings and positive numbers. This encodes a bit string by prefixing it with a tag indicating if the bit string is null followed by the bit string's length when it is not null. It encodes a positive number, , by encoding its associated bit string |n|\>>>>. <\eqnarray*> >>|>>|>|>>>>|>>|>>|>|>>\|>\l>>|>|>||n|\>>>|>>>>> The table below illustrates this prefix code on a few inputs. \; |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>>||>>||>>>|>|>|>|>>|>|>>>>|>|>|>|>>|>|>>>>|>>||>>||>>>|-1>|>>|>|>>>|>>|>|>>\>>>>>|>|>|>|>>>|>>|>|>>\>>>>>|>>||>>||>>>>>>> \; Notice that this prefix code preserves numeric ordering as lexicographical ordering. If and are positive numbers then m\\> where > is the lexicographical ordering on bit strings. When you are parsing a code for a positive number that you know from context is not allowed to exceed some bound . Then during parsing you can abort as soon as the string being parsed lexicographically exceeds >. In some cases you can abort parsing after only a few bits. For example, if from context you know that a the positive number must fit in a 64-bit integer (i.e. it is not allowed to exceed -1>), then you can abort parsing as soon as the bit string being parsed lexicographically meets or exceeds the prefix . In this section we describe a fairly direct serialization for Simplicity DAGs. First, we provide a prefix code for values stripped of witness data: <\eqnarray*> > i j|>>||>>\\>>|> i j|>>||>>\\>>|> i j|>>||>>\\>>|> i j|>>||>>\\>>|> i|>>||>>\>>|> i|>>||>>\>>|> i|>>||>>\>>|> i|>>||>>\>>|>|>>||>>>>|>|>>||>>>>|> b|>>||>>\>\>>>|)>>\BE|)>>>|> h|>>||>>\>\>>>|)>>\BE|)>>>|>v|>>||>>>>>> We define a : <2>>> function for DAGs DAG> that serializes the values held by the witness data: <\eqnarray*> >v|)>>|>|>|>|>| \v.n\>v>>>> <\equation*> witnessData\ \>>|)>|)> The code >>>, is a reserved code for wallet use where it represents a \Punary >>\Q node for representing commitment time Simplicity program where, of course, the disconnected Simplicity expression wouldn't be available. The code is not used for consensus purposes, and like >>, it cannot legally appear on chain For serialization of DAGs, , which is a non-empty list of Nodes, we have the following serialization format <\equation*> lengthCode\|>\\>x.|)>>|)>|)> The above prefixes the serialization of DAG with the number of nodes, followed by the list of nodes serialized with the prefix code for nodes. Again, is a prefix codes. Notice that the does not use a prefix code, and the witnessData simply concatenates values without separating them with deliminators. This works because during deserialization, type inference does not depend on witness data, and once type inference is complete, we can use the inference types of witness nodes to decode the witness values in sequence. A prefix of is reserved for computational jets which are given in Appendix. \ A previx of is used with a special enoding for jetting ,<2>>>> expressions, which we call word jets. \; <\with|par-mode|center> ||||||>>|<2>>>>>>>>>>| n v\Node>>>>>> \; <\eqnarray*> n v>|)>>|>|>>||k, n v|\>>|>|\<1>,\\<2>>|}>>>|> n v>>|)>|)>>|>||,<2>>>|\>>>|>n v|>>|>|>>\\\>>>>>>>> where \>>>>> formally converts a word value >> to a bistring: <\eqnarray*> >>>>|>|>>>>|>>>>|x,y|\>>|>|>>>>\\>>>>>>>> The DAG encoding for Simplicity expressions allows for sharing of subexpressions, however nothing in the previous section mandates sharing of subexpressions. \ Without mandatory sharing would have a malleability vector where a third party could unshare every subexprssion, vastly inflating the weight of a transaction. \ To enforce mandatory sharing we will introduce the notion of an identity Merkle root and require that every sub-DAG have a unique such identity. The identity Merkle root of a Simplicity expression is defined by >. \ This value is the same as except in the presence of and combinators which are defined as follows: <\eqnarray*> || b>>|>||SHA256>>\ |SHA256>|)>,|\>|\>>>| s t>>|>||SHA256>>\ |,|\>|\>>>>> The unique tags used are <\small> <\eqnarray*> >>|>|1f4964656e746974791f7769746e657373]>>>>|>>|>|1f4964656e746974791f646973636f6e6e656374]>>>>>> and \A\<2>>> is the inverse of : <\eqnarray*> >||\>|)>>|>|>>>|>|)>>|>|>\deflate>>|>|)>>|>|>\deflate>>|B>|a,b|\>|)>>|>|\deflate>>>> <\lemma> For all A>, |)>=a>. One of our anti-malleability requirements is that non-hidden nodes in a DAG synethesis are terms with unique identity Merkle root, input, output type triples. \ We also require that hidden nodes are unique. <\definition> We say a well-formed Simplicity DAG DAG>, that has a substitution > yielding the most general unifier for >, has maximized sharing when <\enumerate-numeric> for all > and > such that <\enumerate-alpha> , k\> and |]>\\> h|)> > and |]>\\> h|)> >for any > and >, and >>|)>=\>>|)>> and >>|)>=\>>|)>>, and ,l|]>|)>>=,l|]>|)>>> then =k>, and for all > and > such that <\enumerate-alpha> , k\> and |]>=\> h|)> > and |]>=\> h|)> >for some then =k>. The Coq development for Simplicity is found in the directory. There are two subdirectories: contains modules related to Simplicity, and the directory has a few modules dedicated to other structures that are not by themselves specific to Simplicity, including a short hierarchy for commutative and idempotent monads. We will focus on the contents of the directory. The Coq development for Simplicity begins with the file. This contain the inductive definition of which defines Simplicity's type expressions. The function interprets Simplicity types as Coq types, and it is declared as coercion. The module also provides standard arithmetic notation for Simplicity's sum and product types. The is a record collecting the operations needed to define structurally recursive functions for . These are known as , and it is one of the inputs to that defines catamorphisms from to another type. There are two different ways of representing of Simplicity terms defined in Coq. One representation is an \Pinitial\Q representation, as an inductive type. The other representation is a \Pfinal\Q representation, based on algebras. Generally speaking the \Pinitial\Q representation works well when reasoning about Simplicity term using induction to prove properties about them, while the \Pfinal\Q representation is useful for implicitly capturing shared sub-expressions when defining Simplicity programs. We begin with the \Pinitial\Q representation, which will most readers will find more familiar. The module defines an inductive family, , for the well-typed core Simplicity language. The core language is the pure fragment of Simplicity that has no effects such as failure or read access to the transaction environment. The function provides denotational semantics and interprets terms as Coq functions over the corresponding Coq types. This module also establishes the core Simplicity completeness theorem (Theorem) as the theorem. The proof is built from , a function to produce Simplicity terms representing constant functions, and which transforms Coq functions over Simplicity types into Simplicity terms representing those functions. To explain the \Pfinal\Q representation of terms it is first necessary to understand what an algebra for Simplicity is. We can understand this by way of a mathematical analogy with ring theory. A ring is a mathematical structure consisting of a domain along with constants from that domain that correspond to 0 and 1, and binary functions over that domain that correspond to +> and > operations that satisfy certain ring laws. A term from the language of rings is an expression made out of , , , and >. Given a ring and a term from the language of rings, we can interpret that term in the given ring and compute an element of the domain that the term represents. There are many different rings structures, such as the ring of integers, and the ring of integers modulo for any positive number . A given term can be interpreted as some value for any ring. An alternative way to represent terms is as a function that, given any ring, returns a value from its domain and does so in a \Puniform\Q way. This would be the \Pfinal\Q representation for terms in the language of rings. An algebra for Simplicity is an analogous structure to a ring. An algebra for Simplicity consists of a domain, along with constants from that domain that correspond to > and > and functions over that domain that correspond the other combinators from Simplicity. Unlike the case for rings, the domain of a Simplicity algebra is indexed by a pair of Simplicity types, and naturally the constants and functions that interpret Simplicity combinators must respect these types (and unlike rings, we are not going to impose any extra laws). Core Simplicity algebras are formalized in the file. The record captures the interpretation of constants and combinators for core Simplicity over a given domain. The structure is the type of Simplicity algebras, containing a type family for the domain, and an instance of the record for interpretations. Given any Simplicity algebra and a well-typed term (from the \Pinitial\Q representation) we can interpret that term in the algebra to get out a value from the domain (that has a type corresponding to the type of the term). The function performs this interpretation by recursively evaluating the interpretation of the core Simplicity combinators from the algebra. What sort of Simplicity algebras are there? The most obvious one is the functional semantics of Simplicity. The domain of this algebra is the functions between Simplicity types. This domain is indexed by the input and output Simplicity types. The interpretation of the > and > constants are the identity and constant-unit functions respectively and the interpretation of the other core Simplicity combinators is also in accordance with Simplicity's denotational semantics. This algebra is defined in the structure and the lemma proves that the interpretation of terms in the \Pinitial\Q representation into this algebra results in the same function that the function from produces. The notation denotes this denotation semantics using the domain. Another example of a Simplicity algebra is the \Pinitial\Q representation of terms themselves, which form a trivial algebra. This domain of Simplicity terms is also indexed by input and output Simplicity types and the constants and combinators are interpreted as themselves. This algebra is defined in the structure and the lemma proves that the interpretation of any term in this algebra returns the original term back. There are several other Simplicity algebras. Programs for the Bit Machine form a Simplicity algebra with the translation from Simplicity to Bit Machine code defining the interpretation of core Simplicity combinators. Also 256-bit hashes form a Simplicity algebra with the commitment Merkle root computation defining the interpretation of core Simplicity combinators. Static analysis of resource usage for Simplicity expressions forms yet another set of Simplicity algebras. Instances of Simplicity algebras are declared as . This allows Coq's type inference engine to infer the interpretation of Simplicity terms when they are used in the typing contexts of domain of one of these Simplicity algebras. The \Pfinal\Q representation of a Simplicity term is as a function that selects a value out of any Simplicity algebra and does so in a \Puniform\Q manner. A \Puniform\Q manner means a function that satisfies the property which effectively says that that the values chosen by the function from two domains must each be constructed from a composition of the interpretation of combinators in the two domains in the same way. In other words, the function must act the the interpretation of some \Pinitial\Q represented term under for any domain. Terms in the \Pinitial\Q representation can be converted to the \Pfinal\Q representation by partial application of . The lemma proves that the resulting \Pfinal\Q representation resulting from satisfies the property. Terms in the \Pfinal\Q representation can be converted into the \Pinitial\Q representation by applying the function to the Simplicity algebra. The lemma shows that converting from the \Pinitial\Q representation to the \Pfinal\Q representation and back to the \Pinitial\Q representation returns the original value. The lemma shows that starting from any term in the \Pfinal\Q representation that satisfies the property and converting it to the \Pinitial\Q representation and back to the \Pfinal\Q representation results in an equivalent term. This completes the proof at the two representations are isomorphic. To facilitate the construction of expression in the \Pfinal\Q representation, the nine core combinators are defined as functions parameterized over all Simplicity algebras, and each combinator is proven to be parametric or to preserve parametericity. For the most part, these combinators can be used to write Simplicity expressions in the \Pfinal\Q representation in the same way one would use constructors to write Simplicity expressions in the \Pinitial\Q representation. On top of this, notation is defined for the pair combinator, and \\ t> is defined for the composition combinator. Also we define the , , and notations for sequences of takes and drops over the identity combinator. For every expression built in the \Pfinal\Q representation, it is necessary to prove that the result satisfies the parametericity property. A hint database is provided to facilitate automatic proofs of these results. Users should add their own parametricity lemmas to the hint database as they create new Simplicity expressions. Some examples of this can be found in the module. The \Pinitial\Q inductive representation is the traditional definition one expects for terms and is easy to reason inductively about. The problem with this representation is that, due to lack of sharing between sub-expressions, it is expensive to evaluate with these terms inside Coq itself. For example, one cannot compute Merkle roots of anything but the most trivial of expressions. The \Pfinal\Q algebra representation solves this problem by allowing transparent sharing of expressions. In the \Pfinal\Q representation, terms are really values of a Simplicity algebra. When these values are shared using in Coq's let expressions, or shared via some function argument in Coq, those values of the algebra are shared during computation within Coq. This representation makes it feasible to actually compute Merkle roots for Simplicity expressions directly inside Coq. Both representations are used throughout the Simplicity Coq library. The isomorphism between the two representations is used to transport theorems between them. I typically use as the variable name for an abstract Simplicity algebra. I use this variable name because are the most generic type of Simplicity algebra (formally known as an initial algebra) so it makes sense to think of generic Simplicity algebras as if they are term algebras. The file defines notation for the Simplicity type for bits, and notation for their two values and . The Simplicity expressions and are defined to be the constant functions that return the zero and one bit respectively. A few logical combinators are defined for bits, including the > combinator which does case analysis on one bit of input, and executes > or > expressions according to whether the bit represented true or false. All the combinators and Simplicity expressions are given in the \Pfinal\Q representation and parametricity lemmas are provided. The file defines types for multi-bit words and defines Simplicity expressions for addition and multiplication on those words. > is a Simplicity type of a >-bit word. The module defines a class of types of finite words. The class provides and operations that convert between standard Coq integers and these types of finite words along with proofs that the conversion functions are inverses modulo the word size. declarations provide implementations for the and > types and for pairs of of such types. The file also defines the following Simplicity expressions: <\itemize-dot> term ((Word n * Word n) * (Word n * Word n)) (Word (S n))> The expression defines the sum of two >-bit word, returning a carry bit and a >-bit word result. The expression defines the sum of two >-bit word and one (carry input) bit, returning a carry bit and a >-bit word result. The expression defines the product of two >-bit word and returns a >-bit word. The expression takes a quadruple, ||a,b|\>,|c,d|\>|\>> of >-bit words and returns b+c+d> as a >-bit word. Each of these expressions has an associated correctness lemma. These expressions are all defined in the \Pfinal\Q representation and there are parametricity lemmas for each expression. |The inheritance hierarchy of algebras for Simplicity's partial extensions in Coq.> So far we have only covered the algebra for the core Simplicity language in Coq. The various extensions to this core Simplicity language are captured by extensions to the record type for the core Simplicity algebra. Figure illustrates the names of the algebras extending the language algebra and their inheritance relationship. We use the \Ppacked-classes\Q method for formalizing the inheritance relation of these extensions in Coq. Readers unfamiliar with this style should first read \P\Q and \P\Q. Roughly speaking, there are two dimensions to the inheritance structure. In one direction, the , , and algebras all have semantics that can be interpreted as pure functions. That is, the function semantics of terms from these languages can be evaluated as functions that have no side-effects and can return values within any monad, including the identity monad. The next layer in this direction, , , and , extend the previous layer with assertion and failure expressions. These expressions introduce the failure effect and the functional semantics of terms from these languages return values within a , which includes the monad. The last layer in this direction, , , , and , include primitive terms that are particular to the specific blockchain application. The functional semantics of terms from these language return values within a monad that captures the particular effects of the blockchain application. In the case of Bitcoin, the effects are captured by an environment (a.k.a reader) monad that provides read-only access to the signed transaction data. We break up the language of Simplicity into these layers because it helps us isolate the side-effects of the various language extensions when reasoning about Simplicity programs. When dealing with a sub-expression from the first layer, one can safely ignore the environment and failure effects and reason only about pure functions. Afterwards, various lemmas, such as > or , can be used to lift results into the monads use by the other layers when combining the pure sub-expression with other sub-expressions that do have effects. The other dimension of the inheritance structure breaks the language into feature sets. The , , and algebras exclude witness and delegation features and encompass the set of language features that s are restricted to using. The next layer, , and , add witness features culminating in the algebra defining the Full Simplicity language. The last layer, , , and provides the powerful and dangerous delegation extension, which should only be used with caution. We cover these language extensions in more detail below. The algebra, found in , extends the algebra with the combinator. The and canonical structures define the function semantics by interpreting the terms as pure functions and as Kleisli morphisms for any monad, respectively. The lemma relates these two interpretations. The algebra, found in , extends the algebra with the , , and combinators. The canonical structure defines the functional semantics of Simplicity with assertions by interpreting terms as Kleisli morphisms for a monad with zero. The lemma shows that when reasoning about the functional semantics of Simplicity with assertions, it suffices to reason within the monad and translate the result to any other monad with zero via the homomorphism. The algebra is simply the meet of the and algebras without adding any new combinators. The algebra, found in , extends the algebra with the combinator. The algebra is simply the meet of the and algebras (equiv. the meet of the and algebras) without adding any new combinators. \ Building the functional semantics of Simplicity with delegation involves a simultaneous computation of commitment Merkle roots (see Section) and the functional semantics. To support this the type is the product of the and the types. Whenever forms an algebra from any of the previous Simplicity language algebras, then is also a member of the same algebra. Furthermore whenever is a Simplicity with witnesses algebra, then is a Simplicity with witnesses and delegation algebra. Similarly whenever is a Simplicity with assertions and witnesses algebra, then is a Simplicity with assertions, witnesses and delegation algebra. The projection extracts , from . For example, is a functional semantics for Simplicity with witnesses. Then, when > is a term for Simplicity with witnesses and delegation, is the functional semantics of >. The lemma shows that for Simplicity terms that don't have delegation, then returns the original semantics. The Simplicity language is parameterized by the choice of blockchain-specific primitives. Currently we use Coq's module system to capture this parameterization. A found in defines the parameters that define these blockchain-specific applications of simplicity: <\itemize> A type family Ty -\ Set> of the primitive expression's syntax. A function hash256> that defines the Merkle roots for the primitives. A type that captures the relevant read-only context used to interpret the primitives. A function A -\ env -\ option B> that defines the functional semantics of the primitives. At the moment, this frameworks only supports primitives that use the environment (and failure) side-effect; however this framework could be extended to allow primitives that require other effects that can be captured by commutative and idempotent monads (for example, the writer effect to a commutative and idempotent monoid). Given an instance of the 's parameters, the defines the algebras for the parts of the Simplicity language that depends on the primitives. This includes the , , and algebras. The algebra extends the algebra with the primitives given by the 's type family through the combinator. The arrow is the Kleisli arrow for the monad generated by adding an environment effect for the 's to the monad . The canonical structure provides the functional semantics for Simplicity with primitives by interpreting terms as whenever is a monad zero. The module found in provides these an instance of the parameters used for a Bitcoin or Bitcoin-like application of Simplicity. The structures defining the signed transaction data are specified culminating in the data type. The type lists the typed primitive expressions defined in Section. The type captures the read-only context for interpreting these primitives and it includes a , the index within this transaction that is under consideration, and the commitment Merkle root of the script being evaluated. Lastly, the function defines the functional semantics of the primitives in accordance with Section and the function defines the Merkle roots for the primitives in accordance with Section. We use in the definition of to pre-evaluate the definitions of the Merkle roots as an optimization. The algebra, found in the in , extends the algebra with generic support for jets. The combinator takes a term > from the algebra and the canonical structures defines the functional semantics of a jet to be the functional semantics of >. Operationally, we expect implementations of specific jets to be natively implemented, but this detail goes beyond the scope of the specification of Simplicity within Coq. Because > is restricted to being a term from the algebra, jets cannot contain or sub-expressions. While our generic definition of allows any term from the algebra to be a jet, we expect specific applications of Simplicity to limit themselves to a finite collection of jets through its serialization format. The algebra, found in the in , is the meet of the and the algebras (equiv. the meet of the and algebras) with no additional combinators. It defines the full Simplicity language. The canonical structure provides the functional semantics of the full Simplicity language as the type family when is a monad zero. The algebra is the the meet of the and the algebras (equiv. the meet of the and algebras, or the meet of the and algebras, etc.) defines the full Simplicity with delegation language. The functional semantics are defined via the canonical structure whose domain includes when is a monad zero. Using , one can extract a value as the functional semantics. The file defines a Merkle root of types, and the commitment Merkle root and annotated Merkle roots for part of the Simplicity language. The Merkle root of types is specified by > and defined by . The in the family the parameters are phantom parameters, and the value is always a type. Canonical Structures provide instances of for core Simplicity, and Simplicity with assertions and witnesses. The for delegation is found in and the for primitives, jets, Full Simplicity and Full Simplicity with delegation is found in . These Merkle roots are computed using the SHA-256 compression function with unique tags providing the initial value for each language construct. These tags are in turn the SHA-256 hash of short (less than 56 character) ASCII strings. The Coq definition of SHA-256 is taken from the VST (Verified Software Toolchain) project and the module provides an interface to that project. The VST implementation of SHA-256 is efficient enough that it is practical to compute some commitment Merkle roots of functions inside Coq itself using . See at the end of for an example of computing the commitment Merkle root of a Simplicity function that computes the SHA-256 compression function. The file provides the primary definition of the abstract Bit Machine. This definition, and hence this file, is independent of the rest of the Simplicity language. The type explicitly tracks cell values in the bit machine as being one of , , and undefined. represents the undefined value and and represent and respectively. The record represents read frames. It uses a zipper representation of a list with a cursor: The elements of the list in front of the cursor are in the field and the elements of the list behind the cursor are in the field stored in . The function builds a read frame from a list with the cursor set to the beginning of the frame. The record represents write frames. It uses a similar zipper representation where the field holds the elements behind the cursor in . Because write frames are append only, every cell in front of the cursor must be an undefined value. For this reason we only store the number of cells in front of the cursor in the field. The function builds an empty write frame of a given size and the function builds an filled write frame from a list. The record represents the non-halted states of the Bit Machine. It consists of <\itemize-dot> : a list of inactive read frames, with the bottom of the stack at the end of the list. : the active read frame, which is the top value of the non-empty stack of read frames. : the active write frame, which is the top value of the non-empty stack of write frames. : a list of inactive write frames, with the bottom of the stack at the end of the list. The variant is either a or the state and represents the possible states of the Bit Machine. We make the injection of into a coercion. It is sometimes useful to decompose the Bit Machine's state as <\equation*> \r\|\>\*c>>\r\|w\*\*c>>>\\|]> where we are locally interested in what is immediately in front of the active read frame's cursor, |\>\*c>>>, and what is immediately surrounding the active write frame's cursor, *\*c>>>>. This is captured by the type, noting that the data immediately surrounding the active write frame's cursor is captured by the type. The remainder of the state, consisting of \r\\\r\|w\\\\\|]>> is captured by the type, which happens to be isomorphic to the type. The function combines a value and a value to build a complete value. Sometimes we are interested in of some within another . The context of such a decomposition is isomorphic to and we don't even both giving a type alias to this. The function combines a context, , with a , , to build a combined . makes into a monoid and becomes a monoid action on s with respect to this monoid. This theory is not fully developed in Coq, but will be if it is needed. The lemma proves the monoid action property, which is the only theorem developed so far. The type is constructed using similar fields as the type and contains a sequence of numbers. This is used for counting the number of cells in the various components of the Bit Machine's . The function tallies up the totals and is used later in the function. The > type enumerates the nine basic instructions of the Bit Machine. The type of these instructions are parameterized by the legal states that the instructions can successfully operate in, >, and the resulting state after execution of the instruction, >. In this way, the type family represents a precategory (also known as a directed multi-graph) that captures the machine instructions and their semantics. There is an object (a.k.a. node) for every possible state of the Bit Machine. There is an arrow (a.k.a. directed edge) between two states if there is an instruction of the Bit Machine that successfully transitions from the source state to the target state, and that arrow (a.k.a. directed edge) is labeled with the name of the instruction. The instruction is the only instruction whose final state is the state. No instruction begins from the state. The specific type > is the type of all instructions that transition from state > to state >. A of is the free category generated from the precategory . This free category can also be understood as a collection of all paths through the directed graph of all machine instructions and their associated state transitions. The specific type > is the type of all sequences of instructions that transition from state > to state >. This type captures the semantics of sequences of machine instructions. The notation ~~\ > denotes the > type of single step transitions, which corresponds to \S>. The notation -\\ > denotes the > type of multi-step (including 0 steps) transitions between states > and and the trace of the instructions used. The lemma proves that the only trace that begins from the state is the empty trace. We interpret a Bit Machine as a function taking an initial machine state and, if successful, returning a final machine state along with a thrist of machine instructions that connect the initial state to the final state. The notation \- k -\\ S2> corresponds to |k|S> and denotes that the program when started in state successfully executes and ends in state . The function extracts a \ S2> trace from a program when \- k -\\ S2> holds. For each machine instruction we use to define a single instruction that tries to execute that single instruction once and returns that state transition. If the initial non-halted state given to these single instruction programs is not valid for their instruction, the program fails by returning . However, when the initial state is the state, the program succeeds but ignores its instruction and remains in the state. This corresponds to the |i|> deduction. These single instruction programs have an associated correctness lemma that proves they run successfully when run from an initial state valid for their instruction and a completeness lemma that proves that they were run from either a valid initial state or the state. We also define the trivial program that contains no instructions and always succeeds. These single instruction (and ) programs can be combined into more complex programs using the and combinators. The combinator sequences two programs, running the second program starting from the final state of the first program and combines their thrists. The sequence fails if either program fails. The combinator picks between running two programs by peeking at the cell under the active read frame's cursor from the initial state and running either the first or second program depending on whether the cell holds a or value. When starting from a non-halted state, if the cell holds an undefined value, or if the active read frame's cursor is at the end of the frame, the combinator fails. When started from the state, the program succeeds but remains in the state. The notations ;;; > and \|\|\| > denote the sequence and choice combinations respectively of two programs and correspond to ;k> and k>. We also define the combinator > which corresponds to k>. The function takes a and an initial and extracts the resulting final and the trace to get there, if the program is successful. For denotational semantics we only care about the resulting final state. For operational semantics we will care how we got there. A few lemmas are provided to help reason about the behaviour of when running the program combinators. The function computes the maximum number of cells used by any intermediate state from the trace of execution of a Bit Machine program. A few lemmas are provided to help reason about the behaviour of when running the program combinators. The file defines how to transform Simplicity programs into Bit Machine programs that perform the same computation. The and functions implement > and > respectively. The structure provides a Simplicity algebra for Bit Machine s that interprets Simplicity terms according to the naive translation. The theorem proves that the generated by when started from a state that contains an encoding of Simplicity function's input successfully ends up in a final machine state that contains an encoding of Simplicity function's output (and input). The files defines the static analyses of Simplicity program that compute bounds on the various computational resources used by the Bit Machine when executing translated Simplicity. The file also proves the correctness of these upper bounds. The module defines the algebra which is used to compute an upper bound on additional memory that will be used when Simplicity sub-expressions are naively translated to the Bit Machine and executed. The lemma proves that for naively translated core Simplicity expressions, the maximum memory used by the Bit Machine is the memory needed by the size of the initial state, plus the results of . This bound holds no matter what the starting state is, even if it is not a valid state for holding the input for the Simplicity expression. The function computes the memory used by the Bit Machine for evaluating Simplicity expressions starting from a standard initial state and proves that this upper bound is correct. WARNING: None of the Haskell library development is normative. There is no formalized connection between any of the Haskell library and Simplicity's formal semantics and development in Coq. There could be errors in the Haskell library that cause it to disagree with the formal development defined in Coq. The Haskell library is intended to be used for experimental, exploratory and rapid development of Simplicity related work, but should not be relied upon for production development. For production development, formal developments in Coq should be created. The Haskell Simplicity project is split up into multiple libraries in order so that multiple different applications of Simplicity to different Blockchains can be developed and used without conflicting with each other. We use the Backpack feature of the Glasgow Haskell Compiler to parameterize and reexport common functionally for different Simplicity applications. library> The first library, , is found in the directory. It defines the aspects of Simplicity that are independent of any particular Blockchain application. This include Simplicity's type system, Simplicity's core expression language and the assertions, witness, and delegation extensions, and a few other components. The file contains the development of Simplicity types. There are three different ways that Simplicity types are captured in Haskell. The primary way Simplicity types are captured is by the class which only has instances for the Haskell types that correspond to the Simplicity types: <\itemize-dot> TyC (Either a b)> TyC (a, b)> The class is crafted so that its methods are not exported. This prevents anyone from adding further instances to the class. The second way Simplicity types are captured is by the GADT: <\code> data TyReflect a where \ \ OneR \ :: TyReflect () \ \ SumR \ :: (TyC a, TyC b) =\ TyReflect a -\ TyReflect b -\ TyReflect (Either a b) \ \ ProdR :: (TyC a, TyC b) =\ TyReflect a -\ TyReflect b -\ TyReflect (a, b) This data type provides a concrete, value-level representation of Simplicity types that is tied to the type-level representation of Simplicity types. For each Haskell type corresponding to a Simplicity type, , the type has exactly one value that is built up out of other values of type corresponding to the Simplicity type sub-expression. For example the value of type is . The TyReflect a> produces the value of the GADT that corresponds to the type constrained by the constraint. When users have a Haskell type constrained by they can use to get the corresponding concrete value of the GADT which can then be further processed. The and functions are helper functions for that let you pass types via a proxy. The third way Simplicity types are captured is by the type alias, which is the fixed point of the functor. This is a representation of Simplicity types as a data type. The , , and functions provide smart-constructors that handle the explicit fixed-point constructor. The helps one build memoized functions that consume values. Generally speaking, we use to constrain Haskell types to Simplicity types when creating Simplicity expressions. This way Simplicity type errors are Haskell type errors and can be caught by the Haskell compiler. We use the type when doing computations such as deserializing Simplicity expressions and performing unification for Simplicity's type inference. The GADT links these two representations. For example, the function can test if two Simplicity types are equal or not, and if they are equal then it can unify the Haskell type variables that represent the two Simplicity types. The function turns a value into a value by forgetting about the type parameter. The file also defines the that represents data values of Simplicity's typed, but in an untyped manner. This is mostly used for nodes. There are functions to convert to and from typed and s. Within the directory, there are modules providing data types that are built from Simplicity types. The module provides a type, corresponding to >, and the canonical isomorphism between Haskell's type and . The module provides the type that describes Simplicity types for multi-bit words. Its type parameter is restricted to either be a single word type or a product that doubles the size of a another word type via the GADT. The returns the number of bits a word has, or more generally the number of elements a vector has. The and functions convert values of Simplicity words types to and from Haskell s (modulo the size of the word). The file also provides specializations of these various functions for word sizes between 1 and 512 bits. Terms are represented in tagless-final style. This style is analogous to the \Pfinal\Q representation of terms that is defined in the Coq library. The file develops the core Simplicity term language plus a few extensions. The type class captures Simplicity algebras for core Simplicity expressions. Core Simplicity expressions are represented in Haskell by expressions of type term a b> which are expressions that hold for all Simplicity algebras. This module provides infix operators, \\)> and , for the and Simplicity combinators respectively. It also provides notation for short sequences of string of 's, 's and 's. Note that because is a reserved word in Haskell we use for Simplicity's combinator. Examples of building Simplicity expressions can be found in the next section. This module also provides , , and classes for the failure, witness, and delegation language extensions respectively. Terms that make use of these extension will have these class constraints added to their type signatures. For example, a value of type term a b> is a term in the language of Simplicity with witnesses. This module provides )> and instances of these classes that provide denotational semantics of core Simplicity and some extensions. For example, one can take core Simplicity terms and directly use them as functions. The semantics of depends on the commitment Merkle root; you can find semantics for that extension in and it is discussed in Section. The primary purpose of using tagless-final style is to support transparent sharing of subexpressions in Simplicity. While subexpressions can be shared if we used a GADT to represent Simplicity terms, any recursive function that consumes such a GADT cannot take advantage of that sharing. Sharing results of static analysis between shared sub-expressions is critical to making static analysis practical. Adding explicit sharing to the Simplicity language would make the language more complex and would risk incorrectly implementing the sharing combinator. Explicitly building memoization tables could work, but will have overhead. For instance, we do this when computing Merkle roots of Simplicity types. However, the solution of using tagless-final style lets us write terms in a natural manner and we get sharing for Simplicity expressions at exactly the points where we have sharing in the Haskell representation of the term. The module reexports functionality defined in , which provides instances of Simplicity terms that compute the commitment, identity and annotated Merkle roots. The and return these Merkle root values. The module also provides a memoized computation of the Merkle roots for Simplicity types. The SHA-256 implementation is provided through an abstract interface found in , which in turn references an implementation of a 256-bit word type defined in . The computation differs from > in that it additionally hashes in the input and output types of an expression . This is done so that ensuring the uniqueness of the > and the input and outputs type triples can be effectively done by just comparing the single value. The module provides a typed tensor which allows you to apply multiple interpretations of a Simplicity expression simultaneously. For example, this is used in the construct (see Section) to simultaneously compute a commitment Merkle root alongside another interpretation. The directory contains various developments of Simplicity expressions in Haskell that are independent of any particular blockchain application. The file provides some Simplicity expressions that can apply to any Simplicity type. The function produces a Simplicity expression denoting a constant function for any value for any Simplicity type. The Simplicity expression compares any two values of the same Simplicity type and decides if they are equal or not. The file has Simplicity expressions for bit manipulation. and are Simplicity expressions for the constant functions of those types and provides case analysis combinator for a single bit. There are combinators for various logical operators. These logical operators are short-circuited where possible. There are also a few trinary Boolean Simplicity expressions that are used in hash functions such as SHA-256. The file provides support for vector an multi-bit word expressions that operate on Simplicity's vector and word types. It provides the implementations of logical bit-vector, padding, truncating, shifting and rotating Simplicity expressions. The function provides a generic shift operation that allows shifting in and shifting out an arbitrary word size of bits. The function can perform either left or right shifts, filling in new elements or bits with a provided value. The function can perform either left or right rotates by a constant amount. The combinator takes a Simplicity expression for a binary bit operation and lifts it to a Simplicity expression for a binary operation on arbitrary sized words that performs the bit operation bit-wise. There is also a variant, called the does the same thing for trinary bit operations. The file provides support for arithmetic and number based expressions that operate on Simplicity's word types interpreted as unsigned integers. It provides implementations of the , , , , , , and Simplicity expressions. It also provides implementations of , , , , and . The expression implements the extended euclidean algorithm, which in turn defines , , and expressions. The and expression operate on an interpretation of Simplicity words as signed integers (with returning an unsigned value). The files is a stub module for holding operations for building unbounded loops via the self-delegation method described in Section. At the moment it can be used to build the of an unbounded loop, but the code needed to redeem such a commitment has not been developed yet. The tagless-final style used for Simplicity expressions is designed to perform efficiently for some interpretations of Simplicity when subexpressions are shared. In particular the computation of Merkle roots and serialization (see ) are much faster to compute when subexpressions are shared. However the polymorphism in the tagless-final type used for expression is at odds with subexpression sharing in a naive implementation of Simplicity expressions. In order to realize subexpression sharing between Simplicity expressions, we build libraries of Simplicity expressions as a record type. We use the language extension to bring all function of a library in scope with a single pattern. This approach is similar to \P\Q by . Generating several Simplicity expressions together allows us to share common subexpressions between the different library functions all within a single interpretation. Libraries typically come with some kind of function that given a set library dependencies, constructs an instance of the library of functions. Building a library from a set of dependencies allows us to share dependencies between different libraries when we want to use multiple different libraries. The general approach to using the libraries for your own expressions is to create a clause containing the expression for all the libraries that you want to use and their dependencies that are bound to patterns to bring all the library function into scope. Then you can build your expression using any of the library functions. The file provides a library of Simplicity expressions to help compute SHA-256 hashes. The expression is a constant function the returns the initial value to begin a SHA-256 computation. The expression computes the SHA-256 compression function on a single block of data. To compress multiple blocks, multiple calls to the function can be chained together. This library has no dependencies and you can use the library value directly. The file provides an unpacked module version of the library. However use of this module will lose the subexpression sharing. Therefore this should only be used for testing purposes. The file provides a library of Simplicity expressions that mimic the functional behaviour of the the libsecp256k1 elliptic curve library. This includes Simplicity types for, and operations on secp256k1's underlying finite field, elliptic curve point operations in affine and Jacobian coordinates, and linear combinations of points. This module also include the and expressions that implement Schnorr signatures as specified in BIP-0340. The function builds the library from the its dependency, the SHA-256 library. The value illustrates how to build the library, but using the value will not allow you to share the dependency, so it should only be used for testing purposed. The file provides an unpacked module version of the library. However use of this module will lose the subexpression sharing. Therefore this should only be used for testing purposes. The , while not technically a library, provides a Simplicity program that is similar to the operation of Bitcoin script except with \PUniversal signature hash modes\Q (see Section). \ The combinator uses to pair the commitment root of a given hash mode with its output and produces the message that checks its signature against. The directory has modules related to the Bit Machine and evaluation of Simplicity via the Bit Machine. The file defines , , and , which define the , and functions from Section. They operate on the type. The file also defines variants of these three function that operate on the GADT instead. The file (technically not in the directory) defines the canonical type of a to be a , with the value representing undefined cell values. The and functions transform a value of a Simplicity type to and from a list of s that represent the value. The combinator captures a common pattern of running a Simplicity program through an implementation of the Bit Machine by encoding program inputs and decoding the results. Since there is more than one way to compile and run Simplicity program on the Bit Machine (for example, see naive translation versus TCO translation), this abstraction is used is multiple places. The type alias captures canonical forms of programs for the Bit Machine, which is the explicit fixed point of the functor. Usually programs are built in continuation passing style (analogous to using difference lists to build lists), making use of the type alias. There are smart-constructors for each machine code that make single instruction programs. Programs are composed sequentially using ordinary function composition, . Deterministic choice between two programs is provided by the operator. The program is an alias for the identity function. The file is an implementation of the Bit Machine that follows the formal definition of the Bit Machine and fully tracks undefined values. The type is used for both read frames and write frames. The type is captures the pair of active read and write frames, and the type captures the entire state of the Bit Machine. Lenses are used to access the components of the State. The function interprets in accordance with the semantics of the Bit Machine, and transforms an initial state into a final state (possibly crashing during execution). It is meant to be used, in conjunction with a Simplicity translator, with . The function is a variant of that logs statistics about memory usage during the execution. It is used as part of the testing for static analysis. The file defines the naive translation from Simplicity to the Bit Machine. The type wraps the type with phantom type parameters in order to make an instance suitable to be a Simplicity algebra. The function translates Simplicity terms to via the algebra (recall that a Simplicity term in tagless final form is a polymorphic value that can become any Simplicity algebra). The file provides a similar Simplicity algebra and functions, but this translating using tail composition optimization. \; The file has instances to perform static analysis for bounding the maximum number of cells used by the Bit Machine when executing the naive translation of Simplicity expressions. The type wraps the data needed for the static analysis with phantom type parameters in order to make an instance suitable for a Simplicity Algebra. The function computes the bound on cell use from Simplicity terms via the Algebra. The file provides a similar static analysis that bounds the maximum number of cells used by the Bit Machine when executing the TCO translation of Simplicity expressions. The runs a few of the example Simplicity expressions through the static analysis and compares the result with the maximum cell count of executing the Bit Machine on various inputs. In this file you can see an example of how is used. While Simplicity with assertions expressions can be evaluated directly with the instance, evaluation of sophisticated expressions, such as Schnorr signature verification, can be extremely time and memory consuming. To address this the and files create bindings via and to the C implementation of jets for Simplicity with assertion expressions. The modules provides a that replaces evaluation of subexpressions of Simplicity with assertion expressions that match these jets with optimized implementations. library> To keep the Haskell library of Simplicity modular over different blockchain applications we use the Glasgow Haskell Compiler's Backpack mechanism. The next library, , is found in the directory. The file is a module signature that defines the data types and functions that make up the interface that a blockchain application needs to provide. The remained of the library defines the aspects of Simplicity that are generic over all different Blockchain application through this module signature. This includes the full Simplicity language, including primitives and jets, the semantics of full Simplicity, type inference for full Simplicity expressions, and generic serialization and deserialization of Simplicity expressions. Each different blockchain application needs to provide a module satisfying the signature. At the moment only the Bitcoin blockchain application is provided (see Section). The signature provides an interface to the different possible primitives provided by different blockchain applications. This signature requires <\itemize> , a GADT for primitives, and which are used to generate unique names for the Merkle roots of primitive expressions, , , , , are provide for primitive specific serialization and deserialization operations. and , which provides the type of the context and the denotational semantics for evaluating primitive expressions. The module provides expressions for the blockchain primitives and jet extensions, in addition to re-exporting the module. Discounted jets are characterized by their specification, which consists of a Simplicity expression with assertions and primitives, but not witness nor delegation. Be aware that universal quantifier in the argument means that subexpressions within this specification cannot be shared outside of the specification itself. All the Simplicity extensions are gathered together in the class, whose associated values of type term a b> are terms in the full Simplicity language with delegation. The semantics of full Simplicity is discussed in Section. class> While the class allows any expression to be a jet, in reality there we will have a specific set of known jets that we have accelerated implements of. The defines the class whose instances are types which represent sets of known discounted jets. The method define the specification of discounted jets and the method decides if a given Simplicity expression is known to be substitutable by a some discounted jet. The gives an optional optimized implementation of the jet, which otherwise defaults to that of the . There are also and used for Serialization (see Section) Because the set of discounted jets in use could vary over time, the class allows for different types to represent different sets of discounted jets. You can have a different instance for each version of the set of discounted jets. The module provides an instance which provides semantics for full Simplicity (excluding delegation), where is both a reader monad over and . Semantics for the full Simplicity language with delegation, which depends on computing commitment Merkle roots, is found in the module. The helper type bundles a commitment Merkle root computation with the Simplicity semantics of , allowing commitment Merkle roots and semantics to be evaluated concurrently. This allows us to create and instances using . The is a of for the Kleisli semantics that support the Blockchain primitives, and thus is an instance the class for expressions of full Simplicity with delegation. The function defines the semantics of full Simplicity with delegation by returning a concrete function from and to . The module also provides a function that uses a 's optimized to evaluate subexpressions with known jets. The file defines a concrete term data type for Simplicity expressions in open recursive style via the functor. The parameter allows for these terms to be decorated with type annotations, though nothing in the data type itself enforces that the annotations are well-typed. The traversal provides access to the type annotations. When type annotations are unused, this parameter is set to , as is the case for the functor synonym. The parameter determines the type of data held by nodes. This is usually of the form for some type annotated data structure that represents a type for known jets. The traversal provides access to the jet data. The parameter determines the type of data held by nodes. This is often , but is sometimes a vector or list of s, which may be used in intermediate computations when deserializing Simplicity expressions. The combinator is a traversal indexed by type annotations for accessing this data. While the fixed point of this functor would yield a type for untyped, full Simplicity terms, instead we usually use a list or vector of values to build a DAG structure, where the values are references to other subexpressions within a list or vector. This provides a structure with explicit sharing of subexpressions. This structure is captured by the type synonym. The main functions of this module are the and functions. The normal progression here is to first use the function which discards the type annotations of the input Simplicity DAG (if any) and performs first-order unification to infer new, principle type annotations, with any remaining type variables instantiated at the type. It also adds unification constraints given the input and output types of the intended Simplicity expression provided through the argument. Next one would use to use the inferred type information to decode the witness data into an . Lastly, one would uses the function to type check the inferred type annotations and, if everything is successful, a proper well-typed Simplicity expression of is returned. Note that the one calling specifies the type of the resulting Simplicity expression; it is not inferred from the . The function should never fail after provided the same type constraints in its proxy argument and the witness data has been decoded to an that matches the inferred witness type. There are deserialization functions (see ) that go through this progression of type inference and type checking for you. There are two main methods of serialization found in this Simplicity library. The primary method is serialization via a difference list of s and deserialization via a free monad representation of a binary branching tree. A difference list, represented within the type [Bool]> should be familiar to most Haskell programmers. The same technique is used in the function using the type synonym and is used to avoid quadratic time complexity in some cases of nested appending of lists. A type synonym is defined in . Our free monad representation of binary trees is perhaps less familiar. See Section for details. An alternative serialization method is via the and monads from the package. These are used for serializations to and from . The alternative method is deprecated and will probably be removed. Our free monad representation of binary trees is perhaps less familiar. A binary branching tree with leaves holding values of type can be represented by the free monad over the functor X>, which in Haskell could be written as ) Bool) a> where is from the in the package. \; ) Bool) a>> \; \ In the free monad representation the constructor creates a leaf holding an value while the constructor builds a branch represented as a function BinaryTree a>, which is isomorphic to a pair of binary trees. Given a binary tree (represented as a free monad) we can \Pexecute\Q this monad to produce a value by providing an executable interpretation of each branch. Our interpretation of a branch is to read a bit from a stream of bits and recursively execute either the left branch or the right branch depending on whether we encounter a 0 bit or a 1 bit. This process repeats until we encounter a leaf, after which we halt, returning the value of type held by that leaf. This interpretation captures precisely what it means to use a prefix code to parse a stream of bits. Given a stream of bits we follow branches in a binary tree, left or right, in accordance to the bits that we encounter within the stream until we encounter a leaf, in which case parsing is complete and we have our result, plus a possible remainder of unparsed bits. Where does the stream of bits come from? Well, if we were to interpret this in the state monad, the state would hold a stream of bits. If we were to interpret this the monad, we could grab a stream bits from or from a file handle. In general, we can interpret our free monad in any monad that offers a callback to generate bits for us to consume. \; <\verbatim> runBinaryTree : Monad m =\ m Bool -\ BinaryTree a -\ m a runBinaryTree next = foldFree (\$\ next) \; This ability to interpret a free monad within any other monad is essentially what it means to be a free monad in the first place. This free monad approach to parsing can be extended. For example, suppose when parsing we encounter a prefix that is not a code of any value. We can extend our functor to given a variant to return failure in this case. Thus we build a free monad over the functor 1+X>. In Haskell we could use the type ) Bool))> for this monad or equivalently \; <\verbatim> type BitDecoder a = Free (Sum (Const ()) ((-\) Bool)) a \; runBitDecoder : Monad m =\ m Void -\ m Bool -\ BitDecoder a -\ m a runBitDecoder abort next = foldFree eta \ where \ \ eta (Inl (Const ())) = vacuous abort \ \ eta (Inr f) = f \$\ next \; Our free monad interpreter now requires two callbacks. The callback is as before; it generates bits to be parsed. The callback handles a failure case when the a sequence of bits do not correspond to any coded value. This callback can throw an exception or call , or do whatever is appropriate in case of failure. This implementation of free monads suffers from a similar quadratic complexity issue that lists have. In some cases, nested calls to the free monad's bind operation can have quadratic time complexity. To mitigate this we choose a to use a different representation of free monads. The above interpreters completely characterize their corresponding free monads. Instead of using the type we can directly use the type m Bool -\ m a>. Similarly we can directly use the type m Void -\ m Bool -\ m a> in place of the type with a constraint instead>. This is known as the Van Laarhoven free monad representation and it is what we use in this library. For example, and from the module are decoders a list of bits and positive numbers respectively that use this Van Laarhoven representation of binary trees. Similarly from is a decoder for a 256-bit hash value. In there are several adapter functions for executing these Van Laarhoven free monads within particular monads. <\itemize-dot> evaluates a Van Laarhoven binary tree using a list of bits and returns if all the bits are consumed before decoding is successful. evaluates a Van Laarhoven binary tree using a vector of bits and will return unless the vector is exactly entirely consumed. evaluates a Van Laarhoven bit decoder using a list of bits and returns an if the decoder aborts or the list runs out of bits. evaluates a Van Laarhoven bit decoder within cereal's monad while internally tracking partially consumed bytes. The file provides a that converts Simplicity expressions into a topologically sorted DAG structure with explicit sharing that is suitable for encoding. This conversion <\itemize-dot> finds and shares identical well-typed subexpressions, runs type inference to determine the principle type annotations needed to optimal sharing and pruning of unused witness data, finds subexpressions that matches known jets and replaces them with nodes. \; The file provides and functions that decode and encode a Simplicity expression. The function executes to perform sharing and substitution of jets, and the executes deserialization, type inference and type checking all together. The module also provides, , and , that are used by the and functions to convert between Simplicity DAGs and their serialized representation. The file provides similar and functions for the alternative encoding described in Appendix. The provides also provides a function uses the same substitution mechanism in found in Section > to return a new Simplicity expression that replaces found jets with explicit jets. This substitution can change the commitment root of the overall expression and of subexpressions. Because the commitment root is used in the semantics of , it is even possible for this substitution to change the result of evaluation of expressions. In order to support partial evaluation, the function returns a expression. This result can be unwrapped by the function. The use of lets us share much of the work of substitution in case we want to evaluate the resulting expression with multiple different interpretations. Without we would end up needing to redo the entire substitution for each different interpretation of the resulting expression. Library> To instantiate the library, we need to provide a blockchain specific implementation of the signature. The library provides primitives used for Bitcoin applications. The module implements the signature by providing the primitive expressions and their semantics for Simplicity's Bitcoin application. The GADT enumerates the list of primitive Simplicity expressions for Bitcoin. The provides the context that a Simplicity expression is evaluated within, providing the signed transaction data, the index of the input being considered for redemption, and the commitment Merkle root of the Simplicity program itself. The function is an interpreter for these primitive expressions for the Bitcoin. The module provides the data structures that make up the signed transaction data for Bitcoin. Library> The library assembles all of the previous libraries together. The library is instantiated at all available implementations of the signature, which at the moment is only the module. This Bitcoin instance of the library has its modules reexported under the prefix. Specifically the following modules are reexported: <\itemize-dot> as as as > as as as Some modules build on specific Simplicity blockchain applications. The file provides a library for a signature hash mode for creating a Bitcoin specific transaction digest and a Simplicity program that verifies Schnorr signature over that digest for a given public key. The function hashes the pair of the commitment root of with the output of producing the message that needs to be signed. \ This signature is compatible with using the mode with the program from Section. The file provides an unpacked module version of the library. However use of this module will lose the subexpression sharing. Therefore this should only be used for testing purposes. The file provides similar functionality for the Elements blockchain application. The and provide a canonical of known jets. .> These modules also provide and function that specifically encode and decode this set of jets. Both sets of jets draw upon the module which provides \Pcore\Q jets that are jets that do not depend on any primitives. \ These \Pcore\Q jets include <\itemize> Jets for arithmetic, including 32-bit addition, subtraction and multiplication Jets for hash functions, including the SHA-256 compression function. These modules also reexport specialized instances of and for their specific s. > The directory has a collection of tests for a Simplicity . The file imports the various test modules to build a testing executable to run them all. The has some QuickCheck properties that provide randomized testing for some of the Simplicity expressions developed. The runs a few of the Simplicity expressions through the Bit Machine implementation to test that the value computed by the Bit Machine matches that direct interpretation of the same Simplicity expressions. In this file you can see an example of how is used. The Elements application of Simplicity is based on the Bitcoin application described in Section. The signed transaction data for Elements is similar to Bitcoin's but with added confidential amounts and assets, pegins, and asset issuances. Below we define the record type defining the environment in which Simplicity expressions are evaluated within for the Elements application. <\eqnarray*> |>|>>||>|\<2>>>|>| >|Point>>| X>>>>>|}>>>||>|>>||>|>|>|>|+ExplicitAsset>>||>|>>||>|>|>|>|+ ExplicitAmount>>||>|>>||>|>||>||)>>>>||>||)>>>>||>|<2>>>| AmountWith>>|>>>>>|}>>>||>|ExplicitNonce>>|<2>>>| ConfidentialAmount>>>>>|}>>>||>|>||>|AssetWith>>|AmountWith>>||)>>>>|>>>>>|}>>>||>|Asset>>|Amount>>||)>>>>>>>|}>>>||>||)>>>|Outpoint>>|ElementsUTXO >>|<2>>>|>>||)>>|)> >> prefix|)>>>>||)>>>>>>>|}>>>||>|<2>>>|ElementsSigInput>>|ElementsSigOutput>>|Lock>>>>>|}>>>||>|ElementsSigTx>>|<2>>>|TapEnv>>|<2>>>|<2>>>>>>|}>>>>> \; The Elements protocol imposes limits and other constraints similar to Bitcoin's for transactions to be valid. We will assume that for all transactions the length of the and arrays are less than or equal to >, and the the length of the scriptPubKeys lengths are also less than or equal to >. Also we will assume that for every ELEnv> that |e|\>\|\|>> so that \Pcurrent\Q index being validated is, in fact, an input of the transaction. >The monad we use for the Elements application provides an environment effect (also known as a reader effect) that allows read-access to the value defining the Simplicity program's evaluation context. We call this monad . <\eqnarray*> A>|>|A>>|f>|>|e\ELEnv\f|)>>>>> \; is a commutative, idempotent monad with zero: <\eqnarray*> >>|>|e\ELEnv\\>>>|>>|>|e\ELEnv\\>f\f|)>|)>|)>>>|>>|>|e\ELEnv\\>>>>> \; We define several new primitive expressions for reading data from a value. The language that uses this extension is called . \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\\Lock>>>>>> \; <\with|par-mode|center> |\<2>\|)>|)>>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\<2>\\<2>++<2>|)>|)>|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\<2>\|)>>>>>>> \; <\with|par-mode|center> |\\PubKey>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> \; <\with|par-mode|center> |\\<2>>>>>>> We extend the formal semantics of these new expressions as follows. <\eqnarray*> ||\>>||\>>|>|e\ELEnv\\>|)>>>|||\>>||\>>|>|e\ELEnv\\>|)>>>||>|\>>||\>>|>|e\ELEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\SHA256|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>l\l|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\|)>|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\SHA256|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>l\|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>l\|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>l\|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>\issuanceAssetAmt|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>\issuanceTokenAmt|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>issuanceAssetAmt|)>|i|\>|)>|)>>>||>>|\>>>|>|e\ELEnv\\>issuanceTokenAmt|)>|i|\>|)>|)>>>||>|\>>||\>>|>|e\ELEnv\\>|)>>>||>|\>>|>|e\ELEnv\\>l\ClearAsset|)>|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\ClearAmount|)>|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\SHA256|)>|)>|i|\>|)>|)>>>||>|\>|i,j|\>>|>|e\ELEnv\\>>l\nullDatum|l,|j|\>|\>|)>|)>|i|\>|)>|)>>>|||\>>|>|e\ELEnv\\>l\PrfHash|)>|)>|i|\>|)>|)>>>||>|\>>|>|e\ELEnv\\>l\PrfHash|)>|)>|i|\>|)>|)>>>||>|\>>>|>|e\ELEnv\\>|e,a|\>|)>>>||>|\>||\>>|>|e\ELEnv\\>|)>>>||>|\>>|>|e\ELEnv\\>|i|\>|)>>>||>|\>||\>>|>|e\ELEnv\\>|)>>>||>|\>>||\>>|>|e\ELEnv\\>|)>>>||>|\>>||\>>|>|e\ELEnv\\>|)>>>|||\>>||\>>|>|e\ELEnv\\>|)>|)>>>>> where <\eqnarray*> >|)>>|>||)>>>|>|)>>|>|SHA256|)>>||)>>|>|>>|>|)>>|>||)>>>|>|)>>|>||)>>>>|>|)>>|>|>>>|>|)>>|>||)>>>>|>|)>>|>|>>>|>|)>|)>>|>|>>|>|)>|)>>|>|>>>|>|)>>|>|>>>|>|)>|)>>|>|>>>|>|)>|)>>|>|>>|>|)>>|>|>>>|>|>||)>>>|>|>||)>>>|>|)>>|>|>>|>|)>>|>|>>|>|)>>|>|>>|>|)>>|>||0|\>>>>|>|>||)>>>|>|>||)>>>||\,a|\>>|>||0|\>>>||o\l,a|\>>|>||l,a|\>|+|\>> vwhen o=>and o=>and o=\>>||o\l,a|\>>|>||l,a|\>when o\>or \v\o\>or o\\>>|>|)>>|>||]>>>>>|>>|)>|)>>|>||]>>>\BE>>|>|>,x|\>>|)>|)>>|>||]>>>\BE|)>>>|>|>,x|\>>|)>|)>>|>||]>>>\BE|)>>>||0|\>>|)>>|>||]>>>>>|>|)>>|>||]>>>\BEwhen v\|0|\>>>||>,x|\>>|)>>|>||]>>>\BE|)>>>||>,x|\>>|)>>|>||]>>>\BE|)>>>|>|)>>|>||]>>>>>|>>|)>|)>>|>||]>>>\BE>>|>|>,x|\>>|)>|)>>|>||]>>>\BE|)>>>|>|>,x|\>>|)>|)>>|>||]>>>\BE|)>>>|>|)>>|>||)>|)>>>|>|)>>|>|>>|>|)>>|>||]>>>\|]>>>>>|>>|)>|)>>|>||)>\encAmt|)>\BE|0|\>|)>\BE|)>\encProof|)>|)>\encProof|)>|)>>>|>>|)>|)>>|>||)>\|]>>>\BE|)>\BE|)>\encProof|)>|)>\encProof>|)>>>>> where is defined in the next section and where ElementsSigTx\<2>> follows Element's definition of the transaction ID. An output's scriptPubKey is call a script if it consists of an opcode (|>|\>>) followed by \P\Q, operations, which are operations whose opcode is (96) or less (including (80)). In Elements, pegouts have an instance of a scriptPubKey. For that reason we offer primitives for detecting and parsing scriptPubKeys. Below we define the function <\equation*> nullData\|)>>\\<2>++<2>|)>|)>>|)> which, <\enumerate-numeric> decides if a script is ``'', and if it is push only, returns a list of parsed opcodes in which the pushed data is hashed. We also define <\equation*> nullData\|)>>\\\\<2>++<2>|)>|)>|)> which decides if a script is and returns the parsed element at the given index for the parsed data, if length of the parsed script is long enough. This is used to define the semantics of above. <\eqnarray*> >|)>>|>|>\<2>++<2>|)>>|)>>>|d\l|)>>|>|>r.||0|\>,SHA256|\>>\r|)>|)>|)>when =|n|\>\76>>|l|)>>|>|>when \|n|\>\76>>||76|\>>\n\d\l|)>>|>|>r.||1|\>,SHA256|\>>\r|)>|)>|)>when =|n|\>>>||76|\>\n\l|)>>|>|>when \|n|\>>>||76|\>\\|)>>|>|>>>||77|\>\n\n\d\l|)>>|>|>r.||2|\>,SHA256|\>>\r|)>|)>|)>when =||n,n|\>|\>>>||77|\>\n\n\l|)>>>|>|>when \||n,n|\>|\>>>||77|\>>\l|)>>|>|>when \2>>||78|\>\n\n\n\n\d\l|)>>|>|>r.||3|\>,SHA256|\>>\r|)>|)>|)>when =|||n,n|\>,|n,n|\>|\>|\>>>||78|\>\n\n\n\n\l|)>>|>|>when \|||n,n|\>,|n,n|\>|\>|\>>>||78|\>\l|)>>|>|>when \4>>||79|\>\l|)>>|>|>r.>|)>>|)>>\r|)>|)>|)>>>||80|\>\l|)>>|>|>r.>|)>>|)>>\r|)>|)>|)>>>|l|)>>|>|>r.||x|\>-81|\>>|)>>\r|)>|)>|)>when 81\|x|\>\97>>|l|)>>|>|>when 97\|x|\>>>||>\s,j|\>>|>|l.l|)>|)>>>||x\s,j|\>>|>|>>>>>>>||\,j|\>>|>|>>>>> We extend the definition of the commitment Merkle root to support the new expressions by hashing new unique byte strings. <\eqnarray*> >>|>|>>>>|>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>|>>>|>|>>>>|>>>|>|>>>|>>>|>|>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>>|>|>>>>|>>|>|>>>>|>>|>|>>>>|>>|>|>>>>|>>>|>|>>>>|>>|>|>>>>|>>|>|>>>|>>>>|>|>>>|>>>|>|>>>|>>>|>|>>>|>>>|>|>>>|>>>|>|>>>>> \; where <\equation*> ELprefix\1f5072696d69746976651f456c656d6e74731f]> >>> \; We develop a recommended set of jets and provide an interim encoding. \ An encoding ought to be based on how frequenly jets are used, however we do not currently have good estimates of that. \ As an interim measure we develop a hierarchical encoding of jets by category. The properties for jets listed below may not fully define the jet's semantics. All jets will be formally specified by a Simplicity program that implements their complete semantics. \ Those formal specifications will be found in the Coq library. Implementations MUST implement the COMPLETE specifications as defined in the Coq library. Core Jets> \; The following jets are specified in core Simplicity or Simplicity with assertions, and therefore are applicable to any Simplicity application. Jets for multi-bit logic> It is recommended that jets be supported for multi-bit words up to > in size. : <2>\<2>>> \; >|>\>>\|>\|>> >\<2>\<1>> > \; >>|>\>>\|>\|>\> >>\<1>\<2>>> for n> \; Properties: |bit,i>|>>|\>||\>|)>|\>=0> ||>>|\>||\>|\>>=0> \; Aliases: >>> \ >>\<1>\<2>>> > \; >>|>\>>\|>\|>\> >>\<1>\<2>>> for n> \; Properties: |bit,i>|>>|\>||\>|)>|\>=1> ||>>|\>||\>|\>>=2-1> \; Aliases: >> \ >\<1>\<2>> > \; >>|>\>>\|>\|>\> >> :<2>>\<2>>> for n> \; Properties: |bit,i>|>>|\>|)>|\>=1-|bit,i>|\>> ||>>|\>|\>>=2-1-|x|\>>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>>\<2>>> for n> \; Properties: |bit,i>|>>|\>|x,y|\>|)>|\>=\|bit,i>|\>=1\|bit,i>|\>=1|)>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>>\<2>>> for n> \; Properties: |bit,i>|>>|\>|x,y|\>|)>|\>=\|bit,i>|\>=1\|bit,i>|\>=1|)>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>>\<2>>> for n> \; Properties: |bit,i>|>>|\>|x,y|\>|)>|\>\|bit,i>|\>+|bit,i>|\>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\>\<2>>|)>\<2>>> for n> \; Properties: |bit,i>|>>|\>|x,|y,z|\>|\>|)>|\>=\|bit,i>|\>+|bit,i>|\>+|bit,i>|\>|)>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\>\<2>>|)>\<2>>> for n> \; Properties: |bit,i>|>>|\>|x,|y,z|\>|\>|)>|\>\|bit,i>|\>+|bit,i>|\>+|bit,i>|\>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\>\<2>>|)>\<2>>> for n> \; Properties: |bit,i>|>>|\>|x,|y,z|\>|\>|)>|\>=|bit,i>|\>|)>\|bit,i>|\>+|bit,i>|\>\|bit,i>|\>> > (CAUTION: Not defined when .) >>|>\>>\|>\|>\> >> :<2>>\<2>> for n> \; Properties: ||>>|\>|\>=\|x|\>>\0|)>> \; Aliases: >> \ > \ <2>\<2>> > (CAUTION: Not defined when .) >>|>\>>\|>\|>\> >> :<2>>\<2>> for n> \; Properties: ||>>|\>|\>=\|x|\>>=2-1|)>> \; Aliases: >> \ > \ <2>\<2>> > \; <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>>\<2>> for n> \; Properties: |>>|\>|x,y|\>=\> > \; <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>\<2>>\<2>>> for m\n> \; Properties: ,i>|>,2>|\>|x,y|\>|)>|)>=bit,i>> for i\2> ,i>|>,2>|\>|x,y|\>|)>|)>=bit,2+i>> for i\2-2> ,2-2+i>|>,2>|\>|x,y|\>|)>|)>=bit,i>> for i\2> \; Aliases: >,2> \ > :<2>>\<2>>\<2>>\<2>>> >,2> \>,2>:<2>>\<2>>\<2>>\<2>>> when n\m> >,2> \>,2> :<2>>\<2>>\<2>>\<2>>> when n\m> > \; <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>\<2>>\<2>>> for m\n> \; Properties: ,i>|>,2>|\>|x,y|\>|)>|)>=bit> for i\2> ,2+i>|>,2>|\>|x,y|\>|)>|)>=bit,i>> for i\2-2> ,i>|>,2>|\>|x,y|\>|)>|)>=bit,2-2+i>> for i\2> \; Aliases: >,2> \ > :<2>>\<2>>\<2>>\<2>>> >,2> \>,2> :<2>>\<2>>\<2>>\<2>>> when n\m> >,2> \>,2>:<2>>\<2>>\<2>>\<2>>> when n\m> > \; <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for m\n> \; Properties: ,i>|>,2>|\>|)>=bit,i>> \; Aliases: >,2> \ > :<2>>\<2>>> > \; <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for m\n> \; Properties: ,i>|>,2>|\>|)>=bit,2-2+i>> ||>,2>|\>|\>>=|x|\>> |)>> \; Aliases: >,2> \ > :<2>>\<2>>> > (Note: derived from .) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for n\m> \; Properties: |bit,i>|>,2>|\>|)>|\>=0> when 2-2> ,2-2+i>|>,2>|\>|)>=bit,i>> when 2> ||>,2>|\>|\>>=|x|\>>> > (Note: derived from .) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for n\m> \; Properties: |bit,i>|>,2>|\>|)>|\>=1> when 2-2> ,2-2+i>|>,2>|\>|)>=bit,i>> when 2> > (Note: derived from , and .) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for n\m> \; Properties: ,i>|>,2>|\>|)>=bit,0>> when 2-2> ,2-2+i>|>,2>|\>|)>=bit,i>> when 2> \; Aliases: >>\>> :<2>\<2>>> for n\m> > (Note: derived from .) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for n\m> \; Properties: ,i>|>,2>|\>|)>=bit,i>> when 2> |bit,i>|>,2>|\>|)>|\>=0> when \i\2> > (Note: derived from .) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for n\m> \; Properties: ,i>|>,2>|\>|)>=bit,i>> when 2> |bit,i>|>,2>|\>|)>|\>=1> when \i\2> > (Note: derived from , , and .) (CAUTION: Not defined when .) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>>\<2>>> for n\m>\ Properties: ,i>|>,2>|\>|)>=bit,i>> when 2> |bit,i>|>,2>|\>|)>|\>=bit,2-1>> when \i\2> \; Aliases: >>\>> :<2>\<2>>> for n\m> > Left shift by a given amount. Bits are filled with the provided value. \; <\math> >>|>\>>\|>\|>\ >> :<2>\|lb|\>>>\<2>>|)>\<2>>> for n> > Right shift by a given amount. Bits are filled with the provided value. <\math> >>|>\>>\|>\|>\ >> :<2>\|lb|\>>>\<2>>|)>\<2>>> for n> > Left shift by a given amount. Bits are filled with 0 bits. <\math> >>|>\>>\|>\|>\ >> :<2>|lb|\>>>\<2>>\<2>>> for n> > Right shift by a given amount. Bits are filled with 0 bits. <\math> >>|>\>>\|>\|>\ >> :<2>|lb|\>>>\<2>>\<2>>> for n> > Right rotate by an amount. <\math> >>|>\>>\|>\|>\ >> :<2>|lb|\>>>\<2>>\<2>>> for n> \; Aliases: >> \ > \ <1>\<2>\<2>> > Right rotate by an amount. <\math> >>|>\>>\|>\|>\ >> :<2>|lb|\>>>\<2>>\<2>>> for n> \; Aliases: >> \ > \ <1>\<2>\<2>> <\with|color|red> (NOT IMPLEMENTED)> (CAUTION: Not defined when or .) (Note: Support only recommended up to \2\256>.) <\math> >,2>|>\>>\|>\|>\\ >,2> :<2>\2>\<2>\2>> for n> and m> \; Aliases: >> \ > :<2>>\<2>>> >,1> \ > :<2>>\<2>>> (NOT IMPLEMENTED)> (CAUTION: Not defined when .) <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>|lb|\>>>> for n> (NOT IMPLEMENTED)> (CAUTION: Not defined when .) <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>|lb|\>>>> for n> (NOT IMPLEMENTED)> (CAUTION: Not defined when 1>.) <\math> >>|>\>>\|>\|>\ >> :<2>|lb|\>>>\<2>>\<2>> for n> \; Aliases: >> \ > \ <1>\<2>\<2>> >> \ > \ <2>\<2>\<2>> Jets for arithmetic> > (CAUTION: Not defined when . See Aliases.) >>|>\>>\|>\|>\> >>\<1>\<2>>> for n> \; Properties: |bit,i>|>>|\>|)>|\>=0> when i\2-1> |bit,2-1>|>>|\>|)>|\>=1> ||>>|\>||\>|\>>=1> \; Aliases: >> \ >\<1>\<2>> > (Note: >> is composed from and .) >>|>\>>\|>\|>\> >> :<2>\>\<2>>|)>\<2>\<2>>> for n> \; Properties: ||>>|\>|c,|x,y|\>|\>|\>>=|x|\>>+|y|\>>+|c|\>> > \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|x,y|\>|\>>=|x|\>>+|y|\>>> \; Aliases: >> \ > :<2>\<2>> > (CAUTION: Not defined when . See Aliases.) >>|>\>>\|>\|>\> >> :<2>\<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|c,x|\>|\>>=|x|\>>+|c|\>> > \; >>|>\>>\|>\|>\> >> :<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|\>>=|x|\>>+1> <\with|color|red> (NOT IMPLEMENTED)> (CAUTION: Not defined when 1>.) <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>|lb|\>>>> for n> \; Properties: ||>>|\>|\>|lb|\>>>=-1>|bit,i>|\>> \; Aliases: > \ > :<2>\<2>> >> \ > :<2>\<2>> > (Note: composition of with applied to 1st and 3rd arguments). >>|>\>>\|>\|>\> >> :<2>\>\<2>>|)>\<2>\<2>>> for n> \; Properties: ||>>|\>|c,|x,y|\>|\>|\>>\|x|\>>-|y|\>>-|c|\>+1>|)>> > \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|x,y|\>|\>>\|x|\>>-|y|\>>+1>|)>> > (CAUTION: Not defined when .) >>|>\>>\|>\|>\> >> :<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|\>>\-|x|\>> +1>|)>> > \; >>|>\>>\|>\|>\> >> :<2>\<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|c,x|\>|\>>\|x|\>>-|c|\>+1>|)>> > \; >>|>\>>\|>\|>\> >> :<2>>\<2>\<2>>> for n> \; Properties: ||>>|\>|\>>\|x|\>>-1+1>|)>> > (Note: >> is composed from >> and .) >>|>\>>\|>\|>\> >> :>\<2>>|)>\>\<2>>|)>\<2>>> for n> \; Properties: ||>>|\>||c,c|\>,|x,y|\>|\>|\>>=|x|\>>\|y|\>>+|c|\>>+|c|\>>> > \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> \; Properties: ||>>|\>|x,y|\>|\>>=|x|\>>\|y|\>>> > (CAUTION: Not defined when . See Aliases.) (Note: of ). >>|>\>>\|>\|>\> \; Properties: ||>>|\>|\>=\|x|\>>=0|)>> > (CAUTION: Not defined when . See Aliases.) >>|>\>>\|>\|>\> \; Properties: ||>>|\>|\>=\|x|\>>=1|)>> (unsigned)> (Note: borrow bit from ) >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>> for n> \; Properties: ||>>|\>|x,y|\>|\>=\|x|\>>\|y|\>>|)>> (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>> for n> \; Properties: ||>>|\>|x,y|\>|\>=\|x|\>>\|y|\>>|)>> (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> \; Properties: ||>>|\>|x,y|\>|\>>> if and only if |x|\>>> and |y|\>>> \; Aliases: > \ > :<2>\<2>\<2>> (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> \; Properties: ||>>|\>|x,y|\>|\>>\z> if and only if |x|\>>\z> and |y|\>>\z> \; Aliases: > \ > :<2>\<2>\<2>> (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\>\<2>>|)>\<2>>> for n> \; Properties: ||>>|\>|x,x|\>|\>>\||>>|\>|x,|x,x|\>|\>|\>>\||>>|\>|x,x|\>|\>>> for all i\j\3>. \; Aliases: > \ > :<2>\\<2>|)>\<2>> \; > (Note: helper function for . See by Bunikel and Ziegler (1998).) >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>\<2>>> for n> \; Properties: When \|y|\>> >and|x|\>>\2\|y|\>>>, <\enumerate-alpha> |y|\>>\|\|>>|\>|x,y|\>|)>|\>>=|x|\>>-|\|>>|\>|x,y|\>|)>|\>>>, and |\|>>|\>|x,y|\>|)>|\>>\|y|\>>>. \; When \|y|\>> >or|x|\>>\2\|y|\>>>, then ,i>|>>|\>|x,y|\>|)>=1>. \; (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>\<2>>> for n> \; Properties: |y|\>>\|\|>>|\>|x,y|\>|)>|\>>=|x|\>>-|\|>>|\>|x,y|\>|)>|\>>> \; For all \> such that |y|\>>\||x|\>>-r> we have|\|>>|\>|x,y|\>|)>|\>>\r>. (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> (unsigned)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>> for n> \; Properties: ||>>|\>|x,y|\>|\>=\|x|\>>\||y|\>>|)>> <\with|color|red> (unsigned) (NOT IMPLEMENTED)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\>\<2>>|)>+>\<2>>|)>|)>\>\<2>>|)>|)>\<2>>> for n> \; Properties: Let ||b,|c,c|\>|\>,d|\>\|>>|\>|x,y|\>> \; |c|\>>*|d|\>>=|x|\>>> |c|\>>*|d|\>>=|y|\>>> \; If |s,t|\>>=b> then |s|\>>*|x|\>>-|t|\>>*|y|\>>=|d|\>>> and either |s|\>>*\|c|\>>|2>> or |t|\>>*\|c|\>>|2>>. If |s,t|\>>=b> then |s|\>>*|x|\>>-|t|\>>*|y|\>>=-|d|\>>> and either |s|\>>*\|c|\>>|2>> or |t|\>>*\|c|\>>|2>.> \; |>>|\>||x|\>,|x|\>|\>=||||1|\>,|0|\>|\>>,||1|\>,|1|\>|\>|\>,|x|\>|\>>. (unsigned) (NOT IMPLEMENTED)> (CAUTION: Not defined when 1>.) >>|>\>>\|>\|>\> >> :<2>>\<2>>\>\<2>>|)>+>\<2>>|)>> for n> (unsigned) (NOT IMPLEMENTED)> (CAUTION: Not defined when 1>.) >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> (unsigned)(NOT IMPLEMENTED)> (CAUTION: Not defined when 1>.) >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>\<2>>> for n> (unsigned) (NOT IMPLEMENTED)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>>> for n> (unsigned) (NOT IMPLEMENTED)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>> for n> (signed input/unsigned output) (NOT IMPLEMENTED)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>> for n> (NOT IMPLEMENTED)> (CAUTION: Not defined when . See Aliases.) <\math> >>|>\>>\|>\|>\ >> :<2>>\<2>> for n> \; Properties: |>>|\>=||>>|\>,|>>|\>|\>> (NOT IMPLEMENTED)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>> for n> (NOT IMPLEMENTED)> \; >>|>\>>\|>\|>\> >> :<2>>\<2>>\<2>> for n> (NOT IMPLEMENTED)> (NOT IMPLEMENTED)> (NOT IMPLEMENTED)> (NOT IMPLEMENTED)> Right shift by a signed amount with sign extension. Negative values are a left shift. (unsigned denominator) (NOT IMPLEMENTED)> (unsigned denominator) (NOT IMPLEMENTED)> (signed denominator) (NOT IMPLEMENTED)> (signed denominator) (NOT IMPLEMENTED)> \; Jets for hash functions> Jets for SHA-2> In this section we define |)>64>\\<2>|)>>. This represent a type of SHA-256 contexts for hashing variable length byte strings. The first component is a buffer of bytes representing a partial block. \ The second component is the number of times the compression function has been invoked. \ The third component is the SHA-256 midstate of compressed data so for (excluding the data in the partial block). Note that SHA-256 only allows the compression counter to be less than >. \ The jets below will fail if the compression counter is > or larger, or if executing the function would cause the counter to become > or larger. \; > \; >|>\>>\|>\|>\|>> > :<2>\<2>\<2>> \; > \; >|>\>>\|>\|>\|>> <\math> > :<1>\<2> \; > \; >>|>\>>\|>\|>\|>>> <\math> >> :Ctx8\|)>>\Ctx8 \; > \; >|>\>>\|>\|>\|>> <\math> > :Ctx8\|)>512>\Ctx8 \; > \; >|>\>>\|>\|>\|>> <\math> > :Ctx8\<2> \; > \; >|>\>>\|>\|>\|>> <\math> > :<1>\Ctx8 <\with|color|red> Jets for SHA-3 (NOT IMPLEMENTED)> In this section we define \X\X> and \|)>|)>>. \; > \; <\math> >|>\>>\|>\|>\|> > :<1>\<2>> \; > (Note: we should probably byte-stwap the input before xoring it into place <\math> >|>\>>\|>\|>\|>\\ >:<2>\<2>\<2>> for n,m\5> \; > \; <\math> >|>\>>\|>\|>\|> > :<2>\<2>\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:<2>\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:<2>\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:<2>\<2>> Jets for RIPEMD (NOT IMPLEMENTED)> Jets for SHA-1 (RESERVED) (NOT IMPLEMENTED)> Jets for elliptic curve functions> Jets for secp256k1> In this section we define <2>>, \<2>\<2>>, <2>>, FE\FE>, and GE\FE>, <2>\FE>. (Note: To convert GE to GEJ pair with ). FE and Scalar inputs yield outputs.> \; > (Note: Support only recommended up to \>.) <\math> >>|>\>>\|>\|>\|>\ >>:Point|)>>\Scalar|)>\Point\<1>> for n> \; > \; <\math> >|>\>>\|>\|>\|>\ >:Point\> for n> \; > (Note: Support only recommended up to \>.) <\math> >>|>\>>\|>\|>\|>\ >>:GE|)>>\Scalar|)>\GE\<1>> for n> \; > (Note: Support only recommended up to \>.) <\math> >>|>\>>\|>\|>\|>\ >>:GEJ|)>>\Scalar\GEJ> for n> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\GEJ\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:<1>\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GE\GE> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\GEJ\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\GE\FE\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\GE\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\FE\GEJ> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\<2>> \; > <\math> >|>\>>\|>\|>\|> >:GEJ\GEJ\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\GE\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\GEJ\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:GEJ\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:GE\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:Scalar\<2>> \; <\with|color|red> (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:GE\GE> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:GEJ\GEJ> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:Scalar\<2>\<2>> \; TODO Properties: \|\|>|\>|)>|\>>+|\|>|\>|)>|\>>\|x|\>>> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:<2>\Scalar> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> gi>:FE\FE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\<2>> \; <\with|color|red> (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:FE\<2>> \; > \; <\math> >|>\>>\|>\|>\|> >:<2>\GE> \; > \; <\math> >|>\>>\|>\|>\|> >:FE\GE> \; Jets for digital signatures> Jets for secp256k1 based digital signatures> In this section we define <2>>, <2>>. \; > (Note: this jet can fail.) <\math> >|>\>>\|>\|>\|> >:<2>|)>\Signature\<1>> \; > (Note: this jet can fail.) <\math> >|>\>>\|>\|>\|> >:<2>|)>\Signature\<1>> \; <\with|color|red> (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:<1>\<2>> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> <\math> >:FE\Pubkey\<2> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:Signature\Scalar|)>> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:Pubkey\> \; (NOT IMPLEMENTED)> \; <\math> >|>\>>\|>\|>\|> >:Pubkey\> \; (NOT IMPLEMENTED)> \; <\with|color|red> Jets for Simplicity (NOT IMPLEMENTED)> Tagged hash IVs for basic simplicity combinators, signature hashes, etc. The CMR of various expressions for constants. \; These would be use for Simplicity covenants. Jets for tagged hash IVs> > > > > > > > > > > > > > \; <\math> >|>\>>\|>\|>\|> >:<1>\<2>> \; > Jets for Bitcoin (without primitives)> This section is not recommended for non-Bitcoin(-like) applications. > (Note: |>|\>|0|\>\>>) >|>\>>\|>\|>> > :<2>\<2>+<2>> > \; >|>\>>\|>\|>> > :<2>\+<2>|)>> > \; >|>\>>\|>\|>> > :<1>\Ctx8> \; Creates a Sha256 context initialized with a \PTapData\Q tag. Bitcoin Jets> <\itemize> >\<1>\<2>> >\<1>\<2>> (anyone can pay) >\Index\<2>\<2>> (anyone can pay) In this section we define <2>>, <2>>, <2>>, and >. > \; >|>\>>\|>\|>> >> :Height\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> '>> :Time\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> '>> :Distance\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> '>> :Duration\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> >> :<1>\Height> \; Returns when returns >> and |>|\>\|>|\>> returns >>. Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\Time> \; Returns when returns >> and |>|\>\|>|\>> returns >>. Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\Distance> \; When ||>|\>||\>|\>>>>, returns the greatest of values >|)>> returned by |>|\>\|>|\>|)>> for any input , if there are any. \ Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\Duration> \; When ||>|\>||\>|\>>>>, returns the greatest of values \>|)> returned by |>|\>\|>|\>|)>> for any input , if there are any. \ Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\<2>> \; Returns >> when all the sequence numbers of the transaction inputs are at their maximum value. Otherwise returns >>. > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \PubKey> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \Lock> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \Outpoint> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \|)>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ <2>\> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ \<2>> \; Elements Jets> > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (32 bytes). The result of again (32 bytes). The result of (32 bytes). The result of (32 bytes). The result of (Note: this is in big endian format) (4 bytes). \; Note: the two copies of the values effectively makes this result a BIP-340 style tagged hash. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (Note: this is in big endian format) (4 bytes). The result of (Note: this is in big endian format) (4 bytes). The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). \; Note: the result of is specifically excluded because surjection proofs are dependent on the inputs as well as the output. See also . > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). The result of (32 bytes). > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The result of (32 bytes). The result of (32 bytes). > \; >|>\>>\|>\|>> >> :<2>\|)>> \; If the input value is a valid output index, then >> >returns >> of the SHA256 hash of the following: <\itemize-dot> The serialization of the output's asset and amount fields. The serialization of the output's nonce field. The SHA256 hash of the output's scriptPubKey. The SHA256 hash of the output's range proof.. Otherwise if the input value is not a valid output index then >> >returns >>. \; Note: the result of is specifically excluded because surjection proofs are dependent on the inputs as well as the output. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the serialization of each output's asset and amount fields. \; > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the concatenation of the SHA256 hash of each output's scriptPubKey. \; > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the serialization of each output's nonce field. \; > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the concatenation of the SHA256 hash of each output's range proof. \; Note that if the output's amount is explicit then the range proof is considered the empty string. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the concatenation of the SHA256 hash of each output's surjection proof. \; Note that if the output's asset is explicit then the surjection proof is considered the empty string. > \; >|>\>>\|>\|>> >> :<2>\|)>> \; If the input value is a valid input index, then >> >returns >> of the SHA256 hash of the following: <\itemize-dot> If the input is not a pegin, then the byte . If the input is a pegin, then the byte followed by the parent chain's genesis hash (32 bytes). The input's serialized previous transaction id (32 bytes). The input's previous transaction index in big endian format (4 bytes). The inputs sequence number in big endian format (4 bytes). If the input has no annex, or isn't a taproot spend, then the byte . If the input has an annex, then the byte followed by a SHA256 hash of the annex (32 bytes). Otherwise if the input value is not a valid input index then >> >returns >>. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> If the input is not a pegin, then the byte . If the input is a pegin, then the byte followed by the parent chain's genesis hash (32 bytes). The input's serialized previous transaction id (32 bytes). The input's previous transaction index in big endian format (4 bytes). \; IMPORTANT: the index is serialized in big endian format rather than little endian format. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> The inputs sequence number in big endian format (4 bytes). \; IMPORTANT, the sequence number is serialized in big endian format rather than little endian format. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> If the input has no annex, or isn't a taproot spend, then the byte . If the input has an annex, then the byte followed by a SHA256 hash of the annex (32 bytes). > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the concatenation of the SHA256 hash of each input's scriptSig. \; Note that if an input's UTXO uses segwit, then it's scriptSig will necessarily be the empty string. \ In such cases we still use the SHA256 hash of the empty string. > \; >|>\>>\|>\|>> >> :<2>\|)>> \; If the input value is a valid input index, then > returns >> of the SHA256 hash of the following: <\enumerate> The asset issuance: <\itemize-dot> If the input has no issuance then two bytes . If the input is has a new issuance then the byte followed by a serialization of the calculated issued asset id (32 bytes) followed by the serialization of the (possibly confidential) issued asset amount (9 bytes or 33 bytes). If the input is has a reissuance then the byte followed by a serialization of the issued asset id (32 bytes), followed by the serialization of the (possibly confidential) issued asset amount (9 bytes or 33 bytes). The token issuance: <\itemize-dot> If the input has no issuance then another two bytes . If the input is has a new issuance then the byte followed by a serialization of the calculated issued token id (32 bytes) followed by the serialization of the (possibly confidential) issued token amount (9 bytes or 33 bytes). If the input is has a reissuance then the byte followed by a serialization of the issued token id (32 bytes), followed by the serialization of the explicit 0 amount (i.e ) \ (9 bytes). The range proofs: <\itemize-dot> The SHA256 hash of the range proof of the input's issuance asset amount (32 bytes). The SHA256 hash of the range proof of the input's issuance token amount (32 bytes). These will be the hashes of the empty proof in case there is no issuance. The blinding entropy: <\itemize-dot> If the input has no issuance then another byte. If the input is has a new issuance then the byte followed by 32 bytes and the new issuance's contract hash field (32 bytes). If the input is has reissuance then the byte followed by a serializaiton of the reissuance's blinding nonce field (32 bytes) and the reissuance's entropy field (32 bytes). Otherwise if the input value is not a valid input index then >>> returns >>. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> If the input has no issuance then two bytes . If the input is has a new issuance then the byte followed by a serialization of the calculated issued asset id (32 bytes) followed by the serialization of the (possibly confidential) issued asset amount (9 bytes or 33 bytes). If the input is has a reissuance then the byte followed by a serialization of the issued asset id (32 bytes), followed by the serialization of the (possibly confidential) issued asset amount (9 bytes or 33 bytes). \; IMPORTANT: If there is an issuance but there are no asset issued (i.e. the amount is null) we serialize the vase as the explicit 0 amount, (i.e. ). \; Note, the issuance asset id is serialized in the same format as an explicit asset id would be. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> If the input has no issuance then two bytes . If the input is has a new issuance then the byte followed by a serialization of the calculated issued token id (32 bytes) followed by the serialization of the (possibly confidential) issued token amount (9 bytes or 33 bytes). If the input is has a reissuance then the byte followed by a serialization of the issued token id (32 bytes), followed by the serialization of the explicit 0 amount (i.e ) \ (9 bytes). \; IMPORTANT: If there is an issuance but there are no tokens issued (i.e. the amount is null) we serialize the vase as the explicit 0 amount, (i.e. ). \; Note, the issuance token id is serialized in the same format as an explicit asset id would be. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> The SHA256 hash of the range proof of the input's issuance asset amount (32 bytes). The SHA256 hash of the range proof of the input's issuance token amount (32 bytes). Note that each the range proof is considered to be the empty string in the case there is no issuance, or if the asset or token amount doesn't exist (i.e is null). The SHA256 hash of the empty string is still used in these cases. \; > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the concatenation of the following for every input. <\itemize-dot> If the input has no issuance then the byte . If the input is has a new issuance then the byte followed by 32 bytes and the new issuance's contract hash field (32 bytes). If the input is has reissuance then the byte followed by a serializaiton of the reissuance's blinding nonce field (32 bytes) and the reissuance's entropy field (32 bytes). \; Note that if the issuance is a new issuance then the blinding nonce field is 32 bytes and new issuance's contract hash > \; >|>\>>\|>\|>> >> :<2>\|)>> \; If the input value is a valid input index, then >> >returns >> of the SHA256 hash of the following: <\itemize-dot> The serialization of the input UTXO's asset and amount fields. The SHA256 hash of the input UTXO's scriptPubKey. Otherwise if the input value is not a valid input index then >> >returns >>. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the serialization of each input UTXO's asset and amount fields. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns the SHA256 hash of the concatenation of the SHA256 hash of each input UTXO's scriptPubKey. \; > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a SHA256 hash of the following: <\itemize-dot> The hash of the ASCII string (32 bytes). The hash of the ASCII string again (32 bytes). The result of (1 byte). The byte (1 byte). The result of (32 bytes). \; Note: this matches Element's modified BIP-0341 definition of tapleaf hash. > \; >|>\>>\|>\|>> >> :<1>\<2>> \; Returns a hash of the current input's control block excluding the leaf version and the taproot internal key. \ Using the notation of BIP-0341, it returns the SHA256 hash of >. > \; >|>\>>\|>\|>> <\math> >> :Ctx8\|)>\Outpoint|)>\Ctx8 \; Continues a SHA256 hash with an optional pegin and an outpoint by appending the following: <\itemize-dot> If the input is not a pegin, then the byte . If the input is a pegin, then the byte followed by the given parent genesis hash (32 bytes). The input's previous transaction id (32 bytes). The input's previous transaction index in big endian format (4 bytes). > \; >|>\>>\|>\|>> <\math> >> :Ctx8\Amount|)>\Ctx8 \; Continues a SHA256 hash with the serialization of a confidential asset followed by the serialization of a confidential amount. > \; <\math> >|>\>>\|>\|> <\math> >> :Ctx8\|)>\Ctx8 \; Continues a SHA256 hash with the serialization of an optional nonce. > \; <\math> >|>\>>\|>\|> <\math> >> :Ctx8\|)>|)>\Ctx8 \; Continues a SHA256 hash with an optional hash by appending the following: <\itemize-dot> If there is no hash, then the byte . If there is a hash, then the byte followed by the given hash (32 bytes). > \; <\math> >|>\>>\|>\|> <\math> >> :<2>\<2> \; Returns a SHA256 hash of the following: <\itemize-dot> The hash of the ASCII string (32 bytes). The hash of the ASCII string again (32 bytes). The byte (1 byte) for the Simplicity tapleaf version number. The byte (1 byte). The input (32 bytes) which should be the CMR of a Simplicity program. > \; <\math> >|>\>>\|>\|> <\math> >> :<2>\<2>\<2> \; Returns a SHA256 hash of the following: <\itemize-dot> The hash of the ASCII string (32 bytes). The hash of the ASCII string again (32 bytes). The lexicographically smaller of the two inputs (32 bytes). The lexicographically larger of the two inputs (32 bytes). This builds a taproot from two branches. > \; <\math> >|>\>>\|>\|> <\math> >> :Pubkey\<2>\<2> \; This implements > from BIP-0341. Note that this jet can fail in the following situations: <\enumerate> The input x-only public key is off curve or exceeds the field size. The internal hash value exceeds the secp256k1 group order. The generated tweaked point is infinity, and thus has no valid x-only public key. Note that situations 2 and 3 are cryptographically impossible to occur. In this section we define <2>>, <2>>, <2>>, and >. > \; >|>\>>\|>\|>> >> :Height\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> '>> :Time\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> '>> :Distance\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> '>> :Duration\<1>> \; Asserts that the value returned by is greater than or equal to the input. > \; >|>\>>\|>\|>> >> :<1>\Height> \; Returns when returns >> and |>|\>\|>|\>> returns >>. Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\Time> \; Returns when returns >> and |>|\>\|>|\>> returns >>. Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\Distance> \; When ||>|\>||\>|\>>>>, returns the greatest of values >|)>> returned by |>|\>\|>|\>|)>> for any input , if there are any. \ Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\Duration> \; When ||>|\>||\>|\>>>>, returns the greatest of values \>|)> returned by |>|\>\|>|\>|)>> for any input , if there are any. \ Otherwise returns |0|\>>. > \; >|>\>>\|>\|>> '>> :<1>\<2>> \; Returns >> when all the sequence numbers of the transaction inputs are at their maximum value. Otherwise returns >>. > \; >|>\>>\|>\|>> > :Index\|)>|)>> \; Returns >|)>|)>> when the given input has a new issuance. Returns >|)>|)>> when the given input has a reissuance. Returns |)>> when the given input has no issuance. Otherwise returns > when there is no input of the given index. > \; >|>\>>\|>\|>> > :Index\|)>> \; Returns |)>> when the given input has an issuance with asset ID . Returns |)>> when the given input has no issuance. Otherwise returns > when there is no input of the given index. > \; >|>\>>\|>\|>> > :Index\|)>> \; Returns |)>> when the given input has an issuance with reissuance token ID . Returns |)>> when the given input has no issuance. Otherwise returns > when there is no input of the given index. > \; >|>\>>\|>\|>> > :Index\|)>|)>> \; Returns |)>> when the given input has an reissuance with entropy , or if there is a new issuance whose computed entropy is . Returns |)>> when the given input has no issuance. Otherwise returns > when there is no input of the given index. > \; >|>\>>\|>\|>> > :Outpoint\<2>\<2>> \; Calculate the entropy value from a given ouptoint and contract hash. \ This entropy value is used to compute issued asset and token IDs (see below). > \; >|>\>>\|>\|>> > :<2>\ExplicitAsset> \; Calculate the issued asset id from a given entropy value. > \; >|>\>>\|>\|>> > :<2>\ExplicitAsset> \; Calculate the reissuance token id from a given entropy value for assets with explicit issued amounts. > \; >|>\>>\|>\|>> > :<2>\ExplicitAsset> \; Calculate the reissuance token id from a given entropy value for assets with confidential issued amounts. > \; >|>\>>\|>\|>> > :\ExplicitAsset> \; Returns the asset for liquid BTC. > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \PubKey> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \Lock> > \; >|>\>>\|>\|>> > \ <2>\> > \; >|>\>>\|>\|>> > \ <2>\Amount|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\<2>\\<2>++<2>|)>|)>|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ ExplicitAsset\ExplicitAmount> > \; >|>\>>\|>\|>> > \ \|)>> > \; >|>\>>\|>\|>> > \ \Outpoint> > \; >|>\>>\|>\|>> > \ \Asset> > \; >|>\>>\|>\|>> > \ \Asset\Amount> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \|)>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \> > \; >|>\>>\|>\|>> > \ \|)>> > \; >|>\>>\|>\|>> > \ \|)>> > \; >|>\>>\|>\|>> > \ \> > \; >|>\>>\|>\|>> > \ \> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ <2>\|)>|)>> > \; >|>\>>\|>\|>> > \ <2>\> > \; >|>\>>\|>\|>> > \ <2>\> > \; >|>\>>\|>\|>> > \ <2>\Amount|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ <2>\|)>> \; > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ <2>\|)>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> > \; >|>\>>\|>\|>> > \ \<2>> This appendix presents an alternative, byte-oriented prefix code for Simplicity DAGs. This code is not as compact as the bit-oriented code presented in Section and it imposes some arbitrary limits on the size of the DAG and witness values. Its only advantage is that it might be faster to decode. This code probably should not be used by any application and maybe should be removed from this report. First we define a byte-string serialization for numbers known to be less than a bound by determining the minimum number of bytes needed to fit a number less than . <\eqnarray*> >|>|>>>|>|>|,q|)>\BE|i|\>|)>where 2*q\i\2 and 2\b\2> and i\b>>>> \; For witness data, which is a bit-string, we group the bits into bytes to form a byte-string, padding the least significant bits with zero bits. <\eqnarray*> |)>>|>|>>>|\b\b\b\b\b\b\b\v|)>>|>||||b,b|\>,|b,b|\>|\>,||b,b|\>,|b,b|\>|\>|\>\bytePad>>|>|>|>>|)>when 0\\8>>>> Note that by itself is not a prefix code and forgets how many bits where in the vector. Both issues are addressed by prefixing this encoding with the length of the number of bits in the original bit-string. Next we define a byte-string serialization for Node, \\Node\|)>>>. The first parameter to , , is the index at which the Node occurs in the Dag. It is used to determine the bound on the size of the sub-expression offsets for serialization of those values. <\eqnarray*> > 1 1|)>>|||]>>>>>|> 1 1|)>>|||]>>>>>|> 1 1|)>>|||]>>>>>|> 1 1|)>>|||]>>>>>|> 1 j|)>>|||]>>>\byteCodewhere 1\j>>|> 1 j|)>>|||]>>>\byteCodewhere 1\j>>|> 1 j|)>>|||]>>>\byteCodewhere 1\j>>|> 1 j|)>>|||]>>>\byteCodewhere 1\j>>|> i 1|)>>|=||]>>>\byteCodewhere 1\i>>|> i 1|)>>|||]>>>\byteCodewhere 1\i>>|> i 1|)>>|||]>>>\byteCodewhere 1\i>>|> i 1|)>>|||]>>>\byteCodewhere 1\i>>|> i j|)>>|||]>>>\byteCode\byteCodewhere 1\i and 1\j>>|> i j|)>>|||]>>>\byteCode\byteCodewhere 1\i and 1\j>>|> i j|)>>|||]>>>\byteCode\byteCodewhere 1\i and 1\j>>|> i j|)>>|||]>>>\byteCode\byteCodewhere 1\i and 1\j>>|> 1|)>>|||]>>>>>|> 1|)>>|||]>>>>>|> 1|)>>|||]>>>>>|> 1|)>>|||]>>>>>|> i|)>>|||]>>>\byteCodewhere 1\i>>|> i|)>>|||]>>>\byteCodewhere 1\i>>|> i|)>>|||]>>>\byteCodewhere 1\i>>|> i|)>>|||]>>>\byteCodewhere 1\i>>|>|)>>||>>>>|>|)>>||>>>>|> b|)>>||>>\BE>>|> h|)>>||>>\BE>>|> v|)>>|||>+|\>|)>\bytePadwhere \127>>|> v|)>>|||]>>>\BE||\>|)>\bytePadwhere 127 \\2>>>> The byte codes for primitives begin with a byte between >> and ]>>> inclusive. The codes can contain multiple bytes. However, for the Bitcoin primitives, we only need to use one byte per primitive. <\eqnarray*> >|)>>|||]>>>>>|>|)>>|||]>>>>>>|>|)>>|||]>>>>>>|>|)>>|||]>>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>|>|)>>|||]>>>>>>> We define a byte-string prefix code for Simplicity DAGs as a concatenation of byte-string codes of its nodes, terminated by a sentinel value that has been reserved as an end-of-stream byte. <\equation*> byteCode\>\\>\byteCode\indexed|)>|)>\|]>>> Notice that while > for Node> seems like it could call > for some >, this can never happen for Simplicity DAGs. Recall from Section, that a well-formed Simplicity DAG, Node>, satisfies the condition <\equation*> \|i,a|\>\indexed\\j\ref\0\j\i The condition on DAGs implies that |)>|\|>=0>. This condition means that > never occurs for any >. <\the-glossary|gly> , > <\bibliography|bib|tm-plain|Simplicity.bib> <\bib-list|18> A.W.Appel. Verification of a cryptographic primitive: SHA-256. , 37(2):7\U1, apr 2015. Bitcoinwiki. Script. , 2016. J.Carette, O.KiselyovC.Shan. Finally tagless, partially evaluated: tagless staged interpreters for simpler typed languages. , 19(5):509\U543, sep 2009. Certicom Research. Standards for Efficient Cryptography 2: Recommended Elliptic Curve Domain Parameters. Standard SEC2, Certicom Corp., Mississauga, ON, USA, Sep 2000. The Coq Development Team. . Oct 2017. F.Garillot, G.Gonthier, A.MahboubiL.Rideau. Packaging Mathematical Structures. Tobias NipkowChristian Urban, , 5674. Munich, Germany, 2009. Springer. G.Gentzen. Investigations into logical deduction. M.E.Szabo, , Studies in logic and the foundations of mathematics, 3. \ North-Holland Pub. Co., 1969. D.J.KingP.Wadler. , 134\U143. Springer London, London, 1993. A.MahboubiE.Tassi. Canonical structures for the working Coq user. , ITP'13, 19\U34. Berlin, Heidelberg, 2013. Springer-Verlag. H.G.Mairson. Deciding ML typability is complete for deterministic exponential time. , POPL '90, 382\U401. New York, NY, USA, 1990. ACM. S.Nakamoto. Bitcoin: A peer-to-peer electronic cash system. , Nov 2008. S.Nakamoto. Re: Transactions and Scripts: DUP HASH160 ... EQUALVERIFY CHECKSIG. , Jun 2010. National institute of standards and technology. FIPS 180-4, secure hash standard, federal information processing standard (FIPS), publication 180-4. , DEPARTMENT OF COMMERCE, aug 2015. R.O'Connor. Van Laarhoven free monad. Feb 2014. Blog post, . M.S.PatersonM.N.Wegman. Linear unification. , 16(2):158\U167, 1978. Wikipedia contributors. F-algebra \V Wikipedia, the free encyclopedia. , 2017. P.Wuille. Libsecp256k1. , May 2018. P.Wuille, J.NickT.Ruffing. Bip-0340. 2020. . <\initial> <\collection> <\references> <\collection> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > <\auxiliary> <\collection> <\associate|bib> bitcoin satoshiScript script Coq:manual King1993 gentzen sha sec2 libsecp256k1 bip-0340 unification Mairson:1989 f-algebra Mahboubi:2013 garillot:2009 Appel:2015 Carette:2009 libsecp256k1 bip-0340 oconnor2014 <\associate|figure> |3.1>||Example state of the Bit Machine.>|> |8.1>||The inheritance hierarchy of algebras for Simplicity's partial extensions in Coq.>|> <\associate|gly> > > <\associate|toc> |math-font-series||1Introduction> |.>>>>|> 1.1Bitcoin Script |.>>>>|> 1.2Simplicity's Design Goals |.>>>>|> |1.2.1Static Analysis |.>>>>|> > |1.2.2Pruning and Sharing |.>>>>|> > |1.2.3Formal Semantics |.>>>>|> > |math-font-series||2Type Theory Preliminaries> |.>>>>|> 2.1Algebraic Types |.>>>>|> |2.1.1Records |.>>>>|> > 2.2Functors |.>>>>|> |2.2.1Option Functor |.>>>>|> > |2.2.2List Functors |.>>>>|> > |2.2.3Buffers |.>>>>|> > 2.3Monads |.>>>>|> |2.3.1Kleisli Morphisms |.>>>>|> > |2.3.2Cartesian Strength |.>>>>|> > |2.3.3Identity Monad |.>>>>|> > |2.3.4Monad Zero |.>>>>|> > |2.3.4.1Option Monad |.>>>>|> > 2.4Multi-bit Words |.>>>>|> |2.4.1Byte Strings |.>>>>|> > |2.4.2Bit Strings |.>>>>|> > |math-font-series||3Core Simplicity> |.>>>>|> 3.1Types |.>>>>|> |3.1.1Abstract Syntax |.>>>>|> > |3.1.2Formal Syntax |.>>>>|> > |3.1.3Formal Semantics |.>>>>|> > 3.2Terms |.>>>>|> |3.2.1Identity |.>>>>|> > |3.2.2Composition |.>>>>|> > |3.2.3Constant Unit |.>>>>|> > |3.2.4Left Injection |.>>>>|> > |3.2.5Right Injection |.>>>>|> > |3.2.6Case |.>>>>|> > |3.2.7Pair |.>>>>|> > |3.2.8Take |.>>>>|> > |3.2.9Drop |.>>>>|> > |3.2.10Formal Syntax |.>>>>|> > |3.2.11Formal Semantics |.>>>>|> > 3.3Example Simplicity |.>>>>|> |3.3.1Bit Operations |.>>>>|> > |3.3.2Simplicity Notation |.>>>>|> > |3.3.3Generic Equality |.>>>>|> > |3.3.4Arithmetic |.>>>>|> > |3.3.5Bitwise Operations |.>>>>|> > |3.3.6SHA-256 |.>>>>|> > |3.3.6.1Tagged Hashes |.>>>>|> > |3.3.7Elliptic Curve Operations on secp256k1 |.>>>>|> > |3.3.7.1libsecp256k1 |.>>>>|> > |3.3.7.2libsecp256k1 in Simplicity |.>>>>|> > |3.3.7.3Schnorr Signature Validation |.>>>>|> > 3.4Completeness Theorem |.>>>>|> 3.5Operational Semantics |.>>>>|> |3.5.1Representing Values as Cell Arrays |.>>>>|> > |3.5.2Bit Machine |.>>>>|> > |3.5.2.1Frame Instructions |.>>>>|> > |3.5.2.2Active Write Frame Instructions |.>>>>|> > |3.5.2.3Active Read Frame Instructions |.>>>>|> > |3.5.2.4Abort Instruction |.>>>>|> > |3.5.2.5Bit Machine Programs |.>>>>|> > |3.5.2.6Crashing the Bit Machine |.>>>>|> > |3.5.3Executing Simplicity |.>>>>|> > |3.5.3.1Tail Composition Optimisation (TCO) |.>>>>|> > 3.6Static Analysis |.>>>>|> |3.6.1Space Resources |.>>>>|> > |3.6.1.1Maximum Cell Count Bound |.>>>>|> > |3.6.1.2Maximum Frame Count Bound |.>>>>|> > |3.6.2Time Resources |.>>>>|> > 3.7Commitment Merkle Root |.>>>>|> 3.8Type Merkle Root |.>>>>|> |math-font-series||4Simplicity Extensions> |.>>>>|> 4.1Monadic Semantics |.>>>>|> 4.2Witness |.>>>>|> |4.2.1Elided Computation |.>>>>|> > |4.2.2Type Inference with Witness |.>>>>|> > 4.3Assertions and Failure |.>>>>|> |4.3.1Denotational Semantics |.>>>>|> > |4.3.2Merkle Roots |.>>>>|> > |4.3.2.1Pruning Unused |case> Branches |.>>>>|> > |4.3.2.2Salted Expressions |.>>>>|> > 4.4Blockchain Primitives |.>>>>|> |4.4.1Bitcoin Transactions |.>>>>|> > |4.4.1.1Denotational Semantics |.>>>>|> > |4.4.1.2Merkle Roots |.>>>>|> > 4.5Simplicity Programs |.>>>>|> |4.5.1Example: ||font-shape||checkSigHashAll>>> |.>>>>|> > 4.6Schnorr Signature Aggregation |.>>>>|> 4.7Malleability |.>>>>|> |4.7.1Transaction Weight |.>>>>|> > |math-font-series||5Jets> |.>>>>|> |math-font-series||6Delegation> |.>>>>|> 6.1Implementing |disconnect> on the Bit Machine |.>>>>|> |6.1.1Static Analysis of |disconnect> |.>>>>|> > |6.1.1.1Space Resources |.>>>>|> > 6.2Unbounded Loops |.>>>>|> |6.2.1Adding a |loop> primitive to Simplicity? |.>>>>|> > 6.3Universal Signature Hash Modes |.>>>>|> |6.3.1Side-Effects and Delegation |.>>>>|> > |math-font-series||7Type Inference and Serialization> |.>>>>|> 7.1Explicit Simplicity DAGs |.>>>>|> |7.1.1Type Inference |.>>>>|> > |7.1.2Reconstructing Simplicity Expressions |.>>>>|> > |7.1.2.1syncase |.>>>>|> > |7.1.2.2inflate |.>>>>|> > 7.2Serialization |.>>>>|> |7.2.1Serialization of Bit Strings and Positive Numbers |.>>>>|> > |7.2.2Serialization of Simplicity |.>>>>|> > |7.2.2.1Serialization of Word Jets |.>>>>|> > |7.2.3Identity Merkle Root |.>>>>|> > |math-font-series||8Coq Library Guide> |.>>>>|> 8.1Simplicity Types |.>>>>|> 8.2Simplicity Terms |.>>>>|> |8.2.1The \PInitial\Q Representation of Terms |.>>>>|> > |8.2.2The \PFinal\Q Representation of Terms |.>>>>|> > |8.2.2.1Simplicity Algebras |.>>>>|> > |8.2.2.2The \PFinal\Q Representation |.>>>>|> > |8.2.2.3Constructing \PFinal\Q Terms |.>>>>|> > |8.2.3Why two representations of Terms? |.>>>>|> > 8.3Example Simplicity Expressions |.>>>>|> |8.3.1Bits |.>>>>|> > |8.3.2Arithmetic |.>>>>|> > |8.3.3SHA256 |.>>>>|> > 8.4The Hierarchy of Simplicity Language Extensions |.>>>>|> |8.4.1Witness |.>>>>|> > |8.4.2Assertion |.>>>>|> > |8.4.3Delegation |.>>>>|> > |8.4.4Primitives |.>>>>|> > |8.4.4.1Bitcoin |.>>>>|> > |8.4.5Jets |.>>>>|> > |8.4.6Full Simplicity |.>>>>|> > 8.5Merkle Roots |.>>>>|> 8.6The Bit Machine |.>>>>|> |8.6.1Bit Machine Code |.>>>>|> > |8.6.1.1Bit Machine Programs |.>>>>|> > |8.6.2Translating Simplicity to the Bit Machine |.>>>>|> > |8.6.3Static Analysis |.>>>>|> > |math-font-series||9Haskell Library Guide> |.>>>>|> 9.1|language||Simplicity-Core> library |.>>>>|> |9.1.1Simplicity Types |.>>>>|> > |9.1.2Simplicity Terms |.>>>>|> > |9.1.3Merkle Roots |.>>>>|> > |9.1.4Tensors |.>>>>|> > |9.1.5Example Simplicity Expressions |.>>>>|> > |9.1.5.1Generic |.>>>>|> > |9.1.5.2Bits |.>>>>|> > |9.1.5.3Multi-bit Words |.>>>>|> > |9.1.5.4Arithmetic |.>>>>|> > |9.1.5.5Loop |.>>>>|> > |9.1.6Libraries of Simplicity Expressions |.>>>>|> > |9.1.6.1SHA-256 |.>>>>|> > |9.1.6.2LibSecp256k1 |.>>>>|> > |9.1.6.3CheckSigHash |.>>>>|> > |9.1.7The Bit Machine |.>>>>|> > |9.1.7.1Translating Simplicity to the Bit Machine |.>>>>|> > |9.1.7.2Static Analysis |.>>>>|> > |9.1.7.3Fast Evaluation with FFI |.>>>>|> > 9.2|language||Simplicity-Indef> library |.>>>>|> |9.2.1Primitive Signature |.>>>>|> > |9.2.2Primitive Terms |.>>>>|> > |9.2.3|language||JetType> class |.>>>>|> > |9.2.4Denotational Semantics of Full Simplicity |.>>>>|> > |9.2.5Type Inference |.>>>>|> > |9.2.6Serialization |.>>>>|> > |9.2.6.1Free Monadic Deserializaiton |.>>>>|> > |9.2.6.2Serialization of Simplicity DAGs |.>>>>|> > |9.2.7Jet Substitution |.>>>>|> > 9.3|language||Simplicity-Bitcoin> Library |.>>>>|> 9.4|language||Simplicity> Library |.>>>>|> |9.4.1CheckSigHashAll |.>>>>|> > |9.4.2Known Discounted Jets |.>>>>|> > 9.5Simplicity |language||testsuite> |.>>>>|> |math-font-series||10C Library Guide> |.>>>>|> |math-font-series||Appendix AElements Application> |.>>>>|> A.1Denotational Semantics |.>>>>|> |A.1.1Null Data |.>>>>|> > |A.1.2Merkle Roots |.>>>>|> > |math-font-series||Appendix BCatelogue of Jets> |.>>>>|> B.1|language||110...: >Core Jets |.>>>>|> |B.1.1|language||1100...: >Jets for multi-bit logic |.>>>>|> > |B.1.1.1verify |.>>>>|> > |B.1.1.2|low> |.>>>>|> > |B.1.1.3|high> |.>>>>|> > |B.1.1.4|complement> |.>>>>|> > |B.1.1.5|and> |.>>>>|> > |B.1.1.6|or> |.>>>>|> > |B.1.1.7|xor> |.>>>>|> > |B.1.1.8|maj> |.>>>>|> > |B.1.1.9|xor-xor> |.>>>>|> > |B.1.1.10|ch> |.>>>>|> > |B.1.1.11|some> |.>>>>|> > |B.1.1.12|all> |.>>>>|> > |B.1.1.13|eq> |.>>>>|> > |B.1.1.14|full-left-shift> |.>>>>|> > |B.1.1.15|full-right-shift> |.>>>>|> > |B.1.1.16|leftmost> |.>>>>|> > |B.1.1.17|rightmost> |.>>>>|> > |B.1.1.18|left-pad-low> |.>>>>|> > |B.1.1.19|left-pad-high> |.>>>>|> > |B.1.1.20|left-extend> |.>>>>|> > |B.1.1.21|right-pad-low> |.>>>>|> > |B.1.1.22|right-pad-high> |.>>>>|> > |B.1.1.23|right-extend> |.>>>>|> > |B.1.1.24|left-shift-with> |.>>>>|> > |B.1.1.25|right-shift-with> |.>>>>|> > |B.1.1.26|left-shift> |.>>>>|> > |B.1.1.27|right-shift> |.>>>>|> > |B.1.1.28|left-rotate> |.>>>>|> > |B.1.1.29|right-rotate> |.>>>>|> > |B.1.1.30|transpose> (NOT IMPLEMENTED) |.>>>>|> > |B.1.1.31|find-first-high> (NOT IMPLEMENTED) |.>>>>|> > |B.1.1.32|find-last-high> (NOT IMPLEMENTED) |.>>>>|> > |B.1.1.33|bit> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2|language||110100...: >Jets for arithmetic |.>>>>|> > |B.1.2.1|one> |.>>>>|> > |B.1.2.2|full-add> |.>>>>|> > |B.1.2.3|add> |.>>>>|> > |B.1.2.4|full-increment> |.>>>>|> > |B.1.2.5|increment> |.>>>>|> > |B.1.2.6|popcount> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.7|full-subtract> |.>>>>|> > |B.1.2.8|subtract> |.>>>>|> > |B.1.2.9|negate> |.>>>>|> > |B.1.2.10|full-decrement> |.>>>>|> > |B.1.2.11|decrement> |.>>>>|> > |B.1.2.12|full-multiply> |.>>>>|> > |B.1.2.13|multiply> |.>>>>|> > |B.1.2.14|language||>|is-zero> |.>>>>|> > |B.1.2.15|language||>|is-one> |.>>>>|> > |B.1.2.16|le> (unsigned) |.>>>>|> > |B.1.2.17|lt> (unsigned) |.>>>>|> > |B.1.2.18|min> (unsigned) |.>>>>|> > |B.1.2.19|max> (unsigned) |.>>>>|> > |B.1.2.20|median> (unsigned) |.>>>>|> > |B.1.2.21|div2n1n> |.>>>>|> > |B.1.2.22|div-mod> (unsigned) |.>>>>|> > |B.1.2.23|divide> (unsigned) |.>>>>|> > |B.1.2.24|modulo> (unsigned) |.>>>>|> > |B.1.2.25|divides> (unsigned) |.>>>>|> > |B.1.2.26|eea> (unsigned) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.27|bezout> (unsigned) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.28|gcd> (unsigned) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.29|cofactors> (unsigned)(NOT IMPLEMENTED) |.>>>>|> > |B.1.2.30|lcm> (unsigned) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.31|jacobi> (unsigned) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.32|absolute-value> (signed input/unsigned output) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.33|language||>|sign> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.34|signed-le> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.35|signed-lt> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.36|signed-min> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.37|signed-max> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.38|signed-median> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.39|signed-right-shift> (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.40|signed-divmod> (unsigned denominator) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.41|signed-div> (unsigned denominator) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.42|signed-signed-divmod> (signed denominator) (NOT IMPLEMENTED) |.>>>>|> > |B.1.2.43|signed-signed-div> (signed denominator) (NOT IMPLEMENTED) |.>>>>|> > |B.1.3|language||110101...: >Jets for hash functions |.>>>>|> > |B.1.3.1|language||1101010...: >Jets for SHA-2 |.>>>>|> > ||sha-256-block> |.>>>>|> > ||sha-256-iv> |.>>>>|> > ||sha-256-ctx-8-add> |.>>>>|> > ||sha-256-ctx-8-add-buffer-511> |.>>>>|> > ||sha-256-ctx-8-finalize> |.>>>>|> > ||sha-256-ctx-8-init> |.>>>>|> > |B.1.3.2|language||110101100...: >Jets for SHA-3 (NOT IMPLEMENTED) |.>>>>|> > ||sha3-zero> |.>>>>|> > ||sha3-absorb> |.>>>>|> > ||sha3-xor> |.>>>>|> > ||sha3-permute> |.>>>>|> > ||sha3-squeeze-256> |.>>>>|> > ||sha3-squeeze-512> |.>>>>|> > |B.1.3.3|language||110101101...: >Jets for RIPEMD (NOT IMPLEMENTED) |.>>>>|> > |B.1.3.4|language||110101110000...: >Jets for SHA-1 (RESERVED) (NOT IMPLEMENTED) |.>>>>|> > |B.1.4|language||110110000...: >Jets for elliptic curve functions |.>>>>|> > |B.1.4.1|language||1101100000...: >Jets for secp256k1 |.>>>>|> > ||secp256k1-point-verify> |.>>>>|> > ||secp256k1-decompress> |.>>>>|> > ||secp256k1-linear-verify> |.>>>>|> > ||secp256k1-linear-combination> |.>>>>|> > ||secp256k1-scale> |.>>>>|> > ||secp256k1-generate> |.>>>>|> > ||secp256k1-gej-infinity> |.>>>>|> > ||secp256k1-gej-normalize> |.>>>>|> > ||secp256k1-gej-negate> |.>>>>|> > ||secp256k1-ge-negate> |.>>>>|> > ||secp256k1-gej-double> |.>>>>|> > ||secp256k1-gej-add> |.>>>>|> > ||secp256k1-gej-ge-add-ex> |.>>>>|> > ||secp256k1-gej-ge-add> |.>>>>|> > ||secp256k1-gej-rescale> |.>>>>|> > ||secp256k1-gej-is-infinity> |.>>>>|> > ||secp256k1-gej-equiv> |Does not exist in libsecp256k1> |.>>>>|> > ||secp256k1-gej-ge-equiv> |Does not exist in libsecp256k1> |.>>>>|> > ||secp256k1-gej-x-equiv> |.>>>>|> > ||secp256k1-gej-y-is-odd> |.>>>>|> > ||secp256k1-gej-is-on-curve> |.>>>>|> > ||secp256k1-ge-is-on-curve> |.>>>>|> > ||secp256k1-scalar-normalize> |.>>>>|> > ||secp256k1-scalar-negate> |.>>>>|> > ||secp256k1-scalar-add> |.>>>>|> > ||secp256k1-scalar-square> |.>>>>|> > ||secp256k1-scalar-multiply> |.>>>>|> > ||secp256k1-scalar-multiply-lambda> |.>>>>|> > ||secp256k1-scalar-invert> |.>>>>|> > ||secp256k1-scalar-is-zero> |.>>>>|> > ||secp256k1-ge-scale-lambda> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-gej-scale-lambda> |Consider removing> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-scalar-split-lambda> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-short-scalar> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-fe-normalize> |.>>>>|> > ||secp256k1-fe-negate> |.>>>>|> > ||secp256k1-fe-add> |.>>>>|> > ||secp256k1-fe-square> |.>>>>|> > ||secp256k1-fe-multiply> |.>>>>|> > ||secp256k1-fe-multiply-beta> |.>>>>|> > ||secp256k1-fe-invert> |.>>>>|> > ||secp256k1-fe-square-root> |.>>>>|> > ||secp256k1-fe-is-zero> |.>>>>|> > ||secp256k1-fe-is-odd> |.>>>>|> > ||secp256k1-fe-is-quad> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-hash-to-curve> |.>>>>|> > ||secp256k1-swu> |.>>>>|> > |B.1.5|language||110110001...: >Jets for digital signatures |.>>>>|> > |B.1.5.1|language||1101100010...: >Jets for secp256k1 based digital signatures |.>>>>|> > ||check-sig-verify> |.>>>>|> > ||bip-0340-verify> |.>>>>|> > ||bip-0340-challenge-iv> (NOT IMPLEMENTED) |.>>>>|> > ||bip-0340-challenge-midstate> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-signature-unpack> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-pubkey-unpack> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-pubkey-unpack-neg> (NOT IMPLEMENTED) |.>>>>|> > ||secp256k1-ecdsa> (NOT IMPLEMENTED) |.>>>>|> > |B.1.6|language||110110010...: >Jets for Simplicity (NOT IMPLEMENTED) |.>>>>|> > |B.1.6.1|language||11011000100...: >Jets for tagged hash IVs |.>>>>|> > ||iden-commitment-tag> |.>>>>|> > ||comp-commitment-tag> |.>>>>|> > ||unit-commitment-tag> |.>>>>|> > ||injl-commitment-tag> |.>>>>|> > ||injr-commitment-tag> |.>>>>|> > ||case-commitment-tag> |.>>>>|> > ||pair-commitment-tag> |.>>>>|> > ||take-commitment-tag> |.>>>>|> > ||drop-commitment-tag> |.>>>>|> > ||witness-commitment-tag> |.>>>>|> > ||disconnect-commitment-tag> |.>>>>|> > ||fail-commitment-tag> |.>>>>|> > ||signtaure-tag> |.>>>>|> > ||sighash-tag> |.>>>>|> > |B.1.7|language||110110011...: >Jets for Bitcoin (without primitives) |.>>>>|> > |B.1.7.1|parse-lock> |.>>>>|> > |B.1.7.2|parse-sequence> |.>>>>|> > |B.1.7.3|tapdata-init> |.>>>>|> > B.2|language||111...: >Bitcoin Jets |.>>>>|> |B.2.1Signature Hash Modes |.>>>>|> > |B.2.2Time Locks |.>>>>|> > |B.2.2.1|check-lock-height> |.>>>>|> > |B.2.2.2|check-lock-time> |.>>>>|> > |B.2.2.3|check-lock-distance> |.>>>>|> > |B.2.2.4|check-lock-duration> |.>>>>|> > |B.2.2.5|tx-height-lock> |.>>>>|> > |B.2.2.6|tx-time-lock> |.>>>>|> > |B.2.2.7|tx-distance-lock> |.>>>>|> > |B.2.2.8|tx-duration-lock> |.>>>>|> > |B.2.2.9|is-final> |.>>>>|> > |B.2.3Transaction |.>>>>|> > |B.2.3.1|script-cmr> |.>>>>|> > |B.2.3.2|internal-key> |.>>>>|> > |B.2.3.3|current-index> |.>>>>|> > |B.2.3.4|num-inputs> |.>>>>|> > |B.2.3.5|num-outputs> |.>>>>|> > |B.2.3.6|lock-time> |.>>>>|> > |B.2.3.7|fee> |.>>>>|> > |B.2.3.8|output-value> |.>>>>|> > |B.2.3.9|output-script-hash> |.>>>>|> > |B.2.3.10|total-output-value> |.>>>>|> > |B.2.3.11|current-prev-outpoint> |.>>>>|> > |B.2.3.12|current-value> |.>>>>|> > |B.2.3.13|current-script-hash> |.>>>>|> > |B.2.3.14|current-sequence> |.>>>>|> > |B.2.3.15|current-annex-hash> |.>>>>|> > |B.2.3.16|current-script-sig-hash> |.>>>>|> > |B.2.3.17|input-prev-outpoint> |.>>>>|> > |B.2.3.18|input-value> |.>>>>|> > |B.2.3.19|input-script-hash> |.>>>>|> > |B.2.3.20|input-sequence> |.>>>>|> > |B.2.3.21|input-annex-hash> |.>>>>|> > |B.2.3.22|input-script-sig-hash> |.>>>>|> > |B.2.3.23|total-input-value> |.>>>>|> > |B.2.3.24|tapleaf-version> |.>>>>|> > |B.2.3.25|tappath> |.>>>>|> > |B.2.3.26|version> |.>>>>|> > B.3|language||111...: >Elements Jets |.>>>>|> |B.3.1Signature Hash Modes |.>>>>|> > |B.3.1.1|sig-all-hash> |.>>>>|> > |B.3.1.2|tx-hash> |.>>>>|> > |B.3.1.3|tap-env-hash> |.>>>>|> > |B.3.1.4|outputs-hash> |.>>>>|> > |B.3.1.5|inputs-hash> |.>>>>|> > |B.3.1.6|issuances-hash> |.>>>>|> > |B.3.1.7|input-utxos-hash> |.>>>>|> > |B.3.1.8|output-hash> |.>>>>|> > |B.3.1.9|output-amounts-hash> |.>>>>|> > |B.3.1.10|output-scripts-hash> |.>>>>|> > |B.3.1.11|output-nonces-hash> |.>>>>|> > |B.3.1.12|output-range-proofs-hash> |.>>>>|> > |B.3.1.13|output-surjection-proofs-hash> |.>>>>|> > |B.3.1.14|input-hash> |.>>>>|> > |B.3.1.15|input-outpoints-hash> |.>>>>|> > |B.3.1.16|input-sequences-hash> |.>>>>|> > |B.3.1.17|input-annexes-hash> |.>>>>|> > |B.3.1.18|input-script-sigs-hash> |.>>>>|> > |B.3.1.19|issuance-hash> |.>>>>|> > |B.3.1.20|issuance-asset-amounts-hash> |.>>>>|> > |B.3.1.21|issuance-token-amounts-hash> |.>>>>|> > |B.3.1.22|issuance-range-proofs-hash> |.>>>>|> > |B.3.1.23|issuance-blinding-entropy-hash> |.>>>>|> > |B.3.1.24|input-utxo-hash> |.>>>>|> > |B.3.1.25|input-amounts-hash> |.>>>>|> > |B.3.1.26|input-scripts-hash> |.>>>>|> > |B.3.1.27|tapleaf-hash> |.>>>>|> > |B.3.1.28|tappath-hash> |.>>>>|> > |B.3.1.29|outpoint-hash> |.>>>>|> > |B.3.1.30|asset-amount-hash> |.>>>>|> > |B.3.1.31|nonce-hash> |.>>>>|> > |B.3.1.32|annex-hash> |.>>>>|> > |B.3.1.33|build-tapleaf-simplicity> |.>>>>|> > |B.3.1.34|build-tapbranch> |.>>>>|> > |B.3.1.35|build-taptweak> |.>>>>|> > |B.3.2Time Locks |.>>>>|> > |B.3.2.1|check-lock-height> |.>>>>|> > |B.3.2.2|check-lock-time> |.>>>>|> > |B.3.2.3|check-lock-distance> |.>>>>|> > |B.3.2.4|check-lock-duration> |.>>>>|> > |B.3.2.5|tx-lock-height> |.>>>>|> > |B.3.2.6|tx-lock-time> |.>>>>|> > |B.3.2.7|tx-lock-distance> |.>>>>|> > |B.3.2.8|tx-lock-duration> |.>>>>|> > |B.3.2.9|tx-is-final> |.>>>>|> > |B.3.3Issuance |.>>>>|> > |B.3.3.1|issuance> |.>>>>|> > |B.3.3.2|issuance-asset> |.>>>>|> > |B.3.3.3|issuance-token> |.>>>>|> > |B.3.3.4|issuance-entropy> |.>>>>|> > |B.3.3.5|calculate-issuance-entropy> |.>>>>|> > |B.3.3.6|calculate-asset> |.>>>>|> > |B.3.3.7|calculate-explicit-token> |.>>>>|> > |B.3.3.8|calculate-confidential-token> |.>>>>|> > |B.3.3.9|lbtc-asset> |.>>>>|> > |B.3.4Transaction |.>>>>|> > |B.3.4.1|script-cmr> |.>>>>|> > |B.3.4.2|internal-key> |.>>>>|> > |B.3.4.3|current-index> |.>>>>|> > |B.3.4.4|num-inputs> |.>>>>|> > |B.3.4.5|num-outputs> |.>>>>|> > |B.3.4.6|lock-time> |.>>>>|> > |B.3.4.7|output-asset> |.>>>>|> > |B.3.4.8|output-amount> |.>>>>|> > |B.3.4.9|output-nonce> |.>>>>|> > |B.3.4.10|output-script-hash> |.>>>>|> > |B.3.4.11|output-null-datum> |.>>>>|> > |B.3.4.12|output-is-fee> |.>>>>|> > |B.3.4.13|output-surjection-proof> |.>>>>|> > |B.3.4.14|output-range-proof> |.>>>>|> > |B.3.4.15|total-fee> |.>>>>|> > |B.3.4.16|current-pegin> |.>>>>|> > |B.3.4.17|current-prev-outpoint> |.>>>>|> > |B.3.4.18|current-asset> |.>>>>|> > |B.3.4.19|current-amount> |.>>>>|> > |B.3.4.20|current-script-hash> |.>>>>|> > |B.3.4.21|current-sequence> |.>>>>|> > |B.3.4.22|current-annex-hash> |.>>>>|> > |B.3.4.23|current-script-sig-hash> |.>>>>|> > |B.3.4.24|current-reissuance-blinding> |.>>>>|> > |B.3.4.25|current-new-issuance-contract> |.>>>>|> > |B.3.4.26|current-reissuance-entropy> |.>>>>|> > |B.3.4.27|current-issuance-asset-amount> |.>>>>|> > |B.3.4.28|current-issuance-token-amount> |.>>>>|> > |B.3.4.29|current-issuance-asset-proof> |.>>>>|> > |B.3.4.30|current-issuance-token-proof> |.>>>>|> > |B.3.4.31|input-pegin> |.>>>>|> > |B.3.4.32|input-prev-outpoint> |.>>>>|> > |B.3.4.33|input-asset> |.>>>>|> > |B.3.4.34|input-amount> |.>>>>|> > |B.3.4.35|input-script-hash> |.>>>>|> > |B.3.4.36|input-sequence> |.>>>>|> > |B.3.4.37|input-annex-hash> |.>>>>|> > |B.3.4.38|input-script-sig-hash> |.>>>>|> > |B.3.4.39|reissuance-blinding> |.>>>>|> > |B.3.4.40|new-issuance-contract> |.>>>>|> > |B.3.4.41|reissuance-entropy> |.>>>>|> > |B.3.4.42|issuance-asset-amount> |.>>>>|> > |B.3.4.43|issuance-token-amount> |.>>>>|> > |B.3.4.44|issuance-asset-proof> |.>>>>|> > |B.3.4.45|issuance-token-proof> |.>>>>|> > |B.3.4.46|tapleaf-version> |.>>>>|> > |B.3.4.47|tappath> |.>>>>|> > |B.3.4.48|version> |.>>>>|> > |B.3.4.49|genesis-block-hash> |.>>>>|> > |B.3.4.50|transaction-id> |.>>>>|> > |math-font-series||Appendix CAlternative Serialization of Simplicity DAGs> |.>>>>|> |math-font-series||Glossary> |.>>>>|> |math-font-series||Bibliography> |.>>>>|> ================================================ FILE: Simplicity.C.nix ================================================ { lib, stdenv, gcovr ? null, wideMultiply ? null, withCoverage ? false , withProfiler ? false, gperftools ? null, graphviz ? null, perl ? null, librsvg ? null , withTiming ? true , withValgrind ? false, valgrind ? null , production ? false , enableShaNI ? stdenv.hostPlatform.isx86_64 , gcov-executable ? if stdenv.cc.isGNU then "gcov -r" else if stdenv.cc.isClang then "${stdenv.cc.cc.libllvm}/bin/llvm-cov gcov" else null , doCheck ? true }: assert wideMultiply == null || wideMultiply == "int64" || wideMultiply == "int128" || wideMultiply == "int128_struct"; assert withCoverage -> gcovr != null && gcov-executable != null; assert withProfiler -> gperftools != null && graphviz != null && perl != null && librsvg != null; assert withValgrind -> valgrind != null; stdenv.mkDerivation { name = "libSimplicity-0.0.0"; src = lib.sourceFilesBySuffices ./C ["Makefile" ".c" ".h" ".inc"]; enableParallelBuilding = true; CPPFLAGS = lib.optional (builtins.isString wideMultiply) "-DUSE_FORCE_WIDEMUL_${lib.toUpper wideMultiply}=1"; CFLAGS = lib.optional withCoverage "--coverage" ++ lib.optional withTiming "-DTIMING_FLAG" ++ lib.optional production "-DPRODUCTION"; LDFLAGS = lib.optional withCoverage "--coverage" ++ lib.optional withProfiler "-lprofiler"; preBuild = lib.optional (enableShaNI) '' makeFlagsArray+=(X86_SHANI_CXXFLAGS="-msse4.1 -msha") ''; inherit doCheck; checkInputs = lib.optionals withProfiler [ gperftools ]; nativeCheckInputs = lib.optionals withProfiler [ graphviz ] ++ lib.optionals withValgrind [ valgrind ]; postCheck = lib.optional withCoverage '' mkdir -p $out/shared/coverage ${gcovr}/bin/gcovr --gcov-executable "${gcov-executable}" --verbose --html --html-details -o $out/shared/coverage/coverage.html '' ++ lib.optional withProfiler '' mkdir -p $out/shared/profile CPUPROFILE=./prof.out CPUPROFILE_FREQUENCY=1000 ./test # Until https://github.com/NixOS/nixpkgs/pull/279623 is resolved, we need to explicitly invoke perl ${perl}/bin/perl ${gperftools}/bin/pprof --svg ./test prof.out > $out/shared/profile/test.svg ${librsvg}/bin/rsvg-convert -f pdf -o $out/shared/profile/test.pdf $out/shared/profile/test.svg '' ++ lib.optional withValgrind '' valgrind --leak-check=full --error-exitcode=1 ./test --no-timing ''; meta = { license = lib.licenses.mit; }; } ================================================ FILE: Simplicity.Coq.nix ================================================ { coq, safegcd-bounds, lib, vst, stdenv , alectryon ? null , serapi ? null }: assert alectryon != null -> serapi != null; stdenv.mkDerivation { name = "Simplicity-coq-0.0.0"; src = lib.sourceFilesBySuffices (lib.sourceByRegex ./Coq ["_CoqProject" "C" "C/.*" "Simplicity" "Simplicity/.*" "Util" "Util/.*"]) ["_CoqProject" ".v"]; outputs = [ "out" ] ++ lib.optional (alectryon != null) "doc"; postConfigure = '' coq_makefile -f _CoqProject -o CoqMakefile ''; buildInputs = [ coq ]; nativeBuildInputs = lib.optional (alectryon != null) serapi; propagatedBuildInputs = [ safegcd-bounds vst ]; enableParallelBuilding = true; makefile = "CoqMakefile"; postBuild = lib.optional (alectryon != null) '' ${alectryon}/bin/alectryon --frontend coq --output-directory $doc --webpage-style windowed -R C C \ C/secp256k1/spec_int128.v C/secp256k1/verif_int128_impl.v \ C/divstep.v C/secp256k1/spec_modinv64.v C/secp256k1/verif_modinv64_impl.v ''; installFlags = "COQLIB=$(out)/lib/coq/${coq.coq-version}/"; meta = { license = lib.licenses.mit; }; } ================================================ FILE: Simplicity.Haskell.nix ================================================ { mkDerivation, base, binary, cereal, lens-family, lib, MemoTrie, mtl, prettyprinter, QuickCheck, stdenv, split, tasty, tasty-hunit, tasty-quickcheck, tardis, unification-fd, vector, entropy , doCheck ? true , withValgrind ? false, valgrind ? null }: assert withValgrind -> valgrind != null; mkDerivation (rec { pname = "Simplicity"; version = "0.0.0"; src = lib.sourceFilesBySuffices (lib.sourceByRegex ./. ["^LICENSE$" "^Simplicity\.cabal$" "^Setup.hs$" "^Tests.hs$" "^Haskell$" "^Haskell/.*" "^Haskell-Generate$" "^Haskell-Generate/.*" "^Haskell-Examples$" "^Haskell-Examples/.*" "^C$" "^C/.*"]) ["LICENSE" ".cabal" ".hs" ".hsig" ".h" ".c" ".inc"]; libraryHaskellDepends = [ base binary cereal lens-family MemoTrie mtl split tardis unification-fd vector ]; executableHaskellDepends = [ prettyprinter entropy ]; testHaskellDepends = libraryHaskellDepends ++ [ QuickCheck tasty tasty-hunit tasty-quickcheck ] ++ lib.optionals withValgrind [ valgrind ]; enableParallelBuilding = true; inherit doCheck; preCheck = [ '' export GHCRTS=-N$NIX_BUILD_CORES '' ] ++ lib.optional withValgrind '' valgrind --leak-check=yes dist/build/testsuite/testsuite -p '$2=="C / SPEC"' ''; postCheck = '' unset GHCRTS ''; # Uncomment to make testing deterministic. # testFlags = ["--quickcheck-replay=582534"]; # Cabal's haddock doesn't work for Backpack / internal libraries / modules reexports. # Until that is fix we manually generate some documentation pages haddockFlags = ["--haddock-option='--use-contents=index.html'"]; postHaddock = '' cp ${./manual-index.html} dist/doc/html/Simplicity/index.html cp ${./Simplicity-Primitive.html} dist/doc/html/Simplicity/Simplicity-Primitive.html ''; license = lib.licenses.mit; }) ================================================ FILE: Simplicity.bib ================================================ @incollection{gentzen, author={Gentzen, G.}, title={Investigations into Logical Deduction}, booktitle={The collected papers of Gerhard Gentzen}, editor={Szabo, M.E.}, chapter=3, series={Studies in logic and the foundations of mathematics}, year={1969}, publisher={North-Holland Pub. Co.} } @misc{appel, author = {Appel, A. W.}, title = {Verifiable {C}}, howpublished = "\url{http://vst.cs.princeton.edu/download/VC.pdf}", month = Jul, year = 2016, } @misc{goldfederescrow, title={Escrow protocols for cryptocurrencies: How to buy physical goods using Bitcoin}, author={Goldfeder, S. and Bonneau, J. and Gennaro, R. and Narayanan, A.}, howpublished = "\url{http://fc17.ifca.ai/preproceedings/paper_122.pdf}", month = Apr, year = 2017, note = "To appear in the proceedings of the 21st International Conference on Financial Cryptography and Data Security" } @article{Appel:2015, author = {Appel, A. W.}, title = {Verification of a Cryptographic Primitive: {SHA-256}}, journal = {ACM Trans. Program. Lang. Syst.}, issue_date = {April 2015}, volume = {37}, number = {2}, month = apr, year = {2015}, issn = {0164-0925}, pages = {7:1--7:31}, articleno = {7}, numpages = {31}, url = {http://doi.acm.org/10.1145/2701415}, doi = {10.1145/2701415}, acmid = {2701415}, publisher = {ACM}, address = {New York, NY, USA}, keywords = {Cryptography}, } @article{unification, title = "Linear unification", journal = "Journal of Computer and System Sciences", volume = "16", number = "2", pages = "158 - 167", year = "1978", note = "", issn = "0022-0000", doi = "http://dx.doi.org/10.1016/0022-0000(78)90043-0", url = "http://www.sciencedirect.com/science/article/pii/0022000078900430", author = "M. S. Paterson and M. N. Wegman", } @techreport{sec2, author = "{Certicom Research}", title = "{Standards for Efficient Cryptography 2: Recommended Elliptic Curve Domain Parameters}", institution = "Certicom Corp.", year = 2000, type = "Standard", number = "SEC2", address = "Mississauga, ON, USA", month = Sep } @manual{Coq:manual, author = {{Coq} {Development} {Team}, The}, title = {The {Coq} Proof Assistant Reference Manual, version 8.7}, month = Oct, year = {2017}, url = {http://coq.inria.fr} } @misc{oconnor2014, author = "O'Connor, R.", title = {{van Laarhoven} Free Monad}, year = 2014, month = Feb, day = 02, note = {Blog post, \url{http://r6.ca/blog/20140210T181244Z.html}} } @MISC{script, author = {bitcoinwiki}, title = {Script}, howpublished = "\url{https://en.bitcoin.it/w/index.php?title=Script&oldid=61707}", year = {2016} } @misc{sighash, author = "Bitcoin Developer Guide", title = {Signature Hash Types}, note = "\url{https://bitcoin.org/en/developer-guide\string#signature-hash-types}", year = {2014} } @MISC{bitcoin, author = {Nakamoto, S.}, title = {{Bitcoin: A peer-to-peer electronic cash system}}, howpublished = "\url{http://bitcoin.org/bitcoin.pdf}", month = Nov, year = {2008} } @misc{libsecp256k1, author = "Wuille, P.", title = {{libsecp256k1}}, howpublished = "\url{https://github.com/bitcoin-core/secp256k1/tree/1e6f1f5ad5e7f1e3ef79313ec02023902bf8175c}", month = May, year = {2018}, } @misc{misc, author = {Nakamoto, S.}, title = {{misc changes}}, howpublished = "\url{https://github.com/bitcoin/bitcoin/commit/4bd188c4383d6e614e18f79dc337fbabe8464c82}", month = Aug, year = {2010}, note = "\url{https://bitcoin.svn.sourceforge.net/svnroot/bitcoin/trunk@131}" } @misc{satoshiScript, author = {Nakamoto, S.}, title = {{Re: Transactions and Scripts: DUP HASH160 ... EQUALVERIFY CHECKSIG}}, howpublished = "\url{https://bitcointalk.org/index.php?topic=195.msg1611\string#msg1611}", month = Jun, year = {2010}, } @misc{sidechains, author = "Back, A. and Corallo, M. and Dashjr, L. and Friedenbach, M. and Maxwell, G. and Miller, A. and Poelstra, A. and Tim\'on, J. and Wuille, P.", title = "Enabling Blockchain Innovations with Pegged Sidechains", year = 2014, note = "\url{https://www.blockstream.com/sidechains.pdf}" } @misc{andresen2012-2, author = "Andresen, G.", howpublished = "{Bitcoin} Improvement Proposal", title = "{BIP16}: Pay to Script Hash", note = "\url{https://github.com/bitcoin/bips/blob/master/bip-0016.mediawiki}", year = 2012 } @misc{cltv, author = "Todd, P.", howpublished = "{Bitcoin} Improvement Proposal", title = "{BIP65}: OP\_CHECKLOCKTIMEVERIFY", note = "\url{https://github.com/bitcoin/bips/blob/master/bip-0065.mediawiki}", year = 2014 } @misc{mast, author = "Lau, J.", howpublished = "{Bitcoin} Improvement Proposal", title = "{BIP114}: Merkelized Abstract Syntax Tree", note = "\url{https://github.com/bitcoin/bips/blob/master/bip-0114.mediawiki}", year = 2016 } @misc{csv, author = "BtcDrak and Friedenbach, M. and Lombrozo, E.", howpublished = "{Bitcoin} Improvement Proposal", title = "{BIP112}: CHECKSEQUENCEVERIFY", note = "\url{https://github.com/bitcoin/bips/blob/master/bip-0112.mediawiki}", year = 2015 } @misc{bip-0340, author = "Wuille, P. and Nick, J. and Ruffing, T.", title = "bip-0340", note = "\url{https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki}", year = 2020 } @misc{zkcp, author = "Maxwell, G.", title = {Zero-Knowledge Contingent Payment}, year = 2011, note = "\url{https://en.bitcoin.it/wiki/Zero\_Knowledge\_Contingent\_Payment}" } @misc{urbit, author = "Yarvin, C. and Monk, P. and Dyudin, A. and Pasco, R.", title = {Urbit: A Solid-State Interpreter}, month = May, year = 2016, note = "\url{http://media.urbit.org/whitepaper.pdf}" } @article{compcert, author = {Leroy, X.}, title = {Formal verification of a realistic compiler}, journal = {Communications of the ACM}, year = 2009, volume = 52, number = 7, pages = {107--115}, url = {http://gallium.inria.fr/~xleroy/publi/compcert-CACM.pdf}, urlpublisher = {http://doi.acm.org/10.1145/1538788.1538814}, hal = {http://hal.archives-ouvertes.fr/inria-00415861/}, pubkind = {journal-int-mono}, abstract = {This paper reports on the development and formal verification (proof of semantic preservation) of CompCert, a compiler from Clight (a large subset of the C programming language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of critical software and its formal verification: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well.} } @inproceedings{schnorr1989, author = "Schnorr, C. P.", title = "Efficient Identification and Signatures for Smart Cards", booktitle = {Proceedings of CRYPTO '89}, year = 1989, } @article{ecdsa, author = {{National institute of standards and technology}}, title = {{FIPS} Pub 186-4 Federal Information Processing Standards Publication Digital Signature Standard (DSS)}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.362.5590}, year = {2013} } @techreport{sha, author = {{National institute of standards and technology}}, day = {26}, institution = {DEPARTMENT OF COMMERCE}, keywords = {cryptography, hash, standard}, month = aug, title = {{FIPS} 180-4, Secure Hash Standard, Federal Information Processing Standard ({FIPS}), Publication 180-4}, url = {http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf}, year = {2015} } @misc{oconnor2016, author = "O'Connor, R.", title = {Covenants in Elements Alpha}, year = 2016, note = {Blog post, \url{https://blockstream.com/2016/11/02/covenants-in-elements-alpha.html}} } @Inbook{King1993, author="King, D. J. and Wadler, P.", editor="Launchbury, John and Sansom, Patrick", title="Combining Monads", bookTitle="Functional Programming, Glasgow 1992: Proceedings of the 1992 Glasgow Workshop on Functional Programming, Ayr, Scotland, 6--8 July 1992", year="1993", publisher="Springer London", address="London", pages="134--143", abstract="Monads provide a way of structuring functional programs. Most real applications require a combination of primitive monads. Here we describe how some monads may be combined with others to yield a combined monad.", isbn="978-1-4471-3215-8", doi="10.1007/978-1-4471-3215-8_12", url="https://doi.org/10.1007/978-1-4471-3215-8_12" } @inproceedings{Mairson:1989, author = {Mairson, H. G.}, title = {Deciding {ML} Typability is Complete for Deterministic Exponential Time}, booktitle = {Proceedings of the 17th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages}, series = {POPL '90}, year = {1990}, isbn = {0-89791-343-4}, location = {San Francisco, California, USA}, pages = {382--401}, numpages = {20}, url = {http://doi.acm.org/10.1145/96709.96748}, doi = {10.1145/96709.96748}, acmid = {96748}, publisher = {ACM}, address = {New York, NY, USA}, } @article{Carette:2009, author = {Carette, J. and Kiselyov, O. and Shan, C.}, title = {Finally Tagless, Partially Evaluated: Tagless Staged Interpreters for Simpler Typed Languages}, journal = {J. Funct. Program.}, issue_date = {September 2009}, volume = {19}, number = {5}, month = sep, year = {2009}, issn = {0956-7968}, pages = {509--543}, numpages = {35}, url = {http://dx.doi.org/10.1017/S0956796809007205}, doi = {10.1017/S0956796809007205}, acmid = {1630626}, publisher = {Cambridge University Press}, address = {New York, NY, USA}, } @inproceedings{Mahboubi:2013, author = {Mahboubi, A. and Tassi, E.}, title = {Canonical Structures for the Working {Coq} User}, booktitle = {Proceedings of the 4th International Conference on Interactive Theorem Proving}, series = {ITP'13}, year = {2013}, isbn = {978-3-642-39633-5}, location = {Rennes, France}, pages = {19--34}, numpages = {16}, url = {http://dx.doi.org/10.1007/978-3-642-39634-2_5}, doi = {10.1007/978-3-642-39634-2_5}, acmid = {2529322}, publisher = {Springer-Verlag}, address = {Berlin, Heidelberg}, } @inproceedings{garillot:2009, TITLE = {{Packaging Mathematical Structures}}, AUTHOR = {Garillot, F. and Gonthier, G. and Mahboubi, A. and Rideau, L.}, URL = {https://hal.inria.fr/inria-00368403}, BOOKTITLE = {{Theorem Proving in Higher Order Logics}}, ADDRESS = {Munich, Germany}, EDITOR = {Tobias Nipkow and Christian Urban}, PUBLISHER = {{Springer}}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {5674}, YEAR = {2009}, KEYWORDS = {Formalization of Algebra ; Coercive subtyping ; Type inference ; Coq ; SSReflect}, PDF = {https://hal.inria.fr/inria-00368403/file/main.pdf}, HAL_ID = {inria-00368403}, HAL_VERSION = {v2}, } @misc{f-algebra, author = "{Wikipedia contributors}", title = "F-algebra --- {Wikipedia}{,} The Free Encyclopedia", year = "2017", howpublished = "\url{https://en.wikipedia.org/w/index.php?title=F-algebra&oldid=814231684}", } ================================================ FILE: Simplicity.cabal ================================================ cabal-version: 2.2 name: Simplicity version: 0.0.0 -- synopsis: -- description: license: MIT license-file: LICENSE author: Russell O'Connor maintainer: roconnor@blockstream.com copyright: (c) 2018 Blockstream category: Language build-type: Simple extra-source-files: README.md tested-with: GHC ==8.6.4 library Simplicity-Core C-sources: C/sha256.c, C/frame.c, C/jets.c, C/jets-secp256k1.c Haskell/cbits/frame.c, Haskell/cbits/coreJets.c Include-dirs: C Includes: sha256.h, frame.h, jets.h exposed-modules: Simplicity.Ty, Simplicity.Ty.Bit, Simplicity.Ty.Word, Simplicity.Ty.LibSecp256k1, Simplicity.Ty.Sha256, Simplicity.Term.Core, Simplicity.CoreJets, Simplicity.Functor, Simplicity.Tensor, Simplicity.FFI.Frame, Simplicity.FFI.Jets, Simplicity.BitMachine, Simplicity.BitMachine.Authentic, Simplicity.BitMachine.Ty, Simplicity.BitMachine.Translate, Simplicity.BitMachine.Translate.TCO, Simplicity.BitMachine.StaticAnalysis, Simplicity.BitMachine.StaticAnalysis.TCO, Simplicity.BitMachine.StaticAnalysis.Cost, Simplicity.Programs.Bit, Simplicity.Programs.Generic, Simplicity.Programs.Loop, Simplicity.Programs.Word, Simplicity.Programs.Arith, Simplicity.Programs.Sha256, Simplicity.Programs.Sha256.Lib, Simplicity.Programs.LibSecp256k1, Simplicity.Programs.LibSecp256k1.Lib, Simplicity.Programs.CheckSig, Simplicity.Programs.CheckSig.Lib, Simplicity.Programs.Bitcoin, Simplicity.Programs.Bitcoin.Lib, Simplicity.Programs.Elements, Simplicity.Programs.Elements.Lib, Simplicity.Programs.TimeLock, Simplicity.Digest, Simplicity.Digest.Pure.SHA, Simplicity.Tags, Simplicity.Tree, Simplicity.MerkleRoot, Simplicity.MerkleRoot.Impl, Simplicity.Delegator, Simplicity.Delegator.Impl, Simplicity.Serialization, Simplicity.Word, Simplicity.LibSecp256k1.Schnorr, Simplicity.LibSecp256k1.Spec, Simplicity.Bitcoin, Simplicity.Weight other-extensions: BangPatterns, FlexibleContexts, GADTs, StandaloneDeriving, TypeFamilies NoMonomorphismRestriction, UndecidableInstances, QuantifiedConstraints, RankNTypes, ExistentialQuantification, TypeOperators, TypeFamilies, DeriveTraversable, ScopedTypeVariables, RecordWildCards, ForeignFunctionInterface hs-source-dirs: Haskell/Core default-language: Haskell2010 ghc-options: -O2 build-depends: base >=4.9 && <4.20, binary >=0.7 && <0.9, bytestring >=0.10 && <0.13, containers >=0.5.10 && <0.7, cereal >=0.5 && <0.6, lens-family >=2.0 && <2.2, mtl >=2.2 && <2.4, MemoTrie >=0.6 && <0.7, split >=0.2.3 && <0.3, tardis >=0.4.1 && <0.6, transformers >=0.5 && <0.7, unification-fd >=0.10 && <0.12, vector >=0.12 && <0.14 library Simplicity-Bitcoin exposed-modules: Simplicity.Bitcoin.Primitive, Simplicity.Bitcoin.DataTypes other-extensions: GADTs, ScopedTypeVariables hs-source-dirs: Haskell/Bitcoin default-language: Haskell2010 ghc-options: -O2 build-depends: Simplicity-Core, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, vector >=0.12 && <0.14 library Simplicity-Elements exposed-modules: Simplicity.Elements.Primitive, Simplicity.Elements.DataTypes other-extensions: GADTs, ScopedTypeVariables hs-source-dirs: Haskell/Elements default-language: Haskell2010 ghc-options: -O2 build-depends: Simplicity-Core, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, containers >=0.5.10 && <0.7, lens-family >=2.0 && <2.2, vector >=0.12 && <0.14 library Simplicity-Indef exposed-modules: Simplicity.Term, Simplicity.Semantics, Simplicity.Dag, Simplicity.Inference Simplicity.JetType, Simplicity.Serialization.BitString, Simplicity.Serialization.ByteString, Simplicity.StaticAnalysis.Cost signatures: Simplicity.Primitive other-extensions: EmptyCase, EmptyDataDecls, EmptyDataDeriving, ScopedTypeVariables, DeriveTraversable, FlexibleInstances, GADTs, TypeFamilies, MultiParamTypeClasses, RankNTypes, UndecidableInstances hs-source-dirs: Haskell/Indef default-language: Haskell2010 ghc-options: -O2 build-depends: Simplicity-Core, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, containers >=0.5.10 && <0.7, lens-family >=2.0 && <2.2, mtl >=2.2 && <2.4, transformers >=0.5 && <0.7, unification-fd >=0.10 && <0.12, vector >=0.12 && <0.14 library C-sources: C/rsort.c C/elements/elementsJets.c C/elements/ops.c C/elements/env.c C/elements/txEnv.c C/bitcoin/bitcoinJets.c C/bitcoin/ops.c C/bitcoin/env.c C/bitcoin/txEnv.c Haskell/cbits/bitcoin/jets.c Haskell/cbits/bitcoin/env.c Haskell/cbits/elements/jets.c Haskell/cbits/elements/env.c Include-dirs: C C/include Includes: elements/elementsJets.h elements/primitive.h simplicity/elements/env.h exposed-modules: Simplicity.Bitcoin.Programs.SigHash, Simplicity.Bitcoin.Programs.SigHash.Lib, Simplicity.Bitcoin.Programs.Transaction, Simplicity.Bitcoin.Programs.Transaction.Lib, Simplicity.Bitcoin.Programs.TimeLock, Simplicity.Elements.Programs.TimeLock, Simplicity.Bitcoin.Benchmarks, Simplicity.Elements.Programs.Issuance, Simplicity.Elements.Programs.Issuance.Lib, Simplicity.Elements.Programs.SigHash, Simplicity.Elements.Programs.SigHash.Lib, Simplicity.Elements.Programs.Transaction, Simplicity.Elements.Programs.Transaction.Lib, Simplicity.Elements.Benchmarks, Simplicity.Bitcoin.Jets, Simplicity.Elements.Jets, Simplicity.Bitcoin.FFI.Env, Simplicity.Bitcoin.FFI.Jets, Simplicity.Elements.FFI.Env, Simplicity.Elements.FFI.Jets reexported-modules: Simplicity.Ty, Simplicity.Ty.Bit, Simplicity.Ty.Word, Simplicity.Ty.LibSecp256k1, Simplicity.Ty.Sha256, Simplicity.Term.Core, Simplicity.CoreJets, Simplicity.Functor, Simplicity.Tensor, Simplicity.FFI.Jets, Simplicity.BitMachine, Simplicity.BitMachine.Authentic, Simplicity.BitMachine.Ty, Simplicity.BitMachine.Translate, Simplicity.BitMachine.Translate.TCO, Simplicity.BitMachine.StaticAnalysis, Simplicity.BitMachine.StaticAnalysis.TCO, Simplicity.BitMachine.StaticAnalysis.Cost, Simplicity.Programs.Bit, Simplicity.Programs.Generic, Simplicity.Programs.Loop, Simplicity.Programs.Word, Simplicity.Programs.Arith, Simplicity.Programs.Sha256, Simplicity.Programs.Sha256.Lib, Simplicity.Programs.LibSecp256k1, Simplicity.Programs.LibSecp256k1.Lib, Simplicity.Programs.CheckSig, Simplicity.Programs.CheckSig.Lib, Simplicity.Programs.Bitcoin, Simplicity.Programs.Bitcoin.Lib, Simplicity.Programs.Elements, Simplicity.Programs.Elements.Lib, Simplicity.Programs.TimeLock, Simplicity.Digest, Simplicity.Tags, Simplicity.Tree, Simplicity.MerkleRoot, Simplicity.Delegator, Simplicity.Serialization, Simplicity.Word, Simplicity.LibSecp256k1.Schnorr, Simplicity.LibSecp256k1.Spec, Simplicity.Bitcoin, Simplicity.Bitcoin.Primitive, Simplicity.Bitcoin.DataTypes, Simplicity.Bitcoin.Term, Simplicity.Bitcoin.Semantics, Simplicity.Bitcoin.Dag, Simplicity.Bitcoin.Inference, Simplicity.Bitcoin.JetType, Simplicity.Bitcoin.Serialization.BitString, Simplicity.Bitcoin.Serialization.ByteString, Simplicity.Elements.Primitive, Simplicity.Elements.DataTypes, Simplicity.Elements.Term, Simplicity.Elements.Semantics, Simplicity.Elements.Dag, Simplicity.Elements.Inference, Simplicity.Elements.JetType, Simplicity.Elements.Serialization.BitString, Simplicity.Elements.Serialization.ByteString, Simplicity.Elements.StaticAnalysis.Cost, Simplicity.Weight mixins: Simplicity-Indef (Simplicity.Term as Simplicity.Bitcoin.Term, Simplicity.Semantics as Simplicity.Bitcoin.Semantics, Simplicity.Dag as Simplicity.Bitcoin.Dag, Simplicity.Inference as Simplicity.Bitcoin.Inference, Simplicity.JetType as Simplicity.Bitcoin.JetType, Simplicity.Serialization.BitString as Simplicity.Bitcoin.Serialization.BitString, Simplicity.Serialization.ByteString as Simplicity.Bitcoin.Serialization.ByteString, Simplicity.StaticAnalysis.Cost as Simplicity.Bitcoin.StaticAnalysis.Cost) requires (Simplicity.Primitive as Simplicity.Bitcoin.Primitive), Simplicity-Indef (Simplicity.Term as Simplicity.Elements.Term, Simplicity.Semantics as Simplicity.Elements.Semantics, Simplicity.Dag as Simplicity.Elements.Dag, Simplicity.Inference as Simplicity.Elements.Inference, Simplicity.JetType as Simplicity.Elements.JetType, Simplicity.Serialization.BitString as Simplicity.Elements.Serialization.BitString, Simplicity.Serialization.ByteString as Simplicity.Elements.Serialization.ByteString, Simplicity.StaticAnalysis.Cost as Simplicity.Elements.StaticAnalysis.Cost) requires (Simplicity.Primitive as Simplicity.Elements.Primitive) other-extensions: ConstraintKinds, GADTs, StandaloneDeriving, TypeFamilies hs-source-dirs: Haskell default-language: Haskell2010 ghc-options: -O2 build-depends: Simplicity-Core, Simplicity-Bitcoin, Simplicity-Elements, Simplicity-Indef, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, containers >=0.5.10 && <0.7, lens-family >=2.0 && <2.2, vector >=0.12 && <0.14 Test-Suite testsuite Type: exitcode-stdio-1.0 main-is: Tests.hs other-extensions: RankNTypes, GADTs, ScopedTypeVariables hs-source-dirs: Haskell/Tests default-language: Haskell2010 ghc-options: -threaded -O0 -with-rtsopts=-c other-modules: Simplicity.Programs.Example, Simplicity.Bip0340, Simplicity.Arbitrary, Simplicity.Ty.Arbitrary, Simplicity.Bitcoin.Arbitrary, Simplicity.Elements.Arbitrary, Simplicity.BitMachine.StaticAnalysis.Tests, Simplicity.BitMachine.Tests, Simplicity.Bitcoin.FFI.Primitive, Simplicity.Bitcoin.TestEval, Simplicity.Bitcoin.Tests, Simplicity.Bitcoin.FFI.Tests, Simplicity.Bitcoin.Serialization.Tests, Simplicity.FFI.Bitstream, Simplicity.FFI.Dag, Simplicity.Elements.FFI.Primitive, Simplicity.Elements.TestEval, Simplicity.Elements.Tests, Simplicity.Elements.FFI.Tests, Simplicity.Elements.Regression, Simplicity.Elements.Serialization.Tests, Simplicity.FFI.Tests, Simplicity.Programs.Tests, Simplicity.Serialization.Tests, Simplicity.TestCoreEval, Simplicity.Ty.Tests C-sources: C/rsort.c, C/dag.c, C/bitstream.c C/bitcoin/primitive.c C/elements/primitive.c Haskell/cbits/bitstream.c, Haskell/cbits/dag.c build-depends: Simplicity, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, containers >=0.5.10 && <0.7, lens-family >=2.0 && <2.2, QuickCheck >=2.10 && <2.16, mtl >=2.2 && <2.4, tasty >=0.11 && <1.6, tasty-hunit >=0.9 && <0.11, tasty-quickcheck >=0.8 && <0.12, transformers >=0.5 && <0.7, vector >=0.12 && <0.14 executable GenDecodeJet main-is: GenDecodeJet.hs ghc-options: -main-is GenDecodeJet -- Modules included in this executable, other than Main. -- other-modules: -- LANGUAGE extensions used by modules in this package. -- other-extensions: hs-source-dirs: Haskell-Generate default-language: Haskell2010 other-modules: NameWrangler build-depends: Simplicity, base >=4.9 && <4.20, prettyprinter >=1.7 && <1.8, split >=0.2.3 && <0.3, executable GenPrecomputed main-is: GenPrecomputed.hs ghc-options: -main-is GenPrecomputed -- Modules included in this executable, other than Main. -- other-modules: -- LANGUAGE extensions used by modules in this package. -- other-extensions: hs-source-dirs: Haskell-Generate default-language: Haskell2010 build-depends: Simplicity, base >=4.9 && <4.20, prettyprinter >=1.7 && <1.8, split >=0.2.3 && <0.3, executable GenPrimitive main-is: GenPrimitive.hs ghc-options: -main-is GenPrimitives -- Modules included in this executable, other than Main. -- other-modules: -- LANGUAGE extensions used by modules in this package. -- other-extensions: hs-source-dirs: Haskell-Generate default-language: Haskell2010 other-modules: NameWrangler build-depends: Simplicity, base >=4.9 && <4.20, containers >=0.5.10 && <0.7, mtl >=2.2 && <2.4, split >=0.2.3 && <0.3, unification-fd >=0.10 && <0.12, executable GenTests main-is: GenTests.hs ghc-options: -main-is GenTests -- Modules included in this executable, other than Main. -- other-modules: -- LANGUAGE extensions used by modules in this package. -- other-extensions: hs-source-dirs: Haskell-Generate default-language: Haskell2010 build-depends: Simplicity, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, lens-family >=2.0 && <2.2, split >=0.2.3 && <0.3, vector >=0.12 && <0.14, executable GenRustJets main-is: GenRustJets.hs ghc-options: -main-is GenRustJets -- Modules included in this executable, other than Main. -- other-modules: -- LANGUAGE extensions used by modules in this package. -- other-extensions: hs-source-dirs: Haskell-Generate default-language: Haskell2010 other-modules: NameWrangler other-extensions: OverloadedStrings build-depends: Simplicity, base >=4.9 && <4.20, containers >=0.5.10 && <0.7, prettyprinter >=1.7 && <1.8, split >=0.2.3 && <0.3, transformers >=0.5 && <0.7, unification-fd >=0.10 && <0.12, executable TestnetTransaction main-is: TestnetTransaction.hs ghc-options: -main-is TestnetTransaction -- Modules included in this executable, other than Main. -- other-modules: -- LANGUAGE extensions used by modules in this package. -- other-extensions: hs-source-dirs: Haskell-Examples default-language: Haskell2010 build-depends: Simplicity, array >=0.5 && <0.6, base >=4.9 && <4.20, bytestring >=0.10 && <0.13, cereal >=0.5 && <0.6, entropy >=0.4 && <0.5, lens-family >=2.0 && <2.2, vector >=0.12 && <0.14, ================================================ FILE: alectryon/alectryon.css ================================================ @charset "UTF-8"; /* Copyright © 2019 Clément Pit-Claudel Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ /*******************************/ /* CSS reset for .alectryon-io */ /*******************************/ .alectryon-io blockquote { line-height: inherit; } .alectryon-io blockquote:after { display: none; } .alectryon-io label { display: inline; font-size: inherit; margin: 0; } /* Undo and
, added to improve RSS rendering. */ .alectryon-io small.alectryon-output { font-size: inherit; } .alectryon-io blockquote.alectryon-goal, .alectryon-io blockquote.alectryon-message { font-weight: normal; font-size: inherit; } /***************/ /* Main styles */ /***************/ .alectryon-coqdoc .doc .code, .alectryon-coqdoc .doc .comment, .alectryon-coqdoc .doc .inlinecode, .alectryon-mref, .alectryon-block, .alectryon-io, .alectryon-toggle-label, .alectryon-banner { font-family: 'Iosevka Slab Web', 'Iosevka Web', 'Iosevka Slab', 'Iosevka', 'Fira Code', monospace; font-feature-settings: "COQX" 1 /* Coq ligatures */, "XV00" 1 /* Legacy */, "calt" 1 /* Fallback */; line-height: initial; } .alectryon-io, .alectryon-block, .alectryon-toggle-label, .alectryon-banner { overflow: visible; overflow-wrap: break-word; position: relative; white-space: pre-wrap; } /* CoqIDE doesn't turn off the unicode bidirectional algorithm (and PG simply respects the user's `bidi-display-reordering` setting), so don't turn it off here either. But beware unexpected results like `Definition test_אב := 0.` .alectryon-io span { direction: ltr; unicode-bidi: bidi-override; } In any case, make an exception for comments: .highlight .c { direction: embed; unicode-bidi: initial; } */ .alectryon-mref, .alectryon-mref-marker { align-self: center; box-sizing: border-box; display: inline-block; font-size: 80%; font-weight: bold; line-height: 1; box-shadow: 0 0 0 1pt black; padding: 1pt 0.3em; text-decoration: none; } .alectryon-block .alectryon-mref-marker, .alectryon-io .alectryon-mref-marker { user-select: none; margin: -0.25em 0 -0.25em 0.5em; } .alectryon-inline .alectryon-mref-marker { margin: -0.25em 0.15em -0.25em 0.625em; /* 625 = 0.5em / 80% */ } .alectryon-mref { color: inherit; margin: -0.5em 0.25em; } .alectryon-goal:target .goal-separator .alectryon-mref-marker, :target > .alectryon-mref-marker { animation: blink 0.2s step-start 0s 3 normal none; background-color: #fcaf3e; position: relative; } @keyframes blink { 50% { box-shadow: 0 0 0 3pt #fcaf3e, 0 0 0 4pt black; z-index: 10; } } .alectryon-toggle, .alectryon-io .alectryon-extra-goal-toggle { display: none; } .alectryon-bubble, .alectryon-io label, .alectryon-toggle-label { cursor: pointer; } .alectryon-toggle-label { display: block; font-size: 0.8em; } .alectryon-io .alectryon-input { padding: 0.1em 0; /* Enlarge the hitbox slightly to fill interline gaps */ } .alectryon-io .alectryon-sentence.alectryon-target .alectryon-input { /* FIXME if keywords were ‘bolder’ we wouldn't need !important */ font-weight: bold !important; /* Use !important to avoid a * selector */ } .alectryon-bubble:before, .alectryon-toggle-label:before, .alectryon-io label.alectryon-input:after, .alectryon-io .alectryon-goal > label:before { border: 1px solid #babdb6; border-radius: 1em; box-sizing: border-box; content: ''; display: inline-block; font-weight: bold; height: 0.25em; margin-bottom: 0.15em; vertical-align: middle; width: 0.75em; } .alectryon-toggle-label:before, .alectryon-io .alectryon-goal > label:before { margin-right: 0.25em; } .alectryon-io .alectryon-goal > label:before { margin-top: 0.125em; } .alectryon-io label.alectryon-input { padding-right: 1em; /* Prevent line wraps before the checkbox bubble */ } .alectryon-io label.alectryon-input:after { margin-left: 0.25em; margin-right: -1em; /* Compensate for the anti-wrapping space */ } .alectryon-failed { /* Underlines are broken in Chrome (they reset at each element boundary)… */ /* text-decoration: red wavy underline; */ /* … but it isn't too noticeable with dots */ text-decoration: red dotted underline; text-decoration-skip-ink: none; /* Chrome prints background images in low resolution, yielding a blurry underline */ /* background: bottom / 0.3em auto repeat-x url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAyLjY0NiAxLjg1MiIgaGVpZ2h0PSI4IiB3aWR0aD0iMTAiPjxwYXRoIGQ9Ik0wIC4yNjVjLjc5NCAwIC41MyAxLjMyMiAxLjMyMyAxLjMyMi43OTQgMCAuNTMtMS4zMjIgMS4zMjMtMS4zMjIiIGZpbGw9Im5vbmUiIHN0cm9rZT0icmVkIiBzdHJva2Utd2lkdGg9Ii41MjkiLz48L3N2Zz4=); */ } /* Wrapping :hover rules in a media query ensures that tapping a Coq sentence doesn't trigger its :hover state (otherwise, on mobile, tapping a sentence to hide its output causes it to remain visible (its :hover state gets triggered. We only do it for the default style though, since other styles don't put the output over the main text, so showing too much is not an issue. */ @media (any-hover: hover) { .alectryon-bubble:hover:before, .alectryon-toggle-label:hover:before, .alectryon-io label.alectryon-input:hover:after { background: #eeeeec; } .alectryon-io label.alectryon-input:hover { text-decoration: underline dotted #babdb6; text-shadow: 0 0 1px rgb(46, 52, 54, 0.3); /* #2e3436 + opacity */ } .alectryon-io .alectryon-sentence:hover .alectryon-output { z-index: 2; /* Place hovered goals above .alectryon-sentence.alectryon-target ones */ } } .alectryon-toggle:checked + .alectryon-toggle-label:before, .alectryon-io .alectryon-sentence > .alectryon-toggle:checked + label.alectryon-input:after, .alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal > label:before { background-color: #babdb6; border-color: #babdb6; } /* Disable clicks on sentences when the document-wide toggle is set. */ .alectryon-toggle:checked + label + .alectryon-container label.alectryon-input { cursor: unset; pointer-events: none; } /* Hide individual checkboxes when the document-wide toggle is set. */ .alectryon-toggle:checked + label + .alectryon-container label.alectryon-input:after { display: none; } /* .alectryon-output is displayed by toggles, :hover, and .alectryon-target rules */ .alectryon-io .alectryon-output { box-sizing: border-box; display: none; left: 0; right: 0; position: absolute; padding: 0.25em 0; overflow: visible; /* Let box-shadows overflow */ z-index: 1; /* Default to an index lower than that used by :hover */ } @media (any-hover: hover) { /* See note above about this @media query */ .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) { display: block; } } .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output { display: block; } /* Indicate active (hovered or targeted) goals with a shadow. */ .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-messages, .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output .alectryon-messages, .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-goals, .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output .alectryon-goals { box-shadow: 0 0 3px gray; } .alectryon-io .alectryon-extra-goals .alectryon-goal .goal-hyps { display: none; } .alectryon-io .alectryon-extra-goals .alectryon-extra-goal-toggle:not(:checked) + .alectryon-goal label.goal-separator hr { /* Dashes indicate that the hypotheses are hidden */ border-top-style: dashed; } /* Show just a small preview of the other goals; this is undone by the "extra-goal" toggle and by :hover and .alectryon-target in windowed mode. */ .alectryon-io .alectryon-extra-goals .alectryon-goal .goal-conclusion { max-height: 5.2em; overflow-y: auto; /* Combining ‘overflow-y: auto’ with ‘display: inline-block’ causes extra space to be added below the box. ‘vertical-align: middle’ gets rid of it. */ vertical-align: middle; } .alectryon-io .alectryon-goals, .alectryon-io .alectryon-messages { background: #eeeeec; border: thin solid #d3d7cf; /* Convenient when pre's background is already #EEE */ display: block; padding: 0.25em; } .alectryon-message::before { content: ''; float: right; /* etc/svg/square-bubble-xl.svg */ background: url("data:image/svg+xml,%3Csvg width='14' height='14' viewBox='0 0 3.704 3.704' xmlns='http://www.w3.org/2000/svg'%3E%3Cg fill-rule='evenodd' stroke='%23000' stroke-width='.264'%3E%3Cpath d='M.794.934h2.115M.794 1.463h1.455M.794 1.992h1.852'/%3E%3C/g%3E%3Cpath d='M.132.14v2.646h.794v.661l.926-.661h1.72V.14z' fill='none' stroke='%23000' stroke-width='.265'/%3E%3C/svg%3E") top right no-repeat; height: 14px; width: 14px; } .alectryon-toggle:checked + label + .alectryon-container { width: unset; } /* Show goals when a toggle is set */ .alectryon-toggle:checked + label + .alectryon-container label.alectryon-input + .alectryon-output, .alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output { display: block; position: static; width: unset; background: unset; /* Override the backgrounds set in floating in windowed mode */ padding: 0.25em 0; /* Re-assert so that later :hover rules don't override this padding */ } .alectryon-toggle:checked + label + .alectryon-container label.alectryon-input + .alectryon-output .goal-hyps, .alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output .goal-hyps { /* Overridden back in windowed style */ flex-flow: row wrap; justify-content: flex-start; } .alectryon-toggle:checked + label + .alectryon-container .alectryon-sentence .alectryon-output > div, .alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output > div { display: block; } .alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal .goal-hyps { display: flex; } .alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal .goal-conclusion { max-height: unset; overflow-y: unset; } .alectryon-toggle:checked + label + .alectryon-container .alectryon-sentence > .alectryon-toggle ~ .alectryon-wsp, .alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-wsp { display: none; } .alectryon-io .alectryon-messages, .alectryon-io .alectryon-message, .alectryon-io .alectryon-goals, .alectryon-io .alectryon-goal, .alectryon-io .goal-hyps > span, .alectryon-io .goal-conclusion { border-radius: 0.15em; } .alectryon-io .alectryon-goal, .alectryon-io .alectryon-message { align-items: center; background: #d3d7cf; display: block; flex-direction: column; margin: 0.25em; padding: 0.5em; position: relative; } .alectryon-io .goal-hyps { align-content: space-around; align-items: baseline; display: flex; flex-flow: column nowrap; /* re-stated in windowed mode */ justify-content: space-around; /* LATER use a ‘gap’ property instead of margins once supported */ margin: -0.15em -0.25em; /* -0.15em to cancel the item spacing */ padding-bottom: 0.35em; /* 0.5em-0.15em to cancel the 0.5em of .goal-separator */ } .alectryon-io .goal-hyps > br { display: none; /* Only for RSS readers */ } .alectryon-io .goal-hyps > span, .alectryon-io .goal-conclusion { background: #eeeeec; display: inline-block; padding: 0.15em 0.35em; } .alectryon-io .goal-hyps > span { align-items: baseline; display: inline-flex; margin: 0.15em 0.25em; } .alectryon-block var, .alectryon-inline var, .alectryon-io .goal-hyps > span > var { font-weight: 600; font-style: unset; } .alectryon-io .goal-hyps > span > var { /* Shrink the list of names, but let it grow as long as space is available. */ flex-basis: min-content; flex-grow: 1; } .alectryon-io .goal-hyps > span b { font-weight: 600; margin: 0 0 0 0.5em; white-space: pre; } .alectryon-io .hyp-body, .alectryon-io .hyp-type { display: flex; align-items: baseline; } .alectryon-io .goal-separator { align-items: center; display: flex; flex-direction: row; height: 1em; /* Fixed height to ignore goal name and markers */ margin-top: -0.5em; /* Compensated in .goal-hyps when shown */ } .alectryon-io .goal-separator hr { border: none; border-top: thin solid #555753; display: block; flex-grow: 1; margin: 0; } .alectryon-io .goal-separator .goal-name { font-size: 0.75em; margin-left: 0.5em; } /**********/ /* Banner */ /**********/ .alectryon-banner { background: #eeeeec; border: 1px solid #babcbd; font-size: 0.75em; padding: 0.25em; text-align: center; margin: 1em 0; } .alectryon-banner a { cursor: pointer; text-decoration: underline; } .alectryon-banner kbd { background: #d3d7cf; border-radius: 0.15em; border: 1px solid #babdb6; box-sizing: border-box; display: inline-block; font-family: inherit; font-size: 0.9em; height: 1.3em; line-height: 1.2em; margin: -0.25em 0; padding: 0 0.25em; vertical-align: middle; } /**********/ /* Toggle */ /**********/ .alectryon-toggle-label { margin: 1rem 0; } /******************/ /* Floating style */ /******************/ /* If there's space, display goals to the right of the code, not below it. */ @media (min-width: 80rem) { /* Unlike the windowed case, we don't want to move output blocks to the side when they are both :checked and -targeted, since it gets confusing as things jump around; hence the commented-output part of the selector, which would otherwise increase specificity */ .alectryon-floating .alectryon-sentence.alectryon-target /* > .alectryon-toggle ~ */ .alectryon-output, .alectryon-floating .alectryon-sentence:hover .alectryon-output { top: 0; left: 100%; right: -100%; padding: 0 0.5em; position: absolute; } .alectryon-floating .alectryon-output { min-height: 100%; } .alectryon-floating .alectryon-sentence:hover .alectryon-output { background: white; /* Ensure that short goals hide long ones */ } /* This odd margin-bottom property prevents the sticky div from bumping against the bottom of its container (.alectryon-output). The alternative would be enlarging .alectryon-output, but that would cause overflows, enlarging scrollbars and yielding scrolling towards the bottom of the page. Doing things this way instead makes it possible to restrict .alectryon-output to a reasonable size (100%, through top = bottom = 0). See also https://stackoverflow.com/questions/43909940/. */ /* See note on specificity above */ .alectryon-floating .alectryon-sentence.alectryon-target /* > .alectryon-toggle ~ */ .alectryon-output > div, .alectryon-floating .alectryon-sentence:hover .alectryon-output > div { margin-bottom: -200%; position: sticky; top: 0; } .alectryon-floating .alectryon-toggle:checked + label + .alectryon-container .alectryon-sentence .alectryon-output > div, .alectryon-floating .alectryon-io .alectryon-sentence > .alectryon-toggle:checked ~ .alectryon-output > div { margin-bottom: unset; /* Undo the margin */ } /* Float underneath the current fragment @media (max-width: 80rem) { .alectryon-floating .alectryon-output { top: 100%; } } */ } /********************/ /* Multi-pane style */ /********************/ .alectryon-windowed { border: 0 solid #2e3436; box-sizing: border-box; } .alectryon-windowed .alectryon-sentence:hover .alectryon-output { background: white; /* Ensure that short goals hide long ones */ } .alectryon-windowed .alectryon-output { position: fixed; /* Overwritten by the ‘:checked’ rules */ } /* See note about specificity below */ .alectryon-windowed .alectryon-sentence:hover .alectryon-output, .alectryon-windowed .alectryon-sentence.alectryon-target > .alectryon-toggle ~ .alectryon-output { padding: 0.5em; overflow-y: auto; /* Windowed contents may need to scroll */ } .alectryon-windowed .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-messages, .alectryon-windowed .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output .alectryon-messages, .alectryon-windowed .alectryon-io .alectryon-sentence:hover .alectryon-output:not(:hover) .alectryon-goals, .alectryon-windowed .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output .alectryon-goals { box-shadow: none; /* A shadow is unnecessary here and incompatible with overflow-y set to auto */ } .alectryon-windowed .alectryon-io .alectryon-sentence.alectryon-target .alectryon-output .goal-hyps { /* Restated to override the :checked style */ flex-flow: column nowrap; justify-content: space-around; } .alectryon-windowed .alectryon-sentence.alectryon-target .alectryon-extra-goals .alectryon-goal .goal-conclusion /* Like .alectryon-io .alectryon-extra-goal-toggle:checked + .alectryon-goal .goal-conclusion */ { max-height: unset; overflow-y: unset; } .alectryon-windowed .alectryon-output > div { display: flex; /* Put messages after goals */ flex-direction: column-reverse; } /*********************/ /* Standalone styles */ /*********************/ .alectryon-standalone { font-family: 'IBM Plex Serif', 'PT Serif', 'Merriweather', 'DejaVu Serif', serif; line-height: 1.5; } @media screen and (min-width: 50rem) { html.alectryon-standalone { /* Prevent flickering when hovering a block causes scrollbars to appear. */ margin-left: calc(100vw - 100%); margin-right: 0; } } /* Coqdoc */ .alectryon-coqdoc .doc .code, .alectryon-coqdoc .doc .inlinecode, .alectryon-coqdoc .doc .comment { display: inline; } .alectryon-coqdoc .doc .comment { color: #eeeeec; } .alectryon-coqdoc .doc .paragraph { height: 0.75em; } /* Centered, Floating */ .alectryon-standalone .alectryon-centered, .alectryon-standalone .alectryon-floating { max-width: 50rem; margin: auto; } @media (min-width: 80rem) { .alectryon-standalone .alectryon-floating { max-width: 80rem; } .alectryon-standalone .alectryon-floating > * { width: 50%; margin-left: 0; } } /* Windowed */ .alectryon-standalone .alectryon-windowed { display: block; margin: 0; overflow-y: auto; position: absolute; padding: 0 1em; } .alectryon-standalone .alectryon-windowed > * { /* Override properties of docutils_basic.css */ margin-left: 0; max-width: unset; } .alectryon-standalone .alectryon-windowed .alectryon-io { box-sizing: border-box; width: 100%; } /* No need to predicate the ‘:hover’ rules below on ‘:not(:checked)’, since ‘left’, ‘right’, ‘top’, and ‘bottom’ will be inactived by the :checked rules setting ‘position’ to ‘static’ */ /* Specificity: We want the output to stay inline when hovered while unfolded (:checked), but we want it to move when it's targeted (i.e. when the user is browsing goals one by one using the keyboard, in which case we want to goals to appear in consistent locations). The selectors below ensure that :hover < :checked < -targeted in terms of specificity. */ /* LATER: Reimplement this stuff with CSS variables */ .alectryon-windowed .alectryon-sentence.alectryon-target > .alectryon-toggle ~ .alectryon-output { position: fixed; } @media screen and (min-width: 60rem) { .alectryon-standalone .alectryon-windowed { border-right-width: thin; bottom: 0; left: 0; right: 50%; top: 0; } .alectryon-standalone .alectryon-windowed .alectryon-sentence:hover .alectryon-output, .alectryon-standalone .alectryon-windowed .alectryon-sentence.alectryon-target .alectryon-output { bottom: 0; left: 50%; right: 0; top: 0; } } @media screen and (max-width: 60rem) { .alectryon-standalone .alectryon-windowed { border-bottom-width: 1px; bottom: 40%; left: 0; right: 0; top: 0; } .alectryon-standalone .alectryon-windowed .alectryon-sentence:hover .alectryon-output, .alectryon-standalone .alectryon-windowed .alectryon-sentence.alectryon-target .alectryon-output { bottom: 0; left: 0; right: 0; top: 60%; } } ================================================ FILE: alectryon/alectryon.js ================================================ var Alectryon; (function(Alectryon) { (function (slideshow) { function anchor(sentence) { return "#" + sentence.id; } function current_sentence() { return slideshow.sentences[slideshow.pos]; } function unhighlight() { var sentence = current_sentence(); if (sentence) sentence.classList.remove("alectryon-target"); slideshow.pos = -1; } function highlight(sentence) { sentence.classList.add("alectryon-target"); } function scroll(sentence) { // Put the top of the current fragment close to the top of the // screen, but scroll it out of view if showing it requires pushing // the sentence past half of the screen. If sentence is already in // a reasonable position, don't move. var parent = sentence.parentElement; /* We want to scroll the whole document, so start at root… */ while (parent && !parent.classList.contains("alectryon-root")) parent = parent.parentElement; /* … and work up from there to find a scrollable element. parent.scrollHeight can be greater than parent.clientHeight without showing scrollbars, so we add a 10px buffer. */ while (parent && parent.scrollHeight <= parent.clientHeight + 10) parent = parent.parentElement; /* and elements can have their client rect overflow * the window if their height is unset, so scroll the window * instead */ if (parent && (parent.nodeName == "BODY" || parent.nodeName == "HTML")) parent = null; var rect = function(e) { return e.getBoundingClientRect(); }; var parent_box = parent ? rect(parent) : { y: 0, height: window.innerHeight }, sentence_y = rect(sentence).y - parent_box.y, fragment_y = rect(sentence.parentElement).y - parent_box.y; // The assertion below sometimes fails for the first element in a block. // console.assert(sentence_y >= fragment_y); if (sentence_y < 0.1 * parent_box.height || sentence_y > 0.7 * parent_box.height) { (parent || window).scrollBy( 0, Math.max(sentence_y - 0.5 * parent_box.height, fragment_y - 0.1 * parent_box.height)); } } function highlighted(pos) { return slideshow.pos == pos; } function navigate(pos, inhibitScroll) { unhighlight(); slideshow.pos = Math.min(Math.max(pos, 0), slideshow.sentences.length - 1); var sentence = current_sentence(); highlight(sentence); if (!inhibitScroll) scroll(sentence); } var keys = { PAGE_UP: 33, PAGE_DOWN: 34, ARROW_UP: 38, ARROW_DOWN: 40, h: 72, l: 76, p: 80, n: 78 }; function onkeydown(e) { e = e || window.event; if (e.ctrlKey || e.metaKey) { if (e.keyCode == keys.ARROW_UP) slideshow.previous(); else if (e.keyCode == keys.ARROW_DOWN) slideshow.next(); else return; } else { // if (e.keyCode == keys.PAGE_UP || e.keyCode == keys.p || e.keyCode == keys.h) // slideshow.previous(); // else if (e.keyCode == keys.PAGE_DOWN || e.keyCode == keys.n || e.keyCode == keys.l) // slideshow.next(); // else return; } e.preventDefault(); } function start() { slideshow.navigate(0); } function toggleHighlight(idx) { if (highlighted(idx)) unhighlight(); else navigate(idx, true); } function handleClick(evt) { if (evt.ctrlKey || evt.metaKey) { var sentence = evt.currentTarget; // Ensure that the goal is shown on the side, not inline var checkbox = sentence.getElementsByClassName("alectryon-toggle")[0]; if (checkbox) checkbox.checked = false; toggleHighlight(sentence.alectryon_index); evt.preventDefault(); } } function init() { document.onkeydown = onkeydown; slideshow.pos = -1; slideshow.sentences = Array.from(document.getElementsByClassName("alectryon-sentence")); slideshow.sentences.forEach(function (s, idx) { s.addEventListener('click', handleClick, false); s.alectryon_index = idx; }); } slideshow.start = start; slideshow.end = unhighlight; slideshow.navigate = navigate; slideshow.next = function() { navigate(slideshow.pos + 1); }; slideshow.previous = function() { navigate(slideshow.pos + -1); }; window.addEventListener('DOMContentLoaded', init); })(Alectryon.slideshow || (Alectryon.slideshow = {})); (function (styles) { var styleNames = ["centered", "floating", "windowed"]; function className(style) { return "alectryon-" + style; } function setStyle(style) { var root = document.getElementsByClassName("alectryon-root")[0]; styleNames.forEach(function (s) { root.classList.remove(className(s)); }); root.classList.add(className(style)); } function init() { var banner = document.getElementsByClassName("alectryon-banner")[0]; if (banner) { banner.append(" Style: "); styleNames.forEach(function (styleName, idx) { var s = styleName; var a = document.createElement("a"); a.onclick = function() { setStyle(s); }; a.append(styleName); if (idx > 0) banner.append("; "); banner.appendChild(a); }); banner.append("."); } } window.addEventListener('DOMContentLoaded', init); styles.setStyle = setStyle; })(Alectryon.styles || (Alectryon.styles = {})); })(Alectryon || (Alectryon = {})); ================================================ FILE: alectryon/divstep.v.html ================================================ divstep.v
Built with Alectryon, running Coq+SerAPI v8.17.0+0.17.3. Bubbles () indicate interactive fragments: hover for details, tap to reveal contents. Use Ctrl+↑ Ctrl+↓ to navigate, Ctrl+🖱️ to focus. On Mac, use ⌘ instead of Ctrl.
Require Import ZArith.
Require Import ZArith.Znumtheory.
Require Import ZArith.Zpow_facts.
Require Import Lia.
Require Import List.

Require Import divsteps.divsteps_def.
Require Import extraMath.
Require Import modinv.

Open Scope list_scope.
Open Scope Z_scope.
Arguments Z.add !x !y.
Arguments Z.sub !m !n.
Arguments Z.mul !x !y.


z: Z
Hz1, Hz2: Zodd z
Hz1 = Hz2


z: Z
Hz1, Hz2: Zodd z
Hz1 = Hz2


z: Z
forall Hz1 Hz2 : Zodd z, Hz1 = Hz2

destruct z as [|p|p]; try destruct p; try contradiction; intros [] []; reflexivity.
Defined.

Module Step.

Inductive Step : Set :=
| D : Step
| S : Step
| H : Step.

End Step.
Definition Step := Step.Step.

Definition INC : Z := 1.

Record State : Set :=
 { delta : Z
 ; f : Z
 ; g : Z
 ; oddF : Zodd f
 }.

Definition eta (st : State) := Z.opp (delta st).

Definition init f g oddF :=
{| delta := 1
 ; f := f
 ; g := g
 ; oddF := oddF
 |}.

Definition step (st : State) : State * Step :=
match Zeven_odd_dec (g st) with
| left _ => ({| delta := INC + delta st
              ; f := f st
              ; g := g st / 2
              ; oddF := oddF st
              |}
            , Step.H)
| right oddG =>
    if (0 <? delta st)%Z
    then ({| delta := INC - delta st
           ; f := g st
           ; g := (g st - f st) / 2
           ; oddF := oddG
           |}
         , Step.D)
    else ({| delta := INC + delta st
           ; f := f st
           ; g := (g st + f st) / 2
           ; oddF := oddF st
           |}
         , Step.S)
end.

(* Last step is first in the list to facilitate matrix multiplication. *)
Fixpoint stepN (n : nat) : State -> State * list Step  :=
match n with
| O => fun st => (st, nil)
| (S n) => fun st =>
    let (st0, xs) := stepN n st in
    let (st1, x) := step st0 in
    (st1, x :: xs)
end.

Inductive Spec : State -> (State * Step) -> Set :=
| specH : forall d f' g', Spec {| delta := d; f := 2*f'+1; g := 2*g'; oddF := Zodd_2p_plus_1 f' |}
                               ({| delta := INC + d; f := 2*f'+1; g := g'; oddF := Zodd_2p_plus_1 f' |}, Step.H)
| specD : forall d f' g', Spec {| delta := Z.pos d; f := 2*f'+1; g := 2*g'+1; oddF := Zodd_2p_plus_1 f' |}
                               ({| delta := INC - Z.pos d; f := 2*g'+1; g := g' - f'; oddF := Zodd_2p_plus_1 g' |}, Step.D)
| specS : forall d f' g', (d <= 0) ->
                          Spec {| delta := d; f := 2*f'+1; g := 2*g'+1; oddF := Zodd_2p_plus_1 f' |}
                               ({| delta := INC + d; f := 2*f'+1; g := g' + f' + 1; oddF := Zodd_2p_plus_1 f' |}, Step.S).


st: State
Spec st (step st)


st: State
Spec st (step st)


d0, f0, g0: Z
Hf0: Zodd f0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (step
     {| delta := d0; f := f0; g := g0; oddF := Hf0 |})


d0, f0, g0: Z
Hf0: Zodd f0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  match Zeven_odd_dec g0 with
  | left _ =>
      ({|
         delta := 1 + d0;
         f := f0;
         g := g0 / 2;
         oddF := Hf0
       |}, Step.H)
  | right oddG =>
      if 0 <? d0
      then
       ({|
          delta := 1 - d0;
          f := g0;
          g := (g0 - f0) / 2;
          oddF := oddG
        |}, Step.D)
      else
       ({|
          delta := 1 + d0;
          f := f0;
          g := (g0 + f0) / 2;
          oddF := Hf0
        |}, Step.S)
  end


d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zeven g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  ({|
     delta := 1 + d0;
     f := f0;
     g := g0 / 2;
     oddF := Hf0
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zeven g0
forall Hf0 : Zodd f0,
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  ({|
     delta := 1 + d0;
     f := f0;
     g := g0 / 2;
     oddF := Hf0
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zeven g0
forall Hf0 : Zodd f0,
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  ({|
     delta := 1 + d0;
     f := f0;
     g := g0 / 2;
     oddF := Hf0
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zeven g0
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := g0;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := g0 / 2;
     oddF := Hf0
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zeven g0
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := 2 * Z.div2 g0 / 2;
     oddF := Hf0
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zeven g0
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := Z.div2 g0;
     oddF := Hf0
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zeven g0
Hf0': Zodd (2 * Z.div2 f0 + 1)
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0;
    oddF := Hf0'
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := Z.div2 g0;
     oddF := Hf0'
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zeven g0
Hf0': Zodd (2 * Z.div2 f0 + 1)
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0;
    oddF := Zodd_2p_plus_1 (Z.div2 f0)
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := Z.div2 g0;
     oddF := Zodd_2p_plus_1 (Z.div2 f0)
   |}, Step.H)
d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Zodd f0
Hg0: Zodd g0
forall (Hf0 : Zodd f0) (Hg0 : Zodd g0),
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Zodd g0
forall (Hf0 : Zodd f0) (Hg0 : Zodd g0),
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
forall (Hf0 : Zodd f0) (Hg0 : Zodd g0),
Spec {| delta := d0; f := f0; g := g0; oddF := Hf0 |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - f0) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := f0;
       g := (g0 + f0) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
forall (Hf0 : Zodd (2 * Z.div2 f0 + 1))
  (Hg0 : Zodd g0),
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := g0;
    oddF := Hf0
  |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := g0;
       g := (g0 - (2 * Z.div2 f0 + 1)) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := 2 * Z.div2 f0 + 1;
       g := (g0 + (2 * Z.div2 f0 + 1)) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
forall (Hf0 : Zodd (2 * Z.div2 f0 + 1))
  (Hg0 : Zodd (2 * Z.div2 g0 + 1)),
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  (if 0 <? d0
   then
    ({|
       delta := 1 - d0;
       f := 2 * Z.div2 g0 + 1;
       g :=
         (2 * Z.div2 g0 + 1 - (2 * Z.div2 f0 + 1)) / 2;
       oddF := Hg0
     |}, Step.D)
   else
    ({|
       delta := 1 + d0;
       f := 2 * Z.div2 f0 + 1;
       g :=
         (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
       oddF := Hf0
     |}, Step.S))


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = true
forall (Hf0 : Zodd (2 * Z.div2 f0 + 1))
  (Hg0 : Zodd (2 * Z.div2 g0 + 1)),
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 - d0;
     f := 2 * Z.div2 g0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 - (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hg0
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


p: positive
f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? Z.pos p) = true
forall (Hf0 : Zodd (2 * Z.div2 f0 + 1))
  (Hg0 : Zodd (2 * Z.div2 g0 + 1)),
Spec
  {|
    delta := Z.pos p;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 - Z.pos p;
     f := 2 * Z.div2 g0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 - (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hg0
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


p: positive
f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? Z.pos p) = true
forall (Hf0 : Zodd (2 * Z.div2 f0 + 1))
  (Hg0 : Zodd (2 * Z.div2 g0 + 1)),
Spec
  {|
    delta := Z.pos p;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 - Z.pos p;
     f := 2 * Z.div2 g0 + 1;
     g := (Z.div2 g0 - Z.div2 f0) * 2 / 2;
     oddF := Hg0
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


p: positive
f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? Z.pos p) = true
forall (Hf0 : Zodd (2 * Z.div2 f0 + 1))
  (Hg0 : Zodd (2 * Z.div2 g0 + 1)),
Spec
  {|
    delta := Z.pos p;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 - Z.pos p;
     f := 2 * Z.div2 g0 + 1;
     g := Z.div2 g0 - Z.div2 f0;
     oddF := Hg0
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


p: positive
f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? Z.pos p) = true
Hf0': Zodd (2 * Z.div2 f0 + 1)
Hg0': Zodd (2 * Z.div2 g0 + 1)
Spec
  {|
    delta := Z.pos p;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0'
  |}
  ({|
     delta := 1 - Z.pos p;
     f := 2 * Z.div2 g0 + 1;
     g := Z.div2 g0 - Z.div2 f0;
     oddF := Hg0'
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


p: positive
f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? Z.pos p) = true
Hf0': Zodd (2 * Z.div2 f0 + 1)
Hg0': Zodd (2 * Z.div2 g0 + 1)
Spec
  {|
    delta := Z.pos p;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Zodd_2p_plus_1 (Z.div2 f0)
  |}
  ({|
     delta := 1 - Z.pos p;
     f := 2 * Z.div2 g0 + 1;
     g := Z.div2 g0 - Z.div2 f0;
     oddF := Hg0'
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


p: positive
f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? Z.pos p) = true
Hf0': Zodd (2 * Z.div2 f0 + 1)
Hg0': Zodd (2 * Z.div2 g0 + 1)
Spec
  {|
    delta := Z.pos p;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Zodd_2p_plus_1 (Z.div2 f0)
  |}
  ({|
     delta := 1 - Z.pos p;
     f := 2 * Z.div2 g0 + 1;
     g := Z.div2 g0 - Z.div2 f0;
     oddF := Zodd_2p_plus_1 (Z.div2 g0)
   |}, Step.D)
d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g :=
       (2 * Z.div2 g0 + 1 + (2 * Z.div2 f0 + 1)) / 2;
     oddF := Hf0
   |}, Step.S)


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := (Z.div2 g0 + Z.div2 f0 + 1) * 2 / 2;
     oddF := Hf0
   |}, Step.S)


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
forall Hf0 : Zodd (2 * Z.div2 f0 + 1),
Zodd (2 * Z.div2 g0 + 1) ->
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := Z.div2 g0 + Z.div2 f0 + 1;
     oddF := Hf0
   |}, Step.S)


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
Hf0': Zodd (2 * Z.div2 f0 + 1)
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Hf0'
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := Z.div2 g0 + Z.div2 f0 + 1;
     oddF := Hf0'
   |}, Step.S)


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
Hf0': Zodd (2 * Z.div2 f0 + 1)
Spec
  {|
    delta := d0;
    f := 2 * Z.div2 f0 + 1;
    g := 2 * Z.div2 g0 + 1;
    oddF := Zodd_2p_plus_1 (Z.div2 f0)
  |}
  ({|
     delta := 1 + d0;
     f := 2 * Z.div2 f0 + 1;
     g := Z.div2 g0 + Z.div2 f0 + 1;
     oddF := Zodd_2p_plus_1 (Z.div2 f0)
   |}, Step.S)


d0, f0, g0: Z
Hf0: Z.odd f0 = true
Hg0: Z.odd g0 = true
Hd: (0 <? d0) = false
Hf0': Zodd (2 * Z.div2 f0 + 1)
d0 <= 0

lia.
Qed.


b: Z
n: nat
st: State
- b <= eta st < b ->
- b - Z.of_nat n <= eta (fst (stepN n st)) <
b + Z.of_nat n


b: Z
n: nat
st: State
- b <= eta st < b ->
- b - Z.of_nat n <= eta (fst (stepN n st)) <
b + Z.of_nat n


b: Z
n: nat
st: State
IHn: - b <= eta st < b ->
- b - Z.of_nat n <= eta (fst (stepN n st)) < b + Z.of_nat n
- b <= eta st < b ->
- b - Z.pos (Pos.of_succ_nat n) <=
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) <
b + Z.pos (Pos.of_succ_nat n)


b: Z
n: nat
st, s: State
l: list Step
IHn: - b <= eta st < b -> - b - Z.of_nat n <= eta (fst (s, l)) < b + Z.of_nat n
- b <= eta st < b ->
- b - Z.pos (Pos.of_succ_nat n) <=
eta (fst (let (st1, x) := step s in (st1, x :: l))) <
b + Z.pos (Pos.of_succ_nat n)


b: Z
n: nat
st, s: State
l: list Step
IHn: - b <= eta st < b -> - b - Z.of_nat n <= eta (fst (s, l)) < b + Z.of_nat n
- b <= eta st < b ->
- b - Z.succ (Z.of_nat n) <=
eta (fst (let (st1, x) := step s in (st1, x :: l))) <
b + Z.succ (Z.of_nat n)


b: Z
n: nat
st, s: State
l: list Step
(- b <= eta st < b ->
 - b - Z.of_nat n <= eta (fst (s, l)) < b + Z.of_nat n) ->
- b <= eta st < b ->
- b - Z.succ (Z.of_nat n) <=
eta (fst (let (st1, x) := step s in (st1, x :: l))) <
b + Z.succ (Z.of_nat n)

elim (spec s); intros d f' g'; try generalize (Z.pos d); unfold eta; cbn; try lia.
Qed.


n: nat
st: State
(2 ^ Z.of_nat n | g st) ->
g (fst (stepN n st)) = g st / 2 ^ Z.of_nat n


n: nat
st: State
(2 ^ Z.of_nat n | g st) ->
g (fst (stepN n st)) = g st / 2 ^ Z.of_nat n


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (stepN n st)) = g st / 2 ^ Z.of_nat n
(2 ^ Z.of_nat (S n) | g st) ->
g (fst (stepN (S n) st)) = g st / 2 ^ Z.of_nat (S n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (stepN n st)) = g st / 2 ^ Z.of_nat n
(2 * 2 ^ Z.of_nat n | g st) ->
g (fst (stepN (S n) st)) = g st / (2 * 2 ^ Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (stepN n st)) = g st / 2 ^ Z.of_nat n
(2 * 2 ^ Z.of_nat n | g st) ->
g
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
(2 * 2 ^ Z.of_nat n | g st) ->
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
Hg: (2 * 2 ^ Z.of_nat n | g st)
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
Hg: (2 * 2 ^ Z.of_nat n | g st)
Hdivide: (2 ^ Z.of_nat n | g st)
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
Hg: g st mod (2 * 2 ^ Z.of_nat n) = 0
Hdivide: (2 ^ Z.of_nat n | g st)
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
Hg: g st mod (2 * 2 ^ Z.of_nat n) / 2 ^ Z.of_nat n =
0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
Hg: (g st / 2 ^ Z.of_nat n) mod 2 =
0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> g (fst (s, l)) = g st / 2 ^ Z.of_nat n
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g (fst (let (st1, x) := step s in (st1, x :: l))) =
g st / (2 * 2 ^ Z.of_nat n)


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
g
(fst
({|
delta := d; f := 2 * f' + 1; g := 2 * g'; oddF := Zodd_2p_plus_1 f'
|}, l)) = g st / 2 ^ Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: l)) = g st / (2 * 2 ^ Z.of_nat n)


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
g
(fst
({|
delta := d; f := 2 * f' + 1; g := 2 * g'; oddF := Zodd_2p_plus_1 f'
|}, l)) = g st / 2 ^ Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g' = g st / (2 * 2 ^ Z.of_nat n)


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) -> 2 * g' = g st / 2 ^ Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g' = g st / (2 * 2 ^ Z.of_nat n)


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) -> 2 * g' = g st / 2 ^ Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
2 * g' = 2 * (g st / (2 * 2 ^ Z.of_nat n))


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) -> 2 * g' = g st / 2 ^ Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g' * 2 = g st / 2 ^ Z.of_nat n / 2 * 2


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) -> 2 * g' = g st / 2 ^ Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat n | g st)
g' * 2 = 2 * g' / 2 * 2

rewrite !(Z.mul_comm 2), Z.div_mul; lia.
Qed.


n: nat
st: State
(2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st


n: nat
st: State
(2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
(2 ^ Z.of_nat (S n) | g st) ->
f (fst (stepN (S n) st)) = f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
(2 * 2 ^ Z.of_nat n | g st) ->
f (fst (stepN (S n) st)) = f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: (2 * 2 ^ Z.of_nat n | g st)
f (fst (stepN (S n) st)) = f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: (2 * 2 ^ Z.of_nat n | g st)
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: (2 * 2 ^ Z.of_nat n | g st)
Hg': (2 ^ Z.of_nat n | g st)
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: g st mod (2 * 2 ^ Z.of_nat n) = 0
Hg': (2 ^ Z.of_nat n | g st)
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: g st mod (2 * 2 ^ Z.of_nat n) / 2 ^ Z.of_nat n =
0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: (g st / 2 ^ Z.of_nat n) mod 2 =
0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (stepN n st)) = f st
Hg: g (fst (stepN n st)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (s, l)) = f st
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
f (fst (let (st1, x) := step s in (st1, x :: l))) =
f st


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> f (fst (s, l)) = f st
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
f (fst (let (st1, x) := step s in (st1, x :: l))) =
f (fst (s, l))


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
f
(fst
({|
delta := d; f := 2 * f' + 1; g := 2 * g'; oddF := Zodd_2p_plus_1 f'
|}, l)) = f st
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
f
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: l)) =
f
  (fst
     ({|
        delta := d;
        f := 2 * f' + 1;
        g := 2 * g';
        oddF := Zodd_2p_plus_1 f'
      |}, l))

reflexivity.
Qed.


n: nat
st: State
(2 ^ Z.of_nat n | g st) ->
eta (fst (stepN n st)) = eta st - Z.of_nat n


n: nat
st: State
(2 ^ Z.of_nat n | g st) ->
eta (fst (stepN n st)) = eta st - Z.of_nat n


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
(2 ^ Z.of_nat (S n) | g st) ->
eta (fst (stepN (S n) st)) = eta st - Z.of_nat (S n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
(2 * 2 ^ Z.of_nat n | g st) ->
eta (fst (stepN (S n) st)) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: (2 * 2 ^ Z.of_nat n | g st)
eta (fst (stepN (S n) st)) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: (2 * 2 ^ Z.of_nat n | g st)
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: (2 * 2 ^ Z.of_nat n | g st)
Hg': (2 ^ Z.of_nat n | g st)
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: g st mod (2 * 2 ^ Z.of_nat n) = 0
Hg': (2 ^ Z.of_nat n | g st)
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: g st mod (2 * 2 ^ Z.of_nat n) / 2 ^ Z.of_nat n =
0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: (g st / 2 ^ Z.of_nat n) mod 2 =
0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Hg: g (fst (stepN n st)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (s, l)) = eta st - Z.of_nat n
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta st - Z.succ (Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (s, l)) = eta st - Z.of_nat n
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta st - Z.of_nat n - 1


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) -> eta (fst (s, l)) = eta st - Z.of_nat n
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta (fst (s, l)) - 1


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
eta
(fst
({|
delta := d; f := 2 * f' + 1; g := 2 * g'; oddF := Zodd_2p_plus_1 f'
|}, l)) = eta st - Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
eta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: l)) =
eta
  (fst
     ({|
        delta := d;
        f := 2 * f' + 1;
        g := 2 * g';
        oddF := Zodd_2p_plus_1 f'
      |}, l)) - 1


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
eta
(fst
({|
delta := d; f := 2 * f' + 1; g := 2 * g'; oddF := Zodd_2p_plus_1 f'
|}, l)) = eta st - Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
-
delta
  (fst
     ({|
        delta := 1 + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: l)) =
-
delta
  (fst
     ({|
        delta := d;
        f := 2 * f' + 1;
        g := 2 * g';
        oddF := Zodd_2p_plus_1 f'
      |}, l)) - 1


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
eta
(fst
({|
delta := d; f := 2 * f' + 1; g := 2 * g'; oddF := Zodd_2p_plus_1 f'
|}, l)) = eta st - Z.of_nat n
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
- (1 + d) = - d - 1

ring.
Qed.


n: nat
st: State
0 <= eta st ->
Z.of_nat n <= 1 + eta st ->
eta (fst (stepN n st)) = eta st - Z.of_nat n


n: nat
st: State
0 <= eta st ->
Z.of_nat n <= 1 + eta st ->
eta (fst (stepN n st)) = eta st - Z.of_nat n


n: nat
st: State
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (stepN n st)) = eta st - Z.of_nat n
0 <= eta st ->
Z.of_nat (S n) <= 1 + eta st ->
eta (fst (stepN (S n) st)) = eta st - Z.of_nat (S n)


n: nat
st: State
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (stepN n st)) = eta st - Z.of_nat n
0 <= eta st ->
1 + Z.of_nat n <= 1 + eta st ->
eta (fst (stepN (S n) st)) = eta st - (1 + Z.of_nat n)


n: nat
st: State
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Heta: 0 <= eta st
Hn: 1 + Z.of_nat n <= 1 + eta st
eta (fst (stepN (S n) st)) = eta st - (1 + Z.of_nat n)


n: nat
st: State
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (stepN n st)) = eta st - Z.of_nat n
Heta: 0 <= eta st
Hn: 1 + Z.of_nat n <= 1 + eta st
eta
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
eta st - (1 + Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (s, l)) = eta st - Z.of_nat n
Heta: 0 <= eta st
Hn: 1 + Z.of_nat n <= 1 + eta st
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta st - (1 + Z.of_nat n)


n: nat
st, s: State
l: list Step
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (s, l)) = eta st - Z.of_nat n
Heta: 0 <= eta st
Hn: 1 + Z.of_nat n <= 1 + eta st
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta st - Z.of_nat n - 1


n: nat
st, s: State
l: list Step
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (s, l)) = eta st - Z.of_nat n
Heta: 0 <= eta st
Hn: 1 + Z.of_nat n <= 1 + eta st
Hs: eta (fst (s, l)) = eta st - Z.of_nat n
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta st - Z.of_nat n - 1


n: nat
st, s: State
l: list Step
IHn: 0 <= eta st ->
Z.of_nat n <= 1 + eta st -> eta (fst (s, l)) = eta st - Z.of_nat n
Heta: 0 <= eta st
Hn: 1 + Z.of_nat n <= 1 + eta st
Hs: eta (fst (s, l)) = eta st - Z.of_nat n
eta (fst (let (st1, x) := step s in (st1, x :: l))) =
eta (fst (s, l)) - 1


n: nat
st, s: State
l: list Step
IHn: 0 <= - delta st ->
Z.of_nat n <= 1 + - delta st ->
- delta (fst (s, l)) = - delta st - Z.of_nat n
Heta: 0 <= - delta st
Hn: 1 + Z.of_nat n <= 1 + - delta st
Hs: - delta (fst (s, l)) = - delta st - Z.of_nat n
-
delta (fst (let (st1, x) := step s in (st1, x :: l))) =
- delta (fst (s, l)) - 1


n: nat
st: State
l: list Step
d: positive
f', g': Z
IHn: 0 <= - delta st ->
Z.of_nat n <= 1 + - delta st ->
-
delta
(fst
({|
delta := Z.pos d;
f := 2 * f' + 1;
g := 2 * g' + 1;
oddF := Zodd_2p_plus_1 f'
|}, l)) = - delta st - Z.of_nat n
Heta: 0 <= - delta st
Hn: 1 + Z.of_nat n <= 1 + - delta st
Hs: -
delta
  (fst
     ({|
        delta := Z.pos d;
        f := 2 * f' + 1;
        g := 2 * g' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, l)) = - delta st - Z.of_nat n
- Z.pos_sub 1 d = Z.neg (d + 1)


n: nat
st: State
l: list Step
d: positive
f', g': Z
IHn: 0 <= - delta st ->
Z.of_nat n <= 1 + - delta st ->
-
delta
(fst
({|
delta := Z.pos d;
f := 2 * f' + 1;
g := 2 * g' + 1;
oddF := Zodd_2p_plus_1 f'
|}, l)) = - delta st - Z.of_nat n
Heta: 0 <= - delta st
Hn: 1 + Z.of_nat n <= 1 + - delta st
Hs: Z.neg d = - delta st - Z.of_nat n
- Z.pos_sub 1 d = Z.neg (d + 1)

lia.
Qed.


n, m: nat
st: State
stepN (n + m) st =
(let st1 := stepN m st in
 (fst (stepN n (fst st1)),
  snd (stepN n (fst st1)) ++ snd st1))


n, m: nat
st: State
stepN (n + m) st =
(let st1 := stepN m st in
 (fst (stepN n (fst st1)),
  snd (stepN n (fst st1)) ++ snd st1))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
stepN (S n + m) st =
(let st1 := stepN m st in
 (fst (stepN (S n) (fst st1)),
  snd (stepN (S n) (fst st1)) ++ snd st1))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
(let (st0, xs) := stepN (n + m) st in
 let (st1, x) := step st0 in (st1, x :: xs)) =
(fst
   (let (st0, xs) := stepN n (fst (stepN m st)) in
    let (st1, x) := step st0 in (st1, x :: xs)),
 snd
   (let (st0, xs) := stepN n (fst (stepN m st)) in
    let (st1, x) := step st0 in (st1, x :: xs)) ++
 snd (stepN m st))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
(let (st0, xs) :=
   let st1 := stepN m st in
   (fst (stepN n (fst st1)),
    snd (stepN n (fst st1)) ++ snd st1) in
 let (st1, x) := step st0 in (st1, x :: xs)) =
(fst
   (let (st0, xs) := stepN n (fst (stepN m st)) in
    let (st1, x) := step st0 in (st1, x :: xs)),
 snd
   (let (st0, xs) := stepN n (fst (stepN m st)) in
    let (st1, x) := step st0 in (st1, x :: xs)) ++
 snd (stepN m st))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
(let (st1, x) :=
   step (fst (stepN n (fst (stepN m st)))) in
 (st1,
  x
  :: snd (stepN n (fst (stepN m st))) ++
     snd (stepN m st))) =
(fst
   (let (st0, xs) := stepN n (fst (stepN m st)) in
    let (st1, x) := step st0 in (st1, x :: xs)),
 snd
   (let (st0, xs) := stepN n (fst (stepN m st)) in
    let (st1, x) := step st0 in (st1, x :: xs)) ++
 snd (stepN m st))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
s: State
l: list Step
(let (st1, x) := step (fst (s, l)) in
 (st1, x :: snd (s, l) ++ snd (stepN m st))) =
(fst (let (st1, x) := step s in (st1, x :: l)),
 snd (let (st1, x) := step s in (st1, x :: l)) ++
 snd (stepN m st))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
s: State
l: list Step
(let (st1, x) := step s in
 (st1, x :: l ++ snd (stepN m st))) =
(fst (let (st1, x) := step s in (st1, x :: l)),
 snd (let (st1, x) := step s in (st1, x :: l)) ++
 snd (stepN m st))


n, m: nat
st: State
IHn: stepN (n + m) st =
(let st1 := stepN m st in
(fst (stepN n (fst st1)), snd (stepN n (fst st1)) ++ snd st1))
s: State
l: list Step
s0: State
s1: Step
(s0, s1 :: l ++ snd (stepN m st)) =
(fst (s0, s1 :: l),
 snd (s0, s1 :: l) ++ snd (stepN m st))

reflexivity.
Qed.


n, m: nat
st: State
fst (stepN (n + m) st) =
fst (stepN n (fst (stepN m st)))


n, m: nat
st: State
fst (stepN (n + m) st) =
fst (stepN n (fst (stepN m st)))


n, m: nat
st: State
fst
  (let st1 := stepN m st in
   (fst (stepN n (fst st1)),
    snd (stepN n (fst st1)) ++ snd st1)) =
fst (stepN n (fst (stepN m st)))

reflexivity.
Qed.


n, m: nat
st: State
snd (stepN (n + m) st) =
snd (stepN n (fst (stepN m st))) ++ snd (stepN m st)


n, m: nat
st: State
snd (stepN (n + m) st) =
snd (stepN n (fst (stepN m st))) ++ snd (stepN m st)


n, m: nat
st: State
snd
  (let st1 := stepN m st in
   (fst (stepN n (fst st1)),
    snd (stepN n (fst st1)) ++ snd st1)) =
snd (stepN n (fst (stepN m st))) ++ snd (stepN m st)

reflexivity.
Qed.


n: nat
st: State
Zodd (g st) ->
eta st < 0 ->
0 < Z.of_nat n <= 1 - eta st ->
eta (fst (stepN n st)) = - eta st - Z.of_nat n


n: nat
st: State
Zodd (g st) ->
eta st < 0 ->
0 < Z.of_nat n <= 1 - eta st ->
eta (fst (stepN n st)) = - eta st - Z.of_nat n


n: nat
st: State
Hodd: Zodd (g st)
Heta: eta st < 0
Hn: 0 < Z.of_nat n <= 1 - eta st
eta (fst (stepN n st)) = - eta st - Z.of_nat n


n: nat
st: State
Hodd: Zodd (g st)
Heta: eta st < 0
Hn: 0 < Z.of_nat (S n) <= 1 - eta st
eta (fst (stepN (S n) st)) = - eta st - Z.of_nat (S n)


n: nat
st: State
Hodd: Zodd (g st)
Heta: eta st < 0
Hn: 0 < Z.of_nat (S n) <= 1 - eta st
eta (fst (stepN (n + 1) st)) =
- eta st - Z.of_nat (n + 1)


n: nat
st: State
Hodd: Zodd (g st)
Heta: eta st < 0
Hn: 0 < Z.of_nat (S n) <= 1 - eta st
eta (fst (stepN n (fst (stepN 1 st)))) =
- eta st - Z.of_nat (n + 1)


n: nat
st: State
Hodd: Zodd (g st)
Heta: eta st < 0
Hn: 0 < Z.of_nat (S n) <= 1 - eta st
eta
  (fst
     (stepN n
        (fst
           (let (st1, x) := step st in (st1, x :: nil))))) =
- eta st - Z.of_nat (n + 1)


n: nat
d: positive
f', g': Z
Hodd: Zodd
  (g
     {|
       delta := Z.pos d;
       f := 2 * f' + 1;
       g := 2 * g' + 1;
       oddF := Zodd_2p_plus_1 f'
     |})
Heta: eta
  {|
    delta := Z.pos d;
    f := 2 * f' + 1;
    g := 2 * g' + 1;
    oddF := Zodd_2p_plus_1 f'
  |} < 0
Hn: 0 < Z.of_nat (S n) <=
1 -
eta
  {|
    delta := Z.pos d;
    f := 2 * f' + 1;
    g := 2 * g' + 1;
    oddF := Zodd_2p_plus_1 f'
  |}
eta
  (fst
     (stepN n
        (fst
           ({|
              delta := INC - Z.pos d;
              f := 2 * g' + 1;
              g := g' - f';
              oddF := Zodd_2p_plus_1 g'
            |}, Step.D :: nil)))) =
-
eta
  {|
    delta := Z.pos d;
    f := 2 * f' + 1;
    g := 2 * g' + 1;
    oddF := Zodd_2p_plus_1 f'
  |} - Z.of_nat (n + 1)


n: nat
d: positive
f', g': Z
Hodd: Zodd (2 * g' + 1)
Heta: Z.neg d < 0
Hn: 0 < Z.pos (Pos.of_succ_nat n) <=
Z.pos
  match d with
  | q~1 => (Pos.succ q)~0
  | q~0 => q~1
  | 1 => 2
  end
Z.of_nat n <= 1 + - (1 - Z.pos d)


n: nat
d: positive
f', g': Z
Hodd: Zodd (2 * g' + 1)
Heta: Z.neg d < 0
Hn: 0 < Z.of_nat (S n) <= 1 - - Z.pos d
Z.of_nat n <= 1 + - (1 - Z.pos d)

lia.
Qed.


n: nat
st1, st2: State
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)


n: nat
st1, st2: State
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)


n: nat
forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
forall st1 st2 : State,
eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN (S n) st1)) =
delta (fst (stepN (S n) st2)) /\
snd (stepN (S n) st1) = snd (stepN (S n) st2)


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
delta (fst (stepN (S n) st1)) =
delta (fst (stepN (S n) st2)) /\
snd (stepN (S n) st1) = snd (stepN (S n) st2)


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
delta (fst (stepN (n + 1) st1)) =
delta (fst (stepN (n + 1) st2)) /\
snd (stepN (n + 1) st1) = snd (stepN (n + 1) st2)


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
delta (fst (stepN n (fst (stepN 1 st1)))) =
delta (fst (stepN n (fst (stepN 1 st2)))) /\
snd (stepN n (fst (stepN 1 st1))) ++ snd (stepN 1 st1) =
snd (stepN n (fst (stepN 1 st2))) ++ snd (stepN 1 st2)


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) := step st1 in
            (st1, x :: nil))))) =
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) := step st2 in
            (st1, x :: nil))))) /\
snd
  (stepN n
     (fst
        (let (st1, x) := step st1 in (st1, x :: nil)))) ++
snd (let (st1, x) := step st1 in (st1, x :: nil)) =
snd
  (stepN n
     (fst
        (let (st1, x) := step st2 in (st1, x :: nil)))) ++
snd (let (st1, x) := step st2 in (st1, x :: nil))


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) :=
              match Zeven_odd_dec (g st1) with
              | left _ =>
                  ({|
                     delta := INC + delta st2;
                     f := f st1;
                     g := g st1 / 2;
                     oddF := oddF st1
                   |}, Step.H)
              | right oddG =>
                  if 0 <? delta st2
                  then
                   ({|
                      delta := INC - delta st2;
                      f := g st1;
                      g := (g st1 - f st1) / 2;
                      oddF := oddG
                    |}, Step.D)
                  else
                   ({|
                      delta := INC + delta st2;
                      f := f st1;
                      g := (g st1 + f st1) / 2;
                      oddF := oddF st1
                    |}, Step.S)
              end in
            (st1, x :: nil))))) =
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) :=
              match Zeven_odd_dec (g st2) with
              | left _ =>
                  ({|
                     delta := INC + delta st2;
                     f := f st2;
                     g := g st2 / 2;
                     oddF := oddF st2
                   |}, Step.H)
              | right oddG =>
                  if 0 <? delta st2
                  then
                   ({|
                      delta := INC - delta st2;
                      f := g st2;
                      g := (g st2 - f st2) / 2;
                      oddF := oddG
                    |}, Step.D)
                  else
                   ({|
                      delta := INC + delta st2;
                      f := f st2;
                      g := (g st2 + f st2) / 2;
                      oddF := oddF st2
                    |}, Step.S)
              end in
            (st1, x :: nil))))) /\
snd
  (stepN n
     (fst
        (let (st1, x) :=
           match Zeven_odd_dec (g st1) with
           | left _ =>
               ({|
                  delta := INC + delta st2;
                  f := f st1;
                  g := g st1 / 2;
                  oddF := oddF st1
                |}, Step.H)
           | right oddG =>
               if 0 <? delta st2
               then
                ({|
                   delta := INC - delta st2;
                   f := g st1;
                   g := (g st1 - f st1) / 2;
                   oddF := oddG
                 |}, Step.D)
               else
                ({|
                   delta := INC + delta st2;
                   f := f st1;
                   g := (g st1 + f st1) / 2;
                   oddF := oddF st1
                 |}, Step.S)
           end in
         (st1, x :: nil)))) ++
snd
  (let (st1, x) :=
     match Zeven_odd_dec (g st1) with
     | left _ =>
         ({|
            delta := INC + delta st2;
            f := f st1;
            g := g st1 / 2;
            oddF := oddF st1
          |}, Step.H)
     | right oddG =>
         if 0 <? delta st2
         then
          ({|
             delta := INC - delta st2;
             f := g st1;
             g := (g st1 - f st1) / 2;
             oddF := oddG
           |}, Step.D)
         else
          ({|
             delta := INC + delta st2;
             f := f st1;
             g := (g st1 + f st1) / 2;
             oddF := oddF st1
           |}, Step.S)
     end in
   (st1, x :: nil)) =
snd
  (stepN n
     (fst
        (let (st1, x) :=
           match Zeven_odd_dec (g st2) with
           | left _ =>
               ({|
                  delta := INC + delta st2;
                  f := f st2;
                  g := g st2 / 2;
                  oddF := oddF st2
                |}, Step.H)
           | right oddG =>
               if 0 <? delta st2
               then
                ({|
                   delta := INC - delta st2;
                   f := g st2;
                   g := (g st2 - f st2) / 2;
                   oddF := oddG
                 |}, Step.D)
               else
                ({|
                   delta := INC + delta st2;
                   f := f st2;
                   g := (g st2 + f st2) / 2;
                   oddF := oddF st2
                 |}, Step.S)
           end in
         (st1, x :: nil)))) ++
snd
  (let (st1, x) :=
     match Zeven_odd_dec (g st2) with
     | left _ =>
         ({|
            delta := INC + delta st2;
            f := f st2;
            g := g st2 / 2;
            oddF := oddF st2
          |}, Step.H)
     | right oddG =>
         if 0 <? delta st2
         then
          ({|
             delta := INC - delta st2;
             f := g st2;
             g := (g st2 - f st2) / 2;
             oddF := oddG
           |}, Step.D)
         else
          ({|
             delta := INC + delta st2;
             f := f st2;
             g := (g st2 + f st2) / 2;
             oddF := oddF st2
           |}, Step.S)
     end in
   (st1, x :: nil))


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) =
delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) :=
              match Zeven_odd_dec (g st1) with
              | left _ =>
                  ({|
                     delta := INC + delta st2;
                     f := f st1;
                     g := g st1 / 2;
                     oddF := oddF st1
                   |}, Step.H)
              | right oddG =>
                  if 0 <? delta st2
                  then
                   ({|
                      delta := INC - delta st2;
                      f := g st1;
                      g := (g st1 - f st1) / 2;
                      oddF := oddG
                    |}, Step.D)
                  else
                   ({|
                      delta := INC + delta st2;
                      f := f st1;
                      g := (g st1 + f st1) / 2;
                      oddF := oddF st1
                    |}, Step.S)
              end in
            (st1, x :: nil))))) =
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) :=
              match Zeven_odd_dec (g st2) with
              | left _ =>
                  ({|
                     delta := INC + delta st2;
                     f := f st2;
                     g := g st2 / 2;
                     oddF := oddF st2
                   |}, Step.H)
              | right oddG =>
                  if 0 <? delta st2
                  then
                   ({|
                      delta := INC - delta st2;
                      f := g st2;
                      g := (g st2 - f st2) / 2;
                      oddF := oddG
                    |}, Step.D)
                  else
                   ({|
                      delta := INC + delta st2;
                      f := f st2;
                      g := (g st2 + f st2) / 2;
                      oddF := oddF st2
                    |}, Step.S)
              end in
            (st1, x :: nil))))) /\
snd
  (stepN n
     (fst
        (let (st1, x) :=
           match Zeven_odd_dec (g st1) with
           | left _ =>
               ({|
                  delta := INC + delta st2;
                  f := f st1;
                  g := g st1 / 2;
                  oddF := oddF st1
                |}, Step.H)
           | right oddG =>
               if 0 <? delta st2
               then
                ({|
                   delta := INC - delta st2;
                   f := g st1;
                   g := (g st1 - f st1) / 2;
                   oddF := oddG
                 |}, Step.D)
               else
                ({|
                   delta := INC + delta st2;
                   f := f st1;
                   g := (g st1 + f st1) / 2;
                   oddF := oddF st1
                 |}, Step.S)
           end in
         (st1, x :: nil)))) ++
snd
  (let (st1, x) :=
     match Zeven_odd_dec (g st1) with
     | left _ =>
         ({|
            delta := INC + delta st2;
            f := f st1;
            g := g st1 / 2;
            oddF := oddF st1
          |}, Step.H)
     | right oddG =>
         if 0 <? delta st2
         then
          ({|
             delta := INC - delta st2;
             f := g st1;
             g := (g st1 - f st1) / 2;
             oddF := oddG
           |}, Step.D)
         else
          ({|
             delta := INC + delta st2;
             f := f st1;
             g := (g st1 + f st1) / 2;
             oddF := oddF st1
           |}, Step.S)
     end in
   (st1, x :: nil)) =
snd
  (stepN n
     (fst
        (let (st1, x) :=
           match Zeven_odd_dec (g st2) with
           | left _ =>
               ({|
                  delta := INC + delta st2;
                  f := f st2;
                  g := g st2 / 2;
                  oddF := oddF st2
                |}, Step.H)
           | right oddG =>
               if 0 <? delta st2
               then
                ({|
                   delta := INC - delta st2;
                   f := g st2;
                   g := (g st2 - f st2) / 2;
                   oddF := oddG
                 |}, Step.D)
               else
                ({|
                   delta := INC + delta st2;
                   f := f st2;
                   g := (g st2 + f st2) / 2;
                   oddF := oddF st2
                 |}, Step.S)
           end in
         (st1, x :: nil)))) ++
snd
  (let (st1, x) :=
     match Zeven_odd_dec (g st2) with
     | left _ =>
         ({|
            delta := INC + delta st2;
            f := f st2;
            g := g st2 / 2;
            oddF := oddF st2
          |}, Step.H)
     | right oddG =>
         if 0 <? delta st2
         then
          ({|
             delta := INC - delta st2;
             f := g st2;
             g := (g st2 - f st2) / 2;
             oddF := oddG
           |}, Step.D)
         else
          ({|
             delta := INC + delta st2;
             f := f st2;
             g := (g st2 + f st2) / 2;
             oddF := oddF st2
           |}, Step.S)
     end in
   (st1, x :: nil))


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)

 
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
x, y: Z
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)

 
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
x, y: Z
x mod 2 ^ Z.of_nat (S n) = y mod 2 ^ Z.of_nat (S n) ->
(x / 2) mod 2 ^ Z.of_nat n =
(y / 2) mod 2 ^ Z.of_nat n

 
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
x, y: Z
Z.land x (Z.ones (Z.of_nat (S n))) =
Z.land y (Z.ones (Z.of_nat (S n))) ->
Z.land (Z.shiftr x 1) (Z.ones (Z.of_nat n)) =
Z.land (Z.shiftr y 1) (Z.ones (Z.of_nat n))

 
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
x, y: Z
Z.land x (Z.ones (Z.of_nat (S n))) =
Z.land y (Z.ones (Z.of_nat (S n))) ->
Z.land (Z.shiftr x 1) (Z.ones (Z.of_nat (S n) - 1)) =
Z.land (Z.shiftr y 1) (Z.ones (Z.of_nat (S n) - 1))

 
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
x, y: Z
Z.land x (Z.ones (Z.of_nat (S n))) =
Z.land y (Z.ones (Z.of_nat (S n))) ->
Z.shiftr (Z.land x (Z.ones (Z.of_nat (S n)))) 1 =
Z.shiftr (Z.land y (Z.ones (Z.of_nat (S n)))) 1

 congruence.

n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) :=
              match Zeven_odd_dec (g st1) with
              | left _ =>
                  ({|
                     delta := INC + delta st2;
                     f := f st1;
                     g := g st1 / 2;
                     oddF := oddF st1
                   |}, Step.H)
              | right oddG =>
                  if 0 <? delta st2
                  then
                   ({|
                      delta := INC - delta st2;
                      f := g st1;
                      g := (g st1 - f st1) / 2;
                      oddF := oddG
                    |}, Step.D)
                  else
                   ({|
                      delta := INC + delta st2;
                      f := f st1;
                      g := (g st1 + f st1) / 2;
                      oddF := oddF st1
                    |}, Step.S)
              end in
            (st1, x :: nil))))) =
delta
  (fst
     (stepN n
        (fst
           (let (st1, x) :=
              match Zeven_odd_dec (g st2) with
              | left _ =>
                  ({|
                     delta := INC + delta st2;
                     f := f st2;
                     g := g st2 / 2;
                     oddF := oddF st2
                   |}, Step.H)
              | right oddG =>
                  if 0 <? delta st2
                  then
                   ({|
                      delta := INC - delta st2;
                      f := g st2;
                      g := (g st2 - f st2) / 2;
                      oddF := oddG
                    |}, Step.D)
                  else
                   ({|
                      delta := INC + delta st2;
                      f := f st2;
                      g := (g st2 + f st2) / 2;
                      oddF := oddF st2
                    |}, Step.S)
              end in
            (st1, x :: nil))))) /\
snd
  (stepN n
     (fst
        (let (st1, x) :=
           match Zeven_odd_dec (g st1) with
           | left _ =>
               ({|
                  delta := INC + delta st2;
                  f := f st1;
                  g := g st1 / 2;
                  oddF := oddF st1
                |}, Step.H)
           | right oddG =>
               if 0 <? delta st2
               then
                ({|
                   delta := INC - delta st2;
                   f := g st1;
                   g := (g st1 - f st1) / 2;
                   oddF := oddG
                 |}, Step.D)
               else
                ({|
                   delta := INC + delta st2;
                   f := f st1;
                   g := (g st1 + f st1) / 2;
                   oddF := oddF st1
                 |}, Step.S)
           end in
         (st1, x :: nil)))) ++
snd
  (let (st1, x) :=
     match Zeven_odd_dec (g st1) with
     | left _ =>
         ({|
            delta := INC + delta st2;
            f := f st1;
            g := g st1 / 2;
            oddF := oddF st1
          |}, Step.H)
     | right oddG =>
         if 0 <? delta st2
         then
          ({|
             delta := INC - delta st2;
             f := g st1;
             g := (g st1 - f st1) / 2;
             oddF := oddG
           |}, Step.D)
         else
          ({|
             delta := INC + delta st2;
             f := f st1;
             g := (g st1 + f st1) / 2;
             oddF := oddF st1
           |}, Step.S)
     end in
   (st1, x :: nil)) =
snd
  (stepN n
     (fst
        (let (st1, x) :=
           match Zeven_odd_dec (g st2) with
           | left _ =>
               ({|
                  delta := INC + delta st2;
                  f := f st2;
                  g := g st2 / 2;
                  oddF := oddF st2
                |}, Step.H)
           | right oddG =>
               if 0 <? delta st2
               then
                ({|
                   delta := INC - delta st2;
                   f := g st2;
                   g := (g st2 - f st2) / 2;
                   oddF := oddG
                 |}, Step.D)
               else
                ({|
                   delta := INC + delta st2;
                   f := f st2;
                   g := (g st2 + f st2) / 2;
                   oddF := oddF st2
                 |}, Step.S)
           end in
         (st1, x :: nil)))) ++
snd
  (let (st1, x) :=
     match Zeven_odd_dec (g st2) with
     | left _ =>
         ({|
            delta := INC + delta st2;
            f := f st2;
            g := g st2 / 2;
            oddF := oddF st2
          |}, Step.H)
     | right oddG =>
         if 0 <? delta st2
         then
          ({|
             delta := INC - delta st2;
             f := g st2;
             g := (g st2 - f st2) / 2;
             oddF := oddG
           |}, Step.D)
         else
          ({|
             delta := INC + delta st2;
             f := f st2;
             g := (g st2 + f st2) / 2;
             oddF := oddF st2
           |}, Step.S)
     end in
   (st1, x :: nil))


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zeven (g st1)
z0: Zeven (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := g st1 / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := g st2 / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (f st1') (f st2')
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) =
delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zeven (g st1)
z0: Zeven (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := g st1 / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := g st2 / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (g st1') (g st2')
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) =
delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 - delta st2;
  f := g st1;
  g := (g st1 - f st1) / 2;
  oddF := z
|}: State
st2':= {|
  delta := 1 - delta st2;
  f := g st2;
  g := (g st2 - f st2) / 2;
  oddF := z0
|}: State
eqm (2 ^ Z.of_nat n) (f st1') (f st2')
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) =
delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 - delta st2;
  f := g st1;
  g := (g st1 - f st1) / 2;
  oddF := z
|}: State
st2':= {|
  delta := 1 - delta st2;
  f := g st2;
  g := (g st2 - f st2) / 2;
  oddF := z0
|}: State
eqm (2 ^ Z.of_nat n) (g st1') (g st2')
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) =
delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := (g st1 + f st1) / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := (g st2 + f st2) / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (f st1') (f st2')
n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) =
delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := (g st1 + f st1) / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := (g st2 + f st2) / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (g st1') (g st2')


n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zeven (g st1)
z0: Zeven (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := g st1 / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := g st2 / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (f st1') (f st2')
 eapply extraMath.eqm_2_pow_le;[|apply Hf]; lia.

n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zeven (g st1)
z0: Zeven (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := g st1 / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := g st2 / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (g st1') (g st2')
 apply Hdiv2; apply Hg.

n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 - delta st2;
  f := g st1;
  g := (g st1 - f st1) / 2;
  oddF := z
|}: State
st2':= {|
  delta := 1 - delta st2;
  f := g st2;
  g := (g st2 - f st2) / 2;
  oddF := z0
|}: State
eqm (2 ^ Z.of_nat n) (f st1') (f st2')
 eapply extraMath.eqm_2_pow_le;[|apply Hg]; lia.

n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 - delta st2;
  f := g st1;
  g := (g st1 - f st1) / 2;
  oddF := z
|}: State
st2':= {|
  delta := 1 - delta st2;
  f := g st2;
  g := (g st2 - f st2) / 2;
  oddF := z0
|}: State
eqm (2 ^ Z.of_nat n) (g st1') (g st2')
 apply Hdiv2; apply Zminus_eqm; assumption.

n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := (g st1 + f st1) / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := (g st2 + f st2) / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (f st1') (f st2')
 eapply extraMath.eqm_2_pow_le;[|apply Hf]; lia.

n: nat
IHn: forall st1 st2 : State,
eqm (2 ^ Z.of_nat n) (f st1) (f st2) ->
eqm (2 ^ Z.of_nat n) (g st1) (g st2) ->
delta st1 = delta st2 ->
delta (fst (stepN n st1)) = delta (fst (stepN n st2)) /\
snd (stepN n st1) = snd (stepN n st2)
st1, st2: State
Hf: eqm (2 ^ Z.of_nat (S n)) (f st1) (f st2)
Hg: eqm (2 ^ Z.of_nat (S n)) (g st1) (g st2)
Hdelta: delta st1 = delta st2
Hdiv2: forall x y : Z,
eqm (2 ^ Z.of_nat (S n)) x y ->
eqm (2 ^ Z.of_nat n) (x / 2) (y / 2)
z: Zodd (g st1)
z0: Zodd (g st2)
st1':= {|
  delta := 1 + delta st2;
  f := f st1;
  g := (g st1 + f st1) / 2;
  oddF := oddF st1
|}: State
st2':= {|
  delta := 1 + delta st2;
  f := f st2;
  g := (g st2 + f st2) / 2;
  oddF := oddF st2
|}: State
eqm (2 ^ Z.of_nat n) (g st1') (g st2')
 apply Hdiv2; apply Zplus_eqm; assumption.
Qed.


st: State
Z.abs (f (fst (step st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
Z.abs (f (fst (step st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))

destruct (spec st); cbn;lia.
Qed.


st: State
2 * Z.abs (g (fst (step st))) <=
Z.abs (f st) + Z.abs (g st)


st: State
2 * Z.abs (g (fst (step st))) <=
Z.abs (f st) + Z.abs (g st)

destruct (spec st); cbn;lia.
Qed.


st: State
n: nat
Z.abs (f (fst (stepN n st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
Z.abs (f (fst (stepN n st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st))
Z.abs (f (fst (stepN (S n) st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN (S n) st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st))
Z.abs
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step (fst (stepN n st))))) <=
Z.max (Z.abs (f (fst (stepN n st))))
  (Z.abs (g (fst (stepN n st))))
Z.abs
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step (fst (stepN n st))))) <=
Z.max (Z.abs (f (fst (stepN n st))))
  (Z.abs (g (fst (stepN n st))))
Hg: 2 * Z.abs (g (fst (step (fst (stepN n st))))) <=
Z.abs (f (fst (stepN n st))) +
Z.abs (g (fst (stepN n st)))
Z.abs
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (f (fst (st', xs))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (st', xs))) <= Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step (fst (st', xs))))) <=
Z.max (Z.abs (f (fst (st', xs))))
  (Z.abs (g (fst (st', xs))))
Hg: 2 * Z.abs (g (fst (step (fst (st', xs))))) <=
Z.abs (f (fst (st', xs))) +
Z.abs (g (fst (st', xs)))
Z.abs
  (f
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (f st') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st') <= Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step st'))) <=
Z.max (Z.abs (f st')) (Z.abs (g st'))
Hg: 2 * Z.abs (g (fst (step st'))) <=
Z.abs (f st') + Z.abs (g st')
Z.abs
  (f
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (f st') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st') <= Z.max (Z.abs (f st)) (Z.abs (g st))
st'': State
xs': Step
Hf: Z.abs (f (fst (st'', xs'))) <=
Z.max (Z.abs (f st')) (Z.abs (g st'))
Hg: 2 * Z.abs (g (fst (st'', xs'))) <=
Z.abs (f st') + Z.abs (g st')
Z.abs (f (fst (st'', xs' :: xs))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (st'', xs' :: xs))) <=
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (f st') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st') <= Z.max (Z.abs (f st)) (Z.abs (g st))
st'': State
xs': Step
Hf: Z.abs (f st'') <=
Z.max (Z.abs (f st')) (Z.abs (g st'))
Hg: 2 * Z.abs (g st'') <=
Z.abs (f st') + Z.abs (g st')
Z.abs (f st'') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st'') <= Z.max (Z.abs (f st)) (Z.abs (g st))

lia.
Qed.


st: State
n: nat
Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN n st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN n st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) < Z.max (Z.abs (f st)) (Z.abs (g st))
Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN (S n) st))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN (S n) st))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) < Z.max (Z.abs (f st)) (Z.abs (g st))
Z.abs (g st) < Z.abs (f st) ->
Z.abs
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) < Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step (fst (stepN n st))))) <=
Z.max (Z.abs (f (fst (stepN n st))))
  (Z.abs (g (fst (stepN n st))))
Z.abs (g st) < Z.abs (f st) ->
Z.abs
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (stepN n st))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (stepN n st))) < Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step (fst (stepN n st))))) <=
Z.max (Z.abs (f (fst (stepN n st))))
  (Z.abs (g (fst (stepN n st))))
Hg: 2 * Z.abs (g (fst (step (fst (stepN n st))))) <=
Z.abs (f (fst (stepN n st))) +
Z.abs (g (fst (stepN n st)))
Z.abs (g st) < Z.abs (f st) ->
Z.abs
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (st', xs))) <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (st', xs))) < Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step (fst (st', xs))))) <=
Z.max (Z.abs (f (fst (st', xs))))
  (Z.abs (g (fst (st', xs))))
Hg: 2 * Z.abs (g (fst (step (fst (st', xs))))) <=
Z.abs (f (fst (st', xs))) +
Z.abs (g (fst (st', xs)))
Z.abs (g st) < Z.abs (f st) ->
Z.abs
  (f
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f st') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st') < Z.max (Z.abs (f st)) (Z.abs (g st))
Hf: Z.abs (f (fst (step st'))) <=
Z.max (Z.abs (f st')) (Z.abs (g st'))
Hg: 2 * Z.abs (g (fst (step st'))) <=
Z.abs (f st') + Z.abs (g st')
Z.abs (g st) < Z.abs (f st) ->
Z.abs
  (f
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs
  (g
     (fst (let (st1, x) := step st' in (st1, x :: xs)))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f st') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st') < Z.max (Z.abs (f st)) (Z.abs (g st))
st'': State
xs': Step
Hf: Z.abs (f (fst (st'', xs'))) <=
Z.max (Z.abs (f st')) (Z.abs (g st'))
Hg: 2 * Z.abs (g (fst (st'', xs'))) <=
Z.abs (f st') + Z.abs (g st')
Z.abs (g st) < Z.abs (f st) ->
Z.abs (f (fst (st'', xs' :: xs))) <=
Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g (fst (st'', xs' :: xs))) <
Z.max (Z.abs (f st)) (Z.abs (g st))


st: State
n: nat
st': State
xs: list Step
IHn: Z.abs (g st) < Z.abs (f st) ->
Z.abs (f st') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st') < Z.max (Z.abs (f st)) (Z.abs (g st))
st'': State
xs': Step
Hf: Z.abs (f st'') <=
Z.max (Z.abs (f st')) (Z.abs (g st'))
Hg: 2 * Z.abs (g st'') <=
Z.abs (f st') + Z.abs (g st')
Z.abs (g st) < Z.abs (f st) ->
Z.abs (f st'') <= Z.max (Z.abs (f st)) (Z.abs (g st)) /\
Z.abs (g st'') < Z.max (Z.abs (f st)) (Z.abs (g st))

lia.
Qed.


st: State
n: nat
g st = 0 ->
f (fst (stepN n st)) = f st /\
g (fst (stepN n st)) = 0


st: State
n: nat
g st = 0 ->
f (fst (stepN n st)) = f st /\
g (fst (stepN n st)) = 0


st: State
n: nat
Hg: g st = 0
f (fst (stepN n st)) = f st /\
g (fst (stepN n st)) = 0


st: State
n: nat
Hg: g st = 0
IHn: f (fst (stepN n st)) = f st /\ g (fst (stepN n st)) = 0
f (fst (stepN (S n) st)) = f st /\
g (fst (stepN (S n) st)) = 0


st: State
n: nat
Hg: g st = 0
IHn: f (fst (stepN n st)) = f st /\ g (fst (stepN n st)) = 0
f
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) =
f st /\
g
  (fst
     (let (st0, xs) := stepN n st in
      let (st1, x) := step st0 in (st1, x :: xs))) = 0


st: State
n: nat
Hg: divstep.g st = 0
eta, f, g: Z
Hf: Zodd f
l: list Step
IHn: divstep.f (fst ({| delta := eta; f := f; g := g; oddF := Hf |}, l)) =
divstep.f st /\
divstep.g (fst ({| delta := eta; f := f; g := g; oddF := Hf |}, l)) = 0
divstep.f
  (fst
     (let (st1, x) :=
        step
          {|
            delta := eta; f := f; g := g; oddF := Hf
          |} in
      (st1, x :: l))) = divstep.f st /\
divstep.g
  (fst
     (let (st1, x) :=
        step
          {|
            delta := eta; f := f; g := g; oddF := Hf
          |} in
      (st1, x :: l))) = 0


st: State
n: nat
Hg: divstep.g st = 0
eta, f, g: Z
Hf: Zodd f
l: list Step
IHn: divstep.f (fst ({| delta := eta; f := f; g := g; oddF := Hf |}, l)) =
divstep.f st /\
divstep.g (fst ({| delta := eta; f := f; g := g; oddF := Hf |}, l)) = 0
divstep.f
  (fst
     (let (st1, x) :=
        match
          Zeven_odd_dec
            (divstep.g
               {|
                 delta := eta;
                 f := f;
                 g := g;
                 oddF := Hf
               |})
        with
        | left _ =>
            ({|
               delta :=
                 INC +
                 delta
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |};
               f :=
                 divstep.f
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |};
               g :=
                 divstep.g
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |} / 2;
               oddF :=
                 oddF
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |}
             |}, Step.H)
        | right oddG =>
            if
             0 <?
             delta
               {|
                 delta := eta;
                 f := f;
                 g := g;
                 oddF := Hf
               |}
            then
             ({|
                delta :=
                  INC -
                  delta
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                f :=
                  divstep.g
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                g :=
                  (divstep.g
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |} -
                   divstep.f
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |}) / 2;
                oddF := oddG
              |}, Step.D)
            else
             ({|
                delta :=
                  INC +
                  delta
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                f :=
                  divstep.f
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                g :=
                  (divstep.g
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |} +
                   divstep.f
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |}) / 2;
                oddF :=
                  oddF
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |}
              |}, Step.S)
        end in
      (st1, x :: l))) = divstep.f st /\
divstep.g
  (fst
     (let (st1, x) :=
        match
          Zeven_odd_dec
            (divstep.g
               {|
                 delta := eta;
                 f := f;
                 g := g;
                 oddF := Hf
               |})
        with
        | left _ =>
            ({|
               delta :=
                 INC +
                 delta
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |};
               f :=
                 divstep.f
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |};
               g :=
                 divstep.g
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |} / 2;
               oddF :=
                 oddF
                   {|
                     delta := eta;
                     f := f;
                     g := g;
                     oddF := Hf
                   |}
             |}, Step.H)
        | right oddG =>
            if
             0 <?
             delta
               {|
                 delta := eta;
                 f := f;
                 g := g;
                 oddF := Hf
               |}
            then
             ({|
                delta :=
                  INC -
                  delta
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                f :=
                  divstep.g
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                g :=
                  (divstep.g
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |} -
                   divstep.f
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |}) / 2;
                oddF := oddG
              |}, Step.D)
            else
             ({|
                delta :=
                  INC +
                  delta
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                f :=
                  divstep.f
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |};
                g :=
                  (divstep.g
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |} +
                   divstep.f
                     {|
                       delta := eta;
                       f := f;
                       g := g;
                       oddF := Hf
                     |}) / 2;
                oddF :=
                  oddF
                    {|
                      delta := eta;
                      f := f;
                      g := g;
                      oddF := Hf
                    |}
              |}, Step.S)
        end in
      (st1, x :: l))) = 0


st: State
n: nat
Hg: divstep.g st = 0
eta, f, g: Z
Hf: Zodd f
l: list Step
IHn: f = divstep.f st /\ g = 0
divstep.f
  (fst
     (let (st1, x) :=
        match Zeven_odd_dec g with
        | left _ =>
            ({|
               delta := 1 + eta;
               f := f;
               g := g / 2;
               oddF := Hf
             |}, Step.H)
        | right oddG =>
            if 0 <? eta
            then
             ({|
                delta := 1 - eta;
                f := g;
                g := (g - f) / 2;
                oddF := oddG
              |}, Step.D)
            else
             ({|
                delta := 1 + eta;
                f := f;
                g := (g + f) / 2;
                oddF := Hf
              |}, Step.S)
        end in
      (st1, x :: l))) = divstep.f st /\
divstep.g
  (fst
     (let (st1, x) :=
        match Zeven_odd_dec g with
        | left _ =>
            ({|
               delta := 1 + eta;
               f := f;
               g := g / 2;
               oddF := Hf
             |}, Step.H)
        | right oddG =>
            if 0 <? eta
            then
             ({|
                delta := 1 - eta;
                f := g;
                g := (g - f) / 2;
                oddF := oddG
              |}, Step.D)
            else
             ({|
                delta := 1 + eta;
                f := f;
                g := (g + f) / 2;
                oddF := Hf
              |}, Step.S)
        end in
      (st1, x :: l))) = 0


st: State
n: nat
Hg: g st = 0
eta: Z
Hf: Zodd (f st)
l: list Step
f
  (fst
     (let (st1, x) :=
        match Zeven_odd_dec 0 with
        | left _ =>
            ({|
               delta := 1 + eta;
               f := f st;
               g := 0 / 2;
               oddF := Hf
             |}, Step.H)
        | right oddG =>
            if 0 <? eta
            then
             ({|
                delta := 1 - eta;
                f := 0;
                g := (0 - f st) / 2;
                oddF := oddG
              |}, Step.D)
            else
             ({|
                delta := 1 + eta;
                f := f st;
                g := (0 + f st) / 2;
                oddF := Hf
              |}, Step.S)
        end in
      (st1, x :: l))) = f st /\
g
  (fst
     (let (st1, x) :=
        match Zeven_odd_dec 0 with
        | left _ =>
            ({|
               delta := 1 + eta;
               f := f st;
               g := 0 / 2;
               oddF := Hf
             |}, Step.H)
        | right oddG =>
            if 0 <? eta
            then
             ({|
                delta := 1 - eta;
                f := 0;
                g := (0 - f st) / 2;
                oddF := oddG
              |}, Step.D)
            else
             ({|
                delta := 1 + eta;
                f := f st;
                g := (0 + f st) / 2;
                oddF := Hf
              |}, Step.S)
        end in
      (st1, x :: l))) = 0


st: State
n: nat
Hg: g st = 0
eta: Z
Hf: Zodd (f st)
l: list Step
f st = f st /\ 0 = 0

auto.
Qed.


st: State
n: nat
g st = 0 -> f (fst (stepN n st)) = f st


st: State
n: nat
g st = 0 -> f (fst (stepN n st)) = f st


st: State
n: nat
Hg: g st = 0
f (fst (stepN n st)) = f st


st: State
n: nat
Hg: g st = 0
H: f (fst (stepN n st)) = f st
H0: g (fst (stepN n st)) = 0
f (fst (stepN n st)) = f st

assumption.
Qed.


st: State
n: nat
g st = 0 -> g (fst (stepN n st)) = 0


st: State
n: nat
g st = 0 -> g (fst (stepN n st)) = 0


st: State
n: nat
Hg: g st = 0
g (fst (stepN n st)) = 0


st: State
n: nat
Hg: g st = 0
H: f (fst (stepN n st)) = f st
H0: g (fst (stepN n st)) = 0
g (fst (stepN n st)) = 0

assumption.
Qed.


st: State
d: Z
n: nat
Zis_gcd (f st) (g st) d ->
Zis_gcd (f (fst (stepN n st))) (g (fst (stepN n st)))
  d


st: State
d: Z
n: nat
Zis_gcd (f st) (g st) d ->
Zis_gcd (f (fst (stepN n st))) (g (fst (stepN n st)))
  d


st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
Zis_gcd (f (fst (stepN n st))) (g (fst (stepN n st)))
  d


st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
IHn: Zis_gcd (f (fst (stepN n st)))
  (g (fst (stepN n st))) d
Zis_gcd (f (fst (stepN (S n) st)))
  (g (fst (stepN (S n) st))) d


st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
IHn: Zis_gcd (f (fst (stepN n st)))
  (g (fst (stepN n st))) d
Zis_gcd
  (f
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs))))
  (g
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs))))
  d


st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
st0: State
l: list Step
IHn: Zis_gcd (f (fst (st0, l))) (g (fst (st0, l))) d
Zis_gcd
  (f (fst (let (st1, x) := step st0 in (st1, x :: l))))
  (g (fst (let (st1, x) := step st0 in (st1, x :: l))))
  d


st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
st0: State
l: list Step
IHn: Zis_gcd (f st0) (g st0) d
Zis_gcd
  (f (fst (let (st1, x) := step st0 in (st1, x :: l))))
  (g (fst (let (st1, x) := step st0 in (st1, x :: l))))
  d


st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
(d | g')
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
forall x : Z, (x | 2 * f' + 1) -> (x | g') -> (x | d)
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
(d | g' - f')
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
forall x : Z,
(x | 2 * g' + 1) -> (x | g' - f') -> (x | d)
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
(d | g' + f' + 1)
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
forall x : Z,
(x | 2 * f' + 1) -> (x | g' + f' + 1) -> (x | d)
 

st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
(d | g')
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Z.odd d = true
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Hodd: Z.odd d = true
(d | g')

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g', z1: Z
Hd1: 2 * f' + 1 = z1 * d
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g', z1: Z
Hd1: Z.odd (2 * f' + 1) = Z.odd (z1 * d)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g', z1: Z
Hd1: Z.odd 1 = (Z.odd d && Z.odd z1)%bool
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Z.odd d = true

    destruct (Z.odd d);auto.
  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Hodd: Z.odd d = true
(d | g')

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Hodd: Z.odd d = true
rel_prime d 2

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Hodd: Z.odd d = true
rel_prime (d mod 2) 2

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
Hodd: Z.odd d = true
rel_prime 1 2

  apply rel_prime_1.

st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
forall x : Z, (x | 2 * f' + 1) -> (x | g') -> (x | d)
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
x: Z
Hxf: (x | 2 * f' + 1)
Hxg: (x | g')
(x | d)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g')
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g') -> (x | d)
x: Z
Hxf: (x | 2 * f' + 1)
Hxg: (x | g')
(x | 2 * g')

  auto with *.

st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
(d | g' - f')
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | g' - f')

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g', z1: Z
Hd1: 2 * f' + 1 = z1 * d
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g', z1: Z
Hd1: Z.odd (2 * f' + 1) = Z.odd (z1 * d)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g', z1: Z
Hd1: Z.odd 1 = (Z.odd d && Z.odd z1)%bool
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    destruct (Z.odd d);auto.
  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | g' - f')

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | 2 * (g' - f'))
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime d 2

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | 2 * (g' - f'))
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | 2 * g' + 1 - (2 * f' + 1))

    apply Z.divide_sub_r; assumption.
  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime d 2
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime (d mod 2) 2

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime 1 2

    apply rel_prime_1.

st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
forall x : Z,
(x | 2 * g' + 1) -> (x | g' - f') -> (x | d)
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * g' + 1)
Hxg: (x | g' - f')
(x | d)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * g' + 1)
Hxg: (x | g' - f')
(x | 2 * f' + 1)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * g' + 1)
Hxg: (x | g' - f')
(x | 2 * g' + 1 - 2 * (g' - f'))

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0: positive
f', g': Z
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * g' + 1)
Hxg: (x | g' - f')
(x | 2 * (g' - f'))

  auto with *.

st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
(d | g' + f' + 1)
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | g' + f' + 1)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
z1: Z
Hd1: 2 * f' + 1 = z1 * d
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
z1: Z
Hd1: Z.odd (2 * f' + 1) = Z.odd (z1 * d)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
z1: Z
Hd1: Z.odd 1 = (Z.odd d && Z.odd z1)%bool
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Z.odd d = true

    destruct (Z.odd d);auto.
  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | g' + f' + 1)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | 2 * (g' + f' + 1))
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime d 2

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | 2 * (g' + f' + 1))
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
(d | 2 * g' + 1 + (2 * f' + 1))

    apply Z.divide_add_r; assumption.
  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime d 2
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime (d mod 2) 2

    
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
Hodd: Z.odd d = true
rel_prime 1 2

    apply rel_prime_1.

st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
forall x : Z,
(x | 2 * f' + 1) -> (x | g' + f' + 1) -> (x | d)
 
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * f' + 1)
Hxg: (x | g' + f' + 1)
(x | d)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * f' + 1)
Hxg: (x | g' + f' + 1)
(x | 2 * g' + 1)

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * f' + 1)
Hxg: (x | g' + f' + 1)
(x | 2 * (g' + f' + 1) - (2 * f' + 1))

  
st: State
d: Z
n: nat
Hgcd: Zis_gcd (f st) (g st) d
l: list Step
d0, f', g': Z
l0: d0 <= 0
Hd1: (d | 2 * f' + 1)
Hd2: (d | 2 * g' + 1)
Hdx: forall x : Z,
(x | 2 * f' + 1) -> (x | 2 * g' + 1) -> (x | d)
x: Z
Hxf: (x | 2 * f' + 1)
Hxg: (x | g' + f' + 1)
(x | 2 * (g' + f' + 1))

  auto with *.
Qed.


n: nat
fi, gi: Z
Hf: Zodd fi
delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi)) /\
f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi)) /\
g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))


n: nat
fi, gi: Z
Hf: Zodd fi
delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi)) /\
f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi)) /\
g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))


n: nat
fi, gi: Z
Hf: Zodd fi
IHn: delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)) /\
f (fst (stepN n (init fi gi Hf))) =
divsteps.f (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi)) /\
g (fst (stepN n (init fi gi Hf))) =
divsteps.g (N.iter (N.of_nat n) divsteps.step (divsteps.init fi gi))
delta (fst (stepN (S n) (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat (S n)) divsteps.step
     (divsteps.init fi gi)) /\
f (fst (stepN (S n) (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat (S n)) divsteps.step
     (divsteps.init fi gi)) /\
g (fst (stepN (S n) (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat (S n)) divsteps.step
     (divsteps.init fi gi))


n: nat
fi, gi: Z
Hf: Zodd fi
IHdelta: delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
IHf: f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
IHg: g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
delta (fst (stepN (S n) (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat (S n)) divsteps.step
     (divsteps.init fi gi)) /\
f (fst (stepN (S n) (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat (S n)) divsteps.step
     (divsteps.init fi gi)) /\
g (fst (stepN (S n) (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat (S n)) divsteps.step
     (divsteps.init fi gi))


n: nat
fi, gi: Z
Hf: Zodd fi
IHdelta: delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
IHf: f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
IHg: g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
delta (fst (stepN (S n) (init fi gi Hf))) =
divsteps.delta
  (divsteps.step
     (N.iter (N.of_nat n) divsteps.step
        (divsteps.init fi gi))) /\
f (fst (stepN (S n) (init fi gi Hf))) =
divsteps.f
  (divsteps.step
     (N.iter (N.of_nat n) divsteps.step
        (divsteps.init fi gi))) /\
g (fst (stepN (S n) (init fi gi Hf))) =
divsteps.g
  (divsteps.step
     (N.iter (N.of_nat n) divsteps.step
        (divsteps.init fi gi)))


n: nat
fi, gi: Z
Hf: Zodd fi
delta0, f0, g0, d, e, modulus: Z
IHdelta: delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
IHf: f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
IHg: g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
delta (fst (stepN (S n) (init fi gi Hf))) =
divsteps.delta
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
f (fst (stepN (S n) (init fi gi Hf))) =
divsteps.f
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
g (fst (stepN (S n) (init fi gi Hf))) =
divsteps.g
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |})


n: nat
fi, gi: Z
Hf: Zodd fi
delta0, f0, g0, d, e, modulus: Z
IHdelta: delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
IHf: f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
IHg: g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
delta
  (fst
     (let (st0, xs) := stepN n (init fi gi Hf) in
      let (st1, x) := step st0 in (st1, x :: xs))) =
divsteps.delta
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
f
  (fst
     (let (st0, xs) := stepN n (init fi gi Hf) in
      let (st1, x) := step st0 in (st1, x :: xs))) =
divsteps.f
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
g
  (fst
     (let (st0, xs) := stepN n (init fi gi Hf) in
      let (st1, x) := step st0 in (st1, x :: xs))) =
divsteps.g
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |})


n: nat
fi, gi: Z
Hf: Zodd fi
delta0, f0, g0, d, e, modulus: Z
st0: State
l: list Step
IHdelta: delta (fst (st0, l)) =
divsteps.delta
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
IHf: f (fst (st0, l)) =
divsteps.f
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
IHg: g (fst (st0, l)) =
divsteps.g
  {|
    divsteps.delta := delta0;
    divsteps.f := f0;
    divsteps.g := g0;
    divsteps.d := d;
    divsteps.e := e;
    divsteps.modulus := modulus
  |}
delta
  (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.delta
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
f (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.f
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
g (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.g
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |})


n: nat
fi, gi: Z
Hf: Zodd fi
delta0, f0, g0, d, e, modulus: Z
st0: State
l: list Step
IHdelta: delta st0 = delta0
IHf: f st0 = f0
IHg: g st0 = g0
delta
  (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.delta
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
f (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.f
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
g (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.g
  (divsteps.step
     {|
       divsteps.delta := delta0;
       divsteps.f := f0;
       divsteps.g := g0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |})


n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
st0: State
l: list Step
delta
  (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.delta
  (divsteps.step
     {|
       divsteps.delta := delta st0;
       divsteps.f := f st0;
       divsteps.g := g st0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
f (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.f
  (divsteps.step
     {|
       divsteps.delta := delta st0;
       divsteps.f := f st0;
       divsteps.g := g st0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |}) /\
g (fst (let (st1, x) := step st0 in (st1, x :: l))) =
divsteps.g
  (divsteps.step
     {|
       divsteps.delta := delta st0;
       divsteps.f := f st0;
       divsteps.g := g st0;
       divsteps.d := d;
       divsteps.e := e;
       divsteps.modulus := modulus
     |})


n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
1 + d0 =
divsteps.delta
  (if Z.even (2 * g')
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := 2 * g' / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g';
       divsteps.g := (2 * g' - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
2 * f' + 1 =
divsteps.f
  (if Z.even (2 * g')
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := 2 * g' / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g';
       divsteps.g := (2 * g' - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
g' =
divsteps.g
  (if Z.even (2 * g')
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := 2 * g' / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g';
       divsteps.g := (2 * g' - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |})
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0: positive
f', g': Z
Z.pos_sub 1 d0 =
divsteps.delta
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta :=
        Z.pos
          match d0 with
          | q~1 => (Pos.succ q)~0
          | q~0 => q~1
          | 1 => 2
          end;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := Z.pos_sub 1 d0;
      divsteps.f := 2 * g' + 1;
      divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}) /\
2 * g' + 1 =
divsteps.f
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta :=
        Z.pos
          match d0 with
          | q~1 => (Pos.succ q)~0
          | q~0 => q~1
          | 1 => 2
          end;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := Z.pos_sub 1 d0;
      divsteps.f := 2 * g' + 1;
      divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}) /\
g' - f' =
divsteps.g
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta :=
        Z.pos
          match d0 with
          | q~1 => (Pos.succ q)~0
          | q~0 => q~1
          | 1 => 2
          end;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := Z.pos_sub 1 d0;
      divsteps.f := 2 * g' + 1;
      divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |})
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
l0: d0 <= 0
1 + d0 =
divsteps.delta
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g' + 1;
       divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + 1 + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
2 * f' + 1 =
divsteps.f
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g' + 1;
       divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + 1 + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
g' + f' + 1 =
divsteps.g
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g' + 1;
       divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + 1 + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |})


n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
1 + d0 =
divsteps.delta
  (if Z.even (2 * g')
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := 2 * g' / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g';
       divsteps.g := (2 * g' - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
2 * f' + 1 =
divsteps.f
  (if Z.even (2 * g')
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := 2 * g' / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g';
       divsteps.g := (2 * g' - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
g' =
divsteps.g
  (if Z.even (2 * g')
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := 2 * g' / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g';
       divsteps.g := (2 * g' - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |})
 
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
1 + d0 = 1 + d0 /\
2 * f' + 1 = 2 * f' + 1 /\ g' = 2 * g' / 2

  rewrite (Z.mul_comm 2 g'), Z.div_mul; lia.

n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0: positive
f', g': Z
Z.pos_sub 1 d0 =
divsteps.delta
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta :=
        Z.pos
          match d0 with
          | q~1 => (Pos.succ q)~0
          | q~0 => q~1
          | 1 => 2
          end;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := Z.pos_sub 1 d0;
      divsteps.f := 2 * g' + 1;
      divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}) /\
2 * g' + 1 =
divsteps.f
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta :=
        Z.pos
          match d0 with
          | q~1 => (Pos.succ q)~0
          | q~0 => q~1
          | 1 => 2
          end;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := Z.pos_sub 1 d0;
      divsteps.f := 2 * g' + 1;
      divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}) /\
g' - f' =
divsteps.g
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta :=
        Z.pos
          match d0 with
          | q~1 => (Pos.succ q)~0
          | q~0 => q~1
          | 1 => 2
          end;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := Z.pos_sub 1 d0;
      divsteps.f := 2 * g' + 1;
      divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |})
 
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0: positive
f', g': Z
Z.pos_sub 1 d0 = Z.pos_sub 1 d0 /\
1 + 2 * g' = 1 + 2 * g' /\
g' - f' = (1 + 2 * g' - (2 * f' + 1)) / 2

  
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0: positive
f', g': Z
g' - f' = (1 + 2 * g' - (2 * f' + 1)) / 2

  
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0: positive
f', g': Z
g' - f' = (g' - f') * 2 / 2

  rewrite Z.div_mul; lia.

n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
l0: d0 <= 0
1 + d0 =
divsteps.delta
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g' + 1;
       divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + 1 + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
2 * f' + 1 =
divsteps.f
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g' + 1;
       divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + 1 + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |}) /\
g' + f' + 1 =
divsteps.g
  (if Z.even (2 * g' + 1)
   then
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (2 * g' + 1) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd e then e + modulus else e) / 2;
      divsteps.modulus := modulus
    |}
   else
    if 0 <? d0
    then
     {|
       divsteps.delta := 1 - d0;
       divsteps.f := 2 * g' + 1;
       divsteps.g := (2 * g' + 1 - (2 * f' + 1)) / 2;
       divsteps.d := e;
       divsteps.e :=
         (if Z.odd (e - d)
          then e - d + modulus
          else e - d) / 2;
       divsteps.modulus := modulus
     |}
    else
     {|
       divsteps.delta := 1 + d0;
       divsteps.f := 2 * f' + 1;
       divsteps.g := (2 * g' + 1 + (2 * f' + 1)) / 2;
       divsteps.d := d;
       divsteps.e :=
         (if Z.odd (e + d)
          then e + d + modulus
          else e + d) / 2;
       divsteps.modulus := modulus
     |})
 
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
l0: d0 <= 0
1 + d0 =
divsteps.delta
  (if 0 <? d0
   then
    {|
      divsteps.delta := 1 - d0;
      divsteps.f := 1 + 2 * g';
      divsteps.g := (1 + 2 * g' - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (1 + 2 * g' + (2 * f' + 1)) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd (e + d)
         then e + d + modulus
         else e + d) / 2;
      divsteps.modulus := modulus
    |}) /\
2 * f' + 1 =
divsteps.f
  (if 0 <? d0
   then
    {|
      divsteps.delta := 1 - d0;
      divsteps.f := 1 + 2 * g';
      divsteps.g := (1 + 2 * g' - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (1 + 2 * g' + (2 * f' + 1)) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd (e + d)
         then e + d + modulus
         else e + d) / 2;
      divsteps.modulus := modulus
    |}) /\
g' + f' + 1 =
divsteps.g
  (if 0 <? d0
   then
    {|
      divsteps.delta := 1 - d0;
      divsteps.f := 1 + 2 * g';
      divsteps.g := (1 + 2 * g' - (2 * f' + 1)) / 2;
      divsteps.d := e;
      divsteps.e :=
        (if Z.odd (e - d)
         then e - d + modulus
         else e - d) / 2;
      divsteps.modulus := modulus
    |}
   else
    {|
      divsteps.delta := 1 + d0;
      divsteps.f := 2 * f' + 1;
      divsteps.g := (1 + 2 * g' + (2 * f' + 1)) / 2;
      divsteps.d := d;
      divsteps.e :=
        (if Z.odd (e + d)
         then e + d + modulus
         else e + d) / 2;
      divsteps.modulus := modulus
    |})

  
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
l0: d0 <= 0
1 + d0 = 1 + d0 /\
2 * f' + 1 = 2 * f' + 1 /\
g' + f' + 1 = (1 + 2 * g' + (2 * f' + 1)) / 2

  
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
l0: d0 <= 0
g' + f' + 1 = (1 + 2 * g' + (2 * f' + 1)) / 2

  
n: nat
fi, gi: Z
Hf: Zodd fi
d, e, modulus: Z
l: list Step
d0, f', g': Z
l0: d0 <= 0
g' + f' + 1 = (g' + f' + 1) * 2 / 2

  rewrite Z.div_mul; lia.
Qed.


n: nat
fi, gi: Z
Hf: Zodd fi
g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))


n: nat
fi, gi: Z
Hf: Zodd fi
g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))


n: nat
fi, gi: Z
Hf: Zodd fi
H: delta (fst (stepN n (init fi gi Hf))) =
divsteps.delta
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
H0: f (fst (stepN n (init fi gi Hf))) =
divsteps.f
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi)) /\
g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))
g (fst (stepN n (init fi gi Hf))) =
divsteps.g
  (N.iter (N.of_nat n) divsteps.step
     (divsteps.init fi gi))

tauto.
Qed.

Module Trans.

Record V2 :=
{ x : Z; y : Z }.

Definition scale (c : Z) (vec : V2) :=
{| x := c * (x vec)
 ; y := c * (y vec)
|}.


c1, c2: Z
vec: V2
scale (c1 * c2) vec = scale c1 (scale c2 vec)


c1, c2: Z
vec: V2
scale (c1 * c2) vec = scale c1 (scale c2 vec)


c1, c2, x0, y0: Z
scale (c1 * c2) {| x := x0; y := y0 |} =
scale c1 (scale c2 {| x := x0; y := y0 |})

unfold scale; simpl; f_equal; ring.
Qed.

Record M2x2 :=
{ u : Z; v : Z; q : Z; r : Z}.

Definition I : M2x2 :=
{| u := 1
 ; v := 0
 ; q := 0
 ; r := 1
|}.

Definition ap (m : M2x2) (vec : V2) : V2 :=
{| x := (u m) * (x vec) + (v m) * (y vec)
 ; y := (q m) * (x vec) + (r m) * (y vec)
|}.


m: M2x2
c: Z
vec: V2
ap m (scale c vec) = scale c (ap m vec)


m: M2x2
c: Z
vec: V2
ap m (scale c vec) = scale c (ap m vec)


u0, v0, q0, r0, c, x0, y0: Z
ap {| u := u0; v := v0; q := q0; r := r0 |}
  (scale c {| x := x0; y := y0 |}) =
scale c
  (ap {| u := u0; v := v0; q := q0; r := r0 |}
     {| x := x0; y := y0 |})

unfold ap, scale; simpl; f_equal; ring.
Qed.

Definition mul (m1 m2: M2x2) : M2x2 :=
{| u := (u m1) * (u m2) + (v m1) * (q m2)
 ; v := (u m1) * (v m2) + (v m1) * (r m2)
 ; q := (q m1) * (u m2) + (r m1) * (q m2)
 ; r := (q m1) * (v m2) + (r m1) * (r m2)
|}.


m1, m2, m3: M2x2
mul m1 (mul m2 m3) = mul (mul m1 m2) m3


m1, m2, m3: M2x2
mul m1 (mul m2 m3) = mul (mul m1 m2) m3


u0, v0, q0, r0, u1, v1, q1, r1, u2, v2, q2, r2: Z
mul {| u := u0; v := v0; q := q0; r := r0 |}
  (mul {| u := u1; v := v1; q := q1; r := r1 |}
     {| u := u2; v := v2; q := q2; r := r2 |}) =
mul
  (mul {| u := u0; v := v0; q := q0; r := r0 |}
     {| u := u1; v := v1; q := q1; r := r1 |})
  {| u := u2; v := v2; q := q2; r := r2 |}

unfold mul; simpl; f_equal; ring.
Qed.


m1, m2: M2x2
vec: V2
ap (mul m1 m2) vec = ap m1 (ap m2 vec)


m1, m2: M2x2
vec: V2
ap (mul m1 m2) vec = ap m1 (ap m2 vec)


u0, v0, q0, r0, u1, v1, q1, r1, x0, y0: Z
ap
  (mul {| u := u0; v := v0; q := q0; r := r0 |}
     {| u := u1; v := v1; q := q1; r := r1 |})
  {| x := x0; y := y0 |} =
ap {| u := u0; v := v0; q := q0; r := r0 |}
  (ap {| u := u1; v := v1; q := q1; r := r1 |}
     {| x := x0; y := y0 |})

unfold ap, mul; simpl; f_equal; ring.
Qed.

Definition det (m: M2x2) : Z := (u m) * (r m) - (v m) * (q m).


m1, m2: M2x2
det (mul m1 m2) = det m1 * det m2


m1, m2: M2x2
det (mul m1 m2) = det m1 * det m2


u0, v0, q0, r0, u1, v1, q1, r1: Z
det
  (mul {| u := u0; v := v0; q := q0; r := r0 |}
     {| u := u1; v := v1; q := q1; r := r1 |}) =
det {| u := u0; v := v0; q := q0; r := r0 |} *
det {| u := u1; v := v1; q := q1; r := r1 |}


u0, v0, q0, r0, u1, v1, q1, r1: Z
(u0 * u1 + v0 * q1) * (q0 * v1 + r0 * r1) -
(u0 * v1 + v0 * r1) * (q0 * u1 + r0 * q1) =
(u0 * r0 - v0 * q0) * (u1 * r1 - v1 * q1)

ring.
Qed.

Definition prod : list M2x2 -> M2x2 := fold_right mul I.


l1, l2: list M2x2
prod (l1 ++ l2) = mul (prod l1) (prod l2)


l1, l2: list M2x2
prod (l1 ++ l2) = mul (prod l1) (prod l2)


l2: list M2x2
prod (nil ++ l2) = mul (prod nil) (prod l2)
a: M2x2
l1, l2: list M2x2
IHl1: prod (l1 ++ l2) = mul (prod l1) (prod l2)
prod ((a :: l1) ++ l2) =
mul (prod (a :: l1)) (prod l2)


a: M2x2
l1, l2: list M2x2
IHl1: prod (l1 ++ l2) = mul (prod l1) (prod l2)
prod ((a :: l1) ++ l2) =
mul (prod (a :: l1)) (prod l2)


a: M2x2
l1, l2: list M2x2
IHl1: prod (l1 ++ l2) = mul (prod l1) (prod l2)
mul a (prod (l1 ++ l2)) =
mul (mul a (prod l1)) (prod l2)


a: M2x2
l1, l2: list M2x2
IHl1: prod (l1 ++ l2) = mul (prod l1) (prod l2)
mul a (mul (prod l1) (prod l2)) =
mul (mul a (prod l1)) (prod l2)

destruct (prod l1); destruct (prod l2); unfold mul; cbn; f_equal; ring.
Qed.


ms: list M2x2
det (prod ms) = fold_right Z.mul 1 (map det ms)


ms: list M2x2
det (prod ms) = fold_right Z.mul 1 (map det ms)


a: M2x2
ms: list M2x2
IHms: det (prod ms) = fold_right Z.mul 1 (map det ms)
det (prod (a :: ms)) =
fold_right Z.mul 1 (map det (a :: ms))


a: M2x2
ms: list M2x2
IHms: det (prod ms) = fold_right Z.mul 1 (map det ms)
det (mul a (prod ms)) =
det a * fold_right Z.mul 1 (map det ms)


a: M2x2
ms: list M2x2
IHms: det (prod ms) = fold_right Z.mul 1 (map det ms)
det a * det (prod ms) =
det a * fold_right Z.mul 1 (map det ms)

congruence.
Qed.

Definition bounded (b : Z) (m : M2x2) :=
  (Z.abs (u m) + Z.abs (v m) <= b /\ -b < u m + v m) /\
  (Z.abs (q m) + Z.abs (r m) <= b /\ -b < q m + r m).


bounded 1 I


bounded 1 I


(Z.abs (u I) + Z.abs (v I) <= 1 /\ - (1) < u I + v I) /\
Z.abs (q I) + Z.abs (r I) <= 1 /\ - (1) < q I + r I


(1 <= 1 /\ -1 < 1) /\ 1 <= 1 /\ -1 < 1

lia.
Qed.

Definition trans (s : Step) : M2x2 :=
match s with
| Step.H => {| u := 2; v := 0; q := 0; r := 1 |}
| Step.D => {| u := 0; v := 2; q := -1; r := 1 |}
| Step.S => {| u := 2; v := 0; q := 1; r := 1 |}
end.

Definition fg st := {| x := f st; y := g st |}.


st: State
scale 2 (fg (fst (step st))) =
ap (trans (snd (step st))) (fg st)


st: State
scale 2 (fg (fst (step st))) =
ap (trans (snd (step st))) (fg st)

destruct (spec st);
unfold scale,ap, fg; cbn;
f_equal; ring.
Qed.


s: Step
det (trans s) = 2


s: Step
det (trans s) = 2

destruct s; reflexivity.
Qed.


b: Z
m: M2x2
s: Step
bounded b m -> bounded (2 * b) (mul (trans s) m)


b: Z
m: M2x2
s: Step
bounded b m -> bounded (2 * b) (mul (trans s) m)


b, u, v, q, r: Z
s: Step
bounded b {| u := u; v := v; q := q; r := r |} ->
bounded (2 * b)
  (mul (trans s) {| u := u; v := v; q := q; r := r |})


b, u, v, q, r: Z
s: Step
Huv: Z.abs u + Z.abs v <= b /\ - b < u + v
Hqr: Z.abs q + Z.abs r <= b /\ - b < q + r
bounded (2 * b)
  (mul (trans s) {| u := u; v := v; q := q; r := r |})

destruct s; unfold bounded; simpl; lia.
Qed.

Definition transN (n : nat) (st : State) : M2x2 :=
  prod (map trans (snd (stepN n st))).


n: nat
st: State
{x : Step
| transN (S n) st = mul (trans x) (transN n st)}


n: nat
st: State
{x : Step
| transN (S n) st = mul (trans x) (transN n st)}


n: nat
st: State
{x : Step
| prod (map trans (snd (stepN (S n) st))) =
  mul (trans x) (prod (map trans (snd (stepN n st))))}


n: nat
st: State
{x : Step
| prod
    (map trans
       (snd
          (let (st0, xs) := stepN n st in
           let (st1, x0) := step st0 in
           (st1, x0 :: xs)))) =
  mul (trans x) (prod (map trans (snd (stepN n st))))}


n: nat
st, st0: State
xs: list Step
Hxs: stepN n st = (st0, xs)
{x : Step
| prod
    (map trans
       (snd
          (let (st1, x0) := step st0 in
           (st1, x0 :: xs)))) =
  mul (trans x) (prod (map trans (snd (st0, xs))))}


n: nat
st, st0: State
xs: list Step
Hxs: stepN n st = (st0, xs)
st1: State
x: Step
{x0 : Step
| prod (map trans (snd (st1, x :: xs))) =
  mul (trans x0) (prod (map trans (snd (st0, xs))))}


n: nat
st, st0: State
xs: list Step
Hxs: stepN n st = (st0, xs)
st1: State
x: Step
prod (map trans (snd (st1, x :: xs))) =
mul (trans x) (prod (map trans (snd (st0, xs))))

reflexivity.
Qed.


n: nat
st: State
scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) =
ap (transN n st) (fg st)


n: nat
st: State
scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) =
ap (transN n st) (fg st)


st: State
scale (2 ^ Z.of_nat 0) (fg (fst (stepN 0 st))) =
ap (transN 0 st) (fg st)
n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) = ap (transN n st) (fg st)
scale (2 ^ Z.of_nat (S n)) (fg (fst (stepN (S n) st))) =
ap (transN (S n) st) (fg st)

 
st: State
scale 1 (fg (fst (stepN 0 st))) =
ap (transN 0 st) (fg st)
n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) = ap (transN n st) (fg st)
scale (2 ^ Z.of_nat (S n)) (fg (fst (stepN (S n) st))) =
ap (transN (S n) st) (fg st)

 
delta0, f0, g0: Z
oddF0: Zodd f0
{| x := 1 * f0; y := 1 * g0 |} =
{| x := 1 * f0 + 0 * g0; y := 0 * f0 + 1 * g0 |}
n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) =
ap (transN n st) (fg st)
scale (2 ^ Z.of_nat (S n)) (fg (fst (stepN (S n) st))) =
ap (transN (S n) st) (fg st)

 
n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) = ap (transN n st) (fg st)
scale (2 ^ Z.of_nat (S n)) (fg (fst (stepN (S n) st))) =
ap (transN (S n) st) (fg st)


n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) = ap (transN n st) (fg st)
scale (2 * 2 ^ Z.of_nat n) (fg (fst (stepN (S n) st))) =
ap (transN (S n) st) (fg st)


n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) =
ap (prod (map trans (snd (stepN n st)))) (fg st)
scale (2 * 2 ^ Z.of_nat n) (fg (fst (stepN (S n) st))) =
ap (prod (map trans (snd (stepN (S n) st)))) (fg st)


n: nat
st: State
IHn: scale (2 ^ Z.of_nat n) (fg (fst (stepN n st))) =
ap (prod (map trans (snd (stepN n st)))) (fg st)
scale (2 * 2 ^ Z.of_nat n)
  (fg
     (fst
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
ap
  (prod
     (map trans
        (snd
           (let (st0, xs) := stepN n st in
            let (st1, x) := step st0 in (st1, x :: xs)))))
  (fg st)


n: nat
st, st0: State
xs: list Step
IHn: scale (2 ^ Z.of_nat n) (fg st0) = ap (prod (map trans xs)) (fg st)
scale (2 * 2 ^ Z.of_nat n)
  (fg
     (fst (let (st1, x) := step st0 in (st1, x :: xs)))) =
ap
  (prod
     (map trans
        (snd
           (let (st1, x) := step st0 in (st1, x :: xs)))))
  (fg st)


n: nat
st, st0: State
xs: list Step
IHn: scale (2 ^ Z.of_nat n) (fg st0) = ap (prod (map trans xs)) (fg st)
Htrans: scale 2 (fg (fst (step st0))) =
ap (trans (snd (step st0))) (fg st0)
scale (2 * 2 ^ Z.of_nat n)
  (fg
     (fst (let (st1, x) := step st0 in (st1, x :: xs)))) =
ap
  (prod
     (map trans
        (snd
           (let (st1, x) := step st0 in (st1, x :: xs)))))
  (fg st)


n: nat
st, st0: State
xs: list Step
IHn: scale (2 ^ Z.of_nat n) (fg st0) = ap (prod (map trans xs)) (fg st)
st1: State
x: Step
Htrans: scale 2 (fg st1) = ap (trans x) (fg st0)
scale (2 * 2 ^ Z.of_nat n) (fg st1) =
ap (mul (trans x) (prod (map trans xs))) (fg st)


n: nat
st, st0: State
xs: list Step
IHn: scale (2 ^ Z.of_nat n) (fg st0) = ap (prod (map trans xs)) (fg st)
st1: State
x: Step
Htrans: scale 2 (fg st1) = ap (trans x) (fg st0)
scale (2 ^ Z.of_nat n) (scale 2 (fg st1)) =
scale (2 ^ Z.of_nat n) (ap (trans x) (fg st0))


n: nat
st, st0: State
xs: list Step
IHn: scale (2 ^ Z.of_nat n) (fg st0) = ap (prod (map trans xs)) (fg st)
st1: State
x: Step
Htrans: scale 2 (fg st1) = ap (trans x) (fg st0)
scale 2 (fg st1) = ap (trans x) (fg st0)

apply Htrans.
Qed.


n: nat
st: State
det (transN n st) = 2 ^ Z.of_nat n


n: nat
st: State
det (transN n st) = 2 ^ Z.of_nat n


n: nat
forall st : State, det (transN n st) = 2 ^ Z.of_nat n


n: nat
IHn: forall st : State, det (transN n st) = 2 ^ Z.of_nat n
forall st : State,
det (transN (S n) st) = 2 ^ Z.of_nat (S n)


n: nat
IHn: forall st : State, det (transN n st) = 2 ^ Z.of_nat n
st: State
det (transN (S n) st) = 2 ^ Z.of_nat (S n)


n: nat
IHn: forall st : State, det (transN n st) = 2 ^ Z.of_nat n
st: State
x: Step
det (mul (trans x) (transN n st)) = 2 ^ Z.of_nat (S n)


n: nat
IHn: forall st : State, det (transN n st) = 2 ^ Z.of_nat n
st: State
x: Step
2 * det (transN n st) = 2 * 2 ^ Z.of_nat n

congruence.
Qed.


n: nat
st: State
bounded (2 ^ Z.of_nat n) (transN n st)


n: nat
st: State
bounded (2 ^ Z.of_nat n) (transN n st)


n: nat
st: State
IHn: bounded (2 ^ Z.of_nat n) (transN n st)
bounded (2 ^ Z.of_nat (S n)) (transN (S n) st)


n: nat
st: State
IHn: bounded (2 ^ Z.of_nat n) (transN n st)
x: Step
bounded (2 ^ Z.of_nat (S n))
  (mul (trans x) (transN n st))


n: nat
st: State
IHn: bounded (2 ^ Z.of_nat n) (transN n st)
x: Step
bounded (2 * 2 ^ Z.of_nat n)
  (mul (trans x) (transN n st))

auto using bounded_mul_trans.
Qed.


n, m: nat
st: State
mul (transN n (fst (stepN m st))) (transN m st) =
transN (n + m) st


n, m: nat
st: State
mul (transN n (fst (stepN m st))) (transN m st) =
transN (n + m) st


n, m: nat
st: State
mul
  (prod (map trans (snd (stepN n (fst (stepN m st))))))
  (prod (map trans (snd (stepN m st)))) =
prod (map trans (snd (stepN (n + m) st)))


n, m: nat
st: State
mul
  (prod (map trans (snd (stepN n (fst (stepN m st))))))
  (prod (map trans (snd (stepN m st)))) =
mul
  (prod (map trans (snd (stepN n (fst (stepN m st))))))
  (prod (map trans (snd (stepN m st))))

reflexivity.
Qed.


n: nat
st: State
(2 ^ Z.of_nat n | g st) ->
transN n st =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
(2 ^ Z.of_nat n | g st) ->
transN n st =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
transN n st = {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
(2 ^ Z.of_nat (S n) | g st) ->
transN (S n) st =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
transN n st = {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
(2 * 2 ^ Z.of_nat n | g st) ->
transN (S n) st =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
transN n st = {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: (2 * 2 ^ Z.of_nat n | g st)
transN (S n) st =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: (2 * 2 ^ Z.of_nat n | g st)
prod (map trans (snd (stepN (S n) st))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: (2 * 2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: (2 * 2 ^ Z.of_nat n | g st)
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g st mod (2 * 2 ^ Z.of_nat n) = 0
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g st mod (2 * 2 ^ Z.of_nat n) / 2 ^ Z.of_nat n =
0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: (g st / 2 ^ Z.of_nat n) mod 2 =
0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st: State
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (stepN n st))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g (fst (stepN n st)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        (let (st0, xs) := stepN n st in
         let (st1, x) := step st0 in (st1, x :: xs)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (s, l))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd (let (st1, x) := step s in (st1, x :: l)))) =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (s, l))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd (let (st1, x) := step s in (st1, x :: l)))) =
mul (trans Step.H)
  {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (s, l))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
mul (trans Step.H)
  {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |} =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (s, l))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd (let (st1, x) := step s in (st1, x :: l)))) =
mul (trans Step.H)
  {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}


n: nat
st, s: State
l: list Step
IHn: (2 ^ Z.of_nat n | g st) ->
prod (map trans (snd (s, l))) =
{| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: g (fst (s, l)) mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd (let (st1, x) := step s in (st1, x :: l)))) =
mul (trans Step.H) (prod (map trans (snd (s, l))))


n: nat
st: State
l: list Step
d, f', g': Z
IHn: (2 ^ Z.of_nat n | g st) ->
prod
(map trans
(snd
({|
delta := d;
f := 2 * f' + 1;
g := 2 * g';
oddF := Zodd_2p_plus_1 f'
|}, l))) = {| u := 2 ^ Z.of_nat n; v := 0; q := 0; r := 1 |}
Hg: (2 * g') mod 2 = 0 / 2 ^ Z.of_nat n
Hg': (2 ^ Z.of_nat n | g st)
prod
  (map trans
     (snd
        ({|
           delta := INC + d;
           f := 2 * f' + 1;
           g := g';
           oddF := Zodd_2p_plus_1 f'
         |}, Step.H :: l))) =
mul (trans Step.H)
  (prod
     (map trans
        (snd
           ({|
              delta := d;
              f := 2 * f' + 1;
              g := 2 * g';
              oddF := Zodd_2p_plus_1 f'
            |}, l))))

reflexivity.
Qed.


n: nat
st: State
delta st <= 0 ->
Z.of_nat n <= 1 - delta st ->
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
delta st <= 0 ->
Z.of_nat n <= 1 - delta st ->
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
rel_prime (f st) 2
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
rel_prime (f st) 2

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
rel_prime (f st mod 2) 2

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hfodd: Zodd (f st)
rel_prime (f st mod 2) 2

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hfodd: Z.odd (f st) = true
rel_prime (f st mod 2) 2

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hfodd: Z.odd (f st) = true
rel_prime 1 2

  apply rel_prime_1.

n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
forall x : Z, 0 <= x -> Z.gcd (f st) (2 ^ x) = 1
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
forall x : Z, 0 <= x -> Z.gcd (f st) (2 ^ x) = 1

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
x: Z
Hx: 0 <= x
Z.gcd (f st) (2 ^ x) = 1

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
x: Z
Hx: 0 <= x
rel_prime (f st) (2 ^ x)

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
x: Z
Hx: 0 <= x
rel_prime (f st) 2

  assumption.

n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (modInv (- f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n =
(modInv (- f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n =
(modInv (- f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
eqm (2 ^ Z.of_nat n)
  (- modInv (f st) (2 ^ Z.of_nat n))
  (modInv (- f st) (2 ^ Z.of_nat n))

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n =
modInv (- f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
modInv (- f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(1 * modInv (- f st) (2 ^ Z.of_nat n))
mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(modInv (f st) (2 ^ Z.of_nat n) *
 (f st * modInv (- f st) (2 ^ Z.of_nat n)))
mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(modInv (f st) (2 ^ Z.of_nat n) *
 (- - f st * modInv (- f st) (2 ^ Z.of_nat n)))
mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(- modInv (f st) (2 ^ Z.of_nat n) *
 (- f st * modInv (- f st) (2 ^ Z.of_nat n)))
mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
(- modInv (f st) (2 ^ Z.of_nat n) * 1)
mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  
n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n =
- modInv (f st) (2 ^ Z.of_nat n) mod 2 ^ Z.of_nat n

  reflexivity.

n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
transN n st =
{| u := 2 ^ Z.of_nat n; v := 0; q := w; r := 1 |}


n: nat
st: State
Hdelta: delta st <= 0
Hn: Z.of_nat n <= 1 - delta st
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
transN n st =
{| u := 2 ^ Z.of_nat n; v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat n | f st * w + g st) /\
delta (fst (stepN n st)) = Z.of_nat n + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
IHn: let w :=
  (- modInv (f st) (2 ^ Z.of_nat n) * g st)
  mod 2 ^ Z.of_nat n in
Z.of_nat n <= 1 - delta st ->
transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w; r := 1
|} /\
(2 ^ Z.of_nat n | f st * w + g st) /\
delta (fst (stepN n st)) = Z.of_nat n + delta st
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
transN (S n) st =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta (fst (stepN (S n) st)) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
transN (S n) st =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta (fst (stepN (S n) st)) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
mul (transN 1 (fst (stepN n st)))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta (fst (stepN (S n) st)) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
mul (transN 1 (fst (stepN n st)))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta (fst (stepN (1 + n) st)) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
mul (transN 1 (fst (stepN n st)))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     (let st1 := stepN n st in
      (fst (stepN 1 (fst st1)),
       snd (stepN 1 (fst st1)) ++ snd st1))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
mul
  (prod (map trans (snd (stepN 1 (fst (stepN n st))))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     (fst (stepN 1 (fst (stepN n st))),
      snd (stepN 1 (fst (stepN n st))) ++
      snd (stepN n st))) = Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
mul
  (prod (map trans (snd (stepN 1 (fst (stepN n st))))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     (let (st1, x) := step (fst (stepN n st)) in
      (st1, x :: nil))) = Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step (fst (stepN n st)) in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     (let (st1, x) := step (fst (stepN n st)) in
      (st1, x :: nil))) = Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hst': st' = st'
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
st' = st' ->
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
st' = fst (stepN n st) ->
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
st' = fst (stepN n st) ->
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st



n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
(2 ^ Z.of_nat (S n) | f st * w + g st)
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
st' = fst (stepN n st) ->
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
(2 ^ Z.of_nat (S n) | f st * w + g st)

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
(f st * w + g st) mod 2 ^ Z.of_nat (S n) = 0

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
(f st *
 ((- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
  mod 2 ^ Z.of_nat (S n)) + g st)
mod 2 ^ Z.of_nat (S n) = 0

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
((Z.gcd (f st) (2 ^ Z.of_nat (S n))
  mod 2 ^ Z.of_nat (S n) * - g st)
 mod 2 ^ Z.of_nat (S n) + g st) mod 2 ^ Z.of_nat (S n) =
0

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
((1 mod 2 ^ Z.of_nat (S n) * - g st)
 mod 2 ^ Z.of_nat (S n) + g st) mod 2 ^ Z.of_nat (S n) =
0
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
1 = Z.gcd (f st) (2 ^ Z.of_nat (S n))

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
1 = Z.gcd (f st) (2 ^ Z.of_nat (S n))

   
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Z.gcd (f st) (2 ^ Z.of_nat (S n)) = 1

   
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
rel_prime (f st) (2 ^ Z.of_nat (S n))
 
   
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
rel_prime (f st) 2

   assumption.
  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
((1 mod 2 ^ Z.of_nat (S n) * - g st)
 mod 2 ^ Z.of_nat (S n) + g st) mod 2 ^ Z.of_nat (S n) =
0

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
(1 * - g st + g st) mod 2 ^ Z.of_nat (S n) = 0

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
0 mod 2 ^ Z.of_nat (S n) = 0

  reflexivity.

n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
st' = fst (stepN n st) ->
mul
  (prod
     (map trans
        (snd
           (let (st1, x) := step st' in
            (st1, x :: nil)))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst (let (st1, x) := step st' in (st1, x :: nil))) =
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g';
              oddF := Zodd_2p_plus_1 f'
            |}, Step.H :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: nil)) = Z.of_nat (S n) + delta st
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d: positive
f', g': Z
Hst': {|
  delta := Z.pos d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC - Z.pos d;
              f := 2 * g' + 1;
              g := g' - f';
              oddF := Zodd_2p_plus_1 g'
            |}, Step.D :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC - Z.pos d;
        f := 2 * g' + 1;
        g := g' - f';
        oddF := Zodd_2p_plus_1 g'
      |}, Step.D :: nil)) = 
Z.of_nat (S n) + delta st
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
{|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st) ->
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g' + f' + 1;
              oddF := Zodd_2p_plus_1 f'
            |}, Step.S :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g' + f' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, Step.S :: nil)) = 
Z.of_nat (S n) + delta st


n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g';
              oddF := Zodd_2p_plus_1 f'
            |}, Step.H :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: nil)) = Z.of_nat (S n) + delta st
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g';
              oddF := Zodd_2p_plus_1 f'
            |}, Step.H :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |}
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n) | f st * w + g st)
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: nil)) = 
Z.of_nat (S n) + delta st

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g';
              oddF := Zodd_2p_plus_1 f'
            |}, Step.H :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |}
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g';
              oddF := Zodd_2p_plus_1 f'
            |}, Step.H :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{|
  u := 2 ^ (1 + Z.of_nat n); v := 0; q := w; r := 1
|}

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g';
              oddF := Zodd_2p_plus_1 f'
            |}, Step.H :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{|
  u := 2 ^ 1 * 2 ^ Z.of_nat n; v := 0; q := w; r := 1
|}

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
{|
  u :=
    2 * 2 ^ Z.of_nat n +
    0 *
    ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
     mod 2 ^ Z.of_nat n);
  v := 0;
  q :=
    0 * 2 ^ Z.of_nat n +
    1 *
    ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
     mod 2 ^ Z.of_nat n);
  r := 1
|} =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := w; r := 1 |}

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 * 2 ^ Z.of_nat n +
1 *
((- modInv (f st) (2 ^ Z.of_nat n) * g st)
 mod 2 ^ Z.of_nat n) = w

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n = w

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n =
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n)

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n) =
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat (S n)
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n)
| - modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
  (- modInv (f st) (2 ^ Z.of_nat n) * g st)
  mod 2 ^ Z.of_nat n)

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat (S n)
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: 0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat (S n)

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: 0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ (1 + Z.of_nat n)

      rewrite Z.pow_add_r; lia.
    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n)
| - modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
  (- modInv (f st) (2 ^ Z.of_nat n) * g st)
  mod 2 ^ Z.of_nat n)
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n)
| - modInv (f st) (2 ^ Z.of_nat (S n)) * g st - w0)

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st - w0)
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 w0 mod 2 ^ Z.of_nat (S n)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 (1 * w0) mod 2 ^ Z.of_nat (S n))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 (Z.gcd (f st) (2 ^ Z.of_nat (S n))
  mod 2 ^ Z.of_nat (S n) * w0) mod 2 ^ Z.of_nat (S n))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 modInv (f st) (2 ^ Z.of_nat (S n)) * f st * w0)
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: scale (2 ^ Z.of_nat n)
  (fg (fst (stepN n st))) =
ap (transN n st) (fg st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: scale (2 ^ Z.of_nat n)
  (fg
     {|
       delta := d;
       f := 2 * f' + 1;
       g := 2 * g';
       oddF := Zodd_2p_plus_1 f'
     |}) =
ap
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q := w0;
    r := 1
  |} (fg st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: {|
  x :=
    2 ^ Z.of_nat n *
    x
      {|
        x :=
          f
            {|
              delta := d;
              f := 2 * f' + 1;
              g := 2 * g';
              oddF := Zodd_2p_plus_1 f'
            |};
        y :=
          g
            {|
              delta := d;
              f := 2 * f' + 1;
              g := 2 * g';
              oddF := Zodd_2p_plus_1 f'
            |}
      |};
  y :=
    2 ^ Z.of_nat n *
    y
      {|
        x :=
          f
            {|
              delta := d;
              f := 2 * f' + 1;
              g := 2 * g';
              oddF := Zodd_2p_plus_1 f'
            |};
        y :=
          g
            {|
              delta := d;
              f := 2 * f' + 1;
              g := 2 * g';
              oddF := Zodd_2p_plus_1 f'
            |}
      |}
|} =
{|
  x :=
    u
      {|
        u := 2 ^ Z.of_nat n;
        v := 0;
        q := w0;
        r := 1
      |} * x {| x := f st; y := g st |} +
    v
      {|
        u := 2 ^ Z.of_nat n;
        v := 0;
        q := w0;
        r := 1
      |} * y {| x := f st; y := g st |};
  y :=
    q
      {|
        u := 2 ^ Z.of_nat n;
        v := 0;
        q := w0;
        r := 1
      |} * x {| x := f st; y := g st |} +
    r
      {|
        u := 2 ^ Z.of_nat n;
        v := 0;
        q := w0;
        r := 1
      |} * y {| x := f st; y := g st |}
|}
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: {|
  x := 2 ^ Z.of_nat n * (2 * f' + 1);
  y := 2 ^ Z.of_nat n * (2 * g')
|} =
{|
  x := 2 ^ Z.of_nat n * f st + 0 * g st;
  y := w0 * f st + 1 * g st
|}
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
2 ^ Z.of_nat n * (2 * g') = w0 * f st + 1 * g st ->
2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st ->
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g') = w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (w0 * f st + 1 * g st)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g') = w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * (2 * g'))) mod 2 ^ Z.of_nat (S n) =
0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g') = w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (g' * (2 ^ Z.of_nat n * 2 ^ 1)))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g') = w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g' *
 2 ^ (Z.of_nat n + 1)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g') = w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g' *
 2 ^ Z.of_nat (S n)) mod 2 ^ Z.of_nat (S n) = 0

      apply Z_mod_mult.
  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n) | f st * w + g st)
 assumption.
  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: nil)) = Z.of_nat (S n) + delta st
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: nil)) =
1 + (Z.of_nat n + delta st)

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g';
        oddF := Zodd_2p_plus_1 f'
      |}, Step.H :: nil)) =
1 + delta (fst (stepN n st))

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
INC + d = 1 + delta (fst (stepN n st))

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g';
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
INC + d =
1 +
delta
  {|
    delta := d;
    f := 2 * f' + 1;
    g := 2 * g';
    oddF := Zodd_2p_plus_1 f'
  |}

    reflexivity.

n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d: positive
f', g': Z
Hst': {|
  delta := Z.pos d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC - Z.pos d;
              f := 2 * g' + 1;
              g := g' - f';
              oddF := Zodd_2p_plus_1 g'
            |}, Step.D :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC - Z.pos d;
        f := 2 * g' + 1;
        g := g' - f';
        oddF := Zodd_2p_plus_1 g'
      |}, Step.D :: nil)) = Z.of_nat (S n) + delta st
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
d: positive
f', g': Z
IHn3: delta
  {|
    delta := Z.pos d;
    f := 2 * f' + 1;
    g := 2 * g' + 1;
    oddF := Zodd_2p_plus_1 f'
  |} = Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
Hst': {|
  delta := Z.pos d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC - Z.pos d;
              f := 2 * g' + 1;
              g := g' - f';
              oddF := Zodd_2p_plus_1 g'
            |}, Step.D :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC - Z.pos d;
        f := 2 * g' + 1;
        g := g' - f';
        oddF := Zodd_2p_plus_1 g'
      |}, Step.D :: nil)) = Z.of_nat (S n) + delta st

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
d: positive
f', g': Z
IHn3: Z.pos d = Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
Hst': {|
  delta := Z.pos d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC - Z.pos d;
              f := 2 * g' + 1;
              g := g' - f';
              oddF := Zodd_2p_plus_1 g'
            |}, Step.D :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC - Z.pos d;
        f := 2 * g' + 1;
        g := g' - f';
        oddF := Zodd_2p_plus_1 g'
      |}, Step.D :: nil)) = Z.of_nat (S n) + delta st

  lia.

n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
{|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st) ->
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g' + f' + 1;
              oddF := Zodd_2p_plus_1 f'
            |}, Step.S :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |} /\
(2 ^ Z.of_nat (S n) | f st * w + g st) /\
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g' + f' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, Step.S :: nil)) = Z.of_nat (S n) + delta st
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g' + f' + 1;
              oddF := Zodd_2p_plus_1 f'
            |}, Step.S :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |}
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n) | f st * w + g st)
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g' + f' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, Step.S :: nil)) = 
Z.of_nat (S n) + delta st

  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g' + f' + 1;
              oddF := Zodd_2p_plus_1 f'
            |}, Step.S :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{| u := 2 ^ Z.of_nat (S n); v := 0; q := w; r := 1 |}
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g' + f' + 1;
              oddF := Zodd_2p_plus_1 f'
            |}, Step.S :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{|
  u := 2 ^ (1 + Z.of_nat n); v := 0; q := w; r := 1
|}

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
mul
  (prod
     (map trans
        (snd
           ({|
              delta := INC + d;
              f := 2 * f' + 1;
              g := g' + f' + 1;
              oddF := Zodd_2p_plus_1 f'
            |}, Step.S :: nil))))
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q :=
      (- modInv (f st) (2 ^ Z.of_nat n) * g st)
      mod 2 ^ Z.of_nat n;
    r := 1
  |} =
{|
  u := 2 ^ 1 * 2 ^ Z.of_nat n; v := 0; q := w; r := 1
|}

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
{|
  u :=
    2 * 2 ^ Z.of_nat n +
    0 *
    ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
     mod 2 ^ Z.of_nat n);
  v := 0;
  q :=
    1 * 2 ^ Z.of_nat n +
    1 *
    ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
     mod 2 ^ Z.of_nat n);
  r := 1
|} =
{| u := 2 * 2 ^ Z.of_nat n; v := 0; q := w; r := 1 |}

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
1 * 2 ^ Z.of_nat n +
1 *
((- modInv (f st) (2 ^ Z.of_nat n) * g st)
 mod 2 ^ Z.of_nat n) = w

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n = w

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n =
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n)

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n) =
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat (S n)
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n)
| - modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
  (2 ^ Z.of_nat n +
   (- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n))

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat (S n)
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: 0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat (S n)

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: 0 <=
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
0 <=
2 ^ Z.of_nat n +
(- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n < 2 ^ (1 + Z.of_nat n)

      rewrite Z.pow_add_r; lia.
    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n)
| - modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
  (2 ^ Z.of_nat n +
   (- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n))
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n)
| - modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
  (2 ^ Z.of_nat n + w0))

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 (2 ^ Z.of_nat n + w0)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 (2 ^ Z.of_nat n + w0) mod 2 ^ Z.of_nat (S n))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 (1 * (2 ^ Z.of_nat n + w0)) mod 2 ^ Z.of_nat (S n))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 (Z.gcd (f st) (2 ^ Z.of_nat (S n))
  mod 2 ^ Z.of_nat (S n) * (2 ^ Z.of_nat n + w0))
 mod 2 ^ Z.of_nat (S n)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) * g st -
 modInv (f st) (2 ^ Z.of_nat (S n)) * f st *
 (2 ^ Z.of_nat n + w0)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * f st + 0 * g st +
  (w0 * f st + 1 * g st))) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: scale (2 ^ Z.of_nat n)
  (fg (fst (stepN n st))) =
ap (transN n st) (fg st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * f st + 0 * g st +
  (w0 * f st + 1 * g st))) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: scale (2 ^ Z.of_nat n)
  (fg
     {|
       delta := d;
       f := 2 * f' + 1;
       g := 2 * g' + 1;
       oddF := Zodd_2p_plus_1 f'
     |}) =
ap
  {|
    u := 2 ^ Z.of_nat n;
    v := 0;
    q := w0;
    r := 1
  |} (fg st)
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * f st + 0 * g st +
  (w0 * f st + 1 * g st))) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
HtransN: {|
  x := 2 ^ Z.of_nat n * (2 * f' + 1);
  y := 2 ^ Z.of_nat n * (2 * g' + 1)
|} =
{|
  x := 2 ^ Z.of_nat n * f st + 0 * g st;
  y := w0 * f st + 1 * g st
|}
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * f st + 0 * g st +
  (w0 * f st + 1 * g st))) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
2 ^ Z.of_nat n * (2 * g' + 1) = w0 * f st + 1 * g st ->
2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st ->
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * f st + 0 * g st +
  (w0 * f st + 1 * g st))) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g' + 1) =
w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * f st + 0 * g st +
  (w0 * f st + 1 * g st))) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g' + 1) =
w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 (2 ^ Z.of_nat n * (2 * f' + 1) +
  2 ^ Z.of_nat n * (2 * g' + 1)))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g' + 1) =
w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) *
 ((f' + g' + 1) * (2 ^ Z.of_nat n * 2 ^ 1)))
mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g' + 1) =
w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) * (f' + g' + 1) *
 2 ^ (Z.of_nat n + 1)) mod 2 ^ Z.of_nat (S n) = 0

      
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
w0:= (- modInv (f st) (2 ^ Z.of_nat n) * g st)
mod 2 ^ Z.of_nat n: Z
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n; v := 0; q := w0; r := 1
|}
IHn2: (2 ^ Z.of_nat n | f st * w0 + g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
Hg': 2 ^ Z.of_nat n * (2 * g' + 1) =
w0 * f st + 1 * g st
Hf': 2 ^ Z.of_nat n * (2 * f' + 1) =
2 ^ Z.of_nat n * f st + 0 * g st
(- modInv (f st) (2 ^ Z.of_nat (S n)) * (f' + g' + 1) *
 2 ^ Z.of_nat (S n)) mod 2 ^ Z.of_nat (S n) = 0

      apply Z_mod_mult.
  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
(2 ^ Z.of_nat (S n) | f st * w + g st)
 assumption.
  
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g' + f' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, Step.S :: nil)) = Z.of_nat (S n) + delta st
 
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g' + f' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, Step.S :: nil)) =
1 + (Z.of_nat n + delta st)

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
delta
  (fst
     ({|
        delta := INC + d;
        f := 2 * f' + 1;
        g := g' + f' + 1;
        oddF := Zodd_2p_plus_1 f'
      |}, Step.S :: nil)) =
1 + delta (fst (stepN n st))

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
INC + d = 1 + delta (fst (stepN n st))

    
n: nat
st: State
Hdelta: delta st <= 0
Hrel_prime: rel_prime (f st) 2
Hgcd: forall x : Z,
0 <= x -> Z.gcd (f st) (2 ^ x) = 1
w:= (- modInv (f st) (2 ^ Z.of_nat (S n)) * g st)
mod 2 ^ Z.of_nat (S n): Z
Hn: Z.of_nat (S n) <= 1 - delta st
IHn1: transN n st =
{|
  u := 2 ^ Z.of_nat n;
  v := 0;
  q :=
    (- modInv (f st) (2 ^ Z.of_nat n) * g st)
    mod 2 ^ Z.of_nat n;
  r := 1
|}
IHn2: (2 ^ Z.of_nat n
| f st *
  ((- modInv (f st) (2 ^ Z.of_nat n) * g st)
   mod 2 ^ Z.of_nat n) + 
  g st)
IHn3: delta (fst (stepN n st)) =
Z.of_nat n + delta st
st':= fst (stepN n st): State
Hbound: forall a : Z,
0 <= a mod 2 ^ Z.of_nat n < 2 ^ Z.of_nat n
Hdivide: (2 ^ Z.of_nat (S n) | f st * w + g st)
d, f', g': Z
Hst': d <= 0
Hst'0: {|
  delta := d;
  f := 2 * f' + 1;
  g := 2 * g' + 1;
  oddF := Zodd_2p_plus_1 f'
|} = fst (stepN n st)
INC + d =
1 +
delta
  {|
    delta := d;
    f := 2 * f' + 1;
    g := 2 * g' + 1;
    oddF := Zodd_2p_plus_1 f'
  |}

    reflexivity.
Qed.


n: nat
st: State
Zodd (g st) ->
0 < delta st ->
0 < Z.of_nat n <= 1 + delta st ->
transN n st =
{|
  u := 0;
  v := 2 ^ Z.of_nat n;
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat n) * - f st)
    mod 2 ^ Z.of_nat n
|}


n: nat
st: State
Zodd (g st) ->
0 < delta st ->
0 < Z.of_nat n <= 1 + delta st ->
transN n st =
{|
  u := 0;
  v := 2 ^ Z.of_nat n;
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat n) * - f st)
    mod 2 ^ Z.of_nat n
|}


n: nat
st: State
Hodd: Zodd (g st)
Hdelta: 0 < delta st
Hn0: 0 < Z.of_nat n
Hn: Z.of_nat n <= 1 + delta st
transN n st =
{|
  u := 0;
  v := 2 ^ Z.of_nat n;
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat n) * - f st)
    mod 2 ^ Z.of_nat n
|}


n: nat
st: State
Hodd: Zodd (g st)
Hdelta: 0 < delta st
Hn0: 0 < Z.of_nat (S n)
Hn: Z.of_nat (S n) <= 1 + delta st
transN (S n) st =
{|
  u := 0;
  v := 2 ^ Z.of_nat (S n);
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat (S n)) * - f st)
    mod 2 ^ Z.of_nat (S n)
|}


n: nat
st: State
Hodd: Zodd (g st)
Hdelta: 0 < delta st
Hn0: 0 < Z.of_nat (S n)
Hn: Z.of_nat (S n) <= 1 + delta st
mul (transN n (fst (stepN 1 st))) (transN 1 st) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat (n + 1)) * - f st)
    mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hodd: Zodd (g st)
Hdelta: 0 < delta st
Hn0: 0 < Z.of_nat (S n)
Hn: Z.of_nat (S n) <= 1 + delta st
mul
  (transN n
     (fst (let (st1, x) := step st in (st1, x :: nil))))
  (prod
     (map trans
        (snd
           (let (st1, x) := step st in (st1, x :: nil))))) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat (n + 1)) * - f st)
    mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
Zodd (g st) ->
0 < delta st ->
Z.of_nat (S n) <= 1 + delta st ->
mul
  (transN n
     (fst (let (st1, x) := step st in (st1, x :: nil))))
  (prod
     (map trans
        (snd
           (let (st1, x) := step st in (st1, x :: nil))))) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- g st) (2 ^ Z.of_nat (n + 1)) * - f st)
    mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
d: positive
f', g': Z
Hodd: Zodd (2 * g' + 1)
Hdelta: 0 < Z.pos d
Hn: Z.pos (Pos.of_succ_nat n) <=
Z.pos
  match d with
  | q~1 => (Pos.succ q)~0
  | q~0 => q~1
  | 1 => 2
  end
mul
  (transN n
     {|
       delta := Z.pos_sub 1 d;
       f := 2 * g' + 1;
       g := g' - f';
       oddF := Zodd_2p_plus_1 g'
     |}) (mul {| u := 0; v := 2; q := -1; r := 1 |} I) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
d: positive
f', g': Z
Hodd: Zodd (2 * g' + 1)
Hdelta: 0 < Z.pos d
Hn: Z.of_nat (S n) <= 1 + Z.pos d
mul
  (transN n
     {|
       delta := Z.pos_sub 1 d;
       f := 2 * g' + 1;
       g := g' - f';
       oddF := Zodd_2p_plus_1 g'
     |}) (mul {| u := 0; v := 2; q := -1; r := 1 |} I) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
d: positive
f', g': Z
Hodd: Zodd (2 * g' + 1)
Hdelta: 0 < Z.pos d
Hn: Z.of_nat (S n) <= 1 + Z.pos d
mul
  (transN n
     {|
       delta := 1 - Z.pos d;
       f := 2 * g' + 1;
       g := g' - f';
       oddF := Zodd_2p_plus_1 g'
     |}) (mul {| u := 0; v := 2; q := -1; r := 1 |} I) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
mul
  (transN n
     {|
       delta := 1 - dZ;
       f := 2 * g' + 1;
       g := g' - f';
       oddF := Zodd_2p_plus_1 g'
     |}) (mul {| u := 0; v := 2; q := -1; r := 1 |} I) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
mul
  (transN n
     {|
       delta := 1 - dZ;
       f := 2 * g' + 1;
       g := g' - f';
       oddF := Zodd_2p_plus_1 g'
     |})
  (mul (trans Step.S)
     {| u := 0; v := 1; q := -1; r := 0 |}) =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
st: State
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
mul
  (mul
     (transN n
        {|
          delta := 1 - dZ;
          f := 2 * g' + 1;
          g := g' - f';
          oddF := Zodd_2p_plus_1 g'
        |}) (trans Step.S))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
mul
  (mul
     (transN n
        {|
          delta := 1 - dZ;
          f := 2 * g' + 1;
          g := g' - f';
          oddF := Zodd_2p_plus_1 g'
        |}) (trans Step.S))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
mul
  (mul
     (transN n
        {|
          delta := 1 - dZ;
          f := 2 * g' + 1;
          g := g' - f';
          oddF := Zodd_2p_plus_1 g'
        |}) (trans Step.S))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
mul (mul (transN n st1) (trans Step.S))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
step st0 = (st1, Step.S)
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
mul (mul (transN n st1) (trans Step.S))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 
    2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
step st0 = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
match Zeven_odd_dec (g st0) with
| left _ =>
    ({|
       delta := INC + delta st0;
       f := f st0;
       g := g st0 / 2;
       oddF := oddF st0
     |}, Step.H)
| right oddG =>
    if 0 <? delta st0
    then
     ({|
        delta := INC - delta st0;
        f := g st0;
        g := (g st0 - f st0) / 2;
        oddF := oddG
      |}, Step.D)
    else
     ({|
        delta := INC + delta st0;
        f := f st0;
        g := (g st0 + f st0) / 2;
        oddF := oddF st0
      |}, Step.S)
end = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hoddg: Zodd (g st0)
match Zeven_odd_dec (g st0) with
| left _ =>
    ({|
       delta := INC + delta st0;
       f := f st0;
       g := g st0 / 2;
       oddF := oddF st0
     |}, Step.H)
| right oddG =>
    if 0 <? delta st0
    then
     ({|
        delta := INC - delta st0;
        f := g st0;
        g := (g st0 - f st0) / 2;
        oddF := oddG
      |}, Step.D)
    else
     ({|
        delta := INC + delta st0;
        f := f st0;
        g := (g st0 + f st0) / 2;
        oddF := oddF st0
      |}, Step.S)
end = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hoddg, Hoddg': Zodd (g st0)
(if 0 <? delta st0
 then
  ({|
     delta := INC - delta st0;
     f := g st0;
     g := (g st0 - f st0) / 2;
     oddF := Hoddg'
   |}, Step.D)
 else
  ({|
     delta := INC + delta st0;
     f := f st0;
     g := (g st0 + f st0) / 2;
     oddF := oddF st0
   |}, Step.S)) = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hoddg, Hoddg': Zodd (g st0)
Hd0: - dZ <= 0
({|
   delta := INC + delta st0;
   f := f st0;
   g := (g st0 + f st0) / 2;
   oddF := oddF st0
 |}, Step.S) = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hoddg, Hoddg': Zodd (g st0)
Hd0: - dZ <= 0
({|
   delta := INC + delta st0;
   f := f st0;
   g := (-2 * f' - 1 + (2 * g' + 1)) / 2;
   oddF := oddF st0
 |}, Step.S) = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hoddg, Hoddg': Zodd (g st0)
Hd0: - dZ <= 0
({|
   delta := INC + delta st0;
   f := f st0;
   g := (g' - f') * 2 / 2;
   oddF := oddF st0
 |}, Step.S) = (st1, Step.S)

  
n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hoddg, Hoddg': Zodd (g st0)
Hd0: - dZ <= 0
({|
   delta := INC + delta st0;
   f := f st0;
   g := g' - f';
   oddF := oddF st0
 |}, Step.S) = (st1, Step.S)

  reflexivity.

n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
mul (mul (transN n st1) (trans Step.S))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
mul (mul (transN n st1) (transN 1 st0))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
mul
  (mul (transN n (fst (stepN 1 st0))) (transN 1 st0))
  {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
mul
  {|
    u := 2 ^ Z.of_nat (n + 1);
    v := 0;
    q :=
      (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
       (-2 * f' - 1)) mod 2 ^ Z.of_nat (n + 1);
    r := 1
  |} {| u := 0; v := 1; q := -1; r := 0 |} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
{|
  u := 2 ^ Z.of_nat (n + 1) * 0 + 0;
  v := 2 ^ Z.of_nat (n + 1) * 1 + 0;
  q :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     (-2 * f' - 1)) mod 2 ^ Z.of_nat (n + 1) * 0 + -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     (-2 * f' - 1)) mod 2 ^ Z.of_nat (n + 1) * 1 + 0
|} =
{|
  u := 0;
  v := 2 ^ Z.of_nat (n + 1);
  q := -1;
  r :=
    (modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
     - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)
|}


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
(modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
 (-2 * f' - 1)) mod 2 ^ Z.of_nat (n + 1) * 1 + 0 =
(modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
 - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
(modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
 (-2 * f' - 1)) mod 2 ^ Z.of_nat (n + 1) =
(modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
 - (2 * f' + 1)) mod 2 ^ Z.of_nat (n + 1)


n: nat
Hn0: 0 < Z.of_nat (S n)
f', g': Z
Hodd: Zodd (2 * g' + 1)
dZ: Z
Hdelta: 0 < dZ
Hn: Z.of_nat (S n) <= 1 + dZ
st0:= {|
  delta := - dZ;
  f := 2 * g' + 1;
  g := -2 * f' - 1;
  oddF := Zodd_2p_plus_1 g'
|}: State
st1:= {|
  delta := 1 - dZ;
  f := 2 * g' + 1;
  g := g' - f';
  oddF := Zodd_2p_plus_1 g'
|}: State
Hst01: step st0 = (st1, Step.S)
modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
(-2 * f' - 1) =
modInv (- (2 * g' + 1)) (2 ^ Z.of_nat (n + 1)) *
- (2 * f' + 1)

ring.
Qed.

End Trans.

Definition pre_div62Modulo (M a : Z) : Z :=
  a - (((modInv M (2^62))*a) mod 2^62) * M.


M, a: Z
pre_div62Modulo M a mod M = a mod M


M, a: Z
pre_div62Modulo M a mod M = a mod M


M, a: Z
(a + - ((modInv M (2 ^ 62) * a) mod 2 ^ 62 * M)) mod M =
a mod M


M, a: Z
(a + - ((modInv M (2 ^ 62) * a) mod 2 ^ 62) * M) mod M =
a mod M

apply Z_mod_plus_full.
Qed.


M, a: Z
Zodd M -> (2 ^ 62 | pre_div62Modulo M a)


M, a: Z
Zodd M -> (2 ^ 62 | pre_div62Modulo M a)


M, a: Z
HM: Zodd M
(2 ^ 62 | pre_div62Modulo M a)


M, a: Z
HM: Zodd M
pre_div62Modulo M a mod 2 ^ 62 = 0


M, a: Z
HM: Zodd M
(a - (modInv M (2 ^ 62) * a) mod 2 ^ 62 * M)
mod 2 ^ 62 = 0


M, a: Z
HM: Zodd M
(a - (modInv M (2 ^ 62) * a * M) mod 2 ^ 62)
mod 2 ^ 62 = 0


M, a: Z
HM: Zodd M
(a - (modInv M (2 ^ 62) * M * a) mod 2 ^ 62)
mod 2 ^ 62 = 0


M, a: Z
HM: Zodd M
(a - (Z.gcd M (2 ^ 62) mod 2 ^ 62 * a) mod 2 ^ 62)
mod 2 ^ 62 = 0


M, a: Z
HM: Zodd M
1 = Z.gcd M (2 ^ 62)


M, a: Z
HM: Zodd M
Z.gcd M (2 ^ 62) = 1


M, a: Z
HM: Zodd M
rel_prime M (2 ^ 62)


M, a: Z
HM: Zodd M
rel_prime M 2


M, a: Z
HM: Zodd M
Z.gcd M 2 = 1


M, a: Z
HM: Zodd M
Z.Bezout M 2 1


M, a: Z
HM: exists m : Z, M = 2 * m + 1
Z.Bezout M 2 1


M, a, m: Z
HMm: M = 2 * m + 1
Z.Bezout M 2 1


M, a, m: Z
HMm: M = 2 * m + 1
1 * M + - m * 2 = 1

lia.
Qed.

Definition update_de (M d e : Z) (mtx : Trans.M2x2) : (Z * Z) :=
  let vec := Trans.ap mtx
              {| Trans.x := d + if d <? 0 then M else 0
               ; Trans.y := e + if e <? 0 then M else 0
               |} in
  ( pre_div62Modulo M (Trans.x vec) / 2^62
  , pre_div62Modulo M (Trans.y vec) / 2^62
  ).


m, d, e: Z
mtx: Trans.M2x2
Zodd m ->
Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <= 2 ^ 62 ->
Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <= 2 ^ 62 ->
-2 * m < d < m ->
-2 * m < e < m ->
-2 * m < fst (update_de m d e mtx) < m /\
-2 * m < snd (update_de m d e mtx) < m


m, d, e: Z
mtx: Trans.M2x2
Zodd m ->
Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <= 2 ^ 62 ->
Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <= 2 ^ 62 ->
-2 * m < d < m ->
-2 * m < e < m ->
-2 * m < fst (update_de m d e mtx) < m /\
-2 * m < snd (update_de m d e mtx) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
-2 * m < fst (update_de m d e mtx) < m /\
-2 * m < snd (update_de m d e mtx) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
-2 * m <
fst
  (pre_div62Modulo m
     (Trans.x
        (Trans.ap mtx
           {|
             Trans.x := d + (if d <? 0 then m else 0);
             Trans.y := e + (if e <? 0 then m else 0)
           |})) / 2 ^ 62,
   pre_div62Modulo m
     (Trans.y
        (Trans.ap mtx
           {|
             Trans.x := d + (if d <? 0 then m else 0);
             Trans.y := e + (if e <? 0 then m else 0)
           |})) / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m
     (Trans.x
        (Trans.ap mtx
           {|
             Trans.x := d + (if d <? 0 then m else 0);
             Trans.y := e + (if e <? 0 then m else 0)
           |})) / 2 ^ 62,
   pre_div62Modulo m
     (Trans.y
        (Trans.ap mtx
           {|
             Trans.x := d + (if d <? 0 then m else 0);
             Trans.y := e + (if e <? 0 then m else 0)
           |})) / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m
     (Trans.y
        (Trans.ap mtx
           {|
             Trans.x := d + (if d <? 0 then m else 0);
             Trans.y := e + (if e <? 0 then m else 0)
           |})) / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m
     (Trans.y
        (Trans.ap mtx
           {|
             Trans.x := d + (if d <? 0 then m else 0);
             Trans.y := e + (if e <? 0 then m else 0)
           |})) / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Z.abs x <= 2 ^ 62 * (m - 1)
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Z.abs x <= 2 ^ 62 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Z.abs
  (Trans.u mtx * (d + (if d <? 0 then m else 0)) +
   Trans.v mtx * (e + (if e <? 0 then m else 0))) <=
4611686018427387904 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Z.abs (Trans.u mtx * (d + (if d <? 0 then m else 0))) +
Z.abs (Trans.v mtx * (e + (if e <? 0 then m else 0))) <=
4611686018427387904 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Z.abs (Trans.u mtx) *
Z.abs (d + (if d <? 0 then m else 0)) +
Z.abs (Trans.v mtx) *
Z.abs (e + (if e <? 0 then m else 0)) <=
4611686018427387904 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Z.abs (Trans.u mtx) *
Z.abs (d + (if d <? 0 then m else 0)) +
Z.abs (Trans.v mtx) *
Z.abs (e + (if e <? 0 then m else 0)) <=
(Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx)) * (m - 1)

  destruct (Z.ltb_spec0 d 0); destruct (Z.ltb_spec0 e 0);
  rewrite Z.mul_add_distr_r; apply Z.add_le_mono; apply Zmult_le_compat_l; lia.

m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Z.abs y <= 2 ^ 62 * (m - 1)
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Z.abs y <= 2 ^ 62 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Z.abs
  (Trans.q mtx * (d + (if d <? 0 then m else 0)) +
   Trans.r mtx * (e + (if e <? 0 then m else 0))) <=
4611686018427387904 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Z.abs (Trans.q mtx * (d + (if d <? 0 then m else 0))) +
Z.abs (Trans.r mtx * (e + (if e <? 0 then m else 0))) <=
4611686018427387904 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Z.abs (Trans.q mtx) *
Z.abs (d + (if d <? 0 then m else 0)) +
Z.abs (Trans.r mtx) *
Z.abs (e + (if e <? 0 then m else 0)) <=
4611686018427387904 * (m - 1)

  
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Z.abs (Trans.q mtx) *
Z.abs (d + (if d <? 0 then m else 0)) +
Z.abs (Trans.r mtx) *
Z.abs (e + (if e <? 0 then m else 0)) <=
(Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx)) * (m - 1)

  destruct (Z.ltb_spec0 d 0); destruct (Z.ltb_spec0 e 0);
  rewrite Z.mul_add_distr_r; apply Z.add_le_mono; apply Zmult_le_compat_l; lia.

m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
-2 * m <
fst
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m /\
-2 * m <
snd
  (pre_div62Modulo m x / 2 ^ 62,
   pre_div62Modulo m y / 2 ^ 62) < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
-2 * m < pre_div62Modulo m x / 2 ^ 62 < m /\
-2 * m < pre_div62Modulo m y / 2 ^ 62 < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
-2 * m <
(x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m) / 2 ^ 62 <
m /\
-2 * m <
(y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m) / 2 ^ 62 <
m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
-2 * m <
(x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m) / 2 ^ 62 <
m /\
-2 * m <
(y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m) / 2 ^ 62 <
m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
Hymod: 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 <
2 ^ 62
-2 * m <
(x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m) / 2 ^ 62 <
m /\
-2 * m <
(y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m) / 2 ^ 62 <
m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
Hymod: 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 <
2 ^ 62
-2 * m <
Z.shiftr (x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m)
  62 < m /\
-2 * m <
Z.shiftr (y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m)
  62 < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
Hymod: 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 <
2 ^ 62
-2 * m <
Z.shiftr (x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m)
  62 < m
m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
Hymod: 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 <
2 ^ 62
-2 * m <
Z.shiftr (y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m)
  62 < m


m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
Hymod: 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 <
2 ^ 62
-2 * m <
Z.shiftr (x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m)
  62 < m
 cut (-2*m + 1 <= Z.shiftr (x - (modInv m (2 ^ 62) * x) mod 2 ^ 62 * m) 62 < m);[lia|apply shiftr_bounds;nia].

m, d, e: Z
mtx: Trans.M2x2
Hoddm: Zodd m
Huv: Z.abs (Trans.u mtx) + Z.abs (Trans.v mtx) <=
2 ^ 62
Hqr: Z.abs (Trans.q mtx) + Z.abs (Trans.r mtx) <=
2 ^ 62
Hmd: -2 * m < d < m
Hme: -2 * m < e < m
x:= Trans.x
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
y:= Trans.y
  (Trans.ap mtx
     {|
       Trans.x := d + (if d <? 0 then m else 0);
       Trans.y := e + (if e <? 0 then m else 0)
     |}): Z
Hm1: 1 <= m
Hxbound: Z.abs x <= 2 ^ 62 * (m - 1)
Hybound: Z.abs y <= 2 ^ 62 * (m - 1)
Hxmod: 0 <= (modInv m (2 ^ 62) * x) mod 2 ^ 62 <
2 ^ 62
Hymod: 0 <= (modInv m (2 ^ 62) * y) mod 2 ^ 62 <
2 ^ 62
-2 * m <
Z.shiftr (y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m)
  62 < m
 cut (-2*m + 1 <= Z.shiftr (y - (modInv m (2 ^ 62) * y) mod 2 ^ 62 * m) 62 < m);[lia|apply shiftr_bounds;nia].
Qed.


m, x, d, e: Z
st: State
Zodd m ->
eqm m (x * d) (f st) ->
eqm m (x * e) (g st) ->
eqm m (x * fst (update_de m d e (Trans.transN 62 st)))
  (f (fst (stepN 62 st))) /\
eqm m (x * snd (update_de m d e (Trans.transN 62 st)))
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Zodd m ->
eqm m (x * d) (f st) ->
eqm m (x * e) (g st) ->
eqm m (x * fst (update_de m d e (Trans.transN 62 st)))
  (f (fst (stepN 62 st))) /\
eqm m (x * snd (update_de m d e (Trans.transN 62 st)))
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
eqm m (x * fst (update_de m d e (Trans.transN 62 st)))
  (f (fst (stepN 62 st))) /\
eqm m (x * snd (update_de m d e (Trans.transN 62 st)))
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (f (fst (stepN 62 st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
(forall a : Z, (2 ^ 62 | pre_div62Modulo m a)) ->
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (f (fst (stepN 62 st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
(forall a : Z, pre_div62Modulo m a mod m = a mod m) ->
(forall a : Z, (2 ^ 62 | pre_div62Modulo m a)) ->
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (f (fst (stepN 62 st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
Trans.scale (2 ^ Z.of_nat 62)
  (Trans.fg (fst (stepN 62 st))) =
Trans.ap (Trans.transN 62 st) (Trans.fg st) ->
(forall a : Z, pre_div62Modulo m a mod m = a mod m) ->
(forall a : Z, (2 ^ 62 | pre_div62Modulo m a)) ->
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (f (fst (stepN 62 st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ 62)) 
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
Trans.scale (2 ^ Z.of_nat 62)
  (Trans.fg (fst (stepN 62 st))) =
Trans.ap (Trans.transN 62 st) (Trans.fg st) ->
(forall a : Z, pre_div62Modulo m a mod m = a mod m) ->
(forall a : Z, (2 ^ Z.of_nat 62 | pre_div62Modulo m a)) ->
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat 62))
  (f (fst (stepN 62 st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat 62,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN 62 st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat 62))
  (g (fst (stepN 62 st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
Trans.scale (2 ^ Z.of_nat n)
  (Trans.fg (fst (stepN n st))) =
Trans.ap (Trans.transN n st) (Trans.fg st) ->
(forall a : Z, pre_div62Modulo m a mod m = a mod m) ->
(forall a : Z, (2 ^ Z.of_nat n | pre_div62Modulo m a)) ->
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (f (fst (stepN n st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
2 ^ Z.of_nat n * g (fst (stepN n st)) =
Trans.q (Trans.transN n st) * f st +
Trans.r (Trans.transN n st) * g st ->
2 ^ Z.of_nat n * f (fst (stepN n st)) =
Trans.u (Trans.transN n st) * f st +
Trans.v (Trans.transN n st) * g st ->
(forall a : Z, pre_div62Modulo m a mod m = a mod m) ->
(forall a : Z, (2 ^ Z.of_nat n | pre_div62Modulo m a)) ->
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (f (fst (stepN n st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
Trans.q (Trans.transN n st) * f st +
Trans.r (Trans.transN n st) * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
Trans.u (Trans.transN n st) * f st +
Trans.v (Trans.transN n st) * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (f (fst (stepN n st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap (Trans.transN n st)
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
Trans.q
  {|
    Trans.u := u;
    Trans.v := v;
    Trans.q := q;
    Trans.r := r
  |} * f st +
Trans.r
  {|
    Trans.u := u;
    Trans.v := v;
    Trans.q := q;
    Trans.r := r
  |} * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
Trans.u
  {|
    Trans.u := u;
    Trans.v := v;
    Trans.q := q;
    Trans.r := r
  |} * f st +
Trans.v
  {|
    Trans.u := u;
    Trans.v := v;
    Trans.q := q;
    Trans.r := r
  |} * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
eqm m
  (x *
   fst
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap
              {|
                Trans.u := u;
                Trans.v := v;
                Trans.q := q;
                Trans.r := r
              |}
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap
              {|
                Trans.u := u;
                Trans.v := v;
                Trans.q := q;
                Trans.r := r
              |}
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (f (fst (stepN n st))) /\
eqm m
  (x *
   snd
     (pre_div62Modulo m
        (Trans.x
           (Trans.ap
              {|
                Trans.u := u;
                Trans.v := v;
                Trans.q := q;
                Trans.r := r
              |}
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n,
      pre_div62Modulo m
        (Trans.y
           (Trans.ap
              {|
                Trans.u := u;
                Trans.v := v;
                Trans.q := q;
                Trans.r := r
              |}
              {|
                Trans.x :=
                  d + (if d <? 0 then m else 0);
                Trans.y :=
                  e + (if e <? 0 then m else 0)
              |})) / 2 ^ Z.of_nat n))
  (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
eqm m
  (x *
   (pre_div62Modulo m
      (u * (d + (if d <? 0 then m else 0)) +
       v * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (f (fst (stepN n st))) /\
eqm m
  (x *
   (pre_div62Modulo m
      (q * (d + (if d <? 0 then m else 0)) +
       r * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
eqm m
  (x *
   (pre_div62Modulo m
      (u * (d + (if d <? 0 then m else 0)) +
       v * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (f (fst (stepN n st))) /\
eqm m
  (x *
   (pre_div62Modulo m
      (q * (d + (if d <? 0 then m else 0)) +
       r * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
(modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n) mod m =
1 mod m
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
eqm m
  (x *
   (pre_div62Modulo m
      (u * (d + (if d <? 0 then m else 0)) +
       v * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (f (fst (stepN n st))) /\
eqm m
  (x *
   (pre_div62Modulo m
      (q * (d + (if d <? 0 then m else 0)) +
       r * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
(modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n) mod m =
1 mod m

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Z.gcd (2 ^ Z.of_nat n) m mod m = 1 mod m

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Z.gcd (2 ^ Z.of_nat n) m = 1

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
rel_prime (2 ^ Z.of_nat n) m

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
rel_prime m (2 ^ Z.of_nat n)

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
rel_prime m 2

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
rel_prime 2 m

  
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
~ (2 | m)

  
m, x, d, e: Z
st: State
Hoddm: Z.Odd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
~ (2 | m)

  
x, d, e: Z
st: State
b: Z
Hg: eqm (2 * b + 1) (x * e) (g st)
Hf: eqm (2 * b + 1) (x * d) (f st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre2: forall a : Z,
(2 ^ Z.of_nat n
| pre_div62Modulo (2 * b + 1) a)
Hpre1: forall a : Z,
pre_div62Modulo (2 * b + 1) a mod (2 * b + 1) =
a mod (2 * b + 1)
Hn: 0 < 2 ^ Z.of_nat n
~ (2 | 2 * b + 1)

  
x, d, e: Z
st: State
b: Z
Hg: eqm (2 * b + 1) (x * e) (g st)
Hf: eqm (2 * b + 1) (x * d) (f st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre2: forall a : Z,
(2 ^ Z.of_nat n
| pre_div62Modulo (2 * b + 1) a)
Hpre1: forall a : Z,
pre_div62Modulo (2 * b + 1) a mod (2 * b + 1) =
a mod (2 * b + 1)
Hn: 0 < 2 ^ Z.of_nat n
Hdivide: (2 | 2 * b + 1)
False

  
x, d, e: Z
st: State
b: Z
Hg: eqm (2 * b + 1) (x * e) (g st)
Hf: eqm (2 * b + 1) (x * d) (f st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre2: forall a : Z,
(2 ^ Z.of_nat n
| pre_div62Modulo (2 * b + 1) a)
Hpre1: forall a : Z,
pre_div62Modulo (2 * b + 1) a mod (2 * b + 1) =
a mod (2 * b + 1)
Hn: 0 < 2 ^ Z.of_nat n
Hdivide: (2 | 1)
False

  
x, d, e: Z
st: State
b: Z
Hg: eqm (2 * b + 1) (x * e) (g st)
Hf: eqm (2 * b + 1) (x * d) (f st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre2: forall a : Z,
(2 ^ Z.of_nat n
| pre_div62Modulo (2 * b + 1) a)
Hpre1: forall a : Z,
pre_div62Modulo (2 * b + 1) a mod (2 * b + 1) =
a mod (2 * b + 1)
Hn: 0 < 2 ^ Z.of_nat n
Hdivide: Z.abs 2 = 1
False

  discriminate.

m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
eqm m
  (x *
   (pre_div62Modulo m
      (u * (d + (if d <? 0 then m else 0)) +
       v * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (f (fst (stepN n st))) /\
eqm m
  (x *
   (pre_div62Modulo m
      (q * (d + (if d <? 0 then m else 0)) +
       r * (e + (if e <? 0 then m else 0))) /
    2 ^ Z.of_nat n)) (g (fst (stepN n st)))


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
(x *
 (pre_div62Modulo m
    (u * (d + (if d <? 0 then m else 0)) +
     v * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
f (fst (stepN n st)) mod m /\
(x *
 (pre_div62Modulo m
    (q * (d + (if d <? 0 then m else 0)) +
     r * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
(x mod m *
 (pre_div62Modulo m
    (u * (d + (if d <? 0 then m else 0)) +
     v * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
f (fst (stepN n st)) mod m /\
(x mod m *
 (pre_div62Modulo m
    (q * (d + (if d <? 0 then m else 0)) +
     r * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
((x * 1) mod m *
 (pre_div62Modulo m
    (u * (d + (if d <? 0 then m else 0)) +
     v * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
f (fst (stepN n st)) mod m /\
((x * 1) mod m *
 (pre_div62Modulo m
    (q * (d + (if d <? 0 then m else 0)) +
     r * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
(x * (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n) *
 (pre_div62Modulo m
    (u * (d + (if d <? 0 then m else 0)) +
     v * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
f (fst (stepN n st)) mod m /\
(x * (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n) *
 (pre_div62Modulo m
    (q * (d + (if d <? 0 then m else 0)) +
     r * (e + (if e <? 0 then m else 0))) /
  2 ^ Z.of_nat n)) mod m = 
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
(x *
 (modInv (2 ^ Z.of_nat n) m *
  pre_div62Modulo m
    (u * (d + (if d <? 0 then m else 0)) +
     v * (e + (if e <? 0 then m else 0))))) mod m =
f (fst (stepN n st)) mod m /\
(x *
 (modInv (2 ^ Z.of_nat n) m *
  pre_div62Modulo m
    (q * (d + (if d <? 0 then m else 0)) +
     r * (e + (if e <? 0 then m else 0))))) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
(x * modInv (2 ^ Z.of_nat n) m *
 ((u * (d + (if d <? 0 then m else 0)) +
   v * (e + (if e <? 0 then m else 0))) mod m)) mod m =
f (fst (stepN n st)) mod m /\
(x * modInv (2 ^ Z.of_nat n) m *
 ((q * (d + (if d <? 0 then m else 0)) +
   r * (e + (if e <? 0 then m else 0))) mod m)) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
(x * modInv (2 ^ Z.of_nat n) m *
 ((u * (d + (if d <? 0 then m else 0)) +
   v * (e + (if e <? 0 then m else 0))) mod m)) mod m =
f (fst (stepN n st)) mod m /\
(x * modInv (2 ^ Z.of_nat n) m *
 ((q * (d + (if d <? 0 then m else 0)) +
   r * (e + (if e <? 0 then m else 0))) mod m)) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)

 
m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
a, b: Z
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)

 apply Zplus_eqm;apply Zmult_eqm;try apply eqm_refl;destruct (Z.ltb _ _);unfold eqm;
  rewrite <-Zplus_mod_idemp_r, ?Z_mod_same_full, ?Zmod_0_l;f_equal;try ring.

m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
(x * modInv (2 ^ Z.of_nat n) m *
 ((u * (d + (if d <? 0 then m else 0)) +
   v * (e + (if e <? 0 then m else 0))) mod m)) mod m =
f (fst (stepN n st)) mod m /\
(x * modInv (2 ^ Z.of_nat n) m *
 ((q * (d + (if d <? 0 then m else 0)) +
   r * (e + (if e <? 0 then m else 0))) mod m)) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
(x * modInv (2 ^ Z.of_nat n) m * (u * d + v * e))
mod m = f (fst (stepN n st)) mod m /\
(x * modInv (2 ^ Z.of_nat n) m * (q * d + r * e))
mod m = g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
((u * d * x + v * e * x) * modInv (2 ^ Z.of_nat n) m)
mod m = f (fst (stepN n st)) mod m /\
((q * d * x + r * e * x) * modInv (2 ^ Z.of_nat n) m)
mod m = g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
((u * (x * d) + v * (x * e)) *
 modInv (2 ^ Z.of_nat n) m) mod m =
f (fst (stepN n st)) mod m /\
((q * (x * d) + r * (x * e)) *
 modInv (2 ^ Z.of_nat n) m) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
(((u * ((x * d) mod m)) mod m +
  (v * ((x * e) mod m)) mod m) mod m *
 modInv (2 ^ Z.of_nat n) m) mod m =
f (fst (stepN n st)) mod m /\
(((q * ((x * d) mod m)) mod m +
  (r * ((x * e) mod m)) mod m) mod m *
 modInv (2 ^ Z.of_nat n) m) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
((u * f st + v * g st) * modInv (2 ^ Z.of_nat n) m)
mod m = f (fst (stepN n st)) mod m /\
((q * f st + r * g st) * modInv (2 ^ Z.of_nat n) m)
mod m = g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
(modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n *
 f (fst (stepN n st))) mod m =
f (fst (stepN n st)) mod m /\
(modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n *
 g (fst (stepN n st))) mod m =
g (fst (stepN n st)) mod m


m, x, d, e: Z
st: State
Hoddm: Zodd m
Hf: eqm m (x * d) (f st)
Hg: eqm m (x * e) (g st)
n: nat
u, v, q, r: Z
Hgqr: 2 ^ Z.of_nat n * g (fst (stepN n st)) =
q * f st + r * g st
Hfuv: 2 ^ Z.of_nat n * f (fst (stepN n st)) =
u * f st + v * g st
Hpre1: forall a : Z,
pre_div62Modulo m a mod m = a mod m
Hpre2: forall a : Z,
(2 ^ Z.of_nat n | pre_div62Modulo m a)
Hn: 0 < 2 ^ Z.of_nat n
Hinv: (modInv (2 ^ Z.of_nat n) m * 2 ^ Z.of_nat n)
mod m = 1 mod m
Hab: forall a b : Z,
eqm m
  (a * (d + (if d <? 0 then m else 0)) +
   b * (e + (if e <? 0 then m else 0)))
  (a * d + b * e)
f (fst (stepN n st)) mod m =
f (fst (stepN n st)) mod m /\
g (fst (stepN n st)) mod m =
g (fst (stepN n st)) mod m

auto.
Qed.
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Require Import VST.floyd.proofauto.
Require Import VST.msl.iter_sepcon.
Require Import jets_secp256k1.


compspecs
 make_compspecs prog. Defined.

Definition Int128_modulus : Z := 2^128.
Definition Int128_max_unsigned : Z := Int128_modulus - 1.
Definition Int128_max_signed : Z := 2^127 - 1.
Definition Int128_min_signed : Z := -2^127.
Definition t_secp256k1_uint128 := Tstruct _secp256k1_uint128 noattr.  
(* (secp256k1_uint128_at sh x p) says that the structure pointed to by p
 * is equivalent to x modulo 2^128.
 *)
Definition secp256k1_uint128_at sh x :=
   data_at sh
     t_secp256k1_uint128 (Vlong (Int64.repr x), Vlong (Int64.repr (Z.shiftr x 64))).

(*/
Definition secp256k1_u128_load_spec : ident * funspec :=
DECLARE _secp256k1_u128_load
  WITH r : val, sh : share, hi : Z, lo : Z
  PRE [ tptr t_secp256k1_uint128, tulong, tulong ]
    PROP(writable_share sh;
         0 <= lo < Int64.modulus)
    PARAMS(r; Vlong (Int64.repr hi); Vlong (Int64.repr lo))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (Z.shiftl hi 64 + lo) r).
*)

Definition secp256k1_u128_mul_spec : ident * funspec :=
DECLARE _secp256k1_u128_mul
  WITH r : val, sh : share, a : Z, b : Z
  PRE [ tptr t_secp256k1_uint128, tulong, tulong ]
    PROP(writable_share sh;
         0 <= a < Int64.modulus;
         0 <= b < Int64.modulus)
    PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (a * b) r).

Definition secp256k1_u128_accum_mul_spec : ident * funspec :=
DECLARE _secp256k1_u128_accum_mul
  WITH r : val, sh : share, r0 : Z, a : Z, b : Z
  PRE [ tptr t_secp256k1_uint128, tulong, tulong ]
    PROP(writable_share sh;
         0 <= a < Int64.modulus;
         0 <= b < Int64.modulus)
    PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (r0 + a * b) r).

Definition secp256k1_u128_accum_u64_spec : ident * funspec :=
DECLARE _secp256k1_u128_accum_u64
  WITH r : val, sh : share, r0 : Z, a : Z
  PRE [ tptr t_secp256k1_uint128, tulong ]
    PROP(writable_share sh;
         0 <= a < Int64.modulus)
    PARAMS(r; Vlong (Int64.repr a))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (r0 + a) r).

Definition secp256k1_u128_rshift_spec : ident * funspec :=
DECLARE _secp256k1_u128_rshift
  WITH r : val, sh : share, r0 : Z, n : Z
  PRE [ tptr t_secp256k1_uint128, tuint ]
    PROP(writable_share sh;
         0 <= r0 < Int128_modulus;
         0 <= n < 128)
    PARAMS(r; Vint (Int.repr n))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (Z.shiftr r0 n) r).

Definition secp256k1_u128_to_u64_spec : ident * funspec :=
DECLARE _secp256k1_u128_to_u64
  WITH r : val, sh : share, r0 : Z
  PRE [ tptr t_secp256k1_uint128 ]
    PROP(readable_share sh)
    PARAMS(r)
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tulong ]
  PROP()
  RETURN(Vlong (Int64.repr r0))
  SEP(secp256k1_uint128_at sh r0 r).

Definition secp256k1_u128_hi_u64_spec : ident * funspec :=
DECLARE _secp256k1_u128_hi_u64
  WITH r : val, sh : share, r0 : Z
  PRE [ tptr t_secp256k1_uint128 ]
    PROP(readable_share sh)
    PARAMS(r)
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tulong ]
  PROP()
  RETURN(Vlong (Int64.repr (Z.shiftr r0 64)))
  SEP(secp256k1_uint128_at sh r0 r).

Definition secp256k1_u128_from_u64_spec : ident * funspec :=
DECLARE _secp256k1_u128_from_u64
  WITH r : val, sh : share, a : Z
  PRE [ tptr t_secp256k1_uint128, tulong ]
    PROP(writable_share sh;
         0 <= a < Int64.modulus)
    PARAMS(r; Vlong (Int64.repr a))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh a r).

Definition secp256k1_u128_check_bits_spec : ident * funspec :=
DECLARE _secp256k1_u128_check_bits
  WITH r : val, sh : share, r0 : Z, n : Z
  PRE [ tptr t_secp256k1_uint128, tuint ]
    PROP(readable_share sh;
         0 <= r0 < 2^128;
         0 <= n < 128)
    PARAMS(r; Vint (Int.repr n))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tint ]
  PROP()
  RETURN(Vint (Int.repr (if r0 <? 2^n then 1 else 0)))
  SEP(secp256k1_uint128_at sh r0 r).

(*
Definition secp256k1_i128_load_spec : ident * funspec :=
DECLARE _secp256k1_i128_load
  WITH r : val, sh : share, hi : Z, lo : Z
  PRE [ tptr t_secp256k1_uint128, tlong, tulong ]
    PROP(writable_share sh;
         Int64.min_signed <= hi <= Int64.max_signed;
         0 <= lo < Int64.modulus)
    PARAMS(r; Vlong (Int64.repr hi); Vlong (Int64.repr lo))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (Z.shiftl hi 64 + lo) r).
*)

Definition secp256k1_i128_mul_spec : ident * funspec :=
DECLARE _secp256k1_i128_mul
  WITH r : val, sh : share, a : Z, b : Z
  PRE [ tptr t_secp256k1_uint128, tlong, tlong ]
    PROP(writable_share sh;
         Int64.min_signed <= a <= Int64.max_signed;
         Int64.min_signed <= b <= Int64.max_signed)
    PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (a * b) r).

Definition secp256k1_i128_accum_mul_spec : ident * funspec :=
DECLARE _secp256k1_i128_accum_mul
  WITH r : val, sh : share, r0 : Z, a : Z, b : Z
  PRE [ tptr t_secp256k1_uint128, tlong, tlong ]
    PROP(writable_share sh;
         Int64.min_signed <= a <= Int64.max_signed;
         Int64.min_signed <= b <= Int64.max_signed;
         Int128_min_signed <= r0 <= Int128_max_signed;
         Int128_min_signed <= r0 + a * b <= Int128_max_signed)
    PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (r0 + a * b) r).

Definition secp256k1_i128_dissip_mul_spec : ident * funspec :=
DECLARE _secp256k1_i128_dissip_mul
  WITH r : val, sh : share, r0 : Z, a : Z, b : Z
  PRE [ tptr t_secp256k1_uint128, tlong, tlong ]
    PROP(writable_share sh;
         Int64.min_signed <= a <= Int64.max_signed;
         Int64.min_signed <= b <= Int64.max_signed;
         Int128_min_signed <= r0 <= Int128_max_signed;
         Int128_min_signed <= r0 - a * b <= Int128_max_signed)
   PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (r0 - a * b) r).

Definition secp256k1_i128_det_spec : ident * funspec :=
DECLARE _secp256k1_i128_det
  WITH r : val, sh : share, a : Z, b : Z, c : Z, d : Z
  PRE [ tptr t_secp256k1_uint128, tlong, tlong, tlong, tlong ]
    PROP(writable_share sh;
         Int64.min_signed <= a <= Int64.max_signed;
         Int64.min_signed <= b <= Int64.max_signed;
         Int64.min_signed <= c <= Int64.max_signed;
         Int64.min_signed <= d <= Int64.max_signed)
    PARAMS(r; Vlong (Int64.repr a); Vlong (Int64.repr b);
              Vlong (Int64.repr c); Vlong (Int64.repr d))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (a * d - b * c) r).

Definition secp256k1_i128_rshift_spec : ident * funspec :=
DECLARE _secp256k1_i128_rshift
  WITH r : val, sh : share, r0 : Z, n : Z
  PRE [ tptr t_secp256k1_uint128, tuint ]
    PROP(writable_share sh;
         Int128_min_signed <= r0 <= Int128_max_signed;
         0 <= n < 128)
    PARAMS(r; Vint (Int.repr n))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh (Z.shiftr r0 n) r).

Definition secp256k1_i128_to_u64_spec : ident * funspec :=
DECLARE _secp256k1_i128_to_u64
  WITH r : val, sh : share, r0 : Z
  PRE [ tptr t_secp256k1_uint128 ]
    PROP(readable_share sh)
    PARAMS(r)
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tulong ]
  PROP()
  RETURN(Vlong (Int64.repr r0))
  SEP(secp256k1_uint128_at sh r0 r).

Definition secp256k1_i128_to_i64_spec : ident * funspec :=
DECLARE _secp256k1_i128_to_i64
  WITH r : val, sh : share, r0 : Z
  PRE [ tptr t_secp256k1_uint128 ]
    PROP(readable_share sh;
         Int64.min_signed <= r0 <= Int64.max_signed)
    PARAMS(r)
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tlong ]
  PROP()
  RETURN(Vlong (Int64.repr r0))
  SEP(secp256k1_uint128_at sh r0 r).

Definition secp256k1_i128_from_i64_spec : ident * funspec :=
DECLARE _secp256k1_i128_from_i64
  WITH r : val, sh : share, a : Z
  PRE [ tptr t_secp256k1_uint128, tlong ]
    PROP(writable_share sh;
         Int64.min_signed <= a <= Int64.max_signed)
    PARAMS(r; Vlong (Int64.repr a))
  SEP(data_at_ sh t_secp256k1_uint128 r)
POST [ tvoid ]
  PROP()
  RETURN()
  SEP(secp256k1_uint128_at sh a r).

Definition secp256k1_i128_eq_var_spec : ident * funspec :=
DECLARE _secp256k1_i128_eq_var
  WITH r : val, shr : share, r0 : Z,
       s : val, shs : share, s0 : Z
  PRE [ tptr t_secp256k1_uint128, tptr t_secp256k1_uint128 ]
    PROP(readable_share shr;
         readable_share shs)
    PARAMS(r; s)
  SEP(secp256k1_uint128_at shr r0 r;
      secp256k1_uint128_at shs s0 s)
POST [ tint ]
  PROP()
  RETURN(Vint (Int.repr (if r0 mod 2^128 =? s0 mod 2^128 then 1 else 0)))
  SEP(secp256k1_uint128_at shr r0 r
     ;secp256k1_uint128_at shs s0 s).

Definition secp256k1_i128_eq_var_spec_alias : ident * funspec :=
DECLARE _secp256k1_i128_eq_var
  WITH r : val, shr : share, r0 : Z
  PRE [ tptr t_secp256k1_uint128, tptr t_secp256k1_uint128 ]
    PROP(readable_share shr)
    PARAMS(r; r)
  SEP(secp256k1_uint128_at shr r0 r)
POST [ tint ]
  PROP()
  RETURN(Vint (Int.repr 1))
  SEP(secp256k1_uint128_at shr r0 r).

Definition secp256k1_i128_check_pow2_spec : ident * funspec :=
DECLARE _secp256k1_i128_check_pow2
  WITH r : val, sh : share, r0 : Z, n : Z, sign : Z
  PRE [ tptr t_secp256k1_uint128, tuint, tint ]
    PROP(readable_share sh;
         Int128_min_signed <= r0 <= Int128_max_signed;
         0 <= n < 127;
         sign = -1 \/ sign = 1)
    PARAMS(r; Vint (Int.repr n); Vint (Int.repr sign))
  SEP(secp256k1_uint128_at sh r0 r)
POST [ tint ]
  PROP()
  RETURN(Vint (Int.repr (Z.b2z (r0 =? sign*2^n))))
  SEP(secp256k1_uint128_at sh r0 r).
================================================ FILE: alectryon/spec_modinv64.v.html ================================================ spec_modinv64.v
Built with Alectryon, running Coq+SerAPI v8.17.0+0.17.3. Bubbles () indicate interactive fragments: hover for details, tap to reveal contents. Use Ctrl+↑ Ctrl+↓ to navigate, Ctrl+🖱️ to focus. On Mac, use ⌘ instead of Ctrl.
Require Import VST.floyd.proofauto.
Require Import jets_secp256k1.
Require Import Coq.Logic.Eqdep_dec.

Require Import progressC.
Require Import extraMath.
Require Import modinv.
Require divstep.


compspecs
 make_compspecs prog. Defined.

Opaque Z.shiftr Z.pow.

Definition t_secp256k1_modinv64_signed62 := Tstruct _secp256k1_modinv64_signed62 noattr.
Definition t_secp256k1_modinv64_modinfo := Tstruct _secp256k1_modinv64_modinfo noattr.

Module Signed62.

Definition max_signed n : Z := 2^(n*62)-1.
Definition min_signed n : Z := -2^(n*62).

Fixpoint signed (l : list int64) : Z :=
match l with
| [] => 0
| (a :: l') => Int64.signed a + 2^62 * signed l'
end.


l1, l2: list int64
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                          * signed l2


l1, l2: list int64
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                          * signed l2


l1: list int64
forall l2 : list int64,
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                          * signed l2


l2: list int64
signed ([] ++ l2) = signed []
                      + 2 ^ (Zlength [] * 62)
                          * signed l2
a: int64
l1: list int64
IHl1: forall l2 : list int64,
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                        * signed l2
l2: list int64
signed ((a :: l1) ++ l2) = signed (a :: l1)
                             + 2
                                 ^ (Zlength (a :: l1)
                                      * 62)
                                 * signed l2


l2: list int64
signed ([] ++ l2) = signed []
                      + 2 ^ (Zlength [] * 62)
                          * signed l2
 
l2: list int64
signed ([] ++ l2) = signed [] + 1 * signed l2
 
l2: list int64
signed l2 = 0 + 1 * signed l2
 ring.

a: int64
l1: list int64
IHl1: forall l2 : list int64,
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                        * signed l2
l2: list int64
signed ((a :: l1) ++ l2) = signed (a :: l1)
                             + 2
                                 ^ (Zlength (a :: l1)
                                      * 62)
                                 * signed l2
 
a: int64
l1: list int64
IHl1: forall l2 : list int64,
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                        * signed l2
l2: list int64
signed ((a :: l1) ++ l2) = signed (a :: l1)
                             + 2
                                 ^ (Z.succ
                                      (Zlength l1)
                                      * 62)
                                 * signed l2

  
a: int64
l1: list int64
IHl1: forall l2 : list int64,
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                        * signed l2
l2: list int64
Int64.signed a + 2 ^ 62 * signed (l1 ++ l2) = Int64.signed
                                                a
                                                + 
                                                2 ^ 62
                                                 * 
                                                 signed
                                                 l1
                                                + 
                                                2
                                                 ^ 
                                                 (Z.succ
                                                 (Zlength
                                                 l1)
                                                 * 62)
                                                 * 
                                                 signed
                                                 l2

  
a: int64
l1: list int64
IHl1: forall l2 : list int64,
signed (l1 ++ l2) = signed l1
                      + 2 ^ (Zlength l1 * 62)
                        * signed l2
l2: list int64
Hlen: 0 <= Zlength l1
Int64.signed a + 2 ^ 62 * signed (l1 ++ l2) = Int64.signed
                                                a
                                                + 
                                                2 ^ 62
                                                 * 
                                                 signed
                                                 l1
                                                + 
                                                2
                                                 ^ 
                                                 (Z.succ
                                                 (Zlength
                                                 l1)
                                                 * 62)
                                                 * 
                                                 signed
                                                 l2

  rewrite IHl1, Z.mul_succ_l, Z.pow_add_r; lia.
Qed.

Fixpoint reprn (n : nat) (a : Z) : list int64 :=
match n with
| 0%nat => []
| 1%nat => [Int64.repr a]
| (S n0) => Int64.repr (a mod (2 ^ 62)) :: (reprn n0 (Z.shiftr a 62))
end.


n: nat
forall a : Z, Datatypes.length (reprn n a) = n


n: nat
forall a : Z, Datatypes.length (reprn n a) = n


n: nat
IHn: forall a : Z, Datatypes.length (reprn n a) = n
forall a : Z, Datatypes.length (reprn (S n) a) = S n


n: nat
IHn: forall a : Z, Datatypes.length (reprn (S n) a) = S n
forall a : Z,
Datatypes.length (reprn (S (S n)) a) = S (S n)

intro a; simpl in *; rewrite IHn; reflexivity.
Qed.


n: nat
forall a : Z, Zlength (reprn n a) = Z.of_nat n


n: nat
forall a : Z, Zlength (reprn n a) = Z.of_nat n


n: nat
a: Z
Zlength (reprn n a) = Z.of_nat n

rewrite Zlength_correct, Signed62.reprn_length; reflexivity.
Qed.


n: nat
a: Z
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
                [Int64.repr
                   (Z.shiftr a (62 * Z.of_nat n))]


n: nat
a: Z
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
                [Int64.repr
                   (Z.shiftr a (62 * Z.of_nat n))]


n: nat
IHn: forall a : Z,
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n))]
a: Z
reprn (S (S n)) a = reprn (S n)
                      (a mod 2 ^ (62 * Z.of_nat (S n))) ++
                    [Int64.repr
                       (Z.shiftr a
                          (62 * Z.of_nat (S n)))]


n: nat
IHn: forall a : Z,
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n))]
a: Z
(fun n : nat =>
 reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
                 [Int64.repr
                    (Z.shiftr a (62 * Z.of_nat n))])
  (S n)


n: nat
IHn: forall a : Z,
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n))]
a: Z
(fun n : nat =>
 match n with
 | 0%nat => [Int64.repr a]
 | S _ =>
     Int64.repr (a mod 2 ^ 62)
     :: reprn n (Z.shiftr a 62)
 end = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
       [Int64.repr (Z.shiftr a (62 * Z.of_nat n))])
  (S n)


n: nat
IHn: forall a : Z,
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n))]
a: Z
match S n with
| 0%nat => [Int64.repr a]
| S _ =>
    Int64.repr (a mod 2 ^ 62)
    :: reprn (S n) (Z.shiftr a 62)
end = reprn (S n) (a mod 2 ^ (62 * Z.of_nat (S n))) ++
      [Int64.repr (Z.shiftr a (62 * Z.of_nat (S n)))]


n: nat
IHn: forall a : Z,
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n))]
a: Z
Int64.repr (a mod 2 ^ 62)
:: reprn n (Z.shiftr a 62 mod 2 ^ (62 * Z.of_nat n)) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat n + 62))] = 
reprn (S n) (a mod 2 ^ (62 * Z.of_nat n + 62)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n + 62))]


n: nat
IHn: forall a : Z,
reprn (S n) a = reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n))]
a: Z
Int64.repr (a mod 2 ^ 62)
:: reprn n (Z.shiftr a 62 mod 2 ^ (62 * Z.of_nat n)) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat n + 62))] = 
match n with
| 0%nat =>
    [Int64.repr (a mod 2 ^ (62 * Z.of_nat n + 62))]
| S _ =>
    Int64.repr
      ((a mod 2 ^ (62 * Z.of_nat n + 62)) mod 2 ^ 62)
    :: reprn n
         (Z.shiftr (a mod 2 ^ (62 * Z.of_nat n + 62))
            62)
end ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat n + 62))]


n: nat
IHn: forall a : Z,
reprn (S (S n)) a = reprn (S n) (a mod 2 ^ (62 * Z.of_nat (S n))) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n)))]
a: Z
Int64.repr (a mod 2 ^ 62)
:: reprn (S n)
     (Z.shiftr a 62 mod 2 ^ (62 * Z.of_nat (S n))) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))] = 
(Int64.repr
   ((a mod 2 ^ (62 * Z.of_nat (S n) + 62)) mod 2 ^ 62)
 :: reprn (S n)
      (Z.shiftr (a mod 2 ^ (62 * Z.of_nat (S n) + 62))
         62)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))]


n: nat
IHn: forall a : Z,
reprn (S (S n)) a = reprn (S n) (a mod 2 ^ (62 * Z.of_nat (S n))) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n)))]
a: Z
Int64.repr (a mod 2 ^ 62)
:: reprn (S n)
     (Z.shiftr a 62 mod 2 ^ (62 * Z.of_nat (S n))) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))] = 
(Int64.repr
   ((a mod (2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62))
    mod 2 ^ 62)
 :: reprn (S n)
      (Z.shiftr
         (a mod (2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62))
         62)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))]


n: nat
IHn: forall a : Z,
reprn (S (S n)) a = reprn (S n) (a mod 2 ^ (62 * Z.of_nat (S n))) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n)))]
a: Z
Int64.repr (a mod 2 ^ 62)
:: reprn (S n)
     ((a / 2 ^ 62) mod 2 ^ (62 * Z.of_nat (S n))) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))] = 
(Int64.repr (a mod 2 ^ 62)
 :: reprn (S n)
      (a mod (2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62)
         / 2 ^ 62)) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))]


n: nat
IHn: forall a : Z,
reprn (S (S n)) a = reprn (S n) (a mod 2 ^ (62 * Z.of_nat (S n))) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n)))]
a: Z
Int64.repr (a mod 2 ^ 62)
:: reprn (S n)
     ((a / 2 ^ 62) mod 2 ^ (62 * Z.of_nat (S n))) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))] = 
(Int64.repr (a mod 2 ^ 62)
 :: reprn (S n)
      ((a / 2 ^ 62) mod 2 ^ (62 * Z.of_nat (S n)))) ++
[Int64.repr (Z.shiftr a (62 * Z.of_nat (S n) + 62))]

reflexivity.
Qed.


forall (a : Z) (n : nat) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr
                       (Z.shiftr a
                          (62 * (Z.of_nat n - 1)))


forall (a : Z) (n : nat) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr
                       (Z.shiftr a
                          (62 * (Z.of_nat n - 1)))


a: Z
n: nat
forall d : int64,
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr
                       (Z.shiftr a
                          (62 * (Z.of_nat n - 1)))


n: nat
forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr
                       (Z.shiftr a
                          (62 * (Z.of_nat n - 1)))


n: nat
IHn: forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1)))
forall (a : Z) (d : int64),
(1 <= S n)%nat ->
last (reprn (S n) a) d = Int64.repr
                           (Z.shiftr a
                              (62
                                 * (Z.of_nat (S n) - 1)))


n: nat
IHn: forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1)))
a: Z
d: int64
Hn: (1 <= S n)%nat
last (reprn (S n) a) d = Int64.repr
                           (Z.shiftr a
                              (62
                                 * (Z.of_nat (S n) - 1)))


n: nat
IHn: forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1)))
a: Z
d: int64
Hn: (1 <= S n)%nat
last (reprn (S n) a) d = Int64.repr
                           (Z.shiftr a
                              (62
                                 * (Z.succ
                                      (Z.of_nat n)
                                      - 1)))


n: nat
IHn: forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1)))
a: Z
d: int64
Hn: (1 <= S n)%nat
last (reprn (S n) a) d = Int64.repr
                           (Z.shiftr a
                              (62
                                 * (Z.of_nat n + 1 - 1)))


n: nat
IHn: forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1)))
a: Z
d: int64
Hn: (1 <= S n)%nat
last (reprn (S n) a) d = Int64.repr
                           (Z.shiftr a
                              (62 * Z.of_nat n))


n: nat
IHn: forall (a : Z) (d : int64),
(1 <= n)%nat ->
last (reprn n a) d = Int64.repr (Z.shiftr a (62 * (Z.of_nat n - 1)))
a: Z
d: int64
Hn: (1 <= S n)%nat
last
  (reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat n))]) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat n))

apply last_last.
Qed.


forall (a : Z) (n i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr
                        (Z.shiftr a (62 * Z.of_nat i)
                         mod 2 ^ 62)


forall (a : Z) (n i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr
                        (Z.shiftr a (62 * Z.of_nat i)
                         mod 2 ^ 62)


a: Z
n: nat
forall (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr
                        (Z.shiftr a (62 * Z.of_nat i)
                         mod 2 ^ 62)


n: nat
forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr
                        (Z.shiftr a (62 * Z.of_nat i)
                         mod 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
forall (a : Z) (i : nat) (d : int64),
(0 <= i < S n - 1)%nat ->
nth i (reprn (S n) a) d = Int64.repr
                            (Z.shiftr a
                               (62 * Z.of_nat i)
                             mod 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
nth i (reprn (S n) a) d = Int64.repr
                            (Z.shiftr a
                               (62 * Z.of_nat i)
                             mod 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
nth i
  (reprn n (a mod 2 ^ (62 * Z.of_nat n)) ++
   [Int64.repr (Z.shiftr a (62 * Z.of_nat n))]) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
nth i (reprn n (a mod 2 ^ (62 * Z.of_nat n))) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (i < n - 1)%nat
nth i (reprn n (a mod 2 ^ (62 * Z.of_nat n))) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
nth i (reprn n (a mod 2 ^ (62 * Z.of_nat n))) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (i < n - 1)%nat
nth i (reprn n (a mod 2 ^ (62 * Z.of_nat n))) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
 
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (i < n - 1)%nat
Int64.repr
  (((a / 2 ^ (62 * Z.of_nat i))
    mod 2 ^ (62 * Z.of_nat (n - i))) mod 2 ^ 62) = 
Int64.repr ((a / 2 ^ (62 * Z.of_nat i)) mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (i < n - 1)%nat
(2 ^ 62 | (2 ^ 62) ^ Z.of_nat (n - i))

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (i < n - 1)%nat
0 < Z.of_nat (n - i)

  lia.

n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
nth i (reprn n (a mod 2 ^ (62 * Z.of_nat n))) d = 
Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
 
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
nth i l d = Int64.repr
              (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
nth (n - 1) l d = Int64.repr
                    (Z.shiftr a
                       (62 * Z.of_nat (n - 1))
                     mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
nth (Datatypes.length l - 1) l d = Int64.repr
                                     (Z.shiftr a
                                        (62
                                           * Z.of_nat
                                               (n - 1))
                                      mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
nth
  (Datatypes.length
     (reprn n (a mod 2 ^ (62 * Z.of_nat n)))
     - 1) (reprn n (a mod 2 ^ (62 * Z.of_nat n))) d = 
Int64.repr
  (Z.shiftr a (62 * Z.of_nat (n - 1)) mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
Int64.repr
  (Z.shiftr (a mod 2 ^ (62 * Z.of_nat n))
     (62 * (Z.of_nat n - 1))) = Int64.repr
                                  (Z.shiftr a
                                     (62
                                        * Z.of_nat
                                            (n - 1))
                                   mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
Int64.repr
  (Z.shiftr (a mod 2 ^ (62 * (Z.of_nat n - 1) + 62))
     (62 * (Z.of_nat n - 1))) = Int64.repr
                                  (Z.shiftr a
                                     (62
                                        * Z.of_nat
                                            (n - 1))
                                   mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
Int64.repr
  ((a / 2 ^ (62 * (Z.of_nat n - 1))) mod 2 ^ 62) = 
Int64.repr
  ((a / 2 ^ (62 * Z.of_nat (n - 1))) mod 2 ^ 62)

  
n: nat
IHn: forall (a : Z) (i : nat) (d : int64),
(0 <= i < n - 1)%nat ->
nth i (reprn n a) d = Int64.repr (Z.shiftr a (62 * Z.of_nat i) mod 2 ^ 62)
a: Z
i: nat
d: int64
Hi: (0 <= i < S n - 1)%nat
H: (n - 1 <= i)%nat
l:= reprn n (a mod 2 ^ (62 * Z.of_nat n)): list int64
Z.of_nat n - 1 = Z.of_nat (n - 1)

  lia.
Qed.


forall (a : Z) (n : nat) (i : Z),
0 <= i < Z.of_nat n - 1 ->
Znth i (reprn n a) = Int64.repr
                       (Z.shiftr a (62 * i) mod 2 ^ 62)


forall (a : Z) (n : nat) (i : Z),
0 <= i < Z.of_nat n - 1 ->
Znth i (reprn n a) = Int64.repr
                       (Z.shiftr a (62 * i) mod 2 ^ 62)


a: Z
n: nat
i: Z
Hi: 0 <= i < Z.of_nat n - 1
Znth i (reprn n a) = Int64.repr
                       (Z.shiftr a (62 * i) mod 2 ^ 62)


a: Z
n: nat
i: Z
Hi: 0 <= i < Z.of_nat n - 1
nth (Z.to_nat i) (reprn n a) Inhabitant_int64 = Int64.repr
                                                 (Z.shiftr
                                                 a
                                                 (62
                                                 * i)
                                                 mod 
                                                 2
                                                 ^ 62)


a: Z
n: nat
i: Z
Hi: 0 <= i < Z.of_nat n - 1
Int64.repr (Z.shiftr a (62 * i) mod 2 ^ 62) = Int64.repr
                                                (Z.shiftr
                                                 a
                                                 (62
                                                 * i)
                                                 mod 
                                                 2
                                                 ^ 62)

reflexivity.
Qed.


a: Z
i, n: nat
(i < n)%nat ->
signed (firstn i (reprn n a)) = a
                                mod 2
                                      ^ (62
                                           * Z.of_nat
                                               i)


a: Z
i, n: nat
(i < n)%nat ->
signed (firstn i (reprn n a)) = a
                                mod 2
                                      ^ (62
                                           * Z.of_nat
                                               i)


n: nat
forall (a : Z) (i : nat),
(i < n)%nat ->
signed (firstn i (reprn n a)) = a
                                mod 2
                                      ^ (62
                                           * Z.of_nat
                                               i)


n: nat
IHn: forall (a : Z) (i : nat),
(i < n)%nat -> signed (firstn i (reprn n a)) = a mod 2 ^ (62 * Z.of_nat i)
forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a
                                    mod 2
                                          ^ (62
                                               * Z.of_nat
                                                 i)


n: nat
IHn: forall (a : Z) (i : nat),
(i < n)%nat -> signed (firstn i (reprn n a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
(S i < S n)%nat ->
signed (firstn (S i) (reprn (S n) a)) = a
                                        mod 2
                                              ^ (62
                                                 * Z.of_nat
                                                 (S i))


n: nat
IHn: forall (a : Z) (i : nat),
(i < n)%nat -> signed (firstn i (reprn n a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (S i < S n)%nat
signed (firstn (S i) (reprn (S n) a)) = a
                                        mod 2
                                              ^ (62
                                                 * Z.of_nat
                                                 (S i))


n: nat
IHn: forall (a : Z) (i : nat),
(i < n)%nat -> signed (firstn i (reprn n a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < n)%nat
signed (firstn (S i) (reprn (S n) a)) = a
                                        mod 2
                                              ^ (62
                                                 * Z.of_nat
                                                 (S i))


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
signed (firstn (S i) (reprn (S (S n)) a)) = a
                                            mod 2
                                                 ^ 
                                                 (62
                                                 * Z.of_nat
                                                 (S i))


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
signed (firstn (S i) (reprn (S (S n)) a)) = a
                                            mod (2
                                                 ^ (62
                                                 * Z.of_nat
                                                 i)
                                                 * 2
                                                 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62
      * signed
          (firstn i
             match n with
             | 0%nat => [Int64.repr (Z.shiftr a 62)]
             | S _ =>
                 Int64.repr (Z.shiftr a 62 mod 2 ^ 62)
                 :: reprn n
                      (Z.shiftr (Z.shiftr a 62) 62)
             end) = a
                    mod (2 ^ (62 * Z.of_nat i)
                           * 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62
      * signed
          (firstn i (reprn (S n) (Z.shiftr a 62))) = 
a mod (2 ^ (62 * Z.of_nat i) * 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62 * (Z.shiftr a 62 mod 2 ^ (62 * Z.of_nat i)) = 
a mod (2 ^ (62 * Z.of_nat i) * 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
a mod 2 ^ 62
  + 2 ^ 62 * (Z.shiftr a 62 mod 2 ^ (62 * Z.of_nat i)) = 
a mod (2 ^ (62 * Z.of_nat i) * 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
a mod 2 ^ 62
  + 2 ^ 62 * ((a / 2 ^ 62) mod 2 ^ (62 * Z.of_nat i)) = 
a mod (2 ^ (62 * Z.of_nat i) * 2 ^ 62)


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
a mod (2 ^ (62 * Z.of_nat i) * 2 ^ 62) = a mod 2 ^ 62
                                           + 2 ^ 62
                                               * ((a
                                                 / 2
                                                 ^ 62)
                                                 mod 
                                                 2
                                                 ^ (62
                                                 * Z.of_nat
                                                 i))


n: nat
IHn: forall (a : Z) (i : nat),
(i < S n)%nat ->
signed (firstn i (reprn (S n) a)) = a mod 2 ^ (62 * Z.of_nat i)
a: Z
i: nat
Hi: (i < S n)%nat
(a / 2 ^ 62) mod 2 ^ (62 * Z.of_nat i) * 2 ^ 62
  + a mod 2 ^ 62 = a mod 2 ^ 62
                     + 2 ^ 62
                         * ((a / 2 ^ 62)
                            mod 2 ^ (62 * Z.of_nat i))

ring.
Qed.


a: Z
n: nat
(1 <= n)%nat ->
-2 ^ (62 * Z.of_nat n + 1) <= a <=
2 ^ (62 * Z.of_nat n + 1) - 1 ->
signed (reprn n a) = a


a: Z
n: nat
(1 <= n)%nat ->
-2 ^ (62 * Z.of_nat n + 1) <= a <=
2 ^ (62 * Z.of_nat n + 1) - 1 ->
signed (reprn n a) = a


n: nat
forall a : Z,
(1 <= n)%nat ->
-2 ^ (62 * Z.of_nat n + 1) <= a <=
2 ^ (62 * Z.of_nat n + 1) - 1 ->
signed (reprn n a) = a


n: nat
IHn: forall a : Z,
(1 <= n)%nat ->
-2 ^ (62 * Z.of_nat n + 1) <= a <= 2 ^ (62 * Z.of_nat n + 1) - 1 ->
signed (reprn n a) = a
forall a : Z,
(1 <= S n)%nat ->
-2 ^ (62 * Z.of_nat (S n) + 1) <= a <=
2 ^ (62 * Z.of_nat (S n) + 1) - 1 ->
signed (reprn (S n) a) = a


n: nat
IHn: forall a : Z,
(1 <= n)%nat ->
-2 ^ (62 * Z.of_nat n + 1) <= a <= 2 ^ (62 * Z.of_nat n + 1) - 1 ->
signed (reprn n a) = a
a: Z
-2 ^ (62 * Z.of_nat (S n) + 1) <= a <=
2 ^ (62 * Z.of_nat (S n) + 1) - 1 ->
signed (reprn (S n) a) = a


n: nat
IHn: forall a : Z,
(1 <= n)%nat ->
-2 ^ (62 * Z.of_nat n + 1) <= a <= 2 ^ (62 * Z.of_nat n + 1) - 1 ->
signed (reprn n a) = a
a: Z
-2 ^ (62 * Z.of_nat n + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat n + 62 + 1) - 1 ->
signed (reprn (S n) a) = a


IHn: forall a : Z,
(1 <= 0)%nat ->
-2 ^ (62 * Z.of_nat 0 + 1) <= a <= 2 ^ (62 * Z.of_nat 0 + 1) - 1 ->
signed (reprn 0 a) = a
a: Z
-2 ^ (62 * Z.of_nat 0 + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat 0 + 62 + 1) - 1 ->
signed (reprn 1 a) = a
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-2 ^ (62 * Z.of_nat (S n) + 1) <= a <= 2 ^ (62 * Z.of_nat (S n) + 1) - 1 ->
signed (reprn (S n) a) = a
a: Z
-2 ^ (62 * Z.of_nat (S n) + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat (S n) + 62 + 1) - 1 ->
signed (reprn (S (S n)) a) = a


IHn: forall a : Z,
(1 <= 0)%nat ->
-2 ^ (62 * Z.of_nat 0 + 1) <= a <= 2 ^ (62 * Z.of_nat 0 + 1) - 1 ->
signed (reprn 0 a) = a
a: Z
-2 ^ (62 * Z.of_nat 0 + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat 0 + 62 + 1) - 1 ->
signed (reprn 1 a) = a
 
IHn: forall a : Z,
(1 <= 0)%nat ->
-2 ^ (62 * Z.of_nat 0 + 1) <= a <= 2 ^ (62 * Z.of_nat 0 + 1) - 1 ->
signed (reprn 0 a) = a
a: Z
-2 ^ 63 <= a <= 2 ^ 63 - 1 ->
Int64.signed (Int64.repr a) + 2 ^ 62 * 0 = a
 
IHn: forall a : Z,
(1 <= 0)%nat ->
-2 ^ (62 * Z.of_nat 0 + 1) <= a <= 2 ^ (62 * Z.of_nat 0 + 1) - 1 ->
signed (reprn 0 a) = a
a: Z
Ha: -2 ^ 63 <= a <= 2 ^ 63 - 1
Int64.signed (Int64.repr a) + 2 ^ 62 * 0 = a
 rewrite Int64.signed_repr;[lia|assumption].

n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-2 ^ (62 * Z.of_nat (S n) + 1) <= a <= 2 ^ (62 * Z.of_nat (S n) + 1) - 1 ->
signed (reprn (S n) a) = a
a: Z
-2 ^ (62 * Z.of_nat (S n) + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat (S n) + 62 + 1) - 1 ->
signed (reprn (S (S n)) a) = a
 
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-2 ^ (62 * Z.of_nat (S n) + 1) <= a <= 2 ^ (62 * Z.of_nat (S n) + 1) - 1 ->
signed (reprn (S n) a) = a
a: Z
-2 ^ (62 * Z.of_nat (S n) + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat (S n) + 62 + 1) - 1 ->
signed
  (Int64.repr (a mod 2 ^ 62)
   :: reprn (S n) (Z.shiftr a 62)) = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-2 ^ (62 * Z.of_nat (S n) + 1) <= a <= 2 ^ (62 * Z.of_nat (S n) + 1) - 1 ->
signed (reprn (S n) a) = a
a: Z
-2 ^ (62 * Z.of_nat (S n) + 62 + 1) <= a <=
2 ^ (62 * Z.of_nat (S n) + 62 + 1) - 1 ->
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62 * signed (reprn (S n) (Z.shiftr a 62)) = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1 - 1 -> signed (reprn (S n) a) = a
a: Z
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1 - 1 ->
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62 * signed (reprn (S n) (Z.shiftr a 62)) = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1 - 1 -> signed (reprn (S n) a) = a
a: Z
Ha: -(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1) <=
a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1 - 1
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62 * signed (reprn (S n) (Z.shiftr a 62)) = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1 - 1 -> signed (reprn (S n) a) = a
a: Z
Ha: -(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1) <=
a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1 - 1
Int64.signed (Int64.repr (a mod 2 ^ 62))
  + 2 ^ 62 * Z.shiftr a 62 = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1 - 1 -> signed (reprn (S n) a) = a
a: Z
Ha: -(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1) <=
a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1 - 1
a mod 2 ^ 62 + 2 ^ 62 * Z.shiftr a 62 = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1 - 1 -> signed (reprn (S n) a) = a
a: Z
Ha: -(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1) <=
a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1 - 1
2 ^ 62 * (a / 2 ^ 62) + a mod 2 ^ 62 = a

  
n: nat
IHn: forall a : Z,
(1 <= S n)%nat ->
-(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1) <= a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 1 - 1 -> signed (reprn (S n) a) = a
a: Z
Ha: -(2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1) <=
a <=
2 ^ (62 * Z.of_nat (S n)) * 2 ^ 62 * 2 ^ 1 - 1
a = 2 ^ 62 * (a / 2 ^ 62) + a mod 2 ^ 62

  apply Z_div_mod_eq_full.
Qed.


a: Z
n1, n2: nat
min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1) ->
(1 <= n1 < n2)%nat ->
firstn n1
  (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
     (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
        (Int64.repr
           (Z.shiftl (if 0 <=? a then 0 else -1) 62)))) = 
reprn n1 a


a: Z
n1, n2: nat
min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1) ->
(1 <= n1 < n2)%nat ->
firstn n1
  (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
     (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
        (Int64.repr
           (Z.shiftl (if 0 <=? a then 0 else -1) 62)))) = 
reprn n1 a


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
firstn n1
  (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
     (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
        (Int64.repr
           (Z.shiftl (if 0 <=? a then 0 else -1) 62)))) = 
reprn n1 a


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
forall i : nat,
(0 <= i < Init.Nat.min n1 n2)%nat ->
nth i
  (firstn n1
     (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
        (Int64.or
           (Znth (Z.of_nat n1 - 1) (reprn n2 a))
           (Int64.repr
              (Z.shiftl (if 0 <=? a then 0 else -1) 62)))))
  default = nth i (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
forall i : nat,
(0 <= i < n1)%nat ->
nth i
  (firstn n1
     (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
        (Int64.or
           (Znth (Z.of_nat n1 - 1) (reprn n2 a))
           (Int64.repr
              (Z.shiftl (if 0 <=? a then 0 else -1) 62)))))
  default = nth i (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
i: nat
Hi: (0 <= i < n1)%nat
nth i
  (firstn n1
     (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
        (Int64.or
           (Znth (Z.of_nat n1 - 1) (reprn n2 a))
           (Int64.repr
              (Z.shiftl (if 0 <=? a then 0 else -1) 62)))))
  default = nth i (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
i: nat
Hi: (0 <= i < n1)%nat
nth i
  (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
     (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
        (Int64.repr
           (Z.shiftl (if 0 <=? a then 0 else -1) 62))))
  default = nth i (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Znth (Z.of_nat (n1 - 1))
  (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
     (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
        (Int64.repr
           (Z.shiftl (if 0 <=? a then 0 else -1) 62)))) = 
nth (n1 - 1) (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Znth (Z.of_nat n1 - 1)
  (upd_Znth (Z.of_nat n1 - 1) (reprn n2 a)
     (Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
        (Int64.repr
           (Z.shiftl (if 0 <=? a then 0 else -1) 62)))) = 
nth (n1 - 1) (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Int64.or (Znth (Z.of_nat n1 - 1) (reprn n2 a))
  (Int64.repr
     (Z.shiftl (if 0 <=? a then 0 else -1) 62)) = 
nth (n1 - 1) (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr
     (Z.shiftl (if 0 <=? a then 0 else -1) 62)) = 
nth (n1 - 1) (reprn n1 a) default


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
nth (n1 - 1) (reprn n1 a) default = Int64.or
                                      (Int64.repr
                                         (Z.shiftr a
                                            (62
                                               * (Z.of_nat
                                                 n1
                                                 - 1))
                                          mod 2 ^ 62))
                                      (Int64.repr
                                         (Z.shiftl
                                            (if
                                              0 <=? a
                                             then 0
                                             else -1)
                                            62))


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
nth (Datatypes.length (reprn n1 a) - 1) (reprn n1 a)
  default = Int64.or
              (Int64.repr
                 (Z.shiftr a (62 * (Z.of_nat n1 - 1))
                  mod 2 ^ 62))
              (Int64.repr
                 (Z.shiftl (if 0 <=? a then 0 else -1)
                    62))


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
last (reprn n1 a) default = Int64.or
                              (Int64.repr
                                 (Z.shiftr a
                                    (62
                                       * (Z.of_nat n1
                                            - 1))
                                  mod 2 ^ 62))
                              (Int64.repr
                                 (Z.shiftl
                                    (if 0 <=? a
                                     then 0
                                     else -1) 62))


a: Z
n1, n2: nat
Ha: min_signed (Z.of_nat n1) <= a <=
max_signed (Z.of_nat n1)
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr
     (Z.shiftl (if 0 <=? a then 0 else -1) 62))


a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr
     (Z.shiftl (if 0 <=? a then 0 else -1) 62))


a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl 0 62))
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl (-1) 62))


a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl 0 62))
 
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.repr
  (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62)

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
Int64.repr
  (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62) = 
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1)))

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62 = Z.shiftr
                                                 a
                                                 (62
                                                 * (Z.of_nat
                                                 n1
                                                 - 1))

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
0 <= Z.shiftr a (62 * (Z.of_nat n1 - 1)) < 2 ^ 62

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
2 ^ (62 * (Z.of_nat n1 - 1)) * 0 <= a <
2 ^ (62 * (Z.of_nat n1 - 1)) * 2 ^ 62

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
2 ^ (62 * (Z.of_nat n1 - 1)) * 0 <= a <
2 ^ (62 * (Z.of_nat n1 - 1) + 62)

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: 0 <= a
2 ^ (62 * (Z.of_nat n1 - 1)) * 0 <= a <
2 ^ (Z.of_nat n1 * 62)

  lia.

a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.or
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl (-1) 62))
 
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.add
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl (-1) 62))
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.and
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl (-1) 62)) = Int64.zero

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.and
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl (-1) 62)) = Int64.zero

    
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
forall i : Z,
0 <= i < Int64.zwordsize ->
Int64.testbit
  (Int64.and
     (Int64.repr
        (Z.shiftr a (62 * (Z.of_nat n1 - 1))
         mod 2 ^ 62)) (Int64.repr (Z.shiftl (-1) 62)))
  i = Int64.testbit Int64.zero i

    
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
j: Z
Hj: 0 <= j < Int64.zwordsize
Int64.testbit
  (Int64.and
     (Int64.repr
        (Z.shiftr a (62 * (Z.of_nat n1 - 1))
         mod 2 ^ 62)) (Int64.repr (Z.shiftl (-1) 62)))
  j = Int64.testbit Int64.zero j

    
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
j: Z
Hj: 0 <= j < Int64.zwordsize
Z.testbit
  (Z.land
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62)
     (Z.shiftl (-1) 62)) j = false

    
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
j: Z
Hj: 0 <= j < Int64.zwordsize
(Z.testbit (Z.shiftr a (62 * (Z.of_nat n1 - 1))) j &&
 (j <? 62) && Z.testbit (-1) (j - 62))%bool = false

    
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
j: Z
Hj: 0 <= j < Int64.zwordsize
j < 62 ->
(Z.testbit (Z.shiftr a (62 * (Z.of_nat n1 - 1))) j &&
 true && Z.testbit (-1) (j - 62))%bool = false

    intro; rewrite (Z.testbit_neg_r _ (j - 62)), !andb_false_r by lia; reflexivity.
  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.add
  (Int64.repr
     (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62))
  (Int64.repr (Z.shiftl (-1) 62))

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Int64.repr (Z.shiftr a (62 * (Z.of_nat n1 - 1))) = 
Int64.repr
  (Z.shiftr a (62 * (Z.of_nat n1 - 1)) mod 2 ^ 62
     + Z.shiftl (-1) 62)

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Z.shiftr a (62 * (Z.of_nat n1 - 1)) = Z.shiftr a
                                        (62
                                           * (Z.of_nat
                                                n1
                                                - 1))
                                      mod 2 ^ 62
                                        + Z.shiftl
                                            (-1) 62

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
Z.shiftr a (62 * (Z.of_nat n1 - 1)) = Z.shiftr a
                                        (62
                                           * (Z.of_nat
                                                n1
                                                - 1))
                                      mod 2 ^ 62
                                        + -2 ^ 62

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
0 <=
Z.shiftr a (62 * (Z.of_nat n1 - 1)) + 1 * 2 ^ 62 <
2 ^ 62

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
0 <=
Z.shiftr a (62 * (Z.of_nat n1 - 1)) + 1 * 2 ^ 62 <=
2 ^ 62 - 1

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
0 - 1 * 2 ^ 62 <=
Z.shiftr a (62 * (Z.of_nat n1 - 1)) <=
2 ^ 62 - 1 - 1 * 2 ^ 62

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
0 - 1 * 2 ^ 62 <=
Z.shiftr a (62 * (Z.of_nat n1 - 1)) <
2 ^ 62 - 1 - 1 * 2 ^ 62 + 1

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
2 ^ (62 * (Z.of_nat n1 - 1)) * (0 - 1 * 2 ^ 62) <= a <
2 ^ (62 * (Z.of_nat n1 - 1))
  * (2 ^ 62 - 1 - 1 * 2 ^ 62 + 1)

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
2 ^ (62 * (Z.of_nat n1 - 1)) * (0 - 1 * 2 ^ 62) <= a <
0

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
-(2 ^ 62 * 2 ^ (62 * (Z.of_nat n1 - 1))) <= a < 0

  
a: Z
n1, n2: nat
Ha: -2 ^ (Z.of_nat n1 * 62) <= a <=
2 ^ (Z.of_nat n1 * 62) - 1
Hn: (1 <= n1 < n2)%nat
Hi: (0 <= n1 - 1 < n1)%nat
Ha0: a < 0
-2 ^ (62 + 62 * (Z.of_nat n1 - 1)) <= a < 0

  replace (62 + 62 * (Z.of_nat n1 - 1)) with (Z.of_nat n1 * 62); lia.
Qed.

Definition pad (l : list int64) : list val := map Vlong l ++ repeat Vundef (5 - length l).


i: Z
l: list int64
0 <= i < Zlength l ->
Znth i (pad l) = Vlong (Znth i l)


i: Z
l: list int64
0 <= i < Zlength l ->
Znth i (pad l) = Vlong (Znth i l)


i: Z
l: list int64
Hi: 0 <= i < Zlength l
Znth i (pad l) = Vlong (Znth i l)


i: Z
l: list int64
Hi: 0 <= i < Zlength l
nth (Z.to_nat i) (pad l) Inhabitant_val = Vlong
                                            (nth
                                               (Z.to_nat
                                                 i) l
                                               Inhabitant_int64)
i: Z
l: list int64
Hi: 0 <= i < Zlength l
0 <= i < Zlength (pad l)


i: Z
l: list int64
Hi: 0 <= i < Zlength l
nth (Z.to_nat i) (pad l) Inhabitant_val = Vlong
                                            (nth
                                               (Z.to_nat
                                                 i) l
                                               Inhabitant_int64)
 
i: Z
l: list int64
Hi: 0 <= i < Zlength l
H: (Z.to_nat i < Datatypes.length l)%nat
nth (Z.to_nat i) (pad l) Inhabitant_val = Vlong
                                            (nth
                                               (Z.to_nat
                                                 i) l
                                               Inhabitant_int64)

  
i: Z
l: list int64
Hi: 0 <= i < Zlength l
H: (Z.to_nat i < Datatypes.length l)%nat
nth (Z.to_nat i)
  (map Vlong l ++
   repeat Vundef (5 - Datatypes.length l))
  Inhabitant_val = Vlong
                     (nth (Z.to_nat i) l
                        Inhabitant_int64)

  
i: Z
l: list int64
Hi: 0 <= i < Zlength l
H: (Z.to_nat i < Datatypes.length l)%nat
nth (Z.to_nat i) (map Vlong l) Inhabitant_val = Vlong
                                                 (nth
                                                 (Z.to_nat
                                                 i) l
                                                 Inhabitant_int64)

  
i: Z
l: list int64
Hi: 0 <= i < Zlength l
H: (Z.to_nat i < Datatypes.length l)%nat
nth (Z.to_nat i) (map Vlong l) ?d' = Vlong
                                       (nth
                                          (Z.to_nat i)
                                          l
                                          Inhabitant_int64)

  apply map_nth.

i: Z
l: list int64
Hi: 0 <= i < Zlength l
0 <= i < Zlength (pad l)
 
i: Z
l: list int64
Hi: 0 <= i < Zlength l
0 <= i <
Zlength
  (map Vlong l ++
   repeat Vundef (5 - Datatypes.length l))

  
i: Z
l: list int64
Hi: 0 <= i < Zlength l
0 <= i <
Zlength l
  + Zlength (repeat Vundef (5 - Datatypes.length l))

  
i: Z
l: list int64
Hi: 0 <= i < Zlength l
Hlen: 0
  <= Zlength
       (repeat Vundef (5 - Datatypes.length l))
0 <= i <
Zlength l
  + Zlength (repeat Vundef (5 - Datatypes.length l))

  lia.
Qed.


i: Z
l: list int64
Zlength l <= i -> Znth i (pad l) = Vundef


i: Z
l: list int64
Zlength l <= i -> Znth i (pad l) = Vundef


i: Z
l: list int64
Hi: Zlength l <= i
Znth i (pad l) = Vundef


i: Z
l: list int64
Hi: Zlength l <= i
Hl:= Zlength_nonneg l: 0 <= Zlength l
Znth i (pad l) = Vundef


i: Z
l: list int64
Hi: Zlength l <= i
Hl:= Zlength_nonneg l: 0 <= Zlength l
nth (Z.to_nat i) (pad l) default = Vundef


i: Z
l: list int64
Hi: (Datatypes.length l <= Z.to_nat i)%nat
Hl:= Zlength_nonneg l: 0 <= Zlength l
nth (Z.to_nat i) (pad l) default = Vundef


i: Z
l: list int64
Hi: (Datatypes.length l <= Z.to_nat i)%nat
Hl:= Zlength_nonneg l: 0 <= Zlength l
nth (Z.to_nat i)
  (map Vlong l ++
   repeat Vundef (5 - Datatypes.length l)) default = Vundef


i: Z
l: list int64
Hi: (Datatypes.length l <= Z.to_nat i)%nat
Hl:= Zlength_nonneg l: 0 <= Zlength l
nth (Z.to_nat i - Datatypes.length (map Vlong l))
  (repeat Vundef (5 - Datatypes.length l)) default = Vundef

apply nth_repeat.
Qed.


l: list int64
(Datatypes.length l <= 5)%nat ->
Datatypes.length (pad l) = 5%nat


l: list int64
(Datatypes.length l <= 5)%nat ->
Datatypes.length (pad l) = 5%nat


l: list int64
Hl: (Datatypes.length l <= 5)%nat
Datatypes.length (pad l) = 5%nat


l: list int64
Hl: (Datatypes.length l <= 5)%nat
Datatypes.length
  (map Vlong l ++
   repeat Vundef (5 - Datatypes.length l)) = 5%nat


l: list int64
Hl: (Datatypes.length l <= 5)%nat
(Datatypes.length l + (5 - Datatypes.length l))%nat = 5%nat

lia.
Qed.


l: list int64
Zlength l <= 5 -> Zlength (pad l) = 5


l: list int64
Zlength l <= 5 -> Zlength (pad l) = 5


l: list int64
Hl: Zlength l <= 5
Zlength (pad l) = 5

rewrite Zlength_correct, pad_length in *; try lia.
Qed.


pad [] = repeat Vundef 5


pad [] = repeat Vundef 5

reflexivity.
Qed.


l: list int64
Datatypes.length l = 5%nat -> pad l = map Vlong l


l: list int64
Datatypes.length l = 5%nat -> pad l = map Vlong l


l: list int64
Datatypes.length l = 5%nat ->
map Vlong l ++ repeat Vundef (5 - Datatypes.length l) = 
map Vlong l


l: list int64
map Vlong l ++ repeat Vundef (5 - 5) = map Vlong l


l: list int64
map Vlong l ++ [] = map Vlong l


l: list int64
map Vlong l ++ [] = map Vlong l ++ []

reflexivity.
Qed.



a: int64
i: Z
l: list int64
0 <= i < Zlength l ->
upd_Znth i (pad l) (Vlong a) = pad (upd_Znth i l a)


a: int64
i: Z
l: list int64
0 <= i < Zlength l ->
upd_Znth i (pad l) (Vlong a) = pad (upd_Znth i l a)


a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
upd_Znth i (pad l) (Vlong a) = pad (upd_Znth i l a)


a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
upd_Znth i
  (map Vlong l ++
   repeat Vundef (5 - Datatypes.length l)) (Vlong a) = 
map Vlong (upd_Znth i l a) ++
repeat Vundef (5 - Datatypes.length (upd_Znth i l a))


a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
upd_Znth i (map Vlong l) (Vlong a) ++
repeat Vundef (5 - Datatypes.length l) = map Vlong
                                           (upd_Znth i
                                              l a) ++
                                         repeat Vundef
                                           (5
                                              - Datatypes.length
                                                 (upd_Znth
                                                 i l a))


a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
upd_Znth i (map Vlong l) (Vlong a) = map Vlong
                                       (upd_Znth i l a)
a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
repeat Vundef (5 - Datatypes.length l) = repeat Vundef
                                           (5
                                              - Datatypes.length
                                                 (upd_Znth
                                                 i l a))


a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
upd_Znth i (map Vlong l) (Vlong a) = map Vlong
                                       (upd_Znth i l a)
 apply upd_Znth_map.

a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
repeat Vundef (5 - Datatypes.length l) = repeat Vundef
                                           (5
                                              - Datatypes.length
                                                 (upd_Znth
                                                 i l a))
 
a: int64
i: Z
l: list int64
Hi: 0 <= i < Zlength l
repeat Vundef (5 - Datatypes.length l) = repeat Vundef
                                           (5
                                              - Datatypes.length
                                                 l)

  reflexivity.
Qed.


a: int64
l: list int64
(Datatypes.length l <= 4)%nat ->
upd_Znth (Zlength l) (pad l) (Vlong a) = pad
                                           (l ++ [a])


a: int64
l: list int64
(Datatypes.length l <= 4)%nat ->
upd_Znth (Zlength l) (pad l) (Vlong a) = pad
                                           (l ++ [a])


a: int64
l: list int64
Hl: (Datatypes.length l <= 4)%nat
upd_Znth (Zlength l) (pad l) (Vlong a) = pad
                                           (l ++ [a])


a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
upd_Znth (Zlength l) (pad l) (Vlong a) = pad
                                           (l ++ [a])

(* assert (Hl' : Zlength l <= 4) by lia. *)

a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
Datatypes.length
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Datatypes.length
                                               (pad
                                                 (l ++
                                                 [a]))
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
forall n : nat,
(n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat ->
nth n (upd_Znth (Zlength l) (pad l) (Vlong a)) default = 
nth n (pad (l ++ [a])) default


a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
Datatypes.length
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Datatypes.length
                                               (pad
                                                 (l ++
                                                 [a]))
 
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
Z.of_nat
  (Datatypes.length
     (upd_Znth (Zlength l) (pad l) (Vlong a))) = Z.of_nat
                                                 (Datatypes.length
                                                 (pad
                                                 (l ++
                                                 [a])))

  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
Zlength (l ++ [a]) <= 5

  rewrite Zlength_app, Zlength_cons; simpl; lia.  

a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
forall n : nat,
(n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat ->
nth n (upd_Znth (Zlength l) (pad l) (Vlong a)) default = 
nth n (pad (l ++ [a])) default
 
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
nth n (upd_Znth (Zlength l) (pad l) (Vlong a)) default = 
nth n (pad (l ++ [a])) default

  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Znth
                                               (Z.of_nat
                                                 n)
                                               (pad
                                                 (l ++
                                                 [a]))

  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Znth
                                               (Z.of_nat
                                                 n)
                                               (pad
                                                 (l ++
                                                 [a]))

  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n < Zlength l
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Znth
                                               (Z.of_nat
                                                 n)
                                               (pad
                                                 (l ++
                                                 [a]))
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n = Zlength l
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = 
Znth (Z.of_nat n) (pad (l ++ [a]))
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Zlength l < Z.of_nat n
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = 
Znth (Z.of_nat n) (pad (l ++ [a]))

  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n < Zlength l
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Znth
                                               (Z.of_nat
                                                 n)
                                               (pad
                                                 (l ++
                                                 [a]))
 
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n < Zlength l
Vlong (Znth (Z.of_nat n) l) = Znth (Z.of_nat n)
                                (pad (l ++ [a]))

    
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n < Zlength l
Vlong (Znth (Z.of_nat n) l) = Vlong
                                (Znth (Z.of_nat n)
                                   (l ++ [a]))

    
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n < Zlength l
Vlong (Znth (Z.of_nat n) l) = Vlong
                                (Znth (Z.of_nat n) l)

    reflexivity.
  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n = Zlength l
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Znth
                                               (Z.of_nat
                                                 n)
                                               (pad
                                                 (l ++
                                                 [a]))
 
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n = Zlength l
Vlong a = Znth (Z.of_nat n) (pad (l ++ [a]))

    
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n = Zlength l
Vlong a = Znth (Z.of_nat n)
            (map Vlong (l ++ [a]) ++
             repeat Vundef
               (5 - Datatypes.length (l ++ [a])))

    
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Z.of_nat n = Zlength l
Vlong a = Znth 0 (map Vlong [a])

    reflexivity.
  
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Zlength l < Z.of_nat n
Znth (Z.of_nat n)
  (upd_Znth (Zlength l) (pad l) (Vlong a)) = Znth
                                               (Z.of_nat
                                                 n)
                                               (pad
                                                 (l ++
                                                 [a]))
 
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Zlength l < Z.of_nat n
Vundef = Znth (Z.of_nat n) (pad (l ++ [a]))

    
a: int64
l: list int64
Hl: (Z.to_nat (Zlength l) <= 4)%nat
n: nat
Hn: (n
   < Datatypes.length
       (upd_Znth (Zlength l) (pad l) (Vlong a)))%nat
Hpad:= pad_Zlength l: Zlength l <= 5 -> Zlength (pad l) = 5
Hnl: Zlength l < Z.of_nat n
Vundef = Vundef

    reflexivity.
Qed.

End Signed62.

Definition make_modinfo (m : Z) : (list val * val)%type :=
  (map Vlong (Signed62.reprn 5 m), Vlong (Int64.repr (modInv m (2^62)))).

Definition debruijn64_array (sh: share) (gv: globals) : mpred :=
  Eval cbn in
  let
    is_all_init_int8 := fix is_all_init_int8 (l : list init_data) :=
      match l with
      | [] => True
      | Init_int8 _ :: l' => is_all_init_int8 l'
      | _ => False
      end
  in let
    uninit_int8s := fix uninit_int8s (l: list init_data) :
        is_all_init_int8 l -> list int :=
      match l with
      | [] => fun _ => []
      | x :: l' =>
        match x with
        | Init_int8 i => fun pf => i :: uninit_int8s l' pf
        | _ => False_rec (list int)
        end
      end
  in data_at sh (gvar_info v_debruijn)
    (map Vint (uninit_int8s (gvar_init v_debruijn) I)) (gv _debruijn).


cs: compspecs
forall (sh : Share.t) (v : reptype tulong) (p : val),
data_at sh tulong v p = data_at sh tlong v p


cs: compspecs
forall (sh : Share.t) (v : reptype tulong) (p : val),
data_at sh tulong v p = data_at sh tlong v p

  
cs: compspecs
sh: Share.t
v: reptype tulong
p: val
data_at sh tulong v p = data_at sh tlong v p

  
cs: compspecs
sh: Share.t
v: reptype tulong
p: val
!! field_compatible tulong [] p &&
at_offset
  (data_at_rec sh (nested_field_type tulong []) v)
  (nested_field_offset tulong []) p = !! field_compatible
                                           tlong [] p &&
                                      at_offset
                                        (data_at_rec
                                           sh
                                           (nested_field_type
                                              tlong [])
                                           v)
                                        (nested_field_offset
                                           tlong []) p

  
cs: compspecs
sh: Share.t
v: reptype tulong
p: val
!! field_compatible tulong [] p = !! field_compatible
                                       tlong [] p

  
cs: compspecs
sh: Share.t
v: reptype tulong
p: val
!! (isptr p /\
    complete_legal_cosu_type tulong = true /\
    size_compatible tulong p /\
    align_compatible tulong p /\
    legal_nested_field tulong []) = !! (isptr p /\
                                        complete_legal_cosu_type
                                          tlong = true /\
                                        size_compatible
                                          tlong p /\
                                        align_compatible
                                          tlong p /\
                                        legal_nested_field
                                          tlong [])

  
cs: compspecs
sh: Share.t
v: reptype tulong
p: val
isptr p /\
complete_legal_cosu_type tulong = true /\
size_compatible tulong p /\
align_compatible tulong p /\
legal_nested_field tulong [] <->
isptr p /\
complete_legal_cosu_type tlong = true /\
size_compatible tlong p /\
align_compatible tlong p /\
legal_nested_field tlong []

  
cs: compspecs
sh: Share.t
v: reptype tulong
p: val
align_compatible tulong p <-> align_compatible tlong p

  
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
align_compatible_rec cenv_cs tulong
  (Ptrofs.unsigned i) <->
align_compatible_rec cenv_cs tlong (Ptrofs.unsigned i)

  
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: align_compatible_rec cenv_cs tulong
  (Ptrofs.unsigned i)
align_compatible_rec cenv_cs tlong (Ptrofs.unsigned i)
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: align_compatible_rec cenv_cs tlong
  (Ptrofs.unsigned i)
align_compatible_rec cenv_cs tulong
  (Ptrofs.unsigned i)

  
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: align_compatible_rec cenv_cs tulong
  (Ptrofs.unsigned i)
align_compatible_rec cenv_cs tlong (Ptrofs.unsigned i)
 
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: (align_chunk Mint64 | Ptrofs.unsigned i)
align_compatible_rec cenv_cs tlong (Ptrofs.unsigned i)

    
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: (align_chunk Mint64 | Ptrofs.unsigned i)
(align_chunk Mint64 | Ptrofs.unsigned i)

    auto.
  
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: align_compatible_rec cenv_cs tlong
  (Ptrofs.unsigned i)
align_compatible_rec cenv_cs tulong
  (Ptrofs.unsigned i)
 
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: (align_chunk Mint64 | Ptrofs.unsigned i)
align_compatible_rec cenv_cs tulong
  (Ptrofs.unsigned i)

    
cs: compspecs
sh: Share.t
v: reptype tulong
b: block
i: ptrofs
H: (align_chunk Mint64 | Ptrofs.unsigned i)
(align_chunk Mint64 | Ptrofs.unsigned i)

    auto.
Qed.


gv: ident -> val
headptr (gv _SECP256K1_SIGNED62_ONE) ->
globvar2pred gv
  (_SECP256K1_SIGNED62_ONE, v_SECP256K1_SIGNED62_ONE)
|-- data_at Ers t_secp256k1_modinv64_signed62
      (map Vlong (Signed62.reprn 5 1))
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
headptr (gv _SECP256K1_SIGNED62_ONE) ->
globvar2pred gv
  (_SECP256K1_SIGNED62_ONE, v_SECP256K1_SIGNED62_ONE)
|-- data_at Ers t_secp256k1_modinv64_signed62
      (map Vlong (Signed62.reprn 5 1))
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
globvar2pred gv
  (_SECP256K1_SIGNED62_ONE, v_SECP256K1_SIGNED62_ONE)
|-- data_at Ers t_secp256k1_modinv64_signed62
      (map Vlong (Signed62.reprn 5 1))
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
(if
  gvar_volatile
    (snd
       (_SECP256K1_SIGNED62_ONE,
        v_SECP256K1_SIGNED62_ONE))
 then TT
 else
  init_data_list2pred gv
    (gvar_init
       (snd
          (_SECP256K1_SIGNED62_ONE,
           v_SECP256K1_SIGNED62_ONE)))
    (readonly2share
       (gvar_readonly
          (snd
             (_SECP256K1_SIGNED62_ONE,
              v_SECP256K1_SIGNED62_ONE))))
    (gv
       (fst
          (_SECP256K1_SIGNED62_ONE,
           v_SECP256K1_SIGNED62_ONE))))
|-- data_at Ers t_secp256k1_modinv64_signed62
      (map Vlong (Signed62.reprn 5 1))
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * (mapsto_zeros 32 Ers
       (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
       * emp)
|-- data_at Ers t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr (1 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr 1 62 mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr (Z.shiftr 1 62) 62 mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr (Z.shiftr (Z.shiftr 1 62) 62) 62
             mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr
               (Z.shiftr 
                  (Z.shiftr (Z.shiftr 1 62) 62) 62) 62))]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr (1 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr 1 62 mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr (Z.shiftr 1 62) 62 mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr (Z.shiftr (Z.shiftr 1 62) 62) 62
             mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr
               (Z.shiftr 
                  (Z.shiftr (Z.shiftr 1 62) 62) 62) 62))]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr (1 mod 2 ^ 62));
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr 0 62 mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr (Z.shiftr 0 62) 62 mod 2 ^ 62));
       Vlong
         (Int64.repr
            (Z.shiftr (Z.shiftr (Z.shiftr 0 62) 62) 62))]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr (1 mod 2 ^ 62));
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr 1);
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr (0 mod 2 ^ 62));
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (Tstruct _secp256k1_modinv64_signed62 noattr)
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (Tstruct _secp256k1_modinv64_signed62 noattr)
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)



gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- field_at Ers
      (Tstruct _secp256k1_modinv64_signed62 noattr) []
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- nested_sfieldlist_at Ers
      (Tstruct _secp256k1_modinv64_signed62 noattr) []
      (co_members
         (get_co _secp256k1_modinv64_signed62))
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- nested_sfieldlist_at Ers
      (Tstruct _secp256k1_modinv64_signed62 noattr) []
      [Member_plain _v (tarray tlong 5)]
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- withspacer Ers 40
      (0
         + match
             Maps.PTree.get
               _secp256k1_modinv64_signed62
               (Maps.PTree.Nodes
                  (Maps.PTree.Node101
                     (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001 ...)
                      (Maps.PTree.Node100 ...))))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101 ... ...)
                      (Maps.PTree.Node001 ...)))))))
                     (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 ...)))))))))
           with
           | Some co => co_sizeof co
           | None => 0
           end)
      (field_at Ers
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v)
         [Vlong (Int64.repr 1); 
          Vlong (Int64.repr 0); 
          Vlong (Int64.repr 0); 
          Vlong (Int64.repr 0); 
          Vlong (Int64.repr 0)])
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- withspacer Ers 40 40
      (field_at Ers
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v)
         [Vlong (Int64.repr 1); 
          Vlong (Int64.repr 0); 
          Vlong (Int64.repr 0); 
          Vlong (Int64.repr 0); 
          Vlong (Int64.repr 0)])
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- (if Z.eq_dec (40 - 40) 0
     then
      field_at Ers
        (Tstruct _secp256k1_modinv64_signed62 noattr)
        (DOT _v)
        [Vlong (Int64.repr 1); 
         Vlong (Int64.repr 0); 
         Vlong (Int64.repr 0); 
         Vlong (Int64.repr 0); 
         Vlong (Int64.repr 0)]
        (gv _SECP256K1_SIGNED62_ONE)
     else
      field_at Ers
        (Tstruct _secp256k1_modinv64_signed62 noattr)
        (DOT _v)
        [Vlong (Int64.repr 1); 
         Vlong (Int64.repr 0); 
         Vlong (Int64.repr 0); 
         Vlong (Int64.repr 0); 
         Vlong (Int64.repr 0)]
        (gv _SECP256K1_SIGNED62_ONE)
        * spacer Ers 40 40
            (gv _SECP256K1_SIGNED62_ONE))


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- field_at Ers
      (Tstruct _secp256k1_modinv64_signed62 noattr)
      (DOT _v)
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (nested_field_type
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v))
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v) (gv _SECP256K1_SIGNED62_ONE))


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
field_compatible
  (Tstruct _secp256k1_modinv64_signed62 noattr)
  (DOT _v) (gv _SECP256K1_SIGNED62_ONE)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (nested_field_type
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v))
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v) (gv _SECP256K1_SIGNED62_ONE))


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
field_compatible
  (Tstruct _secp256k1_modinv64_signed62 noattr)
  (DOT _v) (gv _SECP256K1_SIGNED62_ONE)

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
headptr (gv _SECP256K1_SIGNED62_ONE)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type
  (Tstruct _secp256k1_modinv64_signed62 noattr) = true
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
legal_nested_field
  (Tstruct _secp256k1_modinv64_signed62 noattr)
  (DOT _v)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
sizeof (Tstruct _secp256k1_modinv64_signed62 noattr)
  < Ptrofs.modulus
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec cenv_cs
  (Tstruct _secp256k1_modinv64_signed62 noattr) 0

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
headptr (gv _SECP256K1_SIGNED62_ONE)
 assumption.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type
  (Tstruct _secp256k1_modinv64_signed62 noattr) = true
 reflexivity.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
legal_nested_field
  (Tstruct _secp256k1_modinv64_signed62 noattr)
  (DOT _v)
 repeat constructor.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
sizeof (Tstruct _secp256k1_modinv64_signed62 noattr)
  < Ptrofs.modulus
 reflexivity.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec cenv_cs
  (Tstruct _secp256k1_modinv64_signed62 noattr) 0
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Maps.PTree.get _secp256k1_modinv64_signed62 cenv_cs = 
Some ?co
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
plain_members (co_members ?co) = true
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
forall (i0 : ident) (t0 : type) (z0 : Z),
Ctypes.field_type i0 (co_members ?co) = 
Errors.OK t0 ->
Ctypes.field_offset cenv_cs i0 (co_members ?co) = 
Errors.OK (z0, Full) ->
align_compatible_rec cenv_cs t0 (0 + z0)

    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Maps.PTree.get _secp256k1_modinv64_signed62 cenv_cs = 
Some ?co
 reflexivity.
    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
plain_members
  (co_members
     {|
       co_su := Struct;
       co_members :=
         [Member_plain _v (tarray tlong 5)];
       co_attr := noattr;
       co_sizeof := 40;
       co_alignof := 8;
       co_rank := 1;
       co_sizeof_pos := Zgeb0_ge0 40 eq_refl;
       co_alignof_two_p :=
         prove_alignof_two_p 8 eq_refl;
       co_sizeof_alignof := prove_Zdivide 8 40 eq_refl
     |}) = true
 reflexivity.
    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
forall (i0 : ident) (t0 : type) (z0 : Z),
Ctypes.field_type i0
  (co_members
     {|
       co_su := Struct;
       co_members :=
         [Member_plain _v (tarray tlong 5)];
       co_attr := noattr;
       co_sizeof := 40;
       co_alignof := 8;
       co_rank := 1;
       co_sizeof_pos := Zgeb0_ge0 40 eq_refl;
       co_alignof_two_p :=
         prove_alignof_two_p 8 eq_refl;
       co_sizeof_alignof := prove_Zdivide 8 40 eq_refl
     |}) = Errors.OK t0 ->
Ctypes.field_offset cenv_cs i0
  (co_members
     {|
       co_su := Struct;
       co_members :=
         [Member_plain _v (tarray tlong 5)];
       co_attr := noattr;
       co_sizeof := 40;
       co_alignof := 8;
       co_rank := 1;
       co_sizeof_pos := Zgeb0_ge0 40 eq_refl;
       co_alignof_two_p :=
         prove_alignof_two_p 8 eq_refl;
       co_sizeof_alignof := prove_Zdivide 8 40 eq_refl
     |}) = Errors.OK (z0, Full) ->
align_compatible_rec cenv_cs t0 (0 + z0)
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i0: ident
t0: type
z0: Z
H0: (if ident_eq i0 _v
 then Errors.OK (tarray tlong 5)
 else
  Errors.Error
    [Errors.MSG "Unknown field "; Errors.CTX i0]) = 
Errors.OK t0
H1: Ctypes.field_offset
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  i0 [Member_plain _v (tarray tlong 5)] = 
Errors.OK (z0, Full)
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  t0 (0 + z0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i0: ident
t0: type
z0: Z
e: i0 = _v
H0: Errors.OK (tarray tlong 5) = Errors.OK t0
H1: Ctypes.field_offset
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  i0 [Member_plain _v (tarray tlong 5)] = 
Errors.OK (z0, Full)
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  t0 (0 + z0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i0: ident
t0: type
z0: Z
e: i0 = _v
H1: Ctypes.field_offset
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  i0 [Member_plain _v (tarray tlong 5)] = 
Errors.OK (z0, Full)
tarray tlong 5 = t0 ->
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 (...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 (...)))))))))))))
  t0 (0 + z0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i0: ident
z0: Z
e: i0 = _v
H1: Ctypes.field_offset
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  i0 [Member_plain _v (tarray tlong 5)] = 
Errors.OK (z0, Full)
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  (tarray tlong 5) (0 + z0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
z0: Z
H1: Ctypes.field_offset
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  _v [Member_plain _v (tarray tlong 5)] = 
Errors.OK (z0, Full)
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  (tarray tlong 5) (0 + z0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
z0: Z
0 = z0 ->
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 (...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 (...)))))))))))))
  (tarray tlong 5) (0 + z0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  (tarray tlong 5) (0 + 0)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
forall i : Z,
0 <= i < 5 ->
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...)))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 ...))))))))))))
  tlong (0 + 0 + Ctypes.sizeof tlong * i)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
forall i : Z,
0 <= i < 5 ->
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...)))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 ...))))))))))))
  tlong (0 + 0 + Ctypes.sizeof tlong * i)
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i: Z
Hi: 0 <= i < 5
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 ...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 ...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 ...)))))))))))))
  tlong (0 + 0 + Ctypes.sizeof tlong * i)

        
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i: Z
Hi: 0 <= i < 5
i = 0 \/ i = 1 \/ i = 2 \/ i = 3 \/ i = 4 ->
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 (...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 (...)))))))))))))
  tlong (0 + 0 + Ctypes.sizeof tlong * i)

        
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i: Z
i = 0 \/ i = 1 \/ i = 2 \/ i = 3 \/ i = 4 ->
align_compatible_rec
  (Maps.PTree.Nodes
     (Maps.PTree.Node101
        (Maps.PTree.Node101
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node100
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001 (...))))))))))
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node001
                    (Maps.PTree.Node001
                      (Maps.PTree.Node101
                      (Maps.PTree.Node101
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100 (...))))
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100
                      (Maps.PTree.Node100 (...)))))))))))
        (Maps.PTree.Node001
           (Maps.PTree.Node001
              (Maps.PTree.Node001
                 (Maps.PTree.Node100
                    (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001
                      (Maps.PTree.Node100
                      (Maps.PTree.Node001
                      (Maps.PTree.Node001 (...)))))))))))))
  tlong (0 + 0 + Ctypes.sizeof tlong * i)

        intros [->|[->|[->|[->| ->]]]];econstructor;try reflexivity;apply Zmod_divide;try reflexivity;cbn;lia.

gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (nested_field_type
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v))
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v) (gv _SECP256K1_SIGNED62_ONE))


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (nested_field_type
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v))
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (offset_val
         (nested_field_offset
            (Tstruct _secp256k1_modinv64_signed62
               noattr) 
            (DOT _v)) (gv _SECP256K1_SIGNED62_ONE))


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers
      (nested_field_type
         (Tstruct _secp256k1_modinv64_signed62 noattr)
         (DOT _v))
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)


gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (tarray tlong 5)
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)



gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong 5 noattr)
      [Vlong (Int64.repr 1); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (gv _SECP256K1_SIGNED62_ONE)

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
  * mapsto_zeros 32 Ers
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong 1 noattr)
      [Vlong (Int64.repr 1)]
      (gv _SECP256K1_SIGNED62_ONE)
      * data_at Ers (Tarray tlong (5 - 1) noattr)
          [Vlong (Int64.repr 0); 
           Vlong (Int64.repr 0); 
           Vlong (Int64.repr 0); 
           Vlong (Int64.repr 0)]
          (field_address0 
             (Tarray tlong 5 noattr) 
             (SUB 1) (gv _SECP256K1_SIGNED62_ONE))

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
|-- data_at Ers (Tarray tlong 1 noattr)
      [Vlong (Int64.repr 1)]
      (gv _SECP256K1_SIGNED62_ONE)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto_zeros 32 Ers
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
|-- data_at Ers (Tarray tlong 1 noattr)
      [Vlong (Int64.repr 1)]
      (gv _SECP256K1_SIGNED62_ONE)
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
|-- data_at Ers tlong (Vlong (Int64.repr 1))
      (gv _SECP256K1_SIGNED62_ONE)

     
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto Ers (Tlong Unsigned noattr)
  (gv _SECP256K1_SIGNED62_ONE) 
  (Vlong (Int64.repr 1))
|-- data_at Ers tulong 
      (Vlong (Int64.repr 1))
      (gv _SECP256K1_SIGNED62_ONE)

     
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
field_compatible (Tlong Unsigned noattr) []
  (gv _SECP256K1_SIGNED62_ONE)

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
headptr (gv _SECP256K1_SIGNED62_ONE)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type (Tlong Unsigned noattr) = true
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
legal_nested_field (Tlong Unsigned noattr) []
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
sizeof (Tlong Unsigned noattr) < Ptrofs.modulus
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec cenv_cs (Tlong Unsigned noattr) 0

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
headptr (gv _SECP256K1_SIGNED62_ONE)
 assumption.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type (Tlong Unsigned noattr) = true
 reflexivity.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
legal_nested_field (Tlong Unsigned noattr) []
 repeat constructor.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
sizeof (Tlong Unsigned noattr) < Ptrofs.modulus
 reflexivity.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec cenv_cs (Tlong Unsigned noattr) 0
 econstructor;[reflexivity|apply Z.divide_0_r].
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible
  (Tstruct _secp256k1_modinv64_signed62
     noattr) (DOT _v)
  (gv _SECP256K1_SIGNED62_ONE)
mapsto_zeros 32 Ers
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
mapsto_zeros 32 Ers
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
mapsto_zeros 32 Ers
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)

        
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
headptr (gv _SECP256K1_SIGNED62_ONE)
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type (tarray tlong 5) = true
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
legal_nested_field (tarray tlong 5) []
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
sizeof (tarray tlong 5) < Ptrofs.modulus
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec cenv_cs (tarray tlong 5) 0

  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
headptr (gv _SECP256K1_SIGNED62_ONE)
 assumption.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type (tarray tlong 5) = true
 reflexivity.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
legal_nested_field (tarray tlong 5) []
 repeat constructor.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
sizeof (tarray tlong 5) < Ptrofs.modulus
 reflexivity.
  
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
align_compatible_rec cenv_cs (tarray tlong 5) 0
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
forall i : Z,
0 <= i < 5 ->
align_compatible_rec cenv_cs tlong
  (0 + Ctypes.sizeof tlong * i)

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
forall i : Z,
0 <= i < 5 ->
align_compatible_rec cenv_cs tlong
  (0 + Ctypes.sizeof tlong * i)
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i: Z
Hi: 0 <= i < 5
align_compatible_rec cenv_cs tlong
  (0 + Ctypes.sizeof tlong * i)

        
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i: Z
Hi: 0 <= i < 5
i = 0 \/ i = 1 \/ i = 2 \/ i = 3 \/ i = 4 ->
align_compatible_rec cenv_cs tlong
  (0 + Ctypes.sizeof tlong * i)

        
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
i: Z
i = 0 \/ i = 1 \/ i = 2 \/ i = 3 \/ i = 4 ->
align_compatible_rec cenv_cs tlong
  (0 + Ctypes.sizeof tlong * i)

        intros [->|[->|[->|[->| ->]]]];econstructor;try reflexivity;apply Zmod_divide;try reflexivity;cbn;lia.
       
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
mapsto_zeros 32 Ers
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))

    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
readable_share Ers
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type (Tarray tlong (5 - 1) noattr) = true
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
fully_nonvolatile
  (rank_type cenv_cs (Tarray tlong (5 - 1) noattr))
  (Tarray tlong (5 - 1) noattr) = true
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
field_compatible (Tarray tlong (5 - 1) noattr) []
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
data_at Ers (Tarray tlong (5 - 1) noattr)
  (zero_val (Tarray tlong (5 - 1) noattr))
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))

    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
readable_share Ers
 apply readable_Ers.
    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
complete_legal_cosu_type (Tarray tlong (5 - 1) noattr) = true
 reflexivity.
    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
fully_nonvolatile
  (rank_type cenv_cs (Tarray tlong (5 - 1) noattr))
  (Tarray tlong (5 - 1) noattr) = true
 reflexivity.
    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
field_compatible (Tarray tlong (5 - 1) noattr) []
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
 apply (field_compatible0_nested_field_array (Tarray tlong 5 noattr) []); try lia; apply arr_field_compatible0; try lia; assumption.
    
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
data_at Ers (Tarray tlong (5 - 1) noattr)
  (zero_val (Tarray tlong (5 - 1) noattr))
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (field_address0 (Tarray tlong 5 noattr) 
         (SUB 1) (gv _SECP256K1_SIGNED62_ONE))
 
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
data_at Ers (Tarray tlong (5 - 1) noattr)
  (zero_val (Tarray tlong (5 - 1) noattr))
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (offset_val
         (nested_field_offset 
            (Tarray tlong 5 noattr) 
            (SUB 1)) (gv _SECP256K1_SIGNED62_ONE))

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
data_at Ers (Tarray tlong (5 - 1) noattr)
  (zero_val (Tarray tlong (5 - 1) noattr))
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (Tarray tlong (5 - 1) noattr)
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
data_at Ers (tarray tlong (5 - 1))
  (zero_val (tarray tlong (5 - 1)))
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (tarray tlong (5 - 1))
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))

      
gv: ident -> val
Hheadptr: headptr (gv _SECP256K1_SIGNED62_ONE)
Hptr: isptr (gv _SECP256K1_SIGNED62_ONE)
Hcompat: field_compatible (tarray tlong 5) []
  (gv _SECP256K1_SIGNED62_ONE)
data_at Ers (tarray tlong (5 - 1))
  (Zrepeat (Vlong Int64.zero) (5 - 1))
  (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))
|-- data_at Ers (tarray tlong (5 - 1))
      [Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0); 
       Vlong (Int64.repr 0)]
      (offset_val 8 (gv _SECP256K1_SIGNED62_ONE))

      apply derives_refl.
Qed.

Definition secp256k1_modinv64_signed62_assign_spec : ident * funspec :=
DECLARE _secp256k1_modinv64_signed62_assign
  WITH x : Z, ptr_dst : val, ptr_src : val, sh_dst : share, sh_src : share
  PRE [ tptr t_secp256k1_modinv64_signed62
      , tptr t_secp256k1_modinv64_signed62
      ]
    PROP( writable_share sh_dst
        ; readable_share sh_src
        )
    PARAMS(ptr_dst; ptr_src)
    SEP( data_at_ sh_dst t_secp256k1_modinv64_signed62 ptr_dst
       ; data_at sh_src t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptr_src
       )
  POST [ tvoid ]
    PROP()
    RETURN()
    SEP( data_at sh_dst t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptr_dst
       ; data_at sh_src t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptr_src
       ).

Definition secp256k1_modinv64_var_spec : ident * funspec :=
DECLARE _secp256k1_modinv64_var
  WITH x : Z, m : Z, ptrx : val, modinfo : val, shx : share, sh_modinfo : share,
       sh_debruijn : share, sh_SECP256K1_SIGNED62_ONE : share, gv : globals
  PRE [ tptr t_secp256k1_modinv64_signed62
      , tptr t_secp256k1_modinv64_modinfo
      ]
    PROP( Z.Odd m
        ; 0 <= x < m
        ; 1 < m < 2^256
        ; x = 0 \/ rel_prime x m
        ; writable_share shx
        ; readable_share sh_modinfo
        ; readable_share sh_debruijn
        ; readable_share sh_SECP256K1_SIGNED62_ONE
        )
    PARAMS(ptrx; modinfo)
    GLOBALS(gv)
    SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx;
        data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo;
        debruijn64_array sh_debruijn gv;
        data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE))
  POST [ tvoid ]
    PROP()
    RETURN()
    SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 (modInv x m))) ptrx;
        data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo;
        debruijn64_array sh_debruijn gv;
        data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)).

Definition secp256k1_modinv64_var_spec_prime : ident * funspec :=
DECLARE _secp256k1_modinv64_var
  WITH x : Z, m : Z, ptrx : val, modinfo : val, shx : share, sh_modinfo : share,
       sh_debruijn : share, sh_SECP256K1_SIGNED62_ONE : share, gv : globals
  PRE [ tptr t_secp256k1_modinv64_signed62
      , tptr t_secp256k1_modinv64_modinfo
      ]
    PROP( Z.Odd m
        ; 0 <= x < m
        ; m < 2^256
        ; prime m
        ; writable_share shx
        ; readable_share sh_modinfo
        ; readable_share sh_debruijn
        ; readable_share sh_SECP256K1_SIGNED62_ONE
        )
    PARAMS(ptrx; modinfo)
    GLOBALS(gv)
    SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 x)) ptrx;
        data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo;
        debruijn64_array sh_debruijn gv;
        data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE))
  POST [ tvoid ]
    PROP()
    RETURN()
    SEP(data_at shx t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 (modInv x m))) ptrx;
        data_at sh_modinfo t_secp256k1_modinv64_modinfo (make_modinfo m) modinfo;
        debruijn64_array sh_debruijn gv;
        data_at sh_SECP256K1_SIGNED62_ONE t_secp256k1_modinv64_signed62 (map Vlong (Signed62.reprn 5 1)) (gv _SECP256K1_SIGNED62_ONE)).

(* Use with
   forward_call secp256k1_modinv64_var_spec_prime_sub (x, m, ptrx, modinfo, shx, sh_modinfo, sh_debruijn, sh_SECP256K1_SIGNED62_ONE, gv)
*)

funspec_sub (snd secp256k1_modinv64_var_spec)
  (snd secp256k1_modinv64_var_spec_prime)


funspec_sub (snd secp256k1_modinv64_var_spec)
  (snd secp256k1_modinv64_var_spec_prime)


w: (Z * Z * val * val * share * share * share * share
   * globals)%type
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
(let (p, gv) := w in
 let (p0, sh_SECP256K1_SIGNED62_ONE) := p in
 let (p1, sh_debruijn) := p0 in
 let (p2, sh_modinfo) := p1 in
 let (p3, shx) := p2 in
 let (p4, modinfo) := p3 in
 let (p5, ptrx) := p4 in
 let (x, m) := p5 in
 fun x0 : argsEnviron =>
 !! (Z.Odd m /\
     0 <= x < m /\
     m < 2 ^ 256 /\
     prime m /\
     writable_share shx /\
     readable_share sh_modinfo /\
     readable_share sh_debruijn /\
     readable_share sh_SECP256K1_SIGNED62_ONE /\ True) &&
 (!! (snd x0 = [ptrx; modinfo]) &&
  (!! (gvars_denote gv
         (Clight_seplog.mkEnv (fst x0) [] []) /\ True) &&
   (data_at shx t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr (x mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr x 62 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr ... 62 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr ... 62 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr (...) 62))] ptrx
      * (data_at sh_modinfo
           t_secp256k1_modinv64_modinfo
           (make_modinfo m) modinfo
           * (debruijn64_array sh_debruijn gv
                * (data_at sh_SECP256K1_SIGNED62_ONE
                     t_secp256k1_modinv64_signed62
                     [...; ...; ...; ...; ...] (...)
                     * emp))))))) (g, args)
|-- EX (x1 : Z * Z * val * val * share * share * share
               * share
               * globals) (F : mpred),
    F
      * (let (p, gv) := x1 in
         let (p0, sh_SECP256K1_SIGNED62_ONE) := p in
         let (p1, sh_debruijn) := p0 in
         let (p2, sh_modinfo) := p1 in
         let (p3, shx) := p2 in
         let (p4, modinfo) := p3 in
         let (p5, ptrx) := p4 in
         let (x, m) := p5 in
         fun x0 : argsEnviron =>
         !! (Z.Odd m /\
             0 <= x < m /\
             1 < m < 2 ^ 256 /\
             (x = 0 \/ rel_prime x m) /\
             writable_share shx /\
             readable_share sh_modinfo /\
             readable_share sh_debruijn /\
             readable_share sh_SECP256K1_SIGNED62_ONE /\
             True) &&
         (!! (snd x0 = [ptrx; modinfo]) &&
          (!! (gvars_denote gv
                 (Clight_seplog.mkEnv (fst x0) [] []) /\
               True) &&
           (data_at shx t_secp256k1_modinv64_signed62
              [Vlong (Int64.repr ...);
               Vlong (Int64.repr ...);
               Vlong (Int64.repr ...);
               Vlong (Int64.repr ...);
               Vlong (Int64.repr ...)] ptrx
              * (data_at sh_modinfo
                   t_secp256k1_modinv64_modinfo
                   (make_modinfo m) modinfo
                   * (debruijn64_array sh_debruijn gv
                        * (...))))))) (g, args) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (F
           * (let (p, gv) := x1 in
              let (p0, sh_SECP256K1_SIGNED62_ONE) :=
                p in
              let (p1, sh_debruijn) := p0 in
              let (p2, sh_modinfo) := p1 in
              let (p3, shx) := p2 in
              let (p4, modinfo) := p3 in
              let (p5, ptrx) := p4 in
              let (x, m) := p5 in
              fun _ : environ =>
              TT &&
              (TT &&
               (data_at shx
                  t_secp256k1_modinv64_signed62
                  [...; ...; ...; ...; ...] ptrx
                  * (... * ...)))) rho')
        |-- (let (p, gv) := w in
             let (p0, sh_SECP256K1_SIGNED62_ONE) :=
               p in
             let (p1, sh_debruijn) := p0 in
             let (p2, sh_modinfo) := p1 in
             let (p3, shx) := p2 in
             let (p4, modinfo) := p3 in
             let (p5, ptrx) := p4 in
             let (x, m) := p5 in
             fun _ : environ =>
             TT &&
             (TT &&
              (data_at shx
                 t_secp256k1_modinv64_signed62
                 [Vlong (Int64.repr ...);
                  Vlong (Int64.repr ...);
                  Vlong (Int64.repr ...);
                  Vlong (Int64.repr ...);
                  Vlong (Int64.repr ...)] ptrx
                 * (data_at sh_modinfo
                      t_secp256k1_modinv64_modinfo
                      (make_modinfo m) modinfo
                      * (debruijn64_array sh_debruijn
                           gv
                           * (...)))))) rho')


w: (Z * Z * val * val * share * share * share * share
   * globals)%type
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
(let (p, gv) := w in
 let (p0, sh_SECP256K1_SIGNED62_ONE) := p in
 let (p1, sh_debruijn) := p0 in
 let (p2, sh_modinfo) := p1 in
 let (p3, shx) := p2 in
 let (p4, modinfo) := p3 in
 let (p5, ptrx) := p4 in
 let (x, m) := p5 in
 fun x0 : argsEnviron =>
 !! (Z.Odd m /\
     0 <= x < m /\
     m < 2 ^ 256 /\
     prime m /\
     writable_share shx /\
     readable_share sh_modinfo /\
     readable_share sh_debruijn /\
     readable_share sh_SECP256K1_SIGNED62_ONE /\ True) &&
 (!! (snd x0 = [ptrx; modinfo]) &&
  (!! (gvars_denote gv
         (Clight_seplog.mkEnv (fst x0) [] []) /\ True) &&
   (data_at shx t_secp256k1_modinv64_signed62
      [Vlong (Int64.repr (x mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr x 62 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr ... 62 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr ... 62 mod 2 ^ 62));
       Vlong (Int64.repr (Z.shiftr (...) 62))] ptrx
      * (data_at sh_modinfo
           t_secp256k1_modinv64_modinfo
           (make_modinfo m) modinfo
           * (debruijn64_array sh_debruijn gv
                * (data_at sh_SECP256K1_SIGNED62_ONE
                     t_secp256k1_modinv64_signed62
                     [...; ...; ...; ...; ...] 
                     (...)
                     * emp))))))) (
  g, args)
|-- emp
      * (let (p, gv) := w in
         let (p0, sh_SECP256K1_SIGNED62_ONE) := p in
         let (p1, sh_debruijn) := p0 in
         let (p2, sh_modinfo) := p1 in
         let (p3, shx) := p2 in
         let (p4, modinfo) := p3 in
         let (p5, ptrx) := p4 in
         let (x, m) := p5 in
         fun x0 : argsEnviron =>
         !! (Z.Odd m /\
             0 <= x < m /\
             1 < m < 2 ^ 256 /\
             (x = 0 \/ rel_prime x m) /\
             writable_share shx /\
             readable_share sh_modinfo /\
             readable_share sh_debruijn /\
             readable_share sh_SECP256K1_SIGNED62_ONE /\
             True) &&
         (!! (snd x0 = [ptrx; modinfo]) &&
          (!! (gvars_denote gv
                 (Clight_seplog.mkEnv (fst x0) [] []) /\
               True) &&
           (data_at shx t_secp256k1_modinv64_signed62
              [Vlong (Int64.repr (...));
               Vlong (Int64.repr (...));
               Vlong (Int64.repr (...));
               Vlong (Int64.repr (...));
               Vlong (Int64.repr (...))] ptrx
              * (data_at sh_modinfo
                   t_secp256k1_modinv64_modinfo
                   (make_modinfo m) modinfo
                   * (debruijn64_array sh_debruijn gv
                        * 
                        (... * emp))))))) (
          g, args) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (emp
           * (let (p, gv) := w in
              let (p0, sh_SECP256K1_SIGNED62_ONE) :=
                p in
              let (p1, sh_debruijn) := p0 in
              let (p2, sh_modinfo) := p1 in
              let (p3, shx) := p2 in
              let (p4, modinfo) := p3 in
              let (p5, ptrx) := p4 in
              let (x, m) := p5 in
              fun _ : environ =>
              TT &&
              (TT &&
               (data_at shx
                  t_secp256k1_modinv64_signed62
                  [Vlong ...; 
                   Vlong ...; 
                   Vlong ...; 
                   Vlong ...; 
                   Vlong ...] ptrx
                  * (data_at sh_modinfo
                       t_secp256k1_modinv64_modinfo
                       ... modinfo
                       * 
                       (...))))) rho')
        |-- (let (p, gv) := w in
             let (p0, sh_SECP256K1_SIGNED62_ONE) :=
               p in
             let (p1, sh_debruijn) := p0 in
             let (p2, sh_modinfo) := p1 in
             let (p3, shx) := p2 in
             let (p4, modinfo) := p3 in
             let (p5, ptrx) := p4 in
             let (x, m) := p5 in
             fun _ : environ =>
             TT &&
             (TT &&
              (data_at shx
                 t_secp256k1_modinv64_signed62
                 [Vlong (Int64.repr (...));
                  Vlong (Int64.repr (...));
                  Vlong (Int64.repr (...));
                  Vlong (Int64.repr (...));
                  Vlong (Int64.repr (...))] ptrx
                 * (data_at sh_modinfo
                      t_secp256k1_modinv64_modinfo
                      (make_modinfo m) modinfo
                      * (debruijn64_array sh_debruijn
                        gv
                        * (... * emp)))))) rho')


x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
!! (Z.Odd m /\
    0 <= x < m /\
    m < 2 ^ 256 /\
    prime m /\
    writable_share shx /\
    readable_share sh_modinfo /\
    readable_share sh_debruinj /\
    readable_share sh_SECP256K1_SIGNED62_ONE /\ True) &&
(!! (snd (g, args) = [ptrx; modinfo]) &&
 (!! (gvars_denote gv
        (Clight_seplog.mkEnv (fst (g, args)) [] []) /\
      True) &&
  (data_at shx t_secp256k1_modinv64_signed62
     [Vlong (Int64.repr (x mod 2 ^ 62));
      Vlong (Int64.repr (Z.shiftr x 62 mod 2 ^ 62));
      Vlong
        (Int64.repr
           (Z.shiftr (Z.shiftr x 62) 62 mod 2 ^ 62));
      Vlong
        (Int64.repr
           (Z.shiftr (Z.shiftr (Z.shiftr x 62) 62) 62
            mod 2 ^ 62));
      Vlong
        (Int64.repr
           (Z.shiftr
              (Z.shiftr (Z.shiftr (Z.shiftr x 62) 62)
                 62) 62))] ptrx
     * (data_at sh_modinfo
          t_secp256k1_modinv64_modinfo
          (make_modinfo m) modinfo
          * (debruijn64_array sh_debruinj gv
               * (data_at sh_SECP256K1_SIGNED62_ONE
                    t_secp256k1_modinv64_signed62
                    [Vlong (Int64.repr (1 mod 2 ^ 62));
                     Vlong
                       (Int64.repr
                        (Z.shiftr 1 62 mod 2 ^ 62));
                     Vlong
                       (Int64.repr
                        (Z.shiftr (Z.shiftr 1 62) 62
                        mod 
                        2 ^ 62));
                     Vlong
                       (Int64.repr
                        (Z.shiftr
                        (Z.shiftr (Z.shiftr 1 62) 62)
                        62 mod 
                        2 ^ 62));
                     Vlong
                       (Int64.repr
                        (Z.shiftr
                        (Z.shiftr
                        (Z.shiftr (Z.shiftr 1 62) 62)
                        62) 62))]
                    (gv _SECP256K1_SIGNED62_ONE)
                    * emp))))))
|-- emp
      * (!! (Z.Odd m /\
             0 <= x < m /\
             1 < m < 2 ^ 256 /\
             (x = 0 \/ rel_prime x m) /\
             writable_share shx /\
             readable_share sh_modinfo /\
             readable_share sh_debruinj /\
             readable_share sh_SECP256K1_SIGNED62_ONE /\
             True) &&
         (!! (snd (g, args) = [ptrx; modinfo]) &&
          (!! (gvars_denote gv
                 (Clight_seplog.mkEnv 
                    (fst (g, args)) [] []) /\ True) &&
           (data_at shx t_secp256k1_modinv64_signed62
              [Vlong (Int64.repr (x mod 2 ^ 62));
               Vlong
                 (Int64.repr
                    (Z.shiftr x 62 mod 2 ^ 62));
               Vlong
                 (Int64.repr
                    (Z.shiftr (Z.shiftr x 62) 62
                     mod 
                     2 ^ 62));
               Vlong
                 (Int64.repr
                    (Z.shiftr
                       (Z.shiftr (Z.shiftr x 62) 62)
                       62 mod 
                     2 ^ 62));
               Vlong
                 (Int64.repr
                    (Z.shiftr
                       (Z.shiftr
                        (Z.shiftr (Z.shiftr x 62) 62)
                        62) 62))] ptrx
              * (data_at sh_modinfo
                   t_secp256k1_modinv64_modinfo
                   (make_modinfo m) modinfo
                   * (debruijn64_array sh_debruinj gv
                        * 
                        (data_at
                        sh_SECP256K1_SIGNED62_ONE
                        t_secp256k1_modinv64_signed62
                        [Vlong
                        (Int64.repr (1 mod 2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr 1 62 mod 2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr (Z.shiftr 1 62) 62
                        mod 
                        2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr (Z.shiftr ... 62) 62
                        mod 
                        2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr 
                        (Z.shiftr (...) 62) 62))]
                        (gv _SECP256K1_SIGNED62_ONE)
                        * emp))))))) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (emp
           * (TT &&
              (TT &&
               (data_at shx
                  t_secp256k1_modinv64_signed62
                  [Vlong
                     (Int64.repr
                        (modInv x m mod 2 ^ 62));
                   Vlong
                     (Int64.repr
                        (Z.shiftr (modInv x m) 62
                        mod 
                        2 ^ 62));
                   Vlong
                     (Int64.repr
                        (Z.shiftr
                        (Z.shiftr (modInv x m) 62) 62
                        mod 
                        2 ^ 62));
                   Vlong
                     (Int64.repr
                        (Z.shiftr
                        (Z.shiftr 
                        (Z.shiftr (...) 62) 62) 62
                        mod 
                        2 ^ 62));
                   Vlong
                     (Int64.repr
                        (Z.shiftr
                        (Z.shiftr
                        (Z.shiftr (Z.shiftr ... 62) 62)
                        62) 62))] ptrx
                  * (data_at sh_modinfo
                       t_secp256k1_modinv64_modinfo
                       (make_modinfo m) modinfo
                       * 
                       (debruijn64_array sh_debruinj
                        gv
                        * (data_at
                        sh_SECP256K1_SIGNED62_ONE
                        t_secp256k1_modinv64_signed62
                        [Vlong
                        (Int64.repr (1 mod ...));
                        Vlong
                        (Int64.repr (... mod ...));
                        Vlong
                        (Int64.repr (... mod ...));
                        Vlong
                        (Int64.repr (... mod ...));
                        Vlong
                        (Int64.repr (Z.shiftr ... 62))]
                        (gv _SECP256K1_SIGNED62_ONE)
                        * emp)))))))
        |-- TT &&
            (TT &&
             (data_at shx
                t_secp256k1_modinv64_signed62
                [Vlong
                   (Int64.repr (modInv x m mod 2 ^ 62));
                 Vlong
                   (Int64.repr
                      (Z.shiftr (modInv x m) 62
                       mod 
                       2 ^ 62));
                 Vlong
                   (Int64.repr
                      (Z.shiftr
                        (Z.shiftr (modInv x m) 62) 62
                       mod 
                       2 ^ 62));
                 Vlong
                   (Int64.repr
                      (Z.shiftr
                        (Z.shiftr
                        (Z.shiftr (modInv x m) 62) 62)
                        62 mod 
                       2 ^ 62));
                 Vlong
                   (Int64.repr
                      (Z.shiftr
                        (Z.shiftr
                        (Z.shiftr
                        (Z.shiftr (modInv x m) 62) 62)
                        62) 62))] ptrx
                * (data_at sh_modinfo
                     t_secp256k1_modinv64_modinfo
                     (make_modinfo m) modinfo
                     * (debruijn64_array sh_debruinj
                        gv
                        * (data_at
                        sh_SECP256K1_SIGNED62_ONE
                        t_secp256k1_modinv64_signed62
                        [Vlong
                        (Int64.repr (1 mod 2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr 1 62 mod 2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr (Z.shiftr 1 62) 62
                        mod 
                        2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr 
                        (Z.shiftr (...) 62) 62
                        mod 
                        2 ^ 62));
                        Vlong
                        (Int64.repr
                        (Z.shiftr
                        (Z.shiftr (Z.shiftr ... 62) 62)
                        62))]
                        (gv _SECP256K1_SIGNED62_ONE)
                        * emp))))))


x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
1 < m < 2 ^ 256 /\ (x = 0 \/ rel_prime x m)


x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
1 < m < 2 ^ 256
x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
x = 0 \/ rel_prime x m


x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
1 < m < 2 ^ 256
 
x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
m <> 1

  
x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
Hm: m = 1
prime 1

  congruence.

x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
x = 0 \/ rel_prime x m
 
x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
Hx0: x <> 0
x = 0 \/ rel_prime x m

  
x, m: Z
ptrx, modinfo: val
shx, sh_modinfo, sh_debruinj, sh_SECP256K1_SIGNED62_ONE: share
gv: globals
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_modinv64_signed62;
       tptr t_secp256k1_modinv64_modinfo], tvoid))
H0: Z.Odd m
H1: 0 <= x < m
H2: m < 2 ^ 256
H3: prime m
H4: writable_share shx
H5: readable_share sh_modinfo
H6: readable_share sh_debruinj
H7: readable_share sh_SECP256K1_SIGNED62_ONE
H8: snd (g, args) = [ptrx; modinfo]
H9: gvars_denote gv
  (Clight_seplog.mkEnv (fst (g, args)) [] [])
Hx0: x <> 0
rel_prime x m

  apply rel_prime_le_prime;[assumption|lia].
Qed.
================================================ FILE: alectryon/verif_int128_impl.v.html ================================================ verif_int128_impl.v
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Require Import VST.floyd.proofauto.
Require Import jets_secp256k1.
Require Import spec_int128.
Require Import VST.msl.iter_sepcon.
Require Import extraMath.
Require Import progressC.

Opaque Z.shiftl Z.shiftr Z.pow.


varspecs
 mk_varspecs prog. Defined.

Definition secp256k1_umul128_spec : ident * funspec :=
DECLARE _secp256k1_umul128
  WITH a : Z, b : Z, hi : val, sh : share
PRE [ tulong, tulong, tptr tulong ]
  PROP(writable_share sh;
       0 <= a < Int64.modulus;
       0 <= b < Int64.modulus)
  PARAMS(Vlong (Int64.repr a); Vlong (Int64.repr b); hi)
  SEP(data_at_ sh tulong hi)
POST [ tulong ]
  PROP()
  RETURN(Vlong (Int64.repr (a * b)))
  SEP(data_at sh tulong (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi).

Definition secp256k1_mul128_spec : ident * funspec :=
DECLARE _secp256k1_mul128
  WITH a : Z, b : Z, hi : val, sh : share
  PRE [ tlong, tlong, tptr tlong ]
    PROP(writable_share sh;
         Int64.min_signed <= a <= Int64.max_signed;
         Int64.min_signed <= b <= Int64.max_signed)
    PARAMS(Vlong (Int64.repr a); Vlong (Int64.repr b); hi)
  SEP(data_at_ sh tlong hi)
POST [ tulong ]
  PROP()
  RETURN(Vlong (Int64.repr (a * b)))
  SEP(data_at sh tlong (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi).


B: Type
f: B -> mpred
x: B
l: list B
Hl: In x l
iter_sepcon f l = (f x * (f x -* iter_sepcon f l))%logic


B: Type
f: B -> mpred
x: B
l: list B
Hl: In x l
iter_sepcon f l = (f x * (f x -* iter_sepcon f l))%logic


B: Type
f: B -> mpred
x: B
l: list B
Hl: In x l
iter_sepcon f l |-- f x * (f x -* iter_sepcon f l)


B: Type
f: B -> mpred
x: B
l: list B
Hl: exists l' : list B, Permutation l (x :: l')
iter_sepcon f l |-- f x * (f x -* iter_sepcon f l)


B: Type
f: B -> mpred
x: B
l, l': list B
Hl': Permutation l (x :: l')
iter_sepcon f l |-- f x * (f x -* iter_sepcon f l)


B: Type
f: B -> mpred
x: B
l, l': list B
Hl': Permutation l (x :: l')
iter_sepcon f (x :: l')
|-- f x * (f x -* iter_sepcon f (x :: l'))


B: Type
f: B -> mpred
x: B
l, l': list B
Hl': Permutation l (x :: l')
f x * iter_sepcon f l'
|-- f x * (f x -* f x * iter_sepcon f l')


B: Type
f: B -> mpred
x: B
l, l': list B
Hl': Permutation l (x :: l')
iter_sepcon f l' |-- f x -* f x * iter_sepcon f l'

apply wand_frame_intro.
Qed.

Ltac unfold_Int128 :=
  unfold Int128_max_unsigned,
         Int128_max_signed,
         Int128_min_signed,
         Int128_modulus
  in *|-*.

Definition Gprog := ltac:(with_library prog
  [secp256k1_umul128_spec
  ;secp256k1_mul128_spec
(*   ;secp256k1_u128_load_spec *)
  ;secp256k1_u128_mul_spec
  ;secp256k1_u128_accum_mul_spec
  ;secp256k1_u128_accum_u64_spec
  ;secp256k1_u128_rshift_spec
  ;secp256k1_u128_to_u64_spec
  ;secp256k1_u128_hi_u64_spec
  ;secp256k1_u128_from_u64_spec
  ;secp256k1_u128_check_bits_spec
(*   ;secp256k1_i128_load_spec *)
  ;secp256k1_i128_mul_spec
  ;secp256k1_i128_accum_mul_spec
  ;secp256k1_i128_dissip_mul_spec
  ;secp256k1_i128_det_spec
  ;secp256k1_i128_rshift_spec
  ;secp256k1_i128_to_u64_spec
  ;secp256k1_i128_to_i64_spec
  ;secp256k1_i128_from_i64_spec
  ;secp256k1_i128_eq_var_spec
  ;secp256k1_i128_check_pow2_spec
  ]).


semax_body Vprog Gprog f_secp256k1_umul128
  secp256k1_umul128_spec


semax_body Vprog Gprog f_secp256k1_umul128
  secp256k1_umul128_spec


Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)); temp _hi hi)
   SEP (data_at_ sh tulong hi))
  (_ll = ((tulong) (tuint) _a * (tuint) _b);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Vlong
  (Int64.repr
     ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
         + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
         + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
        * 2 ^ 32
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) = 
Vlong (Int64.repr (a * b))
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr (a mod 2 ^ 32 * Z.shiftr b 32)
               32
           + Z.shiftr (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32 * (b mod 2 ^ 32))
                    mod 
                    2 ^ 32) 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi


Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Vlong
  (Int64.repr
     ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
         + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
         + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
        * 2 ^ 32
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) = 
Vlong (Int64.repr (a * b))
 
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Int64.repr
  ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
      + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
      + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
     * 2 ^ 32
     + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32) = 
Int64.repr (a * b)

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Int64.eqm
  ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
      + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
      + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
     * 2 ^ 32
     + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
  (Int64.unsigned (Int64.repr (a * b)))

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Int64.unsigned
  (Int64.repr
     ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
         + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
         + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
        * 2 ^ 32
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) = 
Int64.unsigned (Int64.repr (a * b))

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
    + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
    + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod Int64.modulus = (a * b) mod Int64.modulus

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
    + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
    + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
    + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32
    + (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * ((a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32)
   + 2 ^ 32
       * ((a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   + (2 ^ 32
        * (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32)
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32))
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * ((a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32)
   + 2 ^ 32
       * ((a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   + a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32)))
 mod (2 ^ 32 * 2 ^ 32)
   + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
     mod (2 ^ 32 * 2 ^ 32)
   + a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32)))
 mod (2 ^ 32 * 2 ^ 32)
   + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
     mod (2 ^ 32 * 2 ^ 32)
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 64)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32))) mod 2 ^ 64
   + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
     mod 2 ^ 64
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 64)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32))
   + ((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
      mod 2 ^ 64
        + a mod 2 ^ 32 * (b mod 2 ^ 32))) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32))) mod 2 ^ 64
   + a mod 2 ^ 32
       * (2 ^ 32 * (b / 2 ^ 32) + b mod 2 ^ 32))
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32))) mod 2 ^ 64
   + a mod 2 ^ 32 * b) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
 mod (2 ^ 32 * 2 ^ 32)
   + a mod 2 ^ 32 * b) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * (a / 2 ^ 32 * b) + a mod 2 ^ 32 * b)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32) + a mod 2 ^ 32) * b)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(a * b) mod 2 ^ 64 = (a * b) mod 2 ^ 64

  reflexivity.

Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr (a mod 2 ^ 32 * Z.shiftr b 32)
               32
           + Z.shiftr (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32 * (b mod 2 ^ 32))
                    mod 
                    2 ^ 32) 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi
 
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        (a / 2 ^ 32 * (b / 2 ^ 32)
           + a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32
           + a / 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
           + (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
                + (a mod 2 ^ 32 * (b / 2 ^ 32))
                  mod 2 ^ 32
                + (a / 2 ^ 32 * (b mod 2 ^ 32))
                  mod 2 ^ 32)
               / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        (((a / 2 ^ 32 * (b / 2 ^ 32)
             + a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32
             + a / 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32)
            * 2 ^ 32
            + (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
                 + (a mod 2 ^ 32 * (b / 2 ^ 32))
                   mod 2 ^ 32
                 + (a / 2 ^ 32 * (b mod 2 ^ 32))
                   mod 2 ^ 32))
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((2 ^ 32
            * (a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32)
            + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + (a / 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32))
                 + (2 ^ 32
                      * 
                      (a / 2 ^ 32 * (b mod 2 ^ 32)
                       / 2 ^ 32)
                      + 
                      (a / 2 ^ 32 * (b mod 2 ^ 32))
                      mod 
                      2 ^ 32)))
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * (b / 2 ^ 32)
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + (a / 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32))
                 + a / 2 ^ 32 * (b mod 2 ^ 32)))
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * (b / 2 ^ 32)
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + a / 2 ^ 32
                * (2 ^ 32 * (b / 2 ^ 32)
                     + b mod 2 ^ 32))
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * (b / 2 ^ 32)
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        (((a mod 2 ^ 32 * (b / 2 ^ 32) * 2 ^ 32
             + a mod 2 ^ 32 * (b mod 2 ^ 32))
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        (((a mod 2 ^ 32 * (b / 2 ^ 32 * 2 ^ 32)
             + a mod 2 ^ 32 * (b mod 2 ^ 32))
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32
            * (b / 2 ^ 32 * 2 ^ 32 + b mod 2 ^ 32)
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32
            * (2 ^ 32 * (b / 2 ^ 32) + b mod 2 ^ 32)
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * b / 2 ^ 32 + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a / 2 ^ 32 * b + a mod 2 ^ 32 * b / 2 ^ 32)
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((a / 2 ^ 32 * b * 2 ^ 32 + a mod 2 ^ 32 * b)
           / 2 ^ 32
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((2 ^ 32 * (a / 2 ^ 32) * b + a mod 2 ^ 32 * b)
           / 2 ^ 32
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong
     (Int64.repr
        ((2 ^ 32 * (a / 2 ^ 32) + a mod 2 ^ 32) * b
           / 2 ^ 32
           / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
PNhi: is_pointer_or_null hi
H1: field_compatible tulong [] hi
H2: tc_val' tulong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tulong
  (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32))) hi
|-- data_at sh tulong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_mul128
  secp256k1_mul128_spec


semax_body Vprog Gprog f_secp256k1_mul128
  secp256k1_mul128_spec


Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)); temp _hi hi)
   SEP (data_at_ sh tlong hi))
  (_ll = ((tulong) (tuint) _a * (tuint) _b);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Vlong
  (Int64.repr
     ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
         + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
         + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
        * 2 ^ 32
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) = 
Vlong (Int64.repr (a * b))
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr (a mod 2 ^ 32 * Z.shiftr b 32)
               32
           + Z.shiftr (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32 * (b mod 2 ^ 32))
                    mod 
                    2 ^ 32) 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi


Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Vlong
  (Int64.repr
     ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
         + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
         + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
        * 2 ^ 32
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) = 
Vlong (Int64.repr (a * b))
 
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Int64.repr
  ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
      + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
      + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
     * 2 ^ 32
     + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32) = 
Int64.repr (a * b)

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Int64.eqm
  ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
      + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
      + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
     * 2 ^ 32
     + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
  (Int64.unsigned (Int64.repr (a * b)))

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
Int64.unsigned
  (Int64.repr
     ((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
         + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
         + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
        * 2 ^ 32
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)) = 
Int64.unsigned (Int64.repr (a * b))

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
    + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
    + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod Int64.modulus = (a * b) mod Int64.modulus

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((Z.shiftr (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
    + (a mod 2 ^ 32 * Z.shiftr b 32) mod 2 ^ 32
    + (Z.shiftr a 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
    + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32
    + (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
    + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32
    + (a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   * 2 ^ 32
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * ((a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32)
   + 2 ^ 32
       * ((a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   + (2 ^ 32
        * (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32)
        + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32))
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * ((a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32)
   + 2 ^ 32
       * ((a / 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 32)
   + a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32)))
 mod (2 ^ 32 * 2 ^ 32)
   + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
     mod (2 ^ 32 * 2 ^ 32)
   + a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32)))
 mod (2 ^ 32 * 2 ^ 32)
   + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
     mod (2 ^ 32 * 2 ^ 32)
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 64)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32))) mod 2 ^ 64
   + (2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
     mod 2 ^ 64
   + (a mod 2 ^ 32 * (b mod 2 ^ 32)) mod 2 ^ 64)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * (a mod 2 ^ 32 * (b / 2 ^ 32))
   + ((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
      mod 2 ^ 64
        + a mod 2 ^ 32 * (b mod 2 ^ 32))) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32))) mod 2 ^ 64
   + a mod 2 ^ 32
       * (2 ^ 32 * (b / 2 ^ 32) + b mod 2 ^ 32))
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32))) mod 2 ^ 64
   + a mod 2 ^ 32 * b) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32 * (b mod 2 ^ 32)))
 mod (2 ^ 32 * 2 ^ 32)
   + a mod 2 ^ 32 * b) mod 
2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(2 ^ 32 * (a / 2 ^ 32 * b) + a mod 2 ^ 32 * b)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
((2 ^ 32 * (a / 2 ^ 32) + a mod 2 ^ 32) * b)
mod 2 ^ 64 = (a * b) mod 2 ^ 64

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
(a * b) mod 2 ^ 64 = (a * b) mod 2 ^ 64

  reflexivity.

Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr (a mod 2 ^ 32 * Z.shiftr b 32)
               32
           + Z.shiftr (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32)) 32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32 * (b mod 2 ^ 32))
                    mod 
                    2 ^ 32) 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (Z.shiftr (a * b) 64))) hi
 
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        (a / 2 ^ 32 * (b / 2 ^ 32)
           + a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32
           + a / 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
           + (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
                + (a mod 2 ^ 32 * (b / 2 ^ 32))
                  mod 2 ^ 32
                + (a / 2 ^ 32 * (b mod 2 ^ 32))
                  mod 2 ^ 32)
               / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        (((a / 2 ^ 32 * (b / 2 ^ 32)
             + a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32
             + a / 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32)
            * 2 ^ 32
            + (a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
                 + (a mod 2 ^ 32 * (b / 2 ^ 32))
                   mod 2 ^ 32
                 + (a / 2 ^ 32 * (b mod 2 ^ 32))
                   mod 2 ^ 32))
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((2 ^ 32
            * (a mod 2 ^ 32 * (b / 2 ^ 32) / 2 ^ 32)
            + (a mod 2 ^ 32 * (b / 2 ^ 32)) mod 2 ^ 32
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + (a / 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32))
                 + (2 ^ 32
                      * 
                      (a / 2 ^ 32 * (b mod 2 ^ 32)
                       / 2 ^ 32)
                      + 
                      (a / 2 ^ 32 * (b mod 2 ^ 32))
                      mod 
                      2 ^ 32)))
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * (b / 2 ^ 32)
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + (a / 2 ^ 32 * (2 ^ 32 * (b / 2 ^ 32))
                 + a / 2 ^ 32 * (b mod 2 ^ 32)))
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * (b / 2 ^ 32)
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + a / 2 ^ 32
                * (2 ^ 32 * (b / 2 ^ 32)
                     + b mod 2 ^ 32))
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * (b / 2 ^ 32)
            + a mod 2 ^ 32 * (b mod 2 ^ 32) / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        (((a mod 2 ^ 32 * (b / 2 ^ 32) * 2 ^ 32
             + a mod 2 ^ 32 * (b mod 2 ^ 32))
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        (((a mod 2 ^ 32 * (b / 2 ^ 32 * 2 ^ 32)
             + a mod 2 ^ 32 * (b mod 2 ^ 32))
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32
            * (b / 2 ^ 32 * 2 ^ 32 + b mod 2 ^ 32)
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32
            * (2 ^ 32 * (b / 2 ^ 32) + b mod 2 ^ 32)
            / 2 ^ 32
            + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a mod 2 ^ 32 * b / 2 ^ 32 + a / 2 ^ 32 * b)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a / 2 ^ 32 * b + a mod 2 ^ 32 * b / 2 ^ 32)
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((a / 2 ^ 32 * b * 2 ^ 32 + a mod 2 ^ 32 * b)
           / 2 ^ 32
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((2 ^ 32 * (a / 2 ^ 32) * b + a mod 2 ^ 32 * b)
           / 2 ^ 32
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong
     (Int64.repr
        ((2 ^ 32 * (a / 2 ^ 32) + a mod 2 ^ 32) * b
           / 2 ^ 32
           / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  
Espec: OracleKind
a, b: Z
hi: val
sh: share
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
PNhi: is_pointer_or_null hi
H1: field_compatible tlong [] hi
H2: tc_val' tlong
  (Vlong
     (Int64.repr
        (Z.shiftr a 32 * Z.shiftr b 32
           + Z.shiftr
               (a mod 2 ^ 32 * Z.shiftr b 32) 32
           + Z.shiftr
               (Z.shiftr a 32 * (b mod 2 ^ 32))
               32
           + Z.shiftr
               (Z.shiftr
                  (a mod 2 ^ 32 * (b mod 2 ^ 32))
                  32
                  + (a mod 2 ^ 32 * Z.shiftr b 32)
                    mod 
                    2 ^ 32
                  + (Z.shiftr a 32
                       * 
                       (b mod 2 ^ 32)) mod 
                    2 ^ 32) 32)))
data_at sh tlong
  (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32))) hi
|-- data_at sh tlong
      (Vlong (Int64.repr (a * b / 2 ^ 32 / 2 ^ 32)))
      hi

  entailer!.
Qed.

(*
Lemma body_secp256k1_u128_load: semax_body Vprog Gprog f_secp256k1_u128_load secp256k1_u128_load_spec.
Proof.
start_function.
repeat forward.
entailer!.
unfold secp256k1_uint128_at.
rewrite <- (Int64.repr_unsigned (Int64.repr (_ + lo))), Int64.unsigned_repr_eq.
rewrite Z.shiftl_mul_pow2, <- Zplus_mod_idemp_l, <- Zmult_mod_idemp_r, Z_mod_same_full by lia.
rewrite Z.mul_0_r, Z.add_0_l.
clear_mod.
rewrite Z.shiftr_div_pow2, Z.div_add_l by lia.
rewrite Z.div_small, Z.add_0_r by solve_bounds.
entailer!.
Qed.
*)


semax_body Vprog Gprog f_secp256k1_u128_mul
  secp256k1_u128_mul_spec


semax_body Vprog Gprog f_secp256k1_u128_mul
  secp256k1_u128_mul_spec


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ sh t_secp256k1_uint128 r))
  (_t'1 =
     _secp256k1_umul128
     ([(_a)%expr; (_b)%expr; (&(_r -> _hi))%expr]);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (field_at sh t_secp256k1_uint128 
          (DOT _lo)
          (fst
             (default_val
                (nested_field_type t_secp256k1_uint128
                   []))) r;
   field_at sh t_secp256k1_uint128 
     (DOT _hi)
     (snd
        (default_val
           (nested_field_type t_secp256k1_uint128 [])))
     r))
  (_t'1 =
     _secp256k1_umul128
     ([(_a)%expr; (_b)%expr; (&(_r -> _hi))%expr]);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (field_at sh t_secp256k1_uint128 
          (DOT _lo) Vundef r;
   field_at sh t_secp256k1_uint128 (DOT _hi) Vundef r))
  (_t'1 =
     _secp256k1_umul128
     ([(_a)%expr; (_b)%expr; (&(_r -> _hi))%expr]);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (field_at sh t_secp256k1_uint128 
          (DOT _lo) Vundef r;
   data_at sh
     (nested_field_type t_secp256k1_uint128 (DOT _hi))
     Vundef
     (field_address t_secp256k1_uint128 (DOT _hi) r)))
  (_t'1 =
     _secp256k1_umul128
     ([(_a)%expr; (_b)%expr; (&(_r -> _hi))%expr]);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
H1: field_compatible t_secp256k1_uint128 (DOT _hi) r
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (field_at sh t_secp256k1_uint128 
          (DOT _lo) Vundef r;
   data_at sh
     (nested_field_type t_secp256k1_uint128 (DOT _hi))
     Vundef
     (field_address t_secp256k1_uint128 (DOT _hi) r)))
  (_t'1 =
     _secp256k1_umul128
     ([(_a)%expr; (_b)%expr; (&(_r -> _hi))%expr]);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
H1: field_compatible t_secp256k1_uint128 (DOT _hi) r
semax Delta
  (PROP ( )
   LOCAL (temp _t'1 (Vlong (Int64.repr (a * b)));
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at sh tulong
          (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
          (field_address t_secp256k1_uint128 
             (DOT _hi) r);
   field_at sh t_secp256k1_uint128 (DOT _lo) Vundef r))
  ((_r -> _lo) = _t'1;) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
H1: field_compatible t_secp256k1_uint128 (DOT _hi) r
ENTAIL Delta,
PROP ( )
LOCAL (temp _t'1 (Vlong (Int64.repr (a * b)));
temp _r r; temp _a (Vlong (Int64.repr a));
temp _b (Vlong (Int64.repr b)))
SEP (data_at sh tulong
       (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
       (field_address t_secp256k1_uint128 (DOT _hi) r);
field_at sh t_secp256k1_uint128 
  (DOT _lo) (Vlong (Int64.repr (a * b))) r)
|-- PROP ( )
    RETURN ( ) SEP (secp256k1_uint128_at sh (a * b) r)


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
H1: field_compatible t_secp256k1_uint128 (DOT _hi) r
ENTAIL Delta,
PROP ( )
LOCAL (temp _t'1 (Vlong (Int64.repr (a * b)));
temp _r r; temp _a (Vlong (Int64.repr a));
temp _b (Vlong (Int64.repr b)))
SEP (data_at sh tulong
       (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
       (field_address t_secp256k1_uint128 (DOT _hi) r);
field_at sh t_secp256k1_uint128 
  (DOT _lo) (Vlong (Int64.repr (a * b))) r)
|-- PROP ( )
    RETURN ( ) SEP (data_at sh t_secp256k1_uint128
                      (Vlong (Int64.repr (a * b)),
                       Vlong
                       (Int64.repr
                       (Z.shiftr (a * b) 64))) r)


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
H1: field_compatible t_secp256k1_uint128 (DOT _hi) r
ENTAIL Delta,
PROP ( )
LOCAL (temp _t'1 (Vlong (Int64.repr (a * b)));
temp _r r; temp _a (Vlong (Int64.repr a));
temp _b (Vlong (Int64.repr b)))
SEP (data_at sh tulong
       (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
       (field_address t_secp256k1_uint128 (DOT _hi) r);
field_at sh t_secp256k1_uint128 
  (DOT _lo) (Vlong (Int64.repr (a * b))) r)
|-- PROP ( )
    RETURN ( ) SEP (field_at sh t_secp256k1_uint128
                      (DOT _lo)
                      (Vlong (Int64.repr (a * b))) r
                      * 
                      field_at sh t_secp256k1_uint128
                       (DOT _hi)
                       (Vlong
                       (Int64.repr
                       (Z.shiftr (a * b) 64))) r)

entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_accum_mul
  secp256k1_u128_accum_mul_spec


semax_body Vprog Gprog f_secp256k1_u128_accum_mul
  secp256k1_u128_accum_mul_spec


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tulong v_hi; temp _r r;
   temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tulong v_hi;
   secp256k1_uint128_at sh r0 r))
  ((_t'1 =
      _secp256k1_umul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: 0 <= a < Int64.modulus
H0: 0 <= b < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tulong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tulong
          (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
          v_hi; secp256k1_uint128_at sh r0 r))
  ((_t'5 = (_r -> _lo);
    (_r -> _lo) = (_t'5 + _lo);)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + (Z.shiftr (a * b) 64
                + Z.b2z
                    ((r0 + a * b) mod 2 ^ 64 <?
                     (a * b) mod 2 ^ 64))))) r
|-- secp256k1_uint128_at sh (r0 + a * b) r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + (Z.shiftr (a * b) 64
                + Z.b2z
                    ((r0 + a * b) mod 2 ^ 64 <?
                     (a * b) mod 2 ^ 64))))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64)))
      r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64 + Z.shiftr (a * b) 64
           + Z.b2z
               ((r0 + a * b) mod 2 ^ 64 <?
                (a * b) mod 2 ^ 64)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64)))
      r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: 0 <= a < 2 ^ 64
H0: 0 <= b < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64)))
      r

entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_accum_u64
  secp256k1_u128_accum_u64_spec


semax_body Vprog Gprog f_secp256k1_u128_accum_u64
  secp256k1_u128_accum_u64_spec


Espec: OracleKind
r: val
sh: share
r0, a: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a)))
   SEP (secp256k1_uint128_at sh r0 r))
  ((_t'3 = (_r -> _lo);
    (_r -> _lo) = (_t'3 + _a);)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + Z.b2z ((r0 + a) mod 2 ^ 64 <? a)))) r
|-- secp256k1_uint128_at sh (r0 + a) r


Espec: OracleKind
r: val
sh: share
r0, a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + Z.b2z ((r0 + a) mod 2 ^ 64 <? a)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a)),
       Vlong (Int64.repr (Z.shiftr (r0 + a) 64))) r


Espec: OracleKind
r: val
sh: share
r0, a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + Z.b2z ((r0 + a) mod 2 ^ 64 <? a)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a)),
       Vlong
         (Int64.repr
            (Z.shiftr r0 64 + Z.shiftr a 64
               + Z.b2z
                   ((r0 + a) mod 2 ^ 64 <?
                    a mod 2 ^ 64)))) r


Espec: OracleKind
r: val
sh: share
r0, a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + Z.b2z ((r0 + a) mod 2 ^ 64 <? a)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a)),
       Vlong
         (Int64.repr
            (Z.shiftr r0 64
               + Z.b2z ((r0 + a) mod 2 ^ 64 <? a)))) r

entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_rshift
  secp256k1_u128_rshift_spec


semax_body Vprog Gprog f_secp256k1_u128_rshift
  secp256k1_u128_rshift_spec


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     if (!(_n < (128))) {
       for (;
       ;
       break;) {
         ((_t'5 = _stderr;
           _fprintf
             ([(_t'5)%expr; (___stringlit_6)%expr;
               (___stringlit_159)%expr; ((79))%expr;
               (___stringlit_158)%expr]);)
          _abort([]);)
       }
     }
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
H1: Int.repr
  (Z.b2z (Int.ltu (Int.repr n) (Int.repr 128))) = Int.zero
False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (Int.ltu (Int.repr n) (Int.repr 128))) = Int.zero ->
False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 128)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 128)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < Int128_modulus
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (data_at sh t_secp256k1_uint128
                       (Vlong
                       (Int64.repr (Z.shiftr r0 n)),
                       Vlong
                       (Int64.repr
                       (Z.shiftr (Z.shiftr r0 n) 64)))
                       r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     ((_t'4 = (_r -> _hi);
       (_r -> _lo) = _t'4 >> (_n - (64));)
      (_r -> _hi) = (0);)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = _t'1 >> _n;)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (data_at sh t_secp256k1_uint128
                       (Vlong
                       (Int64.repr (Z.shiftr r0 n)),
                       Vlong
                       (Int64.repr
                       (Z.shiftr (Z.shiftr r0 n) 64)))
                       r)
        * stackframe_of f_secp256k1_u128_rshift)%logic)


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr (Z.shiftr (Z.shiftr r0 64) (n - 64))),
   Vlong (Int64.repr 0)) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 64) n))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr (Z.shiftr (Z.shiftr r0 64) (n - 64))),
   Vlong (Int64.repr 0)) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 (64 + (n - 64)))),
   Vlong (Int64.repr 0)) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 n)),
   Vlong (Int64.repr 0)) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
0 <= r0 < 2 ^ (n + 64)

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
0 <= r0 < 2 ^ 128 -> 0 <= r0 < 2 ^ (n + 64)

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n >= 64
H2: 2 ^ 128 <= 2 ^ (n + 64)
0 <= r0 < 2 ^ 128 -> 0 <= r0 < 2 ^ (n + 64)

  lia.

Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 64) n))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr r0 (64 + n)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
Int64.repr (Z.shiftr r0 n) = 
Int64.repr
  (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
Int64.repr (Z.shiftr r0 n) = 
Int64.repr
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
Int64.eqm (Z.shiftr r0 n)
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
forall i : Z,
0 <= i < Int64.zwordsize ->
Z.testbit (Z.shiftr r0 n) i = 
Z.testbit
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n)) i

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
forall i : Z,
0 <= i < 64 ->
Z.testbit (Z.shiftr r0 n) i = 
Z.testbit
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n)) i

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Z.testbit (Z.shiftr r0 n) i = 
Z.testbit
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n)) i

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (false
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (false || Z.testbit r0 (i + n))%bool

    reflexivity.
  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit r0
                       (i - (64 - n) + 64)
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = Z.testbit r0
                       (i - (64 - n) + 64)

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = Z.testbit r0 (i + n)

    reflexivity.

Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 0)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 0) 64))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr r0),
       Vlong (Int64.repr (Z.shiftr r0 64))) r

  entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_to_u64
  secp256k1_u128_to_u64_spec


semax_body Vprog Gprog f_secp256k1_u128_to_u64
  secp256k1_u128_to_u64_spec


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = (_a -> _lo);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'1 = (_a -> _lo);
   MORE_COMMANDS) POSTCONDITION

repeat progressC.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_hi_u64
  secp256k1_u128_hi_u64_spec


semax_body Vprog Gprog f_secp256k1_u128_hi_u64
  secp256k1_u128_hi_u64_spec


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = (_a -> _hi);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'1 = (_a -> _hi);
   MORE_COMMANDS) POSTCONDITION

repeat progressC.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_from_u64
  secp256k1_u128_from_u64_spec


semax_body Vprog Gprog f_secp256k1_u128_from_u64
  secp256k1_u128_from_u64_spec


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: 0 <= a < Int64.modulus
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a)))
   SEP (data_at_ sh t_secp256k1_uint128 r))
  ((_r -> _hi) = (0);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a), Vlong (Int64.repr 0)) r
|-- secp256k1_uint128_at sh a r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a), Vlong (Int64.repr 0)) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (Z.shiftr a 64))) r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: 0 <= a < 2 ^ 64
0 = Z.shiftr a 64

symmetry; auto using shiftr_small.
Qed.


semax_body Vprog Gprog f_secp256k1_u128_check_bits
  secp256k1_u128_check_bits_spec


semax_body Vprog Gprog f_secp256k1_u128_check_bits
  secp256k1_u128_check_bits_spec


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     if (!(_n < (128))) {
       for (;
       ;
       break;) {
         ((_t'5 = _stderr;
           _fprintf
             ([(_t'5)%expr; (___stringlit_6)%expr;
               (___stringlit_159)%expr; ((103))%expr;
               (___stringlit_158)%expr]);)
          _abort([]);)
       }
     }
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
H1: Int.repr
  (Z.b2z (Int.ltu (Int.repr n) (Int.repr 128))) = Int.zero
False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (Int.ltu (Int.repr n) (Int.repr 128))) = Int.zero ->
False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 128)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 128)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     (_t'4 = (_r -> _hi);
      _t'1 = (tint) (_t'4 >> (_n - (64)) == (0));)
   } else {
     (_t'2 = (_r -> _hi);
      if (_t'2 == (0)) {
        ((_t'3 = (_r -> _lo);
          _t'1 = (tbool) (_t'3 >> _n == (0));)
         _t'1 = (tint) _t'1;)
      } else {
        _t'1 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'2 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n >= 64
Vint (Int.repr (Z.b2z (r0 <? 2 ^ n))) = 
Vint
  (Int.repr
     (Z.b2z (Z.shiftr (Z.shiftr r0 64) (n - 64) =? 0)))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n >= 64
(r0 <? 2 ^ n) = (Z.shiftr (Z.shiftr r0 64) (n - 64) =?
                 0)

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n >= 64
(r0 <? 2 ^ n) = (Z.shiftr r0 (64 + (n - 64)) =? 0)

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n >= 64
(r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)

  assumption.

Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'2 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) = Int64.zero
Vint (Int.repr (Z.b2z (r0 <? 2 ^ n))) = 
Vint
  (Int.repr (Z.b2z (Z.shiftr (r0 mod 2 ^ 64) n =? 0)))
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Vint (Int.repr (Z.b2z (r0 <? 2 ^ n))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) = Int64.zero
Vint (Int.repr (Z.b2z (r0 <? 2 ^ n))) = 
Vint
  (Int.repr (Z.b2z (Z.shiftr (r0 mod 2 ^ 64) n =? 0)))
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) = Int64.zero
Vint (Int.repr (Z.b2z (Z.shiftr r0 n =? 0))) = 
Vint
  (Int.repr (Z.b2z (Z.shiftr (r0 mod 2 ^ 64) n =? 0)))

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) = Int64.zero
Vint
  (Int.repr
     (Z.b2z
        (Z.shiftr
           (2 ^ 64 * (r0 / 2 ^ 64) + r0 mod 2 ^ 64) n =?
         0))) = Vint
                  (Int.repr
                     (Z.b2z
                       (Z.shiftr (r0 mod 2 ^ 64) n =?
                       0)))

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) = Int64.zero
Vint
  (Int.repr
     (Z.b2z
        (Z.shiftr
           (2 ^ 64 * Z.shiftr r0 64 + r0 mod 2 ^ 64) n =?
         0))) = Vint
                  (Int.repr
                     (Z.b2z
                       (Z.shiftr (r0 mod 2 ^ 64) n =?
                       0)))

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.unsigned (Int64.repr (Z.shiftr r0 64)) = 
Int64.unsigned Int64.zero
Vint
  (Int.repr
     (Z.b2z
        (Z.shiftr
           (2 ^ 64 * Z.shiftr r0 64 + r0 mod 2 ^ 64) n =?
         0))) = Vint
                  (Int.repr
                     (Z.b2z
                       (Z.shiftr (r0 mod 2 ^ 64) n =?
                       0)))

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
Vint
  (Int.repr
     (Z.b2z
        (Z.shiftr (2 ^ 64 * 0 + r0 mod 2 ^ 64) n =? 0))) = 
Vint
  (Int.repr (Z.b2z (Z.shiftr (r0 mod 2 ^ 64) n =? 0)))

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
Vint
  (Int.repr (Z.b2z (Z.shiftr (r0 mod 2 ^ 64) n =? 0))) = 
Vint
  (Int.repr (Z.b2z (Z.shiftr (r0 mod 2 ^ 64) n =? 0)))

    reflexivity.
  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Vint (Int.repr (Z.b2z (r0 <? 2 ^ n))) = 
Vint (Int.repr 0)
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Vint (Int.repr (Z.b2z (Z.shiftr r0 n =? 0))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Z.shiftr r0 n = 0 ->
Vint (Int.repr (Z.b2z true)) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Hr0: Z.shiftr r0 n = 0
Vint (Int.repr (Z.b2z true)) = Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Hr0: Z.shiftr r0 n = 0
Int64.repr (Z.shiftr r0 64) = Int64.repr 0

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Hr0: Z.shiftr r0 n = 0
Int64.repr (Z.shiftr r0 (n + (64 - n))) = Int64.repr 0

    
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: 0 <= r0 < 2 ^ 128
H0: 0 <= n < 128
shiftr_small_eq: (r0 <? 2 ^ n) = (Z.shiftr r0 n =? 0)
H1: n < 64
H2: Int64.repr (Z.shiftr r0 64) <> Int64.repr 0
Hr0: Z.shiftr r0 n = 0
Int64.repr 0 = Int64.repr 0

    reflexivity.
Qed.

(*
Lemma body_secp256k1_i128_load: semax_body Vprog Gprog f_secp256k1_i128_load secp256k1_i128_load_spec.
Proof.
start_function.
repeat forward.
entailer!.
unfold secp256k1_uint128_at.
rewrite <- (Int64.repr_unsigned (Int64.repr (_ + lo))), Int64.unsigned_repr_eq.
rewrite Z.shiftl_mul_pow2, <- Zplus_mod_idemp_l, <- Zmult_mod_idemp_r, Z_mod_same_full by lia.
rewrite Z.mul_0_r, Z.add_0_l.
clear_mod.
rewrite Z.shiftr_div_pow2, Z.div_add_l by lia.
rewrite Z.div_small, Z.add_0_r by solve_bounds.
entailer!.
Qed.
*)


semax_body Vprog Gprog f_secp256k1_i128_mul
  secp256k1_i128_mul_spec


semax_body Vprog Gprog f_secp256k1_i128_mul
  secp256k1_i128_mul_spec


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; temp _r r;
   temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   data_at_ sh t_secp256k1_uint128 r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    (_r -> _lo) = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'1 (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
          v_hi; data_at_ sh t_secp256k1_uint128 r))
  ((_r -> _lo) = _t'1;
   MORE_COMMANDS) POSTCONDITION

repeat progressC.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_accum_mul
  secp256k1_i128_accum_mul_spec


semax_body Vprog Gprog f_secp256k1_i128_accum_mul
  secp256k1_i128_accum_mul_spec


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int128_min_signed <= r0 <= Int128_max_signed
H2: Int128_min_signed <= r0 + a * b <=
Int128_max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; temp _r r;
   temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   secp256k1_uint128_at sh r0 r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int128_min_signed <= r0 <= Int128_max_signed
H2: Int128_min_signed <= r0 + a * b <=
Int128_max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
          v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'18 = (_r -> _lo);
    (_r -> _lo) = (_t'18 + _lo);)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'14 = (_r -> _hi);
       if (_t'14 <= (9223372036854775807)LL) {
         (_t'15 = _hi;
          _t'2 =
            (tbool) ((tulong) _t'15
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'2 = (0);
       })
      _t'11 = (_r -> _hi);
      _t'12 = _hi;
      if (!(_t'2
              <= (_t'11 + (tulong) _t'12
                    <= (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'13 = _stderr;
            _fprintf
              ([(_t'13)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((129))%expr; 
                (___stringlit_160)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'14 = (_r -> _hi);
    if (_t'14 <= (9223372036854775807)LL) {
      (_t'15 = _hi;
       _t'2 =
         (tbool) ((tulong) _t'15
                    <= (9223372036854775807)LL);)
    } else {
      _t'2 = (0);
    })
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'14
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'14 <= (9223372036854775807)LL) {
     (_t'15 = _hi;
      _t'2 =
        (tbool) ((tulong) _t'15
                   <= (9223372036854775807)LL);)
   } else {
     _t'2 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
semax Delta
  (PROP ( )
   LOCAL (temp _t'14
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'14 <= (9223372036854775807)LL) {
     (_t'15 = _hi;
      _t'2 =
        (tbool) ((tulong) _t'15
                   <= (9223372036854775807)LL);)
   } else {
     _t'2 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Int.repr
  (Z.b2z
     (negb
        ((Z.shiftr r0 64 mod 2 ^ 64 <=?
          9223372036854775807) &&
         (hi mod 2 ^ 64 <=? 9223372036854775807))
      || negb
           (9223372036854775807 <?
            (Z.shiftr r0 64 + hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'12 (Vlong (Int64.repr hi));
   temp _t'11 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2
     (Vint
        (Int.repr
           (Z.b2z
              ((Z.shiftr r0 64 mod 2 ^ 64 <=?
                9223372036854775807) &&
               (hi mod 2 ^ 64 <=? 9223372036854775807)))));
   temp _t'14 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'13 = _stderr;
       _fprintf
         ([(_t'13)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((129))%expr; 
           (___stringlit_160)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Z.shiftr r0 64 mod 2 ^ 64 <= 9223372036854775807
Int.repr
  (Z.b2z
     (negb
        (true &&
         (hi mod 2 ^ 64 <=? 9223372036854775807))
      || negb
           (9223372036854775807 <?
            (Z.shiftr r0 64 + hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'12 (Vlong (Int64.repr hi));
   temp _t'11 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2
     (Vint
        (Int.repr
           (Z.b2z
              (true &&
               (hi mod 2 ^ 64 <=? 9223372036854775807)))));
   temp _t'14 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'13 = _stderr;
       _fprintf
         ([(_t'13)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((129))%expr; 
           (___stringlit_160)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Z.shiftr r0 64 mod 2 ^ 64 <= 9223372036854775807
Hhi: hi mod 2 ^ 64 <= 9223372036854775807
Int.repr
  (Z.b2z
     (negb (true && true)
      || negb
           (9223372036854775807 <?
            (Z.shiftr r0 64 + hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'12 (Vlong (Int64.repr hi));
   temp _t'11 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'14 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'13 = _stderr;
       _fprintf
         ([(_t'13)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((129))%expr; 
           (___stringlit_160)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Z.shiftr r0 64 mod 2 ^ 64 <= 9223372036854775807
Hhi: hi mod 2 ^ 64 <= 9223372036854775807
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 + hi) mod 2 ^ 64
Int.repr (Z.b2z (negb (true && true) || negb true)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'12 (Vlong (Int64.repr hi));
   temp _t'11 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'14 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'13 = _stderr;
       _fprintf
         ([(_t'13)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((129))%expr; 
           (___stringlit_160)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: hi mod 2 ^ 64 <= 9223372036854775807
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 + hi) mod 2 ^ 64
Int.repr (Z.b2z (negb (true && true) || negb true)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'12 (Vlong (Int64.repr hi));
   temp _t'11 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'14 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'13 = _stderr;
       _fprintf
         ([(_t'13)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((129))%expr; 
           (___stringlit_160)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 + hi) mod 2 ^ 64
Int.repr (Z.b2z (negb (true && true) || negb true)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'12 (Vlong (Int64.repr hi));
   temp _t'11 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'14 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'13 = _stderr;
       _fprintf
         ([(_t'13)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((129))%expr; 
           (___stringlit_160)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 + hi) mod 2 ^ 64
Int64.min_signed <= Z.shiftr r0 64 + hi <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 + hi) mod 2 ^ 64
Int64.min_signed <=
Z.shiftr r0 64
  + (Z.shiftr (a * b) 64
       + Z.b2z
           ((r0 + a * b) mod 2 ^ 64 <?
            (a * b) mod 2 ^ 64)) <= Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 + hi) mod 2 ^ 64
Int64.min_signed <= Z.shiftr (r0 + a * b) 64 <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'9 = (_r -> _hi);
       if (_t'9 > (9223372036854775807)LL) {
         (_t'10 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'10
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'6 = (_r -> _hi);
      _t'7 = _hi;
      if (!(_t'3
              <= (_t'6 + (tulong) _t'7
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'8 = _stderr;
            _fprintf
              ([(_t'8)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((134))%expr; 
                (___stringlit_161)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'9 = (_r -> _hi);
    if (_t'9 > (9223372036854775807)LL) {
      (_t'10 = _hi;
       _t'3 =
         (tbool) ((tulong) _t'10
                    > (9223372036854775807)LL);)
    } else {
      _t'3 = (0);
    })
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'9
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'9 > (9223372036854775807)LL) {
     (_t'10 = _hi;
      _t'3 =
        (tbool) ((tulong) _t'10
                   > (9223372036854775807)LL);)
   } else {
     _t'3 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
semax Delta
  (PROP ( )
   LOCAL (temp _t'9
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'9 > (9223372036854775807)LL) {
     (_t'10 = _hi;
      _t'3 =
        (tbool) ((tulong) _t'10
                   > (9223372036854775807)LL);)
   } else {
     _t'3 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Int.repr
  (Z.b2z
     (negb
        ((2 ^ 63 - 1 <? Z.shiftr r0 64 mod 2 ^ 64) &&
         (2 ^ 63 - 1 <? hi mod 2 ^ 64))
      || (9223372036854775807 <?
          (Z.shiftr r0 64 + hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'7 (Vlong (Int64.repr hi));
   temp _t'6 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3
     (Vint
        (Int.repr
           (Z.b2z
              ((2 ^ 63 - 1 <?
                Z.shiftr r0 64 mod 2 ^ 64) &&
               (2 ^ 63 - 1 <? hi mod 2 ^ 64)))));
   temp _t'9 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'8 = _stderr;
       _fprintf
         ([(_t'8)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((134))%expr; 
           (___stringlit_161)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 2 ^ 63 - 1 < Z.shiftr r0 64 mod 2 ^ 64
Int.repr
  (Z.b2z
     (negb (true && (2 ^ 63 - 1 <? hi mod 2 ^ 64))
      || (9223372036854775807 <?
          (Z.shiftr r0 64 + hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'7 (Vlong (Int64.repr hi));
   temp _t'6 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3
     (Vint
        (Int.repr
           (Z.b2z
              (true && (2 ^ 63 - 1 <? hi mod 2 ^ 64)))));
   temp _t'9 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'8 = _stderr;
       _fprintf
         ([(_t'8)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((134))%expr; 
           (___stringlit_161)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 2 ^ 63 - 1 < Z.shiftr r0 64 mod 2 ^ 64
Hhi: 2 ^ 63 - 1 < hi mod 2 ^ 64
Int.repr
  (Z.b2z
     (negb (true && true)
      || (9223372036854775807 <?
          (Z.shiftr r0 64 + hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'7 (Vlong (Int64.repr hi));
   temp _t'6 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'9 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'8 = _stderr;
       _fprintf
         ([(_t'8)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((134))%expr; 
           (___stringlit_161)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: 2 ^ 63 - 1 < Z.shiftr r0 64 mod 2 ^ 64
Hhi: 2 ^ 63 - 1 < hi mod 2 ^ 64
Hr0hi: (Z.shiftr r0 64 + hi) mod 2 ^ 64
  <= 9223372036854775807
Int.repr (Z.b2z (negb (true && true) || false)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'7 (Vlong (Int64.repr hi));
   temp _t'6 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'9 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'8 = _stderr;
       _fprintf
         ([(_t'8)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((134))%expr; 
           (___stringlit_161)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: 2 ^ 63 - 1 < hi mod 2 ^ 64
Hr0hi: (Z.shiftr r0 64 + hi) mod 2 ^ 64
  <= 9223372036854775807
Int.repr (Z.b2z (negb (true && true) || false)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'7 (Vlong (Int64.repr hi));
   temp _t'6 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'9 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'8 = _stderr;
       _fprintf
         ([(_t'8)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((134))%expr; 
           (___stringlit_161)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: Int64.min_signed <= hi < 0
Hr0hi: (Z.shiftr r0 64 + hi) mod 2 ^ 64
  <= 9223372036854775807
Int.repr (Z.b2z (negb (true && true) || false)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'7 (Vlong (Int64.repr hi));
   temp _t'6 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'9 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'8 = _stderr;
       _fprintf
         ([(_t'8)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((134))%expr; 
           (___stringlit_161)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: Int64.min_signed <= hi < 0
Hr0hi: (Z.shiftr r0 64 + hi) mod 2 ^ 64
  <= 9223372036854775807
Int64.min_signed <= Z.shiftr r0 64 + hi <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: Int64.min_signed <= hi < 0
Hr0hi: (Z.shiftr r0 64 + hi) mod 2 ^ 64
  <= 9223372036854775807
Int64.min_signed <=
Z.shiftr r0 64
  + (Z.shiftr (a * b) 64
       + Z.b2z
           ((r0 + a * b) mod 2 ^ 64 <?
            (a * b) mod 2 ^ 64)) <= Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z
      ((r0 + a * b) mod 2 ^ 64 <?
       (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: Int64.min_signed <= hi < 0
Hr0hi: (Z.shiftr r0 64 + hi) mod 2 ^ 64
  <= 9223372036854775807
Int64.min_signed <= Z.shiftr (r0 + a * b) 64 <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'17 (Vlong (Int64.repr (r0 + a * b)));
   temp _t'16
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       ((r0 + a * b) mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr (r0 + a * b)),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'4 = (_r -> _hi);
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 + a * b) r)
        * stackframe_of f_secp256k1_i128_accum_mul)%logic)


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + (Z.shiftr (a * b) 64
                + Z.b2z
                    ((r0 + a * b) mod 2 ^ 64 <?
                     (a * b) mod 2 ^ 64))))) r
|-- secp256k1_uint128_at sh (r0 + a * b) r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           + (Z.shiftr (a * b) 64
                + Z.b2z
                    ((r0 + a * b) mod 2 ^ 64 <?
                     (a * b) mod 2 ^ 64))))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64)))
      r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 + a * b <= 2 ^ 127 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 + a * b)),
   Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 + a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 + a * b) 64)))
      r

entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_dissip_mul
  secp256k1_i128_dissip_mul_spec


semax_body Vprog Gprog f_secp256k1_i128_dissip_mul
  secp256k1_i128_dissip_mul_spec


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int128_min_signed <= r0 <= Int128_max_signed
H2: Int128_min_signed <= r0 - a * b <=
Int128_max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; temp _r r;
   temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   secp256k1_uint128_at sh r0 r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int128_min_signed <= r0 <= Int128_max_signed
H2: Int128_min_signed <= r0 - a * b <=
Int128_max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at_ Tsh tlong v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'1 =
      _secp256k1_mul128
      ([(_a)%expr; (_b)%expr; (&_hi)%expr]);
    _lo = _t'1;)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong (Int64.repr (Z.shiftr (a * b) 64)))
          v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'17 = _hi;
    _t'18 = (_r -> _lo);
    _hi = (_t'17 + (_t'18 < _lo));)
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'15 = (_r -> _hi);
       if (_t'15 <= (9223372036854775807)LL) {
         (_t'16 = _hi;
          _t'2 =
            (tbool) ((tulong) _t'16
                       > 
                       (9223372036854775807)LL);)
       } else {
         _t'2 = (0);
       })
      _t'12 = (_r -> _hi);
      _t'13 = _hi;
      if (!(_t'2
              <= (_t'12 - (tulong) _t'13
                    <= (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'14 = _stderr;
            _fprintf
              ([(_t'14)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((146))%expr; 
                (___stringlit_162)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'15 = (_r -> _hi);
    if (_t'15 <= (9223372036854775807)LL) {
      (_t'16 = _hi;
       _t'2 =
         (tbool) ((tulong) _t'16
                    > (9223372036854775807)LL);)
    } else {
      _t'2 = (0);
    })
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'15
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'15 <= (9223372036854775807)LL) {
     (_t'16 = _hi;
      _t'2 =
        (tbool) ((tulong) _t'16
                   > (9223372036854775807)LL);)
   } else {
     _t'2 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
semax Delta
  (PROP ( )
   LOCAL (temp _t'15
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'15 <= (9223372036854775807)LL) {
     (_t'16 = _hi;
      _t'2 =
        (tbool) ((tulong) _t'16
                   > (9223372036854775807)LL);)
   } else {
     _t'2 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Int.repr
  (Z.b2z
     (negb
        ((Z.shiftr r0 64 mod 2 ^ 64 <=? 2 ^ 63 - 1) &&
         (2 ^ 63 - 1 <? hi mod 2 ^ 64))
      || negb
           (9223372036854775807 <?
            (Z.shiftr r0 64 - hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'13 (Vlong (Int64.repr hi));
   temp _t'12 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2
     (Vint
        (Int.repr
           (Z.b2z
              ((Z.shiftr r0 64 mod 2 ^ 64 <=?
                2 ^ 63 - 1) &&
               (2 ^ 63 - 1 <? hi mod 2 ^ 64)))));
   temp _t'15 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'14 = _stderr;
       _fprintf
         ([(_t'14)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((146))%expr; 
           (___stringlit_162)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Z.shiftr r0 64 mod 2 ^ 64 <= 2 ^ 63 - 1
Int.repr
  (Z.b2z
     (negb (true && (2 ^ 63 - 1 <? hi mod 2 ^ 64))
      || negb
           (9223372036854775807 <?
            (Z.shiftr r0 64 - hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'13 (Vlong (Int64.repr hi));
   temp _t'12 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2
     (Vint
        (Int.repr
           (Z.b2z
              (true && (2 ^ 63 - 1 <? hi mod 2 ^ 64)))));
   temp _t'15 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'14 = _stderr;
       _fprintf
         ([(_t'14)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((146))%expr; 
           (___stringlit_162)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Z.shiftr r0 64 mod 2 ^ 64 <= 2 ^ 63 - 1
Hhi: 2 ^ 63 - 1 < hi mod 2 ^ 64
Int.repr
  (Z.b2z
     (negb (true && true)
      || negb
           (9223372036854775807 <?
            (Z.shiftr r0 64 - hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'13 (Vlong (Int64.repr hi));
   temp _t'12 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'15 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'14 = _stderr;
       _fprintf
         ([(_t'14)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((146))%expr; 
           (___stringlit_162)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Z.shiftr r0 64 mod 2 ^ 64 <= 2 ^ 63 - 1
Hhi: 2 ^ 63 - 1 < hi mod 2 ^ 64
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 - hi) mod 2 ^ 64
Int.repr (Z.b2z (negb (true && true) || negb true)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'13 (Vlong (Int64.repr hi));
   temp _t'12 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'15 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'14 = _stderr;
       _fprintf
         ([(_t'14)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((146))%expr; 
           (___stringlit_162)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: 2 ^ 63 - 1 < hi mod 2 ^ 64
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 - hi) mod 2 ^ 64
Int.repr (Z.b2z (negb (true && true) || negb true)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'13 (Vlong (Int64.repr hi));
   temp _t'12 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'15 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'14 = _stderr;
       _fprintf
         ([(_t'14)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((146))%expr; 
           (___stringlit_162)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: Int64.min_signed <= hi < 0
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 - hi) mod 2 ^ 64
Int.repr (Z.b2z (negb (true && true) || negb true)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'13 (Vlong (Int64.repr hi));
   temp _t'12 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'2 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'15 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'14 = _stderr;
       _fprintf
         ([(_t'14)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((146))%expr; 
           (___stringlit_162)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: Int64.min_signed <= hi < 0
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 - hi) mod 2 ^ 64
Int64.min_signed <= Z.shiftr r0 64 - hi <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: Int64.min_signed <= hi < 0
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 - hi) mod 2 ^ 64
Int64.min_signed <=
Z.shiftr r0 64
  - (Z.shiftr (a * b) 64
       + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64)) <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 0 <= Z.shiftr r0 64 <= Int64.max_signed
Hhi: Int64.min_signed <= hi < 0
Hr0hi: 9223372036854775807
  < (Z.shiftr r0 64 - hi) mod 2 ^ 64
Int64.min_signed <= Z.shiftr (r0 - a * b) 64 <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   break;) {
     ((_t'10 = (_r -> _hi);
       if (_t'10 > (9223372036854775807)LL) {
         (_t'11 = _hi;
          _t'3 =
            (tbool) ((tulong) _t'11
                       <= 
                       (9223372036854775807)LL);)
       } else {
         _t'3 = (0);
       })
      _t'7 = (_r -> _hi);
      _t'8 = _hi;
      if (!(_t'3
              <= (_t'7 - (tulong) _t'8
                    > (9223372036854775807)LL))) {
        for (;
        ;
        break;) {
          ((_t'9 = _stderr;
            _fprintf
              ([(_t'9)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((151))%expr; 
                (___stringlit_163)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'10 = (_r -> _hi);
    if (_t'10 > (9223372036854775807)LL) {
      (_t'11 = _hi;
       _t'3 =
         (tbool) ((tulong) _t'11
                    <= (9223372036854775807)LL);)
    } else {
      _t'3 = (0);
    })
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'10
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'10 > (9223372036854775807)LL) {
     (_t'11 = _hi;
      _t'3 =
        (tbool) ((tulong) _t'11
                   <= (9223372036854775807)LL);)
   } else {
     _t'3 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
semax Delta
  (PROP ( )
   LOCAL (temp _t'10
            (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_t'10 > (9223372036854775807)LL) {
     (_t'11 = _hi;
      _t'3 =
        (tbool) ((tulong) _t'11
                   <= (9223372036854775807)LL);)
   } else {
     _t'3 = (0);
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Int.repr
  (Z.b2z
     (negb
        ((2 ^ 63 - 1 <? Z.shiftr r0 64 mod 2 ^ 64) &&
         (hi mod 2 ^ 64 <=? 2 ^ 63 - 1))
      || (9223372036854775807 <?
          (Z.shiftr r0 64 - hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'8 (Vlong (Int64.repr hi));
   temp _t'7 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3
     (Vint
        (Int.repr
           (Z.b2z
              ((2 ^ 63 - 1 <?
                Z.shiftr r0 64 mod 2 ^ 64) &&
               (hi mod 2 ^ 64 <=? 2 ^ 63 - 1)))));
   temp _t'10 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'9 = _stderr;
       _fprintf
         ([(_t'9)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((151))%expr; 
           (___stringlit_163)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 2 ^ 63 - 1 < Z.shiftr r0 64 mod 2 ^ 64
Int.repr
  (Z.b2z
     (negb (true && (hi mod 2 ^ 64 <=? 2 ^ 63 - 1))
      || (9223372036854775807 <?
          (Z.shiftr r0 64 - hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'8 (Vlong (Int64.repr hi));
   temp _t'7 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3
     (Vint
        (Int.repr
           (Z.b2z
              (true && (hi mod 2 ^ 64 <=? 2 ^ 63 - 1)))));
   temp _t'10 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'9 = _stderr;
       _fprintf
         ([(_t'9)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((151))%expr; 
           (___stringlit_163)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 2 ^ 63 - 1 < Z.shiftr r0 64 mod 2 ^ 64
Hhi: hi mod 2 ^ 64 <= 2 ^ 63 - 1
Int.repr
  (Z.b2z
     (negb (true && true)
      || (9223372036854775807 <?
          (Z.shiftr r0 64 - hi) mod 2 ^ 64))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'8 (Vlong (Int64.repr hi));
   temp _t'7 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'10 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'9 = _stderr;
       _fprintf
         ([(_t'9)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((151))%expr; 
           (___stringlit_163)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: 2 ^ 63 - 1 < Z.shiftr r0 64 mod 2 ^ 64
Hhi: hi mod 2 ^ 64 <= 2 ^ 63 - 1
Hr0hi: (Z.shiftr r0 64 - hi) mod 2 ^ 64
  <= 9223372036854775807
Int.repr (Z.b2z (negb (true && true) || false)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'8 (Vlong (Int64.repr hi));
   temp _t'7 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'10 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'9 = _stderr;
       _fprintf
         ([(_t'9)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((151))%expr; 
           (___stringlit_163)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: hi mod 2 ^ 64 <= 2 ^ 63 - 1
Hr0hi: (Z.shiftr r0 64 - hi) mod 2 ^ 64
  <= 9223372036854775807
Int.repr (Z.b2z (negb (true && true) || false)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'8 (Vlong (Int64.repr hi));
   temp _t'7 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'10 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'9 = _stderr;
       _fprintf
         ([(_t'9)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((151))%expr; 
           (___stringlit_163)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: (Z.shiftr r0 64 - hi) mod 2 ^ 64
  <= 9223372036854775807
Int.repr (Z.b2z (negb (true && true) || false)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'8 (Vlong (Int64.repr hi));
   temp _t'7 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'3 (Vint (Int.repr (Z.b2z (true && true))));
   temp _t'10 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong (Vlong (Int64.repr hi)) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'9 = _stderr;
       _fprintf
         ([(_t'9)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((151))%expr; 
           (___stringlit_163)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: (Z.shiftr r0 64 - hi) mod 2 ^ 64
  <= 9223372036854775807
Int64.min_signed <= Z.shiftr r0 64 - hi <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: (Z.shiftr r0 64 - hi) mod 2 ^ 64
  <= 9223372036854775807
Int64.min_signed <=
Z.shiftr r0 64
  - (Z.shiftr (a * b) 64
       + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64)) <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
POSTCONDITION:= abbreviate: ret_assert
hi:= Z.shiftr (a * b) 64
  + Z.b2z (r0 mod 2 ^ 64 <? (a * b) mod 2 ^ 64): Z
Hr0: Int64.min_signed <= Z.shiftr r0 64 < 0
Hhi: 0 <= hi <= Int64.max_signed
Hr0hi: (Z.shiftr r0 64 - hi) mod 2 ^ 64
  <= 9223372036854775807
Int64.min_signed <= Z.shiftr (r0 - a * b) 64 <=
Int64.max_signed
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'18 (Vlong (Int64.repr r0));
   temp _t'17
     (Vlong (Int64.repr (Z.shiftr (a * b) 64)));
   temp _lo (Vlong (Int64.repr (a * b)));
   lvar _hi tlong v_hi; 
   temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b)))
   SEP (data_at Tsh tlong
          (Vlong
             (Int64.repr
                (Z.shiftr (a * b) 64
                   + Z.b2z
                       (r0 mod 2 ^ 64 <?
                       (a * b) mod 2 ^ 64)))) v_hi;
   data_at sh t_secp256k1_uint128
     (Vlong (Int64.repr r0),
      Vlong (Int64.repr (Z.shiftr r0 64))) r))
  ((_t'5 = (_r -> _hi);
    _t'6 = _hi;
    (_r -> _hi) = (_t'5 - (tulong) _t'6);)
   MORE_COMMANDS)
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (r0 - a * b) r)
        * stackframe_of f_secp256k1_i128_dissip_mul)%logic)


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 - a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           - (Z.shiftr (a * b) 64
                + Z.b2z
                    (r0 mod 2 ^ 64 <?
                     (a * b) mod 2 ^ 64))))) r
|-- secp256k1_uint128_at sh (r0 - a * b) r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 - a * b)),
   Vlong
     (Int64.repr
        (Z.shiftr r0 64
           - (Z.shiftr (a * b) 64
                + Z.b2z
                    (r0 mod 2 ^ 64 <?
                     (a * b) mod 2 ^ 64))))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 - a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 - a * b) 64)))
      r


Espec: OracleKind
r: val
sh: share
r0, a, b: Z
Delta_specs: Maps.PTree.t funspec
v_hi: val
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: -2 ^ 63 <= b <= 2 ^ 63 - 1
H1: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H2: -2 ^ 127 <= r0 - a * b <= 2 ^ 127 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (r0 - a * b)),
   Vlong (Int64.repr (Z.shiftr (r0 - a * b) 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (r0 - a * b)),
       Vlong (Int64.repr (Z.shiftr (r0 - a * b) 64)))
      r

entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_det
  secp256k1_i128_det_spec


semax_body Vprog Gprog f_secp256k1_i128_det
  secp256k1_i128_det_spec


Espec: OracleKind
r: val
sh: share
a, b, c, d: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int64.min_signed <= c <= Int64.max_signed
H2: Int64.min_signed <= d <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b));
   temp _c (Vlong (Int64.repr c));
   temp _d (Vlong (Int64.repr d)))
   SEP (data_at_ sh t_secp256k1_uint128 r))
  (_secp256k1_i128_mul
     ([(_r)%expr; (_a)%expr; (_d)%expr]);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b, c, d: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int64.min_signed <= c <= Int64.max_signed
H2: Int64.min_signed <= d <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a));
   temp _b (Vlong (Int64.repr b));
   temp _c (Vlong (Int64.repr c));
   temp _d (Vlong (Int64.repr d)))
   SEP (secp256k1_uint128_at sh (a * d) r))
  (_secp256k1_i128_dissip_mul
     ([(_r)%expr; (_b)%expr; (_c)%expr]);)
  POSTCONDITION


Espec: OracleKind
r: val
sh: share
a, b, c, d: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int64.min_signed <= c <= Int64.max_signed
H2: Int64.min_signed <= d <= Int64.max_signed
Int128_min_signed <= a * d <= Int128_max_signed /\
Int128_min_signed <= a * d - b * c <=
Int128_max_signed


Espec: OracleKind
r: val
sh: share
a, b, c, d: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int64.min_signed <= c <= Int64.max_signed
H2: Int64.min_signed <= d <= Int64.max_signed
-2 ^ 127 <= a * d <= 2 ^ 127 - 1 /\
-2 ^ 127 <= a * d - b * c <= 2 ^ 127 - 1


Espec: OracleKind
r: val
sh: share
a, b, c, d: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int64.min_signed <= c <= Int64.max_signed
H2: Int64.min_signed <= d <= Int64.max_signed
Htight: -2 ^ 126 + 2 ^ 63 <= a * d <= 2 ^ 126
-2 ^ 127 <= a * d <= 2 ^ 127 - 1 /\
-2 ^ 127 <= a * d - b * c <= 2 ^ 127 - 1


Espec: OracleKind
r: val
sh: share
a, b, c, d: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
H0: Int64.min_signed <= b <= Int64.max_signed
H1: Int64.min_signed <= c <= Int64.max_signed
H2: Int64.min_signed <= d <= Int64.max_signed
Htight: -2 ^ 126 + 2 ^ 63 <= a * d <= 2 ^ 126
Htight': -2 ^ 126 + 2 ^ 63 <= b * c <= 2 ^ 126
-2 ^ 127 <= a * d <= 2 ^ 127 - 1 /\
-2 ^ 127 <= a * d - b * c <= 2 ^ 127 - 1

lia.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_rshift
  secp256k1_i128_rshift_spec


semax_body Vprog Gprog f_secp256k1_i128_rshift
  secp256k1_i128_rshift_spec


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     if (!(_n < (128))) {
       for (;
       ;
       break;) {
         ((_t'6 = _stderr;
           _fprintf
             ([(_t'6)%expr; (___stringlit_6)%expr;
               (___stringlit_159)%expr; ((165))%expr;
               (___stringlit_158)%expr]);)
          _abort([]);)
       }
     }
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
H1: Int.repr
  (Z.b2z (Int.ltu (Int.repr n) (Int.repr 128))) = Int.zero
False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (Int.ltu (Int.repr n) (Int.repr 128))) = Int.zero ->
False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 128)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 128)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)

 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (secp256k1_uint128_at sh
                       (Z.shiftr r0 n) r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (data_at sh t_secp256k1_uint128
                       (Vlong
                       (Int64.repr (Z.shiftr r0 n)),
                       Vlong
                       (Int64.repr
                       (Z.shiftr (Z.shiftr r0 n) 64)))
                       r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     ((_t'5 = (_r -> _hi);
       (_r -> _lo) =
         (tulong) ((tlong) _t'5 >> (_n - (64)));)
      _t'4 = (_r -> _hi);
      (_r -> _hi) = (tulong) ((tlong) _t'4 >> (63));)
   } else {
     if (_n > (0)) {
       ((_t'2 = (_r -> _hi);
         _t'3 = (_r -> _lo);
         (_r -> _lo) =
           ((1) * _t'2) << ((64) - _n) | _t'3 >> _n;)
        _t'1 = (_r -> _hi);
        (_r -> _hi) = (tulong) ((tlong) _t'1 >> _n);)
     }
   })
  (normal_ret_assert
     (PROP ( )
      RETURN ( ) SEP (data_at sh t_secp256k1_uint128
                       (Vlong
                       (Int64.repr (Z.shiftr r0 n)),
                       Vlong
                       (Int64.repr
                       (Z.shiftr (Z.shiftr r0 n) 64)))
                       r)
        * stackframe_of f_secp256k1_i128_rshift)%logic)


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr (Z.shiftr (Z.shiftr r0 64) (n - 64))),
   Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 64) 63)))
  r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 64) n))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r


Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr (Z.shiftr (Z.shiftr r0 64) (n - 64))),
   Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 64) 63)))
  r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 (64 + (n - 64)))),
   Vlong (Int64.repr (Z.shiftr r0 (64 + 63)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 n)),
   Vlong (Int64.repr (Z.shiftr r0 (64 + 63)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 n)),
   Vlong (Int64.repr (Z.shiftr r0 127))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 n)),
   Vlong (Int64.repr (Z.shiftr r0 127))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr r0 (127 + (n - 63)))))
      r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n >= 64
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr (Z.shiftr r0 n)),
   Vlong (Int64.repr (Z.shiftr r0 127))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 127))) r

  entailer!.

Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 64) n))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr r0 (64 + n)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
data_at sh t_secp256k1_uint128
  (Vlong
     (Int64.repr
        (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
           (Z.shiftr (r0 mod 2 ^ 64) n))),
   Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong (Int64.repr (Z.shiftr r0 (n + 64)))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
Int64.repr (Z.shiftr r0 n) = 
Int64.repr
  (Z.lor (Z.shiftr r0 64 * 2 ^ (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
Int64.repr (Z.shiftr r0 n) = 
Int64.repr
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
Int64.eqm (Z.shiftr r0 n)
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n))

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
forall i : Z,
0 <= i < Int64.zwordsize ->
Z.testbit (Z.shiftr r0 n) i = 
Z.testbit
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n)) i

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
forall i : Z,
0 <= i < 64 ->
Z.testbit (Z.shiftr r0 n) i = 
Z.testbit
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n)) i

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Z.testbit (Z.shiftr r0 n) i = 
Z.testbit
  (Z.lor (Z.shiftl (Z.shiftr r0 64) (64 - n))
     (Z.shiftr (r0 mod 2 ^ 64) n)) i

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

   
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (false
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

   
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hneg: i - (64 - n) < 0
Z.testbit r0 (i + n) = (false || Z.testbit r0 (i + n))%bool
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

   
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit 
                       (Z.shiftr r0 64) 
                       (i - (64 - n))
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = (Z.testbit r0
                       (i - (64 - n) + 64)
                       || 
                       Z.testbit 
                       (r0 mod 2 ^ 64) 
                       (i + n))%bool

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = Z.testbit r0
                       (i - (64 - n) + 64)

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 < n
i: Z
Hi: 0 <= i < 64
Hpos: 0 <= i - (64 - n)
Z.testbit r0 (i + n) = Z.testbit r0 (i + n)

  reflexivity.

Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 n)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 n) 64))) r
 
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr (Z.shiftr r0 0)),
       Vlong
         (Int64.repr (Z.shiftr (Z.shiftr r0 0) 64))) r

  
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 128
H1: n < 64
H2: 0 >= n
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr r0),
       Vlong (Int64.repr (Z.shiftr r0 64))) r

  entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_to_u64
  secp256k1_i128_to_u64_spec


semax_body Vprog Gprog f_secp256k1_i128_to_u64
  secp256k1_i128_to_u64_spec


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = (_a -> _lo);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'1 = (_a -> _lo);
   MORE_COMMANDS) POSTCONDITION

repeat progressC.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_to_i64
  secp256k1_i128_to_i64_spec


semax_body Vprog Gprog f_secp256k1_i128_to_i64
  secp256k1_i128_to_i64_spec


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     (_t'2 = (_a -> _hi);
      _t'3 = (_a -> _lo);
      if (!_t'2 == (-_t'3 >> (63))) {
        for (;
        ;
        break;) {
          ((_t'4 = _stderr;
            _fprintf
              ([(_t'4)%expr; (___stringlit_6)%expr;
                (___stringlit_159)%expr; ((181))%expr;
                (___stringlit_164)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'2 = (_a -> _hi);
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
H0: Int.repr
  (Z.b2z
     (Int64.eq (Int64.repr (Z.shiftr r0 64))
        (Int64.neg
           (Int64.shru (Int64.repr r0)
              (Int64.repr
                 (Int.unsigned (Int.repr 63))))))) = Int.zero
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr
  (Z.b2z
     (Int64.eq (Int64.repr (Z.shiftr r0 64))
        (Int64.neg
           (Int64.shru (Int64.repr r0)
              (Int64.repr (Int.unsigned (Int.repr 63))))))) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr
  (Z.b2z
     (Z.shiftr r0 64 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr
  (Z.b2z
     (Z.shiftr r0 (63 + 1) mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr r0 (63 + 1))));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 (63 + 1))))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr ((r0 + 2 ^ 64) mod 2 ^ 64) 63
      mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 + 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     ((r0 / 2 ^ 63 / 2 ^ 1) mod 2 ^ 64 =?
      -((r0 + 2 ^ 64) / 2 ^ 63) mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (r0 / 2 ^ 63 / 2 ^ 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (r0 / 2 ^ 63 / 2 ^ 1))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     ((r0 / 2 ^ 63 / 2 ^ 1) mod 2 ^ 64 =?
      -((r0 + 2 * 2 ^ 63) / 2 ^ 63) mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (r0 / 2 ^ 63 / 2 ^ 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (r0 / 2 ^ 63 / 2 ^ 1))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     ((r0 / 2 ^ 63 / 2 ^ 1) mod 2 ^ 64 =?
      -(r0 / 2 ^ 63 + 2) mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (r0 / 2 ^ 63 / 2 ^ 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (r0 / 2 ^ 63 / 2 ^ 1))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
Int.repr
  (Z.b2z
     ((-1 / 2 ^ 1) mod 2 ^ 64 =? -(-1 + 2) mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2 (Vlong (Int64.repr (-1 / 2 ^ 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (-1 / 2 ^ 1))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
-1 = r0 / 2 ^ 63
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hneg: r0 < 0
-1 = r0 / 2 ^ 63
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 mod 2 ^ 64 =?
      -Z.shiftr (r0 mod 2 ^ 64) 63 mod 2 ^ 64)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr
  (Z.b2z
     (Z.shiftr (Z.shiftr r0 63) 1 =? -Z.shiftr r0 63)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2
     (Vlong (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong
             (Int64.repr (Z.shiftr (Z.shiftr r0 63) 1)))
          r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
Int.repr (Z.b2z (Z.shiftr 0 1 =? -0)) = Int.zero ->
semax Delta
  (PROP ( )
   LOCAL (temp _t'3 (Vlong (Int64.repr r0));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr 0 1)));
   temp _a r)
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr 0 1))) r))
  (for (;
   ;
   (break;)%C) {
     ((_t'4 = _stderr;
       _fprintf
         ([(_t'4)%expr; 
           (___stringlit_6)%expr;
           (___stringlit_159)%expr; 
           ((181))%expr; 
           (___stringlit_164)%expr]);)
      _abort([]);)
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
0 = Z.shiftr r0 63
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
0 = Z.shiftr r0 63
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 63 <= r0 <= 2 ^ 63 - 1
POSTCONDITION:= abbreviate: ret_assert
Hpos: 0 <= r0
0 = 0
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r)
   SEP (secp256k1_uint128_at sh r0 r))
  (_t'1 = _secp256k1_i128_to_u64(_a);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0: Z
Delta_specs:= abbreviate: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int64.min_signed <= r0 <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
semax Delta
  (PROP ( )
   LOCAL (temp _t'1 (Vlong (Int64.repr r0));
   temp _a r)  SEP (secp256k1_uint128_at sh r0 r))
  (return (tlong) _t'1;) POSTCONDITION

repeat progressC.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_from_i64
  secp256k1_i128_from_i64_spec


semax_body Vprog Gprog f_secp256k1_i128_from_i64
  secp256k1_i128_from_i64_spec


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: writable_share sh
H: Int64.min_signed <= a <= Int64.max_signed
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _a (Vlong (Int64.repr a)))
   SEP (data_at_ sh t_secp256k1_uint128 r))
  ((_r -> _hi) = (tulong) (_a >> (63));
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (Z.shiftr a 63))) r
|-- secp256k1_uint128_at sh a r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (Z.shiftr a 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (Z.shiftr a 64))) r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (Z.shiftr a 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (Z.shiftr a (63 + 1)))) r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (a / 2 ^ 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (a / 2 ^ 63 / 2 ^ 1))) r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: a < 0
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (a / 2 ^ 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (a / 2 ^ 63 / 2 ^ 1))) r
Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: 0 <= a
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (a / 2 ^ 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (a / 2 ^ 63 / 2 ^ 1))) r


Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: a < 0
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (a / 2 ^ 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (a / 2 ^ 63 / 2 ^ 1))) r
 
Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: a < 0
-1 = a / 2 ^ 63

  
Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: a < 0
0 = a / 2 ^ 63 + 1

  
Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: a < 0
0 = (a + 2 ^ 63) / 2 ^ 63

  rewrite Zdiv_small;[reflexivity|rep_lia].

Espec: OracleKind
r: val
sh: share
a: Z
Delta_specs: Maps.PTree.t funspec
SH: writable_share sh
H: -2 ^ 63 <= a <= 2 ^ 63 - 1
H0: 0 <= a
data_at sh t_secp256k1_uint128
  (Vlong (Int64.repr a),
   Vlong (Int64.repr (a / 2 ^ 63))) r
|-- data_at sh t_secp256k1_uint128
      (Vlong (Int64.repr a),
       Vlong (Int64.repr (a / 2 ^ 63 / 2 ^ 1))) r
 rewrite (Zdiv_small a);[entailer!|rep_lia].
Qed.


semax_body Vprog Gprog f_secp256k1_i128_eq_var
  secp256k1_i128_eq_var_spec


semax_body Vprog Gprog f_secp256k1_i128_eq_var
  secp256k1_i128_eq_var_spec


Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _a r; temp _b s)
   SEP (secp256k1_uint128_at shr r0 r;
   secp256k1_uint128_at shs s0 s))
  ((_t'2 = (_a -> _hi);
    _t'3 = (_b -> _hi);
    if (_t'2 == _t'3) {
      (_t'4 = (_a -> _lo);
       _t'5 = (_b -> _lo);
       _t'1 = (tbool) (_t'4 == _t'5);)
    } else {
      _t'1 = (0);
    })
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (if (_t'2 == _t'3) {
     (_t'4 = (_a -> _lo);
      _t'5 = (_b -> _lo);
      _t'1 = (tbool) (_t'4 == _t'5);)
   } else {
     _t'1 = (0);
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (if (_t'2 == _t'3) {
     (_t'4 = (_a -> _lo);
      _t'5 = (_b -> _lo);
      _t'1 = (tbool) (_t'4 == _t'5);)
   } else {
     _t'1 = (0);
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 mod (2 ^ 64 * 2 ^ 64) =? s0 mod (2 ^ 64 * 2 ^ 64)) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (if (_t'2 == _t'3) {
     (_t'4 = (_a -> _lo);
      _t'5 = (_b -> _lo);
      _t'1 = (tbool) (_t'4 == _t'5);)
   } else {
     _t'1 = (0);
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(Z.shiftl (Z.shiftr r0 64 mod 2 ^ 64) 64
   + r0 mod 2 ^ 64 =?
 Z.shiftl (Z.shiftr s0 64 mod 2 ^ 64) 64
   + s0 mod 2 ^ 64) = ((Z.shiftr r0 64 mod 2 ^ 64 =?
                       Z.shiftr s0 64 mod 2 ^ 64) &&
                       (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (if (_t'2 == _t'3) {
     (_t'4 = (_a -> _lo);
      _t'5 = (_b -> _lo);
      _t'1 = (tbool) (_t'4 == _t'5);)
   } else {
     _t'1 = (0);
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (if (_t'2 == _t'3) {
     (_t'4 = (_a -> _lo);
      _t'5 = (_b -> _lo);
      _t'1 = (tbool) (_t'4 == _t'5);)
   } else {
     _t'1 = (0);
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = true
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (_t'4 = (_a -> _lo);
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.repr (Z.shiftr r0 64) <>
Int64.repr (Z.shiftr s0 64)
POSTCONDITION:= abbreviate: ret_assert
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (_t'1 = (0);) POSTCONDITION
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _t'1
            (Vint
               (Int.repr
                  (Z.b2z
                     (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128))));
   temp _t'3 (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (return _t'1;) POSTCONDITION


Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = true
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (_t'4 = (_a -> _lo);
   MORE_COMMANDS) POSTCONDITION
 
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = true
Vint
  (Int.repr (Z.b2z (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128))) = 
bool2val (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = true
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 mod 2 ^ 64 =?
          Z.shiftr s0 64 mod 2 ^ 64) &&
         (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
bool2val (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = true ->
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 mod 2 ^ 64 =?
          Z.shiftr s0 64 mod 2 ^ 64) &&
         (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
bool2val (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
(Z.shiftr r0 64 mod 2 ^ 64 =?
 Z.shiftr s0 64 mod 2 ^ 64) = true ->
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 mod 2 ^ 64 =?
          Z.shiftr s0 64 mod 2 ^ 64) &&
         (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
bool2val (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Vint
  (Int.repr
     (Z.b2z (true && (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
bool2val (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)

  reflexivity.

Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.repr (Z.shiftr r0 64) <>
Int64.repr (Z.shiftr s0 64)
POSTCONDITION:= abbreviate: ret_assert
semax Delta
  (PROP ( )
   LOCAL (temp _t'3
            (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (_t'1 = (0);) POSTCONDITION
 
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.repr (Z.shiftr r0 64) <>
Int64.repr (Z.shiftr s0 64)
Vint
  (Int.repr (Z.b2z (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = false
Vint
  (Int.repr (Z.b2z (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
H: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = false
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 mod 2 ^ 64 =?
          Z.shiftr s0 64 mod 2 ^ 64) &&
         (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr (Z.shiftr s0 64)) = false ->
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 mod 2 ^ 64 =?
          Z.shiftr s0 64 mod 2 ^ 64) &&
         (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
(Z.shiftr r0 64 mod 2 ^ 64 =?
 Z.shiftr s0 64 mod 2 ^ 64) = false ->
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 mod 2 ^ 64 =?
          Z.shiftr s0 64 mod 2 ^ 64) &&
         (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share shr
SH0: readable_share shs
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
Vint
  (Int.repr
     (Z.b2z
        (false && (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64)))) = 
Vint (Int.repr 0)

  reflexivity.

Espec: OracleKind
r: val
shr: share
r0: Z
s: val
shs: share
s0: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share shr
SH0: readable_share shs
POSTCONDITION:= abbreviate: ret_assert
Hrs: (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128) = 
((Z.shiftr r0 64 mod 2 ^ 64 =?
  Z.shiftr s0 64 mod 2 ^ 64) &&
 (r0 mod 2 ^ 64 =? s0 mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _t'1
            (Vint
               (Int.repr
                  (Z.b2z
                     (r0 mod 2 ^ 128 =? s0 mod 2 ^ 128))));
   temp _t'3 (Vlong (Int64.repr (Z.shiftr s0 64)));
   temp _t'2 (Vlong (Int64.repr (Z.shiftr r0 64)));
   temp _a r; temp _b s)
   SEP (data_at shr t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r;
   data_at shs t_secp256k1_uint128
     (Vlong (Int64.repr s0),
      Vlong (Int64.repr (Z.shiftr s0 64))) s))
  (return _t'1;) POSTCONDITION
 repeat progressC.
Qed.

(* Use with
   forward_call secp256k1_i128_eq_var_spec_alias_sub (r, shr, r0)
*)

funspec_sub (snd secp256k1_i128_eq_var_spec)
  (snd secp256k1_i128_eq_var_spec_alias)


funspec_sub (snd secp256k1_i128_eq_var_spec)
  (snd secp256k1_i128_eq_var_spec_alias)


w: (val * share * Z)%type
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
(let (p, r0) := w in
 let (r, shr) := p in
 fun x : argsEnviron =>
 !! (readable_share shr /\ True) &&
 (!! (snd x = [r; r]) &&
  (TT && (secp256k1_uint128_at shr r0 r * emp))))
  (g, args)
|-- EX (x1 : val * share * Z * val * share * Z)
    (F : mpred),
    F
      * (let (p, s0) := x1 in
         let (p0, shs) := p in
         let (p1, s) := p0 in
         let (p2, r0) := p1 in
         let (r, shr) := p2 in
         fun x : argsEnviron =>
         !! (readable_share shr /\
             readable_share shs /\ True) &&
         (!! (snd x = [r; s]) &&
          (TT &&
           (secp256k1_uint128_at shr r0 r
              * (secp256k1_uint128_at shs s0 s * emp)))))
          (g, args) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (F
           * (let (p, s0) := x1 in
              let (p0, shs) := p in
              let (p1, s) := p0 in
              let (p2, r0) := p1 in
              let (r, shr) := p2 in
              fun x : environ =>
              TT &&
              (!! ((Vint (Int.repr ...) = eval_id
                                            ret_temp x /\
                    Vint (...) <> Vundef) /\ True) &&
               (secp256k1_uint128_at shr r0 r
                  * (secp256k1_uint128_at shs s0 s
                       * emp)))) rho')
        |-- (let (p, r0) := w in
             let (r, shr) := p in
             fun x : environ =>
             TT &&
             (!! ((Vint (Int.repr 1) = eval_id
                                         ret_temp x /\
                   Vint (Int.repr 1) <> Vundef) /\
                  True) &&
              (secp256k1_uint128_at shr r0 r * emp)))
              rho')


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
!! (readable_share shr /\ True) &&
(!! (snd (g, args) = [r; r]) &&
 (TT && (secp256k1_uint128_at shr r0 r * emp)))
|-- EX (x1 : val * share * Z * val * share * Z)
    (F : mpred),
    F
      * (let (p, s0) := x1 in
         let (p0, shs) := p in
         let (p1, s) := p0 in
         let (p2, r0) := p1 in
         let (r, shr) := p2 in
         fun x : argsEnviron =>
         !! (readable_share shr /\
             readable_share shs /\ True) &&
         (!! (snd x = [r; s]) &&
          (TT &&
           (secp256k1_uint128_at shr r0 r
              * (secp256k1_uint128_at shs s0 s * emp)))))
          (g, args) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (F
           * (let (p, s0) := x1 in
              let (p0, shs) := p in
              let (p1, s) := p0 in
              let (p2, r0) := p1 in
              let (r, shr) := p2 in
              fun x : environ =>
              TT &&
              (!! ((Vint (Int.repr ...) = 
                    eval_id ret_temp x /\
                    Vint (...) <> Vundef) /\ True) &&
               (secp256k1_uint128_at shr r0 r
                  * (secp256k1_uint128_at shs s0 s
                       * emp)))) rho')
        |-- TT &&
            (!! ((Vint (Int.repr 1) = 
                  eval_id ret_temp rho' /\
                  Vint (Int.repr 1) <> Vundef) /\ True) &&
             (secp256k1_uint128_at shr r0 r * emp)))


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
secp256k1_uint128_at shr r0 r
|-- EX (x1 : val * share * Z * val * share * Z)
    (F : mpred),
    F
      * (let (p, s0) := x1 in
         let (p0, shs) := p in
         let (p1, s) := p0 in
         let (p2, r0) := p1 in
         let (r, shr) := p2 in
         fun x : argsEnviron =>
         !! (readable_share shr /\
             readable_share shs /\ True) &&
         (!! (snd x = [r; s]) &&
          (TT &&
           (secp256k1_uint128_at shr r0 r
              * (secp256k1_uint128_at shs s0 s * emp)))))
          (g, args) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (F
           * (let (p, s0) := x1 in
              let (p0, shs) := p in
              let (p1, s) := p0 in
              let (p2, r0) := p1 in
              let (r, shr) := p2 in
              fun x : environ =>
              TT &&
              (!! ((Vint (Int.repr ...) = 
                    eval_id ret_temp x /\
                    Vint (...) <> Vundef) /\ True) &&
               (secp256k1_uint128_at shr r0 r
                  * (secp256k1_uint128_at shs s0 s
                       * emp)))) rho')
        |-- TT &&
            (!! ((Vint (Int.repr 1) = 
                  eval_id ret_temp rho' /\
                  Vint (Int.repr 1) <> Vundef) /\ True) &&
             secp256k1_uint128_at shr r0 r))


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
sh1, sh2: share
Hsh1: readable_share sh1
Hsh2: readable_share sh2
Hsh: sepalg.join sh1 sh2 shr
secp256k1_uint128_at shr r0 r
|-- EX (x1 : val * share * Z * val * share * Z)
    (F : mpred),
    F
      * (let (p, s0) := x1 in
         let (p0, shs) := p in
         let (p1, s) := p0 in
         let (p2, r0) := p1 in
         let (r, shr) := p2 in
         fun x : argsEnviron =>
         !! (readable_share shr /\
             readable_share shs /\ True) &&
         (!! (snd x = [r; s]) &&
          (TT &&
           (secp256k1_uint128_at shr r0 r
              * (secp256k1_uint128_at shs s0 s * emp)))))
          (g, args) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (F
           * (let (p, s0) := x1 in
              let (p0, shs) := p in
              let (p1, s) := p0 in
              let (p2, r0) := p1 in
              let (r, shr) := p2 in
              fun x : environ =>
              TT &&
              (!! ((Vint (Int.repr ...) = 
                    eval_id ret_temp x /\
                    Vint (...) <> Vundef) /\ True) &&
               (secp256k1_uint128_at shr r0 r
                  * (secp256k1_uint128_at shs s0 s
                       * emp)))) rho')
        |-- TT &&
            (!! ((Vint (Int.repr 1) = 
                  eval_id ret_temp rho' /\
                  Vint (Int.repr 1) <> Vundef) /\ True) &&
             secp256k1_uint128_at shr r0 r))


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
sh1, sh2: share
Hsh1: readable_share sh1
Hsh2: readable_share sh2
Hsh: sepalg.join sh1 sh2 shr
secp256k1_uint128_at shr r0 r
|-- emp
      * (!! (readable_share sh1 /\
             readable_share sh2 /\ True) &&
         (!! (snd (g, args) = [r; r]) &&
          (TT &&
           (secp256k1_uint128_at sh1 r0 r
              * (secp256k1_uint128_at sh2 r0 r * emp))))) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (emp
           * (TT &&
              (!! ((Vint
                      (Int.repr
                        (if
                        r0 mod 2 ^ 128 =?
                        r0 mod 2 ^ 128
                        then 1
                        else 0)) = 
                    eval_id ret_temp rho' /\
                    Vint
                      (Int.repr
                        (if
                        r0 mod 2 ^ 128 =?
                        r0 mod 2 ^ 128
                        then 1
                        else 0)) <> Vundef) /\ True) &&
               (secp256k1_uint128_at sh1 r0 r
                  * (secp256k1_uint128_at sh2 r0 r
                       * emp)))))
        |-- TT &&
            (!! ((Vint (Int.repr 1) = 
                  eval_id ret_temp rho' /\
                  Vint (Int.repr 1) <> Vundef) /\ True) &&
             secp256k1_uint128_at shr r0 r))


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
sh1, sh2: share
Hsh1: readable_share sh1
Hsh2: readable_share sh2
Hsh: sepalg.join sh1 sh2 shr
data_at shr t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- emp
      * (!! (readable_share sh1 /\
             readable_share sh2 /\ True) &&
         (!! (snd (g, args) = [r; r]) &&
          (TT &&
           (data_at sh1 t_secp256k1_uint128
              (Vlong (Int64.repr r0),
               Vlong (Int64.repr (Z.shiftr r0 64))) r
              * (data_at sh2 t_secp256k1_uint128
                   (Vlong (Int64.repr r0),
                    Vlong
                      (Int64.repr (Z.shiftr r0 64))) r
                   * emp))))) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (emp
           * (TT &&
              (!! ((Vint
                      (Int.repr
                        (if
                        r0 mod 2 ^ 128 =?
                        r0 mod 2 ^ 128
                        then 1
                        else 0)) = 
                    eval_id ret_temp rho' /\
                    Vint
                      (Int.repr
                        (if
                        r0 mod 2 ^ 128 =?
                        r0 mod 2 ^ 128
                        then 1
                        else 0)) <> Vundef) /\ True) &&
               (data_at sh1 t_secp256k1_uint128
                  (Vlong (Int64.repr r0),
                   Vlong (Int64.repr (Z.shiftr r0 64)))
                  r
                  * (data_at sh2 t_secp256k1_uint128
                       (Vlong (Int64.repr r0),
                        Vlong
                        (Int64.repr (Z.shiftr r0 64)))
                       r
                       * emp)))))
        |-- TT &&
            (!! ((Vint (Int.repr 1) = 
                  eval_id ret_temp rho' /\
                  Vint (Int.repr 1) <> Vundef) /\ True) &&
             data_at shr t_secp256k1_uint128
               (Vlong (Int64.repr r0),
                Vlong (Int64.repr (Z.shiftr r0 64))) r))


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
sh1, sh2: share
Hsh1: readable_share sh1
Hsh2: readable_share sh2
Hsh: sepalg.join sh1 sh2 shr
data_at sh1 t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
  * data_at sh2 t_secp256k1_uint128
      (Vlong (Int64.repr r0),
       Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- emp
      * (!! (readable_share sh1 /\
             readable_share sh2 /\ True) &&
         (!! (snd (g, args) = [r; r]) &&
          (TT &&
           (data_at sh1 t_secp256k1_uint128
              (Vlong (Int64.repr r0),
               Vlong (Int64.repr (Z.shiftr r0 64))) r
              * (data_at sh2 t_secp256k1_uint128
                   (Vlong (Int64.repr r0),
                    Vlong
                      (Int64.repr (Z.shiftr r0 64))) r
                   * emp))))) &&
    !! (forall rho' : environ,
        !! (ve_of rho' = Map.empty (block * type)) &&
        (emp
           * (TT &&
              (!! ((Vint (Int.repr 1) = 
                    eval_id ret_temp rho' /\
                    Vint (Int.repr 1) <> Vundef) /\
                   True) &&
               (data_at sh1 t_secp256k1_uint128
                  (Vlong (Int64.repr r0),
                   Vlong (Int64.repr (Z.shiftr r0 64)))
                  r
                  * (data_at sh2 t_secp256k1_uint128
                       (Vlong (Int64.repr r0),
                        Vlong
                        (Int64.repr (Z.shiftr r0 64)))
                       r
                       * emp)))))
        |-- TT &&
            (!! ((Vint (Int.repr 1) = 
                  eval_id ret_temp rho' /\
                  Vint (Int.repr 1) <> Vundef) /\ True) &&
             (data_at sh1 t_secp256k1_uint128
                (Vlong (Int64.repr r0),
                 Vlong (Int64.repr (Z.shiftr r0 64)))
                r
                * data_at sh2 t_secp256k1_uint128
                    (Vlong (Int64.repr r0),
                     Vlong
                       (Int64.repr (Z.shiftr r0 64)))
                    r)))


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
sh1, sh2: share
Hsh1: readable_share sh1
Hsh2: readable_share sh2
Hsh: sepalg.join sh1 sh2 shr
H2: field_compatible t_secp256k1_uint128 [] r
H3: value_fits t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64)))
H6: Vint (Int.repr 1) <> Vundef
forall x : environ,
ve_of x = Map.empty (block * type) ->
Vint (Int.repr 1) = eval_id ret_temp x ->
data_at sh1 t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
  * data_at sh2 t_secp256k1_uint128
      (Vlong (Int64.repr r0),
       Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- !! ((Vint (Int.repr 1) = 
         eval_id ret_temp x /\
         Vint (Int.repr 1) <> Vundef) /\ True) &&
    (data_at sh1 t_secp256k1_uint128
       (Vlong (Int64.repr r0),
        Vlong (Int64.repr (Z.shiftr r0 64))) r
       * data_at sh2 t_secp256k1_uint128
           (Vlong (Int64.repr r0),
            Vlong (Int64.repr (Z.shiftr r0 64))) r)


r: val
shr: share
r0: Z
g: genviron
args: list val
H: argsHaveTyps (snd (g, args))
  (fst
     ([tptr t_secp256k1_uint128;
       tptr t_secp256k1_uint128], tint))
H0: readable_share shr
H1: snd (g, args) = [r; r]
sh1, sh2: share
Hsh1: readable_share sh1
Hsh2: readable_share sh2
Hsh: sepalg.join sh1 sh2 shr
H2: field_compatible t_secp256k1_uint128 [] r
H3: value_fits t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64)))
H6: Vint (Int.repr 1) <> Vundef
x: environ
H4: ve_of x = Map.empty (block * type)
H5: Vint (Int.repr 1) = eval_id ret_temp x
data_at sh1 t_secp256k1_uint128
  (Vlong (Int64.repr r0),
   Vlong (Int64.repr (Z.shiftr r0 64))) r
  * data_at sh2 t_secp256k1_uint128
      (Vlong (Int64.repr r0),
       Vlong (Int64.repr (Z.shiftr r0 64))) r
|-- !! ((Vint (Int.repr 1) = 
         eval_id ret_temp x /\
         Vint (Int.repr 1) <> Vundef) /\ True) &&
    (data_at sh1 t_secp256k1_uint128
       (Vlong (Int64.repr r0),
        Vlong (Int64.repr (Z.shiftr r0 64))) r
       * data_at sh2 t_secp256k1_uint128
           (Vlong (Int64.repr r0),
            Vlong (Int64.repr (Z.shiftr r0 64))) r)

entailer!.
Qed.


semax_body Vprog Gprog f_secp256k1_i128_check_pow2
  secp256k1_i128_check_pow2_spec


semax_body Vprog Gprog f_secp256k1_i128_check_pow2
  secp256k1_i128_check_pow2_spec


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: Int128_min_signed <= r0 <= Int128_max_signed
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     if (!(_n < (127))) {
       for (;
       ;
       break;) {
         ((_t'8 = _stderr;
           _fprintf
             ([(_t'8)%expr; (___stringlit_6)%expr;
               (___stringlit_159)%expr; ((195))%expr;
               (___stringlit_165)%expr]);)
          _abort([]);)
       }
     }
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     if (!(_n < (127))) {
       for (;
       ;
       break;) {
         ((_t'8 = _stderr;
           _fprintf
             ([(_t'8)%expr; 
               (___stringlit_6)%expr;
               (___stringlit_159)%expr; 
               ((195))%expr; 
               (___stringlit_165)%expr]);)
          _abort([]);)
       }
     }
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
H2: Int.repr
  (Z.b2z (Int.ltu (Int.repr n) (Int.repr 127))) = Int.zero
False
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     (if (_sign == (1)) {
        _t'1 = (1);
      } else {
        _t'1 = (tbool) (_sign == (-(1)));
      }
      if (!_t'1) {
        for (;
        ;
        break;) {
          ((_t'7 = _stderr;
            _fprintf
              ([(_t'7)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((196))%expr; 
                (___stringlit_166)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (Int.ltu (Int.repr n) (Int.repr 127))) = Int.zero ->
False
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     (if (_sign == (1)) {
        _t'1 = (1);
      } else {
        _t'1 = (tbool) (_sign == (-(1)));
      }
      if (!_t'1) {
        for (;
        ;
        break;) {
          ((_t'7 = _stderr;
            _fprintf
              ([(_t'7)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((196))%expr; 
                (___stringlit_166)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 127)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     (if (_sign == (1)) {
        _t'1 = (1);
      } else {
        _t'1 = (tbool) (_sign == (-(1)));
      }
      if (!_t'1) {
        for (;
        ;
        break;) {
          ((_t'7 = _stderr;
            _fprintf
              ([(_t'7)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((196))%expr; 
                (___stringlit_166)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
Int.repr (Z.b2z (n <? 127)) = Int.zero -> False
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     (if (_sign == (1)) {
        _t'1 = (1);
      } else {
        _t'1 = (tbool) (_sign == (-(1)));
      }
      if (!_t'1) {
        for (;
        ;
        break;) {
          ((_t'7 = _stderr;
            _fprintf
              ([(_t'7)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((196))%expr; 
                (___stringlit_166)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (for (;
   ;
   break;) {
     (if (_sign == (1)) {
        _t'1 = (1);
      } else {
        _t'1 = (tbool) (_sign == (-(1)));
      }
      if (!_t'1) {
        for (;
        ;
        break;) {
          ((_t'7 = _stderr;
            _fprintf
              ([(_t'7)%expr; 
                (___stringlit_6)%expr;
                (___stringlit_159)%expr; 
                ((196))%expr; 
                (___stringlit_166)%expr]);)
           _abort([]);)
        }
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_sign == (1)) {
     _t'1 = (1);
   } else {
     _t'1 = (tbool) (_sign == (-(1)));
   }
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'5 = (_r -> _hi);
      if (_t'5 == (tulong) _sign << (_n - (64))) {
        ((_t'6 = (_r -> _lo);
          _t'2 = (tbool) (_t'6 == (0));)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   } else {
     (_t'3 = (_r -> _hi);
      if (_t'3 == (tulong) ((_sign - (1)) >> (1))) {
        ((_t'4 = (_r -> _lo);
          _t'2 =
            (tbool) (_t'4 == (tulong) _sign << _n);)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
semax Delta
  (PROP ( )
   LOCAL (temp _t'1 (Vint (Int.repr 1)); 
   temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (!_t'1) {
     for (;
     ;
     break;) {
       ((_t'7 = _stderr;
         _fprintf
           ([(_t'7)%expr; 
             (___stringlit_6)%expr;
             (___stringlit_159)%expr; 
             ((196))%expr; 
             (___stringlit_166)%expr]);)
        _abort([]);)
     }
   }) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'5 = (_r -> _hi);
      if (_t'5 == (tulong) _sign << (_n - (64))) {
        ((_t'6 = (_r -> _lo);
          _t'2 = (tbool) (_t'6 == (0));)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   } else {
     (_t'3 = (_r -> _hi);
      if (_t'3 == (tulong) ((_sign - (1)) >> (1))) {
        ((_t'4 = (_r -> _lo);
          _t'2 =
            (tbool) (_t'4 == (tulong) _sign << _n);)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION

 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (secp256k1_uint128_at sh r0 r))
  (if (_n >= (64)) {
     (_t'5 = (_r -> _hi);
      if (_t'5 == (tulong) _sign << (_n - (64))) {
        ((_t'6 = (_r -> _lo);
          _t'2 = (tbool) (_t'6 == (0));)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   } else {
     (_t'3 = (_r -> _hi);
      if (_t'3 == (tulong) ((_sign - (1)) >> (1))) {
        ((_t'4 = (_r -> _lo);
          _t'2 =
            (tbool) (_t'4 == (tulong) _sign << _n);)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (if (_n >= (64)) {
     (_t'5 = (_r -> _hi);
      if (_t'5 == (tulong) _sign << (_n - (64))) {
        ((_t'6 = (_r -> _lo);
          _t'2 = (tbool) (_t'6 == (0));)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   } else {
     (_t'3 = (_r -> _hi);
      if (_t'3 == (tulong) ((_sign - (1)) >> (1))) {
        ((_t'4 = (_r -> _lo);
          _t'2 =
            (tbool) (_t'4 == (tulong) _sign << _n);)
         _t'2 = (tint) _t'2;)
      } else {
        _t'2 = (tint) (0);
      })
   }
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION


Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION
 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(2 ^ 64 * (r0 / 2 ^ 64) + r0 mod 2 ^ 64 =?
 sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                   sign * 2 ^ (n - 64)) &&
                  (r0 mod 2 ^ 64 =? 0))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 / 2 ^ 64 * 2 ^ 64 + r0 mod 2 ^ 64 =? sign * 2 ^ n) = 
((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) &&
 (r0 mod 2 ^ 64 =? 0))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 / 2 ^ 64 * 2 ^ 64 + r0 mod 2 ^ 64 =?
 sign * 2 ^ (n - 64 + 64)) = 
((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) &&
 (r0 mod 2 ^ 64 =? 0))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 / 2 ^ 64 * 2 ^ 64 + r0 mod 2 ^ 64 =?
 sign * 2 ^ (n - 64 + 64) + 0) = 
((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) &&
 (r0 mod 2 ^ 64 =? 0))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 / 2 ^ 64 * 2 ^ 64 + r0 mod 2 ^ 64 =?
 sign * 2 ^ (n - 64 + 64) + 0 mod 2 ^ 64) = 
((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) &&
 (r0 mod 2 ^ 64 =? 0 mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(Z.shiftl (Z.shiftr r0 64) 64 + r0 mod 2 ^ 64 =?
 Z.shiftl (Z.shiftl sign (n - 64)) 64 + 0 mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftl sign (n - 64)) &&
 (r0 mod 2 ^ 64 =? 0 mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'5 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.shl (Int64.repr sign)
     (Int64.repr
        (Int.unsigned (Int.repr (n - 64))))) = true
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint (Int.repr (Z.b2z (r0 mod 2 ^ 64 =? 0)))
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.shl (Int64.repr sign)
     (Int64.repr
        (Int.unsigned (Int.repr (n - 64))))) = true
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint (Int.repr (Z.b2z (r0 mod 2 ^ 64 =? 0)))
 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.shl (Int64.repr sign)
     (Int64.repr
        (Int.unsigned (Int.repr (n - 64))))) = true
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) &&
         (r0 mod 2 ^ 64 =? 0)))) = 
Vint (Int.repr (Z.b2z (r0 mod 2 ^ 64 =? 0)))

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.shl (Int64.repr sign)
     (Int64.repr
        (Int.unsigned (Int.repr (n - 64))))) = true
true = (Z.shiftr r0 64 =? sign * 2 ^ (n - 64))

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.shl (Int64.repr sign)
     (Int64.repr
        (Int.unsigned (Int.repr (n - 64))))) = true
Z.shiftr r0 64 = sign * 2 ^ (n - 64)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.shl (Int64.repr sign)
     (Int64.repr (Int.unsigned (Int.repr (n - 64))))) = true ->
Z.shiftr r0 64 = sign * 2 ^ (n - 64)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
(Z.shiftr r0 64 mod 2 ^ 64 =?
 (sign * 2 ^ (n - 64)) mod 2 ^ 64) = true ->
Z.shiftr r0 64 = sign * 2 ^ (n - 64)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
Z.shiftr r0 64 mod 2 ^ 64 = 
(sign * 2 ^ (n - 64)) mod 
2 ^ 64 -> Z.shiftr r0 64 = 
sign * 2 ^ (n - 64)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
-2 ^ 63 <= sign * 2 ^ (n - 64) <= 2 ^ 63 - 1

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
Hpow:= Z.pow_lt_mono_r 2 (n - 64) 63: 1 < 2 ->
0 <= 63 -> n - 64 < 63 -> 2 ^ (n - 64) < 2 ^ 63
-2 ^ 63 <= sign * 2 ^ (n - 64) <= 2 ^ 63 - 1

    lia.
  
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint (Int.repr 0)
 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 =? sign * 2 ^ (n - 64)) &&
         (r0 mod 2 ^ 64 =? 0)))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Z.shiftr r0 64 = sign * 2 ^ (n - 64) ->
Vint (Int.repr (Z.b2z (true && (r0 mod 2 ^ 64 =? 0)))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Hr0n: Z.shiftr r0 64 = sign * 2 ^ (n - 64)
Vint (Int.repr (Z.b2z (true && (r0 mod 2 ^ 64 =? 0)))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Hr0n: Z.shiftr r0 64 = sign * 2 ^ (n - 64)
Int64.repr (Z.shiftr r0 64) = 
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n >= 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       sign * 2 ^ (n - 64)) &&
                       (r0 mod 2 ^ 64 =? 0))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.shl (Int64.repr sign)
  (Int64.repr (Int.unsigned (Int.repr (n - 64))))
Hr0n: Z.shiftr r0 64 = sign * 2 ^ (n - 64)
Int64.repr (Z.shiftr r0 64) = 
Int64.repr (sign * 2 ^ (n - 64))

    congruence.

Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION
 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(2 ^ 64 * (r0 / 2 ^ 64) + r0 mod 2 ^ 64 =?
 sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                   Z.shiftr (sign - 1) 1) &&
                  (r0 mod 2 ^ 64 =?
                   (sign * 2 ^ n) mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(2 ^ 64 * (r0 / 2 ^ 64) + r0 mod 2 ^ 64 =?
 2 ^ 64 * (sign * 2 ^ n / 2 ^ 64)
   + (sign * 2 ^ n) mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
 (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(r0 / 2 ^ 64 * 2 ^ 64 + r0 mod 2 ^ 64 =?
 sign * 2 ^ n / 2 ^ 64 * 2 ^ 64
   + (sign * 2 ^ n) mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
 (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(Z.shiftl (Z.shiftr r0 64) 64 + r0 mod 2 ^ 64 =?
 Z.shiftl (Z.shiftl sign (n - 64)) 64
   + Z.shiftl sign n mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
 (r0 mod 2 ^ 64 =? Z.shiftl sign n mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(Z.shiftl (Z.shiftr r0 64) 64 + r0 mod 2 ^ 64 =?
 Z.shiftl (Z.shiftl sign (-(64 - n))) 64
   + Z.shiftl sign n mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
 (r0 mod 2 ^ 64 =? Z.shiftl sign n mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(Z.shiftl (Z.shiftr r0 64) 64 + r0 mod 2 ^ 64 =?
 Z.shiftl (Z.shiftr sign (64 - n)) 64
   + Z.shiftl sign n mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
 (r0 mod 2 ^ 64 =? Z.shiftl sign n mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
(Z.shiftl (Z.shiftr r0 64) 64 + r0 mod 2 ^ 64 =?
 Z.shiftl (Z.shiftr (sign - 1) 1) 64
   + Z.shiftl sign n mod 2 ^ 64) = 
((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
 (r0 mod 2 ^ 64 =? Z.shiftl sign n mod 2 ^ 64))%bool
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Z.shiftr (sign - 1) 1 = Z.shiftr sign (64 - n)
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Z.shiftr (sign - 1) 1 = Z.shiftr sign (64 - n)
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Z.shiftr (1 - 1) 1 = Z.shiftr 1 (64 - n)
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
0 <= 1 < 2 ^ (64 - n)
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

   
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
Delta:= abbreviate: tycontext
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
POSTCONDITION:= abbreviate: ret_assert
MORE_COMMANDS:= abbreviate: statement
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
semax Delta
  (PROP ( )
   LOCAL (temp _r r; temp _n (Vint (Int.repr n));
   temp _sign (Vint (Int.repr sign)))
   SEP (data_at sh t_secp256k1_uint128
          (Vlong (Int64.repr r0),
           Vlong (Int64.repr (Z.shiftr r0 64))) r))
  (_t'3 = (_r -> _hi);
   MORE_COMMANDS) POSTCONDITION

  
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr
     (Int.signed
        (Int.shr (Int.repr (sign - 1))
           (Int.repr 1)))) = true
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint
  (Int.repr
     (Z.b2z
        (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint (Int.repr 0)

  
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr
     (Int.signed
        (Int.shr (Int.repr (sign - 1))
           (Int.repr 1)))) = true
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint
  (Int.repr
     (Z.b2z
        (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))
 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr
     (Int.signed
        (Int.shr (Int.repr (sign - 1))
           (Int.repr 1)))) = true
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
         (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))) = 
Vint
  (Int.repr
     (Z.b2z
        (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr
     (Int.signed
        (Int.shr (Int.repr (sign - 1))
           (Int.repr 1)))) = true
true = (Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr
     (Int.signed
        (Int.shr (Int.repr (sign - 1))
           (Int.repr 1)))) = true
Z.shiftr r0 64 = Z.shiftr (sign - 1) 1

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
Int64.eq (Int64.repr (Z.shiftr r0 64))
  (Int64.repr
     (Int.signed
        (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))) = true ->
Z.shiftr r0 64 = Z.shiftr (sign - 1) 1

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
(Z.shiftr r0 64 mod 2 ^ 64 =?
 Z.shiftr (sign - 1) 1 mod 2 ^ 64) = true ->
Z.shiftr r0 64 = Z.shiftr (sign - 1) 1

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
Z.shiftr r0 64 mod 2 ^ 64 = 
Z.shiftr (sign - 1) 1 mod 
2 ^ 64 -> Z.shiftr r0 64 = 
Z.shiftr (sign - 1) 1

    apply (Z_mod_eq_bounded (-2^63) (2^63)); solve_bounds.
  
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Vint (Int.repr (Z.b2z (r0 =? sign * 2 ^ n))) = 
Vint (Int.repr 0)
 
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Vint
  (Int.repr
     (Z.b2z
        ((Z.shiftr r0 64 =? Z.shiftr (sign - 1) 1) &&
         (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Z.shiftr r0 64 = Z.shiftr (sign - 1) 1 ->
Vint
  (Int.repr
     (Z.b2z
        (true &&
         (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Hr0n: Z.shiftr r0 64 = Z.shiftr (sign - 1) 1
Vint
  (Int.repr
     (Z.b2z
        (true &&
         (r0 mod 2 ^ 64 =? (sign * 2 ^ n) mod 2 ^ 64)))) = 
Vint (Int.repr 0)

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Hr0n: Z.shiftr r0 64 = Z.shiftr (sign - 1) 1
Int64.repr (Z.shiftr r0 64) = 
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))

    
Espec: OracleKind
r: val
sh: share
r0, n, sign: Z
Delta_specs: Maps.PTree.t funspec
SH: readable_share sh
H: -2 ^ 127 <= r0 <= 2 ^ 127 - 1
H0: 0 <= n < 127
H1: sign = -1 \/ sign = 1
H2: n < 64
Hr0: (r0 =? sign * 2 ^ n) = ((Z.shiftr r0 64 =?
                       Z.shiftr (sign - 1) 1) &&
                       (r0 mod 2 ^ 64 =?
                       (sign * 2 ^ n) mod 2 ^ 64))%bool
H3: Int64.repr (Z.shiftr r0 64) <>
Int64.repr
  (Int.signed
     (Int.shr (Int.repr (sign - 1)) (Int.repr 1)))
Hr0n: Z.shiftr r0 64 = Z.shiftr (sign - 1) 1
Int64.repr (Z.shiftr r0 64) = 
Int64.repr (Z.shiftr (sign - 1) 1)

    congruence.
Qed.
================================================ FILE: alectryon/verif_modinv64_impl.v.html ================================================ [File too large to display: 32.7 MB] ================================================ FILE: compcert-opensource.nix ================================================ { stdenv, lib, fetchurl , coq, flocq, ocaml, menhir, menhirLib, findlib , ccomp-platform ? if stdenv.isDarwin then "x86_64-macosx" else "x86_64-linux" }: assert lib.versionAtLeast ocaml.version "4.05"; assert lib.versionAtLeast coq.coq-version "8.9"; stdenv.mkDerivation { pname = "compcert"; version = "3.14"; src = fetchurl { url = "https://github.com/AbsInt/CompCert/archive/v3.14.tar.gz"; hash = "sha256-VYh0fbyJeHKu9Hldt8kro/k4T18qwbxFXjsBstPJryA="; }; # Unpack only those files that are open source licensed (GPL2 or GPL3). unpackPhase = '' tar -xf $src --wildcards --no-wildcards-match-slash \ 'CompCert*/MenhirLib' \ 'CompCert*/lib' \ 'CompCert*/common' \ 'CompCert*/cfrontend/C2C.ml' \ 'CompCert*/cfrontend/Clight.v' \ 'CompCert*/cfrontend/ClightBigstep.v' \ 'CompCert*/cfrontend/Cop.v' \ 'CompCert*/cfrontend/CPragmas.ml' \ 'CompCert*/cfrontend/Csem.v' \ 'CompCert*/cfrontend/Cstrategy.v' \ 'CompCert*/cfrontend/Csyntax.v' \ 'CompCert*/cfrontend/Ctypes.v' \ 'CompCert*/cfrontend/Ctyping.v' \ 'CompCert*/cfrontend/PrintClight.ml' \ 'CompCert*/cfrontend/PrintCsyntax.ml' \ 'CompCert*/backend/Cminor.v' \ 'CompCert*/backend/PrintCminor.ml' \ 'CompCert*/cparser' \ 'CompCert*/export' \ 'CompCert*/*/Archi.v' \ 'CompCert*/*/Builtins1.v' \ 'CompCert*/*/CBuiltins.ml' \ 'CompCert*/*/extractionMachdep.v' \ 'CompCert*/extraction/extraction.v' \ 'CompCert*/configure' \ 'CompCert*/Makefile' \ 'CompCert*/Makefile.extr' \ 'CompCert*/Makefile.menhir' \ 'CompCert*/LICENSE' \ 'CompCert*/README.md' \ 'CompCert*/VERSION' cd CompCert* mkdir doc ''; patches = [ ./compcert-opensource.patch ]; buildInputs = [ ocaml findlib coq menhir menhirLib ]; propagatedBuildInputs = [ flocq ]; enableParallelBuilding = true; configurePhase = '' ./configure \ -bindir $out/bin \ -libdir $out/lib \ -install-coqdev \ -use-external-Flocq \ -coqdevdir $out/lib/coq/${coq.coq-version}/user-contrib/compcert \ ${ccomp-platform} ''; preBuild = "make depend"; buildFlags = [ "proof" "export/Clightdefs.vo" "compcert.config" ]; meta = with lib; { description = "Formally verified C compiler"; homepage = "http://compcert.inria.fr"; license = licenses.gpl3; # These particular files are all gpl3 compatible. platforms = [ "x86_64-linux" "x86_64-darwin" ]; }; } ================================================ FILE: compcert-opensource.patch ================================================ --- CompCert-3.9/Makefile 2021-05-10 04:11:36.000000000 -0400 +++ CompCert-3.9-adj/Makefile 2021-06-19 18:50:59.484683789 -0400 @@ -28,7 +28,7 @@ ARCHDIRS=$(ARCH)_$(BITSIZE) $(ARCH) endif -DIRS := lib common $(ARCHDIRS) backend cfrontend driver export cparser +DIRS := lib common $(ARCHDIRS) backend cfrontend export cparser COQINCLUDES := $(foreach d, $(DIRS), -R $(d) compcert.$(d)) @@ -112,41 +112,12 @@ # Back-end modules (in backend/, $(ARCH)/) BACKEND=\ - Cminor.v Cminortyping.v Op.v CminorSel.v \ - SelectOp.v SelectDiv.v SplitLong.v SelectLong.v Selection.v \ - SelectOpproof.v SelectDivproof.v SplitLongproof.v \ - SelectLongproof.v Selectionproof.v \ - Registers.v RTL.v \ - RTLgen.v RTLgenspec.v RTLgenproof.v \ - Tailcall.v Tailcallproof.v \ - Inlining.v Inliningspec.v Inliningproof.v \ - Renumber.v Renumberproof.v \ - RTLtyping.v \ - Kildall.v Liveness.v \ - ValueDomain.v ValueAOp.v ValueAnalysis.v \ - ConstpropOp.v Constprop.v ConstpropOpproof.v Constpropproof.v \ - CSEdomain.v CombineOp.v CSE.v CombineOpproof.v CSEproof.v \ - NeedDomain.v NeedOp.v Deadcode.v Deadcodeproof.v \ - Unusedglob.v Unusedglobproof.v \ - Machregs.v Locations.v Conventions1.v Conventions.v LTL.v \ - Allocation.v Allocproof.v \ - Tunneling.v Tunnelingproof.v \ - Linear.v Lineartyping.v \ - Linearize.v Linearizeproof.v \ - CleanupLabels.v CleanupLabelsproof.v \ - Debugvar.v Debugvarproof.v \ - Mach.v \ - Bounds.v Stacklayout.v Stacking.v Stackingproof.v \ - Asm.v Asmgen.v Asmgenproof0.v Asmgenproof1.v Asmgenproof.v + Cminor.v # C front-end modules (in cfrontend/) -CFRONTEND=Ctypes.v Cop.v Csyntax.v Csem.v Ctyping.v Cstrategy.v Cexec.v \ - Initializers.v Initializersproof.v \ - SimplExpr.v SimplExprspec.v SimplExprproof.v \ - Clight.v ClightBigstep.v SimplLocals.v SimplLocalsproof.v \ - Cshmgen.v Cshmgenproof.v \ - Csharpminor.v Cminorgen.v Cminorgenproof.v +CFRONTEND=Ctypes.v Cop.v Csyntax.v Csem.v Ctyping.v Cstrategy.v \ + Clight.v ClightBigstep.v # Parser @@ -162,30 +133,19 @@ MENHIRLIB= endif -# Putting everything together (in driver/) - -DRIVER=Compopts.v Compiler.v Complements.v - # Library for .v files generated by clightgen ifeq ($(CLIGHTGEN),true) EXPORTLIB=Ctypesdefs.v Clightdefs.v Csyntaxdefs.v else EXPORTLIB= endif # All source files -FILES=$(VLIB) $(COMMON) $(BACKEND) $(CFRONTEND) $(DRIVER) $(FLOCQ) \ +FILES=$(VLIB) $(COMMON) $(BACKEND) $(CFRONTEND) $(FLOCQ) \ $(MENHIRLIB) $(PARSER) $(EXPORTLIB) -# Generated source files - -GENERATED=\ - $(ARCH)/ConstpropOp.v $(ARCH)/SelectOp.v $(ARCH)/SelectLong.v \ - backend/SelectDiv.v backend/SplitLong.v \ - cparser/Parser.v - all: @test -f .depend || $(MAKE) depend $(MAKE) proof @@ -311,20 +271,13 @@ $(MENHIR) --coq --coq-no-version-check cparser/Parser.vy @chmod a-w $@ -depend: $(GENERATED) depend1 +depend: depend1 -depend1: $(FILES) export/Clightdefs.v +depend1: $(FILES) export/Ctypesdefs.v export/Clightdefs.v @echo "Analyzing Coq dependencies" @$(COQDEP) $^ > .depend install: - install -d $(DESTDIR)$(BINDIR) - install -m 0755 ./ccomp $(DESTDIR)$(BINDIR) - install -d $(DESTDIR)$(SHAREDIR) - install -m 0644 ./compcert.ini $(DESTDIR)$(SHAREDIR) - install -d $(DESTDIR)$(MANDIR)/man1 - install -m 0644 ./doc/ccomp.1 $(DESTDIR)$(MANDIR)/man1 - $(MAKE) -C runtime install ifeq ($(CLIGHTGEN),true) install -m 0755 ./clightgen $(DESTDIR)$(BINDIR) endif @@ -348,7 +301,7 @@ rm -f compcert.ini compcert.config rm -f extraction/STAMP extraction/*.ml extraction/*.mli .depend.extr rm -f tools/ndfun tools/modorder tools/*.cm? tools/*.o - rm -f $(GENERATED) .depend + rm -f .depend rm -f .lia.cache $(MAKE) -f Makefile.extr clean $(MAKE) -C runtime clean ================================================ FILE: default.nix ================================================ { nixpkgs ? import {} , ghc ? "ghc98" , coqPackages ? "coqPackages_8_17" , production ? false , secp256k1git ? null , wideMultiply ? null , withAlectryon ? true , withCoverage ? false , withProfiler ? false , withSafegcdCheat ? false , withTiming ? true , withValgrind ? false , doCheck ? true , env ? "stdenv" }: let hp = nixpkgs.haskell.packages.${ghc}; cp = nixpkgs.${coqPackages}; pp = nixpkgs.python3Packages; in rec { haskell = haskellPackages.callPackage ./Simplicity.Haskell.nix { inherit doCheck withValgrind; }; haskellPackages = hp.override { overrides = self: super: { Simplicity = haskell; # Temporary work around for https://github.com/wrengr/unification-fd/issues/70 "unification-fd" = self.callPackage ({ mkDerivation, base, containers, logict, mtl }: mkDerivation { pname = "unification-fd"; version = "0.11.2"; sha256 = "1lyx3g10llkr7vl7c2j15ddlqrkz2r684d1laza7nvq97amrqnqv"; revision = "1"; editedCabalFile = "07xmrqmk99lnp3jyk0dqgnpprm3ghnyjdqva0y13ddh3nw8iiqdj"; libraryHaskellDepends = [ base containers logict mtl ]; description = "Simple generic unification algorithms"; license = nixpkgs.lib.licenses.bsd3; hydraPlatforms = nixpkgs.lib.platforms.none; patches = [ ./unification.patch ]; }) {}; }; }; coq = nixpkgs.callPackage ./Simplicity.Coq.nix { alectryon = if withAlectryon then pp.alectryon else null; inherit (cp) coq serapi; inherit safegcd-bounds vst; }; c = nixpkgs.callPackage ./Simplicity.C.nix { inherit doCheck production wideMultiply withCoverage withProfiler withTiming withValgrind; stdenv = nixpkgs.${env}; }; compcert = nixpkgs.callPackage ./compcert-opensource.nix { inherit (cp) coq flocq; inherit (cp.coq.ocamlPackages) ocaml menhir menhirLib findlib; ccomp-platform = "x86_64-linux"; }; pdf = nixpkgs.runCommand "Simplicity-TR" {} '' export TEXMACS_HOME_PATH=$NIX_BUILD_TOP mkdir -p $out/share/ cp ${./Simplicity-TR.tm} Simplicity-TR.tm cp ${./Simplicity.bib} Simplicity.bib mkdir -p $TEXMACS_HOME_PATH/progs cat < $TEXMACS_HOME_PATH/progs/my-init-buffer.scm ; inspired by http://savannah.gnu.org/bugs/?32944 (generate-all-aux) (print-to-file "Simplicity-TR.pdf") (style-clear-cache) EOF ${nixpkgs.xvfb-run}/bin/xvfb-run ${nixpkgs.texmacs}/bin/texmacs -c Simplicity-TR.tm $out/share/Simplicity-TR.pdf -q ''; vst = nixpkgs.callPackage ./vst.nix { inherit (cp) coq; inherit compcert; }; safegcd-bounds = nixpkgs.callPackage ./safegcd-bounds.nix { inherit (cp) coq; cheating = withSafegcdCheat; }; # $ nix-build -A inheritance -o inheritance.Coq.eps inheritance = nixpkgs.runCommand "inheritance.Coq.eps" { buildInputs = [ nixpkgs.graphviz ]; } "dot ${./inheritance.Coq.dot} -Teps -o $out"; } ================================================ FILE: inheritance.Coq.dot ================================================ digraph { node [fontname=Courier,shape=box] rankdir="BT" Core Assertion->Core Primitive->Assertion Jet->Primitive Witness->Core AssertionWitness->Assertion AssertionWitness->Witness FullSimplicity->Jet FullSimplicity->AssertionWitness Delegation->Witness AssertionDelegation->AssertionWitness AssertionDelegation->Delegation FullSimplicityWithDelegation->FullSimplicity FullSimplicityWithDelegation->AssertionDelegation {rank=same; Assertion Witness} {rank=same; Primitive AssertionWitness Delegation} {rank=same; FullSimplicity AssertionDelegation} } ================================================ FILE: manual-index.html ================================================ Simplicity-0.0.0
Simplicity-0.0.0

Simplicity-0.0.0

 

Signatures

Modules

================================================ FILE: safegcd-bounds.nix ================================================ {lib, stdenv, fetchFromGitHub, coq, cheating ? true } : stdenv.mkDerivation { name = "safegcd-bounds-coq-divsteps"; src = fetchFromGitHub { owner = "sipa"; repo = "safegcd-bounds"; rev ="06abb7f7aba9b00eb4ead96bdd7dbcc04ec45c4f"; sparseCheckout = [ "coq/divsteps" ]; hash = "sha256-I+1TFBJOQxro09hkHBdCrLptoq06RYaeBz5PbPLzjGA="; name = "safegcd-bounds"; }; sourceRoot = "safegcd-bounds/coq/divsteps"; ${if cheating then "postPatch" else null} = '' substituteInPlace divsteps724.v --replace-fail "Time Qed." "Admitted." ''; buildInputs = [ coq ]; enableParallelBuilding = true; preBuild = '' coq_makefile -f _CoqProject -o Makefile ''; installFlags = "COQLIBINSTALL=$(out)/lib/coq/${coq.coq-version}/user-contrib/"; } ================================================ FILE: shell.nix ================================================ { haskell ? true , coq ? true , c ? true , nixpkgs ? import {} , ghc ? "ghc98" , coqPackages ? "coqPackages_8_17" , env ? "stdenv" , withCoverage ? true , withProfiler ? true , withSafegcdCheat ? true , withValgrind ? true }: let simplicity = import ./. {inherit nixpkgs ghc coqPackages env withCoverage withProfiler withSafegcdCheat withValgrind;}; optional = nixpkgs.lib.optional; haskellDevTools = pkgs: with pkgs; [cabal-install hlint hasktags]; haskellPkgs = pkgs: simplicity.haskell.buildInputs ++ simplicity.haskell.propagatedBuildInputs ++ haskellDevTools pkgs; haskellDevEnv = simplicity.haskellPackages.ghcWithPackages haskellPkgs; coqDevEnv = [ nixpkgs.python3Packages.alectryon nixpkgs.${coqPackages}.serapi nixpkgs.${coqPackages}.coq nixpkgs.${coqPackages}.coqide ]; in nixpkgs.mkShell { packages = optional haskell haskellDevEnv ++ optional coq coqDevEnv; inputsFrom = optional coq simplicity.coq ++ optional c simplicity.c; } ================================================ FILE: spelling.ignore.txt ================================================ alo ba catche crate fro fromWord hge ist iterm memoty nd olt outin shiftin shs thn toWord wit ================================================ FILE: unification.patch ================================================ --- unification-fd-0.11.2/unification-fd.cabal 2001-09-08 21:46:40.000000000 -0400 +++ unification-fd-0.11.2/unification-fd.cabal 2024-05-21 17:53:32.740519714 -0400 @@ -70,7 +70,7 @@ -- should be resolved now. Cf., -- -- - Build-Depends: logict >= 0.4 && < 0.8.1 + Build-Depends: logict >= 0.4 && < 0.8.3 -- N.B., Tasty requires base>=4.5.0.0; which -- means we aren't CI testing anything older than -- that anymore, so we might as well just require ================================================ FILE: vst.nix ================================================ {lib, stdenv, fetchFromGitHub, coq, compcert, ignoreCompcertVersion ? compcert.version=="3.14" # Temporarily allow compcert 3.14 } : stdenv.mkDerivation { name = "vst-sha256-2.14"; src = fetchFromGitHub { owner = "PrincetonUniversity"; repo = "VST"; rev ="v2.14"; hash = "sha256-NHc1ZQ2VmXZy4lK2+mtyeNz1Qr9Nhj2QLxkPhhQB7Iw"; }; buildInputs = [ coq ]; propagatedBuildInputs = [ compcert ]; patches = [ ]; postPatch = '' substituteInPlace util/coqflags \ --replace "\`/bin/pwd\`" "$out/lib/coq/${coq.coq-version}/user-contrib/VST" patchShebangs --build util/* ''; enableParallelBuilding = true; makeFlags = lib.optional ignoreCompcertVersion "IGNORECOMPCERTVERSION=true" ++ [ "COMPCERT=inst_dir" "COMPCERT_INST_DIR=${compcert}/lib/coq/${coq.coq-version}/user-contrib/compcert" "INSTALLDIR=$(out)/lib/coq/${coq.coq-version}/user-contrib/VST" ]; buildFlags = [ "default_target" "sha" ]; postBuild = '' gcc -c sha/sha.c -o sha/sha.o ''; postInstall = '' install -d "$out/lib/coq/${coq.coq-version}/user-contrib/sha" find sha -name \*.vo -exec sh -c ' install -m 0644 -T "$0" "$out/lib/coq/${coq.coq-version}/user-contrib/$0" install -m 0644 -T "''${0%.vo}.v" "$out/lib/coq/${coq.coq-version}/user-contrib/''${0%.vo}.v" ' {} \; install -d "$out/lib/sha" install -m 0644 -t "$out/lib/sha" "sha/sha.o" "sha/sha.h" install -d "$out/share" install -m 0644 -t "$out/share" "_CoqProject-export" ''; }