Repository: creachadair/imath Branch: main Commit: 2a1818b001fd Files: 92 Total size: 2.2 MB Directory structure: gitextract_l6z2n_88/ ├── .dockerignore ├── .gitattributes ├── .github/ │ └── workflows/ │ └── unit-tests.yml ├── ChangeLog ├── LICENSE ├── Makefile ├── README.md ├── contrib/ │ ├── Makefile.msvc │ └── README ├── doc.md ├── doc.md.in ├── examples/ │ ├── basecvt.c │ ├── findprime.c │ ├── imcalc.c │ ├── input.c │ ├── pi.c │ ├── randprime.c │ ├── rounding.c │ └── rsakey.c ├── gmp_compat.c ├── gmp_compat.h ├── imath.c ├── imath.h ├── imdrover.c ├── imdrover.h ├── imrat.c ├── imrat.h ├── imtest.c ├── imtimer.c ├── iprime.c ├── iprime.h ├── macros.c ├── rsamath.c ├── rsamath.h ├── tests/ │ ├── add.tc │ ├── bigmul.tc │ ├── bigsqr.tc │ ├── bintest.c │ ├── bug-qread.c │ ├── bug-swap.c │ ├── compare.tc │ ├── conv.tc │ ├── div.tc │ ├── egcd.tc │ ├── emod.tc │ ├── emodv.tc │ ├── expt.tc │ ├── gcd.tc │ ├── gmp-compat-test/ │ │ ├── .gitignore │ │ ├── Makefile │ │ ├── README │ │ ├── genctest.py │ │ ├── gendata.py │ │ ├── genpytest.py │ │ ├── gmp_custom_test.c │ │ ├── gmpapi.py │ │ ├── imath_custom_test.c │ │ ├── runtest │ │ └── runtest.py │ ├── imath-test.scm │ ├── init.tc │ ├── invmod.tc │ ├── isprime.tc │ ├── lcm.tc │ ├── linux/ │ │ └── Dockerfile │ ├── mod.tc │ ├── mul.tc │ ├── neg.tc │ ├── pi1024.txt │ ├── pi1500-10.txt │ ├── pi1698-16.txt │ ├── pi4096-10.txt │ ├── qadd.tc │ ├── qaddz.tc │ ├── qdecompose.tc │ ├── qdiv.tc │ ├── qdivz.tc │ ├── qmisc.tc │ ├── qmul.tc │ ├── qmulz.tc │ ├── qsub.tc │ ├── qsubz.tc │ ├── qtodec.tc │ ├── root.tc │ ├── rtest.c │ ├── set.tc │ ├── sqr.tc │ ├── sub.tc │ ├── test.bc │ └── test.sh └── tools/ ├── findthreshold.py └── mkdoc.py ================================================ FILE CONTENTS ================================================ ================================================ FILE: .dockerignore ================================================ .git ChangeLog LICENSE contrib **/*.gz **/*.md **/*.o **/*.so **/Dockerfile tests/*.bc tests/*.scm tests/linux tests/random.tests ================================================ FILE: .gitattributes ================================================ *.tc linguist-language=fundamental ================================================ FILE: .github/workflows/unit-tests.yml ================================================ name: Unit tests on: push: branches: - main pull_request: types: [opened, reopened, synchronize] workflow_dispatch: permissions: contents: read jobs: build: strategy: fail-fast: false matrix: os: [ubuntu-latest, ubuntu-24.04-arm, macos-latest] compiler: ['gcc', 'clang'] exclude: - os: macos-latest compiler: gcc # gcc is clang on macOS runs-on: ${{ matrix.os }} env: CC: ${{ matrix.compiler }} steps: - uses: actions/checkout@v6 - name: Log compiler version run: | "$CC" --version - name: make test # unit tests run: make test # TODO(creachadair): As of 25-Jan-2024, the GMP compatibility tests # on gcc no longer work correctly when run in containers either # locally or in github actions. They work fine from the CLI, but # for now turn them off in CI. - name: make check # unit and compatibility tests if: matrix.compiler != 'gcc' # `make check` is failing on gcc run: make check ================================================ FILE: ChangeLog ================================================ 1.35 Add mp_rat_set to set an mp_rat from two mp_int values (#71) Use mp_size for length and counter results instead of mp_result (#73) Improve documentation and tests for signed div and mod Add mp_rat_decompose to split mp_rat into integer and fractional parts (#74) 1.34 Minor documentation fixes. Reverse the ChangeLog so new items are first. f1acc48 Fix incorrect usage of CHECK macro in gmp_compat.c (#67) 0353f9d Silence unused-value warnings (#68) 1.33 Make mp_rat_read_cstring more consistent with mp_int_read_cstring. Add some tests for that. Include the standard ubuntu-24.04-arm runner type in the CI matrix. Exclude "gcc" builds from make check because they don't work. Update some of the Python test support code. 1.32 Add const qualifiers to global static data. (#53) Includes documentation and formatting cleanup, and some fixes to the tests and test scripts. 048b49c Reorganize allocation to make cleanup simpler. 18404fb Add a unit test for 4096 decimal digits of pi. e6d37f2 Merge pull request #42 from creachadair/pi-dynamic-output-buffer 9d6dfa1 Update test scripts to use Python 3. 1.31 Improvements to build and test automation; add CI configuration. d419633 Add a Travis CI configuration for imath. 3305c4a Ensure the Makefile respects a $CC set in the environment. d2da4b6 Update instructions for reporting bugs. 1.30 Improve test automation; no functional changes to the library. fc7846a imtest: Ensure the exit code is non-zero when tests fail. 87edcbe test.sh: Exit non-zero if any unit tests fail. 276d1f9 imtest: Make test output easier to read. c8c90c4 Make the Linux test protocol less brittle. f68ba5b Add a .gitattributes file. 33c2843 Add a docker-test target to the Makefile. 1.29 The Documentation Edition. The main improvement here is that the API documentation is now unified in the header files, and doc.md is now generated from a template that includes the text from the headers. The automation for this is still unsatisfactory, but it is better than it was. d239b2e Remove imath.py. e43b0f5 imath: Clean up extraneous whitespace. fbbbbad Remove the mpz struct tag. 718fef2 imath: Add documentation comments to the header. 02600e5 imath: Make radix bound checks into requirements. c21f49d imrat: Add documentation comments to the header. ea5398f Remove the mpq struct tag. c1549c7 Move tools and tests into subdirectories. 7187c49 Remove extraneous whitespace from declarations. afa715c Comment cleanup on Aisle 2. cbf9a03 Add tools/mkdoc.py. 58672fc Remove the "dist" target from Makefile. 894bb90 Move rtest.c into the tests directory. d4cfc69 Add a doc.md.in template file. bd929aa Add a make rule for doc.md from doc.md.in. 6dea44e Update doc.md using the new generator. 56ef9a0 doc: Include mp_int_set_uvalue. 13618b3 doc: Explain the comparator terminology. 9990b2e Make the clean and distclean make-rules equivalent. 13df978 doc: Update the explanation of temp handling macros. b80bd8a doc: Emit one generated comment for the whole file. 3cde6b8 doc: Remove the markdown disclaimer. 045a2a6 doc: Point my address to github instead of e-mail. 08f2efd doc: Add headings for general API functions. 77159d9 mkdoc.py: Link back to source lines. aec8587 doc: Include links back to the source. f8c9f6c imath: Document a constraint on mp_int_redux_const. 1.28 Another round of cleanup, and some more invasive API changes. I removed more macros, and added an API surface for setting the default precision and recursive-multiply threshold. The compile-time switchable statics are now strictly static. The handling of temporary values was greatly reworked to make it less brittle. ba44b37 Add unit tests for mp_int_is_prime. 6f10877 imath: Remove lvalue uses of access macros, and the macros. f4939db Fix formatting. 85137fa docs: Remove macro implementation comments. 37f046e Rework the handling of temporaries. cc8ac74 imtimer: Fix a lingering lvalue use of MP_USED. 9736a8b imath: Drop switchable statics and stdio dependency. 5445ad8 Add functions to set default precision and multiply threshold. 58f2d6e Use alpine:latest rather than a fixed version. 1.27 Another round of cleanup and bug fixes. This release includes a Dockerfile to support basic Linux testing, which I found useful as I do most of my work on macOS. This release also addresses most of issue #29 (Switching from C90 to C99). Part of that change removes most function-like macros from the API headers, replacing them with static functions. Code that used the macros as lvalues will no longer work, but can and should be easily updated to access the members of mpz_t directly. Fixed: #34. 899e202 Add a docker config for basic Linux testing. 40e8887 Move imath-test.scm to the tests directory. 6f01c9f Add .dockerignore to the release tarball. 1dab081 Fix the spelling of __abs__ in imath.py. 8f0a00c Enable source formatting for Python. 99e27c8 Format all Python source with yapf. bf289f0 gmp-compat-test: Remove dependency on Python 3. 9269d57 Clean up the Linux test image. 61ca691 Include stdbool.h and use the bool type where appropriate. d4760ee Replace macros with static inline functions. 8241977 linux test: Layer the image for better caching. 46bb578 imath: Replace accessor macros with inline functions. 50c6cc8 imrat: Replace accessor macros with static functions. 0c5cec9 gmp_compat: Fix lvalue uses of MP_USED. 89c72f2 Remove CHECK and NRCHECK macros. dbe9f50 imath: Replace macros with static functions. 0006998 imath: Replace ROUND_PREC macro with a function. b628a0c Move local variable declarations closer to first use. 54d51da Remove obsolete division spec. 796776f iprime: Move and scope variables closer to first use. 8fd5236 iprime: Use a sentinel instead of a length. ce89180 Include getopt.h explicitly where it is required. e6fc170 Make libimath.so build correctly under GCC. b54d8c9 Use Bourne in preference to Bash. 8f88c01 Makefile: Export CC and CFLAGS for submakes. 58f4392 Use the inherited settings in the gmp-compat-tests. 8a181cd Make the Linux docker test run "make check". 28617f2 gmp_compat: Fix overflow in the uint conversion adapter. 1.26 Another round of fixes. Notably the gmp-compat-test again works on macOS, fixing https://github.com/creachadair/imath/issues/26. Also, this release cleans up some more warnings and fixes some missing #include paths. 2ea0fff gmp_compat: Fix warnings for mixed-sign comparisons. 2a41bae Fix DLL loading. 56c40f4 Make gmp-compat-test work again on macOS. f163906 Comment out a vacuously true assertion. 667d90e gmp_compat: Ensure a definition of ssize_t is available. 6c6fdd8 Fix a vacuously meaningless comparison. 4dac16f Silence a warning about an uninitialized variable. c6119c4 Include strings.h for strcasecmp. 1.25 This version fixes several issues found by clang static analysis. It also includes some additional follow-on cleanup tasks from the previous release. b5a73c4 Cleanup: Use .tc for test files instead of .t. dc307ae Cleanup: Remove dead author URLs, SVN markers. 389a1be bug: Fix a memory leak in test_meta. 8fb98f7 bug: Fix a use of an uninitialized pointer. fe0757a bug: Fix reads of uninitialized fields in free_test. 08fe765 bug: Fix a reachable null pointer indirection. 7b10453 bug: Remove a redundant initialization. cebce44 bug: Fix various dead assignments. ef36352 Remove the findsizes.py script. eebfb85 Fix some more comparison-sign mismatches. 9abcf66 Cleanup: Update a stale reference to doc.txt in the README. 8ec696f Cleanup: Consolidate the USE_32BIT_WORDS macro sections. 1.24 A cosmetic update, consisting mainly of readability updates, documentation fixes, and warning fixes. There are not intended to be any functional changes in this update, but a fair bit of code and the Makefile have been modified, so I'm adding a tag. My intent is to keep the source formatted with clang-format going forward, though I will need to set up some presubmit checks to enforce that. For now it is still a manual step via "make format". 7e45d6a Remove a doc reference to MP_USMALL_MIN. 544687d Fix the spelling of mp_error_string in doc.md. 592d4a0 Fix some mis-converted section breaks in doc.md. df9fe8e Format source files with clang-format. fcb4e21 Build with 64-bit words by default. 1579b70 Minor simplifications to the Makefile. 0fbe8e6 Style cleanup: More invasive manual changes. 1d28177 Add -Wextra and -Wno-unused-parameter to default build flags. 15ba02a Fix warnings for signed/unsigned comparisons. 3556984 Style cleanup: Insert missing brackets. 1.23 Portability fixes from PostgreSQL (#8), from nmisch. 1.22 Remove MP_USMALL_MIN, which was unused by anything in imath. Rework doc.txt into Markdown. Restore imath-test.scm and imath.py, dropped during import. 1.21 Fix a syntax error. TODO: Run tests before merging, or better still set up CI someplace. Remove dead division code. Restore a missing comparison. Drop dead flags from the Makefile. 1.20 Fix broken comments, apparently from a previous bad merge. Remove emacs folding-mode comments throughout. Some minor Makefile cleanup to make clang happier. 1.19 Fix signedness error in compile. Reported by Paweł Sikora. 1.18 Made mp_int_rat() use mp_int_init() to initialize numerator and denominator instead of mp_int_init_size(). Some minor code cleanup inside the testing code (imdrover.c). Fixed an off-by-one bug in s_udiv() which could cause the quotient guessing loop to spin. Reported by Andres Navarro. Added triggering example to div.t as a regression test. 1.17 Fixed a bug in mp_int_swap() where mpz_t structures using their single field as storage would not get swapped correctly. Reported by Andres Navarro Added regression test for this and some hooks for future regressions in the tests/test.sh script. 1.16 Fixed a bug in mp_int_to_uint() which was causing incorrect MP_RANGE errors during small integer conversion. Reported by Andrea Barberio Added mp_int_compare_uvalue(). Added some new testing hooks in imtest.c, new unit tests. Made some code style changes that do not affect functionality. 1.15 Fixed a bug in the definition of MP_DIGIT_MAX that caused errors when IMath is built under 64-bit Linux. Reported by Klaus Stengel . Unpacked the macro definitions in imath.c a bit, to make them more readable. Added mp_int_expt_full() by request of Andrea Barberio . 1.14 Instead of using the preprocessor to delete "static", the static definitions in imath.c now use an explicit STATIC macro, that is made null when DEBUG is defined. This avoids a subtle problem with static variables defined inside functions (although no bugs actually arose from it). Fixed a bug in s_udiv() while building on MinGW. When building with short type digits, the routine was incorrectly discarding overflow when computing the next quotient digit. Reported by Paul DeMarco . 1.13 Cosmetic change -- updated all the files with my new web address. Fixed a buglet caught by Love Hörnquist Âstrand using the LLVM static checker tools, in which a mp_int_copy() failure would be silently ignored and cause an extra copy to be generated. Fixed a bug in the testing suite while building on MinGW. The pi generation tests compare to static files and these tests fail if CR/LF is output instead of just LF. The test script now strips all CR and LF from the output and compares to files lacking them. Reported by Chris Cole . 1.12 Added a new global constant MP_MINERR which is the value of the smallest error code defined by IMath itself. This can be used by clients who wish to define and use additional error codes, so that those codes will not conflict with the existing set. Extended the imcalc example to include memory. Fixed a bug in mp_int_add() in which -1 + 1 = -0 (the sign of zero was recorded incorrectly). Added tests to the regression suite for this fix. 1.11 Those functions which take int parameters to supply one or more of the arithmetic values of the function have been converted to use a typedef "mp_small". This is defined in imath.h, along with some supporting macros. Added mp_int_to_uint() and mp_int_lcm() in imath.{h,c}, based on a patch contributed by Hal Finkel. Added LCM tests as as well as some more GCD tests in tests/lcm.t and tests/gcd.t Also at Hal Finkel's request, added mp_int_root() to compute the integer nth root, i.e., \lfloor a^{1/b}\rfloor; replaced the old mp_int_sqrt() function with a call to mp_int_root() via a macro. The new implementation is probably slightly less efficient for square roots, but more general. Added tests/root.t and moved the sqrt tests there, also. 1.10 All primes less than 1000 are now used in iprime.c for preliminary testing of prime candidates. Removed declaration of s_pad() from rsakey.c example. Added imcalc.c example. Beginning with this release, defining the DEBUG preprocessor macro when compiling imath.c causes all the normally-static helper functions to be exported. This makes it easier to troubleshoot bugs in the back end functions without manually editing the source till you have found where the bug actually is. Fixed a memory leak in the test driver (imtest.c) where the input buffers allocated for test specs were not released before being released. No impact on the core routines, but nevertheless not a good thing. Fixed several uninitialized memory reads and one subtle read past the end of a buffer in s_kmul(), found during a run of Purify. Thanks to Love Hörnquist Âstrand for finding this one, and providing a good test case so I could isolate the problem. Also fixed a buglet in s_kmul(), in which free() was being called instead of s_free(), which would break if you provided a custom version of s_alloc() and s_free() for your application. 1.9 Increased the number of small primes used for primality testing to 100 from 32. Removed an unwanted #define from imath.c, left over from testing; added "static" to the declaration of the s_embar() internal function since it is not used outside imath.c. Reduced the quantity of feedback generated by rsakey.c during the prime finding stage of key generation. 1.8 Fixed a bug in s_udiv() affecting the computation of quotient digits. Thanks to Love Âstrand for isolating this bug. Also in this release, defining USELLONG=Y or USELLONG=N on the command line for make will switch support for the "long long" data type on or off without having to edit the Makefile. The default is still to permit use of "long long", even though the type is not standard ANSI C90. 1.7 Fixed a subtle casting problem in the use of the ctype macros that would permit negative signed character values to produce illogical behaviour in some configurations (e.g., NetBSD). Removed a dead "return" statement. Added the -pedantic switch for gcc, to get more aggressive warnings; to permit the nonstandard "long long" type to still be used, I also added -Wno-long-long when building with long long enabled (the standard configuration). Fixed a bug found by the Samba team running Valgrind on the Heimdal project, and reported by Love Hörnquist Âstrand: One of the intermediate values used during modular exponentiation could be overflowed during recursive multiplication. Fixed by taking a more conservative approach to buffer sizing. Added a "contrib" subdirectory, whose first entry is a Makefile to build IMath with the MSVC++ "nmake" program, contributed by Matus Horvath. 1.6 Defined default_precision and multiply_threshold to be constant and static. If IMATH_TEST is defined at compile time, these are made global, and can be modified by the caller (the imtimer tool makes use of this ability, for example). Implemented a single-digit optimization suggested by J. Shapiro. Documentation updated. 1.5 Changed the API for rational rounding. Removed the two functions mp_rat_set_rounding() and mp_rat_get_rounding(), along with the round_output global variable. Redefined the MP_ROUND_* constants as an enumeration type (mp_round_mode). Added a new parameter to the mp_rat_to_decimal() function to accept a rounding mode. Unit tests and doc.txt updated suitably. This release also incorporates a small patch submitted by Jonathan Shapiro to support compilation in C++. 1.4 Fixed a bug in mp_int_alloc(), it was not returning NULL when out of memory, but rather failing in assert() instead. Also, updated the documentation to have better language about the return values in various error conditions. 1.3 Replaced findsizes.pl with findsizes.py. Fixed two bugs in the rsakey tool that were leading to incorrect output. 1.2 Dropped bugfix component of revision number. Fixed rsakey.c example program to be complete and work faster. 1.1.9 Added mp_rat_alloc() and mp_rat_free(). Fixed a couple of minor bugs in the doc.txt file. Added mp_int_sqrt() to imath.{h,c} and doc.txt. 1.1.8 Added mp_int_alloc() and mp_int_free(). 1.1.7 Fixed a bug in s_udiv(), internal to imath.c, which caused division to fail in some corner cases masked by the use of long long as a word type. As a result, s_udiv() has now been wholly rewritten. I also fixed a few lingering buffer-length errors in s_kmul(), and added a "const" qualifier to the input buffers for the mp_int_read_string() and mp_int_read_cstring() functions, and their analogs in imrat.c. 1.1.6 Fixed a bug in mp_int_read_cstring() which would read the string "-0" with incorrect sign (MP_NEG instead of MP_ZPOS). This would violate an invariant that zero is always signed with positives. Added some tests to tests/neg.t to catch this case. 1.1.5 Added mp_rat_read_cdecimal() and mp_rat_read_ustring() Updated the input.c example. 1.1.4 Added mixed rational/integer operations: mp_rat_add_int, mp_rat_sub_int, mp_rat_mul_int, mp_rat_div_int Added rational exponentiation (with integer exponents): mp_rat_expt Tests for same were added to the tests/ subdirectory. 1.1.3 Rewrote mp_int_to_decimal() to support new rounding modes. The modes are documented in doc.txt. Some of the code sucked anyway, so I rewrote pretty much the entire function. Added new rounding mode constants. 1.1.2 Fixed a bug with leading zeroes after the decimal point in the mp_rat_read_decimal() function (imrat.c). Along the way, I also found a sign-related bug, in which -0.5 would be treated as if it were positive, because the sign of zero is implicitly positive, and the denominator is treated as unsigned always. Thanks to Eric Silva for pointing out the leading zeroes bug. The solution isn't the most efficient possible. 1.1.0 Added imrat.h and imrat.c, containing routines for rational number arithmetic at arbitrary precision. Added support to the test driver, in imath.c and included various tests in the tests/ subdirectory. Fixed a sign-of-zero bug in mp_int_mul(). Tests added to mul.t to regress this fix. 1.0.8 Fixed a small buffer-overrun in s_qmul(). Because it only allocates an extra digit if it absolutely has to, the test for whether it needs to carry a shift out into the "spare" digit had to be written carefully; I missed a subtlety, which is now fixed. Along the way, I fixed a minor performance-related bug in the same routine. Added mp_int_error_string(), which converts mp_result values into descriptive strings. These are statically allocated, so you don't have to free them. This version also adds an "examples" subdirectory. Currently, there is only one program there, but I will add more examples as time permits me. You have to read the source to understand them anyway, so I won't explain them here. 1.0.7 The mp_int_invmod(a, m, c) function would compute a negative value for c when given a < 0. I added some code to insure that the value returned is always the least non-negative member of the congruence class, if the inverse exists. A test for this was added to invmod.t. 1.0.6 Updated copyright notices, added LICENSE file explaining the license I am using. This is basically the BSD license, so you should have no trouble incorporating this code into other open source projects. No new functionality in this release. 1.0.5 Updated the Makefile to include the _GNU_SOURCE macro. For many GCC systems, this is necessary to get the correct definition of the ULLONG_MAX macro in . Also, you may now build with the make option DEBUG=Y to enable debugging, e.g.: make DEBUG=Y imtest By default, the Makefile builds with the optimizer enabled. Cleaned up the definitions triggered by USE_LONG_LONG in imath.h, and added an #error instruction in case the build is unable to find a definition of ULLONG_MAX or ULONG_LONG_MAX in . Also added the mp_int_to_unsigned(), mp_int_read_unsigned(), and mp_int_unsigned_len() prototypes. Fixed a bug in s_qmul() [imath.c:2493] that would grow the value being multiplied even if there was room in the existing digits to hold the result. This was driving an (apparent) bug in the more general mp_int_read_binary() routine. Added the routines mentioned in the previous paragraph, and factored some common code out into a static s_tobin(). Added reset_registers() to imdrover.{h,c}. Added new test driver functions test_to_uns() and test_read_uns(). Renamed test_read_bin to test_read_binary(). Silenced a sign-related warning in pi.c (related to printf). Added many new test vectors to tests/conv.t, including the original bug proof-of-concept from Tom Wu, and a series of new tests for the unsigned conversion routines. Updated `doc.txt' to reflect the changes described above. 1.0.4 Added `findsizes.pl' to the distribution. Revised the type declarations in imath.h to use 32/64 bit operations where the "long long" type is supported. Fixed a sign-related bug in mp_int_invmod(). Fixed several small bugs related to shifting which affect the use of 32-bit digits. Many architectures cannot shift by 32 bits at a time (e.g., MIPS), so I split each of these cases into two shifts of half the size, which should scale properly for both the smaller and larger cases. Fixed several arithmetic issues with 32-bit digits that arose due to missing type-casts on the right-hand sides of assignments. Fixed s_print() and s_print_buf() to handle the sizes of digits transparently. 1.0.3 Fixed a couple of bugs in pi.c that were causing incorrect values to be computed for > 30 digits or so. Added a pi-computation test to the default test suite (make test), checked against a static file computed by bc (set scale=1024, compute 4 * atan(1)). Added command line option to specify output radix for pi. Cleaned up a sign-related bug in mp_int_gcd(), which would cause the sign of gcd(0, x) to be incorrect when x < 0. Test cases added for future regression. Fixed a bug in s_reduce() which would give incorrect results for powers of 2 in certain circumstances. Added tests to drive this case for future regression. Added mp_int_exptmod_evalue() and mp_int_exptmod_bvalue() to make it easier to work with small bases and small exponents. Set default recursive multiplication threshold to 50 digits, since this seems to work best for the platforms I've tested so far. Added iprime.h and iprime.c to the distribution. 1.0.2 Fixed a bug in mp_int_div() which would yield incorrect quotients when the divisor was very close in value to a prefix of the dividend. This is now fixed, and there are regression tests in the tests directory. Added recursive multiplication and squaring (Karatsuba-Ofman) for large input values. Integrated these with the existing code for exponentiation, too. See the code for s_kmul() and s_ksqr() in imath.c. Tests added and verified against GNU bc. Added documentation on mp_get_multiply_threshold() and the reason why it exists. 1.0.1 First released version. ================================================ FILE: LICENSE ================================================ IMath is Copyright © 2002-2009 Michael J. Fromberger You may use it subject to the following Licensing Terms: 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: Makefile ================================================ ## ## Name: Makefile ## Purpose: Makefile for imath library and associated tools ## Author: M. J. Fromberger ## ## Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. ## ## 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. ## # --- begin configuration section --- ## Generic settings for systems with GCC (default) ## To build with debugging, add DEBUG=Y on the "make" command line. ifeq ($(origin CC),default) CC=gcc endif CFLAGS+=-pedantic -Wall -Werror -Wextra -Wno-unused-parameter \ -I. -std=c99 $(DFLAGS$(DEBUG)) CSFLAGS=$(CFLAGS) -fPIC #LIBS= # These are needed to build the GMP compatibility tests. export CC CFLAGS DFLAGS=-O3 -funroll-loops -finline-functions DFLAGSN=$(DFLAGS) DFLAGSY=-g -DDEBUG=1 # --- end of configuration section --- TARGETS=bintest bug-swap bug-qread imtest imtimer rtest HDRS=imath.h imrat.h iprime.h imdrover.h rsamath.h gmp_compat.h SRCS=$(HDRS:.h=.c) $(TARGETS:=.c) OBJS=$(SRCS:.c=.o) OTHER=LICENSE ChangeLog Makefile doc.md doc.md.in \ tools/findthreshold.py tools/mkdoc.py .dockerignore VPATH += examples tests EXAMPLES=basecvt findprime imcalc input pi randprime rounding rsakey .PHONY: all test clean distclean .SUFFIXES: .so .md .c.o: $(CC) $(CFLAGS) -c $< .c.so: $(CC) $(CSFLAGS) -o $@ -c $< all: objs examples test objs: $(OBJS) # N.B.: With a stock installation of Python 2 on macOS, this test may fail # because SIP may block its attempt to load the shared library. If you see # this error on macOS: # # Reason: unsafe use of relative rpath libimath.so # in imath_test.so with restricted binary # # try the Homebrew version of Python 2: brew install python@2 # check: test gmp-compat-test @ echo "Completed running imath and gmp-compat unit tests" test: imtest pi bug-swap bug-qread doc.md @ echo "" @ echo "Running tests, you should not see any 'FAILED' lines here." @ echo "If you do, please see doc.txt for how to report a bug." @ echo "" (cd tests && ./test.sh) gmp-compat-test: libimath.so @ echo "Running gmp-compat unit tests" @ echo "Printing progress after every 100,000 tests" make -C tests/gmp-compat-test TESTS="-p 100000 random.tests" docker-image: clean docker build -t imath/test-runner -f tests/linux/Dockerfile . docker-test: docker-image docker run --rm -it imath/test-runner:latest $(EXAMPLES):%: imath.o imrat.o iprime.o %.o $(CC) $(CFLAGS) -o $@ $^ $(LIBS) $(TARGETS):%: imath.o imrat.o %.o $(CC) $(CFLAGS) -o $@ $^ $(LIBS) examples: $(EXAMPLES) libimath.so: imath.so imrat.so gmp_compat.so $(CC) $(CFLAGS) -shared -o $@ $^ imtest: imtest.o imath.o imrat.o imdrover.o iprime.o rtest: rtest.o imath.o rsamath.o # Requires clang-format: https://clang.llvm.org/docs/ClangFormat.html format-c: @ echo "Formatting C source files and headers ..." find . -type f -name '*.h' -o -name '*.c' -print0 | \ xargs -0 clang-format --style=Google -i # Requires yapf: pip install yapf format-py: @ echo "Formatting Python source files ..." find . -type f -name '*.py' -print0 | \ xargs -0 yapf --style=pep8 -i # Format source files. format: format-c format-py # Generate documentation from header comments. # This rule depends on the header files to ensure the docs get updated when the # headers change. doc.md: doc.md.in imath.h imrat.h tools/mkdoc.py tools/mkdoc.py $< $@ clean distclean: rm -f -- *.o *.so *.pyc *~ core gmon.out examples/*~ rm -f -- tests/*~ tests/gmon.out make -C tests/gmp-compat-test clean rm -f $(TARGETS) $(EXAMPLES) ================================================ FILE: README.md ================================================ IMath ===== Arbitrary precision integer and rational arithmetic library. [![Unit tests](https://github.com/creachadair/imath/workflows/Unit%20tests/badge.svg)](https://github.com/creachadair/imath/actions/workflows/unit-tests.yml) IMath is an open-source ISO C arbitrary precision integer and rational arithmetic library. IMath is copyright © 2002-2009 Michael J. Fromberger. > 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. About IMath ----------- IMath is a library written in portable ISO C that allows you to perform arithmetic on integers and rational numbers of arbitrary precision. While many programming languages, including Java, Perl, and Python provide arbitrary precision numbers as a standard library or language feature, C does not. IMath was designed to be small, self-contained, easy to understand and use, and as portable as possible across various platforms. The API is simple, and the code should be comparatively easy to modify or extend. Simplicity and portability are useful goals for some applications—however, IMath does not attempt to break performance records. If you need the fastest possible implementation, you might consider some other libraries, such as GNU MP (GMP), MIRACL, or the bignum library from OpenSSL. Programming with IMath ---------------------- Detailed descriptions of the IMath API can be found in [doc.md](doc.md). However, the following is a brief synopsis of how to get started with some simple tasks. To do basic integer arithmetic, you must declare variables of type `mpz_t` in your program, and call the functions defined in `imath.h` to operate on them. Here is a simple example that reads one base-10 integer from the command line, multiplies it by another (fixed) value, and prints the result to the standard output in base-10 notation: ```c #include #include #include "imath.h" int main(int argc, char *argv[]) { mpz_t a, b; char *buf; int len; if(argc < 2) { fprintf(stderr, "Usage: testprogram \n"); return 1; } /* Initialize a new zero-valued mpz_t structure */ mp_int_init(&a); /* Initialize a new mpz_t with a small integer value */ mp_int_init_value(&b, 25101); /* Read a string value in the specified radix */ mp_int_read_string(&a, 10, argv[1]); /* Multiply the two together... */ mp_int_mul(&a, &b, &a); /* Print out the result */ len = mp_int_string_len(&a, 10); buf = calloc(len, sizeof(*buf)); mp_int_to_string(&a, 10, buf, len); printf("result = %s\n", buf); free(buf); /* Release memory occupied by mpz_t structures when finished */ mp_int_clear(&b); mp_int_clear(&a); return 0; } ``` This simple example program does not do any error checking, but all the IMath API functions return an `mp_result` value which can be used to detect various problems like range errors, running out of memory, and undefined results. The IMath API also supports operations on arbitrary precision rational numbers. The functions for creating and manipulating rational values (type `mpq_t`) are defined in `imrat.h`, so that you need only include them in your project if you wish to. ================================================ FILE: contrib/Makefile.msvc ================================================ ## ## Name: Makefile.msvc ## Purpose: Makefile for IMath library and associated tools ## for Microsoft Visual Studio 2005 ## Author: Matus Horvath ## ## Copyright (C) 2006 Matus Horvath. Permission has been granted to use, ## modify, and redistribute this file according to the terms of the IMath ## license. ## ## Usage: nmake /f Makefile.msvc ## # --- begin configuration section --- ## Settings for Microsoft Windows systems using nmake. ## To build with debugging, add DEBUG=Y on the "nmake" command line. CC=cl.exe LD=link.exe CFLAGS=$(CFLAGS) -nologo -I. -D_CRT_SECURE_NO_DEPRECATE $(DCFLAGS) LDFLAGS=$(LDFLAGS) -nologo $(DLDFLAGS) LIBS=$(DLIBS) !if "$(DEBUG)" == "Y" DCFLAGS=-ZI -Od -DDEBUG=1 -DTRACEABLE_FREE=1 DLDFLAGS=-DEBUG #DLIBS=-lefence !else DCFLAGS=-O2 -Ob2 DLDFLAGS= #DLIBS= !endif ## Visual Studio C/C++ 2005 compiler supports "long long" 64-bit type. CFLAGS=$(CFLAGS) -DUSE_LONG_LONG # --- end of configuration section --- TARGETS=imtest.exe pi.exe bintest.exe findprime.exe HDRS=imath.h imrat.h iprime.h imdrover.h rsamath.h SRCS=$(HDRS:.h=.c) $(TARGETS:.exe=.c) OBJS=$(SRCS:.c=.obj) EXAMPLES=input.exe basecvt.exe rounding.exe .c.obj: $(CC) $(CFLAGS) -c $< all: objs examples test objs: $(OBJS) # Because Visual Studio does not permit Unix shell syntax, you will # have to run the tests manually once the "test" target is built. test: imtest.exe pi.exe # @ echo "" # @ echo "Running tests, you should not see any 'FAILED' lines here." # @ echo "If you do, please see doc.txt for how to report a bug." # @ echo "" # (cd tests && ./test.sh) $(EXAMPLES): imath.obj imrat.obj iprime.obj examples/$*.obj @move $*.obj examples/$*.obj $(LD) $(LDFLAGS) -out:$@ $** $(LIBS) examples: $(EXAMPLES) imtest.exe: imtest.obj imath.obj imrat.obj imdrover.obj $(LD) $(LDFLAGS) -out:$@ $** $(LIBS) pi.exe: pi.obj imath.obj $(LD) $(LDFLAGS) -out:$@ $** $(LIBS) findprime.exe: findprime.obj imath.obj iprime.obj $(LD) $(LDFLAGS) -out:$@ $** $(LIBS) rtest.exe: rtest.obj imath.obj rsamath.obj $(LD) $(LDFLAGS) -out:$@ $** $(LIBS) bintest.exe: imath.obj bintest.obj $(LD) $(LDFLAGS) -out:$@ $** $(LIBS) clean: del /q /f *.exe *.obj examples\*.obj # End of Makefile.msvc ================================================ FILE: contrib/README ================================================ The files in this directory have been contributed to the IMath project by other authors. ================================================ FILE: doc.md ================================================ # User Documentation for the IMath Library Author: [M. J. Fromberger](https://github.com/creachadair) ## Installation 1. Edit Makefile to select compiler and options. The default is to use gcc. You may want to change CC to `clang` instead of `gcc` (and on macOS that is what you will get anyway), but you should be able to use the default GCC settings for either. By default, the Makefile assumes you can use 64-bit integer types, even though they were not standard in ISO/IEC 9899:1990. If you cannot, add `-DUSE_32BIT_WORDS` to the compiler options. 2. Type `make` or `make test` to build the test driver and run the unit tests. None of these should fail. If they do, see below for how you can report bugs. To build with debugging enabled (and optimization disabled), run `make DEBUG=Y`. This sets the preprocessor macro `DEBUG` to 1, and several other things (see Makefile for details). To use the library in your code, include "imath.h" wherever you intend to use the library's routines. The integer library is just a single source file, so you can compile it into your project in whatever way makes sense. If you wish to use rational arithmetic, you will also need to include "imrat.h". ## Background The basic types defined by the imath library are `mpz_t`, an arbitrary precision signed integer, and `mpq_t`, an arbitrary precision signed rational number. The type `mp_int` is a pointer to an `mpz_t`, and `mp_rat` is a pointer to an `mpq_t`. Most of the functions in the imath library return a value of type `mp_result`. This is a signed integer type which can be used to convey status information and also return small values. Any negative value is considered to be a status message. The following constants are defined for processing these: | Status | Description | | ----------- | -------------------------------------------- | | `MP_OK` | operation successful, all is well (= 0) | | `MP_FALSE` | boolean false (= `MP_OK`) | | `MP_TRUE` | boolean true | | `MP_MEMORY` | out of memory | | `MP_RANGE` | parameter out of range | | `MP_UNDEF` | result is undefined (e.g., division by zero) | | `MP_TRUNC` | output value was truncated | | `MP_BADARG` | an invalid parameter was passed | If you obtain a zero or negative value of an `mp_result`, you can use the `mp_error_string()` routine to obtain a pointer to a brief human-readable string describing the error. These strings are statically allocated, so they need not be freed by the caller; the same strings are reused from call to call. Unless otherwise noted, it is legal to use the same parameter for both inputs and output with most of the functions in this library. For example, you can add a number to itself and replace the original by writing: mp_int_add(a, a, a); /* a = a + a */ Any cases in which this is not legal will be noted in the function summaries below (if you discover that this is not so, please report it as a bug; I will fix either the function or the documentation :) ## The IMath API Each of the API functions is documented here. The general format of the entries is: > ------------ > 
> return_type function_name(parameters ...)
>
> - English description. Unless otherwise noted, any API function that returns `mp_result` may be expected to return `MP_OK`, `MP_BADARG`, or `MP_MEMORY`. Other return values should be documented in the description. Please let me know if you discover this is not the case. The following macros are defined in "imath.h", to define the sizes of the various data types used in the library: | Constant | Description | --------------- | ---------------------------------------- | `MP_DIGIT_BIT` | the number of bits in a single `mpz_t` digit. | `MP_WORD_BIT` | the number of bits in a `mpz_t` word. | `MP_SMALL_MIN` | the minimum value representable by an `mp_small`. | `MP_SMALL_MAX` | the maximum value representable by an `mp_small`. | `MP_USMALL_MAX` | the maximum value representable by an `mp_usmall`. | `MP_MIN_RADIX` | the minimum radix accepted for base conversion. | `MP_MAX_RADIX` | the maximum radix accepted for base conversion. ### Initialization An `mp_int` must be initialized before use. By default, an `mp_int` is initialized with a certain minimum amount of storage for digits, and the storage is expanded automatically as needed. To initialize an `mp_int`, use the following functions: ------------ 
mp_result mp_int_init(mp_int z);
- Initializes `z` with 1-digit precision and sets it to zero. This function cannot fail unless `z == NULL`. ------------ 
mp_int mp_int_alloc(void);
- Allocates a fresh zero-valued `mpz_t` on the heap, returning NULL in case of error. The only possible error is out-of-memory. ------------ 
mp_result mp_int_init_size(mp_int z, mp_size prec);
- Initializes `z` with at least `prec` digits of storage, and sets it to zero. If `prec` is zero, the default precision is used. In either case the size is rounded up to the nearest multiple of the word size. ------------ 
mp_result mp_int_init_copy(mp_int z, mp_int old);
- Initializes `z` to be a copy of an already-initialized value in `old`. The new copy does not share storage with the original. ------------ 
mp_result mp_int_init_value(mp_int z, mp_small value);
- Initializes `z` to the specified signed `value` at default precision. ### Cleanup When you are finished with an `mp_int`, you must free the memory it uses: ------------ 
void mp_int_clear(mp_int z);
- Releases the storage used by `z`. ------------ 
void mp_int_free(mp_int z);
- Releases the storage used by `z` and also `z` itself. This should only be used for `z` allocated by `mp_int_alloc()`. ### Setting Values To set an `mp_int` which has already been initialized to a small integer value, use: ------------ 
mp_result mp_int_set_value(mp_int z, mp_small value);
- Sets `z` to the value of the specified signed `value`. ------------ 
mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue);
- Sets `z` to the value of the specified unsigned `value`. To copy one initialized `mp_int` to another, use: ------------ 
mp_result mp_int_copy(mp_int a, mp_int c);
- Replaces the value of `c` with a copy of the value of `a`. No new memory is allocated unless `a` has more significant digits than `c` has allocated. ### Arithmetic Functions ------------ 
static inline bool mp_int_is_odd(mp_int z);
- Reports whether `z` is odd, having remainder 1 when divided by 2. ------------ 
static inline bool mp_int_is_even(mp_int z);
- Reports whether `z` is even, having remainder 0 when divided by 2. ------------ 
void mp_int_zero(mp_int z);
- Sets `z` to zero. The allocated storage of `z` is not changed. ------------ 
mp_result mp_int_abs(mp_int a, mp_int c);
- Sets `c` to the absolute value of `a`. ------------ 
mp_result mp_int_neg(mp_int a, mp_int c);
- Sets `c` to the additive inverse (negation) of `a`. ------------ 
mp_result mp_int_add(mp_int a, mp_int b, mp_int c);
- Sets `c` to the sum of `a` and `b`. ------------ 
mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c);
- Sets `c` to the sum of `a` and `value`. ------------ 
mp_result mp_int_sub(mp_int a, mp_int b, mp_int c);
- Sets `c` to the difference of `a` less `b`. ------------ 
mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c);
- Sets `c` to the difference of `a` less `value`. ------------ 
mp_result mp_int_mul(mp_int a, mp_int b, mp_int c);
- Sets `c` to the product of `a` and `b`. ------------ 
mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c);
- Sets `c` to the product of `a` and `value`. ------------ 
mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c);
- Sets `c` to the product of `a` and `2^p2`. Requires `p2 >= 0`. ------------ 
mp_result mp_int_sqr(mp_int a, mp_int c);
- Sets `c` to the square of `a`. ------------ 
mp_result mp_int_root(mp_int a, mp_small b, mp_int c);
- Sets `c` to the greatest integer not less than the `b`th root of `a`, using Newton's root-finding algorithm. It returns `MP_UNDEF` if `a < 0` and `b` is even. ------------ 
static inline mp_result mp_int_sqrt(mp_int a, mp_int c);
- Sets `c` to the greatest integer not less than the square root of `a`. This is a special case of `mp_int_root()`. ------------ 
mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r);
- Sets `q` and `r` to the quotient and remainder of `a / b`, so that the equation `a == b*q + r` is satisfied and `0 <= |r| < |b|`. Division by powers of 2 is detected and handled efficiently. Either of `q` or `r` may be NULL, but not both, and `q` and `r` may not point to the same value. ------------ 
mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r);
- Sets `q` and `*r` to the quotient and remainder of `a / value`. Division by powers of 2 is detected and handled efficiently. The remainder is pinned to `0 <= *r < b`. Either of `q` or `r` may be NULL. ------------ 
mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r);
- Sets `q` and `r` to the quotient and remainder of `a / 2^p2`. This is a special case for division by powers of two that is more efficient than using ordinary division. Note that `mp_int_div()` will automatically handle this case, this function is for cases where you have only the exponent. ------------ 
mp_result mp_int_mod(mp_int a, mp_int m, mp_int c);
- Sets `c` to the remainder of `a / m`. It returns `MP_UNDEF` if `m == 0`, or `MP_RANGE` if `m < 0` . Otherwise the remainder is pinned to `0 <= c < m`. ------------ 
static inline mp_result mp_int_mod_value(mp_int a, mp_small value, mp_small* r);
- Sets `*r` to the remainder of `a / value`. The remainder is pinned to `0 <= r < value`. ------------ 
mp_result mp_int_expt(mp_int a, mp_small b, mp_int c);
- Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE` if `b < 0`. ------------ 
mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c);
- Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE` if `b < 0`. ------------ 
mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c);
- Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE`) if `b < 0`. ### Comparison Functions Unless otherwise specified, comparison between values `x` and `y` returns a **comparator**, an integer value < 0 if `x` is less than `y`, 0 if `x` is equal to `y`, and > 0 if `x` is greater than `y`. ------------ 
int mp_int_compare(mp_int a, mp_int b);
- Returns the comparator of `a` and `b`. ------------ 
int mp_int_compare_unsigned(mp_int a, mp_int b);
- Returns the comparator of the magnitudes of `a` and `b`, disregarding their signs. Neither `a` nor `b` is modified by the comparison. ------------ 
int mp_int_compare_zero(mp_int z);
- Returns the comparator of `z` and zero. ------------ 
int mp_int_compare_value(mp_int z, mp_small v);
- Returns the comparator of `z` and the signed value `v`. ------------ 
int mp_int_compare_uvalue(mp_int z, mp_usmall uv);
- Returns the comparator of `z` and the unsigned value `uv`. ------------ 
bool mp_int_divisible_value(mp_int a, mp_small v);
- Reports whether `a` is divisible by `v`. ------------ 
int mp_int_is_pow2(mp_int z);
- Returns `k >= 0` such that `z` is `2^k`, if such a `k` exists. If no such `k` exists, the function returns -1. ### Modular Operations ------------ 
mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c);
- Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`. It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. ------------ 
mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c);
- Sets `c` to the value of `a` raised to the `value` power, modulo `m`. It returns `MP_RANGE` if `value < 0` or `MP_UNDEF` if `m == 0`. ------------ 
mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c);
- Sets `c` to the value of `value` raised to the `b` power, modulo `m`. It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. ------------ 
mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c);
- Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`, given a precomputed reduction constant `mu` defined for Barrett's modular reduction algorithm. It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. ------------ 
mp_result mp_int_redux_const(mp_int m, mp_int c);
- Sets `c` to the reduction constant for Barrett reduction by modulus `m`. Requires that `c` and `m` point to distinct locations. ------------ 
mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c);
- Sets `c` to the multiplicative inverse of `a` modulo `m`, if it exists. The least non-negative representative of the congruence class is computed. It returns `MP_UNDEF` if the inverse does not exist, or `MP_RANGE` if `a == 0` or `m <= 0`. ------------ 
mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c);
- Sets `c` to the greatest common divisor of `a` and `b`. It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a` and `b` are both zero. ------------ 
mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, mp_int x, mp_int y);
- Sets `c` to the greatest common divisor of `a` and `b`, and sets `x` and `y` to values satisfying Bezout's identity `gcd(a, b) = ax + by`. It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a` and `b` are both zero. ------------ 
mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c);
- Sets `c` to the least common multiple of `a` and `b`. It returns `MP_UNDEF` if the LCM is undefined, such as for example if `a` and `b` are both zero. ### Conversion of Values ------------ 
mp_result mp_int_to_int(mp_int z, mp_small *out);
- Returns `MP_OK` if `z` is representable as `mp_small`, else `MP_RANGE`. If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. ------------ 
mp_result mp_int_to_uint(mp_int z, mp_usmall *out);
- Returns `MP_OK` if `z` is representable as `mp_usmall`, or `MP_RANGE`. If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. ------------ 
mp_result mp_int_to_string(mp_int z, mp_size radix, char *str, int limit);
- Converts `z` to a zero-terminated string of characters in the specified `radix`, writing at most `limit` characters to `str` including the terminating NUL value. A leading `-` is used to indicate a negative value. Returns `MP_TRUNC` if `limit` was to small to write all of `z`. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. ------------ 
mp_size mp_int_string_len(mp_int z, mp_size radix);
- Reports the minimum number of characters required to represent `z` as a zero-terminated string in the given `radix`. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. ------------ 
mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str);
- Reads a string of ASCII digits in the specified `radix` from the zero terminated `str` provided into `z`. For values of `radix > 10`, the letters `A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect to case. Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a sign flag. Processing stops when a NUL or any other character out of range for a digit in the given radix is encountered. If the whole string was consumed, `MP_OK` is returned; otherwise `MP_TRUNC`. is returned. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. ------------ 
mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end);
- Reads a string of ASCII digits in the specified `radix` from the zero terminated `str` provided into `z`. For values of `radix > 10`, the letters `A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect to case. Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a sign flag. Processing stops when a NUL or any other character out of range for a digit in the given radix is encountered. If the whole string was consumed, `MP_OK` is returned; otherwise `MP_TRUNC`. is returned. If `end` is not NULL, `*end` is set to point to the first unconsumed byte of the input string (the NUL byte if the whole string was consumed). This emulates the behavior of the standard C `strtol()` function. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. ------------ 
mp_size mp_int_count_bits(mp_int z);
- Returns the number of significant bits in `z`. ------------ 
mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit);
- Converts `z` to 2's complement binary, writing at most `limit` bytes into the given `buf`. Returns `MP_TRUNC` if the buffer limit was too small to contain the whole value. If this occurs, the contents of buf will be effectively garbage, as the function uses the buffer as scratch space. The binary representation of `z` is in base-256 with digits ordered from most significant to least significant (network byte ordering). The high-order bit of the first byte is set for negative values, clear for non-negative values. As a result, non-negative values will be padded with a leading zero byte if the high-order byte of the base-256 magnitude is set. This extra byte is accounted for by the `mp_int_binary_len()` function. ------------ 
mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len);
- Reads a 2's complement binary value from `buf` into `z`, where `len` is the length of the buffer. The contents of `buf` may be overwritten during processing, although they will be restored when the function returns. ------------ 
mp_size mp_int_binary_len(mp_int z);
- Returns the number of bytes to represent `z` in 2's complement binary. ------------ 
mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit);
- Converts the magnitude of `z` to unsigned binary, writing at most `limit` bytes into the given `buf`. The sign of `z` is ignored, but `z` is not modified. Returns `MP_TRUNC` if the buffer limit was too small to contain the whole value. If this occurs, the contents of `buf` will be effectively garbage, as the function uses the buffer as scratch space during conversion. The binary representation of `z` is in base-256 with digits ordered from most significant to least significant (network byte ordering). ------------ 
mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len);
- Reads an unsigned binary value from `buf` into `z`, where `len` is the length of the buffer. The contents of `buf` are not modified during processing. ------------ 
mp_size mp_int_unsigned_len(mp_int z);
- Returns the number of bytes required to represent `z` as an unsigned binary value in base 256. ### Other Functions Ordinarily, integer multiplication and squaring are done using the simple quadratic "schoolbook" algorithm. However, for sufficiently large values, there is a more efficient algorithm usually attributed to Karatsuba and Ofman that is usually faster. See Knuth Vol. 2 for more details about how this algorithm works. The breakpoint between the "normal" and the recursive algorithm is controlled by a static digit threshold defined in `imath.c`. Values with fewer significant digits use the standard algorithm. This value can be modified by calling `mp_int_multiply_threshold(n)`. The `imtimer` program and the `findthreshold.py` script (Python) can help you find a suitable value for for your particular platform. ------------ 
const char *mp_error_string(mp_result res);
- Returns a pointer to a brief, human-readable, zero-terminated string describing `res`. The returned string is statically allocated and must not be freed by the caller. ## Rational Arithmetic ------------ 
mp_result mp_rat_init(mp_rat r);
- Initializes `r` with 1-digit precision and sets it to zero. This function cannot fail unless `r` is NULL. ------------ 
mp_rat mp_rat_alloc(void);
- Allocates a fresh zero-valued `mpq_t` on the heap, returning NULL in case of error. The only possible error is out-of-memory. ------------ 
mp_result mp_rat_reduce(mp_rat r);
- Reduces `r` in-place to lowest terms and canonical form. Zero is represented as 0/1, one as 1/1, and signs are adjusted so that the sign of the value is carried by the numerator. ------------ 
mp_result mp_rat_init_size(mp_rat r, mp_size n_prec, mp_size d_prec);
- Initializes `r` with at least `n_prec` digits of storage for the numerator and `d_prec` digits of storage for the denominator, and value zero. If either precision is zero, the default precision is used, rounded up to the nearest word size. ------------ 
mp_result mp_rat_init_copy(mp_rat r, mp_rat old);
- Initializes `r` to be a copy of an already-initialized value in `old`. The new copy does not share storage with the original. ------------ 
mp_result mp_rat_set(mp_rat r, mp_int numer, mp_int denom);
- Sets the value of `r` to the ratio of signed `numer` to signed `denom`. It returns `MP_UNDEF` if `denom` is zero. At least one of `numer` and `denom` must be non-NULL. If `numer` is NULL, the value of `r` is set to 1 / `denom`. If `denom` is NULL, the value of `r` is set to `numer` / 1. ------------ 
mp_result mp_rat_set_value(mp_rat r, mp_small numer, mp_small denom);
- Sets the value of `r` to the ratio of signed `numer` to signed `denom`. It returns `MP_UNDEF` if `denom` is zero. ------------ 
mp_result mp_rat_set_uvalue(mp_rat r, mp_usmall numer, mp_usmall denom);
- Sets the value of `r` to the ratio of unsigned `numer` to unsigned `denom`. It returns `MP_UNDEF` if `denom` is zero. ------------ 
void mp_rat_clear(mp_rat r);
- Releases the storage used by `r`. ------------ 
void mp_rat_free(mp_rat r);
- Releases the storage used by `r` and also `r` itself. This should only be used for `r` allocated by `mp_rat_alloc()`. ------------ 
mp_result mp_rat_numer(mp_rat r, mp_int z);
- Sets `z` to a copy of the numerator of `r`. ------------ 
mp_int mp_rat_numer_ref(mp_rat r);
- Returns a pointer to the numerator of `r`. ------------ 
mp_result mp_rat_denom(mp_rat r, mp_int z);
- Sets `z` to a copy of the denominator of `r`. ------------ 
mp_int mp_rat_denom_ref(mp_rat r);
- Returns a pointer to the denominator of `r`. ------------ 
mp_sign mp_rat_sign(mp_rat r);
- Reports the sign of `r`. ------------ 
mp_result mp_rat_copy(mp_rat a, mp_rat c);
- Sets `c` to a copy of the value of `a`. No new memory is allocated unless a term of `a` has more significant digits than the corresponding term of `c` has allocated. ------------ 
void mp_rat_zero(mp_rat r);
- Sets `r` to zero. The allocated storage of `r` is not changed. ------------ 
mp_result mp_rat_abs(mp_rat a, mp_rat c);
- Sets `c` to the absolute value of `a`. ------------ 
mp_result mp_rat_neg(mp_rat a, mp_rat c);
- Sets `c` to the absolute value of `a`. ------------ 
mp_result mp_rat_recip(mp_rat a, mp_rat c);
- Sets `c` to the reciprocal of `a` if the reciprocal is defined. It returns `MP_UNDEF` if `a` is zero. ------------ 
mp_result mp_rat_add(mp_rat a, mp_rat b, mp_rat c);
- Sets `c` to the sum of `a` and `b`. ------------ 
mp_result mp_rat_sub(mp_rat a, mp_rat b, mp_rat c);
- Sets `c` to the difference of `a` less `b`. ------------ 
mp_result mp_rat_mul(mp_rat a, mp_rat b, mp_rat c);
- Sets `c` to the product of `a` and `b`. ------------ 
mp_result mp_rat_div(mp_rat a, mp_rat b, mp_rat c);
- Sets `c` to the ratio `a / b` if that ratio is defined. It returns `MP_UNDEF` if `b` is zero. ------------ 
mp_result mp_rat_add_int(mp_rat a, mp_int b, mp_rat c);
- Sets `c` to the sum of `a` and integer `b`. ------------ 
mp_result mp_rat_sub_int(mp_rat a, mp_int b, mp_rat c);
- Sets `c` to the difference of `a` less integer `b`. ------------ 
mp_result mp_rat_mul_int(mp_rat a, mp_int b, mp_rat c);
- Sets `c` to the product of `a` and integer `b`. ------------ 
mp_result mp_rat_div_int(mp_rat a, mp_int b, mp_rat c);
- Sets `c` to the ratio `a / b` if that ratio is defined. It returns `MP_UNDEF` if `b` is zero. ------------ 
mp_result mp_rat_expt(mp_rat a, mp_small b, mp_rat c);
- Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE` if `b < 0`. ------------ 
mp_result mp_rat_decompose(mp_rat r, mp_int ipart, mp_rat fpart);
- Sets `ipart` to the integer part of `r` and `fpart` to the difference of `r - ipart`. If `r < 0` then the signs of `ipart` and `fpart` will also be negative, unless they are zero. At least one of `ipart` and `fpart` must be non-NULL. If `ipart` is NULL the integer part is discarded. If `fpart` is NULL, the fractional part is discarded. ------------ 
int mp_rat_compare(mp_rat a, mp_rat b);
- Returns the comparator of `a` and `b`. ------------ 
int mp_rat_compare_unsigned(mp_rat a, mp_rat b);
- Returns the comparator of the magnitudes of `a` and `b`, disregarding their signs. Neither `a` nor `b` is modified by the comparison. ------------ 
int mp_rat_compare_zero(mp_rat r);
- Returns the comparator of `r` and zero. ------------ 
int mp_rat_compare_value(mp_rat r, mp_small n, mp_small d);
- Returns the comparator of `r` and the signed ratio `n / d`. It returns `MP_UNDEF` if `d` is zero. ------------ 
bool mp_rat_is_integer(mp_rat r);
- Reports whether `r` is an integer, having canonical denominator 1. ------------ 
mp_result mp_rat_to_ints(mp_rat r, mp_small *num, mp_small *den);
- Reports whether the numerator and denominator of `r` can be represented as small signed integers, and if so stores the corresponding values to `num` and `den`. It returns `MP_RANGE` if either cannot be so represented. ------------ 
mp_result mp_rat_to_string(mp_rat r, mp_size radix, char *str, int limit);
- Converts `r` to a zero-terminated string of the format `"n/d"` with `n` and `d` in the specified radix and writing no more than `limit` bytes to the given output buffer `str`. The output of the numerator includes a sign flag if `r` is negative. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. ------------ 
mp_result mp_rat_to_decimal(mp_rat r, mp_size radix, mp_size prec, mp_round_mode round, char *str, int limit);
- Converts the value of `r` to a string in decimal-point notation with the specified radix, writing no more than `limit` bytes of data to the given output buffer. It generates `prec` digits of precision, and requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. Ratios usually must be rounded when they are being converted for output as a decimal value. There are four rounding modes currently supported: ``` MP_ROUND_DOWN Truncates the value toward zero. Example: 12.009 to 2dp becomes 12.00 ``` ``` MP_ROUND_UP Rounds the value away from zero: Example: 12.001 to 2dp becomes 12.01, but 12.000 to 2dp remains 12.00 ``` ``` MP_ROUND_HALF_DOWN Rounds the value to nearest digit, half goes toward zero. Example: 12.005 to 2dp becomes 12.00, but 12.006 to 2dp becomes 12.01 ``` ``` MP_ROUND_HALF_UP Rounds the value to nearest digit, half rounds upward. Example: 12.005 to 2dp becomes 12.01, but 12.004 to 2dp becomes 12.00 ``` ------------ 
mp_size mp_rat_string_len(mp_rat r, mp_size radix);
- Reports the minimum number of characters required to represent `r` as a zero-terminated string in the given `radix`. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. ------------ 
mp_size mp_rat_decimal_len(mp_rat r, mp_size radix, mp_size prec);
- Reports the length in bytes of the buffer needed to convert `r` using the `mp_rat_to_decimal()` function with the specified `radix` and `prec`. The buffer size estimate may slightly exceed the actual required capacity. ------------ 
mp_result mp_rat_read_string(mp_rat r, mp_size radix, const char *str);
- Sets `r` to the value represented by a zero-terminated string `str` in the format `"n/d"` including a sign flag. It returns `MP_UNDEF` if the encoded denominator has value zero. ------------ 
mp_result mp_rat_read_cstring(mp_rat r, mp_size radix, const char *str, char **end);
- Sets `r` to the value represented by a zero-terminated string `str` in the format `"n/d"` including a sign flag. It returns `MP_UNDEF` if the encoded denominator has value zero. If `end` is not NULL then `*end` is set to point to the first unconsumed character in the string, after parsing. ------------ 
mp_result mp_rat_read_ustring(mp_rat r, mp_size radix, const char *str, char **end);
- Sets `r` to the value represented by a zero-terminated string `str` having one of the following formats, each with an optional leading sign flag: ``` n : integer format, e.g. "123" n/d : ratio format, e.g., "-12/5" z.ffff : decimal format, e.g., "1.627" ``` It returns `MP_UNDEF` if the effective denominator is zero. If `end` is not NULL then `*end` is set to point to the first unconsumed character in the string, after parsing. ------------ 
mp_result mp_rat_read_decimal(mp_rat r, mp_size radix, const char *str);
- Sets `r` to the value represented by a zero-terminated string `str` in the format `"z.ffff"` including a sign flag. It returns `MP_UNDEF` if the effective denominator is zero. ------------ 
mp_result mp_rat_read_cdecimal(mp_rat r, mp_size radix, const char *str, char **end);
- Sets `r` to the value represented by a zero-terminated string `str` in the format `"z.ffff"` including a sign flag. It returns `MP_UNDEF` if the effective denominator is zero. If `end` is not NULL then `*end` is set to point to the first unconsumed character in the string, after parsing. ## Representation Details > NOTE: You do not need to read this section to use IMath. This is provided > for the benefit of developers wishing to extend or modify the internals of > the library. IMath uses a signed magnitude representation for arbitrary precision integers. The magnitude is represented as an array of radix-R digits in increasing order of significance; the value of R is chosen to be half the size of the largest available unsigned integer type, so typically 16 or 32 bits. Digits are represented as mp_digit, which must be an unsigned integral type. Digit arrays are allocated using `malloc(3)` and `realloc(3)`. Because this can be an expensive operation, the library takes pains to avoid allocation as much as possible. For this reason, the `mpz_t` structure distinguishes between how many digits are allocated and how many digits are actually consumed by the representation. The fields of an `mpz_t` are: mp_digit single; /* single-digit value (see note) */ mp_digit *digits; /* array of digits */ mp_size alloc; /* how many digits are allocated */ mp_size used; /* how many digits are in use */ mp_sign sign; /* the sign of the value */ The elements of `digits` at indices less than `used` are the significant figures of the value; the elements at indices greater than or equal to `used` are undefined (and may contain garbage). At all times, `used` must be at least 1 and at most `alloc`. To avoid interaction with the memory allocator, single-digit values are stored directly in the `mpz_t` structure, in the `single` field. The semantics of access are the same as the more general case. The number of digits allocated for an `mpz_t` is referred to in the library documentation as its "precision". Operations that affect an `mpz_t` cause precision to increase as needed. In any case, all allocations are measured in digits, and rounded up to the nearest `mp_word` boundary. There is a default minimum precision stored as a static constant default_precision (`imath.c`). This value can be set using `mp_int_default_precision(n)`. Note that the allocated size of an `mpz_t` can only grow; the library never reallocates in order to decrease the size. A simple way to do so explicitly is to use `mp_int_init_copy()`, as in: ``` mpz_t big, new; /* ... */ mp_int_init_copy(&new, &big); mp_int_swap(&new, &big); mp_int_clear(&new); ``` The value of `sign` is 0 for positive values and zero, 1 for negative values. Constants `MP_ZPOS` and `MP_NEG` are defined for these; no other sign values are used. If you are adding to this library, you should be careful to preserve the convention that inputs and outputs can overlap, as described above. So, for example, `mp_int_add(a, a, a)` is legal. Often, this means you must maintain one or more temporary mpz_t structures for intermediate values. The private macros `DECLARE_TEMP(N)`, `CLEANUP_TEMP()`, and `TEMP(K)` can be used to maintain a conventional structure like this: ```c { /* Declare how many temp values you need. Use TEMP(i) to access the ith value (0-indexed). */ DECLARE_TEMP(8); ... /* Perform actions that must return MP_OK or fail. */ REQUIRE(mp_int_copy(x, TEMP(1))); ... REQUIRE(mp_int_expt(TEMP(1), TEMP(2), TEMP(3))); ... /* You can also use REQUIRE directly for more complex cases. */ if (some_difficult_question(TEMP(3)) != answer(x)) { REQUIRE(MP_RANGE); /* falls through to cleanup (below) */ } /* Ensure temporary values are cleaned up at exit. If control reaches here via a REQUIRE failure, the code below the cleanup will not be executed. */ CLEANUP_TEMP(); return MP_OK; } ``` Under the covers, these macros are just maintaining an array of `mpz_t` values, and a jump label to handle cleanup. You may only have one `DECLARE_TEMP` and its corresponding `CLEANUP_TEMP` per function body. "Small" integer values are represented by the types `mp_small` and `mp_usmall`, which are mapped to appropriately-sized types on the host system. The default for `mp_small` is "long" and the default for `mp_usmall` is "unsigned long". You may change these, provided you insure that `mp_small` is signed and `mp_usmall` is unsigned. You will also need to adjust the size macros: MP_SMALL_MIN, MP_SMALL_MAX MP_USMALL_MIN, MP_USMALL_MAX ... which are defined in ``, if you change these. Rational numbers are represented using a pair of arbitrary precision integers, with the convention that the sign of the numerator is the sign of the rational value, and that the result of any rational operation is always represented in lowest terms. The canonical representation for rational zero is 0/1. See "imrat.h". ## Testing and Reporting of Bugs Test vectors are included in the `tests/` subdirectory of the imath distribution. When you run `make test`, it builds the `imtest` program and runs all available test vectors. If any tests fail, you will get a line like this: x y FAILED v Here, _x_ is the line number of the test which failed, _y_ is index of the test within the file, and _v_ is the value(s) actually computed. The name of the file is printed at the beginning of each test, so you can find out what test vector failed by executing the following (with x, y, and v replaced by the above values, and where "foo.t" is the name of the test file that was being processed at the time): % tail +x tests/foo.t | head -1 None of the tests should fail (but see [Note 2](#note2)); if any do, it probably indicates a bug in the library (or at the very least, some assumption I made which I shouldn't have). Please [file an issue](https://github.com/creachadair/imath/issues/new), including the `FAILED` test line(s), as well as the output of the above `tail` command (so I know what inputs caused the failure). If you build with the preprocessor symbol `DEBUG` defined as a positive integer, the digit allocators (`s_alloc`, `s_realloc`) fill all new buffers with the value `0xdeadbeefabad1dea`, or as much of it as will fit in a digit, so that you can more easily catch uninitialized reads in the debugger. ## Notes 1. You can generally use the same variables for both input and output. One exception is that you may not use the same variable for both the quotient and the remainder of `mp_int_div()`. 2. Many of the tests for this library were written under the assumption that the `mp_small` type is 32 bits or more. If you compile with a smaller type, you may see `MP_RANGE` errors in some of the tests that otherwise pass (due to conversion failures). Also, the pi generator (pi.c) will not work correctly if `mp_small` is too short, as its algorithm for arc tangent is fairly simple-minded. ## Contacts The IMath library was written by Michael J. Fromberger. If you discover any bugs or testing failures, please [open an issue](https://github.com/creachadair/imath/issues/new). Please be sure to include a complete description of what went wrong, and if possible, a test vector for `imtest` and/or a minimal test program that will demonstrate the bug on your system. Please also let me know what hardware, operating system, and compiler you're using. ## Acknowledgements The algorithms used in this library came from Vol. 2 of Donald Knuth's "The Art of Computer Programming" (Seminumerical Algorithms). Thanks to Nelson Bolyard, Bryan Olson, Tom St. Denis, Tushar Udeshi, and Eric Silva for excellent feedback on earlier versions of this code. Special thanks to Jonathan Shapiro for some very helpful design advice, as well as feedback and some clever ideas for improving performance in some common use cases. ## License and Disclaimers IMath is Copyright 2002-2009 Michael J. Fromberger You may use it subject to the following Licensing Terms: 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: doc.md.in ================================================ # User Documentation for the IMath Library Author: [M. J. Fromberger](https://github.com/creachadair) ## Installation 1. Edit Makefile to select compiler and options. The default is to use gcc. You may want to change CC to `clang` instead of `gcc` (and on macOS that is what you will get anyway), but you should be able to use the default GCC settings for either. By default, the Makefile assumes you can use 64-bit integer types, even though they were not standard in ISO/IEC 9899:1990. If you cannot, add `-DUSE_32BIT_WORDS` to the compiler options. 2. Type `make` or `make test` to build the test driver and run the unit tests. None of these should fail. If they do, see below for how you can report bugs. To build with debugging enabled (and optimization disabled), run `make DEBUG=Y`. This sets the preprocessor macro `DEBUG` to 1, and several other things (see Makefile for details). To use the library in your code, include "imath.h" wherever you intend to use the library's routines. The integer library is just a single source file, so you can compile it into your project in whatever way makes sense. If you wish to use rational arithmetic, you will also need to include "imrat.h". ## Background The basic types defined by the imath library are `mpz_t`, an arbitrary precision signed integer, and `mpq_t`, an arbitrary precision signed rational number. The type `mp_int` is a pointer to an `mpz_t`, and `mp_rat` is a pointer to an `mpq_t`. Most of the functions in the imath library return a value of type `mp_result`. This is a signed integer type which can be used to convey status information and also return small values. Any negative value is considered to be a status message. The following constants are defined for processing these: | Status | Description | | ----------- | -------------------------------------------- | | `MP_OK` | operation successful, all is well (= 0) | | `MP_FALSE` | boolean false (= `MP_OK`) | | `MP_TRUE` | boolean true | | `MP_MEMORY` | out of memory | | `MP_RANGE` | parameter out of range | | `MP_UNDEF` | result is undefined (e.g., division by zero) | | `MP_TRUNC` | output value was truncated | | `MP_BADARG` | an invalid parameter was passed | If you obtain a zero or negative value of an `mp_result`, you can use the `mp_error_string()` routine to obtain a pointer to a brief human-readable string describing the error. These strings are statically allocated, so they need not be freed by the caller; the same strings are reused from call to call. Unless otherwise noted, it is legal to use the same parameter for both inputs and output with most of the functions in this library. For example, you can add a number to itself and replace the original by writing: mp_int_add(a, a, a); /* a = a + a */ Any cases in which this is not legal will be noted in the function summaries below (if you discover that this is not so, please report it as a bug; I will fix either the function or the documentation :) ## The IMath API Each of the API functions is documented here. The general format of the entries is: > ------------ > 
> return_type function_name(parameters ...)
>
> - English description. Unless otherwise noted, any API function that returns `mp_result` may be expected to return `MP_OK`, `MP_BADARG`, or `MP_MEMORY`. Other return values should be documented in the description. Please let me know if you discover this is not the case. The following macros are defined in "imath.h", to define the sizes of the various data types used in the library: | Constant | Description | --------------- | ---------------------------------------- | `MP_DIGIT_BIT` | the number of bits in a single `mpz_t` digit. | `MP_WORD_BIT` | the number of bits in a `mpz_t` word. | `MP_SMALL_MIN` | the minimum value representable by an `mp_small`. | `MP_SMALL_MAX` | the maximum value representable by an `mp_small`. | `MP_USMALL_MAX` | the maximum value representable by an `mp_usmall`. | `MP_MIN_RADIX` | the minimum radix accepted for base conversion. | `MP_MAX_RADIX` | the maximum radix accepted for base conversion. ### Initialization An `mp_int` must be initialized before use. By default, an `mp_int` is initialized with a certain minimum amount of storage for digits, and the storage is expanded automatically as needed. To initialize an `mp_int`, use the following functions: {{insert "imath.h" mp_int_init mp_int_alloc mp_int_init_size mp_int_init_copy mp_int_init_value }} ### Cleanup When you are finished with an `mp_int`, you must free the memory it uses: {{insert "imath.h" mp_int_clear mp_int_free}} ### Setting Values To set an `mp_int` which has already been initialized to a small integer value, use: {{insert "imath.h" mp_int_set_value mp_int_set_uvalue}} To copy one initialized `mp_int` to another, use: {{insert "imath.h" mp_int_copy}} ### Arithmetic Functions {{insert "imath.h" mp_int_is_odd mp_int_is_even mp_int_zero mp_int_abs mp_int_neg mp_int_add mp_int_add_value mp_int_sub mp_int_sub_value mp_int_mul mp_int_mul_value mp_int_mul_pow2 mp_int_sqr mp_int_root mp_int_sqrt mp_int_div mp_int_div_value mp_int_div_pow2 mp_int_mod mp_int_mod_value mp_int_expt mp_int_expt_value mp_int_expt_full }} ### Comparison Functions Unless otherwise specified, comparison between values `x` and `y` returns a **comparator**, an integer value < 0 if `x` is less than `y`, 0 if `x` is equal to `y`, and > 0 if `x` is greater than `y`. {{insert "imath.h" mp_int_compare mp_int_compare_unsigned mp_int_compare_zero mp_int_compare_value mp_int_compare_uvalue mp_int_divisible_value mp_int_is_pow2 }} ### Modular Operations {{insert "imath.h" mp_int_exptmod mp_int_exptmod_evalue mp_int_exptmod_bvalue mp_int_exptmod_known mp_int_redux_const mp_int_invmod mp_int_gcd mp_int_egcd mp_int_lcm }} ### Conversion of Values {{insert "imath.h" mp_int_to_int mp_int_to_uint mp_int_to_string mp_int_string_len mp_int_read_string mp_int_read_cstring mp_int_count_bits mp_int_to_binary mp_int_read_binary mp_int_binary_len mp_int_to_unsigned mp_int_read_unsigned mp_int_unsigned_len }} ### Other Functions Ordinarily, integer multiplication and squaring are done using the simple quadratic "schoolbook" algorithm. However, for sufficiently large values, there is a more efficient algorithm usually attributed to Karatsuba and Ofman that is usually faster. See Knuth Vol. 2 for more details about how this algorithm works. The breakpoint between the "normal" and the recursive algorithm is controlled by a static digit threshold defined in `imath.c`. Values with fewer significant digits use the standard algorithm. This value can be modified by calling `mp_int_multiply_threshold(n)`. The `imtimer` program and the `findthreshold.py` script (Python) can help you find a suitable value for for your particular platform. {{insert "imath.h" mp_error_string}} ## Rational Arithmetic {{insert "imrat.h"}} ## Representation Details > NOTE: You do not need to read this section to use IMath. This is provided > for the benefit of developers wishing to extend or modify the internals of > the library. IMath uses a signed magnitude representation for arbitrary precision integers. The magnitude is represented as an array of radix-R digits in increasing order of significance; the value of R is chosen to be half the size of the largest available unsigned integer type, so typically 16 or 32 bits. Digits are represented as mp_digit, which must be an unsigned integral type. Digit arrays are allocated using `malloc(3)` and `realloc(3)`. Because this can be an expensive operation, the library takes pains to avoid allocation as much as possible. For this reason, the `mpz_t` structure distinguishes between how many digits are allocated and how many digits are actually consumed by the representation. The fields of an `mpz_t` are: mp_digit single; /* single-digit value (see note) */ mp_digit *digits; /* array of digits */ mp_size alloc; /* how many digits are allocated */ mp_size used; /* how many digits are in use */ mp_sign sign; /* the sign of the value */ The elements of `digits` at indices less than `used` are the significant figures of the value; the elements at indices greater than or equal to `used` are undefined (and may contain garbage). At all times, `used` must be at least 1 and at most `alloc`. To avoid interaction with the memory allocator, single-digit values are stored directly in the `mpz_t` structure, in the `single` field. The semantics of access are the same as the more general case. The number of digits allocated for an `mpz_t` is referred to in the library documentation as its "precision". Operations that affect an `mpz_t` cause precision to increase as needed. In any case, all allocations are measured in digits, and rounded up to the nearest `mp_word` boundary. There is a default minimum precision stored as a static constant default_precision (`imath.c`). This value can be set using `mp_int_default_precision(n)`. Note that the allocated size of an `mpz_t` can only grow; the library never reallocates in order to decrease the size. A simple way to do so explicitly is to use `mp_int_init_copy()`, as in: ``` mpz_t big, new; /* ... */ mp_int_init_copy(&new, &big); mp_int_swap(&new, &big); mp_int_clear(&new); ``` The value of `sign` is 0 for positive values and zero, 1 for negative values. Constants `MP_ZPOS` and `MP_NEG` are defined for these; no other sign values are used. If you are adding to this library, you should be careful to preserve the convention that inputs and outputs can overlap, as described above. So, for example, `mp_int_add(a, a, a)` is legal. Often, this means you must maintain one or more temporary mpz_t structures for intermediate values. The private macros `DECLARE_TEMP(N)`, `CLEANUP_TEMP()`, and `TEMP(K)` can be used to maintain a conventional structure like this: ```c { /* Declare how many temp values you need. Use TEMP(i) to access the ith value (0-indexed). */ DECLARE_TEMP(8); ... /* Perform actions that must return MP_OK or fail. */ REQUIRE(mp_int_copy(x, TEMP(1))); ... REQUIRE(mp_int_expt(TEMP(1), TEMP(2), TEMP(3))); ... /* You can also use REQUIRE directly for more complex cases. */ if (some_difficult_question(TEMP(3)) != answer(x)) { REQUIRE(MP_RANGE); /* falls through to cleanup (below) */ } /* Ensure temporary values are cleaned up at exit. If control reaches here via a REQUIRE failure, the code below the cleanup will not be executed. */ CLEANUP_TEMP(); return MP_OK; } ``` Under the covers, these macros are just maintaining an array of `mpz_t` values, and a jump label to handle cleanup. You may only have one `DECLARE_TEMP` and its corresponding `CLEANUP_TEMP` per function body. "Small" integer values are represented by the types `mp_small` and `mp_usmall`, which are mapped to appropriately-sized types on the host system. The default for `mp_small` is "long" and the default for `mp_usmall` is "unsigned long". You may change these, provided you insure that `mp_small` is signed and `mp_usmall` is unsigned. You will also need to adjust the size macros: MP_SMALL_MIN, MP_SMALL_MAX MP_USMALL_MIN, MP_USMALL_MAX ... which are defined in ``, if you change these. Rational numbers are represented using a pair of arbitrary precision integers, with the convention that the sign of the numerator is the sign of the rational value, and that the result of any rational operation is always represented in lowest terms. The canonical representation for rational zero is 0/1. See "imrat.h". ## Testing and Reporting of Bugs Test vectors are included in the `tests/` subdirectory of the imath distribution. When you run `make test`, it builds the `imtest` program and runs all available test vectors. If any tests fail, you will get a line like this: x y FAILED v Here, _x_ is the line number of the test which failed, _y_ is index of the test within the file, and _v_ is the value(s) actually computed. The name of the file is printed at the beginning of each test, so you can find out what test vector failed by executing the following (with x, y, and v replaced by the above values, and where "foo.t" is the name of the test file that was being processed at the time): % tail +x tests/foo.t | head -1 None of the tests should fail (but see [Note 2](#note2)); if any do, it probably indicates a bug in the library (or at the very least, some assumption I made which I shouldn't have). Please [file an issue](https://github.com/creachadair/imath/issues/new), including the `FAILED` test line(s), as well as the output of the above `tail` command (so I know what inputs caused the failure). If you build with the preprocessor symbol `DEBUG` defined as a positive integer, the digit allocators (`s_alloc`, `s_realloc`) fill all new buffers with the value `0xdeadbeefabad1dea`, or as much of it as will fit in a digit, so that you can more easily catch uninitialized reads in the debugger. ## Notes 1. You can generally use the same variables for both input and output. One exception is that you may not use the same variable for both the quotient and the remainder of `mp_int_div()`. 2. Many of the tests for this library were written under the assumption that the `mp_small` type is 32 bits or more. If you compile with a smaller type, you may see `MP_RANGE` errors in some of the tests that otherwise pass (due to conversion failures). Also, the pi generator (pi.c) will not work correctly if `mp_small` is too short, as its algorithm for arc tangent is fairly simple-minded. ## Contacts The IMath library was written by Michael J. Fromberger. If you discover any bugs or testing failures, please [open an issue](https://github.com/creachadair/imath/issues/new). Please be sure to include a complete description of what went wrong, and if possible, a test vector for `imtest` and/or a minimal test program that will demonstrate the bug on your system. Please also let me know what hardware, operating system, and compiler you're using. ## Acknowledgements The algorithms used in this library came from Vol. 2 of Donald Knuth's "The Art of Computer Programming" (Seminumerical Algorithms). Thanks to Nelson Bolyard, Bryan Olson, Tom St. Denis, Tushar Udeshi, and Eric Silva for excellent feedback on earlier versions of this code. Special thanks to Jonathan Shapiro for some very helpful design advice, as well as feedback and some clever ideas for improving performance in some common use cases. ## License and Disclaimers IMath is Copyright 2002-2009 Michael J. Fromberger You may use it subject to the following Licensing Terms: 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: examples/basecvt.c ================================================ /* Name: basecvt.c Purpose: Convert integers and rationals from one base to another. Author: M. J. Fromberger Copyright (C) 2004-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include "imath.h" #include "imrat.h" int main(int argc, char* argv[]) { mp_size in_rdx, out_rdx; mpq_t value; mp_result res; int ix; if (argc < 4) { fprintf(stderr, "Usage: basecvt +\n"); return 1; } in_rdx = atoi(argv[1]); out_rdx = atoi(argv[2]); if (in_rdx < MP_MIN_RADIX || in_rdx > MP_MAX_RADIX) { fprintf(stderr, "basecvt: input radix %u not allowed (minimum %u, maximum %u)\n", in_rdx, MP_MIN_RADIX, MP_MAX_RADIX); return 3; } if (out_rdx < MP_MIN_RADIX || out_rdx > MP_MAX_RADIX) { fprintf(stderr, "basecvt: output radix %u not allowed (minimum %u, maximum %u)\n", out_rdx, MP_MIN_RADIX, MP_MAX_RADIX); return 3; } if ((res = mp_rat_init(&value)) != MP_OK) { fprintf(stderr, "basecvt: out of memory\n"); return 2; } for (ix = 3; ix < argc; ++ix) { char *buf, *endp = NULL; mp_result len; int is_int; res = mp_rat_read_ustring(&value, in_rdx, argv[ix], &endp); if (res != MP_OK && res != MP_TRUNC) { fprintf(stderr, "basecvt: error reading argument %d: %s\n", ix, mp_error_string(res)); break; } else if (*endp != '\0') { fprintf(stderr, "basecvt: argument %d contains '%s' not in base %u\n", ix, endp, in_rdx); continue; } is_int = mp_rat_is_integer(&value); if (is_int) { len = mp_int_string_len(MP_NUMER_P(&value), out_rdx); } else { len = mp_rat_string_len(&value, out_rdx); } if ((buf = malloc(len)) == NULL) { fprintf(stderr, "basecvt: out of memory\n"); break; } if (is_int) { res = mp_int_to_string(MP_NUMER_P(&value), out_rdx, buf, len); } else { res = mp_rat_to_string(&value, out_rdx, buf, len); } if (res != MP_OK) { fprintf(stderr, "basecvt: error converting argument %d: %s\n", ix, mp_error_string(res)); free(buf); break; } printf("%s\n", buf); free(buf); } mp_rat_clear(&value); return (res != MP_OK); } /* Here there be dragons */ ================================================ FILE: examples/findprime.c ================================================ /* Name: findprime.c Purpose: Find probable primes. Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. Notes: Find the first prime number in sequence starting from the given value. Demonstrates the use of mp_int_find_prime(). 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. */ #include #include "iprime.h" int main(int argc, char* argv[]) { char buf[4096]; mpz_t seed; mp_result res; if (argc < 2) { fprintf(stderr, "Usage: %s \n", argv[0]); return 1; } mp_int_init(&seed); if ((res = mp_int_read_string(&seed, 10, argv[1])) != MP_OK) { fprintf(stderr, "%s: error reading `%s': %d\n", argv[0], argv[1], res); return 2; } if (mp_int_compare_value(&seed, 131) <= 0) { fprintf(stderr, "%s: please enter a start value > 131\n", argv[0]); return 1; } if ((res = mp_int_find_prime(&seed)) != MP_TRUE) { fprintf(stderr, "%s: error finding prime: %d\n", argv[0], res); return 2; } mp_int_to_string(&seed, 10, buf, sizeof(buf)); printf("=> %s\n", buf); mp_int_clear(&seed); return 0; } ================================================ FILE: examples/imcalc.c ================================================ /* Name: imcalc.c Purpose: Simple RPN calculator based on IMath library. Author: M. J. Fromberger This is a very simplistic RPN calculator that will let you test the features of the IMath built-in functions. Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include #include #include #include #include /* for strcasecmp */ #include #include "imath.h" #include "imrat.h" #include "iprime.h" /* A cstate_t represents a stack of operands; numeric operands are pushed on the stack, and commands cause them to be consumed in various ways. */ typedef struct { /* Operand stack */ mp_int* elts; mp_size alloc; /* number of slots available */ mp_size used; /* number of slots free */ /* Named variables */ mp_int* mem; /* named memory slots */ char** names; /* names of memory slots */ mp_size mslots; /* number of memory slots */ mp_size mused; /* number of used memories */ /* I/O components */ FILE* ifp; /* input file handle */ char* ibuf; /* input scratch buffer */ int buflen; /* size of scratch buffer */ } cstate_t; static mp_result state_init(cstate_t* sp, mp_size n_elts); static void state_clear(cstate_t* sp); static void stack_flush(cstate_t* sp); static mp_result stack_push(cstate_t* sp, mp_int elt); static mp_result stack_pop(cstate_t* sp); static mp_result mem_insert(cstate_t* sp, const char* name, mp_int value); static mp_result mem_recall(cstate_t* sp, const char* name, mp_int value); static mp_result mem_clear(cstate_t* sp); typedef mp_result (*op_func)(cstate_t*); static mp_result cf_abs(cstate_t* sp); static mp_result cf_neg(cstate_t* sp); static mp_result cf_add(cstate_t* sp); static mp_result cf_sub(cstate_t* sp); static mp_result cf_mul(cstate_t* sp); static mp_result cf_divmod(cstate_t* sp); static mp_result cf_div(cstate_t* sp); static mp_result cf_mod(cstate_t* sp); static mp_result cf_expt(cstate_t* sp); static mp_result cf_exptmod(cstate_t* sp); static mp_result cf_square(cstate_t* sp); static mp_result cf_invmod(cstate_t* sp); static mp_result cf_gcd(cstate_t* sp); static mp_result cf_xgcd(cstate_t* sp); static mp_result cf_sqrt(cstate_t* sp); static mp_result cf_root(cstate_t* sp); static mp_result cf_cmplt(cstate_t* sp); static mp_result cf_cmpgt(cstate_t* sp); static mp_result cf_cmple(cstate_t* sp); static mp_result cf_cmpge(cstate_t* sp); static mp_result cf_cmpeq(cstate_t* sp); static mp_result cf_cmpne(cstate_t* sp); static mp_result cf_inc(cstate_t* sp); static mp_result cf_dec(cstate_t* sp); static mp_result cf_fact(cstate_t* sp); static mp_result cf_pprint(cstate_t* sp); static mp_result cf_print(cstate_t* sp); static mp_result cf_pstack(cstate_t* sp); static mp_result cf_clstk(cstate_t* sp); static mp_result cf_pop(cstate_t* sp); static mp_result cf_dup(cstate_t* sp); static mp_result cf_copy(cstate_t* sp); static mp_result cf_swap(cstate_t* sp); static mp_result cf_rot(cstate_t* sp); static mp_result cf_pick(cstate_t* sp); static mp_result cf_setr(cstate_t* sp); static mp_result cf_setbin(cstate_t* sp); static mp_result cf_help(cstate_t* sp); static mp_result cf_store(cstate_t* sp); static mp_result cf_recall(cstate_t* sp); static mp_result cf_cmem(cstate_t* sp); static mp_result cf_pmem(cstate_t* sp); static mp_result cf_qrecall(cstate_t* sp); typedef struct { char* name; /* The name of the operator. */ int stack_size; /* Number of stack arguments required. */ op_func handler; /* Function implementing operation. */ char* descript; /* Human-readable description. */ } calcop_t; static calcop_t g_ops[] = { {"abs", 1, cf_abs, "x -- |x|"}, {"neg", 1, cf_neg, "x -- (-x)"}, {"+", 2, cf_add, "x y -- (x+y)"}, {"add", 2, cf_add, "x y -- (x+y)"}, {"-", 2, cf_sub, "x y -- (x-y)"}, {"sub", 2, cf_sub, "x y -- (x-y)"}, {"*", 2, cf_mul, "x y -- (x*y)"}, {"mul", 2, cf_mul, "x y -- (x*y)"}, {"/", 2, cf_divmod, "x y -- q r ; x = yq + r, 0 <= r < y"}, {"//", 2, cf_div, "x y -- (x div y)"}, {"div", 2, cf_div, "x y -- (x div y)"}, {"%", 2, cf_mod, "x y -- (x mod y)"}, {"mod", 2, cf_mod, "x y -- (x mod y)"}, {"^", 2, cf_expt, "x y -- (x^y)"}, {"expt", 2, cf_expt, "x y -- (x^y)"}, {"^^", 3, cf_exptmod, "x y m -- (x^y mod m)"}, {"emod", 3, cf_exptmod, "x y m -- (x^y mod m)"}, {"sqr", 1, cf_square, "x -- (x*x)"}, {"inv", 2, cf_invmod, "x m -- (1/x mod m)"}, {"gcd", 2, cf_gcd, "x y -- gcd(x, y)"}, {"xgcd", 2, cf_xgcd, "x y -- g u v ; g = ux + vy"}, {"sqrt", 1, cf_sqrt, "x -- floor(sqrt(x))"}, {"root", 2, cf_root, "x y -- floor(x^{1/y}) ; y > 0"}, {"<", 2, cf_cmplt, "x y -- (x", 2, cf_cmpgt, "x y -- (x>y)"}, {"<=", 2, cf_cmple, "x y -- (x<=y)"}, {">=", 2, cf_cmpge, "x y -- (x>=y)"}, {"=", 2, cf_cmpeq, "x y -- (x=y)"}, {"<>", 2, cf_cmpne, "x y -- (x<>y)"}, {"inc", 1, cf_inc, "x -- (x+1)"}, {"dec", 1, cf_dec, "x -- (x-1)"}, {"!", 1, cf_fact, "x -- x!"}, {"fact", 1, cf_fact, "x -- x!"}, {".", 1, cf_pprint, "x -- ; print x in current output mode"}, {";", 1, cf_print, "x -- x ; print x in current output mode"}, {"?", 0, cf_pstack, "-- ; print stack"}, {"cls", 0, cf_clstk, "... -- ; clear stack"}, {"$", 1, cf_pop, "x --"}, {"drop", 1, cf_pop, "x --"}, {"dup", 1, cf_dup, "x -- x x"}, {"copy", 2, cf_copy, "vn ... v1 v0 n -- vn ... v0 vn ... v0"}, {"swap", 2, cf_swap, "x y -- y x"}, {"rot", 3, cf_rot, "a b c -- b c a"}, {"pick", 2, cf_pick, "... v2 v1 v0 n -- ... v2 v1 v0 vn"}, {">>", 1, cf_store, "x -- ; save in named variable"}, {"<<", 0, cf_recall, "-- x ; recall from named variable"}, {"clm", 0, cf_cmem, "-- ; clear memory"}, {"??", 0, cf_pmem, "-- ; print memory"}, {"out", 1, cf_setr, "r -- ; set output radix to r"}, {"bin", 0, cf_setbin, "-- ; set output format to binary"}, {"help", 0, cf_help, "-- ; print help message"}, /* This is the end-marker, but it is also used to catch implicit variable lookups from memory. */ {NULL, 0, cf_qrecall, "-- x ; recall from named variable"}, }; #define BUFFER_SIZE 16384 /* max. length of input values, in chars */ /* Token types from the primitive lexical analyzer */ typedef enum { t_eof, t_symbol, t_number, t_error } token_t; static token_t next_token(FILE* ifp, char* buf, int size); static mp_result read_number(char* buf, mp_int* out); static int find_command(cstate_t* ops); static void print_value(mp_int v); static mp_result run_file(FILE* ifp, cstate_t* op_state); /* Error code used internally to signal input problems. */ static mp_result MP_INPUT; static int g_output_radix = 10; /* output radix */ static FILE* g_output_file = NULL; int main(int argc, char* argv[]) { extern char* optarg; extern int optind; int opt, errs = 0; FILE* ifp; cstate_t op_state; mp_result res; MP_INPUT = MP_MINERR - 1; g_output_file = stdout; while ((opt = getopt(argc, argv, "ho:")) != EOF) { switch (opt) { case 'h': fprintf( stderr, "Usage: imcalc [-h] [-o ] input*\n\n" "Options:\n" " -h : display this help message.\n" " -o : send output to file.\n\n" "If no input files are given, the standard input is read. The\n" "special file name \"-\" is interpreted to mean the standard " "input.\n" "Output goes to standard output unless \"-o\" is used.\n\n"); return 0; case 'o': if ((g_output_file = fopen(optarg, "wt")) == NULL) { fprintf(stderr, "Unable to open \"%s\" for writing: %s\n", optarg, strerror(errno)); return 1; } break; default: fprintf(stderr, "Usage: imcalc [-h] [-o ] input*\n" " [use \"imcalc -h\" to get help]\n\n"); return 1; } } if ((res = state_init(&op_state, 1)) != MP_OK) { fprintf(stderr, "Error: state_init: %s\n", mp_error_string(res)); return 1; } if (optind < argc) { int ix; for (ix = optind; ix < argc; ++ix) { if (strcmp(argv[ix], "-") == 0) ifp = stdin; else if ((ifp = fopen(argv[optind], "rt")) == NULL) { fprintf(stderr, "Unable to open \"%s\" for reading: %s\n", argv[optind], strerror(errno)); return 1; } if (run_file(ifp, &op_state) != MP_OK) ++errs; } state_clear(&op_state); return errs > 0; } else { int rv = 1 - (run_file(stdin, &op_state) == MP_OK); state_clear(&op_state); return rv; } } static token_t next_token(FILE* ifp, char* buf, int size) { int ch, pos = 0; token_t res; assert(buf != NULL && size > 0); while ((ch = fgetc(ifp)) != EOF && isspace(ch)) /* empty */ ; if (ch == EOF) { buf[0] = '\0'; return t_eof; } if (ch == '-') { int next = fgetc(ifp); if (next == EOF || !isdigit(next)) res = t_symbol; else res = t_number; ungetc(next, ifp); } else if (isdigit(ch) || ch == '#') res = t_number; else res = t_symbol; buf[pos++] = ch; while ((ch = fgetc(ifp)) != EOF) { if ((res == t_number && ispunct(ch) && ch != '-') || (res == t_symbol && isdigit(ch)) || isspace(ch)) { ungetc(ch, ifp); break; } else if (pos + 1 >= size) { res = t_error; break; } buf[pos++] = ch; } buf[pos] = '\0'; return res; } static mp_result read_number(char* buf, mp_int* out) { int radix = 10, pos = 0; mp_result res; mp_int value; assert(buf != NULL && out != NULL); if (buf[pos] == '#') { switch (buf[1]) { case 'b': case 'B': radix = 2; break; case 'd': case 'D': radix = 10; break; case 'o': case 'O': radix = 8; break; case 'x': case 'X': radix = 16; break; default: return MP_BADARG; } pos += 2; } if ((value = mp_int_alloc()) == NULL) { *out = NULL; return MP_MEMORY; } if ((res = mp_int_read_string(value, radix, buf + pos)) != MP_OK) { mp_int_free(value); *out = NULL; return res; } *out = value; return res; } static int find_command(cstate_t* op) { int ix, jx; char* buf = op->ibuf; /* First, try to find the command by name */ for (ix = 0; g_ops[ix].name != NULL; ++ix) { if (strcasecmp(buf, g_ops[ix].name) == 0) return ix; } /* If we don't find the command, try a variable lookup */ for (jx = 0; (mp_size)jx < op->mused; ++jx) { if (strcmp(buf, op->names[jx]) == 0) return ix; /* sentinel */ } /* If variable lookup fails, report command not found */ return -1; } static void print_value(mp_int v) { if (g_output_radix == 0) { mp_result len = mp_int_binary_len(v); unsigned char* buf = malloc(len); int ix; if (buf != NULL) { mp_int_to_binary(v, buf, len); for (ix = 0; ix < len - 1; ++ix) { fprintf(g_output_file, "%02x.", buf[ix]); } fprintf(g_output_file, "%02x\n", buf[ix]); free(buf); } else { fprintf(g_output_file, "\n"); } } else { mp_result len = mp_int_string_len(v, g_output_radix); char* buf = malloc(len); if (buf != NULL) { mp_int_to_string(v, g_output_radix, buf, len); fputs(buf, g_output_file); fputc('\n', g_output_file); free(buf); } else { fprintf(g_output_file, "\n"); } } } static mp_result run_file(FILE* ifp, cstate_t* op_state) { mp_result res = MP_OK; token_t next; op_state->ifp = ifp; while ((next = next_token(ifp, op_state->ibuf, op_state->buflen)) != t_eof) { mp_int value = NULL; int cpos; switch (next) { case t_number: if ((res = read_number(op_state->ibuf, &value)) != MP_OK) fprintf(stderr, "error: invalid number syntax: %s\n", op_state->ibuf); else if ((res = stack_push(op_state, value)) != MP_OK) goto EXIT; break; case t_symbol: if ((cpos = find_command(op_state)) < 0) { fprintf(stderr, "error: command not understood: %s\n", op_state->ibuf); } else if (op_state->used < (mp_size)g_ops[cpos].stack_size) { fprintf(stderr, "error: not enough arguments (have %d, want %d)\n", op_state->used, g_ops[cpos].stack_size); } else if ((res = (g_ops[cpos].handler)(op_state)) != MP_OK) { if (res == MP_INPUT) { fprintf(stderr, "error: incorrect input format\n"); } else { fprintf(stderr, "error: %s\n", mp_error_string(res)); } } break; default: fprintf(stderr, "error: invalid input token: %s\n", op_state->ibuf); res = MP_BADARG; goto EXIT; } } EXIT: return res; } static mp_result state_init(cstate_t* sp, mp_size n_elts) { int ix; assert(sp != NULL && n_elts > 0); if ((sp->elts = malloc(n_elts * sizeof(*(sp->elts)))) == NULL) return MP_MEMORY; if ((sp->mem = malloc(n_elts * sizeof(*(sp->mem)))) == NULL) { free(sp->elts); return MP_MEMORY; } if ((sp->names = malloc(n_elts * sizeof(*(sp->names)))) == NULL) { free(sp->mem); free(sp->elts); return MP_MEMORY; } if ((sp->ibuf = malloc(BUFFER_SIZE * sizeof(char))) == NULL) { free(sp->names); free(sp->mem); free(sp->elts); return MP_MEMORY; } for (ix = 0; (mp_size)ix < n_elts; ++ix) { sp->elts[ix] = NULL; sp->mem[ix] = NULL; sp->names[ix] = NULL; } sp->alloc = n_elts; sp->used = 0; sp->mslots = n_elts; sp->mused = 0; sp->buflen = BUFFER_SIZE; return MP_OK; } static void state_clear(cstate_t* sp) { assert(sp != NULL); if (sp->elts != NULL) { int ix; for (ix = 0; (mp_size)ix < sp->used; ++ix) { mp_int_clear(sp->elts[ix]); sp->elts[ix] = NULL; } free(sp->elts); sp->elts = NULL; sp->alloc = 0; sp->used = 0; } if (sp->mem != NULL) { int ix; for (ix = 0; (mp_size)ix < sp->mused; ++ix) { mp_int_free(sp->mem[ix]); sp->mem[ix] = NULL; free(sp->names[ix]); sp->names[ix] = NULL; } free(sp->mem); sp->mem = NULL; free(sp->names); sp->names = NULL; sp->mslots = 0; sp->mused = 0; } if (sp->ibuf != NULL) { free(sp->ibuf); sp->buflen = 0; } if (sp->ifp != NULL) { fclose(sp->ifp); sp->ifp = NULL; } } static void stack_flush(cstate_t* sp) { int ix; assert(sp != NULL && sp->elts != NULL); for (ix = 0; (mp_size)ix < sp->used; ++ix) { mp_int_clear(sp->elts[ix]); sp->elts[ix] = NULL; } sp->used = 0; } static mp_result stack_push(cstate_t* sp, mp_int elt) { if (sp->used >= sp->alloc) { mp_size nsize = 2 * sp->alloc; mp_int* tmp; int ix; if ((tmp = malloc(nsize * sizeof(*(sp->elts)))) == NULL) return MP_MEMORY; for (ix = 0; (mp_size)ix < sp->used; ++ix) { tmp[ix] = sp->elts[ix]; } free(sp->elts); sp->elts = tmp; sp->alloc = nsize; } sp->elts[sp->used++] = elt; return MP_OK; } static mp_result stack_pop(cstate_t* sp) { assert(sp != NULL && sp->elts != NULL); if (sp->used == 0) return MP_UNDEF; sp->used -= 1; mp_int_clear(sp->elts[sp->used]); sp->elts[sp->used] = NULL; return MP_OK; } static mp_result mem_insert(cstate_t* sp, const char* name, mp_int value) { int ix; for (ix = 0; (mp_size)ix < sp->mused; ++ix) { if (strcmp(name, sp->names[ix]) == 0) break; } /* Two cases: ix < sp->mused ==> replacing existing entry. otherwise ==> adding new entry, may need to grow dictionary. */ if ((mp_size)ix < sp->mused) { mp_int_free(sp->mem[ix]); /* fall through to the end */ } else { if (sp->mused >= sp->mslots) { mp_size nsize = 2 * sp->mslots; mp_int* tz; char** tc; int jx; if ((tz = malloc(nsize * sizeof(*(sp->mem)))) == NULL) return MP_MEMORY; if ((tc = malloc(nsize * sizeof(*(sp->names)))) == NULL) { free(tz); return MP_MEMORY; } for (jx = 0; (mp_size)jx < sp->mused; ++jx) { tz[jx] = sp->mem[jx]; tc[jx] = sp->names[jx]; } free(sp->mem); sp->mem = tz; free(sp->names); sp->names = tc; sp->mslots = nsize; } sp->mused += 1; sp->names[ix] = malloc(1 + strlen(name)); strcpy(sp->names[ix], name); } sp->mem[ix] = mp_int_alloc(); return mp_int_copy(value, sp->mem[ix]); } static mp_result mem_recall(cstate_t* sp, const char* name, mp_int value) { int ix; for (ix = 0; (mp_size)ix < sp->mused; ++ix) { if (strcmp(name, sp->names[ix]) == 0) { return mp_int_copy(sp->mem[ix], value); } } return MP_UNDEF; /* not found */ } static mp_result mem_clear(cstate_t* sp) { int ix; for (ix = 0; (mp_size)ix < sp->mused; ++ix) { mp_int_free(sp->mem[ix]); free(sp->names[ix]); } sp->mused = 0; return MP_OK; } static mp_result cf_abs(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; return mp_int_abs(a, a); } static mp_result cf_neg(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; return mp_int_neg(a, a); } static mp_result cf_add(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_add(a, b, a); if (res == MP_OK) stack_pop(sp); return res; } static mp_result cf_sub(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_sub(a, b, a); if (res == MP_OK) stack_pop(sp); return res; } static mp_result cf_mul(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_mul(a, b, a); if (res == MP_OK) stack_pop(sp); return res; } static mp_result cf_divmod(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; return mp_int_div(a, b, a, b); } static mp_result cf_div(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_div(a, b, a, NULL); if (res == MP_OK) stack_pop(sp); return res; } static mp_result cf_mod(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_mod(a, b, a); if (res == MP_OK) stack_pop(sp); return res; } static mp_result cf_expt(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; mp_small bval; if ((res = mp_int_to_int(b, &bval)) != MP_OK) return res; stack_pop(sp); return mp_int_expt(a, bval, a); } static mp_result cf_exptmod(cstate_t* sp) { mp_int m = sp->elts[sp->used - 1]; mp_int b = sp->elts[sp->used - 2]; mp_int a = sp->elts[sp->used - 3]; mp_result res = mp_int_exptmod(a, b, m, a); if (res == MP_OK) { stack_pop(sp); stack_pop(sp); } return res; } static mp_result cf_square(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; return mp_int_sqr(a, a); } static mp_result cf_invmod(cstate_t* sp) { mp_int m = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_invmod(a, m, a); stack_pop(sp); return res; } static mp_result cf_gcd(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res = mp_int_gcd(a, b, a); if (res == MP_OK) stack_pop(sp); return res; } static mp_result cf_xgcd(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_int t; mp_result res; if ((t = mp_int_alloc()) == NULL) return MP_MEMORY; if ((res = mp_int_egcd(a, b, a, b, t)) != MP_OK) { mp_int_free(t); return res; } if ((res = stack_push(sp, t)) != MP_OK) mp_int_free(t); return res; } static mp_result cf_sqrt(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; return mp_int_sqrt(a, a); } static mp_result cf_root(cstate_t* sp) { mp_int a = sp->elts[sp->used - 2]; mp_int bp = sp->elts[sp->used - 1]; mp_small b; mp_result res; if ((res = mp_int_to_int(bp, &b)) != MP_OK) return res; stack_pop(sp); return mp_int_root(a, b, a); } static mp_result cf_cmplt(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; res = mp_int_set_value(a, (mp_int_compare(a, b) < 0)); stack_pop(sp); return res; } static mp_result cf_cmpgt(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; res = mp_int_set_value(a, (mp_int_compare(a, b) > 0)); stack_pop(sp); return res; } static mp_result cf_cmple(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; res = mp_int_set_value(a, (mp_int_compare(a, b) <= 0)); stack_pop(sp); return res; } static mp_result cf_cmpge(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; res = mp_int_set_value(a, (mp_int_compare(a, b) >= 0)); stack_pop(sp); return res; } static mp_result cf_cmpeq(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; res = mp_int_set_value(a, (mp_int_compare(a, b) == 0)); stack_pop(sp); return res; } static mp_result cf_cmpne(cstate_t* sp) { mp_int b = sp->elts[sp->used - 1]; mp_int a = sp->elts[sp->used - 2]; mp_result res; res = mp_int_set_value(a, (mp_int_compare(a, b) != 0)); stack_pop(sp); return res; } static mp_result cf_inc(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; return mp_int_add_value(a, 1, a); } static mp_result cf_dec(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; return mp_int_sub_value(a, 1, a); } static mp_result cf_fact(cstate_t* sp) { mpz_t tmp; mp_int x = sp->elts[sp->used - 1]; mp_result res = MP_OK; if (mp_int_compare_zero(x) < 0) return MP_UNDEF; (void)mp_int_init_value(&tmp, 1); while (mp_int_compare_value(x, 1) > 0) { if ((res = mp_int_mul(&tmp, x, &tmp)) != MP_OK) goto CLEANUP; if ((res = mp_int_sub_value(x, 1, x)) != MP_OK) goto CLEANUP; } res = mp_int_copy(&tmp, x); CLEANUP: mp_int_clear(&tmp); return res; } static mp_result cf_pprint(cstate_t* sp) { print_value(sp->elts[sp->used - 1]); stack_pop(sp); return MP_OK; } static mp_result cf_print(cstate_t* sp) { print_value(sp->elts[sp->used - 1]); return MP_OK; } static mp_result cf_pstack(cstate_t* sp) { int ix; if (sp->used == 0) { fprintf(g_output_file, "\n"); } else { for (ix = 0; (mp_size)ix < sp->used; ++ix) { fprintf(g_output_file, "%2d: ", ix); print_value(sp->elts[sp->used - 1 - ix]); } } return MP_OK; } static mp_result cf_clstk(cstate_t* sp) { stack_flush(sp); return MP_OK; } static mp_result cf_pop(cstate_t* sp) { return stack_pop(sp); } static mp_result cf_dup(cstate_t* sp) { mp_int cp = mp_int_alloc(); mp_result res; if (cp == NULL) return MP_MEMORY; if ((res = mp_int_copy(sp->elts[sp->used - 1], cp)) != MP_OK) { mp_int_free(cp); return res; } if ((res = stack_push(sp, cp)) != MP_OK) mp_int_free(cp); return res; } static mp_result cf_copy(cstate_t* sp) { mp_int n = sp->elts[sp->used - 1]; mp_result res; mp_small ncopy; int ix; if ((res = mp_int_to_int(n, &ncopy)) != MP_OK) return res; if (ncopy < 1 || ncopy >= sp->used) return MP_RANGE; stack_pop(sp); for (ix = 0; ix < ncopy; ++ix) { mp_int old = sp->elts[sp->used - ncopy]; mp_int new = mp_int_alloc(); if (new == NULL) return MP_MEMORY; if ((res = mp_int_copy(old, new)) != MP_OK) { mp_int_free(new); return res; } if ((res = stack_push(sp, new)) != MP_OK) return res; } return MP_OK; } static mp_result cf_swap(cstate_t* sp) { mp_int t = sp->elts[sp->used - 1]; sp->elts[sp->used - 1] = sp->elts[sp->used - 2]; sp->elts[sp->used - 2] = t; return MP_OK; } static mp_result cf_rot(cstate_t* sp) { mp_int t = sp->elts[sp->used - 3]; sp->elts[sp->used - 3] = sp->elts[sp->used - 2]; sp->elts[sp->used - 2] = sp->elts[sp->used - 1]; sp->elts[sp->used - 1] = t; return MP_OK; } static mp_result cf_pick(cstate_t* sp) { mp_int n = sp->elts[sp->used - 1]; mp_result res; mp_small pos = 0; if ((res = mp_int_to_int(n, &pos)) != MP_OK) return res; if (pos < 0 || pos >= sp->used - 1) return MP_RANGE; return mp_int_copy(sp->elts[sp->used - 2 - pos], n); } static mp_result cf_setr(cstate_t* sp) { mp_int a = sp->elts[sp->used - 1]; mp_result res; mp_small rdx = 0; if ((res = mp_int_to_int(a, &rdx)) != MP_OK) return res; if (rdx < MP_MIN_RADIX || rdx > MP_MAX_RADIX) return MP_RANGE; g_output_radix = rdx; stack_pop(sp); return MP_OK; } static mp_result cf_setbin(cstate_t* sp) { g_output_radix = 0; return MP_OK; } static mp_result cf_help(cstate_t* sp) { int ix, maxlen = 10; /* minimum width */ for (ix = 0; g_ops[ix].name != NULL; ++ix) { int len = strlen(g_ops[ix].name); if (len > maxlen) maxlen = len; } fprintf(stderr, "Operators understood:\n"); for (ix = 0; g_ops[ix].name != NULL; ++ix) { int len = strlen(g_ops[ix].name); fputs(g_ops[ix].name, stderr); while (len++ <= maxlen) fputc(' ', stderr); fprintf(stderr, "%s\n", g_ops[ix].descript); } fputc('\n', stderr); return MP_OK; } static mp_result cf_store(cstate_t* sp) { mp_result res; if (next_token(sp->ifp, sp->ibuf, sp->buflen) != t_symbol) return MP_INPUT; if ((res = mem_insert(sp, sp->ibuf, sp->elts[sp->used - 1])) != MP_OK) return res; return stack_pop(sp); } static mp_result cf_recall(cstate_t* sp) { mp_result res; mp_int val; if (next_token(sp->ifp, sp->ibuf, sp->buflen) != t_symbol) return MP_INPUT; if ((val = mp_int_alloc()) == NULL) return MP_MEMORY; if ((res = mem_recall(sp, sp->ibuf, val)) != MP_OK) { mp_int_free(val); return res; } return stack_push(sp, val); } static mp_result cf_cmem(cstate_t* sp) { return mem_clear(sp); } static mp_result cf_pmem(cstate_t* sp) { int ix, max_len = 0; if (sp->mused == 0) { fprintf(g_output_file, "\n"); return MP_OK; } for (ix = 0; (mp_size)ix < sp->mused; ++ix) { int ln = strlen(sp->names[ix]); if (ln > max_len) max_len = ln; } max_len += 1; /* allow for a padding space */ for (ix = 0; (mp_size)ix < sp->mused; ++ix) { int ln = strlen(sp->names[ix]); fprintf(g_output_file, "%s:", sp->names[ix]); while (ln++ < max_len) fputc(' ', g_output_file); print_value(sp->mem[ix]); } return MP_OK; } static mp_result cf_qrecall(cstate_t* sp) { mp_result res; mp_int val; if ((val = mp_int_alloc()) == NULL) return MP_MEMORY; if ((res = mem_recall(sp, sp->ibuf, val)) != MP_OK) { mp_int_free(val); return res; } return stack_push(sp, val); } /* Here there be dragons */ ================================================ FILE: examples/input.c ================================================ /* Name: input.c Purpose: Basic I/O demo for IMath. Author: Michael J. Fromberger This program demonstrates how to read and write arbitrary precision integers using IMath. Copyright (C) 2003-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include "imrat.h" int main(int argc, char* argv[]) { mp_size radix = 10; /* Default output radix */ mpq_t value; mp_result res; char* endp; if (argc < 2) { fprintf(stderr, "Usage: input [output-base]\n"); return 1; } if (argc > 2) { if ((radix = atoi(argv[2])) < MP_MIN_RADIX || (radix > MP_MAX_RADIX)) { fprintf(stderr, "Error: Specified radix is out of range (%d)\n", radix); return 1; } } /* Initialize a new value, initially zero; illustrates how to check for errors (e.g., out of memory) and display a message. */ if ((res = mp_rat_init(&value)) != MP_OK) { fprintf(stderr, "Error in mp_rat_init(): %s\n", mp_error_string(res)); return 1; } /* Read value in base 10 */ if ((res = mp_rat_read_ustring(&value, 0, argv[1], &endp)) != MP_OK) { fprintf(stderr, "Error in mp_rat_read_ustring(): %s\n", mp_error_string(res)); if (res == MP_TRUNC) fprintf(stderr, " -- remaining input is: %s\n", endp); mp_rat_clear(&value); return 1; } printf("Here is your value in base %d\n", radix); { mp_result buf_size, res; char* obuf; if (mp_rat_is_integer(&value)) { /* Allocate a buffer big enough to hold the given value, including sign and zero terminator. */ buf_size = mp_int_string_len(MP_NUMER_P(&value), radix); obuf = malloc(buf_size); /* Convert the value to a string in the desired radix. */ res = mp_int_to_string(MP_NUMER_P(&value), radix, obuf, buf_size); if (res != MP_OK) { fprintf(stderr, "Conversion to base %d failed: %s\n", radix, mp_error_string(res)); mp_rat_clear(&value); return 1; } } else { /* Allocate a buffer big enough to hold the given value, including sign and zero terminator. */ buf_size = mp_rat_string_len(&value, radix); obuf = malloc(buf_size); /* Convert the value to a string in the desired radix. */ res = mp_rat_to_string(&value, radix, obuf, buf_size); if (res != MP_OK) { fprintf(stderr, "Conversion to base %d failed: %s\n", radix, mp_error_string(res)); mp_rat_clear(&value); return 1; } } fputs(obuf, stdout); fputc('\n', stdout); free(obuf); } /* When you are done with a value, it must be "cleared" to release the memory it occupies */ mp_rat_clear(&value); return 0; } /* Here there be dragons */ ================================================ FILE: examples/pi.c ================================================ /* Name: pi.c Purpose: Computes digits of the physical constant pi. Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. Notes: Uses Machin's formula, which should be suitable for a few thousand digits. 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. */ #include #include #include #include #include "imath.h" int g_radix = 10; /* use this radix for output */ mp_result arctan(mp_small radix, mp_small mul, mp_small x, mp_small prec, mp_int sum); int main(int argc, char* argv[]) { mp_result res; mpz_t sum1, sum2; int ndigits, out = 0; clock_t start, end; if (argc < 2) { fprintf(stderr, "Usage: %s []\n", argv[0]); return 1; } if ((ndigits = abs(atoi(argv[1]))) == 0) { fprintf(stderr, "%s: you must request at least 1 digit\n", argv[0]); return 1; } else if ((mp_word)ndigits > MP_DIGIT_MAX) { fprintf(stderr, "%s: you may request at most %u digits\n", argv[0], (unsigned int)MP_DIGIT_MAX); return 1; } if (argc > 2) { int radix = atoi(argv[2]); if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX) { fprintf(stderr, "%s: you may only specify a radix between %d and %d\n", argv[0], MP_MIN_RADIX, MP_MAX_RADIX); return 1; } g_radix = radix; } size_t buf_size = ndigits + 2; /* "3" prefix and terminating '\0' */ char* buf = malloc(buf_size); if (!buf) { perror("malloc"); return 1; } mp_int_init(&sum1); mp_int_init(&sum2); start = clock(); /* sum1 = 16 * arctan(1/5) */ if ((res = arctan(g_radix, 16, 5, ndigits, &sum1)) != MP_OK) { fprintf(stderr, "%s: error computing arctan: %d\n", argv[0], res); out = 1; goto CLEANUP; } /* sum2 = 4 * arctan(1/239) */ if ((res = arctan(g_radix, 4, 239, ndigits, &sum2)) != MP_OK) { fprintf(stderr, "%s: error computing arctan: %d\n", argv[0], res); out = 1; goto CLEANUP; } /* pi = sum1 - sum2 */ if ((res = mp_int_sub(&sum1, &sum2, &sum1)) != MP_OK) { fprintf(stderr, "%s: error computing pi: %d\n", argv[0], res); out = 1; goto CLEANUP; } end = clock(); mp_int_to_string(&sum1, g_radix, buf, buf_size); printf("%c.%s\n", buf[0], buf + 1); fprintf(stderr, "Computation took %.2f sec.\n", (double)(end - start) / CLOCKS_PER_SEC); CLEANUP: free(buf); mp_int_clear(&sum1); mp_int_clear(&sum2); return out; } /* Compute mul * atan(1/x) to prec digits of precision, and store the result in sum. Computes atan(1/x) using the formula: 1 1 1 1 atan(1/x) = --- - ---- + ---- - ---- + ... x 3x^3 5x^5 7x^7 */ mp_result arctan(mp_small radix, mp_small mul, mp_small x, mp_small prec, mp_int sum) { mpz_t t, v; mp_result res; mp_small rem, sign = 1, coeff = 1; mp_int_init(&t); mp_int_init(&v); ++prec; /* Compute mul * radix^prec * x The initial multiplication by x saves a special case in the loop for the first term of the series. */ if ((res = mp_int_expt_value(radix, prec, &t)) != MP_OK || (res = mp_int_mul_value(&t, mul, &t)) != MP_OK || (res = mp_int_mul_value(&t, x, &t)) != MP_OK) goto CLEANUP; x *= x; /* assumes x <= sqrt(MP_SMALL_MAX) */ mp_int_zero(sum); do { if ((res = mp_int_div_value(&t, x, &t, &rem)) != MP_OK) goto CLEANUP; if ((res = mp_int_div_value(&t, coeff, &v, &rem)) != MP_OK) goto CLEANUP; /* Add or subtract the result depending on the current sign (1 = add) */ if (sign > 0) res = mp_int_add(sum, &v, sum); else res = mp_int_sub(sum, &v, sum); if (res != MP_OK) goto CLEANUP; sign = -sign; coeff += 2; } while (mp_int_compare_zero(&t) != 0); res = mp_int_div_value(sum, radix, sum, NULL); CLEANUP: mp_int_clear(&v); mp_int_clear(&t); return res; } /* Here there be dragons */ ================================================ FILE: examples/randprime.c ================================================ /* Name: randprime.c Purpose: Generate a probable prime at random. Author: M. J. Fromberger Usage: randprime [-s] [] Generate a randomly-chosen probable prime having significant bits, and write it to the specified output file or to the standard output. If the "-s" option is given, a prime p is chosen such that (p - 1) / 2 is also prime. A prime is obtained by reading random bits from /dev/random, setting the low-order bit, and testing for primality. If the first candidate is not prime, successive odd candidates are tried until a probable prime is found. Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include #include #include #include "imath.h" #include "iprime.h" /* Load the specified buffer with random bytes */ int randomize(unsigned char* buf, size_t len); /* Overwrite the specified value with n_bits random bits */ mp_result mp_int_randomize(mp_int a, mp_size n_bits); /* Find a prime starting from the given odd seed */ mp_result find_prime(mp_int seed, FILE* fb); mp_result find_strong_prime(mp_int seed, FILE* fb); typedef mp_result (*find_f)(mp_int, FILE*); int main(int argc, char* argv[]) { int opt, modbits; FILE* ofp = stdout; mp_result res; find_f find_func = find_prime; char tag = 'p'; mpz_t value; /* Process command-line arguments */ while ((opt = getopt(argc, argv, "s")) != EOF) { switch (opt) { case 's': find_func = find_strong_prime; tag = 'P'; break; default: fprintf(stderr, "Usage: randprime [-s] []\n"); return 1; } } if (optind >= argc) { fprintf(stderr, "Error: You must specify the number of significant bits.\n"); fprintf(stderr, "Usage: randprime [-s] []\n"); return 1; } modbits = (int)strtol(argv[optind++], NULL, 0); if (modbits < CHAR_BIT) { fprintf(stderr, "Error: Invalid value for number of significant bits.\n"); return 1; } if (modbits % 2 == 1) ++modbits; /* Check if output file is specified */ if (optind < argc) { if ((ofp = fopen(argv[optind], "wt")) == NULL) { fprintf(stderr, "Error: Unable to open output file for writing.\n" " - Filename: %s\n" " - Error: %s\n", argv[optind], strerror(errno)); return 1; } } mp_int_init(&value); if ((res = mp_int_randomize(&value, modbits - 1)) != MP_OK) { fprintf(stderr, "Error: Unable to generate random start value.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } fprintf(stderr, "%c: ", tag); find_func(&value, stderr); fputc('\n', stderr); /* Write the completed value to the specified output file */ { int len; char* obuf; len = mp_int_string_len(&value, 10); obuf = malloc(len); mp_int_to_string(&value, 10, obuf, len); fputs(obuf, ofp); fputc('\n', ofp); free(obuf); } EXIT: fclose(ofp); mp_int_clear(&value); return 0; } int randomize(unsigned char* buf, size_t len) { FILE* rnd = fopen("/dev/random", "rb"); size_t nr; if (rnd == NULL) return -1; nr = fread(buf, sizeof(*buf), len, rnd); fclose(rnd); return (int)nr; } mp_result mp_int_randomize(mp_int a, mp_size n_bits) { mp_size n_bytes = (n_bits + CHAR_BIT - 1) / CHAR_BIT; unsigned char* buf; mp_result res = MP_OK; if ((buf = malloc(n_bytes)) == NULL) return MP_MEMORY; if ((mp_size)randomize(buf, n_bytes) != n_bytes) { res = MP_TRUNC; goto CLEANUP; } /* Clear bits beyond the number requested */ if (n_bits % CHAR_BIT != 0) { unsigned char b_mask = (1 << (n_bits % CHAR_BIT)) - 1; unsigned char t_mask = (1 << (n_bits % CHAR_BIT)) >> 1; buf[0] &= b_mask; buf[0] |= t_mask; } /* Set low-order bit to insure value is odd */ buf[n_bytes - 1] |= 1; res = mp_int_read_unsigned(a, buf, n_bytes); CLEANUP: memset(buf, 0, n_bytes); free(buf); return res; } mp_result find_prime(mp_int seed, FILE* fb) { mp_result res; int count = 0; if (mp_int_is_even(seed)) { if ((res = mp_int_add_value(seed, 1, seed)) != MP_OK) { return res; } } while ((res = mp_int_is_prime(seed)) == MP_FALSE) { ++count; if (fb != NULL && (count % 50) == 0) { fputc('.', fb); } if ((res = mp_int_add_value(seed, 2, seed)) != MP_OK) { return res; } } if (res == MP_TRUE && fb != NULL) fputc('+', fb); return res; } mp_result find_strong_prime(mp_int seed, FILE* fb) { mp_result res = MP_OK; mpz_t t; mp_int_init(&t); for (;;) { if (find_prime(seed, fb) != MP_TRUE) break; if (mp_int_copy(seed, &t) != MP_OK) break; if (mp_int_mul_pow2(&t, 1, &t) != MP_OK || mp_int_add_value(&t, 1, &t) != MP_OK) { break; } if ((res = mp_int_is_prime(&t)) == MP_TRUE) { if (fb != NULL) fputc('!', fb); res = mp_int_copy(&t, seed); break; } else if (res != MP_FALSE) break; if (fb != NULL) fputc('x', fb); if (mp_int_add_value(seed, 2, seed) != MP_OK) break; } mp_int_clear(&t); return res; } /* Here there be dragons */ ================================================ FILE: examples/rounding.c ================================================ /* Name: rounding.c Purpose: Demonstrates rounding modes. Author: M. J. Fromberger Bugs: The rounding mode can only be specified by value, not name. Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include "imath.h" #include "imrat.h" int main(int argc, char* argv[]) { mp_result mode, len, res = 0; mp_size prec, radix; mpq_t value; char* buf; if (argc < 5) { fprintf(stderr, "Usage: rounding \n"); return 1; } if ((res = mp_rat_init(&value)) != MP_OK) { fprintf(stderr, "Error initializing: %s\n", mp_error_string(res)); return 2; } mode = atoi(argv[1]); prec = atoi(argv[2]); radix = atoi(argv[3]); printf( "Rounding mode: %d\n" "Precision: %u digits\n" "Radix: %u\n" "Input string: \"%s\"\n", mode, prec, radix, argv[4]); if ((res = mp_rat_read_decimal(&value, radix, argv[4])) != MP_OK) { fprintf(stderr, "Error reading input string: %s\n", mp_error_string(res)); goto CLEANUP; } len = mp_rat_decimal_len(&value, radix, prec); buf = malloc(len); if ((res = mp_rat_to_decimal(&value, radix, prec, mode, buf, len)) != MP_OK) { fprintf(stderr, "Error converting output: %s\n", mp_error_string(res)); } printf("Result string: \"%s\"\n", buf); free(buf); CLEANUP: mp_rat_clear(&value); return res; } /* Here there be dragons */ ================================================ FILE: examples/rsakey.c ================================================ /* Name: rsakey.c Purpose: Generate keys for the RSA cryptosystem. Author: M. J. Fromberger Usage: rsakey [-e ] [] Generates an RSA key pair with a modulus having significant bits, and writes it to the specified output file, or to the standard output. The -e option allows the user to specify an encryption exponent; otherwise, an encryption exponent is chosen at random. Primes p and q are obtained by reading random bits from /dev/random, setting the low-order bit, and testing for primality. If the first candidate is not prime, successive odd candidates are tried until a probable prime is found. Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include #include #include #include "imath.h" #include "iprime.h" typedef struct { mpz_t p; mpz_t q; mpz_t n; mpz_t e; mpz_t d; } rsa_key; /* Load the specified buffer with random bytes */ int randomize(unsigned char* buf, size_t len); /* Overwrite the specified value with n_bits random bits */ mp_result mp_int_randomize(mp_int a, mp_size n_bits); /* Find a prime starting from the given odd seed */ mp_result find_prime(mp_int seed, FILE* fb); /* Initialize/destroy an rsa_key structure */ mp_result rsa_key_init(rsa_key* kp); void rsa_key_clear(rsa_key* kp); void rsa_key_write(rsa_key* kp, FILE* ofp); int main(int argc, char* argv[]) { int opt, modbits; FILE* ofp = stdout; char* expt = NULL; rsa_key the_key; mp_result res; /* Process command-line arguments */ while ((opt = getopt(argc, argv, "e:")) != EOF) { switch (opt) { case 'e': expt = optarg; break; default: fprintf(stderr, "Usage: rsakey [-e ] []\n"); return 1; } } if (optind >= argc) { fprintf(stderr, "Error: You must specify the number of modulus bits.\n"); fprintf(stderr, "Usage: rsakey [-e ] []\n"); return 1; } modbits = (int)strtol(argv[optind++], NULL, 0); if (modbits < CHAR_BIT) { fprintf(stderr, "Error: Invalid value for number of modulus bits.\n"); return 1; } if (modbits % 2 == 1) ++modbits; /* Check if output file is specified */ if (optind < argc) { if ((ofp = fopen(argv[optind], "wt")) == NULL) { fprintf(stderr, "Error: Unable to open output file for writing.\n" " - Filename: %s\n" " - Error: %s\n", argv[optind], strerror(errno)); return 1; } } if ((res = rsa_key_init(&the_key)) != MP_OK) { fprintf(stderr, "Error initializing RSA key structure:\n" " - %s (%d)\n", mp_error_string(res), res); return 1; } /* If specified, try to load the key exponent */ if (expt != NULL) { if ((res = mp_int_read_string(&(the_key.e), 10, expt)) != MP_OK) { fprintf(stderr, "Error: Invalid value for encryption exponent.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } } if ((res = mp_int_randomize(&(the_key.p), (modbits / 2))) != MP_OK) { fprintf(stderr, "Error: Unable to randomize first prime.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } fprintf(stderr, "p: "); find_prime(&(the_key.p), stderr); if ((res = mp_int_randomize(&(the_key.q), (modbits / 2))) != MP_OK) { fprintf(stderr, "Error: Unable to randomize second prime.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } fprintf(stderr, "\nq: "); find_prime(&(the_key.q), stderr); fputc('\n', stderr); /* Temporarily, the key's "n" field will be (p - 1) * (q - 1) for purposes of computing the decryption exponent. */ mp_int_mul(&(the_key.p), &(the_key.q), &(the_key.n)); mp_int_sub(&(the_key.n), &(the_key.p), &(the_key.n)); mp_int_sub(&(the_key.n), &(the_key.q), &(the_key.n)); mp_int_add_value(&(the_key.n), 1, &(the_key.n)); if (expt == NULL && (res = mp_int_randomize(&(the_key.e), (modbits / 2))) != MP_OK) { fprintf(stderr, "Error: Unable to randomize encryption exponent.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } while ((res = mp_int_invmod(&(the_key.e), &(the_key.n), &(the_key.d))) != MP_OK) { if (expt != NULL) { fprintf(stderr, "Error: Unable to compute decryption exponent.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } if ((res = mp_int_randomize(&(the_key.e), (modbits / 2))) != MP_OK) { fprintf(stderr, "Error: Unable to re-randomize encryption exponent.\n" " - %s (%d)\n", mp_error_string(res), res); goto EXIT; } } /* Recompute the real modulus, now that exponents are done. */ mp_int_mul(&(the_key.p), &(the_key.q), &(the_key.n)); /* Write completed key to the specified output file */ rsa_key_write(&the_key, ofp); EXIT: fclose(ofp); rsa_key_clear(&the_key); return 0; } int randomize(unsigned char* buf, size_t len) { FILE* rnd = fopen("/dev/random", "rb"); size_t nr; if (rnd == NULL) return -1; nr = fread(buf, sizeof(*buf), len, rnd); fclose(rnd); return (int)nr; } mp_result mp_int_randomize(mp_int a, mp_size n_bits) { mp_size n_bytes = (n_bits + CHAR_BIT - 1) / CHAR_BIT; unsigned char* buf; mp_result res = MP_OK; if ((buf = malloc(n_bytes)) == NULL) return MP_MEMORY; if ((mp_size)randomize(buf, n_bytes) != n_bytes) { res = MP_TRUNC; goto CLEANUP; } /* Clear bits beyond the number requested */ if (n_bits % CHAR_BIT != 0) { unsigned char b_mask = (1 << (n_bits % CHAR_BIT)) - 1; unsigned char t_mask = (1 << (n_bits % CHAR_BIT)) >> 1; buf[0] &= b_mask; buf[0] |= t_mask; } /* Set low-order bit to insure value is odd */ buf[n_bytes - 1] |= 1; res = mp_int_read_unsigned(a, buf, n_bytes); CLEANUP: memset(buf, 0, n_bytes); free(buf); return res; } mp_result find_prime(mp_int seed, FILE* fb) { mp_result res; int count = 0; if (mp_int_is_even(seed)) if ((res = mp_int_add_value(seed, 1, seed)) != MP_OK) return res; while ((res = mp_int_is_prime(seed)) == MP_FALSE) { ++count; if (fb != NULL && (count % 50) == 0) fputc('.', fb); if ((res = mp_int_add_value(seed, 2, seed)) != MP_OK) return res; } if (res == MP_TRUE && fb != NULL) fputc('+', fb); return res; } mp_result rsa_key_init(rsa_key* kp) { mp_int_init(&(kp->p)); mp_int_init(&(kp->q)); mp_int_init(&(kp->n)); mp_int_init(&(kp->e)); mp_int_init(&(kp->d)); return MP_OK; } void rsa_key_clear(rsa_key* kp) { mp_int_clear(&(kp->p)); mp_int_clear(&(kp->q)); mp_int_clear(&(kp->n)); mp_int_clear(&(kp->e)); mp_int_clear(&(kp->d)); } void rsa_key_write(rsa_key* kp, FILE* ofp) { int len; char* obuf; len = mp_int_string_len(&(kp->n), 10); obuf = malloc(len); mp_int_to_string(&(kp->p), 10, obuf, len); fprintf(ofp, "p = %s\n", obuf); mp_int_to_string(&(kp->q), 10, obuf, len); fprintf(ofp, "q = %s\n", obuf); mp_int_to_string(&(kp->e), 10, obuf, len); fprintf(ofp, "e = %s\n", obuf); mp_int_to_string(&(kp->d), 10, obuf, len); fprintf(ofp, "d = %s\n", obuf); mp_int_to_string(&(kp->n), 10, obuf, len); fprintf(ofp, "n = %s\n", obuf); free(obuf); } /* Here there be dragons */ ================================================ FILE: gmp_compat.c ================================================ /* Name: gmp_compat.c Purpose: Provide GMP compatible routines for imath library Author: David Peixotto Copyright (c) 2012 Qualcomm Innovation Center, Inc. All rights reserved. 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. */ #include "gmp_compat.h" #include #include #include #include #include #if defined(_MSC_VER) #include typedef SSIZE_T ssize_t; #else #include #endif #ifdef NDEBUG #define CHECK(res) ((void)(res)) #else #define CHECK(res) assert(((res) == MP_OK) && "expected MP_OK") #endif /* *(signed char *)&endian_test will thus either be: * 0b00000001 = 1 on big-endian * 0b11111111 = -1 on little-endian */ static const uint16_t endian_test = 0x1FF; #define HOST_ENDIAN (*(signed char*)&endian_test) /************************************************************************* * * Functions with direct translations * *************************************************************************/ /* gmp: mpq_clear */ void GMPQAPI(clear)(mp_rat x) { mp_rat_clear(x); } /* gmp: mpq_cmp */ int GMPQAPI(cmp)(mp_rat op1, mp_rat op2) { return mp_rat_compare(op1, op2); } /* gmp: mpq_init */ void GMPQAPI(init)(mp_rat x) { CHECK(mp_rat_init(x)); } /* gmp: mpq_mul */ void GMPQAPI(mul)(mp_rat product, mp_rat multiplier, mp_rat multiplicand) { CHECK(mp_rat_mul(multiplier, multiplicand, product)); } /* gmp: mpq_set */ void GMPQAPI(set)(mp_rat rop, mp_rat op) { CHECK(mp_rat_copy(op, rop)); } /* gmp: mpz_abs */ void GMPZAPI(abs)(mp_int rop, mp_int op) { CHECK(mp_int_abs(op, rop)); } /* gmp: mpz_add */ void GMPZAPI(add)(mp_int rop, mp_int op1, mp_int op2) { CHECK(mp_int_add(op1, op2, rop)); } /* gmp: mpz_clear */ void GMPZAPI(clear)(mp_int x) { mp_int_clear(x); } /* gmp: mpz_cmp_si */ int GMPZAPI(cmp_si)(mp_int op1, long op2) { return mp_int_compare_value(op1, op2); } /* gmp: mpz_cmpabs */ int GMPZAPI(cmpabs)(mp_int op1, mp_int op2) { return mp_int_compare_unsigned(op1, op2); } /* gmp: mpz_cmp */ int GMPZAPI(cmp)(mp_int op1, mp_int op2) { return mp_int_compare(op1, op2); } /* gmp: mpz_init */ void GMPZAPI(init)(mp_int x) { CHECK(mp_int_init(x)); } /* gmp: mpz_mul */ void GMPZAPI(mul)(mp_int rop, mp_int op1, mp_int op2) { CHECK(mp_int_mul(op1, op2, rop)); } /* gmp: mpz_neg */ void GMPZAPI(neg)(mp_int rop, mp_int op) { CHECK(mp_int_neg(op, rop)); } /* gmp: mpz_set_si */ void GMPZAPI(set_si)(mp_int rop, long op) { CHECK(mp_int_set_value(rop, op)); } /* gmp: mpz_set */ void GMPZAPI(set)(mp_int rop, mp_int op) { CHECK(mp_int_copy(op, rop)); } /* gmp: mpz_sub */ void GMPZAPI(sub)(mp_int rop, mp_int op1, mp_int op2) { CHECK(mp_int_sub(op1, op2, rop)); } /* gmp: mpz_swap */ void GMPZAPI(swap)(mp_int rop1, mp_int rop2) { mp_int_swap(rop1, rop2); } /* gmp: mpq_sgn */ int GMPQAPI(sgn)(mp_rat op) { return mp_rat_compare_zero(op); } /* gmp: mpz_sgn */ int GMPZAPI(sgn)(mp_int op) { return mp_int_compare_zero(op); } /* gmp: mpq_set_ui */ void GMPQAPI(set_ui)(mp_rat rop, unsigned long op1, unsigned long op2) { CHECK(mp_rat_set_uvalue(rop, op1, op2)); } /* gmp: mpz_set_ui */ void GMPZAPI(set_ui)(mp_int rop, unsigned long op) { CHECK(mp_int_set_uvalue(rop, op)); } /* gmp: mpq_den_ref */ mp_int GMPQAPI(denref)(mp_rat op) { return mp_rat_denom_ref(op); } /* gmp: mpq_num_ref */ mp_int GMPQAPI(numref)(mp_rat op) { return mp_rat_numer_ref(op); } /* gmp: mpq_canonicalize */ void GMPQAPI(canonicalize)(mp_rat op) { CHECK(mp_rat_reduce(op)); } /* * Functions that can be implemented as a combination of imath functions */ /* gmp: mpz_addmul */ /* gmp: rop = rop + (op1 * op2) */ void GMPZAPI(addmul)(mp_int rop, mp_int op1, mp_int op2) { mpz_t tempz; mp_int temp = &tempz; mp_int_init(temp); CHECK(mp_int_mul(op1, op2, temp)); CHECK(mp_int_add(rop, temp, rop)); mp_int_clear(temp); } /* gmp: mpz_divexact */ /* gmp: only produces correct results when d divides n */ void GMPZAPI(divexact)(mp_int q, mp_int n, mp_int d) { CHECK(mp_int_div(n, d, q, NULL)); } /* gmp: mpz_divisible_p */ /* gmp: return 1 if d divides n, 0 otherwise */ /* gmp: 0 is considered to divide only 0 */ int GMPZAPI(divisible_p)(mp_int n, mp_int d) { /* variables to hold remainder */ mpz_t rz; mp_int r = &rz; int r_is_zero; /* check for d = 0 */ int n_is_zero = mp_int_compare_zero(n) == 0; int d_is_zero = mp_int_compare_zero(d) == 0; if (d_is_zero) return n_is_zero; /* return true if remainder is 0 */ CHECK(mp_int_init(r)); CHECK(mp_int_div(n, d, NULL, r)); r_is_zero = mp_int_compare_zero(r) == 0; mp_int_clear(r); return r_is_zero; } /* gmp: mpz_submul */ /* gmp: rop = rop - (op1 * op2) */ void GMPZAPI(submul)(mp_int rop, mp_int op1, mp_int op2) { mpz_t tempz; mp_int temp = &tempz; mp_int_init(temp); CHECK(mp_int_mul(op1, op2, temp)); CHECK(mp_int_sub(rop, temp, rop)); mp_int_clear(temp); } /* gmp: mpz_add_ui */ void GMPZAPI(add_ui)(mp_int rop, mp_int op1, unsigned long op2) { mpz_t tempz; mp_int temp = &tempz; CHECK(mp_int_init_uvalue(temp, op2)); CHECK(mp_int_add(op1, temp, rop)); mp_int_clear(temp); } /* gmp: mpz_divexact_ui */ /* gmp: only produces correct results when d divides n */ void GMPZAPI(divexact_ui)(mp_int q, mp_int n, unsigned long d) { mpz_t tempz; mp_int temp = &tempz; CHECK(mp_int_init_uvalue(temp, d)); CHECK(mp_int_div(n, temp, q, NULL)); mp_int_clear(temp); } /* gmp: mpz_mul_ui */ void GMPZAPI(mul_ui)(mp_int rop, mp_int op1, unsigned long op2) { mpz_t tempz; mp_int temp = &tempz; CHECK(mp_int_init_uvalue(temp, op2)); CHECK(mp_int_mul(op1, temp, rop)); mp_int_clear(temp); } /* gmp: mpz_pow_ui */ /* gmp: 0^0 = 1 */ void GMPZAPI(pow_ui)(mp_int rop, mp_int base, unsigned long exp) { mpz_t tempz; mp_int temp = &tempz; /* check for 0^0 */ if (exp == 0 && mp_int_compare_zero(base) == 0) { CHECK(mp_int_set_value(rop, 1)); return; } /* rop = base^exp */ CHECK(mp_int_init_uvalue(temp, exp)); CHECK(mp_int_expt_full(base, temp, rop)); mp_int_clear(temp); } /* gmp: mpz_sub_ui */ void GMPZAPI(sub_ui)(mp_int rop, mp_int op1, unsigned long op2) { mpz_t tempz; mp_int temp = &tempz; CHECK(mp_int_init_uvalue(temp, op2)); CHECK(mp_int_sub(op1, temp, rop)); mp_int_clear(temp); } /************************************************************************* * * Functions with different behavior in corner cases * *************************************************************************/ /* gmp: mpz_gcd */ void GMPZAPI(gcd)(mp_int rop, mp_int op1, mp_int op2) { int op1_is_zero = mp_int_compare_zero(op1) == 0; int op2_is_zero = mp_int_compare_zero(op2) == 0; if (op1_is_zero && op2_is_zero) { mp_int_zero(rop); return; } CHECK(mp_int_gcd(op1, op2, rop)); } /* gmp: mpz_get_str */ char* GMPZAPI(get_str)(char* str, int radix, mp_int op) { int i, r, len; /* Support negative radix like gmp */ r = radix; if (r < 0) r = -r; /* Compute the length of the string needed to hold the int */ len = mp_int_string_len(op, r); if (str == NULL) { str = malloc(len); } /* Convert to string using imath function */ CHECK(mp_int_to_string(op, r, str, len)); /* Change case to match gmp */ for (i = 0; i < len - 1; i++) { if (radix < 0) { str[i] = toupper(str[i]); } else { str[i] = tolower(str[i]); } } return str; } /* gmp: mpq_get_str */ char* GMPQAPI(get_str)(char* str, int radix, mp_rat op) { int i, r, len; /* Only print numerator if it is a whole number */ if (mp_int_compare_value(mp_rat_denom_ref(op), 1) == 0) return GMPZAPI(get_str)(str, radix, mp_rat_numer_ref(op)); /* Support negative radix like gmp */ r = radix; if (r < 0) r = -r; /* Compute the length of the string needed to hold the int */ len = mp_rat_string_len(op, r); if (str == NULL) { str = malloc(len); } /* Convert to string using imath function */ CHECK(mp_rat_to_string(op, r, str, len)); /* Change case to match gmp */ for (i = 0; i < len; i++) { if (radix < 0) { str[i] = toupper(str[i]); } else { str[i] = tolower(str[i]); } } return str; } /* gmp: mpz_set_str */ int GMPZAPI(set_str)(mp_int rop, char* str, int base) { mp_result res = mp_int_read_string(rop, base, str); return ((res == MP_OK) ? 0 : -1); } /* gmp: mpq_set_str */ int GMPQAPI(set_str)(mp_rat rop, char* s, int base) { char* slash; char* str; mp_result resN; mp_result resD; int res = 0; /* Copy string to temporary storage so we can modify it below */ str = malloc(strlen(s) + 1); strcpy(str, s); /* Properly format the string as an int by terminating at the / */ slash = strchr(str, '/'); if (slash) *slash = '\0'; /* Parse numerator */ resN = mp_int_read_string(mp_rat_numer_ref(rop), base, str); /* Parse denominator if given or set to 1 if not */ if (slash) { resD = mp_int_read_string(mp_rat_denom_ref(rop), base, slash + 1); } else { resD = mp_int_set_uvalue(mp_rat_denom_ref(rop), 1); } /* Return failure if either parse failed */ if (resN != MP_OK || resD != MP_OK) { res = -1; } free(str); return res; } static unsigned long get_long_bits(mp_int op) { /* Deal with integer that does not fit into unsigned long. We want to grab * the least significant digits that will fit into the long. Read the digits * into the long starting at the most significant digit that fits into a * long. The long is shifted over by MP_DIGIT_BIT before each digit is added. * * The shift is decomposed into two steps (following the pattern used in the * rest of the imath library) to accommodate architectures that don't deal * well with 32-bit shifts. */ mp_size digits_to_copy = (sizeof(unsigned long) + sizeof(mp_digit) - 1) / sizeof(mp_digit); if (digits_to_copy > MP_USED(op)) { digits_to_copy = MP_USED(op); } mp_digit* digits = MP_DIGITS(op); unsigned long out = 0; for (int i = digits_to_copy - 1; i >= 0; i--) { out <<= (MP_DIGIT_BIT / 2); out <<= (MP_DIGIT_BIT / 2); out |= digits[i]; } return out; } /* gmp: mpz_get_ui */ unsigned long GMPZAPI(get_ui)(mp_int op) { unsigned long out; /* Try a standard conversion that fits into an unsigned long */ mp_result res = mp_int_to_uint(op, &out); if (res == MP_OK) return out; /* Abort the try if we don't have a range error in the conversion. * The range error indicates that the value cannot fit into a long. */ CHECK(res == MP_RANGE ? MP_OK : MP_RANGE); if (res != MP_RANGE) return 0; return get_long_bits(op); } /* gmp: mpz_get_si */ long GMPZAPI(get_si)(mp_int op) { long out; unsigned long uout; int long_msb; /* Try a standard conversion that fits into a long */ mp_result res = mp_int_to_int(op, &out); if (res == MP_OK) return out; /* Abort the try if we don't have a range error in the conversion. * The range error indicates that the value cannot fit into a long. */ CHECK(res == MP_RANGE ? MP_OK : MP_RANGE); if (res != MP_RANGE) return 0; /* get least significant bits into an unsigned long */ uout = get_long_bits(op); /* clear the top bit */ long_msb = (sizeof(unsigned long) * 8) - 1; uout &= (~(1UL << long_msb)); /* convert to negative if needed based on sign of op */ if (MP_SIGN(op) == MP_NEG) { uout = 0 - uout; } out = (long)uout; return out; } /* gmp: mpz_lcm */ void GMPZAPI(lcm)(mp_int rop, mp_int op1, mp_int op2) { int op1_is_zero = mp_int_compare_zero(op1) == 0; int op2_is_zero = mp_int_compare_zero(op2) == 0; if (op1_is_zero || op2_is_zero) { mp_int_zero(rop); return; } CHECK(mp_int_lcm(op1, op2, rop)); CHECK(mp_int_abs(rop, rop)); } /* gmp: mpz_mul_2exp */ /* gmp: allow big values for op2 when op1 == 0 */ void GMPZAPI(mul_2exp)(mp_int rop, mp_int op1, unsigned long op2) { if (mp_int_compare_zero(op1) == 0) mp_int_zero(rop); else CHECK(mp_int_mul_pow2(op1, op2, rop)); } /* * Functions needing expanded functionality */ /* [Note]Overview of division implementation All division operations (N / D) compute q and r such that N = q * D + r, with 0 <= abs(r) < abs(d) The q and r values are not uniquely specified by N and D. To specify which q and r values should be used, GMP implements three different rounding modes for integer division: ceiling - round q twords +infinity, r has opposite sign as d floor - round q twords -infinity, r has same sign as d truncate - round q twords zero, r has same sign as n The imath library only supports truncate as a rounding mode. We need to implement the other rounding modes in terms of truncating division. We first perform the division in truncate mode and then adjust q accordingly. Once we know q, we can easily compute the correct r according the the formula above by computing: r = N - q * D The main task is to compute q. We can compute the correct q from a truncated version as follows. For ceiling rounding mode, if q is less than 0 then the truncated rounding mode is the same as the ceiling rounding mode. If q is greater than zero then we need to round q up by one because the truncated version was rounded down to zero. If q equals zero then check to see if the result of the division is positive. A positive result needs to increment q to one. For floor rounding mode, if q is greater than 0 then the truncated rounding mode is the same as the floor rounding mode. If q is less than zero then we need to round q down by one because the truncated mode rounded q up by one twords zero. If q is zero then we need to check to see if the result of the division is negative. A negative result needs to decrement q to negative one. */ /* gmp: mpz_cdiv_q */ void GMPZAPI(cdiv_q)(mp_int q, mp_int n, mp_int d) { mpz_t rz; mp_int r = &rz; int qsign, rsign, nsign, dsign; CHECK(mp_int_init(r)); /* save signs before division because q can alias with n or d */ nsign = mp_int_compare_zero(n); dsign = mp_int_compare_zero(d); /* truncating division */ CHECK(mp_int_div(n, d, q, r)); /* see: [Note]Overview of division implementation */ qsign = mp_int_compare_zero(q); rsign = mp_int_compare_zero(r); if (qsign > 0) { /* q > 0 */ if (rsign != 0) { /* r != 0 */ CHECK(mp_int_add_value(q, 1, q)); } } else if (qsign == 0) { /* q == 0 */ if (rsign != 0) { /* r != 0 */ if ((nsign > 0 && dsign > 0) || (nsign < 0 && dsign < 0)) { CHECK(mp_int_set_value(q, 1)); } } } mp_int_clear(r); } /* gmp: mpz_fdiv_q */ void GMPZAPI(fdiv_q)(mp_int q, mp_int n, mp_int d) { mpz_t rz; mp_int r = &rz; int qsign, rsign, nsign, dsign; CHECK(mp_int_init(r)); /* save signs before division because q can alias with n or d */ nsign = mp_int_compare_zero(n); dsign = mp_int_compare_zero(d); /* truncating division */ CHECK(mp_int_div(n, d, q, r)); /* see: [Note]Overview of division implementation */ qsign = mp_int_compare_zero(q); rsign = mp_int_compare_zero(r); if (qsign < 0) { /* q < 0 */ if (rsign != 0) { /* r != 0 */ CHECK(mp_int_sub_value(q, 1, q)); } } else if (qsign == 0) { /* q == 0 */ if (rsign != 0) { /* r != 0 */ if ((nsign < 0 && dsign > 0) || (nsign > 0 && dsign < 0)) { CHECK(mp_int_set_value(q, -1)); } } } mp_int_clear(r); } /* gmp: mpz_fdiv_r */ void GMPZAPI(fdiv_r)(mp_int r, mp_int n, mp_int d) { mpz_t qz; mpz_t tempz; mpz_t orig_dz; mpz_t orig_nz; mp_int q = &qz; mp_int temp = &tempz; mp_int orig_d = &orig_dz; mp_int orig_n = &orig_nz; CHECK(mp_int_init(q)); CHECK(mp_int_init(temp)); /* Make a copy of n in case n and d in case they overlap with q */ CHECK(mp_int_init_copy(orig_d, d)); CHECK(mp_int_init_copy(orig_n, n)); /* floor division */ GMPZAPI(fdiv_q)(q, n, d); /* see: [Note]Overview of division implementation */ /* n = q * d + r ==> r = n - q * d */ mp_int_mul(q, orig_d, temp); mp_int_sub(orig_n, temp, r); mp_int_clear(q); mp_int_clear(temp); mp_int_clear(orig_d); mp_int_clear(orig_n); } /* gmp: mpz_tdiv_q */ void GMPZAPI(tdiv_q)(mp_int q, mp_int n, mp_int d) { /* truncating division*/ CHECK(mp_int_div(n, d, q, NULL)); } /* gmp: mpz_fdiv_q_ui */ unsigned long GMPZAPI(fdiv_q_ui)(mp_int q, mp_int n, unsigned long d) { mpz_t tempz; mp_int temp = &tempz; mpz_t rz; mp_int r = &rz; mpz_t orig_nz; mp_int orig_n = &orig_nz; unsigned long rl; CHECK(mp_int_init_uvalue(temp, d)); CHECK(mp_int_init(r)); /* Make a copy of n in case n and q overlap */ CHECK(mp_int_init_copy(orig_n, n)); /* use floor division mode to compute q and r */ GMPZAPI(fdiv_q)(q, n, temp); GMPZAPI(fdiv_r)(r, orig_n, temp); CHECK(mp_int_to_uint(r, &rl)); mp_int_clear(temp); mp_int_clear(r); mp_int_clear(orig_n); return rl; } /* gmp: mpz_export */ void* GMPZAPI(export)(void* rop, size_t* countp, int order, size_t size, int endian, size_t nails, mp_int op) { size_t i, j; size_t num_used_bytes; size_t num_words, num_missing_bytes; ssize_t word_offset; unsigned char* dst; mp_digit* src; int src_bits; /* We do not have a complete implementation. Assert to ensure our * restrictions are in place. */ assert(nails == 0 && "Do not support non-full words"); assert(endian == 1 || endian == 0 || endian == -1); assert(order == 1 || order == -1); /* Test for zero */ if (mp_int_compare_zero(op) == 0) { if (countp) *countp = 0; return rop; } /* Calculate how many words we need */ num_used_bytes = mp_int_unsigned_len(op); num_words = (num_used_bytes + (size - 1)) / size; /* ceil division */ assert(num_used_bytes > 0); /* Check to see if we will have missing bytes in the last word. Missing bytes can only occur when the size of words we output is greater than the size of words used internally by imath. The number of missing bytes is the number of bytes needed to fill out the last word. If this number is greater than the size of a single mp_digit, then we need to pad the word with extra zeros. Otherwise, the missing bytes can be filled directly from the zeros in the last digit in the number. */ num_missing_bytes = (size * num_words) - num_used_bytes; assert(num_missing_bytes < size); /* Allocate space for the result if needed */ if (rop == NULL) { rop = malloc(num_words * size); } if (endian == 0) { endian = HOST_ENDIAN; } /* Initialize dst and src pointers */ dst = (unsigned char*)rop + (order >= 0 ? (num_words - 1) * size : 0) + (endian >= 0 ? size - 1 : 0); src = MP_DIGITS(op); src_bits = MP_DIGIT_BIT; word_offset = (endian >= 0 ? size : -size) + (order < 0 ? size : -size); for (i = 0; i < num_words; i++) { for (j = 0; j < size && i * size + j < num_used_bytes; j++) { if (src_bits == 0) { ++src; src_bits = MP_DIGIT_BIT; } *dst = (*src >> (MP_DIGIT_BIT - src_bits)) & 0xFF; src_bits -= 8; dst -= endian; } for (; j < size; j++) { *dst = 0; dst -= endian; } dst += word_offset; } if (countp) *countp = num_words; return rop; } /* gmp: mpz_import */ void GMPZAPI(import)(mp_int rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op) { mpz_t tmpz; mp_int tmp = &tmpz; size_t total_size; size_t num_digits; ssize_t word_offset; const unsigned char* src; mp_digit* dst; int dst_bits; size_t i, j; if (count == 0 || op == NULL) return; /* We do not have a complete implementation. Assert to ensure our * restrictions are in place. */ assert(nails == 0 && "Do not support non-full words"); assert(endian == 1 || endian == 0 || endian == -1); assert(order == 1 || order == -1); if (endian == 0) { endian = HOST_ENDIAN; } /* Compute number of needed digits by ceil division */ total_size = count * size; num_digits = (total_size + sizeof(mp_digit) - 1) / sizeof(mp_digit); /* Init temporary */ mp_int_init_size(tmp, num_digits); for (i = 0; i < num_digits; i++) tmp->digits[i] = 0; /* Copy bytes */ src = (const unsigned char*)op + (order >= 0 ? (count - 1) * size : 0) + (endian >= 0 ? size - 1 : 0); dst = MP_DIGITS(tmp); dst_bits = 0; word_offset = (endian >= 0 ? size : -size) + (order < 0 ? size : -size); for (i = 0; i < count; i++) { for (j = 0; j < size; j++) { if (dst_bits == MP_DIGIT_BIT) { ++dst; dst_bits = 0; } *dst |= ((mp_digit)*src) << dst_bits; dst_bits += 8; src -= endian; } src += word_offset; } tmp->used = num_digits; /* Remove leading zeros from number */ { mp_size uz_ = tmp->used; mp_digit* dz_ = MP_DIGITS(tmp) + uz_ - 1; while (uz_ > 1 && (*dz_-- == 0)) --uz_; tmp->used = uz_; } /* Copy to destination */ mp_int_copy(tmp, rop); mp_int_clear(tmp); } /* gmp: mpz_sizeinbase */ size_t GMPZAPI(sizeinbase)(mp_int op, int base) { mp_result res; size_t size; /* If op == 0, return 1 */ if (mp_int_compare_zero(op) == 0) return 1; /* Compute string length in base */ res = mp_int_string_len(op, base); assert(res > 0 && "mp_int_string_len should return positive length"); /* Now adjust the final size by getting rid of string artifacts */ size = res; /* subtract one for the null terminator */ size -= 1; /* subtract one for the negative sign */ if (mp_int_compare_zero(op) < 0) size -= 1; return size; } ================================================ FILE: gmp_compat.h ================================================ /* Name: gmp_compat.h Purpose: Provide GMP compatible routines for imath library Author: David Peixotto Copyright (c) 2012 Qualcomm Innovation Center, Inc. All rights reserved. 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. */ #ifndef IMATH_GMP_COMPAT_H_ #define IMATH_GMP_COMPAT_H_ #include "imath.h" #include "imrat.h" #include #define GMPZAPI(fun) impz_ ## fun #define GMPQAPI(fun) impq_ ## fun #ifdef __cplusplus extern "C" { #endif /************************************************************************* * * Functions with direct translations * *************************************************************************/ /* gmp: mpq_clear */ void GMPQAPI(clear)(mp_rat x); /* gmp: mpq_cmp */ int GMPQAPI(cmp)(mp_rat op1, mp_rat op2); /* gmp: mpq_init */ void GMPQAPI(init)(mp_rat x); /* gmp: mpq_mul */ void GMPQAPI(mul)(mp_rat product, mp_rat multiplier, mp_rat multiplicand); /* gmp: mpq_set */ void GMPQAPI(set)(mp_rat rop, mp_rat op); /* gmp: mpz_abs */ void GMPZAPI(abs)(mp_int rop, mp_int op); /* gmp: mpz_add */ void GMPZAPI(add)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_clear */ void GMPZAPI(clear)(mp_int x); /* gmp: mpz_cmp_si */ int GMPZAPI(cmp_si)(mp_int op1, long op2); /* gmp: mpz_cmpabs */ int GMPZAPI(cmpabs)(mp_int op1, mp_int op2); /* gmp: mpz_cmp */ int GMPZAPI(cmp)(mp_int op1, mp_int op2); /* gmp: mpz_init */ void GMPZAPI(init)(mp_int x); /* gmp: mpz_mul */ void GMPZAPI(mul)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_neg */ void GMPZAPI(neg)(mp_int rop, mp_int op); /* gmp: mpz_set_si */ void GMPZAPI(set_si)(mp_int rop, long op); /* gmp: mpz_set */ void GMPZAPI(set)(mp_int rop, mp_int op); /* gmp: mpz_sub */ void GMPZAPI(sub)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_swap */ void GMPZAPI(swap)(mp_int rop1, mp_int rop2); /* gmp: mpq_sgn */ int GMPQAPI(sgn)(mp_rat op); /* gmp: mpz_sgn */ int GMPZAPI(sgn)(mp_int op); /* gmp: mpq_set_ui */ void GMPQAPI(set_ui)(mp_rat rop, unsigned long op1, unsigned long op2); /* gmp: mpz_set_ui */ void GMPZAPI(set_ui)(mp_int rop, unsigned long op); /* gmp: mpq_den_ref */ mp_int GMPQAPI(denref)(mp_rat op); /* gmp: mpq_num_ref */ mp_int GMPQAPI(numref)(mp_rat op); /* gmp: mpq_canonicalize */ void GMPQAPI(canonicalize)(mp_rat op); /************************************************************************* * * Functions that can be implemented as a combination of imath functions * *************************************************************************/ /* gmp: mpz_addmul */ void GMPZAPI(addmul)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_divexact */ void GMPZAPI(divexact)(mp_int q, mp_int n, mp_int d); /* gmp: mpz_divisible_p */ int GMPZAPI(divisible_p)(mp_int n, mp_int d); /* gmp: mpz_submul */ void GMPZAPI(submul)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_add_ui */ void GMPZAPI(add_ui)(mp_int rop, mp_int op1, unsigned long op2); /* gmp: mpz_divexact_ui */ void GMPZAPI(divexact_ui)(mp_int q, mp_int n, unsigned long d); /* gmp: mpz_mul_ui */ void GMPZAPI(mul_ui)(mp_int rop, mp_int op1, unsigned long op2); /* gmp: mpz_pow_ui */ void GMPZAPI(pow_ui)(mp_int rop, mp_int base, unsigned long exp); /* gmp: mpz_sub_ui */ void GMPZAPI(sub_ui)(mp_int rop, mp_int op1, unsigned long op2); /* gmp: mpz_fdiv_q_ui */ unsigned long GMPZAPI(fdiv_q_ui)(mp_int q, mp_int n, unsigned long d); /* gmp: mpz_sizeinbase */ size_t GMPZAPI(sizeinbase)(mp_int op, int base); /************************************************************************* * * Functions with different behavior in corner cases * *************************************************************************/ /* gmp: mpz_gcd */ /* gmp: When op1 = 0 and op2 = 0, return 0.*/ void GMPZAPI(gcd)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_get_str */ /* gmp: If str is NULL then allocate space using the default allocator. */ char* GMPZAPI(get_str)(char *str, int radix, mp_int op); /* gmp: mpq_get_str */ /* gmp: If str is NULL then allocate space using the default allocator. */ /* gmp: If value is a whole number do not print denomenator. */ /* TODO: Need to handle 0 values better. GMP prints 0/4 instead of 0.*/ char* GMPQAPI(get_str)(char *str, int radix, mp_rat op); /* gmp: mpz_set_str */ /* gmp: Allow and ignore spaces in string. */ int GMPZAPI(set_str)(mp_int rop, char *str, int base); /* gmp: mpq_set_str */ int GMPQAPI(set_str)(mp_rat rop, char *str, int base); /* gmp: mpz_get_ui */ /* gmp: Return least significant bits if value is too big for a long. */ unsigned long GMPZAPI(get_ui)(mp_int op); /* gmp: mpz_get_si */ /* gmp: Return least significant bits if value is too bit for a long. */ /* gmp: If value is too big for long, return the least significant (8*sizeof(long)-1) bits from the op and set the sign bit according to the sign of the op. */ long GMPZAPI(get_si)(mp_int op); /* gmp: mpz_lcm */ /* gmp: When op1 = 0 or op2 = 0, return 0.*/ /* gmp: The result of lcm(a,b) is always positive. */ void GMPZAPI(lcm)(mp_int rop, mp_int op1, mp_int op2); /* gmp: mpz_mul_2exp */ /* gmp: allow big values for op2 when op1 == 0 */ void GMPZAPI(mul_2exp)(mp_int rop, mp_int op1, unsigned long op2); /************************************************************************* * * Functions needing expanded functionality * *************************************************************************/ /* gmp: mpz_cdiv_q */ void GMPZAPI(cdiv_q)(mp_int q, mp_int n, mp_int d); /* gmp: mpz_fdiv_q */ void GMPZAPI(fdiv_q)(mp_int q, mp_int n, mp_int d); /* gmp: mpz_fdiv_r */ void GMPZAPI(fdiv_r)(mp_int r, mp_int n, mp_int d); /* gmp: mpz_tdiv_q */ void GMPZAPI(tdiv_q)(mp_int q, mp_int n, mp_int d); /* gmp: mpz_export */ void* GMPZAPI(export)(void *rop, size_t *countp, int order, size_t size, int endian, size_t nails, mp_int op); /* gmp: mpz_import */ void GMPZAPI(import)(mp_int rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op); #ifdef __cplusplus } #endif #endif /* end IMATH_GMP_COMPAT_H_ */ ================================================ FILE: imath.c ================================================ /* Name: imath.c Purpose: Arbitrary precision integer arithmetic routines. Author: M. J. Fromberger Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. 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. */ #include "imath.h" #include #include #include #include #define USE_IMATH_INTERNAL_TEMP_MACROS #include "macros.c" // for temp value handling const mp_result MP_OK = 0; /* no error, all is well */ const mp_result MP_FALSE = 0; /* boolean false */ const mp_result MP_TRUE = -1; /* boolean true */ const mp_result MP_MEMORY = -2; /* out of memory */ const mp_result MP_RANGE = -3; /* argument out of range */ const mp_result MP_UNDEF = -4; /* result undefined */ const mp_result MP_TRUNC = -5; /* output truncated */ const mp_result MP_BADARG = -6; /* invalid null argument */ const mp_result MP_MINERR = -6; const mp_sign MP_NEG = 1; /* value is strictly negative */ const mp_sign MP_ZPOS = 0; /* value is non-negative */ static const char* const s_unknown_err = "unknown result code"; static const char* const s_error_msg[] = { "error code 0", "boolean true", "out of memory", "argument out of range", "result undefined", "output truncated", "invalid argument", NULL, }; /* The ith entry of this table gives the value of log_i(2). An integer value n requires ceil(log_i(n)) digits to be represented in base i. Since it is easy to compute lg(n), by counting bits, we can compute log_i(n) = lg(n) * log_i(2). The use of this table eliminates a dependency upon linkage against the standard math libraries. If MP_MAX_RADIX is increased, this table should be expanded too. */ static const double s_log2[] = { 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* (D)(D) 2 3 */ 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */ 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */ 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */ 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */ 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */ 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */ 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */ 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */ 0.193426404, /* 36 */ }; /* Return the number of digits needed to represent a static value */ #define MP_VALUE_DIGITS(V) \ ((sizeof(V) + (sizeof(mp_digit) - 1)) / sizeof(mp_digit)) /* Round precision P to nearest word boundary */ static inline mp_size s_round_prec(mp_size P) { return 2 * ((P + 1) / 2); } /* Set array P of S digits to zero */ static inline void ZERO(mp_digit* P, mp_size S) { mp_size i__ = S * sizeof(mp_digit); mp_digit* p__ = P; memset(p__, 0, i__); } /* Copy S digits from array P to array Q */ static inline void COPY(mp_digit* P, mp_digit* Q, mp_size S) { mp_size i__ = S * sizeof(mp_digit); mp_digit* p__ = P; mp_digit* q__ = Q; memcpy(q__, p__, i__); } /* Reverse N elements of unsigned char in A. */ static inline void REV(unsigned char* A, int N) { unsigned char* u_ = A; unsigned char* v_ = u_ + N - 1; while (u_ < v_) { unsigned char xch = *u_; *u_++ = *v_; *v_-- = xch; } } /* Strip leading zeroes from z_ in-place. */ static inline void CLAMP(mp_int z_) { mp_size uz_ = MP_USED(z_); mp_digit* dz_ = MP_DIGITS(z_) + uz_ - 1; while (uz_ > 1 && (*dz_-- == 0)) --uz_; z_->used = uz_; } /* Select min/max. */ static inline int MIN(int A, int B) { return (B < A ? B : A); } static inline mp_size MAX(mp_size A, mp_size B) { return (B > A ? B : A); } /* Exchange lvalues A and B of type T, e.g. SWAP(int, x, y) where x and y are variables of type int. */ #define SWAP(T, A, B) \ do { \ T t_ = (A); \ A = (B); \ B = t_; \ } while (0) /* Compare value to zero. */ static inline int CMPZ(mp_int Z) { if (Z->used == 1 && Z->digits[0] == 0) return 0; return (Z->sign == MP_NEG) ? -1 : 1; } static inline mp_word UPPER_HALF(mp_word W) { return (W >> MP_DIGIT_BIT); } static inline mp_digit LOWER_HALF(mp_word W) { return (mp_digit)(W); } /* Report whether the highest-order bit of W is 1. */ static inline bool HIGH_BIT_SET(mp_word W) { return (W >> (MP_WORD_BIT - 1)) != 0; } /* Report whether adding W + V will carry out. */ static inline bool ADD_WILL_OVERFLOW(mp_word W, mp_word V) { return ((MP_WORD_MAX - V) < W); } /* Default number of digits allocated to a new mp_int */ static mp_size default_precision = 8; void mp_int_default_precision(mp_size size) { assert(size > 0); default_precision = size; } /* Minimum number of digits to invoke recursive multiply */ static mp_size multiply_threshold = 32; void mp_int_multiply_threshold(mp_size thresh) { assert(thresh >= sizeof(mp_word)); multiply_threshold = thresh; } /* Allocate a buffer of (at least) num digits, or return NULL if that couldn't be done. */ static mp_digit* s_alloc(mp_size num); /* Release a buffer of digits allocated by s_alloc(). */ static void s_free(void* ptr); /* Insure that z has at least min digits allocated, resizing if necessary. Returns true if successful, false if out of memory. */ static bool s_pad(mp_int z, mp_size min); /* Ensure Z has at least N digits allocated. */ static inline mp_result GROW(mp_int Z, mp_size N) { return s_pad(Z, N) ? MP_OK : MP_MEMORY; } /* Fill in a "fake" mp_int on the stack with a given value */ static void s_fake(mp_int z, mp_small value, mp_digit vbuf[]); static void s_ufake(mp_int z, mp_usmall value, mp_digit vbuf[]); /* Compare two runs of digits of given length, returns <0, 0, >0 */ static int s_cdig(mp_digit* da, mp_digit* db, mp_size len); /* Pack the unsigned digits of v into array t */ static int s_uvpack(mp_usmall v, mp_digit t[]); /* Compare magnitudes of a and b, returns <0, 0, >0 */ static int s_ucmp(mp_int a, mp_int b); /* Compare magnitudes of a and v, returns <0, 0, >0 */ static int s_vcmp(mp_int a, mp_small v); static int s_uvcmp(mp_int a, mp_usmall uv); /* Unsigned magnitude addition; assumes dc is big enough. Carry out is returned (no memory allocated). */ static mp_digit s_uadd(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b); /* Unsigned magnitude subtraction. Assumes dc is big enough. */ static void s_usub(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b); /* Unsigned recursive multiplication. Assumes dc is big enough. */ static int s_kmul(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b); /* Unsigned magnitude multiplication. Assumes dc is big enough. */ static void s_umul(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b); /* Unsigned recursive squaring. Assumes dc is big enough. */ static int s_ksqr(mp_digit* da, mp_digit* dc, mp_size size_a); /* Unsigned magnitude squaring. Assumes dc is big enough. */ static void s_usqr(mp_digit* da, mp_digit* dc, mp_size size_a); /* Single digit addition. Assumes a is big enough. */ static void s_dadd(mp_int a, mp_digit b); /* Single digit multiplication. Assumes a is big enough. */ static void s_dmul(mp_int a, mp_digit b); /* Single digit multiplication on buffers; assumes dc is big enough. */ static void s_dbmul(mp_digit* da, mp_digit b, mp_digit* dc, mp_size size_a); /* Single digit division. Replaces a with the quotient, returns the remainder. */ static mp_digit s_ddiv(mp_int a, mp_digit b); /* Quick division by a power of 2, replaces z (no allocation) */ static void s_qdiv(mp_int z, mp_size p2); /* Quick remainder by a power of 2, replaces z (no allocation) */ static void s_qmod(mp_int z, mp_size p2); /* Quick multiplication by a power of 2, replaces z. Allocates if necessary; returns false in case this fails. */ static int s_qmul(mp_int z, mp_size p2); /* Quick subtraction from a power of 2, replaces z. Allocates if necessary; returns false in case this fails. */ static int s_qsub(mp_int z, mp_size p2); /* Return maximum k such that 2^k divides z. */ static int s_dp2k(mp_int z); /* Return k >= 0 such that z = 2^k, or -1 if there is no such k. */ static int s_isp2(mp_int z); /* Set z to 2^k. May allocate; returns false in case this fails. */ static int s_2expt(mp_int z, mp_small k); /* Normalize a and b for division, returns normalization constant */ static int s_norm(mp_int a, mp_int b); /* Compute constant mu for Barrett reduction, given modulus m, result replaces z, m is untouched. */ static mp_result s_brmu(mp_int z, mp_int m); /* Reduce a modulo m, using Barrett's algorithm. */ static int s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2); /* Modular exponentiation, using Barrett reduction */ static mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c); /* Unsigned magnitude division. Assumes |a| > |b|. Allocates temporaries; overwrites a with quotient, b with remainder. */ static mp_result s_udiv_knuth(mp_int a, mp_int b); /* Compute the number of digits in radix r required to represent the given value. Does not account for sign flags, terminators, etc. */ static int s_outlen(mp_int z, mp_size r); /* Guess how many digits of precision will be needed to represent a radix r value of the specified number of digits. Returns a value guaranteed to be no smaller than the actual number required. */ static mp_size s_inlen(int len, mp_size r); /* Convert a character to a digit value in radix r, or -1 if out of range */ static int s_ch2val(char c, int r); /* Convert a digit value to a character */ static char s_val2ch(int v, int caps); /* Take 2's complement of a buffer in place */ static void s_2comp(unsigned char* buf, int len); /* Convert a value to binary, ignoring sign. On input, *limpos is the bound on how many bytes should be written to buf; on output, *limpos is set to the number of bytes actually written. */ static mp_result s_tobin(mp_int z, unsigned char* buf, int* limpos, int pad); /* Multiply X by Y into Z, ignoring signs. Requires that Z have enough storage preallocated to hold the result. */ static inline void UMUL(mp_int X, mp_int Y, mp_int Z) { mp_size ua_ = MP_USED(X); mp_size ub_ = MP_USED(Y); mp_size o_ = ua_ + ub_; ZERO(MP_DIGITS(Z), o_); (void)s_kmul(MP_DIGITS(X), MP_DIGITS(Y), MP_DIGITS(Z), ua_, ub_); Z->used = o_; CLAMP(Z); } /* Square X into Z. Requires that Z have enough storage to hold the result. */ static inline void USQR(mp_int X, mp_int Z) { mp_size ua_ = MP_USED(X); mp_size o_ = ua_ + ua_; ZERO(MP_DIGITS(Z), o_); (void)s_ksqr(MP_DIGITS(X), MP_DIGITS(Z), ua_); Z->used = o_; CLAMP(Z); } mp_result mp_int_init(mp_int z) { if (z == NULL) return MP_BADARG; z->single = 0; z->digits = &(z->single); z->alloc = 1; z->used = 1; z->sign = MP_ZPOS; return MP_OK; } mp_int mp_int_alloc(void) { mp_int out = malloc(sizeof(mpz_t)); if (out != NULL) mp_int_init(out); return out; } mp_result mp_int_init_size(mp_int z, mp_size prec) { assert(z != NULL); if (prec == 0) { prec = default_precision; } else if (prec == 1) { return mp_int_init(z); } else { prec = s_round_prec(prec); } z->digits = s_alloc(prec); if (MP_DIGITS(z) == NULL) return MP_MEMORY; z->digits[0] = 0; z->used = 1; z->alloc = prec; z->sign = MP_ZPOS; return MP_OK; } mp_result mp_int_init_copy(mp_int z, mp_int old) { assert(z != NULL && old != NULL); mp_size uold = MP_USED(old); if (uold == 1) { mp_int_init(z); } else { mp_size target = MAX(uold, default_precision); mp_result res = mp_int_init_size(z, target); if (res != MP_OK) return res; } z->used = uold; z->sign = old->sign; COPY(MP_DIGITS(old), MP_DIGITS(z), uold); return MP_OK; } mp_result mp_int_init_value(mp_int z, mp_small value) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_init_copy(z, &vtmp); } mp_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(uvalue)]; s_ufake(&vtmp, uvalue, vbuf); return mp_int_init_copy(z, &vtmp); } mp_result mp_int_set_value(mp_int z, mp_small value) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_copy(&vtmp, z); } mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(uvalue)]; s_ufake(&vtmp, uvalue, vbuf); return mp_int_copy(&vtmp, z); } void mp_int_clear(mp_int z) { if (z == NULL) return; if (MP_DIGITS(z) != NULL) { if (MP_DIGITS(z) != &(z->single)) s_free(MP_DIGITS(z)); z->digits = NULL; } } void mp_int_free(mp_int z) { assert(z != NULL); mp_int_clear(z); free(z); /* note: NOT s_free() */ } mp_result mp_int_copy(mp_int a, mp_int c) { assert(a != NULL && c != NULL); if (a != c) { mp_size ua = MP_USED(a); mp_digit *da, *dc; if (!s_pad(c, ua)) return MP_MEMORY; da = MP_DIGITS(a); dc = MP_DIGITS(c); COPY(da, dc, ua); c->used = ua; c->sign = a->sign; } return MP_OK; } void mp_int_swap(mp_int a, mp_int c) { if (a != c) { mpz_t tmp = *a; *a = *c; *c = tmp; if (MP_DIGITS(a) == &(c->single)) a->digits = &(a->single); if (MP_DIGITS(c) == &(a->single)) c->digits = &(c->single); } } void mp_int_zero(mp_int z) { assert(z != NULL); z->digits[0] = 0; z->used = 1; z->sign = MP_ZPOS; } mp_result mp_int_abs(mp_int a, mp_int c) { assert(a != NULL && c != NULL); mp_result res; if ((res = mp_int_copy(a, c)) != MP_OK) return res; c->sign = MP_ZPOS; return MP_OK; } mp_result mp_int_neg(mp_int a, mp_int c) { assert(a != NULL && c != NULL); mp_result res; if ((res = mp_int_copy(a, c)) != MP_OK) return res; if (CMPZ(c) != 0) c->sign = 1 - MP_SIGN(a); return MP_OK; } mp_result mp_int_add(mp_int a, mp_int b, mp_int c) { assert(a != NULL && b != NULL && c != NULL); mp_size ua = MP_USED(a); mp_size ub = MP_USED(b); mp_size max = MAX(ua, ub); if (MP_SIGN(a) == MP_SIGN(b)) { /* Same sign -- add magnitudes, preserve sign of addends */ if (!s_pad(c, max)) return MP_MEMORY; mp_digit carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub); mp_size uc = max; if (carry) { if (!s_pad(c, max + 1)) return MP_MEMORY; c->digits[max] = carry; ++uc; } c->used = uc; c->sign = a->sign; } else { /* Different signs -- subtract magnitudes, preserve sign of greater */ int cmp = s_ucmp(a, b); /* magnitude comparison, sign ignored */ /* Set x to max(a, b), y to min(a, b) to simplify later code. A special case yields zero for equal magnitudes. */ mp_int x, y; if (cmp == 0) { mp_int_zero(c); return MP_OK; } else if (cmp < 0) { x = b; y = a; } else { x = a; y = b; } if (!s_pad(c, MP_USED(x))) return MP_MEMORY; /* Subtract smaller from larger */ s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y)); c->used = x->used; CLAMP(c); /* Give result the sign of the larger */ c->sign = x->sign; } return MP_OK; } mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_add(a, &vtmp, c); } mp_result mp_int_sub(mp_int a, mp_int b, mp_int c) { assert(a != NULL && b != NULL && c != NULL); mp_size ua = MP_USED(a); mp_size ub = MP_USED(b); mp_size max = MAX(ua, ub); if (MP_SIGN(a) != MP_SIGN(b)) { /* Different signs -- add magnitudes and keep sign of a */ if (!s_pad(c, max)) return MP_MEMORY; mp_digit carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub); mp_size uc = max; if (carry) { if (!s_pad(c, max + 1)) return MP_MEMORY; c->digits[max] = carry; ++uc; } c->used = uc; c->sign = a->sign; } else { /* Same signs -- subtract magnitudes */ if (!s_pad(c, max)) return MP_MEMORY; mp_int x, y; mp_sign osign; int cmp = s_ucmp(a, b); if (cmp >= 0) { x = a; y = b; osign = MP_ZPOS; } else { x = b; y = a; osign = MP_NEG; } if (MP_SIGN(a) == MP_NEG && cmp != 0) osign = 1 - osign; s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y)); c->used = x->used; CLAMP(c); c->sign = osign; } return MP_OK; } mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_sub(a, &vtmp, c); } mp_result mp_int_mul(mp_int a, mp_int b, mp_int c) { assert(a != NULL && b != NULL && c != NULL); /* If either input is zero, we can shortcut multiplication */ if (mp_int_compare_zero(a) == 0 || mp_int_compare_zero(b) == 0) { mp_int_zero(c); return MP_OK; } /* Output is positive if inputs have same sign, otherwise negative */ mp_sign osign = (MP_SIGN(a) == MP_SIGN(b)) ? MP_ZPOS : MP_NEG; /* If the output is not identical to any of the inputs, we'll write the results directly; otherwise, allocate a temporary space. */ mp_size ua = MP_USED(a); mp_size ub = MP_USED(b); mp_size osize = MAX(ua, ub); osize = 4 * ((osize + 1) / 2); mp_digit* out; mp_size p = 0; if (c == a || c == b) { p = MAX(s_round_prec(osize), default_precision); if ((out = s_alloc(p)) == NULL) return MP_MEMORY; } else { if (!s_pad(c, osize)) return MP_MEMORY; out = MP_DIGITS(c); } ZERO(out, osize); if (!s_kmul(MP_DIGITS(a), MP_DIGITS(b), out, ua, ub)) return MP_MEMORY; /* If we allocated a new buffer, get rid of whatever memory c was already using, and fix up its fields to reflect that. */ if (out != MP_DIGITS(c)) { if ((void*)MP_DIGITS(c) != (void*)c) s_free(MP_DIGITS(c)); c->digits = out; c->alloc = p; } c->used = osize; /* might not be true, but we'll fix it ... */ CLAMP(c); /* ... right here */ c->sign = osign; return MP_OK; } mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_mul(a, &vtmp, c); } mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c) { assert(a != NULL && c != NULL && p2 >= 0); mp_result res = mp_int_copy(a, c); if (res != MP_OK) return res; if (s_qmul(c, (mp_size)p2)) { return MP_OK; } else { return MP_MEMORY; } } mp_result mp_int_sqr(mp_int a, mp_int c) { assert(a != NULL && c != NULL); /* Get a temporary buffer big enough to hold the result */ mp_size osize = (mp_size)4 * ((MP_USED(a) + 1) / 2); mp_size p = 0; mp_digit* out; if (a == c) { p = s_round_prec(osize); p = MAX(p, default_precision); if ((out = s_alloc(p)) == NULL) return MP_MEMORY; } else { if (!s_pad(c, osize)) return MP_MEMORY; out = MP_DIGITS(c); } ZERO(out, osize); s_ksqr(MP_DIGITS(a), out, MP_USED(a)); /* Get rid of whatever memory c was already using, and fix up its fields to reflect the new digit array it's using */ if (out != MP_DIGITS(c)) { if ((void*)MP_DIGITS(c) != (void*)c) s_free(MP_DIGITS(c)); c->digits = out; c->alloc = p; } c->used = osize; /* might not be true, but we'll fix it ... */ CLAMP(c); /* ... right here */ c->sign = MP_ZPOS; return MP_OK; } mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r) { assert(a != NULL && b != NULL && q != r); int cmp; mp_result res = MP_OK; mp_int qout, rout; mp_sign sa = MP_SIGN(a); mp_sign sb = MP_SIGN(b); if (CMPZ(b) == 0) { return MP_UNDEF; } else if ((cmp = s_ucmp(a, b)) < 0) { /* If |a| < |b|, no division is required: q = 0, r = a */ if (r && (res = mp_int_copy(a, r)) != MP_OK) return res; if (q) mp_int_zero(q); return MP_OK; } else if (cmp == 0) { /* If |a| = |b|, no division is required: q = 1 or -1, r = 0 */ if (r) mp_int_zero(r); if (q) { mp_int_zero(q); q->digits[0] = 1; if (sa != sb) q->sign = MP_NEG; } return MP_OK; } /* When |a| > |b|, real division is required. We need someplace to store quotient and remainder, but q and r are allowed to be NULL or to overlap with the inputs. */ DECLARE_TEMP(2); int lg; if ((lg = s_isp2(b)) < 0) { if (q && b != q) { REQUIRE(mp_int_copy(a, q)); qout = q; } else { REQUIRE(mp_int_copy(a, TEMP(0))); qout = TEMP(0); } if (r && a != r) { REQUIRE(mp_int_copy(b, r)); rout = r; } else { REQUIRE(mp_int_copy(b, TEMP(1))); rout = TEMP(1); } REQUIRE(s_udiv_knuth(qout, rout)); } else { if (q) REQUIRE(mp_int_copy(a, q)); if (r) REQUIRE(mp_int_copy(a, r)); if (q) s_qdiv(q, (mp_size)lg); qout = q; if (r) s_qmod(r, (mp_size)lg); rout = r; } /* Recompute signs for output */ if (rout) { rout->sign = sa; if (CMPZ(rout) == 0) rout->sign = MP_ZPOS; } if (qout) { qout->sign = (sa == sb) ? MP_ZPOS : MP_NEG; if (CMPZ(qout) == 0) qout->sign = MP_ZPOS; } if (q) REQUIRE(mp_int_copy(qout, q)); if (r) REQUIRE(mp_int_copy(rout, r)); CLEANUP_TEMP(); return res; } mp_result mp_int_mod(mp_int a, mp_int m, mp_int c) { DECLARE_TEMP(1); if (CMPZ(m) < 0) { return MP_RANGE; } mp_int out = (m == c) ? TEMP(0) : c; REQUIRE(mp_int_div(a, m, NULL, out)); if (CMPZ(out) < 0) { REQUIRE(mp_int_add(out, m, c)); } else { REQUIRE(mp_int_copy(out, c)); } CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small* r) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); DECLARE_TEMP(1); REQUIRE(mp_int_div(a, &vtmp, q, TEMP(0))); if (r) (void)mp_int_to_int(TEMP(0), r); /* can't fail */ CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r) { assert(a != NULL && p2 >= 0 && q != r); mp_result res = MP_OK; if (q != NULL && (res = mp_int_copy(a, q)) == MP_OK) { s_qdiv(q, (mp_size)p2); } if (res == MP_OK && r != NULL && (res = mp_int_copy(a, r)) == MP_OK) { s_qmod(r, (mp_size)p2); } return res; } mp_result mp_int_expt(mp_int a, mp_small b, mp_int c) { assert(c != NULL); if (b < 0) return MP_RANGE; DECLARE_TEMP(1); REQUIRE(mp_int_copy(a, TEMP(0))); (void)mp_int_set_value(c, 1); unsigned int v = labs(b); while (v != 0) { if (v & 1) { REQUIRE(mp_int_mul(c, TEMP(0), c)); } v >>= 1; if (v == 0) break; REQUIRE(mp_int_sqr(TEMP(0), TEMP(0))); } CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c) { assert(c != NULL); if (b < 0) return MP_RANGE; DECLARE_TEMP(1); REQUIRE(mp_int_set_value(TEMP(0), a)); (void)mp_int_set_value(c, 1); unsigned int v = labs(b); while (v != 0) { if (v & 1) { REQUIRE(mp_int_mul(c, TEMP(0), c)); } v >>= 1; if (v == 0) break; REQUIRE(mp_int_sqr(TEMP(0), TEMP(0))); } CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c) { assert(a != NULL && b != NULL && c != NULL); if (MP_SIGN(b) == MP_NEG) return MP_RANGE; DECLARE_TEMP(1); REQUIRE(mp_int_copy(a, TEMP(0))); (void)mp_int_set_value(c, 1); for (unsigned ix = 0; ix < MP_USED(b); ++ix) { mp_digit d = b->digits[ix]; for (unsigned jx = 0; jx < MP_DIGIT_BIT; ++jx) { if (d & 1) { REQUIRE(mp_int_mul(c, TEMP(0), c)); } d >>= 1; if (d == 0 && ix + 1 == MP_USED(b)) break; REQUIRE(mp_int_sqr(TEMP(0), TEMP(0))); } } CLEANUP_TEMP(); return MP_OK; } int mp_int_compare(mp_int a, mp_int b) { assert(a != NULL && b != NULL); mp_sign sa = MP_SIGN(a); if (sa == MP_SIGN(b)) { int cmp = s_ucmp(a, b); /* If they're both zero or positive, the normal comparison applies; if both negative, the sense is reversed. */ if (sa == MP_ZPOS) { return cmp; } else { return -cmp; } } else if (sa == MP_ZPOS) { return 1; } else { return -1; } } int mp_int_compare_unsigned(mp_int a, mp_int b) { assert(a != NULL && b != NULL); return s_ucmp(a, b); } int mp_int_compare_zero(mp_int z) { assert(z != NULL); if (MP_USED(z) == 1 && z->digits[0] == 0) { return 0; } else if (MP_SIGN(z) == MP_ZPOS) { return 1; } else { return -1; } } int mp_int_compare_value(mp_int z, mp_small value) { assert(z != NULL); mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS; if (vsign == MP_SIGN(z)) { int cmp = s_vcmp(z, value); return (vsign == MP_ZPOS) ? cmp : -cmp; } else { return (value < 0) ? 1 : -1; } } int mp_int_compare_uvalue(mp_int z, mp_usmall uv) { assert(z != NULL); if (MP_SIGN(z) == MP_NEG) { return -1; } else { return s_uvcmp(z, uv); } } mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c) { assert(a != NULL && b != NULL && c != NULL && m != NULL); /* Zero moduli and negative exponents are not considered. */ if (CMPZ(m) == 0) return MP_UNDEF; if (CMPZ(b) < 0) return MP_RANGE; mp_size um = MP_USED(m); DECLARE_TEMP(3); REQUIRE(GROW(TEMP(0), 2 * um)); REQUIRE(GROW(TEMP(1), 2 * um)); mp_int s; if (c == b || c == m) { REQUIRE(GROW(TEMP(2), 2 * um)); s = TEMP(2); } else { s = c; } REQUIRE(mp_int_mod(a, m, TEMP(0))); REQUIRE(s_brmu(TEMP(1), m)); REQUIRE(s_embar(TEMP(0), b, m, TEMP(1), s)); REQUIRE(mp_int_copy(s, c)); CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_exptmod(a, &vtmp, m, c); } mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c) { mpz_t vtmp; mp_digit vbuf[MP_VALUE_DIGITS(value)]; s_fake(&vtmp, value, vbuf); return mp_int_exptmod(&vtmp, b, m, c); } mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c) { assert(a && b && m && c); /* Zero moduli and negative exponents are not considered. */ if (CMPZ(m) == 0) return MP_UNDEF; if (CMPZ(b) < 0) return MP_RANGE; DECLARE_TEMP(2); mp_size um = MP_USED(m); REQUIRE(GROW(TEMP(0), 2 * um)); mp_int s; if (c == b || c == m) { REQUIRE(GROW(TEMP(1), 2 * um)); s = TEMP(1); } else { s = c; } REQUIRE(mp_int_mod(a, m, TEMP(0))); REQUIRE(s_embar(TEMP(0), b, m, mu, s)); REQUIRE(mp_int_copy(s, c)); CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_redux_const(mp_int m, mp_int c) { assert(m != NULL && c != NULL && m != c); return s_brmu(c, m); } mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c) { assert(a != NULL && m != NULL && c != NULL); if (CMPZ(a) == 0 || CMPZ(m) <= 0) return MP_RANGE; DECLARE_TEMP(2); REQUIRE(mp_int_egcd(a, m, TEMP(0), TEMP(1), NULL)); if (mp_int_compare_value(TEMP(0), 1) != 0) { REQUIRE(MP_UNDEF); } /* It is first necessary to constrain the value to the proper range */ REQUIRE(mp_int_mod(TEMP(1), m, TEMP(1))); /* Now, if 'a' was originally negative, the value we have is actually the magnitude of the negative representative; to get the positive value we have to subtract from the modulus. Otherwise, the value is okay as it stands. */ if (MP_SIGN(a) == MP_NEG) { REQUIRE(mp_int_sub(m, TEMP(1), c)); } else { REQUIRE(mp_int_copy(TEMP(1), c)); } CLEANUP_TEMP(); return MP_OK; } /* Binary GCD algorithm due to Josef Stein, 1961 */ mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c) { assert(a != NULL && b != NULL && c != NULL); int ca = CMPZ(a); int cb = CMPZ(b); if (ca == 0 && cb == 0) { return MP_UNDEF; } else if (ca == 0) { return mp_int_abs(b, c); } else if (cb == 0) { return mp_int_abs(a, c); } DECLARE_TEMP(3); REQUIRE(mp_int_copy(a, TEMP(0))); REQUIRE(mp_int_copy(b, TEMP(1))); TEMP(0)->sign = MP_ZPOS; TEMP(1)->sign = MP_ZPOS; int k = 0; { /* Divide out common factors of 2 from u and v */ int div2_u = s_dp2k(TEMP(0)); int div2_v = s_dp2k(TEMP(1)); k = MIN(div2_u, div2_v); s_qdiv(TEMP(0), (mp_size)k); s_qdiv(TEMP(1), (mp_size)k); } if (mp_int_is_odd(TEMP(0))) { REQUIRE(mp_int_neg(TEMP(1), TEMP(2))); } else { REQUIRE(mp_int_copy(TEMP(0), TEMP(2))); } for (;;) { s_qdiv(TEMP(2), s_dp2k(TEMP(2))); if (CMPZ(TEMP(2)) > 0) { REQUIRE(mp_int_copy(TEMP(2), TEMP(0))); } else { REQUIRE(mp_int_neg(TEMP(2), TEMP(1))); } REQUIRE(mp_int_sub(TEMP(0), TEMP(1), TEMP(2))); if (CMPZ(TEMP(2)) == 0) break; } REQUIRE(mp_int_abs(TEMP(0), c)); if (!s_qmul(c, (mp_size)k)) REQUIRE(MP_MEMORY); CLEANUP_TEMP(); return MP_OK; } /* This is the binary GCD algorithm again, but this time we keep track of the elementary matrix operations as we go, so we can get values x and y satisfying c = ax + by. */ mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, mp_int x, mp_int y) { assert(a != NULL && b != NULL && c != NULL && (x != NULL || y != NULL)); mp_result res = MP_OK; int ca = CMPZ(a); int cb = CMPZ(b); if (ca == 0 && cb == 0) { return MP_UNDEF; } else if (ca == 0) { if ((res = mp_int_abs(b, c)) != MP_OK) return res; mp_int_zero(x); (void)mp_int_set_value(y, 1); return MP_OK; } else if (cb == 0) { if ((res = mp_int_abs(a, c)) != MP_OK) return res; (void)mp_int_set_value(x, 1); mp_int_zero(y); return MP_OK; } /* Initialize temporaries: A:0, B:1, C:2, D:3, u:4, v:5, ou:6, ov:7 */ DECLARE_TEMP(8); REQUIRE(mp_int_set_value(TEMP(0), 1)); REQUIRE(mp_int_set_value(TEMP(3), 1)); REQUIRE(mp_int_copy(a, TEMP(4))); REQUIRE(mp_int_copy(b, TEMP(5))); /* We will work with absolute values here */ TEMP(4)->sign = MP_ZPOS; TEMP(5)->sign = MP_ZPOS; int k = 0; { /* Divide out common factors of 2 from u and v */ int div2_u = s_dp2k(TEMP(4)), div2_v = s_dp2k(TEMP(5)); k = MIN(div2_u, div2_v); s_qdiv(TEMP(4), k); s_qdiv(TEMP(5), k); } REQUIRE(mp_int_copy(TEMP(4), TEMP(6))); REQUIRE(mp_int_copy(TEMP(5), TEMP(7))); for (;;) { while (mp_int_is_even(TEMP(4))) { s_qdiv(TEMP(4), 1); if (mp_int_is_odd(TEMP(0)) || mp_int_is_odd(TEMP(1))) { REQUIRE(mp_int_add(TEMP(0), TEMP(7), TEMP(0))); REQUIRE(mp_int_sub(TEMP(1), TEMP(6), TEMP(1))); } s_qdiv(TEMP(0), 1); s_qdiv(TEMP(1), 1); } while (mp_int_is_even(TEMP(5))) { s_qdiv(TEMP(5), 1); if (mp_int_is_odd(TEMP(2)) || mp_int_is_odd(TEMP(3))) { REQUIRE(mp_int_add(TEMP(2), TEMP(7), TEMP(2))); REQUIRE(mp_int_sub(TEMP(3), TEMP(6), TEMP(3))); } s_qdiv(TEMP(2), 1); s_qdiv(TEMP(3), 1); } if (mp_int_compare(TEMP(4), TEMP(5)) >= 0) { REQUIRE(mp_int_sub(TEMP(4), TEMP(5), TEMP(4))); REQUIRE(mp_int_sub(TEMP(0), TEMP(2), TEMP(0))); REQUIRE(mp_int_sub(TEMP(1), TEMP(3), TEMP(1))); } else { REQUIRE(mp_int_sub(TEMP(5), TEMP(4), TEMP(5))); REQUIRE(mp_int_sub(TEMP(2), TEMP(0), TEMP(2))); REQUIRE(mp_int_sub(TEMP(3), TEMP(1), TEMP(3))); } if (CMPZ(TEMP(4)) == 0) { if (x) REQUIRE(mp_int_copy(TEMP(2), x)); if (y) REQUIRE(mp_int_copy(TEMP(3), y)); if (c) { if (!s_qmul(TEMP(5), k)) { REQUIRE(MP_MEMORY); } REQUIRE(mp_int_copy(TEMP(5), c)); } break; } } CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c) { assert(a != NULL && b != NULL && c != NULL); /* Since a * b = gcd(a, b) * lcm(a, b), we can compute lcm(a, b) = (a / gcd(a, b)) * b. This formulation insures everything works even if the input variables share space. */ DECLARE_TEMP(1); REQUIRE(mp_int_gcd(a, b, TEMP(0))); REQUIRE(mp_int_div(a, TEMP(0), TEMP(0), NULL)); REQUIRE(mp_int_mul(TEMP(0), b, TEMP(0))); REQUIRE(mp_int_copy(TEMP(0), c)); CLEANUP_TEMP(); return MP_OK; } bool mp_int_divisible_value(mp_int a, mp_small v) { mp_small rem = 0; if (mp_int_div_value(a, v, NULL, &rem) != MP_OK) { return false; } return rem == 0; } int mp_int_is_pow2(mp_int z) { assert(z != NULL); return s_isp2(z); } /* Implementation of Newton's root finding method, based loosely on a patch contributed by Hal Finkel modified by M. J. Fromberger. */ mp_result mp_int_root(mp_int a, mp_small b, mp_int c) { assert(a != NULL && c != NULL && b > 0); if (b == 1) { return mp_int_copy(a, c); } bool flips = false; if (MP_SIGN(a) == MP_NEG) { if (b % 2 == 0) { return MP_UNDEF; /* root does not exist for negative a with even b */ } else { flips = true; } } DECLARE_TEMP(5); REQUIRE(mp_int_copy(a, TEMP(0))); REQUIRE(mp_int_copy(a, TEMP(1))); TEMP(0)->sign = MP_ZPOS; TEMP(1)->sign = MP_ZPOS; for (;;) { REQUIRE(mp_int_expt(TEMP(1), b, TEMP(2))); if (mp_int_compare_unsigned(TEMP(2), TEMP(0)) <= 0) break; REQUIRE(mp_int_sub(TEMP(2), TEMP(0), TEMP(2))); REQUIRE(mp_int_expt(TEMP(1), b - 1, TEMP(3))); REQUIRE(mp_int_mul_value(TEMP(3), b, TEMP(3))); REQUIRE(mp_int_div(TEMP(2), TEMP(3), TEMP(4), NULL)); REQUIRE(mp_int_sub(TEMP(1), TEMP(4), TEMP(4))); if (mp_int_compare_unsigned(TEMP(1), TEMP(4)) == 0) { REQUIRE(mp_int_sub_value(TEMP(4), 1, TEMP(4))); } REQUIRE(mp_int_copy(TEMP(4), TEMP(1))); } REQUIRE(mp_int_copy(TEMP(1), c)); /* If the original value of a was negative, flip the output sign. */ if (flips) (void)mp_int_neg(c, c); /* cannot fail */ CLEANUP_TEMP(); return MP_OK; } mp_result mp_int_to_int(mp_int z, mp_small* out) { assert(z != NULL); /* Make sure the value is representable as a small integer */ mp_sign sz = MP_SIGN(z); if ((sz == MP_ZPOS && mp_int_compare_value(z, MP_SMALL_MAX) > 0) || mp_int_compare_value(z, MP_SMALL_MIN) < 0) { return MP_RANGE; } mp_usmall uz = MP_USED(z); mp_digit* dz = MP_DIGITS(z) + uz - 1; mp_small uv = 0; while (uz > 0) { uv <<= MP_DIGIT_BIT / 2; uv = (uv << (MP_DIGIT_BIT / 2)) | *dz--; --uz; } if (out) *out = (mp_small)((sz == MP_NEG) ? -uv : uv); return MP_OK; } mp_result mp_int_to_uint(mp_int z, mp_usmall* out) { assert(z != NULL); /* Make sure the value is representable as an unsigned small integer */ mp_size sz = MP_SIGN(z); if (sz == MP_NEG || mp_int_compare_uvalue(z, MP_USMALL_MAX) > 0) { return MP_RANGE; } mp_size uz = MP_USED(z); mp_digit* dz = MP_DIGITS(z) + uz - 1; mp_usmall uv = 0; while (uz > 0) { uv <<= MP_DIGIT_BIT / 2; uv = (uv << (MP_DIGIT_BIT / 2)) | *dz--; --uz; } if (out) *out = uv; return MP_OK; } mp_result mp_int_to_string(mp_int z, mp_size radix, char* str, int limit) { assert(z != NULL && str != NULL && limit >= 2); assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX); int cmp = 0; if (CMPZ(z) == 0) { *str++ = s_val2ch(0, 1); } else { mp_result res; mpz_t tmp; char *h, *t; if ((res = mp_int_init_copy(&tmp, z)) != MP_OK) return res; if (MP_SIGN(z) == MP_NEG) { *str++ = '-'; --limit; } h = str; /* Generate digits in reverse order until finished or limit reached */ for (/* */; limit > 0; --limit) { mp_digit d; if ((cmp = CMPZ(&tmp)) == 0) break; d = s_ddiv(&tmp, (mp_digit)radix); *str++ = s_val2ch(d, 1); } t = str - 1; /* Put digits back in correct output order */ while (h < t) { char tc = *h; *h++ = *t; *t-- = tc; } mp_int_clear(&tmp); } *str = '\0'; if (cmp == 0) { return MP_OK; } else { return MP_TRUNC; } } mp_size mp_int_string_len(mp_int z, mp_size radix) { assert(z != NULL); assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX); int len = s_outlen(z, radix) + 1; /* for terminator */ /* Allow for sign marker on negatives */ if (MP_SIGN(z) == MP_NEG) len += 1; return len; } /* Read zero-terminated string into z */ mp_result mp_int_read_string(mp_int z, mp_size radix, const char* str) { return mp_int_read_cstring(z, radix, str, NULL); } mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char* str, char** end) { assert(z != NULL && str != NULL); assert(radix >= MP_MIN_RADIX && radix <= MP_MAX_RADIX); /* Skip leading whitespace */ while (isspace((unsigned char)*str)) ++str; /* Handle leading sign tag (+/-, positive default) */ switch (*str) { case '-': z->sign = MP_NEG; ++str; break; case '+': ++str; /* fallthrough */ default: z->sign = MP_ZPOS; break; } /* Skip leading zeroes */ int ch; while ((ch = s_ch2val(*str, radix)) == 0) ++str; /* Make sure there is enough space for the value */ if (!s_pad(z, s_inlen(strlen(str), radix))) return MP_MEMORY; z->used = 1; z->digits[0] = 0; while (*str != '\0' && ((ch = s_ch2val(*str, radix)) >= 0)) { s_dmul(z, (mp_digit)radix); s_dadd(z, (mp_digit)ch); ++str; } CLAMP(z); /* Override sign for zero, even if negative specified. */ if (CMPZ(z) == 0) z->sign = MP_ZPOS; if (end != NULL) *end = (char*)str; /* Return a truncation error if the string has unprocessed characters remaining, so the caller can tell if the whole string was done */ if (*str != '\0') { return MP_TRUNC; } else { return MP_OK; } } mp_size mp_int_count_bits(mp_int z) { assert(z != NULL); mp_size uz = MP_USED(z); if (uz == 1 && z->digits[0] == 0) return 1; --uz; mp_size nbits = uz * MP_DIGIT_BIT; mp_digit d = z->digits[uz]; while (d != 0) { d >>= 1; ++nbits; } return nbits; } mp_result mp_int_to_binary(mp_int z, unsigned char* buf, int limit) { static const int PAD_FOR_2C = 1; assert(z != NULL && buf != NULL); int limpos = limit; mp_result res = s_tobin(z, buf, &limpos, PAD_FOR_2C); if (MP_SIGN(z) == MP_NEG) s_2comp(buf, limpos); return res; } mp_result mp_int_read_binary(mp_int z, unsigned char* buf, int len) { assert(z != NULL && buf != NULL && len > 0); /* Figure out how many digits are needed to represent this value */ mp_size need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT; if (!s_pad(z, need)) return MP_MEMORY; mp_int_zero(z); /* If the high-order bit is set, take the 2's complement before reading the value (it will be restored afterward) */ if (buf[0] >> (CHAR_BIT - 1)) { z->sign = MP_NEG; s_2comp(buf, len); } mp_digit* dz = MP_DIGITS(z); unsigned char* tmp = buf; for (int i = len; i > 0; --i, ++tmp) { s_qmul(z, (mp_size)CHAR_BIT); *dz |= *tmp; } /* Restore 2's complement if we took it before */ if (MP_SIGN(z) == MP_NEG) s_2comp(buf, len); return MP_OK; } mp_size mp_int_binary_len(mp_int z) { mp_size res = mp_int_count_bits(z); if (res == 0) return res; mp_size bytes = mp_int_unsigned_len(z); /* If the highest-order bit falls exactly on a byte boundary, we need to pad with an extra byte so that the sign will be read correctly when reading it back in. */ if (bytes * CHAR_BIT == res) ++bytes; return bytes; } mp_result mp_int_to_unsigned(mp_int z, unsigned char* buf, int limit) { static const int NO_PADDING = 0; assert(z != NULL && buf != NULL); return s_tobin(z, buf, &limit, NO_PADDING); } mp_result mp_int_read_unsigned(mp_int z, unsigned char* buf, int len) { assert(z != NULL && buf != NULL && len > 0); /* Figure out how many digits are needed to represent this value */ mp_size need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT; if (!s_pad(z, need)) return MP_MEMORY; mp_int_zero(z); unsigned char* tmp = buf; for (int i = len; i > 0; --i, ++tmp) { (void)s_qmul(z, CHAR_BIT); *MP_DIGITS(z) |= *tmp; } return MP_OK; } mp_size mp_int_unsigned_len(mp_int z) { mp_size res = mp_int_count_bits(z); mp_size bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT; return bytes; } const char* mp_error_string(mp_result res) { if (res > 0) return s_unknown_err; res = -res; int ix; for (ix = 0; ix < res && s_error_msg[ix] != NULL; ++ix); if (s_error_msg[ix] != NULL) { return s_error_msg[ix]; } else { return s_unknown_err; } } /*------------------------------------------------------------------------*/ /* Private functions for internal use. These make assumptions. */ #if DEBUG static const mp_digit fill = (mp_digit)0xdeadbeefabad1dea; #endif static mp_digit* s_alloc(mp_size num) { mp_digit* out = malloc(num * sizeof(mp_digit)); assert(out != NULL); #if DEBUG for (mp_size ix = 0; ix < num; ++ix) out[ix] = fill; #endif return out; } static mp_digit* s_realloc(mp_digit* old, mp_size osize, mp_size nsize) { #if DEBUG mp_digit* new = s_alloc(nsize); assert(new != NULL); for (mp_size ix = 0; ix < nsize; ++ix) new[ix] = fill; memcpy(new, old, osize * sizeof(mp_digit)); #else mp_digit* new = realloc(old, nsize * sizeof(mp_digit)); assert(new != NULL); #endif return new; } static void s_free(void* ptr) { free(ptr); } static bool s_pad(mp_int z, mp_size min) { if (MP_ALLOC(z) < min) { mp_size nsize = s_round_prec(min); mp_digit* tmp; if (z->digits == &(z->single)) { if ((tmp = s_alloc(nsize)) == NULL) return false; tmp[0] = z->single; } else if ((tmp = s_realloc(MP_DIGITS(z), MP_ALLOC(z), nsize)) == NULL) { return false; } z->digits = tmp; z->alloc = nsize; } return true; } /* Note: This will not work correctly when value == MP_SMALL_MIN */ static void s_fake(mp_int z, mp_small value, mp_digit vbuf[]) { mp_usmall uv = (mp_usmall)(value < 0) ? -value : value; s_ufake(z, uv, vbuf); if (value < 0) z->sign = MP_NEG; } static void s_ufake(mp_int z, mp_usmall value, mp_digit vbuf[]) { mp_size ndig = (mp_size)s_uvpack(value, vbuf); z->used = ndig; z->alloc = MP_VALUE_DIGITS(value); z->sign = MP_ZPOS; z->digits = vbuf; } static int s_cdig(mp_digit* da, mp_digit* db, mp_size len) { mp_digit *dat = da + len - 1, *dbt = db + len - 1; for (/* */; len != 0; --len, --dat, --dbt) { if (*dat > *dbt) { return 1; } else if (*dat < *dbt) { return -1; } } return 0; } static int s_uvpack(mp_usmall uv, mp_digit t[]) { int ndig = 0; if (uv == 0) t[ndig++] = 0; else { while (uv != 0) { t[ndig++] = (mp_digit)uv; uv >>= MP_DIGIT_BIT / 2; uv >>= MP_DIGIT_BIT / 2; } } return ndig; } static int s_ucmp(mp_int a, mp_int b) { mp_size ua = MP_USED(a), ub = MP_USED(b); if (ua > ub) { return 1; } else if (ub > ua) { return -1; } else { return s_cdig(MP_DIGITS(a), MP_DIGITS(b), ua); } } static int s_vcmp(mp_int a, mp_small v) { mp_usmall uv = (v < 0) ? -(mp_usmall)v : (mp_usmall)v; return s_uvcmp(a, uv); } static int s_uvcmp(mp_int a, mp_usmall uv) { mpz_t vtmp; mp_digit vdig[MP_VALUE_DIGITS(uv)]; s_ufake(&vtmp, uv, vdig); return s_ucmp(a, &vtmp); } static mp_digit s_uadd(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b) { mp_size pos; mp_word w = 0; /* Insure that da is the longer of the two to simplify later code */ if (size_b > size_a) { SWAP(mp_digit*, da, db); SWAP(mp_size, size_a, size_b); } /* Add corresponding digits until the shorter number runs out */ for (pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc) { w = w + (mp_word)*da + (mp_word)*db; *dc = LOWER_HALF(w); w = UPPER_HALF(w); } /* Propagate carries as far as necessary */ for (/* */; pos < size_a; ++pos, ++da, ++dc) { w = w + *da; *dc = LOWER_HALF(w); w = UPPER_HALF(w); } /* Return carry out */ return (mp_digit)w; } static void s_usub(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b) { mp_size pos; mp_word w = 0; /* We assume that |a| >= |b| so this should definitely hold */ assert(size_a >= size_b); /* Subtract corresponding digits and propagate borrow */ for (pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc) { w = ((mp_word)MP_DIGIT_MAX + 1 + /* MP_RADIX */ (mp_word)*da) - w - (mp_word)*db; *dc = LOWER_HALF(w); w = (UPPER_HALF(w) == 0); } /* Finish the subtraction for remaining upper digits of da */ for (/* */; pos < size_a; ++pos, ++da, ++dc) { w = ((mp_word)MP_DIGIT_MAX + 1 + /* MP_RADIX */ (mp_word)*da) - w; *dc = LOWER_HALF(w); w = (UPPER_HALF(w) == 0); } /* If there is a borrow out at the end, it violates the precondition */ assert(w == 0); } static int s_kmul(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b) { mp_size bot_size; /* Make sure b is the smaller of the two input values */ if (size_b > size_a) { SWAP(mp_digit*, da, db); SWAP(mp_size, size_a, size_b); } /* Insure that the bottom is the larger half in an odd-length split; the code below relies on this being true. */ bot_size = (size_a + 1) / 2; /* If the values are big enough to bother with recursion, use the Karatsuba algorithm to compute the product; otherwise use the normal multiplication algorithm */ if (multiply_threshold && size_a >= multiply_threshold && size_b > bot_size) { mp_digit *t1, *t2, *t3, carry; mp_digit* a_top = da + bot_size; mp_digit* b_top = db + bot_size; mp_size at_size = size_a - bot_size; mp_size bt_size = size_b - bot_size; mp_size buf_size = 2 * bot_size; /* Do a single allocation for all three temporary buffers needed; each buffer must be big enough to hold the product of two bottom halves, and one buffer needs space for the completed product; twice the space is plenty. */ if ((t1 = s_alloc(4 * buf_size)) == NULL) return 0; t2 = t1 + buf_size; t3 = t2 + buf_size; ZERO(t1, 4 * buf_size); /* t1 and t2 are initially used as temporaries to compute the inner product (a1 + a0)(b1 + b0) = a1b1 + a1b0 + a0b1 + a0b0 */ carry = s_uadd(da, a_top, t1, bot_size, at_size); /* t1 = a1 + a0 */ t1[bot_size] = carry; carry = s_uadd(db, b_top, t2, bot_size, bt_size); /* t2 = b1 + b0 */ t2[bot_size] = carry; (void)s_kmul(t1, t2, t3, bot_size + 1, bot_size + 1); /* t3 = t1 * t2 */ /* Now we'll get t1 = a0b0 and t2 = a1b1, and subtract them out so that we're left with only the pieces we want: t3 = a1b0 + a0b1 */ ZERO(t1, buf_size); ZERO(t2, buf_size); (void)s_kmul(da, db, t1, bot_size, bot_size); /* t1 = a0 * b0 */ (void)s_kmul(a_top, b_top, t2, at_size, bt_size); /* t2 = a1 * b1 */ /* Subtract out t1 and t2 to get the inner product */ s_usub(t3, t1, t3, buf_size + 2, buf_size); s_usub(t3, t2, t3, buf_size + 2, buf_size); /* Assemble the output value */ COPY(t1, dc, buf_size); carry = s_uadd(t3, dc + bot_size, dc + bot_size, buf_size + 1, buf_size); assert(carry == 0); carry = s_uadd(t2, dc + 2 * bot_size, dc + 2 * bot_size, buf_size, buf_size); assert(carry == 0); s_free(t1); /* note t2 and t3 are just internal pointers to t1 */ } else { s_umul(da, db, dc, size_a, size_b); } return 1; } static void s_umul(mp_digit* da, mp_digit* db, mp_digit* dc, mp_size size_a, mp_size size_b) { mp_size a, b; mp_word w; for (a = 0; a < size_a; ++a, ++dc, ++da) { mp_digit* dct = dc; mp_digit* dbt = db; if (*da == 0) continue; w = 0; for (b = 0; b < size_b; ++b, ++dbt, ++dct) { w = (mp_word)*da * (mp_word)*dbt + w + (mp_word)*dct; *dct = LOWER_HALF(w); w = UPPER_HALF(w); } *dct = (mp_digit)w; } } static int s_ksqr(mp_digit* da, mp_digit* dc, mp_size size_a) { if (multiply_threshold && size_a > multiply_threshold) { mp_size bot_size = (size_a + 1) / 2; mp_digit* a_top = da + bot_size; mp_digit *t1, *t2, *t3, carry; mp_size at_size = size_a - bot_size; mp_size buf_size = 2 * bot_size; if ((t1 = s_alloc(4 * buf_size)) == NULL) return 0; t2 = t1 + buf_size; t3 = t2 + buf_size; ZERO(t1, 4 * buf_size); (void)s_ksqr(da, t1, bot_size); /* t1 = a0 ^ 2 */ (void)s_ksqr(a_top, t2, at_size); /* t2 = a1 ^ 2 */ (void)s_kmul(da, a_top, t3, bot_size, at_size); /* t3 = a0 * a1 */ /* Quick multiply t3 by 2, shifting left (can't overflow) */ { int i, top = bot_size + at_size; mp_word w, save = 0; for (i = 0; i < top; ++i) { w = t3[i]; w = (w << 1) | save; t3[i] = LOWER_HALF(w); save = UPPER_HALF(w); } t3[i] = LOWER_HALF(save); } /* Assemble the output value */ COPY(t1, dc, 2 * bot_size); carry = s_uadd(t3, dc + bot_size, dc + bot_size, buf_size + 1, buf_size); assert(carry == 0); carry = s_uadd(t2, dc + 2 * bot_size, dc + 2 * bot_size, buf_size, buf_size); assert(carry == 0); s_free(t1); /* note that t2 and t2 are internal pointers only */ } else { s_usqr(da, dc, size_a); } return 1; } static void s_usqr(mp_digit* da, mp_digit* dc, mp_size size_a) { mp_size i, j; mp_word w; for (i = 0; i < size_a; ++i, dc += 2, ++da) { mp_digit *dct = dc, *dat = da; if (*da == 0) continue; /* Take care of the first digit, no rollover */ w = (mp_word)*dat * (mp_word)*dat + (mp_word)*dct; *dct = LOWER_HALF(w); w = UPPER_HALF(w); ++dat; ++dct; for (j = i + 1; j < size_a; ++j, ++dat, ++dct) { mp_word t = (mp_word)*da * (mp_word)*dat; mp_word u = w + (mp_word)*dct, ov = 0; /* Check if doubling t will overflow a word */ if (HIGH_BIT_SET(t)) ov = 1; w = t + t; /* Check if adding u to w will overflow a word */ if (ADD_WILL_OVERFLOW(w, u)) ov = 1; w += u; *dct = LOWER_HALF(w); w = UPPER_HALF(w); if (ov) { w += MP_DIGIT_MAX; /* MP_RADIX */ ++w; } } w = w + *dct; *dct = (mp_digit)w; while ((w = UPPER_HALF(w)) != 0) { ++dct; w = w + *dct; *dct = LOWER_HALF(w); } assert(w == 0); } } static void s_dadd(mp_int a, mp_digit b) { mp_word w = 0; mp_digit* da = MP_DIGITS(a); mp_size ua = MP_USED(a); w = (mp_word)*da + b; *da++ = LOWER_HALF(w); w = UPPER_HALF(w); for (ua -= 1; ua > 0; --ua, ++da) { w = (mp_word)*da + w; *da = LOWER_HALF(w); w = UPPER_HALF(w); } if (w) { *da = (mp_digit)w; a->used += 1; } } static void s_dmul(mp_int a, mp_digit b) { mp_word w = 0; mp_digit* da = MP_DIGITS(a); mp_size ua = MP_USED(a); while (ua > 0) { w = (mp_word)*da * b + w; *da++ = LOWER_HALF(w); w = UPPER_HALF(w); --ua; } if (w) { *da = (mp_digit)w; a->used += 1; } } static void s_dbmul(mp_digit* da, mp_digit b, mp_digit* dc, mp_size size_a) { mp_word w = 0; while (size_a > 0) { w = (mp_word)*da++ * (mp_word)b + w; *dc++ = LOWER_HALF(w); w = UPPER_HALF(w); --size_a; } if (w) *dc = LOWER_HALF(w); } static mp_digit s_ddiv(mp_int a, mp_digit b) { mp_word w = 0, qdigit; mp_size ua = MP_USED(a); mp_digit* da = MP_DIGITS(a) + ua - 1; for (/* */; ua > 0; --ua, --da) { w = (w << MP_DIGIT_BIT) | *da; if (w >= b) { qdigit = w / b; w = w % b; } else { qdigit = 0; } *da = (mp_digit)qdigit; } CLAMP(a); return (mp_digit)w; } static void s_qdiv(mp_int z, mp_size p2) { mp_size ndig = p2 / MP_DIGIT_BIT, nbits = p2 % MP_DIGIT_BIT; mp_size uz = MP_USED(z); if (ndig) { mp_size mark; mp_digit *to, *from; if (ndig >= uz) { mp_int_zero(z); return; } to = MP_DIGITS(z); from = to + ndig; for (mark = ndig; mark < uz; ++mark) { *to++ = *from++; } z->used = uz - ndig; } if (nbits) { mp_digit d = 0, *dz, save; mp_size up = MP_DIGIT_BIT - nbits; uz = MP_USED(z); dz = MP_DIGITS(z) + uz - 1; for (/* */; uz > 0; --uz, --dz) { save = *dz; *dz = (*dz >> nbits) | (d << up); d = save; } CLAMP(z); } if (MP_USED(z) == 1 && z->digits[0] == 0) z->sign = MP_ZPOS; } static void s_qmod(mp_int z, mp_size p2) { mp_size start = p2 / MP_DIGIT_BIT + 1, rest = p2 % MP_DIGIT_BIT; mp_size uz = MP_USED(z); mp_digit mask = (1u << rest) - 1; if (start <= uz) { z->used = start; z->digits[start - 1] &= mask; CLAMP(z); } } static int s_qmul(mp_int z, mp_size p2) { mp_size uz, need, rest, extra, i; mp_digit *from, *to, d; if (p2 == 0) return 1; uz = MP_USED(z); need = p2 / MP_DIGIT_BIT; rest = p2 % MP_DIGIT_BIT; /* Figure out if we need an extra digit at the top end; this occurs if the topmost `rest' bits of the high-order digit of z are not zero, meaning they will be shifted off the end if not preserved */ extra = 0; if (rest != 0) { mp_digit* dz = MP_DIGITS(z) + uz - 1; if ((*dz >> (MP_DIGIT_BIT - rest)) != 0) extra = 1; } if (!s_pad(z, uz + need + extra)) return 0; /* If we need to shift by whole digits, do that in one pass, then to back and shift by partial digits. */ if (need > 0) { from = MP_DIGITS(z) + uz - 1; to = from + need; for (i = 0; i < uz; ++i) *to-- = *from--; ZERO(MP_DIGITS(z), need); uz += need; } if (rest) { d = 0; for (i = need, from = MP_DIGITS(z) + need; i < uz; ++i, ++from) { mp_digit save = *from; *from = (*from << rest) | (d >> (MP_DIGIT_BIT - rest)); d = save; } d >>= (MP_DIGIT_BIT - rest); if (d != 0) { *from = d; uz += extra; } } z->used = uz; CLAMP(z); return 1; } /* Compute z = 2^p2 - |z|; requires that 2^p2 >= |z| The sign of the result is always zero/positive. */ static int s_qsub(mp_int z, mp_size p2) { mp_digit hi = (1u << (p2 % MP_DIGIT_BIT)), *zp; mp_size tdig = (p2 / MP_DIGIT_BIT), pos; mp_word w = 0; if (!s_pad(z, tdig + 1)) return 0; for (pos = 0, zp = MP_DIGITS(z); pos < tdig; ++pos, ++zp) { w = ((mp_word)MP_DIGIT_MAX + 1) - w - (mp_word)*zp; *zp = LOWER_HALF(w); w = UPPER_HALF(w) ? 0 : 1; } w = ((mp_word)MP_DIGIT_MAX + 1 + hi) - w - (mp_word)*zp; *zp = LOWER_HALF(w); assert(UPPER_HALF(w) != 0); /* no borrow out should be possible */ z->sign = MP_ZPOS; CLAMP(z); return 1; } static int s_dp2k(mp_int z) { int k = 0; mp_digit *dp = MP_DIGITS(z), d; if (MP_USED(z) == 1 && *dp == 0) return 1; while (*dp == 0) { k += MP_DIGIT_BIT; ++dp; } d = *dp; while ((d & 1) == 0) { d >>= 1; ++k; } return k; } static int s_isp2(mp_int z) { mp_size uz = MP_USED(z), k = 0; mp_digit *dz = MP_DIGITS(z), d; while (uz > 1) { if (*dz++ != 0) return -1; k += MP_DIGIT_BIT; --uz; } d = *dz; while (d > 1) { if (d & 1) return -1; ++k; d >>= 1; } return (int)k; } static int s_2expt(mp_int z, mp_small k) { mp_size ndig, rest; mp_digit* dz; ndig = (k + MP_DIGIT_BIT) / MP_DIGIT_BIT; rest = k % MP_DIGIT_BIT; if (!s_pad(z, ndig)) return 0; dz = MP_DIGITS(z); ZERO(dz, ndig); *(dz + ndig - 1) = (1u << rest); z->used = ndig; return 1; } static int s_norm(mp_int a, mp_int b) { mp_digit d = b->digits[MP_USED(b) - 1]; int k = 0; while (d < (1u << (mp_digit)(MP_DIGIT_BIT - 1))) { /* d < (MP_RADIX / 2) */ d <<= 1; ++k; } /* These multiplications can't fail */ if (k != 0) { (void)s_qmul(a, (mp_size)k); (void)s_qmul(b, (mp_size)k); } return k; } static mp_result s_brmu(mp_int z, mp_int m) { mp_size um = MP_USED(m) * 2; if (!s_pad(z, um)) return MP_MEMORY; s_2expt(z, MP_DIGIT_BIT * um); return mp_int_div(z, m, z, NULL); } static int s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2) { mp_size um = MP_USED(m), umb_p1, umb_m1; umb_p1 = (um + 1) * MP_DIGIT_BIT; umb_m1 = (um - 1) * MP_DIGIT_BIT; if (mp_int_copy(x, q1) != MP_OK) return 0; /* Compute q2 = floor((floor(x / b^(k-1)) * mu) / b^(k+1)) */ s_qdiv(q1, umb_m1); UMUL(q1, mu, q2); s_qdiv(q2, umb_p1); /* Set x = x mod b^(k+1) */ s_qmod(x, umb_p1); /* Now, q is a guess for the quotient a / m. Compute x - q * m mod b^(k+1), replacing x. This may be off by a factor of 2m, but no more than that. */ UMUL(q2, m, q1); s_qmod(q1, umb_p1); (void)mp_int_sub(x, q1, x); /* can't fail */ /* The result may be < 0; if it is, add b^(k+1) to pin it in the proper range. */ if ((CMPZ(x) < 0) && !s_qsub(x, umb_p1)) return 0; /* If x > m, we need to back it off until it is in range. This will be required at most twice. */ if (mp_int_compare(x, m) >= 0) { (void)mp_int_sub(x, m, x); if (mp_int_compare(x, m) >= 0) { (void)mp_int_sub(x, m, x); } } /* At this point, x has been properly reduced. */ return 1; } /* Perform modular exponentiation using Barrett's method, where mu is the reduction constant for m. Assumes a < m, b > 0. */ static mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c) { mp_digit umu = MP_USED(mu); mp_digit* db = MP_DIGITS(b); mp_digit* dbt = db + MP_USED(b) - 1; DECLARE_TEMP(3); REQUIRE(GROW(TEMP(0), 4 * umu)); REQUIRE(GROW(TEMP(1), 4 * umu)); REQUIRE(GROW(TEMP(2), 4 * umu)); ZERO(TEMP(0)->digits, TEMP(0)->alloc); ZERO(TEMP(1)->digits, TEMP(1)->alloc); ZERO(TEMP(2)->digits, TEMP(2)->alloc); (void)mp_int_set_value(c, 1); /* Take care of low-order digits */ while (db < dbt) { mp_digit d = *db; for (int i = MP_DIGIT_BIT; i > 0; --i, d >>= 1) { if (d & 1) { /* The use of a second temporary avoids allocation */ UMUL(c, a, TEMP(0)); if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) { REQUIRE(MP_MEMORY); } mp_int_copy(TEMP(0), c); } USQR(a, TEMP(0)); assert(MP_SIGN(TEMP(0)) == MP_ZPOS); if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) { REQUIRE(MP_MEMORY); } assert(MP_SIGN(TEMP(0)) == MP_ZPOS); mp_int_copy(TEMP(0), a); } ++db; } /* Take care of highest-order digit */ mp_digit d = *dbt; for (;;) { if (d & 1) { UMUL(c, a, TEMP(0)); if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) { REQUIRE(MP_MEMORY); } mp_int_copy(TEMP(0), c); } d >>= 1; if (!d) break; USQR(a, TEMP(0)); if (!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) { REQUIRE(MP_MEMORY); } (void)mp_int_copy(TEMP(0), a); } CLEANUP_TEMP(); return MP_OK; } /* Division of nonnegative integers This function implements division algorithm for unsigned multi-precision integers. The algorithm is based on Algorithm D from Knuth's "The Art of Computer Programming", 3rd ed. 1998, pg 272-273. We diverge from Knuth's algorithm in that we do not perform the subtraction from the remainder until we have determined that we have the correct quotient digit. This makes our algorithm less efficient than Knuth because we might have to perform multiple multiplication and comparison steps before the subtraction. The advantage is that it is easy to implement and ensure correctness without worrying about underflow from the subtraction. inputs: u a n+m digit integer in base b (b is 2^MP_DIGIT_BIT) v a n digit integer in base b (b is 2^MP_DIGIT_BIT) n >= 1 m >= 0 outputs: u / v stored in u u % v stored in v */ static mp_result s_udiv_knuth(mp_int u, mp_int v) { /* Force signs to positive */ u->sign = MP_ZPOS; v->sign = MP_ZPOS; /* Use simple division algorithm when v is only one digit long */ if (MP_USED(v) == 1) { mp_digit d, rem; d = v->digits[0]; rem = s_ddiv(u, d); mp_int_set_value(v, rem); return MP_OK; } /* Algorithm D The n and m variables are defined as used by Knuth. u is an n digit number with digits u_{n-1}..u_0. v is an n+m digit number with digits from v_{m+n-1}..v_0. We require that n > 1 and m >= 0 */ mp_size n = MP_USED(v); mp_size m = MP_USED(u) - n; assert(n > 1); /* assert(m >= 0) follows because m is unsigned. */ /* D1: Normalize. The normalization step provides the necessary condition for Theorem B, which states that the quotient estimate for q_j, call it qhat qhat = u_{j+n}u_{j+n-1} / v_{n-1} is bounded by qhat - 2 <= q_j <= qhat. That is, qhat is always greater than the actual quotient digit q, and it is never more than two larger than the actual quotient digit. */ int k = s_norm(u, v); /* Extend size of u by one if needed. The algorithm begins with a value of u that has one more digit of input. The normalization step sets u_{m+n}..u_0 = 2^k * u_{m+n-1}..u_0. If the multiplication did not increase the number of digits of u, we need to add a leading zero here. */ if (k == 0 || MP_USED(u) != m + n + 1) { if (!s_pad(u, m + n + 1)) return MP_MEMORY; u->digits[m + n] = 0; u->used = m + n + 1; } /* Add a leading 0 to v. The multiplication in step D4 multiplies qhat * 0v_{n-1}..v_0. We need to add the leading zero to v here to ensure that the multiplication will produce the full n+1 digit result. */ if (!s_pad(v, n + 1)) return MP_MEMORY; v->digits[n] = 0; /* Initialize temporary variables q and t. q allocates space for m+1 digits to store the quotient digits t allocates space for n+1 digits to hold the result of q_j*v */ DECLARE_TEMP(2); REQUIRE(GROW(TEMP(0), m + 1)); REQUIRE(GROW(TEMP(1), n + 1)); /* D2: Initialize j */ int j = m; mpz_t r; r.digits = MP_DIGITS(u) + j; /* The contents of r are shared with u */ r.used = n + 1; r.sign = MP_ZPOS; r.alloc = MP_ALLOC(u); ZERO(TEMP(1)->digits, TEMP(1)->alloc); /* Calculate the m+1 digits of the quotient result */ for (; j >= 0; j--) { /* D3: Calculate q' */ /* r->digits is aligned to position j of the number u */ mp_word pfx, qhat; pfx = r.digits[n]; pfx <<= MP_DIGIT_BIT / 2; pfx <<= MP_DIGIT_BIT / 2; pfx |= r.digits[n - 1]; /* pfx = u_{j+n}{j+n-1} */ qhat = pfx / v->digits[n - 1]; /* Check to see if qhat > b, and decrease qhat if so. Theorem B guarantees that qhat is at most 2 larger than the actual value, so it is possible that qhat is greater than the maximum value that will fit in a digit */ if (qhat > MP_DIGIT_MAX) qhat = MP_DIGIT_MAX; /* D4,D5,D6: Multiply qhat * v and test for a correct value of q We proceed a bit different than the way described by Knuth. This way is simpler but less efficient. Instead of doing the multiply and subtract then checking for underflow, we first do the multiply of qhat * v and see if it is larger than the current remainder r. If it is larger, we decrease qhat by one and try again. We may need to decrease qhat one more time before we get a value that is smaller than r. This way is less efficient than Knuth because we do more multiplies, but we do not need to worry about underflow this way. */ /* t = qhat * v */ s_dbmul(MP_DIGITS(v), (mp_digit)qhat, TEMP(1)->digits, n + 1); TEMP(1)->used = n + 1; CLAMP(TEMP(1)); /* Clamp r for the comparison. Comparisons do not like leading zeros. */ CLAMP(&r); if (s_ucmp(TEMP(1), &r) > 0) { /* would the remainder be negative? */ qhat -= 1; /* try a smaller q */ s_dbmul(MP_DIGITS(v), (mp_digit)qhat, TEMP(1)->digits, n + 1); TEMP(1)->used = n + 1; CLAMP(TEMP(1)); if (s_ucmp(TEMP(1), &r) > 0) { /* would the remainder be negative? */ assert(qhat > 0); qhat -= 1; /* try a smaller q */ s_dbmul(MP_DIGITS(v), (mp_digit)qhat, TEMP(1)->digits, n + 1); TEMP(1)->used = n + 1; CLAMP(TEMP(1)); } assert(s_ucmp(TEMP(1), &r) <= 0 && "The mathematics failed us."); } /* Unclamp r. The D algorithm expects r = u_{j+n}..u_j to always be n+1 digits long. */ r.used = n + 1; /* D4: Multiply and subtract Note: The multiply was completed above so we only need to subtract here. */ s_usub(r.digits, TEMP(1)->digits, r.digits, r.used, TEMP(1)->used); /* D5: Test remainder Note: Not needed because we always check that qhat is the correct value before performing the subtract. Value cast to mp_digit to prevent warning, qhat has been clamped to MP_DIGIT_MAX */ TEMP(0)->digits[j] = (mp_digit)qhat; /* D6: Add back Note: Not needed because we always check that qhat is the correct value before performing the subtract. */ /* D7: Loop on j */ r.digits--; ZERO(TEMP(1)->digits, TEMP(1)->alloc); } /* Get rid of leading zeros in q */ TEMP(0)->used = m + 1; CLAMP(TEMP(0)); /* Denormalize the remainder */ CLAMP(u); /* use u here because the r.digits pointer is off-by-one */ if (k != 0) s_qdiv(u, k); mp_int_copy(u, v); /* ok: 0 <= r < v */ mp_int_copy(TEMP(0), u); /* ok: q <= u */ CLEANUP_TEMP(); return MP_OK; } static int s_outlen(mp_int z, mp_size r) { assert(r >= MP_MIN_RADIX && r <= MP_MAX_RADIX); mp_result bits = mp_int_count_bits(z); double raw = (double)bits * s_log2[r]; return (int)(raw + 0.999999); } static mp_size s_inlen(int len, mp_size r) { double raw = (double)len / s_log2[r]; mp_size bits = (mp_size)(raw + 0.5); return (mp_size)((bits + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT) + 1; } static int s_ch2val(char c, int r) { int out; /* * In some locales, isalpha() accepts characters outside the range A-Z, * producing out<0 or out>=36. The "out >= r" check will always catch * out>=36. Though nothing explicitly catches out<0, our caller reacts the * same way to every negative return value. */ if (isdigit((unsigned char)c)) out = c - '0'; else if (r > 10 && isalpha((unsigned char)c)) out = toupper((unsigned char)c) - 'A' + 10; else return -1; return (out >= r) ? -1 : out; } static char s_val2ch(int v, int caps) { assert(v >= 0); if (v < 10) { return v + '0'; } else { char out = (v - 10) + 'a'; if (caps) { return toupper((unsigned char)out); } else { return out; } } } static void s_2comp(unsigned char* buf, int len) { unsigned short s = 1; for (int i = len - 1; i >= 0; --i) { unsigned char c = ~buf[i]; s = c + s; c = s & UCHAR_MAX; s >>= CHAR_BIT; buf[i] = c; } /* last carry out is ignored */ } static mp_result s_tobin(mp_int z, unsigned char* buf, int* limpos, int pad) { int pos = 0, limit = *limpos; mp_size uz = MP_USED(z); mp_digit* dz = MP_DIGITS(z); while (uz > 0 && pos < limit) { mp_digit d = *dz++; int i; for (i = sizeof(mp_digit); i > 0 && pos < limit; --i) { buf[pos++] = (unsigned char)d; d >>= CHAR_BIT; /* Don't write leading zeroes */ if (d == 0 && uz == 1) i = 0; /* exit loop without signaling truncation */ } /* Detect truncation (loop exited with pos >= limit) */ if (i > 0) break; --uz; } if (pad != 0 && (buf[pos - 1] >> (CHAR_BIT - 1))) { if (pos < limit) { buf[pos++] = 0; } else { uz = 1; } } /* Digits are in reverse order, fix that */ REV(buf, pos); /* Return the number of bytes actually written */ *limpos = pos; return (uz == 0) ? MP_OK : MP_TRUNC; } /* Here there be dragons */ ================================================ FILE: imath.h ================================================ /* Name: imath.h Purpose: Arbitrary precision integer arithmetic routines. Author: M. J. Fromberger Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. 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. */ #ifndef IMATH_H_ #define IMATH_H_ #include #include #include #ifdef __cplusplus extern "C" { #endif typedef unsigned char mp_sign; typedef unsigned int mp_size; typedef int mp_result; typedef long mp_small; /* must be a signed type */ typedef unsigned long mp_usmall; /* must be an unsigned type */ /* Build with words as uint64_t by default. */ #ifdef USE_32BIT_WORDS typedef uint16_t mp_digit; typedef uint32_t mp_word; # define MP_DIGIT_MAX (UINT16_MAX * 1UL) # define MP_WORD_MAX (UINT32_MAX * 1UL) #else typedef uint32_t mp_digit; typedef uint64_t mp_word; # define MP_DIGIT_MAX (UINT32_MAX * UINT64_C(1)) # define MP_WORD_MAX (UINT64_MAX) #endif typedef struct { mp_digit single; mp_digit* digits; mp_size alloc; mp_size used; mp_sign sign; } mpz_t, *mp_int; static inline mp_digit* MP_DIGITS(mp_int Z) { return Z->digits; } static inline mp_size MP_ALLOC(mp_int Z) { return Z->alloc; } static inline mp_size MP_USED(mp_int Z) { return Z->used; } static inline mp_sign MP_SIGN(mp_int Z) { return Z->sign; } extern const mp_result MP_OK; extern const mp_result MP_FALSE; extern const mp_result MP_TRUE; extern const mp_result MP_MEMORY; extern const mp_result MP_RANGE; extern const mp_result MP_UNDEF; extern const mp_result MP_TRUNC; extern const mp_result MP_BADARG; extern const mp_result MP_MINERR; #define MP_DIGIT_BIT (sizeof(mp_digit) * CHAR_BIT) #define MP_WORD_BIT (sizeof(mp_word) * CHAR_BIT) #define MP_SMALL_MIN LONG_MIN #define MP_SMALL_MAX LONG_MAX #define MP_USMALL_MAX ULONG_MAX #define MP_MIN_RADIX 2 #define MP_MAX_RADIX 36 /** Sets the default number of digits allocated to an `mp_int` constructed by `mp_int_init_size()` with `prec == 0`. Allocations are rounded up to multiples of this value. `MP_DEFAULT_PREC` is the default value. Requires `ndigits > 0`. */ void mp_int_default_precision(mp_size ndigits); /** Sets the number of digits below which multiplication will use the standard quadratic "schoolbook" multiplication algorithm rather than Karatsuba-Ofman. Requires `ndigits >= sizeof(mp_word)`. */ void mp_int_multiply_threshold(mp_size ndigits); /** A sign indicating a (strictly) negative value. */ extern const mp_sign MP_NEG; /** A sign indicating a zero or positive value. */ extern const mp_sign MP_ZPOS; /** Reports whether `z` is odd, having remainder 1 when divided by 2. */ static inline bool mp_int_is_odd(mp_int z) { return (z->digits[0] & 1) != 0; } /** Reports whether `z` is even, having remainder 0 when divided by 2. */ static inline bool mp_int_is_even(mp_int z) { return (z->digits[0] & 1) == 0; } /** Initializes `z` with 1-digit precision and sets it to zero. This function cannot fail unless `z == NULL`. */ mp_result mp_int_init(mp_int z); /** Allocates a fresh zero-valued `mpz_t` on the heap, returning NULL in case of error. The only possible error is out-of-memory. */ mp_int mp_int_alloc(void); /** Initializes `z` with at least `prec` digits of storage, and sets it to zero. If `prec` is zero, the default precision is used. In either case the size is rounded up to the nearest multiple of the word size. */ mp_result mp_int_init_size(mp_int z, mp_size prec); /** Initializes `z` to be a copy of an already-initialized value in `old`. The new copy does not share storage with the original. */ mp_result mp_int_init_copy(mp_int z, mp_int old); /** Initializes `z` to the specified signed `value` at default precision. */ mp_result mp_int_init_value(mp_int z, mp_small value); /** Initializes `z` to the specified unsigned `value` at default precision. */ mp_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue); /** Sets `z` to the value of the specified signed `value`. */ mp_result mp_int_set_value(mp_int z, mp_small value); /** Sets `z` to the value of the specified unsigned `value`. */ mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue); /** Releases the storage used by `z`. */ void mp_int_clear(mp_int z); /** Releases the storage used by `z` and also `z` itself. This should only be used for `z` allocated by `mp_int_alloc()`. */ void mp_int_free(mp_int z); /** Replaces the value of `c` with a copy of the value of `a`. No new memory is allocated unless `a` has more significant digits than `c` has allocated. */ mp_result mp_int_copy(mp_int a, mp_int c); /** Swaps the values and storage between `a` and `c`. */ void mp_int_swap(mp_int a, mp_int c); /** Sets `z` to zero. The allocated storage of `z` is not changed. */ void mp_int_zero(mp_int z); /** Sets `c` to the absolute value of `a`. */ mp_result mp_int_abs(mp_int a, mp_int c); /** Sets `c` to the additive inverse (negation) of `a`. */ mp_result mp_int_neg(mp_int a, mp_int c); /** Sets `c` to the sum of `a` and `b`. */ mp_result mp_int_add(mp_int a, mp_int b, mp_int c); /** Sets `c` to the sum of `a` and `value`. */ mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c); /** Sets `c` to the difference of `a` less `b`. */ mp_result mp_int_sub(mp_int a, mp_int b, mp_int c); /** Sets `c` to the difference of `a` less `value`. */ mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c); /** Sets `c` to the product of `a` and `b`. */ mp_result mp_int_mul(mp_int a, mp_int b, mp_int c); /** Sets `c` to the product of `a` and `value`. */ mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c); /** Sets `c` to the product of `a` and `2^p2`. Requires `p2 >= 0`. */ mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c); /** Sets `c` to the square of `a`. */ mp_result mp_int_sqr(mp_int a, mp_int c); /** Sets `q` and `r` to the quotient and remainder of `a / b`, so that the equation `a == b*q + r` is satisfied and `0 <= |r| < |b|`. Division by powers of 2 is detected and handled efficiently. Either of `q` or `r` may be NULL, but not both, and `q` and `r` may not point to the same value. */ mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r); /** Sets `q` and `*r` to the quotient and remainder of `a / value`. Division by powers of 2 is detected and handled efficiently. The remainder is pinned to `0 <= *r < b`. Either of `q` or `r` may be NULL. */ mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r); /** Sets `q` and `r` to the quotient and remainder of `a / 2^p2`. This is a special case for division by powers of two that is more efficient than using ordinary division. Note that `mp_int_div()` will automatically handle this case, this function is for cases where you have only the exponent. */ mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r); /** Sets `c` to the remainder of `a / m`. It returns `MP_UNDEF` if `m == 0`, or `MP_RANGE` if `m < 0` . Otherwise the remainder is pinned to `0 <= c < m`. */ mp_result mp_int_mod(mp_int a, mp_int m, mp_int c); /** Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE` if `b < 0`. */ mp_result mp_int_expt(mp_int a, mp_small b, mp_int c); /** Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE` if `b < 0`. */ mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c); /** Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE`) if `b < 0`. */ mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c); /** Sets `*r` to the remainder of `a / value`. The remainder is pinned to `0 <= r < value`. */ static inline mp_result mp_int_mod_value(mp_int a, mp_small value, mp_small* r) { return mp_int_div_value(a, value, 0, r); } /** Returns the comparator of `a` and `b`. */ int mp_int_compare(mp_int a, mp_int b); /** Returns the comparator of the magnitudes of `a` and `b`, disregarding their signs. Neither `a` nor `b` is modified by the comparison. */ int mp_int_compare_unsigned(mp_int a, mp_int b); /** Returns the comparator of `z` and zero. */ int mp_int_compare_zero(mp_int z); /** Returns the comparator of `z` and the signed value `v`. */ int mp_int_compare_value(mp_int z, mp_small v); /** Returns the comparator of `z` and the unsigned value `uv`. */ int mp_int_compare_uvalue(mp_int z, mp_usmall uv); /** Reports whether `a` is divisible by `v`. */ bool mp_int_divisible_value(mp_int a, mp_small v); /** Returns `k >= 0` such that `z` is `2^k`, if such a `k` exists. If no such `k` exists, the function returns -1. */ int mp_int_is_pow2(mp_int z); /** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`. It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */ mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c); /** Sets `c` to the value of `a` raised to the `value` power, modulo `m`. It returns `MP_RANGE` if `value < 0` or `MP_UNDEF` if `m == 0`. */ mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c); /** Sets `c` to the value of `value` raised to the `b` power, modulo `m`. It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */ mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c); /** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`, given a precomputed reduction constant `mu` defined for Barrett's modular reduction algorithm. It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */ mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c); /** Sets `c` to the reduction constant for Barrett reduction by modulus `m`. Requires that `c` and `m` point to distinct locations. */ mp_result mp_int_redux_const(mp_int m, mp_int c); /** Sets `c` to the multiplicative inverse of `a` modulo `m`, if it exists. The least non-negative representative of the congruence class is computed. It returns `MP_UNDEF` if the inverse does not exist, or `MP_RANGE` if `a == 0` or `m <= 0`. */ mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c); /** Sets `c` to the greatest common divisor of `a` and `b`. It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a` and `b` are both zero. */ mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); /** Sets `c` to the greatest common divisor of `a` and `b`, and sets `x` and `y` to values satisfying Bezout's identity `gcd(a, b) = ax + by`. It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a` and `b` are both zero. */ mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, mp_int x, mp_int y); /** Sets `c` to the least common multiple of `a` and `b`. It returns `MP_UNDEF` if the LCM is undefined, such as for example if `a` and `b` are both zero. */ mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c); /** Sets `c` to the greatest integer not less than the `b`th root of `a`, using Newton's root-finding algorithm. It returns `MP_UNDEF` if `a < 0` and `b` is even. */ mp_result mp_int_root(mp_int a, mp_small b, mp_int c); /** Sets `c` to the greatest integer not less than the square root of `a`. This is a special case of `mp_int_root()`. */ static inline mp_result mp_int_sqrt(mp_int a, mp_int c) { return mp_int_root(a, 2, c); } /** Returns `MP_OK` if `z` is representable as `mp_small`, else `MP_RANGE`. If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */ mp_result mp_int_to_int(mp_int z, mp_small *out); /** Returns `MP_OK` if `z` is representable as `mp_usmall`, or `MP_RANGE`. If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */ mp_result mp_int_to_uint(mp_int z, mp_usmall *out); /** Converts `z` to a zero-terminated string of characters in the specified `radix`, writing at most `limit` characters to `str` including the terminating NUL value. A leading `-` is used to indicate a negative value. Returns `MP_TRUNC` if `limit` was to small to write all of `z`. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ mp_result mp_int_to_string(mp_int z, mp_size radix, char *str, int limit); /** Reports the minimum number of characters required to represent `z` as a zero-terminated string in the given `radix`. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ mp_size mp_int_string_len(mp_int z, mp_size radix); /** Reads a string of ASCII digits in the specified `radix` from the zero terminated `str` provided into `z`. For values of `radix > 10`, the letters `A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect to case. Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a sign flag. Processing stops when a NUL or any other character out of range for a digit in the given radix is encountered. If the whole string was consumed, `MP_OK` is returned; otherwise `MP_TRUNC`. is returned. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str); /** Reads a string of ASCII digits in the specified `radix` from the zero terminated `str` provided into `z`. For values of `radix > 10`, the letters `A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect to case. Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a sign flag. Processing stops when a NUL or any other character out of range for a digit in the given radix is encountered. If the whole string was consumed, `MP_OK` is returned; otherwise `MP_TRUNC`. is returned. If `end` is not NULL, `*end` is set to point to the first unconsumed byte of the input string (the NUL byte if the whole string was consumed). This emulates the behavior of the standard C `strtol()` function. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end); /** Returns the number of significant bits in `z`. */ mp_size mp_int_count_bits(mp_int z); /** Converts `z` to 2's complement binary, writing at most `limit` bytes into the given `buf`. Returns `MP_TRUNC` if the buffer limit was too small to contain the whole value. If this occurs, the contents of buf will be effectively garbage, as the function uses the buffer as scratch space. The binary representation of `z` is in base-256 with digits ordered from most significant to least significant (network byte ordering). The high-order bit of the first byte is set for negative values, clear for non-negative values. As a result, non-negative values will be padded with a leading zero byte if the high-order byte of the base-256 magnitude is set. This extra byte is accounted for by the `mp_int_binary_len()` function. */ mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit); /** Reads a 2's complement binary value from `buf` into `z`, where `len` is the length of the buffer. The contents of `buf` may be overwritten during processing, although they will be restored when the function returns. */ mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len); /** Returns the number of bytes to represent `z` in 2's complement binary. */ mp_size mp_int_binary_len(mp_int z); /** Converts the magnitude of `z` to unsigned binary, writing at most `limit` bytes into the given `buf`. The sign of `z` is ignored, but `z` is not modified. Returns `MP_TRUNC` if the buffer limit was too small to contain the whole value. If this occurs, the contents of `buf` will be effectively garbage, as the function uses the buffer as scratch space during conversion. The binary representation of `z` is in base-256 with digits ordered from most significant to least significant (network byte ordering). */ mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit); /** Reads an unsigned binary value from `buf` into `z`, where `len` is the length of the buffer. The contents of `buf` are not modified during processing. */ mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len); /** Returns the number of bytes required to represent `z` as an unsigned binary value in base 256. */ mp_size mp_int_unsigned_len(mp_int z); /** Returns a pointer to a brief, human-readable, zero-terminated string describing `res`. The returned string is statically allocated and must not be freed by the caller. */ const char *mp_error_string(mp_result res); #ifdef __cplusplus } #endif #endif /* end IMATH_H_ */ ================================================ FILE: imdrover.c ================================================ /* Name: imdrover.c Purpose: Keeper of the hordes of testing code. Author: M. J. Fromberger Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. 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. */ #include "imdrover.h" #include #include #include #include #include "imath.h" #include "imrat.h" #include "iprime.h" /* Globals visible from outside this file */ mp_result imath_errno; char* imath_errmsg; /* Set imath_errno and return failure from a test. */ #define FAIL(E) return (imath_errno = (E), false) /* Check that an expression X yields the expected mp_result value V. */ #define VCHECK(X, V) \ do { \ mp_result res_; \ if ((res_ = (X)) != (V)) { \ FAIL(res_); \ } \ } while (0) #define CHECK(X) VCHECK(X, MP_OK) #define ECHECK(X) VCHECK(X, expect) #define ACHECK(X) \ do { \ if (!(X)) { \ FAIL(MP_BADARG); \ } \ } while (0) #define OUTPUT_LIMIT 2048 #define NUM_REGS 16 #define OTHER_ERROR -1024 static char g_output[OUTPUT_LIMIT]; static mpz_t g_zreg[NUM_REGS]; static mpq_t g_qreg[NUM_REGS]; static unsigned char g_bin1[OUTPUT_LIMIT]; static unsigned char g_bin2[OUTPUT_LIMIT]; extern void trim_line(char* line); /* borrowed from imtest.c */ /* Read in a string with radix tags */ static mp_result read_int_value(mp_int z, char* str); static mp_result read_rat_value(mp_rat q, char* str); /* Read in a string with radix tags, as a long (not an mp_int) */ static bool read_long(long* z, char* str); /* Parse the input and output values and fill in pointers to the registers containing them. Returns true if all is well, false in case of error. Caller allocates in/out to correct sizes. */ static bool parse_int_values(testspec_t* t, mp_int* in, mp_int* out, mp_result* rval); static bool parse_rat_values(testspec_t* t, mp_rat* in, mp_rat* out, mp_result* rval); /* Parse a result code name and return the corresponding result code */ static bool parse_result_code(char* str, mp_result* code); /* Read in a dot-delimited binary sequence to the given buffer, and return the number of bytes read. Returns < 0 in case of a syntax error. Records no more than limit bytes. */ static int parse_binary(char* str, unsigned char* buf, int limit); /* Clean up registers (called from atexit()) */ static void done_testing(void); /* * Utility subroutines for writing tests (explained above) */ static mp_result read_int_value(mp_int z, char* str) { int radix = 10; if (*str == '#') { ++str; switch (*str) { case 'x': case 'X': radix = 16; break; case 'd': case 'D': radix = 10; break; case 'o': case 'O': radix = 8; break; case 'b': case 'B': radix = 2; break; default: return MP_RANGE; } ++str; } return mp_int_read_string(z, radix, str); } static mp_result read_rat_value(mp_rat q, char* str) { int radix = 10; if (*str == '#') { ++str; switch (*str) { case 'x': case 'X': radix = 16; break; case 'd': case 'D': radix = 10; break; case 'o': case 'O': radix = 8; break; case 'b': case 'B': radix = 2; break; default: return MP_RANGE; } ++str; } if (*str == '@') return mp_rat_read_decimal(q, radix, str + 1); else return mp_rat_read_string(q, radix, str); } static bool read_long(long* z, char* str) { char* end; int radix = 10; if (*str == '#') { ++str; switch (*str) { case 'x': case 'X': radix = 16; break; case 'd': case 'D': radix = 10; break; case 'o': case 'O': radix = 8; break; case 'b': case 'B': radix = 2; break; default: return false; } ++str; } *z = strtol(str, &end, radix); return (end != str && *end == '\0'); } static bool parse_int_values(testspec_t* t, mp_int* in, mp_int* out, mp_result* rval) { int pos = 0; char* str; if (rval != NULL) *rval = MP_OK; /* default */ if (in != NULL) { for (int i = 0; i < t->num_inputs; ++i) { str = t->input[i]; trim_line(str); if (strcmp(str, "NULL") == 0) { in[i] = NULL; continue; } else if (*str == '=') { int k = abs(atoi(str + 1)) - 1; if (k < 0 || k >= i) { fprintf(stderr, "Line %d: Invalid input back-reference [%s]\n", t->line, str); return false; } in[i] = in[k]; } else { mp_int reg = g_zreg + pos++; /* grab next free register */ if (read_int_value(reg, str) != MP_OK) { fprintf(stderr, "Line %d: Invalid input value [%s]\n", t->line, str); return false; } in[i] = reg; } } } for (int i = 0; i < t->num_outputs; ++i) { mp_int reg = g_zreg + pos++; str = t->output[i]; trim_line(str); if (strcmp(str, "?") == 0) { mp_int_zero(reg); } else if (strcmp(str, "NULL") == 0) { if (out != NULL) out[i] = NULL; continue; } else if (*str == '$') { mp_result code; if (!parse_result_code(str, &code)) { fprintf(stderr, "Line %d: Invalid result code [%s]\n", t->line, str); return false; } else if (rval == NULL) { fprintf(stderr, "Line %d: Result code not permitted here [%s]\n", t->line, str); return false; } else { *rval = code; } /* Provide a dummy value for the corresponding output */ mp_int_zero(reg); } else if (out != NULL && read_int_value(reg, str) != MP_OK) { fprintf(stderr, "Line %d: Invalid output value [%s]\n", t->line, str); return false; } if (out != NULL) out[i] = reg; } return true; } static bool parse_rat_values(testspec_t* t, mp_rat* in, mp_rat* out, mp_result* rval) { int pos = 0; char* str; if (rval != NULL) *rval = MP_OK; /* default */ if (in != NULL) { for (int i = 0; i < t->num_inputs; ++i) { str = t->input[i]; trim_line(str); if (strcmp(str, "NULL") == 0) { in[i] = NULL; continue; } else if (*str == '=') { int k = abs(atoi(str + 1)) - 1; if (k < 0 || k >= i) { fprintf(stderr, "Line %d: Invalid input back-reference [%s]\n", t->line, str); return false; } in[i] = in[k]; } else { mp_rat reg = g_qreg + pos++; /* grab next free register */ if (read_rat_value(reg, str) != MP_OK) { fprintf(stderr, "Line %d: Invalid input value [%s]\n", t->line, str); return false; } in[i] = reg; } } } for (int i = 0; i < t->num_outputs; ++i) { mp_rat reg = g_qreg + pos++; str = t->output[i]; trim_line(str); if (strcmp(str, "?") == 0) { mp_rat_zero(reg); } else if (strcmp(str, "NULL") == 0) { if (out != NULL) out[i] = NULL; continue; } else if (*str == '$') { mp_result code; if (!parse_result_code(str, &code)) { fprintf(stderr, "Line %d: Invalid result code [%s]\n", t->line, str); return false; } else if (rval == NULL) { fprintf(stderr, "Line %d: Result code not permitted here [%s]\n", t->line, str); return false; } else { *rval = code; } /* Provide a dummy value for the corresponding output */ mp_rat_zero(reg); } else if (out != NULL && read_rat_value(reg, str) != MP_OK) { fprintf(stderr, "Line %d: Invalid output value [%s]\n", t->line, str); return false; } if (out != NULL) out[i] = reg; } return true; } static bool parse_result_code(char* str, mp_result* code) { if (str[0] == '$') { if (str[1] == '#') { long v; if (!read_long(&v, str + 2)) return false; *code = (mp_result)v; } else if (strcmp(str + 1, "MP_OK") == 0 || strcmp(str + 1, "MP_FALSE") == 0) { *code = MP_OK; } else if (strcmp(str + 1, "MP_TRUE") == 0) { *code = MP_TRUE; } else if (strcmp(str + 1, "MP_MEMORY") == 0) { *code = MP_MEMORY; } else if (strcmp(str + 1, "MP_RANGE") == 0) { *code = MP_RANGE; } else if (strcmp(str + 1, "MP_UNDEF") == 0) { *code = MP_UNDEF; } else if (strcmp(str + 1, "MP_TRUNC") == 0) { *code = MP_TRUNC; } else if (strcmp(str + 1, "MP_BADARG") == 0) { *code = MP_BADARG; } else if (strcmp(str + 1, "MP_ROUND_UP") == 0) { *code = MP_ROUND_UP; } else if (strcmp(str + 1, "MP_ROUND_DOWN") == 0) { *code = MP_ROUND_DOWN; } else if (strcmp(str + 1, "MP_ROUND_HALF_UP") == 0) { *code = MP_ROUND_HALF_UP; } else if (strcmp(str + 1, "MP_ROUND_HALF_DOWN") == 0) { *code = MP_ROUND_HALF_DOWN; } else { return false; } } return true; } static int parse_binary(char* str, unsigned char* buf, int limit) { int pos = 0; char* tok; trim_line(str); for (tok = strtok(str, "."); tok != NULL && pos < limit; tok = strtok(NULL, ".")) { long v; if (!read_long(&v, tok) || v > UCHAR_MAX || v < 0) return -1; buf[pos++] = (unsigned char)v; } return pos; } static void done_testing(void) { int i; for (i = 0; i < NUM_REGS; ++i) { mp_int_clear(g_zreg + i); mp_rat_clear(g_qreg + i); } } /* * Global functions visible to callers outside this file. */ void init_testing(void) { static int is_done = 0; if (is_done) return; for (int i = 0; i < NUM_REGS; ++i) { assert(mp_int_init(g_zreg + i) == MP_OK); assert(mp_rat_init(g_qreg + i) == MP_OK); } imath_errmsg = g_output; assert(atexit(done_testing) == 0); is_done = 1; } void reset_registers(void) { for (int i = 0; i < NUM_REGS; ++i) { mp_int_zero(g_zreg + i); mp_rat_zero(g_qreg + i); } } bool test_init(testspec_t* t, FILE* ofp) { mp_int in[2], out[1]; mp_small v; mp_usmall uv; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); if (strcmp(t->code, "initu") == 0) { CHECK(mp_int_to_uint(in[1], &uv)); ECHECK(mp_int_init_uvalue(in[0], uv)); } else { /* initv */ CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_init_value(in[0], v)); } if (expect == MP_OK && mp_int_compare(in[0], out[0]) != 0) { mp_int_to_string(in[0], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_set(testspec_t* t, FILE* ofp) { mp_int in[2], out[1]; mp_small v; mp_usmall uv; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); if (strcmp(t->code, "setu") == 0) { CHECK(mp_int_to_uint(in[1], &uv)); ECHECK(mp_int_set_uvalue(in[0], uv)); } else { /* setv */ CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_set_value(in[0], v)); } if (expect == MP_OK && mp_int_compare(in[0], out[0]) != 0) { mp_int_to_string(in[0], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_neg(testspec_t* t, FILE* ofp) { mp_int in[2], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_neg(in[0], in[1])); if (expect == MP_OK && mp_int_compare(in[1], out[0]) != 0) { mp_int_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_abs(testspec_t* t, FILE* ofp) { mp_int in[2], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_abs(in[0], in[1])); if (expect == MP_OK && mp_int_compare(in[1], out[0]) != 0) { mp_int_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_add(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_small v; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); if (strcmp(t->code, "addv") == 0) { CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_add_value(in[0], v, in[2])); } else { ECHECK(mp_int_add(in[0], in[1], in[2])); } if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_sub(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_small v; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); if (strcmp(t->code, "subv") == 0) { CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_sub_value(in[0], v, in[2])); } else { ECHECK(mp_int_sub(in[0], in[1], in[2])); } if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_mul(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_mul(in[0], in[1], in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_mulp2(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; mp_small p2; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &p2)); ECHECK(mp_int_mul_pow2(in[0], p2, in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_mulv(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; mp_small v; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_mul_value(in[0], v, in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_sqr(testspec_t* t, FILE* ofp) { mp_int in[2], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_sqr(in[0], in[1])); if (expect == MP_OK && mp_int_compare(in[1], out[0]) != 0) { mp_int_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_div(testspec_t* t, FILE* ofp) { mp_int in[4], out[2]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_div(in[0], in[1], in[2], in[3])); if (expect == MP_OK && ((mp_int_compare(in[2], out[0]) != 0) || (mp_int_compare(in[3], out[1]) != 0))) { int len; char* str; mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); str = g_output + (len = strlen(g_output)); *str++ = ','; mp_int_to_string(in[3], 10, str, OUTPUT_LIMIT - (len + 1)); FAIL(OTHER_ERROR); } return true; } bool test_divp2(testspec_t* t, FILE* ofp) { mp_int in[4], out[2]; mp_result expect; mp_small p2; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &p2)); ECHECK(mp_int_div_pow2(in[0], p2, in[2], in[3])); if (expect == MP_OK && ((mp_int_compare(in[2], out[0]) != 0) || (mp_int_compare(in[3], out[1]) != 0))) { int len; char* str; mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); str = g_output + (len = strlen(g_output)); *str++ = ','; mp_int_to_string(in[3], 10, str, OUTPUT_LIMIT - (len + 1)); FAIL(OTHER_ERROR); } return true; } bool test_divv(testspec_t* t, FILE* ofp) { mp_int in[3], out[2]; mp_result expect; mp_small v, rem, orem; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &v)); CHECK(mp_int_to_int(out[1], &orem)); ECHECK(mp_int_div_value(in[0], v, in[2], &rem)); if (expect == MP_OK && ((mp_int_compare(in[2], out[0]) != 0) || (rem != orem))) { char* str; mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); str = g_output + strlen(g_output); *str++ = ','; sprintf(str, "%ld", rem); FAIL(OTHER_ERROR); } return true; } bool test_expt(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; mp_small pow; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &pow)); ECHECK(mp_int_expt(in[0], pow, in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_exptv(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; mp_small a, b; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[0], &a)); CHECK(mp_int_to_int(in[1], &b)); ECHECK(mp_int_expt_value(a, b, in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_exptf(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_expt_full(in[0], in[1], in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_mod(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_mod(in[0], in[1], in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_gcd(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_gcd(in[0], in[1], in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_egcd(testspec_t* t, FILE* ofp) { mp_int in[5], out[3], t1 = g_zreg + 8, t2 = g_zreg + 9; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_egcd(in[0], in[1], in[2], in[3], in[4])); /* If we got an error we expected, return success immediately */ if (expect != MP_OK) return true; if ((mp_int_compare(in[2], out[0]) != 0) || (mp_int_compare(in[3], out[1]) != 0) || (mp_int_compare(in[4], out[2]) != 0)) { int len, len2; char* str; /* Failure might occur because the tester computed x and y in a different way than we did. Verify that the results are correct before reporting an error. */ mp_int_mul(in[3], in[0], t1); mp_int_mul(in[4], in[1], t2); mp_int_add(t1, t2, t2); if (mp_int_compare(t2, in[2]) == 0) return true; mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); str = g_output + (len = strlen(g_output)); *str++ = ','; mp_int_to_string(in[3], 10, str, OUTPUT_LIMIT - (len + 1)); str = str + (len2 = strlen(str)); *str++ = ','; mp_int_to_string(in[4], 10, str, OUTPUT_LIMIT - (len + len2 + 2)); FAIL(OTHER_ERROR); } return true; } bool test_lcm(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_lcm(in[0], in[1], in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_sqrt(testspec_t* t, FILE* ofp) { mp_int in[2], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_sqrt(in[0], in[1])); if (expect == MP_OK && mp_int_compare(in[1], out[0]) != 0) { mp_int_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_root(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_small v; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_root(in[0], v, in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_invmod(testspec_t* t, FILE* ofp) { mp_int in[3], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_invmod(in[0], in[1], in[2])); if (expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) { mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_exptmod(testspec_t* t, FILE* ofp) { mp_int in[4], out[1]; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_exptmod(in[0], in[1], in[2], in[3])); if (expect == MP_OK && mp_int_compare(in[3], out[0]) != 0) { mp_int_to_string(in[3], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_exptmod_ev(testspec_t* t, FILE* ofp) { mp_int in[4], out[1]; mp_result expect; mp_small v; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[1], &v)); ECHECK(mp_int_exptmod_evalue(in[0], v, in[2], in[3])); if (expect == MP_OK && mp_int_compare(in[3], out[0]) != 0) { mp_int_to_string(in[3], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_exptmod_bv(testspec_t* t, FILE* ofp) { mp_int in[4], out[1]; mp_result expect; mp_small v; ACHECK(parse_int_values(t, in, out, &expect)); CHECK(mp_int_to_int(in[0], &v)); ECHECK(mp_int_exptmod_bvalue(v, in[1], in[2], in[3])); if (expect == MP_OK && mp_int_compare(in[3], out[0]) != 0) { mp_int_to_string(in[3], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_comp(testspec_t* t, FILE* ofp) { mp_int in[2]; mp_result res, expect; ACHECK(parse_int_values(t, in, NULL, &expect)); if ((res = mp_int_compare(in[0], in[1])) != expect) { sprintf(g_output, "Incorrect comparison result (want %d, got %d)", expect, res); FAIL(OTHER_ERROR); } return true; } bool test_ucomp(testspec_t* t, FILE* ofp) { mp_int in[2]; mp_result res, expect; ACHECK(parse_int_values(t, in, NULL, &expect)); if ((res = mp_int_compare_unsigned(in[0], in[1])) != expect) { sprintf(g_output, "Incorrect comparison result (want %d, got %d)", expect, res); FAIL(OTHER_ERROR); } return true; } bool test_zcomp(testspec_t* t, FILE* ofp) { mp_int in[1]; mp_result res, expect; ACHECK(parse_int_values(t, in, NULL, &expect)); if ((res = mp_int_compare_zero(in[0])) != expect) { sprintf(g_output, "Incorrect comparison result (want %d, got %d)", expect, res); FAIL(OTHER_ERROR); } return true; } bool test_vcomp(testspec_t* t, FILE* ofp) { mp_int in[2]; mp_result res, expect; mp_small v; ACHECK(parse_int_values(t, in, NULL, &expect)); v = atoi(t->input[1]); if ((res = mp_int_compare_value(in[0], v)) != expect) { sprintf(g_output, "Incorrect comparison result (want %d, got %d)", expect, res); FAIL(OTHER_ERROR); } return true; } bool test_uvcomp(testspec_t* t, FILE* ofp) { mp_int in[2]; mp_result res, expect; mp_usmall v; ACHECK(parse_int_values(t, in, NULL, &expect)); v = strtoul(t->input[1], NULL, 0); if ((res = mp_int_compare_uvalue(in[0], v)) != expect) { sprintf(g_output, "Incorrect comparison result (want %d, got %d)", expect, res); FAIL(OTHER_ERROR); } return true; } bool test_tostr(testspec_t* t, FILE* ofp) { mp_int in[2]; mp_small radix; mp_result len; ACHECK(parse_int_values(t, in, NULL, NULL)); ACHECK(mp_int_to_int(in[1], &radix) == MP_OK); if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX) FAIL(MP_RANGE); trim_line(t->output[0]); len = mp_int_string_len(in[0], radix); CHECK(mp_int_to_string(in[0], radix, g_output, len)); if (strcmp(t->output[0], g_output) != 0) FAIL(OTHER_ERROR); return true; } bool test_tobin(testspec_t* t, FILE* ofp) { mp_int in[1]; int test_len, out_len; ACHECK(parse_int_values(t, in, NULL, NULL)); trim_line(t->output[0]); if ((out_len = parse_binary(t->output[0], g_bin1, sizeof(g_bin1))) < 0) FAIL(MP_BADARG); if ((test_len = mp_int_binary_len(in[0])) != out_len) { sprintf(g_output, "Output lengths do not match (want %d, got %d)", test_len, out_len); FAIL(OTHER_ERROR); } CHECK(mp_int_to_binary(in[0], g_bin2, sizeof(g_bin2))); if (memcmp(g_bin1, g_bin2, test_len) != 0) { int pos = 0, i; for (i = 0; i < test_len - 1; ++i) pos += sprintf(g_output + pos, "%d.", g_bin2[i]); sprintf(g_output + pos, "%d", g_bin2[i]); FAIL(OTHER_ERROR); } return true; } bool test_to_int(testspec_t* t, FILE* ofp) { mp_int in[1], out[1]; mp_small v; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_to_int(in[0], &v)); if (expect == MP_OK && mp_int_compare_value(out[0], v) != 0) { sprintf(g_output, "Incorrect value (got %ld)", v); FAIL(OTHER_ERROR); } return true; } bool test_to_uint(testspec_t* t, FILE* ofp) { mp_int in[1], out[1]; mp_usmall v; mp_result expect; ACHECK(parse_int_values(t, in, out, &expect)); ECHECK(mp_int_to_uint(in[0], &v)); if (expect == MP_OK && mp_int_compare_uvalue(out[0], v) != 0) { sprintf(g_output, "Incorrect value (got %lu)", v); FAIL(OTHER_ERROR); } return true; } bool test_read_binary(testspec_t* t, FILE* ofp) { mp_int out[1], in = g_zreg + 1; int in_len; mp_result expect; ACHECK(parse_int_values(t, NULL, out, &expect)); trim_line(t->input[0]); if ((in_len = parse_binary(t->input[0], g_bin1, sizeof(g_bin1))) < 0) FAIL(MP_BADARG); ECHECK(mp_int_read_binary(in, g_bin1, in_len)); if (expect == MP_OK && mp_int_compare(in, out[0]) != 0) { mp_int_to_string(in, 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_to_uns(testspec_t* t, FILE* ofp) { mp_int in[1]; int test_len, out_len; ACHECK(parse_int_values(t, in, NULL, NULL)); trim_line(t->output[0]); if ((out_len = parse_binary(t->output[0], g_bin1, sizeof(g_bin1))) < 0) FAIL(MP_BADARG); if ((test_len = mp_int_unsigned_len(in[0])) != out_len) { sprintf(g_output, "Output lengths do not match (want %d, got %d)", test_len, out_len); FAIL(OTHER_ERROR); } CHECK(mp_int_to_unsigned(in[0], g_bin2, sizeof(g_bin2))); if (memcmp(g_bin1, g_bin2, test_len) != 0) { int pos = 0, i; for (i = 0; i < test_len - 1; ++i) pos += sprintf(g_output + pos, "%d.", g_bin2[i]); sprintf(g_output + pos, "%d", g_bin2[i]); FAIL(OTHER_ERROR); } return true; } bool test_read_uns(testspec_t* t, FILE* ofp) { mp_int out[1], in = g_zreg + 1; int in_len; mp_result expect; ACHECK(parse_int_values(t, NULL, out, &expect)); trim_line(t->input[0]); if ((in_len = parse_binary(t->input[0], g_bin1, sizeof(g_bin1))) < 0) FAIL(MP_BADARG); ECHECK(mp_int_read_unsigned(in, g_bin1, in_len)); if (expect == MP_OK && mp_int_compare(in, out[0]) != 0) { mp_int_to_string(in, 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_meta(testspec_t* t, FILE* ofp) { mp_int *in = NULL, *out = NULL; int i, j; mp_result expect; if (t->num_inputs > 0) { in = calloc(t->num_inputs, sizeof(mp_int)); } if (t->num_outputs > 0) { out = calloc(t->num_outputs, sizeof(mp_int)); } if (!parse_int_values(t, in, out, &expect)) { if (in != NULL) free(in); if (out != NULL) free(out); FAIL(MP_BADARG); } fprintf(ofp, "Test '%s' defined at line %d\n", t->code, t->line); fprintf(ofp, "Expected result: %d\n", expect); fprintf(ofp, "Input values: %d\n", t->num_inputs); for (i = 0; i < t->num_inputs; ++i) { mp_int_to_string(in[i], 10, g_output, OUTPUT_LIMIT); fprintf(ofp, " %2d.) %s", i + 1, g_output); for (j = i - 1; j >= 0; --j) if (in[j] == in[i]) { fprintf(ofp, " (=> %d)", j + 1); break; } fputc('\n', ofp); } fprintf(ofp, "Output values: %d\n", t->num_outputs); for (i = 0; i < t->num_outputs; ++i) { mp_int_to_string(out[i], 10, g_output, OUTPUT_LIMIT); fprintf(ofp, " %2d.) %s\n", i + 1, g_output); } if (in != NULL) free(in); if (out != NULL) free(out); return true; } bool test_qset(testspec_t* t, FILE* ofp) { mp_int in[2]; mp_rat out[1]; mp_result expect; mpq_t tmp; mp_rat_init(&tmp); ACHECK(parse_rat_values(t, NULL, out, &expect)); ACHECK(parse_int_values(t, in, NULL, &expect)); ECHECK(mp_rat_set(&tmp, in[0], in[1])); if (expect == MP_OK && mp_rat_compare(&tmp, out[0]) != 0) { mp_rat_to_string(&tmp, 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qneg(testspec_t* t, FILE* ofp) { mp_rat in[2], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_neg(in[0], in[1])); if (expect == MP_OK && mp_rat_compare(in[1], out[0]) != 0) { mp_rat_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qrecip(testspec_t* t, FILE* ofp) { mp_rat in[2], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_recip(in[0], in[1])); if (expect == MP_OK && mp_rat_compare(in[1], out[0]) != 0) { mp_rat_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qabs(testspec_t* t, FILE* ofp) { mp_rat in[2], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_abs(in[0], in[1])); if (expect == MP_OK && mp_rat_compare(in[1], out[0]) != 0) { mp_rat_to_string(in[1], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qadd(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_add(in[0], in[1], in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qsub(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_sub(in[0], in[1], in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qmul(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_mul(in[0], in[1], in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qdiv(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); ECHECK(mp_rat_div(in[0], in[1], in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qaddz(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); if (!mp_rat_is_integer(in[1])) { fprintf(stderr, "Line %d: Second argument must be an integer (test_qaddz)\n", t->line); FAIL(MP_BADARG); } ECHECK(mp_rat_add_int(in[0], MP_NUMER_P(in[1]), in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qsubz(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); if (!mp_rat_is_integer(in[1])) { fprintf(stderr, "Line %d: Second argument must be an integer (test_qsubz)\n", t->line); FAIL(MP_BADARG); } ECHECK(mp_rat_sub_int(in[0], MP_NUMER_P(in[1]), in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qmulz(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); if (!mp_rat_is_integer(in[1])) { fprintf(stderr, "Line %d: Second argument must be an integer (test_qmulz)\n", t->line); FAIL(MP_BADARG); } ECHECK(mp_rat_mul_int(in[0], MP_NUMER_P(in[1]), in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qdivz(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); if (!mp_rat_is_integer(in[1])) { fprintf(stderr, "Line %d: Second argument must be an integer (test_qdivz)\n", t->line); FAIL(MP_BADARG); } ECHECK(mp_rat_div_int(in[0], MP_NUMER_P(in[1]), in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qexpt(testspec_t* t, FILE* ofp) { mp_rat in[3], out[1]; mp_result expect; mp_small power; ACHECK(parse_rat_values(t, in, out, &expect)); if (!mp_rat_is_integer(in[1])) { fprintf(stderr, "Line %d: Second argument must be an integer (test_qexpt)\n", t->line); FAIL(MP_BADARG); } CHECK(mp_int_to_int(MP_NUMER_P(in[1]), &power)); ECHECK(mp_rat_expt(in[0], power, in[2])); if (expect == MP_OK && mp_rat_compare(in[2], out[0]) != 0) { mp_rat_to_string(in[2], 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qtostr(testspec_t* t, FILE* ofp) { mp_rat in[2]; long radix; mp_result len; ACHECK(parse_rat_values(t, in, NULL, NULL)); trim_line(t->input[1]); ACHECK(read_long(&radix, t->input[1])); if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX) { fprintf(stderr, "Line %d: Radix %ld out of range\n", t->line, radix); FAIL(MP_RANGE); } trim_line(t->output[0]); len = mp_rat_string_len(in[0], radix); CHECK(mp_rat_to_string(in[0], radix, g_output, len)); if (strcmp(t->output[0], g_output) != 0) FAIL(OTHER_ERROR); return true; } bool test_qtodec(testspec_t* t, FILE* ofp) { mp_rat in[4]; long radix, prec, m; mp_round_mode rmode; mp_result res, expect = MP_OK, len; ACHECK(parse_rat_values(t, in, NULL, NULL)); if (t->output[0][0] == '$' && !parse_result_code(t->output[0], &expect)) { fprintf(stderr, "Line %d: Invalid result code [%s]\n", t->line, t->output[0]); FAIL(OTHER_ERROR); } trim_line(t->input[1]); trim_line(t->input[2]); trim_line(t->input[3]); ACHECK(read_long(&radix, t->input[1])); ACHECK(read_long(&prec, t->input[2])); ACHECK(read_long(&m, t->input[3])); rmode = (mp_round_mode)m; if (prec < 0) { fprintf(stderr, "Line %d: Precision %ld out of range\n", t->line, prec); FAIL(MP_RANGE); } trim_line(t->output[0]); len = mp_rat_decimal_len(in[0], radix, prec); ECHECK((res = mp_rat_to_decimal(in[0], radix, prec, rmode, g_output, len))); if (res == MP_OK && strcmp(t->output[0], g_output) != 0) FAIL(OTHER_ERROR); return true; } bool test_qrdec(testspec_t* t, FILE* ofp) { mp_rat out[1] = {NULL}, reg = g_qreg + 1; long radix; mp_result expect; ACHECK(parse_rat_values(t, NULL, out, &expect)); trim_line(t->input[1]); ACHECK(read_long(&radix, t->input[1])); ECHECK(mp_rat_read_decimal(reg, radix, t->input[0])); if (expect == MP_OK && mp_rat_compare(reg, out[0]) != 0) { mp_rat_to_string(reg, 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } return true; } bool test_qdecompose(testspec_t* t, FILE* ofp) { mp_rat in[3]; // N.B. offset 1 has to be an int, though. mp_rat out[2]; // N.B. offset 0 has to be an int, though. mp_int ipart = NULL; mp_rat fpart = NULL; mp_result expect; ACHECK(parse_rat_values(t, in, out, &expect)); if (in[1] != NULL) { if (!mp_rat_is_integer(in[1])) { fprintf(stderr, "Line %d: argument 2 is not an integer [%s]\n", t->line, t->input[1]); return false; } ipart = MP_NUMER_P(in[1]); } if (in[2] != NULL) { fpart = in[2]; } if (!mp_rat_is_integer(out[0])) { fprintf(stderr, "Line %d: output 2 is not an integer [%s]\n", t->line, t->output[0]); return false; } ECHECK(mp_rat_decompose(in[0], ipart, fpart)); if (expect == MP_OK) { if (ipart != NULL && mp_int_compare(ipart, MP_NUMER_P(out[0])) != 0) { mp_int_to_string(ipart, 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } if (fpart != NULL && mp_rat_compare(fpart, out[1]) != 0) { mp_rat_to_string(fpart, 10, g_output, OUTPUT_LIMIT); FAIL(OTHER_ERROR); } } return true; } bool test_is_prime(testspec_t* t, FILE* OFP) { mp_int in[1] = {NULL}; mp_result expect; ACHECK(parse_int_values(t, in, NULL, &expect)); ECHECK(mp_int_is_prime(in[0])); return true; } /* Here there be dragons */ ================================================ FILE: imdrover.h ================================================ /* Name: imdrover.h Purpose: Keeper of the hordes of testing code. Author: M. J. Fromberger Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. 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. */ #ifndef IMDROVER_H_ #define IMDROVER_H_ #include #include typedef struct { int line; char *file; char *code; int num_inputs; char **input; int num_outputs; char **output; } testspec_t; typedef bool (*test_f)(testspec_t *, FILE *); /* Call this once at the outset to set up test registers */ void init_testing(void); void reset_registers(void); /* Integer tests, and general */ bool test_init(testspec_t* t, FILE* ofp); bool test_set(testspec_t* t, FILE* ofp); bool test_neg(testspec_t* t, FILE* ofp); bool test_abs(testspec_t* t, FILE* ofp); bool test_add(testspec_t* t, FILE* ofp); bool test_sub(testspec_t* t, FILE* ofp); bool test_mul(testspec_t* t, FILE* ofp); bool test_mulp2(testspec_t* t, FILE* ofp); bool test_mulv(testspec_t* t, FILE* ofp); bool test_sqr(testspec_t* t, FILE* ofp); bool test_div(testspec_t* t, FILE* ofp); bool test_divp2(testspec_t* t, FILE* ofp); bool test_divv(testspec_t* t, FILE* ofp); bool test_expt(testspec_t* t, FILE* ofp); bool test_exptv(testspec_t* t, FILE* ofp); bool test_exptf(testspec_t* t, FILE* ofp); bool test_mod(testspec_t* t, FILE* ofp); bool test_gcd(testspec_t* t, FILE* ofp); bool test_egcd(testspec_t* t, FILE* ofp); bool test_lcm(testspec_t* t, FILE* ofp); bool test_sqrt(testspec_t* t, FILE* ofp); bool test_root(testspec_t* t, FILE* ofp); bool test_invmod(testspec_t* t, FILE* ofp); bool test_exptmod(testspec_t* t, FILE* ofp); bool test_exptmod_ev(testspec_t* t, FILE* ofp); bool test_exptmod_bv(testspec_t* t, FILE* ofp); bool test_comp(testspec_t* t, FILE* ofp); bool test_ucomp(testspec_t* t, FILE* ofp); bool test_zcomp(testspec_t* t, FILE* ofp); bool test_vcomp(testspec_t* t, FILE* ofp); bool test_uvcomp(testspec_t* t, FILE* ofp); bool test_tostr(testspec_t* t, FILE* ofp); bool test_tobin(testspec_t* t, FILE* ofp); bool test_to_int(testspec_t* t, FILE* ofp); bool test_to_uint(testspec_t* t, FILE* ofp); bool test_read_binary(testspec_t* t, FILE* ofp); bool test_to_uns(testspec_t* t, FILE* ofp); bool test_read_uns(testspec_t* t, FILE* ofp); bool test_meta(testspec_t* t, FILE* ofp); /* Rational tests */ bool test_qset(testspec_t* t, FILE* ofp); bool test_qneg(testspec_t* t, FILE* ofp); bool test_qrecip(testspec_t* t, FILE* ofp); bool test_qabs(testspec_t* t, FILE* ofp); bool test_qadd(testspec_t* t, FILE* ofp); bool test_qsub(testspec_t* t, FILE* ofp); bool test_qmul(testspec_t* t, FILE* ofp); bool test_qdiv(testspec_t* t, FILE* ofp); bool test_qdiv(testspec_t* t, FILE* ofp); bool test_qaddz(testspec_t* t, FILE* ofp); bool test_qsubz(testspec_t* t, FILE* ofp); bool test_qmulz(testspec_t* t, FILE* ofp); bool test_qdivz(testspec_t* t, FILE* ofp); bool test_qexpt(testspec_t* t, FILE* ofp); bool test_qtostr(testspec_t* t, FILE* ofp); bool test_qtodec(testspec_t* t, FILE* ofp); bool test_qrdec(testspec_t* t, FILE* ofp); bool test_qdecompose(testspec_t* t, FILE* ofp); /* Primality testing tests */ bool test_is_prime(testspec_t* t, FILE *ofp); #endif /* IMDROVER_H_ */ ================================================ FILE: imrat.c ================================================ /* Name: imrat.c Purpose: Arbitrary precision rational arithmetic routines. Author: M. J. Fromberger Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. 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. */ #include "imrat.h" #include #include #include #include #define USE_IMATH_INTERNAL_TEMP_MACROS #include "macros.c" // for temp value handling #define MP_NUMER_SIGN(Q) (MP_NUMER_P(Q)->sign) #define MP_DENOM_SIGN(Q) (MP_DENOM_P(Q)->sign) /* Reduce the given rational, in place, to lowest terms and canonical form. Zero is represented as 0/1, one as 1/1. Signs are adjusted so that the sign of the numerator is definitive. */ static mp_result s_rat_reduce(mp_rat r); /* Common code for addition and subtraction operations on rationals. */ static mp_result s_rat_combine(mp_rat a, mp_rat b, mp_rat c, mp_result (*comb_f)(mp_int, mp_int, mp_int)); mp_result mp_rat_init(mp_rat r) { mp_result res; if ((res = mp_int_init(MP_NUMER_P(r))) != MP_OK) return res; if ((res = mp_int_init(MP_DENOM_P(r))) != MP_OK) { mp_int_clear(MP_NUMER_P(r)); return res; } return mp_int_set_value(MP_DENOM_P(r), 1); } mp_rat mp_rat_alloc(void) { mp_rat out = malloc(sizeof(*out)); if (out != NULL) { if (mp_rat_init(out) != MP_OK) { free(out); return NULL; } } return out; } mp_result mp_rat_reduce(mp_rat r) { return s_rat_reduce(r); } mp_result mp_rat_init_size(mp_rat r, mp_size n_prec, mp_size d_prec) { mp_result res; if ((res = mp_int_init_size(MP_NUMER_P(r), n_prec)) != MP_OK) { return res; } if ((res = mp_int_init_size(MP_DENOM_P(r), d_prec)) != MP_OK) { mp_int_clear(MP_NUMER_P(r)); return res; } return mp_int_set_value(MP_DENOM_P(r), 1); } mp_result mp_rat_init_copy(mp_rat r, mp_rat old) { mp_result res; if ((res = mp_int_init_copy(MP_NUMER_P(r), MP_NUMER_P(old))) != MP_OK) { return res; } if ((res = mp_int_init_copy(MP_DENOM_P(r), MP_DENOM_P(old))) != MP_OK) mp_int_clear(MP_NUMER_P(r)); return res; } mp_result mp_rat_set(mp_rat r, mp_int numer, mp_int denom) { mp_result res; if (numer == NULL && denom == NULL) return MP_BADARG; if (denom != NULL && mp_int_compare_zero(denom) == 0) { return MP_UNDEF; } if (numer == NULL) { mp_int_set_uvalue(MP_NUMER_P(r), 1); } else if ((res = mp_int_copy(numer, MP_NUMER_P(r))) != MP_OK) { return res; } if (denom == NULL) { mp_int_set_uvalue(MP_DENOM_P(r), 1); } else if ((res = mp_int_copy(denom, MP_DENOM_P(r))) != MP_OK) { return res; } return s_rat_reduce(r); } mp_result mp_rat_set_value(mp_rat r, mp_small numer, mp_small denom) { mp_result res; if (denom == 0) return MP_UNDEF; if ((res = mp_int_set_value(MP_NUMER_P(r), numer)) != MP_OK) { return res; } if ((res = mp_int_set_value(MP_DENOM_P(r), denom)) != MP_OK) { return res; } return s_rat_reduce(r); } mp_result mp_rat_set_uvalue(mp_rat r, mp_usmall numer, mp_usmall denom) { mp_result res; if (denom == 0) return MP_UNDEF; if ((res = mp_int_set_uvalue(MP_NUMER_P(r), numer)) != MP_OK) { return res; } if ((res = mp_int_set_uvalue(MP_DENOM_P(r), denom)) != MP_OK) { return res; } return s_rat_reduce(r); } void mp_rat_clear(mp_rat r) { mp_int_clear(MP_NUMER_P(r)); mp_int_clear(MP_DENOM_P(r)); } void mp_rat_free(mp_rat r) { assert(r != NULL); if (r->num.digits != NULL) mp_rat_clear(r); free(r); } mp_result mp_rat_numer(mp_rat r, mp_int z) { return mp_int_copy(MP_NUMER_P(r), z); } mp_int mp_rat_numer_ref(mp_rat r) { return MP_NUMER_P(r); } mp_result mp_rat_denom(mp_rat r, mp_int z) { return mp_int_copy(MP_DENOM_P(r), z); } mp_int mp_rat_denom_ref(mp_rat r) { return MP_DENOM_P(r); } mp_sign mp_rat_sign(mp_rat r) { return MP_NUMER_SIGN(r); } mp_result mp_rat_copy(mp_rat a, mp_rat c) { mp_result res; if ((res = mp_int_copy(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK) { return res; } res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c)); return res; } void mp_rat_zero(mp_rat r) { mp_int_zero(MP_NUMER_P(r)); mp_int_set_value(MP_DENOM_P(r), 1); } mp_result mp_rat_abs(mp_rat a, mp_rat c) { mp_result res; if ((res = mp_int_abs(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK) { return res; } res = mp_int_abs(MP_DENOM_P(a), MP_DENOM_P(c)); return res; } mp_result mp_rat_neg(mp_rat a, mp_rat c) { mp_result res; if ((res = mp_int_neg(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK) { return res; } res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c)); return res; } mp_result mp_rat_recip(mp_rat a, mp_rat c) { mp_result res; if (mp_rat_compare_zero(a) == 0) return MP_UNDEF; if ((res = mp_rat_copy(a, c)) != MP_OK) return res; mp_int_swap(MP_NUMER_P(c), MP_DENOM_P(c)); /* Restore the signs of the swapped elements */ { mp_sign tmp = MP_NUMER_SIGN(c); MP_NUMER_SIGN(c) = MP_DENOM_SIGN(c); MP_DENOM_SIGN(c) = tmp; } return MP_OK; } mp_result mp_rat_add(mp_rat a, mp_rat b, mp_rat c) { return s_rat_combine(a, b, c, mp_int_add); } mp_result mp_rat_sub(mp_rat a, mp_rat b, mp_rat c) { return s_rat_combine(a, b, c, mp_int_sub); } mp_result mp_rat_mul(mp_rat a, mp_rat b, mp_rat c) { mp_result res; if ((res = mp_int_mul(MP_NUMER_P(a), MP_NUMER_P(b), MP_NUMER_P(c))) != MP_OK) return res; if (mp_int_compare_zero(MP_NUMER_P(c)) != 0) { res = mp_int_mul(MP_DENOM_P(a), MP_DENOM_P(b), MP_DENOM_P(c)); if (res != MP_OK) { return res; } } return s_rat_reduce(c); } mp_result mp_rat_div(mp_rat a, mp_rat b, mp_rat c) { mp_result res = MP_OK; if (mp_rat_compare_zero(b) == 0) return MP_UNDEF; if (c == a || c == b) { mpz_t tmp; if ((res = mp_int_init(&tmp)) != MP_OK) return res; if ((res = mp_int_mul(MP_NUMER_P(a), MP_DENOM_P(b), &tmp)) != MP_OK) { goto CLEANUP; } if ((res = mp_int_mul(MP_DENOM_P(a), MP_NUMER_P(b), MP_DENOM_P(c))) != MP_OK) { goto CLEANUP; } res = mp_int_copy(&tmp, MP_NUMER_P(c)); CLEANUP: mp_int_clear(&tmp); } else { if ((res = mp_int_mul(MP_NUMER_P(a), MP_DENOM_P(b), MP_NUMER_P(c))) != MP_OK) { return res; } if ((res = mp_int_mul(MP_DENOM_P(a), MP_NUMER_P(b), MP_DENOM_P(c))) != MP_OK) { return res; } } if (res != MP_OK) { return res; } return s_rat_reduce(c); } mp_result mp_rat_add_int(mp_rat a, mp_int b, mp_rat c) { mpz_t tmp; mp_result res; if ((res = mp_int_init_copy(&tmp, b)) != MP_OK) { return res; } if ((res = mp_int_mul(&tmp, MP_DENOM_P(a), &tmp)) != MP_OK) { goto CLEANUP; } if ((res = mp_rat_copy(a, c)) != MP_OK) { goto CLEANUP; } if ((res = mp_int_add(MP_NUMER_P(c), &tmp, MP_NUMER_P(c))) != MP_OK) { goto CLEANUP; } res = s_rat_reduce(c); CLEANUP: mp_int_clear(&tmp); return res; } mp_result mp_rat_sub_int(mp_rat a, mp_int b, mp_rat c) { mpz_t tmp; mp_result res; if ((res = mp_int_init_copy(&tmp, b)) != MP_OK) { return res; } if ((res = mp_int_mul(&tmp, MP_DENOM_P(a), &tmp)) != MP_OK) { goto CLEANUP; } if ((res = mp_rat_copy(a, c)) != MP_OK) { goto CLEANUP; } if ((res = mp_int_sub(MP_NUMER_P(c), &tmp, MP_NUMER_P(c))) != MP_OK) { goto CLEANUP; } res = s_rat_reduce(c); CLEANUP: mp_int_clear(&tmp); return res; } mp_result mp_rat_mul_int(mp_rat a, mp_int b, mp_rat c) { mp_result res; if ((res = mp_rat_copy(a, c)) != MP_OK) { return res; } if ((res = mp_int_mul(MP_NUMER_P(c), b, MP_NUMER_P(c))) != MP_OK) { return res; } return s_rat_reduce(c); } mp_result mp_rat_div_int(mp_rat a, mp_int b, mp_rat c) { mp_result res; if (mp_int_compare_zero(b) == 0) { return MP_UNDEF; } if ((res = mp_rat_copy(a, c)) != MP_OK) { return res; } if ((res = mp_int_mul(MP_DENOM_P(c), b, MP_DENOM_P(c))) != MP_OK) { return res; } return s_rat_reduce(c); } mp_result mp_rat_expt(mp_rat a, mp_small b, mp_rat c) { mp_result res; /* Special cases for easy powers. */ if (b == 0) { return mp_rat_set_value(c, 1, 1); } else if (b == 1) { return mp_rat_copy(a, c); } /* Since rationals are always stored in lowest terms, it is not necessary to reduce again when raising to an integer power. */ if ((res = mp_int_expt(MP_NUMER_P(a), b, MP_NUMER_P(c))) != MP_OK) { return res; } return mp_int_expt(MP_DENOM_P(a), b, MP_DENOM_P(c)); } mp_result mp_rat_decompose(mp_rat r, mp_int ipart, mp_rat fpart) { if (ipart == NULL && fpart == NULL) { return MP_BADARG; } int cmp; if ((cmp = mp_int_compare_unsigned(MP_NUMER_P(r), MP_DENOM_P(r))) == 0) { // Case 1: The value is 1/1, no division required. if (fpart != NULL) mp_rat_zero(fpart); if (ipart != NULL) { return mp_int_set_uvalue(ipart, 1); } return MP_OK; } else if (cmp < 0) { // Case 2: The numerator is smaller than the denominator, no division // required. if (ipart != NULL) mp_int_zero(ipart); if (fpart != NULL) { return mp_rat_copy(r, fpart); } return MP_OK; } // Case 3: The numerator is strictly greater (magnitude) than the denominator. DECLARE_TEMP(3); REQUIRE(mp_int_copy(MP_NUMER_P(r), TEMP(0))); REQUIRE(mp_int_abs(TEMP(0), TEMP(0))); mp_result res; if ((res = mp_int_div(TEMP(0), MP_DENOM_P(r), TEMP(1), TEMP(2))) != MP_OK) { goto CLEANUP; } if (ipart != NULL) { if ((res = mp_int_copy(TEMP(1), ipart)) != MP_OK) { goto CLEANUP; } ipart->sign = MP_NUMER_SIGN(r); } if (fpart != NULL) { if ((res = mp_rat_set(fpart, TEMP(2), MP_DENOM_P(r))) != MP_OK) { goto CLEANUP; } MP_NUMER_P(fpart)->sign = MP_NUMER_SIGN(r); } CLEANUP_TEMP(); return MP_OK; } int mp_rat_compare(mp_rat a, mp_rat b) { /* Quick check for opposite signs. Works because the sign of the numerator is always definitive. */ if (MP_NUMER_SIGN(a) != MP_NUMER_SIGN(b)) { if (MP_NUMER_SIGN(a) == MP_ZPOS) { return 1; } else { return -1; } } else { /* Compare absolute magnitudes; if both are positive, the answer stands, otherwise it needs to be reflected about zero. */ int cmp = mp_rat_compare_unsigned(a, b); if (MP_NUMER_SIGN(a) == MP_ZPOS) { return cmp; } else { return -cmp; } } } int mp_rat_compare_unsigned(mp_rat a, mp_rat b) { /* If the denominators are equal, we can quickly compare numerators without multiplying. Otherwise, we actually have to do some work. */ if (mp_int_compare_unsigned(MP_DENOM_P(a), MP_DENOM_P(b)) == 0) { return mp_int_compare_unsigned(MP_NUMER_P(a), MP_NUMER_P(b)); } int cmp = INT_MAX; DECLARE_TEMP(2); /* t0 = num(a) * den(b), t1 = num(b) * den(a) */ REQUIRE(mp_int_copy(MP_NUMER_P(a), TEMP(0))); REQUIRE(mp_int_copy(MP_NUMER_P(b), TEMP(1))); mp_result res; if ((res = mp_int_mul(TEMP(0), MP_DENOM_P(b), TEMP(0))) != MP_OK || (res = mp_int_mul(TEMP(1), MP_DENOM_P(a), TEMP(1))) != MP_OK) { goto CLEANUP; } cmp = mp_int_compare_unsigned(TEMP(0), TEMP(1)); CLEANUP_TEMP(); return cmp; } int mp_rat_compare_zero(mp_rat r) { return mp_int_compare_zero(MP_NUMER_P(r)); } int mp_rat_compare_value(mp_rat r, mp_small n, mp_small d) { mpq_t tmp; mp_result res; int out = INT_MAX; if ((res = mp_rat_init(&tmp)) != MP_OK) { return out; } if ((res = mp_rat_set_value(&tmp, n, d)) != MP_OK) { goto CLEANUP; } out = mp_rat_compare(r, &tmp); CLEANUP: mp_rat_clear(&tmp); return out; } bool mp_rat_is_integer(mp_rat r) { return (mp_int_compare_value(MP_DENOM_P(r), 1) == 0); } mp_result mp_rat_to_ints(mp_rat r, mp_small* num, mp_small* den) { mp_result res; if ((res = mp_int_to_int(MP_NUMER_P(r), num)) != MP_OK) { return res; } res = mp_int_to_int(MP_DENOM_P(r), den); return res; } mp_result mp_rat_to_string(mp_rat r, mp_size radix, char* str, int limit) { /* Write the numerator. The sign of the rational number is written by the underlying integer implementation. */ mp_result res; if ((res = mp_int_to_string(MP_NUMER_P(r), radix, str, limit)) != MP_OK) { return res; } /* If the value is zero, don't bother writing any denominator */ if (mp_int_compare_zero(MP_NUMER_P(r)) == 0) { return MP_OK; } /* Locate the end of the numerator, and make sure we are not going to exceed the limit by writing a slash. */ int len = strlen(str); char* start = str + len; limit -= len; if (limit == 0) return MP_TRUNC; *start++ = '/'; limit -= 1; return mp_int_to_string(MP_DENOM_P(r), radix, start, limit); } mp_result mp_rat_to_decimal(mp_rat r, mp_size radix, mp_size prec, mp_round_mode round, char* str, int limit) { DECLARE_TEMP(3); mp_result res = MP_BADARG; REQUIRE(mp_int_copy(MP_NUMER_P(r), TEMP(0))); /* Get the unsigned integer part by dividing denominator into the absolute value of the numerator. */ REQUIRE(mp_int_abs(TEMP(0), TEMP(0))); if ((res = mp_int_div(TEMP(0), MP_DENOM_P(r), TEMP(0), TEMP(1))) != MP_OK) { goto CLEANUP; } /* Now: T0 = integer portion, unsigned; T1 = remainder, from which fractional part is computed. */ /* Count up leading zeroes after the radix point. */ int zprec = (int)prec; int lead_0; for (lead_0 = 0; lead_0 < zprec && mp_int_compare(TEMP(1), MP_DENOM_P(r)) < 0; ++lead_0) { if ((res = mp_int_mul_value(TEMP(1), radix, TEMP(1))) != MP_OK) { goto CLEANUP; } } /* Multiply remainder by a power of the radix sufficient to get the right number of significant figures. */ if (zprec > lead_0) { if ((res = mp_int_expt_value(radix, zprec - lead_0, TEMP(2))) != MP_OK) { goto CLEANUP; } if ((res = mp_int_mul(TEMP(1), TEMP(2), TEMP(1))) != MP_OK) { goto CLEANUP; } } if ((res = mp_int_div(TEMP(1), MP_DENOM_P(r), TEMP(1), TEMP(2))) != MP_OK) { goto CLEANUP; } /* Now: T1 = significant digits of fractional part; T2 = leftovers, to use for rounding. At this point, what we do depends on the rounding mode. The default is MP_ROUND_DOWN, for which everything is as it should be already. */ switch (round) { int cmp; case MP_ROUND_UP: if (mp_int_compare_zero(TEMP(2)) != 0) { if (prec == 0) { res = mp_int_add_value(TEMP(0), 1, TEMP(0)); } else { res = mp_int_add_value(TEMP(1), 1, TEMP(1)); } } break; case MP_ROUND_HALF_UP: case MP_ROUND_HALF_DOWN: if ((res = mp_int_mul_pow2(TEMP(2), 1, TEMP(2))) != MP_OK) { goto CLEANUP; } cmp = mp_int_compare(TEMP(2), MP_DENOM_P(r)); if (round == MP_ROUND_HALF_UP) cmp += 1; if (cmp > 0) { if (prec == 0) { res = mp_int_add_value(TEMP(0), 1, TEMP(0)); } else { res = mp_int_add_value(TEMP(1), 1, TEMP(1)); } } break; case MP_ROUND_DOWN: break; /* No action required */ default: return MP_BADARG; /* Invalid rounding specifier */ } if (res != MP_OK) { goto CLEANUP; } /* The sign of the output should be the sign of the numerator, but if all the displayed digits will be zero due to the precision, a negative shouldn't be shown. */ char* start = str; int left = limit; if (MP_NUMER_SIGN(r) == MP_NEG && (mp_int_compare_zero(TEMP(0)) != 0 || mp_int_compare_zero(TEMP(1)) != 0)) { *start++ = '-'; left -= 1; } if ((res = mp_int_to_string(TEMP(0), radix, start, left)) != MP_OK) { goto CLEANUP; } int len = strlen(start); start += len; left -= len; if (prec == 0) goto CLEANUP; *start++ = '.'; left -= 1; if (left < zprec + 1) { res = MP_TRUNC; goto CLEANUP; } memset(start, '0', lead_0 - 1); left -= lead_0; start += lead_0 - 1; res = mp_int_to_string(TEMP(1), radix, start, left); CLEANUP_TEMP(); return res; } mp_size mp_rat_string_len(mp_rat r, mp_size radix) { mp_size d_len = 0; mp_size n_len = mp_int_string_len(MP_NUMER_P(r), radix); if (mp_int_compare_zero(MP_NUMER_P(r)) != 0) { d_len = mp_int_string_len(MP_DENOM_P(r), radix); } /* Though simplistic, this formula is correct. Space for the sign flag is included in n_len, and the space for the NUL that is counted in n_len counts for the separator here. The space for the NUL counted in d_len counts for the final terminator here. */ return n_len + d_len; } mp_size mp_rat_decimal_len(mp_rat r, mp_size radix, mp_size prec) { int f_len; int z_len = mp_int_string_len(MP_NUMER_P(r), radix); if (prec == 0) { f_len = 1; /* terminator only */ } else { f_len = 1 + prec + 1; /* decimal point, digits, terminator */ } return z_len + f_len; } mp_result mp_rat_read_string(mp_rat r, mp_size radix, const char* str) { return mp_rat_read_cstring(r, radix, str, NULL); } mp_result mp_rat_read_cstring(mp_rat r, mp_size radix, const char* str, char** end) { mp_result res; char* endp; if ((res = mp_int_read_cstring(MP_NUMER_P(r), radix, str, &endp)) != MP_OK && (res != MP_TRUNC)) { return res; } /* Skip whitespace between numerator and (possible) separator */ char* sp = endp; while (isspace((unsigned char)*sp)) { ++sp; } /* If there is no separator, we will stop reading at this point. */ if (*sp != '/') { mp_int_set_value(MP_DENOM_P(r), 1); if (end != NULL) *end = endp; return res; } endp = sp; ++endp; /* skip separator */ if ((res = mp_int_read_cstring(MP_DENOM_P(r), radix, endp, end)) != MP_OK) { return res; } /* Make sure the value is well-defined */ if (mp_int_compare_zero(MP_DENOM_P(r)) == 0) { return MP_UNDEF; } /* Reduce to lowest terms */ return s_rat_reduce(r); } /* Read a string and figure out what format it's in. The radix may be supplied as zero to use "default" behaviour. This function will accept either a/b notation or decimal notation. */ mp_result mp_rat_read_ustring(mp_rat r, mp_size radix, const char* str, char** end) { char* endp = ""; mp_result res; if (radix == 0) radix = 10; /* default to decimal input */ res = mp_rat_read_cstring(r, radix, str, &endp); if (res == MP_TRUNC && *endp == '.') { res = mp_rat_read_cdecimal(r, radix, str, &endp); } if (end != NULL) *end = endp; return res; } mp_result mp_rat_read_decimal(mp_rat r, mp_size radix, const char* str) { return mp_rat_read_cdecimal(r, radix, str, NULL); } mp_result mp_rat_read_cdecimal(mp_rat r, mp_size radix, const char* str, char** end) { mp_result res; mp_sign osign; char* endp; while (isspace((unsigned char)*str)) ++str; switch (*str) { case '-': osign = MP_NEG; break; default: osign = MP_ZPOS; } if ((res = mp_int_read_cstring(MP_NUMER_P(r), radix, str, &endp)) != MP_OK && (res != MP_TRUNC)) { return res; } /* This needs to be here. */ (void)mp_int_set_value(MP_DENOM_P(r), 1); if (*endp != '.') { if (end != NULL) *end = endp; return res; } /* If the character following the decimal point is whitespace or a sign flag, we will consider this a truncated value. This special case is because mp_int_read_string() will consider whitespace or sign flags to be valid starting characters for a value, and we do not want them following the decimal point. Once we have done this check, it is safe to read in the value of the fractional piece as a regular old integer. */ ++endp; if (*endp == '\0') { if (end != NULL) *end = endp; return MP_OK; } else if (isspace((unsigned char)*endp) || *endp == '-' || *endp == '+') { return MP_TRUNC; } else { mpz_t frac; mp_result save_res; char* save = endp; int num_lz = 0; /* Make a temporary to hold the part after the decimal point. */ if ((res = mp_int_init(&frac)) != MP_OK) { return res; } if ((res = mp_int_read_cstring(&frac, radix, endp, &endp)) != MP_OK && (res != MP_TRUNC)) { goto CLEANUP; } /* Save this response for later. */ save_res = res; if (mp_int_compare_zero(&frac) == 0) goto FINISHED; /* Discard trailing zeroes (somewhat inefficiently) */ while (mp_int_divisible_value(&frac, radix)) { if ((res = mp_int_div_value(&frac, radix, &frac, NULL)) != MP_OK) { goto CLEANUP; } } /* Count leading zeros after the decimal point */ while (save[num_lz] == '0') { ++num_lz; } /* Find the least power of the radix that is at least as large as the significant value of the fractional part, ignoring leading zeroes. */ (void)mp_int_set_value(MP_DENOM_P(r), radix); while (mp_int_compare(MP_DENOM_P(r), &frac) < 0) { if ((res = mp_int_mul_value(MP_DENOM_P(r), radix, MP_DENOM_P(r))) != MP_OK) { goto CLEANUP; } } /* Also shift by enough to account for leading zeroes */ while (num_lz > 0) { if ((res = mp_int_mul_value(MP_DENOM_P(r), radix, MP_DENOM_P(r))) != MP_OK) { goto CLEANUP; } --num_lz; } /* Having found this power, shift the numerator leftward that many, digits, and add the nonzero significant digits of the fractional part to get the result. */ if ((res = mp_int_mul(MP_NUMER_P(r), MP_DENOM_P(r), MP_NUMER_P(r))) != MP_OK) { goto CLEANUP; } { /* This addition needs to be unsigned. */ MP_NUMER_SIGN(r) = MP_ZPOS; if ((res = mp_int_add(MP_NUMER_P(r), &frac, MP_NUMER_P(r))) != MP_OK) { goto CLEANUP; } MP_NUMER_SIGN(r) = osign; } if ((res = s_rat_reduce(r)) != MP_OK) goto CLEANUP; /* At this point, what we return depends on whether reading the fractional part was truncated or not. That information is saved from when we called mp_int_read_string() above. */ FINISHED: res = save_res; if (end != NULL) *end = endp; CLEANUP: mp_int_clear(&frac); return res; } } /* Private functions for internal use. Make unchecked assumptions about format and validity of inputs. */ static mp_result s_rat_reduce(mp_rat r) { mpz_t gcd; mp_result res = MP_OK; if (mp_int_compare_zero(MP_NUMER_P(r)) == 0) { mp_int_set_value(MP_DENOM_P(r), 1); return MP_OK; } /* If the greatest common divisor of the numerator and denominator is greater than 1, divide it out. */ if ((res = mp_int_init(&gcd)) != MP_OK) return res; if ((res = mp_int_gcd(MP_NUMER_P(r), MP_DENOM_P(r), &gcd)) != MP_OK) { goto CLEANUP; } if (mp_int_compare_value(&gcd, 1) != 0) { if ((res = mp_int_div(MP_NUMER_P(r), &gcd, MP_NUMER_P(r), NULL)) != MP_OK) { goto CLEANUP; } if ((res = mp_int_div(MP_DENOM_P(r), &gcd, MP_DENOM_P(r), NULL)) != MP_OK) { goto CLEANUP; } } /* Fix up the signs of numerator and denominator */ if (MP_NUMER_SIGN(r) == MP_DENOM_SIGN(r)) { MP_NUMER_SIGN(r) = MP_DENOM_SIGN(r) = MP_ZPOS; } else { MP_NUMER_SIGN(r) = MP_NEG; MP_DENOM_SIGN(r) = MP_ZPOS; } CLEANUP: mp_int_clear(&gcd); return res; } static mp_result s_rat_combine(mp_rat a, mp_rat b, mp_rat c, mp_result (*comb_f)(mp_int, mp_int, mp_int)) { mp_result res = MP_BADARG; /* Shortcut when denominators are already common */ if (mp_int_compare(MP_DENOM_P(a), MP_DENOM_P(b)) == 0) { if ((res = (comb_f)(MP_NUMER_P(a), MP_NUMER_P(b), MP_NUMER_P(c))) != MP_OK) { return res; } if ((res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c))) != MP_OK) { return res; } return s_rat_reduce(c); } DECLARE_TEMP(2); REQUIRE(mp_int_copy(MP_NUMER_P(a), TEMP(0))); REQUIRE(mp_int_copy(MP_NUMER_P(b), TEMP(1))); if ((res = mp_int_mul(TEMP(0), MP_DENOM_P(b), TEMP(0))) != MP_OK) { goto CLEANUP; } if ((res = mp_int_mul(TEMP(1), MP_DENOM_P(a), TEMP(1))) != MP_OK) { goto CLEANUP; } if ((res = (comb_f)(TEMP(0), TEMP(1), MP_NUMER_P(c))) != MP_OK) { goto CLEANUP; } res = mp_int_mul(MP_DENOM_P(a), MP_DENOM_P(b), MP_DENOM_P(c)); CLEANUP_TEMP(); if (res != MP_OK) { return res; } return s_rat_reduce(c); } /* Here there be dragons */ ================================================ FILE: imrat.h ================================================ /* Name: imrat.h Purpose: Arbitrary precision rational arithmetic routines. Author: M. J. Fromberger Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. 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. */ #ifndef IMRAT_H_ #define IMRAT_H_ #include #include "imath.h" #ifdef __cplusplus extern "C" { #endif typedef struct { mpz_t num; /* Numerator */ mpz_t den; /* Denominator, <> 0 */ } mpq_t, *mp_rat; /* Return a pointer to the numerator. */ static inline mp_int MP_NUMER_P(mp_rat Q) { return &(Q->num); } /* Return a pointer to the denominator. */ static inline mp_int MP_DENOM_P(mp_rat Q) { return &(Q->den); } /* Rounding constants */ typedef enum { MP_ROUND_DOWN, MP_ROUND_HALF_UP, MP_ROUND_UP, MP_ROUND_HALF_DOWN } mp_round_mode; /** Initializes `r` with 1-digit precision and sets it to zero. This function cannot fail unless `r` is NULL. */ mp_result mp_rat_init(mp_rat r); /** Allocates a fresh zero-valued `mpq_t` on the heap, returning NULL in case of error. The only possible error is out-of-memory. */ mp_rat mp_rat_alloc(void); /** Reduces `r` in-place to lowest terms and canonical form. Zero is represented as 0/1, one as 1/1, and signs are adjusted so that the sign of the value is carried by the numerator. */ mp_result mp_rat_reduce(mp_rat r); /** Initializes `r` with at least `n_prec` digits of storage for the numerator and `d_prec` digits of storage for the denominator, and value zero. If either precision is zero, the default precision is used, rounded up to the nearest word size. */ mp_result mp_rat_init_size(mp_rat r, mp_size n_prec, mp_size d_prec); /** Initializes `r` to be a copy of an already-initialized value in `old`. The new copy does not share storage with the original. */ mp_result mp_rat_init_copy(mp_rat r, mp_rat old); /** Sets the value of `r` to the ratio of signed `numer` to signed `denom`. It returns `MP_UNDEF` if `denom` is zero. At least one of `numer` and `denom` must be non-NULL. If `numer` is NULL, the value of `r` is set to 1 / `denom`. If `denom` is NULL, the value of `r` is set to `numer` / 1. */ mp_result mp_rat_set(mp_rat r, mp_int numer, mp_int denom); /** Sets the value of `r` to the ratio of signed `numer` to signed `denom`. It returns `MP_UNDEF` if `denom` is zero. */ mp_result mp_rat_set_value(mp_rat r, mp_small numer, mp_small denom); /** Sets the value of `r` to the ratio of unsigned `numer` to unsigned `denom`. It returns `MP_UNDEF` if `denom` is zero. */ mp_result mp_rat_set_uvalue(mp_rat r, mp_usmall numer, mp_usmall denom); /** Releases the storage used by `r`. */ void mp_rat_clear(mp_rat r); /** Releases the storage used by `r` and also `r` itself. This should only be used for `r` allocated by `mp_rat_alloc()`. */ void mp_rat_free(mp_rat r); /** Sets `z` to a copy of the numerator of `r`. */ mp_result mp_rat_numer(mp_rat r, mp_int z); /** Returns a pointer to the numerator of `r`. */ mp_int mp_rat_numer_ref(mp_rat r); /** Sets `z` to a copy of the denominator of `r`. */ mp_result mp_rat_denom(mp_rat r, mp_int z); /** Returns a pointer to the denominator of `r`. */ mp_int mp_rat_denom_ref(mp_rat r); /** Reports the sign of `r`. */ mp_sign mp_rat_sign(mp_rat r); /** Sets `c` to a copy of the value of `a`. No new memory is allocated unless a term of `a` has more significant digits than the corresponding term of `c` has allocated. */ mp_result mp_rat_copy(mp_rat a, mp_rat c); /** Sets `r` to zero. The allocated storage of `r` is not changed. */ void mp_rat_zero(mp_rat r); /** Sets `c` to the absolute value of `a`. */ mp_result mp_rat_abs(mp_rat a, mp_rat c); /** Sets `c` to the absolute value of `a`. */ mp_result mp_rat_neg(mp_rat a, mp_rat c); /** Sets `c` to the reciprocal of `a` if the reciprocal is defined. It returns `MP_UNDEF` if `a` is zero. */ mp_result mp_rat_recip(mp_rat a, mp_rat c); /** Sets `c` to the sum of `a` and `b`. */ mp_result mp_rat_add(mp_rat a, mp_rat b, mp_rat c); /** Sets `c` to the difference of `a` less `b`. */ mp_result mp_rat_sub(mp_rat a, mp_rat b, mp_rat c); /** Sets `c` to the product of `a` and `b`. */ mp_result mp_rat_mul(mp_rat a, mp_rat b, mp_rat c); /** Sets `c` to the ratio `a / b` if that ratio is defined. It returns `MP_UNDEF` if `b` is zero. */ mp_result mp_rat_div(mp_rat a, mp_rat b, mp_rat c); /** Sets `c` to the sum of `a` and integer `b`. */ mp_result mp_rat_add_int(mp_rat a, mp_int b, mp_rat c); /** Sets `c` to the difference of `a` less integer `b`. */ mp_result mp_rat_sub_int(mp_rat a, mp_int b, mp_rat c); /** Sets `c` to the product of `a` and integer `b`. */ mp_result mp_rat_mul_int(mp_rat a, mp_int b, mp_rat c); /** Sets `c` to the ratio `a / b` if that ratio is defined. It returns `MP_UNDEF` if `b` is zero. */ mp_result mp_rat_div_int(mp_rat a, mp_int b, mp_rat c); /** Sets `c` to the value of `a` raised to the `b` power. It returns `MP_RANGE` if `b < 0`. */ mp_result mp_rat_expt(mp_rat a, mp_small b, mp_rat c); /** Sets `ipart` to the integer part of `r` and `fpart` to the difference of `r - ipart`. If `r < 0` then the signs of `ipart` and `fpart` will also be negative, unless they are zero. At least one of `ipart` and `fpart` must be non-NULL. If `ipart` is NULL the integer part is discarded. If `fpart` is NULL, the fractional part is discarded. */ mp_result mp_rat_decompose(mp_rat r, mp_int ipart, mp_rat fpart); /** Returns the comparator of `a` and `b`. */ int mp_rat_compare(mp_rat a, mp_rat b); /** Returns the comparator of the magnitudes of `a` and `b`, disregarding their signs. Neither `a` nor `b` is modified by the comparison. */ int mp_rat_compare_unsigned(mp_rat a, mp_rat b); /** Returns the comparator of `r` and zero. */ int mp_rat_compare_zero(mp_rat r); /** Returns the comparator of `r` and the signed ratio `n / d`. It returns `MP_UNDEF` if `d` is zero. */ int mp_rat_compare_value(mp_rat r, mp_small n, mp_small d); /** Reports whether `r` is an integer, having canonical denominator 1. */ bool mp_rat_is_integer(mp_rat r); /** Reports whether the numerator and denominator of `r` can be represented as small signed integers, and if so stores the corresponding values to `num` and `den`. It returns `MP_RANGE` if either cannot be so represented. */ mp_result mp_rat_to_ints(mp_rat r, mp_small *num, mp_small *den); /** Converts `r` to a zero-terminated string of the format `"n/d"` with `n` and `d` in the specified radix and writing no more than `limit` bytes to the given output buffer `str`. The output of the numerator includes a sign flag if `r` is negative. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ mp_result mp_rat_to_string(mp_rat r, mp_size radix, char *str, int limit); /** Converts the value of `r` to a string in decimal-point notation with the specified radix, writing no more than `limit` bytes of data to the given output buffer. It generates `prec` digits of precision, and requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. Ratios usually must be rounded when they are being converted for output as a decimal value. There are four rounding modes currently supported: MP_ROUND_DOWN Truncates the value toward zero. Example: 12.009 to 2dp becomes 12.00 MP_ROUND_UP Rounds the value away from zero: Example: 12.001 to 2dp becomes 12.01, but 12.000 to 2dp remains 12.00 MP_ROUND_HALF_DOWN Rounds the value to nearest digit, half goes toward zero. Example: 12.005 to 2dp becomes 12.00, but 12.006 to 2dp becomes 12.01 MP_ROUND_HALF_UP Rounds the value to nearest digit, half rounds upward. Example: 12.005 to 2dp becomes 12.01, but 12.004 to 2dp becomes 12.00 */ mp_result mp_rat_to_decimal(mp_rat r, mp_size radix, mp_size prec, mp_round_mode round, char *str, int limit); /** Reports the minimum number of characters required to represent `r` as a zero-terminated string in the given `radix`. Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ mp_size mp_rat_string_len(mp_rat r, mp_size radix); /** Reports the length in bytes of the buffer needed to convert `r` using the `mp_rat_to_decimal()` function with the specified `radix` and `prec`. The buffer size estimate may slightly exceed the actual required capacity. */ mp_size mp_rat_decimal_len(mp_rat r, mp_size radix, mp_size prec); /** Sets `r` to the value represented by a zero-terminated string `str` in the format `"n/d"` including a sign flag. It returns `MP_UNDEF` if the encoded denominator has value zero. */ mp_result mp_rat_read_string(mp_rat r, mp_size radix, const char *str); /** Sets `r` to the value represented by a zero-terminated string `str` in the format `"n/d"` including a sign flag. It returns `MP_UNDEF` if the encoded denominator has value zero. If `end` is not NULL then `*end` is set to point to the first unconsumed character in the string, after parsing. */ mp_result mp_rat_read_cstring(mp_rat r, mp_size radix, const char *str, char **end); /** Sets `r` to the value represented by a zero-terminated string `str` having one of the following formats, each with an optional leading sign flag: n : integer format, e.g. "123" n/d : ratio format, e.g., "-12/5" z.ffff : decimal format, e.g., "1.627" It returns `MP_UNDEF` if the effective denominator is zero. If `end` is not NULL then `*end` is set to point to the first unconsumed character in the string, after parsing. */ mp_result mp_rat_read_ustring(mp_rat r, mp_size radix, const char *str, char **end); /** Sets `r` to the value represented by a zero-terminated string `str` in the format `"z.ffff"` including a sign flag. It returns `MP_UNDEF` if the effective denominator is zero. */ mp_result mp_rat_read_decimal(mp_rat r, mp_size radix, const char *str); /** Sets `r` to the value represented by a zero-terminated string `str` in the format `"z.ffff"` including a sign flag. It returns `MP_UNDEF` if the effective denominator is zero. If `end` is not NULL then `*end` is set to point to the first unconsumed character in the string, after parsing. */ mp_result mp_rat_read_cdecimal(mp_rat r, mp_size radix, const char *str, char **end); #ifdef __cplusplus } #endif #endif /* IMRAT_H_ */ ================================================ FILE: imtest.c ================================================ /* Name: imtest.c Purpose: Test driver for imath library. Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. Reads tests from input files or standard input, and runs them. Tests have the form: code:inputs:outputs The 'code' is a string identifying the test to be performed. The inputs and outputs are comma-separated sequences of values. The format of each input is: 1005 number in decimal notation (signs ok) #x-C0E number in hexadecimal notation #b1011 number in binary notation #o37750 number in octal notation =k use register k for this input For rational tests, the following syntax is also legal: @5.33 use decimal notation (for rationals only) may be combined with radix notation, e.g. #x@A0.5C Each output is a string representing the value to which the corresponding result is compared in order to pass the test. By default, tests are expected to succeed (i.e., return MP_OK). To specify an alternate return value, use the notation $RESULT, where RESULT is the name of an error (e.g., MP_MEMORY, MP_UNDEF, etc.) or a numeric result denoted $#number (e.g., $#-5). Results are written to standard output in the following formats: filenamelinenumberresult filenamelinenumberresultmessage The filename and line give the offset of the test in its input file, the number is the number of the test among all inputs, starting from 1. The result is a textual description of the result code returned by the operation being tested. The exit status is 0 if all tests passed, 1 if one or more tests failed or had errors. Note: There is currently a fixed limit on the length of lines by this test ---- driver. You can increase it if you wish, but the code doesn't check; lines over the length are truncated (split). */ #include #include #include #include #include #include #include #include #include "imath.h" #include "imdrover.h" #ifdef LINE_MAX #undef LINE_MAX #endif #define LINE_MAX 4096 typedef struct { char* code; int num_inputs; int num_outputs; test_f call; } test_t; test_t g_tests[] = { /* What it does... */ {"initu", 2, 1, test_init}, /* r0 = uv(r1) */ {"initv", 2, 1, test_init}, /* r0 = v(r1) */ {"setu", 2, 1, test_set}, /* r0 = uv(r1) */ {"setv", 2, 1, test_set}, /* r0 = v(r1) */ {"neg", 2, 1, test_neg}, /* r1 = -r0 */ {"abs", 2, 1, test_abs}, /* r1 = |r0| */ {"add", 3, 1, test_add}, /* r3 = r1 + r2 */ {"addv", 3, 1, test_add}, /* r3 = r1 + v(r2) */ {"sub", 3, 1, test_sub}, /* r3 = r1 - r2 */ {"subv", 3, 1, test_sub}, /* r3 = r1 - v(r2) */ {"mul", 3, 1, test_mul}, /* r3 = r1 * r2 */ {"mulp2", 3, 1, test_mulp2}, /* r3 = r1 * 2^v(r2) */ {"mulv", 3, 1, test_mulv}, /* r3 = r1 * v(r2) */ {"sqr", 2, 1, test_sqr}, /* r2 = r1 * r1 */ {"div", 4, 2, test_div}, /* r2 = r1 / r2, r3 = r1 % r2 */ {"divp2", 4, 2, test_divp2}, /* r2 = r1 / 2^v(r2),r3 = r1 % 2^v(r2)*/ {"divv", 3, 2, test_divv}, /* r2 = r1 / v(r2), r3 = r1 % v(r2) */ {"expt", 3, 1, test_expt}, /* r3 = r1 ^ v(r2) */ {"exptv", 3, 1, test_exptv}, /* r3 = v(r1) ^ v(r2) */ {"exptf", 3, 1, test_exptf}, /* r3 = r1 ^ r2 */ {"mod", 3, 1, test_mod}, /* r3 = r1 % r2 */ {"gcd", 3, 1, test_gcd}, /* r3 = gcd(r1, r2) */ {"egcd", 5, 3, test_egcd}, /* r3 = gcd(r1, r2) = r1*r4 + r2*r5 */ {"lcm", 3, 1, test_lcm}, /* r3 = lcm(r1, r2) */ {"sqrt", 2, 1, test_sqrt}, /* r2 = sqrt(r1) */ {"root", 3, 1, test_root}, /* r3 = r1^(1/v(r2)) */ {"invmod", 3, 1, test_invmod}, /* r3 = r1^-1 mod r2 */ {"emod", 4, 1, test_exptmod}, /* r4 = r1^r2 mod r3 */ {"emodev", 4, 1, test_exptmod_ev}, /* r4 = r1^v(r2) mod r3 */ {"emodbv", 4, 1, test_exptmod_bv}, /* r4 = v(r1)^r2 mod r3 */ {"cmp", 2, 1, test_comp}, /* rtn = compare(r1, r2) */ {"cmpu", 2, 1, test_ucomp}, /* rtn = compare(|r1|, |r2|) */ {"cmpz", 1, 1, test_zcomp}, /* rtn = compare(r1, 0) */ {"cmpv", 2, 1, test_vcomp}, /* rtn = compare(r1, v(r2)) */ {"cmpuv", 2, 1, test_uvcomp}, /* rtn = compare(r1, v(r2)) */ {"tostr", 2, 1, test_tostr}, /* r1: value, r2: radix, o1: result */ {"tobin", 1, 1, test_tobin}, /* r1: value, o1: result binary */ {"readbin", 1, 1, test_read_binary}, /* r1: 2's comp, o1: result value */ {"to-uns", 1, 1, test_to_uns}, /* r1: value, o1: result binary */ {"readuns", 1, 1, test_read_uns}, /* r1: unsigned, o1: result value */ {"to-int", 1, 1, test_to_int}, /* r1: value, o1: result */ {"to-uint", 1, 1, test_to_uint}, /* r1: value, o1: result */ {"meta", -1, -1, test_meta}, {"qset", 2, 1, test_qset}, /* r3 = r1 / r2 */ {"qneg", 2, 1, test_qneg}, /* r2 = -r1 */ {"qrecip", 2, 1, test_qrecip}, /* r2 = 1 / r1 */ {"qabs", 2, 1, test_qabs}, /* r2 = |r1| */ {"qadd", 3, 1, test_qadd}, /* r3 = r1 + r2 */ {"qsub", 3, 1, test_qsub}, /* r3 = r1 - r2 */ {"qmul", 3, 1, test_qmul}, /* r3 = r1 * r2 */ {"qdiv", 3, 1, test_qdiv}, /* r3 = r1 / r2 */ {"qaddz", 3, 1, test_qaddz}, /* r3 = r1 + r2 */ {"qsubz", 3, 1, test_qsubz}, /* r3 = r1 - r2 */ {"qmulz", 3, 1, test_qmulz}, /* r3 = r1 * r2 */ {"qdivz", 3, 1, test_qdivz}, /* r3 = r1 / r2 */ {"qexpt", 3, 1, test_qexpt}, /* r3 = r1 ^ v(r2) */ {"qtostr", 2, 1, test_qtostr}, /* r1: value, r2: radix; o1: result */ {"qtodec", 4, 1, test_qtodec}, /* r1: val, r2: rdx, r3: prec, r4: rounding mode; o1: res */ {"qrdec", 2, 1, test_qrdec}, /* r1: dec, r2: rdx; o1: result value */ {"qdecompose", 3, 2, test_qdecompose}, /* r2 = ipart(r1), r3 = fpart(r1) */ {"isprime", 1, 1, test_is_prime}, /* rtn = prime(r1) ? MP_TRUE : MP_FALSE */ {NULL, 0, 0, NULL} /* end of list marker */ }; char g_line[LINE_MAX]; extern mp_result imath_errno; extern char* imath_errmsg; const char* g_imath_strerr[] = {"MP_OK", "MP_TRUE", "MP_MEMORY", "MP_RANGE", "MP_UNDEF", "MP_TRUNC", "MP_BADARG"}; bool process_file(char* file_name, FILE* ifp, FILE* ofp); int read_line(FILE* ifp, char* line, int limit); void trim_line(char* line); int is_blank(char* line); int parse_line(char* line, testspec_t* t); int count_fields(char* line, int delim); void parse_fields(char* line, int delim, char** start); int run_test(int test_num, testspec_t* t, FILE* ofp); void free_test(testspec_t* t); int find_test(char* code, test_t* info); char* error_string(mp_result res); int main(int argc, char* argv[]) { int exit_status = 0; init_testing(); if (argc == 1) { fprintf(stderr, "[reading from stdin]\n"); if (!process_file("-", stdin, stdout)) exit_status = 1; } else { FILE* ifp; int i; for (i = 1; i < argc; ++i) { if (strcmp(argv[i], "-") == 0) { ifp = stdin; } else if ((ifp = fopen(argv[i], "r")) == NULL) { fprintf(stderr, "Cannot open '%s': %s\n", argv[i], strerror(errno)); return 1; } if (!process_file(argv[i], ifp, stdout)) exit_status = 1; fclose(ifp); } } return exit_status; } /** Reads and runs test cases from `ifp` and writes test results to `ofp`. The given `file_name` is used for cosmetic attribution. The return value is true if all tests passed, false if any tests failed or had errors. */ bool process_file(char* file_name, FILE* ifp, FILE* ofp) { int res, line_num, test_num = 0, num_failed = 0, num_bogus = 0; clock_t start, finish; start = clock(); while ((line_num = read_line(ifp, g_line, LINE_MAX)) != 0) { testspec_t t; t.line = line_num; t.file = file_name; if (parse_line(g_line, &t)) { if ((res = run_test(++test_num, &t, ofp)) < 0) { ++num_bogus; } else if (res == 0) { ++num_failed; } free_test(&t); } else { fprintf(stderr, "Line %d: Incorrect input syntax.\n", line_num); ++num_bogus; } } finish = clock(); fprintf(ofp, "# %s %d tests: %d passed, %d failed, %d errors. (%.2f seconds)\n", file_name, test_num, (test_num - num_failed - num_bogus), num_failed, num_bogus, ((double)(finish - start) / CLOCKS_PER_SEC)); return num_failed == 0 && num_bogus == 0; } int read_line(FILE* ifp, char* line, int limit) { static FILE* current_fp = NULL; static int current_line = 0; if (ifp != current_fp) { current_fp = ifp; current_line = 0; } do { if (fgets(line, limit, ifp) == NULL) return 0; ++current_line; } while (is_blank(line)); trim_line(line); return current_line; } /** Removes leading and trailing whitespace from a zero-terminated `line`. */ void trim_line(char* line) { int len; char* fnw = line; /* Remove leading whitespace */ while (isspace((unsigned char)*fnw)) ++fnw; len = strlen(fnw); memmove(line, fnw, len); /* Remove trailing whitespace (including linefeeds) */ fnw = line + len - 1; while (fnw >= line && isspace((unsigned char)*fnw)) *fnw-- = '\0'; } /** Reports whether a zero-terminated `line` contains only whitespace after a line-trailing comment (`# ...`) is removed. */ int is_blank(char* line) { while (*line && *line != '#' && isspace((unsigned char)*line)) ++line; return *line == '\0' || *line == '#'; } int parse_line(char* line, testspec_t* t) { char *code_brk, *in_brk; int num_fields; if ((code_brk = strchr(line, ':')) == NULL) return 0; if ((in_brk = strchr(code_brk + 1, ':')) == NULL) return 0; *code_brk = '\0'; t->code = line; *in_brk = '\0'; num_fields = count_fields(code_brk + 1, ','); t->num_inputs = num_fields; t->input = NULL; num_fields = count_fields(in_brk + 1, ','); t->num_outputs = num_fields; t->output = NULL; if (t->num_inputs > 0) { t->input = calloc(t->num_inputs, sizeof(char*)); parse_fields(code_brk + 1, ',', t->input); } if (t->num_outputs > 0) { t->output = calloc(t->num_outputs, sizeof(char*)); parse_fields(in_brk + 1, ',', t->output); } return 1; } /** Returns the number of `delim` separated fields occur in `line`. */ int count_fields(char* line, int delim) { int count = 1; if (*line == '\0') return 0; while (*line) { if (*line == (char)delim && *(line + 1) != '\0') ++count; ++line; } return count; } void parse_fields(char* line, int delim, char** start) { int pos = 0; start[pos++] = line; while ((line = strchr(line, delim)) != NULL) { *line++ = '\0'; start[pos++] = line; } } /** Runs the test cases specified by `t`, and writes its results to `ofp`. The `test_num` is used in log output and should reflect the global ordering of tests, but is not otherwise interpreted by this function. This function returns 0 if the test succeeds, 1 if the test fails, and -1 if the test is broken (e.g., its code is unknown). */ int run_test(int test_num, testspec_t* t, FILE* ofp) { test_t info; /* Look up and reality check test parameters */ if (find_test(t->code, &info) < 0) { fprintf(stderr, "Line %d: Test code '%s' is unknown.\n", t->line, t->code); return -1; } else { int errs = 0; if (info.num_inputs >= 0 && t->num_inputs != info.num_inputs) { fprintf(stderr, "Line %d: Wrong number of inputs to %s (want %d, have %d)\n", t->line, t->code, info.num_inputs, t->num_inputs); ++errs; } if (info.num_outputs >= 0 && t->num_outputs != info.num_outputs) { fprintf(stderr, "Line %d: Wrong number of outputs to %s (want %d, have %d)\n", t->line, t->code, info.num_outputs, t->num_outputs); ++errs; } if (errs) { fprintf(stderr, "Line %d: %d error(s), skipping this test.\n", t->line, errs); return -1; } } /* If return value is true, just print a generic OK message; otherwise, it is assumed that imath_errno has been set to a value indicating the problem. */ if ((info.call)(t, ofp)) { fprintf(ofp, "%s\t%d\t%d\tOK\n", t->file, t->line, test_num); return 1; } else if (imath_errno >= MP_BADARG) { fprintf(ofp, "%s\t%d\t%d\t%s\n", t->file, t->line, test_num, error_string(imath_errno)); } else { fprintf(ofp, "%s\t%d\t%d\tFAILED\t%s\n", t->file, t->line, test_num, imath_errmsg); } return 0; } /** Locates the run instructions for the specified test `code`, and if they are found populates `*info` with a copy. It returns -1 if `code` is unknown. */ int find_test(char* code, test_t* info) { int i = 0; while (g_tests[i].code != NULL) { if (strcmp(g_tests[i].code, code) == 0) { *info = g_tests[i]; return i; } ++i; } return -1; } /** Releases the memory occupied by a test case invocation. */ void free_test(testspec_t* t) { assert(t != NULL); if (t->input != NULL) { free(t->input); t->input = NULL; } if (t->output != NULL) { free(t->output); t->output = NULL; } } /** Returns a static label string describing `res`. Note that this is not the same as the error string returned by `mp_error_string`, but corresponds to the spelling of the constant for its value. */ char* error_string(mp_result res) { int v = abs(res); return (char*)g_imath_strerr[v]; } /* Here there be dragons */ ================================================ FILE: imtimer.c ================================================ /* Name: imtimer.c Purpose: Timing tests for the imath library. Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include #include #include #include "imath.h" double clocks_to_seconds(clock_t start, clock_t end); double get_multiply_time(int nt, int prec); double get_exptmod_time(int nt, int prec); mp_int alloc_values(int nt, int prec); void randomize_values(mp_int values, int nt, int prec); void release_values(mp_int values, int nt); void mp_int_random(mp_int z, int prec); const int g_mul_factor = 1000; int main(int argc, char* argv[]) { int do_mul = 0, do_exp = 0, do_header = 1; int num_tests, precision = 0, opt; mp_size threshold = 0; unsigned int seed = (unsigned int)time(NULL); while ((opt = getopt(argc, argv, "ehmnp:s:t:")) != EOF) { switch (opt) { case 'e': do_exp = 1; break; case 'm': do_mul = 1; break; case 'n': do_header = 0; break; case 'p': precision = atoi(optarg); break; case 's': seed = atoi(optarg); break; case 't': threshold = (mp_size)atoi(optarg); break; default: fprintf(stderr, "Usage: imtimer [options] \n\n" "Options understood:\n" " -e -- test modular exponentiation speed.\n" " -h -- display this help message.\n" " -m -- test multiplication speed.\n" " -n -- no header line.\n" " -p -- use values with digits.\n" " -s -- set random seed to .\n" " -t -- set recursion threshold to digits.\n\n"); return (opt != 'h'); } } if (optind >= argc) { fprintf(stderr, "Usage: imtimer [options] \n" "[use \"imtimer -h\" for help with options]\n\n"); return 1; } else num_tests = atoi(argv[optind]); srand(seed); if (num_tests <= 0) { fprintf(stderr, "You must request at least one test.\n"); return 1; } if (precision < 0) { fprintf(stderr, "Precision must be non-negative (0 means default).\n"); return 1; } mp_int_multiply_threshold(threshold); if (do_header) printf("NUM\tPREC\tBITS\tREC\tRESULT\n"); printf("%d\t%d\t%d\t%u", num_tests, precision, (int)(precision * MP_DIGIT_BIT), threshold); if (do_mul) { double m_time = get_multiply_time(num_tests, precision); printf("\tMUL %.3f %.3f", m_time, m_time / num_tests); } if (do_exp) { double e_time = get_exptmod_time(num_tests, precision); printf("\tEXP %.3f %.3f", e_time, e_time / num_tests); } fputc('\n', stdout); fflush(stdout); return 0; } double clocks_to_seconds(clock_t start, clock_t end) { return (double)(end - start) / CLOCKS_PER_SEC; } mp_int alloc_values(int nt, int prec) { mp_int out = malloc(nt * sizeof(mpz_t)); int i; if (out == NULL) return NULL; for (i = 0; i < nt; ++i) { if (mp_int_init_size(out + i, prec) != MP_OK) { while (--i >= 0) mp_int_clear(out + i); return NULL; } } return out; } void randomize_values(mp_int values, int nt, int prec) { int i; for (i = 0; i < nt; ++i) mp_int_random(values + i, prec); } void release_values(mp_int values, int nt) { int i; for (i = 0; i < nt; ++i) mp_int_clear(values + i); free(values); } double get_multiply_time(int nt, int prec) { clock_t start, end; mp_int values; int i; if ((values = alloc_values(3, prec)) == NULL) return 0.0; randomize_values(values, 2, prec); start = clock(); for (i = 0; i < nt; ++i) mp_int_mul(values, values + 1, values + 2); end = clock(); release_values(values, 3); return clocks_to_seconds(start, end); } double get_exptmod_time(int nt, int prec) { clock_t start, end; mp_int values; int i; if ((values = alloc_values(4, prec)) == NULL) return 0.0; randomize_values(values, 3, prec); start = clock(); for (i = 0; i < nt; ++i) mp_int_exptmod(values, values + 1, values + 2, values + 3); end = clock(); release_values(values, 4); return clocks_to_seconds(start, end); } void mp_int_random(mp_int z, int prec) { int i; if (prec > (int)MP_ALLOC(z)) prec = (int)MP_ALLOC(z); for (i = 0; i < prec; ++i) { mp_digit d = 0; int j; for (j = 0; j < (int)sizeof(d); ++j) { d = (d << CHAR_BIT) | (rand() & UCHAR_MAX); } z->digits[i] = d; } z->used = prec; } ================================================ FILE: iprime.c ================================================ /* Name: iprime.c Purpose: Pseudoprimality testing routines Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include "iprime.h" #include static const int s_ptab[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 0, /* sentinel */ }; mp_result mp_int_is_prime(mp_int z) { /* Reject values less than 2 immediately. */ if (mp_int_compare_value(z, 2) < 0) { return MP_FALSE; } /* First check for divisibility by small primes; this eliminates a large number of composite candidates quickly */ for (int i = 0; s_ptab[i] != 0; i++) { mp_small rem; mp_result res; if (mp_int_compare_value(z, s_ptab[i]) == 0) return MP_TRUE; if ((res = mp_int_div_value(z, s_ptab[i], NULL, &rem)) != MP_OK) return res; if (rem == 0) return MP_FALSE; } /* Now try Fermat's test for several prime witnesses (since we now know from the above that z is not a multiple of any of them) */ mp_result res; mpz_t tmp; if ((res = mp_int_init(&tmp)) != MP_OK) return res; for (int i = 0; i < 10 && s_ptab[i] != 0; i++) { if ((res = mp_int_exptmod_bvalue(s_ptab[i], z, z, &tmp)) != MP_OK) { return res; } if (mp_int_compare_value(&tmp, s_ptab[i]) != 0) { mp_int_clear(&tmp); return MP_FALSE; } } mp_int_clear(&tmp); return MP_TRUE; } /* Find the first apparent prime in ascending order from z */ mp_result mp_int_find_prime(mp_int z) { mp_result res; if (mp_int_is_even(z) && ((res = mp_int_add_value(z, 1, z)) != MP_OK)) return res; while ((res = mp_int_is_prime(z)) == MP_FALSE) { if ((res = mp_int_add_value(z, 2, z)) != MP_OK) break; } return res; } /* Here there be dragons */ ================================================ FILE: iprime.h ================================================ /* Name: iprime.h Purpose: Pseudoprimality testing routines Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #ifndef IPRIME_H_ #define IPRIME_H_ #include "imath.h" #ifdef __cplusplus extern "C" { #endif /* Reports whether z is likely to be prime, meaning z >= 2 and has no positive divisors 1 < d < z. It returns MP_YES if z is probably prime, or MP_NO if z is definitely not prime. */ mp_result mp_int_is_prime(mp_int z); /* Find the first apparent prime in ascending order from z */ mp_result mp_int_find_prime(mp_int z); #ifdef __cplusplus } #endif #endif /* IPRIME_H_ */ ================================================ FILE: macros.c ================================================ /* Name: macros.c Purpose: Support macros for temporary variable handling. Author: M. J. Fromberger Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved. 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. */ // Discourage direct inclusion from the .h files. #if !defined(USE_IMATH_INTERNAL_TEMP_MACROS) #error This file should not be included from library headers. #endif /* Declare a block of N temporary mpz_t values. These values are initialized to zero. You must add CLEANUP_TEMP() at the end of the function. Use TEMP(i) to access a pointer to the ith value. */ #define DECLARE_TEMP(N) \ struct { \ mpz_t value[(N)]; \ int len; \ mp_result err; \ } temp_ = { \ .len = (N), \ .err = MP_OK, \ }; \ do { \ for (int i = 0; i < temp_.len; i++) { \ mp_int_init(TEMP(i)); \ } \ } while (0) /* Clear all allocated temp values. */ #define CLEANUP_TEMP() \ CLEANUP: \ do { \ for (int i = 0; i < temp_.len; i++) { \ mp_int_clear(TEMP(i)); \ } \ if (temp_.err != MP_OK) { \ return temp_.err; \ } \ } while (0) /* A pointer to the kth temp value. */ #define TEMP(K) (temp_.value + (K)) /* Evaluate E, an expression of type mp_result expected to return MP_OK. If the value is not MP_OK, the error is cached and control resumes at the cleanup handler, which returns it. */ #define REQUIRE(E) \ do { \ temp_.err = (E); \ if (temp_.err != MP_OK) goto CLEANUP; \ } while (0) ================================================ FILE: rsamath.c ================================================ /* Name: rsamath.c Purpose: Implements part of PKCS#1, v. 2.1, June 14, 2002 (RSA Labs) Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include "rsamath.h" #include #include static mp_result s_rsa_transform(mp_int msg, mp_int exp, mp_int mod, mp_int out); /* Convert integer to octet string, per PKCS#1 v.2.1 */ mp_result rsa_i2osp(mp_int z, unsigned char* out, int len) { int excess_len = mp_int_binary_len(z); if (excess_len < len) return MP_RANGE; memset(out, 0, len); excess_len -= len; mp_int_to_binary(z, out + excess_len, len); return MP_OK; } /* Convert octet string to integer, per PKCS#1 v.2.1 */ mp_result rsa_os2ip(mp_int z, unsigned char* in, int len) { return mp_int_read_binary(z, in, len); } /* Primitive RSA encryption operation */ mp_result rsa_rsaep(mp_int msg, mp_int exp, mp_int mod, mp_int cipher) { return s_rsa_transform(msg, exp, mod, cipher); } /* Primitive RSA decryption operation */ mp_result rsa_rsadp(mp_int cipher, mp_int exp, mp_int mod, mp_int msg) { return s_rsa_transform(cipher, exp, mod, msg); } /* Primitive RSA signing operation */ mp_result rsa_rsasp(mp_int msg, mp_int exp, mp_int mod, mp_int signature) { return s_rsa_transform(msg, exp, mod, signature); } /* Primitive RSA verification operation */ mp_result rsa_rsavp(mp_int signature, mp_int exp, mp_int mod, mp_int msg) { return s_rsa_transform(signature, exp, mod, msg); } /* Compute the maximum length in bytes a message can have using PKCS#1 v.1.5 encoding with the given modulus */ int rsa_max_message_len(mp_int mod) { int num_bits = mp_int_count_bits(mod); int num_bytes = num_bits / CHAR_BIT; if (num_bytes < 11) { return 0; /* at least eleven bytes are required for padding */ } else { return num_bytes - 11; } } mp_result rsa_pkcs1v15_encode(unsigned char* buf, int msg_len, int buf_len, int tag, random_f filler) { /* Make sure there is enough space for the encoded output */ if (msg_len > (buf_len - 11)) return MP_RANGE; int msg_start = buf_len - msg_len; int pad_len = msg_start - 3; /* Move message to top of buffer -- these might overlap, so we rely on the semantics of memmove() here */ memmove(buf + msg_start, buf, msg_len); /* Set initial bytes as required by the specification */ buf[0] = 0x00; buf[1] = (unsigned char)tag; /* Fill with random padding. We'll just assume the filler function does the right thing and only writes the requested number of nonzero bytes */ (filler)(buf + 2, pad_len); /* Write separator between pad and message body */ buf[msg_start - 1] = 0x00; return MP_OK; } mp_result rsa_pkcs1v15_decode(unsigned char* buf, int buf_len, int tag, int* msg_len) { /* Make sure the buffer is syntactically valid */ if (buf_len < 11 || buf[0] != 0x00 || buf[1] != (unsigned char)tag) return MP_UNDEF; /* Figure out how many bytes of random padding there are */ int i = 2; int pad_len = 0; while (buf[i++] != '\0') ++pad_len; int data_start = i; int data_len = buf_len - data_start; /* Shift the message to the front of the buffer */ memmove(buf, buf + data_start, data_len); /* Zero out the rest of the buffer */ memset(buf + data_len, 0, pad_len + 3); *msg_len = data_len; return MP_OK; } static mp_result s_rsa_transform(mp_int msg, mp_int exp, mp_int mod, mp_int out) { if (mp_int_compare_zero(msg) < 0 || mp_int_compare(msg, mod) >= 0) { return MP_RANGE; } return mp_int_exptmod(msg, exp, mod, out); } /* Here there be dragons */ ================================================ FILE: rsamath.h ================================================ /* Name: rsamath.h Purpose: Implements part of PKCS#1, v. 2.1, June 14, 2002 (RSA Labs) Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #ifndef RSAMATH_H_ #define RSAMATH_H_ #include "imath.h" #ifdef __cplusplus extern "C" { #endif /* Function to fill a buffer with nonzero random bytes */ typedef void (*random_f)(unsigned char *, int); /* Convert integer to octet string, per PKCS#1 v.2.1 */ mp_result rsa_i2osp(mp_int z, unsigned char *out, int len); /* Convert octet string to integer, per PKCS#1 v.2.1 */ mp_result rsa_os2ip(mp_int z, unsigned char *in, int len); /* The following operations assume that you have converted your keys and message data into mp_int values somehow. */ /* Primitive RSA encryption operation */ mp_result rsa_rsaep(mp_int msg, mp_int exp, mp_int mod, mp_int cipher); /* Primitive RSA decryption operation */ mp_result rsa_rsadp(mp_int cipher, mp_int exp, mp_int mod, mp_int msg); /* Primitive RSA signing operation */ mp_result rsa_rsasp(mp_int msg, mp_int exp, mp_int mod, mp_int signature); /* Primitive RSA verification operation */ mp_result rsa_rsavp(mp_int signature, mp_int exp, mp_int mod, mp_int msg); /* Compute the maximum length in bytes a message can have using PKCS#1 v.1.5 encoding with the given modulus */ int rsa_max_message_len(mp_int mod); /* Encode a raw message per PKCS#1 v.1.5 buf - the buffer containing the message msg_len - the length in bytes of the message buf_len - the size in bytes of the buffer tag - the message tag (nonzero byte) filler - function to generate pseudorandom nonzero padding On input, the message is in the first msg_len bytes of the buffer; on output, the contents of the buffer are replaced by the padded message. If there is not enough room, MP_RANGE is returned. */ mp_result rsa_pkcs1v15_encode(unsigned char *buf, int msg_len, int buf_len, int tag, random_f filler); /* Decode a PKCS#1 v.1.5 message back to its raw form buf - the buffer containing the encoded message buf_len - the length in bytes of the buffer tag - the expected message tag (nonzero byte) msg_len - on output, receives the length of the message content On output, the message is packed into the first msg_len bytes of the buffer, and the rest of the buffer is zeroed. If the buffer is not of the correct form, MP_UNDEF is returned and msg_len is undefined. */ mp_result rsa_pkcs1v15_decode(unsigned char *buf, int buf_len, int tag, int *msg_len); #ifdef __cplusplus } #endif #endif /* end RSAMATH_H_ */ ================================================ FILE: tests/add.tc ================================================ # Addition tests add:0,0,0:0 add:0,0,=1:0 add:1,=1,=1:2 add:1,-1,0:0 add:-1,1,0:0 add:-1,1,=1:0 add:103427990038,909510006269847,0:909613434259885 add:128593002,-9007199254740992,0:-9007199126147990 add:-65537,70000,0:4463 add:-1000000,-6543210,0:-7543210 add:#x29C932F25E6CEF8046FA,#x-29C932F25E6CEF8046FA,0:0 add:2,#x7FFFFFFFF,0:#x800000001 add:95031018,=1,=1:190062036 add:#x-176E7F8018D6BA4B550AB36AAAFDC78A9,#x186DAD2485A41B18AAF5EF17922D7E5F1F,=1:#x16F6C52C8416AF73F5A543E0E77DA1E676 add:-628443782411312,-301652218193016,=2:-930096000604328 add:13731535,499104,0:14230639 add:46496,0,0:46496 add:85658949,0,0:85658949 add:3,86618070,0:86618073 add:-364,0,0:-364 add:916376,71094297,0:72010673 add:-76,-48988,0:-49064 add:7,98029,293800191852111:98036 add:213,0,0:213 add:116992,19352187,=1:19469179 add:-54334706,-2638935,0:-56973641 add:4210,4441,0:8651 add:2470,-1654142,0:-1651672 add:-32608,76896,0:44288 add:598200,65918574,0:66516774 add:-524863149,95573,0:-524767576 add:4,6856995,0:6856999 add:86710327,16209386,0:102919713 add:31,-24,0:7 add:5895523,9915789381,0:9921684904 add:41557511,310172,0:41867683 add:-6714,923,0:-5791 add:466232157,987,0:466233144 add:5919,-63,0:5856 add:929994,66871,0:996865 add:23,391,0:414 add:751,-25255,0:-24504 add:-282292,-1608,0:-283900 add:0,-4119448990,0:-4119448990 add:69248,-64165,0:5083 add:816106,580,0:816686 add:15171,219806,0:234977 add:945180,-585066,0:360114 add:27052,6664636892,0:6664663944 add:-481622,-578,0:-482200 add:926,-81,0:845 add:-4084,62941238721,=1:62941234637 add:888598,6601,0:895199 add:-61,143796,0:143735 add:408006264,51,0:408006315 add:-582073,-6752,0:-588825 add:88194084,595557600,0:683751684 add:4963532385,72932,0:4963605317 add:37370180,708428344,0:745798524 add:638718578,-94054,0:638624524 add:12603892606,194259,0:12604086865 add:9812049,8843056,0:18655105 add:-156093,-3718156523,0:-3718312616 add:12264,949557843298,0:949557855562 add:338742,9139,0:347881 add:48848,-6268099,0:-6219251 add:3653,981782890584,0:981782894237 add:608763646,38233135026,0:38841898672 add:-17063,-4811,0:-21874 add:63244008,-380818980,0:-317574972 add:624559862947,21088,0:624559884035 add:-268795562,74755169,0:-194040393 add:368827930,56987680,0:425815610 add:142,-838643130506,0:-838643130364 add:848909,137303147,0:138152056 add:6682221270,4495632518460,0:4502314739730 add:163999538727,754668,0:164000293395 add:570098317,1230642588,0:1800740905 add:814302609847,295465,0:814302905312 add:61148411120,462527703,0:61610938823 add:979075368979,64243429,0:979139612408 add:8280601099859,431312,0:8280601531171 add:29662,3920844058249,0:3920844087911 add:381765363,6285,0:381771648 add:6038301700102,167589011428,0:6205890711530 add:-6720,50309,0:43589 add:92070025383,8403955,0:92078429338 add:9057100,9331,0:9066431 add:46997620390,2556790331006,0:2603787951396 add:9853238961850,760016661497,0:10613255623347 add:642786326083,4994197649,0:647780523732 add:60934395,192791945290,0:192852879685 add:1304866806,9628566351206,0:9629871218012 add:-537871392295,1691988267,0:-536179404028 add:73595697641,63790,0:73595761431 add:87798124384590,168308169,0:87798292692759 add:77155772837617,993653875,0:77156766491492 add:691109994727,83820903066409,0:84512013061136 add:2012749349577,1194,0:2012749350771 add:3909606,1258809350,0:1262718956 add:5961027295,-191014,0:5960836281 add:-9155782013,84622,0:-9155697391 add:-7211667,-624806193439,0:-624813405106 add:1754076,931310,0:2685386 add:53288031910288,1866366148,0:53289898276436 add:767503182,-78473238204,0:-77705735022 add:-89763935864,-14028568280297,0:-14118332216161 add:454616605,67243118209653,0:67243572826258 add:674985,745910,0:1420895 add:9182866281585,-7492901984,0:9175373379601 add:8427973625,2948084578162,0:2956512551787 add:89366530,96670928089,0:96760294619 add:62255464298256,1694823,0:62255465993079 add:5268676160308,-93499502334390,0:-88230826174082 add:7165346,-12994330060,0:-12987164714 add:73330752719,904668539586,0:977999292305 add:8007349,88617667386,0:88625674735 add:951867792,807329,0:952675121 add:645715109491016,58609052382,0:645773718543398 add:2037750169321,85113205892,0:2122863375213 add:6585250,76715488825566,0:76715495410816 add:4585299,4140224,0:8725523 add:20194080,7047624,0:27241704 add:786913195,5197776759303,0:5198563672498 add:751261814658086,65539188,0:751261880197274 add:-6325172443258,2171993016413249,0:2165667843969991 add:3947284565,-78726628505,0:-74779343940 add:-71699817835206,40239308204,0:-71659578527002 add:53023714,-82553833053558,0:-82553780029844 add:2808131187169,890250230608190,0:893058361795359 add:4783795579,-953360022706,0:-948576227127 add:22326520,59606609543578,0:59606631870098 add:37110988189,2635629530529,0:2672740518718 add:5415787,65557975919,0:65563391706 add:687495904,-3296642739961554,0:-3296642052465650 add:72930835789,43382168425705304,0:43382241356541093 add:-995003864534,61722341747,0:-933281522787 add:74285863538462,4701124896071184,0:4775410759609646 add:-7259432400758987,917110091938734,0:-6342322308820253 add:83640964028613,28436773,0:83640992465386 add:12798300129,42764089830,0:55562389959 add:907689161228474,9984041726746,0:917673202955220 add:88648450941,-92224182312398621,0:-92224093663947680 add:3423736794,992566059450,0:995989796244 add:26095203,84516699542499712,0:84516699568594915 add:-664955461457,34154013,0:-664921307444 add:17408598155,57614703283466656,0:57614720692064811 add:734135582143613,8386599520,0:734143968743133 add:75433328059753089,3411724102,0:75433331471477191 add:-5780056339,370823068636155,0:370817288579816 add:747133022687630,743183409891560,0:1490316432579190 add:1351023965,562216806411,0:563567830376 add:8923051674,5453380084794,0:5462303136468 add:244571930,-51111880145,0:-50867308215 add:-41136584383913485,2817501078,0:-41136581566412407 add:-8079768063523410,441741295522855156,0:433661527459331746 add:599579537585,1505732756139,0:2105312293724 add:6728375739,634744472,0:7363120211 add:163686368,10797029513119,0:10797193199487 add:38258778569482,81136715091,0:38339915284573 add:89311393409893347,6487334114,0:89311399897227461 add:4413952309911,-335091846,0:4413617218065 add:-8490298221703,906197882389719833,0:906189392091498130 add:547446627581960679,4111395072,0:547446631693355751 add:-147199257725737,358585065185151457,0:358437865927425720 add:733104781218,1305401890,0:734410183108 add:66789232493812823,152353542633642764,0:219142775127455587 add:91447917877257,890149399042107596,0:890240846959984853 add:67840659340,45844535119015296,0:45844602959674636 add:31351681435877221,-442068622969770457,0:-410716941533893236 add:8505522087730720965,162001047045127445,0:8667523134775848410 add:90408836865703,91766097115,0:90500602962818 add:8278725919,-6565975065136635,0:-6565966786410716 add:778195404262806210,9985183887639111776,0:10763379291901917986 add:6696810212664216,312304914759219,0:7009115127423435 add:3557735824865,584593215289536,0:588150951114401 add:-49412044681,29956396329782239,0:29956346917737558 add:11923449620,7765655187,0:19689104807 add:1724176067,-67142223866,0:-65418047799 add:525722978624,57023088377443306,0:57023614100421930 add:726936921764427,3077076587081089,0:3804013508845516 add:1790333591126,-91682335574328992,0:-91680545240737866 add:-1112879092907469823,1867817571215,0:-1112877225089898608 add:-8476115918476,3323398534004,0:-5152717384472 add:83059391773,-65273298074046515729,0:-65273297990987123956 add:2211388311050688,-245146603838894173,0:-242935215527843485 add:585851683392336,3975804417513631370,0:3976390269197023706 add:139186663640090,15082756961,0:139201746397051 add:-48189710801086,-33546258184494787728,0:-33546306374205588814 add:-100779556817445,-1522038785339961,0:-1622818342157406 add:4885512159295669,480294778789866559,0:485180290949162228 add:-557882003905193311,20195805293900,0:-557861808099899411 add:154553862612072,9109218823125727072,0:9109373376988339144 add:1483847515783086714,78233016786768531473,0:79716864302551618187 add:632462956668123,-2951738540674650223,0:-2951106077717982100 add:-60943119399848141,74036520715371,0:-60869082879132770 add:-7905328383508507808,-207334403231,0:-7905328590842911039 add:-376183968178,-862976187364,0:-1239160155542 add:918327139068056021,-685922087142,0:918326453145968879 add:-9846497109055054870,6775447579440637,0:-9839721661475614233 add:-84073521083215,71309976692297262369,0:71309892618776179154 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addv:1414000736454,15931,0:1414000752385 addv:606227414766,517,0:606227415283 addv:717100323961,499,=2:717100324460 addv:-85406334226225355,-50533,=1:-85406334226275888 addv:-3753831486,-36277,0:-3753867763 addv:-58465715745893828,12779,=1:-58465715745881049 addv:2855399155447860,5468,0:2855399155453328 addv:4552049505281749,-33297,0:4552049505248452 addv:87837072754930,40967,=2:87837072795897 addv:-42693214607695890,-30492,0:-42693214607726382 addv:70742576302309,-20599,0:70742576281710 addv:118600972756003,10194,0:118600972766197 addv:-882812251166,55167,0:-882812195999 addv:-416381834108529,5090,0:-416381834103439 addv:2956620172683281,-15742,0:2956620172667539 addv:2711117679184010399584,9500,=2:2711117679184010409084 addv:1356315685039,40425,=1:1356315725464 addv:100388100074891247,28468,0:100388100074919715 addv:735453579551845,-55120,=2:735453579496725 addv:9573520208716968,57962,=1:9573520208774930 addv:22464333496911435917,45263,=2:22464333496911481180 addv:2318330134061664645524,35817,=1:2318330134061664681341 addv:40085116522469,35577,0:40085116558046 addv:-9824195637526213,46625,=2:-9824195637479588 addv:1387219546869173,16428,0:1387219546885601 addv:519326948996459554946,16498,0:519326948996459571444 addv:901089575144273153684,48818,0:901089575144273202502 addv:-7267047498859484256669593,10213,=1:-7267047498859484256659380 addv:2746871124496359442,58189,0:2746871124496417631 addv:-1505797511965887167260747,10886,0:-1505797511965887167249861 addv:816815491488878842,49097,=1:816815491488927939 addv:16917424131349552780253,38836,=2:16917424131349552819089 addv:957454833834708924361,39916,=1:957454833834708964277 addv:202026277214860503572,-38223,=2:202026277214860465349 addv:968746861113481671,1030,0:968746861113482701 addv:895889431267844251,44333,=2:895889431267888584 addv:-3357720693387242036833,6150,0:-3357720693387242030683 addv:659201417242721199959654444,44813,0:659201417242721199959699257 addv:-400853063392189225718219,-1010,0:-400853063392189225719229 addv:7218879194561993107952676021,-44154,0:7218879194561993107952631867 addv:4721568551140507782,28030,=1:4721568551140535812 addv:17034283717006469465522672,-11569,=1:17034283717006469465511103 addv:41795594273804830816397,-7668,=1:41795594273804830808729 ================================================ FILE: tests/bigmul.tc ================================================ 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sqr:1129243400327281633151431371474891473455867467281646580615131416918186134500058210362967474476291935913056166817170589720180888384893984130837655605609160519483475686999411456978438146043336536562159220682249690564087391733538120293725815373571240283145745271266418667658265953408844001550460545760069911655331444115026283289502832470850559638590225665815329814544221402813003890575490644213046498706732967784948480361985741430703857522843819419578526133778265155095749489410876608829677795172822626775506026922427707604322446404480105940239935673644113523059324254840712255877427181434254002649024354681415060823887,0:1275190657182721248462063420980207026343022717532622175860219061730792418936740434742094796665906100480439897110257178409857469307077098501942134999624668547631597875340226548233364555044904897637802662331582604911532131450166620402887103231322314236615939231233057651679712668806821697694902550747299740911409056026074325413724541784521105637039150272466375734348928193048571410349655195899575836960732640894105648518962149080274129413128568380000791288924018568364735478182966987827049189244120982249845311602108211176904677903690707944807032554116276797233387539070384134761545289596978472118656073247977568361787904215232007927547273675655812990627547232348919520589298481108958425401154144890217117213559902391607690446197638363620347853484948687625457207482930736345600737267824848389507129569922536325291727973935250559919378188248920389764990722709984543141728260567769676565198058565461309218448131493714100586880045778660348267815919731674340804133476623427737669995140408727297933180816128182764727848278876101607499408120957922795369902531715310169128136970642349303253384538063850831674689811408417573400679901877915536329660371027882694070998224914758044726450736635586342639879086413949670062421005617619755229788769 ================================================ FILE: tests/bintest.c ================================================ /* Name: bintest.c Purpose: Test driver for binary input/output formats from IMath. Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include "imath.h" int main(int argc, char* argv[]) { unsigned char buf[512]; mpz_t v, w; mp_result res; int len; if (argc < 2 || argv[1][0] == '\0') { fprintf(stderr, "Usage: bintest \n"); return 1; } mp_int_init(&v); mp_int_init(&w); res = mp_int_read_string(&v, 10, argv[1]); printf("Result code from mp_int_read_string() = %d (%s)\n", res, mp_error_string(res)); len = mp_int_binary_len(&v); printf("%d bytes needed to write this value in 2's complement.\n", len); res = mp_int_to_binary(&v, buf, sizeof(buf)); printf("Result code from mp_int_to_binary() = %d (%s)\n", res, mp_error_string(res)); if (res != MP_OK) { return 1; } int ix; for (ix = 0; ix < (len - 1); ++ix) { printf("%d.", buf[ix]); } printf("%d\n", buf[ix]); /* Try converting back... */ res = mp_int_read_binary(&w, buf, len); printf("Result code from mp_int_read_binary() = %d (%s)\n", res, mp_error_string(res)); if (res == MP_OK) { mp_int_to_string(&w, 10, (char*)buf, sizeof(buf)); printf("[%s]\n\n", buf); } len = mp_int_unsigned_len(&v); printf("%d bytes needed to write this value as unsigned.\n", len); res = mp_int_to_unsigned(&v, buf, sizeof(buf)); printf("Result code from mp_int_to_unsigned() = %d\n", res); if (res == MP_OK) { int ix; for (ix = 0; ix < (len - 1); ++ix) { printf("%d.", buf[ix]); } printf("%d\n", buf[ix]); } else { return 1; } res = mp_int_read_unsigned(&w, buf, len); printf("Result code from mp_int_read_unsigned() = %d (%s)\n", res, mp_error_string(res)); if (res == MP_OK) { mp_int_to_string(&w, 10, (char*)buf, sizeof(buf)); printf("[%s]\n\n", buf); } mp_int_clear(&v); mp_int_clear(&w); return 0; } ================================================ FILE: tests/bug-qread.c ================================================ #include #include "imrat.h" struct test { char* input; int radix; mp_result want; }; int main(int arch, char* argv[]) { struct test tests[] = { {"123", 10, 0}, {" 1ca", 16, 0}, {"1010", 2, 0}, {"123 ", 10, -5}, /* MP_TRUNC */ {"123/456", 8, 0}, {"123 / 456", 8, 0}, {"123 /", 8, -4}, /* MP_UNDEF */ {" -5/-3", 10, 0}, {NULL, 10, 0}, }; int errs = 0; for (int i = 0; tests[i].input != NULL; i++) { mpq_t value; mp_rat_init(&value); mp_result got = mp_rat_read_cstring(&value, tests[i].radix, tests[i].input, NULL); if (got != tests[i].want) { printf("ERROR: test %d: input \"%s\": got \"%s\", want \"%s\"\n", i + 1, tests[i].input, mp_error_string(got), mp_error_string(tests[i].want)); } } printf("REGRESSION: mp_rat_read_cstring inconsistent space handling: %s\n", errs ? "FAILED" : "OK"); return !errs; } ================================================ FILE: tests/bug-swap.c ================================================ /* Regression test for mp_int_swap() bug on self-stored values. */ #include #include "imath.h" int main(int argc, char* argv[]) { mpz_t a, b; int result; mp_int_init_value(&a, 1); mp_int_init_value(&b, 16); mp_int_swap(&a, &b); result = (a.digits == &(a.single) && b.digits == &(b.single) && a.digits[0] == 16 && b.digits[0] == 1); printf("REGRESSION: mp_int_swap() on self-stored values: %s\n", result ? "OK" : "FAILED"); mp_int_clear(&b); mp_int_clear(&a); return !result; } ================================================ FILE: tests/compare.tc ================================================ # Test ordinary signed comparisons cmp:0,0:$#0 cmp:0,1:$#-1 cmp:1,0:$#1 cmp:-1,1:$#-1 cmp:1,-1:$#1 cmp:123456789012345678901234567890,123456789012345678901234567891:$#-1 # Test unsigned comparisons cmpu:0,0:$#0 cmpu:0,1:$#-1 cmpu:1,0:$#1 cmpu:-1,1:$#0 cmpu:1,-1:$#0 cmpu:-25,15:$#1 cmpu:#x-ffffffffffffffff,#xfffffffffffffffe:$#1 # Test zero comparisons cmpz:0:$#0 cmpz:-25:$#-1 cmpz:105:$#1 # Test small-value comparisons cmpv:0,0:$#0 cmpv:0,1:$#-1 cmpv:1,0:$#1 cmpv:-1,1:$#-1 cmpv:1,-1:$#1 cmpv:499,108:$#1 cmpv:499,499:$#0 cmpv:499,-1024:$#1 ================================================ FILE: tests/conv.tc ================================================ # Output conversion tests tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,2:1111011101001010001010000111011010100001010000110010011010011000100100100011101100000111011001111101101000011001110111001111001111010111000101111001010111101110 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,3:22012212212000122111011022212212002120111111102001120012102211211202200102022110202002000211111221202 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,4:33131022022013122201100302122120210203230013121331220121313033033113011321113232 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,5:404041130042310320100141302000203430214122130002340212132414134210033 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,6:44515230120451152500101352430105520150025145320010504454125502 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,7:644641136612541136016610100564613624243140151310023515322 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,8:173512120732412062323044435407317550316717172705712756 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,9:265785018434285762514442046172754680368422060744852 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,10:1411774500397290569709059837552310354075408897518 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,11:184064268501499311A17746095910428222A241708032A tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,12:47706011B225950B02BB45602AA039893118A85950892 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,13:1A188C826B982353CB58422563AC602B783101671A86 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,14:105957B358B89B018958908A9114BC3DDC410B77982 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,15:CB7B3387E23452178846C55DD9D70C7CA9AEA78E8 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,16:F74A2876A1432698923B0767DA19DCF3D71795EE tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,17:17BF7C3673B76D7G7A5GA836277296F806E7453A tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,18:2EBG8HH3HFA6185D6H0596AH96G24C966DD3HG2 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,19:6G3HGBFEG8I3F25EAF61B904EIA40CFDH2124F tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,20:10AHC3D29EBHDF3HD97905CG0JA8061855C3FI tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,21:3BA5A55J5K699B2D09C38A4B237CH51IHA132 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,22:EDEA90DJ0B5CB3FGG1C8587FEB99D3C143CA tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,23:31M26JI1BBD56K3I028MML4EEDMAJK60LGLE tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,24:GGG5M3142FKKG82EJ28111D70EMHC241E4E tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,25:4446F4D5H10982023N297BF0DKBBHLLJB0I tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,26:12E9DEEOBMKAKEP0IM284MIP7FO1O521M46 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,27:85NN0HD48NN2FDDB1F5BMMKIB8CK20MDPK tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,28:2D882A7A0O0JPCJ4APDRIB77IABAKDGJP2 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,29:MFMCI0R7S27AAA3O3L2S8K44HKA7O02CN tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,30:7IGQS73FFSHC50NNH44B6PTTNLC3M6H78 tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,31:2KLUB3U9850CSN6ANIDNIF1LB29MJ43LH tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,32:UT52GTL18CJ9H4HR0TJTK6ESUFBHF5FE tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,33:BTVL87QQBMUGF8PFWU4W3VU7U922QTMW tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,34:4OG10HW0MSWJBIDEE2PDH24GA7RIHIAA tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,35:1W8W9AX2DRUX48GXOLMK0PE42H0FEUWN tostr:#xF74A2876A1432698923B0767DA19DCF3D71795EE,36:SVWI84VBH069WR15W1U2VTK06USY8Z2 # Conversion to binary tobin:0:0 tobin:-1:255 tobin:1:1 tobin:97:97 tobin:8492:33.44 tobin:-69393016:251.221.37.136 tobin:-218193:252.171.175 tobin:662844:10.29.60 tobin:8241131209300:7.126.201.178.194.84 tobin:705223363410:0.164.50.150.139.82 tobin:-28632557663:249.85.93.215.161 tobin:-553325346410701486:248.82.49.135.113.248.93.82 tobin:-907482337424:255.44.181.214.111.112 tobin:4770047168390927:16.242.85.39.8.167.15 tobin:977875907836789049:13.146.28.245.9.6.65.57 tobin:3572115845746903:12.176.210.8.21.16.215 tobin:28949534667733:26.84.86.186.243.213 tobin:-183125616657544851234:246.18.159.29.228.28.174.208.222 tobin:827162476353576735:11.122.171.227.198.150.95.31 tobin:77184512995655260:1.18.54.231.215.68.126.92 tobin:115255556962215997764:6.63.125.254.104.50.175.49.68 tobin:54297489021590339048:2.241.135.110.149.175.144.125.232 tobin:393928929335369918394864191:1.69.217.178.12.173.1.47.149.43.18.63 tobin:-75550878255305302924368236946:255.11.225.199.59.30.217.134.166.120.200.174.110 tobin:35784643040276670536818634:29.153.177.98.228.47.31.93.65.31.202 tobin:-5876364928874055124010543482048:181.212.112.219.201.219.43.162.130.153.141.251.64 tobin:555590330388726236230755046204154:27.100.137.45.209.201.206.212.69.137.217.165.34.250 tobin:2123372635933612270094308954044:26.204.252.173.123.198.84.97.94.88.53.79.188 tobin:373404212231777284568356947010238:18.105.6.21.0.246.144.164.13.115.91.8.162.190 tobin:355087294263155005473388626149338730:68.99.39.192.10.100.204.157.215.128.79.45.43.110.106 tobin:9075406350072985013229496898492710997:6.211.220.20.76.13.2.68.169.142.198.197.165.106.64.85 tobin:8633675426061757629757850232155550:1.169.172.77.223.131.135.137.86.71.95.134.109.237.158 tobin:-217191451486096670046812323372237867852:255.92.154.114.175.151.49.93.18.105.200.58.156.24.75.180.180 tobin:26829035080908738042076334435395170:5.42.198.7.200.110.201.64.35.201.25.125.64.230.98 tobin:16360606577002719669450329100985058711:12.78.240.46.160.248.51.247.149.232.48.220.205.240.69.151 tobin:26026773591715017125540836707619882:5.3.56.17.26.95.176.214.116.53.154.110.71.84.42 tobin:-315068060596719455443436752409094193:195.81.241.253.255.182.14.126.183.113.140.138.49.151.207 tobin:1404578023533398209741079145277644921444663:16.31.175.15.121.161.137.196.26.125.240.115.59.220.1.85.25.55 tobin:713575197074178787527618959331047471995825:8.49.2.79.246.51.45.90.242.199.86.95.47.64.104.90.91.177 tobin:83871430502261490413450673851124769661:63.25.12.201.105.63.89.102.174.73.208.109.149.109.99.125 tobin:1369887131891462493813741667459688172443624:15.185.188.136.198.40.60.46.152.22.161.146.105.88.210.253.87.232 tobin:829432057166494966641315010911028795638578:9.133.123.83.146.186.254.230.112.155.225.249.127.219.248.43.131.50 tobin:312089922808936140630879643949120224211369:3.149.38.92.196.150.155.232.60.223.247.126.50.176.14.127.177.169 tobin:152333180111442438605972376130506110244327899219:26.174.219.37.168.212.28.162.39.139.47.209.114.56.212.157.2.33.192.83 tobin:-2899223787613074281110944570982644571450999:222.183.242.113.50.20.39.238.192.239.78.170.102.70.102.231.209.137 tobin:444765267932710530788173695233378407323077034767:77.231.246.225.189.253.236.180.85.80.95.147.220.91.211.171.195.205.195.15 tobin:2928186048102542874310326072002539929893828809270937:7.211.139.211.153.76.242.8.164.101.41.243.188.255.255.239.194.98.21.205.38.153 tobin:-826647521214480264223642441769570761615607819637146:253.202.98.131.34.175.212.21.119.210.126.69.61.176.197.180.182.201.116.60.110.102 tobin:8400624623087855337736820815095169248114548022:1.120.178.112.248.52.41.234.187.122.100.10.161.143.20.186.83.68.157.54 tobin:-14981001549924280586667180618266982428182337700429:245.191.228.168.55.2.155.157.248.12.207.194.168.98.220.91.66.110.69.189.179 tobin:710160715229320560332911086106093153060357460087262479:7.106.23.173.245.150.209.228.252.222.62.180.93.143.150.200.182.76.119.140.239.205.15 tobin:73883264784349702632503413711514594728450092072160898:0.197.120.251.47.105.95.210.233.70.183.8.43.3.136.2.36.106.51.96.215.206.130 # Conversion from binary readbin:0:0 readbin:255:-1 readbin:1:1 readbin:97:97 readbin:33.44:8492 readbin:251.221.37.136:-69393016 readbin:252.171.175:-218193 readbin:10.29.60:662844 readbin:7.126.201.178.194.84:8241131209300 readbin:0.164.50.150.139.82:705223363410 readbin:249.85.93.215.161:-28632557663 readbin:248.82.49.135.113.248.93.82:-553325346410701486 readbin:255.44.181.214.111.112:-907482337424 readbin:16.242.85.39.8.167.15:4770047168390927 readbin:13.146.28.245.9.6.65.57:977875907836789049 readbin:12.176.210.8.21.16.215:3572115845746903 readbin:26.84.86.186.243.213:28949534667733 readbin:246.18.159.29.228.28.174.208.222:-183125616657544851234 readbin:11.122.171.227.198.150.95.31:827162476353576735 readbin:1.18.54.231.215.68.126.92:77184512995655260 readbin:6.63.125.254.104.50.175.49.68:115255556962215997764 readbin:2.241.135.110.149.175.144.125.232:54297489021590339048 readbin:1.69.217.178.12.173.1.47.149.43.18.63:393928929335369918394864191 readbin:255.11.225.199.59.30.217.134.166.120.200.174.110:-75550878255305302924368236946 readbin:29.153.177.98.228.47.31.93.65.31.202:35784643040276670536818634 readbin:181.212.112.219.201.219.43.162.130.153.141.251.64:-5876364928874055124010543482048 readbin:27.100.137.45.209.201.206.212.69.137.217.165.34.250:555590330388726236230755046204154 readbin:26.204.252.173.123.198.84.97.94.88.53.79.188:2123372635933612270094308954044 readbin:18.105.6.21.0.246.144.164.13.115.91.8.162.190:373404212231777284568356947010238 readbin:68.99.39.192.10.100.204.157.215.128.79.45.43.110.106:355087294263155005473388626149338730 readbin:6.211.220.20.76.13.2.68.169.142.198.197.165.106.64.85:9075406350072985013229496898492710997 readbin:1.169.172.77.223.131.135.137.86.71.95.134.109.237.158:8633675426061757629757850232155550 readbin:255.92.154.114.175.151.49.93.18.105.200.58.156.24.75.180.180:-217191451486096670046812323372237867852 readbin:5.42.198.7.200.110.201.64.35.201.25.125.64.230.98:26829035080908738042076334435395170 readbin:12.78.240.46.160.248.51.247.149.232.48.220.205.240.69.151:16360606577002719669450329100985058711 readbin:5.3.56.17.26.95.176.214.116.53.154.110.71.84.42:26026773591715017125540836707619882 readbin:195.81.241.253.255.182.14.126.183.113.140.138.49.151.207:-315068060596719455443436752409094193 readbin:16.31.175.15.121.161.137.196.26.125.240.115.59.220.1.85.25.55:1404578023533398209741079145277644921444663 readbin:8.49.2.79.246.51.45.90.242.199.86.95.47.64.104.90.91.177:713575197074178787527618959331047471995825 readbin:63.25.12.201.105.63.89.102.174.73.208.109.149.109.99.125:83871430502261490413450673851124769661 readbin:15.185.188.136.198.40.60.46.152.22.161.146.105.88.210.253.87.232:1369887131891462493813741667459688172443624 readbin:9.133.123.83.146.186.254.230.112.155.225.249.127.219.248.43.131.50:829432057166494966641315010911028795638578 readbin:3.149.38.92.196.150.155.232.60.223.247.126.50.176.14.127.177.169:312089922808936140630879643949120224211369 readbin:26.174.219.37.168.212.28.162.39.139.47.209.114.56.212.157.2.33.192.83:152333180111442438605972376130506110244327899219 readbin:222.183.242.113.50.20.39.238.192.239.78.170.102.70.102.231.209.137:-2899223787613074281110944570982644571450999 readbin:77.231.246.225.189.253.236.180.85.80.95.147.220.91.211.171.195.205.195.15:444765267932710530788173695233378407323077034767 readbin:7.211.139.211.153.76.242.8.164.101.41.243.188.255.255.239.194.98.21.205.38.153:2928186048102542874310326072002539929893828809270937 readbin:253.202.98.131.34.175.212.21.119.210.126.69.61.176.197.180.182.201.116.60.110.102:-826647521214480264223642441769570761615607819637146 readbin:1.120.178.112.248.52.41.234.187.122.100.10.161.143.20.186.83.68.157.54:8400624623087855337736820815095169248114548022 readbin:245.191.228.168.55.2.155.157.248.12.207.194.168.98.220.91.66.110.69.189.179:-14981001549924280586667180618266982428182337700429 readbin:7.106.23.173.245.150.209.228.252.222.62.180.93.143.150.200.182.76.119.140.239.205.15:710160715229320560332911086106093153060357460087262479 readbin:0.197.120.251.47.105.95.210.233.70.183.8.43.3.136.2.36.106.51.96.215.206.130:73883264784349702632503413711514594728450092072160898 # # -- From Tom Wu, triggered a bug in s_qmul(): # readbin:22.200.146.12.243.10.174.111.79.92.242.37.59.156.205.75.163.223.107.103.20.203.19.168.35.69.241.146.93.87.91.210:10305260085868809781027103920001537650251216529133196585936939957967423757266 # Conversion to unsigned to-uns:19:19 to-uns:732849:11.46.177 to-uns:2456939301:146.113.235.37 to-uns:65221819301662:59.81.163.94.255.30 to-uns:-844378241131209300:11.183.213.137.94.177.226.84 to-uns:8570522336341023286325:1.208.155.227.240.84.37.160.100.53 to-uns:57663995533253464107014863:47.178.211.118.41.71.211.74.100.90.207 to-uns:290748233742495477004716839092:3.171.117.77.85.127.49.10.213.243.253.144.180 to-uns:7769778759078367890498335721158457:1.127.20.101.49.86.0.169.68.4.237.33.216.119.57 to-uns:46903702894953466773316183125616657544:35.73.83.24.98.4.211.124.18.69.32.88.95.142.132.136 to-uns:-851234028271624763535767352077184512995655:9.197.141.78.121.20.132.41.143.246.59.33.126.2.92.102.177.71 to-uns:-2609311525555696221599776451542974890215903390:117.1.109.101.2.62.220.206.134.57.198.156.134.252.135.230.114.144.158 to-uns:48673939289293353699183948641914875550878255305302:33.77.214.236.147.20.12.74.7.55.12.207.229.43.143.81.121.102.216.82.86 to-uns:924368236946243578464304027667053681863478587636492887:9.166.158.105.220.232.187.149.229.98.114.203.143.151.179.13.117.242.141.170.94.170.87 to-uns:4055124010543482048995555903303887262362307550462041543621:165.97.120.89.181.168.202.95.163.0.0.6.89.126.141.209.204.168.88.165.194.166.83.197 to-uns:23372635933612270094308954044673734042122317772845683569470102:14.139.121.201.25.49.14.230.89.139.204.223.141.232.201.189.74.36.63.100.115.152.44.110.42.150 to-uns:382935508729426315500547338862614933873079907540635007298501322949:3.162.221.90.36.235.220.148.206.72.220.121.230.47.59.194.10.29.105.64.171.5.133.101.247.195.168.197 to-uns:6898492710997158633675426061757629757850232155550392171914514860966700:255.225.26.217.121.147.85.123.62.227.155.115.151.17.14.226.20.151.216.70.129.251.123.127.200.253.229.131.44 to-uns:46812323372237867852342682903508090873804207633443539517026163606065770027:26.126.173.147.234.225.62.206.132.172.56.142.212.124.86.139.56.123.128.83.59.140.190.156.37.116.71.8.107.238.43 to-uns:196694503291009850587117226026773591715017125540836707619882023150680605967194:1.178.221.36.198.34.91.147.187.41.80.248.32.21.173.116.21.184.114.128.226.148.105.231.211.137.139.144.142.36.59.195.90 to-uns:-5544343675240909419388140457802353339820974107914527764492144466356713575197074178:187.9.226.242.27.68.215.247.155.152.75.195.109.94.123.200.36.80.1.19.58.240.99.181.158.175.120.210.195.130.202.54.99.2 to-uns:78752761895933104747199582531838714305022614904134506738511247696618513698871318914624:40.137.215.13.233.153.110.152.75.205.157.188.162.180.175.192.136.147.0.49.169.41.111.20.20.6.222.4.94.232.86.88.35.227.166.64 to-uns:938137416674596881724436242382943205716649496664131501091102879563857843031208992280893614:7.94.95.163.78.130.176.52.11.67.110.168.191.141.240.164.45.130.231.131.248.48.191.162.48.249.20.181.82.141.159.150.82.213.105.159.88.174 to-uns:-630879643949120224211369280152333180111442438605972376130506110244327899219912899223787613074:19.91.70.129.236.212.139.74.185.0.218.23.135.137.133.202.56.181.112.58.173.172.130.179.124.221.173.55.223.123.126.130.88.154.176.35.3.43.146 to-uns:28111094457098264457145099945444765267932710530788173695233378407323077034767182928186048102542874:13.41.35.240.41.168.225.145.107.18.87.253.43.231.202.150.209.215.163.157.127.252.45.194.199.62.14.60.97.225.213.204.55.37.185.133.79.239.24.46.26 # Conversion from unsigned readuns:19:19 readuns:11.46.177:732849 readuns:146.113.235.37:2456939301 readuns:59.81.163.94.255.30:65221819301662 readuns:11.183.213.137.94.177.226.84:844378241131209300 readuns:1.208.155.227.240.84.37.160.100.53:8570522336341023286325 readuns:47.178.211.118.41.71.211.74.100.90.207:57663995533253464107014863 readuns:3.171.117.77.85.127.49.10.213.243.253.144.180:290748233742495477004716839092 readuns:1.127.20.101.49.86.0.169.68.4.237.33.216.119.57:7769778759078367890498335721158457 readuns:35.73.83.24.98.4.211.124.18.69.32.88.95.142.132.136:46903702894953466773316183125616657544 readuns:9.197.141.78.121.20.132.41.143.246.59.33.126.2.92.102.177.71:851234028271624763535767352077184512995655 readuns:117.1.109.101.2.62.220.206.134.57.198.156.134.252.135.230.114.144.158:2609311525555696221599776451542974890215903390 readuns:33.77.214.236.147.20.12.74.7.55.12.207.229.43.143.81.121.102.216.82.86:48673939289293353699183948641914875550878255305302 readuns:9.166.158.105.220.232.187.149.229.98.114.203.143.151.179.13.117.242.141.170.94.170.87:924368236946243578464304027667053681863478587636492887 readuns:165.97.120.89.181.168.202.95.163.0.0.6.89.126.141.209.204.168.88.165.194.166.83.197:4055124010543482048995555903303887262362307550462041543621 readuns:14.139.121.201.25.49.14.230.89.139.204.223.141.232.201.189.74.36.63.100.115.152.44.110.42.150:23372635933612270094308954044673734042122317772845683569470102 readuns:3.162.221.90.36.235.220.148.206.72.220.121.230.47.59.194.10.29.105.64.171.5.133.101.247.195.168.197:382935508729426315500547338862614933873079907540635007298501322949 readuns:255.225.26.217.121.147.85.123.62.227.155.115.151.17.14.226.20.151.216.70.129.251.123.127.200.253.229.131.44:6898492710997158633675426061757629757850232155550392171914514860966700 readuns:26.126.173.147.234.225.62.206.132.172.56.142.212.124.86.139.56.123.128.83.59.140.190.156.37.116.71.8.107.238.43:46812323372237867852342682903508090873804207633443539517026163606065770027 readuns:1.178.221.36.198.34.91.147.187.41.80.248.32.21.173.116.21.184.114.128.226.148.105.231.211.137.139.144.142.36.59.195.90:196694503291009850587117226026773591715017125540836707619882023150680605967194 readuns:187.9.226.242.27.68.215.247.155.152.75.195.109.94.123.200.36.80.1.19.58.240.99.181.158.175.120.210.195.130.202.54.99.2:5544343675240909419388140457802353339820974107914527764492144466356713575197074178 readuns:40.137.215.13.233.153.110.152.75.205.157.188.162.180.175.192.136.147.0.49.169.41.111.20.20.6.222.4.94.232.86.88.35.227.166.64:78752761895933104747199582531838714305022614904134506738511247696618513698871318914624 readuns:7.94.95.163.78.130.176.52.11.67.110.168.191.141.240.164.45.130.231.131.248.48.191.162.48.249.20.181.82.141.159.150.82.213.105.159.88.174:938137416674596881724436242382943205716649496664131501091102879563857843031208992280893614 readuns:19.91.70.129.236.212.139.74.185.0.218.23.135.137.133.202.56.181.112.58.173.172.130.179.124.221.173.55.223.123.126.130.88.154.176.35.3.43.146:630879643949120224211369280152333180111442438605972376130506110244327899219912899223787613074 readuns:13.41.35.240.41.168.225.145.107.18.87.253.43.231.202.150.209.215.163.157.127.252.45.194.199.62.14.60.97.225.213.204.55.37.185.133.79.239.24.46.26:28111094457098264457145099945444765267932710530788173695233378407323077034767182928186048102542874 # Conversion to small signed integers to-int:0:0 to-int:399392010000012093849283940182938492839481928349823984:$MP_RANGE to-int:-29381082039841029384018230948203801985928309481203984:$MP_RANGE to-int:-25:-25 to-int:101:101 to-int:-1235:-1235 # Conversion to small signed integers to-uint:0:0 to-uint:1:1 to-uint:10:10 to-uint:-15:$MP_RANGE to-uint:101:101 to-uint:100000000000000000000000000000000000000000000000000:$MP_RANGE # Tests to trigger off-by-one bug in computing number of digits needed for string tostr:99999999999999999999999999999,10:99999999999999999999999999999 tostr:9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999,10:9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 tostr:832136388736902947561088644572239329432528812529007215254079045034263648726187965907662527121488680217097287175564480588901672671661161,10:832136388736902947561088644572239329432528812529007215254079045034263648726187965907662527121488680217097287175564480588901672671661161 ================================================ FILE: tests/div.tc ================================================ # Division tests # Tests for error conditions div:102233,0,=1,1:$MP_UNDEF,? div:0,=1,583922,-12345:$MP_UNDEF,? # Sign preservation (a == b*q + r) div:5,-3,0,0:-1,2 div:-5,3,0,0:-1,-2 div:-5,-3,0,0:1,-2 # General division tests, verified using GNU bc div:0,847887705,0,0:0,0 div:80000000000000000000,25,0,0:3200000000000000000,0 div:65000,25,0,0:2600,0 div:800000000000000,25,0,0:32000000000000,0 div:-4,58,0,0:0,-4 div:36869,818935,0,0:0,36869 div:364,921,0,0:0,364 div:5169,898,0,0:5,679 div:#x100000000,#xE424,=1,0:#x11F42,#xD2B8 div:-6144,15855207,0,0:0,-6144 div:680441,-8247,0,0:-82,4187 div:-31218529,577983165,0,0:0,-31218529 div:3,6280,0,0:0,3 div:-2,39790,0,0:0,-2 div:-310,611711,0,0:0,-310 div:46573596,6038351,0,0:7,4305139 div:4525534,39110,0,0:115,27884 div:5938,7789378,0,0:0,5938 div:19732849245693930165221819301662844,18446744073709551616,=1,=2:1069719901075515,6029073732495380604 div:9,456578633,=2,=1:0,9 div:538090499,1858,0,0:289607,693 div:572,3804550,0,0:0,572 div:288850,21164,0,0:13,13718 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divp2:5771713949080,24,0,0:344020,16100760 divp2:-192975675937641,21,0,0:-92017972,-1921897 divp2:51399227509,40,0,0:0,51399227509 divp2:76781489061746141,15,0,0:2343185090995,21981 divp2:624421287579358777,15,0,0:19055825426616,5689 divp2:585792449987,17,0,0:4469241,93635 divp2:64111034807,16,0,0:978256,49591 divp2:-4872049514614819145,60,0,0:-4,-260363496187431241 divp2:-513726738058624,27,0,0:-3827562,-62639488 divp2:-5129414645415250,35,0,0:-149285,-21103148370 divp2:9777073958585027,20,0,0:9324144323,950979 divp2:4917705257,31,0,0:2,622737961 divp2:9309157350108809,25,0,0:277434508,16969353 divp2:549889891480003,40,0,0:500,134077592003 divp2:43259632605223,33,0,0:5036,721999911 divp2:80760535636025,12,0,0:19716927645,2105 divp2:95148114869248768947,22,0,0:22685078351318,2276275 divp2:72784357307196492,23,0,0:8676571525,9292 divp2:8695487295473310914,48,0,0:30892,162314927725762 divp2:-999894977194,21,0,0:-476787,-166570 divp2:422873004052896,16,0,0:6452529969,4512 divp2:5850059500167,33,0,0:681,314043015 divp2:279461298693250805,55,0,0:7,27259719560503029 divp2:-2391765116812271696,39,0,0:-4350595,-221690208336 divp2:93848076004932,44,0,0:5,5887145782852 divp2:54463987988137594412,48,0,0:193494,268844485922348 divp2:9735669349328114,31,0,0:4533524,691512562 divp2:-96573804848256945392306,69,0,0:-163,-355587759787924163250 divp2:693910684713664114,18,0,0:2647059191565,48754 divp2:56085146568929935461,53,0,0:6226,6324008912519269 divp2:7090107398039299,30,0,0:6603177,81864451 divp2:767239571830013898753,66,0,0:10,29369808881631834113 divp2:-74636360117262549362461,43,0,0:-8485171760,-6890174916381 divp2:5461169750136459,50,0,0:4,957570122765963 divp2:976702847245116276,37,0,0:7106448,71221928820 divp2:3617864287401198,48,0,0:12,240164566873326 divp2:-1309978694518086461,40,0,0:-1191418,-749976460093 divp2:-2386749120888691269,33,0,0:-277854167,-244046405 divp2:7266512965529689,33,0,0:845933,3826315353 divp2:-6961513563355648932180971,48,0,0:-24732264461,-193888863384555 divp2:5143351773441402886258,50,0,0:4568214,56404232132722 divp2:900799510679250396,62,0,0:0,900799510679250396 divp2:30978095034050773575947556,48,0,0:110056301970,184099523155236 divp2:398942302365209775391228,57,0,0:2768218,44660240185115132 divp2:914903526125867075664,27,0,0:6816562459810,77563984 divp2:2551094792632393428431439,87,0,0:0,2551094792632393428431439 divp2:6909886286515846175008,60,0,0:5993,427709407012247840 divp2:461670131377821667,44,0,0:26242,15985200256995 divp2:7884527998899506514865191,44,0,0:448183527561,3748608715815 divp2:-17784618887403951072,44,0,0:-1010938,-9512034128864 divp2:-2928855265612995457576576,88,0,0:0,-2928855265612995457576576 divp2:8468445340017772238,58,0,0:29,109764431618131662 divp2:97699128177500917404004263,94,0,0:0,97699128177500917404004263 divp2:-901210903909447624384117,51,0,0:-400218038,-507572120280693 divp2:-9099254471589743272646814275,80,0,0:-7526,-878753170044103808133699 divp2:88420842262358445100031098,32,0,0:20587081616362194,3379223674 divp2:5920604485769478876616913,30,0,0:5513992612966782,320526545 # Division by small integers divv:5,-3,0:-1,2 divv:-5,3,0:-1,-2 divv:-5,-3,0:1,-2 divv:-5721818303,-31144,0:183721,-11479 divv:100359289911028,16,0:6272455619439,4 divv:-80498620,-41490,0:1940,-8020 divv:37386622,55859,0:669,16951 divv:501578,15096,0:33,3410 divv:6823,11067,0:0,6823 divv:-56695604,31395,0:-1805,-27629 divv:396,1627,0:0,396 divv:82237128,16423,0:5007,7167 divv:274600467,39390,0:6971,12777 divv:258805,22852,0:11,7433 divv:5139922232,23459,0:219102,8414 divv:8755497783395,46470,0:188411830,43295 divv:56370361453114,52292,0:1077992072,24090 divv:81119249096,17631,0:4600944,5432 divv:3925148017708459,17729,0:221397034108,7727 divv:-289130964,59901,0:-4826,-48738 divv:-2394107507926474,13709,0:-174637647379,-7763 divv:-50229865870,26540,0:-1892609,-23010 divv:3694598237147,64566,0:57222040,2507 divv:-158417511658676756,-64615,0:2451714178730,-37806 divv:4290308067505999,15193,0:282387156421,1746 divv:560784439224,18032,0:31099403,4328 divv:9207709447044,43308,0:212609897,27768 divv:42833310641849859264,57815,0:740868470844069,10029 divv:-95089845960500,-61243,0:1552664728,-23596 divv:80687877739837,-30796,0:-2620076559,28873 divv:87851714436662969875,61349,0:1431999126907740,28615 divv:-5469457537,11848,0:-461635,-6057 divv:-87902672172139257996,27307,0:-3219052703414481,-25329 divv:-694576880064214,41179,0:-16867259527,-1881 divv:47595892116434828,47204,0:1008302095509,27992 divv:-505437926464614447947,63863,0:-7914409383596361,-45404 divv:-747214784268033231559289,38881,0:-19217992959749832348,-36701 divv:40648086806090824914,-26501,0:-1533832187694457,19957 divv:23860923193973296,51883,0:459898679605,27081 divv:-54927711987466879,-11937,0:4601467034218,-6613 divv:4311756940677447464744993405,57924,0:74438176587898754656877,50057 divv:6015889311543917179186719299,-50635,0:-118808913035329656940588,45919 divv:3915173119649887691276,20797,0:188256629304702009,10103 divv:209840208083311316090,36847,0:5694906181868573,6759 divv:80000000000000000000,25,0:3200000000000000000,0 divv:65000,25,0:2600,0 divv:800000000000000,25,0:32000000000000,0 # More regular division tests, all with remainder zero div:2546905999569583642767,14957376976449,0,0:170277583,0 div:8820890915810513585008,1290654714992,0,0:6834431249,0 div:32722399167479650872,485171756,0,0:67444979562,0 div:281565136283209685892638788,662476076955569,0,0:425019326852,0 div:378946105625441540737303,730177609549,0,0:518977986547,0 div:4582336996784637790714331883462,524659399010705751,0,0:8733927201962,0 div:30908196512568974558050436710,558351619821782,0,0:55356150882905,0 div:22323179841972640636983704753,52956211127329649,0,0:421540351297,0 div:52861155259463695471936251160,9468000366853,0,0:5583138277489720,0 div:63260535208765360919938678377,42122224781389,0,0:1501832715082893,0 div:28984143265639802151626094051438,400082299653446,0,0:72445452574997853,0 div:3317964166851176108015612343691026488,4043377664512227983,0,0:820592198441457736,0 div:66344183633702866132053676311141052606577,91178778320288608847,0,0:727627468320008374591,0 div:5695550794829300030546270882518324992076491,700880200540761512031,0,0:8126282908883599504661,0 div:39037424763225371397599506194643545880,7823304879274443640,0,0:4989889230399751117,0 div:436302766535175847931361924986715811355695802824125,539874776595118725233603625,0,0:808155493551392334022517,0 div:346745970223883677972239586841121624456285168,91526846077189641641348,0,0:3788461911289433710716,0 div:52724986995800116311347732059133990047851510404883234,568154076534742483223872266,0,0:92800508125151146767566749,0 div:2377848542111935708145523356022435793438514852230023651,78161062689778162572883876143153,0,0:30422418276855244470867,0 div:232771550187355002750375300477927538332648185231317422242,385169380058229884085331084789,0,0:604335552717520311627548378,0 # Bug fix regression tests div:#xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,#xFFFFFFFFFFFFFFFFFFFFFFFC7,=1,=2:#x100000000000000000000000390000000000000000000000CB1000000000000000000002D369,#xA11260 div:#xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,#xFFFFFFFFFFFFFFFFFFFFFFFC7,0,0:#x100000000000000000000000390000000000000000000000CB1000000000000000000002D369,#xA11260 div:#xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001,65532,=1,=2:#x100040010004001000400100040010004001000400100040010004001000400100040010004001000400100040010004000fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80fe03f80,#xfe01 div:#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div:#xC085B984D2F30F92A00B8814DCF9A909C8672B081225AA88A7293D276E46B240B96E345B76A5E2D4E5CE7F4C208616DD38CA2029C37FAA8EF2561C688DA55150788FF7F34E484596590DDE971387608FB88D92A8868F4A2F165D0222A272C5AC300AFEBB152B25D3FAB5999458B1AC27FAE5E2ED6D50E7F8FDE7E22178E4C954,#xD607ECBE4F4608C16A0FBDF0F4DC57278E937A73D2226CE8388C6B9B9DF9C58464CF3E05F29FC58B59CD34CBA4F47810D92B7B4FCAAD1860C76E091D0B1491B9,=1,=2:#xE64618B3D9A1E9B5DC38D204743994492C406B98FFFFFF95EF529A267E06AF4364F984172C9569DC33FCA47F08195C2937CD1CAAE1F954A2A78AA08AF59EC954,#x5BAA50658645474B56E43FF89470E38A4D69E90D43F0E1D5DBCAFDE8853AEDBAC364F06CE50511DEA15DE5D944D9ABBEA76EF56D1E1E2732AC396304B28CB7A0 div:#xFFFFFFFF400000002,#x7FFFFFFFE,0,0:#x1FFFFFFFF,0 # Spin in s_udiv(), rep. by Andres Navarro. div:45035996273705000,45035996273704960,0,0:1,40 # ISL test failures div:-110768999339257979395151936604514986,384307167128540502,0,0:-288230376151711743,0 div:-1141798147252782335678234520236874583761538254,990352029122461210705605426,0,0:-1152921500311879679,0 div:-11417981504429295188771564013355757832033533955,2475880072806153026764013565,0,0:-4611686014132420607,0 div:-19746054620424668475119147467564405598366894325375493578959094720,137015778031883893401769208133025156060969696320,0,0:-144115188075855871,0 div:81791893044,81791893043,0,0:1,1 div:66461399479760783996783510248698675,57646074961906893,0,0:1152921504606846975,0 div:4951760153682756594365890554,8589934586,0,0:576460752303423489,0 div:9903520270472025075672416238,25769803758,0,0:384307166770626561,0 div:11141460315522012760862883825,48318382095,0,0:230584300062375935,0 ================================================ FILE: tests/egcd.tc ================================================ # Extended greatest common divisor tests, including # constants satisfying Bezout's identity egcd:7,328492456,0,0,0:1,-140782481,3 egcd:930165221,819,0,=1,0:1,-85,96537294 egcd:166,0,0,0,=1:166,1,0 egcd:44,37824113,0,0,0:1,12894584,-15 egcd:0,93,0,0,0:93,0,1 egcd:70522336,34102,0,0,0:2,-2785,5759331 egcd:863,25,0,0,0:1,2,-69 egcd:66399,5533253,0,0,0:1,1229584,-14755 egcd:4107,14863,0,0,0:1,-1643,454 egcd:7,482337424,0,0,0:1,206716039,-3 egcd:477004716,83909,0,0,0:1,26067,-148185319 egcd:76,9778759,0,0,0:1,2187354,-17 egcd:0,8367890,0,0,0:8367890,0,1 egcd:8335,721158457,0,0,0:1,-159892121,1848 egcd:90370,2894953,0,0,0:1,591452,-18463 egcd:67733,1618312,0,0,0:1,-106035,4438 egcd:166575,4485123,0,0,0:3,-397448,14761 egcd:28271,6,0,0,0:1,-1,4712 egcd:763,53576,0,0,0:1,-18397,262 egcd:52077184,5129,0,0,0:1,1375,-13961031 egcd:6552609311,525555,0,0,0:1,173606,-2164516163 egcd:6221599,7764515429,0,0,0:1,2913991310,-2334941 egcd:89021590,33904,0,0,0:2,-5437,14275908 egcd:739392892,9335369,0,0,=2:1,817116,-64718359 egcd:8394864191,48,0,0,0:1,-1,174893004 egcd:55087825,530530,0,0,0:65,-1805,187423 egcd:243,6823694624,0,0,0:1,2218402779,-79 egcd:7846,430402,0,0,0:2,-77457,1412 egcd:67053681,8634785,0,0,0:1,-3793089,29455346 egcd:6364928874,55124010,=1,=2,0:6,4571384,-527837761 egcd:3482048,995555,0,0,0:1,328872,-1150261 egcd:33038872623,62,0,0,0:1,-13,6927505550 egcd:75504,62,0,0,0:2,5,-6089 egcd:15,436212,0,0,0:3,29081,-1 egcd:72635,93361,0,=1,=2:1,-22347,17386 egcd:7009,4308,0,0,0:1,697,-1134 egcd:40446737340,4212231,0,0,0:3,100060,-960797387 egcd:728456835,694701023,0,0,0:1,99101538,-103916923 egcd:9355087294,2631,0,0,0:1,790,-2809015189 egcd:54733,8862614,0,0,0:1,-1246171,7696 egcd:38730799075,40635,0,0,0:5,-514,489913393 egcd:72,98,0,0,0:2,15,-11 egcd:1322949,68,0,0,0:1,-15,291827 egcd:49271099715,8633675426,0,0,0:1,-3947828585,22529669726 egcd:175,762975785,0,0,0:5,-34878893,8 egcd:321,55550,0,0,0:1,26131,-151 egcd:217191,451486096670,0,0,0:1,198071748991,-95284 egcd:681,2323372,0,0,0:1,917749,-269 egcd:78678,523426,0,0,0:2,98880,-14863 egcd:90350809087,38042,0,0,0:1,7341,-17435079373 egcd:633,4435395170,0,0,0:1,406402717,-58 egcd:16360,606577002,0,0,0:2,-128322922,3461 egcd:9669450329,1009,0,0,0:1,293,-2807878044 egcd:5871172260,26773591,0,0,0:1,6401741,-1403835749 egcd:5017125540,8367,0,0,0:3,71,-42573911 egcd:619,8820231506,0,0,0:1,270734085,-19 egcd:60596719455,443,0,0,0:1,-151,20654863742 egcd:6752409,94193,0,0,0:1,3303,-236782 egcd:14045780235,33398209741,0,0,0:1,-7792585660,3277209961 egcd:9145,27764492144,0,0,0:1,-4065243847,1339 egcd:63567135,7519707417,0,0,0:3,-485762107,4106344 egcd:875276189593,31047471995,0,0,0:1,-4089317138,115284166233 egcd:531838714305,22614,0,0,0:3,-2211,51998558297 egcd:4134506738511,2476,0,0,0:1,-377,629527076098 egcd:6185136988713,1891462493,0,0,0:1,-495247968,1619475161045 egcd:374166745968,81724,0,0,0:4,9131,-41805547421 egcd:62423829,4320571,0,0,0:1,-1655596,23920135 egcd:4949666413,1501091102,0,0,0:1,494932087,-1631978715 egcd:956385784303,12089922808,0,0,0:1,1485803831,-117536040949 egcd:6140630879643,9491202,0,0,0:3,631459,-408542209367 egcd:211369,28015233,0,0,0:1,-7466081,56330 egcd:8011144,24386,0,0,0:2,4799,-1576539 egcd:9723,761305061,0,0,0:1,146419877,-1870 egcd:24432,7899,0,0,0:3,892,-2759 egcd:9912899,223787,0,0,0:1,82520,-3655317 egcd:30742811109,445709,0,0,0:1,100330,-6920269141 egcd:6445714509994,5444765,0,0,0:1,1710399,-2024833698457 egcd:7932710,53078817369,0,0,0:1,-4132035559,617539 egcd:3337840732,3077034,0,0,0:2,723227,-784527093 egcd:718292818604,81025428743,0,0,0:1,34254894424,-303670650665 egcd:326072,253,0,0,0:1,-45,57997 egcd:29893828809270,93736826647521,0,0,0:3,-7295461626941,2326612589313 egcd:4480264,223642,0,0,0:2,-23286,466493 egcd:176957076,161560781,0,0,0:1,-31655390,34672061 egcd:37146108400624,62308785533,0,0,0:1,28939329218,-17252518260107 egcd:368208150951,692481145480,0,0,0:1,61559555031,-32732631176 egcd:6314981,15499,0,0,0:1,-3877,1579662 egcd:2805866,671806182,0,0,0:2,45436714,-189771 egcd:98242818233,77004291671,0,0,0:1,37912166082,-48368707255 egcd:607152,2932056,0,0,0:24,13034,-2699 egcd:329110,861060931,0,0,0:1,423790795,-161979 egcd:6035746008,726247945,0,0,0:1,-51545008,428383417 egcd:388326,4784349702632,0,0,0:2,-1147292297345,93121 egcd:34137115145,947284,0,0,0:1,456621,-16455174641 egcd:9207216089,860347,0,0,0:1,-394196,4218585935 egcd:8112578025453,2680608704,0,0,0:1,-855589147,2589349837748 egcd:4997261,749601100642,0,0,0:1,-67513226341,450081 egcd:852403018665805,68601329,0,0,0:1,-30001234,372779110814299 egcd:92080405,52081391,0,0,0:1,-12636003,22340576 egcd:60095571,4414432667835,0,0,0:3,-74437007062,1013343 egcd:4981195051773,905850760614924,0,0,0:3,-146240346450057,804163027486 egcd:9685579,9592868,0,0,0:1,1793043,-1810372 egcd:59530646,36346354116,0,0,0:2,-4115037905,6739902 egcd:1435163995,69604439462,0,0,0:1,7586354849,-156421967 egcd:99926066,887606404471,0,0,0:1,169670756253,-19101407 egcd:70441698,3974125,0,0,0:1,58887,-1043777 egcd:849350185,211717364,0,0,0:1,-59186631,237440024 egcd:20085073436,2395589822,0,0,0:2,-341128500,2860085191 egcd:1126006461820852,819773895887891,0,0,0:61,-706362472938,970229368007 egcd:70904095451052,2233930,0,0,0:2,400136,-12700165688899 egcd:6758999,15939222862291,0,0,0:1,4123564111309,-1748590 egcd:430279300935,431963821489,0,0,0:1,98776246963,-98391051236 egcd:55721139210155,7073166691740,0,0,0:5,-369561824033,2911341799388 egcd:192435034269048,1832500,0,0,0:4,7198,-755878513871 egcd:15747650667716,36009594821,0,0,0:1,7200472117,-3148897400951 egcd:38881764321,552729171,0,0,0:3,63876322,-4493383429 egcd:691050011,51977919,0,0,0:1,22745801,-302406990 egcd:52540041952180,2156326222,0,0,0:2,-170294052,4149305677871 egcd:7905452,6213885,0,0,0:1,2027303,-2579183 egcd:3430895541193263,119720318,0,0,0:1,-12421015,355956329656547 egcd:78945450,1569850634390353,0,0,0:1,-213574967886499,10740367 egcd:3026195347029,48776084,0,0,0:1,709073,-43992736549 egcd:22612793613368,78277930892526,0,0,0:2,14856095743435,-4291603305253 egcd:775918498,7426337401,0,0,0:1,-3568692411,372864079 egcd:66668332441496166,5313627445077186,0,0,0:6,-18855448933863,236573103938824 egcd:3800017785952,66078608868917137,0,0,0:1,-5030282046793581,289279111249 egcd:8238037234,2941537491408,0,0,0:2,282888965705,-792255696 egcd:9547120368107346,29456344,0,0,0:2,-2851235,924116168074373 egcd:721478459,29799838078,0,0,0:1,-4113566985,99592822 egcd:463484777885,77160851,0,0,0:1,-38346752,230338774171 egcd:6668812562,5426227269,0,0,0:1,-1878258319,2308372291 egcd:7020839924454,9619730190140,0,0,0:2,1676947567713,-1223899236455 egcd:5581687877912,4728620673,0,0,0:1,-1477827499,1744435091593 egcd:86212837117,93176774191319388,0,0,0:1,-16333778951401391,15113008971 egcd:10486952786566311,8072710949230,0,0,0:1,162596692991,-211223200405940 egcd:332388514681475,314477095129839383,0,0,0:7,-4152534349932681,4389046916654 egcd:1878789616020411,634591014351511065,0,0,0:3,-55735306584035142,165011657725421 egcd:853435249810090,294022990301,0,0,0:1,-71973674612,208911796010781 egcd:800760331,479138587,0,0,0:59,2283452,-3816219 egcd:310386781,45470476445,0,0,0:1,9204755541,-62832736 egcd:206381927221,426737049973016,0,0,0:1,-51635348161827,24972293048 egcd:80657906841,97722845343178,0,0,0:1,-44940641023991,37092841744 egcd:3626879556739,974287797969673,0,0,0:1,-416739368163900,1551352175437 egcd:12353260720882,167588026304493,0,0,0:1,-4766112882926,351320057681 egcd:5680097354,954648204845001,0,0,0:1,-206590628821018,1229201373 egcd:8495790423,19792054180,0,0,0:1,8077970807,-3467489852 egcd:1808291492597692,96814519920612,0,0,0:4,-3825789187820,71457690917437 egcd:796275712123233,71773988020895279,0,0,0:1,16421100444870785,-182179140537376 egcd:62156477407557,3665981752,0,0,0:1,1292733717,-21918214413059 egcd:2921017132462,944466357361,0,0,0:1,-167559490864,518222951729 egcd:70129038286402,2652828624150588660,0,0,0:2,61204814273941601,-1617984186560 egcd:4099194006860675,712258835980,0,0,0:5,-46544273205,267871728840131 egcd:18993264993,72866008153094,0,0,0:1,-10126377677909,2639543177 egcd:37137778422333201,725902397772208341,0,0,0:3,36710995342741392,-1878165459827929 egcd:77046543323827,91919074661304,0,0,0:11,-3080180234575,2581806232959 egcd:50946730035622,6841431278091013,0,0,0:1,790206978840254,-5884508662999 egcd:778417902091877810,3526771827155035,0,0,0:5,-62143495200058,13716115340897371 egcd:7357629905645982343,273989149651,0,0,0:1,-10489681694,281687051588686593 egcd:59999050131295751,4402788959646093,0,0,0:1,2181599081375342,-29729763077344837 egcd:68611931054045254,72532452638242572,0,0,0:2,5482399071936641,-5186064629726171 egcd:8597485693846941640,9852318416413,0,0,0:1,4640854869916,-4049776069443081003 egcd:570460270963,54720108308,0,0,0:1,16083505887,-167671472335 egcd:43617503830797013,452251304617430,0,0,0:1,76760132288467,-7403152472886549 egcd:73871669508560399,48493623727,0,0,0:1,15908333574,-24233601655059575 egcd:99534170067866609,8533916062,0,0,0:1,-3636610149,42415108188475141 egcd:1885231469789,5484240550249,0,0,0:1,1215645072521,-417883264932 egcd:1988347340743956951,7107237557789347,0,0,0:11,216195821117034,-60483750895153609 egcd:1028936133037327271,5510465055402,0,0,0:1,1073852868395,-200514113917520622 egcd:908361247108559,833255131023,0,0,0:1,70168847825,-76493572911138 egcd:105122420688920,8437707543309,0,0,0:1,1099150493096,-13693928112891 egcd:7268354783435841902,933995610637335,0,0,0:1,177721439316803,-1383028419904388383 egcd:50338474800791504516,946966290251750,0,0,0:2,-82754441959453,4399029230620270937 egcd:38695580832418,77020806554,0,0,0:2,7049841355,-3541870284322 egcd:460793682039951322,360995931125673,0,0,0:1,-12872500500857,16431118446002835 egcd:9791371944228644211,37881615337394730,0,0,0:3,-994456930616087,257040192279396732 egcd:726186734680,24419809216698234959,0,0,0:1,-2766640019167190414,82273258719 egcd:529564016606,376298866055896536,0,0,0:2,28277719651140475,-39795131343 egcd:145541869208926297,19688885314609703455,0,0,0:1,-4361261236227472297,32238803887896062 egcd:39778456127502718844,81278417471936841,0,0,0:1,-7120109086823404,3484651347093815497 egcd:7809654411174,1244628241216910096,0,0,0:2,-284584948977462005,1785681883582 egcd:247581683736939421066,245039298196,0,0,0:2,-51357390229,51890244702955249521 egcd:667668476732052,476696223555,0,0,0:3,60657763034,-84958248556823 egcd:2229399707506,39201358276824482440,0,0,0:2,-5131877014016252583,291852262700 egcd:4767576564991009579,340159717388,0,0,0:1,-29682941117,416027199034854288 egcd:748410307121741,730540185467629182,0,0,0:1,-213318504992896387,218536599371724 egcd:2356182915322420038,81237995138900716,0,0,0:2,5252342047370707,-152336090720664004 egcd:6513077506735657,306517877388663388,0,0,0:1,85680643466766665,-1820594206381108 egcd:216282311653914599395,911124646576,0,0,0:1,429112007291,-101862393081040854019 egcd:59815399922090959,5110979162439569056,0,0,0:1,-1114788966780819601,13046726616842810 egcd:477652083813766,624733750918729402,0,0,0:2,-154413302241487321,118059630163644 egcd:659935429542750939,44886608128116509,0,0,0:1,15839652572247565,-232878989079292726 egcd:54504214226951518003,387724255017508609,0,0,0:1,31301361124239357,-4400178916414896230 egcd:783331167504862965,48609697533,0,0,0:3,-629742688,10148120643700831 egcd:7643973606720,70743283292590583724,0,0,0:12,1182943528930131602,-127819754647 egcd:4273152632680100030114,1455223242316512,0,0,0:2,12098554144849,-35526486240961014982 egcd:5862269731025091,3136791365228,0,0,0:1,-386529556073,722375272334573 egcd:659628551534893059484,5950075862222037,0,0,0:1,2470161881316403,-273843450328876151623 egcd:9482121506846253,34058669367564240,0,0,0:3,-1589045402569649,442399009322730 egcd:65396942933391,3530693943836047978,0,0,0:1,1333698073169157271,-24703295773820 egcd:24559856763503,6667927595346,0,0,0:1,-250002320323,920829011695 egcd:4843560767022,8140092963222,0,0,0:6,-479036307613,285038693786 egcd:7703573212864,4497158779255,0,0,0:1,1735016188064,-2972059668409 egcd:8411329856643749667337,6927690295201914990,0,0,0:1,57955419569688883,-70367197465289023043 egcd:311630305921790132,36794945100846,0,0,0:2,5335676048581,-45189858410215015 egcd:12252240244679740653,21854667756737479,0,0,0:1,7408241549029968,-4153234277439483257 egcd:914930916911818959,73054804640859,0,0,0:3,3000864169057,-37582516567124740 egcd:144437770651525337,7176192389740,0,0,0:1,-2917598661927,58723543558714060 egcd:9658485554428935101,5617211853860547,0,0,0:1,449096244749153,-772196190086168116 egcd:344028716311850,2026849525600172204430,0,0,0:10,4273604619400616489,-725383257448 egcd:936445752013986984,883181511511066630902,0,0,0:6,37504920718991502298,-39766823953131263 egcd:8136225792202716788767,6604882712946357,0,0,0:1,-763274997603269,940240423932206378732 egcd:577476567105329156936,1256480674248716110951,0,0,0:1,165865135596220858037,-76231358802105687681 egcd:58801491048115,31028000846825692159030,0,0,0:5,2620151256531588957285,-4965476229559 egcd:9973707804728263847551,53630829606521208326,0,0,0:1,16368451878013344235,-3044035631088017117934 egcd:17121194233870838,44442113181771232,0,0,0:2,-5375949729958541,2071068923785980 egcd:194930254933589618442,76996294363551631,0,0,0:1,-38281520562566769,96916697409778838629 egcd:6740972199816713986701,3164254690674619824,0,0,0:3,304736351600199807,-649195300386062944621 egcd:33100303896200,74054854499575190726143,0,0,0:1,-30231828546967434629772,13512722683807 egcd:80391303224075976,94483334960558284,0,0,0:4,9695304929308312,-8249266378534037 egcd:954262165857127978158,3790250771466830,0,0,0:22,53714840833849,-13523654091347297164 egcd:50095431507743637803,32894122691956397938,0,0,0:1,11834908275426407707,-18023731548159747940 egcd:2173109072764661515,71129381706084812,0,0,0:11,-844279059631827,25793988931499293 egcd:52743975673113,1252477537471129,0,0,0:1,198187508901071,-8346015665318 egcd:3400327281633151,431371474891473455,0,0,0:1,205422443946739001,-1619262239320730 egcd:74672816465806151314169,181861345000582103629,0,0,0:1,27254332141007722192,-11190710933415108645643 egcd:474476291935913056166,8171705897201808883848,0,0,0:2,-1170007477720025417249,67934506766326698557 egcd:984130837655605609160519,483475686999411456,0,0,0:1,30260545442548343,-61596346486657707977136 egcd:843814604333653656215922,682249690564087391733,0,0,0:3,38030549017256981789,-47036639393790777318635 egcd:81202937258153735712,402831457452712664,0,0,0:8,13421756749885189,-2705563458591282665 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egcd:213839504515148236538273214896810704701481567163944,7404902411186480168131101360415567235929305381970861083,0,0,0:1,3380833338481241432824569741692207456495975720502139882,-97632039668337051697511687169125113631113481270429 egcd:4704143575442564619226639933367529686541295734236339,6208190661916178838888950379033665108451167558784,0,0,0:1,1036231609662380598181323571412442265592690061947,-785185657902980530502486174709506058502162341225648 egcd:7800918125130733756931790281898023131423182325003,49727855698492641147972884260023067177838769605345,0,0,0:1,19886322404414182208422530205281052324435144823897,-3119611145659963799957590789424626986012404758802 egcd:16259480181384339216392327597672842436080220095778,4211887904631546369945283484243515208523965162735,0,0,0:1,60867090942630605523831629233862298664493090172,-234969990011354799892126958820227867474219476729 egcd:250262833515008658954045947163909193707871367256381,9360574256964093238653836590939739950376635341916,0,0,0:1,-4577416570401947847275576528151972968266287934083,122381085779547263818532525602930002569551981217314 egcd:49350305588299753800512832973348076363359882929159394640,82697581133815540138675428448684737574082443779556532,0,0,0:4,-7094756990744589041872300640946840405432374076597223,4233841193026162290519658157361356032844712511769908257 egcd:6929763065061301565614851166591733819231208368855577,7015852829866459363250622386383961076838110347968449,0,0,0:21,-140151926963831515623623343137474264566890746373088,138432157931912474126854600439744488201286606016053 egcd:798771392168930640410188390828161875038624287357,26910611328285765453242714553447940950358339441064142,0,0,0:9,-589064228600178541791155571644660170053125967736035,17484837048696468032579268233817988200645136912 egcd:25397454048672817537966781867771032309891340572691,23256250389273255570062468054746082424429806429,0,0,0:1,6728497363996047750398121428930431990223003005,-7347990314789774434378123575091130429836158761726 egcd:123423695423831974268547456942149055439119884772839,46840700163848752557976957753546114906692522490120,0,0,0:67,338082829316269748785166702372267870226049440293,-890837071341720045931329882131992024423327017348 egcd:255083834192307897983466926757917955799611163337033,19691274316552711716703825178816583758491484527599,0,0,0:1,8267652047084102914471657271320768345286498962274,-107100452212241711960185536892796650356109725315359 egcd:12995280360832692505430343465201277534610726091988596,59465235355121959404752559527335404508679919016,0,0,0:4,-7141155689480540101632551150483184164353752087,1560597880945943136073564871687625551494286751865366 egcd:22991573949171758827108078165749233594263284484912054137,283817289083807864939015806533699958979417645701638,0,0,0:3,-14276343780208855857892287243849657918266920759821,1156503237720469287676414796512164794747302414005802460 egcd:73499010438519566918821582344590421556887663107370504520,3896393550660794088432191407076243899495579652351675,0,0,0:5,-256046171286391936281227275615268399494905890920906,4829886912457785280143525162619404419581682774707946415 egcd:9583870140187439825440257165562832875040106160360,144350435363505176257999415244713117818105415897,0,0,0:1,-47530478459628272998131044625702170795099568341,3155694903939446205334553339280276087238902971313 egcd:2461253900541942202429868097665121039076482321402912,4470103014382515051213146843793545738275750665419,0,0,0:7,-245912852093874846806381542597934573753889813353,135400451502357810057163583858882200066572301755797 egcd:7046608505460840717651450079359511868310129053953828335,58898419892762238699911322923913407676555176583579748895,0,0,0:5,29358649717475420636966955061254137346962695123318402,-3512469624561697691831838742681262193506315801921927 egcd:506826573770755010074059089662551590730419138892682,2122797248606187597520041255704732461621253654865,0,0,0:1,383346693931445995397683618340486631342217567423,-91525599809021126197144665711931909038630799314789 egcd:651539360489382353856038642218105742846167090450124082,62040904220472849789353991154770087142114255535343,0,0,0:3,-2355997477848366312104173979342645132007028304972,24742145675004203493726030544699958619654829318107349 egcd:21241404865403392359971818730574585605571301440311980,633711839015175748736538000969606849077009552352665518,0,0,0:2,-29634494220450461639960895856430281807980194035925990,993319441051141196492952842918573155102238513897539 egcd:705059512890402826453839323123808449258609192987,54700053492589412596920621965162616297504870254670606577,0,0,0:1,17209927692044096764621482310232491609809545108074829881,-221828361412398689301748597143984873381349400098 egcd:415394044144508415296949741318653110880449387898,712027399337932687761182029057846295919208016685209861,0,0,0:1,311602633323208816932778876458826680113268935109136666,-181787776906565417455080707523448468254230808647 egcd:83651009241467439062630103095611805553814512321696,446490369450787055845922775483794833260870810890813375784,0,0,0:72,-1344835414515943831032725871506341368981976803617565435,251958042961384654578843735842923162844346873473 egcd:6070283815502486157201490923461524628539767903594155636,3804770539341434134928308971505690245714256366681925,0,0,0:1,891543412196165172397968883307773535161244063478816,-1422404187036464521764325842283917202125611790642909427 egcd:96178348424332762060134475763000420774833630208152855,2806142261547257037797431000328431629728168038259049468,0,0,0:1,-225250250276381610381864841594193349660878357372833721,7720277532117966753867311498921456722048818963874392 egcd:865765710958745231463327672884696335768725685962,880656889492281564646438436388571726030066590436314543548,0,0,0:2,62379218473169386716154064883279697033462165217514103793,-61324437558888497176774502622595381331609802518 egcd:3070091985634497235831095568321669340142231224753241,3872660861602828375769437905423007683683302354983,0,0,0:9,-130408390759835341307955887188778334976643191426,103382601688896077821738216002703636813104276203725 egcd:9504468312001233029402718544926917268255994088587,210179277000215612334709921044939204096404089694219,0,0,0:1,-54268679178541938321110274347377533333619467634554,2454071347795548035690892610366452456534032251421 egcd:9812086714469743421916608502147765364717936946446424,233160386400300595605996182320148818062281081024933671783,0,0,0:1,14451818554970487550218007381375932641589632889155020753,-608175767043463911892366241689545509336116825541137 egcd:4360347517898600722460235991841444558919923303109907,283395924916312034671252929842416261359155988664543,0,0,0:1,-105355408855707603292421311080809208231429401696971,1621004944361269525623546575360221751817290611287086 egcd:907128595118057734919250855358256235977656150196435477,4751580206547799719609283650403815057095853254068516282,0,0,0:1,-889356095279141478429404461825805439836321286132426239,169787799048096169202610086149258055777141370865005422 egcd:3973997826695458235929341947630757918334953729985,919677988629130382841929983511305489218360268786013503512,0,0,0:1,384594482287927020029873640499023823049367287552218834897,-1661861712108041873322099084387127370672735847462 egcd:324009569902112154788016906941706831494599024684,58395597253468362692345409336860870479092825229925,0,0,0:1,-24289711240864138406494464493033446495436364142986,134772127734877303605549194460068805419486762181 egcd:9872056470535077418025544166904013532879288870389,987664828323257512963011567924222937884833452375999089884,0,0,0:1,-258549889378418898215810868491864809363285916014306422747,2584296853749008257728523207193933514360103172426 egcd:6138432786866037932815463907301440109085864021227742475,9643623319216552530346508247173742908756209280545686430,0,0,0:5,405384190611356540803926039847087441116531679787752407,-258038241909272527261791760130585315013837095770089124 egcd:9769529614309261031704728459798815700297631096679,3517848632227013216032933216030143937697714956834420809911,0,0,0:1,824442973956188793176135575810678140011131714049438939237,-2289586872950597937723114927397934685180169653102 egcd:147669070524401967353624660276651246996312407855626175,618549790847610101709816507641892193136137457678390333,0,0,0:1,-236805668183208014750730197115976279202350305381572622,56533642776931164630044536099572395597955604255694447 egcd:80869456296117844580165320271841144299624178440949,1514427424327350480216517445312029963129987647776900447567,0,0,0:1,42937034698172799579489980026944211003937200326398387877,-2292810203533548889500989218354940644696579422616 egcd:780887627633271006167866160971476360466719486004445,6754024108447725515883403276228352886002003364798583358,0,0,0:1,-1452325437600127814516627181590300017598700651740748185,167915149147974595643816598065833917458080039787797 egcd:7199869643335698558244236956584912995424331052926,1527691037819148269409741859243943945701460882281456,0,0,0:2,57636477641770614383597878932375099638471007783959,-271635504463112985014746084869260309486608865147 egcd:455180951765525170462545338088508018606122351276980553,556221150703226579334767784298557173503136268977244374088,0,0,0:9,-26099094677797268547154896038734560717230667555583420223,21358070869183507434245801704745654317447493932633856 egcd:93476519277392442254618836667858506817969980392044,987802175681385610339163711595695835800228648753133,0,0,0:1,453471836205864432156593588057832292869365167568759,-42912406838557667802187349192829335384746711750815 egcd:9180181445786644280041614496157713989549610132944896,7069909765059709568140852896063908165359626347795742,65537,-59832818838,667:2,210652202891822695654795784473414654009859303252815,-273529013631655892016199829860413659231566937548689 egcd:273907002017625351000357839595395794496103882311,58944774459707213986630692862708398194596783791903184158,0,0,0:1,-12003726808325219248723901188186062373690817244591520681,55779411376906145094866211582214461320097963024 egcd:22771998405981875169000582212334819990253681885689,60821984515441323586153842147099185189621658456861319,0,0,0:1,-23264721625000571047177124342948563692619090190183688,8710406409472299618111529542234963792113787292207 egcd:3842241889401713108515872147470991560356182059740378113,6515515734620532620891823824801930655919134250326,0,0,0:3,153369059865421665432317909089784699996324017593,-90442729379334735477828876314356700692421064332545681 egcd:2864468548588229088711156824748351772387325226285,715849610154437365072792769096891349579259900786933,0,0,0:1,268550748090675670123276782608442742660458501428618,-1074604443019284165403977646554099860591230618013 egcd:3810898561978236785388520202269462480808294248695893,1062108199707865331145512609955734128758543891943,0,0,0:1,339617394241108857543260840698815161575640725383,-1218564586632720303123702323672631316897985132530526 ================================================ FILE: tests/emod.tc ================================================ # Modular exponentiation tests emod:26,73,10858,0:4748 emod:-79268,611,80,0:48 emod:46600826,0,8487413,0:1 emod:1465748,364434193,5,0:3 emod:873883,48223971,348,0:127 emod:-52,183,125544,0:49784 emod:-846,394,969114928,0:877192256 emod:7054382,917,9,0:5 emod:3768,797,42,0:18 emod:357352724,2093262,84225,0:72601 emod:109912993,364,8323,0:5279 emod:-3224,270672,198893010,0:47016406 emod:55,95723840,523703559,0:372050017 emod:791480518,904571,581451304,0:444873224 emod:7278,922,2398,0:2040 emod:-5,925972,33496,0:15809 emod:0,649246,262,0:0 emod:52004,997,2,0:0 emod:-4115715,8,234398,0:3299 emod:-13612,2576,57,0:7 emod:9843599271,9688373,8509,0:5780 emod:3415850521,762,3050240,0:760241 emod:38873,18109,6791035,0:4721568 emod:504242,66851907,859955181,0:352955933 emod:67731070,2628566175,7885095,0:6298660 emod:575051,8,72796410,0:35016721 emod:3,0,6595628337,0:1 emod:80479332,13,9,0:0 emod:35578433693,9608165878,32791508266,0:32575013339 emod:9998073,96042198253,2871019117,0:94477702 emod:8502,88462049796,288668,0:234260 emod:966350153,6125446381,940,0:33 emod:51249,46773,83983261446,0:2570243355 emod:2571204,205,4404831987,0:2226688593 emod:19,439650,888059767,0:247638574 emod:9485028101,55407,3066739,0:2994746 emod:868043,56705619,183207,0:162593 emod:7072012,750002,2399910888,0:1322891440 emod:55779049,27843295,96,0:25 emod:57835434,31279309,90443,0:13168 emod:-6511,7486344275,346901687,0:325667244 emod:635099,3669199,81611251,0:59252827 emod:8010935551,34,9927,0:1405 emod:24885132,4526383,58404,0:15444 emod:613003,6878758,49607641,0:43381288 emod:132639004426,81043,587317316867,0:532884551555 emod:4439384,43262747,10119,0:7922 emod:689907710540,460484866,82087637,0:30398950 emod:84094,867130,62309,0:9025 emod:-33557432,60878,580294942,0:194480658 emod:3869257,4125450573,456883055,0:129529247 emod:9878539157,15920872437,4738245,0:2745542 emod:8582013178,46758,28059,0:26806 emod:48259672,37258629489,7377276929,0:1692584431 emod:920350,289730727,1122526,0:471310 emod:13029603,4503668042,8665149,0:1456593 emod:6938077836,651113,5180493,0:2235984 emod:-352466,9169937470,70675259176,0:18255076720 emod:612474,308813590252,510155,0:383521 emod:180356946205,710633896291,575721,0:242878 emod:83046,3518,9768613,0:8644737 emod:8670878985584,7549509958953,968064799634,0:673069231488 emod:-37831593555,141781,3434657,0:2539127 emod:94250019226,452692809515,99738576,0:82526128 emod:-1746555354919,310727,6925934085655,0:2276231760446 emod:777851791,126226427233,84192406004,0:11526643943 emod:3511,42864,89474,0:53201 emod:611596753206,17005495050,3708625387380,0:2318918831736 emod:482182433948,97822330605,90338471939,0:27830209373 emod:8971927,5117957930887,1928567236065,0:1437815380378 emod:67445777442,3930771,4541604,0:773076 emod:-52133,16783,3337,0:541 emod:22,7787554274,823549,0:503210 emod:46816685133,272923,22855404855,0:4704305202 emod:181225207536,22085689725,67955765111,0:5581219593 emod:207971493064,41707850,9115746425,0:6454330776 emod:42840650,206759347,852090956,0:15995168 emod:27703329637330,20686092,8407250,0:6767250 emod:-4953,669615,741766623319,0:660186892888 emod:11957529241,380932179443,973373783,0:970856001 emod:78726001052485,62593863,24053,0:22766 emod:340516095,798875,2556443616,0:348235359 emod:954899979887,472716,979176,0:21817 emod:1669727071,1008664017563,37837,0:17717 emod:592681,30974401363809,65653048867352,0:2039369146553 emod:-47884,525888510,60238953788774,0:8466915489354 emod:5643430747,31164,8629966388917,0:7441630635230 emod:-9134817647675,7013427758650,14493293680,0:10069704265 emod:16875464,4824632,157384425878173,0:110131510850102 emod:-1891400577,334033142140099,1461471589,0:500051598 emod:337804687158388,2747595,7100373337,0:3797937129 emod:597469670,80669751974,564129148100,0:462736594600 emod:-373150,494511905,69961532,0:44955656 emod:541002,396515,663670,0:448308 emod:7443329,192200716115,819064750,0:75062949 emod:352331718576096,937115695,121165545639266,0:64461611886972 emod:94655436207250,2442730,199021327246786,0:98351560387664 emod:450100,441162616,8233398,0:5554612 emod:-562161185511147,564556372236072,6280258,0:3623203 emod:-87181577138119,6636401624,33493475420,0:22078084821 emod:63757825,675193212577,791180,0:551825 emod:75719430,7834623506500,81861106,0:11697720 emod:7636428268,342917,424075566,0:382499056 emod:2847036414481441,3486471,96180960030,0:59848561291 emod:7605693821889,6857556039961694,9340113967299,0:2791642232520 emod:8460275679756,1249967640481565,3530286614,0:1855000398 emod:-21034390,9455714874055,499517062,0:436407454 emod:-67878984199,6771837956,26518969637,0:25569641018 emod:24845854,38512788750888,97880493,0:44709115 emod:913222119920236,89756684,24503538,0:2358514 emod:282825837874763,49707087,4419250635,0:2888992652 emod:63007338,778023537730086,51807416,0:42047040 emod:86515727,37854772745819,932061443536802,0:913958455659941 emod:16752138958,84132272429,883645897,0:66146743 emod:76020717,31715587905196,205759754,0:84248649 emod:408229656454238,503345091356,5122409740,0:1428721156 emod:335638746639,5761369582225304,4092173299,0:3495108299 emod:4118216,163393347759,33772615,0:18314396 emod:6140126413594,8416471601616,48576280861410361,0:26480949886245014 emod:-654797902884,3118772351656763,49622473264915,0:8452790798791 emod:724850698,6033802538378749,5080656658,0:3131590110 emod:-67747240120320,5206803331886510,16513427532371,0:9305404239198 emod:571096000432,140739165,2954342334466067,0:1353110426217941 emod:-99625731171,97620037702645811,44537854660922914,0:235109017589213 emod:33191179298252,90227008,7699370104843722,0:3200733061202818 emod:63893120170170773,976336027,635053357,0:242474238 emod:42622029452,37698167195197,75773078526,0:28876796648 emod:83620114446490,8610382003,464773010095268,0:378308871158308 emod:9574472571,9560271542,228122075654,0:119978765197 emod:56753833744514594,333744771296,46684214084,0:22141695456 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emod:-9994818638674529038541342163911785506433155975282,2441529131191726286407021656054505236538534218505,868763054397265950319354411340564521520500110285341,0:713646341945805538982296660502179127412919111592110 emod:89928590797284478729252348706855088798121290869809060,59274533239795541803239071337695221071797917061551,458720998639333601494661224903885165927950415283068,0:238541586391208422370502281952541020478014766570928 emod:95798368921402497294705740910984389802169456614551866,5780238728300624701546948669191486225967922222,17602545836464476089657116165016615105637757631075883410,0:78935491841772453025866169047063528694493328256027716 emod:-6285988010245529074539471748460012192454923426879038527,4464035763112866760911458677964807167647554031374417,557426143112327094606990154681823173588434990737834515,0:492308894761273719919857937651384253941194670007301468 emod:9216609859426876786581364775917107940830826147193,2584656223509851604195298909793029088361431700609487947,97854661860659618908160182622420008085466240143877617,0:85437882709473882823892529660893798801236147303713473 emod:9369310120459129777778887291797647697234777683432051,29114272244461903760267994837317966967186291374,9778907141259037429006274419046033685045015909549812,0:6158258816758612931552439105354775382106793792840429 emod:121095461268256661739120249224368430821121813080,24216928007688542369493467184086532629768906571974067315,1289101505296127733900239534120001726302383453437972,0:559264053276767206654909871928116713399654543670428 emod:182013722639261555865084991953687573500429962535766,5312171499532129540711226268300910853763234503893756460,373925090068292154121977949608424249047611823254,0:314492433924568960493434943112384754084000516952 emod:93122409584336684208634425627697110814180323391,14785829877381197130422634393843365096818009069934141,71932199753627287791733451362196318752438103297,0:8651254301747600278741940327234016885952587642 emod:47314169772357749238033685118725095245857710174326752251,7737526111797627477363360414613284237413174897695810,22636439121232576533369780871442014748582558494258753099,0:13481881160769756096301137118624702877253559402875253449 emod:40437135697420911841447145598134529938086874417869482,34142834203311856114775566332299272975314691621831451157,61483400000688184187598139984127464523117551228,0:24693895005298972635867796289890449288509340480 emod:602105062592660782251188458378445123063805101057628877,8347043677742730027972079328186098141974290663352,26831519142227837662521069711039879610686983918942079815,0:19346421778661788162968173970766981230660937987122859431 emod:-631401827295443763663013499197680737231639584989,4430590554183773954781048837898216988481838421600006676,2298393896534361874746279427962482679705626081354993,0:902945851002567106949268418213474969113107638762554 emod:27786418359632188385534950865019584947593363685667,98296086104810263777729111156693306399745439517905843246,885588959591327389647962772187472088293854582596501585,0:219691806105674835153486211154061118027834335467768059 emod:544755872510174513208896610649845089424204895203973,87613019793007744065404211674234696040702876770839324,4802706142382015625537025588688720114067633075179938214,0:4385825975408070392248170302791202812902625274088936755 emod:266945202318091617395513307631280644325314217797596447,327566429748960361523726509719626329764280050772,11519336904029441280173947176416866297494364467208,0:9214541334269337101551342582484701318239260425185 emod:462274575377872280232466472100106379919338255223,55208106570738920386188352962242729542845793547908872955,394947463398055276743090558014108833519958843326036,0:14090943624401742126636618168767136948067183397671 emod:498588690178207860433541173652626793819053542771822736281,7320383073654496423015034860141911017275032239632,864143543362782361157239005190574446540608427530,0:405837700105174778010475141584205874050426805841 emod:9889983273673267055836467894511050393862566401427167421,9249465646754817541871880579390030265752574382697001,25959701663622988366438447815418575609294742760915,0:14146692686195759173905915586727366427907029148496 emod:8977490701791885156174343111351369788045969359197758,310958534312954656622864682281335777958703646747002872696,174885990030766375557335981487351371779234545791,0:172268700100468974308770735824988553302287984097 emod:75891699691571906472460353214537778119193566652164258472,75642710398299172975011498854625838470353049691991252,955726338299637204220414390179262210175010011084260057,0:871551220400711242628454200406202564111664531240532043 emod:817687870329204460156610156013195890028396416937162234,71199838789107588122529185516473983414598608665610,9797217400749418393402581106919553154845468700907872,0:9732835751266971971517518815617086242024182057719936 emod:656535389260219421975691249279051158130957449883966,9965820125071850776397934471591602941345422709213,7172697024967323900460450488928712811727935935053426,0:952029660753929926293707648671191250800460252928490 emod:66765940995445083043566397231259337861214788967954,698949221229345492777837382914330269944860925101870058401,370977162689246158196783733149906357225503977003,0:56780810013712823080333031377883978714594923759 emod:-24860118467430048016063231699711679455683726879672563278,546329058333516554426292196577372643895447816095329334984,102083942512514956911062347152596366057306100868,0:89329427941719016468252169448693561927858667460 emod:518281434431704435940150792966272899127164218411,19290830216216089485046976601623655817078004660590796816,216069676358948655463888215158143195786697578360538582,0:86506166688482117996142986160440612354876384284094157 emod:517542901438648396791987658999334820221431246981278,4954735021213009892606598900462212813613793939697004110,5546708620630276172568015746256008412046274679011721163,0:114558840275328029858937724196533085168759209383758948 emod:97796431105417086121597265848245224080646880891314620699,3566309852926516051758561425477409449674731444065,4237358411463841472327670289343773756088420869185382928335,0:1728379035119996080675313770460691892171354788520339293899 emod:8797217794906750966627546899905389746578400755524,87461473070045326370501974269638901791524473673607812671,63579576817694957532492907897275166360331019259167287988,0:10068755237067361214693799084814132014570304060924282180 emod:3559874918456198560844107856956492116344121248206,45190612746644425408414684724540657030439304479324039,684772758312255825130987448842421703263477856778082,0:500105229544177258096786497048655528691069662344352 emod:244693542815021761876325478432698673186866834942911366704,569049151750280294347914587638406693043104703456596078,40418336644392592645116495825339904699620388961770,0:29946736018608816763137681085572521922498414649586 emod:9552030352913538449959248911819718532447389423411634,15303289522386175735929093158193781525599040386989921,17905297851878021472325954407339512702437837940804355,0:7227207308763570886905006773221274115571235787935329 emod:2427953611523095508885901603899411553216124564768970531,84219397598182701873267938504642229898519369455120690652,5124565221346746692094768907421280792680721722663049,0:2356962294194965054880021165404451023189256523983359 emod:4450272023458109693579519823508011943468990250887770429477,9852180148050086854797451708622242708750405652182828950510,53218591961090046740426308696077544888041718958796756705,0:20722361228858746975332642022116538507546307084688876639 emod:-3004436507840212393446088399233355090512633931853,49762352101558708510764823100128412949214842904414503,62339832791097134323794421391092834208651832053582621969,0:18644587060060960018044094951299852000053162441627275349 emod:88466522329785151709268834138668446416231472463853002,84423940822580221018912007091908955924620089965579353300,4272746558814012659752446371362908792507498696285890777,0:2076687497522815194513922920413442770240123518700437310 emod:-452137704321173773725358540484655780134513962685597,108536825158896375705138771152627679486775845056880757255,7443505375179903958445129175383134980666720252160978,0:2626655033625685458909447520232601675412626580083149 emod:3646226144731352080332815382512112527325988973642,736730185733372156433101295886081895604485817722725,187559548105706428460460100309284194685793795827962,0:153703862976742792640135721867824635074042235940792 emod:7128578973288696116455318246508827884395148700024035843,120044617176238734085406385417402387651027645325661,437777976047468143063879147080739099513994845762621846093,0:383512808517870785600076597930828756369001886406596109329 emod:92651404329219142594991415600374429189694983250618442,1831956594370082650320589803647600704949512437508530740,989079198090857685320779737579388665165981389775724354,0:429473741854566274661236706264645428539362137664132958 emod:783048980600864030214223520282343154949582263988130988029,5640798680918146067495300825091961866365823288705,712576055151408429943237184396668347415006718010549447,0:132303576760619346367560792334725765196706066347238184 emod:54419766013288244584593400647946050509291116271357,37442044497849759156397618484039469808263267657304,55409955411797081810766022756739065410388681698701498,0:625989815794948434601895148375843191288774735399931 # Regression for overflow bug emod:#x02,#x6FDD97BC0A760282D5A180D2308BE3B075BB6456F26B1DD0BEB2C1B0F880CF2C8EB724F2AD0567F7899D9A980C7DB93E418ED09AA3E35357F4F2E05963CB636A0C91B1BC7A000ADAC40F332D6ACCF4A3285112EDBAA95BB27904794ACC8D6FF188E2B04888ABFB11665BD1D915DEC8C6575706067AF3F7179BA57D1465D78129,#xFFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF,0:#xD2C80DADBC0C72DBAC45F380064FDC5FECEEED268C7E86368DFC436908B2D33426C67DFAFAA56FAE89722EAE3644270B0512BE69DE61FDE07585001B5EA4FFDA1B8B98393D657E2EC4073CE4A6953093EF7C3B130CE1BB316C97CAAA88F83C32575D6E1128E107BF66910AAD2B84C44128370DEACFE7EC8A98B2CEA4DB7B09F1 # Jacob Refstrup reported this failed in 1.11. emod:2,#x10001,#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,0:#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 ================================================ FILE: tests/emodv.tc ================================================ # Modular exponentiation tests with small exponents emodev:19,2,84,0:25 emodev:19,2,84,=1:25 emodev:19,2,84,=3:25 emodev:92,693930,16,0:0 emodev:92,693930,16,=1:0 emodev:92,693930,16,=3:0 emodev:522181,0,166284,0:1 emodev:522181,0,166284,=1:1 emodev:522181,0,166284,=3:1 emodev:437824,312,93008,0:26544 emodev:437824,312,93008,=1:26544 emodev:437824,312,93008,=3:26544 emodev:5705223363,2,3286325576,0:818318913 emodev:5705223363,2,3286325576,=1:818318913 emodev:5705223363,2,3286325576,=3:818318913 emodev:6399553325,6,4107014863,0:3307178134 emodev:6399553325,6,4107014863,=1:3307178134 emodev:6399553325,6,4107014863,=3:3307178134 emodev:29074823374249,77004,71683909277697,0:8940258342532 emodev:29074823374249,77004,71683909277697,=1:8940258342532 emodev:29074823374249,77004,71683909277697,=3:8940258342532 emodev:78759078367890,8335,72115845746903,0:20414099940189 emodev:78759078367890,8335,72115845746903,=1:20414099940189 emodev:78759078367890,8335,72115845746903,=3:20414099940189 emodev:-702894953466773316,312561,665754485123402827,0:84548134549060215 emodev:-702894953466773316,312561,665754485123402827,=1:84548134549060215 emodev:-702894953466773316,312561,665754485123402827,=3:84548134549060215 emodev:162476353576735207,8451,299565526093115255,0:235405725752406313 emodev:162476353576735207,8451,299565526093115255,=1:235405725752406313 emodev:162476353576735207,8451,299565526093115255,=3:235405725752406313 emodev:5569622159977645154297,902159,339048673939289293353,0:314927034088061888405 emodev:5569622159977645154297,902159,339048673939289293353,=1:314927034088061888405 emodev:5569622159977645154297,902159,339048673939289293353,=3:314927034088061888405 emodev:6991839486419148755508,2553,530292436823694624357,0:4272543854207020971 emodev:6991839486419148755508,2553,530292436823694624357,=1:4272543854207020971 emodev:6991839486419148755508,2553,530292436823694624357,=3:4272543854207020971 emodev:84643040276670536818634785,63,64928874055124010543482048,0:22546118193382720472157537 emodev:84643040276670536818634785,63,64928874055124010543482048,=1:22546118193382720472157537 emodev:84643040276670536818634785,63,64928874055124010543482048,=3:22546118193382720472157537 emodev:-99555590330388726236230755,0,62041543621233726359336122,0:1 emodev:-99555590330388726236230755,0,62041543621233726359336122,=1:1 emodev:-99555590330388726236230755,0,62041543621233726359336122,=3:1 emodev:700943089540446737340421223177,8456,835694701023829355087294263155,0:258410405038140346743628562611 emodev:700943089540446737340421223177,8456,835694701023829355087294263155,=1:258410405038140346743628562611 emodev:700943089540446737340421223177,8456,835694701023829355087294263155,=3:258410405038140346743628562611 emodev:5473388626149338730799075406,729,850132294968984927109971586336,0:685051590046393947084559076736 emodev:5473388626149338730799075406,729,850132294968984927109971586336,=1:685051590046393947084559076736 emodev:5473388626149338730799075406,729,850132294968984927109971586336,=3:685051590046393947084559076736 emodev:7542606175762975785023215555039217,0,1451486096670046812323372237867852,0:1 emodev:7542606175762975785023215555039217,0,1451486096670046812323372237867852,=1:1 emodev:7542606175762975785023215555039217,0,1451486096670046812323372237867852,=3:1 emodev:-3426829035080908738042076334435395,0,2616360606577002719669450329100985,0:1 emodev:-3426829035080908738042076334435395,0,2616360606577002719669450329100985,=1:1 emodev:-3426829035080908738042076334435395,0,2616360606577002719669450329100985,=3:1 emodev:5871172260267735917150171255408367076,88202,31506806059671945544343675240909419388,0:9882411358511873694991988201288706348 emodev:5871172260267735917150171255408367076,88202,31506806059671945544343675240909419388,=1:9882411358511873694991988201288706348 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emodev:-579340159717388367484103071217417305401854676291827723561829153224200380081237995138900716,651,307750673565730651787738866338890216282311653914599395911124646576595981539992209095900511,=3:151509745004628309027577206278564432986410874344501872366280516978352818925422691489195213 emodev:-97916243956905636477652083813766624733750918729402656599354295427509394488660812811650986,0,504214226951518003387724255017508609607833311675048629650486096975331876439736067207074328,0:1 emodev:-97916243956905636477652083813766624733750918729402656599354295427509394488660812811650986,0,504214226951518003387724255017508609607833311675048629650486096975331876439736067207074328,=1:1 emodev:-97916243956905636477652083813766624733750918729402656599354295427509394488660812811650986,0,504214226951518003387724255017508609607833311675048629650486096975331876439736067207074328,=3:1 emodev:3292590583724934273152632680100030114145522324231651230586226973102509131367913652288365962855,0,3489305948459500758622220373494821215068462533405866936756424017653969429333910353069394383604,0:1 emodev:3292590583724934273152632680100030114145522324231651230586226973102509131367913652288365962855,0,3489305948459500758622220373494821215068462533405866936756424017653969429333910353069394383604,=1:1 emodev:3292590583724934273152632680100030114145522324231651230586226973102509131367913652288365962855,0,3489305948459500758622220373494821215068462533405866936756424017653969429333910353069394383604,=3:1 emodev:-7978102455985676350366679275953460048435607670228140092963222007703573212864449715877925597841,29856,6437496673370692769029520191499051311630305921790132367949451008467412252240244679740653218546,0:5317938765885037665302910560037583058809520625824168737742040261509540549928785850499941206729 emodev:-7978102455985676350366679275953460048435607670228140092963222007703573212864449715877925597841,29856,6437496673370692769029520191499051311630305921790132367949451008467412252240244679740653218546,=1:5317938765885037665302910560037583058809520625824168737742040261509540549928785850499941206729 emodev:-7978102455985676350366679275953460048435607670228140092963222007703573212864449715877925597841,29856,6437496673370692769029520191499051311630305921790132367949451008467412252240244679740653218546,=3:5317938765885037665302910560037583058809520625824168737742040261509540549928785850499941206729 emodev:67756737479519149309169118189597305480464085950144437770651525337717619238974063965848555442893510,0,61721185386054729344028716311850202684952560017220443047936445752013986984883181511511066630902828,0:1 emodev:67756737479519149309169118189597305480464085950144437770651525337717619238974063965848555442893510,0,61721185386054729344028716311850202684952560017220443047936445752013986984883181511511066630902828,=1:1 emodev:67756737479519149309169118189597305480464085950144437770651525337717619238974063965848555442893510,0,61721185386054729344028716311850202684952560017220443047936445752013986984883181511511066630902828,=3:1 emodev:13622579220271678876766048827129463577857747656710532915693612564806742487161109510958801491048115,28000,84682569215903086997370780472826384755153630829606521208326331712119423387083844442113181771232731,0:61921681237911684957734827136839012206257886339643336895704703733211281700691618371720081605408837 emodev:13622579220271678876766048827129463577857747656710532915693612564806742487161109510958801491048115,28000,84682569215903086997370780472826384755153630829606521208326331712119423387083844442113181771232731,=1:61921681237911684957734827136839012206257886339643336895704703733211281700691618371720081605408837 emodev:13622579220271678876766048827129463577857747656710532915693612564806742487161109510958801491048115,28000,84682569215903086997370780472826384755153630829606521208326331712119423387083844442113181771232731,=3:61921681237911684957734827136839012206257886339643336895704703733211281700691618371720081605408837 # Modular exponentiation with small bases emodbv:9,32,84,0:81 emodbv:9,32,84,=2:81 emodbv:9,32,84,=3:81 emodbv:0,45,69,0:0 emodbv:0,45,69,=2:0 emodbv:0,45,69,=3:0 emodbv:-93016,221819,301662,0:211706 emodbv:-93016,221819,301662,=2:211706 emodbv:-93016,221819,301662,=3:211706 emodbv:44378,411312,93008,0:33472 emodbv:44378,411312,93008,=2:33472 emodbv:44378,411312,93008,=3:33472 emodbv:70,2233634102,3286325576,0:2426711328 emodbv:70,2233634102,3286325576,=2:2426711328 emodbv:70,2233634102,3286325576,=3:2426711328 emodbv:39,5533253464,1070148632,0:416533177 emodbv:39,5533253464,1070148632,=2:416533177 emodbv:39,5533253464,1070148632,=3:416533177 emodbv:7482,37424954770047,16839092776977,0:7609954661820 emodbv:7482,37424954770047,16839092776977,=2:7609954661820 emodbv:7482,37424954770047,16839092776977,=3:7609954661820 emodbv:75,7836789049833,57211584574690,0:32805712142475 emodbv:75,7836789049833,57211584574690,=2:32805712142475 emodbv:75,7836789049833,57211584574690,=3:32805712142475 emodbv:702894,534667733161831256,166575448512340282,0:98236745124961586 emodbv:702894,534667733161831256,166575448512340282,=2:98236745124961586 emodbv:702894,534667733161831256,166575448512340282,=3:98236745124961586 emodbv:16247,353576735207718451,299565526093115255,0:280933599223623558 emodbv:16247,353576735207718451,299565526093115255,=2:280933599223623558 emodbv:16247,353576735207718451,299565526093115255,=3:280933599223623558 emodbv:56,6221599776451542974890,2159033904867393928929,0:837205353236184592624 emodbv:56,6221599776451542974890,2159033904867393928929,=2:837205353236184592624 emodbv:56,6221599776451542974890,2159033904867393928929,=3:837205353236184592624 emodbv:35369,1839486419148755508782,5530530292436823694624,0:3355242496236254343057 emodbv:35369,1839486419148755508782,5530530292436823694624,=2:3355242496236254343057 emodbv:35369,1839486419148755508782,5530530292436823694624,=3:3355242496236254343057 emodbv:-5784,43040276670536818634785876,36492887405512401054348204,0:19286493506125729203919284 emodbv:-5784,43040276670536818634785876,36492887405512401054348204,=2:19286493506125729203919284 emodbv:-5784,43040276670536818634785876,36492887405512401054348204,=3:19286493506125729203919284 emodbv:0,95555903303887262362307550,46204154362123372635933612,0:0 emodbv:0,95555903303887262362307550,46204154362123372635933612,=2:0 emodbv:0,95555903303887262362307550,46204154362123372635933612,=3:0 emodbv:70094,89540446737340421223177728456,835694701023829355087294263155,0:418424229988754966300052414286 emodbv:70094,89540446737340421223177728456,835694701023829355087294263155,=2:418424229988754966300052414286 emodbv:70094,89540446737340421223177728456,835694701023829355087294263155,=3:418424229988754966300052414286 emodbv:-5473,886261493387307990754063500729,850132294968984927109971586336,0:19962186036319737098397980927 emodbv:-5473,886261493387307990754063500729,850132294968984927109971586336,=2:19962186036319737098397980927 emodbv:-5473,886261493387307990754063500729,850132294968984927109971586336,=3:19962186036319737098397980927 emodbv:542606,7576297578502321555503921719145148,6096670046812323372237867852342682,0:6019928069694583180163173577702370 emodbv:542606,7576297578502321555503921719145148,6096670046812323372237867852342682,=2:6019928069694583180163173577702370 emodbv:542606,7576297578502321555503921719145148,6096670046812323372237867852342682,=3:6019928069694583180163173577702370 emodbv:35080,873804207633443539517026163606065,7700271966945032910098505871172260,0:5423974510417358397307357591894900 emodbv:35080,873804207633443539517026163606065,7700271966945032910098505871172260,=2:5423974510417358397307357591894900 emodbv:35080,873804207633443539517026163606065,7700271966945032910098505871172260,=3:5423974510417358397307357591894900 emodbv:6,73591715017125540836707619882023150680,60596719455443436752409094193881404578,0:19278231891294150546581628518996450870 emodbv:6,73591715017125540836707619882023150680,60596719455443436752409094193881404578,=2:19278231891294150546581628518996450870 emodbv:6,73591715017125540836707619882023150680,60596719455443436752409094193881404578,=3:19278231891294150546581628518996450870 emodbv:235,33982097410791452776449214446635671357,51970741787875276189593310474719958253,0:12917271140684347997107415362626020816 emodbv:235,33982097410791452776449214446635671357,51970741787875276189593310474719958253,=2:12917271140684347997107415362626020816 emodbv:235,33982097410791452776449214446635671357,51970741787875276189593310474719958253,=3:12917271140684347997107415362626020816 emodbv:83871,305022614904134506738511247696618513698871,318914624938137416674596881724436242382943,0:318195604484243187814770062976379619616506 emodbv:83871,305022614904134506738511247696618513698871,318914624938137416674596881724436242382943,=2:318195604484243187814770062976379619616506 emodbv:83871,305022614904134506738511247696618513698871,318914624938137416674596881724436242382943,=3:318195604484243187814770062976379619616506 emodbv:0,571664949666413150109110287956385784303120,899228089361406308796439491202242113692801,0:0 emodbv:0,571664949666413150109110287956385784303120,899228089361406308796439491202242113692801,=2:0 emodbv:0,571664949666413150109110287956385784303120,899228089361406308796439491202242113692801,=3:0 emodbv:23331,111442438605972376130506110244327899219912899,2237876130742811109445709826445714509994544476,0:1993464329197419695692136638851665690518853959 emodbv:23331,111442438605972376130506110244327899219912899,2237876130742811109445709826445714509994544476,=2:1993464329197419695692136638851665690518853959 emodbv:23331,111442438605972376130506110244327899219912899,2237876130742811109445709826445714509994544476,=3:1993464329197419695692136638851665690518853959 emodbv:-2679,2710530788173695233378407323077034767182928186,481025428743103260720025399298938288092709373,0:154954456135957386487732495151651926343687936 emodbv:-2679,2710530788173695233378407323077034767182928186,481025428743103260720025399298938288092709373,=2:154954456135957386487732495151651926343687936 emodbv:-2679,2710530788173695233378407323077034767182928186,481025428743103260720025399298938288092709373,=3:154954456135957386487732495151651926343687936 emodbv:8,66475212144802642236424417695707616156078196371461,8400624623087855337736820815095169248114548022631,0:5187964347290625676649944455881080044360235674382 emodbv:8,66475212144802642236424417695707616156078196371461,8400624623087855337736820815095169248114548022631,=2:5187964347290625676649944455881080044360235674382 emodbv:8,66475212144802642236424417695707616156078196371461,8400624623087855337736820815095169248114548022631,=3:5187964347290625676649944455881080044360235674382 emodbv:9,10015499242805866671806182669824281823377004291671,1607152293205603329110861060931530603574600872624,0:322976644144573292044502952628119378896898007465 emodbv:9,10015499242805866671806182669824281823377004291671,1607152293205603329110861060931530603574600872624,=2:322976644144573292044502952628119378896898007465 emodbv:9,10015499242805866671806182669824281823377004291671,1607152293205603329110861060931530603574600872624,=3:322976644144573292044502952628119378896898007465 emodbv:-94,73883264784349702632503413711514594728450092072160898,603477481125780254532680608704164997261749601100642928,0:385098763603163293508297247576178742276025427508920032 emodbv:-94,73883264784349702632503413711514594728450092072160898,603477481125780254532680608704164997261749601100642928,=2:385098763603163293508297247576178742276025427508920032 emodbv:-94,73883264784349702632503413711514594728450092072160898,603477481125780254532680608704164997261749601100642928,=3:385098763603163293508297247576178742276025427508920032 emodbv:0,403018665805686013292292080405520813912760095571441443,266783579498119505177390585076061492421096855799592868,0:0 emodbv:0,403018665805686013292292080405520813912760095571441443,266783579498119505177390585076061492421096855799592868,=2:0 emodbv:0,403018665805686013292292080405520813912760095571441443,266783579498119505177390585076061492421096855799592868,=3:0 emodbv:-559530,4636346354116451435163995696044394621599926066887606404471,2007044169839741253208493501852117173644320085073436239558,0:980083462330793649852651395567038357390956681750027115900 emodbv:-559530,4636346354116451435163995696044394621599926066887606404471,2007044169839741253208493501852117173644320085073436239558,=2:980083462330793649852651395567038357390956681750027115900 emodbv:-559530,4636346354116451435163995696044394621599926066887606404471,2007044169839741253208493501852117173644320085073436239558,=3:980083462330793649852651395567038357390956681750027115900 emodbv:-82298,1260064618208528197738958878917070904095451052223393007675,8999159392228622915543027930093543196382148986055721139210,0:8315318460941735744654692360810076563134610768999859190038 emodbv:-82298,1260064618208528197738958878917070904095451052223393007675,8999159392228622915543027930093543196382148986055721139210,=2:8315318460941735744654692360810076563134610768999859190038 emodbv:-82298,1260064618208528197738958878917070904095451052223393007675,8999159392228622915543027930093543196382148986055721139210,=3:8315318460941735744654692360810076563134610768999859190038 emodbv:-5570,31666917408019243503426904818325007415747650667716360095948214,33888176432105527291712269105001105197791973525400419521802156,0:19067105956731919771713581587977175395882533198855245354642060 emodbv:-5570,31666917408019243503426904818325007415747650667716360095948214,33888176432105527291712269105001105197791973525400419521802156,=2:19067105956731919771713581587977175395882533198855245354642060 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expt:16,-2,0:$MP_RANGE expt:9,114,0:6076396096647706909168138770838836135530328017648434830996201971201776350890241322455818405320466786549738961 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expt:9,761,0:1508515174935868832740908844641413400230908698282014024654729092918735474326353646362638387096847659573480147230064829611049820323852929496264239478087068540642226919569780605621815548160687919464946810325130045648382743363240874672014902866728521582870078261816669666838432797381766007612134725161586319767428484319859256110793709691241551836459283171491322903212579581783263716842956174378353601721913353516686324030063352338083503343527729254306613462747468830270057853272630516028854927235895950242106874919224742672988595490274178820331573555174825456815488479104792855190670321093410569224479462267429452231735849215995686173314732407799996091669536594590589720060331368687564979078136565140955509332862196370159944529609 expt:97,144,0:12448864341302864356285624793135454957839907062356377399873019819913674333304037397385881749787740378047787615516124593880867160513889753519548772992938610862712907794913424958325207507075928443769586211194132774382517001523776118917770065797726717096819996931978519564039067219497326081 expt:25,122,0:353737464016668451855824972300304366432911374927310085530570894138105520257533012294512947342224925759920017160034290220932919252862236536572027034708298742771148681640625 expt:60,794,0:71136550947732097223049080592911024204723415862845308040389197768507697553695725763485652390828706079386079253286683076446508807986344183438029484620306186446936364042768259107355223169364392353311443322952870623266797106042061359252992933819289381215897875409197357921675407844235432207568030978595888122411284106189806970016530299277993693667005155741905298746901362592844010565441606260646610040560804127639267467909340287601194961411351728753184912061106832973826776921930054951881992593414738674333726484856598478050587647451437933451435999205268943471465348558111458293504367268910731207434743916849298071460249600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:77,531,0:532813311656570249504626338521175986931059533505926279525440059983661596994102351537446926949363360529365260710018282274969608991708422465645470353238950991164094603760337431471373797674342466447685331328334896929530869521639021347860305641901746618212067382436047417802334922329714967747069071224609067366771145964345230898570999327581370275837424654936614015736099665593408214589717971837806254491231718922616012680565189067437536528526576020597271981783296886490561985553063246822960810078500648480156559918530508398231087164252252053517193755387712164533565474034807917780960207694570186046344187446803758345139338159388892261095589551022214765624192005132067602116482379395414788544646979450596452460362555591887638135655580299669062424023518502777571809123694201495640270788238169354113138409879326088017367705387411669267281998186298445497315171994082486321864442017377055208040226703055135151101106282748423896319916554310684705542590586019379478759401961042716809342108506273015769966750567573 expt:69,147,0:2045579385385676298810517927458702060863220937986515106749791476657551971253912701625142580828008387342063850849956585037595400455275752324351745210872040235629033488870814386789439565218837255775426196335872604764004481418507627655312643367630027383681234193549436923389 expt:63,5,0:992436543 expt:43,146,0:30647461956799913663494655425076773992386225973903296590660647835395776515882377986142610962128804096035118305690037018948311119864211319779734143116465886493057052663022568542180068531441910862918530533350093865623799781552091321941805049 expt:98,726,0:426708164655477000890275450255347996233537359230825603678068055078572185768690530483979279727883872477967005148697167468182222427688835250730805216703200346494527373336005252179998129153425179169405541975856774474069498366622503869407903427510194050762239470842997997171904492470843168606219304544549428357468779947949943413206194819154200161585559598504692063910328095937302046813011102683058231640089632368478947866970023522346778845648102870898031392605132459073175114548205304577635185214718149330416992983890351407166804165953949747506605647268028309196988233767305361741291382876521135508192965016090404300931198517364604358975250384413502392769253607192796721507324069628343907393125548382919869819440252750811077561632309583741878536279703230000857054139878422446147127180603427708828429704600917447413869817618302245994562895269981736545881770397064210337561050137140587310204526285808818450640283721161279575346308077129128490827488909459752308152575975333376251163648250120013220501057296109952540925755870893739088626118741752210805146783700608707536622996922837160677398003341203351388553480766110431344123182677789104679858022371096216510424982048676315996005859351101823572640031789389690671319495099716878889860298319419347560159622529618640118175355266744662407331598655239886273495406443560838728384648401252398353045183922227138034113900212648350987135932227570141916304732230558988327877007227972193394243239402490072781553664 expt:27,994,0:5964603431471868470779586030579897508944005422481111504996101053704042888070620658634603446892718184220478121160877417420632344218074218536055055853341137441998294000251200835878902350186488825026483460943513306200517889603246366106853840145090440733291280737628836962672475155047075274192277218811417069065936482209339531226972570820904792756362193437359255260272908936652780579152117702725740119749377918245976402017781340294169531390247883611378505356757467342298706583634922064709088257785640184257059718176205448907751675016209636121926542527171904829380257098579043693273941177601321704542520456253669795714215535002523967268853493688846286706973999035367452588515476784419866076998252005842676395279638218578241484332229406009518807659452519350666942646794806449473475747553767493845162021519112769640526941059309326051192732830213515976229333540580413722595827300619108280969740698513378110488385074544619780641948295405495780237236276684111403379203230366783709039063472719411695740144082704697603632985497552873504333474571968038639730745252032873211100978857900893481330626200727251839567315077961576806464237728134101031182507236896333266479325934856175889116335417594516961071359041380154522292684361535083826965209299951003822498563135386891475232447007531309326110170827274814394069801400172716308094800028763449103928013302738446528312264064411790429063607977721347425016445446736220565463902437544468120409 expt:-34,885,0:-228476523750723373644687014002375633344738959573253313295673378381427602021772078020242635916606956729056926140060033073714690114938322706601446752472086204645016603045913330963730961808178207763215017501900858842569395980296056740108703232651676106742955978639790402346938757058023705396206982274162272726053788981662544438635344871901487308331092875364378228725341155111018434010367438360637105101040524061771063338296772106596332044158968115550006262659165852163296710243618168537491315057352543683129215465809356035846400682903175992116512861339446629911475952731908088842546841550719832093476305343487020461708563559436380209360381168143472508064742652734842472679645707885058211800145889276047957973692059807305288049119319173129319106681652756562743739107763982095644384826187365922752532925851190935179707337534386963062100373634441547376770817028643050332728353004280762321859734138238987031675696783935311587870039192834643563874032592612926869623391797208269743645539702607895028584122500698098111011232061951530722490246531280555160067707338914792416989446928511604549465504192826378832978906732786898284995067855250035120805001076275382922780012160428673191761070264969953411775690292328243025746069928396010308859738310517827535649006402912255952898688436528776249218886864180489977578374114695105630836780908831245277680459913198577305780224 expt:68,110,0:3766867964664544159080663337184475494042561418541340945804586832720994284771961635397385875362345125057120310938269750846083952813873238584240580179827028286414766076572917365783013027168357407600410624 expt:53,658,0:3745606907993421946887439162000086810348803803092371857142904229709206909828318821048723175183121197130197244352493778939138463422250852343527134762386848777080851567505679505075345465770806895721134211771274772293259989505354294489544040145546102855689216456038976289617392680444976953405298744483530421163275053596226349987392709474693470945596072586963883209895508334043197301264236788171635960039858646321742025220295519025375907766179640091678782720809671950054095805941850551155084902979965473850917202849828979441725255702684409539964150439149357477472547510742865588406211296859461563407639715931477329008440374383580709783691664845736383663038801784370088793404842551953417842873348778874221805705399715354432210347494670220197359227112393213208248173978860627750353040703341367562548515958900446957626661507861996868491462583136836486757565972785201597859791653509981302034055855843211266876872054969345931382022744508783063231741810980521737612696916450990320941990166412615155878082383699204415978877720954451681587069814429903479542778158301091332107305065103043241495237616334706497558758024048371354995778381078122856889 expt:92,804,0:7680919010486502611899642593747149466649196229266501367711103750663463292831658713415279184569662244175409947032999989257086334914196151008717155913095724421214123565414211404671154819304177054262624540117568190722055697928671476680220542928701368559838336428067111425536616146489821648041701273110577053706361418086034761443472306518865080966679098105467798346917600554685542898553062250741733411314786612840508881986382144004386089851397484105951275595996231115064888236880983094071936561219536816852038032287045459246026554363716223803369919418940349582736218979681160219265039593199424543894793508283019529562836802500641291446928979006411204413367433175378170319515975143760263714327381242315380104084348844582613710587726111048178373881327576604839032050152609478011520362808140313650631437624206065559757026169586967629556330683105990075123728304036555187713491828534603673570621146978011206391066697511863181519910465645525817216154078233941728180083417123747740080789188156807592630560128265705528875621630095351201299879483799930273817796360416169388658060657506361895914025279478414056917576529844826749149254978523394656765480215719926358133890602585178838119464948003289948380599052143243657411917203711988600003537438673472852245599607482384889722702462622774797489957621592414208918554109594415643546111991744898184380453126034201383595790269274373055123173862494511611609472258838476906869425218506801608515950342031211116660445405063954103192171748610888916224658384554763772392708457944737818761788668778004849546835031715922094579082757147279920864952420663296 expt:-93,17,0:-2912125755884410842622249251854493 expt:83,344,0:1455002626766365151331492634356788248715003383435775455996374149087127274539469938480434554541764208550166395886013614290542493336553727055035200479566375122407588223498846894540017410056428775935861377005037728217969587830322338737768781971954310027112710091083345708154562101156949905590633490616529984721229205694585229393810736667126990248301840585766896715156041016184889232474489806021208434163212143568783993412750969879402550558174816868622343662524065027291485375058885945026037942093663550462847296831559200222610314374017319326883901944196944190346470731947264070070668533749087738060363624871768516622722491132752341069559484881101460722290741607521 expt:37,509,0:1639372139330474505096339736526839874531950388106785764526499216811362225270703761672667866735996696543474964780972938761569608985235961843219297731833082892285640739207743839560976358344004254125552207884861967683494079795135492763316903001285669079285642352434013330494551450924529881670919372226435491663678910321572802241052671829048684593319302540499062531002552822413972447877352398056117420144161447269350831919710819792646829325266226815447766753199630288869617053962763718694151712581758666586038482541785095213523640877958314344476036711277346617174429612617143676944589174538616885971879400465341144053670575443367839317972672752212894927196448994763102499581012815364079440761668903982747115134081448923972310533501089520501466675410274312105259815806872362946932755486301682363073385077 expt:34,19,0:125342809160496617801464152064 expt:-76,29,0:-3496183156153757826996482351208459912924449087659442176 expt:37,959,0:8043653985532953716889715133535087168670385482210859421739682450017285673683111089377825581114293665656145651712345850663980083336468179806875814073857765425892155354598266669506804046627707739916500884106198506997527648083295900530561613402364276614913200001026056509772329191449641564220726849838723452604518199139241770839665976645631344667870833619675231878104275459443798340311110952188496587631537611487174398583536053876742575306117395796907118640363142612543112228300527887243345970257920772909373983605623295787525934506659963651305156708304203030998266284694349384314377300558457176325498546062335314396443971466680283426513605059525173724321570541512640520991258079091372220776160186495883992700218975056631545666177364476484572440897669270951851900895176798423899545287983761049721641455850562227655219058197710285516766496107629355803471562655222885223162182968326669241365735898955624385521019652649599364538263697078170698660931177959033737136065046900419098588879986481831152277650601951389732469419718135458317284510180252252347215282909809244252103764833246379696609330932880474725472382498914394849425766909318546858182860618752740997875122661035517690985707005948901199463714885386589945448510035753998020104333298915321476036121567051616071951554677670098530225928071546828420949645455483886944027286648764164718652180618519663834711653112733332792953298854502679756506895010313106988391740237915628327936616978344717429852330779137901687317622168225757826112789753604087557655040173 expt:53,855,0:18024719238727749739525445919483313820179132397627088793412502725451984940695378279438673546750025166612239273512610516827961724525198882762072448802914929186534874689268838685049338395668464648214285629458942854743809087942072596640624011936285554457003232121031929203367446328606007087882829501707445687372318602594007967315081778231244881573239906171935915143655956161425143440493226007667195047540127725460951375078510152848109086910835297918453026272054497519156136102101888168736867868647822194907272146486388416624265152334316284765111597489635974901154683366709520639989936829700879404498384693571443613183789387222654028458579806593806268491518181218800476712301946966270100813204092285152986557168694900881657470791233632087214162768980287038944834419004548322680351210051534951796722585140993240046500305409149666028347813321755225701104959869144974670164886058856826565923628643498059733335090448195444279918303399796642120257846094099858071377352515014517392246807264485477604806428498201472579832708245125875380579584993781814239835479412029038694921470435633141289405105409413524512605572562361133641297988371189750573248231052889827586537697292556993264681319509450424190822893352470802584486267244129501288234774550146263799764737409541494978039756256344516245332054030367728222980738023243510101784709043134443224472285495023599866477956084806532775907376656412097028192665531115092097120219791652662455717002643200873090340640713123160526016567186689389757 expt:32,656,0:2389933285405466860396692079116393607592094511377675771193917107985577957215786660857642782380647855358562124487585166367387947413551391813528167636162447060549990168729176552922878656050672076285621550614985470720664776531442576135048333979096784310286244860102378967371399286213595759636919115966603400112237639950891727815590236647193809310063401704857160813929322419325892381145791656471799426867797910499315367811275543479800432663111156312795121794429616492767525864645383481760770859827287365500386734880646418760089786239708463669779102319740012320361344177543946675529942817886591133769700783852263121450795052384716461322528105766425932143907687036561966697338295352111191252732978138183228296826658380107463086196091321472046087589204515401546744232072241940768351560772822305604027448970361890755796703363650465900018004257276623522292065343862084678326596045941765842024484410215769394555885885158749838834979597158322722201614329459219680380702370857126529706245613395378176 expt:44,825,0:705436783209414656391711687641131832457317079567241536806961190125032329799945689381531828701711922651328924171833912445806993257740496413957550233738157646707468341476136656655190568061765250287343123150183203457096310554778580693127605900054156781937329687900011079033154328368560570397733837126414151383627725550551123061599523989519231809246838020349444255196435779598286912941849683826803885007041497453499648698536652839190738405213015416967571009307605140974000980854307563054593796685305388455731431361267420888839574695702395994221207745406708122106371051596919061007969322392348313397932391816147444777599673900815310461704623664643196151052250877625946280731633882993330125061545681460076713485728798412351901806167839675417726868727194522011871552299094826966964668768915141255798918499796543486231511141788910147145213662462426979493734390203264331227425018827335966699727291310495771236126927600243376852048316429905244128279916690719962985233688697060839371456481476421673214751905689846742695604260150120965796700034367974580976289127610455139192549104607458487162099297483432995551188890538592998367871918611578833922235492029074979130410421219592032895629208451572864516745372515998761341772487485436904736855847415242732131193954436562666516079556232801577061434743967882168334814393918596862293538397642429151346165775119942485356314624 expt:59,114,0:7535799365523929401466950149815776414046724006436301251256273386014282698913901410854119082161738764751825402834444249521979494417181418024031729730875375541703751272328798861158409927866104969176716761 expt:33,638,0:648475603635833183196469398829966467819872179533313634773199294300845287950459501715005525988291242251589147926178661960824082441163194476232580397116885117509943674289579029366937003306245475847226805096473463034937358215125841547863811379526289909390311989707533329900551425869234787887523054960552278032611552781528108935648755207909825160440738427953647870234694868460377213725626413535570112216908805974133165357493773798997957325074032229891071788781461177535131032268348271529076288914099185644193139733366057736098900551638267073002144185264974730918597301702988431169584478969558388865801487275460346465072354829295831509446111012459075308582088675497358398567086973619837648636885329011064845212317340840818123718736632174769798597171923150676024529241760831961841633158660369965791581395332178142007133509696793640532076763117981014872625633261577688978190292542653541593712317454035995088612040333001542622676149361438454964780663603604979033175966419868609 expt:69,872,0:29950710056653639866040347513592954608907832187759095021784612336213340883909743941015111690452867673342534673834960600259673961740938823369536279442812481113707789275256589878997231276618632636210489615929064857400027555434720369902556432133478971302553689173725290340815598949062749239632058821352962601488612707115779689919582783658366139458929359238601369623679788087432179938746909197524719589777317181141198765254386641701187353660512871784711559256412459533781485842843404652110331152933616653843115472865088192382607300085255939568539834001519100403938776165952337332146706473461537817329969120309309517770547565346056282486046731066492332789904059680738904349305243649494763250736765491708310216396673397796961838301667209428954933817477191941146364618594356436871426698169064040813675818513426197050972194802492745959927175153699196273914186935407179377493000883694252000018528388345695513167889176432751477073481242404466807236118127264128971920247017078705326478921858295937254808875182604664522156032745827731392987081529736044441817762936554493023891039839715605648021019219907116643520667553628457465780133403776577685023637262452859732368262675698820414066865949360110605575303893868842664652278685058236518116527393248213186175036314144344761002775344535262642684517202791126837476442938864508396830200526809879345482138492481769343790209140327431667550761817827241581355415614928705123841250085260545474358015032657030444618098608485724932887367556645547344897117535819883458173888231937264034262930323293309593162187140783379967834211500900425793093911669240962055595069032779064523361 expt:-35,560,0:4765460083484463473472807029671198741039814209947733085375343877805519722128264213906493004712395811794836067456926301347831701213543102558807372013840371317686389493491044956157976970854534780866809198779109650495115701056756779233669845873333611352227016172179141127201204621485258250872410797565587431587955801098712622722961241140244408879022252575756465947941316439513115927707432620645580331357844859947529159485059102032289565818525572625258477572647406049297215450764812141735725360033399668564250475303073470958824427283582477027047896762000913374878650247253682919902323190143426951007619514663885034098702528525398380830769050070744862297092823136092265705202572748338959960458521661389246148014773201598614888333659845567286582320269709906762495527111679682357140289756441194587185256840255908734955659782455404151202404960940839373506605625152587890625 expt:-83,209,0:-122270392573975557137544098494603104038431911133401401060669780228862020091902727664948350712829411551252088259762269665003646460255858818493536471916081519810436077327712541465284264947694222413222906768064481479603637285266239005383584918898692141414316852928726367305370720092433674542731019975979821342341530442634729485864001750080837642935553282153040722532849483710322964546566862518809499408403 expt:-22,544,0:18964367700820944190420983771842117471035813402172302356001324232625456871631696158159426747244273988396896874782255417862295115980915085588836421854267161890941876064963407590082206716515749082957670650572915503706055302390446576711188138153431530926911613355471966093726010812009574536833618487020923293412479710272640024885745749390406182848296906282562712038022234856787439331540733410267670953621778020862196051822262364620284766229990123269618359711309083829625146905646383609813594662427186141810814135462546643373090731265237443450146344536874441550683786161973931814080708597655835455648574641882644636540462283387226460671638812957375987034299333511378035037854459892174703913394380151030879671916383365880966083883565056 expt:55,53,0:173469266931818817701197572759460512158186359368276122994156906997886835597455501556396484375 expt:56,7,0:1727094849536 expt:69,511,0:4486269579432801228328894978520612039865782962773314299890064827550076871686539386493998487559513347930912978842976457609693197201213966463505628022312395013622414842679517721662844319556038654381323108565877674965192437982575193911756281655521858715295957459295213878788866632588753200138937292160832095681182024559479348223221677348390842846953123958441380139228198612700886931654375724810762399664286697632157511028362743434949776821972216621014709224808699213105247588616225388811148034573781049594047599184470666181439258133413347363982316136095491031694475463436444214376593921337732387516213520549630132463991049105936530704212604782416902497080757979392934118897752584527916561354795284032980721598161111294569421622420394749960961723356836189382523894823797755998521714994563261231632958790842100581461483738927484818446238271808447886746812572795337464271466846423907255769829987902959874517226021350215314613561013455027818736269 expt:65,627,0:497364306835738758369203816929587563621484908670308464881508611000120397210171552818133505588600972283722504217038299267610870712281857521011539651202476710112665851438274405311118329759864306530206464076881590237702559066115100823897031634086082484171733231579340629242599537765843919362377197750957150409164905009889637997973633002262727089466214411540563439873655647562353181575977350122226034217971081813504998125791931120734615674206813835553948971108562651944903797187278504359842148559086576885512335220747304460608200450624832543393270309192761368009850923893828230888362356748911750574377927901251690822238297994571714786631993517145675163841742009468644933432283278288658898061814717433241276039971839163707090134740016885115455078319929919984436448696758395047545344494824758451226738937682595385197871210901912587652241955896134593132930558535330562369949669112499207879073779991774258219495999580367039563626586056205306276658856886524280676036800529831507826841752629258128889348309920708180393144270583624503924679141781718886992556665276474942605349507318130943424722182510632471387490571856915266835130751132965087890625 expt:46,193,0:817074232257484121156770823318605146696751569369000241039998457282648867989095210690478016388511247325018574872571127938218392125122241277384005423186652367061816702091193768108652663491211481548491110769652180143820817287796926886145903321477727282551759124806922035803851540296187694499862514735119610739703337122267136 expt:35,224,0:7434331703617558866735418205564382401519158226603733006962337038114968755942018524978551854012503800960010205708607955416310926336526408147412201804428417291385136369283229527393145734163012864208910675715691737778124973593953966099385511183284037573029373908498077607797410012638709522747893758502294434854784643817993128322996199131011962890625 expt:48,871,0:2296771307785108997996275281694403742355413375274328510033245315525621390174696501258885481415349678804771928342175537874324074456135373852706084607201324469163233145482596686038350670427036741247616932972355015054433455747986815070761138607427191348086868570458350738831195704010357098624395027409387096510181101959230801667175083036850637754119339482591099632372672743060138882768223599588213396264220864703488219466055760560916641000944392297133620617588807928555012293449584277763904964488395570608415840137573373251523555726603443441113068235906294848808710212674698053441585803096252716528906610961258208381697805496015211611434136696039563551082904259850787494200559601774616526509976357060921883050658747159151714704641435607899726584101580154243983256304378508592421407973560468995638307786371450739384529436653347101351955239349662908173828605297840447911481941092339861863239287090444745959885402693797565521445366949111927811171516747397914656348938374407730394789915004848099910670723354943700564628811075303193718039885360453078287438644715151039299030827041903587917146772156422724773803085293734569147130667846393861058073699252566570823424630289221233864648893789083533315907406376875479011330114253420148543906354793351474113233267966052291368733321678620499879469220151506192717633536571962409876554555026897490062209992621985629094620892105629420732687045223957170224155835158216412193474005114831859911410553422254858147750406913717620915044352 expt:-36,518,0:146115200201244140508535808225340127069092033074086594939641038813380464643092784368499957960397457415719662913975450241240449832879511228597374618467828990096974163693493678321796688824401816250266725231269351174696889365960762080267621636961848851793903147492257687807404324628050042266187673582798121678172191086987308854792095986157320245166750739737004704454814011348168427466038007182398317491734265151076778063010496132619211679988260689473089297585811096036931998406782027461402044049893679481715416361137493463388085294521529831982907701884889345802533151813498254699533482401990075682782757616061340632427940899702653394635849940302575034960855494543054252959646383879992036574182030574286127878688271055584323109202843000534198573252028967226364808637164514811988498672481692393863899485418029056 expt:67,225,0:735920003111339161159356395080570801473725293860740494275221824045023812579963935301031775447575688346607267267532812956137018229766093126468162396242424350409934923304882749620115802577608721780903966951407943056069309235411902308234969497397301699503940488310770219419812977280307849553181552764429270926502167344901946040611637758836796263098836023546748650013560091709744036462304218800125741698559917914307 expt:64,327,0:417687513717921146683814441049501323149276759827878850220310682498444752633939174795763205590085370174509431176916209651043434482148970466887815330179965962230671681555803952508317812856112304403464539027712767146228053984109968456131599036017965241520523692299911631594821772907828969071619810063458617810626197420731690747206373943510385502671614727661759398749224149762165354813028102550602008280537871902180618847076481978941607093146933705617051198474299205992992784680935699867987139285893610877812099445086372781691711812234396546078333906858033970549278924593901475494268981324283904 expt:-25,467,0:-68862700495331938784380419966649877120052824256986622780279879321123463371356437053662605722822371713113741286131261775228105217869324551668789632411755509078456849695493437707718952335537901163716308200277822404533843040793058284766310091608343833157319217838813156052838258955825903648017660766106461430902101129851205246720686051369993734795826264711765354552138512394382816264477130422900505062094863105482712026465196187406241972801187592058303442054845271865009183194933559721460674706658198949275466978787964466683095692914947643154576581856285051087744587327756364233631868758575460879749512993364615070536471908013709253282286226749420166015625 expt:39,139,0:143873356853696095816280231561762895966095121358512894018038780434656905244853021253466390417066964861759354168210279589225963338479315659197113508775296585740367513592599261280433915157811377734958643545758755017210195959 expt:-95,925,0:-247933317851371692765238123220353261074803765143732218785336375547364098379952983086176914411708967965243034975624089734549054262155405601872988521853631418092306768960388547432760579266561975163002729996245381862957127425938796307154036020276283894081669921750185924525104091927547088831951444593347428073211061542081598903847868922087058124406471582647813289892107277092495163694211929855009513467354559044835615466736137087947544617589164470286717500588970895846757222008275492885619438633488692498481179512599142893182301567662753282826824205385088400850355763371781678525389031580015072637605912123616365008472820886799996936155624310901771575510951295719809269053623900174867256402312047226014214451002303098027112553312370656182542716538763092449820889312056658510682841044062831350452293919927832336800994362138064805630261807651118108456301725299789286301137388212766815512960048788081683942442538085959986120065061285006871234949930940185524537103913351720159010805686696397758933127125408357428549627886466305653330611608087733791050176139563443301008883800301224683395958487326723987984535755499835378139919056198037756593511533680696923763042182818051706007416822608172896694323975433662457082439992053758519686924061393975580909143061424199971052081917912118305230171515641167651175575831760969677740062001963108837109680812905974982663520916997121589375625626487587266051342244289361033565546995111061042957242305246986582855170773641851842228652472157775674690273006693174629830847980593151580935023679044298283432329850647778394157726704922914014083180482909180414233817825446242940819724654162541194190922934651789175392031213637280829578333494425326947316977013855379710169610940508930766848830071334425047278453644935556250177705704902919191612346964146136409193037371777312838361240210360847413539886474609375 expt:10,790,0:10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:38,727,0:318181364845266673293939034580700586615440320951037592693430676258808017944424452887520229213529156147652152548660229015222939861579338359559018300102639754560937092707601655387811647657615783015052071118531074778468055452194170663662420447464862055872460088793374322229582464089946075887299294193817540314008779527867126627186841075133467621258418817935949751545729428873936316847772054961100333271621441963886222050417381885840563709089357402135650374520106690685058742735682668165890186931960150146694452795036044289394868653254020018082650676484218338479013477191914691177584198123357631992799912818573072108670426678744162041820440354139322736565922639316890634686494961802003379496237970297257659344819835969921578132529764554764775387964765201989940411202080226725613765864563543622841931061034686660258178316702259830705725064960086720549582591661146532434470239211074978214823780252294240896745420707470768467541239033990368271634631401684194520335589793556924858688944215388612471082194103983918698849904549069496888168308090987990818992745725204687937832492824270761610420142018658784694019990897837283216723902382526473775384524270600192 expt:34,140,0:25529857218193114702174428995046692565363901687129767356632099628880917562050351316339403612051006254976853376622453913126272976393819424111873308895894292132165245320628698829331239739743398255119320169479694974976 expt:16,677,0:154606681340974124033724916902627302485363041461934511562903250082108656614988464109648607664350683544053521938530767427600678633466981349875552123311129851630541427823062009528531348391461351902236714300408426870798081310080290256564473876678342716043349504953916566734770683646870083782168391645037091096887725074202784437995895234871118748161377827084898726055250090503083390633622079852383302615813886977424887371916745952542456924382093237294285328320534432277883419048461987671479977721049775052451336009020607051890596444709721396693315217517965349881355454288834865724272352477664124571092063711425076519590380710563089443910597712561034332057450154631167542515719607903185440744035174760067913386635899419010434568177660006643202632247398908883971060098166563478386618325197936106985114484308324182451552256 expt:6,706,0:2370187868170736180128996880721994304027981016428826558124299374475962263011616081209558299337721916323935274576896010123644085589608182399969109349184244152181717235854411892769936008301419019510706362282451476374286734568331276868548412899353395251910059734878220922682256862053827867397853562809960786231614060068494140882400067369125402792475819991480014501511652656632709028304308993356905586688240373617002392227009641266162761580915216325822191118000345304381153590367158129348967240326861414168892378280984649126875465847201669629322152902656 expt:76,281,0:3225666254982005051650393297063271441718814825117776170427014225270006782094402082487845256842905212014111773807699305585198980793893448295836068068070917535721168698915088215578832824619604662314479653278742492907609252295864963415964828492105414048009356278895083198343094504871689181249621303435108028838697311751040340640118912946160635394223543123655902100316582935791118589542551193090214863975492460201159924354445816812213366018820916069793903958454530414527672845513966606441240056930757447014687133057326317955318808576 expt:18,645,0:447471924335366323510556443313429700068812234629235460450763927673222040496888107200760252341703827945191621326306131795482065495578664462850472512309208303012474749490243865165651244373346115911654861626284849310331418035860337441989794201851669712221122090746182713388579296175033571904584078117965994933295275297103840168214754293386003180820988449264532865805743450873842642690490009197041409759427844949926369573051943199612022394939265067082007558614061463253995880975471188662315261624151062500359331883381108257415114898922045511558749525591359567772810243728526346583785738997208574199792837718461074881349077212584333624940968146337548498271397497840948183881043905337007166709139932188874261432029055567751709278200083034120925981318112036767874722249963589907141208823123050935466250723940859117568 expt:38,388,0:9037233162685752053376455537502721342270736042628911593411187820255850239811996204786955561847703657226822474981226433833893660651795689900570630384290367549695011356487125952090574619505343150852674019087633094038448212974827153618462678721327783567647950749746305048046039645769130932898726170627803026748555303885698486663393441172336532741462629794066215797431699115607727238433090103791079601594737166721617874568124700807143370244859773481280231903946961271883712351477922567791456197385467880154554338880438639750996366163411447302912395804684732748389562157940271392193893922966877712008059498487345053696 expt:-53,961,0:-10693273783600734316315714480041535221366626391070652169481102268537307894640601690397477696258749742562195832242552646613189180449413635841376794326217929699139495316029126112610199345461230984883346783455894745072918234142756324123553503913216798272404688802123185365091119718074925049882233927864436065352441795323304595442144701951516685757397182021033950771925191451161942776319733212924587917285871042600950991564279236504812265880751815730359811693631083452415593025707823313397391467358190650783232378570454741033068772420053491342610776102390217648020227762293217888965761840533847099886723514168515183975698570560700046391474030860444256074699445298615381649814262336045393110771426131519842556272342779016381298742869204722523464017593559562643622326956756787868098747774454389349057962560351445716834035262214568687712133450404931561726575840016754345335968416895437533133106784692856314926056588599354521991402833078563695458116405668054338438928149786528236240697114627604940900558577671850669754855161031297481210200709336712927075772035987106414260818355636404688451829315745413124591033509314578360848228738843568098733649384111596453174139763494748428119399833236094765497395040014927396796803419365269517770431524291886017302139482314655716680780294886334131069691255122316199720460643469796601064562003254702066340683252320430491769624200733429385588367602550126577348991899954540173131577135256775953664267528916851026738118382069532086600634832714152507186748303140799773366399952508384413524462895427617680029976682845372011808593897598687010617459593771185880907170544507963089979836763018697440064683745136860496786467398309247801653 expt:24,659,0:3624167720890114802953487528882213552899975941370552554329513099376544209818189786714454437032689083823830559210703982255340689476005362403899468531020537380006871571749241446843383626812449117417305212547159344386130625689077819341774113065166198322275559097572679481175645104461252543777972030011842688825307404880548921803031127032140294965934932124130451113999567382233597289101129667669422461740167339579466317525327207235602937780467185586995750085737222095672175124755623264554299753026627050426905461119988938722765511047677254959618655219659560371687805940337041876822078905563120206071769003516902911102160952293062550519277843309757303919027154659813054662466523344826296354696819676501832559230684594091362492325587744451955871184496572010101281716464201362384124303957980156819470050845018195253142021574427135662512522551131249157276857182203346963051964089533177481641786738454705685271070900224 expt:24,87,0:1197782680101993558280692226488373902822663746844330952273499589865047835820100735571943168026820232018026475094146023424 expt:74,900,0:203492195695385637811035038604720591140552513788947796070956567581984736792471731249691172218148855021082026970704996363773142346074349135425135963357684169839046304274718335440539737845426708166907155882416103467979779965950248991451379072444893391480544023125591578249908365143894932986279251195201771680227260763948792352936603246330319755571622810515846412833416610215943371396912549385505415900612631771649294092252136231153758926269683448101315780244106657481380278801404098349704834462242414233848548074782034341541814977421309404166439064217724352480695426781157497383082801267848091972668055615592471820028314038214611664559270461638562962083716708158789715725864674555451425781736717842336751000970187435030966278734709392131234668572146766791316051896061637266899364682542146271901296285157019816702372549096549022107433241920866238031206698288958221202218632016024210082467069376475499042527317812114570642803224866302666554372000471823903015245471090472707641476693056302565407925873424770841334676265472397398045286273466791200069893478024154625862765074269711308789130828925453589264234500803624442724824603006351547935458354176575577193029177679995128433886548139638707554538291806471117578045308611020975110487218424109419478440720096710842152057246110025136351560085959690150206324456752232548848972311293881638155478974286423259965771742724362278920613669975929606425566174524456931028511307439225074591462541836290927880691511343917965103496059384368500739378244369199231681115377111475866919320958869237569684233879998976599199774623618592008415441793489599256106350578620210330523214745293501592975212532951752926208891738168918126903740755841015125828096229376 expt:69,543,0:312648443078484768295888815598845711939768666257291433888513312757955049368020160698630214239551072326750999792081447984468792281784366584961486617285817648690364818430979007147880947832896589374742603762111790546410744285504068124412810547392012131346756698151463417807121112731347729403260984454420384883458358195998166979494748478670615869985947232052762056592943794463276191202025608190774698452993168999008156807611820727458156566335247124610066310858249753566038784341494062081025248869417660801751147084173434635188719725442490006572202113716375420781068822739057141812677299815087162596322545640703492929693633783845458495004922557983277693860984056624336776034398970301860440468265923692038302131802660874130160823777321529100807734183365271603815201483619478837176405601832237316540578306276376458696902711394652750821782153970726977230649237363702489026445302222042642632912600454038910186382368705894343877258931593200635310200405119407405120535210771274792854910251876704104130656951309 expt:54,530,0:1474662736655096656312338279909177255103797074286295793375027509375168436887287143309336449315957822362332074972461382683286797326877474651509739917544753283401205851132747553963526978426226509486446008694568119578399112394135310582133814792181430889458385225614364665191714345684166126923640114344412210292872490366419258147481273591304234282967518734863233094427554073982927115901949385739053040841288630681194000841739865889168738376527086934295573433603264828521334566838823869117642465232442629165125207009991732054135918621566022150672289445131265256648929940581735965044254187533327954696081027388229809762269205140612326771928146305517366531304549928582772855377825128227036208742669924062385323267632632943920240050640881476505929970785291909572050487719596150442436573679196485824822432870194747280187996123290839971281376461049282852724465409463771310117744414420026630389950888196241467693900151918455422976 expt:-84,689,0:-673640355906192963680854382395597279844991495307708500762664884953750280820203051032786298142078133894280971340126666823703549559943495473379620456496637792111780395798111098844210312668985085973564668031838744003567469055747069065192031462953751775303646522049111090958707099958568715666445558819096127800586726116121938372786122995565072105666246516054767846555535819145164971484723840655291769178603047752590255749910890559652661832177657587633043896917516743806552357328358607488168344891668330944104480564369749820890670196494165679972464070728580289276173364888339312490946125601330630747303595303211714451602985604824640650790788957226193419801364185053958966373216314087383429341884277698769522842899547363770116372724893917923171530322741674875748776826251410886127808937300207685295104886265377799994629948453289346468117865398420831689205702265516443957514776123773586799797709730156072453168535652382546461520516180270928971757408912398951511864855349540254511900269624608773339111608340753334445558782955747228498729808997160178550956563569619227991188807243565793371441378712685201693989991158958417406905444641725997669829449050156320054612300296488530139587379779862430775560465112395949278438701569138898951204188270163608488455419654051297485964746817157884159015683507047747566104920764542724284450774974464 expt:75,389,0:2505136873002946052821571944823592082408787982442343539331511593683631375266061611945471197761357031711510886915023731134485877973866520759948988373363766768657863172035979520149693975667330757807327190596028499425293356360109900636077772084412582887566894237468021689121483843531949402500679864184300241610176967959666214567894484564567187709777650474627724716339736193918464027876178424957702442801379144695328707996397566477572403174056763614383402310541133628718945533392880172251145025200868578667966567102968410404698307362393252463909620132842830908725719886487634875664806284931154944418880613973079280757557147546572939584559289443428088245026515302516929139885052576138027479661467278315711837421986274421215057373046875 expt:-90,493,0:-2764121656403808255688998318308448927779841418065114299643004937365951143205621653706679499387531179825563949289390297858821486365687544518614573344000251044963118567564039833580386521905044421727153991835591278223063849704280112286033144210330626593002183744292468432067084387118208158609151278745306808847873085867331739532972963860539108442723664744816240576949951467742831617638950862455974397049424866492109130205243025439534284350885748646940037382914614547509931290000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:-78,713,0:-115731536307359192637735081399829109511702293973922696694208047458262444229652160307279087329855878256079999392518677233048314972657057388874094275182501289421919041337127404591027574520060185351444059593154392195135354268588962536879418312873113711549229994647861923000955099677819115616815194464713534830563588649882898053840400195424586032548275013843268241516993330630236304363211493713517911756737817101493890807716278347242379720375897560983549657660651681988416735332099874519575576530792228244128002461198707035814595388684169319814963566786245098551322585402939881500335265639906067916278437416968431351004007211662828198106584287898060279705437441896284017744946256629249246220165360343009335114244569954394057846850014421787925696186369699659423147781488451057285691394827566399868414895988087540099866995327706689353227627368171888882696031349643682455531264058160696858927471245322701673243300242916477186602464825933213315337095950543131154067825494224012789649177821755061866161853106394589673669448275431723352429590524472448401745233005597262909298660312513585040969384431420061687766818410927875672704386212307596396632002473179981323601609734932089290982557135462892951962999979904301332318424478936510361126749344194878185769161091829612201395286090063520676684836034985334594621505414563276756705579096792040160061812562668290048 expt:36,763,0:287612717441501252938235364995076989912258567835194305503864222905817654453491398558770456798842563403876433023498607174234086604662738885378449834211542708982978196216184813939600530734616215970579451031345428619291554254395119224829150049864061092082799955573360133603219521595326864695021799168684562013852249376992623873343118112855686115088808687279222093858336092955998950873167464052797680801992263797310300356797391216282203047175649924968146172953919714557432086976362430640363345164555500849478372610459794623063760436116166308460356269543727122939698305973093062079308977070843850732062284240023079465164860441817815804509328285118427837803457119764359138865084351583806289107350041743083265057334370946088906064154344591975302967899967697344349561592938790173718507304039781398805086538649982989194487018155662504702768958902129616878720294795677270817445558061795402174726521022090102401668102031654702766531351739548933899772524672856784086512436602122477055532078885288888908773574437636605795708667526674002708829716332805686493462673251888541522849276838867497234297868970484972490798084656418668432596022103085029156910177825279909646274306163059443534849729765631328256 expt:47,567,0:1200840839795357756556171793866035488669397069402218058853429523017606108853866073051675237735344222717110142579489091060363324010183030955999583202587790744873920391925268687014453103791428866488369403851229457767518484585400595793732678736929295286963479405802380386638374173162627363885156520588965951827128250889143941188182953700926722256155063001822289750113998809814892368365148536721743814094413016337848688568918084494871619775117616358924448269763664022118923055017911137842861355188743612895261789827872451309409128169082116168520009588315723475618309774431818335253416491565575448829636518484518313005184981691618323760943375615590224232297887531959092930319995333870473790498756459817363196667267350757707139114347799391414825307971212091044223074718730556986735254848581373154216006935257074685468225843364862663458199989272421190309964881842705492582909183953774649449964290445535763582719721041629607601034000766219103889698770634063 expt:93,245,0:189811445138907350552800803028132318270856486385053418037712749975151905680839772940450886299589953341083999271531699036629608182153885935579378849451189841246877163907007586748371382526385877632296297367806278260073619502837087612560855634258114918915142457424551221666268613973872509210548656938814203992202491112249204302074777529915290725274509877730873272245110513173712234923547513758360328049613739612358250332564697958770448525150872819149530642122991079434707200113667499693 expt:-32,412,0:132370456868089885903728134916792123229979044535154622595605894871140987448802881098535736981597853547268988767936094287847913714280410812805481072174892167662104073696464879991808809985596015029436652086821140759661740927560170521238888834410398394247502421409940705455667510851752205552056534626811618859097761109564081530555125656725768476650930897040696615149886691980619883285333853446759459196371669470109465000830819767736722846319827541624437545423803544499106306804575519579034243488673510700931803310410369834741948404811173882422130791081531135326386594346734508460627224488365883999000804776390900106160766976 expt:-73,370,0:268817937446766145442198106557555707299852322454026359428476916174845729180692785461163460485079723744959939462749245845895687904735816865076794263717604966012182689168095690958838217033687276040045060280067207626046312195168080651837761881395764886113963753760834412127698107460752445557996802419849779908408253837884316512634805178240609167419868913614668320759158141050801534936091723675844304423297869129029497377604564133226027972677630729381553858132072499006005550335236095584481554598465568525006973584347149020417329885051185116957434174133558557099710477806848859002101511273766789849989896446599654420469118962896980442098745167512954118478569833907613848252608011717544208148049 expt:-65,904,0:7476088006612927635813859446573471148405722216005428337873036043231186079958168234655128261355783807158721704379260915957758217822077621867500440560206384169070769533159985551483020985475710683700979236907363112033644990047101957273046170714199216404483780160537007038623527166449258864160198748783512961234393617386826793415081976514354630915756963837537486398859606568067746395464131895813501401617041983662268869523438391204770495826612433408765458410620435663877807032464442529968477115921940103577390216858052825708753864587656082968468616911026081653819514030331916018123044661418565642911025530870993821616297682244798142168034872991984538769820084587324504721191662886576517902618307361704402178724708336420139149948284282543262975792304028749420427332919952946188081580583790225269482964488371646996041495410496609499748805494361565442458937572152995474884127357284721870748060112844298373068726360209939266659158366899951921314063488385052535648321076683428148126105842193642286024992930678285755041759862538217409572268726649499499606980773383704800598813078039204400082630771801675842668399057762298657807788837860460553823914353025003459058307226171183437694740812857306950156717503856430459650244670803765893833707297125156273455126961026717976027495374263765611273780285988547067568437963799276682277771865186868699849332832741068240987335316519864763484922262355869276408357104152723004824262877136699430206518871186162960291243767646620145129860636993132567141351134152092406933156142883106133693959341914156343195330930009161411582963602590356021133287170265873006021777183311414517741244623039165162481367588043212890625 expt:-77,614,0:2019785527067220859016075096184821912149421106403027443543560963240192036701879476616954690218222713063782827876839369054281035769658427703648498436632136421739556912595801858063198011831673005695866824564211542399160220651543556138188133469744318628351948574415103501052771273393981204066697612765091526265490864745203168780093996025480290335505689022134191478915929217289966800333369370418943444639005411560553516922153999320601289370932595922673608497374963224036658222600028845023713848177941244589411074334426669985928674891448116003285619161392614412835348838786861689490408617856711975955518135283909499974832312293000442708315178452215588031532966458821114754177230599064225634988092966765366270357352136983827262519338412138264927508379009517645365508020391394723293691499336705517066728129446273985998316873616836259122863394701325807912500191267168031985999081769304410020219207253073778474082824985837553109700468359743907719360064109613799688571311209634969765328990761517943042264537196838333401400347380897531424713195839839974898196239469825106641941501788961002992626402375484540632168133513967413294827065585616353005356965040287767941447609 expt:-51,351,0:-227578803811760559923803665892351520428370789673508990418850061972740388632750522239984381328651663024374140778482561178630115570070474657027787117315641203458108979183298782364210915367865734034950589483411688132192087107896659215307961790261180554632888410345697285434656919490027197985190413884000757019718417174783272092501346827675850086279238576158406359659768393692045443493046761068561458216727137559396464882832268384099230639577378336557744586454311460874543212467858982205362934063365853125812601286856625659044169653638370861329579070059094709483721882329882116015560878826102047594205051 expt:50,702,0:47527289157378995587876810145877577731621780159337975811043651439146356231936805088930037426315546580065265737582454716869456561094715587588615614596313199454696177025793364822808942384619882008554402956376005194359554004974096403788137885595666449606725010563408965535017560520176300458833774557317910487124563377753556232426423122662213885097303501569798166547963265331566412324291699762962584993997746712370064075751466905079402279342701902764578049398469516972909332253038883209228515625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:99,984,0:50702746367732423332636756046707088578844764784173362783707521133315788404642161576107293454340562078957046303833670333713130937649400178138638781061468425602312597594693701873663307101648324074767020103581094560099128401539216160840172463185716103882966689828690031541684807314202742848158232180498584873013282070399063315854921210409313246152527668347143019550364225837781560926140640093081116049657971469048051468284711694257785789178809823941465962040360930016157617452358728751181336693124773903638007273836503394835409596627165112284850875254019710400215921524572141759487839278218635745589782578579334381032101526933997551326789078325869307607100354120311604173747476470292725643886125380388270758769897729363768023262199885056661555947313285025375746755494964841587184402442187978403892800295699470235365305791026570731207454053082865363542424265608839239142648022105330036603608639151764223209401458833898013848306012540918241308571343492002358749458954575469142998610765627649222413431262464681890620336354859534385697259957037363331495002282308313059575072371143057132684161422385180562511230179934391119387461580548233050228505428143177483520819923735804035411728110201914987438877780430590906308303881797836439366427239746559919144471214829376603306425594428226006996275012485608462520827573208905537492316802360406651053484551978898843772619804303428095512709190321751942504748924572861274319455120692685486947434437367729541467272766686966807916370179754298758691241170194777607607571459715789461966313236323523592837374223651504636299665197397806178032081657083412157743291936555271637270327920149177481942718892398679774780630393442679911779866113264527251757137767743475728830777662545861851530110286521972777533327238249737517010066472027602218338978796182855291347346819511885654909739106341730048204503382676292182395762019301010339302187086865618764387685077382309395957419707422191992883094903391508671890404797538764337688679015997252261601 expt:52,827,0:1363845534203275602945715020440112734101654002035408092138994948157965218152597293322552516013541102339042395990176596143927924801584852182694494402174469146476365708253904854631754423456184213955558063795789571339488371939150388709770832326123293382199321743931181340567197060909930816221066728909932740981323058976498861029285889367417218324674394634948477294304297443288075797373908416729496901734018773669789061707665790116223052131538693972561939226658646132503581784089567145866185449011839827233650866407425601793037832263017989277208429957875080013654195540329347914131526642439138839114974367753637477200190329282310264113595396994805361388494628682431321748217640801660295524027806208203770728640462587823579475986549878451221998889514922178015943053639821129315654194174336476091685209054536280060360926059507789375655383925910919328884755937580198622348199281035939633612639571160057396942003035048191323428551521466383128724883857629281100336791723016090894181692768913507036769585784474370724499814943464300066137630528362913596888302207349032278219095928598441501164781762405564581223661028609149292490970074970826464288906555662494076317777084113019235504450774633168894206571329889041276981381226535278534026720907837639336650956477462141594816136215684669130211088491324847506030723793623545095412834551391863147335556256713198925300756827943629425257037444345305406856996887201268436359318843454128128 expt:60,323,0:22021853740468578834412999517383915986003725826542069182383222392560149753844176723050212105982537239537599021478108969602682255828632115769764860327553473474873742876444567203370333512921531141121798618506475910567199986084415121901524096659710646681600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:93,407,0:1487853124884939684161385095260700523967859232818286064937128697770803227477244897265636431308165638318966698855220495473642835305695739102629480041222137050463066756784476730673688602838369260908469031821258574541365094727586343393304192201159344658073883254741254481946525006070001016365758933994228518537153685742527173077615516552516989509505043555164058392121782339357054879545731381596514378851078834808332428961106140341211035824086439359162868820393089217972263771995780773037041591155928597930802603797367287480285258739006095757736651824883846891644962424204439039748118255361764570889647940764521065367186406409883179355871269579713473352431638000331921603972636225043550734332376892148456648021902107583989118652297791718607641268173465287735838369363888845836639239193661056146350176700757 expt:40,532,0:1976584504954205257348587370301926826655826657852950374579114824486624409843704559491800622084346918898311307268718866322166100951033139422529427733796274510952318596450843372699872145918879065832419606235085401060175854330319264634942415582511323792390723208128503608909506002101860376290882104576621154915114333409116160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:87,730,0:706406052439804276576366923069975401164592339719248046363175133041504186269361366113522873942837171766575825692907350413361305763457682609785452731784223726861092814681363318067351830762134706310235218630451383037256434744365437287493102400695653964561812007768770271884322063288345456326150855163077971604365104144672964323628928074590169741911380893259497388141831058301465764795085547886037717455631758754798786277409911481103533394944945594049303351200226257695107186231608269522603794233543597973234060805867176925733535004507818576356738265678541985876988343565444956563176444492195721906970792397883768414377487670435384357764529998377542821466271982699148147379912153120661855805478752385210208666518800046101644963551222667137255772127065300202085523460000468880606604031569380116746352741827362128287425183441335754455687265829010585467574413596756689179258204408286889278803328179345980814287315190200086811052836534046524248233679177100752570989171333960664035727831280319345425290977756020974412906899038592201787348761825228061083631544347976763613084792365803249527341553106644812202911851620419765048510696413924148728211652659875437527114828561845302300246793974650997138116778423178153360481516286629888500954470861598210243812921260066728648008448752894712658707214973199057680079905435919626256730123127286301269269533605024856318874090809110868170349185734499760880296308653980901200084758996049 expt:93,605,0:855428814634958918544599433108540171368754753688076725315883503766618616635962892836439002252201637178631493204536270801813620260674345152674646475870593626683064317677060559261922597424647952067084352720270230897768699019551822862416702016439561791131256840774075776817158756158362876954703668271367349100772697424595673989246853166711784033450960087641035381498697333940896283341471626085405973825001412103159308752988378154950172135332537721061626398804507352072137874822359784882151232478545958168287870325307214815056872605634979408681579673200606265939799910966127483516061505432535339722111470845347125788524278717471958918210481766553564146010755715128950367184222764324448405602954498081027273677629683607327120669429941319549473748000856525799606103272316670237148246821455126298282076072799525481524482941289874128889144124068775066511048362399672727230153446359840323405054769633940438256055614689237151453949465506127337023888311827938050913222460384888518805017976698191594508859162464655030117614187828782625057625442536831551817101524758129922535918617854470433795037085700145033888156152683557013427888199380333661049871576750433106831383797201751809880804414028368093423693 expt:19,963,0:27524390933462438193837863038173257600749953407807781713047411800439226575830665293723529758944853530204290511646210815182136606877662463470431698540803603366243306719651411385140530410420060215533879433895666800137273296375613114999995493626942192121350040312694984901577002074624731875041793317359566297539168950875820565444735886011981922691483574660663239016046035782355557105396128292283603712352714496861384151418904174890595393015389865531243654829040983885834314285234495791323218841795533872159352451945484907904644311539896414067347389400151749600657579278895960573693934814752676278273915895909394982922563318173736071016647179057619243763230042827139542125644226762956903187476598431665900029305113678469725913961143048032016348386870923089862955467576132232067430573022824628886621106941902269773912408414386384958744554226394315986912008000652067452553259073901900219599312892013220890882796369063146728028726932516237716682483149607295171755157994925014520354281344751176954994548850375523372990992872608235206800552848373884097904303114896951128191894747953292238976905990208894450092732832100441840572843532041330491790737292506221131878514424077507009732780885474368274416396249038243621795514514228806975329626059 expt:56,854,0:89655113212012673099023948416704807879861978221153827237199661778584008468165651080543902613878620062782298351513276228294432072744284649261971266393894256607375431816304583821803793716587924442301007552505586044505538442132617485337199937369235592237428954101205944468928491652642992561924170992990684875183153689532992782682092920117235762980760669791412674782564117374541646440937370311927125956106266172810510670685525518812212950138056170979608664706763694733342515990968354863012666224960142013969526617072730522216789165659791684923653320596610175398020948129729808736281334106447129989405194534944350195768931899586302086738465979769199582498488866115372356961255007890457956873669299696404273010639537644911751286565659364626323246621985820562215324013173040199503927765343915648047310527662125096994825235508795834438673893661434170547036065620501605840890610501329654028608371726543612867845130909422255505338304701800505808679604352191497405251720910198472034708192083380402820761289291643085960629808979419703266679006005273854103326911946960981639672499634075872556388250454617093178267203875157005188789441834290824824375362710217394654516436622832004430364564578406063107709727937712128720552024767984099273684466490280196940322959059058007593299284990312017697525386129849377270562464418952129091640339393380715993311611910305891157877528570148396220151382371598274439328443130602108218216942517868406522662920683285329640812262460209537817661379779669996166934404739153002496 expt:45,612,0:5835236069718882114506897382533566247377415373160348322335381401959804325982764654985369043691019754782274324932902412422919504450121982411071559141523227598048101908706172870018726600366871511993242258104983964714191482096777425460159405868198347157194247010711764769855120922789922675107180581288360243567263537448253664324716669975682189100014404252781455216273744498335122639653589122310702857513362909180771831512471469920303997788269181344157274446834696917540185278250066349263511743262735271477684129972106758329375646539895223543706592566504943908712300110805454844873245197309482926904374664094429569566237475738252689670337625545730148780598867696059299091915732424441403497739984466234589413447120981326541342694519489432552938181829843044368724644161584697373078490608422316687980922524068552209758486036117805534388377565978109780133632127524991766800756255658237049157308049222993126272044553147845347401604176748405215264533091894230978452810922757566292930209161937682438292540609836578369140625 expt:54,451,0:20397910418377356550287300571804200557786099666116822595739338489264108594693629585863016865675849836447133820178583817056787257865484263341787975124682123033432566176550892031542044673807061607597691619952835660477594361209973279361945781375083740594965736649506183676117824430817491153516247325248281553959922896499435214529883689562648236636643053318925258184450463587681659723559391253678624035379856699358467799364301117153745186153084620238270375863919362076592257374084773424126742009360452069312697567282746968871243121905805216854913928572510658635514695126678391222696789673476384418005261871513244182859164066090813969042874136599996354815022967528679816614580768946293305191453668744093542408847163544646677483277319352956875504219155308754191860667890267580442087522304 expt:56,73,0:41469229998734605907229666533990439080884762393847798172038084645287681671512979662987869210144861737361911662097025032274313216 expt:22,325,0:19380780692127535243822988975518862106688283415440409657318777291773460112826177488864304471507503296260257393000381968404530628735640782306320769328605753305997492221828698343046454208648959261843736522465022722130523152030591371634509064404845763380835114201823755461164985487277973692677490997892134149211679493862203005748191879355934593251640178434694460018581599355100053236481539133268074642752831875821126444829199442221499154432 expt:1,259,0:1 expt:70,28,0:4599865365447399609768010000000000000000000000000000 expt:2,431,0:5545339388241629719156828368286167406872874150751633150340959161229242615611251246079948812208279156194782421922807143657948315648 expt:-79,826,0:27540854187929799985257468247523155680538433703286824739517469481759833990910653892340315597031695813840072524465738129420981768137177778398386187136483179521533720543407277753119393284152155957481914060287817028607256937594519868156459054669091954974712188347267089425432969106634444194388017265965949995692097701957114472823086198047050856806061672798574128287158999679211211045866881231653749742181206820843018712814234776885483960209113108635431190289016087501917845943054954808695879153901235902843669634627518243307894193841992956050535767242625612932115880911409609569876836530027970817956419533492446863797815044925775952042741550534011707510148845849950514957657983203500516405099685290711977967093948805920524360187028296830546987867500833588472504414005192236672391462985520150287811665577020744455460650359790618613062093825277825004505744707271241064882064070718065648023094280188167073044844547232500114457694590999166919669094693398432022411757793919755408026466841256100301169395413642500129881284167587546361348378140644375492018741141892055856217500455547981975199608522237536059854818106117812566998653773404384267708945402650064006573487698794343692465354553659902815430390133210939131290292916108564064726731071156431583014478295860724491974850345289250462234755107356158270289808695989364604670354446702945425544248554707467316099882094498480778646008506840517719579244276824018750506251514906770636895869751648864985470369467283659845225076014465077719158624528591794989379957868089133908677744283634297198521265648631548657239277970447594973921 expt:66,694,0:580084506530496199901715842061550478736929285435953296906334763408916457294745083700943659750072194007911117976928910771034469652824787161140202192812060086123933696794422026495786736350391860998721709184616206282429321340426294474560554065373638494945279261660818135550623361880986266761169809383156965092394530526878349935560951819098684650456236731366518214247980897154666883115720824687584260186753579248039306484564334815454921665784875496640601208054064934367623514543431818401964065471753818112528393669877004534296514842252720036344695851083439754895878703603097422007514258951525128317284811160997854687940441212627578246621158606819889227734453833088076792053010410429208939580294030978672807007323066516188519488729062055117608304054056122408278794377322396923294276347941530691555115638860207628093697674034586478685823166311562429468232346680345400111368599877502918619287029806863424209567337550321781645413583273156313569257554412238414216208778666350590080290958187713067860125458768396034295744470317801851373266428602679222973688293459392062447571375823266655946023131694535754930689276382991650046678195497949989578167243234281923601875893680839438188017891503234218524380143598199558737455868031691457764742432465500138998414409914742091022336 expt:61,929,0:372749204262219234661028605059600082005472058401807779391175774103147347020721809274006944812742694550566021615220848169519541529572954087195954262275827015340392843546317426147733284748546026914169745283094850736754214694252834868482075113112267516722630530017429413488354970058983032863915079743805868398514511489371415564743824566521175475718773953538278821907613967819226017166214104739437588073569813368813398149488565589556629477697737427900926249987010320503591278599110557450366143792209234346301744107084844660292442687200498652998894095601669905889013178322152368594429857818699973029703219264103421059688221938804094297461171047462303386552014767355489371231645242214605709573806038882091320000969833466616172674723281820861230659720784846394592186695882554183766611030058785231355760030032991550909225744604523622367813062613525325165760288801654110165225918836315855062845073372541514571337989620384391488490776891951817514249041749473163422333900356474699047977817400879900507930748372050203706672988848432054792535888114117248293709532406518972437029506673903536575555598954258917589173484915883729820461151786963746755203344621234694493460419788239808892616004989648342937608880857613762630401759659568336317724218590545423848713453198029293212741308983125342860690464093569963158486256404302217070545170719057156149028351035109222842931378174195730467004520244530634927115724793217592798273975809563142500814120034065476390178392762733701597980347726390211680084858484316148662425498700389466706121929317730214556147564067838219041971460802562516019394610534531801572433089111247198407104918760032599577878951582322678994706142652947962481341 expt:-9,601,0:-3160444535448242529092641683723644059539145692308657340859411006936058865374641314408196086827043799075550619379423798587542309132164609200204439951579781831500807632453119338125875367204968679095724562036128784121814572255501838157522005562307704591221323902634201333248104060896549891818729439534161465226719835137730531986768862453929457126667118122860406909711654476082395260883189301675745656233295957116371351513365076222859294597957033255348289403621311527049289776180957730267554140209309181978595028474886982653235278904914878205932888067162450567679909275108376009 expt:97,61,0:15598246895092955513443352386309396583401527586016822407020611754291026801166140429261857563228075418881342331811243126497 expt:74,605,0:767698049587939197359683749977648383836859839557642912409031546875066993197361480792391911022007587571205286132111673072469130312439363390154975794877785145691154425588220181582417662944285388056619181981589072518943031753597130867006603410867195350232262952739727149609075085699454676389509914456400111058880374719374067186562888441743787354629796015365677880935538353010170412164805965916706642591317263073481887535024205339087233459024635435688359086659169461648708865487255695675398023180920346709788305388156864497546177737256623458491643341041204795577475348427124793503135829398978121525554056766257030843704524575334061514903999726663601269068024921811397693529872001218499944501992703297464998852615587466138862714871448007704439720092007333440282216859169819279737835066578327985762318343795059984146296977874262661155133530578457531318820157803398989111207312212355231067323772033741977708388313965862076950112842132301934452667454484343330105847945439333136829953705856876014817393705072041603637057816525800795342430049224928087060220666508991256383019365798391401213524865142728401193068597503580931118244325830426624 expt:36,975,0:248278005620103284639045703633892910971579590446576896390366023318446808572139362706941322105353809474568993267209279242065096446488620910399483811208530728287594195549653360186846362277601130595472769480324082311203270696569975943570941969562919822812104500652408711500447873544596047411274288014555337548896670749271601634625491645631804888387660782682890889223510249234197182987228667338352972908620961079256927945363991111693736862822062801054752644720735597690210678508403694665212607341057194061256992464781310624503950172678945568406904426022068101752528300052652001276542298094132591990104962487076763890948081836407437498998808161080386782802526119075692789537066681886677023071338001090161651248031406605922396939134353858229048521453819325323124966146924584063700897925385709942659537790517149987487173581392712392934799338496185296838242169097046867947616557569663967960878013987948526741195844085783626887255741456401906399763700966299733165267865215995696668857089937482337710909782176011909086961041572658525585707034935545895295838426884822305638121505564930966674346565073344787297923158159728519118453365025481613806608095528043429679151758551183290377061790258979194328969739145711528285504071957396890777097691503292292512140424378576323419960320470786958549180355944550997252189926822915544222112451356508263343401791620402670748174883090503543874879537424232633444841283544725100377811657760945870884387665856213462789220780358446036998302940381411899721937124651210804520592109143837152301285376 expt:-7,998,0:2557666612174935343076642515066804502377520561389767696864275525553001216974247274131608960292888178840788079990848858707874061009535980056363078332058256731224798188707371509890293039384338196239143157226455217716275665577013531086263168378395631166498491605806001681974869749146726373202776324945125013953453368299778708945971227290643969595629713562243419908025456961888745599561183240940509205834167387996660455423008573664383326301867960985504323358173474091543641085509125145760080557840801210219094336590559580686735948781675614855516621028604833789337737476275129016558156702593389621170307048966068339005329960325088885775363738622269191020959920658840427262709698255458449248536217491851761664583813025566114309314584253990687002952980625513485971873761776789106023932689391842584592322920065018940027985924506720083084514443495522449 expt:98,601,0:533177103720501595374014423272499180364132378499160666153205148287497431057729394569971402806644432590292381465328310811262311129879335218558809778840423111439831395996547946125056037438926572002773115800873538665211948124422673756566945099641176492241232608229762984189514655606698161295525325616990201393228718812438865636613600881016384894116920222938495899464735527691752379448855611912417527389079639150256802359259202228730317836086556170590276966277499401959437472907925192927018522051374174184596825818778972688910983212905978633684186938477351015355179910878863238407299688657725777618404474888655212468833055969341513248604687220063488622962824592611061373538419157946717588609988450009564429746027878532253109391471912738954897803162861544906424860818226748531212662795741229276596890126256794061814383421311422736715585563600029962135442113826772475696417325421015883937926780471519318690864459664035455228247945210545963671338082833659176679989196527849975925731239343901932556903446683281672284250829662800543414520052002458669739331249230862598278859245402390741706350229540923193423152041354794777470610379380463931916503753572520250120327494841108274055472875847368852693579726848 expt:71,113,0:155665870729530205341310326859872459537926086918288608509540470629351860391099882586273156224776434943964531186950530766165453973920218517388369336029496210775525110769905804823288221938617835119278838123463111 expt:88,907,0:442367935572376572508225245682376008933489111316498137860990507028355805276660122793212942345797461553842453310264287269547264461627567883151291662994492100078344571908312323703967322111609104550792111450058081718989072815115851882388563478737616122984915164909745468851730941089128173523430879823706000843384957667316760881888264090864169349212921302774263449334569646606880597808832359653989122198423765672987068986676530059825422164710070729150784542517772146017930986715605834667445246856197609230392607836274592038028103289662613608042193082727017234381117193204646042933195569061774171215561867979977536504587733669688385439306083861005747682093252438793416405292269393894857797371282733609831597024792462532979252620533612898923536406352613040278291119133710169841942272610880326076250824796315291769779313197811055736478745579585246354714882550479199964522615379791935029462701848490881087210486616588742015690198161694007740631075914977342479383653037979280440452432330650580558326686619170505019301413395716564578646343919112222038215172712390311828679340129762907111087076354552831143978497060075661718540626266557415357423140554743330726141178661837462646531942496692764465824964428334360066828688839099062489813585188443877907045253387120110743470809899546315304940652259267302446808962933370950281961149706759813262075876658787778751634455269684666084979732880496655480607530401657107712607869822390372442674816531402008096066231847402127938718306972865332558595609085653122439480481119259426244455543280347111130355917037063730253045491171053471360412763262481476838567930318043324002372902635753161108413432524658790895161967566922959535333684336970564087502342071263031219942567744837673438233646370315543730522460987677141774838398907195160788992 expt:54,693,0:3538959212637179650332389010097218547839980601093690465533384462821473107518120134643329245982087864317937908704373458854914106407415643779615995841169386600913075521454433838879465455760020550207139247760073103240863782684441878651997401564323185374793175538443983412787862620393247499479636694089753362683716397696397917283398425558068217711985447159317136026122405227956991309955957305130230342078570923159947618234652978345575496908772641954759715818896470873163820343504250486061693462131428151141184256959845856167488510754499527069147459850959898142673913068231658647704696101725713008481473114205759711924188717911743864320055181356930972595979239402793810079643314094026495828298793070503069066311897901487935228391178144871449270977053884209274680793281139427835365536821473478187015781075924946317138803162094976414459954194354095344108788615082753544608345483223312927636999008063997529650656957732197940704471295178444341702958910607189754168223147765846213872939337214235441488423377963042762703792152968410669091074122567701986969963794378828129171913930842249996279788381704931705888803023880349755565650291290845634952973640558107667121388591534953156403175205437026399021173691121664 expt:38,856,0:197132715335944702010464928289068787258126989327281133977642459352310471635694659935863663034893224402661971507965073109281478523865599215163431556175379522026942698195490717331056237820749570952967717007649366271894056379198300178606041623775325949617283624435203477373703809019861048596220111560408850308709136073536236931756950635354870794668286264213752040997939539541387051080544346518658745783173789667395614130438466933466487546913034843807849350170476768221968845260192149232038583063007145032622472464523166365735920186939572956871374170348147525734840393491062416576459571924060826547986510253181877148984750114103946480014297867097001766341891006238734128868718256859876341374385005847514034681950344623145375661088734911525281809871480522601658340102129823934063220140098540350561496324424874246538855230619339148284533370024488661745011726445642690111494919560707585228174864187763259132194822208827893654702830695772629276887925981051128487055423282643887884462938381948997470435721291697587128910687319970929427859109724267542710439086909913634572523183081655946843912895400563035037344361397713522987937999965880651790361428060580389888264631102954948376159211750103503891634869806965067088907401334445114937251493551662240660610686055435327064505561719003363736562191988450674773018772056555774194438968053446880417310543649670866927616 expt:-31,708,0:765736298588882623745464551248533589516728262330945024485987989003966799697519427922524828295538506333120906420497833190822172854823291505196845183135662558430608661582624850664725007618784585092336587620980112185589698249795027371672676312069829503342898152005067487306044707288099529713186820460094321862725166577558202701116811479992992160597205251212891371390724533853382322337514186669568739285186663884891566968084627353685451588298678227268272695471519080722554889447126207382826609688589782622034263523702002067627492259917412663020367888185843581319175113423749435759149520782360313210168155362235445104891714946334675780994250948917428592423464724255498014927635397210595806788729762917250871841151153544592712985783889618176401395175667540813239941136361290336680403138159551455700446304015319933056996010034922500542872536431111997459504310947292431025900542295004555040557979582695891302414344669597914053356301361988698100342875761385692372383787936620811489997313151757515795773510401149056466969197955066877735357001712514205212720669933441 expt:83,555,0:1225578881193055029211627122654046612502838285027451787523333889078091117395677304740312290856548894569025972732093305262022262904766698517843710251028889032008071021523615947494541437140578410083242439006303675242241181694132064945370271165796403044400021233214176036607316649425463754916274528213700425307672925070793107159063558868221691827352040472536655806967633986881743762489226940035732391901428677713410085277373744973773271636779960125482940121021337248817093605269643954914154264236561300490516647836816796937996874660377751119032325126115584325317487570936637230731531209445181074951179372481656744462723784646444882817173348451279220016187868806676293898865251048319248697918535078227324297131747582957851638254483032160979834998953230605023477565269493853309225765083693484738566931845020418708591682116652295291303636819498565470825532192376545824497931844947390200802139827837145992356261755130151073475298317589343849166306928091630048941968076783492543886466245827183954554006162583165658402103419444975524038123795891288877937208254234082383456107 expt:-14,196,0:437617814535571368432038511337652545614427696923129424177713451048312616488063444444116568548619798360728579274072579602558189605289698688298076102960815381950768025379270967729373733335391251544937988597855682119418496679936 expt:-98,54,0:335898517749742807149149239304847110365424413007280865740297764742923286290279482895371271867934265713885184 expt:36,114,0:2621109035105672045109358354048170185329363187071886946329003212335230440027818091139599929524823562064749950789402494298276879873503833622348138409040138018400021944463278473216 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expt:17,917,0:2097301675874874262337384393256157290550457272641070742685181359655298484419530330975119591493945747194067982196745980906719459748758882521093062942106370414411307130989688371347312396400965251294933801479523245300205124498392914857119952454973605402952283548281059993829706858741240642855866024547671426840363544681591758614171705795900874121429015664043430807387470485214251545286572177964862773770430978379005467765291145746924901839002665096400397942453076588723612807208413217092949289492019664961222972978192822676475920744552252701836678236202368876327668639558452692524803118939191010230124869369557526977853787148876084719302299232475362067256488446210852407409309331633276993895009372306807316745243435453345840085033563601310824164178695180595270040323771052788593322649328459197776655430007609049049177562253219889705605903722950620003852016584473859694998609725264429690598113186546955167630012283368654064816468752154783362082778625443452372549847742049125737902403986921080094805248820329567053386368469178503759368276006576774606472539223477845778733320367553885443289921963031175184555111324035235498303342308177 expt:90,974,0:27052299935047786065293705383293371594928459960636493591858679901229530489397827439967797113560000179030752129693483986009759069814344789464328028124389302229982080849292903566689398199538736384291803478523321463426163427287122485942132332484438824633259632500429907489423839508356778347605611863182944177635491198031896503926679224776089106017711039660784400591006292140993879293923209120615399556982103777565419076004780936708141570335102044570334141660285505239366482840745962298126113781491303989125579971415048181359429126117863548989486391973761921728851807165407598678812115381168882267007400683443822154895256736017606370596941988046175011944197627446203315020223655176866443121247527516304873917419276577740100216553128143639001206191984430353639022361358939550577829476281299576074140336299277402936582067383619719327798911232272710866516643940342077662311510080648261530453984792175767586937809041407061474275004126136100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 expt:88,533,0:25660449281262222538494450001863125622542059254495725488128163750941665069643744134848017926826911153501794213458141136118798686952318128330169211354566747333325537986995462503989216458427236156137402612135248417253059095443287160848570588029400648482452870347054911987033926310964969317423952372643231383031833176623179144615827641601677528585812306167020803446102194410693881507224213793037477717521197480665170498415644315118063624358208859552595534937279894843336541477825309304143549461073381212334783418760579349454160671722140424226639994874257433085267041153503087290920628156801330326875713842007053978145083999034880721014435679044734743002931660496447382048291494534747035171647495659446493320583080918221954598494959009870518773105244525770713362092498386891958081893316423699439660136195380395615149744310401608278793638807731614951269163459033645996046310958400025916261303110642807596573667882890880336479719496725477724544562900521034037056197498694805705196162644018155788990216861162622711326815130754780320976368304128 expt:12,155,0:187539665641051633765939629010126862030861602821510134598513247329704373202067865855904581679588305105558426392209111518109357753525875656563557488739845521658156679168 expt:84,732,0:37362626400287469786015728314475507196576346217451577972340560264817777335475340674816958024184760346347561438501466002380065324994816957074697212139052544975947819746208063697307962302948345421020870897563746896137814303577394468618413663330314199040777371901150981465952170446359267027980870158458849108279054769543589192992244998367449195186118755704549074553943383839728968976499539257576575130852721502719453361944489930498227884992093281287795552589618712166509707464487440188402096761270376491306019370966520073730856558528831146413882339665688468833965993044432654395376803788836651945621982999063779396803021750087040026958788856842217636023983209404960799438677955235981923691837336224814448363848125978496886798250942574484985336211014321720899330415880628445289132294841424914787671230730112190724165482715241239871542120185970126756942511944451784053266847219551455015565798473788074284186189118669182080184743138159319501208245476233431491562603292975987521331235533354675181947901194397959442206360514628651055734093466035888302489823943737682169815612826149059209986740615789135359084267106289623915297355833264060175823550703443673841878097340893266267479095018072578698649320448199760433477235766344924312161142440752268668342566161645418763284828712617629493206149751363684796869848593636426521501235005044720096689821574083797399723544574440327020813476324227172574108126760343901889888256 expt:79,286,0:526439064947238802053645461445020487916872652166019614740851000911432565395604993916756724273343382808249492973087992062325249551325359686735575913143465467581047691930038117373467695602824586884710893085987595912587448288044732217351433963632626007275558435035805433116956578902569644720408764508101410145243233157169608100135310715793917742521403034578354501408583090243486810991762771487300120584737790555454222432759955623420408431532698387943150871884498498636773443364760233971133647087214954160646197476641876831719032258038195184329121 expt:-48,298,0:1023030868022814299054713017964868399102957735431782102215916358604604051659703035572837203405877079107051634525945219766070256763817295621420805604993635631490817683951846687765019250182667988090399985362595946141453130325277952090882208566546530763707685586001179407168248639583706997713561296809021500677647862937784168307555475376888964203999111072179073538018050362405289547337600007038981171944778216894564706920577451010395411246759676715366409166040432558779691978486479294657424378342139756544 expt:67,294,0:734500327961443669234315379892319347436893827696021491142391697563378578446291077887806124176875773502748252261770540334529098051241702520337994712391193396474812051324450141046760676076260316236367877489247807236984474045776385255239037010394553624592302745770678862650712113089224670041590960921068572134081690133046715543153096542269435280673848480153667033339024712187305544312593068136273774422287977966196973980766284625470220034542418965941570269327451886686200812785835233820579323336965260949631248809309330127020161010203411929 expt:-18,16,0:121439531096594251776 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expt:-66,815,0:-8478274364648612330188917253283022359058819830563672517212108821628253393962000107434004509667343937534845252876105916914550690362654306802088184928424521570461209219177571955862371964722226410637046742655117010513197262769697714640814368023744763233323396664955472317206306714935880218313050258650385673367221675620501577511198414613930001668113399143106311450680541330404416353053190642499775032620035730460907253528440201689228392425128611695226403417406791574278689202884590346418539029059209980814013704118450210566908353305850659319394569789593583277865075164609668529102638203772555818321297822419290710586417444995207152787848623117218947477799582750664329264358615866224038190922228629974680499679526981709174616924365577700177072886843030924028404354842213079523220238443352288912242203925033885655177475234008253977458800922719481452623217104266383098663601342961199447190374025272206739771683319522016840242048283276894211421554923410027867743938181352146258867339132020852657862198937040181786435550099700309055348307396827575249256603692440439981038825878568365720841374284500628316724088850430536784223423104076749618800240805402030937435626889672205773792103911906204527061949920720885833279883726692710574946314456869324980999570723090979946872598945360813531346459611164448392012613641192887272701599318084665769391014924333193179500033230229853166710458920123986965349475008600343653534535593116799600793757728203652141876940711203421375996087235090052747651710976 expt:54,664,0:20391845050873191652345159631406874537839455686365280217235427133476142582092996043619608390016389292965226896811762634987782972686518739140212360064330493755768007040302669237780668310608681482526562495176314471562104423826827089408141436551453430030964346636473177072344012300123214143559305872414360567214132682148167038413419037687295369781258678081076745492992503736782832174090246186699082419488498244657442094259244802484573507417869446357085909447262706180711907718273125250308231346034020925518798041278971653974463785808172029353263314071093941305571685611808887063740166405396225068221678544525487393228625876836004989079566259935122474245224409591612160442040129636723080187009657142522509070943421819954801779957035427054617629433447229882724015810298068048100626156055542733454456801321357919554628269944544954700528568251750045531145328694687448392559273455873142746224088225238286750883430569184631252959597186815034796504990060130502168310308220045378042228226870235350079089558343443820937472250762918032769865387382756419568756482286011357857171768933280108973733824989544483820081477750150555112569963683757807113376801387242848256 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exptf:77,531,0:532813311656570249504626338521175986931059533505926279525440059983661596994102351537446926949363360529365260710018282274969608991708422465645470353238950991164094603760337431471373797674342466447685331328334896929530869521639021347860305641901746618212067382436047417802334922329714967747069071224609067366771145964345230898570999327581370275837424654936614015736099665593408214589717971837806254491231718922616012680565189067437536528526576020597271981783296886490561985553063246822960810078500648480156559918530508398231087164252252053517193755387712164533565474034807917780960207694570186046344187446803758345139338159388892261095589551022214765624192005132067602116482379395414788544646979450596452460362555591887638135655580299669062424023518502777571809123694201495640270788238169354113138409879326088017367705387411669267281998186298445497315171994082486321864442017377055208040226703055135151101106282748423896319916554310684705542590586019379478759401961042716809342108506273015769966750567573 exptf:-18,16,0:121439531096594251776 exptf:23,783,0:17096043011003615277598794858486068754024940440179973307979725548138117553890262896641152305435426637168346356686100176044925372354921872747501460658856273444772550524367017737008810328712782564379920672077160208017588610872900933505244440864632694623791999654579846020232116933586706946483379032274515986264401321379356564215058936360373677277919864278279794625946762796494116433783821073561146442740575287992208852561076777520575751129272827760948307704793048037510164918774200200085555861489097574107784367443496372000977637695193822915836028040509766497522766784721558336792917997571201278516192223590838889688612546686389608843721034916667041733614883996563547634015007274594387270209090391868747626612843208187603964244920932750585408044205476476229852915573917584786214180312460069710688659542311237951704151388274748457930956937912692497993167574943229551708370492252437047946879513486746068495028744525641440991301695614236365008498571998939850585670845752278477745811135337129266946940607139194863121256913904896962276321551899101278415815402393374517929767 exptf:-66,815,0:-8478274364648612330188917253283022359058819830563672517212108821628253393962000107434004509667343937534845252876105916914550690362654306802088184928424521570461209219177571955862371964722226410637046742655117010513197262769697714640814368023744763233323396664955472317206306714935880218313050258650385673367221675620501577511198414613930001668113399143106311450680541330404416353053190642499775032620035730460907253528440201689228392425128611695226403417406791574278689202884590346418539029059209980814013704118450210566908353305850659319394569789593583277865075164609668529102638203772555818321297822419290710586417444995207152787848623117218947477799582750664329264358615866224038190922228629974680499679526981709174616924365577700177072886843030924028404354842213079523220238443352288912242203925033885655177475234008253977458800922719481452623217104266383098663601342961199447190374025272206739771683319522016840242048283276894211421554923410027867743938181352146258867339132020852657862198937040181786435550099700309055348307396827575249256603692440439981038825878568365720841374284500628316724088850430536784223423104076749618800240805402030937435626889672205773792103911906204527061949920720885833279883726692710574946314456869324980999570723090979946872598945360813531346459611164448392012613641192887272701599318084665769391014924333193179500033230229853166710458920123986965349475008600343653534535593116799600793757728203652141876940711203421375996087235090052747651710976 exptf:54,664,0:20391845050873191652345159631406874537839455686365280217235427133476142582092996043619608390016389292965226896811762634987782972686518739140212360064330493755768007040302669237780668310608681482526562495176314471562104423826827089408141436551453430030964346636473177072344012300123214143559305872414360567214132682148167038413419037687295369781258678081076745492992503736782832174090246186699082419488498244657442094259244802484573507417869446357085909447262706180711907718273125250308231346034020925518798041278971653974463785808172029353263314071093941305571685611808887063740166405396225068221678544525487393228625876836004989079566259935122474245224409591612160442040129636723080187009657142522509070943421819954801779957035427054617629433447229882724015810298068048100626156055542733454456801321357919554628269944544954700528568251750045531145328694687448392559273455873142746224088225238286750883430569184631252959597186815034796504990060130502168310308220045378042228226870235350079089558343443820937472250762918032769865387382756419568756482286011357857171768933280108973733824989544483820081477750150555112569963683757807113376801387242848256 ================================================ FILE: tests/gcd.tc ================================================ # Greatest common divisor tests gcd:0,0,0:$MP_UNDEF gcd:0,0,=1:$MP_UNDEF gcd:0,0,=2:$MP_UNDEF gcd:0,=1,0:$MP_UNDEF gcd:0,=1,99999:$MP_UNDEF gcd:-7,328492456,0:1 gcd:16522181,930,0:1 gcd:844378,24,0:2 gcd:209,3,0:1 gcd:70522336,34102,0:2 gcd:32557663,995533,0:1 gcd:641,701,0:1 gcd:290748,-233,0:1 gcd:-95,4770,0:5 gcd:6839092,7,0:1 gcd:787590783,-6789049,0:1 gcd:721,15845,0:1 gcd:-37028,-949534667,0:1 gcd:618,-3,0:3 gcd:16657,-544851,0:1 gcd:28271,6,0:1 gcd:-35357673,5207718,0:3 gcd:99,-565,0:1 gcd:9311525,-5,0:5 gcd:6221599,7764515429,0:1 gcd:21590339,486739392,0:1 gcd:335,3699183948,0:1 gcd:14,8755508782,0:2 gcd:-5302,9,0:1 gcd:8236,9462435,0:1 gcd:43040,2766705,0:5 gcd:863478587,63,0:1 gcd:8874055124,10,0:2 gcd:8204,-89955,0:1 gcd:3303887262,3,0:3 gcd:75504,-62,0:2 gcd:436,2123372,0:4 gcd:3361227,943089540,0:3 gcd:37340421,223177728,0:3 gcd:-35694701,238293550,0:1 gcd:4263,15500547338,0:1 gcd:1493,38730799,0:1 gcd:-635007,298501,0:1 gcd:4968,-98492710997,0:1 gcd:3367542606,17576297,0:1 gcd:232155550,3921719,0:1 gcd:4860966,700,0:2 gcd:2323372237,867,0:1 gcd:4268,-29035,0:1 gcd:8,-73804207633,0:1 gcd:395170,26163606,0:2 gcd:-70027196,6945032910,0:2 gcd:5871172260,26773591,0:1 gcd:17125540,836,0:4 gcd:1988202315,-68060596,0:1 gcd:554434367524,-909419,0:1 gcd:-40457802353,3398,0:1 gcd:410791452776,4492144466,0:2 gcd:135751970,7417878752,0:2 gcd:9593,31047471995,0:1 gcd:-18387143,50226,0:1 gcd:413450673851,-124,0:1 gcd:-618513698871,-318914624,0:1 gcd:37416674596,-8817,0:1 gcd:6242382,-943205,0:1 gcd:-4949666413,1501091102,0:1 gcd:-6385784303120,899228089,0:1 gcd:6308,-79643949,0:1 gcd:2421,136928,0:1 gcd:333180111,442438,0:1 gcd:723761305,611024432789,0:1 gcd:-91289,-9223787613074,0:1 gcd:10944,57098,0:2 gcd:57145099,-94544476,0:1 gcd:9327105307,88173695233,0:13 gcd:73230770347,67182928,0:1 gcd:4810254287,-4310,0:1 gcd:7200253992,9893,0:1 gcd:-92709373682,-664752121448,0:2 gcd:-2236424417,-69570761,0:1 gcd:781963714,61084006246,0:2 gcd:78553,-3773682081509,0:1 gcd:24811454802,-26314981001549,0:1 gcd:805866671,8061826,0:1 gcd:4281823377004,2916710,0:2 gcd:15229,320560332911,0:1 gcd:6093153060,357460,0:20 gcd:624794507388,3264784,0:4 gcd:2632503413711,-514594728450,0:1 gcd:7216089,86034,0:3 gcd:112578025,4532680608704,0:1 gcd:-972617496,-1100642928524,0:4 gcd:86658,-56860,0:2 gcd:2292080,40552081391276,0:28 gcd:57144144326678,3579498119,0:1 gcd:77390585076,614924,0:4 gcd:685579,959286825595306,0:1 gcd:346354116,451435163995,0:1 gcd:443946215999,260668,0:1 gcd:640447120070,-441698,0:2 gcd:1253208493501,-8521171736,0:1 gcd:8507343,62395589,0:1 gcd:81126006,461820852819773,0:1 gcd:87891707090,40954510522233,0:11 gcd:-767589,-991593,0:3 gcd:86229155,43027930,0:5 gcd:-431963821,48986055721,0:1 gcd:101557073166691,-74080192,0:1 gcd:-34269048183,250074,0:3 gcd:7650667716360,-959482143,0:3 gcd:-176432105527291,712269105001105,0:1 gcd:91973525400419,-52180215632622,0:1 gcd:9054526,-21388581343089,0:19 gcd:19326311972,3180878,0:2 gcd:501569850634,39035351302,0:2 gcd:-3470290487760846,622612793613,0:3 gcd:827793089252612,77591849874263,0:1 gcd:19866668332,4414961,0:1 gcd:136274450771,8659380001,0:1 gcd:952660786088689,171372582380,0:1 gcd:429415374,9140880954,0:6 gcd:-368107346,2945634,0:2 gcd:2147845929,79983807840463,0:1 gcd:77885771608,-51236668812562,0:2 gcd:62272695670,208399244,0:2 gcd:61973019,-1405255816878779,0:1 gcd:286206733986,212837117931767,0:1 gcd:-131938894,1048695278656631,0:1 gcd:27109492,306933238851468,0:4 gcd:-314477095129839,3837918787896,0:3 gcd:4116345,9101435151,0:3 gcd:63853435249810,902940229903,0:1 gcd:80076033,14791385,0:1 gcd:-31038678,1454704764,0:6 gcd:20638192722,-14267370499730,0:2 gcd:8065790684,-1977228453431,0:7 gcd:362687955673,99742877979696,0:1 gcd:1235326072088,201675880263044,0:4 gcd:568009735,49546482048450,0:5 gcd:849579042,-3197920541,0:1 gcd:1808291492597692,96814519920612,0:4 gcd:6275712123233717,739880208952795162,0:1 gcd:774075573665981,7523229210171,0:1 gcd:2944466357361,497012903828640,0:3 gcd:282862415058866,-6240991940068,0:2 gcd:571225883598025,189932649930728,0:1 gcd:815309478,-371377784,0:2 gcd:320172590239,777220834144,0:1 gcd:654332382,7919190746613,0:9 gcd:-5094673003562,268414312780910,0:2 gcd:-77841790209187781,35267718271550,0:1 gcd:735762990564598234,-32739891496,0:2 gcd:-5999905013129575,144027889596460,0:5 gcd:6861193105404525,-4725324526382425,0:25 gcd:859748569384694164,98523184164,0:4 gcd:570460270963,-54720108308,0:1 gcd:61750383079701,3452251304617,0:1 gcd:-1738716695,8560399484936237,0:1 gcd:9953417006786660,90085339160,0:20 gcd:188523146978,954842405502,0:2 gcd:198834734074395695,171072375577893,0:1 gcd:-102893613303732727,155104650554,0:7 gcd:90836124710855,-98332551310,0:5 gcd:10512242068892,84377075433,0:1 gcd:-726835478343584190,29339956106373,0:3 gcd:5033847480079150451,-69469662902517,0:1 gcd:3869558083241,-8770208065,0:1 gcd:46079368203995132,23609959311256,0:4 gcd:979137194422864421,-1378816153373947,0:1 gcd:-72618673468,-244198092166982349,0:11 gcd:529564016606,376298866055896536,0:2 gcd:554186920892,-629719688885314,0:2 gcd:3455963977845612750,271884481278417471,0:3 gcd:-41270780965441117,-4124462824121691009,0:1 gcd:47581683736,9394210662450,0:2 gcd:8196306676684,76732052476696223555,0:1 gcd:2939970750639,-2013582768244,0:1 gcd:70476757656499,-100957934015971,0:1 gcd:3674841030712174173,540185467629182772,0:3 gcd:82915322420038008,123799513890,0:6 gcd:466513077506,73565730651787738,0:14 gcd:-38890216282311653,91459939591112,0:1 gcd:576595981539992,20909590051109791,0:1 gcd:956905636477652,8381376662473,0:1 gcd:9187294026565993,54295427509,0:1 gcd:8866081281165098,6545042142269515,0:1 gcd:338772425501,-750860960783,0:1 gcd:6750486296504,8609697533187,0:1 gcd:736067207074328,329259058372493427315,0:1 gcd:680100030114145,52232423165123,0:1 gcd:22697310250913136791,365228836596285515,0:1 gcd:30594845950075862222,37349482121506846253,0:1 gcd:866936756424,-1765396942933391,0:1 gcd:6939438360479781,24559856763503,0:1 gcd:927595346004843560,7670228140092963222,0:2 gcd:-357321286444971587,7925597841132985664,0:1 gcd:6673370692769029,520191499051311630305,0:1 gcd:9013236794945,1008467412252240244,0:1 gcd:406532185466775673747,9519149309169118189,0:1 gcd:548046408595014443,777065152533771,0:1 gcd:23897406396584,-8555442893510156172118,0:2 gcd:54729344028716311850,2026849525600172204,0:2 gcd:-7936445752013,-98698488318151151,0:1 gcd:6309028281362257922,271678876766048827,0:1 gcd:6357785774765671053291,56936125648067424,0:33 gcd:11095109588014,9104811531028000846,0:2 gcd:-921590308699737078,472826384755153630,0:2 gcd:652120832633171211942,-3387083844442113181,0:1 gcd:32731949302549,335896184427699,0:7 gcd:3635516318567409721998,16713986701316425,0:1 gcd:6746198240933100303896,2007405485449,0:1 gcd:-19072614334803913032,-240759760944833349,0:3 gcd:828472954262165857,127978158379025077,0:1 gcd:8306750095431507743,6378030328941226919,0:1 gcd:7938532173109072,7646615157112938170608,0:16 gcd:25274397567311,3125247753747112,0:1 gcd:0,-6378030328941226919,0:6378030328941226919 gcd:-6378030328941226919,0,0:6378030328941226919 gcd:-6378030328941226919,0,=1:6378030328941226919 gcd:-6378030328941226919,0,=2:6378030328941226919 gcd:400327281633151431,37147489147345586,0:1 gcd:28164658061513141691,818613450005821036296,0:3 gcd:476291935913056166817,170589720180888384,0:3 gcd:84130837655605609,16051948347568699941145,0:1 gcd:438146043336536562159,-2206822496905640873917,0:1 gcd:8120293725815373571,24028314574527126,0:1 gcd:-667658265953408,8440015504605457600699,0:1 gcd:53314441150262832895,283247085055963859,0:1 gcd:6658153298145442,2140281300389057549,0:1 gcd:213046498706732967,784948480361985741,0:3 gcd:-3857522843819,419578526133778265155,0:1 gcd:-4948941087660882967,-779517282262677550602,0:1 gcd:4277076043224464,448010594023993,0:1 gcd:-644113523059324254840,-71225587742718143,0:1 gcd:264902435468141506,-823887292259809475,0:1 gcd:1538706915662950684,448326823774496344436,0:4 gcd:2036808313025110180,30422160628736748027,0:1 gcd:7385426850078311,9871854919284839,0:1 gcd:804644713550364054117828,8379163811459445,0:3 gcd:981008037679996757191201,-641409668917881464,0:1 gcd:64201713053871850,879119102660231895102,0:2 gcd:1033957429367195,1113485105415049436,0:1 gcd:14455075580451942850,-1885962875546302716,0:2 gcd:2615475057635555327591,71606675442458157933637,0:1 gcd:596676024530775,2621192750454214313695,0:5 gcd:71665682789483848832034,351563529541544408090967,0:3 gcd:5092055214749737510271,-1833800774226189505,0:1 gcd:600508413963341945,5057063373752305154,0:1 gcd:-92318043858914149,958444935645415778103,0:1 gcd:385447683586530283,1775981280157037775814,0:1 gcd:80717517906672139,362327909576030289130356,0:1 gcd:31249856290116188,7875872084416640,0:4 gcd:5339381130045070,-287550419156538713298378,0:2 gcd:-28993892995370333046,698005135756870427,0:1 gcd:9179674525723481348,81469928617693608886,0:2 gcd:7522547789649675160016,285918417200326088447794,0:2 gcd:-901774653467788803,236000195734098992,0:1 gcd:142671415131788790,-2583777714764598301032762,0:6 gcd:951078283105727024828,1487627587101952300275691,0:1 gcd:19185476025869672486,2445736876347152429980675,0:11 gcd:6741226163186521681303,2568160083399218078514720,0:1 gcd:3987919571578399660412212,9884144363611069680876,0:4 gcd:99431631881940059268,-291965406586754754564989,0:1 gcd:36727416735327035,-1612205593089728906670,0:5 gcd:19590774006340220367562,984968880458891391,0:1 gcd:70695613219926859099201753,62591913993270611799645,0:1 gcd:77425442645246583405,-296832015660977965,0:35 gcd:807971872592227526408,40230405885131399744453603,0:1 gcd:965370212546292322,92058451234918953535616,0:2 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gmp_test.c imath_test.c wrappers.py *.tests _T* ================================================ FILE: tests/gmp-compat-test/Makefile ================================================ CFLAGS+=-fPIC -I$(IMATH_DIR) $(shell pkg-config --cflags gmp) IMATH_DIR=../.. LDFLAGS+=$(shell pkg-config --libs gmp) -L$(IMATH_DIR) -limath runtest: imath_test.so gmp_test.so wrappers.py random.tests ./runtest $(TESTS) gmp_test.c: gmp_custom_test.c genctest.py gmpapi.py ./genctest.py gmp > $@ imath_test.c: imath_custom_test.c genctest.py gmpapi.py ./genctest.py imath > $@ gmp_test.so: gmp_test.o $(CC) $(CFLAGS) $(LDFLAGS) -shared -o $@ $^ imath_test.so: imath_test.o $(CC) $(CFLAGS) $(LDFLAGS) -shared -L$(IMATH_DIR) -o $@ $^ -limath wrappers.py: genpytest.py gmpapi.py ./genpytest.py > $@ random.tests: gendata.py ./gendata.py > $@ clean: rm -f -- a.out *.so *.o random.tests gmp_test.c imath_test.c wrappers.py *.pyc rm -rf __pycache__ ================================================ FILE: tests/gmp-compat-test/README ================================================ Overview ================================================== This directory contains a random test generator for the gmp compatibility layer of imath. The tests cases are randomly generated and run with both gmp and imath. The results are compared and any mismatching results are flagged as failures. You should not see any failures when running these tests. Requirements ================================================== These tests use the python ffi to run the imath and gmp functions. To run these tests you will need the following items * libimath.so * python 3 * gmp library and header files Running ================================================== All the tests cases will be generated and run automatically by the makefile. First, make sure you have built libimath.so in the top level imath directory. Use the following command to generate and run the tests $ make TESTS=random.tests This should generate all the needed wrapper files along with the randomized unit tests. By default the unit tests are output to the random.tests file. The tests can be run by hand using the following command line $ ./runtest random.tests You can also write your own unit tests and run them by passing the file name to the runtest script. Testing Methodology ================================================== The goal of our testing is to ensure that we are compatible with the gmp api. To test our compatibility layer we generate inputs for each gmp api that we wrap and then call the gmp version of the api and compare the results to the imath version. The results should be identical. Any output mismatch is considered an error. Testcase Generation -------------------- The test data generation is inspired by the QuickCheck testing methodolgy. We want to test both random data and important values such as 0,1,-1, etc. We generate input data based on the type of the input parameter. Most apis take either an mpz_t or a signed/unsigned long. For each parameter of the given type we generate the following values: mpz_t: 0,1,-1, all min/max values, all min/max values +/- 1 small numbers: 1-4 digits medium numbers: 5-20 digits large numbers: 20-100 digits long : 0,1,-1 short,int,long min/max values random long values unsigned long: 0,1,-1, unsigned short, unsigned int, unsigned long min/max values random unsigned long values The generated data for each parameter is combined to produce a series of inputs to the function. The input data format looks like: mpz_add|0,1,2 Which represents the call mpz_add(0, 1, 2). Additional test cases can be written by hand. Test Structure -------------------- The tests are run using the python ffi (the ctypes module). We have a single description of each api that is used to generate the following: * input data * c function wrapper to call the libgmp or libimath function * python wrapper to call both libgmp and libimath wrappers and compare results The test_gmp.so and test_imath.so libraries are loaded at runtime by the python runner script and used to run each test input and compare the results. The code generation pattern looks something like this: genctest.py ~~generates~~> gmp_test.c <--includes-- gmp_custom_test.c gmp_test.c ~~generates~~> gmp_tests.so <--links-- libgmp.so genpytest.py ~~generates~~> wrappers.py <--calls-- gmp_test.so gmp_test.so --loads--> runtest.py <--includes-- wrappers.py ^ | reads | gendata.py ~~generates~~> random.tests Adding tests for new APIs ================================================== New apis can be tested by modifying the gmpapy.py file. This file contains a list of all apis that will be tested. Adding an api to the apis list will cause code and input data to be generated for that api. Rerunning make will generate the test data and code to run the test. ================================================ FILE: tests/gmp-compat-test/genctest.py ================================================ #!/usr/bin/env python3 import sys import gmpapi from gmpapi import charp, iint, ilong, mpq_t, mpz_t, size_t, ulong, void class APITest(object): def __init__(self, gmpapi): self.api = gmpapi def test_prefix(self): return "test" def test_param_name(self, ty, i): if ty == mpz_t: pname = "p_zs" elif ty == ilong: pname = "p_si" elif ty == ulong: pname = "p_ui" elif ty == iint: pname = "p_i" elif ty == charp: pname = "p_cs" elif ty == mpq_t: pname = "p_qs" else: raise RuntimeError("Unknown param type: " + str(ty)) return pname + str(i) def test_param_type(self, ty): if ty == mpz_t or ty == mpq_t: pty_name = "char *" else: pty_name = str(ty) return pty_name def test_var_name(self, ty, i): if ty == mpz_t: vname = "v_z" elif ty == ilong: vname = "v_si" elif ty == ulong: vname = "v_ui" elif ty == iint: vname = "v_i" elif ty == size_t: vname = "v_st" elif ty == charp: vname = "v_cs" elif ty == mpq_t: vname = "v_q" else: raise RuntimeError("Unknown param type: " + str(ty)) return vname + str(i) def test_var_type(self, ty): if ty == mpz_t: return self.mpz_type() elif ty == mpq_t: return self.mpq_type() else: return str(ty) def init_var_from_param(self, ty, var, param): code = "\t" if ty == mpz_t or ty == mpq_t: code += self.api_call_prefix(ty) + "init(" + var + ");\n\t" code += self.api_call_prefix(ty) + "set_str(" + ",".join( [var, param, "10"]) + ")" if ty == mpq_t: code += ";\n\t" code += self.api_call_prefix(ty) + "canonicalize(" + var + ")" else: code += var + "=" + param return code def init_vars_from_params(self): code = "" for (i, p) in enumerate(self.api.params): param = self.test_param_name(p, i) code += "\t" code += self.test_var_type(p) + " " var = self.test_var_name(p, i) code += var + ";\n" code += self.init_var_from_param(p, var, param) + ";\n\n" return code def make_api_call(self): bare_name = self.api.name.replace("mpz_", "", 1).replace("mpq_", "", 1) call_params = [ self.test_var_name(p, i) for (i, p) in enumerate(self.api.params) ] ret = "\t" ret_ty = self.api.ret_ty if ret_ty != void: ret += self.test_var_type(ret_ty) + " " + self.test_var_name( ret_ty, "_ret") + " = " # call mpq or mpz function if self.api.name.startswith("mpz_"): prefix = self.api_call_prefix(mpz_t) else: prefix = self.api_call_prefix(mpq_t) return ret + prefix + bare_name + "(" + ",".join(call_params) + ");\n" def normalize_cmp(self, ty): cmpval = self.test_var_name(ty, "_ret") code = "" code += """ if ({var} > 0) {var} = 1; else if ({var} < 0) {var} = -1;\n\t """.format(var=cmpval) return code def extract_result(self, ty, pos): code = "" if ty == mpz_t or ty == mpq_t: var = self.test_var_name(ty, pos) code += self.api_call_prefix( ty) + "get_str(out+offset, 10," + var + ");\n" code += "\toffset = offset + strlen(out); " code += "out[offset] = ' '; out[offset+1] = 0; offset += 1;" else: assert pos == -1, "expected a return value, not a param value" if ty == ilong: var = self.test_var_name(ty, "_ret") code += 'offset = sprintf(out+offset, " %ld ", ' + var + ');' elif ty == ulong: var = self.test_var_name(ty, "_ret") code += 'offset = sprintf(out+offset, " %lu ", ' + var + ');' elif ty == iint: var = self.test_var_name(ty, "_ret") code += 'offset = sprintf(out+offset, " %d ", ' + var + ');' elif ty == size_t: var = self.test_var_name(ty, "_ret") code += 'offset = sprintf(out+offset, " %zu ", ' + var + ');' elif ty == charp: var = self.test_var_name(ty, "_ret") code += 'offset = sprintf(out+offset, " %s ", ' + var + ');' else: raise RuntimeError("Unknown param type: " + str(ty)) return code def extract_results(self): ret_ty = self.api.ret_ty code = "\tint offset = 0;\n\t" # normalize cmp return values if ret_ty == iint and "cmp" in self.api.name: code += self.normalize_cmp(ret_ty) # call canonicalize for mpq_set_ui if self.api.name == "mpq_set_ui": code += self.api_call_prefix( mpq_t) + "canonicalize(" + self.test_var_name(mpq_t, 0) + ");\n\t" # get return value if ret_ty != void: code += self.extract_result(ret_ty, -1) + "\n" # get out param values for pos in self.api.out_params: code += "\t" code += self.extract_result(self.api.params[pos], pos) + "\n" return code + "\n" def clear_local_vars(self): code = "" for (i, p) in enumerate(self.api.params): if p == mpz_t or p == mpq_t: var = self.test_var_name(p, i) code += "\t" + self.api_call_prefix( p) + "clear(" + var + ");\n" return code def print_test_code(self, outf): api = self.api params = [ self.test_param_type(p) + " " + self.test_param_name(p, i) for (i, p) in enumerate(api.params) ] code = "void {}_{}(char *out, {})".format(self.test_prefix(), api.name, ", ".join(params)) code += "{\n" code += self.init_vars_from_params() code += self.make_api_call() code += self.extract_results() code += self.clear_local_vars() code += "}\n" outf.write(code) outf.write("\n") class GMPTest(APITest): def __init__(self, gmpapi): super(GMPTest, self).__init__(gmpapi) def api_call_prefix(self, kind): if kind == mpz_t: return "mpz_" elif kind == mpq_t: return "mpq_" else: raise RuntimeError("Unknown call kind: " + str(kind)) def mpz_type(self): return "mpz_t" def mpq_type(self): return "mpq_t" class ImathTest(APITest): def __init__(self, gmpapi): super(ImathTest, self).__init__(gmpapi) def api_call_prefix(self, kind): if kind == mpz_t: return "impz_" elif kind == mpq_t: return "impq_" else: raise RuntimeError("Unknown call kind: " + str(kind)) def mpz_type(self): return "impz_t" def mpq_type(self): return "impq_t" def print_gmp_header(outf): code = "" code += "#include \n" code += "#include \n" code += "#include \n" code += '#include "gmp_custom_test.c"\n' outf.write(code) def print_imath_header(outf): code = "" code += "#include \n" code += "#include \n" code += "#include \n" code += "typedef mpz_t impz_t[1];\n" code += "typedef mpq_t impq_t[1];\n" code += '#include "imath_custom_test.c"\n' outf.write(code) def print_gmp_tests(outf): print_gmp_header(outf) for api in gmpapi.apis: if not api.custom_test: GMPTest(api).print_test_code(outf) def print_imath_tests(outf): print_imath_header(outf) for api in gmpapi.apis: if not api.custom_test: ImathTest(api).print_test_code(outf) def main(): test = sys.argv[1] if test == "gmp": print_gmp_tests(sys.stdout) elif test == "imath": print_imath_tests(sys.stdout) if __name__ == "__main__": main() ================================================ FILE: tests/gmp-compat-test/gendata.py ================================================ #!/usr/bin/env python3 import random import gmpapi MAX_SLONG = "9223372036854775807" MIN_SLONG = "-9223372036854775808" MAX_ULONG = "18446744073709551615" MAX_SINT = "2147483647" MIN_SINT = "-2147483648" MAX_UINT = "4294967295" MAX_SSHORT = "32767" MIN_SSHORT = "-32768" MAX_USHORT = "65535" def plus1(x): return str(int(x) + 1) def minus1(x): return str(int(x) - 1) def apply(fun, lst): return list(map(str, map(fun, lst))) mzero_one = ["-0", "-1"] zero_one = ["0", "1"] mm_slong = [MAX_SLONG, MIN_SLONG] mm_slong1 = [minus1(MAX_SLONG), plus1(MIN_SLONG)] mm_ulong = [MAX_ULONG] mm_ulong1 = [minus1(MAX_ULONG)] mm_sint = [MAX_SINT, MIN_SINT] mm_sint1 = [minus1(MAX_SINT), plus1(MIN_SINT)] mm_uint = [MAX_UINT] mm_uint1 = [minus1(MAX_UINT)] mm_sshort = [MAX_SSHORT, MIN_SSHORT] mm_sshort1 = [minus1(MAX_SSHORT), plus1(MIN_SSHORT)] mm_ushort = [MAX_USHORT] mm_ushort1 = [minus1(MAX_USHORT)] mm_all = mm_slong + mm_ulong + mm_sint + mm_uint + mm_sshort + mm_ushort zero_one_all = mzero_one + zero_one mpz_std_list = zero_one_all + mm_all + apply(plus1, mm_all) + apply( minus1, mm_all) si_std_list = zero_one + mm_slong + mm_sint + mm_sshort + mm_slong1 + mm_sint1 + mm_sshort1 ui_std_list = zero_one + mm_ulong + mm_uint + mm_ushort + mm_ulong1 + mm_uint1 + mm_ushort1 def gen_random_mpz(mindigits=1, maxdigits=100, allowneg=True): sign = random.choice(["", "-"]) if not allowneg: sign = "" return sign + gen_digits(random.randint(mindigits, maxdigits)) def gen_random_si(): si = gen_random_mpz(mindigits=1, maxdigits=19) while int(si) > int(MAX_SLONG) or int(si) < int(MIN_SLONG): si = gen_random_mpz(mindigits=1, maxdigits=19) return si def gen_random_ui(): ui = gen_random_mpz(mindigits=1, maxdigits=20, allowneg=False) while int(ui) > int(MAX_ULONG): ui = gen_random_mpz(mindigits=1, maxdigits=20, allowneg=False) return ui def gen_digits(length): if length == 1: i = random.randint(1, 9) else: digits = [random.randint(1, 9) ] + [random.randint(0, 9) for x in range(length - 1)] digits = map(str, digits) i = "".join(digits) return str(i) def gen_mpzs(mindigits=1, maxdigits=100, count=10): return [ gen_random_mpz(mindigits=mindigits, maxdigits=maxdigits) for x in range(count) ] default_count = 10 def gen_sis(count=default_count): return [gen_random_si() for x in range(count)] def gen_uis(count=default_count): return [gen_random_ui() for x in range(count)] def gen_small_mpzs(count=default_count): return gen_mpzs(mindigits=1, maxdigits=4, count=count) def is_small_mpz(s): return len(s) >= 1 and len(s) <= 4 def gen_medium_mpzs(count=default_count): return gen_mpzs(mindigits=5, maxdigits=20, count=count) def is_medium_mpz(s): return len(s) >= 5 and len(s) <= 20 def gen_large_mpzs(count=default_count): return gen_mpzs(mindigits=21, maxdigits=100, count=count) def is_large_mpz(s): return len(s) >= 21 def gen_mpz_spread(count=default_count): return gen_small_mpzs(count) + gen_medium_mpzs(count) + gen_large_mpzs( count) def gen_mpz_args(count=default_count): return mpz_std_list + gen_mpz_spread(count) def gen_mpq_args(count=4): nums = zero_one + gen_mpz_spread(count) dens = ["1"] + gen_mpz_spread(count) return [n + "/" + d for n in nums for d in dens if int(d) != 0] def gen_si_args(): return si_std_list + gen_sis() def gen_ui_args(): return ui_std_list + gen_uis() def gen_list_for_type(t, is_write_only): if (t == gmpapi.mpz_t or t == gmpapi.mpq_t) and is_write_only: return ["0"] elif t == gmpapi.mpz_t: return gen_mpz_args() elif t == gmpapi.ilong: return gen_si_args() elif t == gmpapi.ulong: return gen_ui_args() elif t == gmpapi.mpq_t: return gen_mpq_args() else: raise RuntimeError("Unknown type: {}".format(t)) def gen_args(api): if api.custom_test or api.name in custom: return custom[api.name](api) types = api.params if len(types) == 1: return [[a] for a in gen_list_for_type(types[0], api.is_write_only(0))] elif len(types) == 2: t1 = gen_list_for_type(types[0], api.is_write_only(0)) t2 = gen_list_for_type(types[1], api.is_write_only(1)) return [(a, b) for a in t1 for b in t2] elif len(types) == 3: t1 = gen_list_for_type(types[0], api.is_write_only(0)) t2 = gen_list_for_type(types[1], api.is_write_only(1)) t3 = gen_list_for_type(types[2], api.is_write_only(2)) return [(a, b, c) for a in t1 for b in t2 for c in t3] elif len(types) == 4: t1 = gen_list_for_type(types[0], api.is_write_only(0)) t2 = gen_list_for_type(types[1], api.is_write_only(1)) t3 = gen_list_for_type(types[2], api.is_write_only(2)) t4 = gen_list_for_type(types[3], api.is_write_only(3)) return [(a, b, c, d) for a in t1 for b in t2 for c in t3 for d in t4] else: raise RuntimeError("Too many args: {}".format(len(types))) ################################################################### # # Fixup and massage random data for better test coverage # ################################################################### def mul_mpzs(a, b): return str(int(a) * int(b)) def mpz_divexact_data(args): # set n = n * d divisible = mul_mpzs(args[1], (args[2])) return [(args[0], divisible, args[2])] def mpz_divisible_p_data(args): (n, d) = get_div_data(args[0], args[1], rate=1.0) return [(n, d), (args[0], args[1])] def mpz_div3_data(args): q = args[0] (n, d) = get_div_data(args[1], args[2], rate=1.0) return [(q, n, d), (q, args[1], args[2])] def mpz_pow_data(args, alwaysallowbase1=True): base = int(args[1]) exp = int(args[2]) # allow special numbers if base == 0 or exp == 0 or exp == 1: return [args] if base == 1 and alwaysallowbase1: return [args] # disallow too big numbers if base > 1000 or base < -1000: base = gen_random_mpz(maxdigits=3) if exp > 1000: exp = gen_random_mpz(maxdigits=3, allowneg=False) return [(args[0], str(base), str(exp))] def mpz_mul_2exp_data(args): return mpz_pow_data(args, alwaysallowbase1=False) def mpz_gcd_data(args): r = args[0] a = args[1] b = args[2] s_ = gen_small_mpzs(1)[0] m_ = gen_medium_mpzs(1)[0] l_ = gen_large_mpzs(1)[0] return [ (r, a, b), (r, mul_mpzs(a, b), b), (r, mul_mpzs(a, s_), mul_mpzs(b, s_)), (r, mul_mpzs(a, m_), mul_mpzs(b, m_)), (r, mul_mpzs(a, l_), mul_mpzs(b, l_)), ] def mpz_export_data(api): rop = ["0"] countp = ["0"] order = ["-1", "1"] size = ["1", "2", "4", "8"] endian = ["0"] nails = ["0"] ops = gen_mpz_args(1000) + gen_mpzs( count=100, mindigits=100, maxdigits=1000) args = [] for r in rop: for c in countp: for o in order: for s in size: for e in endian: for n in nails: for op in ops: args.append((r, c, o, s, e, n, op)) return args def mpz_sizeinbase_data(api): bases = list(map(str, range(2, 37))) ops = gen_mpz_args(1000) + gen_mpzs( count=1000, mindigits=100, maxdigits=2000) return [(op, b) for op in ops for b in bases] def get_str_data(ty): bases = list(range(2, 37)) + list(range(-2, -37, -1)) bases = list(map(str, bases)) if ty == gmpapi.mpz_t: ops = gen_mpz_args(1000) elif ty == gmpapi.mpq_t: ops = gen_mpq_args(20) else: raise RuntimeError("Unsupported get_str type: " + str(ty)) return [("NULL", b, op) for b in bases for op in ops] def mpz_get_str_data(api): return get_str_data(gmpapi.mpz_t) def mpq_get_str_data(api): return get_str_data(gmpapi.mpq_t) def mpq_set_str_data(api): args = gen_mpq_args(20) + gen_mpz_args() # zero does not match results exactly because the # results are not canonicalized first. We choose to # exclude zero from test results. The other option is # to canonicalize the results after parsing the strings. # Instead we exclude zero so that we can independently # test correctness of set_str and canonicalization nonzero = [] for arg in args: if "/" in arg: pos = arg.find("/") if int(arg[:pos]) != 0: nonzero.append(arg) elif int(arg) != 0: nonzero.append(arg) return [("0", q, "10") for q in nonzero] def get_div_data(n, d, rate=0.2): """Generate some inputs that are perfectly divisible""" if random.random() < rate: n = mul_mpzs(n, d) return (n, d) def allow(name, args): if name not in blacklists: return True filters = blacklists[name] for (pos, disallow) in filters: if args[pos] in disallow: return False return True def fixup_args(name, args): if name not in fixups: return [args] return fixups[name](args) # list of values to be excluded for various api calls # list format is (pos, [list of values to exclude]) blacklists = { "mpz_cdiv_q": [(2, ["0", "-0"])], "mpz_fdiv_q": [(2, ["0", "-0"])], "mpz_fdiv_r": [(2, ["0", "-0"])], "mpz_tdiv_q": [(2, ["0", "-0"])], "mpz_fdiv_q_ui": [(2, ["0", "-0"])], "mpz_divexact": [(2, ["0", "-0"])], "mpz_divisible_p": [(1, ["0", "-0"])], "mpz_divexact_ui": [(2, ["0", "-0"])], "mpq_set_ui": [(2, ["0", "-0"])], } fixups = { "mpz_divexact": mpz_divexact_data, "mpz_divisible_p": mpz_divisible_p_data, "mpz_cdiv_q": mpz_div3_data, "mpz_fdiv_q": mpz_div3_data, "mpz_fdiv_r": mpz_div3_data, "mpz_tdiv_q": mpz_div3_data, "mpz_fdiv_q_ui": mpz_div3_data, "mpz_divexact_ui": mpz_divexact_data, "mpz_pow_ui": mpz_pow_data, "mpz_gcd": mpz_gcd_data, "mpz_lcm": mpz_gcd_data, "mpz_mul_2exp": mpz_mul_2exp_data, } custom = { "mpz_export": mpz_export_data, "mpz_import": mpz_export_data, "mpz_sizeinbase": mpz_sizeinbase_data, "mpz_get_str": mpz_get_str_data, "mpq_set_str": mpq_set_str_data, "mpq_get_str": mpq_get_str_data, } if __name__ == "__main__": #apis = [gmpapi.get_api("mpq_set_str"),] apis = gmpapi.apis for api in apis: tests = gen_args(api) for args in tests: expanded_args = fixup_args(api.name, args) for args in expanded_args: if allow(api.name, args): print("{}|{}".format(api.name, ",".join(args))) ================================================ FILE: tests/gmp-compat-test/genpytest.py ================================================ #!/usr/bin/env python3 import sys import gmpapi def print_header(outf): outf.write(""" #AUTOGENERATED FILE import ctypes import os import sys import binascii verbose = False fork = False """) def print_cmp(outf): outf.write(""" def passt(line, name, a_s, b_s): if verbose: print("PASS: {}@{} {} == {}".format(line, name, a_s, b_s)) return True def fail(line, name, a_s, b_s): print("FAIL: {}@{} {} != {}".format(line, name, a_s,b_s)) return False def cstr_eq(line, name, a, b): a_s = a.value.decode("utf-8") b_s = b.value.decode("utf-8") if a_s == b_s: return passt(line, name, a_s, b_s) else: return fail(line, name, a_s, b_s) def bytes_eq(line, name, a, b): if a == b: return passt(line, name, a, b) else: return fail(line, name, a, b) def run_test(test, line, name, gmp_test_so, imath_test_so, *args): if fork: childpid = os.fork() else: childpid = 0 if childpid == 0: eq = test(line, name, gmp_test_so, imath_test_so, *args) if fork: sys.exit(eq != True) else: return eq else: (pid, status) = os.waitpid(childpid, 0) return status == 0 # custom tests def test_mpz_export(line, name, gmp_test_so, imath_test_so, *args): # do not use first two args from the test. need to create our own pointers used_args = args[2:] gbuf = ctypes.create_string_buffer(b'0xdeadbeef'*1024); gsize = ctypes.c_size_t() gout = ctypes.c_void_p() ibuf = ctypes.create_string_buffer(b'0xdeadbeef'*1024); isize = ctypes.c_size_t() iout = ctypes.c_void_p() word_size = args[3].value #Test with a NULL pointer gmp_test_so.test_mpz_export(ctypes.byref(gout), None, ctypes.byref(gsize), *used_args) imath_test_so.test_mpz_export(ctypes.byref(iout), None, ctypes.byref(isize), *used_args) gb = ctypes.string_at(gout.value, gsize.value * word_size) ib = ctypes.string_at(iout.value, isize.value * word_size) if not bytes_eq(line, name, gb, ib): return False #Test with a provided buffer gmp_test_so.test_mpz_export(ctypes.byref(gout), gbuf, ctypes.byref(gsize), *used_args) imath_test_so.test_mpz_export(ctypes.byref(iout), ibuf, ctypes.byref(isize), *used_args) #print("G:gbuf", gbuf.raw[:gsize.value * word_size]) #print("I:ibuf", ibuf.raw[:isize.value * word_size]) gb = ctypes.string_at(gout.value, gsize.value * word_size) ib = ctypes.string_at(iout.value, isize.value * word_size) if not bytes_eq(line, name, gb, ib): return False return True def test_mpz_import(line, name, gmp_test_so, imath_test_so, *args): # do not use first two args from the test. need to create our own pointers gout = ctypes.create_string_buffer(b'0xdeadbeef'*1024); iout = ctypes.create_string_buffer(b'0xdeadbeef'*1024); gmp_test_so.test_mpz_import(gout, *args) imath_test_so.test_mpz_import(iout, *args) #print(gout.raw[:70]) #print(iout.raw[:70]) return cstr_eq(line, name, gout, iout) """) def print_api(name, outf): outf.write(""" def test_{0}(line, name, gmp_test_so, imath_test_so, *args): gout = ctypes.create_string_buffer(1024*4); iout = ctypes.create_string_buffer(1024*4); gmp_test_so.test_{0}(gout, *args) imath_test_so.test_{0}(iout, *args) eq = cstr_eq(line, name, gout, iout) return eq """.format(name)) def print_api_map(outf): outf.write(""" def get_wrapper(name): test_wrappers = { """) for api in gmpapi.apis: outf.write(' "{}" : {},\n'.format(api.name, "test_" + api.name)) outf.write(" }\n") outf.write(" return test_wrappers[name]\n") if __name__ == "__main__": outf = sys.stdout print_header(outf) print_cmp(outf) for api in gmpapi.apis: if not api.custom_test: print_api(api.name, outf) print_api_map(outf) ================================================ FILE: tests/gmp-compat-test/gmp_custom_test.c ================================================ void test_mpz_export(char** out, char* rop, size_t* countp, int order, size_t size, int endian, size_t nails, char* mpzstr) { mpz_t op; mpz_init(op); mpz_set_str(op, mpzstr, 10); // printf("%p,%p,%d,%zi,%d,%zi,%s\n", rop, countp, order, size, endian, nails, // mpzstr); *out = mpz_export(rop, countp, order, size, endian, nails, op); } void test_mpz_import(char* out, void* unused, size_t count, int order, size_t size, int endian, size_t nails, char* mpzstr) { mpz_t op; mpz_t rop; mpz_init(op); mpz_init(rop); mpz_set_str(op, mpzstr, 10); char* data; // printf("%p,%p,%d,%zi,%d,%zi,%s\n", rop, countp, order, size, endian, nails, // mpzstr); data = mpz_export(NULL, &count, order, size, endian, nails, op); mpz_import(rop, count, order, size, endian, nails, data); int eq = mpz_cmpabs(op, rop); sprintf(out, "%2d:", eq); mpz_get_str(out + 3, 10, rop); } ================================================ FILE: tests/gmp-compat-test/gmpapi.py ================================================ #!/usr/bin/env python3 class CType: def __init__(self, name): self.name = name def __str__(self): return self.name class GMPAPI: def __init__(self, ret_ty, name, *params, **kw): out = kw.get('out', [0]) inout = kw.get('inout', []) mixed = kw.get('mixed', False) custom = kw.get('custom', False) self.name = name self.ret_ty = ret_ty self.params = params self.inout_params = inout self.custom_test = custom # most functions with return results dont need extra out params # set mixed to true to check both the return value and an out param if self.ret_ty != void and not mixed: self.out_params = [] else: self.out_params = out #param location of the output result def is_write_only(self, pos): if pos in self.out_params and pos not in self.inout_params: return True return False def __str__(self): return ("{} {}({})".format(self.ret_ty, self.name, ",".join(map(str, self.params)))) def __repr__(self): return str(self) void = CType("void") voidp = CType("void *") charp = CType("char *") iint = CType("int") size_t = CType("size_t") size_tp = CType("size_t*") ilong = CType("long") ulong = CType("unsigned long") mpz_t = CType("mpz_t") mpq_t = CType("mpq_t") apis = [ GMPAPI(void, "mpz_abs", mpz_t, mpz_t), GMPAPI(void, "mpz_add", mpz_t, mpz_t, mpz_t), GMPAPI(iint, "mpz_cmp_si", mpz_t, ilong), GMPAPI(iint, "mpz_cmpabs", mpz_t, mpz_t), GMPAPI(iint, "mpz_cmp", mpz_t, mpz_t), GMPAPI(void, "mpz_mul", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_neg", mpz_t, mpz_t), GMPAPI(void, "mpz_set_si", mpz_t, ilong), GMPAPI(void, "mpz_set", mpz_t, mpz_t), GMPAPI(void, "mpz_sub", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_swap", mpz_t, mpz_t, out=[0, 1], inout=[0, 1]), GMPAPI(iint, "mpz_sgn", mpz_t), GMPAPI(void, "mpz_addmul", mpz_t, mpz_t, mpz_t, inout=[0]), GMPAPI(void, "mpz_divexact", mpz_t, mpz_t, mpz_t), GMPAPI(iint, "mpz_divisible_p", mpz_t, mpz_t), GMPAPI(void, "mpz_submul", mpz_t, mpz_t, mpz_t, inout=[0]), GMPAPI(void, "mpz_set_ui", mpz_t, ulong), GMPAPI(void, "mpz_add_ui", mpz_t, mpz_t, ulong), GMPAPI(void, "mpz_divexact_ui", mpz_t, mpz_t, ulong), GMPAPI(void, "mpz_mul_ui", mpz_t, mpz_t, ulong), GMPAPI(void, "mpz_pow_ui", mpz_t, mpz_t, ulong), GMPAPI(void, "mpz_sub_ui", mpz_t, mpz_t, ulong), GMPAPI(void, "mpz_cdiv_q", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_fdiv_q", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_fdiv_r", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_tdiv_q", mpz_t, mpz_t, mpz_t), GMPAPI(ulong, "mpz_fdiv_q_ui", mpz_t, mpz_t, ulong, out=[0], mixed=True), GMPAPI(ilong, "mpz_get_si", mpz_t), GMPAPI(ulong, "mpz_get_ui", mpz_t), GMPAPI(void, "mpz_gcd", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_lcm", mpz_t, mpz_t, mpz_t), GMPAPI(void, "mpz_mul_2exp", mpz_t, mpz_t, ulong), GMPAPI(void, "mpz_export", voidp, size_tp, iint, size_t, iint, size_t, mpz_t, custom=True), # The mpz_import signature is a bit of a lie, but it is ok because it is custom GMPAPI(void, "mpz_import", voidp, size_t, iint, size_t, iint, size_t, mpz_t, custom=True), GMPAPI(size_t, "mpz_sizeinbase", mpz_t, iint), GMPAPI(charp, "mpz_get_str", charp, iint, mpz_t), # mpq functions GMPAPI(iint, "mpq_set_str", mpq_t, charp, iint, out=[0], mixed=True), GMPAPI(void, "mpq_canonicalize", mpq_t, inout=[0]), GMPAPI(iint, "mpq_cmp", mpq_t, mpq_t), GMPAPI(void, "mpq_mul", mpq_t, mpq_t, mpq_t), GMPAPI(void, "mpq_set", mpq_t, mpq_t), GMPAPI(void, "mpq_set_ui", mpq_t, ulong, ulong), GMPAPI(iint, "mpq_sgn", mpq_t), GMPAPI(charp, "mpq_get_str", charp, iint, mpq_t), ] def get_api(name): for a in apis: if a.name == name: return a raise RuntimeError("Unknown api: {}".format(name)) ================================================ FILE: tests/gmp-compat-test/imath_custom_test.c ================================================ void test_mpz_export(char** out, char* rop, size_t* countp, int order, size_t size, int endian, size_t nails, char* mpzstr) { impz_t op; impz_init(op); impz_set_str(op, mpzstr, 10); // printf("%p,%p,%d,%zi,%d,%zi,%s\n", rop, countp, order, size, endian, nails, // mpzstr); *out = impz_export(rop, countp, order, size, endian, nails, op); } void test_mpz_import(char* out, void* unused, size_t count, int order, size_t size, int endian, size_t nails, char* mpzstr) { impz_t op; impz_t rop; impz_init(op); impz_init(rop); impz_set_str(op, mpzstr, 10); char* data; // printf("%p,%p,%d,%zi,%d,%zi,%s\n", rop, countp, order, size, endian, nails, // mpzstr); data = impz_export(NULL, &count, order, size, endian, nails, op); impz_import(rop, count, order, size, endian, nails, data); int eq = impz_cmpabs(op, rop); sprintf(out, "%2d:", eq); impz_get_str(out + 3, 10, rop); } ================================================ FILE: tests/gmp-compat-test/runtest ================================================ #!/bin/sh if [ "$(uname)" = "Darwin" ] ; then export DYLD_LIBRARY_PATH=.:../.. # for macOS else export LD_LIBRARY_PATH=.:../.. # for everyone else fi python3 runtest.py $@ ================================================ FILE: tests/gmp-compat-test/runtest.py ================================================ #!/usr/bin/env python3 from __future__ import print_function import ctypes from optparse import OptionParser import gmpapi import wrappers from gmpapi import charp, iint, ilong, mpq_t, mpz_t, size_t, size_tp, ulong, voidp def print_failure(line, test): print("FAIL: {}@{}".format(line, test)) def run_tests(test_file, options): passes = 0 failures = 0 fail_lines = [] for (line, test) in enumerate(open(test_file), start=1): if test.startswith("#"): continue if options.skip > 0 and line < options.skip: continue name, args = test.split("|") if options.verbose or (options.progress > 0 and line % options.progress == 0): print("TEST: {}@{}".format(line, test), end="") api = gmpapi.get_api(name) wrapper = wrappers.get_wrapper(name) input_args = args.split(",") if len(api.params) != len(input_args): raise RuntimeError("Mismatch in args length: {} != {}".format( len(api.params), len(input_args))) call_args = [] for i in range(len(api.params)): param = api.params[i] if param == mpz_t: call_args.append(input_args[i].encode('utf-8')) elif param == mpq_t: call_args.append(input_args[i].encode('utf-8')) elif param == ulong: call_args.append(ctypes.c_ulong(int(input_args[i]))) elif param == ilong: call_args.append(ctypes.c_long(int(input_args[i]))) elif param == voidp or param == size_tp: call_args.append(ctypes.c_void_p(None)) elif param == size_t: call_args.append(ctypes.c_size_t(int(input_args[i]))) elif param == iint: call_args.append(ctypes.c_int(int(input_args[i]))) # pass null for charp elif param == charp: if input_args[i] == "NULL": call_args.append(ctypes.c_void_p(None)) else: call_args.append(input_args[i].encode("utf-8")) else: raise RuntimeError("Unknown param type: {}".format(param)) res = wrappers.run_test(wrapper, line, name, gmp_test_so, imath_test_so, *call_args) if not res: failures += 1 print_failure(line, test) fail_lines.append((line, test)) else: passes += 1 return (passes, failures, fail_lines) def parse_args(): parser = OptionParser() parser.add_option("-f", "--fork", help="fork() before each operation", action="store_true", default=False) parser.add_option("-v", "--verbose", help="print PASS and FAIL tests", action="store_true", default=False) parser.add_option("-p", "--progress", help="print progress every N tests ", metavar="N", type="int", default=0) parser.add_option("-s", "--skip", help="skip to test N", metavar="N", type="int", default=0) return parser.parse_args() if __name__ == "__main__": (options, tests) = parse_args() gmp_test_so = ctypes.cdll.LoadLibrary("gmp_test.so") imath_test_so = ctypes.cdll.LoadLibrary("imath_test.so") wrappers.verbose = options.verbose wrappers.fork = options.fork total_pass = 0 total_fail = 0 all_fail_lines = [] for test_file in tests: print("Running tests in {}".format(test_file)) (passes, failures, fail_lines) = run_tests(test_file, options) print(" Tests: {}. Passes: {}. Failures: {}.".format( passes + failures, passes, failures)) total_pass += passes total_fail += failures all_fail_lines += fail_lines print("=" * 70) print("Total") print(" Tests: {}. Passes: {}. Failures: {}.".format( total_pass + total_fail, total_pass, total_fail)) if len(all_fail_lines) > 0: print("Failing Tests:") for (line, test) in all_fail_lines: print(test.rstrip()) ================================================ FILE: tests/imath-test.scm ================================================ ;;; ;;; Name: imath-test.scm ;;; Purpose: Code to generate random rational number test cases. ;;; Notes: Written for DrRacket (nee PLT Scheme) ;;; (require (lib "27.ss" "srfi")) ;; Generate a random natural number with the specified number of digits. (define (random-big-natural digits) (let loop ((d "") (digits digits)) (if (zero? digits) (string->number d 10) (let ((rnd (random 10))) (loop (string-append d (list->string (list (integer->char (+ rnd (char->integer #\0)))))) (- digits 1)))))) ;; Generate a random integer with the specified number of digits and ;; probability (0..1) of being negative. (define (random-big-integer digits pneg) (let ((base (random-big-natural digits))) (if (< (random-real) pneg) (* base -1) base))) ;; Generate a random rational number with the specified number of numerator and ;; denominator digits, and probability pneg (0..1) of being negative. (define (random-big-rational n-digits d-digits pneg) (let ((num (random-big-natural n-digits)) (den (random-big-natural d-digits))) (if (zero? den) (random-big-rational n-digits d-digits pneg) (if (< (random-real) pneg) (- (/ num den)) (/ num den))))) ;; Create a rational generator with a fixed negative probability. ;; Always generates rationals. (define (make-rat-generator prob-neg) (lambda (n-digits d-digits num) (random-big-rational n-digits d-digits prob-neg))) ;; Create a rational generator with a fixed negative probability. With ;; probability prob-backref, generates a back-reference to an earlier input ;; value, rather than a new value. This is used to make sure argument ;; overlapping works the way it should. (define (make-backref-generator prob-neg prob-backref) (lambda (n-digits d-digits num) (if (and (> num 1) (< (random-real) prob-backref)) (let ((ref (+ (random (- num 1)) 1))) (string-append "=" (number->string ref))) (random-big-rational n-digits d-digits prob-neg)))) ;; Just like make-backref-generator, except the second argument is always an ;; integer, and the backreference can only be to the first argument. (define (make-backref-generator-2 prob-neg prob-backref) (lambda (n-digits d-digits num) (case num ((1) (random-big-rational n-digits d-digits prob-neg)) ((2) (random-big-integer n-digits prob-neg)) (else (if (< (random-real) prob-backref) "=1" (random-big-rational n-digits d-digits prob-neg)))))) (define (make-output-test-generator prob-neg max-dig) (lambda (n-digits d-digits num) (cond ((= num 1) (random-big-rational n-digits d-digits prob-neg)) ((= num 2) (let loop ((radishes '(10 16 8 4 2))) (cond ((null? radishes) (+ (random 34) 2)) ((< (random-real) 0.3) (car radishes)) (else (loop (cdr radishes)))))) (else (random max-dig)) ))) ;; Given a test name, an argument generator, and an operation to compute the ;; desired solution, return a function that generates a random test case for a ;; given number of digits of precision in the numerator and denominator. (define (make-test-case-generator name arg-gen op) (lambda (n-digits d-digits) (let ((args (list (arg-gen n-digits d-digits 1) (arg-gen n-digits d-digits 2) (arg-gen n-digits d-digits 3)))) (let* ((arg1 (car args)) (arg2 (if (equal? (cadr args) "=1") arg1 (cadr args))) (soln (if (and (eq? op /) (zero? arg2)) "$MP_UNDEF" (op arg1 arg2)))) (list name args (list soln)))))) ;; Glue strings together with the specified joiner. (define (join-strings joiner lst) (cond ((null? lst) "") ((null? (cdr lst)) (car lst)) (else (string-append (car lst) joiner (join-strings joiner (cdr lst)))))) ;; Convert a test case generated by a test case generator function into a ;; writable string, in the format used by imtest.c (define (test-case->string tcase) (let ((s (open-output-string)) (stringify (lambda (v) (let ((s (open-output-string))) (display v s) (get-output-string s))))) (display (car tcase) s) (display ":" s) (display (join-strings "," (map stringify (cadr tcase))) s) (display ":" s) (display (join-strings "," (map stringify (caddr tcase))) s) (get-output-string s))) (define qadd (make-test-case-generator 'qadd (make-backref-generator 0.3 0.2) +)) (define qsub (make-test-case-generator 'qsub (make-backref-generator 0.3 0.2) -)) (define qmul (make-test-case-generator 'qmul (make-backref-generator 0.3 0.2) *)) (define qdiv (make-test-case-generator 'qdiv (make-backref-generator 0.3 0.2) /)) (define qtodec (make-test-case-generator 'qtodec (make-output-test-generator 0.3 25) (lambda (a b) '?))) (define qaddz (make-test-case-generator 'qaddz (make-backref-generator-2 0.3 0.2) +)) (define qsubz (make-test-case-generator 'qsubz (make-backref-generator-2 0.3 0.2) -)) (define qmulz (make-test-case-generator 'qmulz (make-backref-generator-2 0.3 0.2) *)) (define qdivz (make-test-case-generator 'qdivz (make-backref-generator-2 0.3 0.2) /)) (define (write-test-cases test-fn lo-size hi-size num-each fname) (let ((out (open-output-file fname))) (do ((num lo-size (+ num 1))) ((> num hi-size) (void)) (do ((den hi-size (- den 1))) ((< den lo-size) (void)) (do ((ctr 1 (+ ctr 1))) ((> ctr num-each) (void)) (display (test-case->string (test-fn num den)) out) (newline out)))) (close-output-port out))) (define (write-lots-of-tests) (write-test-cases qadd 1 20 2 "qadd.tc") (write-test-cases qsub 1 20 2 "qsub.tc") (write-test-cases qmul 1 20 2 "qmul.tc") (write-test-cases qdiv 1 20 2 "qdiv.tc") (write-test-cases qtodec 1 20 2 "qtodec.tc") (write-test-cases qaddz 1 20 2 "qaddz.tc") (write-test-cases qsubz 1 20 2 "qsubz.tc") (write-test-cases qmulz 1 20 2 "qmulz.tc") (write-test-cases qdivz 1 20 2 "qdivz.tc")) ================================================ FILE: tests/init.tc ================================================ #Unsigned integer initialization. Assumes sizeof(long) == 8. initu:0,0:0 initu:0,18446744073709551615:18446744073709551615 initu:0,567:567 #Signed integer initialization Assumes sizeof(long) == 8. initv:0,0:0 initv:0,-1:-1 initv:0,9223372036854775807:9223372036854775807 initv:0,-9223372036854775808:-9223372036854775808 initv:0,4324:4324 ================================================ FILE: tests/invmod.tc ================================================ # Modular inverse tests (no undefined cases) invmod:-25,37,=1:34 invmod:-25,37,=2:34 invmod:-5,11,0:2 invmod:22153,514,0:383 invmod:6521,442674856,0:28104185 invmod:83,8990271,0:2924546 invmod:643111,73,0:23 invmod:6756751,5,0:1 invmod:4310757,655173482,0:578093623 invmod:67658,37989,0:29720 invmod:140,456739,0:394753 invmod:8363,2152,0:1827 invmod:6067,5554,0:1061 invmod:134706247,840181,0:713245 invmod:581,8525,0:3096 invmod:991357,2885,0:2243 invmod:9820551,53210,0:5931 invmod:366,3905684875,0:1846129736 invmod:4582993,6971170,0:6590887 invmod:4261,5,0:1 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invmod:24992448558250395162546529057033728367963608818369,97104418275857998682685499767517746419160351530467647181,=1:62070924902659777799435874506647028956762328885724256288 invmod:11569840794297110873922272445085763696814732411121,3856710587570728871230191743757018008573821992755,0:80733435598402588027986814199605794544352758136 invmod:649787313291617912250345498890431010716418004127770,550784775616289426175030973861257697988532404146125403,0:190014706473838692857161698137541544033343388692933291 ================================================ FILE: tests/isprime.tc ================================================ # Primality check tests # Values < 2 are definitionally nonprime. isprime:-39849281983491823000:$MP_FALSE isprime:-1:$MP_FALSE isprime:0:$MP_FALSE isprime:1:$MP_FALSE # Various small primes. isprime:2:$MP_TRUE isprime:3:$MP_TRUE isprime:5:$MP_TRUE isprime:7:$MP_TRUE isprime:23:$MP_TRUE isprime:37:$MP_TRUE isprime:997:$MP_TRUE # Mersenne primes. isprime:162259276829213363391578010288127:$MP_TRUE isprime:170141183460469231731687303715884105727:$MP_TRUE isprime:6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151:$MP_TRUE # M11 * 829 isprime:134512940491417878251618170528857283:$MP_FALSE # M12 * 1013 isprime:172353018845455331744199238664190599101451:$MP_FALSE # M13 * 65537 isprime:449898244251979768890768832669397267280186981265491806615484951724642943610332184687956191170029747169547068359663480993178863727537429685544664092114807500505087:$MP_FALSE # NIST CAVP test vectors (RSA key factors). # http://csrc.nist.gov/groups/STM/cavp/documents/dss/186-2rsatestvectors.zip isprime:#xe55a8129ca50f0243e06db83063bcf28cd006dc7c8ca269b96c642576a6c27606b57d8395b5c06852f9f1c6bc4be816610335871411733986a64094c115f35e7:$MP_TRUE isprime:#xed47455771df4e093355ffff707d2bd626ee5afcd7b6b609894d285311c8bebc914f50cf40d33532b5e44a1cab04444b474e9f843e018efe425ee8e3e8521101:$MP_TRUE ================================================ FILE: tests/lcm.tc ================================================ # Least common multiple tests # Basic tests contributed by Hal Finkel lcm:2,3,0:6 lcm:2,3,=1:6 lcm:2,=1,0:2 lcm:123456,34,0:2098752 lcm:123456,34,=1:2098752 lcm:123456,34,=2:2098752 lcm:-568,34,0:-9656 lcm:25,=1,=1:25 # More involved tests extracted from gcd.t lcm:0,0,0:$MP_UNDEF lcm:0,0,=1:$MP_UNDEF lcm:0,0,=2:$MP_UNDEF lcm:0,=1,0:$MP_UNDEF lcm:0,=1,99999:$MP_UNDEF lcm:-7,328492456,0:-2299447192 lcm:16522181,930,0:15365628330 lcm:844378,24,0:10132536 lcm:209,3,0:627 lcm:70522336,34102,0:1202476351136 lcm:32557663,995533,0:32412227919379 lcm:641,701,0:449341 lcm:290748,-233,0:-67744284 lcm:290748,-233,=1:-67744284 lcm:290748,-233,=2:-67744284 lcm:-95,4770,0:-90630 lcm:6839092,7,0:47873644 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lcm:-540592613733911579302709730020084890208422708295834255759,1487237786400760689794761062671094249214728767786149324317,0:-803989762194224119099880670025468825040986939150865705871247661626924722104597624198557832395582009863760415991603 lcm:6147134348286513705872901614503400707429078163757093529,477008107151085089956583728568535862114663515203848020888,0:225556378452274534034927784413743699904109572650798922040352209009358253405098100518908280809464240096750894904 lcm:7614680849639684551334463800131196276563566036683927,25187069984138015151555984154271413618496480687947851,0:191791499466750257309658251576197471575523021858632537910036998866329759048429339136517641910254745890877 lcm:34751974072174908316243318351151710272413759348773,8306602488518142539700335965542308143538343391985,0:288670834308846061096235572592461254734354939539314534410107250770305649520412166539742961467784405 ================================================ FILE: tests/linux/Dockerfile ================================================ # Build IMath and run tests with GCC on Linux. # # Usage (from the imath root): # # docker run --rm -it "$(docker build -f tests/linux/Dockerfile -q .)" # FROM alpine:latest AS base RUN apk add --no-cache bash build-base gcc gmp-dev make python3 FROM base AS test COPY . /imath WORKDIR /imath CMD make distclean examples check ================================================ FILE: tests/mod.tc ================================================ # Modulo (remainder) tests mod:-52,67,0:15 mod:-17,0,0:$MP_UNDEF mod:-17,-1,0:$MP_RANGE mod:-17,2,=1:1 mod:-17,2,=2:1 mod:-54090198,1,=1:0 mod:-76,427,0:351 mod:-84,576007732,=2:576007648 mod:0,9268611,=2:0 mod:0,807,0:0 mod:8268,487413,0:8268 mod:1146574,836443419,=1:1146574 mod:68387,38,0:25 mod:822,3971,0:822 mod:6236,52183125,0:6236 mod:3339,8463,0:3339 mod:-6911,492807317,0:492800406 mod:38291,7924,0:6595 mod:768,7974,0:768 mod:-753573,5272420932,0:5271667359 mod:422,509441099,0:422 mod:930,3648323446,0:930 mod:2427,67,0:15 mod:88,9301062895,0:88 mod:7238405237,35596,0:29829 mod:791480,518904571,0:791480 mod:451304532,47,0:4 mod:92202398,405459259,0:92202398 mod:349,6205,0:349 mod:-4,9246262,0:9246258 mod:-5200,499,0:289 mod:605,411571,0:605 mod:343980431,136,=2:119 mod:-5765,7596,0:1831 mod:43599271968,8373850989,0:1730017023 mod:41585052,17623,0:12395 mod:-2409446,38,0:20 mod:181096791,3565,0:1921 mod:424266851,9078599,0:6651297 mod:8187966,773,0:350 mod:2,628566175,0:2 mod:5095350857,5051807279,0:43543578 mod:-93,65,0:37 mod:2833717,10804793,=1:2833717 mod:3929,893,=1:357 mod:-8433693,960816587,0:952382894 mod:79150,8266,0:4756 mod:8999807,39604219825,0:8999807 mod:71019,11742958502,0:71019 mod:62049796028,8668788,0:7280312 mod:663,501536125446,0:663 mod:9405339512,4946,0:1182 mod:8398326144,695282,=1:14866 mod:2040205440,4831,0:1675 mod:80471943965,888059767,=1:546564935 mod:69485028101,554070,0:217541 mod:673,944658680,0:673 mod:670561,90183207,0:670561 mod:87072012,7500022,0:4571770 mod:910888567055,779049027843,=2:131839539212 mod:963684578354,34003127,0:1956047 mod:909044,302,0:24 mod:5117486344,275346901,0:161242126 mod:946663509903,66919981611,0:9783767349 mod:80280109,35551,0:5951 mod:92755422,4885132452638,0:92755422 mod:404434561,300368787584,0:404434561 mod:7641992913,2639,=2:464 mod:4268,10435873,0:4268 mod:-16867245244,3938443,0:1106125 mod:7471011989,656899,0:99662 mod:10540460484,86682087637,=2:10540460484 mod:284094,8671306,0:284094 mod:9452633,5574,0:4703 mod:87858,294942647,0:87858 mod:-6925741,254505734568,0:254498808827 mod:5567849,8785,0:6944 mod:5715920872437,47382,0:30681 mod:-7228582013,17846758280596,0:17839529698583 mod:-4825967237258,629489737727,0:209950664558 mod:-97364920350289,7307271,0:982130 mod:-5267574,1302960,0:1247226 mod:36680428,6651498734,0:36680428 mod:80778366511135,18049323,0:11222506 mod:5246691699374,70706752,0:38580718 mod:-76528261247430,881359,0:586489 mod:2510155,9882180356,0:2510155 mod:205710633,89629157572,0:205710633 mod:38304,635189,0:38304 mod:61339988670,8789855847549,0:61339988670 mod:-95895,39680647996348,0:39680647900453 mod:3783159,35551417,0:3783159 mod:434657,27849425,0:434657 mod:-922645,2692809,0:1770164 mod:9973857,61929174655,0:9973857 mod:491931072,76925934085,0:491931072 mod:36870777851,79112622642,0:36870777851 mod:38419240,600490113,0:38419240 mod:4286489,4746879,0:4286489 mod:-5967532,617005,0:202518 mod:-50370862538738,6877482182,0:6694444412 mod:948978223,306059033,0:30801124 mod:1939139989,7192751179579,0:1939139989 mod:871928,56723606527336,0:871928 mod:5777442393,771454160,0:377263273 mod:-2052133016,7833337,0:201278 mod:200227,787554274823,0:200227 mod:3616468166,851332729232285,0:3616468166 mod:-48554766181,2252075,0:2222894 mod:2085689725679,557651117,0:74548099 mod:2079714930,6441707850091,0:2079714930 mod:-464256354428,40650020675934,0:40185764321506 mod:-209095689322770,332963733020,0:5535013790 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mul:-540592613733911579302709730020084890208422708295834255759,1487237786400760689794761062671094249214728767786149324317,0:-803989762194224119099880670025468825040986939150865705871247661626924722104597624198557832395582009863760415991603 mul:6147134348286513705872901614503400707429078163757093529,477008107151085089956583728568535862114663515203848020888,0:2932232919879568942454061197378668098753424444460385986524578717121657294266275306745807650523035121257761633752 mul:7614680849639684551334463800131196276563566036683927,25187069984138015151555984154271413618496480687947851,0:191791499466750257309658251576197471575523021858632537910036998866329759048429339136517641910254745890877 mul:34751974072174908316243318351151710272413759348773,8306602488518142539700335965542308143538343391985,0:288670834308846061096235572592461254734354939539314534410107250770305649520412166539742961467784405 mul:1973284924569393016522181930166284437824113120930085705223363410232863255766399553325346410701486329074823374249547700471683909277697787590783678904983357211584574690370289495346677331618312561665754485123402827162476353576735207718451299565526093115255556962215997764515429748902159033904867393928929335369918394864191487555087825530530292436823694624357846430402766705368186347858763649288740551240105434820489955559033038872623623075504620415436212337263593361227009430895404467373404212231777284568356947010238293550872942631550054733886261493387307990754063500729850132294968984927109971586336754260617576297578,5023215555039217191451486096670046812323372237867852342682903508090873804207633443539517026163606065770027196694503291009850587117226026773591715017125540836707619882023150680605967194554434367524090941938814045780235333982097410791452776449214446635671357519707417878752761895933104747199582531838714305022614904134506738511247696618513698871318914624938137416674596881724436242382943205716649496664131501091102879563857843031208992280893614063087964394912022421136928015233318011144243860597237613050611024432789921991289922378761307428111094457098264457145099945444765267932710530788173695233378407323077034767182,0:9912235527621363370177765461045903296757346464251250997934314384765381968455767811674327750035883028560327843635490083086230089733649800500491928845965808260177110097000550870708488183060088779215210481900113545281854124601490142211180660492441361405426298053896802091578235012988730731854809702026093664780523793649405978324745399501432045298507869343282835244908856693641856464415460033802080004246708824900236489959461486545994943320360059459917374730418136788819890973086342429995201653932338829740545718352667527142958499428354077966431655595175455785104618218647409782931121099857213491801531717606789462812743975739913830932552436532349361163108142395102143904119547756730321871557900417573185916761969667939077354954258105548072267528998411702020631497735552158986372677452750936969993423245268272976429454770189221077520557005286622417163333812030510164503314440581497599501417407932697447376958591635071781976491704916693799964449632893911830806101578411062044010045678256608720149155356874608716245388282176400921764516344436742619757576145128777884235797616593795005421758664915151768829194432974835591116318659671888399376705850603804666493415116788205809451378581533592708248188469927900316495904963905315042780485196 mul:5693930165221819,3016628443782411,0:17176471693318822194099185625609 mul:19732849245693930165,22181930166284437824,0:437712683949801303830876080256140560960 # Power of two multiplication mulp2:7328492456,15,0:240140040798208 mulp2:9301,45,0:327249844798226432 mulp2:221819,104,0:4499023815872409881769555333012783104 mulp2:1,3,0:8 mulp2:28443782,108,0:9230534995215592279593651121258540040192 mulp2:131,76,0:9898080148094776367906816 mulp2:93,36,0:6390911336448 mulp2:85,4,0:1360 mulp2:522,113,0:5420757920310360044185838167705780224 mulp2:634102,29,0:340430919041024 mulp2:86325,31,0:185381525913600 mulp2:6639955332,101,0:16834286724196864462774406457915724529664 mulp2:4641070,109,0:3012226647655029057743003824831688867840 mulp2:86329074,43,0:759358565425078075392 mulp2:337424,112,0:1752005575194255677729274193390761672704 mulp2:477004716,31,0:1024359827628883968 mulp2:90927769,62,0:419330320984095270608306176 mulp2:875907836789,55,0:31557905658990701020815818752 mulp2:983357211,56,0:70858354704507043363946496 mulp2:4574690370289,41,0:10059850511215301155094528 mulp2:534667733161831,94,0:10590185513519716577933182844778629828706304 mulp2:61665754485,104,0:1250730090982990067823267062394063169781760 mulp2:34028271,97,0:5391994769734856490537202784887898112 mulp2:47635357,28,0:12787018778017792 mulp2:35207718451299,38,0:9677823956166718317920256 mulp2:5526093115255,15,0:181079019200675840 mulp2:696221599776,31,0:1495124500903360462848 mulp2:154297489021,86,0:11938189976268266978253598864697196544 mulp2:3390486739392892,71,0:8005560469361491387429364912321724416 mulp2:35369918394,31,0:75956321382209421312 mulp2:41914875550878,28,0:11251438731683187130368 mulp2:5305302924368,42,0:23332969016866530784182272 mulp2:694624357846,102,0:3522163936626521236224897501281415419920384 mulp2:40276670536,50,0:45347499604413458849726464 mulp2:8634785876,54,0:155550473814310487519657984 mulp2:492887405512401,103,0:4998472123541838661247665060074167267342942208 # Multiplication by small integers mulv:39,34165,0:1332435 mulv:1331169483,45488,0:60552237442704 mulv:967,3873,0:3745191 mulv:4609944,12208,0:56278196352 mulv:-9187510646,-19674,0:180755084449404 mulv:-9187510646,-19674,=1:180755084449404 mulv:-705904,-32646,0:23044941984 mulv:-494,61105,0:-30185870 mulv:31884502736,41742,0:1330922913206112 mulv:124758920,14754,0:1840693105680 mulv:1578359,-34693,0:-54758008787 mulv:66733360927656,-31832,0:-2124256345049145792 mulv:25747369,-31317,0:-806330354973 mulv:241723337947,63112,0:15255643304511064 mulv:7902551,11307,0:89354144157 mulv:-9354271604,39887,0:-373113831468748 mulv:952191019,55813,0:53144637343447 mulv:809248646915194,9772,0:7907977777655275768 mulv:-2633237043,16406,0:-43200886927458 mulv:764186567812009651,1311,0:1001848590401544652461 mulv:866541923,29701,0:25737161655023 mulv:-834567728673833890,4681,0:-3906611537922216439090 mulv:332307463075,323,0:107335310573225 mulv:27691642758,54832,0:1518388155706656 mulv:2202473525085705,16772,0:36939885962737444260 mulv:2202473525085705,16772,=1:36939885962737444260 mulv:-16583738845087,37131,0:-615770807056925397 mulv:9196926997210,10181,0:93633913758595010 mulv:514078180671038315,62002,0:31873875357965717606630 mulv:514078180671038315,62002,=1:31873875357965717606630 mulv:-3412120508850357,36908,0:-125934543740648976156 mulv:549214983476935,10691,0:5871657388351912085 mulv:651367312269732,44154,0:28760472305957746728 mulv:-9584205879196113,22814,0:-218654072927980121982 mulv:987433915942054416876759,34616,0:34181012434250155694605889544 mulv:98036280382191791,23951,0:2348066951433875586241 mulv:80662726244584753,2712,0:218757313575313850136 mulv:47866183268822904587301,56393,0:2699317673078730058391665293 mulv:-6912574313961965048871386,30037,0:-207632994668475544172949821282 mulv:-6912574313961965048871386,30037,=1:-207632994668475544172949821282 mulv:727313511777411140493,-48518,0:-35287796964416433714439374 mulv:465780278683330104360026,58793,0:27384619924629026825639008618 mulv:9089195999415213350558115,62437,0:567502130615487675968797026255 mulv:9089195999415213350558115,62437,=1:567502130615487675968797026255 mulv:1956713589673152168482712,-63098,0:-123464714081196555526922161776 ================================================ FILE: tests/neg.tc ================================================ # # Negation tests # neg:0,0:0 neg:0,=1:0 neg:-0,-0:-0 neg:-0,=1:0 neg:-1050000000000000000,58392:1050000000000000000 ================================================ FILE: tests/pi1024.txt ================================================ 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788 ================================================ FILE: tests/pi1500-10.txt ================================================ 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955 ================================================ FILE: tests/pi1698-16.txt ================================================ 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================================================ FILE: tests/pi4096-10.txt ================================================ 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861177 ================================================ FILE: tests/qadd.tc ================================================ ## Rational addition tests ## Generated and verified in PLT Scheme (see imath-test.scm) qadd:3/13356872859954085399,9/62913230326443414581,6/70815656362754309351:308951546718917012334/840324018679312348674627422530435802819 qadd:-1/10707768797352318399,-7/98320256665411314243,1/73359800109931088847:-57758212748959181012/350930192156520858413194622860526552319 qadd:3/8871935578221811012,=1,-3/4866674049828142891:3/4435967789110905506 qadd:9/4322444789227983625,0,-1/968244430692371869:9/4322444789227983625 qadd:2/225379267690226671,1/650264369025696376,1/34848592015687152:217986857963088489/20936586756579823441422616437606328 qadd:-3/68292234169742612,0,=2:-3/68292234169742612 qadd:-6/86190045205685135,4/67524620320880421,7/25266746450126878:-60387541102541986/5819950077953408572132977712241835 qadd:3/32384565517809325,1/12077081878824172,-5/29092772826669868:68615811154281841/391111049368729137348856297003900 qadd:7/8696576917665055,-1/7581339998976754,3/1629599527000648:44372803075172223/65931706440072050529006903131470 qadd:2/2271361357023875,3/7926992193500824,=2:22668068458073273/18005063745747695119878000173000 qadd:1/149242689846961,=1,-8/422836348382141:2/149242689846961 qadd:1/8658078704679,-3/951317712555992,2/558713214761595:925343476441955/8236583628464972469619886568 qadd:1/16676404623347,-5/33326850326497,9/43833507346994:-7150738970034/79396005838055435322703637 qadd:9/79221016041680,=1,=1:9/39610508020840 qadd:-2/2334176395033,=1,3/4196164230632:-4/2334176395033 qadd:6/8258476677649,3/2022168438715,7/2650901397286:36908440665237/16700030889405718666781035 qadd:2/89237876621,3/593210741974,0:1454135113811/52936867002527677989854 qadd:-1/86244958313,4/307620567537,7/284049788408:37359265715/26530723023449966085081 qadd:7/30268895338,4/83657377701,8/72832717953:706677225259/2532216409883104057938 qadd:-2/16397609979,9/46846025410,=1:53886438991/768162853739503566390 qadd:0,1/192040267,0:1/192040267 qadd:9/9089766539,=1,0:18/9089766539 qadd:2/331584881,4/272560309,=2:1871460142/90376877625088229 qadd:5/832601742,-3/639383129,=2:99872917/76050215287258674 qadd:9/36166996,3/22041145,1/5580628:306871293/797162003050420 qadd:8/17901539,=1,3/89155358:16/17901539 qadd:5/5040389,4/3388433,-1/7168517:37103721/17079020420437 qadd:-3/1713461,=1,1/4488431:-6/1713461 qadd:5/516179,-1/59578,=1:-218289/30752912462 qadd:-1/244201,2/201199,9/174458:287203/49132996999 qadd:-1/41212,3/27175,=2:96461/1119936100 qadd:-3/13547,4/29889,0:-35479/404906283 qadd:2/1907,0,-1/9340:2/1907 qadd:4/1341,4/9919,=2:45040/13301379 qadd:3/160,-1/799,1/705:2237/127840 qadd:4/85,2/265,1/5:246/4505 qadd:-2/59,3/89,=2:-1/5251 qadd:-7/55,9/74,-4/33:-23/4070 qadd:1,1/2,1:3/2 qadd:2,4/5,-9/7:14/5 qadd:53/70893980658822810696,=1,9/9193530480905424214:53/35446990329411405348 qadd:86/71933586324624884067,0,7/18408383381035284932:86/71933586324624884067 qadd:35/378921420794267711,24/6551623471410322667,=2:238400935598423718409/2482550474295871845608778066489505237 qadd:36/3722553911462108789,7/3244440092917636530,65/8189167080175627777:142857720725269676603/12077603158395035547949185323620462170 qadd:74/204211327800791583,=1,-4/261650327849481535:148/204211327800791583 qadd:14/190596241295804639,=1,5/7319468293717642:28/190596241295804639 qadd:11/20832946214725250,=1,34/81808092645053823:11/10416473107362625 qadd:-2/36273895397703103,21/88730391521225765,-11/10905700152968561:584291020309313633/3218596940638185709301052104048795 qadd:39/8019234291976340,-41/686183563094027,47/1842385817838468:-302027447010362887/5502666759754131835671079321180 qadd:27/3512663969871511,=1,-21/6043832798535571:54/3512663969871511 qadd:-5/2985747324014,45/607698145828948,29/712218076096765:-1452066049782055/907216556358525513388378636 qadd:19/46107312122174,92/20099305290153,=2:4623759515752915/926724942451947423255152622 qadd:17/10280669487307,=1,29/71287679743652:34/10280669487307 qadd:7/48006164806589,=1,=2:14/48006164806589 qadd:-21/5174158635853,55/5726484671487,45/4364076509257:164322546870688/29629740116054290765023411 qadd:2/515061581267,81/3885600123095,62/1777317903213:49491188328817/2001323343572560546061365 qadd:59/587566787929,17/530520857961,37/408187963651:41289366014492/311716436441482018352769 qadd:87/16848388346,=1,-29/793777748404:87/8424194173 qadd:13/40356316605,-16/35824973661,12/36053750683:-59992136029/481921326476367313635 qadd:62/58964244603,=1,-41/7476886656:124/58964244603 qadd:49/2379119051,-9/250852979,16/749619475:-9120275488/596809101339002929 qadd:35/1381737807,13/332249103,=1:365324816/5667668480949841 qadd:-29/262819147,-44/212418643,12/429833273:-17724183115/55827686560157521 qadd:14/189466127,31/78740185,-7/602930208:6975812527/14918597891213495 qadd:19/15866903,3/8919802,67/8901141:217076947/141529633113206 qadd:8/44756143,33/6935255,44/26346673:1532434759/310395264521465 qadd:9/9886228,0,=2:9/9886228 qadd:-31/5061520,-19/3104202,43/3631883:-96199571/7855990253520 qadd:-31/302786,=1,31/132480:-31/151393 qadd:10/50561,56/854269,-17/764873:11374106/43192694909 qadd:-12/40781,=1,83/13428:-24/40781 qadd:-7/5458,17/6090,1/14614:12539/8309805 qadd:85/8919,25/1261,=2:330160/11246859 qadd:25/2609,3/832,-17/7121:28627/2170688 qadd:29/910,=1,-19/91:29/455 qadd:41/715,2/15,64/97:409/2145 qadd:22/3,-3/31,22:673/93 qadd:35/29,=1,4:70/29 qadd:-14,9/2,-20:-19/2 qadd:-60,=1,43/2:-120 qadd:375/18696391582109365451,-131/32949770573031503434,166/56750232802998421883:9906936667630486913669/616041813174061083543307811398267458734 qadd:615/80348516296708248277,=1,=2:1230/80348516296708248277 qadd:-150/1530888833706527119,136/9537020524274172927,=1:-1222352197257038250866/14600118227441300399114525155221107313 qadd:89/1394353050192727085,=1,819/2322159924711043043:178/1394353050192727085 qadd:62/46458468892037221,813/119745041246081149,-121/356270572095961665:45194927766483291911/5563171273706775007904337294446929 qadd:809/639945078105944091,400/118384885068174771,-713/209608760084814514:117250467754177008713/25253274840505439393971462380909387 qadd:1/576267190309129,=1,207/61006148560056413:2/576267190309129 qadd:-515/3615716945775737,83/23367471127892459,454/27760785001119423:-11734143124365230214/84490161337046038094355667467283 qadd:73/835205561268243,353/4576154733864164,=1:5197412055370031/31587023826011126162743214412 qadd:159/1356415561313968,=1,610/1188572111871663:159/678207780656984 qadd:17/27804219463543,=1,480/45536329454957:34/27804219463543 qadd:-313/103858729128189,97/192554775266034,53/819834763511200:-16731782644278103/6666164748898110732454544142 qadd:-497/99654168988628,739/9692326546155,144/61549637278907:68827344589157057/965880747523495532712125340 qadd:-215/35851399647701,309/1276360474687,-79/2088545670863:10803664989081904/45759309472532992928244587 qadd:-121/9491608537990,-109/8274027606869,1/42153880273:-2035742671072059/78533831076922767571453310 qadd:513/9899067246839,413/3814421378956,43/320124503991:6045112940348935/37759213738065792812120084 qadd:371/929964631846,19/164386836347,-347/394487184823:78656844289811/152873943743766506506562 qadd:149/158337939815,305/905893441427,-73/931434015171:183271194416198/143437301207471553716005 qadd:601/39399444858,=1,100/29792912589:601/19699722429 qadd:7/24017912572,-55/47728203251,=2:-986887768703/1146331812901164171572 qadd:497/5699936840,-145/2007901849,=1:171436377153/11444913720219217160 qadd:-307/2244804442,112/2757559041,399/2539679446:-595152528083/6190180784314060122 qadd:-15/24574214,=1,97/256299894:-15/12287107 qadd:-79/117243052,17/136766977,280/170126053:-8811459299/16034977796293804 qadd:245/15098288,971/75107317,120/16937981:33061730313/1133991902973296 qadd:431/62180997,-385/41204984,-169/77089643:-6180335741/2562166986489048 qadd:-917/102195,=1,=1:-1834/102195 qadd:63/1841195,-479/6792243,=2:-454021096/12505843850385 qadd:-164/387359,-783/642485,=2:-408669637/248872347115 qadd:203/17726,557/813213,584/477219:174955621/14415013638 qadd:696/29969,-780/92741,687/81050:41171916/2779355029 qadd:139/11350,57/11570,949/42570:112759/6565975 qadd:116/1819,288/689,=2:603796/1253291 qadd:101/1329,260/2321,-115/2808:579961/3084609 qadd:-995/559,-419/64,844/991:-297901/35776 qadd:98/479,83/90,-941/427:48577/43110 qadd:502/31,531/97,=1:65155/3007 qadd:895/7,457/97,-217/22:90014/679 qadd:60,=1,559/8:120 qadd:842/9,-78,=1:140/9 qadd:4707/49292519774798173060,-3367/70976135186689855734,4680/92255023230843683243:84058377121001851123459/1749296273614329067191168098769082663020 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qaddz:20175953575026075815/258856713,-707977887059042238,-88657359408605704674/445245889:-183264808544835335630767879/258856713 qaddz:5641506401094150499/81605428,27796153257209226730,-31152461920419370958/183221007:2268316988949659433944840939/81605428 qaddz:64291966735347840169/1472255,-37813006182818155116,58751143690989021203/3131508:-55670323125718207612466411/1472255 qaddz:-40829665387689228845/40252968,65646528058726294873,48548143291840415697/19567973:2642467552429346280592204219/40252968 qaddz:84643493739932974309/2975141,-85925500041436529739,29931128280261616739/3657301:-255640393475285778591243890/2975141 qaddz:49533459783522540811/7076331,28143218875743097472,=1:199150781703665812199676043/7076331 qaddz:45584750001594149227/984336,41115590339049176247,15975001635513275306/154305:40471601316728311544416219/984336 qaddz:6418669402794912089/164220,73293587179171456413,-2508617797150506151/19201:12036279305232939367054949/164220 qaddz:9535512106815022878/7681,28863162607332458363,16912585483283156773/19761:221707487499027427709081/7681 qaddz:31040563813369589503/9684,-10330625966877227525,58520741913037533005/66343:-100010741299425701762597/9684 qaddz:25406696906821168845/637,-96989536360380372540,89275628731812608081/8978:-61756927964655476139135/637 qaddz:12530150187862657939/1219,40341242697614742420,=1:49188504998580233667919/1219 qaddz:80569150582987599935/2,-15179790697208915754,82993038152425243161/355:50209569188569768427/2 qaddz:36661516357580891535/19,-66347692158873159944,2979405734116612133/33:-1223944634661009147401/19 qaddz:-77628572518590925665/92,9553267737685350880,69073840554559304981/47:801272059348461355295/92 qaddz:94231430591775515069/83,1462408193524266778,-64327046129355071262/11:215611310654289657643/83 qaddz:-6524291256793749081/5,46538712122784125243,=1:226169269357126877134/5 qaddz:1240850785353652095/2,42205460810156144332,=1:85651772405665940759/2 ================================================ FILE: tests/qdecompose.tc ================================================ # Decompose rational values into integer and fraction parts. # Error conditions qdecompose:0,NULL,NULL:$MP_BADARG,? # Zero and positive values qdecompose:0,1,NULL:0,0 qdecompose:0,NULL,1:0,0 qdecompose:32,0,1:32,0 qdecompose:32/8,1,NULL:4,? qdecompose:3/7,1,2:0,3/7 qdecompose:3/7,NULL,2:?,3/7 qdecompose:3/7,1,NULL:0,? qdecompose:9/5,1,2:1,4/5 qdecompose:9/5,999,=1:1,4/5 qdecompose:37/19,1,999:1,18/19 # Negative values qdecompose:-2/5,1,2:0,-2/5 qdecompose:-11/3,1,2:-3,-2/3 qdecompose:-11/3,NULL,2:?,-2/3 qdecompose:-11/3,1,NULL:-3,? qdecompose:174/8,999,999:21,@0.75 qdecompose:174/8,999,=1:21,@0.75 qdecompose:174/8,NULL,=1:?,@0.75 ================================================ FILE: tests/qdiv.tc ================================================ ## Rational division tests ## Generated and verified in PLT Scheme (see imath-test.scm) 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qdivz:19413781778784807559/7455,70419417237119401006,87759888274980374477/7600561:19413781778784807559/524976755502725134499730 qdivz:-44073071620584783758/137977,97178052623075418323,2336605012039492891/4902:-44073071620584783758/13408336166774076993952571 qdivz:25141254449395000414/853567,48818099403147552704,72006961628028408314/367953:12570627224697500207/20834759326623223559447584 qdivz:48044965246872284768/97133,69155615859736994978,-45313300536339105253/86233:24022482623436142384/3358646217651916766599037 qdivz:-4395289710243518173/8350,744289141150282917,-29095078709708260253/88548:-4395289710243518173/6214814328604862356950 qdivz:-92303054169340161069/4319,6791173325830567613,=1:-92303054169340161069/29331077594262221520547 qdivz:64997783212580413369/6291,44933069571459793043,-20474362763124554371/1858:64997783212580413369/282673940674053558033513 qdivz:93945477444073241773/141,88011071920496381723,23904352473973528984/197:93945477444073241773/12409561140789989822943 qdivz:-25808752242439690169/552,-34114701969246980307,41196336212393917073/475:25808752242439690169/18831315487024333129464 qdivz:16573231794217629809/25,80794581544602285996,=1:16573231794217629809/2019864538615057149900 qdivz:42187260212039274209/87,70929718370679041273,41380731918827034219/13:42187260212039274209/6170885498249076590751 qdivz:-34161590626563013397/4,-31069588081719868852,=1:34161590626563013397/124278352326879475408 qdivz:60823156242773368161/2,-90388088707709016642,-91947828450656458545/7:-20274385414257789387/60258725805139344428 ================================================ FILE: tests/qmisc.tc ================================================ ## Miscellaneous rational arithmetic tests ## Generated and verified by hand # Set from signed big integers. qset:0,1:0 qset:0,0:$MP_UNDEF qset:1234567,0:$MP_UNDEF qset:6,8:3/4 qset:1000,2:500/1 qset:8,-4:-2/1 qset:-5,-8:5/8 qset:-16,-24:2/3 qset:12,-16:-3/4 qset:0,NULL:0 qset:-31,NULL:-31/1 qset:NULL,1:1 qset:NULL,-1:-1 qset:NULL,15:1/15 qset:NULL,-7:-1/7 qset:NULL,0:$MP_UNDEF qset:NULL,NULL:$MP_BADARG # Basic negation tests qneg:0,0:0 qneg:0,=1:0 qneg:1/37,15/16:-1/37 qneg:65/18,=1:-65/18 qneg:-6/7,=1:6/7 # Basic absolute value tests qabs:0,0:0 qabs:0,=1:0 qabs:1/37,15/16:1/37 qabs:-592384293849818/1000001,55:592384293849818/1000001 # Reciprocal tests qrecip:0,0:$MP_UNDEF qrecip:1/2,5:2 qrecip:-3/2,100/995:-2/3 qrecip:655378011918000000,=1:1/655378011918000000 # Reading decimal fractions qrdec:0,10:0 qrdec:1.10000,10:11/10 qrdec:1.01000,10:101/100 qrdec:1001.001,10:1001001/1000 qrdec:1001.001,2:73/8 qrdec:12.05,10:241/20 qrdec:-5.00138,10:-250069/50000 qrdec:-00000.5,10:-1/2 qrdec:.5,10:1/2 qrdec:-.005,10:-1/200 # Rational exponentiation qexpt:-5/8,0,0:1 qexpt:-5/8,0,=1:1 qexpt:13/8,0,0:1 qexpt:13/8,0,=1:1 qexpt:509252236125428/47889593208724507642867,0,0:1 qexpt:509252236125428/47889593208724507642867,0,=1:1 qexpt:-5/8,1,0:-5/8 qexpt:-5/8,1,=1:-5/8 qexpt:13/8,1,0:13/8 qexpt:13/8,1,=1:13/8 qexpt:509252236125428/47889593208724507642867,1,0:509252236125428/47889593208724507642867 qexpt:509252236125428/47889593208724507642867,1,=1:509252236125428/47889593208724507642867 qexpt:509252236125428/47889593208724507642867,4,15/39:67256115255216568118287656956157205834289880165948820377856/5259743820161714626344840164714583399959974116151536869550562774750827767486998189660536721 qexpt:509252236125428/47889593208724507642867,4,=1:67256115255216568118287656956157205834289880165948820377856/5259743820161714626344840164714583399959974116151536869550562774750827767486998189660536721 ================================================ FILE: tests/qmul.tc ================================================ ## Rational multiplication tests ## Generated and verified in PLT Scheme (see imath-test.scm) qmul:-3/26206484091896184128,1/693472590887743985,-4/70335584174882085859:-3/18173478421265693438940076224084470080 qmul:3/91130421678723294601,2/1511297448571716895,-9/67416878129472613559:6/137725173770319192750843847801453983895 qmul:3/3660941890584665578,-9/8380105656182991401,5/2848423294177090248:-27/30679079844245810042603985831234694778 qmul:7/2164077499217694058,0,-1/333401876099655555:0 qmul:4/904017211204226053,=1,-1/248448496161174245:16/817247118153466254734904646723958809 qmul:0,-4/100568637457389843,0:0 qmul:2/73650052097202983,5/4552230994414799,0:10/335272049897152087881722802145417 qmul:7/999642011115757,=1,7/12191208784714605:49/999284150387555241548053683049 qmul:4/4748171647596839,7/4194009713619088,1/878273774653032:1/711209928998281855823737102244 qmul:-1/3272725541181013,3/1299116858075758,9/9062356618866682:-3/4251652922403362359365945182854 qmul:1/107669261142969,=1,2/427008086776155:1/11592669795072854172258134961 qmul:9/886384410786908,=1,1/143876368001899:81/785677323686054067227784200464 qmul:3/35807911942040,=1,-5/90295680789497:9/1282206557648890844319361600 qmul:2/68986921725007,5/77598287457417,3/43453045339831:10/5353266982819419037696526919 qmul:-1/1109481330540,-4/9404058215555,=2:1/2608406755367394881137425 qmul:0,=1,5/4715212234981:0 qmul:1/68986716212,-3/2931468080,=1:-3/202232356519496512960 qmul:1/26808054670,=1,=1:1/718671795189708808900 qmul:7/43068832781,0,7/19211808304:0 qmul:1/9608906275,4/5041381803,=1:4/48442165241517513825 qmul:1/1228681579,6/2225293505,2/749381381:6/2734177137461844395 qmul:1/8574959114,=1,6/1956551185:1/73529923806771664996 qmul:-5/861495024,=1,-2/67979545:25/742173676376760576 qmul:-2/140727827,1/692019033,-7/753572629:-2/97386334756731291 qmul:3/95516372,=1,0:9/9123377320042384 qmul:3/21198931,1/3432139,1/3530668:3/72757677843409 qmul:7/6222866,4/1833695,0:14/5705419134935 qmul:6/615053,=1,0:36/378290192809 qmul:5/568461,4/392783,-2/643261:20/223281816963 qmul:-5/510613,=1,0:25/260725635769 qmul:2/14663,-8/93277,=1:-16/1367720651 qmul:9/49612,8/73143,1/20024:2/100799181 qmul:3/697,0,=1:0 qmul:-4/2403,0,1/2247:0 qmul:3/196,9/422,3/424:27/82712 qmul:-1/309,2/257,4/233:-2/79413 qmul:5/67,9/11,7/8:45/737 qmul:1,-1/22,=2:-1/22 qmul:0,=1,3/8:0 qmul:0,-4/7,=1:0 qmul:-85/86153854226096021421,=1,-17/21068656717268700162:7225/7422486598011403290090823970405290859241 qmul:-5/43607938850040716426,27/16056333585184134128,32/52338799857236448113:-135/700183613138564743562274537293596786528 qmul:17/1822698577891414141,=1,-7/8417742332722538862:289/3322230105847383502431373884774767881 qmul:16/4598825929956443605,49/4847943197216974161,27/3451375546922816345:112/3184978126045337954130178471819812915 qmul:-13/308229631559916894,7/23027204844472228,=2:-91/7097666865066408240206510971019832 qmul:9/407734736332167529,=1,=1:81/166247615211862175599509955321965841 qmul:85/4942792842537911,76/69829540258955019,-91/17762034363033874:6460/345152951789675772143408751225309 qmul:54/48159800199427181,=1,5/15794694767846184:2916/2319366355248746342818800521606761 qmul:-1/11155623059888,5/2213190858263331,74/4478858739544117:-5/24689522974375729479887366928 qmul:28/7444112023597965,94/2835981424363017,44/965216022716111:376/3015909059971602514096088922915 qmul:61/275448071365986,=1,39/801040431549668:3721/75871640019241316559957752196 qmul:-16/122979260248953,91/861294833601044,69/330950567465674:-364/26480350373125364764230176733 qmul:-5/15361734038378,-4/21146843499433,-42/41820111648961:10/162426092794746228321619837 qmul:31/27515949153680,42/8919478678031,-31/98260871319338:651/122713960891016949829402040 qmul:-96/7797764223407,-71/8834811164017,1/1862795966742:6816/68891774415328515707545919 qmul:15/5131534941574,57/7059500713061,=1:855/36226074579139089973698014 qmul:99/412586992259,-70/740258455507,2/72307587241:-6930/305421009651925904920313 qmul:79/741601059426,-1/218034913785,-91/880841444516:-79/161694923054812571587410 qmul:-31/7229094496,1/4120337146,=1:-31/29786306583812948416 qmul:55/83518896547,9/29598222046,-49/35480447526:495/2472010845035008675162 qmul:-70/3176137243,=1,1/170734393:4900/10087847786371641049 qmul:19/8816510816,16/688207893,1/526411545:19/379224520768191918 qmul:-3/77923064,=1,29/420820637:9/6072003903148096 qmul:7/886358404,71/63529999,3/267607006:497/56310348519761596 qmul:1/2981721,46/37858403,83/6367099:46/112883195251563 qmul:-31/938629,-15/8290882,1/1023462:465/7782062280778 qmul:37/410302,4/1757463,=1:2/9744467349 qmul:28/8167855,=1,81/7643948:784/66713855301025 qmul:-97/992628,13/93468,-47/39726:-97/7136842608 qmul:-23/674165,7/523911,47/942664:-161/353202459315 qmul:-7/19181,54/85811,=1:-378/1645940791 qmul:5/7653,=1,-76/63829:25/58568409 qmul:11/4265,=1,57/520:121/18190225 qmul:65/6957,41/389,96/2993:2665/2706273 qmul:-23/297,-9/83,14/891:23/2739 qmul:2/31,86/985,-4/905:172/30535 qmul:-12/7,-10/3,62/67:40/7 qmul:-28/23,16/87,4/15:-448/2001 qmul:37/2,=1,-16:1369/4 qmul:-20,=1,35/4:400 qmul:437/75577860178450821941,=1,572/74570847326022239185:190969/5712012949153462506928348371418487007481 qmul:-189/57565050795595180562,-59/2655741179562929534,963/98951958258639716842:11151/152877875901493900051494486844412518108 qmul:392/9223441830913061231,10/126887593668291297,102/1854286196997300457:3920/1170340339264017235848151367305406607 qmul:255/3855767718884073169,129/2905792024958436842,-235/3219625969384677757:32895/11204059087625523831085398908193292298 qmul:-47/35122532617610421,-117/122052767037802280,319/272062018205952087:1833/1428934097118272207801649688519960 qmul:979/892962159830670377,-375/273191235681889997,70/47294962936566903:-367125/243949435861310195658594938880518869 qmul:117/20991277911775766,=1,-92/47578690454158995:13689/440633748369405163321411464886756 qmul:-243/11407352500485733,587/76385498874294444,-614/81454021700493267:-47547/290452103861510956341405887722484 qmul:174/900283464250993,229/9496538222605715,-274/3248450234623149:39846/8549576329439440824503236224995 qmul:-690/8145214566421669,141/5752215623742809,71/3004747651790415:-97290/46853030487708234314403900528221 qmul:226/102973529231733,30/68951726615689,=2:2260/2366734212079704520104819679 qmul:-815/885459835828344,37/163413072330166,-43/147651688219350:-30155/144695712197674089868869025104 qmul:75/6638760558632,-138/35179390065353,413/82329576156442:-5175/116773773621297956634138548 qmul:147/95595835551176,6/10399082254439,189/19869218037638:441/497054478539251611118835132 qmul:-610/7116766665669,370/6178271155283,-170/1991438380331:-225700/43969314209382356444079327 qmul:-22/3906839603439,=1,495/2629172214638:484/15263395686999402780626721 qmul:145/9760768489,529/803913134519,3/3085831861:76705/7846809991306273371791 qmul:30/130533848429,-291/232962676405,413/647890196158:-1746/6081902938292888923549 qmul:218/45496969487,53/7721267751,312/52099708697:11554/351294283268204113737 qmul:277/88084217182,-643/95570881719,=2:-178111/8418286301611629495858 qmul:97/9657661098,472/161930139,400/6505391099:22892/781933202007016311 qmul:137/1394596885,923/2175332507,-63/538078336:126451/3033711938101440695 qmul:-99/123912484,299/998630381,359/807136797:-29601/123742771107576404 qmul:281/377026117,-970/10165277,80/672610947:-272570/3832574915539409 qmul:641/45327247,95/3702049,-31/16613945:60895/167803689429103 qmul:-737/25452329,363/67508236,825/73130323:-267531/1718241832881644 qmul:51/7250464,112/8927185,903/6361594:357/4045389591490 qmul:199/4639977,588/7971809,322/8874233:39004/12329670136131 qmul:665/703012,329/294996,787/209117:218785/207385727952 qmul:133/29650,307/137037,809/690522:40831/4063147050 qmul:553/42863,161/16139,552/86389:89033/691765957 qmul:-568/72299,-953/23177,798/52267:541304/1675673923 qmul:-907/7588,47/7619,=2:-42629/57812972 qmul:37/1428,-161/1853,-140/3279:-851/378012 qmul:69/659,194/7,-183/238:13386/4613 qmul:-365/824,264/503,-421/698:-12045/51809 qmul:747/74,-15/94,12/19:-11205/6956 qmul:12/5,113/37,=2:1356/185 qmul:-807/7,943/8,199/3:-761001/56 qmul:591/7,85,-156:50235/7 qmul:853/18759654468263598130,-2841/40750915886836631585,=1:-2423373/764473101302328863323172599481304936050 qmul:-4752/16314480916934323241,1675/15223840982975523171,=2:-2653200/82789687733065614038692540422933105737 qmul:-877/6101604969629738233,=1,3917/3506403215407013175:769129/37229583205410318824680729796101962289 qmul:3511/9447760616772726092,2633/1439700094583390479,-1093/3530171944589695778:9244463/13601941853568925322985028756947678068 qmul:1947/430992381411198689,=1,6905/150990131770718358:3790809/185754432834496165241461379835318721 qmul:8719/646714849991103264,=1,5786/734533820409647257:76020961/418240097199015197424619951911453696 qmul:-901/11042787574357099,-1492/25943871895296763,2003/71983717831437714:1344292/286492666196095454208761540770537 qmul:248/45424964911300681,-2828/10155871660092285,1922/24482631313347631:-100192/65904301971909291827634263335155 qmul:2932/167088922177995,4285/8315956341564334,=1:1256362/138950418199124701072469163033 qmul:63/96864941445455,1217/536600078187501,-1363/813397840648021:25557/17325911717752953043818085985 qmul:2028/952222976621975,=1,-4447/132247057152414:4112784/906728597206814347382052900625 qmul:-2672/564653311125411,=1,593/245849676591157:7139584/318833361764890193787369918921 qmul:8811/12688709770015,-6995/78357482492503,2405/8730288903721:-12326589/198851070731280426018339509 qmul:-6216/89020593811217,2073/8676827195515,-43/383215257478:-12885768/772416309342061967459091755 qmul:649/679490122076,-1037/2294439110154,6125/672996983517:-673013/1559048711054490271159704 qmul:4001/986338046878,5/3558981731,-2511/3763709597086:20005/3510359089429023585818 qmul:-1523/69241899473,=1,7123/515464482213:2319529/4794440642629037677729 qmul:-6869/800191115742,938/461384295473,-3029/66737130644:-3221561/184597807090188234817983 qmul:3554/16260606585,-2909/10951382696,=1:-5169293/89038062790716326580 qmul:-8706/24347671943,-2333/75528831647,6568/10275254341:20311098/1838951215179232380121 qmul:8843/2387867375,3806/2482665293,-478/3437714583:33656458/5928275456199515875 qmul:676/469237349,=1,=2:456976/220183689696547801 qmul:4381/415783140,=1,-9189/160372247:19193161/172875619508259600 qmul:5209/647900590,31/76532430,5022/774082651:161479/49585406551133700 qmul:6785/98653728,1643/10927961,-3657/22982951:11147755/1078084092088608 qmul:-131/3707540,-3070/95931603,8132/10434367:40217/35567025538662 qmul:3495/4205702,1768/4495963,642/2009179:3089580/9454340290513 qmul:-3081/1925708,-557/52210,=2:1716117/100541214680 qmul:1824/515329,4783/215399,-80/428083:8724192/111001351271 qmul:-1259/116291,686/450649,=2:-123382/7486631837 qmul:2158/8127,4919/28127,=2:10615202/228588129 qmul:-8479/13630,228/39107,-6607/63539:-966606/266514205 qmul:-3929/4639,1292/907,4288/3241:-5076268/4207573 qmul:-2277/9067,379/5790,-503/3539:-287661/17499310 qmul:7172/525,4813/272,4472/631:8629709/35700 qmul:759/64,=1,1976/105:576081/4096 qmul:3255/4,-1567/13,4881/26:-5100585/52 qmul:3089/89,=1,-8984/35:9541921/7921 qmul:5031,-5481,=2:-27574911 qmul:1479,6716/7,669/5:9932964/7 qmul:-79907/42073633953804470386,9649/39994826473890828375,-32061/69201000109873943624:-771022643/1682727689108411078225149789999696002750 qmul:7869/4137317017220625920,-46300/94718332275370703049,-79642/60022119059401889179:-6072245/6531329466094147648450013992237207168 qmul:-29138/1677259660137772757,55969/6796400935123913154,-10129/967130263887253020:-815412361/5699664561302987764528483645927572789 qmul:63296/9530224706297545807,2348/322614345457502213,958/9427355800897598701:148619008/3074587205685099009151203658171370891 qmul:8775/40604046784024133,-33221/144310822954936081,=2:-291514275/5859603406703248409743984976442773 qmul:21115/310091896403808544,11297/311633467720059450,=2:47707231/19327002597641657788985081219588160 qmul:-7541/568197224156233,78686/80834506129161047,=2:-593371126/45929941998629309750410745855951 qmul:-69371/45833711711077260,45306/56585412779622335,7626/54270702558063797:-174606807/144084416466306503713223267033450 qmul:-47821/557744909539529,-35381/1596080991630467,27735/4832267108379043:1691954801/890206048294696559875897230043 qmul:39463/2836203973039415,5893/5755385978253006,39369/9842567552327876:232555459/16323448577896515754725680231490 qmul:59563/93078116326943,=1,39162/530318464795213:3547750969/8663535738971933065667725249 qmul:-6422/219350698334991,12009/451668291281128,38643/184068500609632:-12853633/16512292518047925598650058308 qmul:6353/29487362288887,18649/10109618056586,-739/5084432721670:118477097/298105970236825097644959782 qmul:82991/13932554844361,44258/40391647302859,-4103/3232141273561:3673015678/562758841301169080175328099 qmul:68609/2797606749368,71293/8880170450370,=2:4891341437/24843224787493384272866160 qmul:69352/1282840784633,51360/5155457119681,=2:3561918720/6613630656553360226662073 qmul:19996/284659901481,91975/649935845164,992/22386886571:459783025/46252668413338677571971 qmul:95164/291066123381,=1,86173/926768430166:9056186896/84719488180043514871161 qmul:58599/35278850458,=1,=2:3433842801/1244597289637926809764 qmul:16793/50880968745,32965/31422146373,5133/4972604243:110716249/319757849501085622377 qmul:10537/861910652,22310/9378414407,=1:117540235/4041677638131781682 qmul:79317/9648480088,22265/3941357964,=2:588664335/12676037945111406944 qmul:11221/182565205,56092/543156657,49073/666425232:629408332/99161506432319685 qmul:85751/945688766,15325/126345977,14001/74129827:1314134075/119483971078194382 qmul:-70533/6456184,-11237/1159737,36975/90043007:264193107/2495825154536 qmul:56162/84955139,=1,=2:3154170244/7217375642509321 qmul:559/4445450,87073/9891852,=1:48673807/43973733473400 qmul:2247/126982,=1,=2:5049009/16124428324 qmul:87205/903493,=1,4007/74486:7604712025/816299601049 qmul:20400/957959,=1,-9955/111633:416160000/917685445681 qmul:31836/73595,11609/39450,46021/33218:61597354/483887125 qmul:84969/75326,-86068/92037,9321/65618:-1218851982/1155463177 qmul:49337/4359,71033/6220,-25745/2781:3504555121/27112980 qmul:15077/1290,20527/9232,-259/71:309485579/11909280 qmul:52867/502,-63033/451,83228/635:-3332365611/226402 qmul:1852/17,45130/359,67421/50:83580760/6103 qmul:57233/78,37817/35,-23454:166490797/210 qmul:9693/26,82259/68,46811/66:797336487/1768 qmul:-53957/7,=1,57497/7:2911357849/49 qmul:-95413/6,-29374,-4257:1401330731/3 qmul:-198736/12940720433326325129,125852/5925853683093665567,12760/97357765177854120733:-25011323072/76684815841712259623316096046234133143 qmul:921572/61142247716597287729,-236568/70364185507196351425,204596/87367262923771962827:-218014444896/4302224460657604084043267617199724163825 qmul:-175852/3759159397994001893,12753/21663430571600165,=1:-2242640556/81436288626021332583545141049112345 qmul:-268026/6357464651647716983,=1,8534/1795261387346998395:71837936676/40417356796950227447969273156066622289 qmul:841695/829965893010784622,-533003/287367841069761182,-70387/77776025771352596:-448625960085/238505506836045568256258975978143204 qmul:285995/137908752412413419,=1,=1:81793140025/19018823991948344014771004171269561 qmul:523332/10397730659818265,-637807/84218842967037343,38109/5089543807331942:-333784812924/875684845652784039249421848469895 qmul:331806/46798346659133905,390599/19460297756850316,-839360/33343052356070147:5891049627/41395898205229409605128422071090 qmul:-618133/4917065118673735,=1,-92527/257257853329058:382088405689/24177529381277951659005378850225 qmul:821668/9309756380607047,319410/1721325229930259,-409819/4033682794066002:262448975880/16025118542443120997155893935173 qmul:-463245/974985643441198,-676781/102650194991381,67531/763750320751138:313515414345/100082466413036044472790314438 qmul:3292/15168814078843,786853/187996862965898,126658/126696595422875:1295160038/1425844730867715885896148007 qmul:-108514/9407475910099,31445/45805965278381,209927/522813819096:-487460390/61559787842171498837752817 qmul:206519/25307336797263,439291/97571104143841,-52486/22231146494461:90721938029/2469264794249007720607107183 qmul:755819/4678998804414,132779/513422592641,-154155/1796861274557:100356891001/2402303697126375154717374 qmul:-610422/8953796367011,=1,34600/946679301111:372615018084/80170469381899382209074121 qmul:-168796/96200349399,=1,459815/414314841334:28492089616/9254507224489679661201 qmul:448040/938638294207,-940391/987312987781,877652/581123018277:-421332783640/926729778699174474084667 qmul:367299/48916956722,-234746/31600745479,19962/10415742905:-43110985527/772906149489590079919 qmul:540492/60952022291,=1,=2:292131602064/3715149021362560888681 qmul:48241/1850039638,600695/993394588,=2:28978127495/1837819363974679144 qmul:-73469/4702579939,910622/7776354127,71768/6903692213:-66902487718/36568926916190058253 qmul:165889/228901970,3743/140713319,=2:620922527/32209555924338430 qmul:208098/645461621,-637539/213089255,-987707/763332694:-18952941546/19648705135711765 qmul:978743/66626510,16328/1482253,=1:7990457852/49378672163515 qmul:336035/68124509,=1,245361/31402036:112919521225/4640948726491081 qmul:191473/9297613,135059/7858162,-384667/8715020:25860151907/73062149167306 qmul:-118451/7012982,-685529/5952631,=1:81201595579/41745694055642 qmul:142154/901271,422448/305711,332653/165374:3532510176/16207556393 qmul:52759/177236,850321/697129,72248/85023:44862085639/123556355444 qmul:-88178/95391,=1,277011/11863:7775359684/9099442881 qmul:-466226/55653,24107/11550,-273396/37003:-5619655091/321396075 qmul:825492/3685,102991/306,60368/1041:14169707762/187935 qmul:166834/1709,340151/1908,=2:28374375967/1630386 qmul:-212681/290,424751/190,845448/971:-90336467431/55100 qmul:134907/163,-69685/79,=2:-9400994295/12877 qmul:-539594/3,15173/4,-877571/28:-4093629881/6 qmul:247756/31,94120/29,-147220/11:23318794720/899 qmul:910742/5,63428,2990:57766543576/5 qmul:132140,=1,214219/9:17460979600 qmul:-1882407/73787858412488449855,-434970/15504199196668297319,7152438/32357487418268793473:163758114558/228804331024555497710598988747312487749 qmul:697417/2168456434664834658,1334383/40514117254978695797,1660012/19534585395934841435:132945912673/12550442608046308674759866845069218918 qmul:767157/4500296443907797052,4954462/555593595680231401,3839270/8356753330266434437:1900425102267/1250167941448845883802900321752814926 qmul:3855435/1910412651584231024,3929628/9286414633188139915,6450211/7279093857125478452:757521266409/887044200154977924360507801609786148 qmul:-713297/2131510505574811,=1,8006203/547537770085302559:508792610209/4543337035375786395109517685721 qmul:-3176335/541746203963633741,-438253/349884327285711674,2546202/81167937975645853:1392038342755/189548506133403938761872538263992434 qmul:4172837/3155683016816501,1634359/1130730609779385,3449963/73677939584796131:6819913706483/3568227381875371425040637631885 qmul:1250071/25258841326965282,-32307/1353739173264256,=1:-13462014599/11397960991859667942696774520064 qmul:7965329/6993004096201475,2973773/6634186275128268,3335672/4941418095538311:2153370937847/4217535617903234884469745072300 qmul:924761/7142709941575765,8302365/4849337439058259,=2:1535540671953/6927482147203397401610419498627 qmul:6563249/71417076489085,=1,3793878/305677884396037:43076237436001/5100398814247817470124137225 qmul:123256/2387254101849,6673623/563071687944596,-2966203/120995731224497:68547006374/112016266390064743737763167 qmul:11601/9690796184885,-313729/29163002094366,=2:-1213190043/94204236478625099184285970 qmul:-1548191/1118347883822,693213/16160970245026,=2:-1073226127683/18073586874035135921369372 qmul:4730021/1257111596731,45335/50784818897,9472521/3164110107311:214435502035/63842184773302332225707 qmul:8511317/4540489631064,-6359369/2005086337073,=1:-54126605478973/9104073722868052915635672 qmul:-929873/867693641561,8138971/698148180183,9405551/179909067138:-7568209380683/605778736812172445385663 qmul:9281874/795726121805,-9968150/721200783579,4661824/364533493543:-6168207487540/38258553504002986522673 qmul:3865094/4084662077,4259784/19883113093,=2:16464465579696/81215798023679274161 qmul:-416924/286477113,826597/6309334211,-9773164/19019652193:-344628127628/1807479849719412843 qmul:-9662220/20572447,=1,1141747/1832358244:93358495328400/423225575567809 qmul:616787/710447851,-5149637/86667498,5336551/335300034:-3176229156319/61572737705646798 qmul:-9976984/843714569,=1,613447/59557955:99540209736256/711854273942855761 qmul:-6026602/975541545,9908792/76315713,9315535/212827209:-59716345684784/74449148567796585 qmul:317525/4130814,-794909/3724657,-7514646/67549867:-252403480225/15385865280798 qmul:5284147/75357219,-2845520/19763971,1559210/15974883:-791376103760/78387257418771 qmul:6632185/1141092,2427283/1559559,=2:16098189903355/1779600298428 qmul:-1099211/2368184,=1,4294432/3557597:1208264822521/5608295457856 qmul:-90319/172637,8164133/19492,-7639232/876753:-737376328427/3365040404 qmul:-2193898/79229,542172/63719,=1:-1189470066456/5048392651 qmul:-3656336/69523,1911911/39486,833550/557:-3495294509048/1372592589 qmul:106251/11335,-7809497/82381,-4910754/43655:-829766865747/933788635 qmul:656544/4345,-9528986/1963,2350355/5553:-6256198584384/8529235 qmul:-2189554/2039,-5393104/7563,889038/2857:11808492435616/15420957 qmul:3890213/508,186330/17,-1198413/262:362431694145/4318 qmul:3102225/578,5898937/910,=1:522852280995/15028 qmul:-1156863/5,-8420942/61,1460661/13:9741876224946/305 qmul:-2254787/5,2862624/83,3361/52:-6454607381088/415 qmul:-7630885/4,5547065/8,=1:-42329015102525/32 qmul:3371673/8,1927246,=2:3249021651279/4 qmul:-14442357/30313364574216985165,21011896/19717180229164582119,=1:-101153767759624/199231357554069726942322822323082421545 qmul:73015500/34914714923282785961,10709547/16405893500986887200,19061786/4299472658767378545:7819629289785/5728070946486949421088979169452505992 qmul:-5213601/648973976600394322,95110449/6292591997485345693,10223157/1491031081544864086:-495867932016849/4083728451731883302073525200284355146 qmul:81716702/9420867468902388767,-3659716/561353788976535007,16436845/12448406189105001:-299059921776632/5288439649114135016294765892899066369 qmul:-50829049/681481015656967334,78493193/406094838848924705,=2:-3989734353163457/276745923231817683251713267210586470 qmul:-70639608/210570392897683795,=1,32857499/484390875545236076:4989954218393664/44339890365084922016231475805602025 qmul:-42306075/32432310313264277,-86992166/48265729471703217,59197803/99727495871692084:1226765699736150/521789705240781269523990077359703 qmul:98949619/2882304121717510,-30259679/61942044859153494,=2:-2994183708112301/178535811205149016934639997479940 qmul:-33943246/547508652618667,-9155497/325768016112482,3909688/9222108480297609:155383643461631/89180403784000610709262450747 qmul:-4005853/831711723057253,-65053249/3453104157068793,=2:260593752666397/2871987208371849027864998605629 qmul:30466505/131811990296054,80480517/129751865511763,-66851989/905703806093822:2451960073583085/17102851637731408230589483202 qmul:67778441/221052041028359,31145967/736730375785315,=2:2111025086697447/162855753254933795304810748085 qmul:-27930623/83735524881404,=1,26062637/38713631506284:780119701168129/7011638127164228368265011216 qmul:91874289/55178817284824,2081222/10998714287097,=1:31868465250193/101149341002618103726185988 qmul:-81097913/23224035213,86134633/913902046268,-44110346/4612785602109:-6985338973320929/21224493303760787235084 qmul:26946729/330400702820,-5376007/957000244373,72609687/3803755771964:-144865803731103/316193553339750950231860 qmul:5847347/83932240013,4198391/162033797450,41563965/225583428284:24549449018677/13599859577791227366850 qmul:19548965/189470438789,2465153/48226118390,-16293845/384490679461:9638237943329/1827484762488712445942 qmul:-55395086/15848355167,30834213/24733216753,3746720/49399574807:-1708063880877318/391980803523938512751 qmul:-58079954/9010951227,53522457/51897896711,=1:-1036193946842326/155883138682234904799 qmul:15721758/4667399077,-40891342/1328104821,=2:-214294594406412/2066265071898216739 qmul:70233722/7303211237,8646406/3990640707,33916940/2735563757:607269275303132/29144492054192024559 qmul:6933207/288152,3665663/23826937,-56545561/920522000:25414800371241/6865779550424 qmul:41800997/62123962,-38919041/683603632,-76160505/964998499:-1626854716083877/42468166057429984 qmul:-30010802/20468051,19506739/20221851,38792870/36677751:-585412881794678/413901877582401 qmul:11813175/26779288,=1,4038299/10717148:139551103580625/717130265786944 qmul:-54308089/3363111,6223152/1333435,12297998/2068949:-112655830892176/1494829972095 qmul:47572280/4867129,99908399/5832503,6381834/2396879:4752870331579720/28387544493887 qmul:-62682614/784029,8201676/813035,86261045/879573:-171367496953688/212481006005 qmul:-52450671/559382,31930301/348148,81333805/486957:-1674765712681971/194747724536 qmul:53187047/34080,40744921/16199,37085536/50799:2167102028238287/552061920 qmul:11558111/11033,48139409/27484,-90392545/80713:556400632696399/303230972 qmul:-25583995/4897,-94434044/3561,2921273/9343:2416000109525780/17438217 qmul:-5090656/611,=1,=2:25914778510336/373321 qmul:-13641055/103,35989446/451,-35512409/41:-490934012305530/46453 qmul:99505255/181,-312642,12835678/5:-31109521933710/181 qmul:25097277/5,85216417/47,73513489/51:2138700022396509/235 qmul:64784087/19,-41764336/27,-39313651/72:-2705664376921232/513 qmul:22866666,9187561/2,-79296567/8:105044444370813 qmul:32433429/4,-57952559/6,=2:-626533402564937/8 qmul:142379769/6580458265088042332,=1,829632764/47313440042888292183:20271998620493361/43302430978565528007566299412223998224 qmul:952160697/53449785406826630773,=1,123350541/21685565106900565733:906609992911525809/2856879560035817059690375116110870577529 qmul:134379194/7288875631759851537,262306997/2039219084637508550,=1:17624301418710209/7431807146916983147195344504784070675 qmul:893718997/892104296345812908,=1,287136425/3171192156119780019:798733645598686009/795850075558657977797692103339416464 qmul:148747375/98802457575041086,24743438/63078605847781653,=2:1840260725487625/3116160639084092662997866715997579 qmul:881257471/447180652093139622,=1,467458692/434203794165327853:776614730193315841/199970535606445577794662077186302884 qmul:-328833244/8368942920923449,71377107/4810747268694941,=1:-23471165642145108/40260869298696343876296794571509 qmul:158379101/1326421417689989,-189428893/41659788909099497,196884323/11300332885720816:-30001577776765193/55258436265473435094327901835533 qmul:10782829/45891552641500,764396030/8166229459391987,-237359023/5307605981413862:824235167976887/37476094911825545799378366050 qmul:-176383510/8720957474390283,=1,969790455/2816113324098863:31111142599920100/76055099270123743567802604820089 qmul:153319337/75604684811316,-66073159/9855025487116,=2:-10130292931375583/745086095760891109449004656 qmul:-152252295/92990423831326,58928296/433772431956189,=1:-213618293010460/960397197475024603484708967 qmul:968728976/89630394861017,122952071/77095083081384,=1:14888404229613662/863757842303419891847500941 qmul:421854586/98110047748469,777827572/98264750833133,=2:328130128365445192/9640759396230087578575223377 qmul:321360259/1519003205844,=1,648154609/8326351267679:103272416064547081/2307370739364349435752336 qmul:-623994359/2983440638275,548017609/4525469063166,313238822/1462111109367:-341959896648667631/13501468310305737332278650 qmul:105901696/125767654005,11356251/3169320047,37580987/3123470749:400882080367232/132865982367402112745 qmul:257717002/338572086809,=1,-516598417/866703725253:66418053119868004/114631057966201031802481 qmul:-315718685/10965934391,730969133/99436604662,980080011/95127007262:-230780613446350105/1090415282787296730842 qmul:357633989/52052235576,=1,499101847/17405036021:127902070088052121/2709435228459400051776 qmul:83154971/2959266631,=1,=1:6914749202010841/8757258993350090161 qmul:74008543/143708417,-38807917/3997329896,49374533/1136791926:-410302484862133/82064278797276376 qmul:147247586/394684533,-46611929/47003797,417377757/202754149:-6863494024053394/18551671668171801 qmul:190874443/241889832,65505550/154148559,=1:6251667684829325/18643484519776044 qmul:-494401746/19681,407904654/21651245,69321355/12439911:-201668773139125884/426118152845 qmul:365885228/56568973,4250982/8521637,960401966/74768881:1555371518293896/482060253368801 qmul:255177714/7055753,814922797/4572404,187054293/4701449:103975068212473029/16130876620106 qmul:-588905892/5841913,=1,832554893/1175043:346810149632315664/34127947499569 qmul:135837085/706833,-289514879/255430,725428338/928723:-7865371445497543/36109270638 qmul:122186761/430279,=1,619259689/728443:14929604563671121/185140017841 qmul:775073757/30757,695907415/51279,944630725/67207:179793191556069385/525729401 qmul:95477167/3960,-871735667/38397,-714770441/33262:-7566441078001399/13822920 qmul:-884857813/4929,70752241/2056,154069499/3880:-62605673236108933/10134024 qmul:229619449/1615,957611614/1161,10452182/285:219886251162680686/1875015 qmul:111146789/136,146738413/445,169865033/157:16309503427905857/60520 qmul:9871622/41,-808689707/803,=2:-7983079102794754/32923 qmul:-288336467/9,=1,850175175/86:83137918202042089/81 qmul:558230684/47,805462654/41,167574699/11:449633968278875336/1927 qmul:339929608,29235627/2,=2:4969027612872108 qmul:881780865/2,443292701/9,=1:130295673778655455/6 qmul:2838001100/91389568002455572881,=1,1986643253/20570864960839080487:8054250243601210000/8352053139675451489580240654173902640161 qmul:3251591241/344636720089928137,-1113406027/3139375771816261090,-3172679089/93012796738201713479:-3620341285069809507/1081944169128542879223598266129289330 qmul:2151380941/4425085028680839366,6291439247/670381381077695674,-1225149433/257062097818706652:13535282487455191427/2966494612913295666228911591427102684 qmul:6158301795/2455047697567864031,-5798372309/5521291989057645588,-157042968/9556961002892580965:-3967569622065888295/1506115020592873902921765927885671692 qmul:-8451954373/975723814918920513,4784366210/605780426352481313,8465359637/69665667013568159:-40437244910642936330/591074388603853235233268628964873569 qmul:5825412784/511571458045271039,1008046458/332866639017254645,1740022059/196312276491243337:5872286723299119072/170285071856685864496671466706726155 qmul:1850720900/45716430562358967,-3131316310/52356049605863119,539696323/19977050509485334:-5795192539427879000/2393531706325862841899110744238073 qmul:-999008939/40305492823224241,-149362865/49775456964489,4606037138/47949128805635417:149214837289650235/2006224323454918453607620977849 qmul:-4057348745/579860156310338,1212653237/2742714067824482,-3833477943/1278732708982538:-4920157089262137565/1590390608083267111519706094916 qmul:9177815341/2326648645173174,371635999/876014400872787,-2149851912/2031850250792911:487258081841437237/291168245563265658397194145134 qmul:149460870/500654885667917,8207530879/259222934708685,=1:81780313715146982/8652081915938573470536383943 qmul:1089507559/134057483313428,-7987532800/42390827366211,3382946045/262278399004573:-2175619340840108800/1420701908072059536662445327 qmul:6048157042/13712987352923,=1,-2693371451/4466222589529:36580203604694189764/188046022141426146556643929 qmul:2603227553/49609180587155,471640162/92076035059005,-663933503/13520440154956:175398094974254798/652545235855913432995725825 qmul:4393500955/6416432605233,-3583476841/7979065549803,441355864/1454382446413:-2249144131879126165/7313876621863906114274157 qmul:64145470/8127876011853,-4488303205/666124315584,=2:-143952159293615675/2707087922773595548308576 qmul:2220237721/64548387245,-703263819/579214597702,5697314686/589964874375:-120108681442947423/2875951396186583316230 qmul:7022991149/836362149630,-1984639629/975088070,-1171252556/150772930335:-663719359448649701/38834607347798472100 qmul:7911754989/73811019085,=1,8326854813/74451049034:62595867005966390121/5448066538366234237225 qmul:8670773721/75336074123,7789940197/98427175582,=2:67544808748309163037/7415116995363087664586 qmul:3813777004/9138760931,3878060903/1782466818,-496564577/8664398681:7395029745986437306/8144769058571143779 qmul:4360854339/9648497864,=1,=1:19017050565975126921/93093511031612562496 qmul:-1306392307/687643073,-9598905761/422850143,4622499059/88598595:12539936641788380627/290769971751009439 qmul:4779917420/76898307,1792785739/166010625,2225422443/217138286:1713873556834734676/2553187201302375 qmul:-7341873007/81873962,1385231861/3699454,-4877758523/40734069:-10170196408712276027/302888956216748 qmul:908541847/68126894,3798368094/17436611,175898188/3762149:1725488181854314809/593951074658117 qmul:-7938465013/6277994,-362880881/3869862,=2:2880717177705116453/24294970416828 qmul:6036183652/5477115,-1788527459/1739644,-2727500049/825193:-2698970052292225067/2382057561765 qmul:1659028493/577907,1961575125/200776,=2:3254309023535036625/116029855832 qmul:2324185733/425376,-6101126398/443667,=1:-7090075464730639867/94362646896 qmul:158821375/2278,5716179055/50437,-700123827/1726:907851417261300625/114895486 qmul:6937745972/64507,-657862356/10135,=2:-4564081910469430032/653778445 qmul:-688655549/3844,5925620489/6516,-2612322997/6399:-4080711431017943461/25047504 qmul:1356483025/6163,=1,2367819633/2590:1840046197113150625/37982569 qmul:6911498420/997,-520233898/887,8567846181/167:-3595595764057441160/884339 qmul:-5665580795/223,245568655/53,520214901/133:-1391289055621980725/11819 qmul:6848382683/88,-3930604705/78,-4380032639/66:-26918285195440323515/6864 qmul:7058656941/92,-2614182743/76,1606422009/16:-18452619163919369163/6992 qmul:348409636/3,-58882183/4,8721866869/5:-5128779986478847/3 qmul:-7530659939/2,=1,6943419397/7:56710839116859483721/4 qmul:5479036571/2440360696983602620,49554857924/4707522136067292695,14037572034/1860137811841092895:67878219709076284651/2872013000259729052687425327777215225 qmul:-90287321301/55986373996879974676,79056497918/57955348234225101999,68036645565/23598836282510831821:-1189633238075717258553/540784966893457334425356770707772829554 qmul:-31154471814/4775267091317819455,20452466931/8265429859332817919,7980554951/34755849271476873:-637185804528606582834/39469635202867679038129686483630814145 qmul:85271504414/7465316608452879443,=1,-10606469222/1904172971848733911:7271229465026821483396/55730952064442402518704478477891990249 qmul:-16339852699/127321792148125915,3040615183/55882163298738283,-51110404691/61653999585316250:-49683204204562928917/7115017180309586101368162514903945 qmul:-63804908144/277883532447300683,-720647040/27229766739402803,14615586307/46658500039754383:45980818191445493760/7566703769261267728805752794014449 qmul:10341018519/94245221741052416,87590141171/60174320543406768,=2:301923757310378448583/1890380727576845520968582099050496 qmul:94172173704/61262926143770059,=1,=1:8868398300136349079616/3753146119697024991735097864863481 qmul:-27044253543/1053895278738638,=1,-26863808373/192367352651581:731391649698068052849/1110695258547591485248314095044 qmul:13955551844/8914953109146301,65978266931/1477260665198022,38242091460/2633752121605511:460381562366420635382/6584854780113319521064766908311 qmul:21380540693/46366763004112,4413417248/3293403036539,22792743143/98178838808334:5897577941628254554/9544027379514164158953023 qmul:54517956885/536986169058356,53087744133/624679940801624,-12768510380/23381528319939:2894235345764805705705/335444488298664683363875570144 qmul:15631958865/98900123425043,57461678219/38736535635779,10636904565/14357297124671:898238590233274461435/3831048155437119617055413497 qmul:11306366194/20614966646301,=1,48649167285/72083597787241:127833916512826045636/424976849828102699236982601 qmul:-38850808449/5270347545016,-80555988964/460100649873,=1:260805441388343496403/202074194209869310181914 qmul:2473793897/257329894608,35125602539/6570210827640,-58955090604/1845404251483:86893501189425904483/1690711659828941653365120 qmul:8389450307/94247305842,5879374061/445968667154,46708714783/778418252722:49324716521024286727/42031345369212137713668 qmul:10005721251/317400686611,11885509039/202069710332,=2:118923090370474887789/64137064802662680764852 qmul:53843304483/15517809130,-37493619897/27992722981,-69059984171/37850731407:-2018780392284038098251/434385732248122616530 qmul:4936875434/5558111491,-78071231962/38058507841,11261412306/45256951175:-385427947175313421508/211533429761375700931 qmul:-51013899132/7547986135,18679893598/8111901153,-1770753005/1840835446:-317644735934954852312/20409505810444837885 qmul:25767898320/6199052159,24344608263/317305927,55665198980/5479278553:627309390361215818160/1966995991832846393 qmul:-7303061735/68386022,=1,=1:53334710705221210225/4676648004984484 qmul:20359304675/219624604,16344153007/211704953,-82591435031/427080722:332755590724330407725/46495616467463612 qmul:2652747256/1352133,-25367065339/52123374,23447425715/95023951:-33646206485402479892/35238867028371 qmul:48463976225/65809761,-35504206691/75941530,11794361717/16873414:-49162143684574569185/142791255407838 qmul:82320116481/5180912,-76359077209/9271893,46566602503/1634915:-2095296043408850793843/16012287235472 qmul:-730645673/7142476,-70390135745/551403,34012585939/9989481:165370572681565535/12663609948 qmul:-51855352987/140641,=1,21714825731/757834:2688977633406369822169/19779890881 qmul:-59100071699/229458,-12541528262/72971,17155877720/17761:370602609749617428569/8371889859 qmul:19150460726/80285,98656519537/34995,-82017816286/22501:1889317802757170203862/2809573575 qmul:56611908394/98549,76064158111/38373,31178576993/24120:4306137151046664083734/3781620777 qmul:-96850333567/5969,-11666596495/4102,39126150628/3881:1129913762132343047665/24484838 qmul:71357908657/3994,7273127113/380,-93120031916/8579:27315533693694953539/79880 qmul:5232641313/278,-1351690114/51,-35248603917/754:-1178818255481679947/2363 qmul:22060731824/219,89417675500/637,-9595385874/103:1972619359530955112000/139503 qmul:37188356744/5,=1,=2:1382973877319010281536/25 qmul:12414356869/26,=1,12979259021/2:154116256470887483161/676 qmul:11782172818,32822292611/2,46218809976/5:193358961912883223899 qmul:-13859731454,7084622496,13548345935:-98190965247527189184 qmul:321169783966/82442472722749202597,728527457037/49184101549953208178,-116751888207/19107774656803205945:116990502994936318234371/2027429475212472071101744494655719619133 qmul:554171781160/81669314174466653821,=1,-943011129301/98221859405082497556:307106363034046930945600/6669876877727739897311710883496653900041 qmul:908239534764/8881960367460059525,321942265297/2978409748429418777,=2:292400693254215542284908/26454117343606783848277419057572700925 qmul:-293031348403/5516820790390895330,=1,278931224397/2151761313912895609:85867371146880370650409/30435311633289223066668620559015808900 qmul:766830499115/867319503385856977,853658890931/417340410748453263,960525534527/690526698684531078:654611673406576077026065/361967477793198051355224772486965951 qmul:-197174946287/216799088567900459,769225126373/927398327060743836,=1:-151671922975207062127051/201059112046164919860050113345820724 qmul:349764090584/42391126842026521,126613453358/49564405785108583,47812347985/3864181199117983:44284839369460570981072/2101091012486211034301711750729743 qmul:794966910230/98579318608567187,107830796401/4405388705587841,856324471442/41561939350641701:85721915042543174082230/434280216802727167073601578773267 qmul:-179910941947/302835045319248,=1,206545791527/3108222449901933:32367947032256804150809/91709064673510989994239285504 qmul:390922759353/8379914783143840,539029053922/2783352468162407,377026177321/4659432906395457:105359362565312633416233/11662128247327024341591580811440 qmul:-30764803124/12561782256971,-539449006376/482535642547081,580743800830/469238701287641:16596042476595060718624/6061507672904022859307951651 qmul:-569617603186/169437350142461,73746787167/436340763191759,=1:-42007468148734603114062/73932422674350728263711178899 qmul:869918621105/65172531895443,=1,489477033911/47131389526667:756758407345224551421025/4247458913662535154284166249 qmul:-8609389849/44096958877799,224885883076/88640280149647,-627519969739/56922930432434:-1936130238937915295524/3908766788675566748905986953 qmul:471174356951/3605083055021,-674320263703/7196435655733,32653595707/4448011615939:-317722416629289771049553/25943748239031977053085393 qmul:-321789321980/1418987991609,661459092590/3534157194181,275403065624/8396219756123:-212850472922042142128200/5014926619001395811627229 qmul:239520095411/796512451093,194140409620/80232450203,352671980162/687407449757:46500529435313022253820/63906145568388595421879 qmul:2337932296/15976804799,891988698331/936480654559,185442793337/376858000885:2085409185495046197976/14961968615928892428641 qmul:935302241221/78956895643,-101991808861/3724031317,979935584834/36290437707:-95393167413877147259281/294037952067632851831 qmul:961545851/11884552,=1,185080005240/12501042413:924570423575314201/141242576240704 qmul:58050869295/1757344829,=1,11607624876/16788707:3369903425905173797025/3088260848013039241 qmul:363276341759/9253851473,=1,406409104036/7111288491:131969700481801767214081/85633767084344269729 qmul:939766494010/411615661,=1,=2:883161063263847365880100/169427452380466921 qmul:95392761314/73563601,412095417791/369293182,-720870043827/236439997:19655459913964986068687/13583268146334191 qmul:-283241870542/75087435,=1,-46818914283/44014963:80225957228131087373764/5638122894879225 qmul:443163826526/66515353,-29122331797/35808847,186565142908/1472243:-12905963996518321847222/2381838098727991 qmul:-24774947444/1227689,-306928083461/7644000,333533328161/4876266:146233214169883088917/180470283000 qmul:113920584697/1429782,163887873152/2653059,=2:9335101167111804177472/1896648001569 qmul:90035464372/14941,-388195481621/80696,941463087781/51880:-1248262873387818796679/43059962 qmul:67426970975/82846,-112582136156/206687,205395396001/267511:-291964324111311925850/658584277 qmul:588160655449/37102,68128342139/34512,685450911404/43621:3082339259009843589647/98497248 qmul:106389170475/11959,10438395803/2811,-17763245232/3457:370177423523630505475/11205583 qmul:957920630589/1100,-65200663999/4804,-495801128911/3213:-62457061172743590465411/5284400 qmul:86819672583/656,170251645086/1615,-548605083301/1646:7390596041541820438569/529720 qmul:945486048523/580,28855850251/335,140898494269/717:940786338985841645837/6700 qmul:-942729414451/606,-155199725039/485,483080000839/479:146311345908972673138589/293910 qmul:581542707907/80,200631032151/4,19978821934/5:116675513727268918917957/320 qmul:122743007281/50,559800662157/65,225369102329/50:68711616751045272165117/3250 qmul:35327132396,=1,-649864145447/7:1248006283324512700816 qmul:308054644516/9,-604402431775/8,119532524081/5:-46547244066263391973975/18 qmul:3861743183656/92552781226942245973,=1,114427276291/73077495457803798401:14913060416513578545526336/8566017312842233033877184833269634716729 qmul:5469306927311/39880346228597657723,5296888632971/77121945726781675037,-3329987784143/28763591448200709046:28970309693503183254970981/3075649897407170819117742626456739360751 qmul:-4797915047085/1960347615737482622,7417719670675/7273127653602457926,=2:-11863196274329991106244125/4752619484897976601830464968970387324 qmul:1723762402189/606999775863219192,-7434692936637/9420435145331634673,-763069528725/1760517742915668356:-4271881385331661962366131/1906067340583431653778258276488748072 qmul:1247346376719/305242807686295279,-8174066739160/92487214707299057,864841572942/954533768467866835:-10195892530150517269616040/28231057092341186368611708660251903 qmul:8115256720883/749493161740626651,7922190030123/83578659421247020,7349631862907/82560331952121241:21430201962022657324386203/20880544567891147401285999555443340 qmul:1753584378376/56804157255787803,213889152627/40140349321665607,5387174104820/22251532318661783:41674741861198575821528/253348746130016489574409435021269 qmul:3381018621303/55670925159235316,-1242546983419/8405146979568516,2994898998212/76089681788376449:-200051166132548046722617/22282014688187220091206580424336 qmul:7888297086927/3953740879862848,2176178614605/2418237546542311,-2065888373875/9727383036996952:17166343426221456116768835/9561084644983571534390308961728 qmul:1741311395143/229412472933092,2666488500577/3024227444254530,9874403395326/1841428086863885:4643186811072502030497511/693795496698556358912507906760 qmul:6845501734987/168012430428203,3889846647591/491851863425965,-3888780746586/199780562527063:26627951974917556063966317/82637226984836948219538490895 qmul:-1284195095943/549849541303853,161668973970/13553314165481,-1448576168827/183855043551637:-29659214791201502800530/1064611939576677294763556899 qmul:-980146856483/7876738616913,817692682927/16494848113266,-6731998495411/30165003479004:-801458912740049493365741/129925607113876840407267858 qmul:369161816291/12273827592821,4261359385017/20241923902166,1173948411280/40404643959651:1573131170441574491911947/248445884122187978887950286 qmul:621724265513/2926458480357,5890921582229/3168077061735,=2:3662528893906004858368477/9271245983738877773839395 qmul:4707387599849/1922231158856,-798328469963/4676681253515,5101926004665/1755468911768:-3758041540110251059835587/8989662425544269173378840 qmul:9303566596976/14895662221,171128850459/80855092303,=2:1592108656909253425611984/1204390143793264984963 qmul:-1614421541843/173435332903,8142990982280/901238217503,804529656112/153754860089:-1878031436689446098791720/22329507182505589485887 qmul:-5960114035004/31883313095,1873973661895/29899945043,6761957056543/92101155065:-2233819344697646018194516/190661861865852447617 qmul:258875168272/22951320927,3271990041276/1787602169,7831605696304/53881261029:282345657506544241865024/13675943690173430221 qmul:-3741159259/841057,1140691661765/3674903711,117686209034/892146331:-4267509172076226032135/3090803490462527 qmul:20024244473/524834174,-9933799893095/4311996268,1282763801711/933012946:-198916837605195544613935/2263082999606862632 qmul:9690216301431/721938703,=1,6855538744648/1038547:93900291968519089052647761/521195490889322209 qmul:9772645191158/606342281,4046423002077/832945094,-9924558382428/71076263:19772128146319455948017583/252524914121859707 qmul:159522763697/46674038,=1,-924733338517/15943657:25447512137528901107809/2178465823225444 qmul:9885845356901/75377901,=1,5061603222137/99444337:97729938420561060068323801/5681827959165801 qmul:-3014509110363/533159,-6677531265927/3294029,=1:20129478835870717944501501/1756241207611 qmul:278495797709/459094,3008292413757/8715826,=1:837796795511188800682713/4001383421644 qmul:9263458041541/380854,-749140991886/18803,9474188106647/58449:-18166586768414575214493/18746591 qmul:-6233175654833/507607,7036736213809/354450,815399146191/197662:-43861212857395998672188897/179921301150 qmul:759911289647/22797,-4620304106965/4804,581754997430/2403:-3511021252485103785091355/109516788 qmul:5617203937033/39335,3723507511221/6193,2744191857630/46241:20915701051602548624947293/243601655 qmul:6420686828307/451,=1,-1838097053444/3113:41225219347195003296486249/203401 qmul:-230435506159/3050,3395048403224/1759,-7515243692907/841:-391169848615613583728308/2682475 qmul:9537534272745/521,8952214414132/843,5712074011478/809:28460683930581916956810780/146401 qmul:-7519755017367/994,-1817484841018/15,5714574669259/496:325405732196037376760943/355 qmul:-6778271913655/47,1098941771956/15,59404867523/3:-1489785229518322546491836/141 qmul:-2383271627938/37,=1,-1307389832067/19:5679983652534244702131844/1369 qmul:6051325942003/3,-2529633865827/2,819845568100:-5102546345349420428543827/2 qmul:193126426699/2,9833682493639/8,3235704083583/5:1899143961289011867267661/16 qmul:92112640764600/11163413455400457479,51791476178419/14329005607185776493,-13205225377669/4458612884103206586:1590216546630349267393055800/53320204665922099816203131218014747049 qmul:22529406302098/17968547726331516709,90921027222753/2166236440992021142,=2:1024198381852757628328617897/19462061438241829125530785318127130839 qmul:-53737977727933/7683225139372625170,82909671587883/8352188215577205409,=2:-4455398085219896100673435839/64171742466694571547497029664653544530 qmul:9092501686631/9417724412639248549,-76436516279586/7751295678592549727,5796309029559/364193213335723936:-694999153192333594154414766/72999566541866165880702093299195096123 qmul:3136955253055/79379115811095793,2712229195967/40950870811518088,74321528780980/800208315081442781:8508141623777819670429185/3250643916712716666840937120203784 qmul:-15679427832242/304946032535805217,39088311244217/271842618581639769,-44522979753228/676520091746633939:-612882355237913950168644514/82897328010615208848930336644874873 qmul:58297984629025/79211523461014146,62851948787804/71793418809815961,70122280069093/70263603402410591:1832070972167832036692205550/2843433039200075640773122338792153 qmul:3395759457623/8856655409516280,80356132877828/35186041698707317,16595221216126/25184750109463717:68217524549473731850570711/77907661637580389256034066655190 qmul:25595373885269/2107431405075994,56934769844557/4108548181624632,88071750654219/1721697405597152:1457266721243175200282130833/8658483467223618408882342284208 qmul:5741950765088/69374989603141,-20852939430084/837468342763903,71732839501654/4900087435552233:-119736551514904546484107392/58099357572205493945030219323 qmul:60636029091157/828828822290712,15933414624847/515795094226125,=1:966138992713689089520177979/427505840490766008807415251000 qmul:68154525908584/447018537159783,-53054791972077/814484661933752,-70920570409331/22166122764311:-150663508084810679482608707/15170405921529425529107695659 qmul:3803110014020/54088464597551,8401206536763/81355553929736,20928341840506/38139684449589:7987678177453412143854315/1100099249635669192942919134 qmul:-23763903446216/81519641545907,=1,88937586611085/34349668275946:564723107001076681204718656/6645451957773166616788452649 qmul:46601565963875/3780648692562,-40570846513055/430918579048,82143257528821/7547555659366:-1890664979988380613845888125/1629151762478496046640976 qmul:-14254006674106/532459447725,51813993717043/1845962555644,5112664309595/4080729032211:-369278506127408636439494279/491450101449616910854950 qmul:18869803536517/528732466966,25637726635604/291934133291,-45103838882314/248345183985:241889432368388223683175634/77177527243265749182553 qmul:14394788665063/18929691934,7293379245648/106206553763,-1412717946745/2868209191:1418738552638642755032376/27168342487910789833 qmul:19814466847315/45927017182,31387249087211/83776988054,866410007468/44667970667:621921606466960354656188465/3847627169812266743828 qmul:-84789189148688/68506660259,-2668232889482/7021853339,31544016021473/26570873119:226237303159039621969299616/481043721083397754801 qmul:47144909009231/2853410746,-18254711672997/1611442139,47906136756089/4532570474:-860616720813190565726435307/4598106315979825694 qmul:-88984055558977/5497567684,-29028728538235/9008297936,22366306780529/477338571:2583093993052764435041985595/49523727620797500224 qmul:-22301781837379/314747366,-55932418652881/999474189,6168064682011/82717920:1247392598433499880191838899/314581868372736174 qmul:-69455755003925/425627363,69330030826593/45004450,36456142539195/445137553:-192614785420256450548375101/766205015070614 qmul:43441277702263/29813565,11503955305028/11366299,=2:977977528532569481665124/663150477585 qmul:-63910040173409/12354709,-70800414587599/73292555,34497242288193/35625551:4524857340587464687180954991/905508188891495 qmul:-7828296754760/3568223,-2036289302690/840627,7170972735213/4627145:15940676940000630338304400/2999544595821 qmul:21326380201837/9337727,-17663536047163/4880532,26768558322470/1065127:-376699285450651185091238431/45573075430764 qmul:73980502263403/962358,-21947232844793/591723,21986948107511/9185:-1623667309149641199103010579/569449362834 qmul:11206027962511/331874,-1256483151365/547727,36460011888012/776539:-14080185328620131358477515/181776350398 qmul:24401059998574/37451,=1,-59473261910475/49718:595411729054008176882033476/1402577401 qmul:-60818257728179/86203,31465212303166/90637,6184562112579/9476:-1913659391325818531369114714/7813181311 qmul:71004965949889/9037,7059443197743/235,3055009450153/4139:501255523880917233655900527/2123695 qmul:39294675031972/2789,59869119724423/5716,9542643866131/1571:588134401005356710838563039/3985481 qmul:-41787574848379/366,64572657701526/571,-32471089957981/546:-449722461143545734347821059/34831 qmul:56523234971544/89,91170129020768/233,58883776410491/503:5153230625026852353065025792/20737 qmul:22661601391845/32,=1,9300929081980/9:513548177642871241232504025/1024 qmul:31371000692905/28,78617790969393/17,23430144401503/6:2466318774975488254647256665/476 qmul:-97166077882733/5,557907250924,-67696293193377/8:-54209659394622846477895292/5 qmul:49131886852510/3,44123944198873/3,=1:2167892633865493233459221230/9 qmul:11078630778023/19971767689676985138,5498810148139/653213547400621899,-28047430739573/8529087351247312093:5538117031788903405049927/1185984474585002385862227360780030642 qmul:225961652216941/7065181247481573942,-551303465095893/52284679786625043776,12334914241622/807684136438179561:-41524480615330881905534707771/123133579719680720019267336626376961664 qmul:-140752952779551/667166575947606995,=1,=2:19811393716162513576803761601/445111240061654052498343266972930025 qmul:97203673992431/3238422544888880032,=1,810591359275652/4195094984894633475:9448554237626806783045289761/10487380579244570205870590527288321024 qmul:-167516702376095/716105586249718324,97868227848619/242920547738562082,=2:-16394562796592961287264362805/173956761250425686574425765286990568 qmul:-709927885497849/861328058843025997,496445275118167/289296738986245691,-290819441307632/13291786866431071:-352440344430038207159099322783/249179398620640561552626620942228927 qmul:425323787423127/77722671910833479,317441925005700/19142048058380233,=2:135015601830312569987786823900/1487771120942893870562005728220607 qmul:268865886927957/35135976545503325,123771762953727/25295982530865037,276904755282677/20891637935797169:33278004823190660692373645739/888799048899935778999904809748025 qmul:-28086740887571/7601230497184463,100947908107803/430543690291880,118463785601217/2540243084118529:-2835297738166190579370816513/3272661829016980468206671060440 qmul:-103171508624837/2023211396120145,142320636082678/1434318582636373,-735609507967093/4547494153253362:-14683434733096301226416273486/2901929702056803783817555034085 qmul:-220041868728731/487356763210567,11401923921896/63654265331715,-621742292531267/238183796053545:-2508900646876817363255193976/31022336716611231326648232405 qmul:500876116381607/333341742549014,=1,236931212585485/143461697112113:250876883961521120142447902449/111116717325613130586192372196 qmul:27571394309122/1874139359093,126354562695342/663284435945,=1:3483771470829951376257509724/1243087467678324311797885 qmul:1227588316119/3212397849532,273285780765847/3937050058645,177000179976745/33792263075573:30498402857237483359526163/1149761012899184771436740 qmul:935605828517486/1504497672649,142177975023733/2313039446120,394962145699157/847510134854:66511271059509072349527747619/1739981231716436016585940 qmul:848730874297608/1142939979439,56376353318381/3143925208632,-237516636617763/1280813501326:1993681318400848339723780527/149721575554650494388227 qmul:57281039318273/114674810495,6245708686714/18061176617,39223096410155/17868534091:384275708758478900851262/2224663808669387965 qmul:-154031591323851/83034647227,983277618862577/807648489169,313967727668057/230581524944:-151455816346529785816271424027/67062807381567445384363 qmul:-926888573138874/48704635267,6005840682571/273079429,81726441309104/13903294547:-5566745100767635280134365054/13300233988365622543 qmul:169804184361113/49086554885,384285590061633/44857652581,=1:65253301182144623556398477529/2201907625429518408185 qmul:-225793750988921/2498217360,=1,171352487415765/2208376327:50982817985646863065464744241/6241089977805369600 qmul:-929534096793899/9204730148,8408973696/70382485,=1:-1954106942368753656070176/161962945392664445 qmul:-27418637405473/910326852,=1,81707725335094/491085905:751781677172803165010353729/828694977472229904 qmul:-223297515785450/193612253,-474964608127809/679335356,=2:53029208540474751774311289525/65763824408858534 qmul:3933126433661/878772,9000930134181/1427513,476332935917525/79251326:11800598746094380908355547/418152818012 qmul:703078612387607/27834381,373006385325321/46624543,=2:87417603935414581043747898949/432588431270961 qmul:28193205330738/1040371,26659473685633/1938099,=1:250538671876152577201295718/672113998243 qmul:449065926671750/1450887,=1,153785599009868/2460537:201660206497557548032248062500/2105073086769 qmul:108938909775878/133591,917154127926373/709564,=1:49956885396372608707157715247/47395682162 qmul:987814971089463/782828,=1,930147796775719/981962:975778417108476622509149628369/612819677584 qmul:175113052851196/12305,-227591234473631/6533,64742021370129/15710:-39854195870849886350828812676/80388565 qmul:-161174581471221/66310,=1,=1:25977245712423255688851230841/4397016100 qmul:-1469325465654/4457,=1,582669979881900/2099:2158917324019343933647716/19864849 qmul:102435434692175/7466,-187593100206263/1358,174025094651948/1265:-19216180764881294058412092025/10138828 qmul:489625099725000/347,-332985825161621/684,=2:-13586518154314174697304518750/19779 qmul:-832879871119661/546,=1,817644952915049/828:693688879716303117501780754921/298116 qmul:810059612480081/97,-378237813607713/41,=1:-306395176716377100781960464753/3977 qmul:-534858850780477/21,-597970346506983/25,=1:106609910777842848826760190297/175 qmul:950469485177429/4,=1,423712356772633/4:903392242253446925539611050041/16 qmul:463433346779246,599836163536496/3,225455874511593/2:277984080786941465486776362016/3 qmul:2132350013169985/49772441764072596049,-6499905025666569/10288915167781867756,-272858606518027/93421129408183888508:-13860072567083760096603328731465/512104431003906236530336497276926096044 qmul:2042725727410133/27578306884656676115,=1,-7376907052537410/47153921627935428199:4172728397423256990351591077689/760563010624301820302156974840011493225 qmul:1904035906025563/789989122373815219,700724530060177/1554126856272208244,-1373172495932670/1505401488389199241:1334204665467465969877290304651/1227743311244058254809898816344465436 qmul:6705450642041083/4046641113087645351,236666376333371/9320552548004534960,-6289242797407739/4040540787026624125:1586954705134139142713085880793/37716931137448960379165612296160970960 qmul:-5772878945452494/146823071716041731,=1,-1872446183124785/135874056483712011:33326131318848699195882410820036/21557014388133933331867562533476361 qmul:3589764099796053/928994578492406984,1705996612666706/892580995601505897,4870605263289071/654751374199986585:1020687565754102262148510551903/138200484296525657161313541766664108 qmul:2824552679707636/22642111815107669,8553369491681540/46601368890320207,-8526667827191440/6342142386526223:24159442718258634195461218239440/1055153405151710120834997591367483 qmul:35430767900375/179014168662113,8330204183383419/90063013345106792,735637729618171/16696810462910716:295145530984190781866218882125/16122555461179081195997749371496 qmul:-749012909078762/116545251178673,2437513877538073/992308910607094,-4884979809735527/4653837505135631:-912864680167322642003505352813/57824445616769571297747653131 qmul:4715463621576807/1060495506862783,-1063435887535687/201313562930691,8544123110589389/5820955775073193:-1671531080517925550574808003803/71164042986178638246892124351 qmul:8571923230143950/770828515798001,731727930435031/3506899807300,-1965908269773871/252650249852419:125446312900823969405125054249/54064367470267094252504146 qmul:9586220341682297/144114066713962,8236658921505002/167483669474359,492069171252854/82950316475131:39479213650415110088905890174797/12068376358063466929473150179 qmul:7229812835375017/5756294662713,905126544819761/4153935003623,-5202620176105898/3258193118931:6543895511376548680891107310937/23911273890611781218009199 qmul:9842204333944723/52899600131954,1723939662409201/39238775342850,4378255309793533/73130188348848:16967366416823040750958140596323/2075715525304341221590428900 qmul:-4908316732166843/1357513064850,1991070604269898/8806978369757,4254810663841145/2351480888682:-4886402580931743595080769296007/5977794099398240809870725 qmul:274318025224231/1931992361708,-3590098558074758/5846677514951,57908255856314/1134380359933:-492414373405713403344305530549/5647868150127621484948154 qmul:735894125946707/55761889279,3377584488978728/61428633213,=1:2485544585328156063980584648696/3425376643783608023427 qmul:-1690249237930933/34238968152,3446531515472379/225376230292,-428431726758614/563113867237:-66959738707265887616299668961/88697121507880524832 qmul:-1626151698227417/13809511809,3803324818338850/20014571999,8945616470363923/70396608712:-6184783112252203187079466250450/276391468372271236191 qmul:2032027608247493/71600869449,1568676792624142/1225766355,6648151008356102/92054212485:3187594551029383836749262776006/87765936759331588395 qmul:8570254081381348/584635199,833484957898327/779308020,=2:1785794465549524494136774551199/113902724838748995 qmul:-51136063956207/124926985,237718332836713/43997825,=1:-12155979871501058567713827591/5496515623807625 qmul:7279740565485383/495827506,380399580451240/42684993,-8253225185096257/179789767:1384605128452256161054382112460/10582196811408729 qmul:-3582542718233341/437814906,8075748423185005/259890457,473970333141547/96599174:-28931713707765825242358002251705/113783916001752042 qmul:-4332079095957017/44663887,=1,-2662542824998505/6313513:18766909293627765704435111538289/1994862801948769 qmul:3371800081330173/11806858,=1,9890158011622886/66900743:11369035788458161257397040209929/139401895832164 qmul:-3682944955162964/2466265,-355431368138229/155860,-9055791203817172/8090387:327258541047840188915493337689/96098015725 qmul:7504952243792624/7720459,=1,6076575545940466/7559395:56324308181607941582939516805376/59605487170681 qmul:-538608400556109/199304,-938340266223845/397242,-646694290244130/361681:168465983322739554802492073035/26390639856 qmul:-727793735158436/238619,=1,972430738127054/625301:529683720935867681422021966096/56939027161 qmul:6931913813817249/19931,=1,=2:48051429122190398233188769928001/397244761 qmul:6291923102424872/90007,5686581845796881/19366,5042254583042820/677:17889767844699633282716137212116/871537781 qmul:-5554695053757275/6432,6945167426101948/8185,5702999642802475/2694:-1928914357464231764593229833585/2632296 qmul:2346204224991933/394,1993188578793011/992,5657592821492399/465:4676427464769828756406351780263/390848 qmul:10931191773819/59,9918357253026368/565,-1883501998767878/147:108419465214079847823899059392/33335 qmul:5137390097848632/355,2441231132619748/159,3483872315060623/865:4180518882426831300124305994912/18815 qmul:998295698183777/66,-66459889053732/5,-7667707076954093/93:-11057770224018624245927284294/55 qmul:1731949876588457/12,7146744265770853/16,277946983627531/22:12377802849111091588166946843821/192 qmul:4833330269678962/7,=1,=2:23361081495794907533662545397444/49 qmul:4819457078692447/9,=1,-8437238110144547/7:23227166533358735275059214847809/81 qmul:41244630307260683/19566167985724232189,-19443176533044379/82985325719207603055,-72237473765794569/82811331956111155429:-801926628104221886667557960850857/1623704823372057546563828915880965737395 qmul:-37802618179190435/86632766813453833079,18052713986379148/47810592068654841423,7865481647337074/9519629220475921943:-682439853925221807159327605049380/4141963873896940191789582700970256831417 qmul:19604614792857791/565916848676700071,25954734261578645/2626241461504040026,=2:508832567249237638495290647473195/1486234291758457454242685700381041846 qmul:-50232902667050876/443948998116187511,-43501226416110749/2403446154007360893,1072605872716961/3220822759958359344:2185192872457833663604613633466124/1067007512097771979528373151836407323 qmul:-14994187874938337/764476959662103704,-33213154437024890/559246869916170493,-82827329689594088/466257548265395579:249002138774046516984579242103965/213765673407031013718036719955403036 qmul:5736891872168725/77162101379651687,62325478498146677/137153821651647001,-18320014200167058/208017523087093295:357554531025044304704709142076825/10583077090891052476054011258140687 qmul:88925222453111571/10971132513398300,-1434252874823377/1536739410012178,-23821379824785146/29460096443622911:-127541255947683583837180699995267/16859771705805127088751164497400 qmul:24175746316538219/53267154590314585,45382600351882515/10887587811518971,=1:219431646658389958690970919068157/115990164614361176557282717098407 qmul:6404581190281274/1974919158789793,70447714998202471/6402341997956028,49530122164311697/8312624539331270:225594055187891770083262445914027/6322053936443940716188054611102 qmul:92136543904285079/3155539462802804,15181471002529652/4087143424836463,25144211605663718/418936831080179:15204002929958740164475777811549/140186330078331141119949106981 qmul:-97970673283608013/593909853478849,56972616762762010/241259986786383,19037324141894916/620131018874825:-5581645622976766094030156047986130/143286683402609773344371713167 qmul:73158390938899175/379989099030207,71464686184078751/642455545049147,12129094284454088/244856744399541:5228241450180579956236327448930425/244126103730185933897852583429 qmul:1586267657723262/7744841531795,15363089519026552/9850991413231,-22902559865915557/6801969550956:24369972026739044413538846052624/76294367426547369870179645 qmul:18929755299266541/13128569349373,=1,-44651987164496438/25396774874437:358335635690109691215372562104681/172359333161296196535493129 qmul:80561540824410061/2163952339904,=1,2086973582459110/2490108327963:6490161860003088890959828678023721/4682689729375996750729216 qmul:78697609896523577/5434699087585,65526206295867334/2106565485155,456371042378372/32324922977:5156755821071294622615308595133718/11448549520109931362300675 qmul:-47473161024846652/621907871141,-96761692332772358/887316304237,-65934541786023949/449412506848:4593583401150371824007100974445416/551828993796732548324417 qmul:-14783030669421870/467861289269,=1,-23413922007662121/167402876249:218537995773067621857840034296900/218894185996450894554361 qmul:63487097677098051/89903303933,-44532336344734228/31521473625,40321416288169527/20383337494:-942409595769175172584041963929876/944628207908139422375 qmul:74416958364864933/47087590129,-26664478457249131/9883383278,9944734731289232/14129955379:-1984289383173946522947645546623223/465384700882276462862 qmul:10292005168487623/3482492353,-13044085486904942/9174614883,-10587235554824230/4781845077:-618662650918986430811618914898/147237447796163547 qmul:-6144278338130361/94748822,=1,4769179777732015/4767529558:37752156296417990780857029990321/8977339270387684 qmul:42358656711205552/153537321,1887261908080343/399926027,=2:79941879288510016603861603664336/61403570783753667 qmul:-46666950687843206/336186639,38668781410567001/444012970,=1:-53075121036644655437487007224859/4390330236961995 qmul:37185667641742945/20035026,-22282077470907101/78670922,-91228561955942315/41271552:-828573927200719662619441817152445/1576173967713972 qmul:42236447866339404/44996449,16229676747835589/11939847,15179360621924853/92208979:228494631949166233448275154749652/179083572201101 qmul:14470604449517903/1841454,-26915603513076747/6747551,-30708091604466747/2448316:-43276116884198675180320043277949/1380589419906 qmul:9101509000956136/4152121,20427468979289790/3465161,-3271799016139078/320637:185920792781758275773092222651440/14387767756481 qmul:3901016944389149/228999,-12417812802023553/360344,12000955177317426/2675:-16147366050982125724725565208799/27506138552 qmul:8669125566587600/469719,45940493589390645/423401,-42531240992326551/367483:132754635839146726987952004334000/66293164773 qmul:5938430877112711/95612,6188074245922706/6253,=2:18373725585926676351062678057983/298930918 qmul:21515481020492051/20064,43874545790741615/95584,=1:943981957243410623387527502402365/1917797376 qmul:96468586146884551/4608,-79928708129965834/6685,-48993051068173945/9779:-3855304732922400319985402586215267/15402240 qmul:-75478054000012419/5456,26589933777011524/3359,-72036212797226203/9505:-501739114369507496870468176529139/4581676 qmul:-72899856135461282/473,5291266619094049/285,55496817136408/17:-35066597755120434743929959646438/12255 qmul:41749939409527385/879,1093119177525389/32,-62509807806005818/473:45637659429077399966594328277765/28128 qmul:32236549357972163/25,=1,-8149826384158677/14:1039195114508975474515043482898569/625 qmul:24629347956178358/19,54301261705267425/23,24457116479256857/3:1337404668998534392792361387388150/437 qmul:2790015469580797/2,17009277246386333/5,38190184436799791/6:47456146643806530617054620047401/10 qmul:24781556873646101,42986775647721679/2,81575207729973183/7:1065279225528679999746318391523579/2 qmul:515152885774965653/15080197507802975795,=1,-424832628935135224/94106513082678027465:265382495722274809438289573329716409/227412356874347082213525456257355882025 qmul:846127691843273154/45393076460118791167,107731662129978485/4427725736529596013,856145822802565237/90388573766016577258:30384914205492685300912483332697230/66996030967574580526139479740140939057 qmul:678813466845095843/4312328116586154098,456413709574125389/4100698962952630264,=2:309819772511642767874990940604657927/17683559435596311365398737033122421872 qmul:189404516219742695/1881568644309026479,-990060962742696423/9938184412328540522,684558164600705533/1843391051573289937:-187522017676333112700620971556879985/18699376171598111009073165236722482038 qmul:192924629174279610/915194634829559941,-505412960023216745/330833788805155829,115339652249094077/577677115897920453:-97506607892354095477504410264069450/302777308534814344556633116001046089 qmul:530864983303082949/770272174330693891,=1,=1:281817630497382538228809007974536601/593319222548134880807536517544719881 qmul:175427266863787420/37379184998319363,-737495252249552281/10171255350907481,433186573015158365/49314816010026687:-129376776427158427582783706960105020/380193235426716462103801903854603 qmul:463395468161836969/36199229685681434,-381172902361185896/73861948752008031,951086817685754053/44721463664985715:-88316897770133955247493298327094612/1336872823952984931159738037798227 qmul:388421361132459241/3796589587440279,-520242627647240191/4183488460948680,=2:-202073349549868206476119002444555031/15882988730014316745493183881720 qmul:255643017739843159/5399110517536783,649866517463532383/2945752280295836,613430013767040536/234544931788503:166133837652459903075867976537517897/15904442118603209765181251735588 qmul:155181948901437661/35620018080307,17101221587255570/264465563715517,-129836961434774282/466340126852825:2653800894505656514308728430021770/9420268161165298444608023719 qmul:-839143559403582175/463688071748743,=1,-142780189059606272/172165382315553:704161913288513246519800221977730625/215006627882067436250122080049 qmul:346621266229749718/59475689434557,=1,178397168700747228/42081103836349:120146302202715032285390908921079524/3537357633715875158385786249 qmul:-375320695921875535/16168337083266,911110281599467718/34637020854445,777071986002999094/76066266020689:-34195854495148821384333396824647913/56002302873478088643121737 qmul:-379308371310412479/968244496075,364865258770202694/8926182578765,249116584254479273/678952630517:-138396447051877776676786583577018426/8642727152849761420847375 qmul:-10969933869374653/142543298333,=1,395828837569758458/4480744606673:120339449098453146428785278870409/20318591899650640578889 qmul:357124791031669775/761802845389,917629329624700777/456858033563,774468512475077245/2887603961:327708182586752487826277715049915175/348035749907116661791007 qmul:64954492028958167/95392360685,985096782515221787/715883047223,-29344192999567326/73661198051:63986461107637310581155676549984429/68289773848973303627755 qmul:23618182683258131/18112927883,442655807275151908/16356517261,=2:10454725722029641395907751401163948/296264417565537688463 qmul:732585647194345626/45048543997,=1,16467867097466398/1145670835:536681730475158241367430266345331876/2029371316249644736009 qmul:157646812856286773/2982936935,123752181092126225/1627719293,-433800406988365539/1824179539:3901827386637546694386616182784385/971076799780357391 qmul:18335836145139783/1476948589,=1,100294147058610519/4053918910:336202887141414537392732609287089/2181377134549090921 qmul:-500900480985214557/585315200,=1,822543455056953279/726431948:250901291851219289979222443324706249/342593883351040000 qmul:5430413424253854/29413111,737754500982617905/865566667,-431507384954955136/126635381:4006311945939711393067198205655870/25459008454371037 qmul:69732083733340845/57018307,-850680479702859385/88346816,101371097024811051/77572577:-59319722440958347782449205312080325/5037385877160512 qmul:935028252174165503/84545212,137808471873317260/91516351,=2:32213703647625121220176793216620445/1934317324190353 qmul:350565565504682243/9619524,=1,=1:122896215717617656580228756399511049/92535241986576 qmul:-470988077361736572/2840381,624215376275621564/9300947,748400046271858043/8643413:-293997999931687952811725899730638608/26418233140807 qmul:238657877711036557/147228,760003504393876182/402581,40545524725498725/11806:30230137235265489411523617722264229/9878532578 qmul:129309397398813154/103143,99499262875055329/104050,2865516124888405/1398:6433094861999752891251268341498833/5366014575 qmul:576594622826994119/24550,764054211007945383/64450,196951790705325699/2321:440549549615502846208286120014202577/1582247500 qmul:34307832224344795/5419,755936660033161242/53857,=2:25934548104649265347571596038435390/291851083 qmul:-28093068552310343/6519,963611383601696677/3318,306035391422838526/3427:-27070800657309083458092703055830211/21630042 qmul:144703609571824207/1943,353612545017871990/3809,419690158507626277/2547:51169011653965259593108361509261930/7400887 qmul:533530159200500829/854,84950875994057867/97,561763750303203654/161:45323854393331697896795654407471743/82838 qmul:786023983959036523/653,=1,35801962841884787/949:617833703358835705221613270447929529/426409 qmul:977510365280960078/55,232111556352335897/28,846828806350115358/59:113445726117952006128263047051659983/770 qmul:575356062531111409/48,127909051677869039/2,331562163778887361/52:73593248335467179491251257420765951/96 qmul:223865459457586997/2,-255265991273068741/5,785308709687044221/4:-57145238420241926425388851168760777/10 qmul:-89489266878597587/4,408356339430510509/2,320811062710131617/2:-36543509440864137915495881385541783/8 qmul:6960121193016437767/41673724634003604035,=1,6854483270886536984/32457251506686121265:48443287021476560949924862262183946289/1736699324870758821080322609369068281225 qmul:252294933101143378/671664801173160007,101031884553475048/1683990887624654527,6217560315186323017/75520308794957242947:25489832554501428241776271993432144/1131077404713826819460225518267901689 qmul:95022283125541691/1892238412758904932,6220850886629533101/1296487687523964914,-3552806481592836635/292967787422034901:197039818077029516749136819680004597/817754601333936827050096136476518616 qmul:-9650628580381886023/7106748638657239958,4387498480617035975/5131806125901481009,=2:-42342118233424867760904547954540677425/36470456199103234725545247832492957622 qmul:933857454927346529/770907817024018505,2627554012834724721/741765905423985850,939220528406657553/251830131719517146:2453760903109972444306223754689843409/571833134893249499170644981258154250 qmul:5863194086945812212/700078829279068399,9185022137361371361/111682660170098792,=2:13463391871060894578417924384075215133/19546666495663701071851276388818502 qmul:-1393200667079143151/45785790746761243,-6119736754307708291/97236710970831949,=1:8526021328450249564289054954738564941/4452059701413814892014912979352607 qmul:3607026924237321910/1072023164691893,248422707771439167/17526050077246094,942295846706978669/71124490430949583:448033697761760632546411047280624485/9394165834178976731308723857971 qmul:2219105460493025188/4992146804272097,-654894851214548365/261880809182257,=1:-1453280740378971565345857635989217620/1307347444659395118592692582929 qmul:5112830206310124118/4808519639244359,3895059152513717718/2399893258942939,2005821980379451972/672164805197423:19914776090336848562178934098195722724/11539933867717270078741058631101 qmul:4465488275906636401/885680900323781,-1104529468377254183/50717559226303,-1531096850412298649/70636195562356:-4932263391432018452889201367737315383/44919573517776726756551611643 qmul:5805379505512562993/802580360628120,7576393837591505509/381671212464334,827391747551350507/404055288015098:43983841510445403745585851020069028437/306321819340996990853337472080 qmul:1568069089872115495/10344068691049,6482258105462122875/51585142886372,983293776583976867/13619011887634:10164628567748134676970172369881448125/533600261454209647780484228 qmul:5123357244469621862/61996475985149,784192904118738215/19232930497666,7315968239528825344/72839297342337:105728957799431815835771283411022535/31378260887436578268293743 qmul:310186678678899798/454385367511,496289849974746528/1664255858611,4370884482132758378/6990813743219:153942500225716088309659706960401344/756213509947294088987221 qmul:6896960984221904702/8037366999007,=1,1507716158461831143/4162951083794:47568070817879184399769535232769708804/64599268276726789138986049 qmul:4124205900530951507/699562645532,2446863765306479999/780453290054,2180063751257648537/428993105150:593609998745433301395350821902024029/32116233429666446066984 qmul:1901990540997243863/309938083197,1828919653744696177/128932373995,=1:3478587881666366604445148811312811751/39961052858049029262015 qmul:9909007556102284175/35699264171,=1,2257564478754303350/23996542561:98188430746892162461878914652455430625/1274437462350844317241 qmul:7540576467990933273/59047654891,-667411621026349909/24648144492,49933771491922816/70442999897:-1677556121324992297591622679189540719/485138376555706170124 qmul:7181294574913207518/3819238427,-5066099946607930227/3123415729,-1161733643221201723/183317684:-5197308008934802800386778397102263798/1704152767956145469 qmul:-8059696125757072209/4595320696,6578165258606498110/3168033531,=1:-8836335508230093636747850255982004165/2426355008437709596 qmul:1945331074426594741/151710177,23896636516777288/9647063,-8779812176082283037/763148559:46486869590364160149493061329042408/1463557635260151 qmul:-3667612169703754992/456403523,-7174409726077474195/172294113,3512697218966135831/927221535:21444948999024227916663287692324720/64087726296137 qmul:2801308578321040429/7008589,40646058755682747/3928091,2242284013880005543/86049101:113862153067235113557787361284778463/27530375373599 qmul:7755272402005383603/37065862,7920705443805205865/32575293,-9791686678342842374/5250627:20475742777585438947450807922570143865/402477104982522 qmul:-1833317998287765958/869351,2549513447231770664/4194999,=1:-4674068889686691615296143605162256112/3646926575649 qmul:-9862573495076415071/3231099,-1012500145079952918/2881015,=2:3328619031542189525129501104301875726/3102948228495 qmul:1848318375383620325/62739,2496061735601929291/71058,-3577860376337084987/826120:4613516772004977608237698310240439575/4458107862 qmul:3935629218278546095/380289,272948451544220369/89992,728063154313892053/11066:1074223900981319628581080745604409055/34222967688 qmul:1383092141504746774/6843,9725813952719193095/86512,9563731803386892083/450:6725848423871567383357583818792162765/296000808 qmul:4310844810185467807/68701,5335008431625026234/79247,4165066621321185249/74158:22998393409766456521092748601937448838/5444348147 qmul:-1231083168271826293/1767,2942557339085135869/5628,9747542072617181491/4658:-3622532811822443740742409486671603617/9944676 qmul:2563045864459171017/1901,=1,=1:6569204103321259248191885398852814289/3613801 qmul:3519211776742706458/741,3845395982348454948/319,-5561268787397081165/773:4510920942439923739354839714733884728/78793 qmul:8737995292054242122/619,5446863961283262201/940,7037490695241026988/493:23797335825076532425122443838432315261/290930 qmul:-6758789406646036953/11,3116671878311801932/31,40838395516557640/7:-21064928875125413266537275696088793196/341 qmul:-2984260832879482631/3,-2187683625033562767/25,4114578793904862147/65:2176206185639821933770592463208266659/25 qmul:228695312943600692,-8259900599013409474/7,1324126718913604639/5:-269857221767772356131493369277965144 qmul:2275696080893255434/7,-1435737280894850537/2,294080994708276309/2:-1633650851662375193596252292396534029/7 qmul:-84829337473700364773/56707961321161574960,-29927022646809239114/25185347367370413937,=1:1269344751844627231939227965424189665561/714104852184429966256312155357027108760 qmul:17614709128893699831/24236675989376645657,4599289230585863713/53851416063001125139,55430594239089793855/41774891940497902166:81015141996423294341239778695297132503/1305179322688071182919814999640717871323 qmul:67846551326033993002/4393005431010178629,-25740230532097127103/7368476450475338660,11432245987550154811/3453986965906439686:-41580615998568452669495076840090631743/770708501552589672691163995377845170 qmul:78323538212378809869/7187022102980425966,=1,-32829495858735303110/2068874202909402271:6134576638105963615443551925372851797161/51653286708729184578994636138807033156 qmul:12686256534955947787/123247933988654253,81930708153077686114/345994724232647617,16126072813581949987/95957301898986922:1039393981720550346819611040155758929718/42643134932647985540794888997365101 qmul:90635825716321359861/838907685684947420,6188791645900690243/226601399055279660,-65993207203297829068/942167862280779399:186975413670826858643911432008098178741/63365885084811963416497113498492400 qmul:4256124534146569459/8100972293435918,-36362420289668860861/78362919838311158,46047806868639334273/57305818998350828:-154762989115808645716121851999543044199/634815842442898538160822217373044 qmul:60947370495538663/3595354440833372,20498068986391916397/59798876860276456,=1:73488435585690517250320078551597483/12646950439790760312580408864096 qmul:57111050113208289287/8750146592672703,95339879919848747558/9349828098304853,63474468255902925315/5956909304899564:5444960659889742520776395286830698811146/81812366476457707866224945527659 qmul:31476714111665882746/1411948296801679,=1,91546635306734179873/2545140299680338:990783531267546121976022657443420500516/1993597992841162212620657219041 qmul:28478043672580107559/271169292774531,=1,-12639098468391030777/83575724512750:810998971417379900383655158076008938481/73532785343839310404002269961 qmul:97963124075098523020/223158531052969,=1,=2:9596773678553147851290017119785469920400/49799729981718929459883714961 qmul:38023234767709122291/95410827766256,=1,-80027616607132061503/68758430907707:1445766382200323790987914636817593088681/9103226055042166894572257536 qmul:-6852061478866431364/19230239212017,31234498342946092331/39453881908226,=1:-107010351453709150647505423887409134742/379353793468927863275175921 qmul:33119990811859699401/1776514189342,65254455762623773903/8901520474749,11459125607986399870/8150100596607:720408991763668201816403420648589510701/5271225810036644905308386 qmul:27841303391142022233/8340519171100,=1,61584898160284417471/4425828128209:775138174517616267035460754520666306289/69564260043486631075210000 qmul:-78679695834397046203/681862256264,22320479732932316543/573216980545,=1:-1756168556264938480239345612201392236229/390855023683251092383880 qmul:25675370768619544394/174778199339,=1,-39853005701576084539/982343364060:659224664106082973870755584440136827236/30547418964183220036921 qmul:-24756905032793568159/99453729989,14882817849764444595/70923843844,10502311373057494209/91914989726:-52636072589569046967201515845844521515/1007662973634739405388 qmul:95117421914973587797/80826708744,-23193036682039936606/20563195751,-4893123371481302110/94686383639:-1103030927787525886919861317615127598491/831027716905967673372 qmul:-80983109490183607947/8058699274,-15405016985195778462/2629510637,2177028333237582055/2780215797:623773088605123959908040865328237318757/10595217730683588769 qmul:42899406282841568991/1560723895,-22471941706408087493/1005041792,22818416959151070688/2105105663:-964032957227532597560482503451723729563/1568592740248019840 qmul:-10792553451566883852/995956003,86483521167692451511/50100662,91257203536302258983/95707725:-466689012441018414437879124662439450186/24949027536586993 qmul:66678150407960284786/528696663,496074447844907103/89728426,17869991738879780164/44060669:5512887774491427594627575949932372493/7906519900407073 qmul:96591001707842941940/16266781,=1,26004126355523142571/17591389:9329821610924518126580594334274210963600/264608164101961 qmul:-19258452690165788842/64571275,55666814298088453153/92756359,54411077014502701176/23247995:-1072056709571980969162640959031807118826/5989396364987725 qmul:-4640013132163513704/239663,-52209871104438592227/332773,=2:242254487553159440830522450019582378808/79753375499 qmul:-56411630621727285797/272706,15691212266654685658/1914927,15271170464235431859/4561235:-442583435196820139258606231600281499713/261106041231 qmul:62583023330306722367/644511,42379004056489714974/217085,=2:884068733194153019519400490169326874486/46637890145 qmul:53067206328944584675/275618,=1,37102608540172266636/214843:2816128387558776183269875887008244855625/75965281924 qmul:50636929045250773605/38387,30182307121185668404/29215,16057737093809242633/17297:305667868823489166641648659224001135284/224295241 qmul:-26760988055984279099/53119,44684512572473420625/89488,=2:-108709246112676414811336722275383910625/432137552 qmul:-17331655588145624486/2353,24408931125891445861/334,55315381482361596884/2933:-16271045674950697968739133244742498171/30227 qmul:-9697670177570290081/926,-1158917529680599882/175,-11682447562930993064/1259:5619399982923492491507494162417185221/81025 qmul:-24744828849467423601/305,706079506961442174/13,-12411541580915002667/54:-17471816553877228863576699595124348574/3965 qmul:74993389160967099973/124,-20280570219362183984/677,28316389090053904551/13:-380227173716737042352800246412036858108/20987 qmul:43291079967737078989/47,-41261412311052788301/4,81583584176718755579/67:-1786251099939557456367856008793532107689/188 qmul:-63431471455230924013/94,=1,69816003657973600474/97:4023551570975775516902820423729780024169/8836 qmul:10484919345725066249/3,=1,-37631393326791641801/9:109933533686359751306619094875438930001/9 qmul:76285024187842291525,15471681970508023553/4,14287488305535091904/5:1180257633346808064019424884594192288325/4 ================================================ FILE: tests/qmulz.tc ================================================ qmulz:4/21116887005095188595,0,1/17609283250378275381:0 qmulz:8/84271584737450207059,1,=1:8/84271584737450207059 qmulz:-5/7724990270619098661,3,-1/8550465692384773913:-5/2574996756873032887 qmulz:2/8610596429506001887,7,=1:14/8610596429506001887 qmulz:0,0,-1/273384650324881125:0 qmulz:1/140233715878844976,0,0:0 qmulz:0,4,=1:0 qmulz:-9/45090872528594267,8,=1:-72/45090872528594267 qmulz:1/8811965128522223,2,2/1793564191974955:2/8811965128522223 qmulz:-1/3188926048219934,8,-1/5467596237009668:-4/1594463024109967 qmulz:6/640657208066881,5,1/137611762075086:30/640657208066881 qmulz:3/82322597857883,-7,7/654813178322036:-21/82322597857883 qmulz:2/3688100583837,-5,2/10618253469093:-10/3688100583837 qmulz:-7/83059280440216,9,1/11745563556453:-63/83059280440216 qmulz:9/6593641787929,5,=1:45/6593641787929 qmulz:3/6450530990042,8,-3/716358093439:12/3225265495021 qmulz:-9/518988418619,-6,7/365408602532:54/518988418619 qmulz:-1/122175964907,-8,2/24455846617:8/122175964907 qmulz:3/5927038874,3,-8/86686893619:9/5927038874 qmulz:1/7836708131,5,=1:5/7836708131 qmulz:5/498008886,-4,2/1679653213:-10/249004443 qmulz:1/7271098513,6,0:6/7271098513 qmulz:6/363428537,-7,2/874745017:-42/363428537 qmulz:5/766453791,-5,=1:-25/766453791 qmulz:-4/90120677,4,=1:-16/90120677 qmulz:2/53848349,-1,9/89746135:-2/53848349 qmulz:-1/58093,9,7/9595979:-9/58093 qmulz:9/2605786,-7,-5/2800212:-63/2605786 qmulz:-7/355662,7,-1/161621:-49/355662 qmulz:-1/55532,-8,3/126767:2/13883 qmulz:7/6254,8,=1:28/3127 qmulz:7/22045,2,=1:14/22045 qmulz:0,2,2/2115:0 qmulz:-6/3715,8,-4/2861:-48/3715 qmulz:1/93,5,1/5:5/93 qmulz:2/267,5,8/311:10/267 qmulz:1/11,4,3:4/11 qmulz:7/89,4,0:28/89 qmulz:1,-1,0:-1 qmulz:1/2,2,-3/4:1 qmulz:40/4765370066151782869,-24,3/17739079731156497618:-960/4765370066151782869 qmulz:10/7947188161398728933,31,-29/17781982876586594643:310/7947188161398728933 qmulz:8/970140630929619417,53,13/8387936313655403107:424/970140630929619417 qmulz:3/1360678434809756573,41,-31/7551541168373851760:123/1360678434809756573 qmulz:86/511769393768474807,-69,-1/14040574288485846:-5934/511769393768474807 qmulz:56/95496257521849925,9,4/211197580286155545:504/95496257521849925 qmulz:3/12596246629196159,46,37/18952775459563721:138/12596246629196159 qmulz:77/94995682269709624,37,=1:2849/94995682269709624 qmulz:13/113349891854596,-40,60/1320165562768511:-130/28337472963649 qmulz:-41/8305688624807961,27,-89/2632217443748796:-123/922854291645329 qmulz:50/294091273453599,83,31/297861651301595:4150/294091273453599 qmulz:27/300155905937375,-31,=1:-27/9682448578625 qmulz:-31/21736762942232,-27,80/61942176807321:837/21736762942232 qmulz:59/71835777121419,67,=1:3953/71835777121419 qmulz:9/1200430381838,-23,19/83497011269:-207/1200430381838 qmulz:56/4578602367429,97,-20/776186296021:5432/4578602367429 qmulz:31/25481124930,-86,=1:-1333/12740562465 qmulz:45/421348839203,-96,89/480034443271:-4320/421348839203 qmulz:43/18027020463,18,50/87497424067:258/6009006821 qmulz:-23/3151206468,59,57/92709199715:-1357/3151206468 qmulz:-33/718223267,-66,-76/2839068079:2178/718223267 qmulz:98/8237370817,72,79/3563183593:7056/8237370817 qmulz:37/508616845,22,72/569831387:74/46237895 qmulz:41/364836167,-39,17/275414470:-1599/364836167 qmulz:61/59566303,79,-1/1125330:4819/59566303 qmulz:-97/83330456,63,73/93898689:-6111/83330456 qmulz:-1/164718,22,-65/5152738:-11/82359 qmulz:0,24,1/452605:0 qmulz:-1/74711,-40,56/389891:40/74711 qmulz:49/301825,39,54/550045:1911/301825 qmulz:1/29,75,-29/23058:75/29 qmulz:29/24685,14,=1:406/24685 qmulz:8/4141,88,-12/2819:704/4141 qmulz:26/3215,-38,11/500:-988/3215 qmulz:-1/11,11,1/2:-1 qmulz:58/779,41,-35/237:58/19 qmulz:43/87,-51,=1:-731/29 qmulz:-93/46,10,4/85:-465/23 qmulz:76/3,36,0:912 qmulz:73/4,-77,=1:-5621/4 qmulz:432/74155281191151829175,472,=1:203904/74155281191151829175 qmulz:43/114735919860201111,635,=1:27305/114735919860201111 qmulz:301/3325247703900970462,388,=1:58394/1662623851950485231 qmulz:47/344661002338469478,-106,860/1407842422947199591:-2491/172330501169234739 qmulz:805/331439221582368712,128,=1:12880/41429902697796089 qmulz:2/38222077254594263,-769,366/33431432349396613:-1538/38222077254594263 qmulz:262/61689298838409327,985,63/11550912720533723:258070/61689298838409327 qmulz:29/21271356349676377,424,920/27960990422138801:232/401346346220309 qmulz:205/2415752549117554,210,=1:21525/1207876274558777 qmulz:634/9928964068012837,847,95/1012378898508494:536998/9928964068012837 qmulz:760/992730779954457,-482,=1:-366320/992730779954457 qmulz:13/176143690239813,-422,349/7765280463032:-5486/176143690239813 qmulz:-408/41555001527117,-384,-66/88241293613239:156672/41555001527117 qmulz:27/282651453443,321,23/49707873373983:8667/282651453443 qmulz:337/906250195499,80,-199/1511077632489:26960/906250195499 qmulz:149/1870083861838,-448,281/4154228004961:-33376/935041930919 qmulz:662/109646911569,763,126/297204337159:505106/109646911569 qmulz:-887/964555633809,146,-947/9332491491:-129502/964555633809 qmulz:188/73532880181,760,163/15869550943:142880/73532880181 qmulz:-221/8950730813,505,=1:-111605/8950730813 qmulz:22/13208815,793,=1:17446/13208815 qmulz:193/637058385,-354,482/2363181035:-22774/212352795 qmulz:921/151700978,356,-124/176851221:163938/75850489 qmulz:-304/528635925,-222,259/831832289:22496/176211975 qmulz:-4/3008665,170,37/7388125:-136/601733 qmulz:52/12087973,-255,-249/6720565:-13260/12087973 qmulz:-91/601229,444,125/4420518:-40404/601229 qmulz:224/1546297,-262,-392/1085417:-58688/1546297 qmulz:-184/301489,348,643/741106:-64032/301489 qmulz:245/409686,380,356/35003:46550/204843 qmulz:31/27883,-943,151/26608:-29233/27883 qmulz:53/4847,612,=1:32436/4847 qmulz:-105/3832,445,249/1553:-46725/3832 qmulz:-930/539,770,=1:-9300/7 qmulz:951/374,362,106/887:172131/187 qmulz:-963/277,320,383/272:-308160/277 qmulz:487/53,717,11/2:349179/53 qmulz:104/5,428,263/20:44512/5 qmulz:728/5,676,=1:492128/5 qmulz:-100,626,218/3:-62600 qmulz:8051/79574306408456131157,752,-197/7460413732106301606:6054352/79574306408456131157 qmulz:-3008/38400803020121033225,9712,=1:-29213696/38400803020121033225 qmulz:119/587342139200366012,-7227,=1:-860013/587342139200366012 qmulz:3185/2510393047749702379,3840,-1461/382245232883802373:12230400/2510393047749702379 qmulz:-8497/801072423164046277,7259,-2828/415904520883959335:-61679723/801072423164046277 qmulz:2322/194611268129140181,600,-887/21344410544427618:1393200/194611268129140181 qmulz:311/62962162974221664,-8282,579/2914497438443599:-1287851/31481081487110832 qmulz:5073/93332615871851278,6836,=1:17339514/46666307935925639 qmulz:2466/5537476809280789,8950,48/94598016177721:22070700/5537476809280789 qmulz:231/1712288358365785,70,-6151/1963648192541132:3234/342457671673157 qmulz:3639/430934070927460,5689,7044/387572482090793:20702271/430934070927460 qmulz:1017/411489477643922,6940,7618/907239626952957:3528990/205744738821961 qmulz:9453/75593644627417,-2623,-2593/2251196683387:-24795219/75593644627417 qmulz:216/48287649084937,1544,=1:333504/48287649084937 qmulz:-9415/2492316493411,3873,8599/637176704155:-36464295/2492316493411 qmulz:4082/7751065050029,-283,128/8321097090765:-1155206/7751065050029 qmulz:-487/249512316942,-9582,9041/750949778159:777739/41585386157 qmulz:649/133850377085,-5935,=1:-770363/26770075417 qmulz:6342/41044749355,-8924,-9491/43668795550:-56596008/41044749355 qmulz:7139/68729276289,6836,-9917/81477149162:48802204/68729276289 qmulz:143/2037944234,2833,4555/3599790156:405119/2037944234 qmulz:-9325/7317954198,-9218,5503/6043847166:42978925/3658977099 qmulz:7044/653529617,7307,4797/199351315:51470508/653529617 qmulz:-673/115994640,-7148,559/911781164:1202651/28998660 qmulz:3076/13783363,-9612,-2927/62873576:-29566512/13783363 qmulz:-4161/34536929,3313,98/1321839:-13785393/34536929 qmulz:738/526535,-118,=1:-87084/526535 qmulz:2233/2825257,7157,765/8600573:15981581/2825257 qmulz:107/83440,3370,401/179110:36059/8344 qmulz:-1667/14564,-6138,913/586918:465093/662 qmulz:-7994/44789,404,=1:-3229576/44789 qmulz:-5363/98880,145,=1:-155527/19776 qmulz:842/29,-8855,8672/6371:-7455910/29 qmulz:2310/1103,2603,=1:6012930/1103 qmulz:762/293,2709,=1:2064258/293 qmulz:5789/529,7420,-6538/957:42954380/529 qmulz:539/41,3855,-7655/53:2077845/41 qmulz:-579/13,7973,=1:-4616367/13 qmulz:883,5006,1627:4420298 qmulz:3573/2,3540,4139/9:6324210 qmulz:98250/53192196970205269513,57716,80717/96027247156109827970:5670597000/53192196970205269513 qmulz:-6945/12166748375847716977,80289,23625/38713117494337198876:-557607105/12166748375847716977 qmulz:-58986/296440433764715149,-18018,-97378/3396272899236095159:11679228/3257587184227639 qmulz:-6149/262153684309837118,56309,89961/7445277782705094481:-346244041/262153684309837118 qmulz:-15446/149480531273251391,31846,4749/106265662702068574:-491893316/149480531273251391 qmulz:2451/55473133472349607,90444,20837/279735266283810098:221678244/55473133472349607 qmulz:28710/35478143894265917,69724,=1:2001776040/35478143894265917 qmulz:96358/34167706730231777,49135,-2041/69865271163769782:4734550330/34167706730231777 qmulz:7283/1176116854930460,77815,62454/5465876769829379:113345329/235223370986092 qmulz:99551/5426188854503002,-89899,=1:-8949535349/5426188854503002 qmulz:7860/83586510191743,23843,-4213/144664072126997:187405980/83586510191743 qmulz:-3898/13601562574049,-61855,4031/27837453043985:241110790/13601562574049 qmulz:-6928/5371829731249,37664,4835/26749096759358:-260936192/5371829731249 qmulz:76651/81457027187160,-85014,=1:-1086068019/13576171197860 qmulz:14709/484402153529,30047,10715/9214198729207:441961323/484402153529 qmulz:30365/5730836776783,61734,30655/2550068903118:1874552910/5730836776783 qmulz:13241/55328034593,-80183,11617/428864198314:-1061703103/55328034593 qmulz:35410/387788826057,45514,15158/46042980249:1611650740/387788826057 qmulz:-41739/96062733370,-76701,=1:3201423039/96062733370 qmulz:71383/88228655146,74491,74665/42443189917:5317391053/88228655146 qmulz:-3181/8533129823,78945,19451/1917063317:-251124045/8533129823 qmulz:-35563/2781995353,34546,99624/7403972285:-1228559398/2781995353 qmulz:-46639/190543771,20318,=1:-947611202/190543771 qmulz:57710/227557263,65393,41129/661804772:3773830030/227557263 qmulz:-41473/34008654,19343,68754/48463157:-802212239/34008654 qmulz:86172/41261945,23098,-67843/42705974:1990400856/41261945 qmulz:-23642/477003,-74773,75259/5922193:1767783266/477003 qmulz:-2299/7593,-55092,47078/3719425:42218836/2531 qmulz:89923/436747,27372,38454/602545:2461372356/436747 qmulz:35133/245788,37530,-26959/814296:659270745/122894 qmulz:54300/83317,6506,=1:353275800/83317 qmulz:-2710/16637,92724,49071/5768:-251282040/16637 qmulz:-23308/1133,56278,=1:-1311727624/1133 qmulz:12925/464,48445,5188/4977:626151625/464 qmulz:-15500/139,75561,45107/89:-1171195500/139 qmulz:68128/739,-47269,46324/271:-3220342432/739 qmulz:-98213/47,41522,-7190:-4078000186/47 qmulz:95819/64,12916,907/10:309399551/16 qmulz:-1123,10413,63874/9:-11693799 qmulz:30369/4,-41524,7423/2:-315260589 qmulz:-269467/4029498660068277497,646984,265727/52332437650027766625:-174340837528/4029498660068277497 qmulz:-206269/81809654998485085274,50405,=1:-10396988945/81809654998485085274 qmulz:119347/1701867915016265609,618013,703201/8136517399464628384:73757997511/1701867915016265609 qmulz:199044/306712361923985717,233710,201675/571526199709385944:46518573240/306712361923985717 qmulz:267977/894840013682442654,-489375,=1:-43713748125/298280004560814218 qmulz:12471/7140902397278600,350289,253704/144540771450708869:4368454119/7140902397278600 qmulz:832882/5818152789924367,-80256,108955/22849940119123234:-66843777792/5818152789924367 qmulz:494497/18234011706116519,-14822,68902/17499952371352627:-7329434534/18234011706116519 qmulz:232520/1052550357505571,557021,32429/440602163340406:129518522920/1052550357505571 qmulz:526093/2240655675408643,11119,-126354/4970690629417277:5849628067/2240655675408643 qmulz:54605/174895846259434,-184199,544176/97043233594967:-10058186395/174895846259434 qmulz:764692/11187705426133,576048,-646413/892215624306868:440499297216/11187705426133 qmulz:593840/66545119469401,569003,81868/70640307758063:337896741520/66545119469401 qmulz:109999/9745609238872,665854,=1:36621637073/4872804619436 qmulz:-133443/8282237150,-495649,404461/485555508119:6012808137/752930650 qmulz:224276/6824310584317,712269,=1:159744842244/6824310584317 qmulz:787126/341737321975,925666,71517/134877228043:104087967988/48819617425 qmulz:19969/20124955446,-804254,68212/739707535809:-8030074063/10062477723 qmulz:-484342/14331066017,154663,640199/41001808194:-74909786746/14331066017 qmulz:234567/15529177385,951383,104501/13280956901:223163056161/15529177385 qmulz:447401/2005170496,-162639,25513/657762574:-72764851239/2005170496 qmulz:88392/370535737,889107,=1:78589945944/370535737 qmulz:69608/19589055,197889,391089/111921502:4591552504/6529685 qmulz:-742188/976205903,-835265,198303/463857278:619923659820/976205903 qmulz:30951/7100042,826901,37665/16004119:25593412851/7100042 qmulz:-8717/23405419,749796,584744/90701721:-6535971732/23405419 qmulz:375053/1615401,682230,-413113/4604306:85290802730/538467 qmulz:-682135/9626652,-686085,=1:156000863825/3208884 qmulz:459639/139961,-545993,55641/809527:-250959676527/139961 qmulz:137069/131640,556346,=1:38128894937/65820 qmulz:653137/44831,-33774,=1:-22059049038/44831 qmulz:377111/93851,119783,=1:45171486913/93851 qmulz:61290/967,223671,-198269/2596:13708795590/967 qmulz:108931/3561,890354,99191/837:96987151574/3561 qmulz:-566567/566,72845,=1:-41271573115/566 qmulz:-856110/823,-344105,71629/306:294591731550/823 qmulz:103589/16,-597818,73435/68:-30963684401/8 qmulz:531370/87,698278,92947/30:371043980860/87 qmulz:93564,802315,-69936:75067800660 qmulz:254421/2,-51596,=1:-6563552958 qmulz:5908447/27508951891576930555,-8046857,=1:-47544428101079/27508951891576930555 qmulz:3067750/30055512795875714167,9308933,292151/5218560370048727971:28557479210750/30055512795875714167 qmulz:5909595/1610510865059257451,1081732,8279906/1034011738653690921:6392598018540/1610510865059257451 qmulz:7300703/4024857129457733561,-6809974,=1:-49717597611722/4024857129457733561 qmulz:-411181/366261858643871279,-3873525,5670428/945102376345780573:1592719883025/366261858643871279 qmulz:1840028/328098015717866549,7760,-1208094/324612123643160461:14278617280/328098015717866549 qmulz:5902528/35455662246885099,9372866,-2383248/38025857091093589:55323604005248/35455662246885099 qmulz:412808/8383418920359061,7136425,8412475/90427613237122747:2945973331400/8383418920359061 qmulz:4721348/1016481387773127,-4909375,446916/600970820960263:-23178867837500/1016481387773127 qmulz:346575/543489633400996,2082315,=1:721678321125/543489633400996 qmulz:-54603/142207419353230,9721544,-9944420/520274639700813:-37916104788/10157672810945 qmulz:9128453/94269601342538,-1680681,9401887/439581199104749:-15342017516493/94269601342538 qmulz:327135/14576866729679,-981216,=1:-320990096160/14576866729679 qmulz:-2772009/35771247225944,7269361,3999881/49166513232805:-20150734116249/35771247225944 qmulz:7777936/4972983657531,932701,-1921805/2675875584873:7254488685136/4972983657531 qmulz:-4107413/8839115797940,-7894930,-67679/4109002145737:3242773811609/883911579794 qmulz:6418119/522734321117,-4364508,=1:-28011931720452/522734321117 qmulz:-9554439/610908255599,9002767,5125943/687195405407:-86016388132713/610908255599 qmulz:1541453/67134868472,9336624,124122/1242309641:1798995884334/8391858559 qmulz:-4420171/60924329483,4658729,597333/76303665689:-20592378822659/60924329483 qmulz:2321560/479530207,3712372,-8303185/3259591614:8618494340320/479530207 qmulz:6497537/8003497458,685910,622458/2979408511:2228362801835/4001748729 qmulz:8707355/324035343,-5890611,=1:-17097213714635/108011781 qmulz:-6368331/430504267,6080736,2843024/389993407:-38724139571616/430504267 qmulz:7148576/43643579,9752788,1882739/80695462:69718546229888/43643579 qmulz:-78515/22600098,-9269764,=1:363907760230/11300049 qmulz:6642519/3513320,6950670,4303599/4263095:4616995753773/351332 qmulz:8291036/3791843,-6165764,187574/1468847:-4647324662864/344713 qmulz:3378069/104710,4099164,-3130847/477201:6923629417158/52355 qmulz:-1837947/540683,-7963396,4977946/317377:14636299788012/540683 qmulz:-2439283/46175,3316377,4423369/90864:-8089582037691/46175 qmulz:24851/4671,-9457747,=1:-235034470697/4671 qmulz:-3996265/3851,5644784,2130071/6485:-22558052731760/3851 qmulz:-8787752/5255,-8904351,=1:78249228308952/5255 qmulz:1051819/121,7786465,-1689328/223:8189951829835/121 qmulz:2910419/264,-4517287,4103/10:-13147197913253/264 qmulz:1470867/8,9831206,3981716/39:7230198237801/4 qmulz:4240055/91,-8952034,=1:-417111170570 qmulz:327409/4,1172921,-3686633/6:384024891689/4 qmulz:463486,9343153,-1978362/7:4330420611358 qmulz:29585813/42067907033671980893,71292790,-70324603/70286665753964458740:2109255153188270/42067907033671980893 qmulz:-65065601/40632930795671537185,4699856,7303041/5446641871295709464:-305798955253456/40632930795671537185 qmulz:22287116/6961884952768846975,-61223561,47414597/4915453243825873928:-194928086562868/994554993252692425 qmulz:13726613/4388684468226482322,5689324,=1:39047574389806/2194342234113241161 qmulz:86674641/912048412696230206,9154212,418913/1017052367067494:396719019368946/456024206348115103 qmulz:39606657/62493216618497137,-64895609,-93307621/528183512506792540:-2570298126469113/62493216618497137 qmulz:-61860905/97141961244876374,29603964,95495204/34743879357106645:-915664002313710/48570980622438187 qmulz:23026739/8268491868362646,49125662,=1:565601898538109/4134245934181323 qmulz:74731767/2153002560742688,79046765,=1:5907304424083755/2153002560742688 qmulz:-33040734/8080107924352231,16695468,87206576/5598768033775299:-551630517193512/8080107924352231 qmulz:-85831719/652429006985885,-12207796,-56798629/203624822018813:1047816115881324/652429006985885 qmulz:13811539/218314616664013,-33361377,41774225/444858687471486:-460771959529203/218314616664013 qmulz:46578727/4151263590571,94131401,=1:4384520829306527/4151263590571 qmulz:5864747/4619802266479,-14340682,9374233/85220400863050:-84104471737454/4619802266479 qmulz:-20695/10292597787,19239092,=1:-398153008940/10292597787 qmulz:-79354991/1226479246337,-85100492,-31036795/9391557241804:6753148776755572/1226479246337 qmulz:13497139/220655551780,25874045,16158669/209860028875:69845116371451/44131110356 qmulz:-14641436/673965441365,35697635,=1:-104532927640772/134793088273 qmulz:42076810/47634122699,92555216,-99965382/7603386991:3894428238140960/47634122699 qmulz:-2547044/961062465,-61423853,-64578371/3954121219:156449256240532/961062465 qmulz:12398632/375040743,76607359,19460171/1399871191:949826452732888/375040743 qmulz:99063929/927095607,-33074282,-31824927/5567689051:-3276468323773978/927095607 qmulz:13710043/915838933,-63538218,-80907032/55218445:-871111700923374/915838933 qmulz:-14266908/173792753,79812889,39774414/947866123:-1138683144577212/173792753 qmulz:46031321/23827793,47288874,-29016530/26535747:94642145166198/1035991 qmulz:90667631/37118866,68275195,25790129/31607133:6190350186713045/37118866 qmulz:133784/168291,-36246595,-13384939/1286209:-4849214465480/168291 qmulz:20243420/9836407,-29971865,=1:-86676150196900/1405201 qmulz:55262636/961595,-79684445,-18606712/267721:-880714495779404/192319 qmulz:18521596/447339,13342158,98234108/465429:82372686748056/149113 qmulz:-52333722/83537,75454299,80265841/5748:-3948804307570878/83537 qmulz:27849895/19463,2814646,51492641/14404:78387595562170/19463 qmulz:2229413/2657,47131782,=1:105076207503966/2657 qmulz:37693829/4546,76862997,85444575/4597:2897260665345513/4546 qmulz:47895391/838,51616823,67901608/79:2472207919762793/838 qmulz:94793222/407,45108781,26019479/298:4276006691482382/407 qmulz:-28219652,28509688,-69052146/5:-804533473988576 qmulz:89329658/41,24254853,43325377/63:2166677723330274/41 qmulz:-28028843/2,57869496,97143787/2:-811007508936564 qmulz:17180663,49123793,31747639/3:843979332814759 qmulz:-440812167/25592398472985127969,-67895040,305636107/90241943612023813864:29928959710951680/25592398472985127969 qmulz:469436899/89801410067219467595,339956414,=1:159588084783320186/89801410067219467595 qmulz:624505646/8457866426911473529,55679196,735790506/1487411086627672243:34771972266740616/8457866426911473529 qmulz:-530285107/6030437060176995577,933495870,999692847/7638706602391224839:-495018957307008090/6030437060176995577 qmulz:811800624/481147127809268303,96179572,377106279/130131554630880295:78078636565652928/481147127809268303 qmulz:-249975856/304587360170486515,826091985,851744230/630784049926628227:-41300610217022832/60917472034097303 qmulz:-268512055/31691499965821404,202698168,125655067/11939065745546055:-4535575136201270/2640958330485117 qmulz:52009618/27516701583858369,702923265,-368845548/80831610779378597:12186256831987590/9172233861286123 qmulz:375702102/3296151167632583,-434951925,-521756507/7691136311577133:-163412352491446350/3296151167632583 qmulz:-384209743/6191488089335748,227570856,78931552/6926107452102541:-7286245008170834/515957340777979 qmulz:113980250/183755547250927,437813246,556573714/9774511713479:49902063232391500/183755547250927 qmulz:-472996853/423024426303975,-368827764,986763127/429084644953681:58151457223675564/141008142101325 qmulz:-23658043/2283802118115,740396103,17376279/1797109931431:-5838774280602143/761267372705 qmulz:4078811/40918803323,-845485209,=1:-3448574370806499/40918803323 qmulz:154841851/4593031526275,12617826,-972933704/2547790338703:1953767533435926/4593031526275 qmulz:735542560/7626156428987,778206922,-293104268/2631653460189:572404311617600320/7626156428987 qmulz:-457656798/567001008887,493454600,-366343915/981801223003:-225832852194370800/567001008887 qmulz:-945200662/928772265773,975297818,34885945/9938748237:-83804740292795956/84433842343 qmulz:104875267/28207551782,954147586,=1:50033241419577731/14103775891 qmulz:609918635/17074425662,-224065632,-400611797/35807663040:-9761557458560880/1219601833 qmulz:-864006772/2174255357,384303177,=1:-332040547429114644/2174255357 qmulz:-109536551/482079758,63549943,-10441546/8480554803:-6961041572466593/482079758 qmulz:512697337/200332783,429480437,6412690/26797243:220193476343496269/200332783 qmulz:-789241399/555269030,318371906,755945889/20176822:-125636144246868247/277634515 qmulz:-462528503/5399724,117919312,195760496/23231881:-13635260713537484/1349931 qmulz:-768369531/84617918,630525111,869606481/10643699:-484476283822792941/84617918 qmulz:881987483/8541727,899430760,=1:793286672145177080/8541727 qmulz:435026027/9075006,667517326,-976648275/5125397:145193705141721901/4537503 qmulz:-382388178/685121,90758124,-658289938/398425:-34704833675058072/685121 qmulz:215727059/244359,-726765650,401344067/859586:-156783016256723350/244359 qmulz:300168110/44829,-382517050,-848645422/63521:-114819419941275500/44829 qmulz:240997441/17745,-160000865,=1:-7711959804557293/3549 qmulz:497024455/1871,-967339431,891801689/2782:-480791353492785105/1871 qmulz:159802693/5520,17435365,=1:557243656087589/1104 qmulz:-503495399/548,350245727,=1:-176347112063910073/548 qmulz:-10883201/487,215755629,756773575/299:-2348111877288429/487 qmulz:366108695/3,980458645,-27946686:358954435022418275/3 qmulz:890190708/5,-785135991,-213354065/14:-698920763704571628/5 qmulz:10221149,961494206,348141954:9827575542162694 qmulz:-44158489/8,918744696,-871474083/8:-5071297194015543 qmulz:-2894598477/3168041449931268761,-3793825512,=1:10981601549038945224/3168041449931268761 qmulz:-165305510/4444729020519250969,9650534485,2185861399/5133889833495479703:-1595286524815512350/4444729020519250969 qmulz:-6642522053/7993901796893679282,2810456878,=1:-252277321501628791/108025699958022693 qmulz:4075114142/2324601722262376857,7319061324,224603716/1867619918809913859:9942003435865881336/774867240754125619 qmulz:174975715/284043772444194,6235601626,2532940399/455179300056502113:545539426482256295/142021886222097 qmulz:9511153214/515183582083251763,8998409775,1916260097/49971689447357059:85585254052380266850/515183582083251763 qmulz:9561479651/87091900188234189,-9070226563,-31724150/149115720086953:-86724786712084169513/87091900188234189 qmulz:257684521/4786959313773388,7785131961,6853032479/92097657977675380:2006108000292075681/4786959313773388 qmulz:-4787662186/3232352240839707,-4724762630,=1:22620567381476909180/3232352240839707 qmulz:4815469783/4351554535472742,-3809867113,7127662378/9454193567725933:-1411253843068995883/334734964267134 qmulz:-3134766359/276266993500284,-5054392552,-1084728996/261757765208747:3961084934297439542/69066748375071 qmulz:887520891/240452975602433,8724686676,990724100/235457211073037:7743341692379348316/240452975602433 qmulz:7273936918/90562759963967,3897937854,=1:1667844356487076116/5327221174351 qmulz:-119387249/2501098635936,9536603772,7558585050/14605366326499:-94879074095175269/208424886328 qmulz:1526390275/2230210659804,4788548573,9380637171/7768045927396:7309193973192327575/2230210659804 qmulz:3728595181/1876804971571,9224083630,=1:34392873771958987030/1876804971571 qmulz:4093958623/457077991802,1483219640,9490772153/415966894045:3036119917490477860/228538995901 qmulz:2144803614/309751929683,2542484861,3609691879/286244057812:779018674059012522/44250275669 qmulz:3560518143/86265554695,4399548470,-9491920365/12079543438:3132934429688578242/17253110939 qmulz:-2249859505/6734537978,1110886234,=1:-1249668976269277085/3367268989 qmulz:3262790941/1025060151,5749937770,122130955/253972334:18760844867269741570/1025060151 qmulz:-4710833503/6631683846,-3411512444,=1:8035533558548305666/3315841923 qmulz:-9032027690/956483333,9063301527,=1:-81859990354683282630/956483333 qmulz:-266187969/112068472,6338182319,-7905751808/945700693:-1687147878646320111/112068472 qmulz:4156902964/946699,6705660672,=1:27874780723015031808/946699 qmulz:2651274071/91222015,-5032057829,-2464896493/13519125:-13341364445800251859/91222015 qmulz:318661412/1743,370464187,-232620732/1501523:118052640924852044/1743 qmulz:899914724/512321,5465209352,=1:4918222365607298848/512321 qmulz:3131360803/353764,-2320875649,=1:-7267499035915786147/353764 qmulz:6443807425/863022,84008208,110674088/12311:90222119078557400/143837 qmulz:-3068580532/73491,8795547050,=1:-26989844445920030600/73491 qmulz:696531051/11483,376305292,=1:262108320533621892/11483 qmulz:9419114609/574,7568524581,1555156138/2439:71288800449472703829/574 qmulz:6076760418/5639,3137249772,1485476093/6609:19064315235869124696/5639 qmulz:3390029532/479,4688058595,=1:15892657084796427540/479 qmulz:1638519591/92,3009448307,2877648480/173:4931040009121282437/92 qmulz:516117057/8,8303497266,-9173174800/47:2142788285867733081/4 qmulz:927642007/6,-2879248175,-3421337621/43:-2670911555708087225/6 qmulz:2611149335/3,7293202790,1060208041/2:19043641615128644650/3 qmulz:-4787695612/3,-5387504428,-8004477624:25793731309566169936/3 qmulz:1237812305/631690268983111653,77842709902,51259842584/29388862631694313447:96354664171240944110/631690268983111653 qmulz:5976818503/79879634485079515072,-2490419914,82254088463/65538055479070681595:-7442393911117434371/39939817242539757536 qmulz:-17969301863/1215487409718772165,14907617468,39498072491/8401888749150831870:-267879478340623742884/1215487409718772165 qmulz:62921948190/5765043819856032331,-39453740869,-1868833945/7119552876031525503:-2482506238860903577110/5765043819856032331 qmulz:-15610313710/78152311777353923,92919343081,-49673392741/841288090131527967:-1450500095221527940510/78152311777353923 qmulz:44648474983/288454490007214845,47861920531,11617817909/33454275945577992:2136961761466687575973/288454490007214845 qmulz:-13826523213/28036931389675264,-88421093554,=1:611278151271612834501/14018465694837632 qmulz:40547667371/53177876256600915,49909556335,9076503202/2880089154076223:404743217781153169057/10635575251320183 qmulz:76668523587/5077067067443611,85512171223,-39577211701/3956684840165784:6556091916386158136901/5077067067443611 qmulz:-80228153797/602596042922155,22421445270,24751353255/2432806998119141:-359766231894515638038/120519208584431 qmulz:47062274633/166002450060687,86101072410,82448790716/626049533394637:1350704105318413058510/55334150020229 qmulz:8841820465/21786582003342,53402955559,268303508/5469783598063:472179345353051714935/21786582003342 qmulz:23713841211/21537439736900,-82708390631,-1600362701/2915831487207:-1961333642240894094141/21537439736900 qmulz:56721050875/77459601877944,59578456497,32477270555/35734686972211:1126450887340103761625/25819867292648 qmulz:8928356444/2663712341261,-3648881786,-28952940554/2770799359187:-32578517207427328984/2663712341261 qmulz:18227203995/5958086852101,483256270,-90041196376/5523075085255:8808410615152798650/5958086852101 qmulz:59211032239/570207052514,26723970763,-9542991461/881963470657:1582353894402086428357/570207052514 qmulz:1776113132/40223369371,41111960068,44832213814/478452935141:73019492159034412976/40223369371 qmulz:-15285833580/2156369081,34934254636,-90933367585/31370134781:-533999202607239476880/2156369081 qmulz:91516992782/93740428151,-65378876169,-67776976360/2244262427:-5983278138453644812158/93740428151 qmulz:72779505484/1621504307,-52125941410,5672754165/602683781:-3793700238707757692440/1621504307 qmulz:11740145697/1515672656,87909174824,-48408939345/3034260044:129008315067100541541/189459082 qmulz:79961831072/773650431,-41330850050,-74967019083/977759203:-3304890449760262753600/773650431 qmulz:6884563893/49029205,40219988393,-23059747673/353633216:276897079867326893949/49029205 qmulz:30501090798/47322791,28853148760,=1:880052510136961110480/47322791 qmulz:-18451888579/10709259,11599135921,=1:-214025963626968546259/10709259 qmulz:8926155052/4290885,75202195645,=1:134253291715621829708/858177 qmulz:88656392423/4830649,47619732899,36734598432/8696993:4221793726972187424277/4830649 qmulz:34368523182/239537,-72478917605,-71850709745/331701:-2490993359913710419110/239537 qmulz:-7591160179/904815,-41442417941,84402195575/876773:314596032795194371439/904815 qmulz:78012684294/13529,-92124971658,32782603063/49402:-7186916329549251739452/13529 qmulz:-77476701398/48451,84100140997,84733570363/49436:-6515801511554267013806/48451 qmulz:9785922698/313,99923625908,60518701590/3703:977844878839558059784/313 qmulz:13272361617/790,77228020379,-14315026641/2773:1024998213435133392843/790 qmulz:1977713551/2,92621074895,=1:183177954928027402145/2 qmulz:-8125102987/193,40843068681,=1:-331854139338239250147/193 qmulz:87788302687/10,73718602709,708527495/34:6471631008280390179083/10 qmulz:-17073092947/16,82903130217,60258726452/11:-1415412847792085279499/16 qmulz:-6943963154/5,67700561949,=1:-470110207678950427146/5 qmulz:-86521942923/5,52316853740,74747686643/9:-905311166640643816404 qmulz:-745167514955/75202612388076732241,992589631308,139312742559/34578187132141654765:-739645548931882026211140/75202612388076732241 qmulz:27932224059/2111108032966941227,-779689866177,8856089863/3931386633265401342:-21778472038587689752443/2111108032966941227 qmulz:140525061611/3407680707744152962,127477722944,169676929421/277484368047590363:8956907435367794151392/1703840353872076481 qmulz:341584864563/1420632012141667135,55437156492,=1:18936493592077656192996/1420632012141667135 qmulz:-999027740190/525162199932669211,400522397538,500019558441/907820980265694569:-400132985707868959652220/525162199932669211 qmulz:-339453308372/462366486602163829,952918460297,-90778090002/71370169251458863:-323471323956568979706484/462366486602163829 qmulz:-271650817828/7565295758442605,768776296466,16994985550/10329125142493:-208838709661769886195848/7565295758442605 qmulz:225422010721/10111430949630829,746974776114,-168224996466/53086145704663327:24054936569926668959742/1444490135661547 qmulz:349236361403/2805449982440828,193882264108,-1449692674/936603179147519:16927684114413345855881/701362495610207 qmulz:-197651146031/4351789591405316,-808105729932,58049683298/4854765675888749:39930755908819394924973/1087947397851329 qmulz:271384975109/452447489612746,354118404591,-732534914633/555297542185947:96102414415567326325419/452447489612746 qmulz:88111433664/28798189724783,207968836059,-261683363229/138358019377265:18324432302591869690176/28798189724783 qmulz:67604819101/43380824369659,884187650678,50163356115/7011438059051:59775346175424370000478/43380824369659 qmulz:979853557479/27364774048301,185814534089,376723696931/23421481855538:182071032258409566401631/27364774048301 qmulz:-129581462881/1185999957929,-649615443760,=1:84178119512510783072560/1185999957929 qmulz:631378962263/4697504353981,356337990468,353616095948/3759830408947:224984310636568625709084/4697504353981 qmulz:419208380799/252872515073,306292997739,313894879763/25683953874:128400591632237958013461/252872515073 qmulz:59754817607/502657252480,-190176172167,111686020133/78750756618:-11363942481036514944369/502657252480 qmulz:639847514587/81987662799,449279495706,76285885523/11877258141:95823456227461612954474/27329220933 qmulz:699678831667/15232840363,-328557525533,412748319154/35151716111:-229884745600329961453511/15232840363 qmulz:887054398617/2906111779,840756960767,-7837140210/882145159:745797160216227848059239/2906111779 qmulz:-455315204427/506702237,-175722319764,101353072197/4927140688:80009043945732322395228/506702237 qmulz:18629315637/336690086,163583642465,-428561144079/630858776:70870960663503295935/7830002 qmulz:26610877449/497721338,494401478093,656965629789/571606768:13156457144137281224757/497721338 qmulz:308447566844/63211619,626332529102,389974552910/53161277:193190744636760720294088/63211619 qmulz:432089290445/43417161,381832677443,-993787713167/43836749:164985810665060426932135/43417161 qmulz:259672928141/1911242,33898844506,477785491015/5001727:4401306106734735321673/955621 qmulz:72860807605/947904,836184405122,132459766271/26668:30462535531947709276405/473952 qmulz:8111715299/126471,73018318330,-966100886117/960478:592303809904713130670/126471 qmulz:59136150795/124661,-183025911988,998950795145/902212:-10823447930714766230460/124661 qmulz:-52072229129/344,24297646661,-819340099671/44129:-1265232624227073788269/344 qmulz:462624622089/91900,463652425988,182901467689/69000:53624257088336635612233/22975 qmulz:-12928412440/521,528884765734,937253218809/8798:-6837640384641931330960/521 qmulz:27765652319/2634,-126780088278,=1:-586688642016512569447/439 qmulz:-967104161735/274,750172960968,-709612304/49:-362747696286610257079740/137 qmulz:66752761957/243,243055541185,151935508582/7:16224628683052114699045/243 qmulz:751278773537/66,713221018437,659908640320/37:178609270664053141567223/22 qmulz:-586344498928,-568318448089,521816699255/14:333230395676283284148592 qmulz:161194888214,484546649439,184699645268:78106442990787850811946 qmulz:793578182621/4,-808113765664,=1:-160325363376662447831336 qmulz:561935468909/32803049500299178880,2101294187063,-3358814917919/26371576797557955745:1180791734323002866524267/32803049500299178880 qmulz:-5868873358301/6442991402115355335,2339686618745,-1536954575653/43556673213605193423:-88589190087263739148079/41567686465260357 qmulz:-7979894125724/9674261753856826205,-1852913383532,3286095553311/7067777496639467900:14786052624722387839177168/9674261753856826205 qmulz:515507640950/169593134508951507,130457186386,9764491091569/7319120645126181160:67251676398821316106700/169593134508951507 qmulz:-9365485392019/329669514832033195,2420807490629,=1:-22672037190376071733889951/329669514832033195 qmulz:1709304465717/260423845962574106,2761288775682,-9625873444279/32296180368255957:2359941617703735036146997/130211922981287053 qmulz:215090735926/98137745784701417,1193894989684,=1:256795751949495738187384/98137745784701417 qmulz:2462657897367/2405626367061101,-6540272761466,956548940780/2817455913381063:-16106454366958522300460022/2405626367061101 qmulz:242208253035/596343213619654,5151615220303,=1:1247763722818106293369605/596343213619654 qmulz:228002384282/59111672575229,4689640217907,8887530790232/4265423449943033:1069249151107554031737774/59111672575229 qmulz:1065463662219/36125337508585,-1135495312868,5987819337289/651384630027642:-1209828994480848476134092/36125337508585 qmulz:6023110141478/670453839669919,5713937267309,1998947610187/134406089553918:34415673502497927694342702/670453839669919 qmulz:-9838734646098/73658633070811,3898971866431,=1:-38360949586416063311336238/73658633070811 qmulz:-2320378876107/3544145932211,-9742994143220,8635863424885/42773859269883:22607437799961906994044540/3544145932211 qmulz:1282067863135/7152781512234,-430962905775,4287050590505/9492196607247:-184174563899134867034875/2384260504078 qmulz:2972203649953/4110957928466,-1076925462656,6468360579859/5380802762138:-1600420895416743198827584/2055478964233 qmulz:7745401204821/811506016039,-7138418453884,52955801256/2587064107:-55289914893229593626974764/811506016039 qmulz:-4394166471713/351201211519,1682246763941,2661332639201/255305706936:-7392072327257235964900933/351201211519 qmulz:242477453617/2530363014,7850634381002,-728870121674/37749087679:951800916991718980492117/1265181507 qmulz:-4495597725068/18530739005,-295776565976,2058781523476/32738808743:1329692457130130811086368/18530739005 qmulz:-627713346013/6292366913,8991851477846,-476950295807/2244817575:-5644305178010651601927998/6292366913 qmulz:-4583081886485/1415176577,769919000693,-869103658209/9579044:-3528601826136720462334105/1415176577 qmulz:-1182275059809/252123671,-904658392050,-8972966355829/539780886:1069555054567627520118450/252123671 qmulz:4559690190362/241596515,1670678554004,7140063697224/280561433:7617776613940209657309448/241596515 qmulz:1432554287/2209567,7757230863986,=1:11112654329451858207982/2209567 qmulz:1106108950528/6849831,-6298163069823,=1:-2322151514472041772238848/2283277 qmulz:5088803191704/8136929,-8625507078,-35324495791/106583:-43893507948591842880912/8136929 qmulz:7539081819837/6889238,7284561918683,9960043148827/9194287:54918908326619940050314671/6889238 qmulz:391441941525/125384,7929833985877,3351067478098/711859:3104069611402622309842425/125384 qmulz:9009538508471/742821,-4924002212923,9527002197826/376781:-44362987553126188781170733/742821 qmulz:-9259291631862/58961,4703549016027,9448940593567/14975:-43551532044151545221852274/58961 qmulz:3476127453492/36715,3322870685572,308545119513/7234:11550722014520612585417424/36715 qmulz:-646877695651/729,2845152282117,=1:-613488517344009605324389/243 qmulz:-2520612775732/3305,5509026264687,4380524270328/7049:-13886121984613190802175884/3305 qmulz:1963077614302/267,-825362596397,=1:-1620250836669127260869894/267 qmulz:7889439316771/713,5863316933906,=1:46258283145047187204337526/713 qmulz:8748734240327/23,6371236745698,-7157017762004/53:55740257070317659715363246/23 qmulz:-1296384169421/6,2899800596916,464588384950:-626542598053244779017606 qmulz:-5167288008794/7,-3300699869865,1931056190640:17055666858181330775592810/7 qmulz:6696697914261/4,4069021265747,5631057961007/6:27249006223411589102117967/4 qmulz:23865486379535/26918789012953275954,94873123748548,=1:1132096621302455418116582590/13459394506476637977 qmulz:3092832570307/2006024783468333419,-69091492632924,9214275673435/28417924226192114256:-213688418746233489772987668/2006024783468333419 qmulz:99742200190859/1397162492835988177,13135144429552,=1:1310128205228222025079865168/1397162492835988177 qmulz:16157052816541/834217349232726593,19133269076621,18278786726642/1173386622722504913:309137239024056146385187961/834217349232726593 qmulz:-15154486378645/471850975689269841,83584432024123,14569830702843/38977738569109946:-1266679136576350929552053335/471850975689269841 qmulz:-70285613046769/438550102087486245,58305445024728,=1:-1366011315842564998875167944/146183367362495415 qmulz:5620626946546/16483309748982467,18213910616022,=1:102373596810393507725160012/16483309748982467 qmulz:-87110361266406/28658861993511733,50462053430058,8350373847003/21134055318706744:-191120334979871062479392676/1246037477978771 qmulz:42263850161473/2487221560052869,70196784710879,=1:2966786390837768841769764767/2487221560052869 qmulz:2305968062717/1295096854935771,89753857010368,-1448986636213/88097527127243:206969527771576926343249856/1295096854935771 qmulz:54792800436741/962961846570596,81148189103692,=1:1111584132840379068733886943/240740461642649 qmulz:118089073191/117603203952236,-88682518170219,8843505968368/446344763404861:-10472436378965178887498829/117603203952236 qmulz:4370360581061/33937836375304,24828310773456,=1:13563583837330531311889602/4242229546913 qmulz:44999946775270/77691532844719,19675574610517,90987690124989/70801686470002:885399810246118760377514590/77691532844719 qmulz:7388469159437/80827214538,12962289697895,-39739510822103/1124530750930:95771477668585155318285115/80827214538 qmulz:-4438357163019/354300196838,2800216938058,48604674898545/5905387400293:-6214181452518427865638551/177150098419 qmulz:-1115976535244/90660833629,-84198411580247,81927230020875/605448344659:93963451628372333929725268/90660833629 qmulz:-14354364205035/137076592739,-60231717901669,29779963372229/288489332426:864588015455483313484703415/137076592739 qmulz:28410403793917/8317372959,94611442054559,=1:2687949272294801418906317603/8317372959 qmulz:-26238968575867/81875709363,-41798837075253,94070973760679/3467355102:365586124175115989639573117/27291903121 qmulz:49964458440323/3849731307,3475521417184,-94000433574238/5577825597:173652545407342463250710432/3849731307 qmulz:63054816328381/8314862510,31407375891502,=1:990193159097540038129659131/4157431255 qmulz:15690728254037/869383378,22615130488585,1475502145196/107482041:354847866925974243808667645/869383378 qmulz:74263848858589/607431119,87079437180738,43892391010643/973943857:6466854161481322249396658682/607431119 qmulz:23023853281324/23656491,66652947880105,-31945062874493/5458316:1534607692759273053987659020/23656491 qmulz:3506276105087/11638761,41170764577395,440230047929/1761776:48118689355294122721569455/3879587 qmulz:-93363094505152/3545929,76526518299725,24762745460028/9476321:-7144752560167469121292683200/3545929 qmulz:-2458728669037/893246,74281956367289,10383331533388/299139:-182639175712408990493930693/893246 qmulz:-5121601980421/33999,20660659077801,8112621331106/52165:-35271890816556237705911407/11333 qmulz:25877846847031/404920,75489603155313,-38374243475879/901678:1953508388996337946045925703/404920 qmulz:66471726351654/51695,28218300697455,-2687434510961/88806:375143832413983194158568114/10339 qmulz:-3436425362877/67400,87107727529435,8150807016773/30347:-59867840836945902514756899/13480 qmulz:64658311574074/1471,54380155658036,79155462122195/5662:3516129047983934816427358664/1471 qmulz:9680963797950/229,-14929130816650,28202159724489/2789:-144528374970848369095867500/229 qmulz:816481395175/17,-99383084980450,71300027130653/105:-81144439881633403599328750/17 qmulz:638399693884/125,-59707159904100,34949260444218/785:-1524681304218419151860976/5 qmulz:38337688583813/25,46682828260030,66019999840333/85:357942346408931005122578878/5 qmulz:-4362866892015/19,43253153678106,=1:-188707752157445489971723590/19 qmulz:80038414225429,58791342870753,-71193599831017/3:4705565853558550737752978037 qmulz:-8931381288/7,27056505490713,37222461138097/2:-241651966858423345978344/7 qmulz:-103292201629591/24903444183827008678,811061948698381,=1:-83776374339042161969543392171/24903444183827008678 qmulz:-108233246344215/10921524390718392772,336628265620018,=1:-18217184999638624584411247935/5460762195359196386 qmulz:-242546210473995/3227191274694658997,117559616638474,-200514522282738/1463600762469566069:-28513639520437479372093483630/3227191274694658997 qmulz:346557608752347/7091232122596884343,-890608472719639,764299440148772/741441034955506561:-308647142640297959088714242733/7091232122596884343 qmulz:752322662466430/796990587047794081,213680028681761,572521425296816/937517719580878925:160756328093765562145815783230/796990587047794081 qmulz:34927180981080/55520878875379453,-865283782342577,989438973302993/881309897241401311:-30221923265872621723515443160/55520878875379453 qmulz:274082612801409/53154246781994009,971799838064389,448110955601401/45559104250121531:266353438736673897727411924101/53154246781994009 qmulz:-124555667888037/14097174308038652,829678276357628,125094809716795/35133120466800502:-25835282960979923394918724059/3524293577009663 qmulz:505323718065074/2128598622243549,-277690520595781,914993855209755/9726536089876778:-140323606338886062971007852794/2128598622243549 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qmulz:-2298250489792159/192401665676,4151647369458953,4637677731066783/854611972340:-9541525600303367226221251749527/192401665676 qmulz:-4958597485118384/18914385675,-8391716685524037,=1:13870381750888490254448674198736/6304795225 qmulz:-8775066120996947/26819677230,8537625341965974,-8617075263155655/41305030346:-12486371148675098768666305313563/4469946205 qmulz:8632423322860386/9616021081,5042628174507057,-6506115385718735/7975459194:43530101062127611384934782744002/9616021081 qmulz:-3848534615760728/9274753529,2104642248786963,5619621461116310/5343995473:-8099788548249129154859453789064/9274753529 qmulz:271301194709322/33552569,1917863106025352,-3970383512818995/409886044:520318551953609085962402731344/33552569 qmulz:225678582778501/66976167,5457450818595612,-1586701099858817/141482387:410543255441342622436562179204/22325389 qmulz:-5691916212714825/75531979,-3677441922214847,186124889390004/78334747:20931691298371858008446792006775/75531979 qmulz:9683640970785183/21432671,6061708788245552,3666308965635053/8459353:4515339351909479419918957481232/1648667 qmulz:8423905758112927/2462761,-1402202086438487,4991587911230636/4020141:-11812018229987130827123385021449/2462761 qmulz:110629337771891/244490,5329540769616160,1715961548659264/49589:58960356597093007948570735856/24449 qmulz:2768082072858327/11996,8431038603161226,=1:11668903406493550143637918814451/5998 qmulz:-5632710453612631/282213,8269803080914635,-1089107539381719/990995:-5175711807020645232938163194965/31357 qmulz:513164615298521/2937,-761654779947971,6308090089559589/34312:-390854282142280204811013250891/2937 qmulz:2399352646293603/26699,5936082314225321,246326307317325/1064:14242754809253178957252862921563/26699 qmulz:1917463706144480/173,2784408494403777,-5268002443544296/9923:5339002231099637846089019700960/173 qmulz:-299651250103083/304,8512720924447435,1696619119714772/2041:-2550847466789346268098564942105/304 qmulz:567861836090453/137,1194683804539166,398775012895933/117:678415338793138672840757182198/137 qmulz:5855010424286591/141,-3387352251576542,-6842084179082795/92:-19832982743711308513005380748322/141 qmulz:1839091525348225/37,4835017725039396,3258229037788442/47:8892040123028407522020743672100/37 qmulz:689624656142569/50,-1436205069429607,1650564655275659/9:-990442427155607164133701640383/50 qmulz:887987723713419,-3871030680937173,=1:-3437427722790206595690596024487 qmulz:-6321481694612935/6,9155176113205281,-2076666497659035/2:-19291426070194927792191164303245/2 qmulz:47535841066367704/25874740830854221899,20217596491741418,386741628388289/10612132664990412300:961060453575373318717870874364272/25874740830854221899 qmulz:80223166731461168/79315578551274076339,19941312492318563,-6517563635718293/15173501904275140121:1599755236915441531514785120061584/79315578551274076339 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qmulz:-78176595124115512/936929521175,19202167121582858,-99925056698963177/191994309327:-1501160044569585652613332671093296/936929521175 qmulz:82802252720820771/664875719702,97327360089498817,-27164056917268865/462863761311:8058924666781006338043050273527907/664875719702 qmulz:-79012216554892489/70097745469,18109121557124146,-26372881204544091/13780169332:-1430841834090364897003709055939394/70097745469 qmulz:-70054799672271272/45482963493,7787932643225419,22281182451081849/9895333688:-545582061182298824047255613862968/45482963493 qmulz:38317664305319638/2445394649,31654407463814347,-43227662278819145/8020766369:1212922958982242534681702525246386/2445394649 qmulz:91685907685022135/618530726,-65256514026907419,84454182812530114/7990613223:-5983102720917385677413600610719565/618530726 qmulz:-9319036791983210/326561129,48383470752719549,-21563116260711314/160888617:-450887344068437052714708646772290/326561129 qmulz:-10319092612953469/85265494,-55462305741126344,942196671950729/100675391:286160334735311815060828261043668/42632747 qmulz:24190194708441624/10753379,88757165826516370,33675430745281060/75133189:2147053123112872034250339425384880/10753379 qmulz:-11468596832661746/1766525,56376469108104767,96014028182502185/4186386:-34029420792098057856142633744378/92975 qmulz:-40039747951909081/6069939,-55718774097961657,-38493857988408833/3718928:2230965671071745008018063888107217/6069939 qmulz:-37290139983929779/799087,11981560139468355,-11746974507966646/3218933:-446794054826648164153652712643545/799087 qmulz:41894225992589221/366814,74540431481275887,-66854308231170017/431055:3122813682061684114056083763414027/366814 qmulz:4577566343641272/36389,56889856836673491,=1:260417093950126892755280695920552/36389 qmulz:88284563154658136/23691,63742381682886541,-30323740102908723/9056:5627468321311120786042358530547576/23691 qmulz:-35239011702626416/1503,-96377199381969204,-61186369864860723/42751:1132079085629190722429226942964288/501 qmulz:6204324005181542/3263,9242869672214658,5888893248603815/2661:57345758184085853188298483442636/3263 qmulz:13023563233102553/2092,-18292948555955590,78624947167647851/9735:-119119686119189830929040691810635/1046 qmulz:8668988413765031/12,87487198824736036,24608302652702701/174:189606378241098583267909375589279/3 qmulz:-88604450607713147/253,-57197213811690954,-65274907046510203/195:220344682872903450186081523772706/11 qmulz:33666476522294146/13,67039261791546104,=1:2256975733177017899095506408307184/13 qmulz:-19043783688556820/29,-46927274804274505,15813572639616397/59:893672870466066256149790569874100/29 qmulz:-94396743394101937/7,29360199416108739,=1:-2771507210282078156031800042527443/7 qmulz:32378539760159572,74380454651945304,-15922753341092935/8:2408330508326757024819007256049888 qmulz:-515970186826451384/25959078573251600323,-481657180143660888,855482564716356613/45268895425503079014:248520745225026458245551027714268992/25959078573251600323 qmulz:-130967478747895251/18589421418033360838,147641505075499109,-55563959724327169/34005532994986142887:-19336235678282698393435282075831359/18589421418033360838 qmulz:-860266011517441547/2553655932637699066,-299807248907353740,=1:128956993120773018576083159450917890/1276827966318849533 qmulz:145239559532108435/807509961508023596,576064609905367511,401973572562411248/7006133492934535601:83667370204691447066198253378055285/807509961508023596 qmulz:-203788329869580393/934147712305627115,977955003052547263,34371785465644891/24153024504080070:-199295816759679001811043775610614359/934147712305627115 qmulz:-305697857540446967/103403955365462673,-568720855877228261,=1:173856747180237996116028815024134387/103403955365462673 qmulz:226166409746766031/13002990761630932,789981405518661663,-113466700430225377/10401766053678468:178667258252859769569650633510369553/13002990761630932 qmulz:3220063708444885/86759191901981914,-436274250898667434,=1:-702415441123888629947969466687545/43379595950990957 qmulz:-67396315446702174/385366352018695,935081661792652149,-625977217802097815/9842734508647274:-63021058646604060109741387184071926/385366352018695 qmulz:24319453787590069/147313838530763,247065078929176318,=1:6008487769545396355634476406785942/147313838530763 qmulz:100629482109427385/145102206127588,493200833830327566,587248475105746167/360845897573321:24815272242141808191386545620397455/72551103063794 qmulz:68125647111849775/751431108442761,573247979073143838,74386340727896222/930067472967985:4339209947768671307372114758104050/83492345382529 qmulz:315260234123867071/28724643212088,340944306756538261,-53419962261027213/66345800395925:107486181971265805844870978489503531/28724643212088 qmulz:-236430702618704929/20104762237425,598324387971999776,114120042986736600/9261982109063:-141462255442126511362707327398095904/20104762237425 qmulz:40711881042093025/722627757269,-916183636373594020,59862621134038918/36564773153:-37299559216753971995016222423710500/722627757269 qmulz:-520309382707815761/931737166517,259750055972789770,-130681632611383930/845007490973:-135150391281522837582794926345564970/931737166517 qmulz:-744723510370875375/104328014528,392776247476475915,645297290772722121/747416253776:-292509705810980823923192458654093125/104328014528 qmulz:150326873930054465/220440980183,184204467758877126,446972731209163483/312751250617:27690881802141504054899212422667590/220440980183 qmulz:115421167528373279/5250405410,771027268136349173,=1:88992867484509542530759922626948267/5250405410 qmulz:84701761403492795/44355610023,965802039756702720,=1:27268377978159632125207673492300800/14785203341 qmulz:894229992015313913/3163831833,-785572023936143576,681929403708376856/586412675:-702482064691871660107123412278372888/3163831833 qmulz:74634858785325581/142443768,427912086580428045,263236478364528529/7486986306:10645719384821420242829855889439715/47481256 qmulz:-332428641831574483/344279073,908684289900488822,-638499266082892652/390482433:-302072684345308192917372015601929026/344279073 qmulz:415890959805425615/192542692,57300089077177939,200778229355831075/85157704:23830589043243917548894324983507485/192542692 qmulz:806988421881608649/16389833,666714975759989998,994687425328887678/8586277:538031266133389292509645688390292702/16389833 qmulz:99978136901356657/62362649,-421321213914285499,477860583712193259/43057685:-42122910004168208858812125922216843/62362649 qmulz:134226773204000444/2213319,457929073299284411,=1:61466341865261143971298267726278484/2213319 qmulz:203692403587646607/2530234,198709333320751525,654497348349770852/9852495:40475581719402713398336251356325675/2530234 qmulz:1932413671793631/11008,605844360169614539,271988563133914698/256283:1170741924570827879369734025201109/11008 qmulz:78300870419392545/300541,9938443225300603,474105168486707610/456971:778188755154752224021438282204635/300541 qmulz:731791251673481239/82178,-375066073302435963,897701210637687185/8253:-16145298308367486968573476887023421/4834 qmulz:-244865844794445459/20764,633837473482998794,-572503688932727221/18042:-77602574203395710948196720797888223/10382 qmulz:-871079916851090199/6190,-933271236207286315,165562923533871377/1253:162590766166991424800556971016665337/1238 qmulz:278477012608289079/6904,166601452640247459,=1:46394674827457467509510753167200261/6904 qmulz:50351542334760530/697,74118063280217581,=1:3731958801024335445119077930877930/697 qmulz:716113366657554965/773,292433182475186613,55790708408336567/73:209415310824688987980879304679683545/773 qmulz:266171451721629402,838958222079312932,186531239281784779/61:223306727904647880295582119690026664 qmulz:-191048663820313019/17,-335221912735777740,-104282880591219422/9:64043698511459908763402007212397060/17 qmulz:918486165864351700,-754751323324354742,107963234237522909/3:-693228649141232227471800102650761400 qmulz:-263050925547501061/9,429366864986261421,-369906620681745801/4:-37648450411354997741362101140289227/3 qmulz:-8908762588791502798/9682457258957956871,6517968147068840217,=1:-58067030783541555611439264126370427166/9682457258957956871 qmulz:7658247927733463351/71097873025711495885,2645904249530727710,-526743598589435636/3308522377463446025:4052598147189972001038980978729031242/14219574605142299177 qmulz:35178382688557660/101323881670407613,7331418798392863213,232580837460702659/1407098737763013928:257907456139949700482063020643361580/101323881670407613 qmulz:1263699762126537691/454699906557876874,-4542833552105116827,-2210388710075629538/661648401890741827:-5740777679175690401542804846573826457/454699906557876874 qmulz:-1832647602190411445/226947754154888126,5643404261053171972,-1097284930177831457/619682865758859799:-5171185643605123184522851420511009770/113473877077444063 qmulz:1823011844211832737/592442421313405007,-1035458481118632295,-6389536796987914382/963103956263803057:-1887653075268861046971124680746441415/592442421313405007 qmulz:3241180647893831993/47706456259746618,401191978478284716,8203697741103525736/82629569130745973:216722612789009192825658264487286498/7951076043291103 qmulz:669385746027781985/4358673572763459,-3232260578078726488,3369728187950184564/4211286946970669:-2163629158413418191796114556108718680/4358673572763459 qmulz:-8416424642111725238/6365835551441079,4033684793967464839,623945245518632503/408732809111644:-4849886299779875487264451230199129526/909405078777297 qmulz:1670670426691770676/933711771783465,4268278044364566390,-4259333158202693983/1474131926823072:475392393441177774546174414803811976/62247451452231 qmulz:-2026621003312993155/235607922312922,-6449641809771356053,4984273563952773559/458950128766224:13070979555528254543461227718656817215/235607922312922 qmulz:2110680248476630645/95785011231043,4324730695176379682,-1722968689643087720/615704293887179:9128123658289392651639137372596554890/95785011231043 qmulz:-641839465597711103/9456066925611,1548277416348552437,-2507922761391944404/21340298450009:-993745549506159751964209714572608011/9456066925611 qmulz:2741589907602153339/57948673895524,1590482362679123180,-2499147223466166660/93552475783027:1090112598435077963801396817107324505/14487168473881 qmulz:1105127694202188183/6381230280571,6999165228541352101,-1962335544251498845/1250684067374:7734971330358035931095740815664422483/6381230280571 qmulz:3388900892142215022/3450834628513,-921940083605878001,6734092499539471533/5162430112340:-3124363571833628263304768671241531022/3450834628513 qmulz:-386348847054518292/323004206381,514411028349585069,3189676746121428640/214488726717:-198742107714991314988148399870582148/323004206381 qmulz:2621996699851800211/639729174738,901100719762883014,9556760707097111231/962924737943:1181341556726180554328723203646757977/319864587369 qmulz:-2049289271073576417/18016913114,7508216114633285941,-9469235071531039565/67942461077:-530569197538611262694579912395698393/621272866 qmulz:1639764361637752909/49863322429,-3667535081176061352,=1:-6013893321168728538238660340400472968/49863322429 qmulz:4212865081507184639/8422182797,5317645517552525584,826928849605057287/795440204:3200360445247176534048939736551329168/1203168971 qmulz:4093224907870688472/8446810835,-4394239498678494479,221730631562040646/480114129:-17986610567140020861411212830180946088/8446810835 qmulz:8729905651613329077/131452699,-9507557452223167406,=1:-83000079535201453087454918169138464262/131452699 qmulz:4738064793602310889/451996055,4531489655540363995,=1:4294098319897772319607429689642408311/90399211 qmulz:7744273453919740331/974912,4029995544880393387,5229428187412633641/38528578:31209387517632050003517673680169591097/974912 qmulz:-8068802747587440815/29032004,-9849867648134802759,8503993416585326183/5318819:79476639142642740206984820735611208585/29032004 qmulz:2861631232576326878/6980153,2635765392614151917,=1:7542588569248461690745630176942325126/6980153 qmulz:-1779740841595132817/3012373,9922862571979507578,971621845586608480/521437:-17660123784887653006801622709167987226/3012373 qmulz:4023122851061736595/781603,3458044068302173434,3738807635979349585/665988:13912136111164966581427463952914617230/781603 qmulz:586647455438577923/33279,4526301832916840671,3608109198062688989/33159:2655343452827635863034403318209106333/33279 qmulz:9196111739041159411/1211,3157226438241334248,-5764176110323692119/75991:29034207111522241973647178465501807928/1211 qmulz:-128347641900306833/12774,-7554445682363002392,5759447892271827483/18544:161599214865874288341552651985490756/2129 qmulz:836992725257147861/4133,-8611487193024899504,7678442646525158846/9511:-7207752134206937140419355427193560944/4133 qmulz:8699549138022640117/5811,-6972026102209810211,549233631824230415/177:-60653483667750701802929732179724834687/5811 qmulz:3156470757655913741/841,-6926959212561953600,-840701905979711979/41:-21864744193927041320056800380044417600/841 qmulz:509258565369492935/912,8179603403105663140,-6092933483503672408/101:1041383273589253055649823422179978975/228 qmulz:4260013411623757232/75,-7652070371810821485,=1:-2173194827373526007681124278141981968/5 qmulz:-5571230682641213483/85,5687608093861986954,1592299486970268628/23:-31686976723362408587412758204074900782/85 qmulz:1224310285715487476/7,7384878353077411745,1489674084056377327/2:9041382526430324573993691487042805620/7 qmulz:532608537074668190,5378987672829123810,1299009834218541099:2864894755368193556998428824178603900 qmulz:-16831183915817756170/2753858239387681579,59557538310440342273,14474171978684251754/88138472845001942881:-1002423880876383309855786104105657574410/2753858239387681579 qmulz:-76852233908089385223/89591433315005827168,-16827322555441357812,-13261671210390977146/47829058560152879137:323304332269411910681014536231862103019/22397858328751456792 qmulz:69150327729675178449/8650125162732904421,14293920797793407650,50884780102476306733/6026568253305189080:988429307709434226307578722449551734850/8650125162732904421 qmulz:30499040613205460343/8988598618848438770,30570026052354339437,51811261931566266659/3748183226209013484:932356466117503990794086213419264446891/8988598618848438770 qmulz:43819658523452866810/102194429295876731,70504335913014047202,=1:3089475924131090053789938711687559165620/102194429295876731 qmulz:69656424488183436907/30102774811906661,984948427407800828,-39906369295800321023/155750850550041643:68607985758486503850804077075560358996/30102774811906661 qmulz:33641878290673988917/12925928405761371,-5396171272119458800,19436319690765846760/70381750662978231:-181537337172274262921911758331238119600/12925928405761371 qmulz:42954819767647340359/97571649192732270,38715654116595663589,=1:1663023944764940538514016228488546488451/97571649192732270 qmulz:-99002754944524890631/7986465915924126,-97203975364529818705,12484199575939692941/2326957254470028:9623461352648180166996658939078383052855/7986465915924126 qmulz:88352255172275736854/7933296505985257,42489727492090669013,98815810269903702196/2382358470880605:3754063245581654384182755776192399905102/7933296505985257 qmulz:61590480972201025960/675375171340791,-75994828859228936809,-11049721719852020118/20660972971879:-4680558060840013232552967100229808561640/675375171340791 qmulz:-27522646268475576522/580129834806571,5567162029085222334,74438237038085866509/799763096356799:-153223031245801313480018162391200442348/580129834806571 qmulz:24148248964829892922/23286035365313,49985702383172830448,7055168644844378885/36672697526553:1207067185830748414507857319763501289056/23286035365313 qmulz:52980189869726618341/71466611837586,38839808746354627533,32063023501001399398/95171990625945:22126241310599319846248909165943025621/768458191802 qmulz:-80505026028619928191/8017291718590,-1533155918930949021,-3916532593760914985/326976214133:123426757159468755445689924468501751011/8017291718590 qmulz:17292391457368334407/1571629061585,-63370707239731364623,43143296273586046143/3465594785525:-1095831076519720312454034284738713483561/1571629061585 qmulz:-45604879788200428008/529616356051,53301018012216428706,-91229775748273485595/717004201262:-2430786519035835963440363052798417597648/529616356051 qmulz:-50447424829663619798/988121155093,6780140438275382263,16659035028087001517/899562317168:-342040625094459896541992348672744842874/988121155093 qmulz:3593845345146253521/41915442602,-63858823181329772213,3118916835826556491/676191095:-229498734436739670514786299133279211973/41915442602 qmulz:16886813553311884569/11104775518,-56529259575299150290,73272925971647951646/32053123633:-477299533377423659452543589452131437505/5552387759 qmulz:-36701646710377438096/4191403967,41311697381328283293,85676309288704030215/204223664:-1516207322295535412352618149227058530128/4191403967 qmulz:-31991568945242380121/3326501360,49756427012706630969,=1:-1591786165245924544503303159456768567249/3326501360 qmulz:25027541823211097487/727783012,72744111549984214188,27646550684503944351/772714058:455151573552390843680552331807189136389/181945753 qmulz:-10660456145991522967/70536419,85257294987559072920,-49523716090045547608/476186017:-908881654340736383544975893469407753640/70536419 qmulz:33128477737669316703/79965173,30163481878837698924,41486580218368730746/24538333:999270237913666562482186749103918327572/79965173 qmulz:-88082268340996623207/91130108,-98498682060501497133,55248370490574572505/10033543:8675987344487603057841057039320991765531/91130108 qmulz:-44828402098358201492/3408511,-69899774554986777317,53529539851460359205/7667246:3133495200335534468175721510741221156964/3408511 qmulz:97775247222108446692/6123089,-93552521078990120186,-42751923423887600316/1557173:-9147120876749770652720919372526854124712/6123089 qmulz:36516268542348216758/743177,-24090657731418051536,13560217582155473423/145359:-879700927082258851088293609160542840288/743177 qmulz:13823011732367751421/140456,92159940210798638916,-70795417829842533145/263179:318481983697045021949324000379556224909/35114 qmulz:21697263555618348560/7063,34463551544345103980,99869086375772085/122:747764760920293478397871020089083268800/7063 qmulz:-40668672455972057307/50141,18865137997582967131,=1:-26455866140014285075027032694601012973/1729 qmulz:-15581921553193083728/2673,-55246769898174604433,-17101679935689176965/8667:860850834620665736463709777467848966224/2673 qmulz:5779320031390413993/7,19217000507739754005,25876817036248520828/8953:111061195977620116757818678920929791965/7 qmulz:2423549793740192960/491,98696549719389277261,-8414536430516573180/273:239196002715294582270898075501080282560/491 qmulz:27706287293558914219/676,32022217504768731686,-38742274862382707994/961:443608378981976875151437105221950621617/338 qmulz:64017926203955613359/38,64555971256483309833,70053608548103954878/35:4132739403922228262726093720335950859047/38 qmulz:53804889371534152691/9,-61739634189995994475,-2917407728537843404/21:-3321894187431722069404444190953042382225/9 qmulz:-63773122944071670311,68924540068336860054,-11050684739856731468:-4395533167641640581052894142988833656794 qmulz:91952574331161593349/4,-53703503362679036569,87690617237600059250:-4938175384800530690367847777470278179581/4 ================================================ FILE: tests/qsub.tc ================================================ ## Rational subtraction tests ## Generated and verified in PLT Scheme (see imath-test.scm) qsub:1/6908363373906559980,-3/3282386453454754261,=2:24007476575174434201/22675918354053873847004295306757074780 qsub:1/38717857456042735841,4/21180041959354743117,=1:-133691387864816200247/820045845495301036647051443116443956397 qsub:5/43729125372682174,-9/5619593033754393704,0:14245763648563054043/122869944158248625198135913829316248 qsub:-2/2974810045372038215,=1,-4/6399510259263906921:0 qsub:5/554668526872261904,=1,-1/110568531382495635:0 qsub:3/342789991526278043,-4/498606462885016907,-3/85472740226188603:2866979354760162893/170917305187302413099656668837873001 qsub:1/3516821512087322,0,4/43427709377638547:1/3516821512087322 qsub:-8/99244619430310225,9/68745482383862908,2/20174595569499161:-1443165433943695289/6822619236739570045025636310634300 qsub:1/4158186027003720,3/1924897427288305,2/873983495405445:-2109932130744571/1600816317113127793988749498920 qsub:7/3877179943979588,0,-3/8937193062762751:7/3877179943979588 qsub:3/6941436021947,0,-5/715763583943883:3/6941436021947 qsub:3/164894601106681,5/983718669019872,=2:2126683001526211/162209897529226945840780964832 qsub:3/97536769945753,-8/56666447486451,-3/355123038725:950293502025377/5527062252129064526472492603 qsub:0,1/69397821325107,7/899954591994:-1/69397821325107 qsub:0,1/881101320631,1/1676161462807:-1/881101320631 qsub:9/5714833944922,-5/2130613532867,=1:47749691520413/12176102541138516914751374 qsub:1/416320154010,9/647850043316,8/147151224525:-1549515671387/134856514904351145548580 qsub:1/437091275186,9/260061434048,2/56787440467:-1836880021313/56835291917370078966464 qsub:1/40450640622,7/70939336904,8/60816634845:-106107573725/1434770811533343057144 qsub:0,1/44837423526,-1/89874392823:-1/44837423526 qsub:1/320712007,1/384804019,1/5470204:64092012/123411269235156133 qsub:-5/9120926808,1/893326726,=2:-6793780219/4073983841738135304 qsub:3/355507838,=1,-1/715596526:0 qsub:4/397576755,2/95841397,-3/206755309:-411787922/38104311613926735 qsub:0,-6/63950497,-1/12602985:6/63950497 qsub:5/57474807,-3/9692846,8/51541573:220888651/557094453130722 qsub:-5/7525009,-7/6073612,-1/1008717:22307003/45703984962508 qsub:3/1999328,6/812029,-6/2808949:-9559881/1623512316512 qsub:0,7/738513,=2:-7/738513 qsub:7/320723,=1,9/571685:0 qsub:7/14415,=1,-5/47022:0 qsub:-1/22106,3/90671,=1:-22427/286339018 qsub:3/1135,-9/8459,=2:35592/9600965 qsub:5/6528,1/1065,=2:-401/2317440 qsub:3/100,5/979,5/637:2437/97900 qsub:1/117,=1,-6/601:0 qsub:5/76,3/55,7/20:47/4180 qsub:2/5,7/12,8/11:-11/60 qsub:1/3,=1,=1:0 qsub:-2,0,1/3:-2 qsub:-27/133467566250814981,83/42563959651039965219,91/6397136498252123976:-1160304718576896704336/5680908104622192257664942460644145839 qsub:45/40427972021325393238,64/9751620923778714977,-18/31750379913563777419:-2148567267794782993267/394238257869097174193626565778845125526 qsub:2/843174797904089739,59/3829064789486601609,=1:-14029727832456030461/1076190310012343744009826655225930017 qsub:21/135302160124707707,=1,-91/6243239679870796216:0 qsub:33/269586386932708513,71/663560078654965882,82/347777995721589109:2756849123391569683/178886764117376127330118719865953466 qsub:-49/381369757179978313,-79/502081482360917424,66/15964802517749773:5526218181533332951/191478693012546642471803143103825712 qsub:50/84007949326343527,-55/90680207033049248,=2:9154447564601356385/7617858237334741132727849157017696 qsub:7/63509973628647649,31/6358426332168578,-2/8606093719923861:-1924300198162897073/403823488675725185285863631373122 qsub:-61/3288737806026908,52/891085361745265,=1:-225370572979860381/2930546117568816471902431590620 qsub:-68/686724622342265,-2/87939998369281,-97/6330897213879162:-4606470644426578/60390562168923894678643961465 qsub:53/74615069808694,19/206431401793345,8/335314245039321:9523177968682099/15402893455516996957672341430 qsub:-41/794425111656850,40/355792921374903,84/720131909879285:-46364514242645023/282650831289974168794338035550 qsub:-19/9948614096197,=1,-17/6019916154851:0 qsub:26/86905243242955,5/1105886678309,85/28690254896344:-405773162578741/96107350777587172015563095 qsub:29/1328659476658,-75/8718935424058,23/3978732114658:88124647011758/2896124044385949895659541 qsub:89/3664660122749,39/3752130456923,31/2507346317004:191017865878936/13750282860837702636841327 qsub:-1/111730970852,-4/53644158721,5/525620687366:393279724687/5993713934436112600292 qsub:9/134376727834,-63/680315135834,-13/19845761250:12619870308/79081766305636815401 qsub:53/83663624339,-83/23745430735,39/22448823287:8202588649092/1986628796780784659165 qsub:94/82386633297,59/60658096185,-7/3139891864:280349892289/1665805442295916557315 qsub:-56/4452532283,=1,-33/2287829573:0 qsub:5/4288753327,-1/207457757,-40/1852400711:5326042112/889735145545707539 qsub:31/984155769,43/889343448,-34/317681033:-4916350393/291750828323850504 qsub:91/918406649,64/20465291,4/3347977:-56915684055/18795459328119859 qsub:41/61159865,47/95152545,=2:205348138/1163903361321285 qsub:76/19895571,=1,=1:0 qsub:1/1255098,=1,83/1479054:0 qsub:91/7916464,-7/427858,=1:47175163/1693561227056 qsub:25/630098,19/359620,-70/654341:-1490681/113297921380 qsub:1/23261,6/84073,16/99379:-55493/1955622053 qsub:87/25076,=1,7/10664:0 qsub:88/76661,-54/49307,=1:8478710/3779923927 qsub:86/1213,99/1546,=1:12869/1875298 qsub:40/4409,47/6632,=1:58057/29240488 qsub:47/221,-20/453,32/67:25711/100113 qsub:88/281,27/221,3/160:11861/62101 qsub:11/76,=1,0:0 qsub:12/11,34/37,-91/30:70/407 qsub:-21/2,9,-75/4:-39/2 qsub:-78/7,19,=2:-211/7 qsub:716/63229225130372968755,323/1041977709013285590,-85/5331036743812256792:-87453260788697584113/292815302862361288266503618244274402 qsub:28/28432306149803878485,51/36062569591582234426,-327/8530238148665402747:-440295665075695238807/1025342019176473906318007480837287724610 qsub:35/2651717833003975527,94/1600682896707796861,=2:-193237574917600809403/4244559382184525484529422270531420747 qsub:386/5424883893029166991,-201/2832569452810712705,43/716839232710423233:2183773471283797669321/15366360400439276458941965547170320655 qsub:971/506137779607436980,-690/134579589961574473,267/104999489601941375:479911849781820329483/68115814843630618803212580924211540 qsub:846/926665120742753771,-693/971167451265042566,=1:1463786592444954374139/899947003487953107927067006372016386 qsub:-160/248883036705679,=1,950/1477253685625391:0 qsub:306/15329555212551109,173/93038341559131937,683/17162719883913218:25817719465323030865/1426236393814901458412317286668133 qsub:-625/3476582462880142,-872/8679903101365753,437/9209000641481251:-2393359530722111801/30176398901707132402666142576926 qsub:4/92742256929161,-206/1677519242207209,-29/1920847318304748:25814981896236002/155576920564392438731996521649 qsub:105/440859258236711,23/114084068799213,859/777590483782957:1839064284473012/50295017947446948173484508443 qsub:234/109710309040703,435/19164872307439,=2:-43239404312765079/2102584063574743486180689617 qsub:40/98720052152257,200/37673731641681,195/18309401204:-18237061164784160/3719152752436883045979424017 qsub:101/8139505456847,-896/64811418546951,=1:13838950162576963/527532894928902528173923497 qsub:339/2503418324141,=1,203/710577119901:0 qsub:-210/2286964112149,579/5338514331377,-895/8857700286753:-2445240230523441/12208990688052313177599173 qsub:223/305810995184,29/35011322751,41/153998316063:-1060993886863/10706847453191530631184 qsub:212/157864593381,817/922433484280,301/424913103878:6052775079553/13238144265171023231880 qsub:39/74199525578,=1,86/3093865155:0 qsub:-285/57499506881,767/82446691329,5/8259783887:-67599428806492/4740644095387518534849 qsub:419/3764128897,129/517942151,-247/7249378910:-268554866444/1949601017553437447 qsub:245/1908967167,757/2819581996,-985/2094042342:-754290556399/5382489455028325332 qsub:-295/48205876,431/527424726,140/594985499:-88183513363/12712485470444988 qsub:961/845688743,-405/870406786,187/421915568:1178964862261/736093220751009998 qsub:407/45012097,=1,=2:0 qsub:-58/619321,49/12338458,193/39820887:-745977293/7641466147018 qsub:575/7245689,-62/7853229,=2:4964839393/56902054979781 qsub:95/498463,=1,31/397052:0 qsub:194/160465,199/12089,-11/7277:-29587269/1939861385 qsub:266/45609,908/59061,-571/590454:-8567582/897904383 qsub:131/55938,=1,55/8836:0 qsub:199/46692,=1,964/70603:0 qsub:382/8669,-217/474,467/5123:2062241/4109106 qsub:147/745,528/8207,-88/5227:813069/6114215 qsub:396/775,=1,-877/724:0 qsub:6/551,=1,-435/346:0 qsub:55/24,277/11,54/5:-6043/264 qsub:10,-123/13,556/9:253/13 qsub:108,-709/4,-92:1141/4 qsub:181/9,=1,-941:0 qsub:5864/87029719866427538623,7169/77056696318482378212,9879/50543130835616368106:-172055594510838358553119/6706222694429899607884755085022523682076 qsub:5653/86895502758062177839,5653/8154794595245621549,-1891/10149086543140986167:-445121223244401992707370/708614976242596448503974984564128652611 qsub:661/363701500997277796,479/2983031197662645683,=2:1797570602677312732179/1084932924111611507079868138271154668 qsub:-667/1895442338469738028,=1,-1283/8749436718472928966:0 qsub:-9697/818740708549198026,3503/102582377391327177,-1163/20328789690713125:-1287596671870513440149/27996122783345481707441743709517534 qsub:5593/36797958092515142,-896/400288681159053633,1503/320767765005962056:2271785564173480536601/14729806114199011085303985442610886 qsub:6797/6164537725975597,-25/1227246984675396,-8333/22072906026109818:8495711197988056537/7565410336121273997822462311412 qsub:5972/68776879303523725,3471/59251132058857634,=2:115123212592966940773/4075107958209196684815674316366650 qsub:-6611/9413167004921254,=1,-6256/7532100811974283:0 qsub:1837/782359177742283,274/89188711189557,2191/8972155631565142:-16842250748723111/23259202250051923207502312877 qsub:553/12771753856843,7076/381142689332759,4681/186762282268761:120398976909994659/4867860612493178112476219837 qsub:3079/80223061021791,-3585/408207816163306,=2:1544471539729939909/32747680545640939721680601046 qsub:-9557/15580233019419,6164/45700338424117,-8859/38230373237191:-532794690650984885/712021921714050551118928023 qsub:-6948/27781302080773,=1,=1:0 qsub:965/554586285674,=1,1991/3124819638593:0 qsub:745/38448222313,1985/5666404010804,403/1187780069839:4145151266757675/217863161122667045869652 qsub:-859/409102304936,=1,4163/697719670590:0 qsub:958/328712574179,-6903/92390217229,942/905293648915:2357612727663019/30369826134301586329991 qsub:151/12267425536,=1,=1:0 qsub:8671/21057436708,2207/65025757482,2889/90207961763:36954612879419/97805412326212317804 qsub:-563/827856356,2261/803220213,9777/7547919848:-2323996200835/664950958599723828 qsub:75/325694386,7497/1661300549,1948/1110250407:-2317133270667/541076262268017914 qsub:3501/918304436,961/56965645,=2:-683053839851/52311804503101220 qsub:1123/310344294,2131/431751558,2307/53942272:-4902408080/3721989790303057 qsub:1405/9784159,2196/25867783,=1:14858221951/253094501849497 qsub:794/7899253,-2407/48403717,=1:57446053269/382353206723401 qsub:1229/5474993,4511/2921328,-7447/1108510:-21107381311/15994250350704 qsub:-7372/331741,-1691/1178944,5486/4648811:-8130201137/391104061504 qsub:5538/47579,1604/905061,-3007/385287:4935911102/43061897319 qsub:6299/305054,917/272126,5357/926074:358596789/20753281201 qsub:-4585/61734,=1,3775/46277:0 qsub:419/11735,-8692/17091,1813/23231:109161749/200562885 qsub:-1997/1968,4543/2391,=2:-1523939/522832 qsub:2071/1736,755/3768,4076/8723:405803/408828 qsub:838/393,-953/227,-1542/517:564755/89211 qsub:30/29,5248/27,=2:-151382/783 qsub:391/83,-375/8,1924/15:34253/664 qsub:3263/21,607/4,-2267/41:305/84 qsub:9453,3109/2,6826/5:15797/2 qsub:-3878,309,8605/9:-4187 qsub:11222/48066783055662674131,=1,=1:0 qsub:44095/11229138978726519749,=1,=1:0 qsub:32172/9931355060831305057,-22127/1443489042124973960,7360/8565719299009119553:266191022894258949237359/14335802203762393030456814478941315720 qsub:64044/4464944802393435647,12647/913738015734848205,80458/8255357897052863503:2051280563852837813411/4079789804104601810582916593980963635 qsub:41455/753918793466056957,=1,38552/179247636782332451:0 qsub:70832/329222465952924851,20242/279519391122527087,98212/275893153651362115:13134796356171733792442/92024063227018458748454302122939037 qsub:16550/9390796490643017,=1,=1:0 qsub:-52475/54547572128706592,17578/797685580288227,7736/4761258128626551:-1000695773704029186001/43511811726801235561284074892384 qsub:-20996/6762826792669,-44673/3665405594824492,-89646/5844908573159699:-76656740107626131795/24788503162677927378327249148 qsub:45185/5494693252958359,32663/2723960065506187,40281/8753885671043431:-56391030161481820422/14967324993264855317568567867133 qsub:12788/20397625645595,85276/411854703134143,=2:3527370019125661464/8400858054907910680262050085 qsub:5182/89854258440697,64615/978522088368546,=2:-735231447219831283/87924376618197880146621116562 qsub:14899/24106539570023,26806/37583148137177,60169/20330813693322:-86248575618236415/905999647734893551001045071 qsub:77/5504614030045,39585/32999174301133,41462/80693310429705:-215359209958144084/181647717837917119539540985 qsub:82526/6888246953501,26067/1462753317193,18855/1955140329926:-58840753082241049/10075806080878164174842693 qsub:48233/7425592622352,-67581/3978085226579,41398/5449697074565:693703959744755419/29539640309572506699893808 qsub:5505/559716521882,37907/205803582655,=2:-20084225472465199/115191665474511303156710 qsub:21476/65447686805,89325/499062486437,-40113/803762193086:4871751334864387/32662485308453336363785 qsub:21526/16385258133,59161/53875727711,=1:190360658300573/882767705647956223563 qsub:-19280/22598967893,14123/12257869757,=2:-555496952467799/277015205075018712001 qsub:10456/7458705583,-25903/4591932494,70435/2217009577:241216096873713/34249872529756914002 qsub:19521/861174313,=1,-5154/2978985245:0 qsub:682/74110691,2034/18404407,13571/194261092:-138189339920/1363963320215237 qsub:17065/678911302,47417/43292069,6893/55518891:-31453158049449/29391474931063838 qsub:66870/71491241,=1,54717/26772383:0 qsub:61950/53770049,38657/31651038,=2:-117806980093/1701877864160862 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qtodec:25224504315989/2747113245,10,16,0:9182.1858315815444295 qtodec:-354734288655699/8606733226,10,5,0:-41215.90379 qtodec:294622457238131/4699248277,10,15,0:62695.656809649983088 qtodec:84851645314450/3149545649,8,5,0:64474.72505 qtodec:162782722239884/940443795,10,5,0:173091.38845 qtodec:-503919081966818/49953093,10,12,0:-10087845.450667449160 qtodec:696741265176479/547456417,10,10,0:1272688.0963320208 qtodec:123373090223114/171645417,10,19,0:718767.1676844945997014298 qtodec:530906534529992/21770787,10,10,0:24386189.3706457189 qtodec:25200685975741/10321244,4,3,0:21110012200.213 qtodec:-58528486417214/9145779,16,23,0:-61A614.0F20EFF0ECB8777D9D089D6 qtodec:-202870643410118/39728965,4,0,0:-103132222332 qtodec:226786253503/4854200,10,10,0:46719.5940634914 qtodec:947663833947325/1199459,8,24,0:5705715226.174676743125024435532213 qtodec:58508575771048/1950595,10,12,0:29995245.435904429161 qtodec:-162029920997164/5378993,10,23,0:-30122723.89965259296675046797792 qtodec:-638908439370581/780673,2,13,0:-110000110001111110011101001101.0011111111011 qtodec:54048561476435/260446,16,13,0:C5E8D1C.AADE1542405BB qtodec:311253898901698/112463,16,23,0:A4F666A8.42F6DD7D2BF402286E84E52 qtodec:-364014082098529/378836,16,13,0:-3945CA63.2A9FE228A057C qtodec:662955978899037/29150,8,10,0:251345254234.0616507470 qtodec:380819161094198/155,16,19,0:23C0A857C06.F4704F4704F4704F470 qtodec:19950100398461/41364,3,22,0:1020121112200021201.1102012021021112012001 qtodec:843068174103353/67398,8,22,0:135145224047.7022451545330470767051 # Writing decimal fractions, with rounding qtodec:@0.001,10,1,0:0.0 qtodec:@-3.5,10,0,0:-3 qtodec:@12.001,10,2,0:12.00 qtodec:@0.001,10,1,2:0.1 qtodec:@-3.2,10,0,2:-4 qtodec:@12.001,10,2,2:12.01 qtodec:@0.001,10,1,3:0.0 qtodec:@0.051,10,1,3:0.1 qtodec:@0.050,10,1,3:0.0 qtodec:@-3.5,10,0,3:-3 qtodec:@12.001,10,2,3:12.00 qtodec:@0.001,10,1,1:0.0 qtodec:@0.051,10,1,1:0.1 qtodec:@0.050,10,1,1:0.1 qtodec:@-3.5,10,0,1:-4 qtodec:@12.002,10,2,1:12.00 qtodec:@12.005,10,2,1:12.01 ================================================ FILE: tests/root.tc ================================================ # Root-finding tests # Square root tests sqrt:0,0:0 sqrt:0,=1:0 sqrt:1,0:1 sqrt:1,=1:1 sqrt:1,5:1 sqrt:256,=1:16 sqrt:257,=1:16 sqrt:-1,0:$MP_UNDEF sqrt:-1,=1:$MP_UNDEF sqrt:-1029384298,66883:$MP_UNDEF sqrt:394820398429038402938402,=1:628347354915 sqrt:394820398429038402938402,-5839823984:628347354915 sqrt:17179869183,0:131071 sqrt:4295098369,=1:65537 sqrt:26965706504352387672564992041751053514175649974280741932736827760729,=1:5192851481060515336695158019653723 # More general roots root:0,1,0:0 root:0,1,=1:0 root:0,5,0:0 root:0,5,=1:0 root:-1,5,0:-1 root:-1,4,0:$MP_UNDEF root:-1,3,=1:-1 root:-8,3,0:-2 root:-8,3,=1:-2 root:17,2,0:4 root:17,3,0:2 root:29,2,0:5 root:29,3,0:3 root:50,5,=1:2 root:4295098369,2,0:65537 root:4295098369,2,43:65537 root:4295098369,2,=1:65537 root:-4295098369,2,=1:$MP_UNDEF root:-4295098369,4,65537:$MP_UNDEF root:-281487861809153,3,0:-65537 root:-281487861809153,3,=1:-65537 root:-281487861809153,3,8349283:-65537 root:-19991036671350700657170189502736817905009200157042372341654483623953031910930270960998207372480741818129399253027601458115528449927512127290460743651463958852225556661727551760552841554362323271980596910944452290359774556447658518439936535499843549082781717193598437061923,7,=1:-571823748273487384719287348728374273472 root:26965706504352387672564992041751053514175649974280741932736827760729,2,=1:5192851481060515336695158019653723 ================================================ FILE: tests/rtest.c ================================================ /* Name: rtest.c Purpose: Test routines for RSA implementation. Author: M. J. Fromberger Copyright (C) 2002-2008 Michael J. Fromberger, All Rights Reserved. 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. */ #include #include #include #include #include #include "rsamath.h" void random_fill(unsigned char* buf, int len); void print_buf(unsigned char* buf, int len, int brk, FILE* ofp); int main(int argc, char* argv[]) { int buf_len, msg_len, i; unsigned char* buf; mp_result res; if (argc < 3) { fprintf(stderr, "Usage: %s \n", argv[0]); return 1; } srand((unsigned int)time(NULL)); if ((buf_len = atoi(argv[1])) <= 0) { fprintf(stderr, "Buffer length must be positive, not %d\n", buf_len); return 2; } if ((msg_len = atoi(argv[2])) <= 0) { fprintf(stderr, "Message length must be positive, not %d\n", msg_len); return 2; } if (msg_len > buf_len) msg_len = buf_len; buf = calloc(buf_len, sizeof(*buf)); for (i = 0; i < msg_len; ++i) buf[i] = i + 1; printf( "Buffer size: %d bytes\n" "Message len: %d bytes\n\n", buf_len, msg_len); printf("Message:\n"); print_buf(buf, msg_len, 16, stdout); fputc('\n', stdout); if ((res = rsa_pkcs1v15_encode(buf, msg_len, buf_len, 2, random_fill)) != MP_OK) { printf("Error from encoding function: %d\n", res); free(buf); return 1; } printf("Encoded message:\n"); print_buf(buf, buf_len, 16, stdout); fputc('\n', stdout); msg_len = -1; /* make decoder fill this in */ if ((res = rsa_pkcs1v15_decode(buf, buf_len, 2, &msg_len)) != MP_OK) { printf("Error from decoding function: %d\n", res); free(buf); return 1; } printf("Decoded message (%d bytes):\n", msg_len); print_buf(buf, msg_len, 16, stdout); fputc('\n', stdout); free(buf); return 0; } void random_fill(unsigned char* buf, int len) { int i; for (i = 0; i < len; ++i) { unsigned char c = 0; while (c == 0) c = (unsigned char)rand(); buf[i] = c; } } void print_buf(unsigned char* buf, int len, int brk, FILE* ofp) { int i; for (i = 0; i < len; ++i) { fprintf(ofp, "%02X", buf[i]); if ((i + 1) % brk == 0) fputc('\n', ofp); else fputc(' ', ofp); } if (i % brk) fputc('\n', ofp); } ================================================ FILE: tests/set.tc ================================================ #Unsigned integer assignment. Assumes sizeof(long) == 8. setu:0,0:0 setu:0,18446744073709551615:18446744073709551615 setu:0,567:567 #Signed integer assignment. Assumes sizeof(long) == 8. setv:0,0:0 setv:0,-1:-1 setv:0,9223372036854775807:9223372036854775807 setv:0,-9223372036854775808:-9223372036854775808 setv:0,4324:4324 ================================================ FILE: tests/sqr.tc ================================================ # Squaring tests sqr:0,0:0 sqr:495,0:245025 sqr:702,0:492804 sqr:23080,0:532686400 sqr:-485,0:235225 sqr:31727877,0:1006658178927129 sqr:-8234442,0:67806035051364 sqr:80,0:6400 sqr:75029676,0:5629452280664976 sqr:-8153,0:66471409 sqr:5729957,0:32832407221849 sqr:641,0:410881 sqr:-82,0:6724 sqr:7356,0:54110736 sqr:0,=1:0 sqr:7761224,0:60236597978176 sqr:928319,0:861776165761 sqr:912,0:831744 sqr:334190449,0:111683256202821601 sqr:#xAC46D3FD,0:#x73EF407495E70809 sqr:-180,0:32400 sqr:8965915,0:80387631787225 sqr:1771,0:3136441 sqr:131,0:17161 sqr:2518088106,0:6340767709578667236 sqr:31019,0:962178361 sqr:460877681,0:212408236843937761 sqr:2,0:4 sqr:2,=1:4 sqr:-43189,0:1865289721 sqr:400,0:160000 sqr:400,=1:160000 sqr:16978,0:288252484 sqr:32,0:1024 sqr:4185,0:17514225 sqr:246082426,0:60556560386045476 sqr:5024,0:25240576 sqr:4283818927,0:18351104599323431329 sqr:79803747,0:6368638035240009 sqr:27,0:729 sqr:-294872579,0:86949837846111241 sqr:5431,0:29495761 sqr:-64,0:4096 sqr:-27347593472,0:747890868709777014784 sqr:-93,0:8649 sqr:5941698,0:35303775123204 sqr:68188,0:4649603344 sqr:-10073,0:101465329 sqr:712007,0:506953968049 sqr:74981,0:5622150361 sqr:590060947429,0:348171921680809101710041 sqr:3375362,0:11393068631044 sqr:6288,0:39538944 sqr:-14938,0:223143844 sqr:818,0:669124 sqr:-61517636,0:3784419539028496 sqr:-485757743,0:235960584884454049 sqr:52047149,0:2708905719028201 sqr:880295,0:774919287025 sqr:23268913856,0:541442352037948788736 sqr:8611582804,0:74159358390148502416 sqr:-35440071,0:1255998632485041 sqr:-123,0:15129 sqr:-198239315,0:39298826011669225 sqr:-18792,0:353139264 sqr:42334,0:1792167556 sqr:8871716,0:78707344784656 sqr:-742998638,0:552046976069855044 sqr:599309793653,0:359172228768401439084409 sqr:92330620850,0:8524943546546454722500 sqr:-21253,0:451690009 sqr:-8591240,0:73809404737600 sqr:-4406721416023,0:19419193638435754241136529 sqr:7093605833487,0:50319243720880795970579169 sqr:540053945630,0:291658264190530996096900 sqr:6679643648234,0:44617639267392821131318756 sqr:521589,0:272055084921 sqr:13144286787,0:172772275138902783369 sqr:-47469,0:2253305961 sqr:480758624,0:231128854550373376 sqr:-8238434,0:67871794772356 sqr:-867204631,0:752043872027846161 sqr:84079798766,0:7069412560531055122756 sqr:14048677,0:197365325450329 sqr:647598376181,0:419383656832267988144761 sqr:89538606,0:8017161964423236 sqr:8775965118,0:77017563752352753924 sqr:135957585,0:18484464919032225 sqr:76500157735,0:5852274133479880330225 sqr:821777330800,0:675317981416772628640000 sqr:38741,0:1500865081 sqr:262422499893,0:68865568450091585011449 sqr:-114911750278913,0:13204710352163261933292461569 sqr:645965,0:417270781225 sqr:-846535490921,0:716622337388858473428241 sqr:56965538331,0:3245072557340630265561 sqr:-744309142053,0:553996098943672933054809 sqr:8398405793,0:70533219863895958849 sqr:14899711014997,0:222001388330422931958910009 sqr:4321091217,0:18671829305634541089 sqr:818709681211,0:670285542108617246426521 sqr:557620246567,0:310940339381441875285489 sqr:666538614295667,0:444273724347187940858494974889 sqr:-169058708804,0:28580847022475667110416 sqr:-796502,0:634415436004 sqr:-5416597755634,0:29339531246339285978741956 sqr:922525,0:851052375625 sqr:2993210,0:8959306104100 sqr:1714169182508836,0:2938375986263011104043218074896 sqr:-27353337,0:748205045035569 sqr:9130672606905,0:83369182254485348653679025 sqr:1596656380704,0:2549311598042796583535616 sqr:-9683496758810,0:93770109477883775312616100 sqr:909229240,0:826697810870977600 sqr:333499398389171,0:111221848725938992589570067241 sqr:-307250046,0:94402590767002116 sqr:3035000042541,0:9211225258223871809736681 sqr:-2721781933,0:7408096890805216489 sqr:48792067992331,0:2380665898968251261074813561 sqr:9234221,0:85270837476841 sqr:8101724703211,0:65637943166619366033710521 sqr:8164095821,0:66652460574469664041 sqr:804766485,0:647649095379255225 sqr:6183556496806,0:38236370949191691088201636 sqr:48857539680655569,0:2387059183646833479261385610713761 sqr:7026205978661388,0:49367570454577033123192362086544 sqr:644316320534354,0:415143520906928406000094197316 sqr:-2418657837,0:5849905732481518569 sqr:-689024588558,0:474754883637521184519364 sqr:7595432034404,0:57690587789250486239635216 sqr:51477603372463937,0:2649943648972710500135406365539969 sqr:-4859149914716259,0:23611337893687027113016478955081 sqr:-596229664,0:355489812233552896 sqr:539807450614764,0:291392083739210874761534775696 sqr:-1566967626957,0:2455387543931251913079849 sqr:65611170065548,0:4304825637370261946616540304 sqr:30495282,0:929962224259524 sqr:24673048425668,0:608759318615358173321246224 sqr:-417870989,0:174616163447838121 sqr:973135796,0:946993277456553616 sqr:61834268876013338,0:3823476807431111794332536353902244 sqr:82806890204302,0:6856981065307326523299307204 sqr:1316959192994,0:1734381516011407738684036 sqr:80328462383346,0:6452661868872633334658155716 sqr:42624480104111,0:1816846304145754485399100321 sqr:-375979141,0:141360314467097881 sqr:9920379080,0:98413921090901646400 sqr:80353168236771535,0:6456631645686909915006519786256225 sqr:21921266256,0:480541914266444257536 sqr:51036336390,0:2604707632113238232100 sqr:7536279247897084,0:56795504902284238073836255703056 sqr:4057492473172,0:16463245169847433139741584 sqr:270453549401790,0:73145122384026464066855204100 sqr:-97595328880030,0:9524848219201217774132800900 sqr:2730620091663,0:7456286084993650522105569 sqr:596640915610381483,0:355980382180394358404919444789279289 sqr:907362117785845,0:823306012792813655285282364025 sqr:3529407863794686,0:12456719869015768803663561838596 sqr:5637629105915,0:31782861935859962287987225 sqr:701177821774260333,0:491650337748096387958827849257270889 sqr:388674994544,0:151068251383778429767936 sqr:9003508844276352939,0:81063171508962508596780155978893937721 sqr:5782278255807599,0:33434741827585369298571706144801 sqr:54932190594257,0:3017545563483777218801382049 sqr:2330326791,0:5430422952852357681 sqr:2344523846,0:5496792064462631716 sqr:734348606390121,0:539267875707112861194846394641 sqr:1667343410703,0:2780034049214712934954209 sqr:47416690990247089326,0:2248342584464579496535799798615023134276 sqr:2992718026488505861,0:8956361186069257268281338748231351321 sqr:36345508239,0:1320995969151216881121 sqr:9136952501974852622,0:83483901023344519207328952878620274884 sqr:-68684476889,0:4717557365515575118321 sqr:3324362191672831934,0:11051383981423794566026717599410180356 sqr:3950591846438354580,0:15607175937145207775001664097806976400 sqr:452699498737223,0:204936836156932968571605751729 sqr:16407472075973,0:269205139923833746283896729 sqr:-42791759402,0:1831134672718655397604 sqr:-969620447288,0:940163811798981186554944 sqr:-7324554153015094663,0:53649093540450670762129798726851083569 sqr:1246969904304174,0:1554933942240360863251113822276 sqr:527095728932983463,0:277829907459393180154350270231472369 sqr:133034527166,0:17698185418281191991556 sqr:5806610887494202860,0:33716729998766214183769310106832179600 sqr:604840631315943,0:365832189290668488059885979249 sqr:7106121629098296578,0:50496964607538628518974633341246510084 sqr:81378228896850,0:6622416138388112367939922500 sqr:-18768741494576,0:352265657290218942237419776 sqr:81188620065937,0:6591592028211068078227687969 sqr:8219251025608152,0:67556087421960658524081448855104 sqr:20867876779389,0:435468281279762622975213321 sqr:27156769177930279482,0:737490112183384027655411672542630188324 sqr:40320990680365371419,0:1625782289446111137560608246113822073561 sqr:231848755308011786,0:53753845337874323313724120314909796 sqr:841695784516,0:708451793672004705354256 sqr:1766836913116,0:3121712677549275732829456 sqr:664177322904,0:441131516259924282993216 sqr:5979213918247228581465,0:35750999080161375874506971631233196141546225 sqr:1758746127509067,0:3093187941028139358526167210489 sqr:135179542401621982047,0:18273508683911915341791581411360790310209 sqr:112047175441308,0:12554569524375254604552750864 sqr:70541788345164680600,0:4976143902934011567084482333700016360000 sqr:1492832267100,0:2228548177694925742410000 sqr:3521705164411,0:12402407265039108540976921 sqr:-473191108111249626,0:223909824795552331595427695285139876 sqr:855883713881684,0:732536931687904321002750675856 sqr:16916839558930925199,0:286179460662610259828831065810133189601 sqr:296829185936965,0:88107565624001340524953411225 sqr:7414275234516727336390,0:54971477253168072142121335070692704218232100 sqr:90237037450605,0:8142722927861889317814866025 sqr:60553464627047020812,0:3666722078339034795281351845204761139344 sqr:4439551436109999,0:19709616953866354532829227780001 sqr:5735204172472,0:32892566899940238322590784 sqr:-477556465681133,0:228060177913855160813632163689 sqr:6136903544018042,0:37661585108581203963482021513764 sqr:7355012443029717610726,0:54096208037121975042332803663623262070247076 sqr:2615297272121929464,0:6839779821568405573166111210191327296 sqr:1236583510060121661932,0:1529138777352611011481426496873465697972624 sqr:259304999298782298,0:67239082661341488057486265598160804 sqr:67283385405374162098001,0:4527053951608116799312629323426390509928196001 sqr:301048056239861279998,0:90629932165798680163672601418278954880004 sqr:513985608867175879,0:264181206122561507573492869119422641 sqr:8456087728243890247050,0:71505419667756916634176268857406110033702500 sqr:978607251971625,0:957672153611455542449805140625 sqr:190320200462916,0:36221778704244531620691223056 sqr:213818886286553,0:45718516132821882562028621809 sqr:-862217602106683,0:743419193382598324879713262489 sqr:318640018205323583652,0:101531461201888944823553345475699841657104 sqr:-500900129006539730,0:250900939238768144201293108068472900 sqr:820114087330800098,0:672587116238431209810989756836809604 sqr:55403047897851377414057,0:3069497716371613929908572787677424384421199249 sqr:4810813844423644764918,0:23143929845698208536190754736426427483546724 sqr:9103047106745502875,0:82865466627627670814122634036633265625 sqr:963951698125641,0:929202876319306914592621660881 sqr:539175052498265418,0:290709737236507269568171898774714724 sqr:-50157204922004988220,0:2515745205588001416429472062562338768400 sqr:11026905984136936161244,0:121592655582994972607713656480448242767627536 sqr:3502071722216797290044,0:12264506347550524601785650136506422261521936 sqr:-40351577732954785,0:1628249825538692426114606854396225 sqr:-95254896582422725495010,0:9073495322928048629343683310955771449534900100 sqr:60457070221477869,0:3655057339764706108220106456781161 sqr:93325659970487089,0:8709678808926976205678491915693921 sqr:413237232385124613101743,0:170765010229317482334791391007519236011269638049 sqr:951114415591592288075347,0:904618631546136131332571710964234352253549170409 sqr:401010074180215687828,0:160809079594022088656212052683319147357584 sqr:52476554710721850732027,0:2753788794307383662963857897873667915763528729 sqr:5258576802493280623,0:27652629987720455286211141065027268129 sqr:6054103219841182396749,0:36652165796491372073556099894662392045769001 sqr:956352502346019997280,0:914610108743494184401252227637651207398400 sqr:-26892207599979464777,0:723190829600393285039943832095383659729 sqr:764634776535170557034248,0:584666341486990214285762412733243291473444925504 sqr:8999350031831592,0:80988300995427275943650249254464 sqr:7641437781743263624,0:58391571372253409436905597502761613376 sqr:27231085935730852312965,0:741532041239158628505821004397916290307091225 sqr:54460324605443402457738,0:2965926956130264089583329153826508098876076644 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================================================ FILE: tests/sub.tc ================================================ # Subtraction tests sub:0,0,0:0 sub:0,0,=1:0 sub:1,=1,=1:0 sub:1,-1,0:2 sub:1,-1,=2:2 sub:1,-1,=1:2 sub:-1,1,0:-2 sub:-1,1,=1:-2 sub:103427990038,909510006269847,0:-909406578279809 sub:128593002,-9007199254740992,0:9007199383333994 sub:-65537,70000,0:-135537 sub:-1000000,-6543210,0:5543210 sub:#x29C932F25E6CEF8046FA,#x29C932F25E6CEF8046FA,0:0 sub:#x800000001,2,0:#x7FFFFFFFF sub:95031018,=1,=1:0 sub:#x-176E7F8018D6BA4B550AB36AAAFDC78A9,#x186DAD2485A41B18AAF5EF17922D7E5F1F,=1:#x-19E4951C873186BD60469A4E3CDD5AD7C8 sub:-628443782411312,-301652218193016,=2:-326791564218296 sub:950147,37133897,0:-36183750 sub:649972385,297,0:649972088 sub:505,9,0:496 sub:33,-2638,0:2671 sub:-5,71542573,0:-71542578 sub:4,475357,0:-475353 sub:5,775166,0:-775161 sub:0,20805741,0:-20805741 sub:1,39,0:-38 sub:76825770,751287444,0:-674461674 sub:-5846049,574445,0:-6420494 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sub:8237492058118191763481523977841344753346311488313,1647118892275027900093320780430922273315158677508003654,0:-1647110654782969781901557298906944431970405331196515341 sub:-440042339580320057764506833117106015591230779324161,513962930617733479729549861446740257284856596728706,0:-954005270198053537494056694563846272876087376052867 sub:34635151931992497392391616758693644900635250427499823,287128980133325949899403223688828310849990578079457307,0:-252493828201333452507011606930134665949355327651957484 sub:48138028043471938379654489799905392276347294678190375860,8955461479465751553200394404645878189278984773776867,0:48129072581992472628101289405500746398158015693416598993 sub:7624317887859192567599023956675797189693348039462742,-973928186389609942202650295012119719585450666839535260,0:981552504277469134770249318968795516775144014878998002 sub:775402642132715473344595954662582545794117369927872,63796684229986115177275440213147384846517231365197485,0:-63021281587853399703930844258484802300723113995269613 sub:37362432357418646911115330814724472853415155235293,87036796847105652716376950065916449694424391617602112013,0:-87036759484673295297730038950585634969951538202446876720 sub:-300945445086734604702237356948834421909997080585835251,86543393214880176913230280671573673375238923042066,0:-301031988479949484879150587229505995583372319508877317 sub:-654047435982290398129267970179757606710004276417490112,86422930881746427524648992269920847889306495489,0:-654047522405221279875695494828749876630852165723985601 sub:794552108714326403336258405676646043844624401498072689,544976653015779028031808690831373018858631899320,0:794551563737673387557230373867955212471605542866173369 sub:-195959798494693192093817249845807727728979751653,18593677965094459754532848130637776457537309190937253673,0:-18593678161054258249226040224455026303345036919917005326 sub:57601304615929231199752161276702979414912411756145,21951958716061857914468826747760163180070915240014675524,0:-21951901114757241985237626995598886477091500327602919379 sub:311215074108149476976205428525338649682414980832,6243249733271681693520367645680387625166806885842687456,0:-6243249422056607585370890669474959099828157203427706624 sub:-60089258178336658544420554675373945148810656687928409220,-940949437845306471952666460412774999437620754784474,0:-60088317228898813237948602008913532373811219067173624746 sub:3844895658482592533059556269556968661475827694950384997,527322363491124024058755005552497077118499938802,0:3844895131160229041935532210801963108978750576450446195 sub:-6028944995177498518136854918757906591099625985414,15888968609159402431030920451645796896759203224067431,0:-15894997554154579929549057306564554803350302850052845 sub:996013497441974701923950607149438472739078933691,112407411020615162605964831561295393767448218127,0:883606086421359539317985775588143078971630715564 sub:7719318511816366427665580178076378029426275595533,163667549683108101581704958685911902179912256741218,0:-155948231171291735154039378507835524150485981145685 sub:123382564431290774896664572552493052435404643704458759934,12531798191484951858836698658135874099473672299388553,0:123370032633099289944805735853834916561305170032159371381 sub:942048756549299165967164928739420673047263758767141,3639275805983487223033248868875293658626128636190227,0:-2697227049434188057066083940135872985578864877423086 sub:240418823794626925772533604032962688702579243574687,4907674204394917198714890794857507854118108024516422187,0:-4907433785571122571789118261253474891429405445272847500 sub:3950213238876863129818663666502819327768719939127457701,29991402193339371342321385670768500228753395231039352972,0:-26041188954462508212502722004265680900984675291911895271 sub:1920667868219534801099538208015399489683153418341349572065,-233412004414149707586851107620826952570732551540827551954,0:2154079872633684508686389315636226442253885969882177124019 sub:7784321585128756839986661147453831080387260908002873,586237266875238457979621090825032494806800315405801,0:7198084318253518382007040056628798585580460592597072 sub:-34225848774985487393407814198681047162140030645991253741,-789489361585689258214473176784928536166156096643657,0:-34225059285623901704149599725504262233603864489894610084 sub:-944338971240124849797024756328867740674305651345965,649970029057878269623349411694378680589331156335769959,0:-650914368029118394473146436450707548330005461987115924 sub:25816073494421415375915233416338690441492640884943818729,764159631162282034769988362928740167840568754650018844,0:25051913863259133341145245053409950273652072130293799885 sub:7111381553325219432932289055091214481651627513743376,7385563406175559235314072692841151936136627185182905,0:-274181852850339802381783637749937454484999671439529 sub:-438137611853268269308435226684643695607887735487389,5824616025576441892684517623276732904299681537303913,0:-6262753637429710161992952849961376599907569272791302 sub:-9680790659167697968786181797074343179561171865505840566,-932899327759500157755319258322165056527752927868968726,0:-8747891331408197811030862538752178123033418937636871840 sub:567793364811051880825781313748966696400236576537363041402,-976578291468928773578542746545826341079985184892523837,0:568769943102520809599359856495512522741316561722255565239 sub:38007779187090670273244552314378701844162920433585869254,7187767815567041059760334263355184283280579165883650238,0:30820011371523629213484218051023517560882341267702219016 sub:9014053603553462724377168305482782158101121369010869473906,755601637469656651454003843855153366578358802242924461,0:9013298001915993067725714301638927004734543010208626549445 # Small integer subtraction tests subv:3358604991,36411,0:3358568580 subv:674222429,18986,0:674203443 subv:-3,-29805,=1:29802 subv:3,-61063,=1:61066 subv:2717723,-25258,=1:2742981 subv:394,-40508,=2:40902 subv:4744781967,21435,0:4744760532 subv:-14,50287,0:-50301 subv:2197,3582,=2:-1385 subv:-5296,38162,=2:-43458 subv:-258774,57544,=2:-316318 subv:7417476246,-58958,=2:7417535204 subv:6714936,-40949,0:6755885 subv:15862,-58672,0:74534 subv:958081,21046,0:937035 subv:82515,-11287,0:93802 subv:72715,-25449,0:98164 subv:-8346662975566,52150,0:-8346663027716 subv:96216,-33648,=2:129864 subv:71597071124556,40786,0:71597071083770 subv:2795133710510,-24996,=1:2795133735506 subv:8501300888546,1685,0:8501300886861 subv:3877092429,45143,0:3877047286 subv:-9123902,27698,0:-9151600 subv:-71914098152,-49684,0:-71914048468 subv:-5633175963555389,-13681,0:-5633175963541708 subv:-68774492,24946,0:-68799438 subv:2837978518,2447,=1:2837976071 subv:9527903026793981,34045,=2:9527903026759936 subv:-719766995836501,-14683,=1:-719766995821818 subv:6826892934542,-9599,0:6826892944141 subv:474765520,-36545,=2:474802065 subv:137980222,12896,0:137967326 subv:4124108674,61743,0:4124046931 subv:-4977334202151,16161,0:-4977334218312 subv:-6764356933,33130,=1:-6764390063 subv:6639990082377605303,63220,0:6639990082377542083 subv:68384248282,-28652,0:68384276934 subv:-64782488650,-31866,=2:-64782456784 subv:84126983615,63328,0:84126920287 subv:280281352217,19756,=1:280281332461 subv:-337730569530652702,55596,0:-337730569530708298 subv:750462053456012,-18056,=1:750462053474068 subv:-859984251764611,60341,0:-859984251824952 subv:781147832162694072159,10186,0:781147832162694061973 subv:414707731902540,13874,0:414707731888666 subv:4749293013793395,-27594,0:4749293013820989 subv:-476780935041195291,-51859,0:-476780935041143432 subv:-3619074244886709,38416,=1:-3619074244925125 subv:97855199057493,40752,0:97855199016741 subv:777675086535345464853,9892,=2:777675086535345454961 subv:3103441257588144,4992,0:3103441257583152 subv:136564148041720,53068,=2:136564147988652 subv:-4664978338218772692212,46644,0:-4664978338218772738856 subv:235299291342838779459,27155,=1:235299291342838752304 subv:45286262426870,28782,0:45286262398088 subv:422289955984703063,27236,=2:422289955984675827 subv:-6379926829937406097,-63773,0:-6379926829937342324 subv:830836702855178852980658,-61406,=1:830836702855178853042064 subv:4000074483936047411,59077,=2:4000074483935988334 subv:1622930723651719839167208,63514,0:1622930723651719839103694 subv:532951482400205192926144,57956,0:532951482400205192868188 subv:148980429628794512840,63138,=2:148980429628794449702 subv:-9890648040727702186064,-46766,=1:-9890648040727702139298 subv:-10934480308082214085686,63224,=2:-10934480308082214148910 subv:355809482274653919711872,32446,0:355809482274653919679426 subv:-33926193961684655624,11389,=2:-33926193961684667013 subv:-7186493575578045620,15528,=1:-7186493575578061148 subv:34706765155128499193360248,83,=1:34706765155128499193360165 subv:4328479538590740673745630,14623,0:4328479538590740673731007 subv:-963713498430054741223932789,30239,0:-963713498430054741223963028 subv:-831264221344401371,39516,0:-831264221344440887 subv:318721481318817753735405,52833,0:318721481318817753682572 subv:-62693787119478234447,27553,=1:-62693787119478262000 subv:-7016655669525046977522194886,32638,=2:-7016655669525046977522227524 subv:608134301020199755515,29066,0:608134301020199726449 ================================================ FILE: tests/test.bc ================================================ /* e(a, b, m) := a^b (mod m) */ define e(a, b, m) { auto s, sb; sb = obase; obase = 16; s = 1; while(b != 0) { if((b % 2) == 1) { s = (s * a) % m; } b /= 2; a = (a * a) % m; } obase = sb; return (s); } /* g(a, b) := (a, b) */ define g(a, b) { auto r; while(b != 0) { r = a % b; a = b; b = r; } if(a < 0) { return(-a); } else { return(a); } } define a(x) { if(x < 0) { return (-x); } else { return (x); } } xgu = 0; xgv = 0; define x(a, b) { auto u, v, x, y, t, r; if(a(b) > a(a)) { t = b; b = a; a = t; r = 1; } else { r = 0; } u = 1; v = 0; x = 0; y = 1; while(b != 0) { t = a / b; a = a - (t * b); v = v - (t * y); u = u - (t * x); if(a(a) < a(b)) { t = a; a = b; b = t; t = v; v = y; y = t; t = u; u = x; x = t; } } if(r) { xgu = v; xgv = u; } else { xgu = u; xgv = v; } if(a < 0) { return (-a); } else { return (a); } } define i(a, m) { auto c; c = x(a, m); if(c != 1) return(0); return ((xgu + m) % m); } scale = 0 rand_modulus = 2860385147 rand_base = 129 rand_seed = 10342799 define srand(s) { rand_seed = s; } define rand(n) { auto r; r = (rand_seed * rand_base) % rand_modulus; rand_seed = r; return(r % n); } define rand_digits(k) { auto s; s = 0; while(k > 0) { s = (s * 10) + rand(10); k = k - 1; } return(s); } define rval(ndigits, probneg) { auto x; x = rand_digits(ndigits); if(probneg > 0 && rand(100) < probneg) x = x * -1; return(x); } for(i = 2; i < 100; i += 4) { value = rand_digits(i); obase = 256; print "readuns:", value; obase = 10; print ":", value, "\n" } /* for(i = 2; i < 100; i += 4) { for(j = 0; j < 2; ++j) { ndig = rand(7); base = rval(ndig, 20); expt = rand_digits(i); mod = rand_digits(i); result = e(base, expt, mod); if(result < 0) { result = result + mod; } print "emodbv:", base, ",", expt, ",", mod, ",0:", result, "\n"; print "emodbv:", base, ",", expt, ",", mod, ",=2:", result, "\n"; print "emodbv:", base, ",", expt, ",", mod, ",=3:", result, "\n"; } } */ halt ================================================ FILE: tests/test.sh ================================================ #!/bin/bash ## ## Name: test.sh ## Purpose: Run test suites for IMath library. ## ## Copyright (C) 2002-2007 Michael J. Fromberger. All Rights Reserved. ## set -o pipefail if [ ! -f ../imtest ] ; then echo "I can't find the imath test driver 'imtest', did you build it?" echo "I can't proceed with the unit tests until you do so, sorry." exit 2 fi echo "-- Running all available unit tests" if ../imtest *.tc | (grep -v 'OK'||true) ; then echo "ALL PASSED" else echo "FAILED" exit 1 fi pitest() { local digits="${1:?missing digits}" local radix="${2:?missing radix}" local file="${3:?missing golden file}" local tempfile="/tmp/pi.${digits}.${radix}.$$.txt" echo "-- Running test to compute ${digits} base-${radix} digits of pi" 1>&2 ../pi "$digits" "$radix" | tr -d '\r\n' > "$tempfile" if cmp -s "$tempfile" "$file" ; then echo " PASSED $digits digits" else echo " FAILED" echo "Obtained:" cat "$tempfile" echo "Expected:" cat "$file" fi rm -f "$tempfile" } echo "" if [ ! -f ../pi ] ; then echo "I can't find the pi computing program, did you build it?" echo "I can't proceed with the pi test until you do so, sorry." exit 1 fi pitest 1024 10 pi1024.txt pitest 1698 16 pi1698-16.txt pitest 1500 10 pi1500-10.txt pitest 4096 10 pi4096-10.txt echo "" echo "-- Running regression tests" for bug in bug-qread bug-swap ; do ../${bug} done exit 0 ================================================ FILE: tools/findthreshold.py ================================================ #!/usr/bin/env python3 ## ## Name: findthreshold.py ## Purpose: Find a good threshold for recursive multiplication. ## Author: M. J. Fromberger ## ## This tool computes some timing statistics to help you select a suitable ## recursive multiplication breakpoint. It uses the imtimer tool to run a ## series of tests varying precision and breakpoint, and prints out a summary ## of the "best" values for each category. Each summary line contains the ## following fields, tab-separated: ## ## prec -- the precision of the operands (in digits). ## thresh -- the threshold for recursive multiplication (digits). ## trec -- total time using recursive algorithm (sec). ## tnorm -- total time without recursive algorithm (sec). ## ratio -- speedup (ratio of tnorm/trec). ## ## You are responsible for reading and interpreting the resulting table to ## obtain a useful value for your workload. Change the default in imath.c, or ## call mp_int_multiply_threshold(n) during program initialization, to ## establish a satisfactory result. ## import os import sys import time def get_timing_stats(num_tests, precision, threshold, seed=None): """Obtain timing statistics for multiplication. num_tests -- number of tests to run. precision -- number of digits per operand. threshold -- threshold in digits for recursive multiply. seed -- random seed; if None, the clock is used. Returns a tuple of (seed, bits, time) where seed is the random seed used, bits is the number of bits per operand, and time is a float giving the total time taken for the test run. """ if seed is None: seed = int(time.time()) line = os.popen( './imtimer -mn -p %d -t %d -s %d %d' % (precision, threshold, seed, num_tests), 'r').readline() count, prec, bits, thresh, status = line.strip().split('\t') kind, total, unit = status.split() return seed, int(bits), float(total) def check_binary(name): if not os.path.exists(name): os.system('make %s' % name) if not os.path.exists(name): raise ValueError("Unable to build %s" % name) elif not os.path.isfile(name): raise ValueError("Path exists with wrong type") def compute_stats(): check_binary('imtimer') seed = int(time.time()) print("Computing timer statistics (this may take a while)", file=sys.stderr) stats = {} for prec in (32, 40, 64, 80, 128, 150, 256, 384, 512, 600, 768, 1024): sys.stderr.write('%-4d ' % prec) stats[prec] = (None, 1000000., 0.) for thresh in range(8, 65, 2): s, b, t = get_timing_stats(1000, prec, thresh, seed) sp, bp, tp = get_timing_stats(1000, prec, prec + 1, seed) if t < stats[prec][1]: stats[prec] = (thresh, t, tp) sys.stderr.write('+') else: sys.stderr.write('.') sys.stderr.write('\n') return list((p, h, t, tp) for p, (h, t, tp) in stats.items()) if __name__ == "__main__": stats = compute_stats() stats.sort(key=lambda s: s[3] / s[2]) for prec, thresh, trec, tnorm in stats: print("%d\t%d\t%.3f\t%.3f\t%.4f" % (prec, thresh, trec, tnorm, tnorm / trec)) print() # Here there be dragons ================================================ FILE: tools/mkdoc.py ================================================ #!/usr/bin/env python3 ## ## Name: mkdoc.py ## Purpose: Extract documentation from header files. ## ## Copyright (C) 2018 Michael J. Fromberger. All Rights Reserved. ## ## Usage: mkdoc.py