Showing preview only (2,832K chars total). Download the full file or copy to clipboard to get everything.
Repository: MikeMcl/decimal.js
Branch: master
Commit: 1a6e845004b2
Files: 79
Total size: 2.7 MB
Directory structure:
gitextract_lauzzv64/
├── .npmignore
├── CHANGELOG.md
├── LICENCE.md
├── README.md
├── decimal.d.ts
├── decimal.global.d.ts
├── decimal.js
├── decimal.mjs
├── doc/
│ └── API.html
├── package.json
└── test/
├── hypothesis/
│ ├── .gitignore
│ ├── README.txt
│ ├── error_hunt.py
│ ├── evaluate.mjs
│ └── requirements.txt
├── modules/
│ ├── Decimal.js
│ ├── abs.js
│ ├── acos.js
│ ├── acosh.js
│ ├── asin.js
│ ├── asinh.js
│ ├── atan.js
│ ├── atan2.js
│ ├── atanh.js
│ ├── cbrt.js
│ ├── ceil.js
│ ├── clamp.js
│ ├── clone.js
│ ├── cmp.js
│ ├── config.js
│ ├── cos.js
│ ├── cosh.js
│ ├── div.js
│ ├── divToInt.js
│ ├── dpSd.js
│ ├── exp.js
│ ├── floor.js
│ ├── hypot.js
│ ├── immutability.js
│ ├── intPow.js
│ ├── isFiniteEtc.js
│ ├── ln.js
│ ├── log.js
│ ├── log10.js
│ ├── log2.js
│ ├── minAndMax.js
│ ├── minus.js
│ ├── mod.js
│ ├── neg.js
│ ├── plus.js
│ ├── pow.js
│ ├── powSqrt.js
│ ├── random.js
│ ├── round.js
│ ├── sign.js
│ ├── sin.js
│ ├── sinh.js
│ ├── sqrt.js
│ ├── sum.js
│ ├── tan.js
│ ├── tanh.js
│ ├── times.js
│ ├── toBinary.js
│ ├── toDP.js
│ ├── toExponential.js
│ ├── toFixed.js
│ ├── toFraction.js
│ ├── toHex.js
│ ├── toNearest.js
│ ├── toNumber.js
│ ├── toOctal.js
│ ├── toPrecision.js
│ ├── toSD.js
│ ├── toString.js
│ ├── trunc.js
│ └── valueOf.js
├── setup.js
├── test.html
└── test.js
================================================
FILE CONTENTS
================================================
================================================
FILE: .npmignore
================================================
test
excluded
.*
================================================
FILE: CHANGELOG.md
================================================
#### 10.6.0
* 06/07/2025
* Add `BigInt` support to TypeScript definitions
#### 10.5.0
* 23/01/2025
* #216 TypeScript: instantiation without `new` keyword
* #181 Support `BigInt`
* #241 Match `Math.max` and `Math.min` negative zero handling
* #217 Compute `acos` with less cancellation near `x = 1`
#### 10.4.3
* 04/12/2022
* #211 Remove `toStringTag` declaration for type compatibility.
#### 10.4.2
* 12/10/2022
* #209 Correct return type.
#### 10.4.1
* 16/09/2022
* #205 Add './decimal' subpath to *package.json* `exports`.
#### 10.4.0
* 14/08/2022
* #201 Add `exports` field to *package.json*.
* #203 Preserve license comment after bundling.
* #198 Use type predicate on `isDecimal`.
#### 10.3.1
* 25/06/2021
* Remove minified versions. Refresh *README*.
#### 10.3.0
* 22/06/2021
* Support underscores as separators.
* #101 Add `Decimal.clamp` method.
* #161 Fix Decimal instances deemed plain objects.
* #100 Add `Decimal.sum` method.
* #146 `Symbol.for` to `Symbol['for']` for IE8.
* #132 Fix possible infinite loop when `minE` is very low.
* #180 Accept Decimals of different origin.
* Update Typescript definitions.
* Update minification examples in *README*.
* Add minified versions for both *decimal.js* and *decimal.mjs*.
* Add *files* field to *package.json*, and remove build script.
#### 10.2.1
* 28/09/2020
* Correct `sqrt` initial estimate.
#### 10.2.0
* 08/05/2019
* #128 Workaround V8 `Math.pow` change.
* #93 Accept `+` prefix when parsing string values.
* #129 Fix typo.
#### 10.1.1
* 27/02/2019
* Check `Symbol` properly.
#### 10.1.0
* 26/02/2019
* #122 Add custom `util.inspect()` function.
* Add `Symbol.toStringTag`.
* #121 Constructor: add range check for arguments of type number and Decimal.
* Remove premable from uglifyjs build script.
* Move *decimal.min.js.map* to root directory.
#### 10.0.2
* 13/12/2018
* #114 Remove soureMappingURL from *decimal.min.js*.
* Remove *bower.json*.
#### 10.0.1
* 24/05/2018
* Add `browser` field to *package.json*.
#### 10.0.0
* 10/03/2018
* #88 `toNearest` to return the nearest multiple in the direction of the rounding mode.
* #82 #91 `const` to `var`.
* Add trigonometric precision limit explanantion to documentation.
* Put global ts definitions in separate file (see *bignumber.js* #143).
#### 9.0.1
* 15/12/2017
* #80 Typings: correct return type.
#### 9.0.0
* 14/12/2017
* #78 Typings: remove `toFormat`.
#### 8.0.0
* 10/12/2017
* Correct typings: `toFraction` returns `Decimal[]`.
* Type-checking: add `Decimal.isDecimal` method.
* Enable configuration reset with `defaults: true`.
* Add named export, Decimal, to *decimal.mjs*.
#### 7.5.1
* 03/12/2017
* Remove typo.
#### 7.5.0
* 03/12/2017
* Use TypeScript declarations outside modules.
#### 7.4.0
* 25/11/2017
* Add TypeScript typings.
#### 7.3.0
* 26/09/2017
* Rename *decimal.es6.js* to *decimal.mjs*.
* Amend *.travis.yml*.
#### 7.2.4
* 09/09/2017
* Update docs regarding `global.crypto`.
* Fix `import` issues.
#### 7.2.3
* 27/06/2017
* Bugfix: #58 `pow` sometimes throws when result is `Infinity`.
#### 7.2.2
* 25/06/2017
* Bugfix: #57 Powers of -1 for integers over `Number.MAX_SAFE_INTEGER`.
#### 7.2.1
* 04/05/2017
* Fix *README* badges.
#### 7.2.0
* 09/04/2017
* Add *decimal.es6.js*
#### 7.1.2
* 05/04/2017
* `Decimal.default` to `Decimal['default']` IE8 issue
#### 7.1.1
* 10/01/2017
* Remove duplicated for-loop
* Minor refactoring
#### 7.1.0
* 09/11/2016
* Support ES6 imports.
#### 7.0.0
* 09/11/2016
* Remove `require('crypto')` - leave it to the user
* Default `Decimal.crypto` to `false`
* Add `Decimal.set` as `Decimal.config` alias
#### 6.0.0
* 30/06/2016
* Removed base-88 serialization format
* Amended `toJSON` and removed `Decimal.fromJSON` accordingly
#### 5.0.8
* 09/03/2016
* Add newline to single test results
* Correct year
#### 5.0.7
* 29/02/2016
* Add decimal.js-light link
* Remove outdated example from docs
#### 5.0.6
* 22/02/2016
* Add bower.json
#### 5.0.5
* 20/02/2016
* Bugfix: #26 wrong precision applied
#### 5.0.4
* 14/02/2016
* Bugfix: #26 clone
#### 5.0.3
* 06/02/2016
* Refactor tests
#### 5.0.2
* 05/02/2016
* Added immutability tests
* Minor *decimal.js* clean-up
#### 5.0.1
* 28/01/2016
* Bugfix: #20 cos mutates value
* Add pi info to docs
#### 5.0.0
* 25/01/2016
* Added trigonometric functions and `cubeRoot` method
* Added most of JavaScript's `Math` object methods as Decimal methods
* Added `toBinary`, `toHexadecimal` and `toOctal` methods
* Added `isPositive` method
* Removed the 15 significant digit limit for numbers
* `toFraction` now returns an array of two Decimals, not two strings
* String values containing whitespace or a plus sign are no longer accepted
* `valueOf` now returns `'-0'` for minus zero
* `comparedTo` now returns `NaN` not `null` for comparisons with `NaN`
* `Decimal.max` and `Decimal.min` no longer accept an array
* The Decimal constructor and `toString` no longer accept a base argument
* Binary, hexadecimal and octal prefixes are now recognised for string values
* Removed `Decimal.errors` configuration property
* Removed `toFormat` method
* Removed `Decimal.ONE`
* Renamed `exponential` method to `naturalExponential`
* Renamed `Decimal.constructor` method to `Decimal.clone`
* Simplified error handling and amended error messages
* Refactored the test suite
* `Decimal.crypto` is now `undefined` by default, and the `crypto` object will be used if available
* Major internal refactoring
* Removed *bower.json*
#### 4.0.2
* 20/02/2015 Add bower.json. Add source map. Amend travis CI. Amend doc/comments
#### 4.0.1
* 11/12/2014 Assign correct constructor when duplicating a Decimal
#### 4.0.0
* 10/11/2014 `toFormat` amended to use `Decimal.format` object for more flexible configuration
#### 3.0.1
* 8/06/2014 Surround crypto require in try catch. See issue #5
#### 3.0.0
* 4/06/2014 `random` simplified. Major internal changes mean the properties of a Decimal must now be considered read-only
#### 2.1.0
* 4/06/2014 Amend UMD
#### 2.0.3
* 8/05/2014 Fix NaN toNumber
#### 2.0.2
* 30/04/2014 Correct doc links
#### 2.0.1
* 10/04/2014 Update npmignore
#### 2.0.0
* 10/04/2014 Add `toSignificantDigits`
* Remove `toInteger`
* No arguments to `ceil`, `floor`, `round` and `trunc`
#### 1.0.1
* 07/04/2014 Minor documentation clean-up
#### 1.0.0
* 02/04/2014 Initial release
================================================
FILE: LICENCE.md
================================================
The MIT Licence.
Copyright (c) 2025 Michael Mclaughlin
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
'Software'), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
================================================
FILE: README.md
================================================
An arbitrary-precision Decimal type for JavaScript.
[](https://www.npmjs.com/package/decimal.js)
[](https://www.npmjs.com/package/decimal.js)
[](https://cdnjs.com/libraries/decimal.js)
[](https://www.jsdelivr.com/package/npm/decimal.js)
<br>
## Features
- Integers and floats
- Simple but full-featured API
- Replicates many of the methods of JavaScript's `Number.prototype` and `Math` objects
- Also handles hexadecimal, binary and octal values
- Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
- No dependencies
- Wide platform compatibility: uses JavaScript 1.5 (ECMAScript 3) features only
- Comprehensive [documentation](https://mikemcl.github.io/decimal.js/) and test set
- Used under the hood by [math.js](https://github.com/josdejong/mathjs)
- Includes a TypeScript declaration file: *decimal.d.ts*
The library is similar to [bignumber.js](https://github.com/MikeMcl/bignumber.js/), but here
precision is specified in terms of significant digits rather than decimal places, and all
calculations are rounded to the precision (similar to Python's decimal module) rather than just
those involving division.
This library also adds the trigonometric functions, among others, and supports non-integer powers,
which makes it a significantly larger library than *bignumber.js* and the even smaller
[big.js](https://github.com/MikeMcl/big.js/).
For a lighter version of this library without the trigonometric functions see
[decimal.js-light](https://github.com/MikeMcl/decimal.js-light/).
## Load
The library is the single JavaScript file *decimal.js* or ES module *decimal.mjs*.
Browser:
```html
<script src='path/to/decimal.js'></script>
<script type="module">
import Decimal from './path/to/decimal.mjs';
...
</script>
```
[Node.js](https://nodejs.org):
```bash
npm install decimal.js
```
```js
const Decimal = require('decimal.js');
import Decimal from 'decimal.js';
import {Decimal} from 'decimal.js';
```
## Use
*In all examples below, semicolons and `toString` calls are not shown.
If a commented-out value is in quotes it means `toString` has been called on the preceding expression.*
The library exports a single constructor function, `Decimal`, which expects a single argument that is a number, string or Decimal instance.
```js
x = new Decimal(123.4567)
y = new Decimal('123456.7e-3')
z = new Decimal(x)
x.equals(y) && y.equals(z) && x.equals(z) // true
```
If using values with more than a few digits, it is recommended to pass strings rather than numbers to avoid a potential loss of precision.
```js
// Precision loss from using numeric literals with more than 15 significant digits.
new Decimal(1.0000000000000001) // '1'
new Decimal(88259496234518.57) // '88259496234518.56'
new Decimal(99999999999999999999) // '100000000000000000000'
// Precision loss from using numeric literals outside the range of Number values.
new Decimal(2e+308) // 'Infinity'
new Decimal(1e-324) // '0'
// Precision loss from the unexpected result of arithmetic with Number values.
new Decimal(0.7 + 0.1) // '0.7999999999999999'
```
As with JavaScript numbers, strings can contain underscores as separators to improve readability.
```js
x = new Decimal('2_147_483_647')
```
String values in binary, hexadecimal or octal notation are also accepted if the appropriate prefix is included.
```js
x = new Decimal('0xff.f') // '255.9375'
y = new Decimal('0b10101100') // '172'
z = x.plus(y) // '427.9375'
z.toBinary() // '0b110101011.1111'
z.toBinary(13) // '0b1.101010111111p+8'
// Using binary exponential notation to create a Decimal with the value of `Number.MAX_VALUE`.
x = new Decimal('0b1.1111111111111111111111111111111111111111111111111111p+1023')
// '1.7976931348623157081e+308'
```
Decimal instances are immutable in the sense that they are not changed by their methods.
```js
0.3 - 0.1 // 0.19999999999999998
x = new Decimal(0.3)
x.minus(0.1) // '0.2'
x // '0.3'
```
The methods that return a Decimal can be chained.
```js
x.dividedBy(y).plus(z).times(9).floor()
x.times('1.23456780123456789e+9').plus(9876.5432321).dividedBy('4444562598.111772').ceil()
```
Many method names have a shorter alias.
```js
x.squareRoot().dividedBy(y).toPower(3).equals(x.sqrt().div(y).pow(3)) // true
x.comparedTo(y.modulo(z).negated() === x.cmp(y.mod(z).neg()) // true
```
Most of the methods of JavaScript's `Number.prototype` and `Math` objects are replicated.
```js
x = new Decimal(255.5)
x.toExponential(5) // '2.55500e+2'
x.toFixed(5) // '255.50000'
x.toPrecision(5) // '255.50'
Decimal.sqrt('6.98372465832e+9823') // '8.3568682281821340204e+4911'
Decimal.pow(2, 0.0979843) // '1.0702770511687781839'
// Using `toFixed()` to avoid exponential notation:
x = new Decimal('0.0000001')
x.toString() // '1e-7'
x.toFixed() // '0.0000001'
```
And there are `isNaN` and `isFinite` methods, as `NaN` and `Infinity` are valid `Decimal` values.
```js
x = new Decimal(NaN) // 'NaN'
y = new Decimal(Infinity) // 'Infinity'
x.isNaN() && !y.isNaN() && !x.isFinite() && !y.isFinite() // true
```
There is also a `toFraction` method with an optional *maximum denominator* argument.
```js
z = new Decimal(355)
pi = z.dividedBy(113) // '3.1415929204'
pi.toFraction() // [ '7853982301', '2500000000' ]
pi.toFraction(1000) // [ '355', '113' ]
```
All calculations are rounded according to the number of significant digits and rounding mode specified
by the `precision` and `rounding` properties of the Decimal constructor.
For advanced usage, multiple Decimal constructors can be created, each with their own independent
configuration which applies to all Decimal numbers created from it.
```js
// Set the precision and rounding of the default Decimal constructor
Decimal.set({ precision: 5, rounding: 4 })
// Create another Decimal constructor, optionally passing in a configuration object
Dec = Decimal.clone({ precision: 9, rounding: 1 })
x = new Decimal(5)
y = new Dec(5)
x.div(3) // '1.6667'
y.div(3) // '1.66666666'
```
The value of a Decimal is stored in a floating point format in terms of its digits, exponent and sign, but these properties should be considered read-only.
```js
x = new Decimal(-12345.67);
x.d // [ 12345, 6700000 ] digits (base 10000000)
x.e // 4 exponent (base 10)
x.s // -1 sign
```
For further information see the [API](http://mikemcl.github.io/decimal.js/) reference in the *doc* directory.
## Test
To run the tests using Node.js from the root directory:
```bash
npm test
```
Each separate test module can also be executed individually, for example:
```bash
node test/modules/toFraction
```
To run the tests in a browser, open *test/test.html*.
## Minify
Two minification examples:
Using [uglify-js](https://github.com/mishoo/UglifyJS) to minify the *decimal.js* file:
```bash
npm install uglify-js -g
uglifyjs decimal.js --source-map url=decimal.min.js.map -c -m -o decimal.min.js
```
Using [terser](https://github.com/terser/terser) to minify the ES module version, *decimal.mjs*:
```bash
npm install terser -g
terser decimal.mjs --source-map url=decimal.min.mjs.map -c -m --toplevel -o decimal.min.mjs
```
```js
import Decimal from './decimal.min.mjs';
```
## Licence
[The MIT Licence](LICENCE.md)
================================================
FILE: decimal.d.ts
================================================
// Type definitions for decimal.js >=7.0.0
// Project: https://github.com/MikeMcl/decimal.js
// Definitions by: Michael Mclaughlin <https://github.com/MikeMcl>
// Definitions: https://github.com/MikeMcl/decimal.js
//
// Documentation: http://mikemcl.github.io/decimal.js/
//
// Exports:
//
// class Decimal (default export)
// type Decimal.Constructor
// type Decimal.Instance
// type Decimal.Modulo
// type Decimal.Rounding
// type Decimal.Value
// interface Decimal.Config
//
// Example (alternative syntax commented-out):
//
// import {Decimal} from "decimal.js"
// //import Decimal from "decimal.js"
//
// let r: Decimal.Rounding = Decimal.ROUND_UP;
// let c: Decimal.Configuration = {precision: 4, rounding: r};
// Decimal.set(c);
// let v: Decimal.Value = '12345.6789';
// let d: Decimal = new Decimal(v);
// //let d: Decimal.Instance = new Decimal(v);
//
// The use of compiler option `--strictNullChecks` is recommended.
export default Decimal;
export namespace Decimal {
export type Constructor = typeof Decimal;
export type Instance = Decimal;
export type Rounding = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
export type Modulo = Rounding | 9;
export type Value = string | number | bigint | Decimal;
// http://mikemcl.github.io/decimal.js/#constructor-properties
export interface Config {
precision?: number;
rounding?: Rounding;
toExpNeg?: number;
toExpPos?: number;
minE?: number;
maxE?: number;
crypto?: boolean;
modulo?: Modulo;
defaults?: boolean;
}
}
export declare class Decimal {
readonly d: number[];
readonly e: number;
readonly s: number;
constructor(n: Decimal.Value);
absoluteValue(): Decimal;
abs(): Decimal;
ceil(): Decimal;
clampedTo(min: Decimal.Value, max: Decimal.Value): Decimal;
clamp(min: Decimal.Value, max: Decimal.Value): Decimal;
comparedTo(n: Decimal.Value): number;
cmp(n: Decimal.Value): number;
cosine(): Decimal;
cos(): Decimal;
cubeRoot(): Decimal;
cbrt(): Decimal;
decimalPlaces(): number;
dp(): number;
dividedBy(n: Decimal.Value): Decimal;
div(n: Decimal.Value): Decimal;
dividedToIntegerBy(n: Decimal.Value): Decimal;
divToInt(n: Decimal.Value): Decimal;
equals(n: Decimal.Value): boolean;
eq(n: Decimal.Value): boolean;
floor(): Decimal;
greaterThan(n: Decimal.Value): boolean;
gt(n: Decimal.Value): boolean;
greaterThanOrEqualTo(n: Decimal.Value): boolean;
gte(n: Decimal.Value): boolean;
hyperbolicCosine(): Decimal;
cosh(): Decimal;
hyperbolicSine(): Decimal;
sinh(): Decimal;
hyperbolicTangent(): Decimal;
tanh(): Decimal;
inverseCosine(): Decimal;
acos(): Decimal;
inverseHyperbolicCosine(): Decimal;
acosh(): Decimal;
inverseHyperbolicSine(): Decimal;
asinh(): Decimal;
inverseHyperbolicTangent(): Decimal;
atanh(): Decimal;
inverseSine(): Decimal;
asin(): Decimal;
inverseTangent(): Decimal;
atan(): Decimal;
isFinite(): boolean;
isInteger(): boolean;
isInt(): boolean;
isNaN(): boolean;
isNegative(): boolean;
isNeg(): boolean;
isPositive(): boolean;
isPos(): boolean;
isZero(): boolean;
lessThan(n: Decimal.Value): boolean;
lt(n: Decimal.Value): boolean;
lessThanOrEqualTo(n: Decimal.Value): boolean;
lte(n: Decimal.Value): boolean;
logarithm(n?: Decimal.Value): Decimal;
log(n?: Decimal.Value): Decimal;
minus(n: Decimal.Value): Decimal;
sub(n: Decimal.Value): Decimal;
modulo(n: Decimal.Value): Decimal;
mod(n: Decimal.Value): Decimal;
naturalExponential(): Decimal;
exp(): Decimal;
naturalLogarithm(): Decimal;
ln(): Decimal;
negated(): Decimal;
neg(): Decimal;
plus(n: Decimal.Value): Decimal;
add(n: Decimal.Value): Decimal;
precision(includeZeros?: boolean): number;
sd(includeZeros?: boolean): number;
round(): Decimal;
sine() : Decimal;
sin() : Decimal;
squareRoot(): Decimal;
sqrt(): Decimal;
tangent() : Decimal;
tan() : Decimal;
times(n: Decimal.Value): Decimal;
mul(n: Decimal.Value) : Decimal;
toBinary(significantDigits?: number): string;
toBinary(significantDigits: number, rounding: Decimal.Rounding): string;
toDecimalPlaces(decimalPlaces?: number): Decimal;
toDecimalPlaces(decimalPlaces: number, rounding: Decimal.Rounding): Decimal;
toDP(decimalPlaces?: number): Decimal;
toDP(decimalPlaces: number, rounding: Decimal.Rounding): Decimal;
toExponential(decimalPlaces?: number): string;
toExponential(decimalPlaces: number, rounding: Decimal.Rounding): string;
toFixed(decimalPlaces?: number): string;
toFixed(decimalPlaces: number, rounding: Decimal.Rounding): string;
toFraction(max_denominator?: Decimal.Value): Decimal[];
toHexadecimal(significantDigits?: number): string;
toHexadecimal(significantDigits: number, rounding: Decimal.Rounding): string;
toHex(significantDigits?: number): string;
toHex(significantDigits: number, rounding?: Decimal.Rounding): string;
toJSON(): string;
toNearest(n: Decimal.Value, rounding?: Decimal.Rounding): Decimal;
toNumber(): number;
toOctal(significantDigits?: number): string;
toOctal(significantDigits: number, rounding: Decimal.Rounding): string;
toPower(n: Decimal.Value): Decimal;
pow(n: Decimal.Value): Decimal;
toPrecision(significantDigits?: number): string;
toPrecision(significantDigits: number, rounding: Decimal.Rounding): string;
toSignificantDigits(significantDigits?: number): Decimal;
toSignificantDigits(significantDigits: number, rounding: Decimal.Rounding): Decimal;
toSD(significantDigits?: number): Decimal;
toSD(significantDigits: number, rounding: Decimal.Rounding): Decimal;
toString(): string;
truncated(): Decimal;
trunc(): Decimal;
valueOf(): string;
static abs(n: Decimal.Value): Decimal;
static acos(n: Decimal.Value): Decimal;
static acosh(n: Decimal.Value): Decimal;
static add(x: Decimal.Value, y: Decimal.Value): Decimal;
static asin(n: Decimal.Value): Decimal;
static asinh(n: Decimal.Value): Decimal;
static atan(n: Decimal.Value): Decimal;
static atanh(n: Decimal.Value): Decimal;
static atan2(y: Decimal.Value, x: Decimal.Value): Decimal;
static cbrt(n: Decimal.Value): Decimal;
static ceil(n: Decimal.Value): Decimal;
static clamp(n: Decimal.Value, min: Decimal.Value, max: Decimal.Value): Decimal;
static clone(object?: Decimal.Config): Decimal.Constructor;
static config(object: Decimal.Config): Decimal.Constructor;
static cos(n: Decimal.Value): Decimal;
static cosh(n: Decimal.Value): Decimal;
static div(x: Decimal.Value, y: Decimal.Value): Decimal;
static exp(n: Decimal.Value): Decimal;
static floor(n: Decimal.Value): Decimal;
static hypot(...n: Decimal.Value[]): Decimal;
static isDecimal(object: any): object is Decimal;
static ln(n: Decimal.Value): Decimal;
static log(n: Decimal.Value, base?: Decimal.Value): Decimal;
static log2(n: Decimal.Value): Decimal;
static log10(n: Decimal.Value): Decimal;
static max(...n: Decimal.Value[]): Decimal;
static min(...n: Decimal.Value[]): Decimal;
static mod(x: Decimal.Value, y: Decimal.Value): Decimal;
static mul(x: Decimal.Value, y: Decimal.Value): Decimal;
static noConflict(): Decimal.Constructor; // Browser only
static pow(base: Decimal.Value, exponent: Decimal.Value): Decimal;
static random(significantDigits?: number): Decimal;
static round(n: Decimal.Value): Decimal;
static set(object: Decimal.Config): Decimal.Constructor;
static sign(n: Decimal.Value): number;
static sin(n: Decimal.Value): Decimal;
static sinh(n: Decimal.Value): Decimal;
static sqrt(n: Decimal.Value): Decimal;
static sub(x: Decimal.Value, y: Decimal.Value): Decimal;
static sum(...n: Decimal.Value[]): Decimal;
static tan(n: Decimal.Value): Decimal;
static tanh(n: Decimal.Value): Decimal;
static trunc(n: Decimal.Value): Decimal;
static readonly default?: Decimal.Constructor;
static readonly Decimal?: Decimal.Constructor;
static readonly precision: number;
static readonly rounding: Decimal.Rounding;
static readonly toExpNeg: number;
static readonly toExpPos: number;
static readonly minE: number;
static readonly maxE: number;
static readonly crypto: boolean;
static readonly modulo: Decimal.Modulo;
static readonly ROUND_UP: 0;
static readonly ROUND_DOWN: 1;
static readonly ROUND_CEIL: 2;
static readonly ROUND_FLOOR: 3;
static readonly ROUND_HALF_UP: 4;
static readonly ROUND_HALF_DOWN: 5;
static readonly ROUND_HALF_EVEN: 6;
static readonly ROUND_HALF_CEIL: 7;
static readonly ROUND_HALF_FLOOR: 8;
static readonly EUCLID: 9;
}
export declare function Decimal(n: Decimal.Value): Decimal;
================================================
FILE: decimal.global.d.ts
================================================
// Type definitions for decimal.js >=7.0.0
// Project: https://github.com/MikeMcl/decimal.js
// Definitions by: Michael Mclaughlin <https://github.com/MikeMcl>
// Definitions: https://github.com/MikeMcl/decimal.js
//
// Documentation: http://mikemcl.github.io/decimal.js/
//
// Exports (available globally or when using import):
//
// class Decimal (default export)
// type Decimal.Constructor
// type Decimal.Instance
// type Decimal.Modulo
// type Decimal.Rounding
// type Decimal.Value
// interface Decimal.Config
//
// Example (alternative syntax commented-out):
//
// import {Decimal} from "decimal.js"
// //import Decimal from "decimal.js"
//
// let r: Decimal.Rounding = Decimal.ROUND_UP;
// let c: Decimal.Configuration = {precision: 4, rounding: r};
// Decimal.set(c);
// let v: Decimal.Value = '12345.6789';
// let d: Decimal = new Decimal(v);
// //let d: Decimal.Instance = new Decimal(v);
//
// The use of compiler option `--strictNullChecks` is recommended.
export default Decimal;
export namespace Decimal {
export type Config = DecimalConfig;
export type Constructor = DecimalConstructor;
export type Instance = DecimalInstance;
export type Modulo = DecimalModulo;
export type Rounding = DecimalRounding;
export type Value = DecimalValue;
}
declare global {
const Decimal: DecimalConstructor;
type Decimal = DecimalInstance;
namespace Decimal {
type Config = DecimalConfig;
type Constructor = DecimalConstructor;
type Instance = DecimalInstance;
type Modulo = DecimalModulo;
type Rounding = DecimalRounding;
type Value = DecimalValue;
}
}
type DecimalInstance = Decimal;
type DecimalConstructor = typeof Decimal;
type DecimalValue = string | number | bigint |Decimal;
type DecimalRounding = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
type DecimalModulo = DecimalRounding | 9;
// http://mikemcl.github.io/decimal.js/#constructor-properties
interface DecimalConfig {
precision?: number;
rounding?: DecimalRounding;
toExpNeg?: number;
toExpPos?: number;
minE?: number;
maxE?: number;
crypto?: boolean;
modulo?: DecimalModulo;
defaults?: boolean;
}
export declare class Decimal {
readonly d: number[];
readonly e: number;
readonly s: number;
constructor(n: DecimalValue);
absoluteValue(): Decimal;
abs(): Decimal;
ceil(): Decimal;
clampedTo(min: Decimal.Value, max: Decimal.Value): Decimal;
clamp(min: Decimal.Value, max: Decimal.Value): Decimal;
comparedTo(n: DecimalValue): number;
cmp(n: DecimalValue): number;
cosine(): Decimal;
cos(): Decimal;
cubeRoot(): Decimal;
cbrt(): Decimal;
decimalPlaces(): number;
dp(): number;
dividedBy(n: DecimalValue): Decimal;
div(n: DecimalValue): Decimal;
dividedToIntegerBy(n: DecimalValue): Decimal;
divToInt(n: DecimalValue): Decimal;
equals(n: DecimalValue): boolean;
eq(n: DecimalValue): boolean;
floor(): Decimal;
greaterThan(n: DecimalValue): boolean;
gt(n: DecimalValue): boolean;
greaterThanOrEqualTo(n: DecimalValue): boolean;
gte(n: DecimalValue): boolean;
hyperbolicCosine(): Decimal;
cosh(): Decimal;
hyperbolicSine(): Decimal;
sinh(): Decimal;
hyperbolicTangent(): Decimal;
tanh(): Decimal;
inverseCosine(): Decimal;
acos(): Decimal;
inverseHyperbolicCosine(): Decimal;
acosh(): Decimal;
inverseHyperbolicSine(): Decimal;
asinh(): Decimal;
inverseHyperbolicTangent(): Decimal;
atanh(): Decimal;
inverseSine(): Decimal;
asin(): Decimal;
inverseTangent(): Decimal;
atan(): Decimal;
isFinite(): boolean;
isInteger(): boolean;
isInt(): boolean;
isNaN(): boolean;
isNegative(): boolean;
isNeg(): boolean;
isPositive(): boolean;
isPos(): boolean;
isZero(): boolean;
lessThan(n: DecimalValue): boolean;
lt(n: DecimalValue): boolean;
lessThanOrEqualTo(n: DecimalValue): boolean;
lte(n: DecimalValue): boolean;
logarithm(n?: DecimalValue): Decimal;
log(n?: DecimalValue): Decimal;
minus(n: DecimalValue): Decimal;
sub(n: DecimalValue): Decimal;
modulo(n: DecimalValue): Decimal;
mod(n: DecimalValue): Decimal;
naturalExponential(): Decimal;
exp(): Decimal;
naturalLogarithm(): Decimal;
ln(): Decimal;
negated(): Decimal;
neg(): Decimal;
plus(n: DecimalValue): Decimal;
add(n: DecimalValue): Decimal;
precision(includeZeros?: boolean): number;
sd(includeZeros?: boolean): number;
round(): Decimal;
sine() : Decimal;
sin() : Decimal;
squareRoot(): Decimal;
sqrt(): Decimal;
tangent() : Decimal;
tan() : Decimal;
times(n: DecimalValue): Decimal;
mul(n: DecimalValue) : Decimal;
toBinary(significantDigits?: number): string;
toBinary(significantDigits: number, rounding: DecimalRounding): string;
toDecimalPlaces(decimalPlaces?: number): Decimal;
toDecimalPlaces(decimalPlaces: number, rounding: DecimalRounding): Decimal;
toDP(decimalPlaces?: number): Decimal;
toDP(decimalPlaces: number, rounding: DecimalRounding): Decimal;
toExponential(decimalPlaces?: number): string;
toExponential(decimalPlaces: number, rounding: DecimalRounding): string;
toFixed(decimalPlaces?: number): string;
toFixed(decimalPlaces: number, rounding: DecimalRounding): string;
toFraction(max_denominator?: DecimalValue): Decimal[];
toHexadecimal(significantDigits?: number): string;
toHexadecimal(significantDigits: number, rounding: DecimalRounding): string;
toHex(significantDigits?: number): string;
toHex(significantDigits: number, rounding?: DecimalRounding): string;
toJSON(): string;
toNearest(n: DecimalValue, rounding?: DecimalRounding): Decimal;
toNumber(): number;
toOctal(significantDigits?: number): string;
toOctal(significantDigits: number, rounding: DecimalRounding): string;
toPower(n: DecimalValue): Decimal;
pow(n: DecimalValue): Decimal;
toPrecision(significantDigits?: number): string;
toPrecision(significantDigits: number, rounding: DecimalRounding): string;
toSignificantDigits(significantDigits?: number): Decimal;
toSignificantDigits(significantDigits: number, rounding: DecimalRounding): Decimal;
toSD(significantDigits?: number): Decimal;
toSD(significantDigits: number, rounding: DecimalRounding): Decimal;
toString(): string;
truncated(): Decimal;
trunc(): Decimal;
valueOf(): string;
static abs(n: DecimalValue): Decimal;
static acos(n: DecimalValue): Decimal;
static acosh(n: DecimalValue): Decimal;
static add(x: DecimalValue, y: DecimalValue): Decimal;
static asin(n: DecimalValue): Decimal;
static asinh(n: DecimalValue): Decimal;
static atan(n: DecimalValue): Decimal;
static atanh(n: DecimalValue): Decimal;
static atan2(y: DecimalValue, x: DecimalValue): Decimal;
static cbrt(n: DecimalValue): Decimal;
static ceil(n: DecimalValue): Decimal;
static clamp(n: Decimal.Value, min: Decimal.Value, max: Decimal.Value): Decimal;
static clone(object?: DecimalConfig): DecimalConstructor;
static config(object: DecimalConfig): DecimalConstructor;
static cos(n: DecimalValue): Decimal;
static cosh(n: DecimalValue): Decimal;
static div(x: DecimalValue, y: DecimalValue): Decimal;
static exp(n: DecimalValue): Decimal;
static floor(n: DecimalValue): Decimal;
static hypot(...n: DecimalValue[]): Decimal;
static isDecimal(object: any): object is Decimal;
static ln(n: DecimalValue): Decimal;
static log(n: DecimalValue, base?: DecimalValue): Decimal;
static log2(n: DecimalValue): Decimal;
static log10(n: DecimalValue): Decimal;
static max(...n: DecimalValue[]): Decimal;
static min(...n: DecimalValue[]): Decimal;
static mod(x: DecimalValue, y: DecimalValue): Decimal;
static mul(x: DecimalValue, y: DecimalValue): Decimal;
static noConflict(): DecimalConstructor; // Browser only
static pow(base: DecimalValue, exponent: DecimalValue): Decimal;
static random(significantDigits?: number): Decimal;
static round(n: DecimalValue): Decimal;
static set(object: DecimalConfig): DecimalConstructor;
static sign(n: DecimalValue): number;
static sin(n: DecimalValue): Decimal;
static sinh(n: DecimalValue): Decimal;
static sqrt(n: DecimalValue): Decimal;
static sub(x: DecimalValue, y: DecimalValue): Decimal;
static sum(...n: Decimal.Value[]): Decimal;
static tan(n: DecimalValue): Decimal;
static tanh(n: DecimalValue): Decimal;
static trunc(n: DecimalValue): Decimal;
static readonly default?: DecimalConstructor;
static readonly Decimal?: DecimalConstructor;
static readonly precision: number;
static readonly rounding: DecimalRounding;
static readonly toExpNeg: number;
static readonly toExpPos: number;
static readonly minE: number;
static readonly maxE: number;
static readonly crypto: boolean;
static readonly modulo: DecimalModulo;
static readonly ROUND_UP: 0;
static readonly ROUND_DOWN: 1;
static readonly ROUND_CEIL: 2;
static readonly ROUND_FLOOR: 3;
static readonly ROUND_HALF_UP: 4;
static readonly ROUND_HALF_DOWN: 5;
static readonly ROUND_HALF_EVEN: 6;
static readonly ROUND_HALF_CEIL: 7;
static readonly ROUND_HALF_FLOOR: 8;
static readonly EUCLID: 9;
}
export declare function Decimal(n: Decimal.Value): Decimal;
================================================
FILE: decimal.js
================================================
;(function (globalScope) {
'use strict';
/*!
* decimal.js v10.6.0
* An arbitrary-precision Decimal type for JavaScript.
* https://github.com/MikeMcl/decimal.js
* Copyright (c) 2025 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licence
*/
// ----------------------------------- EDITABLE DEFAULTS ------------------------------------ //
// The maximum exponent magnitude.
// The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.
var EXP_LIMIT = 9e15, // 0 to 9e15
// The limit on the value of `precision`, and on the value of the first argument to
// `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
MAX_DIGITS = 1e9, // 0 to 1e9
// Base conversion alphabet.
NUMERALS = '0123456789abcdef',
// The natural logarithm of 10 (1025 digits).
LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
// Pi (1025 digits).
PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
// The initial configuration properties of the Decimal constructor.
DEFAULTS = {
// These values must be integers within the stated ranges (inclusive).
// Most of these values can be changed at run-time using the `Decimal.config` method.
// The maximum number of significant digits of the result of a calculation or base conversion.
// E.g. `Decimal.config({ precision: 20 });`
precision: 20, // 1 to MAX_DIGITS
// The rounding mode used when rounding to `precision`.
//
// ROUND_UP 0 Away from zero.
// ROUND_DOWN 1 Towards zero.
// ROUND_CEIL 2 Towards +Infinity.
// ROUND_FLOOR 3 Towards -Infinity.
// ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up.
// ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
// ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
// ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
// ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
//
// E.g.
// `Decimal.rounding = 4;`
// `Decimal.rounding = Decimal.ROUND_HALF_UP;`
rounding: 4, // 0 to 8
// The modulo mode used when calculating the modulus: a mod n.
// The quotient (q = a / n) is calculated according to the corresponding rounding mode.
// The remainder (r) is calculated as: r = a - n * q.
//
// UP 0 The remainder is positive if the dividend is negative, else is negative.
// DOWN 1 The remainder has the same sign as the dividend (JavaScript %).
// FLOOR 3 The remainder has the same sign as the divisor (Python %).
// HALF_EVEN 6 The IEEE 754 remainder function.
// EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.
//
// Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian
// division (9) are commonly used for the modulus operation. The other rounding modes can also
// be used, but they may not give useful results.
modulo: 1, // 0 to 9
// The exponent value at and beneath which `toString` returns exponential notation.
// JavaScript numbers: -7
toExpNeg: -7, // 0 to -EXP_LIMIT
// The exponent value at and above which `toString` returns exponential notation.
// JavaScript numbers: 21
toExpPos: 21, // 0 to EXP_LIMIT
// The minimum exponent value, beneath which underflow to zero occurs.
// JavaScript numbers: -324 (5e-324)
minE: -EXP_LIMIT, // -1 to -EXP_LIMIT
// The maximum exponent value, above which overflow to Infinity occurs.
// JavaScript numbers: 308 (1.7976931348623157e+308)
maxE: EXP_LIMIT, // 1 to EXP_LIMIT
// Whether to use cryptographically-secure random number generation, if available.
crypto: false // true/false
},
// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
Decimal, inexact, noConflict, quadrant,
external = true,
decimalError = '[DecimalError] ',
invalidArgument = decimalError + 'Invalid argument: ',
precisionLimitExceeded = decimalError + 'Precision limit exceeded',
cryptoUnavailable = decimalError + 'crypto unavailable',
tag = '[object Decimal]',
mathfloor = Math.floor,
mathpow = Math.pow,
isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,
isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,
isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,
isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
BASE = 1e7,
LOG_BASE = 7,
MAX_SAFE_INTEGER = 9007199254740991,
LN10_PRECISION = LN10.length - 1,
PI_PRECISION = PI.length - 1,
// Decimal.prototype object
P = { toStringTag: tag };
// Decimal prototype methods
/*
* absoluteValue abs
* ceil
* clampedTo clamp
* comparedTo cmp
* cosine cos
* cubeRoot cbrt
* decimalPlaces dp
* dividedBy div
* dividedToIntegerBy divToInt
* equals eq
* floor
* greaterThan gt
* greaterThanOrEqualTo gte
* hyperbolicCosine cosh
* hyperbolicSine sinh
* hyperbolicTangent tanh
* inverseCosine acos
* inverseHyperbolicCosine acosh
* inverseHyperbolicSine asinh
* inverseHyperbolicTangent atanh
* inverseSine asin
* inverseTangent atan
* isFinite
* isInteger isInt
* isNaN
* isNegative isNeg
* isPositive isPos
* isZero
* lessThan lt
* lessThanOrEqualTo lte
* logarithm log
* [maximum] [max]
* [minimum] [min]
* minus sub
* modulo mod
* naturalExponential exp
* naturalLogarithm ln
* negated neg
* plus add
* precision sd
* round
* sine sin
* squareRoot sqrt
* tangent tan
* times mul
* toBinary
* toDecimalPlaces toDP
* toExponential
* toFixed
* toFraction
* toHexadecimal toHex
* toNearest
* toNumber
* toOctal
* toPower pow
* toPrecision
* toSignificantDigits toSD
* toString
* truncated trunc
* valueOf toJSON
*/
/*
* Return a new Decimal whose value is the absolute value of this Decimal.
*
*/
P.absoluteValue = P.abs = function () {
var x = new this.constructor(this);
if (x.s < 0) x.s = 1;
return finalise(x);
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
* direction of positive Infinity.
*
*/
P.ceil = function () {
return finalise(new this.constructor(this), this.e + 1, 2);
};
/*
* Return a new Decimal whose value is the value of this Decimal clamped to the range
* delineated by `min` and `max`.
*
* min {number|string|bigint|Decimal}
* max {number|string|bigint|Decimal}
*
*/
P.clampedTo = P.clamp = function (min, max) {
var k,
x = this,
Ctor = x.constructor;
min = new Ctor(min);
max = new Ctor(max);
if (!min.s || !max.s) return new Ctor(NaN);
if (min.gt(max)) throw Error(invalidArgument + max);
k = x.cmp(min);
return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x);
};
/*
* Return
* 1 if the value of this Decimal is greater than the value of `y`,
* -1 if the value of this Decimal is less than the value of `y`,
* 0 if they have the same value,
* NaN if the value of either Decimal is NaN.
*
*/
P.comparedTo = P.cmp = function (y) {
var i, j, xdL, ydL,
x = this,
xd = x.d,
yd = (y = new x.constructor(y)).d,
xs = x.s,
ys = y.s;
// Either NaN or ±Infinity?
if (!xd || !yd) {
return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
}
// Either zero?
if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;
// Signs differ?
if (xs !== ys) return xs;
// Compare exponents.
if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
xdL = xd.length;
ydL = yd.length;
// Compare digit by digit.
for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;
}
// Compare lengths.
return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
};
/*
* Return a new Decimal whose value is the cosine of the value in radians of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-1, 1]
*
* cos(0) = 1
* cos(-0) = 1
* cos(Infinity) = NaN
* cos(-Infinity) = NaN
* cos(NaN) = NaN
*
*/
P.cosine = P.cos = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.d) return new Ctor(NaN);
// cos(0) = cos(-0) = 1
if (!x.d[0]) return new Ctor(1);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
Ctor.rounding = 1;
x = cosine(Ctor, toLessThanHalfPi(Ctor, x));
Ctor.precision = pr;
Ctor.rounding = rm;
return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);
};
/*
*
* Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
* cbrt(0) = 0
* cbrt(-0) = -0
* cbrt(1) = 1
* cbrt(-1) = -1
* cbrt(N) = N
* cbrt(-I) = -I
* cbrt(I) = I
*
* Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))
*
*/
P.cubeRoot = P.cbrt = function () {
var e, m, n, r, rep, s, sd, t, t3, t3plusx,
x = this,
Ctor = x.constructor;
if (!x.isFinite() || x.isZero()) return new Ctor(x);
external = false;
// Initial estimate.
s = x.s * mathpow(x.s * x, 1 / 3);
// Math.cbrt underflow/overflow?
// Pass x to Math.pow as integer, then adjust the exponent of the result.
if (!s || Math.abs(s) == 1 / 0) {
n = digitsToString(x.d);
e = x.e;
// Adjust n exponent so it is a multiple of 3 away from x exponent.
if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');
s = mathpow(n, 1 / 3);
// Rarely, e may be one less than the result exponent value.
e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));
if (s == 1 / 0) {
n = '5e' + e;
} else {
n = s.toExponential();
n = n.slice(0, n.indexOf('e') + 1) + e;
}
r = new Ctor(n);
r.s = x.s;
} else {
r = new Ctor(s.toString());
}
sd = (e = Ctor.precision) + 3;
// Halley's method.
// TODO? Compare Newton's method.
for (;;) {
t = r;
t3 = t.times(t).times(t);
t3plusx = t3.plus(x);
r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);
// TODO? Replace with for-loop and checkRoundingDigits.
if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
n = n.slice(sd - 3, sd + 1);
// The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999
// , i.e. approaching a rounding boundary, continue the iteration.
if (n == '9999' || !rep && n == '4999') {
// On the first iteration only, check to see if rounding up gives the exact result as the
// nines may infinitely repeat.
if (!rep) {
finalise(t, e + 1, 0);
if (t.times(t).times(t).eq(x)) {
r = t;
break;
}
}
sd += 4;
rep = 1;
} else {
// If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
// If not, then there are further digits and m will be truthy.
if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
// Truncate to the first rounding digit.
finalise(r, e + 1, 1);
m = !r.times(r).times(r).eq(x);
}
break;
}
}
}
external = true;
return finalise(r, e, Ctor.rounding, m);
};
/*
* Return the number of decimal places of the value of this Decimal.
*
*/
P.decimalPlaces = P.dp = function () {
var w,
d = this.d,
n = NaN;
if (d) {
w = d.length - 1;
n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;
// Subtract the number of trailing zeros of the last word.
w = d[w];
if (w) for (; w % 10 == 0; w /= 10) n--;
if (n < 0) n = 0;
}
return n;
};
/*
* n / 0 = I
* n / N = N
* n / I = 0
* 0 / n = 0
* 0 / 0 = N
* 0 / N = N
* 0 / I = 0
* N / n = N
* N / 0 = N
* N / N = N
* N / I = N
* I / n = I
* I / 0 = I
* I / N = N
* I / I = N
*
* Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
*/
P.dividedBy = P.div = function (y) {
return divide(this, new this.constructor(y));
};
/*
* Return a new Decimal whose value is the integer part of dividing the value of this Decimal
* by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.
*
*/
P.dividedToIntegerBy = P.divToInt = function (y) {
var x = this,
Ctor = x.constructor;
return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
};
/*
* Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
*
*/
P.equals = P.eq = function (y) {
return this.cmp(y) === 0;
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
* direction of negative Infinity.
*
*/
P.floor = function () {
return finalise(new this.constructor(this), this.e + 1, 3);
};
/*
* Return true if the value of this Decimal is greater than the value of `y`, otherwise return
* false.
*
*/
P.greaterThan = P.gt = function (y) {
return this.cmp(y) > 0;
};
/*
* Return true if the value of this Decimal is greater than or equal to the value of `y`,
* otherwise return false.
*
*/
P.greaterThanOrEqualTo = P.gte = function (y) {
var k = this.cmp(y);
return k == 1 || k === 0;
};
/*
* Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [1, Infinity]
*
* cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...
*
* cosh(0) = 1
* cosh(-0) = 1
* cosh(Infinity) = Infinity
* cosh(-Infinity) = Infinity
* cosh(NaN) = NaN
*
* x time taken (ms) result
* 1000 9 9.8503555700852349694e+433
* 10000 25 4.4034091128314607936e+4342
* 100000 171 1.4033316802130615897e+43429
* 1000000 3817 1.5166076984010437725e+434294
* 10000000 abandoned after 2 minute wait
*
* TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))
*
*/
P.hyperbolicCosine = P.cosh = function () {
var k, n, pr, rm, len,
x = this,
Ctor = x.constructor,
one = new Ctor(1);
if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);
if (x.isZero()) return one;
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
Ctor.rounding = 1;
len = x.d.length;
// Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1
// i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))
// Estimate the optimum number of times to use the argument reduction.
// TODO? Estimation reused from cosine() and may not be optimal here.
if (len < 32) {
k = Math.ceil(len / 3);
n = (1 / tinyPow(4, k)).toString();
} else {
k = 16;
n = '2.3283064365386962890625e-10';
}
x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);
// Reverse argument reduction
var cosh2_x,
i = k,
d8 = new Ctor(8);
for (; i--;) {
cosh2_x = x.times(x);
x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));
}
return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);
};
/*
* Return a new Decimal whose value is the hyperbolic sine of the value in radians of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-Infinity, Infinity]
*
* sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...
*
* sinh(0) = 0
* sinh(-0) = -0
* sinh(Infinity) = Infinity
* sinh(-Infinity) = -Infinity
* sinh(NaN) = NaN
*
* x time taken (ms)
* 10 2 ms
* 100 5 ms
* 1000 14 ms
* 10000 82 ms
* 100000 886 ms 1.4033316802130615897e+43429
* 200000 2613 ms
* 300000 5407 ms
* 400000 8824 ms
* 500000 13026 ms 8.7080643612718084129e+217146
* 1000000 48543 ms
*
* TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))
*
*/
P.hyperbolicSine = P.sinh = function () {
var k, pr, rm, len,
x = this,
Ctor = x.constructor;
if (!x.isFinite() || x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
Ctor.rounding = 1;
len = x.d.length;
if (len < 3) {
x = taylorSeries(Ctor, 2, x, x, true);
} else {
// Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))
// i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))
// 3 multiplications and 1 addition
// Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))
// i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))
// 4 multiplications and 2 additions
// Estimate the optimum number of times to use the argument reduction.
k = 1.4 * Math.sqrt(len);
k = k > 16 ? 16 : k | 0;
x = x.times(1 / tinyPow(5, k));
x = taylorSeries(Ctor, 2, x, x, true);
// Reverse argument reduction
var sinh2_x,
d5 = new Ctor(5),
d16 = new Ctor(16),
d20 = new Ctor(20);
for (; k--;) {
sinh2_x = x.times(x);
x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));
}
}
Ctor.precision = pr;
Ctor.rounding = rm;
return finalise(x, pr, rm, true);
};
/*
* Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-1, 1]
*
* tanh(x) = sinh(x) / cosh(x)
*
* tanh(0) = 0
* tanh(-0) = -0
* tanh(Infinity) = 1
* tanh(-Infinity) = -1
* tanh(NaN) = NaN
*
*/
P.hyperbolicTangent = P.tanh = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.isFinite()) return new Ctor(x.s);
if (x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + 7;
Ctor.rounding = 1;
return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);
};
/*
* Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of
* this Decimal.
*
* Domain: [-1, 1]
* Range: [0, pi]
*
* acos(x) = pi/2 - asin(x)
*
* acos(0) = pi/2
* acos(-0) = pi/2
* acos(1) = 0
* acos(-1) = pi
* acos(1/2) = pi/3
* acos(-1/2) = 2*pi/3
* acos(|x| > 1) = NaN
* acos(NaN) = NaN
*
*/
P.inverseCosine = P.acos = function () {
var x = this,
Ctor = x.constructor,
k = x.abs().cmp(1),
pr = Ctor.precision,
rm = Ctor.rounding;
if (k !== -1) {
return k === 0
// |x| is 1
? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)
// |x| > 1 or x is NaN
: new Ctor(NaN);
}
if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);
// TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3
Ctor.precision = pr + 6;
Ctor.rounding = 1;
// See https://github.com/MikeMcl/decimal.js/pull/217
x = new Ctor(1).minus(x).div(x.plus(1)).sqrt().atan();
Ctor.precision = pr;
Ctor.rounding = rm;
return x.times(2);
};
/*
* Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the
* value of this Decimal.
*
* Domain: [1, Infinity]
* Range: [0, Infinity]
*
* acosh(x) = ln(x + sqrt(x^2 - 1))
*
* acosh(x < 1) = NaN
* acosh(NaN) = NaN
* acosh(Infinity) = Infinity
* acosh(-Infinity) = NaN
* acosh(0) = NaN
* acosh(-0) = NaN
* acosh(1) = 0
* acosh(-1) = NaN
*
*/
P.inverseHyperbolicCosine = P.acosh = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);
if (!x.isFinite()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;
Ctor.rounding = 1;
external = false;
x = x.times(x).minus(1).sqrt().plus(x);
external = true;
Ctor.precision = pr;
Ctor.rounding = rm;
return x.ln();
};
/*
* Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value
* of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-Infinity, Infinity]
*
* asinh(x) = ln(x + sqrt(x^2 + 1))
*
* asinh(NaN) = NaN
* asinh(Infinity) = Infinity
* asinh(-Infinity) = -Infinity
* asinh(0) = 0
* asinh(-0) = -0
*
*/
P.inverseHyperbolicSine = P.asinh = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.isFinite() || x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;
Ctor.rounding = 1;
external = false;
x = x.times(x).plus(1).sqrt().plus(x);
external = true;
Ctor.precision = pr;
Ctor.rounding = rm;
return x.ln();
};
/*
* Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the
* value of this Decimal.
*
* Domain: [-1, 1]
* Range: [-Infinity, Infinity]
*
* atanh(x) = 0.5 * ln((1 + x) / (1 - x))
*
* atanh(|x| > 1) = NaN
* atanh(NaN) = NaN
* atanh(Infinity) = NaN
* atanh(-Infinity) = NaN
* atanh(0) = 0
* atanh(-0) = -0
* atanh(1) = Infinity
* atanh(-1) = -Infinity
*
*/
P.inverseHyperbolicTangent = P.atanh = function () {
var pr, rm, wpr, xsd,
x = this,
Ctor = x.constructor;
if (!x.isFinite()) return new Ctor(NaN);
if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);
pr = Ctor.precision;
rm = Ctor.rounding;
xsd = x.sd();
if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);
Ctor.precision = wpr = xsd - x.e;
x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);
Ctor.precision = pr + 4;
Ctor.rounding = 1;
x = x.ln();
Ctor.precision = pr;
Ctor.rounding = rm;
return x.times(0.5);
};
/*
* Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-pi/2, pi/2]
*
* asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))
*
* asin(0) = 0
* asin(-0) = -0
* asin(1/2) = pi/6
* asin(-1/2) = -pi/6
* asin(1) = pi/2
* asin(-1) = -pi/2
* asin(|x| > 1) = NaN
* asin(NaN) = NaN
*
* TODO? Compare performance of Taylor series.
*
*/
P.inverseSine = P.asin = function () {
var halfPi, k,
pr, rm,
x = this,
Ctor = x.constructor;
if (x.isZero()) return new Ctor(x);
k = x.abs().cmp(1);
pr = Ctor.precision;
rm = Ctor.rounding;
if (k !== -1) {
// |x| is 1
if (k === 0) {
halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
halfPi.s = x.s;
return halfPi;
}
// |x| > 1 or x is NaN
return new Ctor(NaN);
}
// TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6
Ctor.precision = pr + 6;
Ctor.rounding = 1;
x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();
Ctor.precision = pr;
Ctor.rounding = rm;
return x.times(2);
};
/*
* Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value
* of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-pi/2, pi/2]
*
* atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
*
* atan(0) = 0
* atan(-0) = -0
* atan(1) = pi/4
* atan(-1) = -pi/4
* atan(Infinity) = pi/2
* atan(-Infinity) = -pi/2
* atan(NaN) = NaN
*
*/
P.inverseTangent = P.atan = function () {
var i, j, k, n, px, t, r, wpr, x2,
x = this,
Ctor = x.constructor,
pr = Ctor.precision,
rm = Ctor.rounding;
if (!x.isFinite()) {
if (!x.s) return new Ctor(NaN);
if (pr + 4 <= PI_PRECISION) {
r = getPi(Ctor, pr + 4, rm).times(0.5);
r.s = x.s;
return r;
}
} else if (x.isZero()) {
return new Ctor(x);
} else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {
r = getPi(Ctor, pr + 4, rm).times(0.25);
r.s = x.s;
return r;
}
Ctor.precision = wpr = pr + 10;
Ctor.rounding = 1;
// TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);
// Argument reduction
// Ensure |x| < 0.42
// atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
k = Math.min(28, wpr / LOG_BASE + 2 | 0);
for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));
external = false;
j = Math.ceil(wpr / LOG_BASE);
n = 1;
x2 = x.times(x);
r = new Ctor(x);
px = x;
// atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
for (; i !== -1;) {
px = px.times(x2);
t = r.minus(px.div(n += 2));
px = px.times(x2);
r = t.plus(px.div(n += 2));
if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);
}
if (k) r = r.times(2 << (k - 1));
external = true;
return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);
};
/*
* Return true if the value of this Decimal is a finite number, otherwise return false.
*
*/
P.isFinite = function () {
return !!this.d;
};
/*
* Return true if the value of this Decimal is an integer, otherwise return false.
*
*/
P.isInteger = P.isInt = function () {
return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
};
/*
* Return true if the value of this Decimal is NaN, otherwise return false.
*
*/
P.isNaN = function () {
return !this.s;
};
/*
* Return true if the value of this Decimal is negative, otherwise return false.
*
*/
P.isNegative = P.isNeg = function () {
return this.s < 0;
};
/*
* Return true if the value of this Decimal is positive, otherwise return false.
*
*/
P.isPositive = P.isPos = function () {
return this.s > 0;
};
/*
* Return true if the value of this Decimal is 0 or -0, otherwise return false.
*
*/
P.isZero = function () {
return !!this.d && this.d[0] === 0;
};
/*
* Return true if the value of this Decimal is less than `y`, otherwise return false.
*
*/
P.lessThan = P.lt = function (y) {
return this.cmp(y) < 0;
};
/*
* Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
*
*/
P.lessThanOrEqualTo = P.lte = function (y) {
return this.cmp(y) < 1;
};
/*
* Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* If no base is specified, return log[10](arg).
*
* log[base](arg) = ln(arg) / ln(base)
*
* The result will always be correctly rounded if the base of the log is 10, and 'almost always'
* otherwise:
*
* Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen
* rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error
* between the result and the correctly rounded result will be one ulp (unit in the last place).
*
* log[-b](a) = NaN
* log[0](a) = NaN
* log[1](a) = NaN
* log[NaN](a) = NaN
* log[Infinity](a) = NaN
* log[b](0) = -Infinity
* log[b](-0) = -Infinity
* log[b](-a) = NaN
* log[b](1) = 0
* log[b](Infinity) = Infinity
* log[b](NaN) = NaN
*
* [base] {number|string|bigint|Decimal} The base of the logarithm.
*
*/
P.logarithm = P.log = function (base) {
var isBase10, d, denominator, k, inf, num, sd, r,
arg = this,
Ctor = arg.constructor,
pr = Ctor.precision,
rm = Ctor.rounding,
guard = 5;
// Default base is 10.
if (base == null) {
base = new Ctor(10);
isBase10 = true;
} else {
base = new Ctor(base);
d = base.d;
// Return NaN if base is negative, or non-finite, or is 0 or 1.
if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);
isBase10 = base.eq(10);
}
d = arg.d;
// Is arg negative, non-finite, 0 or 1?
if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {
return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);
}
// The result will have a non-terminating decimal expansion if base is 10 and arg is not an
// integer power of 10.
if (isBase10) {
if (d.length > 1) {
inf = true;
} else {
for (k = d[0]; k % 10 === 0;) k /= 10;
inf = k !== 1;
}
}
external = false;
sd = pr + guard;
num = naturalLogarithm(arg, sd);
denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
// The result will have 5 rounding digits.
r = divide(num, denominator, sd, 1);
// If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,
// calculate 10 further digits.
//
// If the result is known to have an infinite decimal expansion, repeat this until it is clear
// that the result is above or below the boundary. Otherwise, if after calculating the 10
// further digits, the last 14 are nines, round up and assume the result is exact.
// Also assume the result is exact if the last 14 are zero.
//
// Example of a result that will be incorrectly rounded:
// log[1048576](4503599627370502) = 2.60000000000000009610279511444746...
// The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it
// will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so
// the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal
// place is still 2.6.
if (checkRoundingDigits(r.d, k = pr, rm)) {
do {
sd += 10;
num = naturalLogarithm(arg, sd);
denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
r = divide(num, denominator, sd, 1);
if (!inf) {
// Check for 14 nines from the 2nd rounding digit, as the first may be 4.
if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {
r = finalise(r, pr + 1, 0);
}
break;
}
} while (checkRoundingDigits(r.d, k += 10, rm));
}
external = true;
return finalise(r, pr, rm);
};
/*
* Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.
*
* arguments {number|string|bigint|Decimal}
*
P.max = function () {
Array.prototype.push.call(arguments, this);
return maxOrMin(this.constructor, arguments, -1);
};
*/
/*
* Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
*
* arguments {number|string|bigint|Decimal}
*
P.min = function () {
Array.prototype.push.call(arguments, this);
return maxOrMin(this.constructor, arguments, 1);
};
*/
/*
* n - 0 = n
* n - N = N
* n - I = -I
* 0 - n = -n
* 0 - 0 = 0
* 0 - N = N
* 0 - I = -I
* N - n = N
* N - 0 = N
* N - N = N
* N - I = N
* I - n = I
* I - 0 = I
* I - N = N
* I - I = N
*
* Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
*/
P.minus = P.sub = function (y) {
var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd,
x = this,
Ctor = x.constructor;
y = new Ctor(y);
// If either is not finite...
if (!x.d || !y.d) {
// Return NaN if either is NaN.
if (!x.s || !y.s) y = new Ctor(NaN);
// Return y negated if x is finite and y is ±Infinity.
else if (x.d) y.s = -y.s;
// Return x if y is finite and x is ±Infinity.
// Return x if both are ±Infinity with different signs.
// Return NaN if both are ±Infinity with the same sign.
else y = new Ctor(y.d || x.s !== y.s ? x : NaN);
return y;
}
// If signs differ...
if (x.s != y.s) {
y.s = -y.s;
return x.plus(y);
}
xd = x.d;
yd = y.d;
pr = Ctor.precision;
rm = Ctor.rounding;
// If either is zero...
if (!xd[0] || !yd[0]) {
// Return y negated if x is zero and y is non-zero.
if (yd[0]) y.s = -y.s;
// Return x if y is zero and x is non-zero.
else if (xd[0]) y = new Ctor(x);
// Return zero if both are zero.
// From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity.
else return new Ctor(rm === 3 ? -0 : 0);
return external ? finalise(y, pr, rm) : y;
}
// x and y are finite, non-zero numbers with the same sign.
// Calculate base 1e7 exponents.
e = mathfloor(y.e / LOG_BASE);
xe = mathfloor(x.e / LOG_BASE);
xd = xd.slice();
k = xe - e;
// If base 1e7 exponents differ...
if (k) {
xLTy = k < 0;
if (xLTy) {
d = xd;
k = -k;
len = yd.length;
} else {
d = yd;
e = xe;
len = xd.length;
}
// Numbers with massively different exponents would result in a very high number of
// zeros needing to be prepended, but this can be avoided while still ensuring correct
// rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
if (k > i) {
k = i;
d.length = 1;
}
// Prepend zeros to equalise exponents.
d.reverse();
for (i = k; i--;) d.push(0);
d.reverse();
// Base 1e7 exponents equal.
} else {
// Check digits to determine which is the bigger number.
i = xd.length;
len = yd.length;
xLTy = i < len;
if (xLTy) len = i;
for (i = 0; i < len; i++) {
if (xd[i] != yd[i]) {
xLTy = xd[i] < yd[i];
break;
}
}
k = 0;
}
if (xLTy) {
d = xd;
xd = yd;
yd = d;
y.s = -y.s;
}
len = xd.length;
// Append zeros to `xd` if shorter.
// Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length.
for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
// Subtract yd from xd.
for (i = yd.length; i > k;) {
if (xd[--i] < yd[i]) {
for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
--xd[j];
xd[i] += BASE;
}
xd[i] -= yd[i];
}
// Remove trailing zeros.
for (; xd[--len] === 0;) xd.pop();
// Remove leading zeros and adjust exponent accordingly.
for (; xd[0] === 0; xd.shift()) --e;
// Zero?
if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0);
y.d = xd;
y.e = getBase10Exponent(xd, e);
return external ? finalise(y, pr, rm) : y;
};
/*
* n % 0 = N
* n % N = N
* n % I = n
* 0 % n = 0
* -0 % n = -0
* 0 % 0 = N
* 0 % N = N
* 0 % I = 0
* N % n = N
* N % 0 = N
* N % N = N
* N % I = N
* I % n = N
* I % 0 = N
* I % N = N
* I % I = N
*
* Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
* The result depends on the modulo mode.
*
*/
P.modulo = P.mod = function (y) {
var q,
x = this,
Ctor = x.constructor;
y = new Ctor(y);
// Return NaN if x is ±Infinity or NaN, or y is NaN or ±0.
if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN);
// Return x if y is ±Infinity or x is ±0.
if (!y.d || x.d && !x.d[0]) {
return finalise(new Ctor(x), Ctor.precision, Ctor.rounding);
}
// Prevent rounding of intermediate calculations.
external = false;
if (Ctor.modulo == 9) {
// Euclidian division: q = sign(y) * floor(x / abs(y))
// result = x - q * y where 0 <= result < abs(y)
q = divide(x, y.abs(), 0, 3, 1);
q.s *= y.s;
} else {
q = divide(x, y, 0, Ctor.modulo, 1);
}
q = q.times(y);
external = true;
return x.minus(q);
};
/*
* Return a new Decimal whose value is the natural exponential of the value of this Decimal,
* i.e. the base e raised to the power the value of this Decimal, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
*/
P.naturalExponential = P.exp = function () {
return naturalExponential(this);
};
/*
* Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
* rounded to `precision` significant digits using rounding mode `rounding`.
*
*/
P.naturalLogarithm = P.ln = function () {
return naturalLogarithm(this);
};
/*
* Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
* -1.
*
*/
P.negated = P.neg = function () {
var x = new this.constructor(this);
x.s = -x.s;
return finalise(x);
};
/*
* n + 0 = n
* n + N = N
* n + I = I
* 0 + n = n
* 0 + 0 = 0
* 0 + N = N
* 0 + I = I
* N + n = N
* N + 0 = N
* N + N = N
* N + I = N
* I + n = I
* I + 0 = I
* I + N = N
* I + I = I
*
* Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
*/
P.plus = P.add = function (y) {
var carry, d, e, i, k, len, pr, rm, xd, yd,
x = this,
Ctor = x.constructor;
y = new Ctor(y);
// If either is not finite...
if (!x.d || !y.d) {
// Return NaN if either is NaN.
if (!x.s || !y.s) y = new Ctor(NaN);
// Return x if y is finite and x is ±Infinity.
// Return x if both are ±Infinity with the same sign.
// Return NaN if both are ±Infinity with different signs.
// Return y if x is finite and y is ±Infinity.
else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN);
return y;
}
// If signs differ...
if (x.s != y.s) {
y.s = -y.s;
return x.minus(y);
}
xd = x.d;
yd = y.d;
pr = Ctor.precision;
rm = Ctor.rounding;
// If either is zero...
if (!xd[0] || !yd[0]) {
// Return x if y is zero.
// Return y if y is non-zero.
if (!yd[0]) y = new Ctor(x);
return external ? finalise(y, pr, rm) : y;
}
// x and y are finite, non-zero numbers with the same sign.
// Calculate base 1e7 exponents.
k = mathfloor(x.e / LOG_BASE);
e = mathfloor(y.e / LOG_BASE);
xd = xd.slice();
i = k - e;
// If base 1e7 exponents differ...
if (i) {
if (i < 0) {
d = xd;
i = -i;
len = yd.length;
} else {
d = yd;
e = k;
len = xd.length;
}
// Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
k = Math.ceil(pr / LOG_BASE);
len = k > len ? k + 1 : len + 1;
if (i > len) {
i = len;
d.length = 1;
}
// Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
d.reverse();
for (; i--;) d.push(0);
d.reverse();
}
len = xd.length;
i = yd.length;
// If yd is longer than xd, swap xd and yd so xd points to the longer array.
if (len - i < 0) {
i = len;
d = yd;
yd = xd;
xd = d;
}
// Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
for (carry = 0; i;) {
carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
xd[i] %= BASE;
}
if (carry) {
xd.unshift(carry);
++e;
}
// Remove trailing zeros.
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
for (len = xd.length; xd[--len] == 0;) xd.pop();
y.d = xd;
y.e = getBase10Exponent(xd, e);
return external ? finalise(y, pr, rm) : y;
};
/*
* Return the number of significant digits of the value of this Decimal.
*
* [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
*
*/
P.precision = P.sd = function (z) {
var k,
x = this;
if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
if (x.d) {
k = getPrecision(x.d);
if (z && x.e + 1 > k) k = x.e + 1;
} else {
k = NaN;
}
return k;
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
* rounding mode `rounding`.
*
*/
P.round = function () {
var x = this,
Ctor = x.constructor;
return finalise(new Ctor(x), x.e + 1, Ctor.rounding);
};
/*
* Return a new Decimal whose value is the sine of the value in radians of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-1, 1]
*
* sin(x) = x - x^3/3! + x^5/5! - ...
*
* sin(0) = 0
* sin(-0) = -0
* sin(Infinity) = NaN
* sin(-Infinity) = NaN
* sin(NaN) = NaN
*
*/
P.sine = P.sin = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.isFinite()) return new Ctor(NaN);
if (x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
Ctor.rounding = 1;
x = sine(Ctor, toLessThanHalfPi(Ctor, x));
Ctor.precision = pr;
Ctor.rounding = rm;
return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true);
};
/*
* Return a new Decimal whose value is the square root of this Decimal, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* sqrt(-n) = N
* sqrt(N) = N
* sqrt(-I) = N
* sqrt(I) = I
* sqrt(0) = 0
* sqrt(-0) = -0
*
*/
P.squareRoot = P.sqrt = function () {
var m, n, sd, r, rep, t,
x = this,
d = x.d,
e = x.e,
s = x.s,
Ctor = x.constructor;
// Negative/NaN/Infinity/zero?
if (s !== 1 || !d || !d[0]) {
return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0);
}
external = false;
// Initial estimate.
s = Math.sqrt(+x);
// Math.sqrt underflow/overflow?
// Pass x to Math.sqrt as integer, then adjust the exponent of the result.
if (s == 0 || s == 1 / 0) {
n = digitsToString(d);
if ((n.length + e) % 2 == 0) n += '0';
s = Math.sqrt(n);
e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
if (s == 1 / 0) {
n = '5e' + e;
} else {
n = s.toExponential();
n = n.slice(0, n.indexOf('e') + 1) + e;
}
r = new Ctor(n);
} else {
r = new Ctor(s.toString());
}
sd = (e = Ctor.precision) + 3;
// Newton-Raphson iteration.
for (;;) {
t = r;
r = t.plus(divide(x, t, sd + 2, 1)).times(0.5);
// TODO? Replace with for-loop and checkRoundingDigits.
if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
n = n.slice(sd - 3, sd + 1);
// The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
// 4999, i.e. approaching a rounding boundary, continue the iteration.
if (n == '9999' || !rep && n == '4999') {
// On the first iteration only, check to see if rounding up gives the exact result as the
// nines may infinitely repeat.
if (!rep) {
finalise(t, e + 1, 0);
if (t.times(t).eq(x)) {
r = t;
break;
}
}
sd += 4;
rep = 1;
} else {
// If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
// If not, then there are further digits and m will be truthy.
if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
// Truncate to the first rounding digit.
finalise(r, e + 1, 1);
m = !r.times(r).eq(x);
}
break;
}
}
}
external = true;
return finalise(r, e, Ctor.rounding, m);
};
/*
* Return a new Decimal whose value is the tangent of the value in radians of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-Infinity, Infinity]
*
* tan(0) = 0
* tan(-0) = -0
* tan(Infinity) = NaN
* tan(-Infinity) = NaN
* tan(NaN) = NaN
*
*/
P.tangent = P.tan = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.isFinite()) return new Ctor(NaN);
if (x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + 10;
Ctor.rounding = 1;
x = x.sin();
x.s = 1;
x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0);
Ctor.precision = pr;
Ctor.rounding = rm;
return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true);
};
/*
* n * 0 = 0
* n * N = N
* n * I = I
* 0 * n = 0
* 0 * 0 = 0
* 0 * N = N
* 0 * I = N
* N * n = N
* N * 0 = N
* N * N = N
* N * I = N
* I * n = I
* I * 0 = N
* I * N = N
* I * I = I
*
* Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
*/
P.times = P.mul = function (y) {
var carry, e, i, k, r, rL, t, xdL, ydL,
x = this,
Ctor = x.constructor,
xd = x.d,
yd = (y = new Ctor(y)).d;
y.s *= x.s;
// If either is NaN, ±Infinity or ±0...
if (!xd || !xd[0] || !yd || !yd[0]) {
return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd
// Return NaN if either is NaN.
// Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity.
? NaN
// Return ±Infinity if either is ±Infinity.
// Return ±0 if either is ±0.
: !xd || !yd ? y.s / 0 : y.s * 0);
}
e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE);
xdL = xd.length;
ydL = yd.length;
// Ensure xd points to the longer array.
if (xdL < ydL) {
r = xd;
xd = yd;
yd = r;
rL = xdL;
xdL = ydL;
ydL = rL;
}
// Initialise the result array with zeros.
r = [];
rL = xdL + ydL;
for (i = rL; i--;) r.push(0);
// Multiply!
for (i = ydL; --i >= 0;) {
carry = 0;
for (k = xdL + i; k > i;) {
t = r[k] + yd[i] * xd[k - i - 1] + carry;
r[k--] = t % BASE | 0;
carry = t / BASE | 0;
}
r[k] = (r[k] + carry) % BASE | 0;
}
// Remove trailing zeros.
for (; !r[--rL];) r.pop();
if (carry) ++e;
else r.shift();
y.d = r;
y.e = getBase10Exponent(r, e);
return external ? finalise(y, Ctor.precision, Ctor.rounding) : y;
};
/*
* Return a string representing the value of this Decimal in base 2, round to `sd` significant
* digits using rounding mode `rm`.
*
* If the optional `sd` argument is present then return binary exponential notation.
*
* [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
*/
P.toBinary = function (sd, rm) {
return toStringBinary(this, 2, sd, rm);
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
* decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
*
* If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
*
* [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
*/
P.toDecimalPlaces = P.toDP = function (dp, rm) {
var x = this,
Ctor = x.constructor;
x = new Ctor(x);
if (dp === void 0) return x;
checkInt32(dp, 0, MAX_DIGITS);
if (rm === void 0) rm = Ctor.rounding;
else checkInt32(rm, 0, 8);
return finalise(x, dp + x.e + 1, rm);
};
/*
* Return a string representing the value of this Decimal in exponential notation rounded to
* `dp` fixed decimal places using rounding mode `rounding`.
*
* [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
*/
P.toExponential = function (dp, rm) {
var str,
x = this,
Ctor = x.constructor;
if (dp === void 0) {
str = finiteToString(x, true);
} else {
checkInt32(dp, 0, MAX_DIGITS);
if (rm === void 0) rm = Ctor.rounding;
else checkInt32(rm, 0, 8);
x = finalise(new Ctor(x), dp + 1, rm);
str = finiteToString(x, true, dp + 1);
}
return x.isNeg() && !x.isZero() ? '-' + str : str;
};
/*
* Return a string representing the value of this Decimal in normal (fixed-point) notation to
* `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
* omitted.
*
* As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
*
* [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
* (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
* (-0).toFixed(3) is '0.000'.
* (-0.5).toFixed(0) is '-0'.
*
*/
P.toFixed = function (dp, rm) {
var str, y,
x = this,
Ctor = x.constructor;
if (dp === void 0) {
str = finiteToString(x);
} else {
checkInt32(dp, 0, MAX_DIGITS);
if (rm === void 0) rm = Ctor.rounding;
else checkInt32(rm, 0, 8);
y = finalise(new Ctor(x), dp + x.e + 1, rm);
str = finiteToString(y, false, dp + y.e + 1);
}
// To determine whether to add the minus sign look at the value before it was rounded,
// i.e. look at `x` rather than `y`.
return x.isNeg() && !x.isZero() ? '-' + str : str;
};
/*
* Return an array representing the value of this Decimal as a simple fraction with an integer
* numerator and an integer denominator.
*
* The denominator will be a positive non-zero value less than or equal to the specified maximum
* denominator. If a maximum denominator is not specified, the denominator will be the lowest
* value necessary to represent the number exactly.
*
* [maxD] {number|string|bigint|Decimal} Maximum denominator. Integer >= 1 and < Infinity.
*
*/
P.toFraction = function (maxD) {
var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r,
x = this,
xd = x.d,
Ctor = x.constructor;
if (!xd) return new Ctor(x);
n1 = d0 = new Ctor(1);
d1 = n0 = new Ctor(0);
d = new Ctor(d1);
e = d.e = getPrecision(xd) - x.e - 1;
k = e % LOG_BASE;
d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k);
if (maxD == null) {
// d is 10**e, the minimum max-denominator needed.
maxD = e > 0 ? d : n1;
} else {
n = new Ctor(maxD);
if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n);
maxD = n.gt(d) ? (e > 0 ? d : n1) : n;
}
external = false;
n = new Ctor(digitsToString(xd));
pr = Ctor.precision;
Ctor.precision = e = xd.length * LOG_BASE * 2;
for (;;) {
q = divide(n, d, 0, 1, 1);
d2 = d0.plus(q.times(d1));
if (d2.cmp(maxD) == 1) break;
d0 = d1;
d1 = d2;
d2 = n1;
n1 = n0.plus(q.times(d2));
n0 = d2;
d2 = d;
d = n.minus(q.times(d2));
n = d2;
}
d2 = divide(maxD.minus(d0), d1, 0, 1, 1);
n0 = n0.plus(d2.times(n1));
d0 = d0.plus(d2.times(d1));
n0.s = n1.s = x.s;
// Determine which fraction is closer to x, n0/d0 or n1/d1?
r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1
? [n1, d1] : [n0, d0];
Ctor.precision = pr;
external = true;
return r;
};
/*
* Return a string representing the value of this Decimal in base 16, round to `sd` significant
* digits using rounding mode `rm`.
*
* If the optional `sd` argument is present then return binary exponential notation.
*
* [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
*/
P.toHexadecimal = P.toHex = function (sd, rm) {
return toStringBinary(this, 16, sd, rm);
};
/*
* Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding
* mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal.
*
* The return value will always have the same sign as this Decimal, unless either this Decimal
* or `y` is NaN, in which case the return value will be also be NaN.
*
* The return value is not affected by the value of `precision`.
*
* y {number|string|bigint|Decimal} The magnitude to round to a multiple of.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* 'toNearest() rounding mode not an integer: {rm}'
* 'toNearest() rounding mode out of range: {rm}'
*
*/
P.toNearest = function (y, rm) {
var x = this,
Ctor = x.constructor;
x = new Ctor(x);
if (y == null) {
// If x is not finite, return x.
if (!x.d) return x;
y = new Ctor(1);
rm = Ctor.rounding;
} else {
y = new Ctor(y);
if (rm === void 0) {
rm = Ctor.rounding;
} else {
checkInt32(rm, 0, 8);
}
// If x is not finite, return x if y is not NaN, else NaN.
if (!x.d) return y.s ? x : y;
// If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN.
if (!y.d) {
if (y.s) y.s = x.s;
return y;
}
}
// If y is not zero, calculate the nearest multiple of y to x.
if (y.d[0]) {
external = false;
x = divide(x, y, 0, rm, 1).times(y);
external = true;
finalise(x);
// If y is zero, return zero with the sign of x.
} else {
y.s = x.s;
x = y;
}
return x;
};
/*
* Return the value of this Decimal converted to a number primitive.
* Zero keeps its sign.
*
*/
P.toNumber = function () {
return +this;
};
/*
* Return a string representing the value of this Decimal in base 8, round to `sd` significant
* digits using rounding mode `rm`.
*
* If the optional `sd` argument is present then return binary exponential notation.
*
* [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
*/
P.toOctal = function (sd, rm) {
return toStringBinary(this, 8, sd, rm);
};
/*
* Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded
* to `precision` significant digits using rounding mode `rounding`.
*
* ECMAScript compliant.
*
* pow(x, NaN) = NaN
* pow(x, ±0) = 1
* pow(NaN, non-zero) = NaN
* pow(abs(x) > 1, +Infinity) = +Infinity
* pow(abs(x) > 1, -Infinity) = +0
* pow(abs(x) == 1, ±Infinity) = NaN
* pow(abs(x) < 1, +Infinity) = +0
* pow(abs(x) < 1, -Infinity) = +Infinity
* pow(+Infinity, y > 0) = +Infinity
* pow(+Infinity, y < 0) = +0
* pow(-Infinity, odd integer > 0) = -Infinity
* pow(-Infinity, even integer > 0) = +Infinity
* pow(-Infinity, odd integer < 0) = -0
* pow(-Infinity, even integer < 0) = +0
* pow(+0, y > 0) = +0
* pow(+0, y < 0) = +Infinity
* pow(-0, odd integer > 0) = -0
* pow(-0, even integer > 0) = +0
* pow(-0, odd integer < 0) = -Infinity
* pow(-0, even integer < 0) = +Infinity
* pow(finite x < 0, finite non-integer) = NaN
*
* For non-integer or very large exponents pow(x, y) is calculated using
*
* x^y = exp(y*ln(x))
*
* Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the
* probability of an incorrectly rounded result
* P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14
* i.e. 1 in 250,000,000,000,000
*
* If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place).
*
* y {number|string|bigint|Decimal} The power to which to raise this Decimal.
*
*/
P.toPower = P.pow = function (y) {
var e, k, pr, r, rm, s,
x = this,
Ctor = x.constructor,
yn = +(y = new Ctor(y));
// Either ±Infinity, NaN or ±0?
if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn));
x = new Ctor(x);
if (x.eq(1)) return x;
pr = Ctor.precision;
rm = Ctor.rounding;
if (y.eq(1)) return finalise(x, pr, rm);
// y exponent
e = mathfloor(y.e / LOG_BASE);
// If y is a small integer use the 'exponentiation by squaring' algorithm.
if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
r = intPow(Ctor, x, k, pr);
return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm);
}
s = x.s;
// if x is negative
if (s < 0) {
// if y is not an integer
if (e < y.d.length - 1) return new Ctor(NaN);
// Result is positive if x is negative and the last digit of integer y is even.
if ((y.d[e] & 1) == 0) s = 1;
// if x.eq(-1)
if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) {
x.s = s;
return x;
}
}
// Estimate result exponent.
// x^y = 10^e, where e = y * log10(x)
// log10(x) = log10(x_significand) + x_exponent
// log10(x_significand) = ln(x_significand) / ln(10)
k = mathpow(+x, yn);
e = k == 0 || !isFinite(k)
? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1))
: new Ctor(k + '').e;
// Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1.
// Overflow/underflow?
if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0);
external = false;
Ctor.rounding = x.s = 1;
// Estimate the extra guard digits needed to ensure five correct rounding digits from
// naturalLogarithm(x). Example of failure without these extra digits (precision: 10):
// new Decimal(2.32456).pow('2087987436534566.46411')
// should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815
k = Math.min(12, (e + '').length);
// r = x^y = exp(y*ln(x))
r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr);
// r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40)
if (r.d) {
// Truncate to the required precision plus five rounding digits.
r = finalise(r, pr + 5, 1);
// If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate
// the result.
if (checkRoundingDigits(r.d, pr, rm)) {
e = pr + 10;
// Truncate to the increased precision plus five rounding digits.
r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1);
// Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9).
if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) {
r = finalise(r, pr + 1, 0);
}
}
}
r.s = s;
external = true;
Ctor.rounding = rm;
return finalise(r, pr, rm);
};
/*
* Return a string representing the value of this Decimal rounded to `sd` significant digits
* using rounding mode `rounding`.
*
* Return exponential notation if `sd` is less than the number of digits necessary to represent
* the integer part of the value in normal notation.
*
* [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
*/
P.toPrecision = function (sd, rm) {
var str,
x = this,
Ctor = x.constructor;
if (sd === void 0) {
str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
} else {
checkInt32(sd, 1, MAX_DIGITS);
if (rm === void 0) rm = Ctor.rounding;
else checkInt32(rm, 0, 8);
x = finalise(new Ctor(x), sd, rm);
str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd);
}
return x.isNeg() && !x.isZero() ? '-' + str : str;
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
* significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
* omitted.
*
* [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* 'toSD() digits out of range: {sd}'
* 'toSD() digits not an integer: {sd}'
* 'toSD() rounding mode not an integer: {rm}'
* 'toSD() rounding mode out of range: {rm}'
*
*/
P.toSignificantDigits = P.toSD = function (sd, rm) {
var x = this,
Ctor = x.constructor;
if (sd === void 0) {
sd = Ctor.precision;
rm = Ctor.rounding;
} else {
checkInt32(sd, 1, MAX_DIGITS);
if (rm === void 0) rm = Ctor.rounding;
else checkInt32(rm, 0, 8);
}
return finalise(new Ctor(x), sd, rm);
};
/*
* Return a string representing the value of this Decimal.
*
* Return exponential notation if this Decimal has a positive exponent equal to or greater than
* `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
*
*/
P.toString = function () {
var x = this,
Ctor = x.constructor,
str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
return x.isNeg() && !x.isZero() ? '-' + str : str;
};
/*
* Return a new Decimal whose value is the value of this Decimal truncated to a whole number.
*
*/
P.truncated = P.trunc = function () {
return finalise(new this.constructor(this), this.e + 1, 1);
};
/*
* Return a string representing the value of this Decimal.
* Unlike `toString`, negative zero will include the minus sign.
*
*/
P.valueOf = P.toJSON = function () {
var x = this,
Ctor = x.constructor,
str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos);
return x.isNeg() ? '-' + str : str;
};
// Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
/*
* digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower,
* finiteToString, naturalExponential, naturalLogarithm
* checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest,
* P.toPrecision, P.toSignificantDigits, toStringBinary, random
* checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm
* convertBase toStringBinary, parseOther
* cos P.cos
* divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy,
* P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction,
* P.toNearest, toStringBinary, naturalExponential, naturalLogarithm,
* taylorSeries, atan2, parseOther
* finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh,
* P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus,
* P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot,
* P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed,
* P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits,
* P.truncated, divide, getLn10, getPi, naturalExponential,
* naturalLogarithm, ceil, floor, round, trunc
* finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf,
* toStringBinary
* getBase10Exponent P.minus, P.plus, P.times, parseOther
* getLn10 P.logarithm, naturalLogarithm
* getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2
* getPrecision P.precision, P.toFraction
* getZeroString digitsToString, finiteToString
* intPow P.toPower, parseOther
* isOdd toLessThanHalfPi
* maxOrMin max, min
* naturalExponential P.naturalExponential, P.toPower
* naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm,
* P.toPower, naturalExponential
* nonFiniteToString finiteToString, toStringBinary
* parseDecimal Decimal
* parseOther Decimal
* sin P.sin
* taylorSeries P.cosh, P.sinh, cos, sin
* toLessThanHalfPi P.cos, P.sin
* toStringBinary P.toBinary, P.toHexadecimal, P.toOctal
* truncate intPow
*
* Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi,
* naturalLogarithm, config, parseOther, random, Decimal
*/
function digitsToString(d) {
var i, k, ws,
indexOfLastWord = d.length - 1,
str = '',
w = d[0];
if (indexOfLastWord > 0) {
str += w;
for (i = 1; i < indexOfLastWord; i++) {
ws = d[i] + '';
k = LOG_BASE - ws.length;
if (k) str += getZeroString(k);
str += ws;
}
w = d[i];
ws = w + '';
k = LOG_BASE - ws.length;
if (k) str += getZeroString(k);
} else if (w === 0) {
return '0';
}
// Remove trailing zeros of last w.
for (; w % 10 === 0;) w /= 10;
return str + w;
}
function checkInt32(i, min, max) {
if (i !== ~~i || i < min || i > max) {
throw Error(invalidArgument + i);
}
}
/*
* Check 5 rounding digits if `repeating` is null, 4 otherwise.
* `repeating == null` if caller is `log` or `pow`,
* `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`.
*/
function checkRoundingDigits(d, i, rm, repeating) {
var di, k, r, rd;
// Get the length of the first word of the array d.
for (k = d[0]; k >= 10; k /= 10) --i;
// Is the rounding digit in the first word of d?
if (--i < 0) {
i += LOG_BASE;
di = 0;
} else {
di = Math.ceil((i + 1) / LOG_BASE);
i %= LOG_BASE;
}
// i is the index (0 - 6) of the rounding digit.
// E.g. if within the word 3487563 the first rounding digit is 5,
// then i = 4, k = 1000, rd = 3487563 % 1000 = 563
k = mathpow(10, LOG_BASE - i);
rd = d[di] % k | 0;
if (repeating == null) {
if (i < 3) {
if (i == 0) rd = rd / 100 | 0;
else if (i == 1) rd = rd / 10 | 0;
r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0;
} else {
r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) &&
(d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 ||
(rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0;
}
} else {
if (i < 4) {
if (i == 0) rd = rd / 1000 | 0;
else if (i == 1) rd = rd / 100 | 0;
else if (i == 2) rd = rd / 10 | 0;
r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999;
} else {
r = ((repeating || rm < 4) && rd + 1 == k ||
(!repeating && rm > 3) && rd + 1 == k / 2) &&
(d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1;
}
}
return r;
}
// Convert string of `baseIn` to an array of numbers of `baseOut`.
// Eg. convertBase('255', 10, 16) returns [15, 15].
// Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
function convertBase(str, baseIn, baseOut) {
var j,
arr = [0],
arrL,
i = 0,
strL = str.length;
for (; i < strL;) {
for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn;
arr[0] += NUMERALS.indexOf(str.charAt(i++));
for (j = 0; j < arr.length; j++) {
if (arr[j] > baseOut - 1) {
if (arr[j + 1] === void 0) arr[j + 1] = 0;
arr[j + 1] += arr[j] / baseOut | 0;
arr[j] %= baseOut;
}
}
}
return arr.reverse();
}
/*
* cos(x) = 1 - x^2/2! + x^4/4! - ...
* |x| < pi/2
*
*/
function cosine(Ctor, x) {
var k, len, y;
if (x.isZero()) return x;
// Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1
// i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1
// Estimate the optimum number of times to use the argument reduction.
len = x.d.length;
if (len < 32) {
k = Math.ceil(len / 3);
y = (1 / tinyPow(4, k)).toString();
} else {
k = 16;
y = '2.3283064365386962890625e-10';
}
Ctor.precision += k;
x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1));
// Reverse argument reduction
for (var i = k; i--;) {
var cos2x = x.times(x);
x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1);
}
Ctor.precision -= k;
return x;
}
/*
* Perform division in the specified base.
*/
var divide = (function () {
// Assumes non-zero x and k, and hence non-zero result.
function multiplyInteger(x, k, base) {
var temp,
carry = 0,
i = x.length;
for (x = x.slice(); i--;) {
temp = x[i] * k + carry;
x[i] = temp % base | 0;
carry = temp / base | 0;
}
if (carry) x.unshift(carry);
return x;
}
function compare(a, b, aL, bL) {
var i, r;
if (aL != bL) {
r = aL > bL ? 1 : -1;
} else {
for (i = r = 0; i < aL; i++) {
if (a[i] != b[i]) {
r = a[i] > b[i] ? 1 : -1;
break;
}
}
}
return r;
}
function subtract(a, b, aL, base) {
var i = 0;
// Subtract b from a.
for (; aL--;) {
a[aL] -= i;
i = a[aL] < b[aL] ? 1 : 0;
a[aL] = i * base + a[aL] - b[aL];
}
// Remove leading zeros.
for (; !a[0] && a.length > 1;) a.shift();
}
return function (x, y, pr, rm, dp, base) {
var cmp, e, i, k, logBase, more, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0,
yL, yz,
Ctor = x.constructor,
sign = x.s == y.s ? 1 : -1,
xd = x.d,
yd = y.d;
// Either NaN, Infinity or 0?
if (!xd || !xd[0] || !yd || !yd[0]) {
return new Ctor(// Return NaN if either NaN, or both Infinity or 0.
!x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN :
// Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0.
xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0);
}
if (base) {
logBase = 1;
e = x.e - y.e;
} else {
base = BASE;
logBase = LOG_BASE;
e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase);
}
yL = yd.length;
xL = xd.length;
q = new Ctor(sign);
qd = q.d = [];
// Result exponent may be one less than e.
// The digit array of a Decimal from toStringBinary may have trailing zeros.
for (i = 0; yd[i] == (xd[i] || 0); i++);
if (yd[i] > (xd[i] || 0)) e--;
if (pr == null) {
sd = pr = Ctor.precision;
rm = Ctor.rounding;
} else if (dp) {
sd = pr + (x.e - y.e) + 1;
} else {
sd = pr;
}
if (sd < 0) {
qd.push(1);
more = true;
} else {
// Convert precision in number of base 10 digits to base 1e7 digits.
sd = sd / logBase + 2 | 0;
i = 0;
// divisor < 1e7
if (yL == 1) {
k = 0;
yd = yd[0];
sd++;
// k is the carry.
for (; (i < xL || k) && sd--; i++) {
t = k * base + (xd[i] || 0);
qd[i] = t / yd | 0;
k = t % yd | 0;
}
more = k || i < xL;
// divisor >= 1e7
} else {
// Normalise xd and yd so highest order digit of yd is >= base/2
k = base / (yd[0] + 1) | 0;
if (k > 1) {
yd = multiplyInteger(yd, k, base);
xd = multiplyInteger(xd, k, base);
yL = yd.length;
xL = xd.length;
}
xi = yL;
rem = xd.slice(0, yL);
remL = rem.length;
// Add zeros to make remainder as long as divisor.
for (; remL < yL;) rem[remL++] = 0;
yz = yd.slice();
yz.unshift(0);
yd0 = yd[0];
if (yd[1] >= base / 2) ++yd0;
do {
k = 0;
// Compare divisor and remainder.
cmp = compare(yd, rem, yL, remL);
// If divisor < remainder.
if (cmp < 0) {
// Calculate trial digit, k.
rem0 = rem[0];
if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
// k will be how many times the divisor goes into the current remainder.
k = rem0 / yd0 | 0;
// Algorithm:
// 1. product = divisor * trial digit (k)
// 2. if product > remainder: product -= divisor, k--
// 3. remainder -= product
// 4. if product was < remainder at 2:
// 5. compare new remainder and divisor
// 6. If remainder > divisor: remainder -= divisor, k++
if (k > 1) {
if (k >= base) k = base - 1;
// product = divisor * trial digit.
prod = multiplyInteger(yd, k, base);
prodL = prod.length;
remL = rem.length;
// Compare product and remainder.
cmp = compare(prod, rem, prodL, remL);
// product > remainder.
if (cmp == 1) {
k--;
// Subtract divisor from product.
subtract(prod, yL < prodL ? yz : yd, prodL, base);
}
} else {
// cmp is -1.
// If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
// to avoid it. If k is 1 there is a need to compare yd and rem again below.
if (k == 0) cmp = k = 1;
prod = yd.slice();
}
prodL = prod.length;
if (prodL < remL) prod.unshift(0);
// Subtract product from remainder.
subtract(rem, prod, remL, base);
// If product was < previous remainder.
if (cmp == -1) {
remL = rem.length;
// Compare divisor and new remainder.
cmp = compare(yd, rem, yL, remL);
// If divisor < new remainder, subtract divisor from remainder.
if (cmp < 1) {
k++;
// Subtract divisor from remainder.
subtract(rem, yL < remL ? yz : yd, remL, base);
}
}
remL = rem.length;
} else if (cmp === 0) {
k++;
rem = [0];
} // if cmp === 1, k will be 0
// Add the next digit, k, to the result array.
qd[i++] = k;
// Update the remainder.
if (cmp && rem[0]) {
rem[remL++] = xd[xi] || 0;
} else {
rem = [xd[xi]];
remL = 1;
}
} while ((xi++ < xL || rem[0] !== void 0) && sd--);
more = rem[0] !== void 0;
}
// Leading zero?
if (!qd[0]) qd.shift();
}
// logBase is 1 when divide is being used for base conversion.
if (logBase == 1) {
q.e = e;
inexact = more;
} else {
// To calculate q.e, first get the number of digits of qd[0].
for (i = 1, k = qd[0]; k >= 10; k /= 10) i++;
q.e = i + e * logBase - 1;
finalise(q, dp ? pr + q.e + 1 : pr, rm, more);
}
return q;
};
})();
/*
* Round `x` to `sd` significant digits using rounding mode `rm`.
* Check for over/under-flow.
*/
function finalise(x, sd, rm, isTruncated) {
var digits, i, j, k, rd, roundUp, w, xd, xdi,
Ctor = x.constructor;
// Don't round if sd is null or undefined.
out: if (sd != null) {
xd = x.d;
// Infinity/NaN.
if (!xd) return x;
// rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
// w: the word of xd containing rd, a base 1e7 number.
// xdi: the index of w within xd.
// digits: the number of digits of w.
// i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
// they had leading zeros)
// j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
// Get the length of the first word of the digits array xd.
for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++;
i = sd - digits;
// Is the rounding digit in the first word of xd?
if (i < 0) {
i += LOG_BASE;
j = sd;
w = xd[xdi = 0];
// Get the rounding digit at index j of w.
rd = w / mathpow(10, digits - j - 1) % 10 | 0;
} else {
xdi = Math.ceil((i + 1) / LOG_BASE);
k = xd.length;
if (xdi >= k) {
if (isTruncated) {
// Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`.
for (; k++ <= xdi;) xd.push(0);
w = rd = 0;
digits = 1;
i %= LOG_BASE;
j = i - LOG_BASE + 1;
} else {
break out;
}
} else {
w = k = xd[xdi];
// Get the number of digits of w.
for (digits = 1; k >= 10; k /= 10) digits++;
// Get the index of rd within w.
i %= LOG_BASE;
// Get the index of rd within w, adjusted for leading zeros.
// The number of leading zeros of w is given by LOG_BASE - digits.
j = i - LOG_BASE + digits;
// Get the rounding digit at index j of w.
rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0;
}
}
// Are there any non-zero digits after the rounding digit?
isTruncated = isTruncated || sd < 0 ||
xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1));
// The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right
// of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression
// will give 714.
roundUp = rm < 4
? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
: rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 &&
// Check whether the digit to the left of the rounding digit is odd.
((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
rm == (x.s < 0 ? 8 : 7));
if (sd < 1 || !xd[0]) {
xd.length = 0;
if (roundUp) {
// Convert sd to decimal places.
sd -= x.e + 1;
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
x.e = -sd || 0;
} else {
// Zero.
xd[0] = x.e = 0;
}
return x;
}
// Remove excess digits.
if (i == 0) {
xd.length = xdi;
k = 1;
xdi--;
} else {
xd.length = xdi + 1;
k = mathpow(10, LOG_BASE - i);
// E.g. 56700 becomes 56000 if 7 is the rounding digit.
// j > 0 means i > number of leading zeros of w.
xd[xdi] = j > 0 ? (w / mathpow(10, digits - j) % mathpow(10, j) | 0) * k : 0;
}
if (roundUp) {
for (;;) {
// Is the digit to be rounded up in the first word of xd?
if (xdi == 0) {
// i will be the length of xd[0] before k is added.
for (i = 1, j = xd[0]; j >= 10; j /= 10) i++;
j = xd[0] += k;
for (k = 1; j >= 10; j /= 10) k++;
// if i != k the length has increased.
if (i != k) {
x.e++;
if (xd[0] == BASE) xd[0] = 1;
}
break;
} else {
xd[xdi] += k;
if (xd[xdi] != BASE) break;
xd[xdi--] = 0;
k = 1;
}
}
}
// Remove trailing zeros.
for (i = xd.length; xd[--i] === 0;) xd.pop();
}
if (external) {
// Overflow?
if (x.e > Ctor.maxE) {
// Infinity.
x.d = null;
x.e = NaN;
// Underflow?
} else if (x.e < Ctor.minE) {
// Zero.
x.e = 0;
x.d = [0];
// Ctor.underflow = true;
} // else Ctor.underflow = false;
}
return x;
}
function finiteToString(x, isExp, sd) {
if (!x.isFinite()) return nonFiniteToString(x);
var k,
e = x.e,
str = digitsToString(x.d),
len = str.length;
if (isExp) {
if (sd && (k = sd - len) > 0) {
str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
} else if (len > 1) {
str = str.charAt(0) + '.' + str.slice(1);
}
str = str + (x.e < 0 ? 'e' : 'e+') + x.e;
} else if (e < 0) {
str = '0.' + getZeroString(-e - 1) + str;
if (sd && (k = sd - len) > 0) str += getZeroString(k);
} else if (e >= len) {
str += getZeroString(e + 1 - len);
if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
} else {
if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
if (sd && (k = sd - len) > 0) {
if (e + 1 === len) str += '.';
str += getZeroString(k);
}
}
return str;
}
// Calculate the base 10 exponent from the base 1e7 exponent.
function getBase10Exponent(digits, e) {
var w = digits[0];
// Add the number of digits of the first word of the digits array.
for ( e *= LOG_BASE; w >= 10; w /= 10) e++;
return e;
}
function getLn10(Ctor, sd, pr) {
if (sd > LN10_PRECISION) {
// Reset global state in case the exception is caught.
external = true;
if (pr) Ctor.precision = pr;
throw Error(precisionLimitExceeded);
}
return finalise(new Ctor(LN10), sd, 1, true);
}
function getPi(Ctor, sd, rm) {
if (sd > PI_PRECISION) throw Error(precisionLimitExceeded);
return finalise(new Ctor(PI), sd, rm, true);
}
function getPrecision(digits) {
var w = digits.length - 1,
len = w * LOG_BASE + 1;
w = digits[w];
// If non-zero...
if (w) {
// Subtract the number of trailing zeros of the last word.
for (; w % 10 == 0; w /= 10) len--;
// Add the number of digits of the first word.
for (w = digits[0]; w >= 10; w /= 10) len++;
}
return len;
}
function getZeroString(k) {
var zs = '';
for (; k--;) zs += '0';
return zs;
}
/*
* Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an
* integer of type number.
*
* Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`.
*
*/
function intPow(Ctor, x, n, pr) {
var isTruncated,
r = new Ctor(1),
// Max n of 9007199254740991 takes 53 loop iterations.
// Maximum digits array length; leaves [28, 34] guard digits.
k = Math.ceil(pr / LOG_BASE + 4);
external = false;
for (;;) {
if (n % 2) {
r = r.times(x);
if (truncate(r.d, k)) isTruncated = true;
}
n = mathfloor(n / 2);
if (n === 0) {
// To ensure correct rounding when r.d is truncated, increment the last word if it is zero.
n = r.d.length - 1;
if (isTruncated && r.d[n] === 0) ++r.d[n];
break;
}
x = x.times(x);
truncate(x.d, k);
}
external = true;
return r;
}
function isOdd(n) {
return n.d[n.d.length - 1] & 1;
}
/*
* Handle `max` (`n` is -1) and `min` (`n` is 1).
*/
function maxOrMin(Ctor, args, n) {
var k, y,
x = new Ctor(args[0]),
i = 0;
for (; ++i < args.length;) {
y = new Ctor(args[i]);
// NaN?
if (!y.s) {
x = y;
break;
}
k = x.cmp(y);
if (k === n || k === 0 && x.s === n) {
x = y;
}
}
return x;
}
/*
* Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant
* digits.
*
* Taylor/Maclaurin series.
*
* exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
*
* Argument reduction:
* Repeat x = x / 32, k += 5, until |x| < 0.1
* exp(x) = exp(x / 2^k)^(2^k)
*
* Previously, the argument was initially reduced by
* exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10)
* to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
* found to be slower than just dividing repeatedly by 32 as above.
*
* Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000
* Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000
* (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
*
* exp(Infinity) = Infinity
* exp(-Infinity) = 0
* exp(NaN) = NaN
* exp(±0) = 1
*
* exp(x) is non-terminating for any finite, non-zero x.
*
* The result will always be correctly rounded.
*
*/
function naturalExponential(x, sd) {
var denominator, guard, j, pow, sum, t, wpr,
rep = 0,
i = 0,
k = 0,
Ctor = x.constructor,
rm = Ctor.rounding,
pr = Ctor.precision;
// 0/NaN/Infinity?
if (!x.d || !x.d[0] || x.e > 17) {
return new Ctor(x.d
? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0
: x.s ? x.s < 0 ? 0 : x : 0 / 0);
}
if (sd == null) {
external = false;
wpr = pr;
} else {
wpr = sd;
}
t = new Ctor(0.03125);
// while abs(x) >= 0.1
while (x.e > -2) {
// x = x / 2^5
x = x.times(t);
k += 5;
}
// Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision
// necessary to ensure the first 4 rounding digits are correct.
guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
wpr += guard;
denominator = pow = sum = new Ctor(1);
Ctor.precision = wpr;
for (;;) {
pow = finalise(pow.times(x), wpr, 1);
denominator = denominator.times(++i);
t = sum.plus(divide(pow, denominator, wpr, 1));
if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
j = k;
while (j--) sum = finalise(sum.times(sum), wpr, 1);
// Check to see if the first 4 rounding digits are [49]999.
// If so, repeat the summation with a higher precision, otherwise
// e.g. with precision: 18, rounding: 1
// exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123)
// `wpr - guard` is the index of first rounding digit.
if (sd == null) {
if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
Ctor.precision = wpr += 10;
denominator = pow = t = new Ctor(1);
i = 0;
rep++;
} else {
return finalise(sum, Ctor.precision = pr, rm, external = true);
}
} else {
Ctor.precision = pr;
return sum;
}
}
sum = t;
}
}
/*
* Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant
* digits.
*
* ln(-n) = NaN
* ln(0) = -Infinity
* ln(-0) = -Infinity
* ln(1) = 0
* ln(Infinity) = Infinity
* ln(-Infinity) = NaN
* ln(NaN) = NaN
*
* ln(n) (n != 1) is non-terminating.
*
*/
function naturalLogarithm(y, sd) {
var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2,
n = 1,
guard = 10,
x = y,
xd = x.d,
Ctor = x.constructor,
rm = Ctor.rounding,
pr = Ctor.precision;
// Is x negative or Infinity, NaN, 0 or 1?
if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) {
return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x);
}
if (sd == null) {
external = false;
wpr = pr;
} else {
wpr = sd;
}
Ctor.precision = wpr += guard;
c = digitsToString(xd);
c0 = c.charAt(0);
if (Math.abs(e = x.e) < 1.5e15) {
// Argument reduction.
// The series converges faster the closer the argument is to 1, so using
// ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b
// multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
// 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
// later be divided by this number, then separate out the power of 10 using
// ln(a*10^b) = ln(a) + b*ln(10).
// max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
//while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
// max n is 6 (gives 0.7 - 1.3)
while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
x = x.times(y);
c = digitsToString(x.d);
c0 = c.charAt(0);
n++;
}
e = x.e;
if (c0 > 1) {
x = new Ctor('0.' + c);
e++;
} else {
x = new Ctor(c0 + '.' + c.slice(1));
}
} else {
// The argument reduction method above may result in overflow if the argument y is a massive
// number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
// function using ln(x*10^e) = ln(x) + e*ln(10).
t = getLn10(Ctor, wpr + 2, pr).times(e + '');
x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
Ctor.precision = pr;
return sd == null ? finalise(x, pr, rm, external = true) : x;
}
// x1 is x reduced to a value near 1.
x1 = x;
// Taylor series.
// ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
// where x = (y - 1)/(y + 1) (|x| < 1)
sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1);
x2 = finalise(x.times(x), wpr, 1);
denominator = 3;
for (;;) {
numerator = finalise(numerator.times(x2), wpr, 1);
t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1));
if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
sum = sum.times(2);
// Reverse the argument reduction. Check that e is not 0 because, besides preventing an
// unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0.
if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
sum = divide(sum, new Ctor(n), wpr, 1);
// Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has
// been repeated previously) and the first 4 rounding digits 9999?
// If so, restart the summation with a higher precision, otherwise
// e.g. with precision: 12, rounding: 1
// ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463.
// `wpr - guard` is the index of first rounding digit.
if (sd == null) {
if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) {
Ctor.precision = wpr += guard;
t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1);
x2 = finalise(x.times(x), wpr, 1);
denominator = rep = 1;
} else {
return finalise(sum, Ctor.precision = pr, rm, external = true);
}
} else {
Ctor.precision = pr;
return sum;
}
}
sum = t;
denominator += 2;
}
}
// ±Infinity, NaN.
function nonFiniteToString(x) {
// Unsigned.
return String(x.s * x.s / 0);
}
/*
* Parse the value of a new Decimal `x` from string `str`.
*/
function parseDecimal(x, str) {
var e, i, len;
// TODO BigInt str: no need to check for decimal point, exponential form or leading zeros.
// Decimal point?
if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
// Exponential form?
if ((i = str.search(/e/i)) > 0) {
// Determine exponent.
if (e < 0) e = i;
e += +str.slice(i + 1);
str = str.substring(0, i);
} else if (e < 0) {
// Integer.
e = str.length;
}
// Determine leading zeros.
for (i = 0; str.charCodeAt(i) === 48; i++);
// Determine trailing zeros.
for (len = str.length; str.charCodeAt(len - 1) === 48; --len);
str = str.slice(i, len);
if (str) {
len -= i;
x.e = e = e - i - 1;
x.d = [];
// Transform base
// e is the base 10 exponent.
// i is where to slice str to get the first word of the digits array.
i = (e + 1) % LOG_BASE;
if (e < 0) i += LOG_BASE;
if (i < len) {
if (i) x.d.push(+str.slice(0, i));
for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
str = str.slice(i);
i = LOG_BASE - str.length;
} else {
i -= len;
}
for (; i--;) str += '0';
x.d.push(+str);
if (external) {
// Overflow?
if (x.e > x.constructor.maxE) {
// Infinity.
x.d = null;
x.e = NaN;
// Underflow?
} else if (x.e < x.constructor.minE) {
// Zero.
x.e = 0;
x.d = [0];
// x.constructor.underflow = true;
} // else x.constructor.underflow = false;
}
} else {
// Zero.
x.e = 0;
x.d = [0];
}
return x;
}
/*
* Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value.
*/
function parseOther(x, str) {
var base, Ctor, divisor, i, isFloat, len, p, xd, xe;
if (str.indexOf('_') > -1) {
str = str.replace(/(\d)_(?=\d)/g, '$1');
if (isDecimal.test(str)) return parseDecimal(x, str);
} else if (str === 'Infinity' || str === 'NaN') {
if (!+str) x.s = NaN;
x.e = NaN;
x.d = null;
return x;
}
if (isHex.test(str)) {
base = 16;
str = str.toLowerCase();
} else if (isBinary.test(str)) {
base = 2;
} else if (isOctal.test(str)) {
base = 8;
} else {
throw Error(invalidArgument + str);
}
// Is there a binary exponent part?
i = str.search(/p/i);
if (i > 0) {
p = +str.slice(i + 1);
str = str.substring(2, i);
} else {
str = str.slice(2);
}
// Convert `str` as an integer then divide the result by `base` raised to a power such that the
// fraction part will be restored.
i = str.indexOf('.');
isFloat = i >= 0;
Ctor = x.constructor;
if (isFloat) {
str = str.replace('.', '');
len = str.length;
i = len - i;
// log[10](16) = 1.2041... , log[10](88) = 1.9444....
divisor = intPow(Ctor, new Ctor(base), i, i * 2);
}
xd = convertBase(str, base, BASE);
xe = xd.length - 1;
// Remove trailing zeros.
for (i = xe; xd[i] === 0; --i) xd.pop();
if (i < 0) return new Ctor(x.s * 0);
x.e = getBase10Exponent(xd, xe);
x.d = xd;
external = false;
// At what precision to perform the division to ensure exact conversion?
// maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount)
// log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412
// E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits.
// maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount
// Therefore using 4 * the number of digits of str will always be enough.
if (isFloat) x = divide(x, divisor, len * 4);
// Multiply by the binary exponent part if present.
if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p));
external = true;
return x;
}
/*
* sin(x) = x - x^3/3! + x^5/5! - ...
* |x| < pi/2
*
*/
function sine(Ctor, x) {
var k,
len = x.d.length;
if (len < 3) {
return x.isZero() ? x : taylorSeries(Ctor, 2, x, x);
}
// Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x)
// i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5)
// and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20))
// Estimate the optimum number of times to use the argument reduction.
k = 1.4 * Math.sqrt(len);
k = k > 16 ? 16 : k | 0;
x = x.times(1 / tinyPow(5, k));
x = taylorSeries(Ctor, 2, x, x);
// Reverse argument reduction
var sin2_x,
d5 = new Ctor(5),
d16 = new Ctor(16),
d20 = new Ctor(20);
for (; k--;) {
sin2_x = x.times(x);
x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));
}
return x;
}
// Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`.
function taylorSeries(Ctor, n, x, y, isHyperbolic) {
var j, t, u, x2,
i = 1,
pr = Ctor.precision,
k = Math.ceil(pr / LOG_BASE);
external = false;
x2 = x.times(x);
u = new Ctor(y);
for (;;) {
t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1);
u = isHyperbolic ? y.plus(t) : y.minus(t);
y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1);
t = u.plus(y);
if (t.d[k] !== void 0) {
for (j = k; t.d[j] === u.d[j] && j--;);
if (j == -1) break;
}
j = u;
u = y;
y = t;
t = j;
i++;
}
external = true;
t.d.length = k + 1;
return t;
}
// Exponent e must be positive and non-zero.
function tinyPow(b, e) {
var n = b;
while (--e) n *= b;
return n;
}
// Return the absolute value of `x` reduced to less than or equal to half pi.
function toLessThanHalfPi(Ctor, x) {
var t,
isNeg = x.s < 0,
pi = getPi(Ctor, Ctor.precision, 1),
halfPi = pi.times(0.5);
x = x.abs();
if (x.lte(halfPi)) {
quadrant = isNeg ? 4 : 1;
return x;
}
t = x.divToInt(pi);
if (t.isZero()) {
quadrant = isNeg ? 3 : 2;
} else {
x = x.minus(t.times(pi));
// 0 <= x < pi
if (x.lte(halfPi)) {
quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1);
return x;
}
quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2);
}
return x.minus(pi).abs();
}
/*
* Return the value of Decimal `x` as a string in base `baseOut`.
*
* If the optional `sd` argument is present include a binary exponent suffix.
*/
function toStringBinary(x, baseOut, sd, rm) {
var base, e, i, k, len, roundUp, str, xd, y,
Ctor = x.constructor,
isExp = sd !== void 0;
if (isExp) {
checkInt32(sd, 1, MAX_DIGITS);
if (rm === void 0) rm = Ctor.rounding;
else checkInt32(rm, 0, 8);
} else {
sd = Ctor.precision;
rm = Ctor.rounding;
}
if (!x.isFinite()) {
str = nonFiniteToString(x);
} else {
str = finiteToString(x);
i = str.indexOf('.');
// Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required:
// maxBinaryExponent = floor((decimalExponent + 1) * log[2](10))
// minBinaryExponent = floor(decimalExponent * log[2](10))
// log[2](10) = 3.321928094887362347870319429489390175864
if (isExp) {
base = 2;
if (baseOut == 16) {
sd = sd * 4 - 3;
} else if (baseOut == 8) {
sd = sd * 3 - 2;
}
} else {
base = baseOut;
}
// Convert the number as an integer then divide the result by its base raised to a power such
// that the fraction part will be restored.
// Non-integer.
if (i >= 0) {
str = str.replace('.', '');
y = new Ctor(1);
y.e = str.length - i;
y.d = convertBase(finiteToString(y), 10, base);
y.e = y.d.length;
}
xd = convertBase(str, 10, base);
e = len = xd.length;
// Remove trailing zeros.
for (; xd[--len] == 0;) xd.pop();
if (!xd[0]) {
str = isExp ? '0p+0' : '0';
} else {
if (i < 0) {
e--;
} else {
x = new Ctor(x);
x.d = xd;
x.e = e;
x = divide(x, y, sd, rm, 0, base);
xd = x.d;
e = x.e;
roundUp = inexact;
}
// The rounding digit, i.e. the digit after the digit that may be rounded up.
i = xd[sd];
k = base / 2;
roundUp = roundUp || xd[sd + 1] !== void 0;
roundUp = rm < 4
? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2))
: i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 ||
rm === (x.s < 0 ? 8 : 7));
xd.length = sd;
if (roundUp) {
// Rounding up may mean the previous digit has to be rounded up and so on.
for (; ++xd[--sd] > base - 1;) {
xd[sd] = 0;
if (!sd) {
++e;
xd.unshift(1);
}
}
}
// Determine trailing zeros.
for (len = xd.length; !xd[len - 1]; --len);
// E.g. [4, 11, 15] becomes 4bf.
for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]);
// Add binary exponent suffix?
if (isExp) {
if (len > 1) {
if (baseOut == 16 || baseOut == 8) {
i = baseOut == 16 ? 4 : 3;
for (--len; len % i; len++) str += '0';
xd = convertBase(str, base, baseOut);
for (len = xd.length; !xd[len - 1]; --len);
// xd[0] will always be be 1
for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]);
} else {
str = str.charAt(0) + '.' + str.slice(1);
}
}
str = str + (e < 0 ? 'p' : 'p+') + e;
} else if (e < 0) {
for (; ++e;) str = '0' + str;
str = '0.' + str;
} else {
if (++e > len) for (e -= len; e-- ;) str += '0';
else if (e < len) str = str.slice(0, e) + '.' + str.slice(e);
}
}
str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str;
}
return x.s < 0 ? '-' + str : str;
}
// Does not strip trailing zeros.
function truncate(arr, len) {
if (arr.length > len) {
arr.length = len;
return true;
}
}
// Decimal methods
/*
* abs
* acos
* acosh
* add
* asin
* asinh
* atan
* atanh
* atan2
* cbrt
* ceil
* clamp
* clone
* config
* cos
* cosh
* div
* exp
* floor
* hypot
* ln
* log
* log2
* log10
* max
* min
* mod
* mul
* pow
* random
* round
* set
* sign
* sin
* sinh
* sqrt
* sub
* sum
* tan
* tanh
* trunc
*/
/*
* Return a new Decimal whose value is the absolute value of `x`.
*
* x {number|string|bigint|Decimal}
*
*/
function abs(x) {
return new this(x).abs();
}
/*
* Return a new Decimal whose value is the arccosine in radians of `x`.
*
* x {number|string|bigint|Decimal}
*
*/
function acos(x) {
return new this(x).acos();
}
/*
* Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function acosh(x) {
return new this(x).acosh();
}
/*
* Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
* y {number|string|bigint|Decimal}
*
*/
function add(x, y) {
return new this(x).plus(y);
}
/*
* Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function asin(x) {
return new this(x).asin();
}
/*
* Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function asinh(x) {
return new this(x).asinh();
}
/*
* Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function atan(x) {
return new this(x).atan();
}
/*
* Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function atanh(x) {
return new this(x).atanh();
}
/*
* Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi
* (inclusive), rounded to `precision` significant digits using rounding mode `rounding`.
*
* Domain: [-Infinity, Infinity]
* Range: [-pi, pi]
*
* y {number|string|bigint|Decimal} The y-coordinate.
* x {number|string|bigint|Decimal} The x-coordinate.
*
* atan2(±0, -0) = ±pi
* atan2(±0, +0) = ±0
* atan2(±0, -x) = ±pi for x > 0
* atan2(±0, x) = ±0 for x > 0
* atan2(-y, ±0) = -pi/2 for y > 0
* atan2(y, ±0) = pi/2 for y > 0
* atan2(±y, -Infinity) = ±pi for finite y > 0
* atan2(±y, +Infinity) = ±0 for finite y > 0
* atan2(±Infinity, x) = ±pi/2 for finite x
* atan2(±Infinity, -Infinity) = ±3*pi/4
* atan2(±Infinity, +Infinity) = ±pi/4
* atan2(NaN, x) = NaN
* atan2(y, NaN) = NaN
*
*/
function atan2(y, x) {
y = new this(y);
x = new this(x);
var r,
pr = this.precision,
rm = this.rounding,
wpr = pr + 4;
// Either NaN
if (!y.s || !x.s) {
r = new this(NaN);
// Both ±Infinity
} else if (!y.d && !x.d) {
r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75);
r.s = y.s;
// x is ±Infinity or y is ±0
} else if (!x.d || y.isZero()) {
r = x.s < 0 ? getPi(this, pr, rm) : new this(0);
r.s = y.s;
// y is ±Infinity or x is ±0
} else if (!y.d || x.isZero()) {
r = getPi(this, wpr, 1).times(0.5);
r.s = y.s;
// Both non-zero and finite
} else if (x.s < 0) {
this.precision = wpr;
this.rounding = 1;
r = this.atan(divide(y, x, wpr, 1));
x = getPi(this, wpr, 1);
this.precision = pr;
this.rounding = rm;
r = y.s < 0 ? r.minus(x) : r.plus(x);
} else {
r = this.atan(divide(y, x, wpr, 1));
}
return r;
}
/*
* Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function cbrt(x) {
return new this(x).cbrt();
}
/*
* Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`.
*
* x {number|string|bigint|Decimal}
*
*/
function ceil(x) {
return finalise(x = new this(x), x.e + 1, 2);
}
/*
* Return a new Decimal whose value is `x` clamped to the range delineated by `min` and `max`.
*
* x {number|string|bigint|Decimal}
* min {number|string|bigint|Decimal}
* max {number|string|bigint|Decimal}
*
*/
function clamp(x, min, max) {
return new this(x).clamp(min, max);
}
/*
* Configure global settings for a Decimal constructor.
*
* `obj` is an object with one or more of the following properties,
*
* precision {number}
* rounding {number}
* toExpNeg {number}
* toExpPos {number}
* maxE {number}
* minE {number}
* modulo {number}
* crypto {boolean|number}
* defaults {true}
*
* E.g. Decimal.config({ precision: 20, rounding: 4 })
*
*/
function config(obj) {
if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected');
var i, p, v,
useDefaults = obj.defaults === true,
ps = [
'precision', 1, MAX_DIGITS,
'rounding', 0, 8,
'toExpNeg', -EXP_LIMIT, 0,
'toExpPos', 0, EXP_LIMIT,
'maxE', 0, EXP_LIMIT,
'minE', -EXP_LIMIT, 0,
'modulo', 0, 9
];
for (i = 0; i < ps.length; i += 3) {
if (p = ps[i], useDefaults) this[p] = DEFAULTS[p];
if ((v = obj[p]) !== void 0) {
if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
else throw Error(invalidArgument + p + ': ' + v);
}
}
if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p];
if ((v = obj[p]) !== void 0) {
if (v === true || v === false || v === 0 || v === 1) {
if (v) {
if (typeof crypto != 'undefined' && crypto &&
(crypto.getRandomValues || crypto.randomBytes)) {
this[p] = true;
} else {
throw Error(cryptoUnavailable);
}
} else {
this[p] = false;
}
} else {
throw Error(invalidArgument + p + ': ' + v);
}
}
return this;
}
/*
* Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function cos(x) {
return new this(x).cos();
}
/*
* Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function cosh(x) {
return new this(x).cosh();
}
/*
* Create and return a Decimal constructor with the same configuration properties as this Decimal
* constructor.
*
*/
function clone(obj) {
var i, p, ps;
/*
* The Decimal constructor and exported function.
* Return a new Decimal instance.
*
* v {number|string|bigint|Decimal} A numeric value.
*
*/
function Decimal(v) {
var e, i, t,
x = this;
// Decimal called without new.
if (!(x instanceof Decimal)) return new Decimal(v);
// Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
// which points to Object.
x.constructor = Decimal;
if (isDecimalInstance(v)) {
x.s = v.s;
if (external) {
if (!v.d || v.e > Decimal.maxE) {
// Infinity.
x.e = NaN;
x.d = null;
} else if (v.e < Decimal.minE) {
// Zero.
x.e = 0;
x.d = [0];
} else {
x.e = v.e;
x.d = v.d.slice();
}
} else {
x.e = v.e;
x.d = v.d ? v.d.slice() : v.d;
}
return;
}
t = typeof v;
if (t === 'number') {
if (v === 0) {
x.s = 1 / v < 0 ? -1 : 1;
x.e = 0;
x.d = [0];
return;
}
if (v < 0) {
v = -v;
x.s = -1;
} else {
x.s = 1;
}
// Fast path for small integers.
if (v === ~~v && v < 1e7) {
for (e = 0, i = v; i >= 10; i /= 10) e++;
if (external) {
if (e > Decimal.maxE) {
x.e = NaN;
x.d = null;
} else if (e < Decimal.minE) {
x.e = 0;
x.d = [0];
} else {
x.e = e;
x.d = [v];
}
} else {
x.e = e;
x.d = [v];
}
return;
}
// Infinity or NaN?
if (v * 0 !== 0) {
if (!v) x.s = NaN;
x.e = NaN;
x.d = null;
return;
}
return parseDecimal(x, v.toString());
}
if (t === 'string') {
if ((i = v.charCodeAt(0)) === 45) { // minus sign
v = v.slice(1);
x.s = -1;
} else {
if (i === 43) v = v.slice(1); // plus sign
x.s = 1;
}
return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v);
}
if (t === 'bigint') {
if (v < 0) {
v = -v;
x.s = -1;
} else {
x.s = 1;
}
return parseDecimal(x, v.toString());
}
throw Error(invalidArgument + v);
}
Decimal.prototype = P;
Decimal.ROUND_UP = 0;
Decimal.ROUND_DOWN = 1;
Decimal.ROUND_CEIL = 2;
Decimal.ROUND_FLOOR = 3;
Decimal.ROUND_HALF_UP = 4;
Decimal.ROUND_HALF_DOWN = 5;
Decimal.ROUND_HALF_EVEN = 6;
Decimal.ROUND_HALF_CEIL = 7;
Decimal.ROUND_HALF_FLOOR = 8;
Decimal.EUCLID = 9;
Decimal.config = Decimal.set = config;
Decimal.clone = clone;
Decimal.isDecimal = isDecimalInstance;
Decimal.abs = abs;
Decimal.acos = acos;
Decimal.acosh = acosh; // ES6
Decimal.add = add;
Decimal.asin = asin;
Decimal.asinh = asinh; // ES6
Decimal.atan = atan;
Decimal.atanh = atanh; // ES6
Decimal.atan2 = atan2;
Decimal.cbrt = cbrt; // ES6
Decimal.ceil = ceil;
Decimal.clamp = clamp;
Decimal.cos = cos;
Decimal.cosh = cosh; // ES6
Decimal.div = div;
Decimal.exp = exp;
Decimal.floor = floor;
Decimal.hypot = hypot; // ES6
Decimal.ln = ln;
Decimal.log = log;
Decimal.log10 = log10; // ES6
Decimal.log2 = log2; // ES6
Decimal.max = max;
Decimal.min = min;
Decimal.mod = mod;
Decimal.mul = mul;
Decimal.pow = pow;
Decimal.random = random;
Decimal.round = round;
Decimal.sign = sign; // ES6
Decimal.sin = sin;
Decimal.sinh = sinh; // ES6
Decimal.sqrt = sqrt;
Decimal.sub = sub;
Decimal.sum = sum;
Decimal.tan = tan;
Decimal.tanh = tanh; // ES6
Decimal.trunc = trunc; // ES6
if (obj === void 0) obj = {};
if (obj) {
if (obj.defaults !== true) {
ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'];
for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
}
}
Decimal.config(obj);
return Decimal;
}
/*
* Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
* y {number|string|bigint|Decimal}
*
*/
function div(x, y) {
return new this(x).div(y);
}
/*
* Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} The power to which to raise the base of the natural log.
*
*/
function exp(x) {
return new this(x).exp();
}
/*
* Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`.
*
* x {number|string|bigint|Decimal}
*
*/
function floor(x) {
return finalise(x = new this(x), x.e + 1, 3);
}
/*
* Return a new Decimal whose value is the square root of the sum of the squares of the arguments,
* rounded to `precision` significant digits using rounding mode `rounding`.
*
* hypot(a, b, ...) = sqrt(a^2 + b^2 + ...)
*
* arguments {number|string|bigint|Decimal}
*
*/
function hypot() {
var i, n,
t = new this(0);
external = false;
for (i = 0; i < arguments.length;) {
n = new this(arguments[i++]);
if (!n.d) {
if (n.s) {
external = true;
return new this(1 / 0);
}
t = n;
} else if (t.d) {
t = t.plus(n.times(n));
}
}
external = true;
return t.sqrt();
}
/*
* Return true if object is a Decimal instance (where Decimal is any Decimal constructor),
* otherwise return false.
*
*/
function isDecimalInstance(obj) {
return obj instanceof Decimal || obj && obj.toStringTag === tag || false;
}
/*
* Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function ln(x) {
return new this(x).ln();
}
/*
* Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base
* is specified, rounded to `precision` significant digits using rounding mode `rounding`.
*
* log[y](x)
*
* x {number|string|bigint|Decimal} The argument of the logarithm.
* y {number|string|bigint|Decimal} The base of the logarithm.
*
*/
function log(x, y) {
return new this(x).log(y);
}
/*
* Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function log2(x) {
return new this(x).log(2);
}
/*
* Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function log10(x) {
return new this(x).log(10);
}
/*
* Return a new Decimal whose value is the maximum of the arguments.
*
* arguments {number|string|bigint|Decimal}
*
*/
function max() {
return maxOrMin(this, arguments, -1);
}
/*
* Return a new Decimal whose value is the minimum of the arguments.
*
* arguments {number|string|bigint|Decimal}
*
*/
function min() {
return maxOrMin(this, arguments, 1);
}
/*
* Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
* using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
* y {number|string|bigint|Decimal}
*
*/
function mod(x, y) {
return new this(x).mod(y);
}
/*
* Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
* y {number|string|bigint|Decimal}
*
*/
function mul(x, y) {
return new this(x).mul(y);
}
/*
* Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} The base.
* y {number|string|bigint|Decimal} The exponent.
*
*/
function pow(x, y) {
return new this(x).pow(y);
}
/*
* Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with
* `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros
* are produced).
*
* [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive.
*
*/
function random(sd) {
var d, e, k, n,
i = 0,
r = new this(1),
rd = [];
if (sd === void 0) sd = this.precision;
else checkInt32(sd, 1, MAX_DIGITS);
k = Math.ceil(sd / LOG_BASE);
if (!this.crypto) {
for (; i < k;) rd[i++] = Math.random() * 1e7 | 0;
// Browsers supporting crypto.getRandomValues.
} else if (crypto.getRandomValues) {
d = crypto.getRandomValues(new Uint32Array(k));
for (; i < k;) {
n = d[i];
// 0 <= n < 4294967296
// Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865).
if (n >= 4.29e9) {
d[i] = crypto.getRandomValues(new Uint32Array(1))[0];
} else {
// 0 <= n <= 4289999999
// 0 <= (n % 1e7) <= 9999999
rd[i++] = n % 1e7;
}
}
// Node.js supporting crypto.randomBytes.
} else if (crypto.randomBytes) {
// buffer
d = crypto.randomBytes(k *= 4);
for (; i < k;) {
// 0 <= n < 2147483648
n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24);
// Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286).
if (n >= 2.14e9) {
crypto.randomBytes(4).copy(d, i);
} else {
// 0 <= n <= 2139999999
// 0 <= (n % 1e7) <= 9999999
rd.push(n % 1e7);
i += 4;
}
}
i = k / 4;
} else {
throw Error(cryptoUnavailable);
}
k = rd[--i];
sd %= LOG_BASE;
// Convert trailing digits to zeros according to sd.
if (k && sd) {
n = mathpow(10, LOG_BASE - sd);
rd[i] = (k / n | 0) * n;
}
// Remove trailing words which are zero.
for (; rd[i] === 0; i--) rd.pop();
// Zero?
if (i < 0) {
e = 0;
rd = [0];
} else {
e = -1;
// Remove leading words which are zero and adjust exponent accordingly.
for (; rd[0] === 0; e -= LOG_BASE) rd.shift();
// Count the digits of the first word of rd to determine leading zeros.
for (k = 1, n = rd[0]; n >= 10; n /= 10) k++;
// Adjust the exponent for leading zeros of the first word of rd.
if (k < LOG_BASE) e -= LOG_BASE - k;
}
r.e = e;
r.d = rd;
return r;
}
/*
* Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`.
*
* To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL).
*
* x {number|string|bigint|Decimal}
*
*/
function round(x) {
return finalise(x = new this(x), x.e + 1, this.rounding);
}
/*
* Return
* 1 if x > 0,
* -1 if x < 0,
* 0 if x is 0,
* -0 if x is -0,
* NaN otherwise
*
* x {number|string|bigint|Decimal}
*
*/
function sign(x) {
x = new this(x);
return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN;
}
/*
* Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits
* using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function sin(x) {
return new this(x).sin();
}
/*
* Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function sinh(x) {
return new this(x).sinh();
}
/*
* Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
*
*/
function sqrt(x) {
return new this(x).sqrt();
}
/*
* Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits
* using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal}
* y {number|string|bigint|Decimal}
*
*/
function sub(x, y) {
return new this(x).sub(y);
}
/*
* Return a new Decimal whose value is the sum of the arguments, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* Only the result is rounded, not the intermediate calculations.
*
* arguments {number|string|bigint|Decimal}
*
*/
function sum() {
var i = 0,
args = arguments,
x = new this(args[i]);
external = false;
for (; x.s && ++i < args.length;) x = x.plus(args[i]);
external = true;
return finalise(x, this.precision, this.rounding);
}
/*
* Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant
* digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function tan(x) {
return new this(x).tan();
}
/*
* Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* x {number|string|bigint|Decimal} A value in radians.
*
*/
function tanh(x) {
return new this(x).tanh();
}
/*
* Return a new Decimal whose value is `x` truncated to an integer.
*
* x {number|string|bigint|Decimal}
*
*/
function trunc(x) {
return finalise(x = new this(x), x.e + 1, 1);
}
// Create and configure initial Decimal constructor.
Decimal = clone(DEFAULTS);
Decimal.prototype.constructor = Decimal;
Decimal['default'] = Decimal.Decimal = Decimal;
// Create the internal constants from their string values.
LN10 = new Decimal(LN10);
PI = new Decimal(PI);
// Export.
// AMD.
if (typeof define == 'function' && define.amd) {
define(function () {
return Decimal;
});
// Node and other environments that support module.exports.
} else if (typeof module != 'undefined' && module.exports) {
if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
P[Symbol['for']('nodejs.util.inspect.custom')] = P.toString;
P[Symbol.toStringTag] = 'Decimal';
}
module.exports = Decimal;
// Browser.
} else {
if (!globalScope) {
globalScope = typeof self != 'undefined' && self && self.self == self ? self : window;
}
noConflict = globalScope.Decimal;
Decimal.noConflict = function () {
globalScope.Decimal = noConflict;
return Decimal;
};
globalScope.Decimal = Decimal;
}
})(this);
================================================
FILE: decimal.mjs
================================================
/*!
* decimal.js v10.6.0
* An arbitrary-precision Decimal type for JavaScript.
* https://github.com/MikeMcl/decimal.js
* Copyright (c) 2025 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licence
*/
// ----------------------------------- EDITABLE DEFAULTS ------------------------------------ //
// The maximum exponent magnitude.
// The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.
var EXP_LIMIT = 9e15, // 0 to 9e15
// The limit on the value of `precision`, and on the value of the first argument to
// `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
MAX_DIGITS = 1e9, // 0 to 1e9
// Base conversion alphabet.
NUMERALS = '0123456789abcdef',
// The natural logarithm of 10 (1025 digits).
LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
// Pi (1025 digits).
PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
// The initial configuration properties of the Decimal constructor.
DEFAULTS = {
// These values must be integers within the stated ranges (inclusive).
// Most of these values can be changed at run-time using the `Decimal.config` method.
// The maximum number of significant digits of the result of a calculation or base conversion.
// E.g. `Decimal.config({ precision: 20 });`
precision: 20, // 1 to MAX_DIGITS
// The rounding mode used when rounding to `precision`.
//
// ROUND_UP 0 Away from zero.
// ROUND_DOWN 1 Towards zero.
// ROUND_CEIL 2 Towards +Infinity.
// ROUND_FLOOR 3 Towards -Infinity.
// ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up.
// ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
// ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
// ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
// ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
//
// E.g.
// `Decimal.rounding = 4;`
// `Decimal.rounding = Decimal.ROUND_HALF_UP;`
rounding: 4, // 0 to 8
// The modulo mode used when calculating the modulus: a mod n.
// The quotient (q = a / n) is calculated according to the corresponding rounding mode.
// The remainder (r) is calculated as: r = a - n * q.
//
// UP 0 The remainder is positive if the dividend is negative, else is negative.
// DOWN 1 The remainder has the same sign as the dividend (JavaScript %).
// FLOOR 3 The remainder has the same sign as the divisor (Python %).
// HALF_EVEN 6 The IEEE 754 remainder function.
// EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive.
//
// Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian
// division (9) are commonly used for the modulus operation. The other rounding modes can also
// be used, but they may not give useful results.
modulo: 1, // 0 to 9
// The exponent value at and beneath which `toString` returns exponential notation.
// JavaScript numbers: -7
toExpNeg: -7, // 0 to -EXP_LIMIT
// The exponent value at and above which `toString` returns exponential notation.
// JavaScript numbers: 21
toExpPos: 21, // 0 to EXP_LIMIT
// The minimum exponent value, beneath which underflow to zero occurs.
// JavaScript numbers: -324 (5e-324)
minE: -EXP_LIMIT, // -1 to -EXP_LIMIT
// The maximum exponent value, above which overflow to Infinity occurs.
// JavaScript numbers: 308 (1.7976931348623157e+308)
maxE: EXP_LIMIT, // 1 to EXP_LIMIT
// Whether to use cryptographically-secure random number generation, if available.
crypto: false // true/false
},
// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- //
inexact, quadrant,
external = true,
decimalError = '[DecimalError] ',
invalidArgument = decimalError + 'Invalid argument: ',
precisionLimitExceeded = decimalError + 'Precision limit exceeded',
cryptoUnavailable = decimalError + 'crypto unavailable',
tag = '[object Decimal]',
mathfloor = Math.floor,
mathpow = Math.pow,
isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,
isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,
isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,
isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
BASE = 1e7,
LOG_BASE = 7,
MAX_SAFE_INTEGER = 9007199254740991,
LN10_PRECISION = LN10.length - 1,
PI_PRECISION = PI.length - 1,
// Decimal.prototype object
P = { toStringTag: tag };
// Decimal prototype methods
/*
* absoluteValue abs
* ceil
* clampedTo clamp
* comparedTo cmp
* cosine cos
* cubeRoot cbrt
* decimalPlaces dp
* dividedBy div
* dividedToIntegerBy divToInt
* equals eq
* floor
* greaterThan gt
* greaterThanOrEqualTo gte
* hyperbolicCosine cosh
* hyperbolicSine sinh
* hyperbolicTangent tanh
* inverseCosine acos
* inverseHyperbolicCosine acosh
* inverseHyperbolicSine asinh
* inverseHyperbolicTangent atanh
* inverseSine asin
* inverseTangent atan
* isFinite
* isInteger isInt
* isNaN
* isNegative isNeg
* isPositive isPos
* isZero
* lessThan lt
* lessThanOrEqualTo lte
* logarithm log
* [maximum] [max]
* [minimum] [min]
* minus sub
* modulo mod
* naturalExponential exp
* naturalLogarithm ln
* negated neg
* plus add
* precision sd
* round
* sine sin
* squareRoot sqrt
* tangent tan
* times mul
* toBinary
* toDecimalPlaces toDP
* toExponential
* toFixed
* toFraction
* toHexadecimal toHex
* toNearest
* toNumber
* toOctal
* toPower pow
* toPrecision
* toSignificantDigits toSD
* toString
* truncated trunc
* valueOf toJSON
*/
/*
* Return a new Decimal whose value is the absolute value of this Decimal.
*
*/
P.absoluteValue = P.abs = function () {
var x = new this.constructor(this);
if (x.s < 0) x.s = 1;
return finalise(x);
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
* direction of positive Infinity.
*
*/
P.ceil = function () {
return finalise(new this.constructor(this), this.e + 1, 2);
};
/*
* Return a new Decimal whose value is the value of this Decimal clamped to the range
* delineated by `min` and `max`.
*
* min {number|string|bigint|Decimal}
* max {number|string|bigint|Decimal}
*
*/
P.clampedTo = P.clamp = function (min, max) {
var k,
x = this,
Ctor = x.constructor;
min = new Ctor(min);
max = new Ctor(max);
if (!min.s || !max.s) return new Ctor(NaN);
if (min.gt(max)) throw Error(invalidArgument + max);
k = x.cmp(min);
return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x);
};
/*
* Return
* 1 if the value of this Decimal is greater than the value of `y`,
* -1 if the value of this Decimal is less than the value of `y`,
* 0 if they have the same value,
* NaN if the value of either Decimal is NaN.
*
*/
P.comparedTo = P.cmp = function (y) {
var i, j, xdL, ydL,
x = this,
xd = x.d,
yd = (y = new x.constructor(y)).d,
xs = x.s,
ys = y.s;
// Either NaN or ±Infinity?
if (!xd || !yd) {
return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1;
}
// Either zero?
if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0;
// Signs differ?
if (xs !== ys) return xs;
// Compare exponents.
if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1;
xdL = xd.length;
ydL = yd.length;
// Compare digit by digit.
for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1;
}
// Compare lengths.
return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1;
};
/*
* Return a new Decimal whose value is the cosine of the value in radians of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-1, 1]
*
* cos(0) = 1
* cos(-0) = 1
* cos(Infinity) = NaN
* cos(-Infinity) = NaN
* cos(NaN) = NaN
*
*/
P.cosine = P.cos = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.d) return new Ctor(NaN);
// cos(0) = cos(-0) = 1
if (!x.d[0]) return new Ctor(1);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE;
Ctor.rounding = 1;
x = cosine(Ctor, toLessThanHalfPi(Ctor, x));
Ctor.precision = pr;
Ctor.rounding = rm;
return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true);
};
/*
*
* Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
* cbrt(0) = 0
* cbrt(-0) = -0
* cbrt(1) = 1
* cbrt(-1) = -1
* cbrt(N) = N
* cbrt(-I) = -I
* cbrt(I) = I
*
* Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3))
*
*/
P.cubeRoot = P.cbrt = function () {
var e, m, n, r, rep, s, sd, t, t3, t3plusx,
x = this,
Ctor = x.constructor;
if (!x.isFinite() || x.isZero()) return new Ctor(x);
external = false;
// Initial estimate.
s = x.s * mathpow(x.s * x, 1 / 3);
// Math.cbrt underflow/overflow?
// Pass x to Math.pow as integer, then adjust the exponent of the result.
if (!s || Math.abs(s) == 1 / 0) {
n = digitsToString(x.d);
e = x.e;
// Adjust n exponent so it is a multiple of 3 away from x exponent.
if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00');
s = mathpow(n, 1 / 3);
// Rarely, e may be one less than the result exponent value.
e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2));
if (s == 1 / 0) {
n = '5e' + e;
} else {
n = s.toExponential();
n = n.slice(0, n.indexOf('e') + 1) + e;
}
r = new Ctor(n);
r.s = x.s;
} else {
r = new Ctor(s.toString());
}
sd = (e = Ctor.precision) + 3;
// Halley's method.
// TODO? Compare Newton's method.
for (;;) {
t = r;
t3 = t.times(t).times(t);
t3plusx = t3.plus(x);
r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1);
// TODO? Replace with for-loop and checkRoundingDigits.
if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) {
n = n.slice(sd - 3, sd + 1);
// The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999
// , i.e. approaching a rounding boundary, continue the iteration.
if (n == '9999' || !rep && n == '4999') {
// On the first iteration only, check to see if rounding up gives the exact result as the
// nines may infinitely repeat.
if (!rep) {
finalise(t, e + 1, 0);
if (t.times(t).times(t).eq(x)) {
r = t;
break;
}
}
sd += 4;
rep = 1;
} else {
// If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result.
// If not, then there are further digits and m will be truthy.
if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
// Truncate to the first rounding digit.
finalise(r, e + 1, 1);
m = !r.times(r).times(r).eq(x);
}
break;
}
}
}
external = true;
return finalise(r, e, Ctor.rounding, m);
};
/*
* Return the number of decimal places of the value of this Decimal.
*
*/
P.decimalPlaces = P.dp = function () {
var w,
d = this.d,
n = NaN;
if (d) {
w = d.length - 1;
n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE;
// Subtract the number of trailing zeros of the last word.
w = d[w];
if (w) for (; w % 10 == 0; w /= 10) n--;
if (n < 0) n = 0;
}
return n;
};
/*
* n / 0 = I
* n / N = N
* n / I = 0
* 0 / n = 0
* 0 / 0 = N
* 0 / N = N
* 0 / I = 0
* N / n = N
* N / 0 = N
* N / N = N
* N / I = N
* I / n = I
* I / 0 = I
* I / N = N
* I / I = N
*
* Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to
* `precision` significant digits using rounding mode `rounding`.
*
*/
P.dividedBy = P.div = function (y) {
return divide(this, new this.constructor(y));
};
/*
* Return a new Decimal whose value is the integer part of dividing the value of this Decimal
* by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`.
*
*/
P.dividedToIntegerBy = P.divToInt = function (y) {
var x = this,
Ctor = x.constructor;
return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding);
};
/*
* Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
*
*/
P.equals = P.eq = function (y) {
return this.cmp(y) === 0;
};
/*
* Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the
* direction of negative Infinity.
*
*/
P.floor = function () {
return finalise(new this.constructor(this), this.e + 1, 3);
};
/*
* Return true if the value of this Decimal is greater than the value of `y`, otherwise return
* false.
*
*/
P.greaterThan = P.gt = function (y) {
return this.cmp(y) > 0;
};
/*
* Return true if the value of this Decimal is greater than or equal to the value of `y`,
* otherwise return false.
*
*/
P.greaterThanOrEqualTo = P.gte = function (y) {
var k = this.cmp(y);
return k == 1 || k === 0;
};
/*
* Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [1, Infinity]
*
* cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ...
*
* cosh(0) = 1
* cosh(-0) = 1
* cosh(Infinity) = Infinity
* cosh(-Infinity) = Infinity
* cosh(NaN) = NaN
*
* x time taken (ms) result
* 1000 9 9.8503555700852349694e+433
* 10000 25 4.4034091128314607936e+4342
* 100000 171 1.4033316802130615897e+43429
* 1000000 3817 1.5166076984010437725e+434294
* 10000000 abandoned after 2 minute wait
*
* TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x))
*
*/
P.hyperbolicCosine = P.cosh = function () {
var k, n, pr, rm, len,
x = this,
Ctor = x.constructor,
one = new Ctor(1);
if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN);
if (x.isZero()) return one;
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
Ctor.rounding = 1;
len = x.d.length;
// Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1
// i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4))
// Estimate the optimum number of times to use the argument reduction.
// TODO? Estimation reused from cosine() and may not be optimal here.
if (len < 32) {
k = Math.ceil(len / 3);
n = (1 / tinyPow(4, k)).toString();
} else {
k = 16;
n = '2.3283064365386962890625e-10';
}
x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true);
// Reverse argument reduction
var cosh2_x,
i = k,
d8 = new Ctor(8);
for (; i--;) {
cosh2_x = x.times(x);
x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));
}
return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true);
};
/*
* Return a new Decimal whose value is the hyperbolic sine of the value in radians of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-Infinity, Infinity]
*
* sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ...
*
* sinh(0) = 0
* sinh(-0) = -0
* sinh(Infinity) = Infinity
* sinh(-Infinity) = -Infinity
* sinh(NaN) = NaN
*
* x time taken (ms)
* 10 2 ms
* 100 5 ms
* 1000 14 ms
* 10000 82 ms
* 100000 886 ms 1.4033316802130615897e+43429
* 200000 2613 ms
* 300000 5407 ms
* 400000 8824 ms
* 500000 13026 ms 8.7080643612718084129e+217146
* 1000000 48543 ms
*
* TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x))
*
*/
P.hyperbolicSine = P.sinh = function () {
var k, pr, rm, len,
x = this,
Ctor = x.constructor;
if (!x.isFinite() || x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(x.e, x.sd()) + 4;
Ctor.rounding = 1;
len = x.d.length;
if (len < 3) {
x = taylorSeries(Ctor, 2, x, x, true);
} else {
// Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x))
// i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3))
// 3 multiplications and 1 addition
// Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x)))
// i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5)))
// 4 multiplications and 2 additions
// Estimate the optimum number of times to use the argument reduction.
k = 1.4 * Math.sqrt(len);
k = k > 16 ? 16 : k | 0;
x = x.times(1 / tinyPow(5, k));
x = taylorSeries(Ctor, 2, x, x, true);
// Reverse argument reduction
var sinh2_x,
d5 = new Ctor(5),
d16 = new Ctor(16),
d20 = new Ctor(20);
for (; k--;) {
sinh2_x = x.times(x);
x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));
}
}
Ctor.precision = pr;
Ctor.rounding = rm;
return finalise(x, pr, rm, true);
};
/*
* Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-1, 1]
*
* tanh(x) = sinh(x) / cosh(x)
*
* tanh(0) = 0
* tanh(-0) = -0
* tanh(Infinity) = 1
* tanh(-Infinity) = -1
* tanh(NaN) = NaN
*
*/
P.hyperbolicTangent = P.tanh = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.isFinite()) return new Ctor(x.s);
if (x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + 7;
Ctor.rounding = 1;
return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm);
};
/*
* Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of
* this Decimal.
*
* Domain: [-1, 1]
* Range: [0, pi]
*
* acos(x) = pi/2 - asin(x)
*
* acos(0) = pi/2
* acos(-0) = pi/2
* acos(1) = 0
* acos(-1) = pi
* acos(1/2) = pi/3
* acos(-1/2) = 2*pi/3
* acos(|x| > 1) = NaN
* acos(NaN) = NaN
*
*/
P.inverseCosine = P.acos = function () {
var x = this,
Ctor = x.constructor,
k = x.abs().cmp(1),
pr = Ctor.precision,
rm = Ctor.rounding;
if (k !== -1) {
return k === 0
// |x| is 1
? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0)
// |x| > 1 or x is NaN
: new Ctor(NaN);
}
if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5);
// TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3
Ctor.precision = pr + 6;
Ctor.rounding = 1;
// See https://github.com/MikeMcl/decimal.js/pull/217
x = new Ctor(1).minus(x).div(x.plus(1)).sqrt().atan();
Ctor.precision = pr;
Ctor.rounding = rm;
return x.times(2);
};
/*
* Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the
* value of this Decimal.
*
* Domain: [1, Infinity]
* Range: [0, Infinity]
*
* acosh(x) = ln(x + sqrt(x^2 - 1))
*
* acosh(x < 1) = NaN
* acosh(NaN) = NaN
* acosh(Infinity) = Infinity
* acosh(-Infinity) = NaN
* acosh(0) = NaN
* acosh(-0) = NaN
* acosh(1) = 0
* acosh(-1) = NaN
*
*/
P.inverseHyperbolicCosine = P.acosh = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN);
if (!x.isFinite()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4;
Ctor.rounding = 1;
external = false;
x = x.times(x).minus(1).sqrt().plus(x);
external = true;
Ctor.precision = pr;
Ctor.rounding = rm;
return x.ln();
};
/*
* Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value
* of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-Infinity, Infinity]
*
* asinh(x) = ln(x + sqrt(x^2 + 1))
*
* asinh(NaN) = NaN
* asinh(Infinity) = Infinity
* asinh(-Infinity) = -Infinity
* asinh(0) = 0
* asinh(-0) = -0
*
*/
P.inverseHyperbolicSine = P.asinh = function () {
var pr, rm,
x = this,
Ctor = x.constructor;
if (!x.isFinite() || x.isZero()) return new Ctor(x);
pr = Ctor.precision;
rm = Ctor.rounding;
Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6;
Ctor.rounding = 1;
external = false;
x = x.times(x).plus(1).sqrt().plus(x);
external = true;
Ctor.precision = pr;
Ctor.rounding = rm;
return x.ln();
};
/*
* Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the
* value of this Decimal.
*
* Domain: [-1, 1]
* Range: [-Infinity, Infinity]
*
* atanh(x) = 0.5 * ln((1 + x) / (1 - x))
*
* atanh(|x| > 1) = NaN
* atanh(NaN) = NaN
* atanh(Infinity) = NaN
* atanh(-Infinity) = NaN
* atanh(0) = 0
* atanh(-0) = -0
* atanh(1) = Infinity
* atanh(-1) = -Infinity
*
*/
P.inverseHyperbolicTangent = P.atanh = function () {
var pr, rm, wpr, xsd,
x = this,
Ctor = x.constructor;
if (!x.isFinite()) return new Ctor(NaN);
if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN);
pr = Ctor.precision;
rm = Ctor.rounding;
xsd = x.sd();
if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true);
Ctor.precision = wpr = xsd - x.e;
x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1);
Ctor.precision = pr + 4;
Ctor.rounding = 1;
x = x.ln();
Ctor.precision = pr;
Ctor.rounding = rm;
return x.times(0.5);
};
/*
* Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this
* Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-pi/2, pi/2]
*
* asin(x) = 2*atan(x/(1 + sqrt(1 - x^2)))
*
* asin(0) = 0
* asin(-0) = -0
* asin(1/2) = pi/6
* asin(-1/2) = -pi/6
* asin(1) = pi/2
* asin(-1) = -pi/2
* asin(|x| > 1) = NaN
* asin(NaN) = NaN
*
* TODO? Compare performance of Taylor series.
*
*/
P.inverseSine = P.asin = function () {
var halfPi, k,
pr, rm,
x = this,
Ctor = x.constructor;
if (x.isZero()) return new Ctor(x);
k = x.abs().cmp(1);
pr = Ctor.precision;
rm = Ctor.rounding;
if (k !== -1) {
// |x| is 1
if (k === 0) {
halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
halfPi.s = x.s;
return halfPi;
}
// |x| > 1 or x is NaN
return new Ctor(NaN);
}
// TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6
Ctor.precision = pr + 6;
Ctor.rounding = 1;
x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();
Ctor.precision = pr;
Ctor.rounding = rm;
return x.times(2);
};
/*
* Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value
* of this Decimal.
*
* Domain: [-Infinity, Infinity]
* Range: [-pi/2, pi/2]
*
* atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
*
* atan(0) = 0
* atan(-0) = -0
* atan(1) = pi/4
* atan(-1) = -pi/4
* atan(Infinity) = pi/2
* atan(-Infinity) = -pi/2
* atan(NaN) = NaN
*
*/
P.inverseTangent = P.atan = function () {
var i, j, k, n, px, t, r, wpr, x2,
x = this,
Ctor = x.constructor,
pr = Ctor.precision,
rm = Ctor.rounding;
if (!x.isFinite()) {
if (!x.s) return new Ctor(NaN);
if (pr + 4 <= PI_PRECISION) {
r = getPi(Ctor, pr + 4, rm).times(0.5);
r.s = x.s;
return r;
}
} else if (x.isZero()) {
return new Ctor(x);
} else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) {
r = getPi(Ctor, pr + 4, rm).times(0.25);
r.s = x.s;
return r;
}
Ctor.precision = wpr = pr + 10;
Ctor.rounding = 1;
// TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x);
// Argument reduction
// Ensure |x| < 0.42
// atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
k = Math.min(28, wpr / LOG_BASE + 2 | 0);
for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1));
external = false;
j = Math.ceil(wpr / LOG_BASE);
n = 1;
x2 = x.times(x);
r = new Ctor(x);
px = x;
// atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
for (; i !== -1;) {
px = px.times(x2);
t = r.minus(px.div(n += 2));
px = px.times(x2);
r = t.plus(px.div(n += 2));
if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;);
}
if (k) r = r.times(2 << (k - 1));
external = true;
return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true);
};
/*
* Return true if the value of this Decimal is a finite number, otherwise return false.
*
*/
P.isFinite = function () {
return !!this.d;
};
/*
* Return true if the value of this Decimal is an integer, otherwise return false.
*
*/
P.isInteger = P.isInt = function () {
return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2;
};
/*
* Return true if the value of this Decimal is NaN, otherwise return false.
*
*/
P.isNaN = function () {
return !this.s;
};
/*
* Return true if the value of this Decimal is negative, otherwise return false.
*
*/
P.isNegative = P.isNeg = function () {
return this.s < 0;
};
/*
* Return true if the value of this Decimal is positive, otherwise return false.
*
*/
P.isPositive = P.isPos = function () {
return this.s > 0;
};
/*
* Return true if the value of this Decimal is 0 or -0, otherwise return false.
*
*/
P.isZero = function () {
return !!this.d && this.d[0] === 0;
};
/*
* Return true if the value of this Decimal is less than `y`, otherwise return false.
*
*/
P.lessThan = P.lt = function (y) {
return this.cmp(y) < 0;
};
/*
* Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
*
*/
P.lessThanOrEqualTo = P.lte = function (y) {
return this.cmp(y) < 1;
};
/*
* Return the logarithm of the value of this Decimal to the specified base, rounded to `precision`
* significant digits using rounding mode `rounding`.
*
* If no base is specified, return log[10](arg).
*
* log[base](arg) = ln(arg) / ln(base)
*
* The result will always be correctly rounded if the base of the log is 10, and 'almost always'
* otherwise:
*
* Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen
* rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error
* between the result and the correctly rounded result will be one ulp (unit in the last place).
*
* log[-b](a) = NaN
* log[0](a) = NaN
* log[1](a) = NaN
* log[NaN](a) = NaN
* log[Infinity](a) = NaN
* log[b](0) = -Infinity
* log[b](-0) = -Infinity
* log[b](-a) = NaN
* log[b](1) = 0
* log[b](Infinity) = Infinity
* log[b](NaN) = NaN
*
* [base] {number|string|bigint|Decimal} The base of the logarithm.
*
*/
P.logarithm = P.log = function (base) {
var isBase10, d, denominator, k, inf, num, sd, r,
arg = this,
Ctor = arg.constructor,
pr = Ctor.precision,
rm = Ctor.rounding,
guard = 5;
// Default base is 10.
if (base == null) {
base = new Ctor(10);
isBase10 = true;
} else {
base = new Ctor(base);
d = base.d;
// Return NaN if base is negative, or non-finite, or is 0 or 1.
if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN);
isBase10 = base.eq(10);
}
d = arg.d;
// Is arg negative, non-finite, 0 or 1?
if (arg.s < 0 || !d || !d[0] || arg.eq(1)) {
return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0);
}
// The result will have a non-terminating decimal expansion if base is 10 and arg is not an
// integer power of 10.
if (isBase10) {
if (d.length > 1) {
inf = true;
} else {
for (k = d[0]; k % 10 === 0;) k /= 10;
inf = k !== 1;
}
}
external = false;
sd = pr + guard;
num = naturalLogarithm(arg, sd);
denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
// The result will have 5 rounding digits.
r = divide(num, denominator, sd, 1);
// If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000,
// calculate 10 further digits.
//
// If the result is known to have an infinite decimal expansion, repeat this until it is clear
// that the result is above or below the boundary. Otherwise, if after calculating the 10
// further digits, the last 14 are nines, round up and assume the result is exact.
// Also assume the result is exact if the last 14 are zero.
//
// Example of a result that will be incorrectly rounded:
// log[1048576](4503599627370502) = 2.60000000000000009610279511444746...
// The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it
// will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so
// the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal
// place is still 2.6.
if (checkRoundingDigits(r.d, k = pr, rm)) {
do {
sd += 10;
num = naturalLogarithm(arg, sd);
denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd);
r = divide(num, denominator, sd, 1);
if (!inf) {
// Check for 14 nines from the 2nd rounding digit, as the first may be 4.
if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) {
r = finalise(r, pr + 1, 0);
}
break;
}
} while (checkRoundingDigits(r.d, k += 10, rm));
}
external = true;
return finalise(r, pr, rm);
};
/*
* Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal.
*
* arguments {number|string|bigint|Decimal}
*
P.max = function () {
Array.prototype.push.call(arguments, this);
return maxOrMin(this.constructor, arguments, -1);
};
*/
/*
* Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
*
* arguments {number|string|bigint|Decimal}
*
P.min = function () {
Array.prototype.push.call(arguments, this);
return maxOrMin(this.constructor, arguments, 1);
};
*/
/*
* n - 0 = n
* n - N = N
* n - I = -I
* 0 - n = -n
* 0 - 0 = 0
* 0 - N = N
* 0 - I = -I
* N - n = N
* N - 0 = N
* N - N = N
* N - I = N
* I - n = I
* I - 0 = I
* I - N = N
* I - I = N
*
* Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to
gitextract_lauzzv64/
├── .npmignore
├── CHANGELOG.md
├── LICENCE.md
├── README.md
├── decimal.d.ts
├── decimal.global.d.ts
├── decimal.js
├── decimal.mjs
├── doc/
│ └── API.html
├── package.json
└── test/
├── hypothesis/
│ ├── .gitignore
│ ├── README.txt
│ ├── error_hunt.py
│ ├── evaluate.mjs
│ └── requirements.txt
├── modules/
│ ├── Decimal.js
│ ├── abs.js
│ ├── acos.js
│ ├── acosh.js
│ ├── asin.js
│ ├── asinh.js
│ ├── atan.js
│ ├── atan2.js
│ ├── atanh.js
│ ├── cbrt.js
│ ├── ceil.js
│ ├── clamp.js
│ ├── clone.js
│ ├── cmp.js
│ ├── config.js
│ ├── cos.js
│ ├── cosh.js
│ ├── div.js
│ ├── divToInt.js
│ ├── dpSd.js
│ ├── exp.js
│ ├── floor.js
│ ├── hypot.js
│ ├── immutability.js
│ ├── intPow.js
│ ├── isFiniteEtc.js
│ ├── ln.js
│ ├── log.js
│ ├── log10.js
│ ├── log2.js
│ ├── minAndMax.js
│ ├── minus.js
│ ├── mod.js
│ ├── neg.js
│ ├── plus.js
│ ├── pow.js
│ ├── powSqrt.js
│ ├── random.js
│ ├── round.js
│ ├── sign.js
│ ├── sin.js
│ ├── sinh.js
│ ├── sqrt.js
│ ├── sum.js
│ ├── tan.js
│ ├── tanh.js
│ ├── times.js
│ ├── toBinary.js
│ ├── toDP.js
│ ├── toExponential.js
│ ├── toFixed.js
│ ├── toFraction.js
│ ├── toHex.js
│ ├── toNearest.js
│ ├── toNumber.js
│ ├── toOctal.js
│ ├── toPrecision.js
│ ├── toSD.js
│ ├── toString.js
│ ├── trunc.js
│ └── valueOf.js
├── setup.js
├── test.html
└── test.js
SYMBOL INDEX (232 symbols across 55 files)
FILE: decimal.d.ts
type Constructor (line 35) | type Constructor = typeof Decimal;
type Instance (line 36) | type Instance = Decimal;
type Rounding (line 37) | type Rounding = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
type Modulo (line 38) | type Modulo = Rounding | 9;
type Value (line 39) | type Value = string | number | bigint | Decimal;
type Config (line 42) | interface Config {
class Decimal (line 55) | class Decimal {
FILE: decimal.global.d.ts
type Config (line 35) | type Config = DecimalConfig;
type Constructor (line 36) | type Constructor = DecimalConstructor;
type Instance (line 37) | type Instance = DecimalInstance;
type Modulo (line 38) | type Modulo = DecimalModulo;
type Rounding (line 39) | type Rounding = DecimalRounding;
type Value (line 40) | type Value = DecimalValue;
type Decimal (line 45) | type Decimal = DecimalInstance;
type Config (line 48) | type Config = DecimalConfig;
type Constructor (line 49) | type Constructor = DecimalConstructor;
type Instance (line 50) | type Instance = DecimalInstance;
type Modulo (line 51) | type Modulo = DecimalModulo;
type Rounding (line 52) | type Rounding = DecimalRounding;
type Value (line 53) | type Value = DecimalValue;
type DecimalInstance (line 57) | type DecimalInstance = Decimal;
type DecimalConstructor (line 58) | type DecimalConstructor = typeof Decimal;
type DecimalValue (line 59) | type DecimalValue = string | number | bigint |Decimal;
type DecimalRounding (line 60) | type DecimalRounding = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
type DecimalModulo (line 61) | type DecimalModulo = DecimalRounding | 9;
type DecimalConfig (line 64) | interface DecimalConfig {
class Decimal (line 76) | class Decimal {
FILE: decimal.js
function digitsToString (line 2519) | function digitsToString(d) {
function checkInt32 (line 2549) | function checkInt32(i, min, max) {
function checkRoundingDigits (line 2561) | function checkRoundingDigits(d, i, rm, repeating) {
function convertBase (line 2612) | function convertBase(str, baseIn, baseOut) {
function cosine (line 2640) | function cosine(Ctor, x) {
function multiplyInteger (line 2680) | function multiplyInteger(x, k, base) {
function compare (line 2696) | function compare(a, b, aL, bL) {
function subtract (line 2713) | function subtract(a, b, aL, base) {
function finalise (line 2945) | function finalise(x, sd, rm, isTruncated) {
function finiteToString (line 3112) | function finiteToString(x, isExp, sd) {
function getBase10Exponent (line 3146) | function getBase10Exponent(digits, e) {
function getLn10 (line 3155) | function getLn10(Ctor, sd, pr) {
function getPi (line 3167) | function getPi(Ctor, sd, rm) {
function getPrecision (line 3173) | function getPrecision(digits) {
function getZeroString (line 3193) | function getZeroString(k) {
function intPow (line 3207) | function intPow(Ctor, x, n, pr) {
function isOdd (line 3242) | function isOdd(n) {
function maxOrMin (line 3250) | function maxOrMin(Ctor, args, n) {
function naturalExponential (line 3306) | function naturalExponential(x, sd) {
function naturalLogarithm (line 3397) | function naturalLogarithm(y, sd) {
function nonFiniteToString (line 3513) | function nonFiniteToString(x) {
function parseDecimal (line 3522) | function parseDecimal(x, str) {
function parseOther (line 3606) | function parseOther(x, str) {
function sine (line 3686) | function sine(Ctor, x) {
function taylorSeries (line 3720) | function taylorSeries(Ctor, n, x, y, isHyperbolic) {
function tinyPow (line 3756) | function tinyPow(b, e) {
function toLessThanHalfPi (line 3764) | function toLessThanHalfPi(Ctor, x) {
function toStringBinary (line 3802) | function toStringBinary(x, baseOut, sd, rm) {
function truncate (line 3935) | function truncate(arr, len) {
function abs (line 3997) | function abs(x) {
function acos (line 4008) | function acos(x) {
function acosh (line 4020) | function acosh(x) {
function add (line 4033) | function add(x, y) {
function asin (line 4045) | function asin(x) {
function asinh (line 4057) | function asinh(x) {
function atan (line 4069) | function atan(x) {
function atanh (line 4081) | function atanh(x) {
function atan2 (line 4111) | function atan2(y, x) {
function cbrt (line 4162) | function cbrt(x) {
function ceil (line 4173) | function ceil(x) {
function clamp (line 4186) | function clamp(x, min, max) {
function config (line 4209) | function config(obj) {
function cos (line 4260) | function cos(x) {
function cosh (line 4272) | function cosh(x) {
function clone (line 4282) | function clone(obj) {
function div (line 4484) | function div(x, y) {
function exp (line 4496) | function exp(x) {
function floor (line 4507) | function floor(x) {
function hypot (line 4521) | function hypot() {
function isDecimalInstance (line 4551) | function isDecimalInstance(obj) {
function ln (line 4563) | function ln(x) {
function log (line 4578) | function log(x, y) {
function log2 (line 4590) | function log2(x) {
function log10 (line 4602) | function log10(x) {
function max (line 4613) | function max() {
function min (line 4624) | function min() {
function mod (line 4637) | function mod(x, y) {
function mul (line 4650) | function mul(x, y) {
function pow (line 4663) | function pow(x, y) {
function random (line 4676) | function random(sd) {
function round (line 4781) | function round(x) {
function sign (line 4797) | function sign(x) {
function sin (line 4810) | function sin(x) {
function sinh (line 4822) | function sinh(x) {
function sqrt (line 4834) | function sqrt(x) {
function sub (line 4847) | function sub(x, y) {
function sum (line 4861) | function sum() {
function tan (line 4881) | function tan(x) {
function tanh (line 4893) | function tanh(x) {
function trunc (line 4904) | function trunc(x) {
FILE: decimal.mjs
function digitsToString (line 2515) | function digitsToString(d) {
function checkInt32 (line 2545) | function checkInt32(i, min, max) {
function checkRoundingDigits (line 2557) | function checkRoundingDigits(d, i, rm, repeating) {
function convertBase (line 2608) | function convertBase(str, baseIn, baseOut) {
function cosine (line 2636) | function cosine(Ctor, x) {
function multiplyInteger (line 2676) | function multiplyInteger(x, k, base) {
function compare (line 2692) | function compare(a, b, aL, bL) {
function subtract (line 2709) | function subtract(a, b, aL, base) {
function finalise (line 2941) | function finalise(x, sd, rm, isTruncated) {
function finiteToString (line 3108) | function finiteToString(x, isExp, sd) {
function getBase10Exponent (line 3142) | function getBase10Exponent(digits, e) {
function getLn10 (line 3151) | function getLn10(Ctor, sd, pr) {
function getPi (line 3163) | function getPi(Ctor, sd, rm) {
function getPrecision (line 3169) | function getPrecision(digits) {
function getZeroString (line 3189) | function getZeroString(k) {
function intPow (line 3203) | function intPow(Ctor, x, n, pr) {
function isOdd (line 3238) | function isOdd(n) {
function maxOrMin (line 3246) | function maxOrMin(Ctor, args, n) {
function naturalExponential (line 3302) | function naturalExponential(x, sd) {
function naturalLogarithm (line 3393) | function naturalLogarithm(y, sd) {
function nonFiniteToString (line 3509) | function nonFiniteToString(x) {
function parseDecimal (line 3518) | function parseDecimal(x, str) {
function parseOther (line 3601) | function parseOther(x, str) {
function sine (line 3681) | function sine(Ctor, x) {
function taylorSeries (line 3715) | function taylorSeries(Ctor, n, x, y, isHyperbolic) {
function tinyPow (line 3751) | function tinyPow(b, e) {
function toLessThanHalfPi (line 3759) | function toLessThanHalfPi(Ctor, x) {
function toStringBinary (line 3797) | function toStringBinary(x, baseOut, sd, rm) {
function truncate (line 3930) | function truncate(arr, len) {
function abs (line 3992) | function abs(x) {
function acos (line 4003) | function acos(x) {
function acosh (line 4015) | function acosh(x) {
function add (line 4028) | function add(x, y) {
function asin (line 4040) | function asin(x) {
function asinh (line 4052) | function asinh(x) {
function atan (line 4064) | function atan(x) {
function atanh (line 4076) | function atanh(x) {
function atan2 (line 4106) | function atan2(y, x) {
function cbrt (line 4157) | function cbrt(x) {
function ceil (line 4168) | function ceil(x) {
function clamp (line 4181) | function clamp(x, min, max) {
function config (line 4204) | function config(obj) {
function cos (line 4255) | function cos(x) {
function cosh (line 4267) | function cosh(x) {
function clone (line 4277) | function clone(obj) {
function div (line 4479) | function div(x, y) {
function exp (line 4491) | function exp(x) {
function floor (line 4502) | function floor(x) {
function hypot (line 4516) | function hypot() {
function isDecimalInstance (line 4546) | function isDecimalInstance(obj) {
function ln (line 4558) | function ln(x) {
function log (line 4573) | function log(x, y) {
function log2 (line 4585) | function log2(x) {
function log10 (line 4597) | function log10(x) {
function max (line 4608) | function max() {
function min (line 4619) | function min() {
function mod (line 4632) | function mod(x, y) {
function mul (line 4645) | function mul(x, y) {
function pow (line 4658) | function pow(x, y) {
function random (line 4671) | function random(sd) {
function round (line 4776) | function round(x) {
function sign (line 4792) | function sign(x) {
function sin (line 4805) | function sin(x) {
function sinh (line 4817) | function sinh(x) {
function sqrt (line 4829) | function sqrt(x) {
function sub (line 4842) | function sub(x, y) {
function sum (line 4856) | function sum() {
function tan (line 4876) | function tan(x) {
function tanh (line 4888) | function tanh(x) {
function trunc (line 4899) | function trunc(x) {
FILE: test/hypothesis/error_hunt.py
function get_decimal (line 18) | def get_decimal(func: str, args: list, config: dict):
function assert_matches (line 25) | def assert_matches(x, mpfunc, jsfunc=None):
function test_matches (line 43) | def test_matches(x, fn):
function test_positive_domain (line 61) | def test_positive_domain(x, fn):
function test_inverse_trig (line 72) | def test_inverse_trig(x, fn):
function test_small_domain (line 86) | def test_small_domain(x, fn):
function test_acosh (line 98) | def test_acosh(x):
FILE: test/modules/Decimal.js
function randInt (line 103) | function randInt() {
FILE: test/modules/abs.js
function t (line 5) | function t(expected, value){
FILE: test/modules/acos.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/acosh.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/asin.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/asinh.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/atan.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/atan2.js
function t (line 5) | function t(y, x, pr, rm, expected) {
FILE: test/modules/atanh.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/cbrt.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/ceil.js
function t (line 5) | function t(expected, n) {
FILE: test/modules/clamp.js
function t (line 5) | function t(x, min, max, expected) {
FILE: test/modules/clone.js
function t (line 5) | function t(expression) {
FILE: test/modules/cmp.js
function t (line 7) | function t(a, b, expected) {
FILE: test/modules/cos.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/cosh.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/divToInt.js
function t (line 5) | function t(dividend, divisor, expected) {
FILE: test/modules/dpSd.js
function t (line 5) | function t(n, dp, sd, zs) {
function tx (line 12) | function tx(fn, msg) {
FILE: test/modules/exp.js
function t (line 5) | function t(n, expected, pr, rm) {
FILE: test/modules/floor.js
function t (line 5) | function t(expected, n) {
FILE: test/modules/hypot.js
function t (line 5) | function t(a, b, pr, rm, expected) {
FILE: test/modules/immutability.js
function randInt (line 17) | function randInt() {
FILE: test/modules/intPow.js
function t (line 6) | function t(expected, n, exp) {
function tx (line 10) | function tx(fn, msg) {
FILE: test/modules/isFiniteEtc.js
function t (line 5) | function t(actual) {
FILE: test/modules/ln.js
function t (line 5) | function t(n, expected, sd, rm) {
FILE: test/modules/log.js
function t (line 5) | function t(n, base, expected, sd, rm) {
FILE: test/modules/log10.js
function t (line 5) | function t(n, expected, sd, rm) {
FILE: test/modules/log2.js
function t (line 5) | function t(n, expected, sd, rm) {
FILE: test/modules/minAndMax.js
function t (line 5) | function t(min, max, arr) {
FILE: test/modules/neg.js
function t (line 5) | function t(expected, n) {
FILE: test/modules/random.js
function tx (line 6) | function tx(fn, msg) {
FILE: test/modules/round.js
function t (line 5) | function t(expected, n, rm) {
FILE: test/modules/sign.js
function t (line 5) | function t(n, expected) {
FILE: test/modules/sin.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/sinh.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/sqrt.js
function t (line 5) | function t(expected, n, sd, rm) {
FILE: test/modules/sum.js
function t (line 6) | function t() {
FILE: test/modules/tan.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/tanh.js
function t (line 5) | function t(n, pr, rm, expected) {
FILE: test/modules/toDP.js
function t (line 5) | function t(expected, n, dp, rm) {
function tx (line 9) | function tx(fn, msg) {
FILE: test/modules/toExponential.js
function t (line 5) | function t(expected, n, dp) {
function tx (line 9) | function tx(fn, msg) {
FILE: test/modules/toFixed.js
function t (line 5) | function t(expected, n, dp) {
function tx (line 9) | function tx(fn, msg) {
FILE: test/modules/toFraction.js
function t (line 5) | function t(expected, n, maxDenominator) {
function tx (line 9) | function tx(fn, msg) {
FILE: test/modules/toNearest.js
function isMinusZero (line 5) | function isMinusZero(n) {
FILE: test/modules/toPrecision.js
function t (line 5) | function t(expected, n, sd, rm) {
function tx (line 9) | function tx(fn, msg) {
FILE: test/modules/toSD.js
function t (line 5) | function t(expected, n, sd, rm) {
function tx (line 9) | function tx(fn, msg) {
FILE: test/modules/toString.js
function t (line 5) | function t(expected, n) {
FILE: test/modules/trunc.js
function t (line 5) | function t(expected, n) {
FILE: test/modules/valueOf.js
function t (line 5) | function t(expected, n) {
FILE: test/setup.js
function T (line 6) | function T(name, tests) {
Condensed preview — 79 files, each showing path, character count, and a content snippet. Download the .json file or copy for the full structured content (2,867K chars).
[
{
"path": ".npmignore",
"chars": 17,
"preview": "test\nexcluded\n.*\n"
},
{
"path": "CHANGELOG.md",
"chars": 6333,
"preview": "#### 10.6.0\n* 06/07/2025\n* Add `BigInt` support to TypeScript definitions\n\n#### 10.5.0\n* 23/01/2025\n* #216 TypeScript: i"
},
{
"path": "LICENCE.md",
"chars": 1081,
"preview": "The MIT Licence.\n\nCopyright (c) 2025 Michael Mclaughlin\n\nPermission is hereby granted, free of charge, to any person obt"
},
{
"path": "README.md",
"chars": 8328,
"preview": "\n\nAn arbitrary-precision Decim"
},
{
"path": "decimal.d.ts",
"chars": 8718,
"preview": "// Type definitions for decimal.js >=7.0.0\n// Project: https://github.com/MikeMcl/decimal.js\n// Definitions by: Michael "
},
{
"path": "decimal.global.d.ts",
"chars": 9226,
"preview": "// Type definitions for decimal.js >=7.0.0\n// Project: https://github.com/MikeMcl/decimal.js\n// Definitions by: Michael "
},
{
"path": "decimal.js",
"chars": 131665,
"preview": ";(function (globalScope) {\n 'use strict';\n\n\n /*!\n * decimal.js v10.6.0\n * An arbitrary-precision Decimal type fo"
},
{
"path": "decimal.mjs",
"chars": 122816,
"preview": "/*!\n * decimal.js v10.6.0\n * An arbitrary-precision Decimal type for JavaScript.\n * https://github.com/MikeMcl/decima"
},
{
"path": "doc/API.html",
"chars": 107048,
"preview": "<!DOCTYPE HTML>\n<html>\n<head>\n <meta charset=\"utf-8\">\n <meta http-equiv=\"X-UA-Compatible\" content=\"IE=edge\">\n <meta n"
},
{
"path": "package.json",
"chars": 1135,
"preview": "{\n \"name\": \"decimal.js\",\n \"description\": \"An arbitrary-precision Decimal type for JavaScript.\",\n \"version\": \"10.6.0\","
},
{
"path": "test/hypothesis/.gitignore",
"chars": 43,
"preview": "__pycache__\n.hypothesis\n.ipynb_checkpoints\n"
},
{
"path": "test/hypothesis/README.txt",
"chars": 66,
"preview": "See decimal PR #217\nhttps://github.com/MikeMcl/decimal.js/pull/217"
},
{
"path": "test/hypothesis/error_hunt.py",
"chars": 2660,
"preview": "from decimal import Decimal, getcontext\nimport json\nimport subprocess\nimport hypothesis\nfrom hypothesis import given, se"
},
{
"path": "test/hypothesis/evaluate.mjs",
"chars": 685,
"preview": "// listen for test cases, and provide the results.\n// give JSON of the test case, receive the result\n// Example: \n// > {"
},
{
"path": "test/hypothesis/requirements.txt",
"chars": 22,
"preview": "hypothesis\nmpmath\nnode"
},
{
"path": "test/modules/Decimal.js",
"chars": 10212,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('Decimal', function () {\n\n Decimal.config({\n precision: 40,\n "
},
{
"path": "test/modules/abs.js",
"chars": 4247,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('absoluteValue', function () {\n\n function t(expected, value){\n "
},
{
"path": "test/modules/acos.js",
"chars": 101479,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('acos', function () {\n\n function t(n, pr, rm, expected) {\n Dec"
},
{
"path": "test/modules/acosh.js",
"chars": 108755,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('acosh', function () {\n\n function t(n, pr, rm, expected) {\n De"
},
{
"path": "test/modules/asin.js",
"chars": 98229,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('asin', function () {\n\n function t(n, pr, rm, expected) {\n Dec"
},
{
"path": "test/modules/asinh.js",
"chars": 109204,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('asinh', function () {\n\n function t(n, pr, rm, expected) {\n D"
},
{
"path": "test/modules/atan.js",
"chars": 110161,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('atan', function () {\n\n function t(n, pr, rm, expected) {\n Dec"
},
{
"path": "test/modules/atan2.js",
"chars": 155765,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('atan2', function () {\n\n function t(y, x, pr, rm, expected) {\n "
},
{
"path": "test/modules/atanh.js",
"chars": 107083,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('atanh', function () {\n\n function t(n, pr, rm, expected) {\n De"
},
{
"path": "test/modules/cbrt.js",
"chars": 106246,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('cubeRoot', function () {\n\n function t(n, pr, rm, expected) {\n "
},
{
"path": "test/modules/ceil.js",
"chars": 2282,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('ceil', function () {\n\n function t(expected, n) {\n T.assertEqu"
},
{
"path": "test/modules/clamp.js",
"chars": 1079,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('clamp', function () {\n\n function t(x, min, max, expected) {\n "
},
{
"path": "test/modules/clone.js",
"chars": 3513,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('clone', function () {\n\n function t(expression) {\n T.assert(ex"
},
{
"path": "test/modules/cmp.js",
"chars": 42866,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('comparedTo', function () {\n\n var N = NaN, I = Infinity;\n\n funct"
},
{
"path": "test/modules/config.js",
"chars": 12984,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('config', function () {\n\n var MAX_DIGITS = 1e9;\n var EXP_LIMIT ="
},
{
"path": "test/modules/cos.js",
"chars": 6594,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('cos', function () {\n\n function t(n, pr, rm, expected) {\n Deci"
},
{
"path": "test/modules/cosh.js",
"chars": 7796,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('cosh', function () {\n\n function t(n, pr, rm, expected) {\n Dec"
},
{
"path": "test/modules/div.js",
"chars": 139864,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('dividedBy', function () {\n\n Decimal.config({\n precision: 40,\n"
},
{
"path": "test/modules/divToInt.js",
"chars": 131989,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('dividedToIntegerBy', function () {\n\n function t(dividend, diviso"
},
{
"path": "test/modules/dpSd.js",
"chars": 1947,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('decimalPlaces and precision', function () {\n\n function t(n, dp, "
},
{
"path": "test/modules/exp.js",
"chars": 6170,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('exp', function () {\n\n function t(n, expected, pr, rm) {\n Deci"
},
{
"path": "test/modules/floor.js",
"chars": 4716,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('floor', function () {\n\n function t(expected, n) {\n T.assertEq"
},
{
"path": "test/modules/hypot.js",
"chars": 16888,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('hypot', function () {\n\n function t(a, b, pr, rm, expected) {\n "
},
{
"path": "test/modules/immutability.js",
"chars": 8178,
"preview": "// Tests immutability of operand[s] for all applicable methods.\n// Also tests each Decimal.prototype method against its "
},
{
"path": "test/modules/intPow.js",
"chars": 49043,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('integer pow', function () {\n\n // Highest finite exponent here is"
},
{
"path": "test/modules/isFiniteEtc.js",
"chars": 7517,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('isFinite, isInteger, isNaN, isNegative, isZero, isDecimal', funct"
},
{
"path": "test/modules/ln.js",
"chars": 50573,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('ln', function () {\n\n function t(n, expected, sd, rm) {\n Decim"
},
{
"path": "test/modules/log.js",
"chars": 12163,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('log', function () {\n\n function t(n, base, expected, sd, rm) {\n "
},
{
"path": "test/modules/log10.js",
"chars": 43176,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('log10', function () {\n\n function t(n, expected, sd, rm) {\n De"
},
{
"path": "test/modules/log2.js",
"chars": 9859,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('log2', function () {\n\n function t(n, expected, sd, rm) {\n Dec"
},
{
"path": "test/modules/minAndMax.js",
"chars": 2699,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('min and max', function () {\n\n function t(min, max, arr) {\n T."
},
{
"path": "test/modules/minus.js",
"chars": 97591,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('minus', function () {\n\n var t = function (minuend, subtrahend, e"
},
{
"path": "test/modules/mod.js",
"chars": 86915,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('modulo', function () {\n\n var t = function (a, b, expected, sd, r"
},
{
"path": "test/modules/neg.js",
"chars": 6448,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('negated', function () {\n\n function t(expected, n) {\n T.assert"
},
{
"path": "test/modules/plus.js",
"chars": 136382,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('plus', function () {\n\n var t = function (addendA, addendB, expec"
},
{
"path": "test/modules/pow.js",
"chars": 7527,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('pow', function () {\n\n t = function (base, exp, expected, sd, rm)"
},
{
"path": "test/modules/powSqrt.js",
"chars": 1155,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('pow against sqrt', function () {\n\n Decimal.config({\n toExpNeg"
},
{
"path": "test/modules/random.js",
"chars": 719,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('random', function () {\n var i, sd, maxDigits;\n\n function tx(fn,"
},
{
"path": "test/modules/round.js",
"chars": 60341,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('round', function () {\n\n function t(expected, n, rm) {\n Decima"
},
{
"path": "test/modules/sign.js",
"chars": 586,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('sign', function () {\n\n function t(n, expected) {\n T.assertEqu"
},
{
"path": "test/modules/sin.js",
"chars": 8620,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('sin', function () {\n\n function t(n, pr, rm, expected) {\n Deci"
},
{
"path": "test/modules/sinh.js",
"chars": 7288,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('sinh', function () {\n\n function t(n, pr, rm, expected) {\n Dec"
},
{
"path": "test/modules/sqrt.js",
"chars": 60863,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('sqrt', function () {\n\n function t(expected, n, sd, rm) {\n Dec"
},
{
"path": "test/modules/sum.js",
"chars": 1720,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('sum', function () {\n var expected;\n\n function t() {\n T.asser"
},
{
"path": "test/modules/tan.js",
"chars": 6860,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('tan', function () {\n\n function t(n, pr, rm, expected) {\n Deci"
},
{
"path": "test/modules/tanh.js",
"chars": 7626,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('tanh', function () {\n\n function t(n, pr, rm, expected) {\n Dec"
},
{
"path": "test/modules/times.js",
"chars": 105077,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('times', function () {\n\n var t = function (multiplicand, multipli"
},
{
"path": "test/modules/toBinary.js",
"chars": 43829,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toBinary', function () {\n\n var t = function (expected, n, sd, rm"
},
{
"path": "test/modules/toDP.js",
"chars": 43925,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toDecimalPlaces', function () {\n\n function t(expected, n, dp, rm"
},
{
"path": "test/modules/toExponential.js",
"chars": 37406,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toExponential', function () {\n\n function t(expected, n, dp) {\n "
},
{
"path": "test/modules/toFixed.js",
"chars": 30055,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toFixed', function () {\n\n function t(expected, n, dp) {\n T.as"
},
{
"path": "test/modules/toFraction.js",
"chars": 17903,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toFraction', function () {\n\n function t(expected, n, maxDenomina"
},
{
"path": "test/modules/toHex.js",
"chars": 22763,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toHex', function () {\n\n var t = function (expected, n, sd, rm) {"
},
{
"path": "test/modules/toNearest.js",
"chars": 7443,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toNearest', function () {\n\n function isMinusZero(n) {\n return"
},
{
"path": "test/modules/toNumber.js",
"chars": 1527,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toNumber', function () {\n\n Decimal.config({\n precision: 20,\n "
},
{
"path": "test/modules/toOctal.js",
"chars": 22911,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toOctal', function () {\n\n var t = function (expected, n, sd, rm)"
},
{
"path": "test/modules/toPrecision.js",
"chars": 33887,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toPrecision', function () {\n\n function t(expected, n, sd, rm) {\n"
},
{
"path": "test/modules/toSD.js",
"chars": 53726,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toSignificantDigits', function () {\n\n function t(expected, n, sd"
},
{
"path": "test/modules/toString.js",
"chars": 23223,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('toString', function () {\n\n function t(expected, n) {\n T.asser"
},
{
"path": "test/modules/trunc.js",
"chars": 5183,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('trunc', function () {\n\n function t(expected, n) {\n T.assertEq"
},
{
"path": "test/modules/valueOf.js",
"chars": 1630,
"preview": "if (typeof T === 'undefined') require('../setup');\n\nT('valueOf', function () {\n\n function t(expected, n) {\n T.assert"
},
{
"path": "test/setup.js",
"chars": 2886,
"preview": "// Adds global: T\n\nT = (function () {\n var passed, testNumber, write;\n\n function T(name, tests) {\n var time;\n wr"
},
{
"path": "test/test.html",
"chars": 2184,
"preview": "<!DOCTYPE html>\n<html lang='en'>\n<head>\n <meta charset='utf-8' />\n <title>Testing decimal.js</title>\n <style>\n body "
},
{
"path": "test/test.js",
"chars": 1025,
"preview": "var time = new Date(),\n passed = 0,\n total = 0;\n\nconsole.log('\\n Testing decimal.js\\n');\n\n[\n 'abs',\n 'acos',\n 'acos"
}
]
About this extraction
This page contains the full source code of the MikeMcl/decimal.js GitHub repository, extracted and formatted as plain text for AI agents and large language models (LLMs). The extraction includes 79 files (2.7 MB), approximately 708.4k tokens, and a symbol index with 232 extracted functions, classes, methods, constants, and types. Use this with OpenClaw, Claude, ChatGPT, Cursor, Windsurf, or any other AI tool that accepts text input. You can copy the full output to your clipboard or download it as a .txt file.
Extracted by GitExtract — free GitHub repo to text converter for AI. Built by Nikandr Surkov.