diff options
Diffstat (limited to 'alarm/node_modules/decimal.js')
| -rw-r--r-- | alarm/node_modules/decimal.js/LICENCE.md | 23 | ||||
| -rw-r--r-- | alarm/node_modules/decimal.js/README.md | 246 | ||||
| -rw-r--r-- | alarm/node_modules/decimal.js/decimal.d.ts | 300 | ||||
| -rw-r--r-- | alarm/node_modules/decimal.js/decimal.js | 4934 | ||||
| -rw-r--r-- | alarm/node_modules/decimal.js/decimal.mjs | 4898 | ||||
| -rw-r--r-- | alarm/node_modules/decimal.js/package.json | 55 |
6 files changed, 0 insertions, 10456 deletions
diff --git a/alarm/node_modules/decimal.js/LICENCE.md b/alarm/node_modules/decimal.js/LICENCE.md deleted file mode 100644 index b795a60..0000000 --- a/alarm/node_modules/decimal.js/LICENCE.md +++ /dev/null @@ -1,23 +0,0 @@ -The MIT Licence.
-
-Copyright (c) 2022 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.
-
diff --git a/alarm/node_modules/decimal.js/README.md b/alarm/node_modules/decimal.js/README.md deleted file mode 100644 index 3bc5c94..0000000 --- a/alarm/node_modules/decimal.js/README.md +++ /dev/null @@ -1,246 +0,0 @@ -
-
-An arbitrary-precision Decimal type for JavaScript.
-
-[](https://www.npmjs.com/package/decimal.js)
-[](https://www.npmjs.com/package/decimal.js)
-[](https://travis-ci.org/MikeMcl/decimal.js)
-[](https://cdnjs.com/libraries/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 (Expat).](LICENCE.md)
diff --git a/alarm/node_modules/decimal.js/decimal.d.ts b/alarm/node_modules/decimal.js/decimal.d.ts deleted file mode 100644 index abff45e..0000000 --- a/alarm/node_modules/decimal.js/decimal.d.ts +++ /dev/null @@ -1,300 +0,0 @@ -// 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 | 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;
- private readonly toStringTag: string;
-
- 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): Decimal;
- 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;
-}
diff --git a/alarm/node_modules/decimal.js/decimal.js b/alarm/node_modules/decimal.js/decimal.js deleted file mode 100644 index dc21fa7..0000000 --- a/alarm/node_modules/decimal.js/decimal.js +++ /dev/null @@ -1,4934 +0,0 @@ -;(function (globalScope) {
- 'use strict';
-
-
- /*!
- * decimal.js v10.4.1
- * An arbitrary-precision Decimal type for JavaScript.
- * https://github.com/MikeMcl/decimal.js
- * Copyright (c) 2022 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|Decimal}
- * max {number|string|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 halfPi,
- 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;
-
- x = x.asin();
- halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
-
- Ctor.precision = pr;
- Ctor.rounding = rm;
-
- return halfPi.minus(x);
- };
-
-
- /*
- * 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|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|Decimal}
- *
- P.max = function () {
- Array.prototype.push.call(arguments, this);
- return maxOrMin(this.constructor, arguments, 'lt');
- };
- */
-
-
- /*
- * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
- *
- * arguments {number|string|Decimal}
- *
- P.min = function () {
- Array.prototype.push.call(arguments, this);
- return maxOrMin(this.constructor, arguments, 'gt');
- };
- */
-
-
- /*
- * 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|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|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|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` and `min`. `ltgt` is 'lt' or 'gt'.
- */
- function maxOrMin(Ctor, args, ltgt) {
- var y,
- x = new Ctor(args[0]),
- i = 0;
-
- for (; ++i < args.length;) {
- y = new Ctor(args[i]);
- if (!y.s) {
- x = y;
- break;
- } else if (x[ltgt](y)) {
- 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;
-
- // 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|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|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|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|Decimal}
- * y {number|string|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|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|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|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|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|Decimal} The y-coordinate.
- * x {number|string|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|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|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|Decimal}
- * min {number|string|Decimal}
- * max {number|string|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|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|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|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;
-
- // Duplicate.
- 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, NaN.
- } else if (v * 0 !== 0) {
- if (!v) x.s = NaN;
- x.e = NaN;
- x.d = null;
- return;
- }
-
- return parseDecimal(x, v.toString());
-
- } else if (t !== 'string') {
- throw Error(invalidArgument + v);
- }
-
- // Minus sign?
- if ((i = v.charCodeAt(0)) === 45) {
- v = v.slice(1);
- x.s = -1;
- } else {
- // Plus sign?
- if (i === 43) v = v.slice(1);
- x.s = 1;
- }
-
- return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, 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|Decimal}
- * y {number|string|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|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|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|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|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|Decimal} The argument of the logarithm.
- * y {number|string|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|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|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|Decimal}
- *
- */
- function max() {
- return maxOrMin(this, arguments, 'lt');
- }
-
-
- /*
- * Return a new Decimal whose value is the minimum of the arguments.
- *
- * arguments {number|string|Decimal}
- *
- */
- function min() {
- return maxOrMin(this, arguments, 'gt');
- }
-
-
- /*
- * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
- * using rounding mode `rounding`.
- *
- * x {number|string|Decimal}
- * y {number|string|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|Decimal}
- * y {number|string|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|Decimal} The base.
- * y {number|string|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|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|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|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|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|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|Decimal}
- * y {number|string|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|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|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|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|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);
diff --git a/alarm/node_modules/decimal.js/decimal.mjs b/alarm/node_modules/decimal.js/decimal.mjs deleted file mode 100644 index 5d9101b..0000000 --- a/alarm/node_modules/decimal.js/decimal.mjs +++ /dev/null @@ -1,4898 +0,0 @@ -/*!
- * decimal.js v10.4.1
- * An arbitrary-precision Decimal type for JavaScript.
- * https://github.com/MikeMcl/decimal.js
- * Copyright (c) 2022 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|Decimal}
- * max {number|string|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 halfPi,
- 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;
-
- x = x.asin();
- halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
-
- Ctor.precision = pr;
- Ctor.rounding = rm;
-
- return halfPi.minus(x);
-};
-
-
-/*
- * 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|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|Decimal}
- *
-P.max = function () {
- Array.prototype.push.call(arguments, this);
- return maxOrMin(this.constructor, arguments, 'lt');
-};
- */
-
-
-/*
- * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal.
- *
- * arguments {number|string|Decimal}
- *
-P.min = function () {
- Array.prototype.push.call(arguments, this);
- return maxOrMin(this.constructor, arguments, 'gt');
-};
- */
-
-
-/*
- * 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|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|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|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` and `min`. `ltgt` is 'lt' or 'gt'.
- */
-function maxOrMin(Ctor, args, ltgt) {
- var y,
- x = new Ctor(args[0]),
- i = 0;
-
- for (; ++i < args.length;) {
- y = new Ctor(args[i]);
- if (!y.s) {
- x = y;
- break;
- } else if (x[ltgt](y)) {
- 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;
-
- // 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|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|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|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|Decimal}
- * y {number|string|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|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|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|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|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|Decimal} The y-coordinate.
- * x {number|string|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|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|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|Decimal}
- * min {number|string|Decimal}
- * max {number|string|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|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|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|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;
-
- // Duplicate.
- 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, NaN.
- } else if (v * 0 !== 0) {
- if (!v) x.s = NaN;
- x.e = NaN;
- x.d = null;
- return;
- }
-
- return parseDecimal(x, v.toString());
-
- } else if (t !== 'string') {
- throw Error(invalidArgument + v);
- }
-
- // Minus sign?
- if ((i = v.charCodeAt(0)) === 45) {
- v = v.slice(1);
- x.s = -1;
- } else {
- // Plus sign?
- if (i === 43) v = v.slice(1);
- x.s = 1;
- }
-
- return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, 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|Decimal}
- * y {number|string|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|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|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|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|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|Decimal} The argument of the logarithm.
- * y {number|string|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|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|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|Decimal}
- *
- */
-function max() {
- return maxOrMin(this, arguments, 'lt');
-}
-
-
-/*
- * Return a new Decimal whose value is the minimum of the arguments.
- *
- * arguments {number|string|Decimal}
- *
- */
-function min() {
- return maxOrMin(this, arguments, 'gt');
-}
-
-
-/*
- * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits
- * using rounding mode `rounding`.
- *
- * x {number|string|Decimal}
- * y {number|string|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|Decimal}
- * y {number|string|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|Decimal} The base.
- * y {number|string|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|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|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|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|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|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|Decimal}
- * y {number|string|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|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|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|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|Decimal}
- *
- */
-function trunc(x) {
- return finalise(x = new this(x), x.e + 1, 1);
-}
-
-
-P[Symbol.for('nodejs.util.inspect.custom')] = P.toString;
-P[Symbol.toStringTag] = 'Decimal';
-
-// Create and configure initial Decimal constructor.
-export var Decimal = P.constructor = clone(DEFAULTS);
-
-// Create the internal constants from their string values.
-LN10 = new Decimal(LN10);
-PI = new Decimal(PI);
-
-export default Decimal;
diff --git a/alarm/node_modules/decimal.js/package.json b/alarm/node_modules/decimal.js/package.json deleted file mode 100644 index bf742d7..0000000 --- a/alarm/node_modules/decimal.js/package.json +++ /dev/null @@ -1,55 +0,0 @@ -{
- "name": "decimal.js",
- "description": "An arbitrary-precision Decimal type for JavaScript.",
- "version": "10.4.1",
- "keywords": [
- "arbitrary",
- "precision",
- "arithmetic",
- "big",
- "number",
- "decimal",
- "float",
- "biginteger",
- "bigdecimal",
- "bignumber",
- "bigint",
- "bignum"
- ],
- "repository" : {
- "type": "git",
- "url": "https://github.com/MikeMcl/decimal.js.git"
- },
- "main": "decimal",
- "module": "decimal.mjs",
- "browser": "decimal.js",
- "exports": {
- ".": {
- "types": "./decimal.d.ts",
- "import": "./decimal.mjs",
- "require": "./decimal.js"
- },
- "./decimal.mjs": "./decimal.mjs",
- "./decimal.js": "./decimal.js",
- "./package.json": "./package.json",
- "./decimal": {
- "types": "./decimal.d.ts",
- "import": "./decimal.mjs",
- "require": "./decimal.js"
- }
- },
- "author": {
- "name": "Michael Mclaughlin",
- "email": "M8ch88l@gmail.com"
- },
- "license": "MIT",
- "scripts": {
- "test": "node ./test/test.js"
- },
- "types": "decimal.d.ts",
- "files": [
- "decimal.js",
- "decimal.mjs",
- "decimal.d.ts"
- ]
-}
|