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0!==s.onabort?s.onabort=r:s.onreadystatechange=function(){4===s.readyState&&e.setTimeout(function(){n&&r()})},n=n("abort");try{s.send(t.hasContent&&t.data||null)}catch(e){if(n)throw e}},abort:function(){n&&n()}}}),b.ajaxPrefilter(function(e){e.crossDomain&&(e.contents.script=!1)}),b.ajaxSetup({accepts:{script:"text/javascript, application/javascript, application/ecmascript, application/x-ecmascript"},contents:{script:/\b(?:java|ecma)script\b/},converters:{"text script":function(e){return b.globalEval(e),e}}}),b.ajaxPrefilter("script",function(e){void 0===e.cache&&(e.cache=!1),e.crossDomain&&(e.type="GET")}),b.ajaxTransport("script",function(e){var t,n;if(e.crossDomain)return{send:function(i,o){t=b(" +``` + +[Node.js](http://nodejs.org): + +```bash +$ npm install --save decimal.js +``` + +```js +var Decimal = require('decimal.js'); +``` + +ES6 module (*decimal.mjs*): + +```js +//import Decimal from 'decimal.js'; +import {Decimal} from 'decimal.js'; +``` + +AMD loader libraries such as [requireJS](http://requirejs.org/): + +```js +require(['decimal'], function(Decimal) { + // Use Decimal here in local scope. No global Decimal. +}); +``` + +## Use + +*In all examples below, `var`, 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 function object, `Decimal`, the constructor of Decimal instances. + +It accepts a value of type number, string or Decimal. + +```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 +``` + +A value can also be in binary, hexadecimal or octal 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`: + +```js +x = new Decimal('0b1.1111111111111111111111111111111111111111111111111111p+1023') +``` + +A Decimal is immutable in the sense that it is not changed by its 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.cmp(y.mod(z).neg()) == 1 && x.comparedTo(y.modulo(z).negated()) == 1 // true +``` + +Like JavaScript's Number type, there are `toExponential`, `toFixed` and `toPrecision` methods, + +```js +x = new Decimal(255.5) +x.toExponential(5) // '2.55500e+2' +x.toFixed(5) // '255.50000' +x.toPrecision(5) // '255.50' +``` + +and almost all of the methods of JavaScript's Math object are also replicated. + +```js +Decimal.sqrt('6.98372465832e+9823') // '8.3568682281821340204e+4911' +Decimal.pow(2, 0.0979843) // '1.0702770511687781839' +``` + +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 +``` + +and 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 +Decimal9 = Decimal.clone({ precision: 9, rounding: 1 }) + +x = new Decimal(5) +y = new Decimal9(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. + +```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 + +The library can be tested using Node.js or a browser. + +The *test* directory contains the file *test.js* which runs all the tests when executed by Node, +and the file *test.html* which runs all the tests when opened in a browser. + +To run all the tests, from a command-line at the root directory using npm + +```bash +$ npm test +``` + +or at the *test* directory using Node + +```bash +$ node test +``` + +Each separate test module can also be executed individually, for example, at the *test/modules* directory + +```bash +$ node toFraction +``` + +## Build + +For Node, if [uglify-js](https://github.com/mishoo/UglifyJS2) is installed + +```bash +npm install uglify-js -g +``` + +then + +```bash +npm run build +``` + +will create *decimal.min.js*, and a source map will also be added to the *doc* directory. + +## Licence + +MIT. + +See *LICENCE.md* diff --git a/node_modules/decimal.js/decimal.d.ts b/node_modules/decimal.js/decimal.d.ts new file mode 100644 index 0000000..428089d --- /dev/null +++ b/node_modules/decimal.js/decimal.d.ts @@ -0,0 +1,295 @@ +// Type definitions for decimal.js >=7.0.0 +// Project: https://github.com/MikeMcl/decimal.js +// Definitions by: Michael Mclaughlin +// 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 name: string; + + constructor(n: Decimal.Value); + + absoluteValue(): Decimal; + abs(): Decimal; + + ceil(): 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 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): boolean + 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 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/node_modules/decimal.js/decimal.global.d.ts b/node_modules/decimal.js/decimal.global.d.ts new file mode 100644 index 0000000..0b0446b --- /dev/null +++ b/node_modules/decimal.js/decimal.global.d.ts @@ -0,0 +1,316 @@ +// Type definitions for decimal.js >=7.0.0 +// Project: https://github.com/MikeMcl/decimal.js +// Definitions by: Michael Mclaughlin +// Definitions: https://github.com/MikeMcl/decimal.js +// +// Documentation: http://mikemcl.github.io/decimal.js/ +// +// Exports (available globally or when using import): +// +// class Decimal (default export) +// type Decimal.Constructor +// type Decimal.Instance +// type Decimal.Modulo +// type Decimal.Rounding +// type Decimal.Value +// interface Decimal.Config +// +// Example (alternative syntax commented-out): +// +// import {Decimal} from "decimal.js" +// //import Decimal from "decimal.js" +// +// let r: Decimal.Rounding = Decimal.ROUND_UP; +// let c: Decimal.Configuration = {precision: 4, rounding: r}; +// Decimal.set(c); +// let v: Decimal.Value = '12345.6789'; +// let d: Decimal = new Decimal(v); +// //let d: Decimal.Instance = new Decimal(v); +// +// The use of compiler option `--strictNullChecks` is recommended. + +export default Decimal; + +export namespace Decimal { + export type Config = DecimalConfig; + export type Constructor = DecimalConstructor; + export type Instance = DecimalInstance; + export type Modulo = DecimalModulo; + export type Rounding = DecimalRounding; + export type Value = DecimalValue; +} + +declare global { + const Decimal: DecimalConstructor; + type Decimal = DecimalInstance; + + namespace Decimal { + type Config = DecimalConfig; + type Constructor = DecimalConstructor; + type Instance = DecimalInstance; + type Modulo = DecimalModulo; + type Rounding = DecimalRounding; + type Value = DecimalValue; + } +} + +type DecimalInstance = Decimal; +type DecimalConstructor = typeof Decimal; +type DecimalValue = string | number | Decimal; +type DecimalRounding = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8; +type DecimalModulo = DecimalRounding | 9; + +// http://mikemcl.github.io/decimal.js/#constructor-properties +interface DecimalConfig { + precision?: number; + rounding?: DecimalRounding; + toExpNeg?: number; + toExpPos?: number; + minE?: number; + maxE?: number; + crypto?: boolean; + modulo?: DecimalModulo; + defaults?: boolean; +} + +export declare class Decimal { + readonly d: number[]; + readonly e: number; + readonly s: number; + private readonly name: string; + + constructor(n: DecimalValue); + + absoluteValue(): Decimal; + abs(): Decimal; + + ceil(): Decimal; + + comparedTo(n: DecimalValue): number; + cmp(n: DecimalValue): number; + + cosine(): Decimal; + cos(): Decimal; + + cubeRoot(): Decimal; + cbrt(): Decimal; + + decimalPlaces(): number; + dp(): number; + + dividedBy(n: DecimalValue): Decimal; + div(n: DecimalValue): Decimal; + + dividedToIntegerBy(n: DecimalValue): Decimal; + divToInt(n: DecimalValue): Decimal; + + equals(n: DecimalValue): boolean; + eq(n: DecimalValue): boolean; + + floor(): Decimal; + + greaterThan(n: DecimalValue): boolean; + gt(n: DecimalValue): boolean; + + greaterThanOrEqualTo(n: DecimalValue): boolean; + gte(n: DecimalValue): boolean; + + hyperbolicCosine(): Decimal; + cosh(): Decimal; + + hyperbolicSine(): Decimal; + sinh(): Decimal; + + hyperbolicTangent(): Decimal; + tanh(): Decimal; + + inverseCosine(): Decimal; + acos(): Decimal; + + inverseHyperbolicCosine(): Decimal; + acosh(): Decimal; + + inverseHyperbolicSine(): Decimal; + asinh(): Decimal; + + inverseHyperbolicTangent(): Decimal; + atanh(): Decimal; + + inverseSine(): Decimal; + asin(): Decimal; + + inverseTangent(): Decimal; + atan(): Decimal; + + isFinite(): boolean; + + isInteger(): boolean; + isInt(): boolean; + + isNaN(): boolean; + + isNegative(): boolean; + isNeg(): boolean; + + isPositive(): boolean; + isPos(): boolean; + + isZero(): boolean; + + lessThan(n: DecimalValue): boolean; + lt(n: DecimalValue): boolean; + + lessThanOrEqualTo(n: DecimalValue): boolean; + lte(n: DecimalValue): boolean; + + logarithm(n?: DecimalValue): Decimal; + log(n?: DecimalValue): Decimal; + + minus(n: DecimalValue): Decimal; + sub(n: DecimalValue): Decimal; + + modulo(n: DecimalValue): Decimal; + mod(n: DecimalValue): Decimal; + + naturalExponential(): Decimal; + exp(): Decimal; + + naturalLogarithm(): Decimal; + ln(): Decimal; + + negated(): Decimal; + neg(): Decimal; + + plus(n: DecimalValue): Decimal; + add(n: DecimalValue): Decimal; + + precision(includeZeros?: boolean): number; + sd(includeZeros?: boolean): number; + + round(): Decimal; + + sine() : Decimal; + sin() : Decimal; + + squareRoot(): Decimal; + sqrt(): Decimal; + + tangent() : Decimal; + tan() : Decimal; + + times(n: DecimalValue): Decimal; + mul(n: DecimalValue) : Decimal; + + toBinary(significantDigits?: number): string; + toBinary(significantDigits: number, rounding: DecimalRounding): string; + + toDecimalPlaces(decimalPlaces?: number): Decimal; + toDecimalPlaces(decimalPlaces: number, rounding: DecimalRounding): Decimal; + toDP(decimalPlaces?: number): Decimal; + toDP(decimalPlaces: number, rounding: DecimalRounding): Decimal; + + toExponential(decimalPlaces?: number): string; + toExponential(decimalPlaces: number, rounding: DecimalRounding): string; + + toFixed(decimalPlaces?: number): string; + toFixed(decimalPlaces: number, rounding: DecimalRounding): string; + + toFraction(max_denominator?: DecimalValue): Decimal[]; + + toHexadecimal(significantDigits?: number): string; + toHexadecimal(significantDigits: number, rounding: DecimalRounding): string; + toHex(significantDigits?: number): string; + toHex(significantDigits: number, rounding?: DecimalRounding): string; + + toJSON(): string; + + toNearest(n: DecimalValue, rounding?: DecimalRounding): Decimal; + + toNumber(): number; + + toOctal(significantDigits?: number): string; + toOctal(significantDigits: number, rounding: DecimalRounding): string; + + toPower(n: DecimalValue): Decimal; + pow(n: DecimalValue): Decimal; + + toPrecision(significantDigits?: number): string; + toPrecision(significantDigits: number, rounding: DecimalRounding): string; + + toSignificantDigits(significantDigits?: number): Decimal; + toSignificantDigits(significantDigits: number, rounding: DecimalRounding): Decimal; + toSD(significantDigits?: number): Decimal; + toSD(significantDigits: number, rounding: DecimalRounding): Decimal; + + toString(): string; + + truncated(): Decimal; + trunc(): Decimal; + + valueOf(): string; + + static abs(n: DecimalValue): Decimal; + static acos(n: DecimalValue): Decimal; + static acosh(n: DecimalValue): Decimal; + static add(x: DecimalValue, y: DecimalValue): Decimal; + static asin(n: DecimalValue): Decimal; + static asinh(n: DecimalValue): Decimal; + static atan(n: DecimalValue): Decimal; + static atanh(n: DecimalValue): Decimal; + static atan2(y: DecimalValue, x: DecimalValue): Decimal; + static cbrt(n: DecimalValue): Decimal; + static ceil(n: DecimalValue): Decimal; + static clone(object?: DecimalConfig): DecimalConstructor; + static config(object: DecimalConfig): DecimalConstructor; + static cos(n: DecimalValue): Decimal; + static cosh(n: DecimalValue): Decimal; + static div(x: DecimalValue, y: DecimalValue): Decimal; + static exp(n: DecimalValue): Decimal; + static floor(n: DecimalValue): Decimal; + static hypot(...n: DecimalValue[]): Decimal; + static isDecimal(object: any): boolean + static ln(n: DecimalValue): Decimal; + static log(n: DecimalValue, base?: DecimalValue): Decimal; + static log2(n: DecimalValue): Decimal; + static log10(n: DecimalValue): Decimal; + static max(...n: DecimalValue[]): Decimal; + static min(...n: DecimalValue[]): Decimal; + static mod(x: DecimalValue, y: DecimalValue): Decimal; + static mul(x: DecimalValue, y: DecimalValue): Decimal; + static noConflict(): DecimalConstructor; // Browser only + static pow(base: DecimalValue, exponent: DecimalValue): Decimal; + static random(significantDigits?: number): Decimal; + static round(n: DecimalValue): Decimal; + static set(object: DecimalConfig): DecimalConstructor; + static sign(n: DecimalValue): Decimal; + static sin(n: DecimalValue): Decimal; + static sinh(n: DecimalValue): Decimal; + static sqrt(n: DecimalValue): Decimal; + static sub(x: DecimalValue, y: DecimalValue): Decimal; + static tan(n: DecimalValue): Decimal; + static tanh(n: DecimalValue): Decimal; + static trunc(n: DecimalValue): Decimal; + + static readonly default?: DecimalConstructor; + static readonly Decimal?: DecimalConstructor; + + static readonly precision: number; + static readonly rounding: DecimalRounding; + static readonly toExpNeg: number; + static readonly toExpPos: number; + static readonly minE: number; + static readonly maxE: number; + static readonly crypto: boolean; + static readonly modulo: DecimalModulo; + + static readonly ROUND_UP: 0; + static readonly ROUND_DOWN: 1; + static readonly ROUND_CEIL: 2; + static readonly ROUND_FLOOR: 3; + static readonly ROUND_HALF_UP: 4; + static readonly ROUND_HALF_DOWN: 5; + static readonly ROUND_HALF_EVEN: 6; + static readonly ROUND_HALF_CEIL: 7; + static readonly ROUND_HALF_FLOOR: 8; + static readonly EUCLID: 9; +} diff --git a/node_modules/decimal.js/decimal.js b/node_modules/decimal.js/decimal.js new file mode 100644 index 0000000..23cc2d3 --- /dev/null +++ b/node_modules/decimal.js/decimal.js @@ -0,0 +1,4877 @@ +;(function (globalScope) { + 'use strict'; + + + /* + * decimal.js v10.2.0 + * An arbitrary-precision Decimal type for JavaScript. + * https://github.com/MikeMcl/decimal.js + * Copyright (c) 2019 Michael Mclaughlin + * 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', + + 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 = { name: '[object Decimal]' }; + + + // Decimal prototype methods + + + /* + * absoluteValue abs + * ceil + * 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 + * 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 = '1e' + 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; + }; + + + /* + // Add aliases to match BigDecimal method names. + // P.add = P.plus; + P.subtract = P.minus; + P.multiply = P.times; + P.divide = P.div; + P.remainder = P.mod; + P.compareTo = P.cmp; + P.negate = P.neg; + */ + + + // 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, y, + len = x.d.length; + + // 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. + 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 === '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 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 + * 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 + * 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); + } + + + /* + * 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 (v instanceof Decimal) { + 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.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.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.name === '[object Decimal]' || 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 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['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/node_modules/decimal.js/decimal.min.js b/node_modules/decimal.js/decimal.min.js new file mode 100644 index 0000000..98a5552 --- /dev/null +++ b/node_modules/decimal.js/decimal.min.js @@ -0,0 +1,3 @@ +/* decimal.js v10.2.0 https://github.com/MikeMcl/decimal.js/LICENCE */ +!function(n){"use strict";var h,R,e,o,u=9e15,g=1e9,m="0123456789abcdef",t="2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058",r="3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789",c={precision:20,rounding:4,modulo:1,toExpNeg:-7,toExpPos:21,minE:-u,maxE:u,crypto:!1},N=!0,f="[DecimalError] ",w=f+"Invalid argument: ",s=f+"Precision limit exceeded",a=f+"crypto unavailable",L=Math.floor,v=Math.pow,l=/^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,d=/^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,p=/^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,b=/^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,T=1e7,U=7,E=t.length-1,x=r.length-1,y={name:"[object Decimal]"};function M(n){var e,i,t,r=n.length-1,s="",o=n[0];if(0i-1&&(void 0===s[t+1]&&(s[t+1]=0),s[t+1]+=s[t]/i|0,s[t]%=i)}return s.reverse()}y.absoluteValue=y.abs=function(){var n=new this.constructor(this);return n.s<0&&(n.s=1),_(n)},y.ceil=function(){return _(new this.constructor(this),this.e+1,2)},y.comparedTo=y.cmp=function(n){var e,i,t,r,s=this,o=s.d,u=(n=new s.constructor(n)).d,c=s.s,f=n.s;if(!o||!u)return c&&f?c!==f?c:o===u?0:!o^c<0?1:-1:NaN;if(!o[0]||!u[0])return o[0]?c:u[0]?-f:0;if(c!==f)return c;if(s.e!==n.e)return s.e>n.e^c<0?1:-1;for(e=0,i=(t=o.length)<(r=u.length)?t:r;eu[e]^c<0?1:-1;return t===r?0:rthis.d.length-2},y.isNaN=function(){return!this.s},y.isNegative=y.isNeg=function(){return this.s<0},y.isPositive=y.isPos=function(){return 0e&&(e=this.e+1)):e=NaN,e},y.round=function(){var n=this.constructor;return _(new n(this),this.e+1,n.rounding)},y.sine=y.sin=function(){var n,e,i=this,t=i.constructor;return i.isFinite()?i.isZero()?new t(i):(n=t.precision,e=t.rounding,t.precision=n+Math.max(i.e,i.sd())+U,t.rounding=1,i=function(n,e){var i,t=e.d.length;if(t<3)return W(n,2,e,e);i=16<(i=1.4*Math.sqrt(t))?16:0|i,e=e.times(1/J(5,i)),e=W(n,2,e,e);for(var r,s=new n(5),o=new n(16),u=new n(20);i--;)r=e.times(e),e=e.times(s.plus(r.times(o.times(r).minus(u))));return e}(t,z(t,i)),t.precision=n,t.rounding=e,_(2=n.d.length-1&&(i=f<0?-f:f)<=9007199254740991)return r=I(c,u,i,t),n.s<0?new c(1).div(r):_(r,t,s);if((o=u.s)<0){if(ec.maxE+1||e=r.toExpPos):(q(n,1,g),void 0===e?e=r.rounding:q(e,0,8),A(t=_(new r(t),n,e),n<=t.e||t.e<=r.toExpNeg,n)),t.isNeg()&&!t.isZero()?"-"+i:i},y.toSignificantDigits=y.toSD=function(n,e){var i=this.constructor;return void 0===n?(n=i.precision,e=i.rounding):(q(n,1,g),void 0===e?e=i.rounding:q(e,0,8)),_(new i(this),n,e)},y.toString=function(){var n=this,e=n.constructor,i=A(n,n.e<=e.toExpNeg||n.e>=e.toExpPos);return n.isNeg()&&!n.isZero()?"-"+i:i},y.truncated=y.trunc=function(){return _(new this.constructor(this),this.e+1,1)},y.valueOf=y.toJSON=function(){var n=this,e=n.constructor,i=A(n,n.e<=e.toExpNeg||n.e>=e.toExpPos);return n.isNeg()?"-"+i:i};var F=function(){function S(n,e,i){var t,r=0,s=n.length;for(n=n.slice();s--;)t=n[s]*e+r,n[s]=t%i|0,r=t/i|0;return r&&n.unshift(r),n}function Z(n,e,i,t){var r,s;if(i!=t)s=te[r]?1:-1;break}return s}function P(n,e,i,t){for(var r=0;i--;)n[i]-=r,r=n[i](F[c]||0)&&u--,null==i?(N=i=O.precision,t=O.rounding):N=r?i+(n.e-e.e)+1:i,N<0)g.push(1),h=!0;else{if(N=N/a+2|0,c=0,1==M){for(A=A[f=0],N++;(c=s/2&&++y;f=0,(o=Z(A,m,M,w))<0?(v=m[0],M!=w&&(v=v*s+(m[1]||0)),1<(f=v/y|0)?(s<=f&&(f=s-1),1==(o=Z(l=S(A,f,s),m,d=l.length,w=m.length))&&(f--,P(l,Md.maxE?(n.d=null,n.e=NaN):n.en.constructor.maxE?(n.d=null,n.e=NaN):n.er-1;)h[i]=0,i||(++s,h.unshift(1));for(c=h.length;!h[c-1];--c);for(o=0,a="";oc)for(s-=c;s--;)a+="0";else se)return n.length=e,!0}function Q(n){return new this(n).abs()}function X(n){return new this(n).acos()}function Y(n){return new this(n).acosh()}function nn(n,e){return new this(n).plus(e)}function en(n){return new this(n).asin()}function tn(n){return new this(n).asinh()}function rn(n){return new this(n).atan()}function sn(n){return new this(n).atanh()}function on(n,e){n=new this(n),e=new this(e);var i,t=this.precision,r=this.rounding,s=t+4;return n.s&&e.s?n.d||e.d?!e.d||n.isZero()?(i=e.s<0?P(this,t,r):new this(0)).s=n.s:!n.d||e.isZero()?(i=P(this,s,1).times(.5)).s=n.s:i=e.s<0?(this.precision=s,this.rounding=1,i=this.atan(F(n,e,s,1)),e=P(this,s,1),this.precision=t,this.rounding=r,n.s<0?i.minus(e):i.plus(e)):this.atan(F(n,e,s,1)):(i=P(this,s,1).times(0s.maxE?(r.e=NaN,r.d=null):n.e + * 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', + + 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 = { name: '[object Decimal]' }; + + +// Decimal prototype methods + + +/* + * absoluteValue abs + * ceil + * 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 + * 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 = '1e' + 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; +}; + + +/* +// Add aliases to match BigDecimal method names. +// P.add = P.plus; +P.subtract = P.minus; +P.multiply = P.times; +P.divide = P.div; +P.remainder = P.mod; +P.compareTo = P.cmp; +P.negate = P.neg; + */ + + +// 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, y, + len = x.d.length; + + // 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. + 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 === '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 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 + * 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 + * 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); +} + + +/* + * 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 (v instanceof Decimal) { + 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.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.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.name === '[object Decimal]' || 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 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 = clone(DEFAULTS); + +// Create the internal constants from their string values. +LN10 = new Decimal(LN10); +PI = new Decimal(PI); + +export default Decimal; diff --git a/node_modules/decimal.js/doc/API.html b/node_modules/decimal.js/doc/API.html new file mode 100644 index 0000000..cfdb617 --- /dev/null +++ b/node_modules/decimal.js/doc/API.html @@ -0,0 +1,2678 @@ + + + + + + + decimal.js API + + + + +
+ + API + + CONSTRUCTOR + + + Methods + + + Properties + + + INSTANCE + + Methods + + + Properties +
    +
  • ddigits
    • +
  • eexponent
    • +
  • ssign
    • +
+ + Zero, NaN & Infinity + Errors + Pi + FAQ + +
+ +
+ +

decimal.js

+ +

An arbitrary-precision Decimal type for JavaScript.

+

Hosted on GitHub.

+ +

API

+ +

+ See the README on GitHub for a quick-start + introduction. +

+

+ In all examples below, var and semicolons are not shown, and if a commented-out + value is in quotes it means toString has been called on the preceding expression. +


+

+ When the library is loaded, it defines a single function object, + Decimal, the constructor of Decimal instances. +

+

+ + If necessary, multiple Decimal constructors can be created, each with their own independent + configuration, e.g. precision and range, which applies to all Decimal instances created from + it. + +

+

+ + A new Decimal constructor is created by calling the clone + method of an already existing Decimal constructor. + +

+ + + +

CONSTRUCTOR

+ +
+ DecimalDecimal(value) ⇒ Decimal +
+
+
value: number|string|Decimal
+
+ A legitimate value is an integer or float, including ±0, or + is ±Infinity, or NaN. +
+
+ The number of digits of value is not limited, except by JavaScript's maximum + array size and, in practice, the processing time required. +
+
+ The allowable range of value is defined in terms of a maximum exponent, see + maxE, and a minimum exponent, see minE. +
+
+ As well as in decimal, a string value may be expressed in binary, hexadecimal + or octal, if the appropriate prefix is included: 0x or 0X for + hexadecimal, 0b or 0B for binary, and 0o or + 0O for octal. +
+
+ Both decimal and non-decimal string values may use exponential (floating-point), as well as + normal (fixed-point) notation. +
+
+ In exponential notation, e or E defines a power-of-ten exponent + for decimal values, and p or P defines a power-of-two exponent for + non-decimal values, i.e. binary, hexadecimal or octal. +
+
+

Returns a new Decimal object instance.

+

Throws on an invalid value.

+ 
+x = new Decimal(9)                       // '9'
+y = new Decimal(x)                       // '9'
+
+new Decimal('5032485723458348569331745.33434346346912144534543')
+new Decimal('4.321e+4')                  // '43210'
+new Decimal('-735.0918e-430')            // '-7.350918e-428'
+new Decimal('5.6700000')                 // '5.67'
+new Decimal(Infinity)                    // 'Infinity'
+new Decimal(NaN)                         // 'NaN'
+new Decimal('.5')                        // '0.5'
+new Decimal('-0b10110100.1')             // '-180.5'
+new Decimal('0xff.8')                    // '255.5'
+
+new Decimal(0.046875)                    // '0.046875'
+new Decimal('0.046875000000')            // '0.046875'
+
+new Decimal(4.6875e-2)                   // '0.046875'
+new Decimal('468.75e-4')                 // '0.046875'
+
+new Decimal('0b0.000011')                // '0.046875'
+new Decimal('0o0.03')                    // '0.046875'
+new Decimal('0x0.0c')                    // '0.046875'
+
+new Decimal('0b1.1p-5')                  // '0.046875'
+new Decimal('0o1.4p-5')                  // '0.046875'
+new Decimal('0x1.8p-5')                  // '0.046875'
+ + + +

Methods

+

The methods of a Decimal constructor.

+ + + +
abs.abs(x) ⇒ Decimal
+

x: number|string|Decimal

+

See absoluteValue.

+ 
a = Decimal.abs(x)
+b = new Decimal(x).abs()
+a.equals(b)                    // true
+ + + +
acos.acos(x) ⇒ Decimal
+

x: number|string|Decimal

+

See inverseCosine.

+ 
a = Decimal.acos(x)
+b = new Decimal(x).acos()
+a.equals(b)                    // true
+ + + +
acosh.acosh(x) ⇒ Decimal
+

x: number|string|Decimal

+

See inverseHyperbolicCosine.

+ 
a = Decimal.acosh(x)
+b = new Decimal(x).acosh()
+a.equals(b)                    // true
+ + + +
add.add(x, y) ⇒ Decimal
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

See plus.

+ 
a = Decimal.add(x, y)
+b = new Decimal(x).plus(y)
+a.equals(b)                    // true
+ + + +
asin.asin(x) ⇒ Decimal
+

x: number|string|Decimal

+

See inverseSine.

+ 
a = Decimal.asin(x)
+b = new Decimal(x).asin()
+a.equals(b)                    // true
+ + + +
asinh.asinh(x) ⇒ Decimal
+

x: number|string|Decimal

+

See inverseHyperbolicSine.

+ 
a = Decimal.asinh(x)
+b = new Decimal(x).asinh()
+a.equals(b)                    // true
+ + + +
atan.atan(x) ⇒ Decimal
+

x: number|string|Decimal

+

See inverseTangent.

+ 
a = Decimal.atan(x)
+b = new Decimal(x).atan()
+a.equals(b)                    // true
+ + + +
atanh.atanh(x) ⇒ Decimal
+

x: number|string|Decimal

+

See inverseHyperbolicTangent.

+ 
a = Decimal.atanh(x)
+b = new Decimal(x).atanh()
+a.equals(b)                    // true
+ + + +
atan2.atan2(y, x) ⇒ Decimal
+

+ y: number|string|Decimal
+ x: number|string|Decimal +

+

+ Returns a new Decimal whose value is the inverse tangent in radians of the quotient of + y and x, rounded to precision + significant digits using rounding mode rounding. +

+

+ The signs of y and x are used to determine the quadrant of the + result. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-pi, pi] +

+

+ See Pi and + Math.atan2(). +

+ 
r = Decimal.atan2(y, x)
+ + + +
cbrt.cbrt(x) ⇒ Decimal
+

x: number|string|Decimal

+

See cubeRoot.

+ 
a = Decimal.cbrt(x)
+b = new Decimal(x).cbrt()
+a.equals(b)                    // true
+ + + +
ceil.ceil(x) ⇒ Decimal
+

x: number|string|Decimal

+

See ceil.

+ 
a = Decimal.ceil(x)
+b = new Decimal(x).ceil()
+a.equals(b)                    // true
+ + + +
+ clone + .clone([object]) ⇒ Decimal constructor +
+

object: object

+

+ Returns a new independent Decimal constructor with configuration settings as described by + object (see set), or with the same + settings as this Decimal constructor if object is omitted. +

+ 
Decimal.set({ precision: 5 })
+Decimal9 = Decimal.clone({ precision: 9 })
+
+a = new Decimal(1)
+b = new Decimal9(1)
+
+a.div(3)                           // 0.33333
+b.div(3)                           // 0.333333333
+
+// Decimal9 = Decimal.clone({ precision: 9 }) is equivalent to:
+Decimal9 = Decimal.clone()
+Decimal9.set({ precision: 9 })
+

+ If object has a 'defaults' property with value true + then the new constructor will use the default configuration. +

+ 
+D1 = Decimal.clone({ defaults: true })
+
+// Use the defaults except for precision
+D2 = Decimal.clone({ defaults: true, precision: 50 })
+

+ It is not inefficient in terms of memory usage to use multiple Decimal constructors as + functions are shared between them. +

+ + +
cos.cos(x) ⇒ Decimal
+

x: number|string|Decimal

+

See cosine.

+ 
a = Decimal.cos(x)
+b = new Decimal(x).cos()
+a.equals(b)                    // true
+ + + +
cosh.cosh(x) ⇒ Decimal
+

x: number|string|Decimal

+

See hyperbolicCosine.

+ 
a = Decimal.cosh(x)
+b = new Decimal(x).cosh()
+a.equals(b)                    // true
+ + + +
div.div(x, y) ⇒ Decimal
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

See dividedBy.

+ 
a = Decimal.div(x, y)
+b = new Decimal(x).div(y)
+a.equals(b)                    // true
+ + + +
exp.exp(x) ⇒ Decimal
+

x: number|string|Decimal

+

See naturalExponential.

+ 
a = Decimal.exp(x)
+b = new Decimal(x).exp()
+a.equals(b)                    // true
+ + + +
floor.floor(x) ⇒ Decimal
+

x: number|string|Decimal

+

See floor.

+ 
a = Decimal.floor(x)
+b = new Decimal(x).floor()
+a.equals(b)                    // true
+ + + +
+ hypot.hypot([x [, y, ...]]) ⇒ Decimal +
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

+ Returns 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. +

+ 
r = Decimal.hypot(x, y)
+ + + +
ln.ln(x) ⇒ Decimal
+

x: number|string|Decimal

+

See naturalLogarithm.

+ 
a = Decimal.ln(x)
+b = new Decimal(x).ln()
+a.equals(b)                    // true
+ + + +
+ isDecimal.isDecimal(object) ⇒ boolean +
+

object: any

+

+ Returns true if object is a Decimal instance (where Decimal is any + Decimal constructor), or false if it is not. +

+ 
a = new Decimal(1)
+b = {}
+a instanceof Decimal           // true
+Decimal.isDecimal(a)           // true
+Decimal.isDecimal(b)           // false
+ + + +
log.log(x [, base]) ⇒ Decimal
+

+ x: number|string|Decimal
+ base: number|string|Decimal +

+

See logarithm.

+

+ The default base is 10, which is not the same as JavaScript's + Math.log(), which returns the natural logarithm (base e). +

+ 
a = Decimal.log(x, y)
+b = new Decimal(x).log(y)
+a.equals(b)                    // true
+ + + +
log2.log2(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the base 2 logarithm of x, + rounded to precision significant digits using rounding + mode rounding. +

+ 
r = Decimal.log2(x)
+ + + +
log10.log10(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the base 10 logarithm of x, + rounded to precision significant digits using rounding + mode rounding. +

+ 
r = Decimal.log10(x)
+ + + +
+ max.max([x [, y, ...]]) ⇒ Decimal +
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

Returns a new Decimal whose value is the maximum of the arguments.

+ 
r = Decimal.max(x, y, z)
+ + + +
+ min.min([x [, y, ...]]) ⇒ Decimal +
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

Returns a new Decimal whose value is the minimum of the arguments.

+ 
r = Decimal.min(x, y, z)
+ + + +
mod.mod(x, y) ⇒ Decimal
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

See modulo.

+ 
a = Decimal.mod(x, y)
+b = new Decimal(x).mod(y)
+a.equals(b)                    // true
+ + + +
mul.mul(x, y) ⇒ Decimal
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

See times.

+ 
a = Decimal.mul(x, y)
+b = new Decimal(x).mul(y)
+a.equals(b)                    // true
+ + + +
+ noConflict.noConflict() ⇒ Decimal constructor +
+

Browsers only.

+

+ Reverts the Decimal variable to the value it had before this library was loaded + and returns a reference to the original Decimal constructor so it can be assigned to a + variable with a different name. +

+ 
+<script> Decimal = 1 </script>
+<script src='/path/to/decimal.js'></script>
+<script>
+  a = new Decimal(2)      // '2'
+  D = Decimal.noConflict()
+  Decimal                 // 1
+  b = new D(3)            // '3'
+</script>
+ + + +
pow.pow(base, exponent) ⇒ Decimal
+

+ base: number|string|Decimal
+ exponent: number|string|Decimal +

+

See toPower.

+ 
a = Decimal.pow(x, y)
+b = new Decimal(x).pow(y)
+a.equals(b)                    // true
+ + + +
+ random.random([dp]) ⇒ Decimal +
+

dp: number: integer, 0 to 1e+9 inclusive

+

+ Returns a new Decimal with a pseudo-random value equal to or greater than 0 and + less than 1. +

+

+ The return value will have dp decimal places (or less if trailing zeros are + produced). If dp is omitted then the number of decimal places will + default to the current precision setting. +

+

+ If the value of this Decimal constructor's + crypto property is true, and the + crypto object is available globally in the host environment, the random digits of + the return value are generated by either crypto.getRandomValues (Web Cryptography + API in modern browsers) or crypto.randomBytes (Node.js), otherwise, if the the + value of the property is false the return value is generated by + Math.random (fastest). +

+

To make the crypto object available globally in Node.js use

+ 
global.crypto = require('crypto')
+

+ If the value of this Decimal constructor's + crypto property is set true and the + crypto object and associated method are not available, an exception will be + thrown. +

+

+ If one of the crypto methods is used, the value of the returned Decimal should be + cryptographically-secure and statistically indistinguishable from a random value. +

+ 
Decimal.set({ precision: 10 })
+Decimal.random()                    // '0.4117936847'
+Decimal.random(20)                  // '0.78193327636914089009'
+ + +
round.round(x) ⇒ Decimal
+

x: number|string|Decimal

+

See round.

+ 
a = Decimal.round(x)
+b = new Decimal(x).round()
+a.equals(b)                    // true
+ + + +
set.set(object) ⇒ Decimal constructor
+

object: object

+

+ Configures the 'global' settings for this particular Decimal constructor, i.e. + the settings which apply to operations performed on the Decimal instances created by it. +

+

Returns this Decimal constructor.

+

+ The configuration object, object, can contain some or all of the properties + described in detail at Properties and shown in the + example below. +

+

+ The values of the configuration object properties are checked for validity and then stored as + equivalently-named properties of this Decimal constructor. +

+

+ If object has a 'defaults' property with value true + then any unspecified properties will be reset to their default values. +

+

Throws on an invalid object or configuration property value.

+ 
+// Defaults
+Decimal.set({
+    precision: 20,
+    rounding: 4,
+    toExpNeg: -7,
+    toExpPos: 21,
+    maxE: 9e15,
+    minE: -9e15,
+    modulo: 1,
+    crypto: false
+})
+
+// Reset all properties to their default values
+Decimal.set({ defaults: true })
+
+// Set precision to 50 and all other properties to their default values
+Decimal.set({ precision: 50, defaults: true })
+

+ The properties of a Decimal constructor can also be set by direct assignment, but that will + by-pass the validity checking that this method performs - this is not a problem if the user + knows that the assignment is valid. +

+ 
Decimal.precision = 40
+ + + +
sign.sign(x) ⇒ number
+

x: number|string|Decimal

+ + + + + + + + + + + + + + + + + + + + + + +
Returns 
1if the value of x is non-zero and its sign is positive
-1if the value of x is non-zero and its sign is negative
0if the value of x is positive zero
-0if the value of x is negative zero
NaNif the value of x is NaN
+ 
r = Decimal.sign(x)
+ + + +
sin.sin(x) ⇒ Decimal
+

x: number|string|Decimal

+

See sine.

+ 
a = Decimal.sin(x)
+b = new Decimal(x).sin()
+a.equals(b)                    // true
+ + + +
sinh.sinh(x) ⇒ Decimal
+

x: number|string|Decimal

+

See hyperbolicSine.

+ 
a = Decimal.sinh(x)
+b = new Decimal(x).sinh()
+a.equals(b)                    // true
+ + + +
sqrt.sqrt(x) ⇒ Decimal
+

x: number|string|Decimal

+

See squareRoot.

+ 
a = Decimal.sqrt(x)
+b = new Decimal(x).sqrt()
+a.equals(b)                    // true
+ + + +
sub.sub(x, y) ⇒ Decimal
+

+ x: number|string|Decimal
+ y: number|string|Decimal +

+

See minus.

+ 
a = Decimal.sub(x, y)
+b = new Decimal(x).sub(y)
+a.equals(b)                    // true
+ + + +
tan.tan(x) ⇒ Decimal
+

x: number|string|Decimal

+

See tangent.

+ 
a = Decimal.tan(x)
+b = new Decimal(x).tan()
+a.equals(b)                    // true
+ + + +
tanh.tanh(x) ⇒ Decimal
+

x: number|string|Decimal

+

See hyperbolicTangent.

+ 
a = Decimal.tanh(x)
+b = new Decimal(x).tanh()
+a.equals(b)                    // true
+ + + +
trunc.trunc(x) ⇒ Decimal
+

x: number|string|Decimal

+

See truncated.

+ 
a = Decimal.trunc(x)
+b = new Decimal(x).trunc()
+a.equals(b)                    // true
+ + + + +

Properties

+

The properties of a Decimal constructor.

+ + + +
Configuration properties
+

+ The values of the configuration properties precision, + rounding, minE, + maxE, toExpNeg, + toExpPos, modulo, and + crypto are set using the + set method. +

+

+ As simple object properties they can be set directly without using + set, and it is fine to do so, but the values assigned + will not then be checked for validity. For example: +

+ 
Decimal.set({ precision: 0 })
+// '[DecimalError] Invalid argument: precision: 0'
+
+Decimal.precision = 0
+// No error is thrown and the results of calculations are unreliable
+ + + +
precision
+

+ number: integer, 1 to 1e+9 inclusive
+ Default value: 20 +

+

The maximum number of significant digits of the result of an operation.

+

+ All functions which return a Decimal will round the return value to precision + significant digits except Decimal, + absoluteValue, + ceil, floor, + negated, round, + toDecimalPlaces, + toNearest and + truncated. +

+

+ See Pi for the precision limit of the trigonometric methods. +

+ 
Decimal.set({ precision: 5 })
+Decimal.precision                  // 5
+ + + +
rounding
+

+ number: integer, 0 to 8 inclusive
+ Default value: 4 (ROUND_HALF_UP) +

+

+ The default rounding mode used when rounding the result of an operation to + precision significant digits, and when rounding the + return value of the round, + toBinary, + toDecimalPlaces, + toExponential, + toFixed, + toHexadecimal, + toNearest, + toOctal, + toPrecision and + toSignificantDigits methods. +

+

+ The rounding modes are available as enumerated properties of the + constructor. +

+ 
Decimal.set({ rounding: Decimal.ROUND_UP })
+Decimal.set({ rounding: 0 })       // equivalent
+Decimal.rounding                   // 0
+ + + +
minE
+

+ number: integer, -9e15 to 0 inclusive
+ Default value: -9e15 +

+

+ The negative exponent limit, i.e. the exponent value below which underflow to zero occurs. +

+

+ If the Decimal to be returned by a calculation would have an exponent lower than + minE then the value of that Decimal becomes zero. +

+ JavaScript numbers underflow to zero for exponents below -324. +

+ 
Decimal.set({ minE: -500 })
+Decimal.minE                       // -500
+new Decimal('1e-500')              // '1e-500'
+new Decimal('9.9e-501')            // '0'
+
+Decimal.set({ minE: -3 })
+new Decimal(0.001)                 // '0.01'       e is -3
+new Decimal(0.0001)                // '0'          e is -4
+

+ The smallest possible magnitude of a non-zero Decimal is 1e-9000000000000000 +

+ + + +
maxE
+

+ number: integer, 0 to 9e15 inclusive
+ Default value: 9e15 +

+

+ The positive exponent limit, i.e. the exponent value above which overflow to + Infinity occurs. +

+

+ If the Decimal to be returned by a calculation would have an exponent higher than + maxE then the value of that Decimal becomes Infinity. +

+ JavaScript numbers overflow to Infinity for exponents above 308. +

+ 
Decimal.set({ maxE: 500 })
+Decimal.maxE                       // 500
+new Decimal('9.999e500')           // '9.999e+500'
+new Decimal('1e501')               // 'Infinity'
+
+Decimal.set({ maxE: 4 })
+new Decimal(99999)                 // '99999'      e is 4
+new Decimal(100000)                // 'Infinity'
+

+ The largest possible magnitude of a finite Decimal is 9.999...e+9000000000000000 +

+ + + +
toExpNeg
+

+ number: integer, -9e15 to 0 inclusive
+ Default value: -7 +

+

+ The negative exponent value at and below which toString + returns exponential notation. +

+ 
Decimal.set({ toExpNeg: -7 })
+Decimal.toExpNeg                   // -7
+new Decimal(0.00000123)            // '0.00000123'       e is -6
+new Decimal(0.000000123)           // '1.23e-7'
+
+// Always return exponential notation:
+Decimal.set({ toExpNeg: 0 })
+

+ JavaScript numbers use exponential notation for negative exponents of -7 and + below. +

+

+ Regardless of the value of toExpNeg, the + toFixed method will always return a value in normal + notation and the toExponential method will always + return a value in exponential form. +

+ + + +
toExpPos
+

+ number: integer, 0 to 9e15 inclusive
+ Default value: 20 +

+

+ The positive exponent value at and above which toString + returns exponential notation. +

+ 
Decimal.set({ toExpPos: 2 })
+Decimal.toExpPos                   // 2
+new Decimal(12.3)                  // '12.3'        e is 1
+new Decimal(123)                   // '1.23e+2'
+
+// Always return exponential notation:
+Decimal.set({ toExpPos: 0 })
+

+ JavaScript numbers use exponential notation for positive exponents of 20 and + above. +

+

+ Regardless of the value of toExpPos, the + toFixed method will always return a value in normal + notation and the toExponential method will always + return a value in exponential form. +

+ + + +
modulo
+

+ number: integer, 0 to 9 inclusive
+ Default value: 1 (ROUND_DOWN) +

+

The modulo mode used when calculating the modulus: a mod n.

+

+ The quotient, q = a / n, is calculated according to the + rounding mode that corresponds to the chosen + modulo mode. +

+

The remainder, r, is calculated as: r = a - n * q.

+

+ The modes that are most commonly used for the modulus/remainder operation are shown in the + following table. Although the other rounding modes can + be used, they may not give useful results. +

+ + + + + + + + + + + + + + + + + + + + + + +
PropertyValueDescription
ROUND_UP0The remainder is positive if the dividend is negative, else is negative
ROUND_DOWN1 + The remainder has the same sign as the dividend.
+ This uses truncating division and matches the behaviour of JavaScript's remainder + operator %. +
ROUND_FLOOR3 + The remainder has the same sign as the divisor.
+ (This matches Python's % operator) +
ROUND_HALF_EVEN6The IEEE 754 remainder function
EUCLID9 + The remainder is always positive.
+ Euclidian division: q = sign(x) * floor(a / abs(x)). +
+

+ The rounding/modulo modes are available as enumerated properties of the Decimal constructor. +

+ 
Decimal.set({ modulo: Decimal.EUCLID })
+Decimal.set({ modulo: 9 })         // equivalent
+Decimal.modulo                     // 9
+ + + +
crypto
+

+ boolean: true/false
Default value: false +

+

+ The value that determines whether cryptographically-secure pseudo-random number generation is + used. +

+

See random.

+ 
+// Node.js
+global.crypto = require('crypto')
+
+Decimal.crypto                     // false
+Decimal.set({ crypto: true })
+Decimal.crypto                     // true
+ + + +
Rounding modes
+

+ The library's enumerated rounding modes are stored as properties of the Decimal constructor. +
They are not referenced internally by the library itself. +

+

Rounding modes 0 to 6 (inclusive) are the same as those of Java's BigDecimal class.

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
PropertyValueDescription
ROUND_UP0Rounds away from zero
ROUND_DOWN1Rounds towards zero
ROUND_CEIL2Rounds towards Infinity
ROUND_FLOOR3Rounds towards -Infinity
ROUND_HALF_UP4Rounds towards nearest neighbour.
If equidistant, rounds away from zero
ROUND_HALF_DOWN5Rounds towards nearest neighbour.
If equidistant, rounds towards zero
ROUND_HALF_EVEN6 + Rounds towards nearest neighbour.
If equidistant, rounds towards even neighbour +
ROUND_HALF_CEIL7Rounds towards nearest neighbour.
If equidistant, rounds towards Infinity
ROUND_HALF_FLOOR8Rounds towards nearest neighbour.
If equidistant, rounds towards -Infinity
EUCLID9Not a rounding mode, see modulo
+ 
Decimal.set({ rounding: Decimal.ROUND_CEIL })
+Decimal.set({ rounding: 2 })       // equivalent
+Decimal.rounding                   // 2
+ + + + +

INSTANCE

+ +

Methods

+

The methods inherited by a Decimal instance from its constructor's prototype object.

+

A Decimal instance is immutable in the sense that it is not changed by its methods.

+

Methods that return a Decimal can be chained:

+ 
x = new Decimal(2).times('999.999999999999999').dividedBy(4).ceil()
+

Methods do not round their arguments before execution.

+

+ The treatment of ±0, ±Infinity and NaN + is consistent with how JavaScript treats these values. +

+

+ Many method names have a shorter alias. (Internally, the library always uses the shorter + method names.) +

+ + + +
absoluteValue.abs() ⇒ Decimal
+

+ Returns a new Decimal whose value is the absolute value, i.e. the magnitude, of the value of + this Decimal. +

+

+ The return value is not affected by the value of the + precision setting. +

+ 
+x = new Decimal(-0.8)
+y = x.absoluteValue()         // '0.8'
+z = y.abs()                   // '0.8'
+ + + +
ceil.ceil() ⇒ Decimal
+

+ Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in + the direction of positive Infinity. +

+

+ The return value is not affected by the value of the + precision setting. +

+ 
+x = new Decimal(1.3)
+x.ceil()                      // '2'
+y = new Decimal(-1.8)
+y.ceil()                      // '-1'
+ + + +
comparedTo.cmp(x) ⇒ number
+

x: number|string|Decimal

+ + + + + + + + + + + + + + + + + + +
Returns 
1if the value of this Decimal is greater than the value of x
-1if the value of this Decimal is less than the value of x
0if this Decimal and x have the same value
NaNif the value of either this Decimal or x is NaN
+ 
+x = new Decimal(Infinity)
+y = new Decimal(5)
+x.comparedTo(y)                // 1
+x.comparedTo(x.minus(1))       // 0
+y.cmp(NaN)                     // NaN
+ + + +
cosine.cos() ⇒ Decimal
+

+ Returns a new Decimal whose value is the cosine of the value in radians of this Decimal, + rounded to precision significant digits using rounding + mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-1, 1] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0.25)
+x.cosine()                      // '0.96891242171064478414'
+y = new Decimal(-0.25)
+y.cos()                         // '0.96891242171064478414'
+ + + +
cubeRoot.cbrt() ⇒ Decimal
+

+ Returns a new Decimal whose value is the cube root of this Decimal, rounded to + precision significant digits using rounding mode + rounding. +

+

+ The return value will be correctly rounded, i.e. rounded as if the result was first calculated + to an infinite number of correct digits before rounding. +

+ 
+x = new Decimal(125)
+x.cubeRoot()                    // '5'
+y = new Decimal(3)
+y.cbrt()                        // '1.4422495703074083823'
+ + + +
decimalPlaces.dp() ⇒ number
+

+ Returns the number of decimal places, i.e. the number of digits after the decimal point, of + the value of this Decimal. +

+ 
+x = new Decimal(1.234)
+x.decimalPlaces()              // '3'
+y = new Decimal(987.654321)
+y.dp()                         // '6'
+ + + +
dividedBy.div(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the value of this Decimal divided by x, + rounded to precision significant digits using rounding + mode rounding. +

+ 
+x = new Decimal(355)
+y = new Decimal(113)
+x.dividedBy(y)             // '3.14159292035398230088'
+x.div(5)                   // '71'
+ + + +
+ dividedToIntegerBy.divToInt(x) ⇒ Decimal +
+

x: number|string|Decimal

+

+ Return a new Decimal whose value is the integer part of dividing this Decimal by + x, rounded to precision significant digits + using rounding mode rounding. +

+ 
+x = new Decimal(5)
+y = new Decimal(3)
+x.dividedToIntegerBy(y)     // '1'
+x.divToInt(0.7)             // '7'
+ + + +
equals.eq(x) ⇒ boolean
+

x: number|string|Decimal

+

+ Returns true if the value of this Decimal equals the value of x, + otherwise returns false.
As with JavaScript, NaN does not + equal NaN. +

+

Note: This method uses the cmp method internally.

+ 
+0 === 1e-324                     // true
+x = new Decimal(0)
+x.equals('1e-324')               // false
+new Decimal(-0).eq(x)            // true  ( -0 === 0 )
+
+y = new Decimal(NaN)
+y.equals(NaN)                    // false
+ + + +
floor.floor() ⇒ Decimal
+

+ Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in + the direction of negative Infinity. +

+

+ The return value is not affected by the value of the + precision setting. +

+ 
+x = new Decimal(1.8)
+x.floor()                   // '1'
+y = new Decimal(-1.3)
+y.floor()                   // '-2'
+ + + +
greaterThan.gt(x) ⇒ boolean
+

x: number|string|Decimal

+

+ Returns true if the value of this Decimal is greater than the value of + x, otherwise returns false. +

+

Note: This method uses the cmp method internally.

+ 
+0.1 > (0.3 - 0.2)                            // true
+x = new Decimal(0.1)
+x.greaterThan(Decimal(0.3).minus(0.2))       // false
+new Decimal(0).gt(x)                         // false
+ + + +
+ greaterThanOrEqualTo.gte(x) ⇒ boolean +
+

x: number|string|Decimal

+

+ Returns true if the value of this Decimal is greater than or equal to the value + of x, otherwise returns false. +

+

Note: This method uses the cmp method internally.

+ 
+(0.3 - 0.2) >= 0.1                       // false
+x = new Decimal(0.3).minus(0.2)
+x.greaterThanOrEqualTo(0.1)              // true
+new Decimal(1).gte(x)                    // true
+ + + +
hyperbolicCosine.cosh() ⇒ Decimal
+

+ Returns a new Decimal whose value is the hyperbolic cosine of the value in radians of this + Decimal, rounded to precision significant digits using + rounding mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [1, Infinity] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(1)
+x.hyperbolicCosine()                     // '1.5430806348152437785'
+y = new Decimal(0.5)
+y.cosh()                                 // '1.1276259652063807852'
+ + + +
hyperbolicSine.sinh() ⇒ Decimal
+

+ Returns a new Decimal whose value is the hyperbolic sine of the value in radians of this + Decimal, rounded to precision significant digits using + rounding mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-Infinity, Infinity] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(1)
+x.hyperbolicSine()                       // '1.1752011936438014569'
+y = new Decimal(0.5)
+y.sinh()                                 // '0.52109530549374736162'
+ + + +
hyperbolicTangent.tanh() ⇒ Decimal
+

+ Returns a new Decimal whose value is the hyperbolic tangent of the value in radians of this + Decimal, rounded to precision significant digits using + rounding mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-1, 1] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(1)
+x.hyperbolicTangent()                    // '0.76159415595576488812'
+y = new Decimal(0.5)
+y.tanh()                                 // '0.4621171572600097585'
+ + + +
inverseCosine.acos() ⇒ Decimal
+

+ Returns a new Decimal whose value is the inverse cosine in radians of the value of this + Decimal, rounded to precision significant digits using + rounding mode rounding. +

+

+ Domain: [-1, 1]
+ Range: [0, pi] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0)
+x.inverseCosine()                        // '1.5707963267948966192'
+y = new Decimal(0.5)
+y.acos()                                 // '1.0471975511965977462'
+ + + +
+ inverseHyperbolicCosine.acosh() ⇒ Decimal +
+

+ Returns a new Decimal whose value is the inverse hyperbolic cosine in radians of the value of + this Decimal, rounded to precision significant + digits using rounding mode rounding. +

+

+ Domain: [1, Infinity]
+ Range: [0, Infinity] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(5)
+x.inverseHyperbolicCosine()              // '2.2924316695611776878'
+y = new Decimal(50)
+y.acosh()                                // '4.6050701709847571595'
+ + + +
+ inverseHyperbolicSine.asinh() ⇒ Decimal +
+

+ Returns a new Decimal whose value is the inverse hyperbolic sine in radians of the value of + this Decimal, rounded to precision significant digits + using rounding mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-Infinity, Infinity] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(5)
+x.inverseHyperbolicSine()                // '2.3124383412727526203'
+y = new Decimal(50)
+y.asinh()                                // '4.6052701709914238266'
+ + + +
+ inverseHyperbolicTangent.atanh() ⇒ Decimal +
+

+ Returns a new Decimal whose value is the inverse hyperbolic tangent in radians of the value of + this Decimal, rounded to precision significant + digits using rounding mode rounding. +

+

+ Domain: [-1, 1]
+ Range: [-Infinity, Infinity] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0.5)
+x.inverseHyperbolicTangent()             // '0.5493061443340548457'
+y = new Decimal(0.75)
+y.atanh()                                // '0.97295507452765665255'
+ + + +
inverseSine.asin() ⇒ Decimal
+

+ Returns a new Decimal whose value is the inverse sine in radians of the value of this Decimal, + rounded to precision significant digits using rounding + mode rounding. +

+

+ Domain: [-1, 1]
+ Range: [-pi/2, pi/2] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0.5)
+x.inverseSine()                          // '0.52359877559829887308'
+y = new Decimal(0.75)
+y.asin()                                 // '0.84806207898148100805'
+ + + +
inverseTangent.atan() ⇒ Decimal
+

+ Returns a new Decimal whose value is the inverse tangent in radians of the value of this + Decimal, rounded to precision significant digits using + rounding mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-pi/2, pi/2] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0.5)
+x.inverseTangent()                       // '0.46364760900080611621'
+y = new Decimal(0.75)
+y.atan()                                 // '0.6435011087932843868'
+ + + +
isFinite.isFinite() ⇒ boolean
+

+ Returns true if the value of this Decimal is a finite number, otherwise returns + false.
+ The only possible non-finite values of a Decimal are NaN, Infinity + and -Infinity. +

+ 
+x = new Decimal(1)
+x.isFinite()                             // true
+y = new Decimal(Infinity)
+y.isFinite()                             // false
+

+ Note: The native method isFinite() can be used if + n <= Number.MAX_VALUE. +

+ + + +
isInteger.isInt() ⇒ boolean
+

+ Returns true if the value of this Decimal is a whole number, otherwise returns + false. +

+ 
+x = new Decimal(1)
+x.isInteger()                            // true
+y = new Decimal(123.456)
+y.isInt()                                // false
+ + + +
isNaN.isNaN() ⇒ boolean
+

+ Returns true if the value of this Decimal is NaN, otherwise returns + false. +

+ 
+x = new Decimal(NaN)
+x.isNaN()                                // true
+y = new Decimal('Infinity')
+y.isNaN()                                // false
+

Note: The native method isNaN() can also be used.

+ + + +
isNegative.isNeg() ⇒ boolean
+

+ Returns true if the value of this Decimal is negative, otherwise returns + false. +

+ 
+x = new Decimal(-0)
+x.isNegative()                           // true
+y = new Decimal(2)
+y.isNeg                                  // false
+

Note: n < 0 can be used if n <= -Number.MIN_VALUE.

+ + + +
isPositive.isPos() ⇒ boolean
+

+ Returns true if the value of this Decimal is positive, otherwise returns + false. +

+ 
+x = new Decimal(0)
+x.isPositive()                           // true
+y = new Decimal(-2)
+y.isPos                                  // false
+

Note: n < 0 can be used if n <= -Number.MIN_VALUE.

+ + + +
isZero.isZero() ⇒ boolean
+

+ Returns true if the value of this Decimal is zero or minus zero, otherwise + returns false. +

+ 
+x = new Decimal(-0)
+x.isZero() && x.isNeg()                  // true
+y = new Decimal(Infinity)
+y.isZero()                               // false
+

Note: n == 0 can be used if n >= Number.MIN_VALUE.

+ + + +
lessThan.lt(x) ⇒ boolean
+

x: number|string|Decimal

+

+ Returns true if the value of this Decimal is less than the value of + x, otherwise returns false. +

+

Note: This method uses the cmp method internally.

+ 
+(0.3 - 0.2) < 0.1                        // true
+x = new Decimal(0.3).minus(0.2)
+x.lessThan(0.1)                          // false
+new Decimal(0).lt(x)                     // true
+ + + +
lessThanOrEqualTo.lte(x) ⇒ boolean
+

x: number|string|Decimal

+

+ Returns true if the value of this Decimal is less than or equal to the value of + x, otherwise returns false. +

+

Note: This method uses the cmp method internally.

+ 
+0.1 <= (0.3 - 0.2)                              // false
+x = new Decimal(0.1)
+x.lessThanOrEqualTo(Decimal(0.3).minus(0.2))    // true
+new Decimal(-1).lte(x)                          // true
+ + + +
logarithm.log(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the base x logarithm of the value of this + Decimal, rounded to precision significant digits using + rounding mode rounding. +

+

+ If x is omitted, the base 10 logarithm of the value of this Decimal will be + returned. +

+ 
+x = new Decimal(1000)
+x.logarithm()                            // '3'
+y = new Decimal(256)
+y.log(2)                                 // '8'
+

+ The return value will almost always be correctly rounded, i.e. rounded as if the result + was first calculated to an infinite number of correct digits before rounding. If a result is + incorrectly rounded the maximum error will be 1 ulp (unit in the last + place). +

+

Logarithms to base 2 or 10 will always be correctly rounded.

+

+ See toPower for the circumstances in which this method may + return an incorrectly rounded result, and see naturalLogarithm + for the precision limit. +

+

The performance of this method degrades exponentially with increasing digits.

+ + + +
minus.minus(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the value of this Decimal minus x, rounded + to precision significant digits using rounding mode + rounding. +

+ 
+0.3 - 0.1                                // 0.19999999999999998
+x = new Decimal(0.3)
+x.minus(0.1)                             // '0.2'
+ + + +
modulo.mod(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the value of this Decimal modulo x, + rounded to precision significant digits using rounding + mode rounding. +

+

+ The value returned, and in particular its sign, is dependent on the value of the + modulo property of this Decimal's constructor. If it is + 1 (default value), the result will have the same sign as this Decimal, and it + will match that of Javascript's % operator (within the limits of double + precision) and BigDecimal's remainder method. +

+

+ See modulo for a description of the other modulo modes. +

+ 
+1 % 0.9                                  // 0.09999999999999998
+x = new Decimal(1)
+x.modulo(0.9)                            // '0.1'
+
+y = new Decimal(8)
+z = new Decimal(-3)
+Decimal.modulo = 1
+y.mod(z)                                 // '2'
+Decimal.modulo = 3
+y.mod(z)                                 // '-1'
+ + + +
naturalExponential.exp() ⇒ Decimal
+

+ Returns a new Decimal whose value is the base e (Euler's number, the base of the + natural logarithm) exponential of the value of this Decimal, rounded to + precision significant digits using rounding mode + rounding. +

+

+ The naturalLogarithm function is the inverse of this function. +

+ 
+x = new Decimal(1)
+x.naturalExponential()                   // '2.7182818284590452354'
+y = new Decimal(2)
+y.exp()                                  // '7.3890560989306502272'
+

+ The return value will be correctly rounded, i.e. rounded as if the result was first calculated + to an infinite number of correct digits before rounding. (The mathematical result of the + exponential function is non-terminating, unless its argument is 0). +

+

The performance of this method degrades exponentially with increasing digits.

+ + + +
naturalLogarithm.ln() ⇒ Decimal
+

+ Returns a new Decimal whose value is the natural logarithm of the value of this Decimal, + rounded to precision significant digits using rounding + mode rounding. +

+

+ The natural logarithm is the inverse of the naturalExponential + function. +

+ 
+x = new Decimal(10)
+x.naturalLogarithm()                     // '2.3026'
+y = new Decimal('1.23e+30')
+y.ln()                                   // '69.28'
+

+ The return value will be correctly rounded, i.e. rounded as if the result was first calculated + to an infinite number of correct digits before rounding. (The mathematical result of the + natural logarithm function is non-terminating, unless its argument is 1). +

+

+ Internally, this method is dependent on a constant whose value is the natural logarithm of + 10. This LN10 variable in the source code currently has a precision + of 1025 digits, meaning that this method can accurately calculate up to + 1000 digits. +

+

+ If more than 1000 digits is required then the precision of LN10 + will need to be increased to 25 digits more than is required - though, as the + time-taken by this method increases exponentially with increasing digits, it is unlikely to be + viable to calculate over 1000 digits anyway. +

+ + + +
negated.neg() ⇒ Decimal
+

+ Returns a new Decimal whose value is the value of this Decimal negated, i.e. multiplied by + -1. +

+

+ The return value is not affected by the value of the + precision setting. +

+ 
+x = new Decimal(1.8)
+x.negated()                              // '-1.8'
+y = new Decimal(-1.3)
+y.neg()                                  // '1.3'
+ + + +
plus.plus(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the value of this Decimal plus x, rounded to + precision significant digits using rounding mode + rounding. +

+ 
+0.1 + 0.2                                // 0.30000000000000004
+x = new Decimal(0.1)
+y = x.plus(0.2)                          // '0.3'
+new Decimal(0.7).plus(x).plus(y)         // '1.1'
+ + + +
precision.sd([include_zeros]) ⇒ number
+

Returns the number of significant digits of the value of this Decimal.

+

+ If include_zeros is true or 1 then any trailing zeros + of the integer part of a number are counted as significant digits, otherwise they are not. +

+ 
+x = new Decimal(1.234)
+x.precision()                            // '4'
+y = new Decimal(987000)
+y.sd()                                   // '3'
+y.sd(true)                               // '6'
+ + + +
round.round() ⇒ Decimal
+

+ Returns a new Decimal whose value is the value of this Decimal rounded to a whole number using + rounding mode rounding. +

+

+ To emulate Math.round, set rounding to + 7, i.e. ROUND_HALF_CEIL. +

+ 
+Decimal.set({ rounding: 4 })
+x = 1234.5
+x.round()                                // '1235'
+
+Decimal.rounding = Decimal.ROUND_DOWN
+x.round()                                // '1234'
+x                                        // '1234.5'
+ + + +
sine.sin() ⇒ Decimal
+

+ Returns a new Decimal whose value is the sine of the value in radians of this Decimal, + rounded to precision significant digits using rounding + mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-1, 1] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0.5)
+x.sine()                                 // '0.47942553860420300027'
+y = new Decimal(0.75)
+y.sin()                                  // '0.68163876002333416673'
+ + + +
squareRoot.sqrt() ⇒ Decimal
+

+ Returns a new Decimal whose value is the square root of this Decimal, rounded to + precision significant digits using rounding mode + rounding. +

+

+ The return value will be correctly rounded, i.e. rounded as if the result was first calculated + to an infinite number of correct digits before rounding. +

+

+ This method is much faster than using the toPower method with + an exponent of 0.5. +

+ 
+x = new Decimal(16)
+x.squareRoot()                           // '4'
+y = new Decimal(3)
+y.sqrt()                                 // '1.73205080756887729353'
+y.sqrt().eq( y.pow(0.5) )                // true
+ + + +
tangent.tan() ⇒ Decimal
+

+ Returns a new Decimal whose value is the tangent of the value in radians of this Decimal, + rounded to precision significant digits using rounding + mode rounding. +

+

+ Domain: [-Infinity, Infinity]
+ Range: [-Infinity, Infinity] +

+

See Pi for the precision limit of this method.

+ 
+x = new Decimal(0.5)
+x.tangent()                              // '0.54630248984379051326'
+y = new Decimal(0.75)
+y.tan()                                  // '0.93159645994407246117'
+ + + +
times.times(x) ⇒ Decimal
+

x: number|string|Decimal

+

+ Returns a new Decimal whose value is the value of this Decimal times x, + rounded to precision significant digits using rounding + mode rounding. +

+ 
+0.6 * 3                                  // 1.7999999999999998
+x = new Decimal(0.6)
+y = x.times(3)                           // '1.8'
+new Decimal('7e+500').times(y)           // '1.26e+501'
+ + + +
+ toBinary.toBinary([sd [, rm]]) ⇒ string +
+

+ sd: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a string representing the value of this Decimal in binary, rounded to sd + significant digits using rounding mode rm. +

+

+ If sd is defined, the return value will use binary exponential notation. +

+

+ If sd is omitted, the return value will be rounded to + precision significant digits. +

+

+ If rm is omitted, rounding mode rounding + will be used. +

+

Throws on an invalid sd or rm value.

+ 
+x = new Decimal(256)
+x.toBinary()                             // '0b100000000'
+x.toBinary(1)                            // '0b1p+8'
+ + + +
+ toDecimalPlaces.toDP([dp [, rm]]) ⇒ Decimal +
+

+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive. +

+

+ Returns a new Decimal whose value is the value of this Decimal rounded to dp + decimal places using rounding mode rm. +

+

+ If dp is omitted, the return value will have the same value as this Decimal. +

+

+ If rm is omitted, rounding mode rounding + is used. +

+

Throws on an invalid dp or rm value.

+ 
+x = new Decimal(12.34567)
+x.toDecimalPlaces(0)                      // '12'
+x.toDecimalPlaces(1, Decimal.ROUND_UP)    // '12.4'
+
+y = new Decimal(9876.54321)
+y.toDP(3)                           // '9876.543'
+y.toDP(1, 0)                        // '9876.6'
+y.toDP(1, Decimal.ROUND_DOWN)       // '9876.5'
+ + + +
+ toExponential.toExponential([dp [, rm]]) ⇒ string +
+

+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a string representing the value of this Decimal in exponential notation rounded + using rounding mode rm to dp decimal places, i.e with one digit + before the decimal point and dp digits after it. +

+

+ If the value of this Decimal in exponential notation has fewer than dp fraction + digits, the return value will be appended with zeros accordingly. +

+

+ If dp is omitted, the number of digits after the decimal point defaults to the + minimum number of digits necessary to represent the value exactly. +

+

+ If rm is omitted, rounding mode rounding is + used. +

+

Throws on an invalid dp or rm value.

+ 
+x = 45.6
+y = new Decimal(x)
+x.toExponential()                        // '4.56e+1'
+y.toExponential()                        // '4.56e+1'
+x.toExponential(0)                       // '5e+1'
+y.toExponential(0)                       // '5e+1'
+x.toExponential(1)                       // '4.6e+1'
+y.toExponential(1)                       // '4.6e+1'
+y.toExponential(1, Decimal.ROUND_DOWN)   // '4.5e+1'
+x.toExponential(3)                       // '4.560e+1'
+y.toExponential(3)                       // '4.560e+1'
+ + + +
+ toFixed.toFixed([dp [, rm]]) ⇒ string +
+

+ dp: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a string representing the value of this Decimal in normal (fixed-point) notation + rounded to dp decimal places using rounding mode rm. +

+

+ If the value of this Decimal in normal notation has fewer than dp fraction + digits, the return value will be appended with zeros accordingly. +

+

+ Unlike Number.prototype.toFixed, which returns exponential notation if a number + is greater or equal to 1021, this method will always return normal + notation. +

+

+ If dp is omitted, the return value will be unrounded and in normal notation. This + is unlike Number.prototype.toFixed, which returns the value to zero decimal + places, but is useful when because of the current + toExpNeg or + toExpNeg values, + toString returns exponential notation. +

+

+ If rm is omitted, rounding mode rounding is + used. +

+

Throws on an invalid dp or rm value.

+ 
+x = 3.456
+y = new Decimal(x)
+x.toFixed()                       // '3'
+y.toFixed()                       // '3.456'
+y.toFixed(0)                      // '3'
+x.toFixed(2)                      // '3.46'
+y.toFixed(2)                      // '3.46'
+y.toFixed(2, Decimal.ROUND_DOWN)  // '3.45'
+x.toFixed(5)                      // '3.45600'
+y.toFixed(5)                      // '3.45600'
+ + + +
+ toFraction + .toFraction([max_denominator]) ⇒ [Decimal, Decimal] +
+

+ max_denominator: number|string|Decimal: 1 >= integer < + Infinity +

+

+ Returns an array of two Decimals 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 max_denominator. +

+

+ If a maximum denominator is omitted, the denominator will be the lowest value necessary to + represent the number exactly. +

+

Throws on an invalid max_denominator value.

+ 
+x = new Decimal(1.75)
+x.toFraction()                       // '7, 4'
+
+pi = new Decimal('3.14159265358')
+pi.toFraction()                      // '157079632679,50000000000'
+pi.toFraction(100000)                // '312689, 99532'
+pi.toFraction(10000)                 // '355, 113'
+pi.toFraction(100)                   // '311, 99'
+pi.toFraction(10)                    // '22, 7'
+pi.toFraction(1)                     // '3, 1'
+ + + +
+ toHexadecimal.toHex([sd [, rm]]) ⇒ string +
+

+ sd: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a string representing the value of this Decimal in hexadecimal, rounded to + sd significant digits using rounding mode rm. +

+

+ If sd is defined, the return value will use binary exponential notation. +

+

+ If sd is omitted, the return value will be rounded to + precision significant digits. +

+

+ If rm is omitted, rounding mode rounding + will be used. +

+

Throws on an invalid sd or rm value.

+ 
+x = new Decimal(256)
+x.toHexadecimal()                        // '0x100'
+x.toHex(1)                               // '0x1p+8'
+ + + +
toJSON.toJSON() ⇒ string
+

As valueOf.

+ + + +
+ toNearest.toNearest(x [, rm]) ⇒ Decimal +
+

+ x: number|string|Decimal
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a new Decimal whose value is the nearest multiple of x in the direction + of rounding mode rm, or 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 x is NaN, in which case the return value will be also be + NaN. +

+

+ The return value is not affected by the value of the + precision setting. +

+ 
+x = new Decimal(1.39)
+x.toNearest(0.25)                        // '1.5'
+
+y = new Decimal(9.499)
+y.toNearest(0.5, Decimal.ROUND_UP)       // '9.5'
+y.toNearest(0.5, Decimal.ROUND_DOWN)     // '9'
+ + + +
toNumber.toNumber() ⇒ number
+

Returns the value of this Decimal converted to a primitive number.

+

+ Type coercion with, for example, JavaScript's unary plus operator will also work, except that + a Decimal with the value minus zero will convert to positive zero. +

+ 
+x = new Decimal(456.789)
+x.toNumber()                   // 456.789
++x                             // 456.789
+
+y = new Decimal('45987349857634085409857349856430985')
+y.toNumber()                   // 4.598734985763409e+34
+
+z = new Decimal(-0)
+1 / +z                         // Infinity
+1 / z.toNumber()               // -Infinity
+ + + +
+ toOctal.toOctal([sd [, rm]]) ⇒ string +
+

+ sd: number: integer, 0 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a string representing the value of this Decimal in octal, rounded to sd + significant digits using rounding mode rm. +

+

+ If sd is defined, the return value will use binary exponential notation. +

+

+ If sd is omitted, the return value will be rounded to + precision significant digits. +

+

+ If rm is omitted, rounding mode rounding + will be used. +

+

Throws on an invalid sd or rm value.

+ 
+x = new Decimal(256)
+x.toOctal()                              // '0o400'
+x.toOctal(1)                             // '0o1p+8'
+ + + +
toPower.pow(x) ⇒ Decimal
+

x: number|string|Decimal: integer or non-integer

+

+ Returns a new Decimal whose value is the value of this Decimal raised to the power + x, rounded to precision significant digits + using rounding mode rounding. +

+

+ The performance of this method degrades exponentially with increasing digits. For + non-integer exponents in particular, the performance of this method may not be adequate. +

+ 
+Math.pow(0.7, 2)               // 0.48999999999999994
+x = new Decimal(0.7)
+x.toPower(2)                   // '0.49'
+new Decimal(3).pow(-2)         // '0.11111111111111111111'
+
+new Decimal(1217652.23).pow('98765.489305603941')
+// '4.8227010515242461181e+601039'
+

Is the pow function guaranteed to be correctly rounded?

+

+ The return value will almost always be correctly rounded, i.e. rounded as if the result + was first calculated to an infinite number of correct digits before rounding. If a result is + incorrectly rounded the maximum error will be 1 ulp (unit in the last + place). +

+

For non-integer and larger exponents this method uses the formula

+
xy = exp(y*ln(x))
+

+ As the mathematical return values of the exp and + ln functions are both non-terminating (excluding arguments of + 0 or 1), the values of the Decimals returned by the functions as + implemented by this library will necessarily be rounded approximations, which means that there + can be no guarantee of correct rounding when they are combined in the above formula. +

+

+ The return value may, depending on the rounding mode, be incorrectly rounded only if the first + 15 rounding digits are 15 zeros (and there are non-zero digits + following at some point), or 15 nines, or a 5 or 4 + followed by 14 nines. +

+

+ Therefore, assuming the first 15 rounding digits are each equally likely to be + any digit, 0-9, the probability of an incorrectly rounded result is less than + 1 in 250,000,000,000,000. +

+

+ An example of incorrect rounding: +

+ 
+Decimal.set({ precision: 20, rounding: 1 })
+new Decimal(28).pow('6.166675020000903537297764507632802193308677149')
+// 839756321.64088511
+

As the exact mathematical result begins

+ 
839756321.6408851099999999999999999999999999998969466049426031167...
+

+ and the rounding mode is set to ROUND_DOWN, the correct + return value should be +

+ 
839756321.64088510999
+ + + +
+ toPrecision.toPrecision([sd [, rm]]) ⇒ string +
+

+ sd: number: integer, 1 to 1e+9 inclusive
+ rm: number: integer, 0 to 8 inclusive +

+

+ Returns a string representing the value of this Decimal rounded to sd significant + digits using rounding mode rm. +

+

+ If sd is less than the number of digits necessary to represent the integer part + of the value in normal (fixed-point) notation, then exponential notation is used. +

+

+ If sd is omitted, the return value is the same as + toString. +

+

+ If rm is omitted, rounding mode rounding is + used. +

+

Throws on an invalid sd or rm value.

+ 
+x = 45.6
+y = new Decimal(x)
+x.toPrecision()                          // '45.6'
+y.toPrecision()                          // '45.6'
+x.toPrecision(1)                         // '5e+1'
+y.toPrecision(1)                         // '5e+1'
+y.toPrecision(2, Decimal.ROUND_UP)       // '4.6e+1'
+y.toPrecision(2, Decimal.DOWN)           // '4.5e+1'
+x.toPrecision(5)                         // '45.600'
+y.toPrecision(5)                         // '45.600'
+ + + +
+ toSignificantDigits.toSD([sd [, rm]]) ⇒ Decimal +
+

+ sd: number: integer, 1 to 1e+9 inclusive.
+ rm: number: integer, 0 to 8 inclusive. +

+

+ Returns a new Decimal whose value is the value of this Decimal rounded to sd + significant digits using rounding mode rm. +

+

+ If sd is omitted, the return value will be rounded to + precision significant digits. +

+

+ If rm is omitted, rounding mode rounding + will be used. +

+

Throws on an invalid sd or rm value.

+ 
+Decimal.set({ precision: 5, rounding: 4 })
+x = new Decimal(9876.54321)
+
+x.toSignificantDigits()                          // '9876.5'
+x.toSignificantDigits(6)                         // '9876.54'
+x.toSignificantDigits(6, Decimal.ROUND_UP)       // '9876.55'
+x.toSD(2)                                        // '9900'
+x.toSD(2, 1)                                     // '9800'
+x                                                // '9876.54321'
+ + + +
toString.toString() ⇒ string
+

Returns a string representing the value of this Decimal.

+

+ If this Decimal has a positive exponent that is equal to or greater than + toExpPos, or a negative exponent equal to or less than + toExpNeg, then exponential notation will be returned. +

+ 
+x = new Decimal(750000)
+x.toString()                             // '750000'
+Decimal.set({ toExpPos: 5 })
+x.toString()                             // '7.5e+5'
+
+Decimal.set({ precision: 4 })
+y = new Decimal('1.23456789')
+y.toString()                             // '1.23456789'
+ + + +
truncated.trunc() ⇒ Decimal
+

+ Returns a new Decimal whose value is the value of this Decimal truncated to a whole number. +

+

+ The return value is not affected by the value of the + precision setting. +

+ 
+x = new Decimal(123.456)
+x.truncated()                            // '123'
+y = new Decimal(-12.3)
+y.trunc()                                // '-12'
+ + + +
valueOf.valueOf() ⇒ string
+

As toString, but zero is signed.

+ 
+x = new Decimal(-0)
+x.valueOf()                              // '-0'
+ + + + + + +

Properties

+

+ The value of a Decimal is stored in a normalised base 10000000 floating point + format. +

+

+ A Decimal instance is an object with three properties: +

+ + + + + + + + + + + + + + + + + + + + + + + + + +
PropertyDescriptionTypeValue
ddigitsnumber[] Array of integers, each 0 - 1e7, or null
eexponentnumberInteger, -9e15 to 9e15 inclusive, or NaN
ssignnumber-1, 1, or NaN
+

All the properties are best considered to be read-only.

+

+ As with JavaScript numbers, the original exponent and fractional trailing zeros of a value + are not preserved. +

+ 
+x = new Decimal(0.123)                   // '0.123'
+x.toExponential()                        // '1.23e-1'
+x.d                                      // [ 1230000 ]
+x.e                                      // -1
+x.s                                      // 1
+
+y = new Number(-123.4567000e+2)          // '-12345.67'
+y.toExponential()                        // '-1.234567e+4'
+z = new Decimal('-123.4567000e+2')       // '-12345.67'
+z.toExponential()                        // '-1.234567e+4'
+z.d                                      // [ 12345, 6700000 ]
+z.e                                      // 4
+z.s                                      // -1
+ + + +

Zero, NaN and Infinity

+

+ The table below shows how ±0, NaN and + ±Infinity are stored. +

+ + + + + + + + + + + + + + + + + + + + + + + + + +
±0NaN±Infinity
 d [0]nullnull
 e 0NaNNaN
 s ±1NaN±1
+ 
+x = new Number(-0)                       // 0
+1 / x == -Infinity                       // true
+
+y = new Decimal(-0)
+y.d                                      // '0' ( [0].toString() )
+y.e                                      //  0
+y.s                                      // -1
+y.toString()                             // '0'
+y.valueOf()                              // '-0'
+ + + +

Errors

+

+ The errors that are thrown are generic Error objects whose message + property begins with "[DecimalError]". +

+

To determine if an exception is a Decimal Error:

+ 
+try {
+    // ...
+} catch (e) {
+    if ( e instanceof Error && /DecimalError/.test(e.message) ) {
+        // ...
+    }
+}
+ + + +

Pi

+

+ The maximum precision of the trigonometric methods is dependent on the internal value of the + constant pi, which is defined as the string PI near the top of the source file. +

+

+ It has a precision of 1025 digits, meaning that the trigonometric methods + can calculate up to just over 1000 digits, but the actual figure depends on the + precision of the argument passed to them. To calculate the actual figure use: +

+

maximum_result_precision = 1000 - argument_precision

+ For example, the following both work fine: + 
+Decimal.set({precision: 991}).tan(123456789)
+Decimal.set({precision: 9}).tan(991_digit_number)
+

+ as, for each, the result precision plus the argument precision, i.e. 991 + 9 and + 9 + 991, is less than or equal to 1000. +

+

+ If greater precision is required then the value of PI will need to be extended to + about 25 digits more than the precision required. The time taken by the methods + will then be the limiting factor. +

+

+ The value can also be shortened to reduce the size of the source file if such high precision + is not required. +

+

To get the value of pi:

+ 
+pi = Decimal.acos(-1)
+ + + +

FAQ

+
Why are trailing fractional zeros removed from Decimals?
+

+ Some arbitrary-precision libraries retain trailing fractional zeros as they can indicate the + precision of a value. This can be useful but the results of arithmetic operations can be + misleading. +

+ 
+x = new BigDecimal("1.0")
+y = new BigDecimal("1.1000")
+z = x.add(y)                      // 2.1000
+
+x = new BigDecimal("1.20")
+y = new BigDecimal("3.45000")
+z = x.multiply(y)                 // 4.1400000
+

+ To specify the precision of a value is to specify that the value lies + within a certain range. +

+

+ In the first example, x has a value of 1.0. The trailing zero shows + the precision of the value, implying that it is in the range 0.95 to + 1.05. Similarly, the precision indicated by the trailing zeros of y + indicates that the value is in the range 1.09995 to 1.10005. +

+

+ If we add the two lowest values in the ranges we have, 0.95 + 1.09995 = 2.04995, + and if we add the two highest values we have, 1.05 + 1.10005 = 2.15005, so the + range of the result of the addition implied by the precision of its operands is + 2.04995 to 2.15005. +

+

+ The result given by BigDecimal of 2.1000 however, indicates that the value is in + the range 2.09995 to 2.10005 and therefore the precision implied by + its trailing zeros may be misleading. +

+

+ In the second example, the true range is 4.122744 to 4.157256 yet + the BigDecimal answer of 4.1400000 indicates a range of 4.13999995 + to 4.14000005. Again, the precision implied by the trailing zeros may be + misleading. +

+

+ This library, like binary floating point and most calculators, does not retain trailing + fractional zeros. Instead, the toExponential, toFixed and + toPrecision methods enable trailing zeros to be added if and when required.
+

+
+ + + diff --git a/node_modules/decimal.js/package.json b/node_modules/decimal.js/package.json new file mode 100644 index 0000000..e294b28 --- /dev/null +++ b/node_modules/decimal.js/package.json @@ -0,0 +1,65 @@ +{ + "_from": "decimal.js@^10.2.0", + "_id": "decimal.js@10.2.0", + "_inBundle": false, + "_integrity": "sha512-vDPw+rDgn3bZe1+F/pyEwb1oMG2XTlRVgAa6B4KccTEpYgF8w6eQllVbQcfIJnZyvzFtFpxnpGtx8dd7DJp/Rw==", + "_location": "/decimal.js", + "_phantomChildren": {}, + "_requested": { + "type": "range", + "registry": true, + "raw": "decimal.js@^10.2.0", + "name": "decimal.js", + "escapedName": "decimal.js", + "rawSpec": "^10.2.0", + "saveSpec": null, + "fetchSpec": "^10.2.0" + }, + "_requiredBy": [ + "/jsdom" + ], + "_resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-10.2.0.tgz", + "_shasum": "39466113a9e036111d02f82489b5fd6b0b5ed231", + "_spec": "decimal.js@^10.2.0", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\jsdom", + "author": { + "name": "Michael Mclaughlin", + "email": "M8ch88l@gmail.com" + }, + "browser": "decimal.js", + "bugs": { + "url": "https://github.com/MikeMcl/decimal.js/issues" + }, + "bundleDependencies": false, + "deprecated": false, + "description": "An arbitrary-precision Decimal type for JavaScript.", + "homepage": "https://github.com/MikeMcl/decimal.js#readme", + "keywords": [ + "arbitrary", + "precision", + "arithmetic", + "big", + "number", + "decimal", + "float", + "biginteger", + "bigdecimal", + "bignumber", + "bigint", + "bignum" + ], + "license": "MIT", + "main": "decimal", + "module": "decimal.mjs", + "name": "decimal.js", + "repository": { + "type": "git", + "url": "git+https://github.com/MikeMcl/decimal.js.git" + }, + "scripts": { + "build": "uglifyjs decimal.js --source-map url=decimal.min.js.map -c -m -o decimal.min.js", + "test": "node ./test/test.js" + }, + "types": "decimal.d.ts", + "version": "10.2.0" +} diff --git a/node_modules/deep-is/package.json b/node_modules/deep-is/package.json index a4ebe68..c0e88e1 100644 --- a/node_modules/deep-is/package.json +++ b/node_modules/deep-is/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/deep-is/-/deep-is-0.1.3.tgz", "_shasum": "b369d6fb5dbc13eecf524f91b070feedc357cf34", "_spec": "deep-is@~0.1.3", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\optionator", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\optionator", "author": { "name": "Thorsten Lorenz", "email": "thlorenz@gmx.de", diff --git a/node_modules/delayed-stream/package.json b/node_modules/delayed-stream/package.json index dc1b5b9..6b546f8 100644 --- a/node_modules/delayed-stream/package.json +++ b/node_modules/delayed-stream/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/delayed-stream/-/delayed-stream-1.0.0.tgz", "_shasum": "df3ae199acadfb7d440aaae0b29e2272b24ec619", "_spec": "delayed-stream@~1.0.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\combined-stream", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\combined-stream", "author": { "name": "Felix Geisendörfer", "email": "felix@debuggable.com", diff --git a/node_modules/domexception/README.md b/node_modules/domexception/README.md index 0e9eef3..fc1ef59 100644 --- a/node_modules/domexception/README.md +++ b/node_modules/domexception/README.md @@ -17,3 +17,15 @@ console.assert(e2.code === 7); console.assert(DOMException.INUSE_ATTRIBUTE_ERR === 10); ``` + +## APIs + +This package exposes two flavors of the `DOMException` interface depending on the imported module. + +### `domexception` module + +This module default-exports the `DOMException` interface constructor. + +### `domexception/webidl2js-wrapper` module + +This module exports the `DOMException` [interface wrapper API](https://github.com/jsdom/webidl2js#for-interfaces) generated by [webidl2js](https://github.com/jsdom/webidl2js). diff --git a/node_modules/domexception/index.js b/node_modules/domexception/index.js new file mode 100644 index 0000000..6651596 --- /dev/null +++ b/node_modules/domexception/index.js @@ -0,0 +1,7 @@ +"use strict"; +const DOMException = require("./webidl2js-wrapper.js"); + +const sharedGlobalObject = { Error }; +DOMException.install(sharedGlobalObject); + +module.exports = sharedGlobalObject.DOMException; diff --git a/node_modules/domexception/lib/DOMException-impl.js b/node_modules/domexception/lib/DOMException-impl.js index 7852f92..7395751 100644 --- a/node_modules/domexception/lib/DOMException-impl.js +++ b/node_modules/domexception/lib/DOMException-impl.js @@ -3,7 +3,7 @@ const legacyErrorCodes = require("./legacy-error-codes.json"); const idlUtils = require("./utils.js"); exports.implementation = class DOMExceptionImpl { - constructor([message, name]) { + constructor(globalObject, [message, name]) { this.name = name; this.message = message; } diff --git a/node_modules/domexception/lib/DOMException.js b/node_modules/domexception/lib/DOMException.js index 768ad24..b63c31d 100644 --- a/node_modules/domexception/lib/DOMException.js +++ b/node_modules/domexception/lib/DOMException.js @@ -4,303 +4,20 @@ const conversions = require("webidl-conversions"); const utils = require("./utils.js"); const impl = utils.implSymbol; - -function DOMException() { - const args = []; - for (let i = 0; i < arguments.length && i < 2; ++i) { - args[i] = arguments[i]; - } - - if (args[0] !== undefined) { - args[0] = conversions["DOMString"](args[0], { context: "Failed to construct 'DOMException': parameter 1" }); - } else { - args[0] = ""; - } - - if (args[1] !== undefined) { - args[1] = conversions["DOMString"](args[1], { context: "Failed to construct 'DOMException': parameter 2" }); - } else { - args[1] = "Error"; - } - - iface.setup(this, args); -} - -Object.defineProperty(DOMException, "prototype", { - value: DOMException.prototype, - writable: false, - enumerable: false, - configurable: false -}); - -Object.defineProperty(DOMException.prototype, "name", { - get() { - return this[impl]["name"]; - }, - - enumerable: true, - configurable: true -}); - -Object.defineProperty(DOMException.prototype, "message", { - get() { - return this[impl]["message"]; - }, - - enumerable: true, - configurable: true -}); - -Object.defineProperty(DOMException.prototype, "code", { - get() { - return this[impl]["code"]; - }, - - enumerable: true, - configurable: true -}); - -Object.defineProperty(DOMException, "INDEX_SIZE_ERR", { - value: 1, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INDEX_SIZE_ERR", { - value: 1, - enumerable: true -}); - -Object.defineProperty(DOMException, "DOMSTRING_SIZE_ERR", { - value: 2, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "DOMSTRING_SIZE_ERR", { - value: 2, - enumerable: true -}); - -Object.defineProperty(DOMException, "HIERARCHY_REQUEST_ERR", { - value: 3, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "HIERARCHY_REQUEST_ERR", { - value: 3, - enumerable: true -}); - -Object.defineProperty(DOMException, "WRONG_DOCUMENT_ERR", { - value: 4, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "WRONG_DOCUMENT_ERR", { - value: 4, - enumerable: true -}); - -Object.defineProperty(DOMException, "INVALID_CHARACTER_ERR", { - value: 5, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INVALID_CHARACTER_ERR", { - value: 5, - enumerable: true -}); - -Object.defineProperty(DOMException, "NO_DATA_ALLOWED_ERR", { - value: 6, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "NO_DATA_ALLOWED_ERR", { - value: 6, - enumerable: true -}); - -Object.defineProperty(DOMException, "NO_MODIFICATION_ALLOWED_ERR", { - value: 7, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "NO_MODIFICATION_ALLOWED_ERR", { - value: 7, - enumerable: true -}); - -Object.defineProperty(DOMException, "NOT_FOUND_ERR", { - value: 8, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "NOT_FOUND_ERR", { - value: 8, - enumerable: true -}); - -Object.defineProperty(DOMException, "NOT_SUPPORTED_ERR", { - value: 9, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "NOT_SUPPORTED_ERR", { - value: 9, - enumerable: true -}); - -Object.defineProperty(DOMException, "INUSE_ATTRIBUTE_ERR", { - value: 10, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INUSE_ATTRIBUTE_ERR", { - value: 10, - enumerable: true -}); - -Object.defineProperty(DOMException, "INVALID_STATE_ERR", { - value: 11, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INVALID_STATE_ERR", { - value: 11, - enumerable: true -}); - -Object.defineProperty(DOMException, "SYNTAX_ERR", { - value: 12, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "SYNTAX_ERR", { - value: 12, - enumerable: true -}); - -Object.defineProperty(DOMException, "INVALID_MODIFICATION_ERR", { - value: 13, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INVALID_MODIFICATION_ERR", { - value: 13, - enumerable: true -}); - -Object.defineProperty(DOMException, "NAMESPACE_ERR", { - value: 14, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "NAMESPACE_ERR", { - value: 14, - enumerable: true -}); - -Object.defineProperty(DOMException, "INVALID_ACCESS_ERR", { - value: 15, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INVALID_ACCESS_ERR", { - value: 15, - enumerable: true -}); - -Object.defineProperty(DOMException, "VALIDATION_ERR", { - value: 16, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "VALIDATION_ERR", { - value: 16, - enumerable: true -}); - -Object.defineProperty(DOMException, "TYPE_MISMATCH_ERR", { - value: 17, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "TYPE_MISMATCH_ERR", { - value: 17, - enumerable: true -}); - -Object.defineProperty(DOMException, "SECURITY_ERR", { - value: 18, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "SECURITY_ERR", { - value: 18, - enumerable: true -}); - -Object.defineProperty(DOMException, "NETWORK_ERR", { - value: 19, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "NETWORK_ERR", { - value: 19, - enumerable: true -}); - -Object.defineProperty(DOMException, "ABORT_ERR", { - value: 20, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "ABORT_ERR", { - value: 20, - enumerable: true -}); - -Object.defineProperty(DOMException, "URL_MISMATCH_ERR", { - value: 21, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "URL_MISMATCH_ERR", { - value: 21, - enumerable: true -}); - -Object.defineProperty(DOMException, "QUOTA_EXCEEDED_ERR", { - value: 22, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "QUOTA_EXCEEDED_ERR", { - value: 22, - enumerable: true -}); - -Object.defineProperty(DOMException, "TIMEOUT_ERR", { - value: 23, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "TIMEOUT_ERR", { - value: 23, - enumerable: true -}); - -Object.defineProperty(DOMException, "INVALID_NODE_TYPE_ERR", { - value: 24, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "INVALID_NODE_TYPE_ERR", { - value: 24, - enumerable: true -}); - -Object.defineProperty(DOMException, "DATA_CLONE_ERR", { - value: 25, - enumerable: true -}); -Object.defineProperty(DOMException.prototype, "DATA_CLONE_ERR", { - value: 25, - enumerable: true -}); - -Object.defineProperty(DOMException.prototype, Symbol.toStringTag, { - value: "DOMException", - writable: false, - enumerable: false, - configurable: true -}); +const ctorRegistry = utils.ctorRegistrySymbol; const iface = { - mixedInto: [], + // When an interface-module that implements this interface as a mixin is loaded, it will append its own `.is()` + // method into this array. It allows objects that directly implements *those* interfaces to be recognized as + // implementing this mixin interface. + _mixedIntoPredicates: [], is(obj) { if (obj) { - if (obj[impl] instanceof Impl.implementation) { + if (utils.hasOwn(obj, impl) && obj[impl] instanceof Impl.implementation) { return true; } - for (let i = 0; i < module.exports.mixedInto.length; ++i) { - if (obj instanceof module.exports.mixedInto[i]) { + for (const isMixedInto of module.exports._mixedIntoPredicates) { + if (isMixedInto(obj)) { return true; } } @@ -314,8 +31,8 @@ const iface = { } const wrapper = utils.wrapperForImpl(obj); - for (let i = 0; i < module.exports.mixedInto.length; ++i) { - if (wrapper instanceof module.exports.mixedInto[i]) { + for (const isMixedInto of module.exports._mixedIntoPredicates) { + if (isMixedInto(wrapper)) { return true; } } @@ -329,40 +46,160 @@ const iface = { throw new TypeError(`${context} is not of type 'DOMException'.`); }, - create(constructorArgs, privateData) { - let obj = Object.create(DOMException.prototype); - this.setup(obj, constructorArgs, privateData); + create(globalObject, constructorArgs, privateData) { + if (globalObject[ctorRegistry] === undefined) { + throw new Error("Internal error: invalid global object"); + } + + const ctor = globalObject[ctorRegistry]["DOMException"]; + if (ctor === undefined) { + throw new Error("Internal error: constructor DOMException is not installed on the passed global object"); + } + + let obj = Object.create(ctor.prototype); + obj = iface.setup(obj, globalObject, constructorArgs, privateData); return obj; }, - createImpl(constructorArgs, privateData) { - let obj = Object.create(DOMException.prototype); - this.setup(obj, constructorArgs, privateData); + createImpl(globalObject, constructorArgs, privateData) { + const obj = iface.create(globalObject, constructorArgs, privateData); return utils.implForWrapper(obj); }, _internalSetup(obj) {}, - setup(obj, constructorArgs, privateData) { - if (!privateData) privateData = {}; - + setup(obj, globalObject, constructorArgs = [], privateData = {}) { privateData.wrapper = obj; - this._internalSetup(obj); + iface._internalSetup(obj); Object.defineProperty(obj, impl, { - value: new Impl.implementation(constructorArgs, privateData), - writable: false, - enumerable: false, + value: new Impl.implementation(globalObject, constructorArgs, privateData), configurable: true }); + obj[impl][utils.wrapperSymbol] = obj; if (Impl.init) { Impl.init(obj[impl], privateData); } + return obj; }, - interface: DOMException, - expose: { - Window: { DOMException }, - Worker: { DOMException } + + install(globalObject) { + class DOMException { + constructor() { + const args = []; + { + let curArg = arguments[0]; + if (curArg !== undefined) { + curArg = conversions["DOMString"](curArg, { context: "Failed to construct 'DOMException': parameter 1" }); + } else { + curArg = ""; + } + args.push(curArg); + } + { + let curArg = arguments[1]; + if (curArg !== undefined) { + curArg = conversions["DOMString"](curArg, { context: "Failed to construct 'DOMException': parameter 2" }); + } else { + curArg = "Error"; + } + args.push(curArg); + } + return iface.setup(Object.create(new.target.prototype), globalObject, args); + } + + get name() { + if (!this || !module.exports.is(this)) { + throw new TypeError("Illegal invocation"); + } + + return this[impl]["name"]; + } + + get message() { + if (!this || !module.exports.is(this)) { + throw new TypeError("Illegal invocation"); + } + + return this[impl]["message"]; + } + + get code() { + if (!this || !module.exports.is(this)) { + throw new TypeError("Illegal invocation"); + } + + return this[impl]["code"]; + } + } + Object.defineProperties(DOMException.prototype, { + name: { enumerable: true }, + message: { enumerable: true }, + code: { enumerable: true }, + [Symbol.toStringTag]: { value: "DOMException", configurable: true }, + INDEX_SIZE_ERR: { value: 1, enumerable: true }, + DOMSTRING_SIZE_ERR: { value: 2, enumerable: true }, + HIERARCHY_REQUEST_ERR: { value: 3, enumerable: true }, + WRONG_DOCUMENT_ERR: { value: 4, enumerable: true }, + INVALID_CHARACTER_ERR: { value: 5, enumerable: true }, + NO_DATA_ALLOWED_ERR: { value: 6, enumerable: true }, + NO_MODIFICATION_ALLOWED_ERR: { value: 7, enumerable: true }, + NOT_FOUND_ERR: { value: 8, enumerable: true }, + NOT_SUPPORTED_ERR: { value: 9, enumerable: true }, + INUSE_ATTRIBUTE_ERR: { value: 10, enumerable: true }, + INVALID_STATE_ERR: { value: 11, enumerable: true }, + SYNTAX_ERR: { value: 12, enumerable: true }, + INVALID_MODIFICATION_ERR: { value: 13, enumerable: true }, + NAMESPACE_ERR: { value: 14, enumerable: true }, + INVALID_ACCESS_ERR: { value: 15, enumerable: true }, + VALIDATION_ERR: { value: 16, enumerable: true }, + TYPE_MISMATCH_ERR: { value: 17, enumerable: true }, + SECURITY_ERR: { value: 18, enumerable: true }, + NETWORK_ERR: { value: 19, enumerable: true }, + ABORT_ERR: { value: 20, enumerable: true }, + URL_MISMATCH_ERR: { value: 21, enumerable: true }, + QUOTA_EXCEEDED_ERR: { value: 22, enumerable: true }, + TIMEOUT_ERR: { value: 23, enumerable: true }, + INVALID_NODE_TYPE_ERR: { value: 24, enumerable: true }, + DATA_CLONE_ERR: { value: 25, enumerable: true } + }); + Object.defineProperties(DOMException, { + INDEX_SIZE_ERR: { value: 1, enumerable: true }, + DOMSTRING_SIZE_ERR: { value: 2, enumerable: true }, + HIERARCHY_REQUEST_ERR: { value: 3, enumerable: true }, + WRONG_DOCUMENT_ERR: { value: 4, enumerable: true }, + INVALID_CHARACTER_ERR: { value: 5, enumerable: true }, + NO_DATA_ALLOWED_ERR: { value: 6, enumerable: true }, + NO_MODIFICATION_ALLOWED_ERR: { value: 7, enumerable: true }, + NOT_FOUND_ERR: { value: 8, enumerable: true }, + NOT_SUPPORTED_ERR: { value: 9, enumerable: true }, + INUSE_ATTRIBUTE_ERR: { value: 10, enumerable: true }, + INVALID_STATE_ERR: { value: 11, enumerable: true }, + SYNTAX_ERR: { value: 12, enumerable: true }, + INVALID_MODIFICATION_ERR: { value: 13, enumerable: true }, + NAMESPACE_ERR: { value: 14, enumerable: true }, + INVALID_ACCESS_ERR: { value: 15, enumerable: true }, + VALIDATION_ERR: { value: 16, enumerable: true }, + TYPE_MISMATCH_ERR: { value: 17, enumerable: true }, + SECURITY_ERR: { value: 18, enumerable: true }, + NETWORK_ERR: { value: 19, enumerable: true }, + ABORT_ERR: { value: 20, enumerable: true }, + URL_MISMATCH_ERR: { value: 21, enumerable: true }, + QUOTA_EXCEEDED_ERR: { value: 22, enumerable: true }, + TIMEOUT_ERR: { value: 23, enumerable: true }, + INVALID_NODE_TYPE_ERR: { value: 24, enumerable: true }, + DATA_CLONE_ERR: { value: 25, enumerable: true } + }); + if (globalObject[ctorRegistry] === undefined) { + globalObject[ctorRegistry] = Object.create(null); + } + globalObject[ctorRegistry]["DOMException"] = DOMException; + + Object.defineProperty(globalObject, "DOMException", { + configurable: true, + writable: true, + value: DOMException + }); } }; // iface module.exports = iface; -const Impl = require(".//DOMException-impl.js"); +const Impl = require("./DOMException-impl.js"); diff --git a/node_modules/domexception/lib/public-api.js b/node_modules/domexception/lib/public-api.js deleted file mode 100644 index 6c434fd..0000000 --- a/node_modules/domexception/lib/public-api.js +++ /dev/null @@ -1,5 +0,0 @@ -"use strict"; - -module.exports = require("./DOMException").interface; - -Object.setPrototypeOf(module.exports.prototype, Error.prototype); diff --git a/node_modules/domexception/lib/utils.js b/node_modules/domexception/lib/utils.js index b505596..c020d0b 100644 --- a/node_modules/domexception/lib/utils.js +++ b/node_modules/domexception/lib/utils.js @@ -5,35 +5,14 @@ function isObject(value) { return typeof value === "object" && value !== null || typeof value === "function"; } -function getReferenceToBytes(bufferSource) { - // Node.js' Buffer does not allow subclassing for now, so we can get away with a prototype object check for perf. - if (Object.getPrototypeOf(bufferSource) === Buffer.prototype) { - return bufferSource; - } - if (bufferSource instanceof ArrayBuffer) { - return Buffer.from(bufferSource); - } - return Buffer.from(bufferSource.buffer, bufferSource.byteOffset, bufferSource.byteLength); -} - -function getCopyToBytes(bufferSource) { - return Buffer.from(getReferenceToBytes(bufferSource)); -} - -function mixin(target, source) { - const keys = Object.getOwnPropertyNames(source); - for (let i = 0; i < keys.length; ++i) { - if (keys[i] in target) { - continue; - } - - Object.defineProperty(target, keys[i], Object.getOwnPropertyDescriptor(source, keys[i])); - } +function hasOwn(obj, prop) { + return Object.prototype.hasOwnProperty.call(obj, prop); } const wrapperSymbol = Symbol("wrapper"); const implSymbol = Symbol("impl"); const sameObjectCaches = Symbol("SameObject caches"); +const ctorRegistrySymbol = Symbol.for("[webidl2js] constructor registry"); function getSameObject(wrapper, prop, creator) { if (!wrapper[sameObjectCaches]) { @@ -69,18 +48,68 @@ function tryImplForWrapper(wrapper) { const iterInternalSymbol = Symbol("internal"); const IteratorPrototype = Object.getPrototypeOf(Object.getPrototypeOf([][Symbol.iterator]())); +function isArrayIndexPropName(P) { + if (typeof P !== "string") { + return false; + } + const i = P >>> 0; + if (i === Math.pow(2, 32) - 1) { + return false; + } + const s = `${i}`; + if (P !== s) { + return false; + } + return true; +} + +const byteLengthGetter = + Object.getOwnPropertyDescriptor(ArrayBuffer.prototype, "byteLength").get; +function isArrayBuffer(value) { + try { + byteLengthGetter.call(value); + return true; + } catch (e) { + return false; + } +} + +const supportsPropertyIndex = Symbol("supports property index"); +const supportedPropertyIndices = Symbol("supported property indices"); +const supportsPropertyName = Symbol("supports property name"); +const supportedPropertyNames = Symbol("supported property names"); +const indexedGet = Symbol("indexed property get"); +const indexedSetNew = Symbol("indexed property set new"); +const indexedSetExisting = Symbol("indexed property set existing"); +const namedGet = Symbol("named property get"); +const namedSetNew = Symbol("named property set new"); +const namedSetExisting = Symbol("named property set existing"); +const namedDelete = Symbol("named property delete"); + module.exports = exports = { isObject, - getReferenceToBytes, - getCopyToBytes, - mixin, + hasOwn, wrapperSymbol, implSymbol, getSameObject, + ctorRegistrySymbol, wrapperForImpl, implForWrapper, tryWrapperForImpl, tryImplForWrapper, iterInternalSymbol, - IteratorPrototype + IteratorPrototype, + isArrayBuffer, + isArrayIndexPropName, + supportsPropertyIndex, + supportedPropertyIndices, + supportsPropertyName, + supportedPropertyNames, + indexedGet, + indexedSetNew, + indexedSetExisting, + namedGet, + namedSetNew, + namedSetExisting, + namedDelete }; diff --git a/node_modules/domexception/node_modules/webidl-conversions/LICENSE.md b/node_modules/domexception/node_modules/webidl-conversions/LICENSE.md new file mode 100644 index 0000000..d4a994f --- /dev/null +++ b/node_modules/domexception/node_modules/webidl-conversions/LICENSE.md @@ -0,0 +1,12 @@ +# The BSD 2-Clause License + +Copyright (c) 2014, Domenic Denicola +All rights reserved. + +Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: + +1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. + +2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/node_modules/domexception/node_modules/webidl-conversions/README.md b/node_modules/domexception/node_modules/webidl-conversions/README.md new file mode 100644 index 0000000..b2905df --- /dev/null +++ b/node_modules/domexception/node_modules/webidl-conversions/README.md @@ -0,0 +1,79 @@ +# Web IDL Type Conversions on JavaScript Values + +This package implements, in JavaScript, the algorithms to convert a given JavaScript value according to a given [Web IDL](http://heycam.github.io/webidl/) [type](http://heycam.github.io/webidl/#idl-types). + +The goal is that you should be able to write code like + +```js +"use strict"; +const conversions = require("webidl-conversions"); + +function doStuff(x, y) { + x = conversions["boolean"](x); + y = conversions["unsigned long"](y); + // actual algorithm code here +} +``` + +and your function `doStuff` will behave the same as a Web IDL operation declared as + +```webidl +void doStuff(boolean x, unsigned long y); +``` + +## API + +This package's main module's default export is an object with a variety of methods, each corresponding to a different Web IDL type. Each method, when invoked on a JavaScript value, will give back the new JavaScript value that results after passing through the Web IDL conversion rules. (See below for more details on what that means.) Alternately, the method could throw an error, if the Web IDL algorithm is specified to do so: for example `conversions["float"](NaN)` [will throw a `TypeError`](http://heycam.github.io/webidl/#es-float). + +Each method also accepts a second, optional, parameter for miscellaneous options. For conversion methods that throw errors, a string option `{ context }` may be provided to provide more information in the error message. (For example, `conversions["float"](NaN, { context: "Argument 1 of Interface's operation" })` will throw an error with message `"Argument 1 of Interface's operation is not a finite floating-point value."`) Specific conversions may also accept other options, the details of which can be found below. + +## Conversions implemented + +Conversions for all of the basic types from the Web IDL specification are implemented: + +- [`any`](https://heycam.github.io/webidl/#es-any) +- [`void`](https://heycam.github.io/webidl/#es-void) +- [`boolean`](https://heycam.github.io/webidl/#es-boolean) +- [Integer types](https://heycam.github.io/webidl/#es-integer-types), which can additionally be provided the boolean options `{ clamp, enforceRange }` as a second parameter +- [`float`](https://heycam.github.io/webidl/#es-float), [`unrestricted float`](https://heycam.github.io/webidl/#es-unrestricted-float) +- [`double`](https://heycam.github.io/webidl/#es-double), [`unrestricted double`](https://heycam.github.io/webidl/#es-unrestricted-double) +- [`DOMString`](https://heycam.github.io/webidl/#es-DOMString), which can additionally be provided the boolean option `{ treatNullAsEmptyString }` as a second parameter +- [`ByteString`](https://heycam.github.io/webidl/#es-ByteString), [`USVString`](https://heycam.github.io/webidl/#es-USVString) +- [`object`](https://heycam.github.io/webidl/#es-object) +- [Buffer source types](https://heycam.github.io/webidl/#es-buffer-source-types) + +Additionally, for convenience, the following derived type definitions are implemented: + +- [`ArrayBufferView`](https://heycam.github.io/webidl/#ArrayBufferView) +- [`BufferSource`](https://heycam.github.io/webidl/#BufferSource) +- [`DOMTimeStamp`](https://heycam.github.io/webidl/#DOMTimeStamp) +- [`Function`](https://heycam.github.io/webidl/#Function) +- [`VoidFunction`](https://heycam.github.io/webidl/#VoidFunction) (although it will not censor the return type) + +Derived types, such as nullable types, promise types, sequences, records, etc. are not handled by this library. You may wish to investigate the [webidl2js](https://github.com/jsdom/webidl2js) project. + +### A note on the `long long` types + +The `long long` and `unsigned long long` Web IDL types can hold values that cannot be stored in JavaScript numbers, so the conversion is imperfect. For example, converting the JavaScript number `18446744073709552000` to a Web IDL `long long` is supposed to produce the Web IDL value `-18446744073709551232`. Since we are representing our Web IDL values in JavaScript, we can't represent `-18446744073709551232`, so we instead the best we could do is `-18446744073709552000` as the output. + +This library actually doesn't even get that far. Producing those results would require doing accurate modular arithmetic on 64-bit intermediate values, but JavaScript does not make this easy. We could pull in a big-integer library as a dependency, but in lieu of that, we for now have decided to just produce inaccurate results if you pass in numbers that are not strictly between `Number.MIN_SAFE_INTEGER` and `Number.MAX_SAFE_INTEGER`. + +## Background + +What's actually going on here, conceptually, is pretty weird. Let's try to explain. + +Web IDL, as part of its madness-inducing design, has its own type system. When people write algorithms in web platform specs, they usually operate on Web IDL values, i.e. instances of Web IDL types. For example, if they were specifying the algorithm for our `doStuff` operation above, they would treat `x` as a Web IDL value of [Web IDL type `boolean`](http://heycam.github.io/webidl/#idl-boolean). Crucially, they would _not_ treat `x` as a JavaScript variable whose value is either the JavaScript `true` or `false`. They're instead working in a different type system altogether, with its own rules. + +Separately from its type system, Web IDL defines a ["binding"](http://heycam.github.io/webidl/#ecmascript-binding) of the type system into JavaScript. This contains rules like: when you pass a JavaScript value to the JavaScript method that manifests a given Web IDL operation, how does that get converted into a Web IDL value? For example, a JavaScript `true` passed in the position of a Web IDL `boolean` argument becomes a Web IDL `true`. But, a JavaScript `true` passed in the position of a [Web IDL `unsigned long`](http://heycam.github.io/webidl/#idl-unsigned-long) becomes a Web IDL `1`. And so on. + +Finally, we have the actual implementation code. This is usually C++, although these days [some smart people are using Rust](https://github.com/servo/servo). The implementation, of course, has its own type system. So when they implement the Web IDL algorithms, they don't actually use Web IDL values, since those aren't "real" outside of specs. Instead, implementations apply the Web IDL binding rules in such a way as to convert incoming JavaScript values into C++ values. For example, if code in the browser called `doStuff(true, true)`, then the implementation code would eventually receive a C++ `bool` containing `true` and a C++ `uint32_t` containing `1`. + +The upside of all this is that implementations can abstract all the conversion logic away, letting Web IDL handle it, and focus on implementing the relevant methods in C++ with values of the correct type already provided. That is payoff of Web IDL, in a nutshell. + +And getting to that payoff is the goal of _this_ project—but for JavaScript implementations, instead of C++ ones. That is, this library is designed to make it easier for JavaScript developers to write functions that behave like a given Web IDL operation. So conceptually, the conversion pipeline, which in its general form is JavaScript values ↦ Web IDL values ↦ implementation-language values, in this case becomes JavaScript values ↦ Web IDL values ↦ JavaScript values. And that intermediate step is where all the logic is performed: a JavaScript `true` becomes a Web IDL `1` in an unsigned long context, which then becomes a JavaScript `1`. + +## Don't use this + +Seriously, why would you ever use this? You really shouldn't. Web IDL is … strange, and you shouldn't be emulating its semantics. If you're looking for a generic argument-processing library, you should find one with better rules than those from Web IDL. In general, your JavaScript should not be trying to become more like Web IDL; if anything, we should fix Web IDL to make it more like JavaScript. + +The _only_ people who should use this are those trying to create faithful implementations (or polyfills) of web platform interfaces defined in Web IDL. Its main consumer is the [jsdom](https://github.com/jsdom/jsdom) project. diff --git a/node_modules/domexception/node_modules/webidl-conversions/lib/index.js b/node_modules/domexception/node_modules/webidl-conversions/lib/index.js new file mode 100644 index 0000000..bae66dc --- /dev/null +++ b/node_modules/domexception/node_modules/webidl-conversions/lib/index.js @@ -0,0 +1,361 @@ +"use strict"; + +function _(message, opts) { + return `${opts && opts.context ? opts.context : "Value"} ${message}.`; +} + +function type(V) { + if (V === null) { + return "Null"; + } + switch (typeof V) { + case "undefined": + return "Undefined"; + case "boolean": + return "Boolean"; + case "number": + return "Number"; + case "string": + return "String"; + case "symbol": + return "Symbol"; + case "object": + // Falls through + case "function": + // Falls through + default: + // Per ES spec, typeof returns an implemention-defined value that is not any of the existing ones for + // uncallable non-standard exotic objects. Yet Type() which the Web IDL spec depends on returns Object for + // such cases. So treat the default case as an object. + return "Object"; + } +} + +// Round x to the nearest integer, choosing the even integer if it lies halfway between two. +function evenRound(x) { + // There are four cases for numbers with fractional part being .5: + // + // case | x | floor(x) | round(x) | expected | x <> 0 | x % 1 | x & 1 | example + // 1 | 2n + 0.5 | 2n | 2n + 1 | 2n | > | 0.5 | 0 | 0.5 -> 0 + // 2 | 2n + 1.5 | 2n + 1 | 2n + 2 | 2n + 2 | > | 0.5 | 1 | 1.5 -> 2 + // 3 | -2n - 0.5 | -2n - 1 | -2n | -2n | < | -0.5 | 0 | -0.5 -> 0 + // 4 | -2n - 1.5 | -2n - 2 | -2n - 1 | -2n - 2 | < | -0.5 | 1 | -1.5 -> -2 + // (where n is a non-negative integer) + // + // Branch here for cases 1 and 4 + if ((x > 0 && (x % 1) === +0.5 && (x & 1) === 0) || + (x < 0 && (x % 1) === -0.5 && (x & 1) === 1)) { + return censorNegativeZero(Math.floor(x)); + } + + return censorNegativeZero(Math.round(x)); +} + +function integerPart(n) { + return censorNegativeZero(Math.trunc(n)); +} + +function sign(x) { + return x < 0 ? -1 : 1; +} + +function modulo(x, y) { + // https://tc39.github.io/ecma262/#eqn-modulo + // Note that http://stackoverflow.com/a/4467559/3191 does NOT work for large modulos + const signMightNotMatch = x % y; + if (sign(y) !== sign(signMightNotMatch)) { + return signMightNotMatch + y; + } + return signMightNotMatch; +} + +function censorNegativeZero(x) { + return x === 0 ? 0 : x; +} + +function createIntegerConversion(bitLength, typeOpts) { + const isSigned = !typeOpts.unsigned; + + let lowerBound; + let upperBound; + if (bitLength === 64) { + upperBound = Math.pow(2, 53) - 1; + lowerBound = !isSigned ? 0 : -Math.pow(2, 53) + 1; + } else if (!isSigned) { + lowerBound = 0; + upperBound = Math.pow(2, bitLength) - 1; + } else { + lowerBound = -Math.pow(2, bitLength - 1); + upperBound = Math.pow(2, bitLength - 1) - 1; + } + + const twoToTheBitLength = Math.pow(2, bitLength); + const twoToOneLessThanTheBitLength = Math.pow(2, bitLength - 1); + + return (V, opts) => { + if (opts === undefined) { + opts = {}; + } + + let x = +V; + x = censorNegativeZero(x); // Spec discussion ongoing: https://github.com/heycam/webidl/issues/306 + + if (opts.enforceRange) { + if (!Number.isFinite(x)) { + throw new TypeError(_("is not a finite number", opts)); + } + + x = integerPart(x); + + if (x < lowerBound || x > upperBound) { + throw new TypeError(_( + `is outside the accepted range of ${lowerBound} to ${upperBound}, inclusive`, opts)); + } + + return x; + } + + if (!Number.isNaN(x) && opts.clamp) { + x = Math.min(Math.max(x, lowerBound), upperBound); + x = evenRound(x); + return x; + } + + if (!Number.isFinite(x) || x === 0) { + return 0; + } + x = integerPart(x); + + // Math.pow(2, 64) is not accurately representable in JavaScript, so try to avoid these per-spec operations if + // possible. Hopefully it's an optimization for the non-64-bitLength cases too. + if (x >= lowerBound && x <= upperBound) { + return x; + } + + // These will not work great for bitLength of 64, but oh well. See the README for more details. + x = modulo(x, twoToTheBitLength); + if (isSigned && x >= twoToOneLessThanTheBitLength) { + return x - twoToTheBitLength; + } + return x; + }; +} + +exports.any = V => { + return V; +}; + +exports.void = function () { + return undefined; +}; + +exports.boolean = function (val) { + return !!val; +}; + +exports.byte = createIntegerConversion(8, { unsigned: false }); +exports.octet = createIntegerConversion(8, { unsigned: true }); + +exports.short = createIntegerConversion(16, { unsigned: false }); +exports["unsigned short"] = createIntegerConversion(16, { unsigned: true }); + +exports.long = createIntegerConversion(32, { unsigned: false }); +exports["unsigned long"] = createIntegerConversion(32, { unsigned: true }); + +exports["long long"] = createIntegerConversion(64, { unsigned: false }); +exports["unsigned long long"] = createIntegerConversion(64, { unsigned: true }); + +exports.double = (V, opts) => { + const x = +V; + + if (!Number.isFinite(x)) { + throw new TypeError(_("is not a finite floating-point value", opts)); + } + + return x; +}; + +exports["unrestricted double"] = V => { + const x = +V; + + return x; +}; + +exports.float = (V, opts) => { + const x = +V; + + if (!Number.isFinite(x)) { + throw new TypeError(_("is not a finite floating-point value", opts)); + } + + if (Object.is(x, -0)) { + return x; + } + + const y = Math.fround(x); + + if (!Number.isFinite(y)) { + throw new TypeError(_("is outside the range of a single-precision floating-point value", opts)); + } + + return y; +}; + +exports["unrestricted float"] = V => { + const x = +V; + + if (isNaN(x)) { + return x; + } + + if (Object.is(x, -0)) { + return x; + } + + return Math.fround(x); +}; + +exports.DOMString = function (V, opts) { + if (opts === undefined) { + opts = {}; + } + + if (opts.treatNullAsEmptyString && V === null) { + return ""; + } + + if (typeof V === "symbol") { + throw new TypeError(_("is a symbol, which cannot be converted to a string", opts)); + } + + return String(V); +}; + +exports.ByteString = (V, opts) => { + const x = exports.DOMString(V, opts); + let c; + for (let i = 0; (c = x.codePointAt(i)) !== undefined; ++i) { + if (c > 255) { + throw new TypeError(_("is not a valid ByteString", opts)); + } + } + + return x; +}; + +exports.USVString = (V, opts) => { + const S = exports.DOMString(V, opts); + const n = S.length; + const U = []; + for (let i = 0; i < n; ++i) { + const c = S.charCodeAt(i); + if (c < 0xD800 || c > 0xDFFF) { + U.push(String.fromCodePoint(c)); + } else if (0xDC00 <= c && c <= 0xDFFF) { + U.push(String.fromCodePoint(0xFFFD)); + } else if (i === n - 1) { + U.push(String.fromCodePoint(0xFFFD)); + } else { + const d = S.charCodeAt(i + 1); + if (0xDC00 <= d && d <= 0xDFFF) { + const a = c & 0x3FF; + const b = d & 0x3FF; + U.push(String.fromCodePoint((2 << 15) + ((2 << 9) * a) + b)); + ++i; + } else { + U.push(String.fromCodePoint(0xFFFD)); + } + } + } + + return U.join(""); +}; + +exports.object = (V, opts) => { + if (type(V) !== "Object") { + throw new TypeError(_("is not an object", opts)); + } + + return V; +}; + +// Not exported, but used in Function and VoidFunction. + +// Neither Function nor VoidFunction is defined with [TreatNonObjectAsNull], so +// handling for that is omitted. +function convertCallbackFunction(V, opts) { + if (typeof V !== "function") { + throw new TypeError(_("is not a function", opts)); + } + return V; +} + +const abByteLengthGetter = + Object.getOwnPropertyDescriptor(ArrayBuffer.prototype, "byteLength").get; + +function isArrayBuffer(V) { + try { + abByteLengthGetter.call(V); + return true; + } catch (e) { + return false; + } +} + +// I don't think we can reliably detect detached ArrayBuffers. +exports.ArrayBuffer = (V, opts) => { + if (!isArrayBuffer(V)) { + throw new TypeError(_("is not a view on an ArrayBuffer object", opts)); + } + return V; +}; + +const dvByteLengthGetter = + Object.getOwnPropertyDescriptor(DataView.prototype, "byteLength").get; +exports.DataView = (V, opts) => { + try { + dvByteLengthGetter.call(V); + return V; + } catch (e) { + throw new TypeError(_("is not a view on an DataView object", opts)); + } +}; + +[ + Int8Array, Int16Array, Int32Array, Uint8Array, + Uint16Array, Uint32Array, Uint8ClampedArray, Float32Array, Float64Array +].forEach(func => { + const name = func.name; + const article = /^[AEIOU]/.test(name) ? "an" : "a"; + exports[name] = (V, opts) => { + if (!ArrayBuffer.isView(V) || V.constructor.name !== name) { + throw new TypeError(_(`is not ${article} ${name} object`, opts)); + } + + return V; + }; +}); + +// Common definitions + +exports.ArrayBufferView = (V, opts) => { + if (!ArrayBuffer.isView(V)) { + throw new TypeError(_("is not a view on an ArrayBuffer object", opts)); + } + + return V; +}; + +exports.BufferSource = (V, opts) => { + if (!ArrayBuffer.isView(V) && !isArrayBuffer(V)) { + throw new TypeError(_("is not an ArrayBuffer object or a view on one", opts)); + } + + return V; +}; + +exports.DOMTimeStamp = exports["unsigned long long"]; + +exports.Function = convertCallbackFunction; + +exports.VoidFunction = convertCallbackFunction; diff --git a/node_modules/domexception/node_modules/webidl-conversions/package.json b/node_modules/domexception/node_modules/webidl-conversions/package.json new file mode 100644 index 0000000..d7490a0 --- /dev/null +++ b/node_modules/domexception/node_modules/webidl-conversions/package.json @@ -0,0 +1,66 @@ +{ + "_from": "webidl-conversions@^5.0.0", + "_id": "webidl-conversions@5.0.0", + "_inBundle": false, + "_integrity": "sha512-VlZwKPCkYKxQgeSbH5EyngOmRp7Ww7I9rQLERETtf5ofd9pGeswWiOtogpEO850jziPRarreGxn5QIiTqpb2wA==", + "_location": "/domexception/webidl-conversions", + "_phantomChildren": {}, + "_requested": { + "type": "range", + "registry": true, + "raw": "webidl-conversions@^5.0.0", + "name": "webidl-conversions", + "escapedName": "webidl-conversions", + "rawSpec": "^5.0.0", + "saveSpec": null, + "fetchSpec": "^5.0.0" + }, + "_requiredBy": [ + "/domexception" + ], + "_resolved": "https://registry.npmjs.org/webidl-conversions/-/webidl-conversions-5.0.0.tgz", + "_shasum": "ae59c8a00b121543a2acc65c0434f57b0fc11aff", + "_spec": "webidl-conversions@^5.0.0", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\domexception", + "author": { + "name": "Domenic Denicola", + "email": "d@domenic.me", + "url": "https://domenic.me/" + }, + "bugs": { + "url": "https://github.com/jsdom/webidl-conversions/issues" + }, + "bundleDependencies": false, + "deprecated": false, + "description": "Implements the WebIDL algorithms for converting to and from JavaScript values", + "devDependencies": { + "eslint": "^6.7.2", + "mocha": "^6.2.2", + "nyc": "^14.1.1" + }, + "engines": { + "node": ">=8" + }, + "files": [ + "lib/" + ], + "homepage": "https://github.com/jsdom/webidl-conversions#readme", + "keywords": [ + "webidl", + "web", + "types" + ], + "license": "BSD-2-Clause", + "main": "lib/index.js", + "name": "webidl-conversions", + "repository": { + "type": "git", + "url": "git+https://github.com/jsdom/webidl-conversions.git" + }, + "scripts": { + "coverage": "nyc mocha test/*.js", + "lint": "eslint .", + "test": "mocha test/*.js" + }, + "version": "5.0.0" +} diff --git a/node_modules/domexception/package.json b/node_modules/domexception/package.json index 72200f5..658612b 100644 --- a/node_modules/domexception/package.json +++ b/node_modules/domexception/package.json @@ -1,28 +1,27 @@ { - "_from": "domexception@^1.0.1", - "_id": "domexception@1.0.1", + "_from": "domexception@^2.0.1", + "_id": "domexception@2.0.1", "_inBundle": false, - "_integrity": "sha512-raigMkn7CJNNo6Ihro1fzG7wr3fHuYVytzquZKX5n0yizGsTcYgzdIUwj1X9pK0VvjeihV+XiclP+DjwbsSKug==", + "_integrity": "sha512-yxJ2mFy/sibVQlu5qHjOkf9J3K6zgmCxgJ94u2EdvDOV09H+32LtRswEcUsmUWN72pVLOEnTSRaIVVzVQgS0dg==", "_location": "/domexception", "_phantomChildren": {}, "_requested": { "type": "range", "registry": true, - "raw": "domexception@^1.0.1", + "raw": "domexception@^2.0.1", "name": "domexception", "escapedName": "domexception", - "rawSpec": "^1.0.1", + "rawSpec": "^2.0.1", "saveSpec": null, - "fetchSpec": "^1.0.1" + "fetchSpec": "^2.0.1" }, "_requiredBy": [ - "/jsdom", - "/w3c-xmlserializer" + "/jsdom" ], - "_resolved": "https://registry.npmjs.org/domexception/-/domexception-1.0.1.tgz", - "_shasum": "937442644ca6a31261ef36e3ec677fe805582c90", - "_spec": "domexception@^1.0.1", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\jsdom", + "_resolved": "https://registry.npmjs.org/domexception/-/domexception-2.0.1.tgz", + "_shasum": "fb44aefba793e1574b0af6aed2801d057529f304", + "_spec": "domexception@^2.0.1", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\jsdom", "author": { "name": "Domenic Denicola", "email": "d@domenic.me", @@ -33,18 +32,23 @@ }, "bundleDependencies": false, "dependencies": { - "webidl-conversions": "^4.0.2" + "webidl-conversions": "^5.0.0" }, "deprecated": false, "description": "An implementation of the DOMException class from browsers", "devDependencies": { - "eslint": "^4.3.0", + "eslint": "^6.7.2", "mkdirp": "^0.5.1", - "mocha": "^3.5.0", - "request": "^2.81.0", - "webidl2js": "^7.2.0" + "mocha": "^6.2.2", + "request": "^2.88.0", + "webidl2js": "^12.0.0" + }, + "engines": { + "node": ">=8" }, "files": [ + "index.js", + "webidl2js-wrapper.js", "lib/" ], "homepage": "https://github.com/jsdom/domexception#readme", @@ -57,17 +61,18 @@ "exception" ], "license": "MIT", - "main": "lib/public-api.js", + "main": "index.js", "name": "domexception", "repository": { "type": "git", "url": "git+https://github.com/jsdom/domexception.git" }, "scripts": { + "init-wpt": "node scripts/get-latest-platform-tests.js", "lint": "eslint lib", - "prepublish": "node scripts/generate.js", - "pretest": "npm run prepublish", + "prepare": "node scripts/generate.js", + "pretest": "npm run prepare && npm run init-wpt", "test": "mocha" }, - "version": "1.0.1" + "version": "2.0.1" } diff --git a/node_modules/domexception/webidl2js-wrapper.js b/node_modules/domexception/webidl2js-wrapper.js new file mode 100644 index 0000000..05d3470 --- /dev/null +++ b/node_modules/domexception/webidl2js-wrapper.js @@ -0,0 +1,15 @@ +"use strict"; +const DOMException = require("./lib/DOMException.js"); + +// Special install function to make the DOMException inherit from Error. +// https://heycam.github.io/webidl/#es-DOMException-specialness +function installOverride(globalObject) { + if (typeof globalObject.Error !== "function") { + throw new Error("Internal error: Error constructor is not present on the given global object."); + } + + DOMException.install(globalObject); + Object.setPrototypeOf(globalObject.DOMException.prototype, globalObject.Error.prototype); +} + +module.exports = {...DOMException, install: installOverride }; diff --git a/node_modules/ecc-jsbn/package.json b/node_modules/ecc-jsbn/package.json index a359f80..19f089e 100644 --- a/node_modules/ecc-jsbn/package.json +++ b/node_modules/ecc-jsbn/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/ecc-jsbn/-/ecc-jsbn-0.1.2.tgz", "_shasum": "3a83a904e54353287874c564b7549386849a98c9", "_spec": "ecc-jsbn@~0.1.1", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\sshpk", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\sshpk", "author": { "name": "Jeremie Miller", "email": "jeremie@jabber.org", diff --git a/node_modules/escodegen/LICENSE.BSD b/node_modules/escodegen/LICENSE.BSD index 3e580c3..426019d 100644 --- a/node_modules/escodegen/LICENSE.BSD +++ b/node_modules/escodegen/LICENSE.BSD @@ -1,3 +1,5 @@ +Copyright (C) 2012 Yusuke Suzuki (twitter: @Constellation) and other contributors. + Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: diff --git a/node_modules/escodegen/escodegen.js b/node_modules/escodegen/escodegen.js index 6fe6646..4c055b8 100644 --- a/node_modules/escodegen/escodegen.js +++ b/node_modules/escodegen/escodegen.js @@ -983,7 +983,7 @@ result.push('['); } - result.push(this.generateExpression(expr, Precedence.Sequence, E_TTT)); + result.push(this.generateExpression(expr, Precedence.Assignment, E_TTT)); if (computed) { result.push(']'); @@ -2223,13 +2223,19 @@ multiline = false; if (expr.properties.length === 1) { property = expr.properties[0]; - if (property.value.type !== Syntax.Identifier) { + if ( + property.type === Syntax.Property + && property.value.type !== Syntax.Identifier + ) { multiline = true; } } else { for (i = 0, iz = expr.properties.length; i < iz; ++i) { property = expr.properties[i]; - if (!property.shorthand) { + if ( + property.type === Syntax.Property + && !property.shorthand + ) { multiline = true; break; } diff --git a/node_modules/escodegen/package.json b/node_modules/escodegen/package.json index cea0279..377603b 100644 --- a/node_modules/escodegen/package.json +++ b/node_modules/escodegen/package.json @@ -1,27 +1,27 @@ { - "_from": "escodegen@^1.11.0", - "_id": "escodegen@1.14.1", + "_from": "escodegen@^1.14.1", + "_id": "escodegen@1.14.3", "_inBundle": false, - "_integrity": "sha512-Bmt7NcRySdIfNPfU2ZoXDrrXsG9ZjvDxcAlMfDUgRBjLOWTuIACXPBFJH7Z+cLb40JeQco5toikyc9t9P8E9SQ==", + "_integrity": "sha512-qFcX0XJkdg+PB3xjZZG/wKSuT1PnQWx57+TVSjIMmILd2yC/6ByYElPwJnslDsuWuSAp4AwJGumarAAmJch5Kw==", "_location": "/escodegen", "_phantomChildren": {}, "_requested": { "type": "range", "registry": true, - "raw": "escodegen@^1.11.0", + "raw": "escodegen@^1.14.1", "name": "escodegen", "escapedName": "escodegen", - "rawSpec": "^1.11.0", + "rawSpec": "^1.14.1", "saveSpec": null, - "fetchSpec": "^1.11.0" + "fetchSpec": "^1.14.1" }, "_requiredBy": [ "/jsdom" ], - "_resolved": "https://registry.npmjs.org/escodegen/-/escodegen-1.14.1.tgz", - "_shasum": "ba01d0c8278b5e95a9a45350142026659027a457", - "_spec": "escodegen@^1.11.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\jsdom", + "_resolved": "https://registry.npmjs.org/escodegen/-/escodegen-1.14.3.tgz", + "_shasum": "4e7b81fba61581dc97582ed78cab7f0e8d63f503", + "_spec": "escodegen@^1.14.1", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\jsdom", "bin": { "esgenerate": "bin/esgenerate.js", "escodegen": "bin/escodegen.js" @@ -86,5 +86,5 @@ "test": "gulp travis", "unit-test": "gulp test" }, - "version": "1.14.1" + "version": "1.14.3" } diff --git a/node_modules/esprima/package.json b/node_modules/esprima/package.json index b84b85f..acd470e 100644 --- a/node_modules/esprima/package.json +++ b/node_modules/esprima/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/esprima/-/esprima-4.0.1.tgz", "_shasum": "13b04cdb3e6c5d19df91ab6987a8695619b0aa71", "_spec": "esprima@^4.0.1", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\escodegen", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\escodegen", "author": { "name": "Ariya Hidayat", "email": "ariya.hidayat@gmail.com" diff --git a/node_modules/estraverse/package.json b/node_modules/estraverse/package.json index 0fb9caf..2da7b23 100644 --- a/node_modules/estraverse/package.json +++ b/node_modules/estraverse/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/estraverse/-/estraverse-4.3.0.tgz", "_shasum": "398ad3f3c5a24948be7725e83d11a7de28cdbd1d", "_spec": "estraverse@^4.2.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\escodegen", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\escodegen", "bugs": { "url": "https://github.com/estools/estraverse/issues" }, diff --git a/node_modules/esutils/package.json b/node_modules/esutils/package.json index 4e3fa8c..f4894b3 100644 --- a/node_modules/esutils/package.json +++ b/node_modules/esutils/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/esutils/-/esutils-2.0.3.tgz", "_shasum": "74d2eb4de0b8da1293711910d50775b9b710ef64", "_spec": "esutils@^2.0.2", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\escodegen", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\escodegen", "bugs": { "url": "https://github.com/estools/esutils/issues" }, diff --git a/node_modules/extend/package.json b/node_modules/extend/package.json index 329d2dc..16f35cf 100644 --- a/node_modules/extend/package.json +++ b/node_modules/extend/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/extend/-/extend-3.0.2.tgz", "_shasum": "f8b1136b4071fbd8eb140aff858b1019ec2915fa", "_spec": "extend@~3.0.2", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Stefan Thomas", "email": "justmoon@members.fsf.org", diff --git a/node_modules/extsprintf/package.json b/node_modules/extsprintf/package.json index c86ae4c..a18eaba 100644 --- a/node_modules/extsprintf/package.json +++ b/node_modules/extsprintf/package.json @@ -22,7 +22,7 @@ "_resolved": "https://registry.npmjs.org/extsprintf/-/extsprintf-1.3.0.tgz", "_shasum": "96918440e3041a7a414f8c52e3c574eb3c3e1e05", "_spec": "extsprintf@1.3.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\jsprim", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\jsprim", "bugs": { "url": "https://github.com/davepacheco/node-extsprintf/issues" }, diff --git a/node_modules/fast-deep-equal/es6/index.d.ts b/node_modules/fast-deep-equal/es6/index.d.ts index 0fc8d3b..c7eb9c7 100644 --- a/node_modules/fast-deep-equal/es6/index.d.ts +++ b/node_modules/fast-deep-equal/es6/index.d.ts @@ -1,2 +1,2 @@ -const equal: (a: any, b: any) => boolean; +declare const equal: (a: any, b: any) => boolean; export = equal; diff --git a/node_modules/fast-deep-equal/es6/react.d.ts b/node_modules/fast-deep-equal/es6/react.d.ts index 0fc8d3b..c7eb9c7 100644 --- a/node_modules/fast-deep-equal/es6/react.d.ts +++ b/node_modules/fast-deep-equal/es6/react.d.ts @@ -1,2 +1,2 @@ -const equal: (a: any, b: any) => boolean; +declare const equal: (a: any, b: any) => boolean; export = equal; diff --git a/node_modules/fast-deep-equal/package.json b/node_modules/fast-deep-equal/package.json index c45e3c3..1029020 100644 --- a/node_modules/fast-deep-equal/package.json +++ b/node_modules/fast-deep-equal/package.json @@ -1,8 +1,8 @@ { "_from": "fast-deep-equal@^3.1.1", - "_id": "fast-deep-equal@3.1.1", + "_id": "fast-deep-equal@3.1.3", "_inBundle": false, - "_integrity": "sha512-8UEa58QDLauDNfpbrX55Q9jrGHThw2ZMdOky5Gl1CDtVeJDPVrG4Jxx1N8jw2gkWaff5UUuX1KJd+9zGe2B+ZA==", + "_integrity": "sha512-f3qQ9oQy9j2AhBe/H9VC91wLmKBCCU/gDOnKNAYG5hswO7BLKj09Hc5HYNz9cGI++xlpDCIgDaitVs03ATR84Q==", "_location": "/fast-deep-equal", "_phantomChildren": {}, "_requested": { @@ -18,10 +18,10 @@ "_requiredBy": [ "/ajv" ], - "_resolved": "https://registry.npmjs.org/fast-deep-equal/-/fast-deep-equal-3.1.1.tgz", - "_shasum": "545145077c501491e33b15ec408c294376e94ae4", + "_resolved": "https://registry.npmjs.org/fast-deep-equal/-/fast-deep-equal-3.1.3.tgz", + "_shasum": "3a7d56b559d6cbc3eb512325244e619a65c6c525", "_spec": "fast-deep-equal@^3.1.1", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\ajv", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\ajv", "author": { "name": "Evgeny Poberezkin" }, @@ -32,16 +32,16 @@ "deprecated": false, "description": "Fast deep equal", "devDependencies": { - "coveralls": "^2.13.1", + "coveralls": "^3.1.0", "dot": "^1.1.2", - "eslint": "^4.0.0", - "mocha": "^3.4.2", - "nyc": "^11.0.2", + "eslint": "^7.2.0", + "mocha": "^7.2.0", + "nyc": "^15.1.0", "pre-commit": "^1.2.2", "react": "^16.12.0", "react-test-renderer": "^16.12.0", - "sinon": "^7.5.0", - "typescript": "^2.6.1" + "sinon": "^9.0.2", + "typescript": "^3.9.5" }, "files": [ "index.js", @@ -84,5 +84,5 @@ "test-ts": "tsc --target ES5 --noImplicitAny index.d.ts" }, "types": "index.d.ts", - "version": "3.1.1" + "version": "3.1.3" } diff --git a/node_modules/fast-deep-equal/react.d.ts b/node_modules/fast-deep-equal/react.d.ts index 0fc8d3b..c7eb9c7 100644 --- a/node_modules/fast-deep-equal/react.d.ts +++ b/node_modules/fast-deep-equal/react.d.ts @@ -1,2 +1,2 @@ -const equal: (a: any, b: any) => boolean; +declare const equal: (a: any, b: any) => boolean; export = equal; diff --git a/node_modules/fast-json-stable-stringify/package.json b/node_modules/fast-json-stable-stringify/package.json index de6955d..1501217 100644 --- a/node_modules/fast-json-stable-stringify/package.json +++ b/node_modules/fast-json-stable-stringify/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/fast-json-stable-stringify/-/fast-json-stable-stringify-2.1.0.tgz", "_shasum": "874bf69c6f404c2b5d99c481341399fd55892633", "_spec": "fast-json-stable-stringify@^2.0.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\ajv", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\ajv", "author": { "name": "James Halliday", "email": "mail@substack.net", diff --git a/node_modules/fast-levenshtein/package.json b/node_modules/fast-levenshtein/package.json index e3a558b..ac84849 100644 --- a/node_modules/fast-levenshtein/package.json +++ b/node_modules/fast-levenshtein/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/fast-levenshtein/-/fast-levenshtein-2.0.6.tgz", "_shasum": "3d8a5c66883a16a30ca8643e851f19baa7797917", "_spec": "fast-levenshtein@~2.0.6", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\optionator", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\optionator", "author": { "name": "Ramesh Nair", "email": "ram@hiddentao.com", diff --git a/node_modules/forever-agent/package.json b/node_modules/forever-agent/package.json index fa5b1bb..c6d1d4e 100644 --- a/node_modules/forever-agent/package.json +++ b/node_modules/forever-agent/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/forever-agent/-/forever-agent-0.6.1.tgz", "_shasum": "fbc71f0c41adeb37f96c577ad1ed42d8fdacca91", "_spec": "forever-agent@~0.6.1", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Mikeal Rogers", "email": "mikeal.rogers@gmail.com", diff --git a/node_modules/form-data/package.json b/node_modules/form-data/package.json index 0f133c4..566e1d5 100644 --- a/node_modules/form-data/package.json +++ b/node_modules/form-data/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/form-data/-/form-data-2.3.3.tgz", "_shasum": "dcce52c05f644f298c6a7ab936bd724ceffbf3a6", "_spec": "form-data@~2.3.2", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Felix Geisendörfer", "email": "felix@debuggable.com", diff --git a/node_modules/getpass/package.json b/node_modules/getpass/package.json index 8709d66..863249f 100644 --- a/node_modules/getpass/package.json +++ b/node_modules/getpass/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/getpass/-/getpass-0.1.7.tgz", "_shasum": "5eff8e3e684d569ae4cb2b1282604e8ba62149fa", "_spec": "getpass@^0.1.1", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\sshpk", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\sshpk", "author": { "name": "Alex Wilson", "email": "alex.wilson@joyent.com" diff --git a/node_modules/har-schema/package.json b/node_modules/har-schema/package.json index a4e2b5e..cfbe26d 100644 --- a/node_modules/har-schema/package.json +++ b/node_modules/har-schema/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/har-schema/-/har-schema-2.0.0.tgz", "_shasum": "a94c2224ebcac04782a0d9035521f24735b7ec92", "_spec": "har-schema@^2.0.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\har-validator", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\har-validator", "author": { "name": "Ahmad Nassri", "email": "ahmad@ahmadnassri.com", diff --git a/node_modules/har-validator/package.json b/node_modules/har-validator/package.json index b9fb3db..d6f130a 100644 --- a/node_modules/har-validator/package.json +++ b/node_modules/har-validator/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/har-validator/-/har-validator-5.1.3.tgz", "_shasum": "1ef89ebd3e4996557675eed9893110dc350fa080", "_spec": "har-validator@~5.1.3", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Ahmad Nassri", "email": "ahmad@ahmadnassri.com", diff --git a/node_modules/html-encoding-sniffer/LICENSE.txt b/node_modules/html-encoding-sniffer/LICENSE.txt index 82d5c89..6abf703 100644 --- a/node_modules/html-encoding-sniffer/LICENSE.txt +++ b/node_modules/html-encoding-sniffer/LICENSE.txt @@ -1,4 +1,4 @@ -Copyright © 2016 Domenic Denicola +Copyright © 2016–2020 Domenic Denicola 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: diff --git a/node_modules/html-encoding-sniffer/lib/html-encoding-sniffer.js b/node_modules/html-encoding-sniffer/lib/html-encoding-sniffer.js index 851b9e2..25b7537 100644 --- a/node_modules/html-encoding-sniffer/lib/html-encoding-sniffer.js +++ b/node_modules/html-encoding-sniffer/lib/html-encoding-sniffer.js @@ -2,27 +2,19 @@ const whatwgEncoding = require("whatwg-encoding"); // https://html.spec.whatwg.org/#encoding-sniffing-algorithm -module.exports = function sniffHTMLEncoding(buffer, options) { +module.exports = (buffer, { transportLayerEncodingLabel, defaultEncoding = "windows-1252" } = {}) => { let encoding = whatwgEncoding.getBOMEncoding(buffer); // see https://github.com/whatwg/html/issues/1910 - if (options === undefined) { - options = {}; - } - - if (encoding === null && options.transportLayerEncodingLabel !== undefined) { - encoding = whatwgEncoding.labelToName(options.transportLayerEncodingLabel); + if (encoding === null && transportLayerEncodingLabel !== undefined) { + encoding = whatwgEncoding.labelToName(transportLayerEncodingLabel); } if (encoding === null) { encoding = prescanMetaCharset(buffer); } - if (encoding === null && options.defaultEncoding !== undefined) { - encoding = options.defaultEncoding; - } - if (encoding === null) { - encoding = "windows-1252"; + encoding = defaultEncoding; } return encoding; @@ -35,8 +27,8 @@ function prescanMetaCharset(buffer) { let c = buffer[i]; if (c === 0x3C) { // "<" - let c1 = buffer[i + 1]; - let c2 = buffer[i + 2]; + const c1 = buffer[i + 1]; + const c2 = buffer[i + 2]; const c3 = buffer[i + 3]; const c4 = buffer[i + 4]; const c5 = buffer[i + 5]; @@ -45,11 +37,10 @@ function prescanMetaCharset(buffer) { i += 4; for (; i < l; i++) { c = buffer[i]; - c1 = buffer[i + 1]; - c2 = buffer[i + 2]; + const cMinus1 = buffer[i - 1]; + const cMinus2 = buffer[i - 2]; // --> (comment end) - if (c === 0x2D && c1 === 0x2D && c2 === 0x3E) { - i += 2; + if (c === 0x3E && cMinus1 === 0x2D && cMinus2 === 0x2D) { break; } } @@ -60,6 +51,7 @@ function prescanMetaCharset(buffer) { (isSpaceCharacter(c5) || c5 === 0x2F)) { // "meta" + space or / i += 6; + const attributeList = new Set(); let gotPragma = false; let needPragma = null; let charset = null; @@ -67,7 +59,8 @@ function prescanMetaCharset(buffer) { let attrRes; do { attrRes = getAttribute(buffer, i, l); - if (attrRes.attr) { + if (attrRes.attr && !attributeList.has(attrRes.attr.name)) { + attributeList.add(attrRes.attr.name); if (attrRes.attr.name === "http-equiv") { gotPragma = attrRes.attr.value === "content-type"; } else if (attrRes.attr.name === "content" && !charset) { @@ -140,7 +133,6 @@ function getAttribute(buffer, i, l) { } // ">" if (c === 0x3E) { - i++; break; } let name = ""; @@ -249,12 +241,12 @@ function extractCharacterEncodingFromMeta(string) { let position = 0; while (true) { - let subPosition = string.substring(position).search(/charset/i); + const indexOfCharset = string.substring(position).search(/charset/i); - if (subPosition === -1) { + if (indexOfCharset === -1) { return null; } - subPosition += "charset".length; + let subPosition = position + indexOfCharset + "charset".length; while (isSpaceCharacter(string[subPosition].charCodeAt(0))) { ++subPosition; @@ -290,10 +282,11 @@ function extractCharacterEncodingFromMeta(string) { return null; } - let end = string.substring(position + 1).search(/\x09|\x0A|\x0C|\x0D|\x20|;/); - if (end === -1) { - end = string.length; - } + const indexOfASCIIWhitespaceOrSemicolon = string.substring(position + 1).search(/\x09|\x0A|\x0C|\x0D|\x20|;/); + const end = indexOfASCIIWhitespaceOrSemicolon === -1 ? + string.length : + position + indexOfASCIIWhitespaceOrSemicolon + 1; + return whatwgEncoding.labelToName(string.substring(position, end)); } diff --git a/node_modules/html-encoding-sniffer/package.json b/node_modules/html-encoding-sniffer/package.json index 622fbed..31b4dbe 100644 --- a/node_modules/html-encoding-sniffer/package.json +++ b/node_modules/html-encoding-sniffer/package.json @@ -1,27 +1,27 @@ { - "_from": "html-encoding-sniffer@^1.0.2", - "_id": "html-encoding-sniffer@1.0.2", + "_from": "html-encoding-sniffer@^2.0.1", + "_id": "html-encoding-sniffer@2.0.1", "_inBundle": false, - "_integrity": "sha512-71lZziiDnsuabfdYiUeWdCVyKuqwWi23L8YeIgV9jSSZHCtb6wB1BKWooH7L3tn4/FuZJMVWyNaIDr4RGmaSYw==", + "_integrity": "sha512-D5JbOMBIR/TVZkubHT+OyT2705QvogUW4IBn6nHd756OwieSF9aDYFj4dv6HHEVGYbHaLETa3WggZYWWMyy3ZQ==", "_location": "/html-encoding-sniffer", "_phantomChildren": {}, "_requested": { "type": "range", "registry": true, - "raw": "html-encoding-sniffer@^1.0.2", + "raw": "html-encoding-sniffer@^2.0.1", "name": "html-encoding-sniffer", "escapedName": "html-encoding-sniffer", - "rawSpec": "^1.0.2", + "rawSpec": "^2.0.1", "saveSpec": null, - "fetchSpec": "^1.0.2" + "fetchSpec": "^2.0.1" }, "_requiredBy": [ "/jsdom" ], - "_resolved": "https://registry.npmjs.org/html-encoding-sniffer/-/html-encoding-sniffer-1.0.2.tgz", - "_shasum": "e70d84b94da53aa375e11fe3a351be6642ca46f8", - "_spec": "html-encoding-sniffer@^1.0.2", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\jsdom", + "_resolved": "https://registry.npmjs.org/html-encoding-sniffer/-/html-encoding-sniffer-2.0.1.tgz", + "_shasum": "42a6dc4fd33f00281176e8b23759ca4e4fa185f3", + "_spec": "html-encoding-sniffer@^2.0.1", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\jsdom", "author": { "name": "Domenic Denicola", "email": "d@domenic.me", @@ -32,13 +32,16 @@ }, "bundleDependencies": false, "dependencies": { - "whatwg-encoding": "^1.0.1" + "whatwg-encoding": "^1.0.5" }, "deprecated": false, "description": "Sniff the encoding from a HTML byte stream", "devDependencies": { - "eslint": "^3.8.0", - "mocha": "^3.1.2" + "eslint": "^6.8.0", + "mocha": "^7.0.0" + }, + "engines": { + "node": ">=10" }, "files": [ "lib/" @@ -56,8 +59,8 @@ "url": "git+https://github.com/jsdom/html-encoding-sniffer.git" }, "scripts": { - "lint": "eslint lib test", + "lint": "eslint .", "test": "mocha" }, - "version": "1.0.2" + "version": "2.0.1" } diff --git a/node_modules/http-signature/package.json b/node_modules/http-signature/package.json index 1c99515..5c3e867 100644 --- a/node_modules/http-signature/package.json +++ b/node_modules/http-signature/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/http-signature/-/http-signature-1.2.0.tgz", "_shasum": "9aecd925114772f3d95b65a60abb8f7c18fbace1", "_spec": "http-signature@~1.2.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Joyent, Inc" }, diff --git a/node_modules/iconv-lite/package.json b/node_modules/iconv-lite/package.json index bea1d22..98eead2 100644 --- a/node_modules/iconv-lite/package.json +++ b/node_modules/iconv-lite/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/iconv-lite/-/iconv-lite-0.4.24.tgz", "_shasum": "2022b4b25fbddc21d2f524974a474aafe733908b", "_spec": "iconv-lite@0.4.24", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\whatwg-encoding", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\whatwg-encoding", "author": { "name": "Alexander Shtuchkin", "email": "ashtuchkin@gmail.com" diff --git a/node_modules/ip-regex/index.js b/node_modules/ip-regex/index.js new file mode 100644 index 0000000..973e5f4 --- /dev/null +++ b/node_modules/ip-regex/index.js @@ -0,0 +1,24 @@ +'use strict'; + +const v4 = '(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])(?:\\.(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])){3}'; + +const v6seg = '[0-9a-fA-F]{1,4}'; +const v6 = ` +( +(?:${v6seg}:){7}(?:${v6seg}|:)| // 1:2:3:4:5:6:7:: 1:2:3:4:5:6:7:8 +(?:${v6seg}:){6}(?:${v4}|:${v6seg}|:)| // 1:2:3:4:5:6:: 1:2:3:4:5:6::8 1:2:3:4:5:6::8 1:2:3:4:5:6::1.2.3.4 +(?:${v6seg}:){5}(?::${v4}|(:${v6seg}){1,2}|:)| // 1:2:3:4:5:: 1:2:3:4:5::7:8 1:2:3:4:5::8 1:2:3:4:5::7:1.2.3.4 +(?:${v6seg}:){4}(?:(:${v6seg}){0,1}:${v4}|(:${v6seg}){1,3}|:)| // 1:2:3:4:: 1:2:3:4::6:7:8 1:2:3:4::8 1:2:3:4::6:7:1.2.3.4 +(?:${v6seg}:){3}(?:(:${v6seg}){0,2}:${v4}|(:${v6seg}){1,4}|:)| // 1:2:3:: 1:2:3::5:6:7:8 1:2:3::8 1:2:3::5:6:7:1.2.3.4 +(?:${v6seg}:){2}(?:(:${v6seg}){0,3}:${v4}|(:${v6seg}){1,5}|:)| // 1:2:: 1:2::4:5:6:7:8 1:2::8 1:2::4:5:6:7:1.2.3.4 +(?:${v6seg}:){1}(?:(:${v6seg}){0,4}:${v4}|(:${v6seg}){1,6}|:)| // 1:: 1::3:4:5:6:7:8 1::8 1::3:4:5:6:7:1.2.3.4 +(?::((?::${v6seg}){0,5}:${v4}|(?::${v6seg}){1,7}|:)) // ::2:3:4:5:6:7:8 ::2:3:4:5:6:7:8 ::8 ::1.2.3.4 +)(%[0-9a-zA-Z]{1,})? // %eth0 %1 +`.replace(/\s*\/\/.*$/gm, '').replace(/\n/g, '').trim(); + +const ip = module.exports = opts => opts && opts.exact ? + new RegExp(`(?:^${v4}$)|(?:^${v6}$)`) : + new RegExp(`(?:${v4})|(?:${v6})`, 'g'); + +ip.v4 = opts => opts && opts.exact ? new RegExp(`^${v4}$`) : new RegExp(v4, 'g'); +ip.v6 = opts => opts && opts.exact ? new RegExp(`^${v6}$`) : new RegExp(v6, 'g'); diff --git a/node_modules/array-equal/LICENSE b/node_modules/ip-regex/license similarity index 93% rename from node_modules/array-equal/LICENSE rename to node_modules/ip-regex/license index a7ae8ee..654d0bf 100644 --- a/node_modules/array-equal/LICENSE +++ b/node_modules/ip-regex/license @@ -1,7 +1,6 @@ - The MIT License (MIT) -Copyright (c) 2014 Jonathan Ong me@jongleberry.com +Copyright (c) Sindre Sorhus (sindresorhus.com) Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal diff --git a/node_modules/ip-regex/package.json b/node_modules/ip-regex/package.json new file mode 100644 index 0000000..7961bdf --- /dev/null +++ b/node_modules/ip-regex/package.json @@ -0,0 +1,77 @@ +{ + "_from": "ip-regex@^2.1.0", + "_id": "ip-regex@2.1.0", + "_inBundle": false, + "_integrity": "sha1-+ni/XS5pE8kRzp+BnuUUa7bYROk=", + "_location": "/ip-regex", + "_phantomChildren": {}, + "_requested": { + "type": "range", + "registry": true, + "raw": "ip-regex@^2.1.0", + "name": "ip-regex", + "escapedName": "ip-regex", + "rawSpec": "^2.1.0", + "saveSpec": null, + "fetchSpec": "^2.1.0" + }, + "_requiredBy": [ + "/tough-cookie" + ], + "_resolved": "https://registry.npmjs.org/ip-regex/-/ip-regex-2.1.0.tgz", + "_shasum": "fa78bf5d2e6913c911ce9f819ee5146bb6d844e9", + "_spec": "ip-regex@^2.1.0", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\tough-cookie", + "author": { + "name": "Sindre Sorhus", + "email": "sindresorhus@gmail.com", + "url": "sindresorhus.com" + }, + "bugs": { + "url": "https://github.com/sindresorhus/ip-regex/issues" + }, + "bundleDependencies": false, + "deprecated": false, + "description": "Regular expression for matching IP addresses (IPv4 & IPv6)", + "devDependencies": { + "ava": "*", + "xo": "*" + }, + "engines": { + "node": ">=4" + }, + "files": [ + "index.js" + ], + "homepage": "https://github.com/sindresorhus/ip-regex#readme", + "keywords": [ + "ip", + "ipv6", + "ipv4", + "regex", + "regexp", + "re", + "match", + "test", + "find", + "text", + "pattern", + "internet", + "protocol", + "address", + "validate" + ], + "license": "MIT", + "name": "ip-regex", + "repository": { + "type": "git", + "url": "git+https://github.com/sindresorhus/ip-regex.git" + }, + "scripts": { + "test": "xo && ava" + }, + "version": "2.1.0", + "xo": { + "esnext": true + } +} diff --git a/node_modules/ip-regex/readme.md b/node_modules/ip-regex/readme.md new file mode 100644 index 0000000..66bc7f2 --- /dev/null +++ b/node_modules/ip-regex/readme.md @@ -0,0 +1,63 @@ +# ip-regex [![Build Status](https://travis-ci.org/sindresorhus/ip-regex.svg?branch=master)](https://travis-ci.org/sindresorhus/ip-regex) + +> Regular expression for matching IP addresses + + +## Install + +``` +$ npm install --save ip-regex +``` + + +## Usage + +```js +const ipRegex = require('ip-regex'); + +// Contains an IP address? +ipRegex().test('unicorn 192.168.0.1'); +//=> true + +// Is an IP address? +ipRegex({exact: true}).test('unicorn 192.168.0.1'); +//=> false + +ipRegex.v6({exact: true}).test('1:2:3:4:5:6:7:8'); +//=> true + +'unicorn 192.168.0.1 cake 1:2:3:4:5:6:7:8 rainbow'.match(ipRegex()); +//=> ['192.168.0.1', '1:2:3:4:5:6:7:8'] +``` + + +## API + +### ipRegex([options]) + +Returns a regex for matching both IPv4 and IPv6. + +### ipRegex.v4([options]) + +Returns a regex for matching IPv4. + +### ipRegex.v6([options]) + +Returns a regex for matching IPv6. + +#### options.exact + +Type: `boolean`
+Default: `false` *(Matches any IP address in a string)* + +Only match an exact string. Useful with `RegExp#test()` to check if a string is an IP address. + + +## Related + +- [is-ip](https://github.com/sindresorhus/is-ip) - Check if a string is an IP address + + +## License + +MIT © [Sindre Sorhus](https://sindresorhus.com) diff --git a/node_modules/is-potential-custom-element-name/LICENSE-MIT.txt b/node_modules/is-potential-custom-element-name/LICENSE-MIT.txt new file mode 100644 index 0000000..a41e0a7 --- /dev/null +++ b/node_modules/is-potential-custom-element-name/LICENSE-MIT.txt @@ -0,0 +1,20 @@ +Copyright Mathias Bynens + +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/node_modules/is-potential-custom-element-name/index.js b/node_modules/is-potential-custom-element-name/index.js new file mode 100644 index 0000000..f750dcf --- /dev/null +++ b/node_modules/is-potential-custom-element-name/index.js @@ -0,0 +1,9 @@ +// Generated using `npm run build`. Do not edit. + +var regex = /^[a-z](?:[\-\.0-9_a-z\xB7\xC0-\xD6\xD8-\xF6\xF8-\u037D\u037F-\u1FFF\u200C\u200D\u203F\u2040\u2070-\u218F\u2C00-\u2FEF\u3001-\uD7FF\uF900-\uFDCF\uFDF0-\uFFFD]|[\uD800-\uDB7F][\uDC00-\uDFFF])*-(?:[\-\.0-9_a-z\xB7\xC0-\xD6\xD8-\xF6\xF8-\u037D\u037F-\u1FFF\u200C\u200D\u203F\u2040\u2070-\u218F\u2C00-\u2FEF\u3001-\uD7FF\uF900-\uFDCF\uFDF0-\uFFFD]|[\uD800-\uDB7F][\uDC00-\uDFFF])*$/; + +var isPotentialCustomElementName = function(string) { + return regex.test(string); +}; + +module.exports = isPotentialCustomElementName; diff --git a/node_modules/is-potential-custom-element-name/package.json b/node_modules/is-potential-custom-element-name/package.json new file mode 100644 index 0000000..26005d4 --- /dev/null +++ b/node_modules/is-potential-custom-element-name/package.json @@ -0,0 +1,63 @@ +{ + "_from": "is-potential-custom-element-name@^1.0.0", + "_id": "is-potential-custom-element-name@1.0.0", + "_inBundle": false, + "_integrity": "sha1-DFLlS8yjkbssSUsh6GJtczbG45c=", + "_location": "/is-potential-custom-element-name", + "_phantomChildren": {}, + "_requested": { + "type": "range", + "registry": true, + "raw": "is-potential-custom-element-name@^1.0.0", + "name": "is-potential-custom-element-name", + "escapedName": "is-potential-custom-element-name", + "rawSpec": "^1.0.0", + "saveSpec": null, + "fetchSpec": "^1.0.0" + }, + "_requiredBy": [ + "/jsdom" + ], + "_resolved": "https://registry.npmjs.org/is-potential-custom-element-name/-/is-potential-custom-element-name-1.0.0.tgz", + "_shasum": "0c52e54bcca391bb2c494b21e8626d7336c6e397", + "_spec": "is-potential-custom-element-name@^1.0.0", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\jsdom", + "author": { + "name": "Mathias Bynens", + "url": "https://mathiasbynens.be/" + }, + "bugs": { + "url": "https://github.com/mathiasbynens/is-potential-custom-element-name/issues" + }, + "bundleDependencies": false, + "dependencies": {}, + "deprecated": false, + "description": "Check whether a given string matches the `PotentialCustomElementName` production as defined in the HTML Standard.", + "devDependencies": { + "mocha": "^2.2.1", + "regenerate": "^1.3.1" + }, + "files": [ + "LICENSE-MIT.txt", + "index.js" + ], + "homepage": "https://github.com/mathiasbynens/is-potential-custom-element-name", + "keywords": [ + "html", + "custom element", + "custom element name", + "web components" + ], + "license": "MIT", + "main": "index.js", + "name": "is-potential-custom-element-name", + "repository": { + "type": "git", + "url": "git+https://github.com/mathiasbynens/is-potential-custom-element-name.git" + }, + "scripts": { + "build": "node build.js", + "test": "mocha" + }, + "version": "1.0.0" +} diff --git a/node_modules/is-typedarray/package.json b/node_modules/is-typedarray/package.json index ee5e195..1d5e4dc 100644 --- a/node_modules/is-typedarray/package.json +++ b/node_modules/is-typedarray/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/is-typedarray/-/is-typedarray-1.0.0.tgz", "_shasum": "e479c80858df0c1b11ddda6940f96011fcda4a9a", "_spec": "is-typedarray@~1.0.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Hugh Kennedy", "email": "hughskennedy@gmail.com", diff --git a/node_modules/isstream/package.json b/node_modules/isstream/package.json index 68cce0c..be0ce9f 100644 --- a/node_modules/isstream/package.json +++ b/node_modules/isstream/package.json @@ -21,7 +21,7 @@ "_resolved": "https://registry.npmjs.org/isstream/-/isstream-0.1.2.tgz", "_shasum": "47e63f7af55afa6f92e1500e690eb8b8529c099a", "_spec": "isstream@~0.1.2", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\request", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\request", "author": { "name": "Rod Vagg", "email": "rod@vagg.org" diff --git a/node_modules/jsbn/package.json b/node_modules/jsbn/package.json index 47574d8..99d7943 100644 --- a/node_modules/jsbn/package.json +++ b/node_modules/jsbn/package.json @@ -22,7 +22,7 @@ "_resolved": "https://registry.npmjs.org/jsbn/-/jsbn-0.1.1.tgz", "_shasum": "a5e654c2e5a2deb5f201d96cefbca80c0ef2f513", "_spec": "jsbn@~0.1.0", - "_where": "F:\\projects\\p\\minifyfromhtml\\node_modules\\sshpk", + "_where": "D:\\Projects\\minifyfromhtml\\node_modules\\sshpk", "author": { "name": "Tom Wu" }, diff --git a/node_modules/jsdom/Changelog.md b/node_modules/jsdom/Changelog.md index bb9e023..6766f59 100644 --- a/node_modules/jsdom/Changelog.md +++ b/node_modules/jsdom/Changelog.md @@ -1,3 +1,5 @@ +# jsdom Changelog + +## 16.3.0 + +* Added firing of `focusin` and `focusout` when using `el.focus()` and `el.blur()`. (trueadm) +* Fixed elements with the `contenteditable=""` attribute to be considered as focusable. (jamieliu386) +* Fixed `window.NodeFilter` to be per-`Window`, instead of shared across all `Window`s. (ExE-Boss) +* Fixed edge-case behavior involving use of objects with `handleEvent` properties as event listeners. (ExE-Boss) +* Fixed a second failing image load sometimes firing a `load` event instead of an `error` event, when the `canvas` package is installed. (strager) +* Fixed drawing an empty canvas into another canvas. (zjffun) + +## 16.2.2 + +* Updated `StyleSheetList` for better spec compliance; notably it no longer inherits from `Array.prototype`. (ExE-Boss) +* Fixed `requestAnimationFrame()` from preventing process exit. This likely regressed in v16.1.0. +* Fixed `setTimeout()` to no longer leak the closures passed in to it. This likely regressed in v16.1.0. (AviVahl) +* Fixed infinite recursion that could occur when calling `click()` on a `