valki/dockerized_openAger
3
1
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Intial Commit

Browse Source
This commit is contained in:
valki
2020-10-17 18:42:50 +02:00
commit 664c6d8ca3
5892 changed files with 759183 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

118
nodered/rootfs/data/node_modules/decimal.js/CHANGELOG.md generated vendored Normal file
View File

@@ -0,0 +1,118 @@
#### 7.1.1
* 10/01/2017
* Remove duplicated for-loop
* Minor refactoring
#### 7.1.0
* 09/11/2016
* Support ES6 imports.
#### 7.0.0
* 09/11/2016
* Remove `require('crypto')` - leave it to the user
* Default `Decimal.crypto` to `false`
* Add `Decimal.set` as `Decimal.config` alias
#### 6.0.0
* 30/06/2016
* Removed base-88 serialization format
* Amended `toJSON` and removed `Decimal.fromJSON` accordingly
#### 5.0.8
* 09/03/2016
* Add newline to single test results
* Correct year
#### 5.0.7
* 29/02/2016
* Add decimal.js-light link
* Remove outdated example from docs
#### 5.0.6
* 22/02/2016
* Add bower.json
#### 5.0.5
* 20/02/2016
* Bugfix: #26 wrong precision applied
#### 5.0.4
* 14/02/2016
* Bugfix: #26 clone
#### 5.0.3
* 06/02/2016
* Refactor tests
#### 5.0.2
* 05/02/2016
* Added immutability tests
* Minor *decimal.js* clean-up
#### 5.0.1
* 28/01/2016
* Bugfix: #20 cos mutates value
* Add pi info to docs
#### 5.0.0
* 25/01/2016
* Added trigonometric functions and `cubeRoot` method
* Added most of JavaScript's `Math` object methods as Decimal methods
* Added `toBinary`, `toHexadecimal` and `toOctal` methods
* Added `isPositive` method
* Removed the 15 significant digit limit for numbers
* `toFraction` now returns an array of two Decimals, not two strings
* String values containing whitespace or a plus sign are no longer accepted
* `valueOf` now returns `'-0'` for minus zero
* `comparedTo` now returns `NaN` not `null` for comparisons with `NaN`
* `Decimal.max` and `Decimal.min` no longer accept an array
* The Decimal constructor and `toString` no longer accept a base argument
* Binary, hexadecimal and octal prefixes are now recognised for string values
* Removed `Decimal.errors` configuration property
* Removed `toFormat` method
* Removed `Decimal.ONE`
* Renamed `exponential` method to `naturalExponential`
* Renamed `Decimal.constructor` method to `Decimal.clone`
* Simplified error handling and amended error messages
* Refactored the test suite
* `Decimal.crypto` is now `undefined` by default, and the `crypto` object will be used if available
* Major internal refactoring
* Removed *bower.json*
#### 4.0.2
* 20/02/2015 Add bower.json. Add source map. Amend travis CI. Amend doc/comments
#### 4.0.1
* 11/12/2014 Assign correct constructor when duplicating a Decimal
#### 4.0.0
* 10/11/2014 `toFormat` amended to use `Decimal.format` object for more flexible configuration
#### 3.0.1
* 8/06/2014 Surround crypto require in try catch. See issue #5
#### 3.0.0
* 4/06/2014 `random` simplified. Major internal changes mean the properties of a Decimal must now be considered read-only
#### 2.1.0
* 4/06/2014 Amend UMD
#### 2.0.3
* 8/05/2014 Fix NaN toNumber
#### 2.0.2
* 30/04/2014 Correct doc links
#### 2.0.1
* 10/04/2014 Update npmignore
#### 2.0.0
* 10/04/2014 Add `toSignificantDigits`
* Remove `toInteger`
* No arguments to `ceil`, `floor`, `round` and `trunc`
#### 1.0.1
* 07/04/2014 Minor documentation clean-up
#### 1.0.0
* 02/04/2014 Initial release

23
nodered/rootfs/data/node_modules/decimal.js/LICENCE.md generated vendored Normal file
View File

@@ -0,0 +1,23 @@
The MIT Licence.
Copyright (c) 2016, 2017 Michael Mclaughlin
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
'Software'), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

232
nodered/rootfs/data/node_modules/decimal.js/README.md generated vendored Normal file
View File

@@ -0,0 +1,232 @@
![decimal.js](https://raw.githubusercontent.com/MikeMcl/decimal.js/gh-pages/decimaljs.png)
An arbitrary-precision Decimal type for JavaScript.
<br>
[![Build Status](https://travis-ci.org/MikeMcl/decimal.js.svg)](https://travis-ci.org/MikeMcl/decimal.js)
<br>
## Features
- Integers and floats
- Simple but full-featured API
- Replicates many of the methods of JavaScript's `Number.prototype` and `Math` objects
- Also handles hexadecimal, binary and octal values
- Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
- No dependencies
- Wide platform compatibility: uses JavaScript 1.5 (ECMAScript 3) features only
- Comprehensive [documentation](http://mikemcl.github.io/decimal.js/) and test set
![API](https://raw.githubusercontent.com/MikeMcl/decimal.js/gh-pages/API.png)
The library is similar to [bignumber.js](https://github.com/MikeMcl/bignumber.js/), but here
precision is specified in terms of significant digits rather than decimal places, and all
calculations are rounded to the precision (similar to Python's decimal module) rather than just
those involving division.
This library also adds the trigonometric functions, among others, and supports non-integer powers,
which makes it a significantly larger library than *bignumber.js* and the even smaller
[big.js](https://github.com/MikeMcl/big.js/).
For a lighter version of this library without the trigonometric functions see the
[v4.x.x](https://github.com/MikeMcl/decimal.js/tree/v4.x.x) branch where version 4 continues to be supported, or better, see [decimal.js-light](https://github.com/MikeMcl/decimal.js-light/), which is lighter still.
## Load
The library is the single JavaScript file *decimal.js* (or minified, *decimal.min.js*).
It can be loaded using a script tag in an HTML document for the browser
```html
<script src='path/to/decimal.js'></script>
```
or as a [Node.js](http://nodejs.org) module using `require`.
```js
var Decimal = require('decimal.js');
```
For Node, the library is available from the [npm](https://npmjs.org/) registry
```bash
$ npm install decimal.js
```
To load with 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'
```
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.
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
Decimal10 = Decimal.clone({ precision: 10, rounding: 1 })
x = new Decimal(5)
y = new Decimal10(5)
x.div(3) // '1.6667'
y.div(3) // '1.666666666'
```
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.
## Feedback
<a href='mailto:M8ch88l@gmail.com'>M8ch88l@gmail.com</a>
**BTC** 16MjxmTB5EZxY5Uk9xyhfsu4n9gYxEJYkY
**Monero** 4B7GE8BUQ5dHjHxVubTDmsTn4bUYWG6bsRXQwunDifX6hcNAfkmGxcZYQGbpYgArKLNxfA15LK2j6bUENiE9eTHRAWkEB5R
## Licence
MIT.
See *LICENCE.md*

33
nodered/rootfs/data/node_modules/decimal.js/bower.json generated vendored Normal file
View File

@@ -0,0 +1,33 @@
{
"name": "decimal.js",
"main": "decimal.js",
"version": "7.1.1",
"homepage": "https://github.com/MikeMcl/decimal.js",
"authors": [
"Michael Mclaughlin <M8ch88l@gmail.com>"
],
"description": "An arbitrary-precision Decimal type for JavaScript",
"moduleType": [
"amd",
"globals",
"node"
],
"keywords": [
"arbitrary",
"precision",
"arithmetic",
"bignumber",
"decimal",
"float",
"biginteger",
"bigdecimal",
"bignum",
"math"
],
"license": "MIT",
"ignore": [
".*",
"*.json",
"test"
]
}

4799
nodered/rootfs/data/node_modules/decimal.js/decimal.js generated vendored Normal file
View File

@@ -0,0 +1,4799 @@
/*! decimal.js v7.1.1 https://github.com/MikeMcl/decimal.js/LICENCE */
;(function (globalScope) {
'use strict';
/*
* decimal.js v7.1.1
* An arbitrary-precision Decimal type for JavaScript.
* https://github.com/MikeMcl/decimal.js
* Copyright (c) 2016 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licence
*/
// ----------------------------------- EDITABLE DEFAULTS ------------------------------------ //
// The maximum exponent magnitude.
// The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`.
var EXP_LIMIT = 9e15, // 0 to 9e15
// The limit on the value of `precision`, and on the value of the first argument to
// `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
MAX_DIGITS = 1e9, // 0 to 1e9
// Base conversion alphabet.
NUMERALS = '0123456789abcdef',
// The natural logarithm of 10 (1025 digits).
LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',
// Pi (1025 digits).
PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',
// The initial configuration properties of the Decimal constructor.
Decimal = {
// 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, 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 = {};
// 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 * Math.pow(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 = Math.pow(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 = Math.pow(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(Math.pow(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 the magnitude of `y` to the value
* of this Decimal.
*
* If the value of this Decimal is equidistant from two multiples of `y`, the rounding mode `rm`,
* or `Decimal.rounding` if `rm` is omitted, determines the direction of the nearest multiple.
*
* In the context of this method, rounding mode 4 (ROUND_HALF_UP) is the same as rounding mode 0
* (ROUND_UP), and so on.
*
* 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) 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;
if (rm < 4) rm = [4, 5, 7, 8][rm];
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, sign, yIsInt,
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);
e = mathfloor(y.e / LOG_BASE);
k = y.d.length - 1;
yIsInt = e >= k;
sign = x.s;
if (!yIsInt) {
if (sign < 0) return new Ctor(NaN);
// If y is a small integer use the 'exponentiation by squaring' algorithm.
} else if ((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);
}
// Result is negative if x is negative and the last digit of integer y is odd.
sign = sign < 0 && y.d[Math.max(e, k)] & 1 ? -1 : 1;
// 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;
// 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 ? sign / 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);
// 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 = sign;
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 = Math.pow(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 ? Math.pow(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;
// Max k before Math.pow precision loss is 22
x = x.times(Math.pow(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;
}
// 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}
*
* 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,
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 ((v = obj[p = ps[i]]) !== void 0) {
if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
else throw Error(invalidArgument + p + ': ' + v);
}
}
if ((v = obj[p = 'crypto']) !== 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;
x.e = v.e;
x.d = (v = v.d) ? v.slice() : v;
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++;
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 (v.charCodeAt(0) === 45) {
v = v.slice(1);
x.s = -1;
} else {
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.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) {
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 + ...)
*
*/
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 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
*
*/
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(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) {
module.exports = Decimal.default = Decimal.Decimal = Decimal;
// Browser.
} else {
if (!globalScope) {
globalScope = typeof self != 'undefined' && self && self.self == self
? self : Function('return this')();
}
noConflict = globalScope.Decimal;
Decimal.noConflict = function () {
globalScope.Decimal = noConflict;
return Decimal;
};
globalScope.Decimal = Decimal;
}
})(this);

3
nodered/rootfs/data/node_modules/decimal.js/decimal.min.js generated vendored Normal file
View File

File diff suppressed because one or more lines are too long

2629
nodered/rootfs/data/node_modules/decimal.js/doc/API.html generated vendored Normal file
View File

@@ -0,0 +1,2629 @@
<!DOCTYPE HTML>
<html>
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="Author" content="MMclaughlin">
<title>decimal.js API</title>
<style>
html{font-size:100%}
body{background:#fff;font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;
line-height:1.65em;min-height:100%;margin:0}
body,i{color:#000}
.nav{background:#fff;position:fixed;top:0;bottom:0;left:0;width:210px;overflow-y:auto;
padding:15px 0 30px 15px}
div.container{width:600px;margin:50px 0 50px 240px}
p{margin:0 0 1em;width:600px}
pre,ul{margin:1em 0}
h1,h2,h3,h4,h5{margin:0;padding:1.5em 0 0}
h1,h2{padding:.75em 0}
h1{font:400 3em Consolas, monaco, monospace;color:#000;margin-bottom:1em}
h2{font-size:2.25em;color:#f00}
h3{font-size:1.75em;color:#69d2e7}
h4{font-size:1.75em;color:#f00;padding-bottom:.75em}
h5{font-size:1.2em;margin-bottom:.4em}
h6{font-size:1.1em;margin-bottom:0.8em;padding:0.5em 0}
dd dt{font-size:1.2em}
dt{padding-top:.5em}
dd{padding-top:.35em}
b{font-weight:700}
a,a:visited{color:#f00;text-decoration:none}
a:active,a:hover{outline:0;text-decoration:underline}
.nav a,.nav b,.nav a:visited{display:block;color:#f00;font-weight:700;margin-top:15px}
.nav b{color:#69d2e7;margin-top:20px;cursor:default;width:auto}
ul{list-style-type:none;padding:0 0 0 20px}
.nav ul{line-height:14px;padding-left:0;margin:5px 0 0}
.nav ul a,.nav ul a:visited,span{display:inline;color:#000;font-family:Verdana,Geneva,sans-serif;
font-size:11px;font-weight:400;margin:0}
.inset{margin-left:20px;font-size:.9em}
.nav li{width:auto;margin:0 0 3px}
.alias{font-style:italic;margin-left:20px}
table{border-collapse:collapse;border-spacing:0;border:2px solid #a7dbd8;margin:1.75em 0;padding:0}
td,th{text-align:left;margin:0;padding:2px 5px;border:1px dotted #a7dbd8}
th{border-top:2px solid #a7dbd8;border-bottom:2px solid #a7dbd8;color:#f00}
code,pre{font-family:Consolas, monaco, monospace;font-weight:400}
pre{background:#f5f5f5;white-space:pre-wrap;word-wrap:break-word;border-left:5px solid #a7dbd8;
padding:1px 0 1px 15px;margin:1.2em 0}
code,.nav-title{color:#f00}
.end{margin-bottom:25px}
.centre{text-align:center}
#modes,#configProps{color:#f00}
.spacer{line-height:0px}
#faq{margin:3em 0 0}
li span{float:right;margin-right:10px;color:#c0c0c0}
#js{font:inherit;color:#f00}
</style>
</head>
<body>
<div class="nav">
<a class='nav-title' href="#">API</a>
<b>CONSTRUCTOR</b>
<ul><li><a href="#decimal"><strong>Decimal</strong></a></li></ul>
<a href="#methods">Methods</a>
<ul>
<li><a href="#Dabs" >abs</a></li>
<li><a href="#Dacos" >acos</a></li>
<li><a href="#Dacosh" >acosh</a></li>
<li><a href="#Dadd" >add</a></li>
<li><a href="#Dasin" >asin</a></li>
<li><a href="#Dasinh" >asinh</a></li>
<li><a href="#Datan" >atan</a></li>
<li><a href="#Datanh" >atanh</a></li>
<li><a href="#Datan2" >atan2</a></li>
<li><a href="#Dcbrt" >cbrt</a></li>
<li><a href="#Dceil" >ceil</a></li>
<li><a href="#Dclone" ><strong>clone</strong></a></li>
<li><a href="#Dcos" >cos</a></li>
<li><a href="#Dcosh" >cosh</a></li>
<li><a href="#Ddiv" >div</a></li>
<li><a href="#Dexp" >exp</a></li>
<li><a href="#Dfloor" >floor</a></li>
<li><a href="#Dhypot" >hypot</a></li>
<li><a href="#Dln" >ln</a></li>
<li><a href="#Dlog" >log</a></li>
<li><a href="#Dlog2" >log2</a></li>
<li><a href="#Dlog10" >log10</a></li>
<li><a href="#Dmax" >max</a></li>
<li><a href="#Dmin" >min</a></li>
<li><a href="#Dmod" >mod</a></li>
<li><a href="#Dmul" >mul</a></li>
<li><a href="#DnoConflict"><strong>noConflict</strong></a></li>
<li><a href="#Dpow" >pow</a></li>
<li><a href="#Drandom" >random</a></li>
<li><a href="#Dround" >round</a></li>
<li><a href="#Dset" ><strong>set</strong></a></li>
<li><a href="#Dsign" >sign</a></li>
<li><a href="#Dsin" >sin</a></li>
<li><a href="#Dsinh" >sinh</a></li>
<li><a href="#Dsqrt" >sqrt</a></li>
<li><a href="#Dsub" >sub</a></li>
<li><a href="#Dtan" >tan</a></li>
<li><a href="#Dtanh" >tanh</a></li>
<li><a href="#Dtrunc" >trunc</a></li>
</ul>
<a href="#constructor-properties">Properties</a>
<ul>
<li><a href="#precision">precision</a></li>
<li><a href="#rounding" >rounding</a></li>
<li><a href="#minE" >minE</a></li>
<li><a href="#maxE" >maxE</a></li>
<li><a href="#toExpNeg" >toExpNeg</a></li>
<li><a href="#toExpPos" >toExpPos</a></li>
<li><a href="#modulo" >modulo</a></li>
<li><a href="#crypto" >crypto</a></li>
<li class='spacer'>&nbsp;</li>
<li><a href="#modes">ROUND_UP</a></li>
<li><a href="#modes">ROUND_DOWN</a></li>
<li><a href="#modes">ROUND_CEIL</a></li>
<li><a href="#modes">ROUND_FLOOR</a></li>
<li><a href="#modes">ROUND_HALF_UP</a></li>
<li><a href="#modes">ROUND_HALF_DOWN</a></li>
<li><a href="#modes">ROUND_HALF_EVEN</a></li>
<li><a href="#modes">ROUND_HALF_CEIL</a></li>
<li><a href="#modes">ROUND_HALF_FLOOR</a></li>
<li><a href="#modes">EUCLID</a></li>
</ul>
<b> INSTANCE </b>
<a href="#prototype-methods">Methods</a>
<ul>
<li><a href="#abs" >absoluteValue </a><span>abs</span> </li>
<li><a href="#ceil" >ceil </a> </li>
<li><a href="#cmp" >comparedTo </a><span>cmp</span> </li>
<li><a href="#cos" >cosine </a><span>cos</span> </li>
<li><a href="#cbrt" >cubeRoot </a><span>cbrt</span> </li>
<li><a href="#dp" >decimalPlaces </a><span>dp</span> </li>
<li><a href="#div" >dividedBy </a><span>div</span> </li>
<li><a href="#divToInt" >dividedToIntegerBy </a><span>divToInt</span></li>
<li><a href="#eq" >equals </a><span>eq</span> </li>
<li><a href="#floor" >floor </a> </li>
<li><a href="#gt" >greaterThan </a><span>gt</span> </li>
<li><a href="#gte" >greaterThanOrEqualTo </a><span>gte</span> </li>
<li><a href="#cosh" >hyperbolicCosine </a><span>cosh</span> </li>
<li><a href="#sinh" >hyperbolicSine </a><span>sinh</span> </li>
<li><a href="#tanh" >hyperbolicTangent </a><span>tanh</span> </li>
<li><a href="#acos" >inverseCosine </a><span>acos</span> </li>
<li><a href="#acosh" >inverseHyperbolicCosine </a><span>acosh</span> </li>
<li><a href="#asinh" >inverseHyperbolicSine </a><span>asinh</span> </li>
<li><a href="#atanh" >inverseHyperbolicTangent</a><span>atanh</span> </li>
<li><a href="#asin" >inverseSine </a><span>asin</span> </li>
<li><a href="#atan" >inverseTangent </a><span>atan</span> </li>
<li><a href="#isFinite" >isFinite </a> </li>
<li><a href="#isInt" >isInteger </a><span>isInt</span> </li>
<li><a href="#isNaN" >isNaN </a> </li>
<li><a href="#isNeg" >isNegative </a><span>isNeg</span> </li>
<li><a href="#isPos" >isPositive </a><span>isPos</span> </li>
<li><a href="#isZero" >isZero </a> </li>
<li><a href="#lt" >lessThan </a><span>lt</span> </li>
<li><a href="#lte" >lessThanOrEqualTo </a><span>lte</span> </li>
<li><a href="#log" >logarithm </a><span>log</span> </li>
<li><a href="#sub" >minus </a><span>sub</span> </li>
<li><a href="#mod" >modulo </a><span>mod</span> </li>
<li><a href="#exp" >naturalExponential </a><span>exp</span> </li>
<li><a href="#ln" >naturalLogarithm </a><span>ln</span> </li>
<li><a href="#neg" >negated </a><span>neg</span> </li>
<li><a href="#add" >plus </a><span>add</span> </li>
<li><a href="#sd" >precision </a><span>sd</span> </li>
<li><a href="#round" >round </a> </li>
<li><a href="#sin" >sine </a><span>sin</span> </li>
<li><a href="#sqrt" >squareRoot </a><span>sqrt</span> </li>
<li><a href="#tan" >tangent </a><span>tan</span> </li>
<li><a href="#mul" >times </a><span>mul</span> </li>
<li><a href="#toBinary" >toBinary </a> </li>
<li><a href="#toDP" >toDecimalPlaces </a><span>toDP</span> </li>
<li><a href="#toExponential">toExponential </a> </li>
<li><a href="#toFixed" >toFixed </a> </li>
<li><a href="#toFraction" >toFraction </a> </li>
<li><a href="#toHex" >toHexadecimal </a><span>toHex</span> </li>
<li><a href="#toJSON" >toJSON </a> </li>
<li><a href="#toNearest" >toNearest </a> </li>
<li><a href="#toNumber" >toNumber </a> </li>
<li><a href="#toOctal" >toOctal </a> </li>
<li><a href="#pow" >toPower </a><span>pow</span> </li>
<li><a href="#toPrecision" >toPrecision </a> </li>
<li><a href="#toSD" >toSignificantDigits </a><span>toSD</span> </li>
<li><a href="#toString" >toString </a> </li>
<li><a href="#trunc" >truncated </a><span>trunc</span> </li>
<li><a href="#valueOf" >valueOf </a> </li>
</ul>
<a href="#instance-properties">Properties</a>
<ul>
<li><a href="#digits" >d</a><span>digits</span></li>
<li><a href="#exponent">e</a><span>exponent</span></li>
<li><a href="#sign" >s</a><span>sign</span></li>
</ul>
<a href="#zero-nan-infinity">Zero, NaN &amp; Infinity</a>
<a href="#Errors">Errors</a>
<a href="#Pi">Pi</a>
<a class='end' href="#faq">FAQ</a>
</div>
<div class="container">
<h1>decimal<span id='js'>.js</span></h1>
<p>An arbitrary-precision Decimal type for JavaScript.</p>
<p><a href='https://github.com/MikeMcl/decimal.js'>Hosted on GitHub</a>.</p>
<h2>API</h2>
<p>
See the <a href='https://github.com/MikeMcl/decimal.js'>README</a> on GitHub for a quick-start
introduction.
</p>
<p>
In all examples below, <code>var</code> and semicolons are not shown, and if a commented-out
value is in quotes it means <code>toString</code> has been called on the preceding expression.
</p><br />
<p>
When the library is loaded, it defines a single function object,
<a href='#decimal'><code>Decimal</code></a>, the constructor of Decimal instances.
</p>
<p>
<i>
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.
</i>
</p>
<p>
<i>
A new Decimal constructor is created by calling the <code><a href='#Dclone'>clone</a></code>
method of an already existing Decimal constructor.
</i>
</p>
<h3 class='end'>CONSTRUCTOR</h3>
<h5 id="decimal">
Decimal<code class='inset'>Decimal(value) <i>&rArr; Decimal</i></code>
</h5>
<dl>
<dt><code>value</code>: <i>number|string|Decimal</i></dt>
<dd>
A legitimate <code>value</code> is an integer or float, including <code>&plusmn;0</code>, or
is <code>&plusmn;Infinity</code>, or <code>NaN</code>.
</dd>
<dd>
The number of digits of <code>value</code> is not limited, except by JavaScript's maximum
array size and, in practice, the processing time required.
</dd>
<dd>
The allowable range of <code>value</code> is defined in terms of a maximum exponent, see
<a href='#maxE'>maxE</a>, and a minimum exponent, see <a href='#minE'>minE</a>.
</dd>
<dd>
As well as in decimal, a string <code>value</code> may be expressed in binary, hexadecimal
or octal, if the appropriate prefix is included: <code>0x</code> or <code>0X</code> for
hexadecimal, <code>0b</code> or <code>0B</code> for binary, and <code>0o</code> or
<code>0O</code> for octal.
</dd>
<dd>
Both decimal and non-decimal string values may use exponential (floating-point), as well as
normal (fixed-point) notation.
</dd>
<dd>
In exponential notation, <code>e</code> or <code>E</code> defines a power-of-ten exponent
for decimal values, and <code>p</code> or <code>P</code> defines a power-of-two exponent for
non-decimal values, i.e. binary, hexadecimal or octal.
</dd>
</dl>
<p>Returns a new Decimal object instance.</p>
<p>Throws on an invalid <code>value</code>.</p>
<pre>
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'</pre>
<h4 id="methods">Methods</h4>
<p>The methods of a Decimal constructor.</p>
<h5 id="Dabs">abs<code class='inset'>.abs(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#abs'>absoluteValue</a></code>.</p>
<pre>a = Decimal.abs(x)
b = new Decimal(x).abs()
a.equals(b) // true</pre>
<h5 id="Dacos">acos<code class='inset'>.acos(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#acos'>inverseCosine</a></code>.</p>
<pre>a = Decimal.acos(x)
b = new Decimal(x).acos()
a.equals(b) // true</pre>
<h5 id="Dacosh">acosh<code class='inset'>.acosh(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#acos'>inverseHyperbolicCosine</a></code>.</p>
<pre>a = Decimal.acosh(x)
b = new Decimal(x).acosh()
a.equals(b) // true</pre>
<h5 id="Dadd">add<code class='inset'>.add(x, y) <i>&rArr; Decimal</i></code></h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href='#add'>plus</a></code>.</p>
<pre>a = Decimal.add(x, y)
b = new Decimal(x).plus(y)
a.equals(b) // true</pre>
<h5 id="Dasin">asin<code class='inset'>.asin(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#asin'>inverseSine</a></code>.</p>
<pre>a = Decimal.asin(x)
b = new Decimal(x).asin()
a.equals(b) // true</pre>
<h5 id="Dasinh">asinh<code class='inset'>.asinh(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#asin'>inverseHyperbolicSine</a></code>.</p>
<pre>a = Decimal.asinh(x)
b = new Decimal(x).asinh()
a.equals(b) // true</pre>
<h5 id="Datan">atan<code class='inset'>.atan(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#atan'>inverseTangent</a></code>.</p>
<pre>a = Decimal.atan(x)
b = new Decimal(x).atan()
a.equals(b) // true</pre>
<h5 id="Datanh">atanh<code class='inset'>.atanh(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#atan'>inverseHyperbolicTangent</a></code>.</p>
<pre>a = Decimal.atanh(x)
b = new Decimal(x).atanh()
a.equals(b) // true</pre>
<h5 id="Datan2">atan2<code class='inset'>.atan2(y, x) <i>&rArr; Decimal</i></code></h5>
<p>
<code>y</code>: <i>number|string|Decimal</i><br />
<code>x</code>: <i>number|string|Decimal</i>
</p>
<p>
Returns a new Decimal whose value is the inverse tangent in radians of the quotient of
<code>y</code> and <code>x</code>, rounded to <a href='#precision'><code>precision</code></a>
significant digits using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The signs of <code>y</code> and <code>x</code> are used to determine the quadrant of the
result.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-pi, pi</code>]
</p>
<p>
See <a href='#Pi'><code>Pi</code></a> and
<a href='https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/atan2'><code>Math.atan2()</code>.</a>
</p>
<pre>r = Decimal.atan2(y, x)</pre>
<h5 id="Dcbrt">cbrt<code class='inset'>.cbrt(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#cbrt'>cubeRoot</a></code>.</p>
<pre>a = Decimal.cbrt(x)
b = new Decimal(x).cbrt()
a.equals(b) // true</pre>
<h5 id="Dceil">ceil<code class='inset'>.ceil(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#ceil'>ceil</a></code>.</p>
<pre>a = Decimal.ceil(x)
b = new Decimal(x).ceil()
a.equals(b) // true</pre>
<h5 id="Dclone">
clone
<code class='inset'>.clone([object]) <i>&rArr; Decimal constructor</i></code>
</h5>
<p><code>object</code>: <i>object</i></p>
<p>
Returns a new independent Decimal constructor with configuration settings as described by
<code>object</code> (see <a href='#Dset'><code>set</code></a>), or with the same
settings as <code>this</code> Decimal constructor if <code>object</code> is omitted.
</p>
<pre>Decimal.set({ precision: 5 })
D9 = Decimal.clone({ precision: 9 })
a = new Decimal(1)
b = new D9(1)
a.div(3) // 0.33333
b.div(3) // 0.333333333
// D9 = Decimal.clone({ precision: 9 }) is equivalent to:
D9 = Decimal.clone()
D9.set({ precision: 9 })</pre>
<p>
It is not inefficient in terms of memory usage to use multiple Decimal constructors as
functions are shared between them.
</p>
<h5 id="Dcos">cos<code class='inset'>.cos(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#cos'>cosine</a></code>.</p>
<pre>a = Decimal.cos(x)
b = new Decimal(x).cos()
a.equals(b) // true</pre>
<h5 id="Dcosh">cosh<code class='inset'>.cosh(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#cos'>hyperbolicCosine</a></code>.</p>
<pre>a = Decimal.cosh(x)
b = new Decimal(x).cosh()
a.equals(b) // true</pre>
<h5 id="Ddiv">div<code class='inset'>.div(x, y) <i>&rArr; Decimal</i></code></h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href='#div'>dividedBy</a></code>.</p>
<pre>a = Decimal.div(x, y)
b = new Decimal(x).div(y)
a.equals(b) // true</pre>
<h5 id="Dexp">exp<code class='inset'>.exp(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#exp'>naturalExponential</a></code>.</p>
<pre>a = Decimal.exp(x)
b = new Decimal(x).exp()
a.equals(b) // true</pre>
<h5 id="Dfloor">floor<code class='inset'>.floor(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#floor'>floor</a></code>.</p>
<pre>a = Decimal.floor(x)
b = new Decimal(x).floor()
a.equals(b) // true</pre>
<h5 id="Dhypot">
hypot<code class='inset'>.hypot([x [, y, ...]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>
Returns a new Decimal whose value is the square root of the sum of the squares of the
arguments, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>r = Decimal.hypot(x, y)</pre>
<h5 id="Dln">ln<code class='inset'>.ln(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#ln'>naturalLogarithm</a></code>.</p>
<pre>a = Decimal.ln(x)
b = new Decimal(x).ln()
a.equals(b) // true</pre>
<h5 id="Dlog">log<code class='inset'>.log(x [, base]) <i>&rArr; Decimal</i></code></h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>base</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href='#log'>logarithm</a></code>.</p>
<p>
The default base is <code>10</code>, which is not the same as JavaScript's
<code>Math.log()</code>, which returns the natural logarithm (base <code>e</code>).
</p>
<pre>a = Decimal.log(x, y)
b = new Decimal(x).log(y)
a.equals(b) // true</pre>
<h5 id="Dlog2">log2<code class='inset'>.log2(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the base <code>2</code> logarithm of <code>x</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>r = Decimal.log2(x)</pre>
<h5 id="Dlog10">log10<code class='inset'>.log10(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the base <code>10</code> logarithm of <code>x</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>r = Decimal.log10(x)</pre>
<h5 id="Dmax">
max<code class='inset'>.max([x [, y, ...]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>Returns a new Decimal whose value is the maximum of the <code>arguments</code>.</p>
<pre>r = Decimal.max(x, y, z)</pre>
<h5 id="Dmin">
min<code class='inset'>.min([x [, y, ...]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>Returns a new Decimal whose value is the minimum of the <code>arguments</code>.</p>
<pre>r = Decimal.min(x, y, z)</pre>
<h5 id="Dmod">mod<code class='inset'>.mod(x, y) <i>&rArr; Decimal</i></code></h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href='#mod'>modulo</a></code>.</p>
<pre>a = Decimal.mod(x, y)
b = new Decimal(x).mod(y)
a.equals(b) // true</pre>
<h5 id="Dmul">mul<code class='inset'>.mul(x, y) <i>&rArr; Decimal</i></code></h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href='#mul'>times</a></code>.</p>
<pre>a = Decimal.mul(x, y)
b = new Decimal(x).mul(y)
a.equals(b) // true</pre>
<h5 id="DnoConflict">
noConflict<code class='inset'>.noConflict() <i>&rArr; Decimal constructor</i></code>
</h5>
<p><i>Browsers only.</i></p>
<p>
Reverts the <code>Decimal</code> 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.
</p>
<pre>
&lt;script&gt; Decimal = 1 &lt;/script&gt;
&lt;script src='/path/to/decimal.js'&gt;&lt;/script&gt;
&lt;script&gt;
a = new Decimal(2) // '2'
D = Decimal.noConflict()
Decimal // 1
b = new D(3) // '3'
&lt;/script&gt;</pre>
<h5 id="Dpow">pow<code class='inset'>.pow(base, exponent) <i>&rArr; Decimal</i></code></h5>
<p>
<code>base</code>: <i>number|string|Decimal</i><br />
<code>exponent</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href="#pow">toPower</a></code>.</p>
<pre>a = Decimal.pow(x, y)
b = new Decimal(x).pow(y)
a.equals(b) // true</pre>
<h5 id="Drandom">
random<code class='inset'>.random([dp]) <i>&rArr; Decimal</i></code>
</h5>
<p><code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive</p>
<p>
Returns a new Decimal with a pseudo-random value equal to or greater than <code>0</code> and
less than <code>1</code>.
</p>
<p>
The return value will have <code>dp</code> decimal places (or less if trailing zeros are
produced). If <code>dp</code> is omitted then the number of decimal places will
default to the current <a href='#precision'><code>precision</code></a> setting.
</p>
<p>
If the value of <code>this</code> Decimal constructor's
<a href='#crypto'><code>crypto</code></a> property is <code>true</code>, and the
<code>crypto</code> object is available in the host environment, the random digits of the
return value are generated by either <code>crypto.getRandomValues</code> (Web Cryptography API
in modern browsers) or <code>crypto.randomBytes</code> (Node.js), otherwise, if the the value
of the property is <code>false</code> the return value is generated by
<code>Math.random</code> (fastest).
</p>
<p>
If the value of <code>this</code> Decimal constructor's
<a href='#crypto'><code>crypto</code></a> property is set <code>true</code> and the
<code>crypto</code> object and associated method are not available, an exception will be
thrown.
</p>
<p>
If one of the <code>crypto</code> methods is used, the value of the returned Decimal should be
cryptographically-secure and statistically indistinguishable from a random value.
</p>
<pre>Decimal.set({ precision: 10 })
Decimal.random() // '0.4117936847'
Decimal.random(20) // '0.78193327636914089009'</pre>
<h5 id="Dround">round<code class='inset'>.round(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#round'>round</a></code>.</p>
<pre>a = Decimal.round(x)
b = new Decimal(x).round()
a.equals(b) // true</pre>
<h5 id="Dset">set<code class='inset'>.set(object) <i>&rArr; Decimal constructor</i></code></h5>
<p><code>object</code>: <i>object</i></p>
<p>
Configures the 'global' settings for <code>this</code> particular Decimal constructor, i.e.
the settings which apply to operations performed on the Decimal instances created by it.
</p>
<p>Returns <code>this</code> Decimal constructor.</p>
<p>
The configuration object, <code>object</code>, can contain some or all of the properties
described in detail at <a href="#constructor-properties">Properties</a> and shown in the
example below.
</p>
<p>
The values of the configuration object properties are checked for validity and then stored as
equivalently-named properties of <code>this</code> Decimal constructor.
</p>
<p>Throws on an invalid <code>object</code> or configuration property value.</p>
<pre>
// Defaults
Decimal.set({
precision: 20,
rounding: 4,
toExpNeg: -7,
toExpPos: 21,
maxE: 9e15,
minE: -9e15,
modulo: 1,
crypto: false
})</pre>
<p>
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 assingment is valid.
</p>
<pre>Decimal.precision = 40</pre>
<h5 id="Dsign">sign<code class='inset'>.sign(x) <i>&rArr; number</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<table>
<tr><th>Returns</th><th>&nbsp;</th></tr>
<tr>
<td class='centre'><code>1</code></td>
<td>if the value of <code>x</code> is non-zero and its sign is positive</td>
</tr>
<tr>
<td class='centre'><code>-1</code></td>
<td>if the value of <code>x</code> is non-zero and its sign is negative</td>
</tr>
<tr>
<td class='centre'><code>0</code></td>
<td>if the value of <code>x</code> is positive zero</td>
</tr>
<tr>
<td class='centre'><code>-0</code></td>
<td>if the value of <code>x</code> is negative zero</td>
</tr>
<tr>
<td class='centre'><code>NaN</code></td>
<td>if the value of <code>x</code> is <code>NaN</code></td>
</tr>
</table>
<pre>r = Decimal.sign(x)</pre>
<h5 id="Dsin">sin<code class='inset'>.sin(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#sin'>sine</a></code>.</p>
<pre>a = Decimal.sin(x)
b = new Decimal(x).sin()
a.equals(b) // true</pre>
<h5 id="Dsinh">sinh<code class='inset'>.sinh(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#sin'>hyperbolicSine</a></code>.</p>
<pre>a = Decimal.sinh(x)
b = new Decimal(x).sinh()
a.equals(b) // true</pre>
<h5 id="Dsqrt">sqrt<code class='inset'>.sqrt(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <a href='#sqrt'>squareRoot</a>.</p>
<pre>a = Decimal.sqrt(x)
b = new Decimal(x).sqrt()
a.equals(b) // true</pre>
<h5 id="Dsub">sub<code class='inset'>.sub(x, y) <i>&rArr; Decimal</i></code></h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>y</code>: <i>number|string|Decimal</i>
</p>
<p>See <code><a href='#sub'>minus</a></code>.</p>
<pre>a = Decimal.sub(x, y)
b = new Decimal(x).sub(y)
a.equals(b) // true</pre>
<h5 id="Dtan">tan<code class='inset'>.tan(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#tan'>tangent</a></code>.</p>
<pre>a = Decimal.tan(x)
b = new Decimal(x).tan()
a.equals(b) // true</pre>
<h5 id="Dtanh">tanh<code class='inset'>.tanh(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#tan'>hyperbolicTangent</a></code>.</p>
<pre>a = Decimal.tanh(x)
b = new Decimal(x).tanh()
a.equals(b) // true</pre>
<h5 id="Dtrunc">trunc<code class='inset'>.trunc(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>See <code><a href='#trunc'>truncated</a></code>.</p>
<pre>a = Decimal.trunc(x)
b = new Decimal(x).trunc()
a.equals(b) // true</pre>
<h4 id="constructor-properties">Properties</h4>
<p>The properties of a Decimal constructor.</p>
<h6 id='configProps'>Configuration properties</h6>
<p>
The values of the configuration properties <a href='#precision'><code>precision</code></a>,
<a href='#rounding'><code>rounding</code></a>, <a href='#minE'><code>minE</code></a>,
<a href='#maxE'><code>maxE</code></a>, <a href='#toExpNeg'><code>toExpNeg</code></a>,
<a href='#toExpPos'><code>toExpPos</code></a>, <a href='#modulo'><code>modulo</code></a>, and
<a href='#crypto'><code>crypto</code></a> are set using the
<a href='#Dset'><code>set</code></a> method.
</p>
<p>
As simple object properties they can be set directly without using
<a href='#Dset'><code>set</code></a>, and it is fine to do so, but the values assigned
will not then be checked for validity. For example:
</p>
<pre>Decimal.set({ precision: 0 })
// '[DecimalError] Invalid argument: precision: 0'
Decimal.precision = 0
// No error is thrown and the results of calculations are unreliable</pre>
<h5 id="precision">precision</h5>
<p>
<i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive<br />
Default value: <code>20</code>
</p>
<p>The <i>maximum</i> number of significant digits of the result of an operation.</p>
<p>
All functions which return a Decimal will round the return value to <code>precision</code>
significant digits except <a href='#decimal'><code>Decimal</code></a>,
<a href='#abs'><code>absoluteValue</code></a>,
<a href='#ceil'><code>ceil</code></a>, <a href='#floor'><code>floor</code></a>,
<a href='#neg'><code>negated</code></a>, <a href='#round'><code>round</code></a>,
<a href='#toDP'><code>toDecimalPlaces</code></a>,
<a href='#toNearest'><code>toNearest</code></a> and
<a href='#trunc'><code>truncated</code></a>.
</p>
<pre>Decimal.set({ precision: 5 })
Decimal.precision // 5</pre>
<h5 id="rounding">rounding</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />
Default value: <code>4</code> <a href="#modes">(<code>ROUND_HALF_UP</code>)</a>
</p>
<p>
The default rounding mode used when rounding the result of an operation to
<code><a href='#precision'>precision</a></code> significant digits, and when rounding the
return value of the <a href='#round'><code>round</code></a>,
<a href='#toBinary'><code>toBinary</code></a>,
<a href='#toDP'><code>toDecimalPlaces</code></a>,
<a href='#toExponential'><code>toExponential</code></a>,
<a href='#toFixed'><code>toFixed</code></a>,
<a href='#toHexadecimal'><code>toHexadecimal</code></a>,
<a href='#toNearest'><code>toNearest</code></a>,
<a href='#toOctal'><code>toOctal</code></a>,
<a href='#toPrecision'><code>toPrecision</code></a> and
<a href='#toSD'><code>toSignificantDigits</code></a> methods.
</p>
<p>
The <a href='#modes'>rounding modes</a> are available as enumerated properties of the
constructor.
</p>
<pre>Decimal.set({ rounding: Decimal.ROUND_UP })
Decimal.set({ rounding: 0 }) // equivalent
Decimal.rounding // 0</pre>
<h5 id="minE">minE</h5>
<p>
<i>number</i>: integer, <code>-9e15</code> to <code>0</code> inclusive<br />
Default value: <code>-9e15</code>
</p>
<p>
The negative exponent limit, i.e. the exponent value below which underflow to zero occurs.
</p>
<p>
If the <code>Decimal</code> to be returned by a calculation would have an exponent lower than
<code>minE</code> then the value of that <code>Decimal</code> becomes zero.
<p>
JavaScript numbers underflow to zero for exponents below <code>-324</code>.
</p>
<pre>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</pre>
<p>
The smallest possible magnitude of a non-zero Decimal is <code>1e-9000000000000000</code>
</p>
<h5 id="maxE">maxE</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>9e15</code> inclusive<br />
Default value: <code>9e15</code>
</p>
<p>
The positive exponent limit, i.e. the exponent value above which overflow to
<code>Infinity</code> occurs.
</p>
<p>
If the <code>Decimal</code> to be returned by a calculation would have an exponent higher than
<code>maxE</code> then the value of that <code>Decimal</code> becomes <code>Infinity</code>.
<p>
JavaScript numbers overflow to <code>Infinity</code> for exponents above <code>308</code>.
</p>
<pre>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'</pre>
<p>
The largest possible magnitude of a finite Decimal is <code>9.999...e+9000000000000000</code>
</p>
<h5 id="toExpNeg">toExpNeg</h5>
<p>
<i>number</i>: integer, <code>-9e15</code> to <code>0</code> inclusive<br />
Default value: <code>-7</code>
</p>
<p>
The negative exponent value at and below which <a href='#toString'><code>toString</code></a>
returns exponential notation.
</p>
<pre>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 })</pre>
<p>
JavaScript numbers use exponential notation for negative exponents of <code>-7</code> and
below.
</p>
<p>
Regardless of the value of <code>toExpNeg</code>, the
<a href='#toFixed'><code>toFixed</code></a> method will always return a value in normal
notation and the <a href='#toExponential'><code>toExponential</code></a> method will always
return a value in exponential form.
</p>
<h5 id="toExpPos">toExpPos</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>9e15</code> inclusive<br />
Default value: <code>20</code>
</p>
<p>
The positive exponent value at and above which <a href='#toString'><code>toString</code></a>
returns exponential notation.
</p>
<pre>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 })</pre>
<p>
JavaScript numbers use exponential notation for positive exponents of <code>20</code> and
above.
</p>
<p>
Regardless of the value of <code>toExpPos</code>, the
<a href='#toFixed'><code>toFixed</code></a> method will always return a value in normal
notation and the <a href='#toExponential'><code>toExponential</code></a> method will always
return a value in exponential form.
</p>
<h5 id="modulo">modulo</h5>
<p>
<i>number</i>: integer, <code>0</code> to <code>9</code> inclusive<br />
Default value: <code>1</code> (<code>ROUND_DOWN</code>)
</p>
<p>The modulo mode used when calculating the modulus: <code>a mod n</code>.</p>
<p>
The quotient, <code>q = a / n</code>, is calculated according to the
<a href='#rounding'><code>rounding</code></a> mode that corresponds to the chosen
<code>modulo</code> mode.
</p>
<p>The remainder, <code>r</code>, is calculated as: <code>r = a - n * q</code>.</p>
<p>
The modes that are most commonly used for the modulus/remainder operation are shown in the
following table. Although the other <a href='#rounding'><code>rounding</code></a> modes can
be used, they may not give useful results.
</p>
<table>
<tr><th>Property</th><th>Value</th><th>Description</th></tr>
<tr>
<td>ROUND_UP</td><td class='centre'>0</td>
<td>The remainder is positive if the dividend is negative, else is negative</td>
</tr>
<tr>
<td>ROUND_DOWN</td><td class='centre'>1</td>
<td>
The remainder has the same sign as the dividend.<br />
This uses truncating division and matches the behaviour of JavaScript's remainder
operator <code>%</code>.
</td>
</tr>
<tr>
<td>ROUND_FLOOR</td><td class='centre'>3</td>
<td>
The remainder has the same sign as the divisor.<br />
(This matches Python's <code>%</code> operator)
</td>
</tr>
<tr>
<td>ROUND_HALF_EVEN</td><td class='centre'>6</td>
<td>The <i>IEEE 754</i> remainder function</td>
</tr>
<tr>
<td>EUCLID</td><td class='centre'>9</td>
<td>
The remainder is always positive.<br />
Euclidian division: <code>q = sign(x) * floor(a / abs(x))</code>.
</td>
</tr>
</table>
<p>
The rounding/modulo modes are available as enumerated properties of the Decimal constructor.
</p>
<pre>Decimal.set({ modulo: Decimal.EUCLID })
Decimal.set({ modulo: 9 }) // equivalent
Decimal.modulo // 9</pre>
<h5 id="crypto">crypto</h5>
<p>
<i>boolean</i>: <code>true/false</code><br /> Default value: <code>false</code>
</p>
<p>
The value that determines whether cryptographically-secure pseudo-random number generation is
used.
</p>
<p>See <a href='#Drandom'><code>random</code></a>.</p>
<pre>Decimal.crypto // false
Decimal.set({ crypto: true })
Decimal.crypto // true</pre>
<h6 id="modes">Rounding modes</h6>
<p>
The library's enumerated rounding modes are stored as properties of the Decimal constructor.
<br />They are not referenced internally by the library itself.
</p>
<p>Rounding modes 0 to 6 (inclusive) are the same as those of Java's BigDecimal class.</p>
<table>
<tr><th>Property</th><th>Value</th><th>Description</th></tr>
<tr><td><b>ROUND_UP</b></td><td class='centre'>0</td><td>Rounds away from zero</td></tr>
<tr><td><b>ROUND_DOWN</b></td><td class='centre'>1</td><td>Rounds towards zero</td></tr>
<tr><td><b>ROUND_CEIL</b></td><td class='centre'>2</td><td>Rounds towards Infinity</td></tr>
<tr><td><b>ROUND_FLOOR</b></td><td class='centre'>3</td><td>Rounds towards -Infinity</td></tr>
<tr>
<td><b>ROUND_HALF_UP</b></td><td class='centre'>4</td>
<td>Rounds towards nearest neighbour.<br />If equidistant, rounds away from zero</td>
</tr>
<tr>
<td><b>ROUND_HALF_DOWN</b></td><td class='centre'>5</td>
<td>Rounds towards nearest neighbour.<br />If equidistant, rounds towards zero</td>
</tr>
<tr>
<td><b>ROUND_HALF_EVEN</b></td><td class='centre'>6</td>
<td>
Rounds towards nearest neighbour.<br />If equidistant, rounds towards even neighbour
</td>
</tr>
<tr>
<td><b>ROUND_HALF_CEIL</b></td><td class='centre'>7</td>
<td>Rounds towards nearest neighbour.<br />If equidistant, rounds towards Infinity</td>
</tr>
<tr>
<td><b>ROUND_HALF_FLOOR</b></td><td class='centre'>8</td>
<td>Rounds towards nearest neighbour.<br />If equidistant, rounds towards -Infinity</td>
</tr>
<tr>
<td><b>EUCLID</b></td><td class='centre'>9</td>
<td>Not a rounding mode, see <a href='#modulo'>modulo</a></td>
</tr>
</table>
<pre>Decimal.set({ rounding: Decimal.ROUND_CEIL })
Decimal.set({ rounding: 2 }) // equivalent
Decimal.rounding // 2</pre>
<h3>INSTANCE</h3>
<h4 id="prototype-methods">Methods</h4>
<p>The methods inherited by a Decimal instance from its constructor's prototype object.</p>
<p>A Decimal instance is immutable in the sense that it is not changed by its methods.</p>
<p>Methods that return a Decimal can be chained:</p>
<pre>x = new Decimal(2).times('999.999999999999999').dividedBy(4).ceil()</pre>
<p>Methods do not round their arguments before execution.</p>
<p>
The treatment of <code>&plusmn;0</code>, <code>&plusmn;Infinity</code> and <code>NaN</code>
is consistent with how JavaScript treats these values.
</p>
<p>
Many method names have a shorter alias. (Internally, the library always uses the shorter
method names.)
</p>
<h5 id="abs">absoluteValue<code class='inset'>.abs() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the absolute value, i.e. the magnitude, of the value of
this Decimal.
</p>
<p>
The return value is not affected by the value of the
<a href='#precision'><code>precision</code></a> setting.
</p>
<pre>
x = new Decimal(-0.8)
y = x.absoluteValue() // '0.8'
z = y.abs() // '0.8'</pre>
<h5 id="ceil">ceil<code class='inset'>.ceil() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in
the direction of positive <code>Infinity</code>.
</p>
<p>
The return value is not affected by the value of the
<a href='#precision'><code>precision</code></a> setting.
</p>
<pre>
x = new Decimal(1.3)
x.ceil() // '2'
y = new Decimal(-1.8)
y.ceil() // '-1'</pre>
<h5 id="cmp">comparedTo<code class='inset'>.cmp(x) <i>&rArr; number</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<table>
<tr><th>Returns</th><th>&nbsp;</th></tr>
<tr>
<td class='centre'><code>1</code></td>
<td>if the value of this Decimal is greater than the value of <code>x</code></td>
</tr>
<tr>
<td class='centre'><code>-1</code></td>
<td>if the value of this Decimal is less than the value of <code>x</code></td>
</tr>
<tr>
<td class='centre'><code>0</code></td>
<td>if this Decimal and <code>x</code> have the same value</td>
</tr>
<tr>
<td class='centre'><code>NaN</code></td>
<td>if the value of either this Decimal or <code>x</code> is <code>NaN</code> </td>
</tr>
</table>
<pre>
x = new Decimal(Infinity)
y = new Decimal(5)
x.comparedTo(y) // 1
x.comparedTo(x.minus(1)) // 0
y.cmp(NaN) // NaN</pre>
<h5 id="cos">cosine<code class='inset'>.cos() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the cosine of the value in radians of this Decimal,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-1, 1</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0.25)
x.cosine() // '0.96891242171064478414'
y = new Decimal(-0.25)
y.cos() // '0.96891242171064478414'</pre>
<h5 id="cbrt">cubeRoot<code class='inset'>.cbrt() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the cube root of this Decimal, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<p>
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.
</p>
<pre>
x = new Decimal(125)
x.cubeRoot() // '5'
y = new Decimal(3)
y.cbrt() // '1.4422495703074083823'</pre>
<h5 id="dp">decimalPlaces<code class='inset'>.dp() <i>&rArr; number</i></code></h5>
<p>
Returns the number of decimal places, i.e. the number of digits after the decimal point, of
the value of this Decimal.
</p>
<pre>
x = new Decimal(1.234)
x.decimalPlaces() // '3'
y = new Decimal(987.654321)
y.dp() // '6'</pre>
<h5 id="div">dividedBy<code class='inset'>.div(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the value of this Decimal divided by <code>x</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
x = new Decimal(355)
y = new Decimal(113)
x.dividedBy(y) // '3.14159292035398230088'
x.div(5) // '71'</pre>
<h5 id="divToInt">
dividedToIntegerBy<code class='inset'>.divToInt(x) <i>&rArr; Decimal</i></code>
</h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Return a new Decimal whose value is the integer part of dividing this Decimal by
<code>x</code>, rounded to <code><a href='#precision'>precision</a></code> significant digits
using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
x = new Decimal(5)
y = new Decimal(3)
x.dividedToIntegerBy(y) // '1'
x.divToInt(0.7) // '7'</pre>
<h5 id="eq">equals<code class='inset'>.eq(x) <i>&rArr; boolean</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns <code>true</code> if the value of this Decimal equals the value of <code>x</code>,
otherwise returns <code>false</code>.<br /> As with JavaScript, <code>NaN</code> does not
equal <code>NaN</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
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</pre>
<h5 id="floor">floor<code class='inset'>.floor() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to a whole number in
the direction of negative <code>Infinity</code>.
</p>
<p>
The return value is not affected by the value of the
<a href='#precision'><code>precision</code></a> setting.
</p>
<pre>
x = new Decimal(1.8)
x.floor() // '1'
y = new Decimal(-1.3)
y.floor() // '-2'</pre>
<h5 id="gt">greaterThan<code class='inset'>.gt(x) <i>&rArr; boolean</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns <code>true</code> if the value of this Decimal is greater than the value of
<code>x</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
0.1 &gt; (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</pre>
<h5 id="gte">
greaterThanOrEqualTo<code class='inset'>.gte(x) <i>&rArr; boolean</i></code>
</h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns <code>true</code> if the value of this Decimal is greater than or equal to the value
of <code>x</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
(0.3 - 0.2) &gt;= 0.1 // false
x = new Decimal(0.3).minus(0.2)
x.greaterThanOrEqualTo(0.1) // true
new Decimal(1).gte(x) // true</pre>
<h5 id="cosh">hyperbolicCosine<code class='inset'>.cosh() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the hyperbolic cosine of the value in radians of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>1, Infinity</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(1)
x.hyperbolicCosine() // '1.5430806348152437785'
y = new Decimal(0.5)
y.cosh() // '1.1276259652063807852'</pre>
<h5 id="sinh">hyperbolicSine<code class='inset'>.sinh() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the hyperbolic sine of the value in radians of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-Infinity, Infinity</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(1)
x.hyperbolicSine() // '1.1752011936438014569'
y = new Decimal(0.5)
y.sinh() // '0.52109530549374736162'</pre>
<h5 id="tanh">hyperbolicTangent<code class='inset'>.tanh() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the hyperbolic tangent of the value in radians of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-1, 1</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(1)
x.hyperbolicTangent() // '0.76159415595576488812'
y = new Decimal(0.5)
y.tanh() // '0.4621171572600097585'</pre>
<h5 id="acos">inverseCosine<code class='inset'>.acos() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the inverse cosine in radians of the value of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-1, 1</code>]<br />
Range: [<code>0, pi</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0)
x.inverseCosine() // '1.5707963267948966192'
y = new Decimal(0.5)
y.acos() // '1.0471975511965977462'</pre>
<h5 id="acosh">
inverseHyperbolicCosine<code class='inset'>.acosh() <i>&rArr; Decimal</i></code>
</h5>
<p>
Returns a new Decimal whose value is the inverse hyperbolic cosine in radians of the value of
this Decimal, rounded to <a href='#precision'><code>precision</code></a> significant
digits using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>1, Infinity</code>]<br />
Range: [<code>0, Infinity</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(5)
x.inverseHyperbolicCosine() // '2.2924316695611776878'
y = new Decimal(50)
y.acosh() // '4.6050701709847571595'</pre>
<h5 id="asinh">
inverseHyperbolicSine<code class='inset'>.asinh() <i>&rArr; Decimal</i></code>
</h5>
<p>
Returns a new Decimal whose value is the inverse hyperbolic sine in radians of the value of
this Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits
using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-Infinity, Infinity</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(5)
x.inverseHyperbolicSine() // '2.3124383412727526203'
y = new Decimal(50)
y.asinh() // '4.6052701709914238266'</pre>
<h5 id="atanh">
inverseHyperbolicTangent<code class='inset'>.atanh() <i>&rArr; Decimal</i></code>
</h5>
<p>
Returns a new Decimal whose value is the inverse hyperbolic tangent in radians of the value of
this Decimal, rounded to <a href='#precision'><code>precision</code></a> significant
digits using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-1, 1</code>]<br />
Range: [<code>-Infinity, Infinity</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0.5)
x.inverseHyperbolicTangent() // '0.5493061443340548457'
y = new Decimal(0.75)
y.atanh() // '0.97295507452765665255'</pre>
<h5 id="asin">inverseSine<code class='inset'>.asin() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the inverse sine in radians of the value of this Decimal,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-1, 1</code>]<br />
Range: [<code>-pi/2, pi/2</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0.5)
x.inverseSine() // '0.52359877559829887308'
y = new Decimal(0.75)
y.asin() // '0.84806207898148100805'</pre>
<h5 id="atan">inverseTangent<code class='inset'>.atan() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the inverse tangent in radians of the value of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-pi/2, pi/2</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0.5)
x.inverseTangent() // '0.46364760900080611621'
y = new Decimal(0.75)
y.atan() // '0.6435011087932843868'</pre>
<h5 id="isFinite">isFinite<code class='inset'>.isFinite() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is a finite number, otherwise returns
<code>false</code>.<br />
The only possible non-finite values of a Decimal are <code>NaN</code>, <code>Infinity</code>
and <code>-Infinity</code>.
</p>
<pre>
x = new Decimal(1)
x.isFinite() // true
y = new Decimal(Infinity)
y.isFinite() // false</pre>
<p>
Note: The native method <code>isFinite()</code> can be used if
<code>n &lt;= Number.MAX_VALUE</code>.
</p>
<h5 id="isInt">isInteger<code class='inset'>.isInt() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is a whole number, otherwise returns
<code>false</code>.
</p>
<pre>
x = new Decimal(1)
x.isInteger() // true
y = new Decimal(123.456)
y.isInt() // false</pre>
<h5 id="isNaN">isNaN<code class='inset'>.isNaN() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is <code>NaN</code>, otherwise returns
<code>false</code>.
</p>
<pre>
x = new Decimal(NaN)
x.isNaN() // true
y = new Decimal('Infinity')
y.isNaN() // false</pre>
<p>Note: The native method <code>isNaN()</code> can also be used.</p>
<h5 id="isNeg">isNegative<code class='inset'>.isNeg() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is negative, otherwise returns
<code>false</code>.
</p>
<pre>
x = new Decimal(-0)
x.isNegative() // true
y = new Decimal(2)
y.isNeg // false</pre>
<p>Note: <code>n &lt; 0</code> can be used if <code>n &lt;= -Number.MIN_VALUE</code>.</p>
<h5 id="isPos">isPositive<code class='inset'>.isPos() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is positive, otherwise returns
<code>false</code>.
</p>
<pre>
x = new Decimal(0)
x.isPositive() // true
y = new Decimal(-2)
y.isPos // false</pre>
<p>Note: <code>n &lt; 0</code> can be used if <code>n &lt;= -Number.MIN_VALUE</code>.</p>
<h5 id="isZero">isZero<code class='inset'>.isZero() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this Decimal is zero or minus zero, otherwise
returns <code>false</code>.
</p>
<pre>
x = new Decimal(-0)
x.isZero() && x.isNeg() // true
y = new Decimal(Infinity)
y.isZero() // false</pre>
<p>Note: <code>n == 0</code> can be used if <code>n &gt;= Number.MIN_VALUE</code>.</p>
<h5 id="lt">lessThan<code class='inset'>.lt(x) <i>&rArr; boolean</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns <code>true</code> if the value of this Decimal is less than the value of
<code>x</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
(0.3 - 0.2) &lt; 0.1 // true
x = new Decimal(0.3).minus(0.2)
x.lessThan(0.1) // false
new Decimal(0).lt(x) // true</pre>
<h5 id="lte">lessThanOrEqualTo<code class='inset'>.lte(x) <i>&rArr; boolean</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns <code>true</code> if the value of this Decimal is less than or equal to the value of
<code>x</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <code>cmp</code> method internally.</p>
<pre>
0.1 &lt;= (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</pre>
<h5 id="log">logarithm<code class='inset'>.log(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the base <code>x</code> logarithm of the value of this
Decimal, rounded to <a href='#precision'><code>precision</code></a> significant digits using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
If <code>x</code> is omitted, the base 10 logarithm of the value of this Decimal will be
returned.
</p>
<pre>
x = new Decimal(1000)
x.logarithm() // '3'
y = new Decimal(256)
y.log(2) // '8'</pre>
<p>
The return value will <i>almost always</i> 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 <code>1</code> <i>ulp</i> (unit in the last
place).
</p>
<p>Logarithms to base <code>2</code> or <code>10</code> will always be correctly rounded.</p>
<p>
See <a href='#pow'><code>toPower</code></a> for the circumstances in which this method may
return an incorrectly rounded result.
</p>
<p>The performance of this method degrades exponentially with increasing digits.</p>
<h5 id="sub">minus<code class='inset'>.minus(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the value of this Decimal minus <code>x</code>, rounded
to <a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
0.3 - 0.1 // 0.19999999999999998
x = new Decimal(0.3)
x.minus(0.1) // '0.2'</pre>
<h5 id="mod">modulo<code class='inset'>.mod(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the value of this Decimal modulo <code>x</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The value returned, and in particular its sign, is dependent on the value of the
<a href='#modulo'><code>modulo</code></a> property of this Decimal's constructor. If it is
<code>1</code> (default value), the result will have the same sign as this Decimal, and it
will match that of Javascript's <code>%</code> operator (within the limits of double
precision) and BigDecimal's <code>remainder</code> method.
</p>
<p>
See <a href='#modulo'><code>modulo</code></a> for a description of the other modulo modes.
</p>
<pre>
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'</pre>
<h5 id="exp">naturalExponential<code class='inset'>.exp() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the base <code>e</code> (Euler's number, the base of the
natural logarithm) exponential of the value of this Decimal, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The <code><a href='#ln'>naturalLogarithm</a></code> function is the inverse of this function.
</p>
<pre>
x = new Decimal(1)
x.naturalExponential() // '2.7182818284590452354'
y = new Decimal(2)
y.exp() // '7.3890560989306502272'</pre>
<p>
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 <code>0</code>).
</p>
<p>The performance of this method degrades exponentially with increasing digits.</p>
<h5 id="ln">naturalLogarithm<code class='inset'>.ln() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the natural logarithm of the value of this Decimal,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
The natural logarithm is the inverse of the <code><a href='#exp'>naturalExponential</a></code>
function.
</p>
<pre>
x = new Decimal(10)
x.naturalLogarithm() // '2.3026'
y = new Decimal('1.23e+30')
y.ln() // '69.28'</pre>
<p>
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 <code>1</code>).
</p>
<p>
Internally, this method is dependent on a constant whose value is the natural logarithm of
<code>10</code>. This <code>LN10</code> variable in the source code currently has a precision
of <code>1025</code> digits, meaning that this method can accurately calculate up to
<code>1000</code> digits.
</p>
<p>
If more than <code>1000</code> digits is required then the precision of <code>LN10</code>
will need to be increased to <code>25</code> 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 <code>1000</code> digits anyway.
</p>
<h5 id="neg">negated<code class='inset'>.neg() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal negated, i.e. multiplied by
<code>-1</code>.
</p>
<p>
The return value is not affected by the value of the
<a href='#precision'><code>precision</code></a> setting.
</p>
<pre>
x = new Decimal(1.8)
x.negated() // '-1.8'
y = new Decimal(-1.3)
y.neg() // '1.3'</pre>
<h5 id="add">plus<code class='inset'>.plus(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the value of this Decimal plus <code>x</code>, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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'</pre>
<h5 id="sd">precision<code class='inset'>.sd([include_zeros]) <i>&rArr; number</i></code></h5>
<p>Returns the number of significant digits of the value of this Decimal.</p>
<p>
If <code>include_zeros</code> is <code>true</code> or <code>1</code> then any trailing zeros
of the integer part of a number are counted as significant digits, otherwise they are not.
</p>
<pre>
x = new Decimal(1.234)
x.precision() // '4'
y = new Decimal(987000)
y.sd() // '3'
y.sd(true) // '6'</pre>
<h5 id="round">round<code class='inset'>.round() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to a whole number using
rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
To emulate <code>Math.round</code>, set <a href='#rounding'><code>rounding</code></a> to
<code>7</code>, i.e. <a href='#modes'><code>ROUND_HALF_CEIL</code></a>.
</p>
<pre>
Decimal.set({ rounding: 4 })
x = 1234.5
x.round() // '1235'
Decimal.rounding = Decimal.ROUND_DOWN
x.round() // '1234'
x // '1234.5'</pre>
<h5 id="sin">sine<code class='inset'>.sin() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the sine of the value in radians of this Decimal,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-1, 1</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0.5)
x.sine() // '0.47942553860420300027'
y = new Decimal(0.75)
y.sin() // '0.68163876002333416673'</pre>
<h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the square root of this Decimal, rounded to
<a href='#precision'><code>precision</code></a> significant digits using rounding mode
<a href='#rounding'><code>rounding</code></a>.
</p>
<p>
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.
</p>
<p>
This method is much faster than using the <a href='#pow'><code>toPower</code></a> method with
an exponent of <code>0.5</code>.
</p>
<pre>
x = new Decimal(16)
x.squareRoot() // '4'
y = new Decimal(3)
y.sqrt() // '1.73205080756887729353'
y.sqrt().eq( y.pow(0.5) ) // true</pre>
<h5 id="tan">tangent<code class='inset'>.tan() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the tangent of the value in radians of this Decimal,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
Domain: [<code>-Infinity, Infinity</code>]<br />
Range: [<code>-Infinity, Infinity</code>]
</p>
<p>See <a href='#Pi'><code>Pi</code></a>.</p>
<pre>
x = new Decimal(0.5)
x.tangent() // '0.54630248984379051326'
y = new Decimal(0.75)
y.tan() // '0.93159645994407246117'</pre>
<h5 id="mul">times<code class='inset'>.times(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i></p>
<p>
Returns a new Decimal whose value is the value of this Decimal times <code>x</code>,
rounded to <a href='#precision'><code>precision</code></a> significant digits using rounding
mode <a href='#rounding'><code>rounding</code></a>.
</p>
<pre>
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'</pre>
<h5 id="toBinary">
toBinary<code class='inset'>.toBinary([sd [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a string representing the value of this Decimal in binary, rounded to <code>sd</code>
significant digits using rounding mode <code>rm</code>.
</p>
<p>
If <code>sd</code> is defined, the return value will use binary exponential notation.
</p>
<p>
If <code>sd</code> is omitted, the return value will be rounded to
<a href='#precision'><code>precision</code></a> significant digits.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
will be used.
</p>
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
<pre>
x = new Decimal(256)
x.toBinary() // '0b100000000'
x.toBinary(1) // '0b1p+8'</pre>
<h5 id="toDP">
toDecimalPlaces<code class='inset'>.toDP([dp [, rm]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive.
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to <code>dp</code>
decimal places using rounding mode <code>rm</code>.
</p>
<p>
If <code>dp</code> is omitted, the return value will have the same value as this Decimal.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
is used.
</p>
<p>Throws on an invalid <code>dp</code> or <code>rm</code> value.</p>
<pre>
x = new Decimal(12.24567)
x.toDecimalPlaces(0) // '12'
x.toDecimalPlaces(1, 0) // '12.3'
y = new Decimal(9876.54321)
y.toDP(3) // '9876.543'
y.toDP(1, 0) // '9876.6'
y.toDP(1, Decimal.ROUND_DOWN) // '9876.5'</pre>
<h5 id="toExponential">
toExponential<code class='inset'>.toExponential([dp [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a string representing the value of this Decimal in exponential notation rounded
using rounding mode <code>rm</code> to <code>dp</code> decimal places, i.e with one digit
before the decimal point and <code>dp</code> digits after it.
</p>
<p>
If the value of this Decimal in exponential notation has fewer than <code>dp</code> fraction
digits, the return value will be appended with zeros accordingly.
</p>
<p>
If <code>dp</code> is omitted, the number of digits after the decimal point defaults to the
minimum number of digits necessary to represent the value exactly.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a> is
used.
</p>
<p>Throws on an invalid <code>dp</code> or <code>rm</code> value.</p>
<pre>
x = 45.6
b = 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, 1) // '4.5e+1' (ROUND_DOWN)
x.toExponential(3) // '4.560e+1'
y.toExponential(3) // '4.560e+1'</pre>
<h5 id="toFixed">
toFixed<code class='inset'>.toFixed([dp [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>dp</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a string representing the value of this Decimal in normal (fixed-point) notation
rounded to <code>dp</code> decimal places using rounding mode <code>rm</code>.
</p>
<p>
If the value of this Decimal in normal notation has fewer than <code>dp</code> fraction
digits, the return value will be appended with zeros accordingly.
</p>
<p>
Unlike <code>Number.prototype.toFixed</code>, which returns exponential notation if a number
is greater or equal to <code>10<sup>21</sup></code>, this method will always return normal
notation.
</p>
<p>
If <code>dp</code> is omitted, the return value will be unrounded and in normal notation. This
is unlike <code>Number.prototype.toFixed</code>, which returns the value to zero decimal
places, but is useful when because of the current
<a href="#toExpNeg"><code>toExpNeg</code></a> or
<a href="#toExpPos"><code>toExpNeg</code></a> values,
<code><a href='#toString'>toString</a></code> returns exponential notation.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a> is
used.
</p>
<p>Throws on an invalid <code>dp</code> or <code>rm</code> value.</p>
<pre>
x = 3.456
b = 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, 1) // '3.45' (ROUND_DOWN)
x.toFixed(5) // '3.45600'
y.toFixed(5) // '3.45600'</pre>
<h5 id="toFraction">
toFraction
<code class='inset'>.toFraction([max_denominator]) <i>&rArr; [Decimal, Decimal]</i></code>
</h5>
<p>
<code>max_denominator</code>: <i>number|string|Decimal</i>: <code>1</code> &gt;= integer &lt;
<code>Infinity</code>
</p>
<p>
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 <code>max_denominator</code>.
</p>
<p>
If a maximum denominator is omitted, the denominator will be the lowest value necessary to
represent the number exactly.
</p>
<p>Throws on an invalid <code>max_denominator</code> value.</p>
<pre>
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'</pre>
<h5 id="toHex">
toHexadecimal<code class='inset'>.toHex([sd [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a string representing the value of this Decimal in hexadecimal, rounded to
<code>sd</code> significant digits using rounding mode <code>rm</code>.
</p>
<p>
If <code>sd</code> is defined, the return value will use binary exponential notation.
</p>
<p>
If <code>sd</code> is omitted, the return value will be rounded to
<a href='#precision'><code>precision</code></a> significant digits.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
will be used.
</p>
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
<pre>
x = new Decimal(256)
x.toHexadecimal() // '0x100'
x.toHex(1) // '0x1p+8'</pre>
<h5 id="toJSON">toJSON<code class='inset'>.toJSON() <i>&rArr; string</i></code></h5>
<p>As <a href='#valueOf'><code>valueOf</code></a>.</p>
<h5 id="toNearest">
toNearest<code class='inset'>.toNearest(n [, rm]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>x</code>: <i>number|string|Decimal</i><br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a new Decimal whose value is the nearest multiple of <code>x</code> to the value of
this Decimal.
</p>
<p>
If the value of this Decimal is equidistant from two multiples of <code>x</code>, the rounding
mode <code>rm</code>, or <a href='#rounding'><code>rounding</code></a> if <code>rm</code> is
omitted, determines the direction of the nearest.
</p>
<p>
In this context, rounding mode <a href='#rounding'><code>ROUND_HALF_UP</code></a> is
interpreted the same as rounding mode <a href='#rounding'><code>ROUND_UP</code></a>, and so
on, i.e. the rounding is either up, down, to ceil, to floor or to even.
</p>
<p>
The return value will always have the same sign as this Decimal, unless either this Decimal
or <code>x</code> is <code>NaN</code>, in which case the return value will be also be
<code>NaN</code>.
</p>
<p>
The return value is not affected by the value of the
<a href='#precision'><code>precision</code></a> setting.
</p>
<pre>
x = new Decimal(1.39)
x.toNearest(0.25) // '1.5'
y = new Decimal(0.75) // equidistant from 0.5 and 1
y.toNearest(0.5, 0) // '1' (ROUND_UP)
y.toNearest(0.5, 1) // '0.5' (ROUND_DOWN)</pre>
<h5 id="toNumber">toNumber<code class='inset'>.toNumber() <i>&rArr; number</i></code></h5>
<p>Returns the value of this Decimal converted to a primitive number.</p>
<p>
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.
</p>
<pre>
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</pre>
<h5 id="toOctal">
toOctal<code class='inset'>.toOctal([sd [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a string representing the value of this Decimal in octal, rounded to <code>sd</code>
significant digits using rounding mode <code>rm</code>.
</p>
<p>
If <code>sd</code> is defined, the return value will use binary exponential notation.
</p>
<p>
If <code>sd</code> is omitted, the return value will be rounded to
<a href='#precision'><code>precision</code></a> significant digits.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
will be used.
</p>
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
<pre>
x = new Decimal(256)
x.toOctal() // '0o400'
x.toOctal(1) // '0o1p+8'</pre>
<h5 id="pow">toPower<code class='inset'>.pow(x) <i>&rArr; Decimal</i></code></h5>
<p><code>x</code>: <i>number|string|Decimal</i>: integer or non-integer</p>
<p>
Returns a new Decimal whose value is the value of this Decimal raised to the power
<code>x</code>, rounded to <a href='#precision'><code>precision</code></a> significant digits
using rounding mode <a href='#rounding'><code>rounding</code></a>.
</p>
<p>
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.
</p>
<pre>
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'</pre>
<p><i>Is the pow function guaranteed to be correctly rounded?</i></p>
<p>
The return value will <i>almost always</i> 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 <code>1</code> <i>ulp</i> (unit in the last
place).
</p>
<p>For non-integer and larger exponents this method uses the formula</p>
<blockquote><code>x<sup>y</sup> = exp(y*ln(x))</code></blockquote>
<p>
As the mathematical return values of the <a href='#exp'><code>exp</code></a> and
<a href='#ln'><code>ln</code></a> functions are both non-terminating (excluding arguments of
<code>0</code> or <code>1</code>), 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.
</p>
<p>
The return value may, depending on the rounding mode, be incorrectly rounded only if the first
<code>15</code> rounding digits are <code>15</code> zeros (and there are non-zero digits
following at some point), or <code>15</code> nines, or a <code>5</code> or <code>4</code>
followed by <code>14</code> nines.
</p>
<p>
Therefore, assuming the first <code>15</code> rounding digits are each equally likely to be
any digit, <code>0-9</code>, the probability of an incorrectly rounded result is less than
<code>1</code> in <code>250,000,000,000,000</code>.
</p>
<p>
An example of incorrect rounding:
</p>
<pre>
Decimal.set({ precision: 20, rounding: 1 })
new Decimal(28).pow('6.166675020000903537297764507632802193308677149')
// 839756321.64088511</pre>
<p>As the exact mathematical result begins</p>
<pre>839756321.6408851099999999999999999999999999998969466049426031167...</pre>
<p>
and the rounding mode is set to <code><a href='#modes'>ROUND_DOWN</a></code>, the correct
return value should be
</p>
<pre>839756321.64088510999</pre>
<h5 id="toPrecision">
toPrecision<code class='inset'>.toPrecision([sd [, rm]]) <i>&rArr; string</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a string representing the value of this Decimal rounded to <code>sd</code> significant
digits using rounding mode <code>rm</code>.
</p>
<p>
If <code>sd</code> 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.
</p>
<p>
If <code>sd</code> is omitted, the return value is the same as
<code><a href='#toString'>toString</a></code>.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a> is
used.
</p>
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
<pre>
x = 45.6
b = new Decimal(x)
x.toPrecision() // '45.6'
y.toPrecision() // '45.6'
x.toPrecision(1) // '5e+1'
y.toPrecision(1) // '5e+1'
y.toPrecision(2, 0) // '4.6e+1' (ROUND_UP)
y.toPrecision(2, 1) // '4.5e+1' (ROUND_DOWN)
x.toPrecision(5) // '45.600'
y.toPrecision(5) // '45.600'</pre>
<h5 id="toSD">
toSignificantDigits<code class='inset'>.toSD([sd [, rm]]) <i>&rArr; Decimal</i></code>
</h5>
<p>
<code>sd</code>: <i>number</i>: integer, <code>1</code> to <code>1e+9</code> inclusive.<br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive.
</p>
<p>
Returns a new Decimal whose value is the value of this Decimal rounded to <code>sd</code>
significant digits using rounding mode <code>rm</code>.
</p>
<p>
If <code>sd</code> is omitted, the return value will be rounded to
<a href='#precision'><code>precision</code></a> significant digits.
</p>
<p>
If <code>rm</code> is omitted, rounding mode <a href='#rounding'><code>rounding</code></a>
will be used.
</p>
<p>Throws on an invalid <code>sd</code> or <code>rm</code> value.</p>
<pre>
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'</pre>
<h5 id="toString">toString<code class='inset'>.toString() <i>&rArr; string</i></code></h5>
<p>Returns a string representing the value of this Decimal.</p>
<p>
If this Decimal has a positive exponent that is equal to or greater than
<a href="#toExpPos"><code>toExpPos</code></a>, or a negative exponent equal to or less than
<a href="#toExpPos"><code>toExpNeg</code></a>, then exponential notation will be returned.
</p>
<pre>
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'</pre>
<h5 id="trunc">truncated<code class='inset'>.trunc() <i>&rArr; Decimal</i></code></h5>
<p>
Returns a new Decimal whose value is the value of this Decimal truncated to a whole number.
</p>
<p>
The return value is not affected by the value of the
<a href='#precision'><code>precision</code></a> setting.
</p>
<pre>
x = new Decimal(123.456)
x.truncated() // '123'
y = new Decimal(-12.3)
y.trunc() // '-12'</pre>
<h5 id="valueOf">valueOf<code class='inset'>.valueOf() <i>&rArr; string</i></code></h5>
<p>As <a href='#toString'><code>toString</code></a>, but zero is signed.</p>
<pre>
x = new Decimal(-0)
x.valueOf() // '-0'</pre>
<h4 id="instance-properties">Properties</h4>
<p>
The value of a Decimal is stored in a normalised base <code>10000000</code> floating point
format.
</p>
<p>
A Decimal instance is an object with three properties:
</p>
<table>
<tr>
<th>Property</th>
<th>Description</th>
<th>Type</th>
<th>Value</th>
</tr>
<tr>
<td class='centre' id='digits'><b>d</b></td>
<td>digits</td>
<td><i>number</i><code style='color:#000'>[]</code></td>
<td> Array of integers, each <code>0</code> - <code>1e7</code>, or <code>null</code></td>
</tr>
<tr>
<td class='centre' id='exponent'><b>e</b></td>
<td>exponent</td>
<td><i>number</i></td>
<td>Integer, <code>-9e15</code> to <code>9e15</code> inclusive, or <code>NaN</code></td>
</tr>
<tr>
<td class='centre' id='sign'><b>s</b></td>
<td>sign</td>
<td><i>number</i></td>
<td><code>-1</code>, <code>1</code>, or <code>NaN</code></td>
</tr>
</table>
<p>The properties are best considered to be read-only.</p>
<p>
As with JavaScript numbers, the original exponent and fractional trailing zeros of a number
are not preserved.
</p>
<pre>
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</pre>
<h4 id="zero-nan-infinity">Zero, NaN and Infinity</h4>
<p>
The table below shows how <code>&plusmn;0</code>, <code>NaN</code> and
<code>&plusmn;Infinity</code> are stored.
</p>
<table>
<tr>
<th> </th>
<th>&plusmn;0</th>
<th>NaN</th>
<th>&plusmn;Infinity</th>
</tr>
<tr>
<td><b>&nbsp;d&nbsp;</b></td>
<td><code>[0]</code></td>
<td><code>null</code></td>
<td><code>null</code></td>
</tr>
<tr>
<td><b>&nbsp;e&nbsp;</b></td>
<td><code>0</code></td>
<td><code>NaN</code></td>
<td><code>NaN</code></td>
</tr>
<tr>
<td><b>&nbsp;s&nbsp;</b></td>
<td><code>&plusmn;1</code></td>
<td><code>NaN</code></td>
<td><code>&plusmn;1</code></td>
</tr>
</table>
<pre>
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'</pre>
<h4 id='Errors'>Errors</h4>
<p>
The errors that are thrown are generic <code>Error</code> objects whose <code>message</code>
property begins with <code>"[DecimalError]"</code>.
</p>
<p>To determine if an exception is a Decimal Error:</p>
<pre>
try {
// ...
} catch (e) {
if ( e instanceof Error && /DecimalError/.test(e.message) ) {
// ...
}
}</pre>
<h4 id='Pi'>Pi</h4>
<p>
The maximum precision of the trigonometric methods is dependent on the internal value of the
constant pi, which is defined as the string <code>PI</code> near the top of the source file.
</p>
<p>
It has a precision of <code>1025</code> digits, meaning that the trigonometric methods
can accurately calculate up to at least <code>1000</code> digits.
</p>
<p>
If greater precision is required then the value of <code>PI</code> will need to be extended to
about <code>25</code> digits more than the precision required.
</p>
<p>The value can also be shortened to reduce the size of the source file.</p>
<p>To get the value of pi:</p>
<pre>
pi = Decimal.acos(-1)</pre>
<h2 id='faq'>FAQ</h2>
<h6>Why are trailing fractional zeros removed from Decimals?</h6>
<p>
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.
</p>
<pre>
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</pre>
<p>
To specify the precision of a value is to specify that the value lies
within a certain range.
</p>
<p>
In the first example, <code>x</code> has a value of <code>1.0</code>. The trailing zero shows
the precision of the value, implying that it is in the range <code>0.95</code> to
<code>1.05</code>. Similarly, the precision indicated by the trailing zeros of <code>y</code>
indicates that the value is in the range <code>1.09995</code> to <code>1.10005</code>.
</p>
<p>
If we add the two lowest values in the ranges we have, <code>0.95 + 1.09995 = 2.04995</code>,
and if we add the two highest values we have, <code>1.05 + 1.10005 = 2.15005</code>, so the
range of the result of the addition implied by the precision of its operands is
<code>2.04995</code> to <code>2.15005</code>.
</p>
<p>
The result given by BigDecimal of <code>2.1000</code> however, indicates that the value is in
the range <code>2.09995</code> to <code>2.10005</code> and therefore the precision implied by
its trailing zeros may be misleading.
</p>
<p>
In the second example, the true range is <code>4.122744</code> to <code>4.157256</code> yet
the BigDecimal answer of <code>4.1400000</code> indicates a range of <code>4.13999995</code>
to <code>4.14000005</code>. Again, the precision implied by the trailing zeros may be
misleading.
</p>
<p>
This library, like binary floating point and most calculators, does not retain trailing
fractional zeros. Instead, the <code>toExponential</code>, <code>toFixed</code> and
<code>toPrecision</code> methods enable trailing zeros to be added if and when required.<br />
</p>
</div>
</body>
</html>

1
nodered/rootfs/data/node_modules/decimal.js/doc/decimal.js.map generated vendored Normal file
View File

File diff suppressed because one or more lines are too long

62
nodered/rootfs/data/node_modules/decimal.js/package.json generated vendored Normal file
View File

@@ -0,0 +1,62 @@
{
"_from": "decimal.js@7.1.1",
"_id": "decimal.js@7.1.1",
"_inBundle": false,
"_integrity": "sha1-GtytfXDXqRxCbXVvHrZWbDvmy88=",
"_location": "/decimal.js",
"_phantomChildren": {},
"_requested": {
"type": "version",
"registry": true,
"raw": "decimal.js@7.1.1",
"name": "decimal.js",
"escapedName": "decimal.js",
"rawSpec": "7.1.1",
"saveSpec": null,
"fetchSpec": "7.1.1"
},
"_requiredBy": [
"/mathjs"
],
"_resolved": "https://registry.npmjs.org/decimal.js/-/decimal.js-7.1.1.tgz",
"_shasum": "1adcad7d70d7a91c426d756f1eb6566c3be6cbcf",
"_spec": "decimal.js@7.1.1",
"_where": "/data/node_modules/mathjs",
"author": {
"name": "Michael Mclaughlin",
"email": "M8ch88l@gmail.com"
},
"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.js",
"name": "decimal.js",
"repository": {
"type": "git",
"url": "git+https://github.com/MikeMcl/decimal.js.git"
},
"scripts": {
"build": "uglifyjs decimal.js --source-map doc/decimal.js.map -c -m -o decimal.min.js --preamble \"/* decimal.js v7.1.1 https://github.com/MikeMcl/decimal.js/LICENCE */\"",
"test": "node ./test/test.js"
},
"version": "7.1.1"
}