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#### 7.2.1
* 24/05/2018
* Add `browser` field to *package.json*.
#### 7.2.0
* 22/05/2018
* #166 Correct *.mjs* file. Remove extension from `main` field in *package.json*.
#### 7.1.0
* 18/05/2018
* Add `module` field to *package.json* for *bignumber.mjs*.
#### 7.0.2
* 17/05/2018
* #165 Bugfix: upper-case letters for bases 11-36 in a custom alphabet.
* Add note to *README* regarding creating BigNumbers from Number values.
#### 7.0.1
* 26/04/2018
* #158 Fix global object variable name typo.
#### 7.0.0
* 26/04/2018
* #143 Remove global BigNumber from typings.
* #144 Enable compatibility with `Object.freeze(Object.prototype)`.
* #148 #123 #11 Only throw on a number primitive with more than 15 significant digits if `BigNumber.DEBUG` is `true`.
* Only throw on an invalid BigNumber value if `BigNumber.DEBUG` is `true`. Return BigNumber `NaN` instead.
* #154 `exponentiatedBy`: allow BigNumber exponent.
* #156 Prevent Content Security Policy *unsafe-eval* issue.
* `toFraction`: allow `Infinity` maximum denominator.
* Comment-out some excess tests to reduce test time.
* Amend indentation and other spacing.
#### 6.0.0
* 26/01/2018
* #137 Implement `APLHABET` configuration option.
* Remove `ERRORS` configuration option.
* Remove `toDigits` method; extend `precision` method accordingly.
* Remove s`round` method; extend `decimalPlaces` method accordingly.
* Remove methods: `ceil`, `floor`, and `truncated`.
* Remove method aliases: `add`, `cmp`, `isInt`, `isNeg`, `trunc`, `mul`, `neg` and `sub`.
* Rename methods: `shift` to `shiftedBy`, `another` to `clone`, `toPower` to `exponentiatedBy`, and `equals` to `isEqualTo`.
* Rename methods: add `is` prefix to `greaterThan`, `greaterThanOrEqualTo`, `lessThan` and `lessThanOrEqualTo`.
* Add methods: `multipliedBy`, `isBigNumber`, `isPositive`, `integerValue`, `maximum` and `minimum`.
* Refactor test suite.
* Add *CHANGELOG.md*.
* Rewrite *bignumber.d.ts*.
* Redo API image.
#### 5.0.0
* 27/11/2017
* #81 Don't throw on constructor call without `new`.
#### 4.1.0
* 26/09/2017
* Remove node 0.6 from *.travis.yml*.
* Add *bignumber.mjs*.
#### 4.0.4
* 03/09/2017
* Add missing aliases to *bignumber.d.ts*.
#### 4.0.3
* 30/08/2017
* Add types: *bignumber.d.ts*.
#### 4.0.2
* 03/05/2017
* #120 Workaround Safari/Webkit bug.
#### 4.0.1
* 05/04/2017
* #121 BigNumber.default to BigNumber['default'].
#### 4.0.0
* 09/01/2017
* Replace BigNumber.isBigNumber method with isBigNumber prototype property.
#### 3.1.2
* 08/01/2017
* Minor documentation edit.
#### 3.1.1
* 08/01/2017
* Uncomment `isBigNumber` tests.
* Ignore dot files.
#### 3.1.0
* 08/01/2017
* Add `isBigNumber` method.
#### 3.0.2
* 08/01/2017
* Bugfix: Possible incorrect value of `ERRORS` after a `BigNumber.another` call (due to `parseNumeric` declaration in outer scope).
#### 3.0.1
* 23/11/2016
* Apply fix for old ipads with `%` issue, see #57 and #102.
* Correct error message.
#### 3.0.0
* 09/11/2016
* Remove `require('crypto')` - leave it to the user.
* Add `BigNumber.set` as `BigNumber.config` alias.
* Default `POW_PRECISION` to `0`.
#### 2.4.0
* 14/07/2016
* #97 Add exports to support ES6 imports.
#### 2.3.0
* 07/03/2016
* #86 Add modulus parameter to `toPower`.
#### 2.2.0
* 03/03/2016
* #91 Permit larger JS integers.
#### 2.1.4
* 15/12/2015
* Correct UMD.
#### 2.1.3
* 13/12/2015
* Refactor re global object and crypto availability when bundling.
#### 2.1.2
* 10/12/2015
* Bugfix: `window.crypto` not assigned to `crypto`.
#### 2.1.1
* 09/12/2015
* Prevent code bundler from adding `crypto` shim.
#### 2.1.0
* 26/10/2015
* For `valueOf` and `toJSON`, include the minus sign with negative zero.
#### 2.0.8
* 2/10/2015
* Internal round function bugfix.
#### 2.0.6
* 31/03/2015
* Add bower.json. Tweak division after in-depth review.
#### 2.0.5
* 25/03/2015
* Amend README. Remove bitcoin address.
#### 2.0.4
* 25/03/2015
* Critical bugfix #58: division.
#### 2.0.3
* 18/02/2015
* Amend README. Add source map.
#### 2.0.2
* 18/02/2015
* Correct links.
#### 2.0.1
* 18/02/2015
* Add `max`, `min`, `precision`, `random`, `shiftedBy`, `toDigits` and `truncated` methods.
* Add the short-forms: `add`, `mul`, `sd`, `sub` and `trunc`.
* Add an `another` method to enable multiple independent constructors to be created.
* Add support for the base 2, 8 and 16 prefixes `0b`, `0o` and `0x`.
* Enable a rounding mode to be specified as a second parameter to `toExponential`, `toFixed`, `toFormat` and `toPrecision`.
* Add a `CRYPTO` configuration property so cryptographically-secure pseudo-random number generation can be specified.
* Add a `MODULO_MODE` configuration property to enable the rounding mode used by the `modulo` operation to be specified.
* Add a `POW_PRECISION` configuration property to enable the number of significant digits calculated by the power operation to be limited.
* Improve code quality.
* Improve documentation.
#### 2.0.0
* 29/12/2014
* Add `dividedToIntegerBy`, `isInteger` and `toFormat` methods.
* Remove the following short-forms: `isF`, `isZ`, `toE`, `toF`, `toFr`, `toN`, `toP`, `toS`.
* Store a BigNumber's coefficient in base 1e14, rather than base 10.
* Add fast path for integers to BigNumber constructor.
* Incorporate the library into the online documentation.
#### 1.5.0
* 13/11/2014
* Add `toJSON` and `decimalPlaces` methods.
#### 1.4.1
* 08/06/2014
* Amend README.
#### 1.4.0
* 08/05/2014
* Add `toNumber`.
#### 1.3.0
* 08/11/2013
* Ensure correct rounding of `sqrt` in all, rather than almost all, cases.
* Maximum radix to 64.
#### 1.2.1
* 17/10/2013
* Sign of zero when x < 0 and x + (-x) = 0.
#### 1.2.0
* 19/9/2013
* Throw Error objects for stack.
#### 1.1.1
* 22/8/2013
* Show original value in constructor error message.
#### 1.1.0
* 1/8/2013
* Allow numbers with trailing radix point.
#### 1.0.1
* Bugfix: error messages with incorrect method name
#### 1.0.0
* 8/11/2012
* Initial release

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The MIT Licence.
Copyright (c) 2018 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.

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![bignumber.js](https://raw.githubusercontent.com/MikeMcl/bignumber.js/gh-pages/bignumberjs.png)
A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.
[![Build Status](https://travis-ci.org/MikeMcl/bignumber.js.svg)](https://travis-ci.org/MikeMcl/bignumber.js)
<br />
## Features
- Integers and decimals
- Simple API but full-featured
- Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
- 8 KB minified and gzipped
- Replicates the `toExponential`, `toFixed`, `toPrecision` and `toString` methods of JavaScript's Number type
- Includes a `toFraction` and a correctly-rounded `squareRoot` method
- Supports cryptographically-secure pseudo-random number generation
- No dependencies
- Wide platform compatibility: uses JavaScript 1.5 (ECMAScript 3) features only
- Comprehensive [documentation](http://mikemcl.github.io/bignumber.js/) and test set
![API](https://raw.githubusercontent.com/MikeMcl/bignumber.js/gh-pages/API.png)
If a smaller and simpler library is required see [big.js](https://github.com/MikeMcl/big.js/).
It's less than half the size but only works with decimal numbers and only has half the methods.
It also does not allow `NaN` or `Infinity`, or have the configuration options of this library.
See also [decimal.js](https://github.com/MikeMcl/decimal.js/), which among other things adds support for non-integer powers, and performs all operations to a specified number of significant digits.
## Load
The library is the single JavaScript file *bignumber.js* (or minified, *bignumber.min.js*).
Browser:
```html
<script src='path/to/bignumber.js'></script>
```
[Node.js](http://nodejs.org):
```bash
$ npm install --save bignumber.js
```
```javascript
var BigNumber = require('bignumber.js');
```
ES6 module (*bignumber.mjs*):
```javascript
//import BigNumber from 'bignumber.js';
import {BigNumber} from 'bignumber.js';
```
AMD loader libraries such as [requireJS](http://requirejs.org/):
```javascript
require(['bignumber'], function(BigNumber) {
// Use BigNumber here in local scope. No global BigNumber.
});
```
## 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: `BigNumber`, the constructor of BigNumber instances.
It accepts a value of type Number, String or BigNumber,
```javascript
x = new BigNumber(123.4567)
y = BigNumber('123456.7e-3')
z = new BigNumber(x)
x.isEqualTo(y) && y.isEqualTo(z) && x.isEqualTo(z) // true
```
and a base can be specified.
```javascript
a = new BigNumber(1011, 2) // "11"
b = new BigNumber('zz.9', 36) // "1295.25"
c = x.plus(y) // "1306.25"
```
Note that a BigNumber is created from a Number's decimal `toString()` value not from its underlying binary value. If the latter is required, then pass the Number's `toString(2)` value and specify base 2.
```javascript
new BigNumber(Number.MAX_VALUE.toString(2), 2)
```
If the limited precision of Number values is not well understood, **it is recommended to pass String values rather than Number values** to avoid a potential loss of precision.
```javascript
// Precision loss from using numeric literals with more than 15 significant digits.
new BigNumber(1.0000000000000001); // '1'
new BigNumber(88259496234518.57); // '88259496234518.56'
new BigNumber(99999999999999999999); // '100000000000000000000'
// Precision loss from using numeric literals outside the range of Number values.
new BigNumber(2e+308); // 'Infinity'
new BigNumber(1e-324); // '0'
// Precision loss from the unexpected result of arithmetic with Number values.
new BigNumber(0.7 + 0.1); // '0.7999999999999999'
```
A BigNumber is immutable in the sense that it is not changed by its methods.
```javascript
0.3 - 0.1 // 0.19999999999999998
x = new BigNumber(0.3)
x.minus(0.1) // "0.2"
x // "0.3"
```
The methods that return a BigNumber can be chained.
```javascript
x.dividedBy(y).plus(z).times(9)
x.times('1.23456780123456789e+9').plus(9876.5432321).dividedBy('4444562598.111772').integerValue()
```
Some of the longer method names have a shorter alias.
```javascript
x.squareRoot().dividedBy(y).exponentiatedBy(3).isEqualTo( x.sqrt().div(y).pow(3) ) // true
x.modulo(y).multipliedBy(z).eq( x.mod(y).times(z) ) // true
```
As with JavaScript's Number type, there are `toExponential`, `toFixed` and `toPrecision` methods
```javascript
x = new BigNumber(255.5)
x.toExponential(5) // "2.55500e+2"
x.toFixed(5) // "255.50000"
x.toPrecision(5) // "255.50"
x.toNumber() // 255.5
```
and a base can be specified for `toString`.
```javascript
x.toString(16) // "ff.8"
```
There is also a `toFormat` method which may be useful for internationalisation
```javascript
y = new BigNumber('1234567.898765')
y.toFormat(2) // "1,234,567.90"
```
The maximum number of decimal places of the result of an operation involving division (i.e. a division, square root, base conversion or negative power operation) is set using the `config` method of the `BigNumber` constructor.
The other arithmetic operations always give the exact result.
```javascript
BigNumber.config({ DECIMAL_PLACES: 10, ROUNDING_MODE: 4 })
x = new BigNumber(2);
y = new BigNumber(3);
z = x.dividedBy(y) // "0.6666666667"
z.squareRoot() // "0.8164965809"
z.exponentiatedBy(-3) // "3.3749999995"
z.toString(2) // "0.1010101011"
z.multipliedBy(z) // "0.44444444448888888889"
z.multipliedBy(z).decimalPlaces(10) // "0.4444444445"
```
There is a `toFraction` method with an optional *maximum denominator* argument
```javascript
y = new BigNumber(355)
pi = y.dividedBy(113) // "3.1415929204"
pi.toFraction() // [ "7853982301", "2500000000" ]
pi.toFraction(1000) // [ "355", "113" ]
```
and `isNaN` and `isFinite` methods, as `NaN` and `Infinity` are valid `BigNumber` values.
```javascript
x = new BigNumber(NaN) // "NaN"
y = new BigNumber(Infinity) // "Infinity"
x.isNaN() && !y.isNaN() && !x.isFinite() && !y.isFinite() // true
```
The value of a BigNumber is stored in a decimal floating point format in terms of a coefficient, exponent and sign.
```javascript
x = new BigNumber(-123.456);
x.c // [ 123, 45600000000000 ] coefficient (i.e. significand)
x.e // 2 exponent
x.s // -1 sign
```
For advanced usage, multiple BigNumber constructors can be created, each with their own independent configuration which applies to all BigNumber's created from it.
```javascript
// Set DECIMAL_PLACES for the original BigNumber constructor
BigNumber.config({ DECIMAL_PLACES: 10 })
// Create another BigNumber constructor, optionally passing in a configuration object
BN = BigNumber.clone({ DECIMAL_PLACES: 5 })
x = new BigNumber(1)
y = new BN(1)
x.div(3) // '0.3333333333'
y.div(3) // '0.33333'
```
For futher information see the [API](http://mikemcl.github.io/bignumber.js/) reference in the *doc* directory.
## Test
The *test/modules* directory contains the test scripts for each method.
The tests can be run with Node.js or a browser. For Node.js use
$ npm test
or
$ node test/test
To test a single method, use, for example
$ node test/methods/toFraction
For the browser, open *test/test.html*.
## Performance
See the [README](https://github.com/MikeMcl/bignumber.js/tree/master/perf) in the *perf* directory.
## Build
For Node, if [uglify-js](https://github.com/mishoo/UglifyJS2) is installed
npm install uglify-js -g
then
npm run build
will create *bignumber.min.js*.
A source map will also be created in the root directory.
## Feedback
Open an issue, or email
Michael
<a href="mailto:M8ch88l@gmail.com">M8ch88l@gmail.com</a>
## Licence
The MIT Licence.
See [LICENCE](https://github.com/MikeMcl/bignumber.js/blob/master/LICENCE).

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// Type definitions for bignumber.js >=6.0.0
// Project: https://github.com/MikeMcl/bignumber.js
// Definitions by: Michael Mclaughlin <https://github.com/MikeMcl>
// Definitions: https://github.com/MikeMcl/bignumber.js
// Documentation: http://mikemcl.github.io/bignumber.js/
//
// Exports:
//
// class BigNumber (default export)
// type BigNumber.Constructor
// type BigNumber.Instance
// type BigNumber.ModuloMode
// type BigNumber.RoundingMOde
// type BigNumber.Value
// interface BigNumber.Config
// interface BigNumber.Format
//
// Example (alternative syntax commented-out):
//
// import {BigNumber} from "bignumber.js"
// //import BigNumber from "bignumber.js"
//
// let rm: BigNumber.RoundingMode = BigNumber.ROUND_UP;
// let f: BigNumber.Format = { decimalSeparator: ',' };
// let c: BigNumber.Config = { DECIMAL_PLACES: 4, ROUNDING_MODE: rm, FORMAT: f };
// BigNumber.config(c);
//
// let v: BigNumber.Value = '12345.6789';
// let b: BigNumber = new BigNumber(v);
// //let b: BigNumber.Instance = new BigNumber(v);
//
// The use of compiler option `--strictNullChecks` is recommended.
export default BigNumber;
export namespace BigNumber {
/**
* See `BigNumber.config` and `BigNumber.clone`.
*/
export interface Config {
/**
* An integer, 0 to 1e+9. Default value: 20.
*
* The maximum number of decimal places of the result of operations involving division, i.e.
* division, square root and base conversion operations, and exponentiation when the exponent is
* negative.
*
* ```ts
* BigNumber.config({ DECIMAL_PLACES: 5 })
* BigNumber.set({ DECIMAL_PLACES: 5 })
* ```
*/
DECIMAL_PLACES?: number;
/**
* An integer, 0 to 8. Default value: `BigNumber.ROUND_HALF_UP` (4).
*
* The rounding mode used in operations that involve division (see `DECIMAL_PLACES`) and the
* default rounding mode of the `decimalPlaces`, `precision`, `toExponential`, `toFixed`,
* `toFormat` and `toPrecision` methods.
*
* The modes are available as enumerated properties of the BigNumber constructor.
*
* ```ts
* BigNumber.config({ ROUNDING_MODE: 0 })
* BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP })
* ```
*/
ROUNDING_MODE?: BigNumber.RoundingMode;
/**
* An integer, 0 to 1e+9, or an array, [-1e+9 to 0, 0 to 1e+9].
* Default value: `[-7, 20]`.
*
* The exponent value(s) at which `toString` returns exponential notation.
*
* If a single number is assigned, the value is the exponent magnitude.
*
* If an array of two numbers is assigned then the first number is the negative exponent value at
* and beneath which exponential notation is used, and the second number is the positive exponent
* value at and above which exponential notation is used.
*
* For example, to emulate JavaScript numbers in terms of the exponent values at which they begin
* to use exponential notation, use `[-7, 20]`.
*
* ```ts
* BigNumber.config({ EXPONENTIAL_AT: 2 })
* new BigNumber(12.3) // '12.3' e is only 1
* new BigNumber(123) // '1.23e+2'
* new BigNumber(0.123) // '0.123' e is only -1
* new BigNumber(0.0123) // '1.23e-2'
*
* BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
* new BigNumber(123456789) // '123456789' e is only 8
* new BigNumber(0.000000123) // '1.23e-7'
*
* // Almost never return exponential notation:
* BigNumber.config({ EXPONENTIAL_AT: 1e+9 })
*
* // Always return exponential notation:
* BigNumber.config({ EXPONENTIAL_AT: 0 })
* ```
*
* Regardless of the value of `EXPONENTIAL_AT`, the `toFixed` method will always return a value in
* normal notation and the `toExponential` method will always return a value in exponential form.
* Calling `toString` with a base argument, e.g. `toString(10)`, will also always return normal
* notation.
*/
EXPONENTIAL_AT?: number|[number, number];
/**
* An integer, magnitude 1 to 1e+9, or an array, [-1e+9 to -1, 1 to 1e+9].
* Default value: `[-1e+9, 1e+9]`.
*
* The exponent value(s) beyond which overflow to Infinity and underflow to zero occurs.
*
* If a single number is assigned, it is the maximum exponent magnitude: values wth a positive
* exponent of greater magnitude become Infinity and those with a negative exponent of greater
* magnitude become zero.
*
* If an array of two numbers is assigned then the first number is the negative exponent limit and
* the second number is the positive exponent limit.
*
* For example, to emulate JavaScript numbers in terms of the exponent values at which they
* become zero and Infinity, use [-324, 308].
*
* ```ts
* BigNumber.config({ RANGE: 500 })
* BigNumber.config().RANGE // [ -500, 500 ]
* new BigNumber('9.999e499') // '9.999e+499'
* new BigNumber('1e500') // 'Infinity'
* new BigNumber('1e-499') // '1e-499'
* new BigNumber('1e-500') // '0'
*
* BigNumber.config({ RANGE: [-3, 4] })
* new BigNumber(99999) // '99999' e is only 4
* new BigNumber(100000) // 'Infinity' e is 5
* new BigNumber(0.001) // '0.01' e is only -3
* new BigNumber(0.0001) // '0' e is -4
* ```
* The largest possible magnitude of a finite BigNumber is 9.999...e+1000000000.
* The smallest possible magnitude of a non-zero BigNumber is 1e-1000000000.
*/
RANGE?: number|[number, number];
/**
* A boolean: `true` or `false`. Default value: `false`.
*
* The value that determines whether cryptographically-secure pseudo-random number generation is
* used. If `CRYPTO` is set to true then the random method will generate random digits using
* `crypto.getRandomValues` in browsers that support it, or `crypto.randomBytes` if using a
* version of Node.js that supports it.
*
* If neither function is supported by the host environment then attempting to set `CRYPTO` to
* `true` will fail and an exception will be thrown.
*
* If `CRYPTO` is `false` then the source of randomness used will be `Math.random` (which is
* assumed to generate at least 30 bits of randomness).
*
* See `BigNumber.random`.
*
* ```ts
* BigNumber.config({ CRYPTO: true })
* BigNumber.config().CRYPTO // true
* BigNumber.random() // 0.54340758610486147524
* ```
*/
CRYPTO?: boolean;
/**
* An integer, 0, 1, 3, 6 or 9. Default value: `BigNumber.ROUND_DOWN` (1).
*
* The modulo mode used when calculating the modulus: `a mod n`.
* The quotient, `q = a / n`, is calculated according to the `ROUNDING_MODE` that corresponds to
* the chosen `MODULO_MODE`.
* The remainder, `r`, is calculated as: `r = a - n * q`.
*
* The modes that are most commonly used for the modulus/remainder operation are shown in the
* following table. Although the other rounding modes can be used, they may not give useful
* results.
*
* Property | Value | Description
* :------------------|:------|:------------------------------------------------------------------
* `ROUND_UP` | 0 | The remainder is positive if the dividend is negative.
* `ROUND_DOWN` | 1 | The remainder has the same sign as the dividend.
* | | Uses 'truncating division' and matches JavaScript's `%` operator .
* `ROUND_FLOOR` | 3 | The remainder has the same sign as the divisor.
* | | This matches Python's `%` operator.
* `ROUND_HALF_EVEN` | 6 | The IEEE 754 remainder function.
* `EUCLID` | 9 | The remainder is always positive.
* | | Euclidian division: `q = sign(n) * floor(a / abs(n))`
*
* The rounding/modulo modes are available as enumerated properties of the BigNumber constructor.
*
* See `modulo`.
*
* ```ts
* BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
* BigNumber.set({ MODULO_MODE: 9 }) // equivalent
* ```
*/
MODULO_MODE?: BigNumber.ModuloMode;
/**
* An integer, 0 to 1e+9. Default value: 0.
*
* The maximum precision, i.e. number of significant digits, of the result of the power operation
* - unless a modulus is specified.
*
* If set to 0, the number of significant digits will not be limited.
*
* See `exponentiatedBy`.
*
* ```ts
* BigNumber.config({ POW_PRECISION: 100 })
* ```
*/
POW_PRECISION?: number;
/**
* An object including any number of the properties shown below.
*
* The object configures the format of the string returned by the `toFormat` method.
* The example below shows the properties of the object that are recognised, and
* their default values.
*
* Unlike the other configuration properties, the values of the properties of the `FORMAT` object
* will not be checked for validity - the existing object will simply be replaced by the object
* that is passed in.
*
* See `toFormat`.
*
* ```ts
* BigNumber.config({
* FORMAT: {
* // the decimal separator
* decimalSeparator: '.',
* // the grouping separator of the integer part
* groupSeparator: ',',
* // the primary grouping size of the integer part
* groupSize: 3,
* // the secondary grouping size of the integer part
* secondaryGroupSize: 0,
* // the grouping separator of the fraction part
* fractionGroupSeparator: ' ',
* // the grouping size of the fraction part
* fractionGroupSize: 0
* }
* })
* ```
*/
FORMAT?: BigNumber.Format;
/**
* A string representing the alphabet used for base conversion.
* Default value: `'0123456789abcdefghijklmnopqrstuvwxyz'`.
*
* The length of the alphabet corresponds to the maximum value of the base argument that can be
* passed to the BigNumber constructor or `toString`. There is no maximum length, but it must be
* at least 2 characters long, and it must not contain a repeated character, or `'.'` - the
* decimal separator for all values whatever their base.
*
* ```ts
* // duodecimal (base 12)
* BigNumber.config({ ALPHABET: '0123456789TE' })
* x = new BigNumber('T', 12)
* x.toString() // '10'
* x.toString(12) // 'T'
* ```
*/
ALPHABET?: string;
}
export type Constructor = typeof BigNumber;
/**
* See `FORMAT` and `toFormat`.
*/
export interface Format {
/**
* The decimal separator.
*/
decimalSeparator?: string;
/**
* The grouping separator of the integer part.
*/
groupSeparator?: string;
/**
* The primary grouping size of the integer part.
*/
groupSize?: number;
/**
* The secondary grouping size of the integer part.
*/
secondaryGroupSize?: number;
/**
* The grouping separator of the fraction part.
*/
fractionGroupSeparator?: string;
/**
* The grouping size of the fraction part.
*/
fractionGroupSize?: number;
}
export type Instance = BigNumber;
export type ModuloMode = 0 | 1 | 3 | 6 | 9;
export type RoundingMode = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
export type Value = string | number | BigNumber;
}
export declare class BigNumber {
/**
* Used internally by the `BigNumber.isBigNumber` method.
*/
private readonly _isBigNumber: true;
/**
* The coefficient of the value of this BigNumber, an array of base 1e14 integer numbers.
*/
readonly c: number[];
/**
* The exponent of the value of this BigNumber, an integer number, -1000000000 to 1000000000.
*/
readonly e: number;
/**
* The sign of the value of this BigNumber, -1 or 1.
*/
readonly s: number;
/**
* Returns a new instance of a BigNumber object with value `n`, where `n` is a numeric value in
* the specified `base`, or base 10 if `base` is omitted or is `null` or `undefined`.
*
* ```ts
* x = new BigNumber(123.4567) // '123.4567'
* // 'new' is optional
* y = BigNumber(x) // '123.4567'
* ```
*
* If `n` is a base 10 value it can be in normal (fixed-point) or exponential notation.
* Values in other bases must be in normal notation. Values in any base can have fraction digits,
* i.e. digits after the decimal point.
*
* ```ts
* new BigNumber(43210) // '43210'
* new BigNumber('4.321e+4') // '43210'
* new BigNumber('-735.0918e-430') // '-7.350918e-428'
* new BigNumber('123412421.234324', 5) // '607236.557696'
* ```
*
* Signed `0`, signed `Infinity` and `NaN` are supported.
*
* ```ts
* new BigNumber('-Infinity') // '-Infinity'
* new BigNumber(NaN) // 'NaN'
* new BigNumber(-0) // '0'
* new BigNumber('.5') // '0.5'
* new BigNumber('+2') // '2'
* ```
*
* String values in hexadecimal literal form, e.g. `'0xff'`, are valid, as are string values with
* the octal and binary prefixs `'0o'` and `'0b'`. String values in octal literal form without the
* prefix will be interpreted as decimals, e.g. `'011'` is interpreted as 11, not 9.
*
* ```ts
* new BigNumber(-10110100.1, 2) // '-180.5'
* new BigNumber('-0b10110100.1') // '-180.5'
* new BigNumber('ff.8', 16) // '255.5'
* new BigNumber('0xff.8') // '255.5'
* ```
*
* If a base is specified, `n` is rounded according to the current `DECIMAL_PLACES` and
* `ROUNDING_MODE` settings. This includes base 10, so don't include a `base` parameter for decimal
* values unless this behaviour is desired.
*
* ```ts
* BigNumber.config({ DECIMAL_PLACES: 5 })
* new BigNumber(1.23456789) // '1.23456789'
* new BigNumber(1.23456789, 10) // '1.23457'
* ```
*
* An error is thrown if `base` is invalid.
*
* There is no limit to the number of digits of a value of type string (other than that of
* JavaScript's maximum array size). See `RANGE` to set the maximum and minimum possible exponent
* value of a BigNumber.
*
* ```ts
* new BigNumber('5032485723458348569331745.33434346346912144534543')
* new BigNumber('4.321e10000000')
* ```
*
* BigNumber `NaN` is returned if `n` is invalid (unless `BigNumber.DEBUG` is `true`, see below).
*
* ```ts
* new BigNumber('.1*') // 'NaN'
* new BigNumber('blurgh') // 'NaN'
* new BigNumber(9, 2) // 'NaN'
* ```
*
* To aid in debugging, if `BigNumber.DEBUG` is `true` then an error will be thrown on an
* invalid `n`. An error will also be thrown if `n` is of type number with more than 15
* significant digits, as calling `toString` or `valueOf` on these numbers may not result in the
* intended value.
*
* ```ts
* console.log(823456789123456.3) // 823456789123456.2
* new BigNumber(823456789123456.3) // '823456789123456.2'
* BigNumber.DEBUG = true
* // 'Error: Number has more than 15 significant digits'
* new BigNumber(823456789123456.3)
* // 'Error: Not a base 2 number'
* new BigNumber(9, 2)
* ```
*
* @param n A numeric value.
* @param base The base of `n`, integer, 2 to 36 (or `ALPHABET.length`, see `ALPHABET`).
*/
constructor(n: BigNumber.Value, base?: number);
/**
* Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of this
* BigNumber.
*
* The return value is always exact and unrounded.
*
* ```ts
* x = new BigNumber(-0.8)
* x.absoluteValue() // '0.8'
* ```
*/
absoluteValue(): BigNumber;
/**
* Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of this
* BigNumber.
*
* The return value is always exact and unrounded.
*
* ```ts
* x = new BigNumber(-0.8)
* x.abs() // '0.8'
* ```
*/
abs(): BigNumber;
/**
* Returns | |
* :-------:|:--------------------------------------------------------------|
* 1 | If the value of this BigNumber is greater than the value of `n`
* -1 | If the value of this BigNumber is less than the value of `n`
* 0 | If this BigNumber and `n` have the same value
* `null` | If the value of either this BigNumber or `n` is `NaN`
*
* ```ts
*
* x = new BigNumber(Infinity)
* y = new BigNumber(5)
* x.comparedTo(y) // 1
* x.comparedTo(x.minus(1)) // 0
* y.comparedTo(NaN) // null
* y.comparedTo('110', 2) // -1
* ```
* @param n A numeric value.
* @param [base] The base of n.
*/
comparedTo(n: BigNumber.Value, base?: number): number;
/**
* Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
* `roundingMode` to a maximum of `decimalPlaces` decimal places.
*
* If `decimalPlaces` is omitted, or is `null` or `undefined`, the return value is the number of
* decimal places of the value of this BigNumber, or `null` if the value of this BigNumber is
* ±`Infinity` or `NaN`.
*
* If `roundingMode` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `decimalPlaces` or `roundingMode` is invalid.
*
* ```ts
* x = new BigNumber(1234.56)
* x.decimalPlaces() // 2
* x.decimalPlaces(1) // '1234.6'
* x.decimalPlaces(2) // '1234.56'
* x.decimalPlaces(10) // '1234.56'
* x.decimalPlaces(0, 1) // '1234'
* x.decimalPlaces(0, 6) // '1235'
* x.decimalPlaces(1, 1) // '1234.5'
* x.decimalPlaces(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
* x // '1234.56'
* y = new BigNumber('9.9e-101')
* y.decimalPlaces() // 102
* ```
*
* @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
decimalPlaces(): number;
decimalPlaces(decimalPlaces: number, roundingMode?: BigNumber.RoundingMode): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
* `roundingMode` to a maximum of `decimalPlaces` decimal places.
*
* If `decimalPlaces` is omitted, or is `null` or `undefined`, the return value is the number of
* decimal places of the value of this BigNumber, or `null` if the value of this BigNumber is
* ±`Infinity` or `NaN`.
*
* If `roundingMode` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `decimalPlaces` or `roundingMode` is invalid.
*
* ```ts
* x = new BigNumber(1234.56)
* x.dp() // 2
* x.dp(1) // '1234.6'
* x.dp(2) // '1234.56'
* x.dp(10) // '1234.56'
* x.dp(0, 1) // '1234'
* x.dp(0, 6) // '1235'
* x.dp(1, 1) // '1234.5'
* x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
* x // '1234.56'
* y = new BigNumber('9.9e-101')
* y.dp() // 102
* ```
*
* @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
dp(): number;
dp(decimalPlaces: number, roundingMode?: BigNumber.RoundingMode): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber divided by `n`, rounded
* according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
*
* ```ts
* x = new BigNumber(355)
* y = new BigNumber(113)
* x.dividedBy(y) // '3.14159292035398230088'
* x.dividedBy(5) // '71'
* x.dividedBy(47, 16) // '5'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
dividedBy(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber divided by `n`, rounded
* according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
*
* ```ts
* x = new BigNumber(355)
* y = new BigNumber(113)
* x.div(y) // '3.14159292035398230088'
* x.div(5) // '71'
* x.div(47, 16) // '5'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
div(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
* `n`.
*
* ```ts
* x = new BigNumber(5)
* y = new BigNumber(3)
* x.dividedToIntegerBy(y) // '1'
* x.dividedToIntegerBy(0.7) // '7'
* x.dividedToIntegerBy('0.f', 16) // '5'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
dividedToIntegerBy(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
* `n`.
*
* ```ts
* x = new BigNumber(5)
* y = new BigNumber(3)
* x.idiv(y) // '1'
* x.idiv(0.7) // '7'
* x.idiv('0.f', 16) // '5'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
idiv(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber exponentiated by `n`, i.e.
* raised to the power `n`, and optionally modulo a modulus `m`.
*
* If `n` is negative the result is rounded according to the current `DECIMAL_PLACES` and
* `ROUNDING_MODE` settings.
*
* As the number of digits of the result of the power operation can grow so large so quickly,
* e.g. 123.456**10000 has over 50000 digits, the number of significant digits calculated is
* limited to the value of the `POW_PRECISION` setting (unless a modulus `m` is specified).
*
* By default `POW_PRECISION` is set to 0. This means that an unlimited number of significant
* digits will be calculated, and that the method's performance will decrease dramatically for
* larger exponents.
*
* If `m` is specified and the value of `m`, `n` and this BigNumber are integers and `n` is
* positive, then a fast modular exponentiation algorithm is used, otherwise the operation will
* be performed as `x.exponentiatedBy(n).modulo(m)` with a `POW_PRECISION` of 0.
*
* Throws if `n` is not an integer.
*
* ```ts
* Math.pow(0.7, 2) // 0.48999999999999994
* x = new BigNumber(0.7)
* x.exponentiatedBy(2) // '0.49'
* BigNumber(3).exponentiatedBy(-2) // '0.11111111111111111111'
* ```
*
* @param n The exponent, an integer.
* @param [m] The modulus.
*/
exponentiatedBy(n: number, m?: BigNumber.Value): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber exponentiated by `n`, i.e.
* raised to the power `n`, and optionally modulo a modulus `m`.
*
* If `n` is negative the result is rounded according to the current `DECIMAL_PLACES` and
* `ROUNDING_MODE` settings.
*
* As the number of digits of the result of the power operation can grow so large so quickly,
* e.g. 123.456**10000 has over 50000 digits, the number of significant digits calculated is
* limited to the value of the `POW_PRECISION` setting (unless a modulus `m` is specified).
*
* By default `POW_PRECISION` is set to 0. This means that an unlimited number of significant
* digits will be calculated, and that the method's performance will decrease dramatically for
* larger exponents.
*
* If `m` is specified and the value of `m`, `n` and this BigNumber are integers and `n` is
* positive, then a fast modular exponentiation algorithm is used, otherwise the operation will
* be performed as `x.pow(n).modulo(m)` with a `POW_PRECISION` of 0.
*
* Throws if `n` is not an integer.
*
* ```ts
* Math.pow(0.7, 2) // 0.48999999999999994
* x = new BigNumber(0.7)
* x.pow(2) // '0.49'
* BigNumber(3).pow(-2) // '0.11111111111111111111'
* ```
*
* @param n The exponent, an integer.
* @param [m] The modulus.
*/
pow(n: number, m?: BigNumber.Value): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
* rounding mode `rm`.
*
* If `rm` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `rm` is invalid.
*
* ```ts
* x = new BigNumber(123.456)
* x.integerValue() // '123'
* x.integerValue(BigNumber.ROUND_CEIL) // '124'
* y = new BigNumber(-12.7)
* y.integerValue() // '-13'
* x.integerValue(BigNumber.ROUND_DOWN) // '-12'
* ```
*
* @param {BigNumber.RoundingMode} [rm] The roundng mode, an integer, 0 to 8.
*/
integerValue(rm?: BigNumber.RoundingMode): BigNumber;
/**
* Returns `true` if the value of this BigNumber is equal to the value of `n`, otherwise returns
* `false`.
*
* As with JavaScript, `NaN` does not equal `NaN`.
*
* ```ts
* 0 === 1e-324 // true
* x = new BigNumber(0)
* x.isEqualTo('1e-324') // false
* BigNumber(-0).isEqualTo(x) // true ( -0 === 0 )
* BigNumber(255).isEqualTo('ff', 16) // true
*
* y = new BigNumber(NaN)
* y.isEqualTo(NaN) // false
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
isEqualTo(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is equal to the value of `n`, otherwise returns
* `false`.
*
* As with JavaScript, `NaN` does not equal `NaN`.
*
* ```ts
* 0 === 1e-324 // true
* x = new BigNumber(0)
* x.eq('1e-324') // false
* BigNumber(-0).eq(x) // true ( -0 === 0 )
* BigNumber(255).eq('ff', 16) // true
*
* y = new BigNumber(NaN)
* y.eq(NaN) // false
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
eq(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is a finite number, otherwise returns `false`.
*
* The only possible non-finite values of a BigNumber are `NaN`, `Infinity` and `-Infinity`.
*
* ```ts
* x = new BigNumber(1)
* x.isFinite() // true
* y = new BigNumber(Infinity)
* y.isFinite() // false
* ```
*/
isFinite(): boolean;
/**
* Returns `true` if the value of this BigNumber is greater than the value of `n`, otherwise
* returns `false`.
*
* ```ts
* 0.1 > (0.3 - 0.2) // true
* x = new BigNumber(0.1)
* x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false
* BigNumber(0).isGreaterThan(x) // false
* BigNumber(11, 3).isGreaterThan(11.1, 2) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
isGreaterThan(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is greater than the value of `n`, otherwise
* returns `false`.
*
* ```ts
* 0.1 > (0.3 - 0 // true
* x = new BigNumber(0.1)
* x.gt(BigNumber(0.3).minus(0.2)) // false
* BigNumber(0).gt(x) // false
* BigNumber(11, 3).gt(11.1, 2) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
gt(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is greater than or equal to the value of `n`,
* otherwise returns `false`.
*
* ```ts
* (0.3 - 0.2) >= 0.1 // false
* x = new BigNumber(0.3).minus(0.2)
* x.isGreaterThanOrEqualTo(0.1) // true
* BigNumber(1).isGreaterThanOrEqualTo(x) // true
* BigNumber(10, 18).isGreaterThanOrEqualTo('i', 36) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
isGreaterThanOrEqualTo(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is greater than or equal to the value of `n`,
* otherwise returns `false`.
*
* ```ts
* (0.3 - 0.2) >= 0.1 // false
* x = new BigNumber(0.3).minus(0.2)
* x.gte(0.1) // true
* BigNumber(1).gte(x) // true
* BigNumber(10, 18).gte('i', 36) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
gte(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is an integer, otherwise returns `false`.
*
* ```ts
* x = new BigNumber(1)
* x.isInteger() // true
* y = new BigNumber(123.456)
* y.isInteger() // false
* ```
*/
isInteger(): boolean;
/**
* Returns `true` if the value of this BigNumber is less than the value of `n`, otherwise returns
* `false`.
*
* ```ts
* (0.3 - 0.2) < 0.1 // true
* x = new BigNumber(0.3).minus(0.2)
* x.isLessThan(0.1) // false
* BigNumber(0).isLessThan(x) // true
* BigNumber(11.1, 2).isLessThan(11, 3) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
isLessThan(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is less than the value of `n`, otherwise returns
* `false`.
*
* ```ts
* (0.3 - 0.2) < 0.1 // true
* x = new BigNumber(0.3).minus(0.2)
* x.lt(0.1) // false
* BigNumber(0).lt(x) // true
* BigNumber(11.1, 2).lt(11, 3) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
lt(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is less than or equal to the value of `n`,
* otherwise returns `false`.
*
* ```ts
* 0.1 <= (0.3 - 0.2) // false
* x = new BigNumber(0.1)
* x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true
* BigNumber(-1).isLessThanOrEqualTo(x) // true
* BigNumber(10, 18).isLessThanOrEqualTo('i', 36) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
isLessThanOrEqualTo(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is less than or equal to the value of `n`,
* otherwise returns `false`.
*
* ```ts
* 0.1 <= (0.3 - 0.2) // false
* x = new BigNumber(0.1)
* x.lte(BigNumber(0.3).minus(0.2)) // true
* BigNumber(-1).lte(x) // true
* BigNumber(10, 18).lte('i', 36) // true
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
lte(n: BigNumber.Value, base?: number): boolean;
/**
* Returns `true` if the value of this BigNumber is `NaN`, otherwise returns `false`.
*
* ```ts
* x = new BigNumber(NaN)
* x.isNaN() // true
* y = new BigNumber('Infinity')
* y.isNaN() // false
* ```
*/
isNaN(): boolean;
/**
* Returns `true` if the value of this BigNumber is negative, otherwise returns `false`.
*
* ```ts
* x = new BigNumber(-0)
* x.isNegative() // true
* y = new BigNumber(2)
* y.isNegative() // false
* ```
*/
isNegative(): boolean;
/**
* Returns `true` if the value of this BigNumber is positive, otherwise returns `false`.
*
* ```ts
* x = new BigNumber(-0)
* x.isPositive() // false
* y = new BigNumber(2)
* y.isPositive() // true
* ```
*/
isPositive(): boolean;
/**
* Returns `true` if the value of this BigNumber is zero or minus zero, otherwise returns `false`.
*
* ```ts
* x = new BigNumber(-0)
* x.isZero() // true
* ```
*/
isZero(): boolean;
/**
* Returns a BigNumber whose value is the value of this BigNumber minus `n`.
*
* The return value is always exact and unrounded.
*
* ```ts
* 0.3 - 0.1 // 0.19999999999999998
* x = new BigNumber(0.3)
* x.minus(0.1) // '0.2'
* x.minus(0.6, 20) // '0'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
minus(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber modulo `n`, i.e. the integer
* remainder of dividing this BigNumber by `n`.
*
* The value returned, and in particular its sign, is dependent on the value of the `MODULO_MODE`
* setting of this BigNumber constructor. If it is 1 (default value), the result will have the
* same sign as this BigNumber, and it will match that of Javascript's `%` operator (within the
* limits of double precision) and BigDecimal's `remainder` method.
*
* The return value is always exact and unrounded.
*
* See `MODULO_MODE` for a description of the other modulo modes.
*
* ```ts
* 1 % 0.9 // 0.09999999999999998
* x = new BigNumber(1)
* x.modulo(0.9) // '0.1'
* y = new BigNumber(33)
* y.modulo('a', 33) // '3'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
modulo(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber modulo `n`, i.e. the integer
* remainder of dividing this BigNumber by `n`.
*
* The value returned, and in particular its sign, is dependent on the value of the `MODULO_MODE`
* setting of this BigNumber constructor. If it is 1 (default value), the result will have the
* same sign as this BigNumber, and it will match that of Javascript's `%` operator (within the
* limits of double precision) and BigDecimal's `remainder` method.
*
* The return value is always exact and unrounded.
*
* See `MODULO_MODE` for a description of the other modulo modes.
*
* ```ts
* 1 % 0.9 // 0.09999999999999998
* x = new BigNumber(1)
* x.mod(0.9) // '0.1'
* y = new BigNumber(33)
* y.mod('a', 33) // '3'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
mod(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber multiplied by `n`.
*
* The return value is always exact and unrounded.
*
* ```ts
* 0.6 * 3 // 1.7999999999999998
* x = new BigNumber(0.6)
* y = x.multipliedBy(3) // '1.8'
* BigNumber('7e+500').multipliedBy(y) // '1.26e+501'
* x.multipliedBy('-a', 16) // '-6'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
multipliedBy(n: BigNumber.Value, base?: number) : BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber multiplied by `n`.
*
* The return value is always exact and unrounded.
*
* ```ts
* 0.6 * 3 // 1.7999999999999998
* x = new BigNumber(0.6)
* y = x.times(3) // '1.8'
* BigNumber('7e+500').times(y) // '1.26e+501'
* x.times('-a', 16) // '-6'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
times(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by -1.
*
* ```ts
* x = new BigNumber(1.8)
* x.negated() // '-1.8'
* y = new BigNumber(-1.3)
* y.negated() // '1.3'
* ```
*/
negated(): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber plus `n`.
*
* The return value is always exact and unrounded.
*
* ```ts
* 0.1 + 0.2 // 0.30000000000000004
* x = new BigNumber(0.1)
* y = x.plus(0.2) // '0.3'
* BigNumber(0.7).plus(x).plus(y) // '1'
* x.plus('0.1', 8) // '0.225'
* ```
*
* @param n A numeric value.
* @param [base] The base of n.
*/
plus(n: BigNumber.Value, base?: number): BigNumber;
/**
* Returns the number of significant digits of the value of this BigNumber, or `null` if the value
* of this BigNumber is ±`Infinity` or `NaN`.
*
* If `includeZeros` is true then any trailing zeros of the integer part of the value of this
* BigNumber are counted as significant digits, otherwise they are not.
*
* Throws if `includeZeros` is invalid.
*
* ```ts
* x = new BigNumber(9876.54321)
* x.precision() // 9
* y = new BigNumber(987000)
* y.precision(false) // 3
* y.precision(true) // 6
* ```
*
* @param [includeZeros] Whether to include integer trailing zeros in the significant digit count.
*/
precision(includeZeros?: boolean): number;
/**
* Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of
* `significantDigits` significant digits using rounding mode `roundingMode`.
*
* If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` will be used.
*
* Throws if `significantDigits` or `roundingMode` is invalid.
*
* ```ts
* x = new BigNumber(9876.54321)
* x.precision(6) // '9876.54'
* x.precision(6, BigNumber.ROUND_UP) // '9876.55'
* x.precision(2) // '9900'
* x.precision(2, 1) // '9800'
* x // '9876.54321'
* ```
*
* @param significantDigits Significant digits, integer, 1 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
precision(significantDigits: number, roundingMode?: BigNumber.RoundingMode): BigNumber;
/**
* Returns the number of significant digits of the value of this BigNumber,
* or `null` if the value of this BigNumber is ±`Infinity` or `NaN`.
*
* If `includeZeros` is true then any trailing zeros of the integer part of
* the value of this BigNumber are counted as significant digits, otherwise
* they are not.
*
* Throws if `includeZeros` is invalid.
*
* ```ts
* x = new BigNumber(9876.54321)
* x.sd() // 9
* y = new BigNumber(987000)
* y.sd(false) // 3
* y.sd(true) // 6
* ```
*
* @param [includeZeros] Whether to include integer trailing zeros in the significant digit count.
*/
sd(includeZeros?: boolean): number;
/*
* Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of
* `significantDigits` significant digits using rounding mode `roundingMode`.
*
* If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` will be used.
*
* Throws if `significantDigits` or `roundingMode` is invalid.
*
* ```ts
* x = new BigNumber(9876.54321)
* x.sd(6) // '9876.54'
* x.sd(6, BigNumber.ROUND_UP) // '9876.55'
* x.sd(2) // '9900'
* x.sd(2, 1) // '9800'
* x // '9876.54321'
* ```
*
* @param significantDigits Significant digits, integer, 1 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
sd(significantDigits: number, roundingMode?: BigNumber.RoundingMode): BigNumber;
/**
* Returns a BigNumber whose value is the value of this BigNumber shifted by `n` places.
*
* The shift is of the decimal point, i.e. of powers of ten, and is to the left if `n` is negative
* or to the right if `n` is positive.
*
* The return value is always exact and unrounded.
*
* Throws if `n` is invalid.
*
* ```ts
* x = new BigNumber(1.23)
* x.shiftedBy(3) // '1230'
* x.shiftedBy(-3) // '0.00123'
* ```
*
* @param n The shift value, integer, -9007199254740991 to 9007199254740991.
*/
shiftedBy(n: number): BigNumber;
/**
* Returns a BigNumber whose value is the square root of the value of this BigNumber, rounded
* according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
*
* 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.
*
* ```ts
* x = new BigNumber(16)
* x.squareRoot() // '4'
* y = new BigNumber(3)
* y.squareRoot() // '1.73205080756887729353'
* ```
*/
squareRoot(): BigNumber;
/**
* Returns a BigNumber whose value is the square root of the value of this BigNumber, rounded
* according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
*
* 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.
*
* ```ts
* x = new BigNumber(16)
* x.sqrt() // '4'
* y = new BigNumber(3)
* y.sqrt() // '1.73205080756887729353'
* ```
*/
sqrt(): BigNumber;
/**
* Returns a string representing the value of this BigNumber in exponential notation rounded using
* rounding mode `roundingMode` to `decimalPlaces` decimal places, i.e with one digit before the
* decimal point and `decimalPlaces` digits after it.
*
* If the value of this BigNumber in exponential notation has fewer than `decimalPlaces` fraction
* digits, the return value will be appended with zeros accordingly.
*
* If `decimalPlaces` is omitted, or is `null` or `undefined`, the number of digits after the
* decimal point defaults to the minimum number of digits necessary to represent the value
* exactly.
*
* If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `decimalPlaces` or `roundingMode` is invalid.
*
* ```ts
* x = 45.6
* y = new BigNumber(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'
* ```
*
* @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
toExponential(decimalPlaces?: number, roundingMode?: BigNumber.RoundingMode): string;
/**
* Returns a string representing the value of this BigNumber in normal (fixed-point) notation
* rounded to `decimalPlaces` decimal places using rounding mode `roundingMode`.
*
* If the value of this BigNumber in normal notation has fewer than `decimalPlaces` fraction
* digits, the return value will be appended with zeros accordingly.
*
* Unlike `Number.prototype.toFixed`, which returns exponential notation if a number is greater or
* equal to 10**21, this method will always return normal notation.
*
* If `decimalPlaces` is omitted or is `null` or `undefined`, the return value will be unrounded
* and in normal notation. This is also unlike `Number.prototype.toFixed`, which returns the value
* to zero decimal places. It is useful when normal notation is required and the current
* `EXPONENTIAL_AT` setting causes `toString` to return exponential notation.
*
* If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `decimalPlaces` or `roundingMode` is invalid.
*
* ```ts
* x = 3.456
* y = new BigNumber(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'
* ```
*
* @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
toFixed(decimalPlaces?: number, roundingMode?: BigNumber.RoundingMode): string;
/**
* Returns a string representing the value of this BigNumber in normal (fixed-point) notation
* rounded to `decimalPlaces` decimal places using rounding mode `roundingMode`, and formatted
* according to the properties of the `FORMAT` object.
*
* The properties of the `FORMAT` object are shown in the examples below.
*
* If `decimalPlaces` is omitted or is `null` or `undefined`, then the return value is not
* rounded to a fixed number of decimal places.
*
* If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `decimalPlaces` or `roundingMode` is invalid.
*
* ```ts
* format = {
* decimalSeparator: '.',
* groupSeparator: ',',
* groupSize: 3,
* secondaryGroupSize: 0,
* fractionGroupSeparator: ' ',
* fractionGroupSize: 0
* }
* BigNumber.config({ FORMAT: format })
*
* x = new BigNumber('123456789.123456789')
* x.toFormat() // '123,456,789.123456789'
* x.toFormat(1) // '123,456,789.1'
*
* format.groupSeparator = ' '
* format.fractionGroupSize = 5
* x.toFormat() // '123 456 789.12345 6789'
*
* BigNumber.config({
* FORMAT: {
* decimalSeparator: ',',
* groupSeparator: '.',
* groupSize: 3,
* secondaryGroupSize: 2
* }
* })
*
* x.toFormat(6) // '12.34.56.789,123'
* ```
*
* @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
* @param [roundingMode] Rounding mode, integer, 0 to 8.
*/
toFormat(decimalPlaces?: number, roundingMode?: BigNumber.RoundingMode): string;
/**
* Returns a string array representing the value of this BigNumber as a simple fraction with an
* integer numerator and an integer denominator. The denominator will be a positive non-zero value
* less than or equal to `max_denominator`.
*
* If a maximum denominator, `max_denominator`, is not specified, or is `null` or `undefined`, the
* denominator will be the lowest value necessary to represent the number exactly.
*
* Throws if `max_denominator` is invalid.
*
* ```ts
* x = new BigNumber(1.75)
* x.toFraction() // '7, 4'
*
* pi = new BigNumber('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'
* ```
*
* @param [max_denominator] The maximum denominator, integer > 0, or Infinity.
*/
toFraction(max_denominator?: BigNumber.Value): BigNumber[];
/**
* As `valueOf`.
*/
toJSON(): string;
/**
* Returns the value of this BigNumber as a JavaScript primitive number.
*
* Using the unary plus operator gives the same result.
*
* ```ts
* x = new BigNumber(456.789)
* x.toNumber() // 456.789
* +x // 456.789
*
* y = new BigNumber('45987349857634085409857349856430985')
* y.toNumber() // 4.598734985763409e+34
*
* z = new BigNumber(-0)
* 1 / z.toNumber() // -Infinity
* 1 / +z // -Infinity
* ```
*/
toNumber(): number;
/**
* Returns a string representing the value of this BigNumber rounded to `significantDigits`
* significant digits using rounding mode `roundingMode`.
*
* If `significantDigits` is less than the number of digits necessary to represent the integer
* part of the value in normal (fixed-point) notation, then exponential notation is used.
*
* If `significantDigits` is omitted, or is `null` or `undefined`, then the return value is the
* same as `n.toString()`.
*
* If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
*
* Throws if `significantDigits` or `roundingMode` is invalid.
*
* ```ts
* x = 45.6
* y = new BigNumber(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'
* ```
*
* @param [significantDigits] Significant digits, integer, 1 to 1e+9.
* @param [roundingMode] Rounding mode, integer 0 to 8.
*/
toPrecision(significantDigits?: number, roundingMode?: BigNumber.RoundingMode): string;
/**
* Returns a string representing the value of this BigNumber in base `base`, or base 10 if `base`
* is omitted or is `null` or `undefined`.
*
* For bases above 10, and using the default base conversion alphabet (see `ALPHABET`), values
* from 10 to 35 are represented by a-z (the same as `Number.prototype.toString`).
*
* If a base is specified the value is rounded according to the current `DECIMAL_PLACES` and
* `ROUNDING_MODE` settings, otherwise it is not.
*
* If a base is not specified, and this BigNumber has a positive exponent that is equal to or
* greater than the positive component of the current `EXPONENTIAL_AT` setting, or a negative
* exponent equal to or less than the negative component of the setting, then exponential notation
* is returned.
*
* If `base` is `null` or `undefined` it is ignored.
*
* Throws if `base` is invalid.
*
* ```ts
* x = new BigNumber(750000)
* x.toString() // '750000'
* BigNumber.config({ EXPONENTIAL_AT: 5 })
* x.toString() // '7.5e+5'
*
* y = new BigNumber(362.875)
* y.toString(2) // '101101010.111'
* y.toString(9) // '442.77777777777777777778'
* y.toString(32) // 'ba.s'
*
* BigNumber.config({ DECIMAL_PLACES: 4 });
* z = new BigNumber('1.23456789')
* z.toString() // '1.23456789'
* z.toString(10) // '1.2346'
* ```
*
* @param [base] The base, integer, 2 to 36 (or `ALPHABET.length`, see `ALPHABET`).
*/
toString(base?: number): string;
/**
* As `toString`, but does not accept a base argument and includes the minus sign for negative
* zero.
*
* ``ts
* x = new BigNumber('-0')
* x.toString() // '0'
* x.valueOf() // '-0'
* y = new BigNumber('1.777e+457')
* y.valueOf() // '1.777e+457'
* ```
*/
valueOf(): string;
/**
* Returns a new independent BigNumber constructor with configuration as described by `object`, or
* with the default configuration if object is `null` or `undefined`.
*
* Throws if `object` is not an object.
*
* ```ts
* BigNumber.config({ DECIMAL_PLACES: 5 })
* BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
*
* x = new BigNumber(1)
* y = new BN(1)
*
* x.div(3) // 0.33333
* y.div(3) // 0.333333333
*
* // BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
* BN = BigNumber.clone()
* BN.config({ DECIMAL_PLACES: 9 })
* ```
*
* @param [object] The configuration object.
*/
static clone(object?: BigNumber.Config): BigNumber.Constructor;
/**
* Configures the settings that apply to this BigNumber constructor.
*
* The configuration object, `object`, contains any number of the properties shown in the example
* below.
*
* Returns an object with the above properties and their current values.
*
* Throws if `object` is not an object, or if an invalid value is assigned to one or more of the
* properties.
*
* ```ts
* BigNumber.config({
* DECIMAL_PLACES: 40,
* ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
* EXPONENTIAL_AT: [-10, 20],
* RANGE: [-500, 500],
* CRYPTO: true,
* MODULO_MODE: BigNumber.ROUND_FLOOR,
* POW_PRECISION: 80,
* FORMAT: {
* groupSize: 3,
* groupSeparator: ' ',
* decimalSeparator: ','
* },
* ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
* });
*
* BigNumber.config().DECIMAL_PLACES // 40
* ```
*
* @param object The configuration object.
*/
static config(object: BigNumber.Config): BigNumber.Config;
/**
* Returns `true` if `value` is a BigNumber instance, otherwise returns `false`.
*
* ```ts
* x = 42
* y = new BigNumber(x)
*
* BigNumber.isBigNumber(x) // false
* y instanceof BigNumber // true
* BigNumber.isBigNumber(y) // true
*
* BN = BigNumber.clone();
* z = new BN(x)
* z instanceof BigNumber // false
* BigNumber.isBigNumber(z) // true
* ```
*
* @param value The value to test.
*/
static isBigNumber(value: any): boolean;
/**
*
* Returns a BigNumber whose value is the maximum of the arguments.
*
* Accepts either an argument list or an array of values.
*
* The return value is always exact and unrounded.
*
* ```ts
* x = new BigNumber('3257869345.0378653')
* BigNumber.maximum(4e9, x, '123456789.9') // '4000000000'
*
* arr = [12, '13', new BigNumber(14)]
* BigNumber.maximum(arr) // '14'
* ```
*
* @param n A numeric value.
*/
static maximum(...n: BigNumber.Value[]): BigNumber;
/**
* Returns a BigNumber whose value is the maximum of the arguments.
*
* Accepts either an argument list or an array of values.
*
* The return value is always exact and unrounded.
*
* ```ts
* x = new BigNumber('3257869345.0378653')
* BigNumber.max(4e9, x, '123456789.9') // '4000000000'
*
* arr = [12, '13', new BigNumber(14)]
* BigNumber.max(arr) // '14'
* ```
*
* @param n A numeric value.
*/
static max(...n: BigNumber.Value[]): BigNumber;
/**
* Returns a BigNumber whose value is the minimum of the arguments.
*
* Accepts either an argument list or an array of values.
*
* The return value is always exact and unrounded.
*
* ```ts
* x = new BigNumber('3257869345.0378653')
* BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9'
*
* arr = [2, new BigNumber(-14), '-15.9999', -12]
* BigNumber.minimum(arr) // '-15.9999'
* ```
*
* @param n A numeric value.
*/
static minimum(...n: BigNumber.Value[]): BigNumber;
/**
* Returns a BigNumber whose value is the minimum of the arguments.
*
* Accepts either an argument list or an array of values.
*
* The return value is always exact and unrounded.
*
* ```ts
* x = new BigNumber('3257869345.0378653')
* BigNumber.min(4e9, x, '123456789.9') // '123456789.9'
*
* arr = [2, new BigNumber(-14), '-15.9999', -12]
* BigNumber.min(arr) // '-15.9999'
* ```
*
* @param n A numeric value.
*/
static min(...n: BigNumber.Value[]): BigNumber;
/**
* Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and less than 1.
*
* The return value will have `decimalPlaces` decimal places, or less if trailing zeros are
* produced. If `decimalPlaces` is omitted, the current `DECIMAL_PLACES` setting will be used.
*
* Depending on the value of this BigNumber constructor's `CRYPTO` setting and the support for the
* `crypto` object in the host environment, the random digits of the return value are generated by
* either `Math.random` (fastest), `crypto.getRandomValues` (Web Cryptography API in recent
* browsers) or `crypto.randomBytes` (Node.js).
*
* If `CRYPTO` is true, i.e. one of the `crypto` methods is to be used, the value of a returned
* BigNumber should be cryptographically secure and statistically indistinguishable from a random
* value.
*
* Throws if `decimalPlaces` is invalid.
*
* ```ts
* BigNumber.config({ DECIMAL_PLACES: 10 })
* BigNumber.random() // '0.4117936847'
* BigNumber.random(20) // '0.78193327636914089009'
* ```
*
* @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
*/
static random(decimalPlaces?: number): BigNumber;
/**
* Configures the settings that apply to this BigNumber constructor.
*
* The configuration object, `object`, contains any number of the properties shown in the example
* below.
*
* Returns an object with the above properties and their current values.
*
* Throws if `object` is not an object, or if an invalid value is assigned to one or more of the
* properties.
*
* ```ts
* BigNumber.set({
* DECIMAL_PLACES: 40,
* ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
* EXPONENTIAL_AT: [-10, 20],
* RANGE: [-500, 500],
* CRYPTO: true,
* MODULO_MODE: BigNumber.ROUND_FLOOR,
* POW_PRECISION: 80,
* FORMAT: {
* groupSize: 3,
* groupSeparator: ' ',
* decimalSeparator: ','
* },
* ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
* });
*
* BigNumber.set().DECIMAL_PLACES // 40
* ```
*
* @param object The configuration object.
*/
static set(object: BigNumber.Config): BigNumber.Config;
/**
* Helps ES6 import.
*/
private static readonly default?: BigNumber.Constructor;
/**
* Helps ES6 import.
*/
private static readonly BigNumber?: BigNumber.Constructor;
/**
* Rounds away from zero.
*/
static readonly ROUND_UP: 0;
/**
* Rounds towards zero.
*/
static readonly ROUND_DOWN: 1;
/**
* Rounds towards Infinity.
*/
static readonly ROUND_CEIL: 2;
/**
* Rounds towards -Infinity.
*/
static readonly ROUND_FLOOR: 3;
/**
* Rounds towards nearest neighbour. If equidistant, rounds away from zero .
*/
static readonly ROUND_HALF_UP: 4;
/**
* Rounds towards nearest neighbour. If equidistant, rounds towards zero.
*/
static readonly ROUND_HALF_DOWN: 5;
/**
* Rounds towards nearest neighbour. If equidistant, rounds towards even neighbour.
*/
static readonly ROUND_HALF_EVEN: 6;
/**
* Rounds towards nearest neighbour. If equidistant, rounds towards Infinity.
*/
static readonly ROUND_HALF_CEIL: 7;
/**
* Rounds towards nearest neighbour. If equidistant, rounds towards -Infinity.
*/
static readonly ROUND_HALF_FLOOR: 8;
/**
* See `MODULO_MODE`.
*/
static readonly EUCLID: 9;
/**
* To aid in debugging, if a `BigNumber.DEBUG` property is `true` then an error will be thrown
* on an invalid `BigNumber.Value`.
*
* ```ts
* // No error, and BigNumber NaN is returned.
* new BigNumber('blurgh') // 'NaN'
* new BigNumber(9, 2) // 'NaN'
* BigNumber.DEBUG = true
* new BigNumber('blurgh') // '[BigNumber Error] Not a number'
* new BigNumber(9, 2) // '[BigNumber Error] Not a base 2 number'
* ```
*
* An error will also be thrown if a `BigNumber.Value` is of type number with more than 15
* significant digits, as calling `toString` or `valueOf` on such numbers may not result
* in the intended value.
*
* ```ts
* console.log(823456789123456.3) // 823456789123456.2
* // No error, and the returned BigNumber does not have the same value as the number literal.
* new BigNumber(823456789123456.3) // '823456789123456.2'
* BigNumber.DEBUG = true
* new BigNumber(823456789123456.3)
* // '[BigNumber Error] Number primitive has more than 15 significant digits'
* ```
*
*/
static DEBUG?: boolean;
}

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@@ -0,0 +1,2814 @@
;(function (globalObject) {
'use strict';
/*
* bignumber.js v7.2.1
* A JavaScript library for arbitrary-precision arithmetic.
* https://github.com/MikeMcl/bignumber.js
* Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licensed.
*
* BigNumber.prototype methods | BigNumber methods
* |
* absoluteValue abs | clone
* comparedTo | config set
* decimalPlaces dp | DECIMAL_PLACES
* dividedBy div | ROUNDING_MODE
* dividedToIntegerBy idiv | EXPONENTIAL_AT
* exponentiatedBy pow | RANGE
* integerValue | CRYPTO
* isEqualTo eq | MODULO_MODE
* isFinite | POW_PRECISION
* isGreaterThan gt | FORMAT
* isGreaterThanOrEqualTo gte | ALPHABET
* isInteger | isBigNumber
* isLessThan lt | maximum max
* isLessThanOrEqualTo lte | minimum min
* isNaN | random
* isNegative |
* isPositive |
* isZero |
* minus |
* modulo mod |
* multipliedBy times |
* negated |
* plus |
* precision sd |
* shiftedBy |
* squareRoot sqrt |
* toExponential |
* toFixed |
* toFormat |
* toFraction |
* toJSON |
* toNumber |
* toPrecision |
* toString |
* valueOf |
*
*/
var BigNumber,
isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
mathceil = Math.ceil,
mathfloor = Math.floor,
bignumberError = '[BigNumber Error] ',
tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
BASE = 1e14,
LOG_BASE = 14,
MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1
// MAX_INT32 = 0x7fffffff, // 2^31 - 1
POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
SQRT_BASE = 1e7,
// EDITABLE
// The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
// the arguments to toExponential, toFixed, toFormat, and toPrecision.
MAX = 1E9; // 0 to MAX_INT32
/*
* Create and return a BigNumber constructor.
*/
function clone(configObject) {
var div, convertBase, parseNumeric,
P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
ONE = new BigNumber(1),
//----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
// The default values below must be integers within the inclusive ranges stated.
// The values can also be changed at run-time using BigNumber.set.
// The maximum number of decimal places for operations involving division.
DECIMAL_PLACES = 20, // 0 to MAX
// The rounding mode used when rounding to the above decimal places, and when using
// toExponential, toFixed, toFormat and toPrecision, and round (default value).
// UP 0 Away from zero.
// DOWN 1 Towards zero.
// CEIL 2 Towards +Infinity.
// FLOOR 3 Towards -Infinity.
// HALF_UP 4 Towards nearest neighbour. If equidistant, up.
// HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
// HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
// HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
// HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
ROUNDING_MODE = 4, // 0 to 8
// EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
// The exponent value at and beneath which toString returns exponential notation.
// Number type: -7
TO_EXP_NEG = -7, // 0 to -MAX
// The exponent value at and above which toString returns exponential notation.
// Number type: 21
TO_EXP_POS = 21, // 0 to MAX
// RANGE : [MIN_EXP, MAX_EXP]
// The minimum exponent value, beneath which underflow to zero occurs.
// Number type: -324 (5e-324)
MIN_EXP = -1e7, // -1 to -MAX
// The maximum exponent value, above which overflow to Infinity occurs.
// Number type: 308 (1.7976931348623157e+308)
// For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
MAX_EXP = 1e7, // 1 to MAX
// Whether to use cryptographically-secure random number generation, if available.
CRYPTO = false, // true or false
// 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.
// This modulo mode is commonly known as 'truncated division' and is
// equivalent to (a % n) in JavaScript.
// FLOOR 3 The remainder has the same sign as the divisor (Python %).
// HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
// EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)).
// The remainder is always positive.
//
// The truncated division, floored division, Euclidian division and IEEE 754 remainder
// modes are commonly used for the modulus operation.
// Although the other rounding modes can also be used, they may not give useful results.
MODULO_MODE = 1, // 0 to 9
// The maximum number of significant digits of the result of the exponentiatedBy operation.
// If POW_PRECISION is 0, there will be unlimited significant digits.
POW_PRECISION = 0, // 0 to MAX
// The format specification used by the BigNumber.prototype.toFormat method.
FORMAT = {
decimalSeparator: '.',
groupSeparator: ',',
groupSize: 3,
secondaryGroupSize: 0,
fractionGroupSeparator: '\xA0', // non-breaking space
fractionGroupSize: 0
},
// The alphabet used for base conversion.
// It must be at least 2 characters long, with no '.' or repeated character.
// '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
//------------------------------------------------------------------------------------------
// CONSTRUCTOR
/*
* The BigNumber constructor and exported function.
* Create and return a new instance of a BigNumber object.
*
* n {number|string|BigNumber} A numeric value.
* [b] {number} The base of n. Integer, 2 to ALPHABET.length inclusive.
*/
function BigNumber(n, b) {
var alphabet, c, caseChanged, e, i, isNum, len, str,
x = this;
// Enable constructor usage without new.
if (!(x instanceof BigNumber)) {
// Don't throw on constructor call without new (#81).
// '[BigNumber Error] Constructor call without new: {n}'
//throw Error(bignumberError + ' Constructor call without new: ' + n);
return new BigNumber(n, b);
}
if (b == null) {
// Duplicate.
if (n instanceof BigNumber) {
x.s = n.s;
x.e = n.e;
x.c = (n = n.c) ? n.slice() : n;
return;
}
isNum = typeof n == 'number';
if (isNum && n * 0 == 0) {
// Use `1 / n` to handle minus zero also.
x.s = 1 / n < 0 ? (n = -n, -1) : 1;
// Faster path for integers.
if (n === ~~n) {
for (e = 0, i = n; i >= 10; i /= 10, e++);
x.e = e;
x.c = [n];
return;
}
str = n + '';
} else {
if (!isNumeric.test(str = n + '')) return parseNumeric(x, str, isNum);
x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
}
// 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;
}
} else {
// '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
intCheck(b, 2, ALPHABET.length, 'Base');
str = n + '';
// Allow exponential notation to be used with base 10 argument, while
// also rounding to DECIMAL_PLACES as with other bases.
if (b == 10) {
x = new BigNumber(n instanceof BigNumber ? n : str);
return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
}
isNum = typeof n == 'number';
if (isNum) {
// Avoid potential interpretation of Infinity and NaN as base 44+ values.
if (n * 0 != 0) return parseNumeric(x, str, isNum, b);
x.s = 1 / n < 0 ? (str = str.slice(1), -1) : 1;
// '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
throw Error
(tooManyDigits + n);
}
// Prevent later check for length on converted number.
isNum = false;
} else {
x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
}
alphabet = ALPHABET.slice(0, b);
e = i = 0;
// Check that str is a valid base b number.
// Don't use RegExp so alphabet can contain special characters.
for (len = str.length; i < len; i++) {
if (alphabet.indexOf(c = str.charAt(i)) < 0) {
if (c == '.') {
// If '.' is not the first character and it has not be found before.
if (i > e) {
e = len;
continue;
}
} else if (!caseChanged) {
// Allow e.g. hexadecimal 'FF' as well as 'ff'.
if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
str == str.toLowerCase() && (str = str.toUpperCase())) {
caseChanged = true;
i = -1;
e = 0;
continue;
}
}
return parseNumeric(x, n + '', isNum, b);
}
}
str = convertBase(str, b, 10, x.s);
// Decimal point?
if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
else e = str.length;
}
// Determine leading zeros.
for (i = 0; str.charCodeAt(i) === 48; i++);
// Determine trailing zeros.
for (len = str.length; str.charCodeAt(--len) === 48;);
str = str.slice(i, ++len);
if (str) {
len -= i;
// '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
if (isNum && BigNumber.DEBUG &&
len > 15 && (n > MAX_SAFE_INTEGER || n !== mathfloor(n))) {
throw Error
(tooManyDigits + (x.s * n));
}
e = e - i - 1;
// Overflow?
if (e > MAX_EXP) {
// Infinity.
x.c = x.e = null;
// Underflow?
} else if (e < MIN_EXP) {
// Zero.
x.c = [x.e = 0];
} else {
x.e = e;
x.c = [];
// Transform base
// e is the base 10 exponent.
// i is where to slice str to get the first element of the coefficient array.
i = (e + 1) % LOG_BASE;
if (e < 0) i += LOG_BASE;
if (i < len) {
if (i) x.c.push(+str.slice(0, i));
for (len -= LOG_BASE; i < len;) {
x.c.push(+str.slice(i, i += LOG_BASE));
}
str = str.slice(i);
i = LOG_BASE - str.length;
} else {
i -= len;
}
for (; i--; str += '0');
x.c.push(+str);
}
} else {
// Zero.
x.c = [x.e = 0];
}
}
// CONSTRUCTOR PROPERTIES
BigNumber.clone = clone;
BigNumber.ROUND_UP = 0;
BigNumber.ROUND_DOWN = 1;
BigNumber.ROUND_CEIL = 2;
BigNumber.ROUND_FLOOR = 3;
BigNumber.ROUND_HALF_UP = 4;
BigNumber.ROUND_HALF_DOWN = 5;
BigNumber.ROUND_HALF_EVEN = 6;
BigNumber.ROUND_HALF_CEIL = 7;
BigNumber.ROUND_HALF_FLOOR = 8;
BigNumber.EUCLID = 9;
/*
* Configure infrequently-changing library-wide settings.
*
* Accept an object with the following optional properties (if the value of a property is
* a number, it must be an integer within the inclusive range stated):
*
* DECIMAL_PLACES {number} 0 to MAX
* ROUNDING_MODE {number} 0 to 8
* EXPONENTIAL_AT {number|number[]} -MAX to MAX or [-MAX to 0, 0 to MAX]
* RANGE {number|number[]} -MAX to MAX (not zero) or [-MAX to -1, 1 to MAX]
* CRYPTO {boolean} true or false
* MODULO_MODE {number} 0 to 9
* POW_PRECISION {number} 0 to MAX
* ALPHABET {string} A string of two or more unique characters which does
* not contain '.'.
* FORMAT {object} An object with some of the following properties:
* decimalSeparator {string}
* groupSeparator {string}
* groupSize {number}
* secondaryGroupSize {number}
* fractionGroupSeparator {string}
* fractionGroupSize {number}
*
* (The values assigned to the above FORMAT object properties are not checked for validity.)
*
* E.g.
* BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
*
* Ignore properties/parameters set to null or undefined, except for ALPHABET.
*
* Return an object with the properties current values.
*/
BigNumber.config = BigNumber.set = function (obj) {
var p, v;
if (obj != null) {
if (typeof obj == 'object') {
// DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
// '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
v = obj[p];
intCheck(v, 0, MAX, p);
DECIMAL_PLACES = v;
}
// ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
// '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
v = obj[p];
intCheck(v, 0, 8, p);
ROUNDING_MODE = v;
}
// EXPONENTIAL_AT {number|number[]}
// Integer, -MAX to MAX inclusive or
// [integer -MAX to 0 inclusive, 0 to MAX inclusive].
// '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
v = obj[p];
if (isArray(v)) {
intCheck(v[0], -MAX, 0, p);
intCheck(v[1], 0, MAX, p);
TO_EXP_NEG = v[0];
TO_EXP_POS = v[1];
} else {
intCheck(v, -MAX, MAX, p);
TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
}
}
// RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
// [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
// '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
if (obj.hasOwnProperty(p = 'RANGE')) {
v = obj[p];
if (isArray(v)) {
intCheck(v[0], -MAX, -1, p);
intCheck(v[1], 1, MAX, p);
MIN_EXP = v[0];
MAX_EXP = v[1];
} else {
intCheck(v, -MAX, MAX, p);
if (v) {
MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
} else {
throw Error
(bignumberError + p + ' cannot be zero: ' + v);
}
}
}
// CRYPTO {boolean} true or false.
// '[BigNumber Error] CRYPTO not true or false: {v}'
// '[BigNumber Error] crypto unavailable'
if (obj.hasOwnProperty(p = 'CRYPTO')) {
v = obj[p];
if (v === !!v) {
if (v) {
if (typeof crypto != 'undefined' && crypto &&
(crypto.getRandomValues || crypto.randomBytes)) {
CRYPTO = v;
} else {
CRYPTO = !v;
throw Error
(bignumberError + 'crypto unavailable');
}
} else {
CRYPTO = v;
}
} else {
throw Error
(bignumberError + p + ' not true or false: ' + v);
}
}
// MODULO_MODE {number} Integer, 0 to 9 inclusive.
// '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
v = obj[p];
intCheck(v, 0, 9, p);
MODULO_MODE = v;
}
// POW_PRECISION {number} Integer, 0 to MAX inclusive.
// '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
v = obj[p];
intCheck(v, 0, MAX, p);
POW_PRECISION = v;
}
// FORMAT {object}
// '[BigNumber Error] FORMAT not an object: {v}'
if (obj.hasOwnProperty(p = 'FORMAT')) {
v = obj[p];
if (typeof v == 'object') FORMAT = v;
else throw Error
(bignumberError + p + ' not an object: ' + v);
}
// ALPHABET {string}
// '[BigNumber Error] ALPHABET invalid: {v}'
if (obj.hasOwnProperty(p = 'ALPHABET')) {
v = obj[p];
// Disallow if only one character, or contains '.' or a repeated character.
if (typeof v == 'string' && !/^.$|\.|(.).*\1/.test(v)) {
ALPHABET = v;
} else {
throw Error
(bignumberError + p + ' invalid: ' + v);
}
}
} else {
// '[BigNumber Error] Object expected: {v}'
throw Error
(bignumberError + 'Object expected: ' + obj);
}
}
return {
DECIMAL_PLACES: DECIMAL_PLACES,
ROUNDING_MODE: ROUNDING_MODE,
EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
RANGE: [MIN_EXP, MAX_EXP],
CRYPTO: CRYPTO,
MODULO_MODE: MODULO_MODE,
POW_PRECISION: POW_PRECISION,
FORMAT: FORMAT,
ALPHABET: ALPHABET
};
};
/*
* Return true if v is a BigNumber instance, otherwise return false.
*
* v {any}
*/
BigNumber.isBigNumber = function (v) {
return v instanceof BigNumber || v && v._isBigNumber === true || false;
};
/*
* Return a new BigNumber whose value is the maximum of the arguments.
*
* arguments {number|string|BigNumber}
*/
BigNumber.maximum = BigNumber.max = function () {
return maxOrMin(arguments, P.lt);
};
/*
* Return a new BigNumber whose value is the minimum of the arguments.
*
* arguments {number|string|BigNumber}
*/
BigNumber.minimum = BigNumber.min = function () {
return maxOrMin(arguments, P.gt);
};
/*
* Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
* and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
* zeros are produced).
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
* '[BigNumber Error] crypto unavailable'
*/
BigNumber.random = (function () {
var pow2_53 = 0x20000000000000;
// Return a 53 bit integer n, where 0 <= n < 9007199254740992.
// Check if Math.random() produces more than 32 bits of randomness.
// If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
// 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
? function () { return mathfloor(Math.random() * pow2_53); }
: function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
(Math.random() * 0x800000 | 0); };
return function (dp) {
var a, b, e, k, v,
i = 0,
c = [],
rand = new BigNumber(ONE);
if (dp == null) dp = DECIMAL_PLACES;
else intCheck(dp, 0, MAX);
k = mathceil(dp / LOG_BASE);
if (CRYPTO) {
// Browsers supporting crypto.getRandomValues.
if (crypto.getRandomValues) {
a = crypto.getRandomValues(new Uint32Array(k *= 2));
for (; i < k;) {
// 53 bits:
// ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
// 11111 11111111 11111111 11111111 11100000 00000000 00000000
// ((Math.pow(2, 32) - 1) >>> 11).toString(2)
// 11111 11111111 11111111
// 0x20000 is 2^21.
v = a[i] * 0x20000 + (a[i + 1] >>> 11);
// Rejection sampling:
// 0 <= v < 9007199254740992
// Probability that v >= 9e15, is
// 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
if (v >= 9e15) {
b = crypto.getRandomValues(new Uint32Array(2));
a[i] = b[0];
a[i + 1] = b[1];
} else {
// 0 <= v <= 8999999999999999
// 0 <= (v % 1e14) <= 99999999999999
c.push(v % 1e14);
i += 2;
}
}
i = k / 2;
// Node.js supporting crypto.randomBytes.
} else if (crypto.randomBytes) {
// buffer
a = crypto.randomBytes(k *= 7);
for (; i < k;) {
// 0x1000000000000 is 2^48, 0x10000000000 is 2^40
// 0x100000000 is 2^32, 0x1000000 is 2^24
// 11111 11111111 11111111 11111111 11111111 11111111 11111111
// 0 <= v < 9007199254740992
v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
(a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
(a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
if (v >= 9e15) {
crypto.randomBytes(7).copy(a, i);
} else {
// 0 <= (v % 1e14) <= 99999999999999
c.push(v % 1e14);
i += 7;
}
}
i = k / 7;
} else {
CRYPTO = false;
throw Error
(bignumberError + 'crypto unavailable');
}
}
// Use Math.random.
if (!CRYPTO) {
for (; i < k;) {
v = random53bitInt();
if (v < 9e15) c[i++] = v % 1e14;
}
}
k = c[--i];
dp %= LOG_BASE;
// Convert trailing digits to zeros according to dp.
if (k && dp) {
v = POWS_TEN[LOG_BASE - dp];
c[i] = mathfloor(k / v) * v;
}
// Remove trailing elements which are zero.
for (; c[i] === 0; c.pop(), i--);
// Zero?
if (i < 0) {
c = [e = 0];
} else {
// Remove leading elements which are zero and adjust exponent accordingly.
for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
// Count the digits of the first element of c to determine leading zeros, and...
for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
// adjust the exponent accordingly.
if (i < LOG_BASE) e -= LOG_BASE - i;
}
rand.e = e;
rand.c = c;
return rand;
};
})();
// PRIVATE FUNCTIONS
// Called by BigNumber and BigNumber.prototype.toString.
convertBase = (function () {
var decimal = '0123456789';
/*
* Convert string of baseIn to an array of numbers of baseOut.
* Eg. toBaseOut('255', 10, 16) returns [15, 15].
* Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
*/
function toBaseOut(str, baseIn, baseOut, alphabet) {
var j,
arr = [0],
arrL,
i = 0,
len = str.length;
for (; i < len;) {
for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
arr[0] += alphabet.indexOf(str.charAt(i++));
for (j = 0; j < arr.length; j++) {
if (arr[j] > baseOut - 1) {
if (arr[j + 1] == null) arr[j + 1] = 0;
arr[j + 1] += arr[j] / baseOut | 0;
arr[j] %= baseOut;
}
}
}
return arr.reverse();
}
// Convert a numeric string of baseIn to a numeric string of baseOut.
// If the caller is toString, we are converting from base 10 to baseOut.
// If the caller is BigNumber, we are converting from baseIn to base 10.
return function (str, baseIn, baseOut, sign, callerIsToString) {
var alphabet, d, e, k, r, x, xc, y,
i = str.indexOf('.'),
dp = DECIMAL_PLACES,
rm = ROUNDING_MODE;
// Non-integer.
if (i >= 0) {
k = POW_PRECISION;
// Unlimited precision.
POW_PRECISION = 0;
str = str.replace('.', '');
y = new BigNumber(baseIn);
x = y.pow(str.length - i);
POW_PRECISION = k;
// Convert str as if an integer, then restore the fraction part by dividing the
// result by its base raised to a power.
y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
10, baseOut, decimal);
y.e = y.c.length;
}
// Convert the number as integer.
xc = toBaseOut(str, baseIn, baseOut, callerIsToString
? (alphabet = ALPHABET, decimal)
: (alphabet = decimal, ALPHABET));
// xc now represents str as an integer and converted to baseOut. e is the exponent.
e = k = xc.length;
// Remove trailing zeros.
for (; xc[--k] == 0; xc.pop());
// Zero?
if (!xc[0]) return alphabet.charAt(0);
// Does str represent an integer? If so, no need for the division.
if (i < 0) {
--e;
} else {
x.c = xc;
x.e = e;
// The sign is needed for correct rounding.
x.s = sign;
x = div(x, y, dp, rm, baseOut);
xc = x.c;
r = x.r;
e = x.e;
}
// xc now represents str converted to baseOut.
// THe index of the rounding digit.
d = e + dp + 1;
// The rounding digit: the digit to the right of the digit that may be rounded up.
i = xc[d];
// Look at the rounding digits and mode to determine whether to round up.
k = baseOut / 2;
r = r || d < 0 || xc[d + 1] != null;
r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
: i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
rm == (x.s < 0 ? 8 : 7));
// If the index of the rounding digit is not greater than zero, or xc represents
// zero, then the result of the base conversion is zero or, if rounding up, a value
// such as 0.00001.
if (d < 1 || !xc[0]) {
// 1^-dp or 0
str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0))
: alphabet.charAt(0);
} else {
// Truncate xc to the required number of decimal places.
xc.length = d;
// Round up?
if (r) {
// Rounding up may mean the previous digit has to be rounded up and so on.
for (--baseOut; ++xc[--d] > baseOut;) {
xc[d] = 0;
if (!d) {
++e;
xc = [1].concat(xc);
}
}
}
// Determine trailing zeros.
for (k = xc.length; !xc[--k];);
// E.g. [4, 11, 15] becomes 4bf.
for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
// Add leading zeros, decimal point and trailing zeros as required.
str = toFixedPoint(str, e, alphabet.charAt(0));
}
// The caller will add the sign.
return str;
};
})();
// Perform division in the specified base. Called by div and convertBase.
div = (function () {
// Assume non-zero x and k.
function multiply(x, k, base) {
var m, temp, xlo, xhi,
carry = 0,
i = x.length,
klo = k % SQRT_BASE,
khi = k / SQRT_BASE | 0;
for (x = x.slice(); i--;) {
xlo = x[i] % SQRT_BASE;
xhi = x[i] / SQRT_BASE | 0;
m = khi * xlo + xhi * klo;
temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
x[i] = temp % base;
}
if (carry) x = [carry].concat(x);
return x;
}
function compare(a, b, aL, bL) {
var i, cmp;
if (aL != bL) {
cmp = aL > bL ? 1 : -1;
} else {
for (i = cmp = 0; i < aL; i++) {
if (a[i] != b[i]) {
cmp = a[i] > b[i] ? 1 : -1;
break;
}
}
}
return cmp;
}
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.splice(0, 1));
}
// x: dividend, y: divisor.
return function (x, y, dp, rm, base) {
var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
yL, yz,
s = x.s == y.s ? 1 : -1,
xc = x.c,
yc = y.c;
// Either NaN, Infinity or 0?
if (!xc || !xc[0] || !yc || !yc[0]) {
return new BigNumber(
// Return NaN if either NaN, or both Infinity or 0.
!x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
// Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
xc && xc[0] == 0 || !yc ? s * 0 : s / 0
);
}
q = new BigNumber(s);
qc = q.c = [];
e = x.e - y.e;
s = dp + e + 1;
if (!base) {
base = BASE;
e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
s = s / LOG_BASE | 0;
}
// Result exponent may be one less then the current value of e.
// The coefficients of the BigNumbers from convertBase may have trailing zeros.
for (i = 0; yc[i] == (xc[i] || 0); i++);
if (yc[i] > (xc[i] || 0)) e--;
if (s < 0) {
qc.push(1);
more = true;
} else {
xL = xc.length;
yL = yc.length;
i = 0;
s += 2;
// Normalise xc and yc so highest order digit of yc is >= base / 2.
n = mathfloor(base / (yc[0] + 1));
// Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
// if (n > 1 || n++ == 1 && yc[0] < base / 2) {
if (n > 1) {
yc = multiply(yc, n, base);
xc = multiply(xc, n, base);
yL = yc.length;
xL = xc.length;
}
xi = yL;
rem = xc.slice(0, yL);
remL = rem.length;
// Add zeros to make remainder as long as divisor.
for (; remL < yL; rem[remL++] = 0);
yz = yc.slice();
yz = [0].concat(yz);
yc0 = yc[0];
if (yc[1] >= base / 2) yc0++;
// Not necessary, but to prevent trial digit n > base, when using base 3.
// else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
do {
n = 0;
// Compare divisor and remainder.
cmp = compare(yc, rem, yL, remL);
// If divisor < remainder.
if (cmp < 0) {
// Calculate trial digit, n.
rem0 = rem[0];
if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
// n is how many times the divisor goes into the current remainder.
n = mathfloor(rem0 / yc0);
// Algorithm:
// product = divisor multiplied by trial digit (n).
// Compare product and remainder.
// If product is greater than remainder:
// Subtract divisor from product, decrement trial digit.
// Subtract product from remainder.
// If product was less than remainder at the last compare:
// Compare new remainder and divisor.
// If remainder is greater than divisor:
// Subtract divisor from remainder, increment trial digit.
if (n > 1) {
// n may be > base only when base is 3.
if (n >= base) n = base - 1;
// product = divisor * trial digit.
prod = multiply(yc, n, base);
prodL = prod.length;
remL = rem.length;
// Compare product and remainder.
// If product > remainder then trial digit n too high.
// n is 1 too high about 5% of the time, and is not known to have
// ever been more than 1 too high.
while (compare(prod, rem, prodL, remL) == 1) {
n--;
// Subtract divisor from product.
subtract(prod, yL < prodL ? yz : yc, prodL, base);
prodL = prod.length;
cmp = 1;
}
} else {
// n is 0 or 1, cmp is -1.
// If n is 0, there is no need to compare yc and rem again below,
// so change cmp to 1 to avoid it.
// If n is 1, leave cmp as -1, so yc and rem are compared again.
if (n == 0) {
// divisor < remainder, so n must be at least 1.
cmp = n = 1;
}
// product = divisor
prod = yc.slice();
prodL = prod.length;
}
if (prodL < remL) prod = [0].concat(prod);
// Subtract product from remainder.
subtract(rem, prod, remL, base);
remL = rem.length;
// If product was < remainder.
if (cmp == -1) {
// Compare divisor and new remainder.
// If divisor < new remainder, subtract divisor from remainder.
// Trial digit n too low.
// n is 1 too low about 5% of the time, and very rarely 2 too low.
while (compare(yc, rem, yL, remL) < 1) {
n++;
// Subtract divisor from remainder.
subtract(rem, yL < remL ? yz : yc, remL, base);
remL = rem.length;
}
}
} else if (cmp === 0) {
n++;
rem = [0];
} // else cmp === 1 and n will be 0
// Add the next digit, n, to the result array.
qc[i++] = n;
// Update the remainder.
if (rem[0]) {
rem[remL++] = xc[xi] || 0;
} else {
rem = [xc[xi]];
remL = 1;
}
} while ((xi++ < xL || rem[0] != null) && s--);
more = rem[0] != null;
// Leading zero?
if (!qc[0]) qc.splice(0, 1);
}
if (base == BASE) {
// To calculate q.e, first get the number of digits of qc[0].
for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
// Caller is convertBase.
} else {
q.e = e;
q.r = +more;
}
return q;
};
})();
/*
* Return a string representing the value of BigNumber n in fixed-point or exponential
* notation rounded to the specified decimal places or significant digits.
*
* n: a BigNumber.
* i: the index of the last digit required (i.e. the digit that may be rounded up).
* rm: the rounding mode.
* id: 1 (toExponential) or 2 (toPrecision).
*/
function format(n, i, rm, id) {
var c0, e, ne, len, str;
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
if (!n.c) return n.toString();
c0 = n.c[0];
ne = n.e;
if (i == null) {
str = coeffToString(n.c);
str = id == 1 || id == 2 && ne <= TO_EXP_NEG
? toExponential(str, ne)
: toFixedPoint(str, ne, '0');
} else {
n = round(new BigNumber(n), i, rm);
// n.e may have changed if the value was rounded up.
e = n.e;
str = coeffToString(n.c);
len = str.length;
// toPrecision returns exponential notation if the number of significant digits
// specified is less than the number of digits necessary to represent the integer
// part of the value in fixed-point notation.
// Exponential notation.
if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
// Append zeros?
for (; len < i; str += '0', len++);
str = toExponential(str, e);
// Fixed-point notation.
} else {
i -= ne;
str = toFixedPoint(str, e, '0');
// Append zeros?
if (e + 1 > len) {
if (--i > 0) for (str += '.'; i--; str += '0');
} else {
i += e - len;
if (i > 0) {
if (e + 1 == len) str += '.';
for (; i--; str += '0');
}
}
}
}
return n.s < 0 && c0 ? '-' + str : str;
}
// Handle BigNumber.max and BigNumber.min.
function maxOrMin(args, method) {
var m, n,
i = 0;
if (isArray(args[0])) args = args[0];
m = new BigNumber(args[0]);
for (; ++i < args.length;) {
n = new BigNumber(args[i]);
// If any number is NaN, return NaN.
if (!n.s) {
m = n;
break;
} else if (method.call(m, n)) {
m = n;
}
}
return m;
}
/*
* Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
* Called by minus, plus and times.
*/
function normalise(n, c, e) {
var i = 1,
j = c.length;
// Remove trailing zeros.
for (; !c[--j]; c.pop());
// Calculate the base 10 exponent. First get the number of digits of c[0].
for (j = c[0]; j >= 10; j /= 10, i++);
// Overflow?
if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
// Infinity.
n.c = n.e = null;
// Underflow?
} else if (e < MIN_EXP) {
// Zero.
n.c = [n.e = 0];
} else {
n.e = e;
n.c = c;
}
return n;
}
// Handle values that fail the validity test in BigNumber.
parseNumeric = (function () {
var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
dotAfter = /^([^.]+)\.$/,
dotBefore = /^\.([^.]+)$/,
isInfinityOrNaN = /^-?(Infinity|NaN)$/,
whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
return function (x, str, isNum, b) {
var base,
s = isNum ? str : str.replace(whitespaceOrPlus, '');
// No exception on ±Infinity or NaN.
if (isInfinityOrNaN.test(s)) {
x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
x.c = x.e = null;
} else {
if (!isNum) {
// basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
s = s.replace(basePrefix, function (m, p1, p2) {
base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
return !b || b == base ? p1 : m;
});
if (b) {
base = b;
// E.g. '1.' to '1', '.1' to '0.1'
s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
}
if (str != s) return new BigNumber(s, base);
}
// '[BigNumber Error] Not a number: {n}'
// '[BigNumber Error] Not a base {b} number: {n}'
if (BigNumber.DEBUG) {
throw Error
(bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
}
// NaN
x.c = x.e = x.s = null;
}
}
})();
/*
* Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
* If r is truthy, it is known that there are more digits after the rounding digit.
*/
function round(x, sd, rm, r) {
var d, i, j, k, n, ni, rd,
xc = x.c,
pows10 = POWS_TEN;
// if x is not Infinity or NaN...
if (xc) {
// rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
// n is a base 1e14 number, the value of the element of array x.c containing rd.
// ni is the index of n within x.c.
// d is the number of digits of n.
// i is the index of rd within n including leading zeros.
// j is the actual index of rd within n (if < 0, rd is a leading zero).
out: {
// Get the number of digits of the first element of xc.
for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
i = sd - d;
// If the rounding digit is in the first element of xc...
if (i < 0) {
i += LOG_BASE;
j = sd;
n = xc[ni = 0];
// Get the rounding digit at index j of n.
rd = n / pows10[d - j - 1] % 10 | 0;
} else {
ni = mathceil((i + 1) / LOG_BASE);
if (ni >= xc.length) {
if (r) {
// Needed by sqrt.
for (; xc.length <= ni; xc.push(0));
n = rd = 0;
d = 1;
i %= LOG_BASE;
j = i - LOG_BASE + 1;
} else {
break out;
}
} else {
n = k = xc[ni];
// Get the number of digits of n.
for (d = 1; k >= 10; k /= 10, d++);
// Get the index of rd within n.
i %= LOG_BASE;
// Get the index of rd within n, adjusted for leading zeros.
// The number of leading zeros of n is given by LOG_BASE - d.
j = i - LOG_BASE + d;
// Get the rounding digit at index j of n.
rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
}
}
r = r || sd < 0 ||
// Are there any non-zero digits after the rounding digit?
// The expression n % pows10[d - j - 1] returns all digits of n to the right
// of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
r = rm < 4
? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
: rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
// Check whether the digit to the left of the rounding digit is odd.
((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
rm == (x.s < 0 ? 8 : 7));
if (sd < 1 || !xc[0]) {
xc.length = 0;
if (r) {
// Convert sd to decimal places.
sd -= x.e + 1;
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
x.e = -sd || 0;
} else {
// Zero.
xc[0] = x.e = 0;
}
return x;
}
// Remove excess digits.
if (i == 0) {
xc.length = ni;
k = 1;
ni--;
} else {
xc.length = ni + 1;
k = pows10[LOG_BASE - i];
// E.g. 56700 becomes 56000 if 7 is the rounding digit.
// j > 0 means i > number of leading zeros of n.
xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
}
// Round up?
if (r) {
for (; ;) {
// If the digit to be rounded up is in the first element of xc...
if (ni == 0) {
// i will be the length of xc[0] before k is added.
for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
j = xc[0] += k;
for (k = 1; j >= 10; j /= 10, k++);
// if i != k the length has increased.
if (i != k) {
x.e++;
if (xc[0] == BASE) xc[0] = 1;
}
break;
} else {
xc[ni] += k;
if (xc[ni] != BASE) break;
xc[ni--] = 0;
k = 1;
}
}
}
// Remove trailing zeros.
for (i = xc.length; xc[--i] === 0; xc.pop());
}
// Overflow? Infinity.
if (x.e > MAX_EXP) {
x.c = x.e = null;
// Underflow? Zero.
} else if (x.e < MIN_EXP) {
x.c = [x.e = 0];
}
}
return x;
}
// PROTOTYPE/INSTANCE METHODS
/*
* Return a new BigNumber whose value is the absolute value of this BigNumber.
*/
P.absoluteValue = P.abs = function () {
var x = new BigNumber(this);
if (x.s < 0) x.s = 1;
return x;
};
/*
* Return
* 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
* -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
* 0 if they have the same value,
* or null if the value of either is NaN.
*/
P.comparedTo = function (y, b) {
return compare(this, new BigNumber(y, b));
};
/*
* If dp is undefined or null or true or false, return the number of decimal places of the
* value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
*
* Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
* BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
* ROUNDING_MODE if rm is omitted.
*
* [dp] {number} Decimal places: integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.decimalPlaces = P.dp = function (dp, rm) {
var c, n, v,
x = this;
if (dp != null) {
intCheck(dp, 0, MAX);
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
return round(new BigNumber(x), dp + x.e + 1, rm);
}
if (!(c = x.c)) return null;
n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
// Subtract the number of trailing zeros of the last number.
if (v = c[v]) for (; v % 10 == 0; v /= 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 BigNumber whose value is the value of this BigNumber divided by the value of
* BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
*/
P.dividedBy = P.div = function (y, b) {
return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
};
/*
* Return a new BigNumber whose value is the integer part of dividing the value of this
* BigNumber by the value of BigNumber(y, b).
*/
P.dividedToIntegerBy = P.idiv = function (y, b) {
return div(this, new BigNumber(y, b), 0, 1);
};
/*
* Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
*
* If m is present, return the result modulo m.
* If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
* If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
*
* The modular power operation works efficiently when x, n, and m are integers, otherwise it
* is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
*
* n {number|string|BigNumber} The exponent. An integer.
* [m] {number|string|BigNumber} The modulus.
*
* '[BigNumber Error] Exponent not an integer: {n}'
*/
P.exponentiatedBy = P.pow = function (n, m) {
var half, isModExp, k, more, nIsBig, nIsNeg, nIsOdd, y,
x = this;
n = new BigNumber(n);
// Allow NaN and ±Infinity, but not other non-integers.
if (n.c && !n.isInteger()) {
throw Error
(bignumberError + 'Exponent not an integer: ' + n);
}
if (m != null) m = new BigNumber(m);
// Exponent of MAX_SAFE_INTEGER is 15.
nIsBig = n.e > 14;
// If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
// The sign of the result of pow when x is negative depends on the evenness of n.
// If +n overflows to ±Infinity, the evenness of n would be not be known.
y = new BigNumber(Math.pow(+x.valueOf(), nIsBig ? 2 - isOdd(n) : +n));
return m ? y.mod(m) : y;
}
nIsNeg = n.s < 0;
if (m) {
// x % m returns NaN if abs(m) is zero, or m is NaN.
if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
isModExp = !nIsNeg && x.isInteger() && m.isInteger();
if (isModExp) x = x.mod(m);
// Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
// Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
} else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
// [1, 240000000]
? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
// [80000000000000] [99999750000000]
: x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
// If x is negative and n is odd, k = -0, else k = 0.
k = x.s < 0 && isOdd(n) ? -0 : 0;
// If x >= 1, k = ±Infinity.
if (x.e > -1) k = 1 / k;
// If n is negative return ±0, else return ±Infinity.
return new BigNumber(nIsNeg ? 1 / k : k);
} else if (POW_PRECISION) {
// Truncating each coefficient array to a length of k after each multiplication
// equates to truncating significant digits to POW_PRECISION + [28, 41],
// i.e. there will be a minimum of 28 guard digits retained.
k = mathceil(POW_PRECISION / LOG_BASE + 2);
}
if (nIsBig) {
half = new BigNumber(0.5);
nIsOdd = isOdd(n);
} else {
nIsOdd = n % 2;
}
if (nIsNeg) n.s = 1;
y = new BigNumber(ONE);
// Performs 54 loop iterations for n of 9007199254740991.
for (; ;) {
if (nIsOdd) {
y = y.times(x);
if (!y.c) break;
if (k) {
if (y.c.length > k) y.c.length = k;
} else if (isModExp) {
y = y.mod(m); //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
}
}
if (nIsBig) {
n = n.times(half);
round(n, n.e + 1, 1);
if (!n.c[0]) break;
nIsBig = n.e > 14;
nIsOdd = isOdd(n);
} else {
n = mathfloor(n / 2);
if (!n) break;
nIsOdd = n % 2;
}
x = x.times(x);
if (k) {
if (x.c && x.c.length > k) x.c.length = k;
} else if (isModExp) {
x = x.mod(m); //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
}
}
if (isModExp) return y;
if (nIsNeg) y = ONE.div(y);
return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
};
/*
* Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
* using rounding mode rm, or ROUNDING_MODE if rm is omitted.
*
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
*/
P.integerValue = function (rm) {
var n = new BigNumber(this);
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
return round(n, n.e + 1, rm);
};
/*
* Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
* otherwise return false.
*/
P.isEqualTo = P.eq = function (y, b) {
return compare(this, new BigNumber(y, b)) === 0;
};
/*
* Return true if the value of this BigNumber is a finite number, otherwise return false.
*/
P.isFinite = function () {
return !!this.c;
};
/*
* Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
* otherwise return false.
*/
P.isGreaterThan = P.gt = function (y, b) {
return compare(this, new BigNumber(y, b)) > 0;
};
/*
* Return true if the value of this BigNumber is greater than or equal to the value of
* BigNumber(y, b), otherwise return false.
*/
P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
};
/*
* Return true if the value of this BigNumber is an integer, otherwise return false.
*/
P.isInteger = function () {
return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
};
/*
* Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
* otherwise return false.
*/
P.isLessThan = P.lt = function (y, b) {
return compare(this, new BigNumber(y, b)) < 0;
};
/*
* Return true if the value of this BigNumber is less than or equal to the value of
* BigNumber(y, b), otherwise return false.
*/
P.isLessThanOrEqualTo = P.lte = function (y, b) {
return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
};
/*
* Return true if the value of this BigNumber is NaN, otherwise return false.
*/
P.isNaN = function () {
return !this.s;
};
/*
* Return true if the value of this BigNumber is negative, otherwise return false.
*/
P.isNegative = function () {
return this.s < 0;
};
/*
* Return true if the value of this BigNumber is positive, otherwise return false.
*/
P.isPositive = function () {
return this.s > 0;
};
/*
* Return true if the value of this BigNumber is 0 or -0, otherwise return false.
*/
P.isZero = function () {
return !!this.c && this.c[0] == 0;
};
/*
* 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 BigNumber whose value is the value of this BigNumber minus the value of
* BigNumber(y, b).
*/
P.minus = function (y, b) {
var i, j, t, xLTy,
x = this,
a = x.s;
y = new BigNumber(y, b);
b = y.s;
// Either NaN?
if (!a || !b) return new BigNumber(NaN);
// Signs differ?
if (a != b) {
y.s = -b;
return x.plus(y);
}
var xe = x.e / LOG_BASE,
ye = y.e / LOG_BASE,
xc = x.c,
yc = y.c;
if (!xe || !ye) {
// Either Infinity?
if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
// Either zero?
if (!xc[0] || !yc[0]) {
// Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
// IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
ROUNDING_MODE == 3 ? -0 : 0);
}
}
xe = bitFloor(xe);
ye = bitFloor(ye);
xc = xc.slice();
// Determine which is the bigger number.
if (a = xe - ye) {
if (xLTy = a < 0) {
a = -a;
t = xc;
} else {
ye = xe;
t = yc;
}
t.reverse();
// Prepend zeros to equalise exponents.
for (b = a; b--; t.push(0));
t.reverse();
} else {
// Exponents equal. Check digit by digit.
j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
for (a = b = 0; b < j; b++) {
if (xc[b] != yc[b]) {
xLTy = xc[b] < yc[b];
break;
}
}
}
// x < y? Point xc to the array of the bigger number.
if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
b = (j = yc.length) - (i = xc.length);
// Append zeros to xc if shorter.
// No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
if (b > 0) for (; b--; xc[i++] = 0);
b = BASE - 1;
// Subtract yc from xc.
for (; j > a;) {
if (xc[--j] < yc[j]) {
for (i = j; i && !xc[--i]; xc[i] = b);
--xc[i];
xc[j] += BASE;
}
xc[j] -= yc[j];
}
// Remove leading zeros and adjust exponent accordingly.
for (; xc[0] == 0; xc.splice(0, 1), --ye);
// Zero?
if (!xc[0]) {
// Following IEEE 754 (2008) 6.3,
// n - n = +0 but n - n = -0 when rounding towards -Infinity.
y.s = ROUNDING_MODE == 3 ? -1 : 1;
y.c = [y.e = 0];
return y;
}
// No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
// for finite x and y.
return normalise(y, xc, ye);
};
/*
* 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 BigNumber whose value is the value of this BigNumber modulo the value of
* BigNumber(y, b). The result depends on the value of MODULO_MODE.
*/
P.modulo = P.mod = function (y, b) {
var q, s,
x = this;
y = new BigNumber(y, b);
// Return NaN if x is Infinity or NaN, or y is NaN or zero.
if (!x.c || !y.s || y.c && !y.c[0]) {
return new BigNumber(NaN);
// Return x if y is Infinity or x is zero.
} else if (!y.c || x.c && !x.c[0]) {
return new BigNumber(x);
}
if (MODULO_MODE == 9) {
// Euclidian division: q = sign(y) * floor(x / abs(y))
// r = x - qy where 0 <= r < abs(y)
s = y.s;
y.s = 1;
q = div(x, y, 0, 3);
y.s = s;
q.s *= s;
} else {
q = div(x, y, 0, MODULO_MODE);
}
y = x.minus(q.times(y));
// To match JavaScript %, ensure sign of zero is sign of dividend.
if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
return y;
};
/*
* 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 BigNumber whose value is the value of this BigNumber multiplied by the value
* of BigNumber(y, b).
*/
P.multipliedBy = P.times = function (y, b) {
var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
base, sqrtBase,
x = this,
xc = x.c,
yc = (y = new BigNumber(y, b)).c;
// Either NaN, ±Infinity or ±0?
if (!xc || !yc || !xc[0] || !yc[0]) {
// Return NaN if either is NaN, or one is 0 and the other is Infinity.
if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
y.c = y.e = y.s = null;
} else {
y.s *= x.s;
// Return ±Infinity if either is ±Infinity.
if (!xc || !yc) {
y.c = y.e = null;
// Return ±0 if either is ±0.
} else {
y.c = [0];
y.e = 0;
}
}
return y;
}
e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
y.s *= x.s;
xcL = xc.length;
ycL = yc.length;
// Ensure xc points to longer array and xcL to its length.
if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
// Initialise the result array with zeros.
for (i = xcL + ycL, zc = []; i--; zc.push(0));
base = BASE;
sqrtBase = SQRT_BASE;
for (i = ycL; --i >= 0;) {
c = 0;
ylo = yc[i] % sqrtBase;
yhi = yc[i] / sqrtBase | 0;
for (k = xcL, j = i + k; j > i;) {
xlo = xc[--k] % sqrtBase;
xhi = xc[k] / sqrtBase | 0;
m = yhi * xlo + xhi * ylo;
xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
zc[j--] = xlo % base;
}
zc[j] = c;
}
if (c) {
++e;
} else {
zc.splice(0, 1);
}
return normalise(y, zc, e);
};
/*
* Return a new BigNumber whose value is the value of this BigNumber negated,
* i.e. multiplied by -1.
*/
P.negated = function () {
var x = new BigNumber(this);
x.s = -x.s || null;
return 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 BigNumber whose value is the value of this BigNumber plus the value of
* BigNumber(y, b).
*/
P.plus = function (y, b) {
var t,
x = this,
a = x.s;
y = new BigNumber(y, b);
b = y.s;
// Either NaN?
if (!a || !b) return new BigNumber(NaN);
// Signs differ?
if (a != b) {
y.s = -b;
return x.minus(y);
}
var xe = x.e / LOG_BASE,
ye = y.e / LOG_BASE,
xc = x.c,
yc = y.c;
if (!xe || !ye) {
// Return ±Infinity if either ±Infinity.
if (!xc || !yc) return new BigNumber(a / 0);
// Either zero?
// Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
}
xe = bitFloor(xe);
ye = bitFloor(ye);
xc = xc.slice();
// Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
if (a = xe - ye) {
if (a > 0) {
ye = xe;
t = yc;
} else {
a = -a;
t = xc;
}
t.reverse();
for (; a--; t.push(0));
t.reverse();
}
a = xc.length;
b = yc.length;
// Point xc to the longer array, and b to the shorter length.
if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
// Only start adding at yc.length - 1 as the further digits of xc can be ignored.
for (a = 0; b;) {
a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
}
if (a) {
xc = [a].concat(xc);
++ye;
}
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
// ye = MAX_EXP + 1 possible
return normalise(y, xc, ye);
};
/*
* If sd is undefined or null or true or false, return the number of significant digits of
* the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
* If sd is true include integer-part trailing zeros in the count.
*
* Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
* BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
* ROUNDING_MODE if rm is omitted.
*
* sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
* boolean: whether to count integer-part trailing zeros: true or false.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
*/
P.precision = P.sd = function (sd, rm) {
var c, n, v,
x = this;
if (sd != null && sd !== !!sd) {
intCheck(sd, 1, MAX);
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
return round(new BigNumber(x), sd, rm);
}
if (!(c = x.c)) return null;
v = c.length - 1;
n = v * LOG_BASE + 1;
if (v = c[v]) {
// Subtract the number of trailing zeros of the last element.
for (; v % 10 == 0; v /= 10, n--);
// Add the number of digits of the first element.
for (v = c[0]; v >= 10; v /= 10, n++);
}
if (sd && x.e + 1 > n) n = x.e + 1;
return n;
};
/*
* Return a new BigNumber whose value is the value of this BigNumber shifted by k places
* (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
*
* k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
*/
P.shiftedBy = function (k) {
intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
return this.times('1e' + k);
};
/*
* sqrt(-n) = N
* sqrt(N) = N
* sqrt(-I) = N
* sqrt(I) = I
* sqrt(0) = 0
* sqrt(-0) = -0
*
* Return a new BigNumber whose value is the square root of the value of this BigNumber,
* rounded according to DECIMAL_PLACES and ROUNDING_MODE.
*/
P.squareRoot = P.sqrt = function () {
var m, n, r, rep, t,
x = this,
c = x.c,
s = x.s,
e = x.e,
dp = DECIMAL_PLACES + 4,
half = new BigNumber('0.5');
// Negative/NaN/Infinity/zero?
if (s !== 1 || !c || !c[0]) {
return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
}
// 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 = coeffToString(c);
if ((n.length + e) % 2 == 0) n += '0';
s = Math.sqrt(n);
e = bitFloor((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 BigNumber(n);
} else {
r = new BigNumber(s + '');
}
// Check for zero.
// r could be zero if MIN_EXP is changed after the this value was created.
// This would cause a division by zero (x/t) and hence Infinity below, which would cause
// coeffToString to throw.
if (r.c[0]) {
e = r.e;
s = e + dp;
if (s < 3) s = 0;
// Newton-Raphson iteration.
for (; ;) {
t = r;
r = half.times(t.plus(div(x, t, dp, 1)));
if (coeffToString(t.c ).slice(0, s) === (n =
coeffToString(r.c)).slice(0, s)) {
// The exponent of r may here be one less than the final result exponent,
// e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
// are indexed correctly.
if (r.e < e) --s;
n = n.slice(s - 3, s + 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) {
round(t, t.e + DECIMAL_PLACES + 2, 0);
if (t.times(t).eq(x)) {
r = t;
break;
}
}
dp += 4;
s += 4;
rep = 1;
} else {
// If rounding digits are null, 0{0,4} or 50{0,3}, check for 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.
round(r, r.e + DECIMAL_PLACES + 2, 1);
m = !r.times(r).eq(x);
}
break;
}
}
}
}
return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
};
/*
* Return a string representing the value of this BigNumber in exponential notation and
* rounded using ROUNDING_MODE to dp fixed decimal places.
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.toExponential = function (dp, rm) {
if (dp != null) {
intCheck(dp, 0, MAX);
dp++;
}
return format(this, dp, rm, 1);
};
/*
* Return a string representing the value of this BigNumber in fixed-point notation rounding
* to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
*
* Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
* but e.g. (-0.00001).toFixed(0) is '-0'.
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.toFixed = function (dp, rm) {
if (dp != null) {
intCheck(dp, 0, MAX);
dp = dp + this.e + 1;
}
return format(this, dp, rm);
};
/*
* Return a string representing the value of this BigNumber in fixed-point notation rounded
* using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
* of the FORMAT object (see BigNumber.set).
*
* FORMAT = {
* decimalSeparator : '.',
* groupSeparator : ',',
* groupSize : 3,
* secondaryGroupSize : 0,
* fractionGroupSeparator : '\xA0', // non-breaking space
* fractionGroupSize : 0
* };
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.toFormat = function (dp, rm) {
var str = this.toFixed(dp, rm);
if (this.c) {
var i,
arr = str.split('.'),
g1 = +FORMAT.groupSize,
g2 = +FORMAT.secondaryGroupSize,
groupSeparator = FORMAT.groupSeparator,
intPart = arr[0],
fractionPart = arr[1],
isNeg = this.s < 0,
intDigits = isNeg ? intPart.slice(1) : intPart,
len = intDigits.length;
if (g2) i = g1, g1 = g2, g2 = i, len -= i;
if (g1 > 0 && len > 0) {
i = len % g1 || g1;
intPart = intDigits.substr(0, i);
for (; i < len; i += g1) {
intPart += groupSeparator + intDigits.substr(i, g1);
}
if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
if (isNeg) intPart = '-' + intPart;
}
str = fractionPart
? intPart + FORMAT.decimalSeparator + ((g2 = +FORMAT.fractionGroupSize)
? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
'$&' + FORMAT.fractionGroupSeparator)
: fractionPart)
: intPart;
}
return str;
};
/*
* Return a string array representing the value of this BigNumber 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.
*
* [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
*
* '[BigNumber Error] Argument {not an integer|out of range} : {md}'
*/
P.toFraction = function (md) {
var arr, d, d0, d1, d2, e, exp, n, n0, n1, q, s,
x = this,
xc = x.c;
if (md != null) {
n = new BigNumber(md);
// Throw if md is less than one or is not an integer, unless it is Infinity.
if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
throw Error
(bignumberError + 'Argument ' +
(n.isInteger() ? 'out of range: ' : 'not an integer: ') + md);
}
}
if (!xc) return x.toString();
d = new BigNumber(ONE);
n1 = d0 = new BigNumber(ONE);
d1 = n0 = new BigNumber(ONE);
s = coeffToString(xc);
// Determine initial denominator.
// d is a power of 10 and the minimum max denominator that specifies the value exactly.
e = d.e = s.length - x.e - 1;
d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
exp = MAX_EXP;
MAX_EXP = 1 / 0;
n = new BigNumber(s);
// n0 = d1 = 0
n0.c[0] = 0;
for (; ;) {
q = div(n, d, 0, 1);
d2 = d0.plus(q.times(d1));
if (d2.comparedTo(md) == 1) break;
d0 = d1;
d1 = d2;
n1 = n0.plus(q.times(d2 = n1));
n0 = d2;
d = n.minus(q.times(d2 = d));
n = d2;
}
d2 = div(md.minus(d0), d1, 0, 1);
n0 = n0.plus(d2.times(n1));
d0 = d0.plus(d2.times(d1));
n0.s = n1.s = x.s;
e *= 2;
// Determine which fraction is closer to x, n0/d0 or n1/d1
arr = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1
? [n1.toString(), d1.toString()]
: [n0.toString(), d0.toString()];
MAX_EXP = exp;
return arr;
};
/*
* Return the value of this BigNumber converted to a number primitive.
*/
P.toNumber = function () {
return +this;
};
/*
* Return a string representing the value of this BigNumber rounded to sd significant digits
* using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
* necessary to represent the integer part of the value in fixed-point notation, then use
* exponential notation.
*
* [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
*/
P.toPrecision = function (sd, rm) {
if (sd != null) intCheck(sd, 1, MAX);
return format(this, sd, rm, 2);
};
/*
* Return a string representing the value of this BigNumber in base b, or base 10 if b is
* omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
* ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
* that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
* TO_EXP_NEG, return exponential notation.
*
* [b] {number} Integer, 2 to ALPHABET.length inclusive.
*
* '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
*/
P.toString = function (b) {
var str,
n = this,
s = n.s,
e = n.e;
// Infinity or NaN?
if (e === null) {
if (s) {
str = 'Infinity';
if (s < 0) str = '-' + str;
} else {
str = 'NaN';
}
} else {
str = coeffToString(n.c);
if (b == null) {
str = e <= TO_EXP_NEG || e >= TO_EXP_POS
? toExponential(str, e)
: toFixedPoint(str, e, '0');
} else {
intCheck(b, 2, ALPHABET.length, 'Base');
str = convertBase(toFixedPoint(str, e, '0'), 10, b, s, true);
}
if (s < 0 && n.c[0]) str = '-' + str;
}
return str;
};
/*
* Return as toString, but do not accept a base argument, and include the minus sign for
* negative zero.
*/
P.valueOf = P.toJSON = function () {
var str,
n = this,
e = n.e;
if (e === null) return n.toString();
str = coeffToString(n.c);
str = e <= TO_EXP_NEG || e >= TO_EXP_POS
? toExponential(str, e)
: toFixedPoint(str, e, '0');
return n.s < 0 ? '-' + str : str;
};
P._isBigNumber = true;
if (configObject != null) BigNumber.set(configObject);
return BigNumber;
}
// PRIVATE HELPER FUNCTIONS
function bitFloor(n) {
var i = n | 0;
return n > 0 || n === i ? i : i - 1;
}
// Return a coefficient array as a string of base 10 digits.
function coeffToString(a) {
var s, z,
i = 1,
j = a.length,
r = a[0] + '';
for (; i < j;) {
s = a[i++] + '';
z = LOG_BASE - s.length;
for (; z--; s = '0' + s);
r += s;
}
// Determine trailing zeros.
for (j = r.length; r.charCodeAt(--j) === 48;);
return r.slice(0, j + 1 || 1);
}
// Compare the value of BigNumbers x and y.
function compare(x, y) {
var a, b,
xc = x.c,
yc = y.c,
i = x.s,
j = y.s,
k = x.e,
l = y.e;
// Either NaN?
if (!i || !j) return null;
a = xc && !xc[0];
b = yc && !yc[0];
// Either zero?
if (a || b) return a ? b ? 0 : -j : i;
// Signs differ?
if (i != j) return i;
a = i < 0;
b = k == l;
// Either Infinity?
if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
// Compare exponents.
if (!b) return k > l ^ a ? 1 : -1;
j = (k = xc.length) < (l = yc.length) ? k : l;
// Compare digit by digit.
for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
// Compare lengths.
return k == l ? 0 : k > l ^ a ? 1 : -1;
}
/*
* Check that n is a primitive number, an integer, and in range, otherwise throw.
*/
function intCheck(n, min, max, name) {
if (n < min || n > max || n !== (n < 0 ? mathceil(n) : mathfloor(n))) {
throw Error
(bignumberError + (name || 'Argument') + (typeof n == 'number'
? n < min || n > max ? ' out of range: ' : ' not an integer: '
: ' not a primitive number: ') + n);
}
}
function isArray(obj) {
return Object.prototype.toString.call(obj) == '[object Array]';
}
// Assumes finite n.
function isOdd(n) {
var k = n.c.length - 1;
return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
}
function toExponential(str, e) {
return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
(e < 0 ? 'e' : 'e+') + e;
}
function toFixedPoint(str, e, z) {
var len, zs;
// Negative exponent?
if (e < 0) {
// Prepend zeros.
for (zs = z + '.'; ++e; zs += z);
str = zs + str;
// Positive exponent
} else {
len = str.length;
// Append zeros.
if (++e > len) {
for (zs = z, e -= len; --e; zs += z);
str += zs;
} else if (e < len) {
str = str.slice(0, e) + '.' + str.slice(e);
}
}
return str;
}
// EXPORT
BigNumber = clone();
BigNumber['default'] = BigNumber.BigNumber = BigNumber;
// AMD.
if (typeof define == 'function' && define.amd) {
define(function () { return BigNumber; });
// Node.js and other environments that support module.exports.
} else if (typeof module != 'undefined' && module.exports) {
module.exports = BigNumber;
// Browser.
} else {
if (!globalObject) {
globalObject = typeof self != 'undefined' && self ? self : window;
}
globalObject.BigNumber = BigNumber;
}
})(this);

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/*
* bignumber.js v7.2.1
* A JavaScript library for arbitrary-precision arithmetic.
* https://github.com/MikeMcl/bignumber.js
* Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
* MIT Licensed.
*
* BigNumber.prototype methods | BigNumber methods
* |
* absoluteValue abs | clone
* comparedTo | config set
* decimalPlaces dp | DECIMAL_PLACES
* dividedBy div | ROUNDING_MODE
* dividedToIntegerBy idiv | EXPONENTIAL_AT
* exponentiatedBy pow | RANGE
* integerValue | CRYPTO
* isEqualTo eq | MODULO_MODE
* isFinite | POW_PRECISION
* isGreaterThan gt | FORMAT
* isGreaterThanOrEqualTo gte | ALPHABET
* isInteger | isBigNumber
* isLessThan lt | maximum max
* isLessThanOrEqualTo lte | minimum min
* isNaN | random
* isNegative |
* isPositive |
* isZero |
* minus |
* modulo mod |
* multipliedBy times |
* negated |
* plus |
* precision sd |
* shiftedBy |
* squareRoot sqrt |
* toExponential |
* toFixed |
* toFormat |
* toFraction |
* toJSON |
* toNumber |
* toPrecision |
* toString |
* valueOf |
*
*/
var isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
mathceil = Math.ceil,
mathfloor = Math.floor,
bignumberError = '[BigNumber Error] ',
tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
BASE = 1e14,
LOG_BASE = 14,
MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1
// MAX_INT32 = 0x7fffffff, // 2^31 - 1
POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
SQRT_BASE = 1e7,
// EDITABLE
// The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
// the arguments to toExponential, toFixed, toFormat, and toPrecision.
MAX = 1E9; // 0 to MAX_INT32
/*
* Create and return a BigNumber constructor.
*/
function clone(configObject) {
var div, convertBase, parseNumeric,
P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
ONE = new BigNumber(1),
//----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
// The default values below must be integers within the inclusive ranges stated.
// The values can also be changed at run-time using BigNumber.set.
// The maximum number of decimal places for operations involving division.
DECIMAL_PLACES = 20, // 0 to MAX
// The rounding mode used when rounding to the above decimal places, and when using
// toExponential, toFixed, toFormat and toPrecision, and round (default value).
// UP 0 Away from zero.
// DOWN 1 Towards zero.
// CEIL 2 Towards +Infinity.
// FLOOR 3 Towards -Infinity.
// HALF_UP 4 Towards nearest neighbour. If equidistant, up.
// HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
// HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
// HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
// HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
ROUNDING_MODE = 4, // 0 to 8
// EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
// The exponent value at and beneath which toString returns exponential notation.
// Number type: -7
TO_EXP_NEG = -7, // 0 to -MAX
// The exponent value at and above which toString returns exponential notation.
// Number type: 21
TO_EXP_POS = 21, // 0 to MAX
// RANGE : [MIN_EXP, MAX_EXP]
// The minimum exponent value, beneath which underflow to zero occurs.
// Number type: -324 (5e-324)
MIN_EXP = -1e7, // -1 to -MAX
// The maximum exponent value, above which overflow to Infinity occurs.
// Number type: 308 (1.7976931348623157e+308)
// For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
MAX_EXP = 1e7, // 1 to MAX
// Whether to use cryptographically-secure random number generation, if available.
CRYPTO = false, // true or false
// 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.
// This modulo mode is commonly known as 'truncated division' and is
// equivalent to (a % n) in JavaScript.
// FLOOR 3 The remainder has the same sign as the divisor (Python %).
// HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
// EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)).
// The remainder is always positive.
//
// The truncated division, floored division, Euclidian division and IEEE 754 remainder
// modes are commonly used for the modulus operation.
// Although the other rounding modes can also be used, they may not give useful results.
MODULO_MODE = 1, // 0 to 9
// The maximum number of significant digits of the result of the exponentiatedBy operation.
// If POW_PRECISION is 0, there will be unlimited significant digits.
POW_PRECISION = 0, // 0 to MAX
// The format specification used by the BigNumber.prototype.toFormat method.
FORMAT = {
decimalSeparator: '.',
groupSeparator: ',',
groupSize: 3,
secondaryGroupSize: 0,
fractionGroupSeparator: '\xA0', // non-breaking space
fractionGroupSize: 0
},
// The alphabet used for base conversion.
// It must be at least 2 characters long, with no '.' or repeated character.
// '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
//------------------------------------------------------------------------------------------
// CONSTRUCTOR
/*
* The BigNumber constructor and exported function.
* Create and return a new instance of a BigNumber object.
*
* n {number|string|BigNumber} A numeric value.
* [b] {number} The base of n. Integer, 2 to ALPHABET.length inclusive.
*/
function BigNumber(n, b) {
var alphabet, c, caseChanged, e, i, isNum, len, str,
x = this;
// Enable constructor usage without new.
if (!(x instanceof BigNumber)) {
// Don't throw on constructor call without new (#81).
// '[BigNumber Error] Constructor call without new: {n}'
//throw Error(bignumberError + ' Constructor call without new: ' + n);
return new BigNumber(n, b);
}
if (b == null) {
// Duplicate.
if (n instanceof BigNumber) {
x.s = n.s;
x.e = n.e;
x.c = (n = n.c) ? n.slice() : n;
return;
}
isNum = typeof n == 'number';
if (isNum && n * 0 == 0) {
// Use `1 / n` to handle minus zero also.
x.s = 1 / n < 0 ? (n = -n, -1) : 1;
// Faster path for integers.
if (n === ~~n) {
for (e = 0, i = n; i >= 10; i /= 10, e++);
x.e = e;
x.c = [n];
return;
}
str = n + '';
} else {
if (!isNumeric.test(str = n + '')) return parseNumeric(x, str, isNum);
x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
}
// 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;
}
} else {
// '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
intCheck(b, 2, ALPHABET.length, 'Base');
str = n + '';
// Allow exponential notation to be used with base 10 argument, while
// also rounding to DECIMAL_PLACES as with other bases.
if (b == 10) {
x = new BigNumber(n instanceof BigNumber ? n : str);
return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
}
isNum = typeof n == 'number';
if (isNum) {
// Avoid potential interpretation of Infinity and NaN as base 44+ values.
if (n * 0 != 0) return parseNumeric(x, str, isNum, b);
x.s = 1 / n < 0 ? (str = str.slice(1), -1) : 1;
// '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
throw Error
(tooManyDigits + n);
}
// Prevent later check for length on converted number.
isNum = false;
} else {
x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
}
alphabet = ALPHABET.slice(0, b);
e = i = 0;
// Check that str is a valid base b number.
// Don't use RegExp so alphabet can contain special characters.
for (len = str.length; i < len; i++) {
if (alphabet.indexOf(c = str.charAt(i)) < 0) {
if (c == '.') {
// If '.' is not the first character and it has not be found before.
if (i > e) {
e = len;
continue;
}
} else if (!caseChanged) {
// Allow e.g. hexadecimal 'FF' as well as 'ff'.
if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
str == str.toLowerCase() && (str = str.toUpperCase())) {
caseChanged = true;
i = -1;
e = 0;
continue;
}
}
return parseNumeric(x, n + '', isNum, b);
}
}
str = convertBase(str, b, 10, x.s);
// Decimal point?
if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
else e = str.length;
}
// Determine leading zeros.
for (i = 0; str.charCodeAt(i) === 48; i++);
// Determine trailing zeros.
for (len = str.length; str.charCodeAt(--len) === 48;);
str = str.slice(i, ++len);
if (str) {
len -= i;
// '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
if (isNum && BigNumber.DEBUG &&
len > 15 && (n > MAX_SAFE_INTEGER || n !== mathfloor(n))) {
throw Error
(tooManyDigits + (x.s * n));
}
e = e - i - 1;
// Overflow?
if (e > MAX_EXP) {
// Infinity.
x.c = x.e = null;
// Underflow?
} else if (e < MIN_EXP) {
// Zero.
x.c = [x.e = 0];
} else {
x.e = e;
x.c = [];
// Transform base
// e is the base 10 exponent.
// i is where to slice str to get the first element of the coefficient array.
i = (e + 1) % LOG_BASE;
if (e < 0) i += LOG_BASE;
if (i < len) {
if (i) x.c.push(+str.slice(0, i));
for (len -= LOG_BASE; i < len;) {
x.c.push(+str.slice(i, i += LOG_BASE));
}
str = str.slice(i);
i = LOG_BASE - str.length;
} else {
i -= len;
}
for (; i--; str += '0');
x.c.push(+str);
}
} else {
// Zero.
x.c = [x.e = 0];
}
}
// CONSTRUCTOR PROPERTIES
BigNumber.clone = clone;
BigNumber.ROUND_UP = 0;
BigNumber.ROUND_DOWN = 1;
BigNumber.ROUND_CEIL = 2;
BigNumber.ROUND_FLOOR = 3;
BigNumber.ROUND_HALF_UP = 4;
BigNumber.ROUND_HALF_DOWN = 5;
BigNumber.ROUND_HALF_EVEN = 6;
BigNumber.ROUND_HALF_CEIL = 7;
BigNumber.ROUND_HALF_FLOOR = 8;
BigNumber.EUCLID = 9;
/*
* Configure infrequently-changing library-wide settings.
*
* Accept an object with the following optional properties (if the value of a property is
* a number, it must be an integer within the inclusive range stated):
*
* DECIMAL_PLACES {number} 0 to MAX
* ROUNDING_MODE {number} 0 to 8
* EXPONENTIAL_AT {number|number[]} -MAX to MAX or [-MAX to 0, 0 to MAX]
* RANGE {number|number[]} -MAX to MAX (not zero) or [-MAX to -1, 1 to MAX]
* CRYPTO {boolean} true or false
* MODULO_MODE {number} 0 to 9
* POW_PRECISION {number} 0 to MAX
* ALPHABET {string} A string of two or more unique characters which does
* not contain '.'.
* FORMAT {object} An object with some of the following properties:
* decimalSeparator {string}
* groupSeparator {string}
* groupSize {number}
* secondaryGroupSize {number}
* fractionGroupSeparator {string}
* fractionGroupSize {number}
*
* (The values assigned to the above FORMAT object properties are not checked for validity.)
*
* E.g.
* BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
*
* Ignore properties/parameters set to null or undefined, except for ALPHABET.
*
* Return an object with the properties current values.
*/
BigNumber.config = BigNumber.set = function (obj) {
var p, v;
if (obj != null) {
if (typeof obj == 'object') {
// DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
// '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
v = obj[p];
intCheck(v, 0, MAX, p);
DECIMAL_PLACES = v;
}
// ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
// '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
v = obj[p];
intCheck(v, 0, 8, p);
ROUNDING_MODE = v;
}
// EXPONENTIAL_AT {number|number[]}
// Integer, -MAX to MAX inclusive or
// [integer -MAX to 0 inclusive, 0 to MAX inclusive].
// '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
v = obj[p];
if (isArray(v)) {
intCheck(v[0], -MAX, 0, p);
intCheck(v[1], 0, MAX, p);
TO_EXP_NEG = v[0];
TO_EXP_POS = v[1];
} else {
intCheck(v, -MAX, MAX, p);
TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
}
}
// RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
// [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
// '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
if (obj.hasOwnProperty(p = 'RANGE')) {
v = obj[p];
if (isArray(v)) {
intCheck(v[0], -MAX, -1, p);
intCheck(v[1], 1, MAX, p);
MIN_EXP = v[0];
MAX_EXP = v[1];
} else {
intCheck(v, -MAX, MAX, p);
if (v) {
MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
} else {
throw Error
(bignumberError + p + ' cannot be zero: ' + v);
}
}
}
// CRYPTO {boolean} true or false.
// '[BigNumber Error] CRYPTO not true or false: {v}'
// '[BigNumber Error] crypto unavailable'
if (obj.hasOwnProperty(p = 'CRYPTO')) {
v = obj[p];
if (v === !!v) {
if (v) {
if (typeof crypto != 'undefined' && crypto &&
(crypto.getRandomValues || crypto.randomBytes)) {
CRYPTO = v;
} else {
CRYPTO = !v;
throw Error
(bignumberError + 'crypto unavailable');
}
} else {
CRYPTO = v;
}
} else {
throw Error
(bignumberError + p + ' not true or false: ' + v);
}
}
// MODULO_MODE {number} Integer, 0 to 9 inclusive.
// '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
v = obj[p];
intCheck(v, 0, 9, p);
MODULO_MODE = v;
}
// POW_PRECISION {number} Integer, 0 to MAX inclusive.
// '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
v = obj[p];
intCheck(v, 0, MAX, p);
POW_PRECISION = v;
}
// FORMAT {object}
// '[BigNumber Error] FORMAT not an object: {v}'
if (obj.hasOwnProperty(p = 'FORMAT')) {
v = obj[p];
if (typeof v == 'object') FORMAT = v;
else throw Error
(bignumberError + p + ' not an object: ' + v);
}
// ALPHABET {string}
// '[BigNumber Error] ALPHABET invalid: {v}'
if (obj.hasOwnProperty(p = 'ALPHABET')) {
v = obj[p];
// Disallow if only one character, or contains '.' or a repeated character.
if (typeof v == 'string' && !/^.$|\.|(.).*\1/.test(v)) {
ALPHABET = v;
} else {
throw Error
(bignumberError + p + ' invalid: ' + v);
}
}
} else {
// '[BigNumber Error] Object expected: {v}'
throw Error
(bignumberError + 'Object expected: ' + obj);
}
}
return {
DECIMAL_PLACES: DECIMAL_PLACES,
ROUNDING_MODE: ROUNDING_MODE,
EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
RANGE: [MIN_EXP, MAX_EXP],
CRYPTO: CRYPTO,
MODULO_MODE: MODULO_MODE,
POW_PRECISION: POW_PRECISION,
FORMAT: FORMAT,
ALPHABET: ALPHABET
};
};
/*
* Return true if v is a BigNumber instance, otherwise return false.
*
* v {any}
*/
BigNumber.isBigNumber = function (v) {
return v instanceof BigNumber || v && v._isBigNumber === true || false;
};
/*
* Return a new BigNumber whose value is the maximum of the arguments.
*
* arguments {number|string|BigNumber}
*/
BigNumber.maximum = BigNumber.max = function () {
return maxOrMin(arguments, P.lt);
};
/*
* Return a new BigNumber whose value is the minimum of the arguments.
*
* arguments {number|string|BigNumber}
*/
BigNumber.minimum = BigNumber.min = function () {
return maxOrMin(arguments, P.gt);
};
/*
* Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
* and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
* zeros are produced).
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
* '[BigNumber Error] crypto unavailable'
*/
BigNumber.random = (function () {
var pow2_53 = 0x20000000000000;
// Return a 53 bit integer n, where 0 <= n < 9007199254740992.
// Check if Math.random() produces more than 32 bits of randomness.
// If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
// 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
? function () { return mathfloor(Math.random() * pow2_53); }
: function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
(Math.random() * 0x800000 | 0); };
return function (dp) {
var a, b, e, k, v,
i = 0,
c = [],
rand = new BigNumber(ONE);
if (dp == null) dp = DECIMAL_PLACES;
else intCheck(dp, 0, MAX);
k = mathceil(dp / LOG_BASE);
if (CRYPTO) {
// Browsers supporting crypto.getRandomValues.
if (crypto.getRandomValues) {
a = crypto.getRandomValues(new Uint32Array(k *= 2));
for (; i < k;) {
// 53 bits:
// ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
// 11111 11111111 11111111 11111111 11100000 00000000 00000000
// ((Math.pow(2, 32) - 1) >>> 11).toString(2)
// 11111 11111111 11111111
// 0x20000 is 2^21.
v = a[i] * 0x20000 + (a[i + 1] >>> 11);
// Rejection sampling:
// 0 <= v < 9007199254740992
// Probability that v >= 9e15, is
// 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
if (v >= 9e15) {
b = crypto.getRandomValues(new Uint32Array(2));
a[i] = b[0];
a[i + 1] = b[1];
} else {
// 0 <= v <= 8999999999999999
// 0 <= (v % 1e14) <= 99999999999999
c.push(v % 1e14);
i += 2;
}
}
i = k / 2;
// Node.js supporting crypto.randomBytes.
} else if (crypto.randomBytes) {
// buffer
a = crypto.randomBytes(k *= 7);
for (; i < k;) {
// 0x1000000000000 is 2^48, 0x10000000000 is 2^40
// 0x100000000 is 2^32, 0x1000000 is 2^24
// 11111 11111111 11111111 11111111 11111111 11111111 11111111
// 0 <= v < 9007199254740992
v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
(a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
(a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
if (v >= 9e15) {
crypto.randomBytes(7).copy(a, i);
} else {
// 0 <= (v % 1e14) <= 99999999999999
c.push(v % 1e14);
i += 7;
}
}
i = k / 7;
} else {
CRYPTO = false;
throw Error
(bignumberError + 'crypto unavailable');
}
}
// Use Math.random.
if (!CRYPTO) {
for (; i < k;) {
v = random53bitInt();
if (v < 9e15) c[i++] = v % 1e14;
}
}
k = c[--i];
dp %= LOG_BASE;
// Convert trailing digits to zeros according to dp.
if (k && dp) {
v = POWS_TEN[LOG_BASE - dp];
c[i] = mathfloor(k / v) * v;
}
// Remove trailing elements which are zero.
for (; c[i] === 0; c.pop(), i--);
// Zero?
if (i < 0) {
c = [e = 0];
} else {
// Remove leading elements which are zero and adjust exponent accordingly.
for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
// Count the digits of the first element of c to determine leading zeros, and...
for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
// adjust the exponent accordingly.
if (i < LOG_BASE) e -= LOG_BASE - i;
}
rand.e = e;
rand.c = c;
return rand;
};
})();
// PRIVATE FUNCTIONS
// Called by BigNumber and BigNumber.prototype.toString.
convertBase = (function () {
var decimal = '0123456789';
/*
* Convert string of baseIn to an array of numbers of baseOut.
* Eg. toBaseOut('255', 10, 16) returns [15, 15].
* Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
*/
function toBaseOut(str, baseIn, baseOut, alphabet) {
var j,
arr = [0],
arrL,
i = 0,
len = str.length;
for (; i < len;) {
for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
arr[0] += alphabet.indexOf(str.charAt(i++));
for (j = 0; j < arr.length; j++) {
if (arr[j] > baseOut - 1) {
if (arr[j + 1] == null) arr[j + 1] = 0;
arr[j + 1] += arr[j] / baseOut | 0;
arr[j] %= baseOut;
}
}
}
return arr.reverse();
}
// Convert a numeric string of baseIn to a numeric string of baseOut.
// If the caller is toString, we are converting from base 10 to baseOut.
// If the caller is BigNumber, we are converting from baseIn to base 10.
return function (str, baseIn, baseOut, sign, callerIsToString) {
var alphabet, d, e, k, r, x, xc, y,
i = str.indexOf('.'),
dp = DECIMAL_PLACES,
rm = ROUNDING_MODE;
// Non-integer.
if (i >= 0) {
k = POW_PRECISION;
// Unlimited precision.
POW_PRECISION = 0;
str = str.replace('.', '');
y = new BigNumber(baseIn);
x = y.pow(str.length - i);
POW_PRECISION = k;
// Convert str as if an integer, then restore the fraction part by dividing the
// result by its base raised to a power.
y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
10, baseOut, decimal);
y.e = y.c.length;
}
// Convert the number as integer.
xc = toBaseOut(str, baseIn, baseOut, callerIsToString
? (alphabet = ALPHABET, decimal)
: (alphabet = decimal, ALPHABET));
// xc now represents str as an integer and converted to baseOut. e is the exponent.
e = k = xc.length;
// Remove trailing zeros.
for (; xc[--k] == 0; xc.pop());
// Zero?
if (!xc[0]) return alphabet.charAt(0);
// Does str represent an integer? If so, no need for the division.
if (i < 0) {
--e;
} else {
x.c = xc;
x.e = e;
// The sign is needed for correct rounding.
x.s = sign;
x = div(x, y, dp, rm, baseOut);
xc = x.c;
r = x.r;
e = x.e;
}
// xc now represents str converted to baseOut.
// THe index of the rounding digit.
d = e + dp + 1;
// The rounding digit: the digit to the right of the digit that may be rounded up.
i = xc[d];
// Look at the rounding digits and mode to determine whether to round up.
k = baseOut / 2;
r = r || d < 0 || xc[d + 1] != null;
r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
: i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
rm == (x.s < 0 ? 8 : 7));
// If the index of the rounding digit is not greater than zero, or xc represents
// zero, then the result of the base conversion is zero or, if rounding up, a value
// such as 0.00001.
if (d < 1 || !xc[0]) {
// 1^-dp or 0
str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0))
: alphabet.charAt(0);
} else {
// Truncate xc to the required number of decimal places.
xc.length = d;
// Round up?
if (r) {
// Rounding up may mean the previous digit has to be rounded up and so on.
for (--baseOut; ++xc[--d] > baseOut;) {
xc[d] = 0;
if (!d) {
++e;
xc = [1].concat(xc);
}
}
}
// Determine trailing zeros.
for (k = xc.length; !xc[--k];);
// E.g. [4, 11, 15] becomes 4bf.
for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
// Add leading zeros, decimal point and trailing zeros as required.
str = toFixedPoint(str, e, alphabet.charAt(0));
}
// The caller will add the sign.
return str;
};
})();
// Perform division in the specified base. Called by div and convertBase.
div = (function () {
// Assume non-zero x and k.
function multiply(x, k, base) {
var m, temp, xlo, xhi,
carry = 0,
i = x.length,
klo = k % SQRT_BASE,
khi = k / SQRT_BASE | 0;
for (x = x.slice(); i--;) {
xlo = x[i] % SQRT_BASE;
xhi = x[i] / SQRT_BASE | 0;
m = khi * xlo + xhi * klo;
temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
x[i] = temp % base;
}
if (carry) x = [carry].concat(x);
return x;
}
function compare(a, b, aL, bL) {
var i, cmp;
if (aL != bL) {
cmp = aL > bL ? 1 : -1;
} else {
for (i = cmp = 0; i < aL; i++) {
if (a[i] != b[i]) {
cmp = a[i] > b[i] ? 1 : -1;
break;
}
}
}
return cmp;
}
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.splice(0, 1));
}
// x: dividend, y: divisor.
return function (x, y, dp, rm, base) {
var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
yL, yz,
s = x.s == y.s ? 1 : -1,
xc = x.c,
yc = y.c;
// Either NaN, Infinity or 0?
if (!xc || !xc[0] || !yc || !yc[0]) {
return new BigNumber(
// Return NaN if either NaN, or both Infinity or 0.
!x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
// Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
xc && xc[0] == 0 || !yc ? s * 0 : s / 0
);
}
q = new BigNumber(s);
qc = q.c = [];
e = x.e - y.e;
s = dp + e + 1;
if (!base) {
base = BASE;
e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
s = s / LOG_BASE | 0;
}
// Result exponent may be one less then the current value of e.
// The coefficients of the BigNumbers from convertBase may have trailing zeros.
for (i = 0; yc[i] == (xc[i] || 0); i++);
if (yc[i] > (xc[i] || 0)) e--;
if (s < 0) {
qc.push(1);
more = true;
} else {
xL = xc.length;
yL = yc.length;
i = 0;
s += 2;
// Normalise xc and yc so highest order digit of yc is >= base / 2.
n = mathfloor(base / (yc[0] + 1));
// Not necessary, but to handle odd bases where yc[0] == (base / 2) - 1.
// if (n > 1 || n++ == 1 && yc[0] < base / 2) {
if (n > 1) {
yc = multiply(yc, n, base);
xc = multiply(xc, n, base);
yL = yc.length;
xL = xc.length;
}
xi = yL;
rem = xc.slice(0, yL);
remL = rem.length;
// Add zeros to make remainder as long as divisor.
for (; remL < yL; rem[remL++] = 0);
yz = yc.slice();
yz = [0].concat(yz);
yc0 = yc[0];
if (yc[1] >= base / 2) yc0++;
// Not necessary, but to prevent trial digit n > base, when using base 3.
// else if (base == 3 && yc0 == 1) yc0 = 1 + 1e-15;
do {
n = 0;
// Compare divisor and remainder.
cmp = compare(yc, rem, yL, remL);
// If divisor < remainder.
if (cmp < 0) {
// Calculate trial digit, n.
rem0 = rem[0];
if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
// n is how many times the divisor goes into the current remainder.
n = mathfloor(rem0 / yc0);
// Algorithm:
// product = divisor multiplied by trial digit (n).
// Compare product and remainder.
// If product is greater than remainder:
// Subtract divisor from product, decrement trial digit.
// Subtract product from remainder.
// If product was less than remainder at the last compare:
// Compare new remainder and divisor.
// If remainder is greater than divisor:
// Subtract divisor from remainder, increment trial digit.
if (n > 1) {
// n may be > base only when base is 3.
if (n >= base) n = base - 1;
// product = divisor * trial digit.
prod = multiply(yc, n, base);
prodL = prod.length;
remL = rem.length;
// Compare product and remainder.
// If product > remainder then trial digit n too high.
// n is 1 too high about 5% of the time, and is not known to have
// ever been more than 1 too high.
while (compare(prod, rem, prodL, remL) == 1) {
n--;
// Subtract divisor from product.
subtract(prod, yL < prodL ? yz : yc, prodL, base);
prodL = prod.length;
cmp = 1;
}
} else {
// n is 0 or 1, cmp is -1.
// If n is 0, there is no need to compare yc and rem again below,
// so change cmp to 1 to avoid it.
// If n is 1, leave cmp as -1, so yc and rem are compared again.
if (n == 0) {
// divisor < remainder, so n must be at least 1.
cmp = n = 1;
}
// product = divisor
prod = yc.slice();
prodL = prod.length;
}
if (prodL < remL) prod = [0].concat(prod);
// Subtract product from remainder.
subtract(rem, prod, remL, base);
remL = rem.length;
// If product was < remainder.
if (cmp == -1) {
// Compare divisor and new remainder.
// If divisor < new remainder, subtract divisor from remainder.
// Trial digit n too low.
// n is 1 too low about 5% of the time, and very rarely 2 too low.
while (compare(yc, rem, yL, remL) < 1) {
n++;
// Subtract divisor from remainder.
subtract(rem, yL < remL ? yz : yc, remL, base);
remL = rem.length;
}
}
} else if (cmp === 0) {
n++;
rem = [0];
} // else cmp === 1 and n will be 0
// Add the next digit, n, to the result array.
qc[i++] = n;
// Update the remainder.
if (rem[0]) {
rem[remL++] = xc[xi] || 0;
} else {
rem = [xc[xi]];
remL = 1;
}
} while ((xi++ < xL || rem[0] != null) && s--);
more = rem[0] != null;
// Leading zero?
if (!qc[0]) qc.splice(0, 1);
}
if (base == BASE) {
// To calculate q.e, first get the number of digits of qc[0].
for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
// Caller is convertBase.
} else {
q.e = e;
q.r = +more;
}
return q;
};
})();
/*
* Return a string representing the value of BigNumber n in fixed-point or exponential
* notation rounded to the specified decimal places or significant digits.
*
* n: a BigNumber.
* i: the index of the last digit required (i.e. the digit that may be rounded up).
* rm: the rounding mode.
* id: 1 (toExponential) or 2 (toPrecision).
*/
function format(n, i, rm, id) {
var c0, e, ne, len, str;
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
if (!n.c) return n.toString();
c0 = n.c[0];
ne = n.e;
if (i == null) {
str = coeffToString(n.c);
str = id == 1 || id == 2 && ne <= TO_EXP_NEG
? toExponential(str, ne)
: toFixedPoint(str, ne, '0');
} else {
n = round(new BigNumber(n), i, rm);
// n.e may have changed if the value was rounded up.
e = n.e;
str = coeffToString(n.c);
len = str.length;
// toPrecision returns exponential notation if the number of significant digits
// specified is less than the number of digits necessary to represent the integer
// part of the value in fixed-point notation.
// Exponential notation.
if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
// Append zeros?
for (; len < i; str += '0', len++);
str = toExponential(str, e);
// Fixed-point notation.
} else {
i -= ne;
str = toFixedPoint(str, e, '0');
// Append zeros?
if (e + 1 > len) {
if (--i > 0) for (str += '.'; i--; str += '0');
} else {
i += e - len;
if (i > 0) {
if (e + 1 == len) str += '.';
for (; i--; str += '0');
}
}
}
}
return n.s < 0 && c0 ? '-' + str : str;
}
// Handle BigNumber.max and BigNumber.min.
function maxOrMin(args, method) {
var m, n,
i = 0;
if (isArray(args[0])) args = args[0];
m = new BigNumber(args[0]);
for (; ++i < args.length;) {
n = new BigNumber(args[i]);
// If any number is NaN, return NaN.
if (!n.s) {
m = n;
break;
} else if (method.call(m, n)) {
m = n;
}
}
return m;
}
/*
* Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
* Called by minus, plus and times.
*/
function normalise(n, c, e) {
var i = 1,
j = c.length;
// Remove trailing zeros.
for (; !c[--j]; c.pop());
// Calculate the base 10 exponent. First get the number of digits of c[0].
for (j = c[0]; j >= 10; j /= 10, i++);
// Overflow?
if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
// Infinity.
n.c = n.e = null;
// Underflow?
} else if (e < MIN_EXP) {
// Zero.
n.c = [n.e = 0];
} else {
n.e = e;
n.c = c;
}
return n;
}
// Handle values that fail the validity test in BigNumber.
parseNumeric = (function () {
var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
dotAfter = /^([^.]+)\.$/,
dotBefore = /^\.([^.]+)$/,
isInfinityOrNaN = /^-?(Infinity|NaN)$/,
whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
return function (x, str, isNum, b) {
var base,
s = isNum ? str : str.replace(whitespaceOrPlus, '');
// No exception on ±Infinity or NaN.
if (isInfinityOrNaN.test(s)) {
x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
x.c = x.e = null;
} else {
if (!isNum) {
// basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
s = s.replace(basePrefix, function (m, p1, p2) {
base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
return !b || b == base ? p1 : m;
});
if (b) {
base = b;
// E.g. '1.' to '1', '.1' to '0.1'
s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
}
if (str != s) return new BigNumber(s, base);
}
// '[BigNumber Error] Not a number: {n}'
// '[BigNumber Error] Not a base {b} number: {n}'
if (BigNumber.DEBUG) {
throw Error
(bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
}
// NaN
x.c = x.e = x.s = null;
}
}
})();
/*
* Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
* If r is truthy, it is known that there are more digits after the rounding digit.
*/
function round(x, sd, rm, r) {
var d, i, j, k, n, ni, rd,
xc = x.c,
pows10 = POWS_TEN;
// if x is not Infinity or NaN...
if (xc) {
// rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
// n is a base 1e14 number, the value of the element of array x.c containing rd.
// ni is the index of n within x.c.
// d is the number of digits of n.
// i is the index of rd within n including leading zeros.
// j is the actual index of rd within n (if < 0, rd is a leading zero).
out: {
// Get the number of digits of the first element of xc.
for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
i = sd - d;
// If the rounding digit is in the first element of xc...
if (i < 0) {
i += LOG_BASE;
j = sd;
n = xc[ni = 0];
// Get the rounding digit at index j of n.
rd = n / pows10[d - j - 1] % 10 | 0;
} else {
ni = mathceil((i + 1) / LOG_BASE);
if (ni >= xc.length) {
if (r) {
// Needed by sqrt.
for (; xc.length <= ni; xc.push(0));
n = rd = 0;
d = 1;
i %= LOG_BASE;
j = i - LOG_BASE + 1;
} else {
break out;
}
} else {
n = k = xc[ni];
// Get the number of digits of n.
for (d = 1; k >= 10; k /= 10, d++);
// Get the index of rd within n.
i %= LOG_BASE;
// Get the index of rd within n, adjusted for leading zeros.
// The number of leading zeros of n is given by LOG_BASE - d.
j = i - LOG_BASE + d;
// Get the rounding digit at index j of n.
rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
}
}
r = r || sd < 0 ||
// Are there any non-zero digits after the rounding digit?
// The expression n % pows10[d - j - 1] returns all digits of n to the right
// of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
r = rm < 4
? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
: rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
// Check whether the digit to the left of the rounding digit is odd.
((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
rm == (x.s < 0 ? 8 : 7));
if (sd < 1 || !xc[0]) {
xc.length = 0;
if (r) {
// Convert sd to decimal places.
sd -= x.e + 1;
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
x.e = -sd || 0;
} else {
// Zero.
xc[0] = x.e = 0;
}
return x;
}
// Remove excess digits.
if (i == 0) {
xc.length = ni;
k = 1;
ni--;
} else {
xc.length = ni + 1;
k = pows10[LOG_BASE - i];
// E.g. 56700 becomes 56000 if 7 is the rounding digit.
// j > 0 means i > number of leading zeros of n.
xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
}
// Round up?
if (r) {
for (; ;) {
// If the digit to be rounded up is in the first element of xc...
if (ni == 0) {
// i will be the length of xc[0] before k is added.
for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
j = xc[0] += k;
for (k = 1; j >= 10; j /= 10, k++);
// if i != k the length has increased.
if (i != k) {
x.e++;
if (xc[0] == BASE) xc[0] = 1;
}
break;
} else {
xc[ni] += k;
if (xc[ni] != BASE) break;
xc[ni--] = 0;
k = 1;
}
}
}
// Remove trailing zeros.
for (i = xc.length; xc[--i] === 0; xc.pop());
}
// Overflow? Infinity.
if (x.e > MAX_EXP) {
x.c = x.e = null;
// Underflow? Zero.
} else if (x.e < MIN_EXP) {
x.c = [x.e = 0];
}
}
return x;
}
// PROTOTYPE/INSTANCE METHODS
/*
* Return a new BigNumber whose value is the absolute value of this BigNumber.
*/
P.absoluteValue = P.abs = function () {
var x = new BigNumber(this);
if (x.s < 0) x.s = 1;
return x;
};
/*
* Return
* 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
* -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
* 0 if they have the same value,
* or null if the value of either is NaN.
*/
P.comparedTo = function (y, b) {
return compare(this, new BigNumber(y, b));
};
/*
* If dp is undefined or null or true or false, return the number of decimal places of the
* value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
*
* Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
* BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
* ROUNDING_MODE if rm is omitted.
*
* [dp] {number} Decimal places: integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.decimalPlaces = P.dp = function (dp, rm) {
var c, n, v,
x = this;
if (dp != null) {
intCheck(dp, 0, MAX);
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
return round(new BigNumber(x), dp + x.e + 1, rm);
}
if (!(c = x.c)) return null;
n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
// Subtract the number of trailing zeros of the last number.
if (v = c[v]) for (; v % 10 == 0; v /= 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 BigNumber whose value is the value of this BigNumber divided by the value of
* BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
*/
P.dividedBy = P.div = function (y, b) {
return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
};
/*
* Return a new BigNumber whose value is the integer part of dividing the value of this
* BigNumber by the value of BigNumber(y, b).
*/
P.dividedToIntegerBy = P.idiv = function (y, b) {
return div(this, new BigNumber(y, b), 0, 1);
};
/*
* Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
*
* If m is present, return the result modulo m.
* If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
* If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
*
* The modular power operation works efficiently when x, n, and m are integers, otherwise it
* is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
*
* n {number|string|BigNumber} The exponent. An integer.
* [m] {number|string|BigNumber} The modulus.
*
* '[BigNumber Error] Exponent not an integer: {n}'
*/
P.exponentiatedBy = P.pow = function (n, m) {
var half, isModExp, k, more, nIsBig, nIsNeg, nIsOdd, y,
x = this;
n = new BigNumber(n);
// Allow NaN and ±Infinity, but not other non-integers.
if (n.c && !n.isInteger()) {
throw Error
(bignumberError + 'Exponent not an integer: ' + n);
}
if (m != null) m = new BigNumber(m);
// Exponent of MAX_SAFE_INTEGER is 15.
nIsBig = n.e > 14;
// If x is NaN, ±Infinity, ±0 or ±1, or n is ±Infinity, NaN or ±0.
if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
// The sign of the result of pow when x is negative depends on the evenness of n.
// If +n overflows to ±Infinity, the evenness of n would be not be known.
y = new BigNumber(Math.pow(+x.valueOf(), nIsBig ? 2 - isOdd(n) : +n));
return m ? y.mod(m) : y;
}
nIsNeg = n.s < 0;
if (m) {
// x % m returns NaN if abs(m) is zero, or m is NaN.
if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
isModExp = !nIsNeg && x.isInteger() && m.isInteger();
if (isModExp) x = x.mod(m);
// Overflow to ±Infinity: >=2**1e10 or >=1.0000024**1e15.
// Underflow to ±0: <=0.79**1e10 or <=0.9999975**1e15.
} else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
// [1, 240000000]
? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
// [80000000000000] [99999750000000]
: x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
// If x is negative and n is odd, k = -0, else k = 0.
k = x.s < 0 && isOdd(n) ? -0 : 0;
// If x >= 1, k = ±Infinity.
if (x.e > -1) k = 1 / k;
// If n is negative return ±0, else return ±Infinity.
return new BigNumber(nIsNeg ? 1 / k : k);
} else if (POW_PRECISION) {
// Truncating each coefficient array to a length of k after each multiplication
// equates to truncating significant digits to POW_PRECISION + [28, 41],
// i.e. there will be a minimum of 28 guard digits retained.
k = mathceil(POW_PRECISION / LOG_BASE + 2);
}
if (nIsBig) {
half = new BigNumber(0.5);
nIsOdd = isOdd(n);
} else {
nIsOdd = n % 2;
}
if (nIsNeg) n.s = 1;
y = new BigNumber(ONE);
// Performs 54 loop iterations for n of 9007199254740991.
for (; ;) {
if (nIsOdd) {
y = y.times(x);
if (!y.c) break;
if (k) {
if (y.c.length > k) y.c.length = k;
} else if (isModExp) {
y = y.mod(m); //y = y.minus(div(y, m, 0, MODULO_MODE).times(m));
}
}
if (nIsBig) {
n = n.times(half);
round(n, n.e + 1, 1);
if (!n.c[0]) break;
nIsBig = n.e > 14;
nIsOdd = isOdd(n);
} else {
n = mathfloor(n / 2);
if (!n) break;
nIsOdd = n % 2;
}
x = x.times(x);
if (k) {
if (x.c && x.c.length > k) x.c.length = k;
} else if (isModExp) {
x = x.mod(m); //x = x.minus(div(x, m, 0, MODULO_MODE).times(m));
}
}
if (isModExp) return y;
if (nIsNeg) y = ONE.div(y);
return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
};
/*
* Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
* using rounding mode rm, or ROUNDING_MODE if rm is omitted.
*
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
*/
P.integerValue = function (rm) {
var n = new BigNumber(this);
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
return round(n, n.e + 1, rm);
};
/*
* Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
* otherwise return false.
*/
P.isEqualTo = P.eq = function (y, b) {
return compare(this, new BigNumber(y, b)) === 0;
};
/*
* Return true if the value of this BigNumber is a finite number, otherwise return false.
*/
P.isFinite = function () {
return !!this.c;
};
/*
* Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
* otherwise return false.
*/
P.isGreaterThan = P.gt = function (y, b) {
return compare(this, new BigNumber(y, b)) > 0;
};
/*
* Return true if the value of this BigNumber is greater than or equal to the value of
* BigNumber(y, b), otherwise return false.
*/
P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;
};
/*
* Return true if the value of this BigNumber is an integer, otherwise return false.
*/
P.isInteger = function () {
return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
};
/*
* Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
* otherwise return false.
*/
P.isLessThan = P.lt = function (y, b) {
return compare(this, new BigNumber(y, b)) < 0;
};
/*
* Return true if the value of this BigNumber is less than or equal to the value of
* BigNumber(y, b), otherwise return false.
*/
P.isLessThanOrEqualTo = P.lte = function (y, b) {
return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
};
/*
* Return true if the value of this BigNumber is NaN, otherwise return false.
*/
P.isNaN = function () {
return !this.s;
};
/*
* Return true if the value of this BigNumber is negative, otherwise return false.
*/
P.isNegative = function () {
return this.s < 0;
};
/*
* Return true if the value of this BigNumber is positive, otherwise return false.
*/
P.isPositive = function () {
return this.s > 0;
};
/*
* Return true if the value of this BigNumber is 0 or -0, otherwise return false.
*/
P.isZero = function () {
return !!this.c && this.c[0] == 0;
};
/*
* 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 BigNumber whose value is the value of this BigNumber minus the value of
* BigNumber(y, b).
*/
P.minus = function (y, b) {
var i, j, t, xLTy,
x = this,
a = x.s;
y = new BigNumber(y, b);
b = y.s;
// Either NaN?
if (!a || !b) return new BigNumber(NaN);
// Signs differ?
if (a != b) {
y.s = -b;
return x.plus(y);
}
var xe = x.e / LOG_BASE,
ye = y.e / LOG_BASE,
xc = x.c,
yc = y.c;
if (!xe || !ye) {
// Either Infinity?
if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
// Either zero?
if (!xc[0] || !yc[0]) {
// Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
// IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
ROUNDING_MODE == 3 ? -0 : 0);
}
}
xe = bitFloor(xe);
ye = bitFloor(ye);
xc = xc.slice();
// Determine which is the bigger number.
if (a = xe - ye) {
if (xLTy = a < 0) {
a = -a;
t = xc;
} else {
ye = xe;
t = yc;
}
t.reverse();
// Prepend zeros to equalise exponents.
for (b = a; b--; t.push(0));
t.reverse();
} else {
// Exponents equal. Check digit by digit.
j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
for (a = b = 0; b < j; b++) {
if (xc[b] != yc[b]) {
xLTy = xc[b] < yc[b];
break;
}
}
}
// x < y? Point xc to the array of the bigger number.
if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
b = (j = yc.length) - (i = xc.length);
// Append zeros to xc if shorter.
// No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
if (b > 0) for (; b--; xc[i++] = 0);
b = BASE - 1;
// Subtract yc from xc.
for (; j > a;) {
if (xc[--j] < yc[j]) {
for (i = j; i && !xc[--i]; xc[i] = b);
--xc[i];
xc[j] += BASE;
}
xc[j] -= yc[j];
}
// Remove leading zeros and adjust exponent accordingly.
for (; xc[0] == 0; xc.splice(0, 1), --ye);
// Zero?
if (!xc[0]) {
// Following IEEE 754 (2008) 6.3,
// n - n = +0 but n - n = -0 when rounding towards -Infinity.
y.s = ROUNDING_MODE == 3 ? -1 : 1;
y.c = [y.e = 0];
return y;
}
// No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
// for finite x and y.
return normalise(y, xc, ye);
};
/*
* 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 BigNumber whose value is the value of this BigNumber modulo the value of
* BigNumber(y, b). The result depends on the value of MODULO_MODE.
*/
P.modulo = P.mod = function (y, b) {
var q, s,
x = this;
y = new BigNumber(y, b);
// Return NaN if x is Infinity or NaN, or y is NaN or zero.
if (!x.c || !y.s || y.c && !y.c[0]) {
return new BigNumber(NaN);
// Return x if y is Infinity or x is zero.
} else if (!y.c || x.c && !x.c[0]) {
return new BigNumber(x);
}
if (MODULO_MODE == 9) {
// Euclidian division: q = sign(y) * floor(x / abs(y))
// r = x - qy where 0 <= r < abs(y)
s = y.s;
y.s = 1;
q = div(x, y, 0, 3);
y.s = s;
q.s *= s;
} else {
q = div(x, y, 0, MODULO_MODE);
}
y = x.minus(q.times(y));
// To match JavaScript %, ensure sign of zero is sign of dividend.
if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
return y;
};
/*
* 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 BigNumber whose value is the value of this BigNumber multiplied by the value
* of BigNumber(y, b).
*/
P.multipliedBy = P.times = function (y, b) {
var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
base, sqrtBase,
x = this,
xc = x.c,
yc = (y = new BigNumber(y, b)).c;
// Either NaN, ±Infinity or ±0?
if (!xc || !yc || !xc[0] || !yc[0]) {
// Return NaN if either is NaN, or one is 0 and the other is Infinity.
if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
y.c = y.e = y.s = null;
} else {
y.s *= x.s;
// Return ±Infinity if either is ±Infinity.
if (!xc || !yc) {
y.c = y.e = null;
// Return ±0 if either is ±0.
} else {
y.c = [0];
y.e = 0;
}
}
return y;
}
e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
y.s *= x.s;
xcL = xc.length;
ycL = yc.length;
// Ensure xc points to longer array and xcL to its length.
if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
// Initialise the result array with zeros.
for (i = xcL + ycL, zc = []; i--; zc.push(0));
base = BASE;
sqrtBase = SQRT_BASE;
for (i = ycL; --i >= 0;) {
c = 0;
ylo = yc[i] % sqrtBase;
yhi = yc[i] / sqrtBase | 0;
for (k = xcL, j = i + k; j > i;) {
xlo = xc[--k] % sqrtBase;
xhi = xc[k] / sqrtBase | 0;
m = yhi * xlo + xhi * ylo;
xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
zc[j--] = xlo % base;
}
zc[j] = c;
}
if (c) {
++e;
} else {
zc.splice(0, 1);
}
return normalise(y, zc, e);
};
/*
* Return a new BigNumber whose value is the value of this BigNumber negated,
* i.e. multiplied by -1.
*/
P.negated = function () {
var x = new BigNumber(this);
x.s = -x.s || null;
return 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 BigNumber whose value is the value of this BigNumber plus the value of
* BigNumber(y, b).
*/
P.plus = function (y, b) {
var t,
x = this,
a = x.s;
y = new BigNumber(y, b);
b = y.s;
// Either NaN?
if (!a || !b) return new BigNumber(NaN);
// Signs differ?
if (a != b) {
y.s = -b;
return x.minus(y);
}
var xe = x.e / LOG_BASE,
ye = y.e / LOG_BASE,
xc = x.c,
yc = y.c;
if (!xe || !ye) {
// Return ±Infinity if either ±Infinity.
if (!xc || !yc) return new BigNumber(a / 0);
// Either zero?
// Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
}
xe = bitFloor(xe);
ye = bitFloor(ye);
xc = xc.slice();
// Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
if (a = xe - ye) {
if (a > 0) {
ye = xe;
t = yc;
} else {
a = -a;
t = xc;
}
t.reverse();
for (; a--; t.push(0));
t.reverse();
}
a = xc.length;
b = yc.length;
// Point xc to the longer array, and b to the shorter length.
if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
// Only start adding at yc.length - 1 as the further digits of xc can be ignored.
for (a = 0; b;) {
a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
}
if (a) {
xc = [a].concat(xc);
++ye;
}
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
// ye = MAX_EXP + 1 possible
return normalise(y, xc, ye);
};
/*
* If sd is undefined or null or true or false, return the number of significant digits of
* the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
* If sd is true include integer-part trailing zeros in the count.
*
* Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
* BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
* ROUNDING_MODE if rm is omitted.
*
* sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
* boolean: whether to count integer-part trailing zeros: true or false.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
*/
P.precision = P.sd = function (sd, rm) {
var c, n, v,
x = this;
if (sd != null && sd !== !!sd) {
intCheck(sd, 1, MAX);
if (rm == null) rm = ROUNDING_MODE;
else intCheck(rm, 0, 8);
return round(new BigNumber(x), sd, rm);
}
if (!(c = x.c)) return null;
v = c.length - 1;
n = v * LOG_BASE + 1;
if (v = c[v]) {
// Subtract the number of trailing zeros of the last element.
for (; v % 10 == 0; v /= 10, n--);
// Add the number of digits of the first element.
for (v = c[0]; v >= 10; v /= 10, n++);
}
if (sd && x.e + 1 > n) n = x.e + 1;
return n;
};
/*
* Return a new BigNumber whose value is the value of this BigNumber shifted by k places
* (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
*
* k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
*/
P.shiftedBy = function (k) {
intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
return this.times('1e' + k);
};
/*
* sqrt(-n) = N
* sqrt(N) = N
* sqrt(-I) = N
* sqrt(I) = I
* sqrt(0) = 0
* sqrt(-0) = -0
*
* Return a new BigNumber whose value is the square root of the value of this BigNumber,
* rounded according to DECIMAL_PLACES and ROUNDING_MODE.
*/
P.squareRoot = P.sqrt = function () {
var m, n, r, rep, t,
x = this,
c = x.c,
s = x.s,
e = x.e,
dp = DECIMAL_PLACES + 4,
half = new BigNumber('0.5');
// Negative/NaN/Infinity/zero?
if (s !== 1 || !c || !c[0]) {
return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
}
// 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 = coeffToString(c);
if ((n.length + e) % 2 == 0) n += '0';
s = Math.sqrt(n);
e = bitFloor((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 BigNumber(n);
} else {
r = new BigNumber(s + '');
}
// Check for zero.
// r could be zero if MIN_EXP is changed after the this value was created.
// This would cause a division by zero (x/t) and hence Infinity below, which would cause
// coeffToString to throw.
if (r.c[0]) {
e = r.e;
s = e + dp;
if (s < 3) s = 0;
// Newton-Raphson iteration.
for (; ;) {
t = r;
r = half.times(t.plus(div(x, t, dp, 1)));
if (coeffToString(t.c ).slice(0, s) === (n =
coeffToString(r.c)).slice(0, s)) {
// The exponent of r may here be one less than the final result exponent,
// e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
// are indexed correctly.
if (r.e < e) --s;
n = n.slice(s - 3, s + 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) {
round(t, t.e + DECIMAL_PLACES + 2, 0);
if (t.times(t).eq(x)) {
r = t;
break;
}
}
dp += 4;
s += 4;
rep = 1;
} else {
// If rounding digits are null, 0{0,4} or 50{0,3}, check for 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.
round(r, r.e + DECIMAL_PLACES + 2, 1);
m = !r.times(r).eq(x);
}
break;
}
}
}
}
return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
};
/*
* Return a string representing the value of this BigNumber in exponential notation and
* rounded using ROUNDING_MODE to dp fixed decimal places.
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.toExponential = function (dp, rm) {
if (dp != null) {
intCheck(dp, 0, MAX);
dp++;
}
return format(this, dp, rm, 1);
};
/*
* Return a string representing the value of this BigNumber in fixed-point notation rounding
* to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
*
* Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
* but e.g. (-0.00001).toFixed(0) is '-0'.
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.toFixed = function (dp, rm) {
if (dp != null) {
intCheck(dp, 0, MAX);
dp = dp + this.e + 1;
}
return format(this, dp, rm);
};
/*
* Return a string representing the value of this BigNumber in fixed-point notation rounded
* using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
* of the FORMAT object (see BigNumber.set).
*
* FORMAT = {
* decimalSeparator : '.',
* groupSeparator : ',',
* groupSize : 3,
* secondaryGroupSize : 0,
* fractionGroupSeparator : '\xA0', // non-breaking space
* fractionGroupSize : 0
* };
*
* [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
*/
P.toFormat = function (dp, rm) {
var str = this.toFixed(dp, rm);
if (this.c) {
var i,
arr = str.split('.'),
g1 = +FORMAT.groupSize,
g2 = +FORMAT.secondaryGroupSize,
groupSeparator = FORMAT.groupSeparator,
intPart = arr[0],
fractionPart = arr[1],
isNeg = this.s < 0,
intDigits = isNeg ? intPart.slice(1) : intPart,
len = intDigits.length;
if (g2) i = g1, g1 = g2, g2 = i, len -= i;
if (g1 > 0 && len > 0) {
i = len % g1 || g1;
intPart = intDigits.substr(0, i);
for (; i < len; i += g1) {
intPart += groupSeparator + intDigits.substr(i, g1);
}
if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
if (isNeg) intPart = '-' + intPart;
}
str = fractionPart
? intPart + FORMAT.decimalSeparator + ((g2 = +FORMAT.fractionGroupSize)
? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
'$&' + FORMAT.fractionGroupSeparator)
: fractionPart)
: intPart;
}
return str;
};
/*
* Return a string array representing the value of this BigNumber 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.
*
* [md] {number|string|BigNumber} Integer >= 1, or Infinity. The maximum denominator.
*
* '[BigNumber Error] Argument {not an integer|out of range} : {md}'
*/
P.toFraction = function (md) {
var arr, d, d0, d1, d2, e, exp, n, n0, n1, q, s,
x = this,
xc = x.c;
if (md != null) {
n = new BigNumber(md);
// Throw if md is less than one or is not an integer, unless it is Infinity.
if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
throw Error
(bignumberError + 'Argument ' +
(n.isInteger() ? 'out of range: ' : 'not an integer: ') + md);
}
}
if (!xc) return x.toString();
d = new BigNumber(ONE);
n1 = d0 = new BigNumber(ONE);
d1 = n0 = new BigNumber(ONE);
s = coeffToString(xc);
// Determine initial denominator.
// d is a power of 10 and the minimum max denominator that specifies the value exactly.
e = d.e = s.length - x.e - 1;
d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;
exp = MAX_EXP;
MAX_EXP = 1 / 0;
n = new BigNumber(s);
// n0 = d1 = 0
n0.c[0] = 0;
for (; ;) {
q = div(n, d, 0, 1);
d2 = d0.plus(q.times(d1));
if (d2.comparedTo(md) == 1) break;
d0 = d1;
d1 = d2;
n1 = n0.plus(q.times(d2 = n1));
n0 = d2;
d = n.minus(q.times(d2 = d));
n = d2;
}
d2 = div(md.minus(d0), d1, 0, 1);
n0 = n0.plus(d2.times(n1));
d0 = d0.plus(d2.times(d1));
n0.s = n1.s = x.s;
e *= 2;
// Determine which fraction is closer to x, n0/d0 or n1/d1
arr = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1
? [n1.toString(), d1.toString()]
: [n0.toString(), d0.toString()];
MAX_EXP = exp;
return arr;
};
/*
* Return the value of this BigNumber converted to a number primitive.
*/
P.toNumber = function () {
return +this;
};
/*
* Return a string representing the value of this BigNumber rounded to sd significant digits
* using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
* necessary to represent the integer part of the value in fixed-point notation, then use
* exponential notation.
*
* [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
*
* '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
*/
P.toPrecision = function (sd, rm) {
if (sd != null) intCheck(sd, 1, MAX);
return format(this, sd, rm, 2);
};
/*
* Return a string representing the value of this BigNumber in base b, or base 10 if b is
* omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
* ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
* that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
* TO_EXP_NEG, return exponential notation.
*
* [b] {number} Integer, 2 to ALPHABET.length inclusive.
*
* '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
*/
P.toString = function (b) {
var str,
n = this,
s = n.s,
e = n.e;
// Infinity or NaN?
if (e === null) {
if (s) {
str = 'Infinity';
if (s < 0) str = '-' + str;
} else {
str = 'NaN';
}
} else {
str = coeffToString(n.c);
if (b == null) {
str = e <= TO_EXP_NEG || e >= TO_EXP_POS
? toExponential(str, e)
: toFixedPoint(str, e, '0');
} else {
intCheck(b, 2, ALPHABET.length, 'Base');
str = convertBase(toFixedPoint(str, e, '0'), 10, b, s, true);
}
if (s < 0 && n.c[0]) str = '-' + str;
}
return str;
};
/*
* Return as toString, but do not accept a base argument, and include the minus sign for
* negative zero.
*/
P.valueOf = P.toJSON = function () {
var str,
n = this,
e = n.e;
if (e === null) return n.toString();
str = coeffToString(n.c);
str = e <= TO_EXP_NEG || e >= TO_EXP_POS
? toExponential(str, e)
: toFixedPoint(str, e, '0');
return n.s < 0 ? '-' + str : str;
};
P._isBigNumber = true;
if (configObject != null) BigNumber.set(configObject);
return BigNumber;
}
// PRIVATE HELPER FUNCTIONS
function bitFloor(n) {
var i = n | 0;
return n > 0 || n === i ? i : i - 1;
}
// Return a coefficient array as a string of base 10 digits.
function coeffToString(a) {
var s, z,
i = 1,
j = a.length,
r = a[0] + '';
for (; i < j;) {
s = a[i++] + '';
z = LOG_BASE - s.length;
for (; z--; s = '0' + s);
r += s;
}
// Determine trailing zeros.
for (j = r.length; r.charCodeAt(--j) === 48;);
return r.slice(0, j + 1 || 1);
}
// Compare the value of BigNumbers x and y.
function compare(x, y) {
var a, b,
xc = x.c,
yc = y.c,
i = x.s,
j = y.s,
k = x.e,
l = y.e;
// Either NaN?
if (!i || !j) return null;
a = xc && !xc[0];
b = yc && !yc[0];
// Either zero?
if (a || b) return a ? b ? 0 : -j : i;
// Signs differ?
if (i != j) return i;
a = i < 0;
b = k == l;
// Either Infinity?
if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
// Compare exponents.
if (!b) return k > l ^ a ? 1 : -1;
j = (k = xc.length) < (l = yc.length) ? k : l;
// Compare digit by digit.
for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
// Compare lengths.
return k == l ? 0 : k > l ^ a ? 1 : -1;
}
/*
* Check that n is a primitive number, an integer, and in range, otherwise throw.
*/
function intCheck(n, min, max, name) {
if (n < min || n > max || n !== (n < 0 ? mathceil(n) : mathfloor(n))) {
throw Error
(bignumberError + (name || 'Argument') + (typeof n == 'number'
? n < min || n > max ? ' out of range: ' : ' not an integer: '
: ' not a primitive number: ') + n);
}
}
function isArray(obj) {
return Object.prototype.toString.call(obj) == '[object Array]';
}
// Assumes finite n.
function isOdd(n) {
var k = n.c.length - 1;
return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
}
function toExponential(str, e) {
return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
(e < 0 ? 'e' : 'e+') + e;
}
function toFixedPoint(str, e, z) {
var len, zs;
// Negative exponent?
if (e < 0) {
// Prepend zeros.
for (zs = z + '.'; ++e; zs += z);
str = zs + str;
// Positive exponent
} else {
len = str.length;
// Append zeros.
if (++e > len) {
for (zs = z, e -= len; --e; zs += z);
str += zs;
} else if (e < len) {
str = str.slice(0, e) + '.' + str.slice(e);
}
}
return str;
}
// EXPORTS
export var BigNumber = clone();
export default BigNumber;

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

@@ -0,0 +1,36 @@
{
"name": "bignumber.js",
"main": "bignumber.js",
"version": "7.2.1",
"homepage": "https://github.com/MikeMcl/bignumber.js",
"authors": [
"Michael Mclaughlin <M8ch88l@gmail.com>"
],
"description": "A library for arbitrary-precision decimal and non-decimal arithmetic",
"moduleType": [
"amd",
"globals",
"node"
],
"keywords": [
"arbitrary",
"precision",
"arithmetic",
"big",
"number",
"decimal",
"float",
"biginteger",
"bigdecimal",
"bignumber",
"bigint",
"bignum"
],
"license": "MIT",
"ignore": [
".*",
"*.json",
"test"
]
}

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<!DOCTYPE HTML>
<html>
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="Author" content="M Mclaughlin">
<title>bignumber.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:200px;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 Verdana,sans-serif;color:#000;margin-bottom:1em}
h2{font-size:2.25em;color:#ff2a00}
h3{font-size:1.75em;color:#4dc71f}
h4{font-size:1.75em;color:#ff2a00;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{padding-top:.35em}
dt{padding-top:.5em}
b{font-weight:700}
dt b{font-size:1.3em}
a,a:visited{color:#ff2a00;text-decoration:none}
a:active,a:hover{outline:0;text-decoration:underline}
.nav a,.nav b,.nav a:visited{display:block;color:#ff2a00;font-weight:700; margin-top:15px}
.nav b{color:#4dc71f;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,ul.inset{margin-left:20px}
.inset{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:#ff2a00}
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 #abef98;
padding:1px 0 1px 15px;margin:1.2em 0}
code,.nav-title{color:#ff2a00}
.end{margin-bottom:25px}
.centre{text-align:center}
.error-table{font-size:13px;width:100%}
#faq{margin:3em 0 0}
li span{float:right;margin-right:10px;color:#c0c0c0}
#js{font:inherit;color:#4dc71f}
</style>
</head>
<body>
<div class="nav">
<a class='nav-title' href="#">API</a>
<b> CONSTRUCTOR </b>
<ul>
<li><a href="#bignumber">BigNumber</a></li>
</ul>
<a href="#methods">Methods</a>
<ul>
<li><a href="#clone">clone</a></li>
<li><a href="#config" >config</a><span>set</span></li>
<li>
<ul class="inset">
<li><a href="#decimal-places">DECIMAL_PLACES</a></li>
<li><a href="#rounding-mode" >ROUNDING_MODE</a></li>
<li><a href="#exponential-at">EXPONENTIAL_AT</a></li>
<li><a href="#range" >RANGE</a></li>
<li><a href="#crypto" >CRYPTO</a></li>
<li><a href="#modulo-mode" >MODULO_MODE</a></li>
<li><a href="#pow-precision" >POW_PRECISION</a></li>
<li><a href="#format" >FORMAT</a></li>
<li><a href="#alphabet" >ALPHABET</a></li>
</ul>
</li>
<li><a href="#isBigNumber">isBigNumber</a></li>
<li><a href="#max" >maximum</a><span>max</span></li>
<li><a href="#min" >minimum</a><span>min</span></li>
<li><a href="#random" >random</a></li>
</ul>
<a href="#constructor-properties">Properties</a>
<ul>
<li><a href="#round-up" >ROUND_UP</a></li>
<li><a href="#round-down" >ROUND_DOWN</a></li>
<li><a href="#round-ceil" >ROUND_CEIL</a></li>
<li><a href="#round-floor" >ROUND_FLOOR</a></li>
<li><a href="#round-half-up" >ROUND_HALF_UP</a></li>
<li><a href="#round-half-down" >ROUND_HALF_DOWN</a></li>
<li><a href="#round-half-even" >ROUND_HALF_EVEN</a></li>
<li><a href="#round-half-ceil" >ROUND_HALF_CEIL</a></li>
<li><a href="#round-half-floor">ROUND_HALF_FLOOR</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="#cmp" >comparedTo </a> </li>
<li><a href="#dp" >decimalPlaces </a><span>dp</span> </li>
<li><a href="#div" >dividedBy </a><span>div</span> </li>
<li><a href="#divInt" >dividedToIntegerBy </a><span>idiv</span> </li>
<li><a href="#pow" >exponentiatedBy </a><span>pow</span> </li>
<li><a href="#int" >integerValue </a> </li>
<li><a href="#eq" >isEqualTo </a><span>eq</span> </li>
<li><a href="#isF" >isFinite </a> </li>
<li><a href="#gt" >isGreaterThan </a><span>gt</span> </li>
<li><a href="#gte" >isGreaterThanOrEqualTo</a><span>gte</span> </li>
<li><a href="#isInt" >isInteger </a> </li>
<li><a href="#lt" >isLessThan </a><span>lt</span> </li>
<li><a href="#lte" >isLessThanOrEqualTo </a><span>lte</span> </li>
<li><a href="#isNaN" >isNaN </a> </li>
<li><a href="#isNeg" >isNegative </a> </li>
<li><a href="#isPos" >isPositive </a> </li>
<li><a href="#isZ" >isZero </a> </li>
<li><a href="#minus" >minus </a> </li>
<li><a href="#mod" >modulo </a><span>mod</span> </li>
<li><a href="#times" >multipliedBy </a><span>times</span></li>
<li><a href="#neg" >negated </a> </li>
<li><a href="#plus" >plus </a> </li>
<li><a href="#sd" >precision </a><span>sd</span> </li>
<li><a href="#shift" >shiftedBy </a> </li>
<li><a href="#sqrt" >squareRoot </a><span>sqrt</span> </li>
<li><a href="#toE" >toExponential </a> </li>
<li><a href="#toFix" >toFixed </a> </li>
<li><a href="#toFor" >toFormat </a> </li>
<li><a href="#toFr" >toFraction </a> </li>
<li><a href="#toJSON" >toJSON </a> </li>
<li><a href="#toN" >toNumber </a> </li>
<li><a href="#toP" >toPrecision </a> </li>
<li><a href="#toS" >toString </a> </li>
<li><a href="#valueOf">valueOf </a> </li>
</ul>
<a href="#instance-properties">Properties</a>
<ul>
<li><a href="#coefficient">c: coefficient</a></li>
<li><a href="#exponent" >e: exponent</a></li>
<li><a href="#sign" >s: sign</a></li>
</ul>
<a href="#zero-nan-infinity">Zero, NaN &amp; Infinity</a>
<a href="#Errors">Errors</a>
<a class='end' href="#faq">FAQ</a>
</div>
<div class="container">
<h1>bignumber<span id='js'>.js</span></h1>
<p>A JavaScript library for arbitrary-precision arithmetic.</p>
<p><a href="https://github.com/MikeMcl/bignumber.js">Hosted on GitHub</a>. </p>
<h2>API</h2>
<p>
See the <a href='https://github.com/MikeMcl/bignumber.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>
<h3>CONSTRUCTOR</h3>
<h5 id="bignumber">
BigNumber<code class='inset'>BigNumber(n [, base]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i>: integer, <code>2</code> to <code>36</code> inclusive. (See
<a href='#alphabet'><code>ALPHABET</code></a> to extend this range).
</p>
<p>
Returns a new instance of a BigNumber object with value <code>n</code>, where <code>n</code>
is a numeric value in the specified <code>base</code>, or base <code>10</code> if
<code>base</code> is omitted or is <code>null</code> or <code>undefined</code>.
</p>
<pre>
x = new BigNumber(123.4567) // '123.4567'
// 'new' is optional
y = BigNumber(x) // '123.4567'</pre>
<p>
If <code>n</code> is a base <code>10</code> value it can be in normal (fixed-point) or
exponential notation. Values in other bases must be in normal notation. Values in any base can
have fraction digits, i.e. digits after the decimal point.
</p>
<pre>
new BigNumber(43210) // '43210'
new BigNumber('4.321e+4') // '43210'
new BigNumber('-735.0918e-430') // '-7.350918e-428'
new BigNumber('123412421.234324', 5) // '607236.557696'</pre>
<p>
Signed <code>0</code>, signed <code>Infinity</code> and <code>NaN</code> are supported.
</p>
<pre>
new BigNumber('-Infinity') // '-Infinity'
new BigNumber(NaN) // 'NaN'
new BigNumber(-0) // '0'
new BigNumber('.5') // '0.5'
new BigNumber('+2') // '2'</pre>
<p>
String values in hexadecimal literal form, e.g. <code>'0xff'</code>, are valid, as are
string values with the octal and binary prefixs <code>'0o'</code> and <code>'0b'</code>.
String values in octal literal form without the prefix will be interpreted as
decimals, e.g. <code>'011'</code> is interpreted as 11, not 9.
</p>
<pre>
new BigNumber(-10110100.1, 2) // '-180.5'
new BigNumber('-0b10110100.1') // '-180.5'
new BigNumber('ff.8', 16) // '255.5'
new BigNumber('0xff.8') // '255.5'</pre>
<p>
If a base is specified, <code>n</code> is rounded according to the current
<a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings. <em>This includes base
<code>10</code> so don't include a <code>base</code> parameter for decimal values unless
this behaviour is wanted.</em>
</p>
<pre>BigNumber.config({ DECIMAL_PLACES: 5 })
new BigNumber(1.23456789) // '1.23456789'
new BigNumber(1.23456789, 10) // '1.23457'</pre>
<p>An error is thrown if <code>base</code> is invalid. See <a href='#Errors'>Errors</a>.</p>
<p>
There is no limit to the number of digits of a value of type <em>string</em> (other than
that of JavaScript's maximum array size). See <a href='#range'><code>RANGE</code></a> to set
the maximum and minimum possible exponent value of a BigNumber.
</p>
<pre>
new BigNumber('5032485723458348569331745.33434346346912144534543')
new BigNumber('4.321e10000000')</pre>
<p>BigNumber <code>NaN</code> is returned if <code>n</code> is invalid
(unless <code>BigNumber.DEBUG</code> is <code>true</code>, see below).</p>
<pre>
new BigNumber('.1*') // 'NaN'
new BigNumber('blurgh') // 'NaN'
new BigNumber(9, 2) // 'NaN'</pre>
<p>
To aid in debugging, if <code>BigNumber.DEBUG</code> is <code>true</code> then an error will
be thrown on an invalid <code>n</code>. An error will also be thrown if <code>n</code> is of
type <em>number</em> with more than <code>15</code> significant digits, as calling
<code><a href='#toS'>toString</a></code> or <code><a href='#valueOf'>valueOf</a></code> on
these numbers may not result in the intended value.
</p>
<pre>
console.log(823456789123456.3) // 823456789123456.2
new BigNumber(823456789123456.3) // '823456789123456.2'
BigNumber.DEBUG = true
// '[BigNumber Error] Number primitive has more than 15 significant digits'
new BigNumber(823456789123456.3)
// '[BigNumber Error] Not a base 2 number'
new BigNumber(9, 2)</pre>
<h4 id="methods">Methods</h4>
<p>The static methods of a BigNumber constructor.</p>
<h5 id="clone">clone
<code class='inset'>.clone([object]) <i>&rArr; BigNumber constructor</i></code>
</h5>
<p><code>object</code>: <i>object</i></p>
<p>
Returns a new independent BigNumber constructor with configuration as described by
<code>object</code> (see <a href='#config'><code>config</code></a>), or with the default
configuration if <code>object</code> is <code>null</code> or <code>undefined</code>.
</p>
<p>
Throws if <code>object</code> is not an object. See <a href='#Errors'>Errors</a>.
</p>
<pre>BigNumber.config({ DECIMAL_PLACES: 5 })
BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
x = new BigNumber(1)
y = new BN(1)
x.div(3) // 0.33333
y.div(3) // 0.333333333
// BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
BN = BigNumber.clone()
BN.config({ DECIMAL_PLACES: 9 })</pre>
<h5 id="config">config<code class='inset'>set([object]) <i>&rArr; object</i></code></h5>
<p>
<code>object</code>: <i>object</i>: an object that contains some or all of the following
properties.
</p>
<p>Configures the settings for this particular BigNumber constructor.</p>
<dl class='inset'>
<dt id="decimal-places"><code><b>DECIMAL_PLACES</b></code></dt>
<dd>
<i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive<br />
Default value: <code>20</code>
</dd>
<dd>
The <u>maximum</u> number of decimal places of the results of operations involving
division, i.e. division, square root and base conversion operations, and power
operations with negative exponents.<br />
</dd>
<dd>
<pre>BigNumber.config({ DECIMAL_PLACES: 5 })
BigNumber.set({ DECIMAL_PLACES: 5 }) // equivalent</pre>
</dd>
<dt id="rounding-mode"><code><b>ROUNDING_MODE</b></code></dt>
<dd>
<i>number</i>: integer, <code>0</code> to <code>8</code> inclusive<br />
Default value: <code>4</code> <a href="#round-half-up">(<code>ROUND_HALF_UP</code>)</a>
</dd>
<dd>
The rounding mode used in the above operations and the default rounding mode of
<a href='#dp'><code>decimalPlaces</code></a>,
<a href='#sd'><code>precision</code></a>,
<a href='#toE'><code>toExponential</code></a>,
<a href='#toFix'><code>toFixed</code></a>,
<a href='#toFor'><code>toFormat</code></a> and
<a href='#toP'><code>toPrecision</code></a>.
</dd>
<dd>The modes are available as enumerated properties of the BigNumber constructor.</dd>
<dd>
<pre>BigNumber.config({ ROUNDING_MODE: 0 })
BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP }) // equivalent</pre>
</dd>
<dt id="exponential-at"><code><b>EXPONENTIAL_AT</b></code></dt>
<dd>
<i>number</i>: integer, magnitude <code>0</code> to <code>1e+9</code> inclusive, or
<br />
<i>number</i>[]: [ integer <code>-1e+9</code> to <code>0</code> inclusive, integer
<code>0</code> to <code>1e+9</code> inclusive ]<br />
Default value: <code>[-7, 20]</code>
</dd>
<dd>
The exponent value(s) at which <code>toString</code> returns exponential notation.
</dd>
<dd>
If a single number is assigned, the value is the exponent magnitude.<br />
If an array of two numbers is assigned then the first number is the negative exponent
value at and beneath which exponential notation is used, and the second number is the
positive exponent value at and above which the same.
</dd>
<dd>
For example, to emulate JavaScript numbers in terms of the exponent values at which they
begin to use exponential notation, use <code>[-7, 20]</code>.
</dd>
<dd>
<pre>BigNumber.config({ EXPONENTIAL_AT: 2 })
new BigNumber(12.3) // '12.3' e is only 1
new BigNumber(123) // '1.23e+2'
new BigNumber(0.123) // '0.123' e is only -1
new BigNumber(0.0123) // '1.23e-2'
BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
new BigNumber(123456789) // '123456789' e is only 8
new BigNumber(0.000000123) // '1.23e-7'
// Almost never return exponential notation:
BigNumber.config({ EXPONENTIAL_AT: 1e+9 })
// Always return exponential notation:
BigNumber.config({ EXPONENTIAL_AT: 0 })</pre>
</dd>
<dd>
Regardless of the value of <code>EXPONENTIAL_AT</code>, the <code>toFixed</code> method
will always return a value in normal notation and the <code>toExponential</code> method
will always return a value in exponential form.
</dd>
<dd>
Calling <code>toString</code> with a base argument, e.g. <code>toString(10)</code>, will
also always return normal notation.
</dd>
<dt id="range"><code><b>RANGE</b></code></dt>
<dd>
<i>number</i>: integer, magnitude <code>1</code> to <code>1e+9</code> inclusive, or
<br />
<i>number</i>[]: [ integer <code>-1e+9</code> to <code>-1</code> inclusive, integer
<code>1</code> to <code>1e+9</code> inclusive ]<br />
Default value: <code>[-1e+9, 1e+9]</code>
</dd>
<dd>
The exponent value(s) beyond which overflow to <code>Infinity</code> and underflow to
zero occurs.
</dd>
<dd>
If a single number is assigned, it is the maximum exponent magnitude: values wth a
positive exponent of greater magnitude become <code>Infinity</code> and those with a
negative exponent of greater magnitude become zero.
<dd>
If an array of two numbers is assigned then the first number is the negative exponent
limit and the second number is the positive exponent limit.
</dd>
<dd>
For example, to emulate JavaScript numbers in terms of the exponent values at which they
become zero and <code>Infinity</code>, use <code>[-324, 308]</code>.
</dd>
<dd>
<pre>BigNumber.config({ RANGE: 500 })
BigNumber.config().RANGE // [ -500, 500 ]
new BigNumber('9.999e499') // '9.999e+499'
new BigNumber('1e500') // 'Infinity'
new BigNumber('1e-499') // '1e-499'
new BigNumber('1e-500') // '0'
BigNumber.config({ RANGE: [-3, 4] })
new BigNumber(99999) // '99999' e is only 4
new BigNumber(100000) // 'Infinity' e is 5
new BigNumber(0.001) // '0.01' e is only -3
new BigNumber(0.0001) // '0' e is -4</pre>
</dd>
<dd>
The largest possible magnitude of a finite BigNumber is
<code>9.999...e+1000000000</code>.<br />
The smallest possible magnitude of a non-zero BigNumber is <code>1e-1000000000</code>.
</dd>
<dt id="crypto"><code><b>CRYPTO</b></code></dt>
<dd>
<i>boolean</i>: <code>true</code> or <code>false</code>.<br />
Default value: <code>false</code>
</dd>
<dd>
The value that determines whether cryptographically-secure pseudo-random number
generation is used.
</dd>
<dd>
If <code>CRYPTO</code> is set to <code>true</code> then the
<a href='#random'><code>random</code></a> method will generate random digits using
<code>crypto.getRandomValues</code> in browsers that support it, or
<code>crypto.randomBytes</code> if using a version of Node.js that supports it.
</dd>
<dd>
If neither function is supported by the host environment then attempting to set
<code>CRYPTO</code> to <code>true</code> will fail and an exception will be thrown.
</dd>
<dd>
If <code>CRYPTO</code> is <code>false</code> then the source of randomness used will be
<code>Math.random</code> (which is assumed to generate at least <code>30</code> bits of
randomness).
</dd>
<dd>See <a href='#random'><code>random</code></a>.</dd>
<dd>
<pre>BigNumber.config({ CRYPTO: true })
BigNumber.config().CRYPTO // true
BigNumber.random() // 0.54340758610486147524</pre>
</dd>
<dt id="modulo-mode"><code><b>MODULO_MODE</b></code></dt>
<dd>
<i>number</i>: integer, <code>0</code> to <code>9</code> inclusive<br />
Default value: <code>1</code> (<a href="#round-down"><code>ROUND_DOWN</code></a>)
</dd>
<dd>The modulo mode used when calculating the modulus: <code>a mod n</code>.</dd>
<dd>
The quotient, <code>q = a / n</code>, is calculated according to the
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> that corresponds to the chosen
<code>MODULO_MODE</code>.
</dd>
<dd>The remainder, <code>r</code>, is calculated as: <code>r = a - n * q</code>.</dd>
<dd>
The modes that are most commonly used for the modulus/remainder operation are shown in
the following table. Although the other rounding modes can be used, they may not give
useful results.
</dd>
<dd>
<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>
The remainder is positive if the dividend is negative, otherwise it is negative.
</td>
</tr>
<tr>
<td><b>ROUND_DOWN</b></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><b>ROUND_FLOOR</b></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><b>ROUND_HALF_EVEN</b></td><td class='centre'>6</td>
<td>The <i>IEEE 754</i> remainder function.</td>
</tr>
<tr>
<td><b>EUCLID</b></td><td class='centre'>9</td>
<td>
The remainder is always positive. Euclidian division: <br />
<code>q = sign(n) * floor(a / abs(n))</code>
</td>
</tr>
</table>
</dd>
<dd>
The rounding/modulo modes are available as enumerated properties of the BigNumber
constructor.
</dd>
<dd>See <a href='#mod'><code>modulo</code></a>.</dd>
<dd>
<pre>BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
BigNumber.config({ MODULO_MODE: 9 }) // equivalent</pre>
</dd>
<dt id="pow-precision"><code><b>POW_PRECISION</b></code></dt>
<dd>
<i>number</i>: integer, <code>0</code> to <code>1e+9</code> inclusive.<br />
Default value: <code>0</code>
</dd>
<dd>
The <i>maximum</i> precision, i.e. number of significant digits, of the result of the power
operation (unless a modulus is specified).
</dd>
<dd>If set to <code>0</code>, the number of significant digits will not be limited.</dd>
<dd>See <a href='#pow'><code>exponentiatedBy</code></a>.</dd>
<dd><pre>BigNumber.config({ POW_PRECISION: 100 })</pre></dd>
<dt id="format"><code><b>FORMAT</b></code></dt>
<dd><i>object</i></dd>
<dd>
The <code>FORMAT</code> object configures the format of the string returned by the
<a href='#toFor'><code>toFormat</code></a> method.
</dd>
<dd>
The example below shows the properties of the <code>FORMAT</code> object that are
recognised, and their default values.
</dd>
<dd>
Unlike the other configuration properties, the values of the properties of the
<code>FORMAT</code> object will not be checked for validity. The existing
<code>FORMAT</code> object will simply be replaced by the object that is passed in.
The object can include any number of the properties shown below.
</dd>
<dd>See <a href='#toFor'><code>toFormat</code></a> for examples of usage.</dd>
<dd>
<pre>
BigNumber.config({
FORMAT: {
// the decimal separator
decimalSeparator: '.',
// the grouping separator of the integer part
groupSeparator: ',',
// the primary grouping size of the integer part
groupSize: 3,
// the secondary grouping size of the integer part
secondaryGroupSize: 0,
// the grouping separator of the fraction part
fractionGroupSeparator: ' ',
// the grouping size of the fraction part
fractionGroupSize: 0
}
});</pre>
</dd>
<dt id="alphabet"><code><b>ALPHABET</b></code></dt>
<dd>
<i>string</i><br />
Default value: <code>'0123456789abcdefghijklmnopqrstuvwxyz'</code>
</dd>
<dd>
The alphabet used for base conversion. The length of the alphabet corresponds to the
maximum value of the base argument that can be passed to the
<a href='#bignumber'><code>BigNumber</code></a> constructor or
<a href='#toS'><code>toString</code></a>.
</dd>
<dd>
There is no maximum length for the alphabet, but it must be at least 2 characters long, and
it must not contain a repeated character, or <code>'.'</code>, as that is used as the
decimal separator for all values whatever their base.
</dd>
<dd>
<pre>// duodecimal (base 12)
BigNumber.config({ ALPHABET: '0123456789TE' })
x = new BigNumber('T', 12)
x.toString() // '10'
x.toString(12) // 'T'</pre>
</dd>
</dl>
<br /><br />
<p>Returns an object with the above properties and their current values.</p>
<p>
Throws if <code>object</code> is not an object, or if an invalid value is assigned to
one or more of the above properties. See <a href='#Errors'>Errors</a>.
</p>
<pre>
BigNumber.config({
DECIMAL_PLACES: 40,
ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
EXPONENTIAL_AT: [-10, 20],
RANGE: [-500, 500],
CRYPTO: true,
MODULO_MODE: BigNumber.ROUND_FLOOR,
POW_PRECISION: 80,
FORMAT: {
groupSize: 3,
groupSeparator: ' ',
decimalSeparator: ','
},
ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
});
obj = BigNumber.config();
obj.DECIMAL_PLACES // 40
obj.RANGE // [-500, 500]</pre>
<h5 id="isBigNumber">
isBigNumber<code class='inset'>.isBigNumber(value) <i>&rArr; boolean</i></code>
</h5>
<p><code>value</code>: <i>any</i><br /></p>
<p>
Returns <code>true</code> if <code>value</code> is a BigNumber instance, otherwise returns
<code>false</code>.
</p>
<pre>x = 42
y = new BigNumber(x)
BigNumber.isBigNumber(x) // false
y instanceof BigNumber // true
BigNumber.isBigNumber(y) // true
BN = BigNumber.clone();
z = new BN(x)
z instanceof BigNumber // false
BigNumber.isBigNumber(z) // true</pre>
<h5 id="max">
maximum<code class='inset'>.max([arg1 [, arg2, ...]]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>arg1</code>, <code>arg2</code>, ...: <i>number|string|BigNumber</i><br />
<i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>
</p>
<p>
Returns a BigNumber whose value is the maximum of <code>arg1</code>,
<code>arg2</code>,... .
</p>
<p>The argument to this method can also be an array of values.</p>
<p>The return value is always exact and unrounded.</p>
<pre>x = new BigNumber('3257869345.0378653')
BigNumber.maximum(4e9, x, '123456789.9') // '4000000000'
arr = [12, '13', new BigNumber(14)]
BigNumber.max(arr) // '14'</pre>
<h5 id="min">
minimum<code class='inset'>.min([arg1 [, arg2, ...]]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>arg1</code>, <code>arg2</code>, ...: <i>number|string|BigNumber</i><br />
<i>See <code><a href="#bignumber">BigNumber</a></code> for further parameter details.</i>
</p>
<p>
Returns a BigNumber whose value is the minimum of <code>arg1</code>,
<code>arg2</code>,... .
</p>
<p>The argument to this method can also be an array of values.</p>
<p>The return value is always exact and unrounded.</p>
<pre>x = new BigNumber('3257869345.0378653')
BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9'
arr = [2, new BigNumber(-14), '-15.9999', -12]
BigNumber.min(arr) // '-15.9999'</pre>
<h5 id="random">
random<code class='inset'>.random([dp]) <i>&rArr; BigNumber</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 BigNumber 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).<br />
If <code>dp</code> is omitted then the number of decimal places will default to the current
<a href='#decimal-places'><code>DECIMAL_PLACES</code></a> setting.
</p>
<p>
Depending on the value of this BigNumber constructor's
<a href='#crypto'><code>CRYPTO</code></a> setting and the support for the
<code>crypto</code> object in the host environment, the random digits of the return value are
generated by either <code>Math.random</code> (fastest), <code>crypto.getRandomValues</code>
(Web Cryptography API in recent browsers) or <code>crypto.randomBytes</code> (Node.js).
</p>
<p>
If <a href='#crypto'><code>CRYPTO</code></a> is <code>true</code>, i.e. one of the
<code>crypto</code> methods is to be used, the value of a returned BigNumber should be
cryptographically-secure and statistically indistinguishable from a random value.
</p>
<p>
Throws if <code>dp</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>BigNumber.config({ DECIMAL_PLACES: 10 })
BigNumber.random() // '0.4117936847'
BigNumber.random(20) // '0.78193327636914089009'</pre>
<h4 id="constructor-properties">Properties</h4>
<p>
The library's enumerated rounding modes are stored as properties of the constructor.<br />
(They are not referenced internally by the library itself.)
</p>
<p>
Rounding modes <code>0</code> to <code>6</code> (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 id="round-up"><b>ROUND_UP</b></td>
<td class='centre'>0</td>
<td>Rounds away from zero</td>
</tr>
<tr>
<td id="round-down"><b>ROUND_DOWN</b></td>
<td class='centre'>1</td>
<td>Rounds towards zero</td>
</tr>
<tr>
<td id="round-ceil"><b>ROUND_CEIL</b></td>
<td class='centre'>2</td>
<td>Rounds towards <code>Infinity</code></td>
</tr>
<tr>
<td id="round-floor"><b>ROUND_FLOOR</b></td>
<td class='centre'>3</td>
<td>Rounds towards <code>-Infinity</code></td>
</tr>
<tr>
<td id="round-half-up"><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 id="round-half-down"><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 id="round-half-even"><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 id="round-half-ceil"><b>ROUND_HALF_CEIL</b></td>
<td class='centre'>7</td>
<td>
Rounds towards nearest neighbour.<br />
If equidistant, rounds towards <code>Infinity</code>
</td>
</tr>
<tr>
<td id="round-half-floor"><b>ROUND_HALF_FLOOR</b></td>
<td class='centre'>8</td>
<td>
Rounds towards nearest neighbour.<br />
If equidistant, rounds towards <code>-Infinity</code>
</td>
</tr>
</table>
<pre>
BigNumber.config({ ROUNDING_MODE: BigNumber.ROUND_CEIL })
BigNumber.config({ ROUNDING_MODE: 2 }) // equivalent</pre>
<h3>INSTANCE</h3>
<h4 id="prototype-methods">Methods</h4>
<p>The methods inherited by a BigNumber instance from its constructor's prototype object.</p>
<p>A BigNumber is immutable in the sense that it is not changed by its methods. </p>
<p>
The treatment of &plusmn;<code>0</code>, &plusmn;<code>Infinity</code> and <code>NaN</code> is
consistent with how JavaScript treats these values.
</p>
<p>Many method names have a shorter alias.</p>
<h5 id="abs">absoluteValue<code class='inset'>.abs() <i>&rArr; BigNumber</i></code></h5>
<p>
Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of
this BigNumber.
</p>
<p>The return value is always exact and unrounded.</p>
<pre>
x = new BigNumber(-0.8)
y = x.absoluteValue() // '0.8'
z = y.abs() // '0.8'</pre>
<h5 id="cmp">
comparedTo<code class='inset'>.comparedTo(n [, base]) <i>&rArr; number</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</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 BigNumber is greater than the value of <code>n</code></td>
</tr>
<tr>
<td class='centre'><code>-1</code></td>
<td>If the value of this BigNumber is less than the value of <code>n</code></td>
</tr>
<tr>
<td class='centre'><code>0</code></td>
<td>If this BigNumber and <code>n</code> have the same value</td>
</tr>
<tr>
<td class='centre'><code>null</code></td>
<td>If the value of either this BigNumber or <code>n</code> is <code>NaN</code></td>
</tr>
</table>
<pre>
x = new BigNumber(Infinity)
y = new BigNumber(5)
x.comparedTo(y) // 1
x.comparedTo(x.minus(1)) // 0
y.comparedTo(NaN) // null
y.comparedTo('110', 2) // -1</pre>
<h5 id="dp">
decimalPlaces<code class='inset'>.dp([dp [, rm]]) <i>&rArr; BigNumber|number</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>
If <code>dp</code> is a number, returns a BigNumber whose value is the value of this BigNumber
rounded by rounding mode <code>rm</code> to a maximum of <code>dp</code> decimal places.
</p>
<p>
If <code>dp</code> is omitted, or is <code>null</code> or <code>undefined</code>, the return
value is the number of decimal places of the value of this BigNumber, or <code>null</code> if
the value of this BigNumber is &plusmn;<code>Infinity</code> or <code>NaN</code>.
</p>
<p>
If <code>rm</code> is omitted, or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
</p>
<p>
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = new BigNumber(1234.56)
x.decimalPlaces(1) // '1234.6'
x.dp() // 2
x.decimalPlaces(2) // '1234.56'
x.dp(10) // '1234.56'
x.decimalPlaces(0, 1) // '1234'
x.dp(0, 6) // '1235'
x.decimalPlaces(1, 1) // '1234.5'
x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
x // '1234.56'
y = new BigNumber('9.9e-101')
y.dp() // 102</pre>
<h5 id="div">dividedBy<code class='inset'>.div(n [, base]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns a BigNumber whose value is the value of this BigNumber divided by
<code>n</code>, rounded according to the current
<a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.
</p>
<pre>
x = new BigNumber(355)
y = new BigNumber(113)
x.dividedBy(y) // '3.14159292035398230088'
x.div(5) // '71'
x.div(47, 16) // '5'</pre>
<h5 id="divInt">
dividedToIntegerBy<code class='inset'>.idiv(n [, base]) &rArr;
<i>BigNumber</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
<code>n</code>.
</p>
<pre>
x = new BigNumber(5)
y = new BigNumber(3)
x.dividedToIntegerBy(y) // '1'
x.idiv(0.7) // '7'
x.idiv('0.f', 16) // '5'</pre>
<h5 id="pow">
exponentiatedBy<code class='inset'>.pow(n [, m]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i>: integer<br />
<code>m</code>: <i>number|string|BigNumber</i>
</p>
<p>
Returns a BigNumber whose value is the value of this BigNumber exponentiated by
<code>n</code>, i.e. raised to the power <code>n</code>, and optionally modulo a modulus
<code>m</code>.
</p>
<p>
Throws if <code>n</code> is not an integer. See <a href='#Errors'>Errors</a>.
</p>
<p>
If <code>n</code> is negative the result is rounded according to the current
<a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.
</p>
<p>
As the number of digits of the result of the power operation can grow so large so quickly,
e.g. 123.456<sup>10000</sup> has over <code>50000</code> digits, the number of significant
digits calculated is limited to the value of the
<a href='#pow-precision'><code>POW_PRECISION</code></a> setting (unless a modulus
<code>m</code> is specified).
</p>
<p>
By default <a href='#pow-precision'><code>POW_PRECISION</code></a> is set to <code>0</code>.
This means that an unlimited number of significant digits will be calculated, and that the
method's performance will decrease dramatically for larger exponents.
</p>
<p>
If <code>m</code> is specified and the value of <code>m</code>, <code>n</code> and this
BigNumber are integers, and <code>n</code> is positive, then a fast modular exponentiation
algorithm is used, otherwise the operation will be performed as
<code>x.exponentiatedBy(n).modulo(m)</code> with a
<a href='#pow-precision'><code>POW_PRECISION</code></a> of <code>0</code>.
</p>
<pre>
Math.pow(0.7, 2) // 0.48999999999999994
x = new BigNumber(0.7)
x.exponentiatedBy(2) // '0.49'
BigNumber(3).pow(-2) // '0.11111111111111111111'</pre>
<h5 id="int">
integerValue<code class='inset'>.integerValue([rm]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive
</p>
<p>
Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
rounding mode <code>rm</code>.
</p>
<p>
If <code>rm</code> is omitted, or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
</p>
<p>
Throws if <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = new BigNumber(123.456)
x.integerValue() // '123'
x.integerValue(BigNumber.ROUND_CEIL) // '124'
y = new BigNumber(-12.7)
y.integerValue() // '-13'
y.integerValue(BigNumber.ROUND_DOWN) // '-12'</pre>
<p>
The following is an example of how to add a prototype method that emulates JavaScript's
<code>Math.round</code> function. <code>Math.ceil</code>, <code>Math.floor</code> and
<code>Math.trunc</code> can be emulated in the same way with
<code>BigNumber.ROUND_CEIL</code>, <code>BigNumber.ROUND_FLOOR</code> and
<code> BigNumber.ROUND_DOWN</code> respectively.
</p>
<pre>
BigNumber.prototype.round = function (n) {
return n.integerValue(BigNumber.ROUND_HALF_CEIL);
};
x.round() // '123'</pre>
<h5 id="eq">isEqualTo<code class='inset'>.eq(n [, base]) <i>&rArr; boolean</i></code></h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this BigNumber is equal to the value of
<code>n</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 <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
<pre>
0 === 1e-324 // true
x = new BigNumber(0)
x.isEqualTo('1e-324') // false
BigNumber(-0).eq(x) // true ( -0 === 0 )
BigNumber(255).eq('ff', 16) // true
y = new BigNumber(NaN)
y.isEqualTo(NaN) // false</pre>
<h5 id="isF">isFinite<code class='inset'>.isFinite() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this BigNumber is a finite number, otherwise
returns <code>false</code>.
</p>
<p>
The only possible non-finite values of a BigNumber are <code>NaN</code>, <code>Infinity</code>
and <code>-Infinity</code>.
</p>
<pre>
x = new BigNumber(1)
x.isFinite() // true
y = new BigNumber(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="gt">isGreaterThan<code class='inset'>.gt(n [, base]) <i>&rArr; boolean</i></code></h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this BigNumber is greater than the value of
<code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
<pre>
0.1 &gt; (0.3 - 0.2) // true
x = new BigNumber(0.1)
x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false
BigNumber(0).gt(x) // false
BigNumber(11, 3).gt(11.1, 2) // true</pre>
<h5 id="gte">
isGreaterThanOrEqualTo<code class='inset'>.gte(n [, base]) <i>&rArr; boolean</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this BigNumber is greater than or equal to the value
of <code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
<pre>
(0.3 - 0.2) &gt;= 0.1 // false
x = new BigNumber(0.3).minus(0.2)
x.isGreaterThanOrEqualTo(0.1) // true
BigNumber(1).gte(x) // true
BigNumber(10, 18).gte('i', 36) // true</pre>
<h5 id="isInt">isInteger<code class='inset'>.isInteger() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this BigNumber is an integer, otherwise returns
<code>false</code>.
</p>
<pre>
x = new BigNumber(1)
x.isInteger() // true
y = new BigNumber(123.456)
y.isInteger() // false</pre>
<h5 id="lt">isLessThan<code class='inset'>.lt(n [, base]) <i>&rArr; boolean</i></code></h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this BigNumber is less than the value of
<code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
<pre>
(0.3 - 0.2) &lt; 0.1 // true
x = new BigNumber(0.3).minus(0.2)
x.isLessThan(0.1) // false
BigNumber(0).lt(x) // true
BigNumber(11.1, 2).lt(11, 3) // true</pre>
<h5 id="lte">
isLessThanOrEqualTo<code class='inset'>.lte(n [, base]) <i>&rArr; boolean</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns <code>true</code> if the value of this BigNumber is less than or equal to the value of
<code>n</code>, otherwise returns <code>false</code>.
</p>
<p>Note: This method uses the <a href='#cmp'><code>comparedTo</code></a> method internally.</p>
<pre>
0.1 &lt;= (0.3 - 0.2) // false
x = new BigNumber(0.1)
x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true
BigNumber(-1).lte(x) // true
BigNumber(10, 18).lte('i', 36) // true</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 BigNumber is <code>NaN</code>, otherwise
returns <code>false</code>.
</p>
<pre>
x = new BigNumber(NaN)
x.isNaN() // true
y = new BigNumber('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'>.isNegative() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this BigNumber is negative, otherwise returns
<code>false</code>.
</p>
<pre>
x = new BigNumber(-0)
x.isNegative() // true
y = new BigNumber(2)
y.isNegative() // 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'>.isPositive() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this BigNumber is positive, otherwise returns
<code>false</code>.
</p>
<pre>
x = new BigNumber(-0)
x.isPositive() // false
y = new BigNumber(2)
y.isPositive() // true</pre>
<h5 id="isZ">isZero<code class='inset'>.isZero() <i>&rArr; boolean</i></code></h5>
<p>
Returns <code>true</code> if the value of this BigNumber is zero or minus zero, otherwise
returns <code>false</code>.
</p>
<pre>
x = new BigNumber(-0)
x.isZero() && x.isneg() // true
y = new BigNumber(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="minus">
minus<code class='inset'>.minus(n [, base]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>Returns a BigNumber whose value is the value of this BigNumber minus <code>n</code>.</p>
<p>The return value is always exact and unrounded.</p>
<pre>
0.3 - 0.1 // 0.19999999999999998
x = new BigNumber(0.3)
x.minus(0.1) // '0.2'
x.minus(0.6, 20) // '0'</pre>
<h5 id="mod">modulo<code class='inset'>.mod(n [, base]) <i>&rArr; BigNumber</i></code></h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns a BigNumber whose value is the value of this BigNumber modulo <code>n</code>, i.e.
the integer remainder of dividing this BigNumber by <code>n</code>.
</p>
<p>
The value returned, and in particular its sign, is dependent on the value of the
<a href='#modulo-mode'><code>MODULO_MODE</code></a> setting of this BigNumber constructor.
If it is <code>1</code> (default value), the result will have the same sign as this BigNumber,
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>The return value is always exact and unrounded.</p>
<p>
See <a href='#modulo-mode'><code>MODULO_MODE</code></a> for a description of the other
modulo modes.
</p>
<pre>
1 % 0.9 // 0.09999999999999998
x = new BigNumber(1)
x.modulo(0.9) // '0.1'
y = new BigNumber(33)
y.mod('a', 33) // '3'</pre>
<h5 id="times">
multipliedBy<code class='inset'>.times(n [, base]) <i>&rArr; BigNumber</i></code>
</h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>
Returns a BigNumber whose value is the value of this BigNumber multiplied by <code>n</code>.
</p>
<p>The return value is always exact and unrounded.</p>
<pre>
0.6 * 3 // 1.7999999999999998
x = new BigNumber(0.6)
y = x.multipliedBy(3) // '1.8'
BigNumber('7e+500').times(y) // '1.26e+501'
x.multipliedBy('-a', 16) // '-6'</pre>
<h5 id="neg">negated<code class='inset'>.negated() <i>&rArr; BigNumber</i></code></h5>
<p>
Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by
<code>-1</code>.
</p>
<pre>
x = new BigNumber(1.8)
x.negated() // '-1.8'
y = new BigNumber(-1.3)
y.negated() // '1.3'</pre>
<h5 id="plus">plus<code class='inset'>.plus(n [, base]) <i>&rArr; BigNumber</i></code></h5>
<p>
<code>n</code>: <i>number|string|BigNumber</i><br />
<code>base</code>: <i>number</i><br />
<i>See <a href="#bignumber">BigNumber</a> for further parameter details.</i>
</p>
<p>Returns a BigNumber whose value is the value of this BigNumber plus <code>n</code>.</p>
<p>The return value is always exact and unrounded.</p>
<pre>
0.1 + 0.2 // 0.30000000000000004
x = new BigNumber(0.1)
y = x.plus(0.2) // '0.3'
BigNumber(0.7).plus(x).plus(y) // '1'
x.plus('0.1', 8) // '0.225'</pre>
<h5 id="sd">
precision<code class='inset'>.sd([d [, rm]]) <i>&rArr; BigNumber|number</i></code>
</h5>
<p>
<code>d</code>: <i>number|boolean</i>: integer, <code>1</code> to <code>1e+9</code>
inclusive, or <code>true</code> or <code>false</code><br />
<code>rm</code>: <i>number</i>: integer, <code>0</code> to <code>8</code> inclusive.
</p>
<p>
If <code>d</code> is a number, returns a BigNumber whose value is the value of this BigNumber
rounded to a precision of <code>d</code> significant digits using rounding mode
<code>rm</code>.
</p>
<p>
If <code>d</code> is omitted or is <code>null</code> or <code>undefined</code>, the return
value is the number of significant digits of the value of this BigNumber, or <code>null</code>
if the value of this BigNumber is &plusmn;<code>Infinity</code> or <code>NaN</code>.</p>
</p>
<p>
If <code>d</code> is <code>true</code> then any trailing zeros of the integer
part of a number are counted as significant digits, otherwise they are not.
</p>
<p>
If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> will be used.
</p>
<p>
Throws if <code>d</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = new BigNumber(9876.54321)
x.precision(6) // '9876.54'
x.sd() // 9
x.precision(6, BigNumber.ROUND_UP) // '9876.55'
x.sd(2) // '9900'
x.precision(2, 1) // '9800'
x // '9876.54321'
y = new BigNumber(987000)
y.precision() // 3
y.sd(true) // 6</pre>
<h5 id="shift">shiftedBy<code class='inset'>.shiftedBy(n) <i>&rArr; BigNumber</i></code></h5>
<p>
<code>n</code>: <i>number</i>: integer,
<code>-9007199254740991</code> to <code>9007199254740991</code> inclusive
</p>
<p>
Returns a BigNumber whose value is the value of this BigNumber shifted by <code>n</code>
places.
<p>
The shift is of the decimal point, i.e. of powers of ten, and is to the left if <code>n</code>
is negative or to the right if <code>n</code> is positive.
</p>
<p>The return value is always exact and unrounded.</p>
<p>
Throws if <code>n</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = new BigNumber(1.23)
x.shiftedBy(3) // '1230'
x.shiftedBy(-3) // '0.00123'</pre>
<h5 id="sqrt">squareRoot<code class='inset'>.sqrt() <i>&rArr; BigNumber</i></code></h5>
<p>
Returns a BigNumber whose value is the square root of the value of this BigNumber,
rounded according to the current
<a href='#decimal-places'><code>DECIMAL_PLACES</code></a> and
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.
</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 BigNumber(16)
x.squareRoot() // '4'
y = new BigNumber(3)
y.sqrt() // '1.73205080756887729353'</pre>
<h5 id="toE">
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 BigNumber 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 BigNumber 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, or is <code>null</code> or <code>undefined</code>, the number
of digits after the decimal point defaults to the minimum number of digits necessary to
represent the value exactly.<br />
If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
</p>
<p>
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = 45.6
y = new BigNumber(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="toFix">
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 BigNumber 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 BigNumber 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 or is <code>null</code> or <code>undefined</code>, the return
value will be unrounded and in normal notation. This is also unlike
<code>Number.prototype.toFixed</code>, which returns the value to zero decimal places.<br />
It is useful when fixed-point notation is required and the current
<a href="#exponential-at"><code>EXPONENTIAL_AT</code></a> setting causes
<code><a href='#toS'>toString</a></code> to return exponential notation.<br />
If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
</p>
<p>
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = 3.456
y = new BigNumber(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="toFor">
toFormat<code class='inset'>.toFormat([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>
<p>
Returns a string representing the value of this BigNumber in normal (fixed-point) notation
rounded to <code>dp</code> decimal places using rounding mode <code>rm</code>, and formatted
according to the properties of the <a href='#format'><code>FORMAT</code></a> object.
</p>
<p>
See the examples below for the properties of the
<a href='#format'><code>FORMAT</code></a> object, their types and their usage.
</p>
<p>
If <code>dp</code> is omitted or is <code>null</code> or <code>undefined</code>, then the
return value is not rounded to a fixed number of decimal places.<br />
If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
</p>
<p>
Throws if <code>dp</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
format = {
decimalSeparator: '.',
groupSeparator: ',',
groupSize: 3,
secondaryGroupSize: 0,
fractionGroupSeparator: ' ',
fractionGroupSize: 0
}
BigNumber.config({ FORMAT: format })
x = new BigNumber('123456789.123456789')
x.toFormat() // '123,456,789.123456789'
x.toFormat(1) // '123,456,789.1'
// If a reference to the object assigned to FORMAT has been retained,
// the format properties can be changed directly
format.groupSeparator = ' '
format.fractionGroupSize = 5
x.toFormat() // '123 456 789.12345 6789'
BigNumber.config({
FORMAT: {
decimalSeparator: ',',
groupSeparator: '.',
groupSize: 3,
secondaryGroupSize: 2
}
})
x.toFormat(6) // '12.34.56.789,123'</pre>
<h5 id="toFr">
toFraction<code class='inset'>.toFraction([max]) <i>&rArr; [string, string]</i></code>
</h5>
<p>
<code>max</code>: <i>number|string|BigNumber</i>: integer &gt;= <code>1</code> and &lt;=
<code>Infinity</code>
</p>
<p>
Returns a string array representing the value of this BigNumber 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</code>.
</p>
<p>
If a maximum denominator, <code>max</code>, is not specified, or is <code>null</code> or
<code>undefined</code>, the denominator will be the lowest value necessary to represent the
number exactly.
</p>
<p>
Throws if <code>max</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = new BigNumber(1.75)
x.toFraction() // '7, 4'
pi = new BigNumber('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="toJSON">toJSON<code class='inset'>.toJSON() <i>&rArr; string</i></code></h5>
<p>As <code>valueOf</code>.</p>
<pre>
x = new BigNumber('177.7e+457')
y = new BigNumber(235.4325)
z = new BigNumber('0.0098074')
// Serialize an array of three BigNumbers
str = JSON.stringify( [x, y, z] )
// "["1.777e+459","235.4325","0.0098074"]"
// Return an array of three BigNumbers
JSON.parse(str, function (key, val) {
return key === '' ? val : new BigNumber(val)
})</pre>
<h5 id="toN">toNumber<code class='inset'>.toNumber() <i>&rArr; number</i></code></h5>
<p>Returns the value of this BigNumber as a JavaScript number primitive.</p>
<p>
This method is identical to using type coercion with the unary plus operator.
</p>
<pre>
x = new BigNumber(456.789)
x.toNumber() // 456.789
+x // 456.789
y = new BigNumber('45987349857634085409857349856430985')
y.toNumber() // 4.598734985763409e+34
z = new BigNumber(-0)
1 / z.toNumber() // -Infinity
1 / +z // -Infinity</pre>
<h5 id="toP">
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 BigNumber 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, or is <code>null</code> or <code>undefined</code>, then the
return value is the same as <code>n.toString()</code>.<br />
If <code>rm</code> is omitted or is <code>null</code> or <code>undefined</code>,
<a href='#rounding-mode'><code>ROUNDING_MODE</code></a> is used.
</p>
<p>
Throws if <code>sd</code> or <code>rm</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = 45.6
y = new BigNumber(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="toS">toString<code class='inset'>.toString([base]) <i>&rArr; string</i></code></h5>
<p>
<code>base</code>: <i>number</i>: integer, <code>2</code> to <code>ALPHABET.length</code>
inclusive (see <a href='#alphabet'><code>ALPHABET</code></a>).
</p>
<p>
Returns a string representing the value of this BigNumber in the specified base, or base
<code>10</code> if <code>base</code> is omitted or is <code>null</code> or
<code>undefined</code>.
</p>
<p>
For bases above <code>10</code>, and using the default base conversion alphabet
(see <a href='#alphabet'><code>ALPHABET</code></a>), values from <code>10</code> to
<code>35</code> are represented by <code>a-z</code>
(as with <code>Number.prototype.toString</code>).
</p>
<p>
If a base is specified the value is rounded according to the current
<a href='#decimal-places'><code>DECIMAL_PLACES</code></a>
and <a href='#rounding-mode'><code>ROUNDING_MODE</code></a> settings.
</p>
<p>
If a base is not specified, and this BigNumber has a positive
exponent that is equal to or greater than the positive component of the
current <a href="#exponential-at"><code>EXPONENTIAL_AT</code></a> setting,
or a negative exponent equal to or less than the negative component of the
setting, then exponential notation is returned.
</p>
<p>If <code>base</code> is <code>null</code> or <code>undefined</code> it is ignored.</p>
<p>
Throws if <code>base</code> is invalid. See <a href='#Errors'>Errors</a>.
</p>
<pre>
x = new BigNumber(750000)
x.toString() // '750000'
BigNumber.config({ EXPONENTIAL_AT: 5 })
x.toString() // '7.5e+5'
y = new BigNumber(362.875)
y.toString(2) // '101101010.111'
y.toString(9) // '442.77777777777777777778'
y.toString(32) // 'ba.s'
BigNumber.config({ DECIMAL_PLACES: 4 });
z = new BigNumber('1.23456789')
z.toString() // '1.23456789'
z.toString(10) // '1.2346'</pre>
<h5 id="valueOf">valueOf<code class='inset'>.valueOf() <i>&rArr; string</i></code></h5>
<p>
As <code>toString</code>, but does not accept a base argument and includes the minus sign
for negative zero.
</p>
<pre>
x = new BigNumber('-0')
x.toString() // '0'
x.valueOf() // '-0'
y = new BigNumber('1.777e+457')
y.valueOf() // '1.777e+457'</pre>
<h4 id="instance-properties">Properties</h4>
<p>The properties of a BigNumber instance:</p>
<table>
<tr>
<th>Property</th>
<th>Description</th>
<th>Type</th>
<th>Value</th>
</tr>
<tr>
<td class='centre' id='coefficient'><b>c</b></td>
<td>coefficient<sup>*</sup></td>
<td><i>number</i><code>[]</code></td>
<td> Array of base <code>1e14</code> numbers</td>
</tr>
<tr>
<td class='centre' id='exponent'><b>e</b></td>
<td>exponent</td>
<td><i>number</i></td>
<td>Integer, <code>-1000000000</code> to <code>1000000000</code> inclusive</td>
</tr>
<tr>
<td class='centre' id='sign'><b>s</b></td>
<td>sign</td>
<td><i>number</i></td>
<td><code>-1</code> or <code>1</code></td>
</tr>
</table>
<p><sup>*</sup>significand</p>
<p>
The value of any of the <code>c</code>, <code>e</code> and <code>s</code> properties may also
be <code>null</code>.
</p>
<p>
The above properties are best considered to be read-only. In early versions of this library it
was okay to change the exponent of a BigNumber by writing to its exponent property directly,
but this is no longer reliable as the value of the first element of the coefficient array is
now dependent on the exponent.
</p>
<p>
Note that, as with JavaScript numbers, the original exponent and fractional trailing zeros are
not necessarily preserved.
</p>
<pre>x = new BigNumber(0.123) // '0.123'
x.toExponential() // '1.23e-1'
x.c // '1,2,3'
x.e // -1
x.s // 1
y = new Number(-123.4567000e+2) // '-12345.67'
y.toExponential() // '-1.234567e+4'
z = new BigNumber('-123.4567000e+2') // '-12345.67'
z.toExponential() // '-1.234567e+4'
z.c // '1,2,3,4,5,6,7'
z.e // 4
z.s // -1</pre>
<h4 id="zero-nan-infinity">Zero, NaN and Infinity</h4>
<p>
The table below shows how &plusmn;<code>0</code>, <code>NaN</code> and
&plusmn;<code>Infinity</code> are stored.
</p>
<table>
<tr>
<th> </th>
<th class='centre'>c</th>
<th class='centre'>e</th>
<th class='centre'>s</th>
</tr>
<tr>
<td>&plusmn;0</td>
<td><code>[0]</code></td>
<td><code>0</code></td>
<td><code>&plusmn;1</code></td>
</tr>
<tr>
<td>NaN</td>
<td><code>null</code></td>
<td><code>null</code></td>
<td><code>null</code></td>
</tr>
<tr>
<td>&plusmn;Infinity</td>
<td><code>null</code></td>
<td><code>null</code></td>
<td><code>&plusmn;1</code></td>
</tr>
</table>
<pre>
x = new Number(-0) // 0
1 / x == -Infinity // true
y = new BigNumber(-0) // '0'
y.c // '0' ( [0].toString() )
y.e // 0
y.s // -1</pre>
<h4 id='Errors'>Errors</h4>
<p>The table below shows the errors that are thrown.</p>
<p>
The errors are generic <code>Error</code> objects whose message begins
<code>'[BigNumber Error]'</code>.
</p>
<table class='error-table'>
<tr>
<th>Method</th>
<th>Throws</th>
</tr>
<tr>
<td rowspan=6>
<code>BigNumber</code><br />
<code>comparedTo</code><br />
<code>dividedBy</code><br />
<code>dividedToIntegerBy</code><br />
<code>isEqualTo</code><br />
<code>isGreaterThan</code><br />
<code>isGreaterThanOrEqualTo</code><br />
<code>isLessThan</code><br />
<code>isLessThanOrEqualTo</code><br />
<code>minus</code><br />
<code>modulo</code><br />
<code>plus</code><br />
<code>multipliedBy</code>
</td>
<td>Base not a primitive number</td>
</tr>
<tr>
<td>Base not an integer</td>
</tr>
<tr>
<td>Base out of range</td>
</tr>
<tr>
<td>Number primitive has more than 15 significant digits<sup>*</sup></td>
</tr>
<tr>
<td>Not a base... number<sup>*</sup></td>
</tr>
<tr>
<td>Not a number<sup>*</sup></td>
</tr>
<tr>
<td><code>clone</code></td>
<td>Object expected</td>
</tr>
<tr>
<td rowspan=24><code>config</code></td>
<td>Object expected</td>
</tr>
<tr>
<td><code>DECIMAL_PLACES</code> not a primitive number</td>
</tr>
<tr>
<td><code>DECIMAL_PLACES</code> not an integer</td>
</tr>
<tr>
<td><code>DECIMAL_PLACES</code> out of range</td>
</tr>
<tr>
<td><code>ROUNDING_MODE</code> not a primitive number</td>
</tr>
<tr>
<td><code>ROUNDING_MODE</code> not an integer</td>
</tr>
<tr>
<td><code>ROUNDING_MODE</code> out of range</td>
</tr>
<tr>
<td><code>EXPONENTIAL_AT</code> not a primitive number</td>
</tr>
<tr>
<td><code>EXPONENTIAL_AT</code> not an integer</td>
</tr>
<tr>
<td><code>EXPONENTIAL_AT</code> out of range</td>
</tr>
<tr>
<td><code>RANGE</code> not a primitive number</td>
</tr>
<tr>
<td><code>RANGE</code> not an integer</td>
</tr>
<tr>
<td><code>RANGE</code> cannot be zero</td>
</tr>
<tr>
<td><code>RANGE</code> cannot be zero</td>
</tr>
<tr>
<td><code>CRYPTO</code> not true or false</td>
</tr>
<tr>
<td><code>crypto</code> unavailable</td>
</tr>
<tr>
<td><code>MODULO_MODE</code> not a primitive number</td>
</tr>
<tr>
<td><code>MODULO_MODE</code> not an integer</td>
</tr>
<tr>
<td><code>MODULO_MODE</code> out of range</td>
</tr>
<tr>
<td><code>POW_PRECISION</code> not a primitive number</td>
</tr>
<tr>
<td><code>POW_PRECISION</code> not an integer</td>
</tr>
<tr>
<td><code>POW_PRECISION</code> out of range</td>
</tr>
<tr>
<td><code>FORMAT</code> not an object</td>
</tr>
<tr>
<td><code>ALPHABET</code> invalid</td>
</tr>
<tr>
<td rowspan=3>
<code>decimalPlaces</code><br />
<code>precision</code><br />
<code>random</code><br />
<code>shiftedBy</code><br />
<code>toExponential</code><br />
<code>toFixed</code><br />
<code>toFormat</code><br />
<code>toPrecision</code>
</td>
<td>Argument not a primitive number</td>
</tr>
<tr>
<td>Argument not an integer</td>
</tr>
<tr>
<td>Argument out of range</td>
</tr>
<tr>
<td>
<code>decimalPlaces</code><br />
<code>precision</code>
</td>
<td>Argument not true or false</td>
</tr>
<tr>
<td><code>exponentiatedBy</code></td>
<td>Argument not an integer</td>
</tr>
<tr>
<td>
<code>minimum</code><br />
<code>maximum</code>
</td>
<td>Not a number<sup>*</sup></td>
</tr>
<tr>
<td>
<code>random</code>
</td>
<td>crypto unavailable</td>
</tr>
<tr>
<td rowspan=2><code>toFraction</code></td>
<td>Argument not an integer</td>
</tr>
<tr>
<td>Argument out of range</td>
</tr>
<tr>
<td rowspan=3><code>toString</code></td>
<td>Base not a primitive number</td>
</tr>
<tr>
<td>Base not an integer</td>
</tr>
<tr>
<td>Base out of range</td>
</tr>
</table>
<p><sup>*</sup>Only thrown if <code>BigNumber.DEBUG</code> is <code>true</code>.</p>
<p>To determine if an exception is a BigNumber Error:</p>
<pre>
try {
// ...
} catch (e) {
if (e instanceof Error && e.message.indexOf('[BigNumber Error]') === 0) {
// ...
}
}</pre>
<h4 id='faq'>FAQ</h4>
<h6>Why are trailing fractional zeros removed from BigNumbers?</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>

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nodered/rootfs/data/node_modules/bignumber.js/package.json generated vendored Normal file
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{
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"_id": "bignumber.js@7.2.1",
"_inBundle": false,
"_integrity": "sha512-S4XzBk5sMB+Rcb/LNcpzXr57VRTxgAvaAEDAl1AwRx27j00hT84O6OkteE7u8UB3NuaaygCRrEpqox4uDOrbdQ==",
"_location": "/bignumber.js",
"_phantomChildren": {},
"_requested": {
"type": "version",
"registry": true,
"raw": "bignumber.js@7.2.1",
"name": "bignumber.js",
"escapedName": "bignumber.js",
"rawSpec": "7.2.1",
"saveSpec": null,
"fetchSpec": "7.2.1"
},
"_requiredBy": [
"/mysql"
],
"_resolved": "https://registry.npmjs.org/bignumber.js/-/bignumber.js-7.2.1.tgz",
"_shasum": "80c048759d826800807c4bfd521e50edbba57a5f",
"_spec": "bignumber.js@7.2.1",
"_where": "/data/node_modules/mysql",
"author": {
"name": "Michael Mclaughlin",
"email": "M8ch88l@gmail.com"
},
"browser": "bignumber.js",
"bugs": {
"url": "https://github.com/MikeMcl/bignumber.js/issues"
},
"bundleDependencies": false,
"deprecated": false,
"description": "A library for arbitrary-precision decimal and non-decimal arithmetic",
"engines": {
"node": "*"
},
"homepage": "https://github.com/MikeMcl/bignumber.js#readme",
"keywords": [
"arbitrary",
"precision",
"arithmetic",
"big",
"number",
"decimal",
"float",
"biginteger",
"bigdecimal",
"bignumber",
"bigint",
"bignum"
],
"license": "MIT",
"main": "bignumber",
"module": "bignumber.mjs",
"name": "bignumber.js",
"repository": {
"type": "git",
"url": "git+https://github.com/MikeMcl/bignumber.js.git"
},
"scripts": {
"build": "uglifyjs bignumber.js --source-map bignumber.js.map -c -m -o bignumber.min.js --preamble \"/* bignumber.js v7.2.1 https://github.com/MikeMcl/bignumber.js/LICENCE */\"",
"test": "node test/test"
},
"types": "bignumber.d.ts",
"version": "7.2.1"
}