A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.
[](https://travis-ci.org/MikeMcl/bignumber.js)
## 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
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
```
[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
M8ch88l@gmail.com
## Licence
The MIT Licence.
See [LICENCE](https://github.com/MikeMcl/bignumber.js/blob/master/LICENCE).