A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.

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 and test set

If a smaller and simpler library is required see big.js. It's less than half the size but only works with decimal numbers and only has half the methods. It also has fewer configuration options than this library, and does not allow NaN or Infinity.

See also 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 ES module bignumber.mjs.

Browser

<script src='path/to/bignumber.js'></script>

ES module

<script type="module">
import BigNumber from './path/to/bignumber.mjs';

Get a minified version from a CDN:

<script src='https://cdn.jsdelivr.net/npm/[email protected]/bignumber.min.js'></script>

Node.js

npm install bignumber.js

const BigNumber = require('bignumber.js');

ES module

import BigNumber from "bignumber.js";
import { BigNumber } from "./node_modules/bignumber.js/bignumber.mjs";

Deno

import BigNumber from 'https://raw.githubusercontent.com/mikemcl/bignumber.js/v9.1.0/bignumber.mjs';
import BigNumber from 'https://unpkg.com/bignumber.js@latest/bignumber.mjs';

Use

The library exports a single constructor function, BigNumber, which accepts a value of type Number, String or BigNumber,

let x = new BigDecimal(123.4567);
let y = BigDecimal('123456.7e-3');
let z = new BigDecimal(x);
x.isEqualTo(y) && y.isEqualTo(z) && x.isEqualTo(z);      // true

To get the string value of a BigNumber use toString() or toFixed(). Using toFixed() prevents exponential notation being returned, no matter how large or small the value.

let x = new BigDecimal('1111222233334444555566');
x.toString();                       // "1.111222233334444555566e+21"
x.toFixed();                        // "1111222233334444555566"

If the limited precision of Number values is not well understood, it is recommended to create BigNumbers from String values rather than Number values to avoid a potential loss of precision.

In all further examples below, let, 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.

// Precision loss from using numeric literals with more than 15 significant digits.
new BigDecimal(1.0000000000000001)         // '1'
new BigDecimal(88259496234518.57)          // '88259496234518.56'
new BigDecimal(99999999999999999999)       // '100000000000000000000'

// Precision loss from using numeric literals outside the range of Number values.
new BigDecimal(2e+308)                     // 'Infinity'
new BigDecimal(1e-324)                     // '0'

// Precision loss from the unexpected result of arithmetic with Number values.
new BigDecimal(0.7 + 0.1)                  // '0.7999999999999999'

When creating a BigNumber from a Number, 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.

new BigDecimal(Number.MAX_VALUE.toString(2), 2)

BigNumbers can be created from values in bases from 2 to 36. See ALPHABET to extend this range.

a = new BigDecimal(1011, 2)          // "11"
b = new BigDecimal('zz.9', 36)       // "1295.25"
c = a.plus(b)                       // "1306.25"

Performance is better if base 10 is NOT specified for decimal values. Only specify base 10 when you want to limit the number of decimal places of the input value to the current DECIMAL_PLACES setting.

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

0.3 - 0.1                           // 0.19999999999999998
x = new BigDecimal(0.3)
x.minus(0.1)                        // "0.2"
x                                   // "0.3"

The methods that return a BigNumber can be chained.

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.

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.

x = new BigDecimal(255.5)
x.toExponential(5)                  // "2.55500e+2"
x.toFixed(5)                        // "255.50000"
x.toPrecision(5)                    // "255.50"
x.toNumber()                        //  255.5

A base can be specified for toString.

Performance is better if base 10 is NOT specified, i.e. use toString() not toString(10). Only specify base 10 when you want to limit the number of decimal places of the string to the current DECIMAL_PLACES setting.

x.toString(16)                     // "ff.8"

There is a toFormat method which may be useful for internationalisation.

y = new BigDecimal('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 set or config method of the BigNumber constructor.

The other arithmetic operations always give the exact result.

BigDecimal.set({DECIMAL_PLACES: 10, ROUNDING_MODE: 4})

x = new BigDecimal(2)
y = new BigDecimal(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

y = new BigDecimal(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.

x = new BigDecimal(NaN)                                           // "NaN"
y = new BigDecimal(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.

x = new BigDecimal(-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 its own independent configuration.

// Set DECIMAL_PLACES for the original BigNumber constructor
BigDecimal.set({DECIMAL_PLACES: 10})

// Create another BigNumber constructor, optionally passing in a configuration object
BN = BigDecimal.clone({DECIMAL_PLACES: 5})

x = new BigDecimal(1)
y = new BN(1)

x.div(3)                            // '0.3333333333'
y.div(3)                            // '0.33333'

To avoid having to call toString or valueOf on a BigNumber to get its value in the Node.js REPL or when using console.log use

BigDecimal.prototype[require('util').inspect.custom] = BigDecimal.prototype.valueOf;

For further information see the API 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.

Minify

To minify using, for example, terser

npm install -g terser

terser big.js -c -m -o big.min.js

Licence

The MIT Licence.

See LICENCE.