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

Note: This is version 2 of the library, for version 1.x.x see the tagged releases or switch to the 'original' branch. The advantages of version 2 are that it is considerably faster for numbers with many digits and that there are a few added methods (see Change Log below). The disadvantages are more lines of code and increased code complexity, and the loss of simplicity in no longer having the coefficient of a BigNumber stored in base 10. The 'original' version will continue to be supported.

• Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
• 6 KB minified and gzipped
• Simple API but full-featured
• Works with numbers with or without fraction digits in bases from 2 to 64 inclusive
• Replicates the toExponential, toFixed, toPrecision and toString methods of JavaScript's Number type
• Includes a toFraction and a correctly-rounded squareRoot method
• No dependencies
• ECMAScript 3 compliant
• Comprehensive documentation and test set

If an even smaller and simpler library is required see big.js. It's 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.

The library is the single JavaScript file bignumber.js (or minified, bignumber.min.js).

It can be loaded via a script tag in an HTML document for the browser

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

or as a CommonJS, Node.js or AMD module using require.

For Node, put the bignumber.js file into the same directory as the file that is requiring it and use

var BigNumber = require('./bignumber.js');

or put it in a node_modules directory within the directory and use require('bignumber.js').

The library is also available from the npm registry, so

$ npm install bignumber.js

will install this directory in a node_modules directory within the current directory.

To load with AMD loader libraries such as requireJS:

require(['path/to/bignumber'], function(BigNumber) {  
    // Use BigNumber here in local scope. No global BigNumber.
});

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 (up to 15 significant digits only), String or BigNumber Object,

x = new BigNumber(123.4567)
y = BigNumber('123456.7e-3')                     // 'new' is optional
z = new BigNumber(x)
x.equals(y) && y.equals(z) && x.equals(z)        // true

and a base from 2 to 64 inclusive can be specified.

x = new BigNumber(1011, 2)           // "11"
y = new BigNumber('zz.9', 36)        // "1295.25"
z = x.plus(y)                        // "1306.25"

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

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.

x.dividedBy(y).plus(z).times(9).floor()
x.times('1.23456780123456789e+9').plus(9876.5432321).dividedBy('4444562598.111772').ceil()

Many method names have a shorter alias.

x.squareRoot().dividedBy(y).toPower(3).equals(x.sqrt().div(y).pow(3))         // true
x.cmp(y.mod(z).neg()) == 1 && x.comparedTo(y.modulo(z).negated()) == 1        // true

Like JavaScript's Number type, there are toExponential, toFixed and toPrecision methods

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.

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

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

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.

BigNumber.config({ DECIMAL_PLACES: 10, ROUNDING_MODE: 4 })
// Alternatively, BigNumber.config( 10, 4 );

x = new BigNumber(2);
y = new BigNumber(3);
z = x.div(y)                 // "0.6666666667"
z.sqrt()                     // "0.8164965809"
z.pow(-3)                    // "3.3749999995"
z.toString(2)                // "0.1010101011"
z.times(z)                   // "0.44444444448888888889"
z.times(z).round(10)         // "0.4444444445"

There is a toFraction method with an optional maximum denominator argument

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.

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.

x = new BigNumber(-123.456);
x.c                            // [ 123, 45600000000000 ]  coefficient (i.e. significand)
x.e                            // 2                        exponent
x.s                            // -1                       sign

For futher information see the API reference from the doc folder.

The test directory contains the test scripts for each method.

The tests can be run with Node or a browser. For Node use

$ npm test

or

$ node test/every-test

To test a single method

$ node test/toFraction

For the browser, see every-test.html and single-test.html in the test/browser directory.

bignumber-vs-number.html enables some of the methods of bignumber.js to be compared with those of JavaScript's Number type.

The perf directory contains two applications and a lib directory containing the BigDecimal libraries used by both.

bignumber-vs-bigdecimal.html tests the performance of bignumber.js against the JavaScript translations of two versions of BigDecimal, its use should be more or less self-explanatory. (The GWT version doesn't work in IE 6.)

• GWT: java.math.BigDecimal https://github.com/iriscouch/bigdecimal.js
• ICU4J: com.ibm.icu.math.BigDecimal https://github.com/dtrebbien/BigDecimal.js

The BigDecimal in Node's npm registry is the GWT version. Despite its seeming popularity I have found it to have some serious bugs, see the Node script perf/lib/bigdecimal_GWT/bugs.js for examples of flaws in its remainder, divide and compareTo methods.

bigtime.js is a Node command-line application which tests the performance of bignumber.js against the GWT version of BigDecimal from the npm registry.

For example, to compare the time taken by the bignumber.js plus method and the BigDecimal add method:

$ node bigtime plus 10000 40

This will time 10000 calls to each, using operands of up to 40 random digits and will check that the results match.

For help:

$ node bigtime -h

See the README in the directory for more information.

I.e. minify.

For Node, if uglify-js is installed globally ( npm install uglify-js -g ) then

npm run build

will create bignumber.min.js.

Open an issue, or email

Michael [email protected]

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Thank you

MIT.

See LICENCE.

####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