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# bignumber.js #

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

  - Faster, smaller, and perhaps easier to use than JavaScript versions of Java's BigDecimal
  - 5 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
  - Stores values in an accessible decimal floating point format
  - No dependencies
  - Comprehensive [documentation](http://mikemcl.github.io/bignumber.js/) and test set 

If an even smaller and simpler library is required see [big.js](https://github.com/MikeMcl/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](https://github.com/MikeMcl/decimal.js/).

## Load

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](http://nodejs.org) 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'); 

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

The library is also available from the [npm](https://npmjs.org/) 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](http://requirejs.org/):

    require(['path/to/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 *(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()

Method names over 5 letters in length 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"

The maximum number of decimal places of, and the rounding mode applied to, the results of operations involving division (i.e. division, square root, base conversion, and negative power operations) is set by a configuration object passed to 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                                 // "1,2,3,4,5,6"    coefficient (i.e. significand)
    x.e                                 // 2                exponent 
    x.s                                 // -1               sign

For futher information see the [API](http://mikemcl.github.io/bignumber.js/) reference from the *doc* folder.

## Test

The *test* directory contains the test scripts for each method. 

The tests can be run with Node or a browser.   

For a quick test of all the methods, from a command-line shell at the *test/* directory

    $ node quick-test

To test a single method in more depth, e.g.

    $ node toFraction

To test all the methods in more depth

    $ node every-test

For the browser, see *quick-test.html*, *single-test.html* and *every-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.  

## Performance

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.

## Build

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*.   

## Feedback

Open an issue, or email  

Michael   
<a href="mailto:M8ch88l@gmail.com">M8ch88l@gmail.com</a>

Bitcoin donation to:  
**1CauoGYrEoJFhcyxGVaiLTE6f3WCaSUjnm**  
Thank you

## Licence

MIT.

See LICENCE.

## Change Log

####1.4.0
* 08/05/2014 Added `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   
