binomcoef

Computes the binomial coefficient.

The binomial coefficient of two non-negative integers n and k is defined as

It can be generalized for any two real numbers n and k as follows

where Γ denotes the Gamma function and Beta is the Beta function.

Installation

$ npm install math-binomcoef

Usage

var binomcoef = require( 'math-binomcoef' );

binomcoef( x, y )

Computes the Binomial coefficient.

var val = binomcoef( 8, 2 );
// returns 28

val = binomcoef( 0, 0 );
// returns 1

val = binomcoef( -4, 2 );
// returns 10

val = binomcoef( 2, -1 );
// returns 0

val = binomcoef( 3, 1.5 );
// returns ~3.395

Implementation

Instead of evaluating the factorial form, which is inefficient and prone to overflow for large inputs arguments, this module computes the following multiplicative representation of the binomial coefficient for integer arguments

For non-integer inputs, the function computes - ln( n + 1 ) - ln( Beta( n - k + 1, k + 1 ) ) and returns the power this value to base e.

Examples

var binomcoef = require( 'math-binomcoef' );

for ( var x = 5; x > 0; x-- ) {
	for ( var y = 0; y < 5; y++ ) {
		console.log( 'x: %d, \t y: %d, \t f(x,y): %d', x, y, binomcoef( x, y ) );
	}
}

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

This repository uses tape for unit tests. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

Browser Support

This repository uses Testling for browser testing. To run the tests in a (headless) local web browser, execute the following command in the top-level application directory:

$ make test-browsers

To view the tests in a local web browser,

$ make view-browser-tests

License

MIT license.

Copyright

Copyright © 2016. The Compute.io Authors.