IEEE-754 compliant LogGamma function
The log(gamma) function in JavaScript as defined in IEEE-745.
Version
1.0.0
Introduction
This is a port of the implementation of lngamma by Sun Microsystems who published the original under the following license:
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
Developed at SunPro, a Sun Microsystems, Inc. business.
Permission to use, copy, modify, and distribute this
software is freely granted, provided that this notice
is preserved.
That license is compatible with the MIT license.
A normal gamma function is implemented, too, but only with Math.exp() which induces a large error, especially for larger numbers. See the examples for details.
To implement a better exponential function is planned for a later version.
Example
The correct results to 38 decimal digits in the comments
> var g = require('ieee745gamma')
> g.gamma(11)
3628800.0000000084 // 3628800.0000000000000000000000000000000
> g.gamma(171)
7.257415615308056e+306 // 7.2574156153079989673967282111292631147 E306
// errors of gamma due to Math.exp():
> g.lngamma(171)
706.5730622457874 // 706.57306224578734711072226272129831468
> g.lngamma(11)
15.104412573075518 // 15.104412573075515295225709329251070372
> g.lngamma(1000000)
12815504.569147611 // 12815504.569147611659976971785017113154
> g.lngamma(.0001)
9.210282658633961 // 9.2102826586339622584486579752729991548
> g.lngamma(3)
0.6931471805599453 // 0.69314718055994530941723212145817656808
> g.lngamma(3) - Math.log(2)
0 // 0
Methods
gamma(x)
Returns exp(log(gamma(x))) for real x, x not a negative integer, over the range of ca. -177.6 <= x <= 171.7, Infinity otherwise.
lngamma(x)
Returns log(gamma(x)) for real x, x not a negative integer, over the range of ca. -10^14 <= x <= 10^305, Infinity otherwise.
Install
With npm do:
npm install ieee745gamma
License
MIT