package edu.northwestern.at.utils.math;
/* Please see the license information at the end of this file. */
import edu.northwestern.at.utils.math.distributions.Gamma;
/** Defines methods for factorials.
*/
public class Factorial
{
// n! for n = 0, ..., 20
protected static final long[] longFactorials =
{
1L,
1L,
2L,
6L,
24L,
120L,
720L,
5040L,
40320L,
362880L,
3628800L,
39916800L,
479001600L,
6227020800L,
87178291200L,
1307674368000L,
20922789888000L,
355687428096000L,
6402373705728000L,
121645100408832000L,
2432902008176640000L
};
// n! for n = 21, ..., 170
protected static final double[] doubleFactorials =
{
5.109094217170944E19,
1.1240007277776077E21,
2.585201673888498E22,
6.204484017332394E23,
1.5511210043330984E25,
4.032914611266057E26,
1.0888869450418352E28,
3.048883446117138E29,
8.841761993739701E30,
2.652528598121911E32,
8.222838654177924E33,
2.6313083693369355E35,
8.68331761881189E36,
2.952327990396041E38,
1.0333147966386144E40,
3.719933267899013E41,
1.3763753091226346E43,
5.23022617466601E44,
2.0397882081197447E46,
8.15915283247898E47,
3.34525266131638E49,
1.4050061177528801E51,
6.041526306337384E52,
2.6582715747884495E54,
1.196222208654802E56,
5.502622159812089E57,
2.5862324151116827E59,
1.2413915592536068E61,
6.082818640342679E62,
3.0414093201713376E64,
1.5511187532873816E66,
8.06581751709439E67,
4.274883284060024E69,
2.308436973392413E71,
1.2696403353658264E73,
7.109985878048632E74,
4.052691950487723E76,
2.350561331282879E78,
1.386831185456898E80,
8.32098711274139E81,
5.075802138772246E83,
3.146997326038794E85,
1.9826083154044396E87,
1.2688693218588414E89,
8.247650592082472E90,
5.443449390774432E92,
3.6471110918188705E94,
2.48003554243683E96,
1.7112245242814127E98,
1.1978571669969892E100,
8.504785885678624E101,
6.123445837688612E103,
4.470115461512686E105,
3.307885441519387E107,
2.4809140811395404E109,
1.8854947016660506E111,
1.451830920282859E113,
1.1324281178206295E115,
8.94618213078298E116,
7.15694570462638E118,
5.797126020747369E120,
4.7536433370128435E122,
3.94552396972066E124,
3.314240134565354E126,
2.8171041143805494E128,
2.4227095383672744E130,
2.107757298379527E132,
1.854826422573984E134,
1.6507955160908465E136,
1.4857159644817605E138,
1.3520015276784033E140,
1.2438414054641305E142,
1.156772507081641E144,
1.0873661566567426E146,
1.0329978488239061E148,
9.916779348709491E149,
9.619275968248216E151,
9.426890448883248E153,
9.332621544394415E155,
9.332621544394418E157,
9.42594775983836E159,
9.614466715035125E161,
9.902900716486178E163,
1.0299016745145631E166,
1.0813967582402912E168,
1.1462805637347086E170,
1.2265202031961373E172,
1.324641819451829E174,
1.4438595832024942E176,
1.5882455415227423E178,
1.7629525510902457E180,
1.974506857221075E182,
2.2311927486598138E184,
2.543559733472186E186,
2.925093693493014E188,
3.393108684451899E190,
3.96993716080872E192,
4.6845258497542896E194,
5.574585761207606E196,
6.689502913449135E198,
8.094298525273444E200,
9.875044200833601E202,
1.2146304367025332E205,
1.506141741511141E207,
1.882677176888926E209,
2.3721732428800483E211,
3.0126600184576624E213,
3.856204823625808E215,
4.974504222477287E217,
6.466855489220473E219,
8.471580690878813E221,
1.1182486511960037E224,
1.4872707060906847E226,
1.99294274616152E228,
2.690472707318049E230,
3.6590428819525483E232,
5.0128887482749884E234,
6.917786472619482E236,
9.615723196941089E238,
1.3462012475717523E241,
1.8981437590761713E243,
2.6953641378881633E245,
3.8543707171800694E247,
5.550293832739308E249,
8.047926057471989E251,
1.1749972043909107E254,
1.72724589045464E256,
2.5563239178728637E258,
3.8089226376305687E260,
5.7133839564458575E262,
8.627209774233244E264,
1.3113358856834527E267,
2.0063439050956838E269,
3.0897696138473515E271,
4.789142901463393E273,
7.471062926282892E275,
1.1729568794264134E278,
1.8532718694937346E280,
2.946702272495036E282,
4.714723635992061E284,
7.590705053947223E286,
1.2296942187394494E289,
2.0044015765453032E291,
3.287218585534299E293,
5.423910666131583E295,
9.003691705778434E297,
1.5036165148649983E300,
2.5260757449731988E302,
4.2690680090047056E304,
7.257415615308004E306
};
/** Compute factorial of an integer.
*
* @param n Number for which to compute factorial.
*
* @return n!
*/
public static double factorial( int n )
{
if ( n < 0 ) throw new IllegalArgumentException();
int l1 = longFactorials.length;
if ( n < l1 ) return longFactorials[ n ];
int l2 = doubleFactorials.length;
if ( n < ( l1 + l2 ) )
{
return doubleFactorials[ n - l1 ];
}
else
{
return Double.POSITIVE_INFINITY;
}
}
/** Computes the natural log of n factorial.
*
* @param n The number for which the log factorial is desired.
*
* @return The natural log of n! .
*
* <p>
* We use the LogGamma function to compute log(n!) using the relation:
* </p>
*
* <p>
* log(n!) = logGamma( n + 1 )
* </p>
*/
public static double logFactorial( int n )
{
if ( n <= 1 )
{
return 0.0D;
}
else
{
return Gamma.logGamma( n + 1.0D );
}
}
}
/*
Copyright (c) 2008, 2009 by Northwestern University.
All rights reserved.
Developed by:
Academic and Research Technologies
Northwestern University
http://www.it.northwestern.edu/about/departments/at/
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal with the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimers.
* Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following
disclaimers in the documentation and/or other materials provided
with the distribution.
* Neither the names of Academic and Research Technologies,
Northwestern University, nor the names of its contributors may be
used to endorse or promote products derived from this Software
without specific prior written permission.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE SOFTWARE.
*/