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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.numbers.combinatorics;
/**
* Factorial of a number.
*/
public final class Factorial {
/** All long-representable factorials. */
static final long[] FACTORIALS = {
1L, 1L, 2L,
6L, 24L, 120L,
720L, 5040L, 40320L,
362880L, 3628800L, 39916800L,
479001600L, 6227020800L, 87178291200L,
1307674368000L, 20922789888000L, 355687428096000L,
6402373705728000L, 121645100408832000L, 2432902008176640000L
};
/** All factorials that can be represented as a double (values up to 170!). */
private static final double[] DOUBLE_FACTORIALS = {
1,
1,
2,
6,
24,
120,
720,
5040,
40320,
362880,
3628800,
3.99168E7,
4.790016E8,
6.2270208E9,
8.71782912E10,
1.307674368E12,
2.0922789888E13,
3.55687428096E14,
6.402373705728E15,
1.21645100408832E17,
2.43290200817664E18,
5.109094217170944E19,
1.1240007277776077E21,
2.585201673888498E22,
6.204484017332394E23,
1.5511210043330986E25,
4.0329146112660565E26,
1.0888869450418352E28,
3.0488834461171387E29,
8.841761993739702E30,
2.6525285981219107E32,
8.222838654177922E33,
2.631308369336935E35,
8.683317618811886E36,
2.9523279903960416E38,
1.0333147966386145E40,
3.7199332678990125E41,
1.3763753091226346E43,
5.230226174666011E44,
2.0397882081197444E46,
8.159152832478977E47,
3.345252661316381E49,
1.40500611775288E51,
6.041526306337383E52,
2.658271574788449E54,
1.1962222086548019E56,
5.502622159812089E57,
2.5862324151116818E59,
1.2413915592536073E61,
6.082818640342675E62,
3.0414093201713376E64,
1.5511187532873822E66,
8.065817517094388E67,
4.2748832840600255E69,
2.308436973392414E71,
1.2696403353658276E73,
7.109985878048635E74,
4.0526919504877214E76,
2.3505613312828785E78,
1.3868311854568984E80,
8.32098711274139E81,
5.075802138772248E83,
3.146997326038794E85,
1.98260831540444E87,
1.2688693218588417E89,
8.247650592082472E90,
5.443449390774431E92,
3.647111091818868E94,
2.4800355424368305E96,
1.711224524281413E98,
1.1978571669969892E100,
8.504785885678623E101,
6.1234458376886085E103,
4.4701154615126844E105,
3.307885441519386E107,
2.48091408113954E109,
1.8854947016660504E111,
1.4518309202828587E113,
1.1324281178206297E115,
8.946182130782976E116,
7.156945704626381E118,
5.797126020747368E120,
4.753643337012842E122,
3.945523969720659E124,
3.314240134565353E126,
2.81710411438055E128,
2.4227095383672734E130,
2.107757298379528E132,
1.8548264225739844E134,
1.650795516090846E136,
1.4857159644817615E138,
1.352001527678403E140,
1.2438414054641308E142,
1.1567725070816416E144,
1.087366156656743E146,
1.032997848823906E148,
9.916779348709496E149,
9.619275968248212E151,
9.426890448883248E153,
9.332621544394415E155,
9.332621544394415E157,
9.42594775983836E159,
9.614466715035127E161,
9.90290071648618E163,
1.0299016745145628E166,
1.081396758240291E168,
1.1462805637347084E170,
1.226520203196138E172,
1.324641819451829E174,
1.4438595832024937E176,
1.588245541522743E178,
1.7629525510902446E180,
1.974506857221074E182,
2.2311927486598138E184,
2.5435597334721877E186,
2.925093693493016E188,
3.393108684451898E190,
3.969937160808721E192,
4.684525849754291E194,
5.574585761207606E196,
6.689502913449127E198,
8.094298525273444E200,
9.875044200833601E202,
1.214630436702533E205,
1.506141741511141E207,
1.882677176888926E209,
2.372173242880047E211,
3.0126600184576594E213,
3.856204823625804E215,
4.974504222477287E217,
6.466855489220474E219,
8.47158069087882E221,
1.1182486511960043E224,
1.4872707060906857E226,
1.9929427461615188E228,
2.6904727073180504E230,
3.659042881952549E232,
5.012888748274992E234,
6.917786472619489E236,
9.615723196941089E238,
1.3462012475717526E241,
1.898143759076171E243,
2.695364137888163E245,
3.854370717180073E247,
5.5502938327393044E249,
8.047926057471992E251,
1.1749972043909107E254,
1.727245890454639E256,
2.5563239178728654E258,
3.80892263763057E260,
5.713383956445855E262,
8.62720977423324E264,
1.3113358856834524E267,
2.0063439050956823E269,
3.0897696138473508E271,
4.789142901463394E273,
7.471062926282894E275,
1.1729568794264145E278,
1.853271869493735E280,
2.9467022724950384E282,
4.7147236359920616E284,
7.590705053947219E286,
1.2296942187394494E289,
2.0044015765453026E291,
3.287218585534296E293,
5.423910666131589E295,
9.003691705778438E297,
1.503616514864999E300,
2.5260757449731984E302,
4.269068009004705E304,
7.257415615307999E306
};
/** Private constructor. */
private Factorial() {
// intentionally empty.
}
/**
* Computes the factorial of {@code n}.
*
* @param n Argument.
* @return {@code n!}
* @throws IllegalArgumentException if {@code n < 0}.
* @throws IllegalArgumentException if {@code n > 20} (the factorial
* value is too large to fit in a {@code long}).
*/
public static long value(int n) {
if (n < 0 ||
n > 20) {
throw new CombinatoricsException(CombinatoricsException.OUT_OF_RANGE,
n, 0, 20);
}
return FACTORIALS[n];
}
/**
* Computes the factorial of {@code n}.
*
* The result should be small enough to fit into a {@code double}: The
* largest {@code n} for which {@code n!} does not exceed
* {@code Double.MAX_VALUE} is 170. {@code Double.POSITIVE_INFINITY} is
* returned for {@code n > 170}.
*
* @param n Argument.
* @return {@code n!}
* @throws IllegalArgumentException if {@code n < 0}.
* @since 1.1
*/
public static double doubleValue(int n) {
if (n < 0) {
throw new CombinatoricsException(CombinatoricsException.NEGATIVE, n);
}
if (n < DOUBLE_FACTORIALS.length) {
return DOUBLE_FACTORIALS[n];
}
return Double.POSITIVE_INFINITY;
}
/**
* Return the factorial of {@code n}.
*
*
Note: This is an internal method that exposes the tabulated factorials that can
* be represented as a double. No checks are performed on the argument.
*
* @param n Argument (must be in [0, 170])
* @return n!
*/
static double uncheckedFactorial(int n) {
return DOUBLE_FACTORIALS[n];
}
}