/*
    * 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;
  
  /**
   * <a href="http://mathworld.wolfram.com/Factorial.html">Factorial of a number</a>.
   */
  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}.
      *
      * <p>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}.
      *
      * <p>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];
     }
 }