mathnet-numerics/src/Numerics/SpecialFunctions/Factorial.cs

// <copyright file="Factorial.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
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namespace MathNet.Numerics
{
    using System;

    public partial class SpecialFunctions
    {
        /// <summary>
        /// Computes the factorial function x -> x! of an integer number > 0. The function can represent all number up
        /// to 22! exactly, all numbers up to 170! using a double representation. All larger values will overflow.
        /// </summary>
        /// <returns>A value value! for value > 0</returns>
        /// <remarks>
        /// If you need to multiply or divide various such factorials, consider using the logarithmic version 
        /// <see cref="FactorialLn"/> instead so you can add instead of multiply and subtract instead of divide, and
        /// then exponentiate the result using <see cref="System.Math.Exp"/>. This will also circumvent the problem that
        /// factorials become very large even for small parameters.
        /// </remarks>
        /// <exception cref="ArgumentOutOfRangeException" />
        public static double Factorial(int x)
        {
            if (x < 0)
            {
                throw new ArgumentOutOfRangeException("x", Properties.Resources.ArgumentPositive);
            }

            if (x <= FactorialMaxArgument)
            {
                if (factorialCache == null)
                {
                    factorialCache = GenerateFactorials(FactorialMaxArgument);
                }

                return factorialCache[x];
            }

            return Double.PositiveInfinity;
        }

        /// <summary>
        /// Computes the logarithmic factorial function x -> ln(x!) of an integer number > 0.
        /// </summary>
        /// <returns>A value value! for value > 0</returns>
        public static double FactorialLn(int x)
        {
            if (x < 0)
            {
                throw new ArgumentOutOfRangeException("x", Properties.Resources.ArgumentPositive);
            }

            if (x <= 1)
            {
                return 0d;
            }

            if (x <= FactorialMaxArgument)
            {
                if (factorialCache == null)
                {
                    factorialCache = GenerateFactorials(FactorialMaxArgument);
                }

                return Math.Log(factorialCache[x]);
            }

            return GammaLn(x + 1.0);
        }

        /// <summary>
        /// Computes the binomial coefficient: n choose k.
        /// </summary>
        /// <param name="n">A nonnegative value n.</param>
        /// <param name="k">A nonnegative value h.</param>
        /// <returns>The binomial coefficient: n choose k.</returns>
        public static double Binomial(int n, int k)
        {
            if (k < 0 || n < 0 || k > n)
            {
                return 0.0;
            }

            return Math.Floor(0.5 + Math.Exp(FactorialLn(n) - FactorialLn(k) - FactorialLn(n - k)));
        }

        /// <summary>
        /// Computes the natural logarithm of the binomial coefficient: ln(n choose k).
        /// </summary>
        /// <param name="n">A nonnegative value n.</param>
        /// <param name="k">A nonnegative value h.</param>
        /// <returns>The logarithmic binomial coefficient: ln(n choose k).</returns>
        public static double BinomialLn(int n, int k)
        {
            if (k < 0 || n < 0 || k > n)
            {
                return Double.NegativeInfinity;
            }

            return FactorialLn(n) - FactorialLn(k) - FactorialLn(n - k);
        }

        private static double[] GenerateFactorials(int max)
        {
            var cache = new double[max + 1];
            cache[0] = 1.0;
            for (int i = 1; i < cache.Length; i++)
            {
                cache[i] = cache[i - 1] * i;
            }

            return cache;
        }

        private const int FactorialMaxArgument = 170;
        private static double[] factorialCache;
    }
}