Christoph Ruegg
17 years ago
6 changed files with 197 additions and 2 deletions
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// <copyright file="Factorial.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://mathnet.opensourcedotnet.info
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//
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// Copyright (c) 2009 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace MathNet.Numerics |
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{ |
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using System; |
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public partial class SpecialFunctions |
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{ |
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/// <summary>
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/// Computes the factorial function x -> x! of an integer number > 0. The function can represent all number up
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/// to 22! exactly, all numbers up to 170! using a double representation. All larger values will overflow.
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/// </summary>
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/// <returns>A value value! for value > 0</returns>
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/// <remarks>
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/// If you need to multiply or divide various such factorials, consider using the logarithmic version
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/// <see cref="FactorialLn"/> instead so you can add instead of multiply and subtract instead of divide, and
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/// then exponentiate the result using <see cref="System.Math.Exp"/>. This will also circumvent the problem that
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/// factorials become very large even for small parameters.
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/// </remarks>
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/// <exception cref="ArgumentOutOfRangeException" />
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public static double Factorial(int x) |
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{ |
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if (x < 0) |
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{ |
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throw new ArgumentOutOfRangeException("x", Properties.Resources.ArgumentPositive); |
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} |
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if (x <= FactorialMaxArgument) |
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{ |
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if (factorialCache == null) |
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{ |
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factorialCache = GenerateFactorials(FactorialMaxArgument); |
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} |
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return factorialCache[x]; |
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} |
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return Double.PositiveInfinity; |
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} |
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/// <summary>
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/// Computes the logarithmic factorial function x -> ln(x!) of an integer number > 0.
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/// </summary>
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/// <returns>A value value! for value > 0</returns>
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public static double FactorialLn(int x) |
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{ |
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if (x < 0) |
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{ |
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throw new ArgumentOutOfRangeException("x", Properties.Resources.ArgumentPositive); |
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} |
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if (x <= 1) |
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{ |
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return 0d; |
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} |
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if (x <= FactorialMaxArgument) |
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{ |
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if (factorialCache == null) |
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{ |
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factorialCache = GenerateFactorials(FactorialMaxArgument); |
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} |
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return Math.Log(factorialCache[x]); |
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} |
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return GammaLn(x + 1.0); |
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} |
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private static double[] GenerateFactorials(int max) |
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{ |
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var cache = new double[max + 1]; |
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cache[0] = 1.0; |
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for (int i = 1; i < cache.Length; i++) |
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{ |
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cache[i] = cache[i - 1] * i; |
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} |
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return cache; |
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} |
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private const int FactorialMaxArgument = 170; |
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private static double[] factorialCache; |
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} |
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} |
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@ -0,0 +1,82 @@ |
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// <copyright file="FactorialTest.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://mathnet.opensourcedotnet.info
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//
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// Copyright (c) 2009 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace MathNet.Numerics.UnitTests.SpecialFunctionsTests |
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{ |
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using System; |
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using MbUnit.Framework; |
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[TestFixture] |
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public class FactorialTest |
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{ |
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[Test] |
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public void CanComputeFactorial() |
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{ |
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// exact
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double factorial = 1.0; |
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for (int i = 1; i < 23; i++) |
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{ |
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factorial *= i; |
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AssertHelpers.AlmostEqual(factorial, SpecialFunctions.Factorial(i), 14); |
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AssertHelpers.AlmostEqual(Math.Log(factorial), SpecialFunctions.FactorialLn(i), 14); |
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} |
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// approximation
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for (int i = 23; i < 171; i++) |
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{ |
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factorial *= i; |
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AssertHelpers.AlmostEqual(factorial, SpecialFunctions.Factorial(i), 14); |
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AssertHelpers.AlmostEqual(Math.Log(factorial), SpecialFunctions.FactorialLn(i), 14); |
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} |
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} |
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[Test] |
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public void ThrowsOnNegativeArgument() |
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{ |
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Assert.Throws<ArgumentOutOfRangeException>(() => SpecialFunctions.Factorial(Int32.MinValue)); |
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Assert.Throws<ArgumentOutOfRangeException>(() => SpecialFunctions.Factorial(-1)); |
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Assert.Throws<ArgumentOutOfRangeException>(() => SpecialFunctions.FactorialLn(-1)); |
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} |
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[Test] |
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public void FactorialOverflowsToInfinity() |
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{ |
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Assert.AreEqual(Double.PositiveInfinity, SpecialFunctions.Factorial(172)); |
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Assert.AreEqual(Double.PositiveInfinity, SpecialFunctions.Factorial(Int32.MaxValue)); |
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} |
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[Test] |
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public void FactorialLnDoesNotOverflow() |
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{ |
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AssertHelpers.AlmostEqual(6078.2118847500501140, SpecialFunctions.FactorialLn(1 << 10), 14); |
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AssertHelpers.AlmostEqual(29978.648060844048236, SpecialFunctions.FactorialLn(1 << 12), 14); |
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AssertHelpers.AlmostEqual(307933.81973375485425, SpecialFunctions.FactorialLn(1 << 15), 14); |
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AssertHelpers.AlmostEqual(1413421.9939462073242, SpecialFunctions.FactorialLn(1 << 17), 14); |
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} |
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} |
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} |
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