mathnet-numerics/src/UnitTests/SpecialFunctionsTests/FactorialTest.cs

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namespace MathNet.Numerics.UnitTests.SpecialFunctionsTests
{
    using System;
    using MbUnit.Framework;

    [TestFixture]
    public class FactorialTest
    {
        [Test]
        public void CanComputeFactorial()
        {
            // exact
            double factorial = 1.0;
            for (int i = 1; i < 23; i++)
            {
                factorial *= i;
                AssertHelpers.AlmostEqual(factorial, SpecialFunctions.Factorial(i), 14);
                AssertHelpers.AlmostEqual(Math.Log(factorial), SpecialFunctions.FactorialLn(i), 14);
            }

            // approximation
            for (int i = 23; i < 171; i++)
            {
                factorial *= i;
                AssertHelpers.AlmostEqual(factorial, SpecialFunctions.Factorial(i), 14);
                AssertHelpers.AlmostEqual(Math.Log(factorial), SpecialFunctions.FactorialLn(i), 14);
            }
        }

        [Test]
        public void ThrowsOnNegativeArgument()
        {
            Assert.Throws<ArgumentOutOfRangeException>(() => SpecialFunctions.Factorial(Int32.MinValue));
            Assert.Throws<ArgumentOutOfRangeException>(() => SpecialFunctions.Factorial(-1));
            Assert.Throws<ArgumentOutOfRangeException>(() => SpecialFunctions.FactorialLn(-1));
        }

        [Test]
        public void FactorialOverflowsToInfinity()
        {
            Assert.AreEqual(Double.PositiveInfinity, SpecialFunctions.Factorial(172));
            Assert.AreEqual(Double.PositiveInfinity, SpecialFunctions.Factorial(Int32.MaxValue));
        }

        [Test]
        public void FactorialLnDoesNotOverflow()
        {
            AssertHelpers.AlmostEqual(6078.2118847500501140, SpecialFunctions.FactorialLn(1 << 10), 14);
            AssertHelpers.AlmostEqual(29978.648060844048236, SpecialFunctions.FactorialLn(1 << 12), 14);
            AssertHelpers.AlmostEqual(307933.81973375485425, SpecialFunctions.FactorialLn(1 << 15), 14);
            AssertHelpers.AlmostEqual(1413421.9939462073242, SpecialFunctions.FactorialLn(1 << 17), 14);
        }

        [Test]
        public void CanComputeBinomial()
        {
            AssertHelpers.AlmostEqual(1, SpecialFunctions.Binomial(1, 1), 14);
            AssertHelpers.AlmostEqual(10, SpecialFunctions.Binomial(5, 2), 14);
            AssertHelpers.AlmostEqual(35, SpecialFunctions.Binomial(7, 3), 14);
            AssertHelpers.AlmostEqual(1, SpecialFunctions.Binomial(1, 0), 14);
            AssertHelpers.AlmostEqual(0, SpecialFunctions.Binomial(0, 1), 14);
            AssertHelpers.AlmostEqual(0, SpecialFunctions.Binomial(5, 7), 14);
            AssertHelpers.AlmostEqual(0, SpecialFunctions.Binomial(5, -7), 14);
        }

        [Test]
        public void CanComputeBinomialLn()
        {
            AssertHelpers.AlmostEqual(Math.Log(1), SpecialFunctions.BinomialLn(1, 1), 14);
            AssertHelpers.AlmostEqual(Math.Log(10), SpecialFunctions.BinomialLn(5, 2), 14);
            AssertHelpers.AlmostEqual(Math.Log(35), SpecialFunctions.BinomialLn(7, 3), 14);
            AssertHelpers.AlmostEqual(Math.Log(1), SpecialFunctions.BinomialLn(1, 0), 14);
            AssertHelpers.AlmostEqual(Math.Log(0), SpecialFunctions.BinomialLn(0, 1), 14);
            AssertHelpers.AlmostEqual(Math.Log(0), SpecialFunctions.BinomialLn(5, 7), 14);
            AssertHelpers.AlmostEqual(Math.Log(0), SpecialFunctions.BinomialLn(5, -7), 14);
        }
    }
}