functions: Binomial, BinomialLn

Signed-off-by: Christoph Ruegg <git@cdrnet.ch>

src/Numerics/SpecialFunctions/Factorial.cs

@@ -93,6 +93,38 @@ namespace MathNet.Numerics
             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];

src/UnitTests/SpecialFunctionsTests/FactorialTest.cs

@@ -78,5 +78,29 @@ namespace MathNet.Numerics.UnitTests.SpecialFunctionsTests
             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);
+        }
     }
 }