number theory: ported from iridium, as needed by quadrature

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

src/Managed.UnitTests/Managed.UnitTests.csproj

@@ -64,6 +64,7 @@
     <Compile Include="DistributionTests\Continuous\NormalTests.cs" />
     <Compile Include="InterpolationTests\InterpolationContract.cs" />
     <Compile Include="InterpolationTests\InterpolationTest.cs" />
+    <Compile Include="NumberTheoryTests\IntegerTheoryTest.cs" />
     <Compile Include="PrecisionTest.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
     <Compile Include="SpecialFunctionsTest\ErfTests.cs" />

src/Managed.UnitTests/NumberTheoryTests/IntegerTheoryTest.cs

@@ -0,0 +1,136 @@
+// <copyright file="IntegerTheoryTest.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics.UnitTests.NumberTheoryTests
+{
+    using System;
+    using NumberTheory;
+    using MbUnit.Framework;
+
+    [TestFixture]
+    public class IntegerTheoryTest
+    {
+        [Test]
+        public void TestEvenOdd32()
+        {
+            Assert.IsTrue(IntegerTheory.IsEven(0), "0 is even");
+            Assert.IsFalse(IntegerTheory.IsOdd(0), "0 is not odd");
+
+            Assert.IsFalse(IntegerTheory.IsEven(1), "1 is not even");
+            Assert.IsTrue(IntegerTheory.IsOdd(1), "1 is odd");
+
+            Assert.IsFalse(IntegerTheory.IsEven(-1), "-1 is not even");
+            Assert.IsTrue(IntegerTheory.IsOdd(-1), "-1 is odd");
+
+            Assert.IsFalse(IntegerTheory.IsEven(Int32.MaxValue), "Int32.Max is not even");
+            Assert.IsTrue(IntegerTheory.IsOdd(Int32.MaxValue), "Int32.Max is odd");
+
+            Assert.IsTrue(IntegerTheory.IsEven(Int32.MinValue), "Int32.Min is even");
+            Assert.IsFalse(IntegerTheory.IsOdd(Int32.MinValue), "Int32.Min is not odd");
+        }
+
+        [Test]
+        public void TestEvenOdd64()
+        {
+            Assert.IsTrue(IntegerTheory.IsEven((long)0), "0 is even");
+            Assert.IsFalse(IntegerTheory.IsOdd((long)0), "0 is not odd");
+
+            Assert.IsFalse(IntegerTheory.IsEven((long)1), "1 is not even");
+            Assert.IsTrue(IntegerTheory.IsOdd((long)1), "1 is odd");
+
+            Assert.IsFalse(IntegerTheory.IsEven((long)-1), "-1 is not even");
+            Assert.IsTrue(IntegerTheory.IsOdd((long)-1), "-1 is odd");
+
+            Assert.IsFalse(IntegerTheory.IsEven(Int64.MaxValue), "Int64.Max is not even");
+            Assert.IsTrue(IntegerTheory.IsOdd(Int64.MaxValue), "Int64.Max is odd");
+
+            Assert.IsTrue(IntegerTheory.IsEven(Int64.MinValue), "Int64.Min is even");
+            Assert.IsFalse(IntegerTheory.IsOdd(Int64.MinValue), "Int64.Min is not odd");
+        }
+
+        [Test]
+        public void TestIsPerfectSquare32()
+        {
+            // Test all known suares
+            int lastRadix = (int)Math.Floor(Math.Sqrt(Int32.MaxValue));
+            for (int i = 0; i <= lastRadix; i++)
+            {
+                Assert.IsTrue(IntegerTheory.IsPerfectSquare(i * i), i + "^2 (+)");
+            }
+
+            // Test 1-offset from all known squares
+            for (int i = 2; i <= lastRadix; i++)
+            {
+                Assert.IsFalse(IntegerTheory.IsPerfectSquare((i * i) - 1), i + "^2-1 (-)");
+                Assert.IsFalse(IntegerTheory.IsPerfectSquare((i * i) + 1), i + "^2+1 (-)");
+            }
+
+            // Selected Cases
+            Assert.IsTrue(IntegerTheory.IsPerfectSquare(100000000), "100000000 (+)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(100000001), "100000001 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(99999999), "99999999 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(-4), "-4 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int32.MinValue), "Int32.MinValue (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int32.MaxValue), "Int32.MaxValue (-)");
+            Assert.IsTrue(IntegerTheory.IsPerfectSquare(1), "1 (+)");
+            Assert.IsTrue(IntegerTheory.IsPerfectSquare(0), "0 (+)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(-1), "-1 (-)");
+        }
+
+        [Test]
+        public void TestIsPerfectSquare64()
+        {
+            // Test all known suares
+            for (int i = 0; i < 32; i++)
+            {
+                long t = ((long)1) << i;
+                Assert.IsTrue(IntegerTheory.IsPerfectSquare(t * t), t + "^2 (+)");
+            }
+
+            // Test 1-offset from all known squares
+            for (int i = 1; i < 32; i++)
+            {
+                long t = ((long)1) << i;
+                Assert.IsFalse(IntegerTheory.IsPerfectSquare((t * t) - 1), t + "^2-1 (-)");
+                Assert.IsFalse(IntegerTheory.IsPerfectSquare((t * t) + 1), t + "^2+1 (-)");
+            }
+
+            // Selected Cases
+            Assert.IsTrue(IntegerTheory.IsPerfectSquare((long)1000000000000000000), "1000000000000000000 (+)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)1000000000000000001), "1000000000000000001 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)999999999999999999), "999999999999999999 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)999999999999999993), "999999999999999993 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)-4), "-4 (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int64.MinValue), "Int32.MinValue (-)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare(Int64.MaxValue), "Int32.MaxValue (-)");
+            Assert.IsTrue(IntegerTheory.IsPerfectSquare((long)1), "1 (+)");
+            Assert.IsTrue(IntegerTheory.IsPerfectSquare((long)0), "0 (+)");
+            Assert.IsFalse(IntegerTheory.IsPerfectSquare((long)-1), "-1 (-)");
+        }
+    }
+}

src/Managed/Managed.csproj

@@ -65,6 +65,7 @@
     <Compile Include="Interpolation\IInterpolation.cs" />
     <Compile Include="Interpolation\Interpolate.cs" />
     <Compile Include="Interpolation\SplineBoundaryCondition.cs" />
+    <Compile Include="NumberTheory\IntegerTheory.cs" />
     <Compile Include="Precision.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
     <Compile Include="Properties\Resources.Designer.cs">

src/Managed/NumberTheory/IntegerTheory.cs

@@ -0,0 +1,126 @@
+// <copyright file="IntegerTheory.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+namespace MathNet.Numerics.NumberTheory
+{
+    using System;
+
+    /// <summary>
+    /// Number Theory for Integers
+    /// </summary>
+    public static class IntegerTheory
+    {
+        /// <summary>
+        /// Find out whether the provided 32 bit integer is an even number.
+        /// </summary>
+        /// <returns>True if and only if it is an even number.</returns>
+        public static bool IsEven(this int number)
+        {
+            return (number & 0x1) == 0x0;
+        }
+
+        /// <summary>
+        /// Find out whether the provided 64 bit integer is an even number.
+        /// </summary>
+        /// <returns>True if and only if it is an even number.</returns>
+        public static bool IsEven(this long number)
+        {
+            return (number & 0x1) == 0x0;
+        }
+
+        /// <summary>
+        /// Find out whether the provided 32 bit integer is an odd number.
+        /// </summary>
+        /// <returns>True if and only if it is an odd number.</returns>
+        public static bool IsOdd(this int number)
+        {
+            return (number & 0x1) == 0x1;
+        }
+
+        /// <summary>
+        /// Find out whether the provided 64 bit integer is an odd number.
+        /// </summary>
+        /// <returns>True if and only if it is an odd number.</returns>
+        public static bool IsOdd(this long number)
+        {
+            return (number & 0x1) == 0x1;
+        }
+
+        /// <summary>
+        /// Find out whether the provided 32 bit integer is a perfect square, i.e. a square of an integer.
+        /// </summary>
+        /// <returns>True if and only if it is a perfect square.</returns>
+        public static bool IsPerfectSquare(int number)
+        {
+            if (number < 0)
+            {
+                return false;
+            }
+
+            int lastHexDigit = number & 0xF;
+            if (lastHexDigit > 9)
+            {
+                return false; // return immediately in 6 cases out of 16.
+            }
+
+            if (lastHexDigit == 0 || lastHexDigit == 1 || lastHexDigit == 4 || lastHexDigit == 9)
+            {
+                int t = (int)Math.Floor(Math.Sqrt(number) + 0.5);
+                return (t * t) == number;
+            }
+
+            return false;
+        }
+
+        /// <summary>
+        /// Find out whether the provided 64 bit integer is a perfect square, i.e. a square of an integer.
+        /// </summary>
+        /// <returns>True if and only if it is a perfect square.</returns>
+        public static bool IsPerfectSquare(long number)
+        {
+            if (number < 0)
+            {
+                return false;
+            }
+
+            int lastHexDigit = (int)(number & 0xF);
+            if (lastHexDigit > 9)
+            {
+                return false; // return immediately in 6 cases out of 16.
+            }
+
+            if (lastHexDigit == 0 || lastHexDigit == 1 || lastHexDigit == 4 || lastHexDigit == 9)
+            {
+                long t = (long)Math.Floor(Math.Sqrt(number) + 0.5);
+                return (t * t) == number;
+            }
+
+            return false;
+        }
+    }
+}

src/Native.UnitTests/Native.UnitTests.csproj

@@ -78,12 +78,15 @@
     <Compile Include="..\Managed.UnitTests\InterpolationTests\InterpolationTest.cs">
       <Link>InterpolationTests\InterpolationTest.cs</Link>
     </Compile>
+    <Compile Include="..\Managed.UnitTests\NumberTheoryTests\IntegerTheoryTest.cs">
+      <Link>NumberTheoryTests\IntegerTheoryTest.cs</Link>
+    </Compile>
     <Compile Include="..\Managed.UnitTests\PrecisionTest.cs">
       <Link>PrecisionTest.cs</Link>
     </Compile>
     <Compile Include="..\Managed.UnitTests\SpecialFunctionsTest\ErfTests.cs">
       <Link>SpecialFunctionsTest\ErfTests.cs</Link>
-	</Compile>
+    </Compile>
     <Compile Include="Properties\AssemblyInfo.cs" />
   </ItemGroup>
   <ItemGroup>

src/Native/Native.csproj

@@ -104,6 +104,9 @@
     <Compile Include="..\Managed\Interpolation\SplineBoundaryCondition.cs">
       <Link>Interpolation\SplineBoundaryCondition.cs</Link>
     </Compile>
+    <Compile Include="..\Managed\NumberTheory\IntegerTheory.cs">
+      <Link>NumberTheory\IntegerTheory.cs</Link>
+    </Compile>
     <Compile Include="..\Managed\Precision.cs">
       <Link>Precision.cs</Link>
     </Compile>