number theory: gcd/lcm for pairs and lists (from Iridium)

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

src/Managed.UnitTests/Managed.UnitTests.csproj

@@ -67,6 +67,7 @@
     <Compile Include="IntegrationTests\IntegrationTest.cs" />
     <Compile Include="InterpolationTests\InterpolationContract.cs" />
     <Compile Include="InterpolationTests\InterpolationTest.cs" />
+    <Compile Include="NumberTheoryTests\GcdRelatedTest.cs" />
     <Compile Include="NumberTheoryTests\IntegerTheoryTest.cs" />
     <Compile Include="PrecisionTest.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />

src/Managed.UnitTests/NumberTheoryTests/GcdRelatedTest.cs

@@ -0,0 +1,131 @@
+// <copyright file="GcdRelatedTest.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 MbUnit.Framework;
+    using NumberTheory;
+
+    [TestFixture]
+    public class GcdRelatedTest
+    {
+        [Test]
+        public void GcdHandlesNormalInputCorrectly()
+        {
+            Assert.AreEqual(0, IntegerTheory.GreatestCommonDivisor(0, 0), "Gcd(0,0)");
+            Assert.AreEqual(6, IntegerTheory.GreatestCommonDivisor(0, 6), "Gcd(0,6)");
+            Assert.AreEqual(1, IntegerTheory.GreatestCommonDivisor(7, 13), "Gcd(7,13)");
+            Assert.AreEqual(7, IntegerTheory.GreatestCommonDivisor(7, 14), "Gcd(7,14)");
+            Assert.AreEqual(1, IntegerTheory.GreatestCommonDivisor(7, 15), "Gcd(7,15)");
+            Assert.AreEqual(3, IntegerTheory.GreatestCommonDivisor(6, 15), "Gcd(6,15)");
+        }
+
+        [Test]
+        public void GcdHandlesNegativeInputCorrectly()
+        {
+            Assert.AreEqual(5, IntegerTheory.GreatestCommonDivisor(-5, 0), "Gcd(-5,0)");
+            Assert.AreEqual(5, IntegerTheory.GreatestCommonDivisor(0, -5), "Gcd(0, -5)");
+            Assert.AreEqual(1, IntegerTheory.GreatestCommonDivisor(-7, 15), "Gcd(-7,15)");
+            Assert.AreEqual(1, IntegerTheory.GreatestCommonDivisor(-7, -15), "Gcd(-7,-15)");
+        }
+
+        [Test]
+        public void GcdSupportsLargeInput()
+        {
+            Assert.AreEqual(Int32.MaxValue, IntegerTheory.GreatestCommonDivisor(0, Int32.MaxValue), "Gcd(0,Int32Max)");
+            Assert.AreEqual(Int64.MaxValue, IntegerTheory.GreatestCommonDivisor(0, Int64.MaxValue), "Gcd(0,Int64Max)");
+            Assert.AreEqual(1, IntegerTheory.GreatestCommonDivisor(Int32.MaxValue, Int64.MaxValue), "Gcd(Int32Max,Int64Max)");
+            Assert.AreEqual(1 << 18, IntegerTheory.GreatestCommonDivisor(1 << 18, 1 << 20), "Gcd(1>>18,1<<20)");
+        }
+
+        [Test]
+        public void ListGcdHandlesNormalInputCorrectly()
+        {
+            Assert.AreEqual(2, IntegerTheory.GreatestCommonDivisor(-10, 6, -8), "Gcd(-10,6,-8)");
+            Assert.AreEqual(1, IntegerTheory.GreatestCommonDivisor(-10, 6, -8, 5, 9, 13), "Gcd(-10,6,-8,5,9,13)");
+            Assert.AreEqual(5, IntegerTheory.GreatestCommonDivisor(-10, 20, 120, 60, -15, 1000), "Gcd(-10,20,120,60,-15,1000)");
+            Assert.AreEqual(3, IntegerTheory.GreatestCommonDivisor(Int64.MaxValue - 1, Int64.MaxValue - 4, Int64.MaxValue - 7), "Gcd(Int64Max-1,Int64Max-4,Int64Max-7)");
+            Assert.AreEqual(123, IntegerTheory.GreatestCommonDivisor(492, -2 * 492, 492 / 4), "Gcd(492, -984, 123)");
+        }
+
+        [Test]
+        public void ListGcdHandlesSpecialInputCorrectly()
+        {
+            Assert.AreEqual(0, IntegerTheory.GreatestCommonDivisor(), "Gcd()");
+            Assert.AreEqual(100, IntegerTheory.GreatestCommonDivisor(-100), "Gcd(-100)");
+        }
+
+        [Test]
+        public void LcmHandlesNormalInputCorrectly()
+        {
+            Assert.AreEqual(10, IntegerTheory.LeastCommonMultiple(10, 10), "Lcm(10,10)");
+
+            Assert.AreEqual(0, IntegerTheory.LeastCommonMultiple(0, 10), "Lcm(0,10)");
+            Assert.AreEqual(0, IntegerTheory.LeastCommonMultiple(10, 0), "Lcm(10,0)");
+
+            Assert.AreEqual(77, IntegerTheory.LeastCommonMultiple(11, 7), "Lcm(11,7)");
+            Assert.AreEqual(33, IntegerTheory.LeastCommonMultiple(11, 33), "Lcm(11,33)");
+            Assert.AreEqual(374, IntegerTheory.LeastCommonMultiple(11, 34), "Lcm(11,34)");
+        }
+
+        [Test]
+        public void LcmHandlesNegativeInputCorrectly()
+        {
+            Assert.AreEqual(352, IntegerTheory.LeastCommonMultiple(11, -32), "Lcm(11,-32)");
+            Assert.AreEqual(352, IntegerTheory.LeastCommonMultiple(-11, 32), "Lcm(-11,32)");
+            Assert.AreEqual(352, IntegerTheory.LeastCommonMultiple(-11, -32), "Lcm(-11,-32)");
+        }
+
+        [Test]
+        public void LcmSupportsLargeInput()
+        {
+            Assert.AreEqual(Int32.MaxValue, IntegerTheory.LeastCommonMultiple(Int32.MaxValue, Int32.MaxValue), "Lcm(Int32Max,Int32Max)");
+            Assert.AreEqual(Int64.MaxValue, IntegerTheory.LeastCommonMultiple(Int64.MaxValue, Int64.MaxValue), "Lcm(Int64Max,Int64Max)");
+            Assert.AreEqual(Int64.MaxValue, IntegerTheory.LeastCommonMultiple(-Int64.MaxValue, -Int64.MaxValue), "Lcm(-Int64Max,-Int64Max)");
+            Assert.AreEqual(Int64.MaxValue, IntegerTheory.LeastCommonMultiple(-Int64.MaxValue, Int64.MaxValue), "Lcm(-Int64Max,Int64Max)");
+        }
+
+        [Test]
+        public void ListLcmHandlesNormalInputCorrectly()
+        {
+            Assert.AreEqual(120, IntegerTheory.LeastCommonMultiple(-10, 6, -8), "Lcm(-10,6,-8)");
+            Assert.AreEqual(4680, IntegerTheory.LeastCommonMultiple(-10, 6, -8, 5, 9, 13), "Lcm(-10,6,-8,5,9,13)");
+            Assert.AreEqual(3000, IntegerTheory.LeastCommonMultiple(-10, 20, 120, 60, -15, 1000), "Lcm(-10,20,120,60,-15,1000)");
+            Assert.AreEqual(984, IntegerTheory.LeastCommonMultiple(492, -2 * 492, 492 / 4), "Lcm(492, -984, 123)");
+            Assert.AreEqual(2016, IntegerTheory.LeastCommonMultiple(32, 42, 36, 18), "Lcm(32,42,36,18)");
+        }
+
+        [Test]
+        public void ListLcmHandlesSpecialInputCorrectly()
+        {
+            Assert.AreEqual(1, IntegerTheory.LeastCommonMultiple(), "Lcm()");
+            Assert.AreEqual(100, IntegerTheory.LeastCommonMultiple(-100), "Lcm(-100)");
+        }
+    }
+}

src/Managed/Managed.csproj

@@ -71,6 +71,7 @@
     <Compile Include="Interpolation\Interpolate.cs" />
     <Compile Include="Interpolation\SplineBoundaryCondition.cs" />
     <Compile Include="NumberTheory\IntegerTheory.cs" />
+    <Compile Include="NumberTheory\IntegerTheory.Euclid.cs" />
     <Compile Include="Precision.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
     <Compile Include="Properties\Resources.Designer.cs">

src/Managed/NumberTheory/IntegerTheory.Euclid.cs

@@ -0,0 +1,200 @@
+// <copyright file="IntegerTheory.Euclid.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;
+    using System.Collections.Generic;
+
+    /// <summary>
+    /// Number theory utility functions for integers.
+    /// </summary>
+    public static partial class IntegerTheory
+    {
+        /// <summary>
+        /// Returns the greatest common divisor (<c>gcd</c>) of two integers using Euclid's algorithm.
+        /// </summary>
+        /// <param name="a">First Integer: a.</param>
+        /// <param name="b">Second Integer: b.</param>
+        /// <returns>Greatest common divisor <c>gcd</c>(a,b)</returns>
+        public static long GreatestCommonDivisor(long a, long b)
+        {
+            while (b != 0)
+            {
+                long remainder = a % b;
+                a = b;
+                b = remainder;
+            }
+
+            return Math.Abs(a);
+        }
+
+        /// <summary>
+        /// Returns the greatest common divisor (<c>gcd</c>) of a set of integers using Euclid's
+        /// algorithm.
+        /// </summary>
+        /// <param name="integers">List of Integers.</param>
+        /// <returns>Greatest common divisor <c>gcd</c>(list of integers)</returns>
+        public static long GreatestCommonDivisor(IList<long> integers)
+        {
+            if (null == integers)
+            {
+                throw new ArgumentNullException("integers");
+            }
+
+            if (integers.Count == 0)
+            {
+                return 0;
+            }
+
+            long gcd = Math.Abs(integers[0]);
+
+            for (int i = 1; (i < integers.Count) && (gcd > 1); i++)
+            {
+                gcd = GreatestCommonDivisor(gcd, integers[i]);
+            }
+
+            return gcd;
+        }
+
+        /// <summary>
+        /// Returns the greatest common divisor (<c>gcd</c>) of a set of integers using Euclid's algorithm.
+        /// </summary>
+        /// <param name="integers">List of Integers.</param>
+        /// <returns>Greatest common divisor <c>gcd</c>(list of integers)</returns>
+        public static long GreatestCommonDivisor(params long[] integers)
+        {
+            return GreatestCommonDivisor((IList<long>)integers);
+        }
+
+        /// <summary>
+        /// Computes the extended greatest common divisor, such that a*x + b*y = <c>gcd</c>(a,b).
+        /// </summary>
+        /// <param name="a">First Integer: a.</param>
+        /// <param name="b">Second Integer: b.</param>
+        /// <param name="x">Resulting x, such that a*x + b*y = <c>gcd</c>(a,b).</param>
+        /// <param name="y">Resulting y, such that a*x + b*y = <c>gcd</c>(a,b)</param>
+        /// <returns>Greatest common divisor <c>gcd</c>(a,b)</returns>
+        /// <example>
+        /// <code>
+        /// long x,y,d;
+        /// d = Fn.GreatestCommonDivisor(45,18,out x, out y);
+        /// -> d == 9 &amp;&amp; x == 1 &amp;&amp; y == -2
+        /// </code>
+        /// The <c>gcd</c> of 45 and 18 is 9: 18 = 2*9, 45 = 5*9. 9 = 1*45 -2*18, therefore x=1 and y=-2.
+        /// </example>
+        public static long ExtendedGreatestCommonDivisor(
+            long a,
+            long b,
+            out long x,
+            out long y)
+        {
+            long mp = 1, np = 0, m = 0, n = 1;
+
+            while (b != 0)
+            {
+                long quot = a / b;
+                long rem = a % b;
+                a = b;
+                b = rem;
+
+                long tmp = m;
+                m = mp - (quot * m);
+                mp = tmp;
+
+                tmp = n;
+                n = np - (quot * n);
+                np = tmp;
+            }
+
+            if (a >= 0)
+            {
+                x = mp;
+                y = np;
+                return a;
+            }
+
+            x = -mp;
+            y = -np;
+            return -a;
+        }
+
+        /// <summary>
+        /// Returns the least common multiple (<c>lcm</c>) of two integers using Euclid's algorithm.
+        /// </summary>
+        /// <param name="a">First Integer: a.</param>
+        /// <param name="b">Second Integer: b.</param>
+        /// <returns>Least common multiple <c>lcm</c>(a,b)</returns>
+        public static long LeastCommonMultiple(long a, long b)
+        {
+            if ((a == 0) || (b == 0))
+            {
+                return 0;
+            }
+
+            return Math.Abs((a / GreatestCommonDivisor(a, b)) * b);
+        }
+
+        /// <summary>
+        /// Returns the least common multiple (<c>lcm</c>) of a set of integers using Euclid's algorithm.
+        /// </summary>
+        /// <param name="integers">List of Integers.</param>
+        /// <returns>Least common multiple <c>lcm</c>(list of integers)</returns>
+        public static long LeastCommonMultiple(IList<long> integers)
+        {
+            if (null == integers)
+            {
+                throw new ArgumentNullException("integers");
+            }
+
+            if (integers.Count == 0)
+            {
+                return 1;
+            }
+
+            long lcm = Math.Abs(integers[0]);
+
+            for (int i = 1; i < integers.Count; i++)
+            {
+                lcm = LeastCommonMultiple(lcm, integers[i]);
+            }
+
+            return lcm;
+        }
+
+        /// <summary>
+        /// Returns the least common multiple (<c>lcm</c>) of a set of integers using Euclid's algorithm.
+        /// </summary>
+        /// <param name="integers">List of Integers.</param>
+        /// <returns>Least common multiple <c>lcm</c>(list of integers)</returns>
+        public static long LeastCommonMultiple(params long[] integers)
+        {
+            return LeastCommonMultiple((IList<long>)integers);
+        }
+    }
+}

src/Managed/NumberTheory/IntegerTheory.cs

@@ -33,7 +33,7 @@ namespace MathNet.Numerics.NumberTheory
     /// <summary>
     /// Number theory utility functions for integers.
     /// </summary>
-    public static class IntegerTheory
+    public static partial class IntegerTheory
     {
         /// <summary>
         /// Find out whether the provided 32 bit integer is an even number.

src/Native.UnitTests/Native.UnitTests.csproj

@@ -83,6 +83,9 @@
     <Compile Include="..\Managed.UnitTests\InterpolationTests\InterpolationTest.cs">
       <Link>InterpolationTests\InterpolationTest.cs</Link>
     </Compile>
+    <Compile Include="..\Managed.UnitTests\NumberTheoryTests\GcdRelatedTest.cs">
+      <Link>NumberTheoryTests\GcdRelatedTest.cs</Link>
+    </Compile>
     <Compile Include="..\Managed.UnitTests\NumberTheoryTests\IntegerTheoryTest.cs">
       <Link>NumberTheoryTests\IntegerTheoryTest.cs</Link>
     </Compile>

src/Native/Native.csproj

@@ -122,6 +122,9 @@
     <Compile Include="..\Managed\NumberTheory\IntegerTheory.cs">
       <Link>NumberTheory\IntegerTheory.cs</Link>
     </Compile>
+    <Compile Include="..\Managed\NumberTheory\IntegerTheory.Euclid.cs">
+      <Link>NumberTheory\IntegerTheory.Euclid.cs</Link>
+    </Compile>
     <Compile Include="..\Managed\Precision.cs">
       <Link>Precision.cs</Link>
     </Compile>