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Accumulators.sln

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+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 16
+VisualStudioVersion = 16.0.29519.181
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "CompensatedAccumulators", "CompensatedAccumulators\CompensatedAccumulators.csproj", "{B44E95B2-6403-4C76-873E-C338502A8CAD}"
+EndProject
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "CompensatedAccumulators.Test", "CompensatedAccumulators.Test\CompensatedAccumulators.Test.csproj", "{E9E5D48D-A70E-4D08-9EA0-CC9EC712576F}"
+EndProject
+Global
+ GlobalSection(SolutionConfigurationPlatforms) = preSolution
+ Debug|Any CPU = Debug|Any CPU
+ Release|Any CPU = Release|Any CPU
+ EndGlobalSection
+ GlobalSection(ProjectConfigurationPlatforms) = postSolution
+ {B44E95B2-6403-4C76-873E-C338502A8CAD}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+ {B44E95B2-6403-4C76-873E-C338502A8CAD}.Debug|Any CPU.Build.0 = Debug|Any CPU
+ {B44E95B2-6403-4C76-873E-C338502A8CAD}.Release|Any CPU.ActiveCfg = Release|Any CPU
+ {B44E95B2-6403-4C76-873E-C338502A8CAD}.Release|Any CPU.Build.0 = Release|Any CPU
+ {E9E5D48D-A70E-4D08-9EA0-CC9EC712576F}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+ {E9E5D48D-A70E-4D08-9EA0-CC9EC712576F}.Debug|Any CPU.Build.0 = Debug|Any CPU
+ {E9E5D48D-A70E-4D08-9EA0-CC9EC712576F}.Release|Any CPU.ActiveCfg = Release|Any CPU
+ {E9E5D48D-A70E-4D08-9EA0-CC9EC712576F}.Release|Any CPU.Build.0 = Release|Any CPU
+ EndGlobalSection
+ GlobalSection(SolutionProperties) = preSolution
+ HideSolutionNode = FALSE
+ EndGlobalSection
+ GlobalSection(ExtensibilityGlobals) = postSolution
+ SolutionGuid = {6B955F72-BAF7-4423-A591-D2AE25DF73A8}
+ EndGlobalSection
+EndGlobal

CompensatedAccumulators.Test/CompensatedAccumulators.Test.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+ <PropertyGroup>
+ <TargetFramework>netcoreapp3.1</TargetFramework>
+
+ <IsPackable>false</IsPackable>
+ </PropertyGroup>
+
+ <ItemGroup>
+ <PackageReference Include="Microsoft.NET.Test.Sdk" Version="16.2.0" />
+ <PackageReference Include="xunit" Version="2.4.0" />
+ <PackageReference Include="xunit.runner.visualstudio" Version="2.4.0" />
+ <PackageReference Include="coverlet.collector" Version="1.0.1" />
+ </ItemGroup>
+
+ <ItemGroup>
+ <ProjectReference Include="..\CompensatedAccumulators\CompensatedAccumulators.csproj" />
+ </ItemGroup>
+
+</Project>

CompensatedAccumulators.Test/CompensatedSumTest.cs

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+//---------------------------------------------------------------------------
+// PROJECT : Compensated Accumulators
+// COPYRIGHT : Andy Thomas (C) 2019
+// WEB URL : https://kuiper.zone
+// LICENSE : GPLv3
+//---------------------------------------------------------------------------
+
+using System;
+using System.Diagnostics;
+using Xunit;
+using Xunit.Abstractions;
+
+namespace CompensatedAccumulators.Test
+{
+ public class CompensatedSumTest
+ {
+ /// <summary>
+ /// Implementation kind used in test theory data.
+ /// </summary>
+ public enum SumKind {Naive, Pairwise, Kahan, Neumaier, Klein};
+
+ private readonly ITestOutputHelper helper;
+
+ /// <summary>
+ /// Constructor with test helper.
+ /// </summary>
+ public CompensatedSumTest(ITestOutputHelper hlp)
+ {
+ helper = hlp;
+ }
+
+ /// <summary>
+ /// Test result of summation is not lost due to presence (and subtraction) of high values.
+ /// Not all accumulators will pass this test.
+ /// </summary>
+ [Theory]
+ [InlineData(SumKind.Neumaier)]
+ [InlineData(SumKind.Klein)]
+ public void Add_PetersTest_ExpectSumOf2(SumKind kind)
+ {
+ // https://en.wikipedia.org/wiki/Kahan_summation_algorithm
+ var sum = CreateSum(kind);
+ sum.Add(1.0);
+ sum.Add(1E100);
+ sum.Add(1.0);
+ sum.Add(-1E100);
+
+ // Only Neumaier and Klein both give correct answer 2.0.
+ // Others expected to give 0.
+ helper.WriteLine(sum.Value.ToString());
+
+ Assert.Equal(2.0, sum.Value, 10);
+ }
+
+ /// <summary>
+ /// PSRNG zero sum sequence. Expect better result than naive summation.
+ /// </summary>
+ [Theory]
+ [InlineData(SumKind.Pairwise)]
+ [InlineData(SumKind.Kahan)]
+ [InlineData(SumKind.Neumaier)]
+ [InlineData(SumKind.Klein)]
+ [InlineData(SumKind.Naive)]
+ public void Add_PsrngZeroSum_ExpectBetterAccuracyThanNaive(SumKind kind)
+ {
+ const double Spread = 1E7;
+
+ var sum = CreateSum(kind);
+ var naive = CreateSum(SumKind.Naive);
+
+ var rand = new Random(2002);
+
+ for(int n = 0; n < 1000000; ++n)
+ {
+ double x = rand.NextDouble() * Spread;
+ sum.Add(x);
+ naive.Add(x);
+ }
+
+ rand = new Random(2002);
+
+ for(int n = 0; n < 1000000; ++n)
+ {
+ double x = rand.NextDouble() * Spread;
+ sum.Add(-x);
+ naive.Add(-x);
+ }
+
+ helper.WriteLine("RESULT: " + Math.Abs(sum.Value));
+ helper.WriteLine("NAIVE: " + Math.Abs(naive.Value));
+
+ // Since we also test Naive as we want output, test
+ // LTE instead of LT.
+ Assert.True(Math.Abs(sum.Value) <= Math.Abs(naive.Value));
+ }
+
+ /// <summary>
+ /// Calling resets fully resets the accumulator.
+ /// </summary>
+ [Theory]
+ [InlineData(SumKind.Pairwise)]
+ [InlineData(SumKind.Kahan)]
+ [InlineData(SumKind.Neumaier)]
+ [InlineData(SumKind.Klein)]
+ public void Reset_PerformsFullReset(SumKind kind)
+ {
+ var sum = CreateSum(kind);
+
+ sum.Add(1.5);
+ sum.Clear();
+ Assert.Equal(0.0, sum.Value, 10);
+
+ // Restarts
+ sum.Add(1.5);
+ Assert.Equal(1.5, sum.Value, 10);
+ }
+
+ /// <summary>
+ /// Measure accumulator performance. Result written to helper. NaiveSum also test for comparison.
+ /// </summary>
+ [Theory]
+ [InlineData(SumKind.Pairwise)]
+ [InlineData(SumKind.Kahan)]
+ [InlineData(SumKind.Neumaier)]
+ [InlineData(SumKind.Klein)]
+ [InlineData(SumKind.Naive)]
+ public void Add_MeasurePerformance(SumKind kind)
+ {
+ const long TicksPerSecond = 1000 * 1000 * 10;
+
+ var sum = CreateSum(kind);
+
+ // JIT
+ sum.Add(1);
+ sum.Clear();
+
+ double elap;
+ long count = 0;
+ var sw = Stopwatch.StartNew();
+
+ do
+ {
+ for(int n = 0; n < 1000; ++n)
+ {
+ sum.Add(++count);
+ }
+
+ elap = (double)sw.ElapsedTicks / TicksPerSecond;
+
+ } while (elap < 1.0);
+
+ helper.WriteLine("Count: " + count);
+ helper.WriteLine("Elapsed: " + elap + " sec");
+
+ helper.WriteLine("RATE: " + count / elap + " per sec");
+ helper.WriteLine("TIME: " + 1E9 * elap / count + " ns");
+ }
+
+ private static ICompensatedSum CreateSum(SumKind kind)
+ {
+ switch(kind)
+ {
+ case SumKind.Pairwise: return new PairwiseSum();
+ case SumKind.Kahan: return new KahanSum();
+ case SumKind.Neumaier: return new NeumaierSum();
+ case SumKind.Klein: return new KleinSum();
+ default: return new NaiveSum();
+ }
+ }
+
+ }
+}

CompensatedAccumulators.Test/NaiveSum.cs

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+//---------------------------------------------------------------------------
+// PROJECT : Compensated Accumulators
+// COPYRIGHT : Andy Thomas (C) 2019
+// WEB URL : https://kuiper.zone
+// LICENSE : GPLv3
+//---------------------------------------------------------------------------
+
+namespace CompensatedAccumulators.Test
+{
+ /// <summary>
+ /// Naive sum implementation for test comparison only.
+ /// </summary>
+ public class NaiveSum : ICompensatedSum
+ {
+ /// <summary>
+ /// Default constructor.
+ /// </summary>
+ public NaiveSum()
+ {
+ }
+
+ /// <summary>
+ /// Constructor with initial value.
+ /// </summary>
+ public NaiveSum(double x)
+ {
+ Value = x;
+ }
+
+ /// <summary>
+ /// Implements <see cref="ICompensatedSum.Value"/>.
+ /// </summary>
+ public double Value { get; set; }
+
+ /// <summary>
+ /// Implements <see cref="ICompensatedSum.Add(double)"/>.
+ /// </summary>
+ public void Add(double x)
+ {
+ Value += x;
+ }
+
+ /// <summary>
+ /// Implements <see cref="ICompensatedSum.Clear()"/>.
+ /// </summary>
+ public void Clear()
+ {
+ Value = 0;
+ }
+
+ /// <summary>
+ /// Implements <see cref="ICompensatedSum.Clone()"/>.
+ /// </summary>
+ public ICompensatedSum Clone()
+ {
+ return new NaiveSum(Value);
+ }
+
+ }
+
+}

CompensatedAccumulators/CompensatedAccumulators.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+ <PropertyGroup>
+ <TargetFramework>netstandard2.0</TargetFramework>
+ </PropertyGroup>
+
+</Project>

CompensatedAccumulators/ICompensatedSum.cs

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+//---------------------------------------------------------------------------
+// PROJECT : Compensated Accumulators
+// COPYRIGHT : Andy Thomas (C) 2019
+// WEB URL : https://kuiper.zone
+// LICENSE : GPLv3
+//---------------------------------------------------------------------------
+
+namespace CompensatedAccumulators
+{
+ /// <summary>
+ /// An interface for a compensated sum algorithm. A "compensated sum" offers reduced numerical
+ /// error when summing finite precision values in comparison to "naive" summation.
+ /// </summary>
+ public interface ICompensatedSum
+ {
+ /// <summary>
+ /// Get or sets the current summation value.
+ /// </summary>
+ double Value { get; set; }
+
+ /// <summary>
+ /// Adds 'x' to the <see cref="Value"/> sum, using a compensation technique designed to reduce numerical
+ /// error.
+ void Add(double x);
+
+ /// <summary>
+ /// Sets the sum value to zero and resets initial state.
+ /// </summary>
+ void Clear();
+
+ /// <summary>
+ /// Creates a "deep" copy of the instance with the same value and internal state. Returns the new instance.
+ /// </summary>
+ ICompensatedSum Clone();
+ }
+}