Add shift-first multiply helper and document benchmarks
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Marek Lemańczyk committed
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@@ -0,0 +1,160 @@
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#r "nuget: ILGPU, 1.5.3"
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#r "nuget: PeterO.Numbers, 1.8.1"
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using System;
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using System.Numerics;
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using ILGPU;
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using ILGPU.Runtime;
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using ILGPU.Runtime.CPU;
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using PeterO.Numbers;
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var context = Context.CreateDefault();
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var accelerator = context.CreateCPUAccelerator(0);
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try
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{
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Console.WriteLine("ILGPU numeric type support probe (CPU accelerator)");
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Console.WriteLine();
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ProbeResult[] results =
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[
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ProbeBigInteger(accelerator),
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ProbeEInteger(accelerator),
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ProbeERational(accelerator)
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];
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foreach (ProbeResult result in results)
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{
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Console.WriteLine($"{result.Type}: {(result.Supported ? "supported" : "unsupported")}");
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Console.WriteLine($" Details: {result.Details}");
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Console.WriteLine();
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}
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}
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finally
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{
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accelerator.Dispose();
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context.Dispose();
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}
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record ProbeResult(string Type, bool Supported, string Details)
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{
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public static ProbeResult Success(string type, string details) => new(type, true, details);
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public static ProbeResult Failure(string type, Exception exception) =>
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new(type, false, $"{exception.GetType().Name}: {exception.Message}");
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public static ProbeResult Failure(string type, string details) => new(type, false, details);
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}
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static ProbeResult ProbeBigInteger(Accelerator accelerator)
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{
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try
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{
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var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<int, Stride1D.Dense>>(BigIntegerKernel);
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using var buffer = accelerator.Allocate1D<int>(1);
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var extent = new Index1D((int)buffer.Length);
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kernel(extent, buffer.View);
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accelerator.Synchronize();
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return ProbeResult.Success(
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"System.Numerics.BigInteger",
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"Addition, subtraction, multiplication, division, and modulo compile on the CPU accelerator.");
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}
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catch (Exception ex)
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{
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return ProbeResult.Failure("System.Numerics.BigInteger", ex);
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}
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}
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static ProbeResult ProbeEInteger(Accelerator accelerator)
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{
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try
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{
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var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<int, Stride1D.Dense>>(EIntegerKernel);
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using var buffer = accelerator.Allocate1D<int>(1);
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kernel(new Index1D((int)buffer.Length), buffer.View);
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accelerator.Synchronize();
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return ProbeResult.Success(
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"PeterO.Numbers.EInteger",
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"Addition, subtraction, multiplication, division, and remainder compile on the CPU accelerator.");
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}
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catch (Exception ex)
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{
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return ProbeResult.Failure("PeterO.Numbers.EInteger", ex);
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}
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}
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static ProbeResult ProbeERational(Accelerator accelerator)
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{
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bool hasRemainder = HasERationalRemainder();
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try
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{
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var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<int, Stride1D.Dense>>(ERationalKernel);
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using var buffer = accelerator.Allocate1D<int>(1);
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kernel(new Index1D((int)buffer.Length), buffer.View);
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accelerator.Synchronize();
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string details = "Addition, subtraction, multiplication, and division compile on the CPU accelerator.";
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details += hasRemainder
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? " ERational exposes a remainder API that requires further investigation."
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: " ERational does not expose a remainder/modulo API.";
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return ProbeResult.Success("PeterO.Numbers.ERational", details);
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}
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catch (Exception ex)
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{
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string details = $"{ex.GetType().Name}: {ex.Message}";
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if (!hasRemainder)
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{
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details += " ERational does not expose a remainder/modulo API.";
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}
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return ProbeResult.Failure("PeterO.Numbers.ERational", details);
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}
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}
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static void BigIntegerKernel(Index1D index, ArrayView1D<int, Stride1D.Dense> data)
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{
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BigInteger value = new BigInteger(data[index]);
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value += BigInteger.One;
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value -= BigInteger.One;
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value *= new BigInteger(2);
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value /= new BigInteger(3);
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value %= new BigInteger(5);
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int comparison = value.CompareTo(BigInteger.Zero);
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data[index] = comparison;
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}
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static void EIntegerKernel(Index1D index, ArrayView1D<int, Stride1D.Dense> data)
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{
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EInteger value = EInteger.FromInt32(data[index]);
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value = value + EInteger.One;
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value = value - EInteger.One;
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value = value * EInteger.FromInt32(2);
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value = value.Divide(EInteger.FromInt32(3));
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value = value.Remainder(EInteger.FromInt32(5));
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int comparison = value.CompareTo(EInteger.Zero);
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data[index] = comparison;
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}
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static void ERationalKernel(Index1D index, ArrayView1D<int, Stride1D.Dense> data)
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{
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ERational value = ERational.FromInt32(data[index]);
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ERational adjusted = (value + ERational.FromInt32(1)) - ERational.FromInt32(1);
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ERational product = adjusted * ERational.FromInt32(2);
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ERational quotient = product / ERational.FromInt32(3);
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int comparison = quotient.CompareTo(ERational.FromInt32(0));
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data[index] = comparison;
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}
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static bool HasERationalRemainder()
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{
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foreach (var method in typeof(ERational).GetMethods())
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{
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if (string.Equals(method.Name, "Remainder", StringComparison.Ordinal))
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{
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return true;
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}
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}
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return false;
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}
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@@ -0,0 +1,11 @@
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<Project Sdk="Microsoft.NET.Sdk">
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<PropertyGroup>
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<OutputType>Exe</OutputType>
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<TargetFramework>net8.0</TargetFramework>
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<Nullable>enable</Nullable>
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<ImplicitUsings>enable</ImplicitUsings>
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</PropertyGroup>
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<ItemGroup>
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<ProjectReference Include="../../PerfectNumbers.Core/PerfectNumbers.Core.csproj" />
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</ItemGroup>
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</Project>
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@@ -0,0 +1,95 @@
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using System.Diagnostics;
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using PerfectNumbers.Core;
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namespace HeuristicMultiplyShiftTiming;
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internal static class Program
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{
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private static readonly MultiplyShiftInput[] Inputs =
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[
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new(0x3FFF_FFFF_FFFF_FFFFUL, 3UL, 3, "NearOverflowShift"),
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new(0x2000_0000_0000_0000UL, 7UL, 4, "HalfRange"),
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new(0x1234_5678_9ABC_DEF0UL, 5UL, 5, "MixedBits"),
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new(0x0000_0000_1000_0000UL, 11UL, 3, "Sparse"),
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];
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private const int Iterations = 200_000_000;
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public static void Main()
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{
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Console.WriteLine($"Timing each method for {Iterations:N0} iterations per input...\n");
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foreach (MultiplyShiftInput input in Inputs)
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{
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Console.WriteLine($"Input: {input.Name} (value=0x{input.Value:X16}, multiplier={input.Multiplier}, shift={input.Shift})");
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Measurement safe = MeasureSafe(input);
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Console.WriteLine($" MultiplyShiftRight (UInt128 product): {safe.AverageNanoseconds:F3} ns | checksum=0x{safe.Checksum:X16}");
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Measurement shiftFirst = MeasureShiftFirst(input);
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Console.WriteLine($" MultiplyShiftRightShiftFirst (shift-first): {shiftFirst.AverageNanoseconds:F3} ns | checksum=0x{shiftFirst.Checksum:X16}");
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Measurement naive = MeasureNaive(input);
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Console.WriteLine($" Naive ((value * multiplier) >> shift): {naive.AverageNanoseconds:F3} ns | checksum=0x{naive.Checksum:X16}\n");
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}
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}
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private static Measurement MeasureSafe(MultiplyShiftInput input)
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{
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ulong checksum = 0UL;
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Stopwatch sw = Stopwatch.StartNew();
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ulong value = input.Value;
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for (int i = 0; i < Iterations; i++)
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{
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checksum += HeuristicArithmetic.MultiplyShiftRight(value, input.Multiplier, input.Shift);
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value += 1UL;
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}
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sw.Stop();
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return CreateMeasurement(sw, checksum);
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}
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private static Measurement MeasureShiftFirst(MultiplyShiftInput input)
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{
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ulong checksum = 0UL;
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Stopwatch sw = Stopwatch.StartNew();
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ulong value = input.Value;
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for (int i = 0; i < Iterations; i++)
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{
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checksum += HeuristicArithmetic.MultiplyShiftRightShiftFirst(value, input.Multiplier, input.Shift);
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value += 1UL;
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}
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sw.Stop();
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return CreateMeasurement(sw, checksum);
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}
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private static Measurement MeasureNaive(MultiplyShiftInput input)
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{
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ulong checksum = 0UL;
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Stopwatch sw = Stopwatch.StartNew();
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ulong value = input.Value;
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for (int i = 0; i < Iterations; i++)
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{
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checksum += (value * input.Multiplier) >> input.Shift;
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value += 1UL;
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}
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sw.Stop();
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return CreateMeasurement(sw, checksum);
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}
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private static Measurement CreateMeasurement(Stopwatch sw, ulong checksum)
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{
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double elapsedNanoseconds = sw.ElapsedTicks * (1_000_000_000.0 / Stopwatch.Frequency);
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double averageNanoseconds = elapsedNanoseconds / Iterations;
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return new Measurement(averageNanoseconds, checksum);
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}
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private readonly record struct MultiplyShiftInput(ulong Value, ulong Multiplier, int Shift, string Name);
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private readonly record struct Measurement(double AverageNanoseconds, ulong Checksum);
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}
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