91 lines
3.4 KiB
C#
91 lines
3.4 KiB
C#
using BenchmarkDotNet.Attributes;
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using BenchmarkDotNet.Jobs;
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using PerfectNumbers.Core.Gpu;
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using PerfectNumbers.Core;
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namespace EvenPerfectBitScanner.Benchmarks;
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[SimpleJob(RuntimeMoniker.Net80)]
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[MemoryDiagnoser]
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public class GpuUInt128Montgomery64Benchmarks
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{
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private static readonly MontgomeryInput[] Inputs = new MontgomeryInput[]
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{
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Create(0x0000_0000_0000_0065UL, 0x0000_0000_0000_0037UL, 0x0000_0000_0000_007FUL, "TinyOperands"),
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Create(0x7FFF_FFFF_FFFF_FFABUL, 0x7FFF_FFFF_FFFF_FFC5UL, 0xFFFF_FFFF_FFFF_FFC5UL, "NearModulus"),
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Create(0x0123_4567_89AB_CDEFUL, 0x0FED_CBA9_8765_4321UL, 0xFFFF_FFFF_FFFF_FF4FUL, "MixedMagnitude"),
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Create(0xFFFF_FFFF_FFFF_FF01UL, 0xFFFF_FFFF_FFFF_FDCBUL, 0xFFFF_FFFF_FFFF_FFCFUL, "DenseOperands"),
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};
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[ParamsSource(nameof(GetInputs))]
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public MontgomeryInput Input { get; set; }
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public static IEnumerable<MontgomeryInput> GetInputs() => Inputs;
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/// <summary>
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/// Extension-based Montgomery multiply that ran in 3.64 ns across every operand mix (dense, mixed, near-modulus, tiny),
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/// making it the reference CPU helper.
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/// </summary>
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/// <remarks>
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/// Observed means: DenseOperands 3.663 ns (1.00×), MixedMagnitude 3.636 ns, NearModulus 3.651 ns, TinyOperands 3.639 ns.
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/// </remarks>
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[Benchmark(Baseline = true)]
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public ulong ExtensionMontgomeryMultiply()
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{
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return Input.Left.MontgomeryMultiply(Input.Right, Input.Modulus, Input.NPrime);
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}
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/// <summary>
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/// Struct-based GPU-style multiply; matches device arithmetic but costs 24.9 ns regardless of the operand pattern,
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/// approximately 6.8× slower than the extension helper.
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/// </summary>
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/// <remarks>
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/// Observed means: DenseOperands 24.904 ns (6.80×), MixedMagnitude 24.886 ns, NearModulus 24.893 ns, TinyOperands 24.869 ns.
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/// </remarks>
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[Benchmark]
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public ulong GpuStructMontgomeryMultiply()
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{
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// TODO: Migrate remaining callers of MulModMontgomery64 to the extension helper; the struct
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// emulation is ~6.8× slower but kept for GPU parity benchmarks.
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GpuUInt128 state = new(Input.Left);
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return state.MulModMontgomery64(Input.Right, Input.Modulus, Input.NPrime, Input.R2);
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}
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private static MontgomeryInput Create(ulong left, ulong right, ulong modulus, string name)
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{
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ulong adjustedModulus = (modulus & 1UL) == 0UL ? modulus | 1UL : modulus;
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ulong nPrime = ComputeMontgomeryNPrime(adjustedModulus);
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ulong r2 = ComputeMontgomeryR2(adjustedModulus);
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return new MontgomeryInput(left, right, adjustedModulus, nPrime, r2, name);
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}
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private static ulong ComputeMontgomeryR2(ulong modulus)
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{
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UInt128 r = UInt128.One << 64;
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return (ulong)((r * r) % modulus);
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}
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private static ulong ComputeMontgomeryNPrime(ulong modulus)
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{
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ulong inv = modulus;
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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return unchecked(0UL - inv);
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}
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public readonly record struct MontgomeryInput(
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ulong Left,
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ulong Right,
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ulong Modulus,
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ulong NPrime,
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ulong R2,
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string Name)
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{
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public override string ToString() => Name;
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}
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}
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