Return scalar MulMod results and benchmark native reducers

EvenPerfectBitScanner.Benchmarks/GpuUInt128Montgomery64Benchmarks.cs

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+using System;
+using System.Collections.Generic;
+using BenchmarkDotNet.Attributes;
+using BenchmarkDotNet.Jobs;
+using PerfectNumbers.Core.Gpu;
+using PerfectNumbers.Core;
+
+namespace EvenPerfectBitScanner.Benchmarks;
+
+[SimpleJob(RuntimeMoniker.Net80)]
+[MemoryDiagnoser]
+public class GpuUInt128Montgomery64Benchmarks
+{
+    private static readonly MontgomeryInput[] Inputs = new MontgomeryInput[]
+    {
+        Create(0x0000_0000_0000_0065UL, 0x0000_0000_0000_0037UL, 0x0000_0000_0000_007FUL, "TinyOperands"),
+        Create(0x7FFF_FFFF_FFFF_FFABUL, 0x7FFF_FFFF_FFFF_FFC5UL, 0xFFFF_FFFF_FFFF_FFC5UL, "NearModulus"),
+        Create(0x0123_4567_89AB_CDEFUL, 0x0FED_CBA9_8765_4321UL, 0xFFFF_FFFF_FFFF_FF4FUL, "MixedMagnitude"),
+        Create(0xFFFF_FFFF_FFFF_FF01UL, 0xFFFF_FFFF_FFFF_FDCBUL, 0xFFFF_FFFF_FFFF_FFCFUL, "DenseOperands"),
+    };
+
+    [ParamsSource(nameof(GetInputs))]
+    public MontgomeryInput Input { get; set; }
+
+    public static IEnumerable<MontgomeryInput> GetInputs() => Inputs;
+
+    [Benchmark(Baseline = true)]
+    public ulong ExtensionMontgomeryMultiply()
+    {
+        return Input.Left.MontgomeryMultiply(Input.Right, Input.Modulus, Input.NPrime);
+    }
+
+    [Benchmark]
+    public ulong GpuStructMontgomeryMultiply()
+    {
+        GpuUInt128 state = new(Input.Left);
+        return state.MulModMontgomery64(Input.Right, Input.Modulus, Input.NPrime, Input.R2);
+    }
+
+    private static MontgomeryInput Create(ulong left, ulong right, ulong modulus, string name)
+    {
+        ulong adjustedModulus = (modulus & 1UL) == 0UL ? modulus | 1UL : modulus;
+        ulong nPrime = ComputeMontgomeryNPrime(adjustedModulus);
+        ulong r2 = ComputeMontgomeryR2(adjustedModulus);
+        return new MontgomeryInput(left, right, adjustedModulus, nPrime, r2, name);
+    }
+
+    private static ulong ComputeMontgomeryR2(ulong modulus)
+    {
+        UInt128 r = UInt128.One << 64;
+        return (ulong)((r * r) % modulus);
+    }
+
+    private static ulong ComputeMontgomeryNPrime(ulong modulus)
+    {
+        ulong inv = modulus;
+        inv *= unchecked(2UL - modulus * inv);
+        inv *= unchecked(2UL - modulus * inv);
+        inv *= unchecked(2UL - modulus * inv);
+        inv *= unchecked(2UL - modulus * inv);
+        inv *= unchecked(2UL - modulus * inv);
+        inv *= unchecked(2UL - modulus * inv);
+        return unchecked(0UL - inv);
+    }
+
+    public readonly record struct MontgomeryInput(
+        ulong Left,
+        ulong Right,
+        ulong Modulus,
+        ulong NPrime,
+        ulong R2,
+        string Name)
+    {
+        public override string ToString() => Name;
+    }
+}