Return scalar MulMod results and benchmark native reducers

EvenPerfectBitScanner.Benchmarks/GpuUInt128MulModByLimbBenchmarks.cs

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+using System.Collections.Generic;
+using BenchmarkDotNet.Attributes;
+using BenchmarkDotNet.Jobs;
+using PerfectNumbers.Core.Gpu;
+
+namespace EvenPerfectBitScanner.Benchmarks;
+
+[SimpleJob(RuntimeMoniker.Net80)]
+[MemoryDiagnoser]
+public class GpuUInt128MulModByLimbBenchmarks
+{
+    private static readonly MulModByLimbInput[] Inputs = new MulModByLimbInput[]
+    {
+        new(
+            new GpuUInt128(0UL, 17UL),
+            new GpuUInt128(0UL, 19UL),
+            new GpuUInt128(0x0000_0000_0000_0001UL, 0x0000_0000_0000_00FFUL),
+            "TinyOperands"),
+        new(
+            new GpuUInt128(0x0123_4567_89AB_CDEFUL, 0xFEDC_BA98_7654_3210UL),
+            new GpuUInt128(0x0F1E_2D3C_4B5A_6978UL, 0x8776_6554_4332_2110UL),
+            new GpuUInt128(0x0FFF_FFFF_FFFF_FFFFUL, 0xFFFF_FFFF_FFFF_FFC3UL),
+            "MixedMagnitude"),
+        new(
+            new GpuUInt128(0x8000_0000_0000_0000UL, 0x0000_0000_0000_0001UL),
+            new GpuUInt128(0x7FFF_FFFF_FFFF_FFFFUL, 0x8000_0000_0000_0000UL),
+            new GpuUInt128(0x7FFF_FFFF_FFFF_FFFFUL, 0xFFFF_FFFF_FFFF_FFF1UL),
+            "HighWordDominant"),
+    };
+
+    [ParamsSource(nameof(GetInputs))]
+    public MulModByLimbInput Input { get; set; }
+
+    public static IEnumerable<MulModByLimbInput> GetInputs() => Inputs;
+
+    [Benchmark(Baseline = true)]
+    public GpuUInt128 LegacyAllocating()
+    {
+        return MulModByLimbLegacy(Input.Left, Input.Right, Input.Modulus);
+    }
+
+    [Benchmark]
+    public GpuUInt128 InPlaceReduction()
+    {
+        GpuUInt128 value = Input.Left;
+        value.MulModByLimb(Input.Right, Input.Modulus);
+        return value;
+    }
+
+    private static GpuUInt128 MulModByLimbLegacy(GpuUInt128 left, GpuUInt128 right, GpuUInt128 modulus)
+    {
+        var (p3, p2, p1, p0) = MultiplyFullLegacy(left, right);
+
+        GpuUInt128 remainder = new(p3, p2);
+        while (remainder.CompareTo(modulus) >= 0)
+        {
+            remainder.Sub(modulus);
+        }
+
+        ulong limb = p1;
+        for (int i = 0; i < 2; i++)
+        {
+            remainder <<= 64;
+            remainder = new GpuUInt128(remainder.High, limb);
+            while (remainder.CompareTo(modulus) >= 0)
+            {
+                remainder.Sub(modulus);
+            }
+
+            limb = p0;
+        }
+
+        return remainder;
+    }
+
+    private static (ulong P3, ulong P2, ulong P1, ulong P0) MultiplyFullLegacy(GpuUInt128 left, GpuUInt128 right)
+    {
+        var (h0, l0) = Mul64Legacy(left.Low, right.Low);
+        var (h1, l1) = Mul64Legacy(left.Low, right.High);
+        var (h2, l2) = Mul64Legacy(left.High, right.Low);
+        var (h3, l3) = Mul64Legacy(left.High, right.High);
+
+        ulong carry = 0UL;
+        ulong sum0 = l0;
+        ulong sum1 = h0;
+
+        sum1 += l1;
+        if (sum1 < l1)
+        {
+            carry++;
+        }
+
+        sum1 += l2;
+        if (sum1 < l2)
+        {
+            carry++;
+        }
+
+        ulong sum2 = h1 + h2;
+        ulong carry2 = sum2 < h2 ? 1UL : 0UL;
+        sum2 += l3;
+        if (sum2 < l3)
+        {
+            carry2++;
+        }
+
+        sum2 += carry;
+        if (sum2 < carry)
+        {
+            carry2++;
+        }
+
+        ulong p1 = sum1;
+        ulong p2 = sum2;
+        ulong p3 = h3 + carry2;
+
+        return (p3, p2, p1, sum0);
+    }
+
+    private static (ulong High, ulong Low) Mul64Legacy(ulong left, ulong right)
+    {
+        ulong a0 = (uint)left;
+        ulong a1 = left >> 32;
+        ulong b0 = (uint)right;
+        ulong b1 = right >> 32;
+
+        ulong lo = a0 * b0;
+        ulong mid1 = a1 * b0;
+        b0 = a0 * b1;
+        b1 *= a1;
+
+        a0 = (lo >> 32) + (uint)mid1 + (uint)b0;
+        a1 = (lo & 0xFFFF_FFFFUL) | (a0 << 32);
+        b1 += (mid1 >> 32) + (b0 >> 32) + (a0 >> 32);
+
+        return (b1, a1);
+    }
+
+    public readonly record struct MulModByLimbInput(GpuUInt128 Left, GpuUInt128 Right, GpuUInt128 Modulus, string Name)
+    {
+        public override string ToString() => Name;
+    }
+}
+