Split MulHigh extensions into CPU and GPU variants

EvenPerfectBitScanner.Benchmarks/Mul64Benchmarks.cs

@@ -89,7 +89,7 @@ public class Mul64Benchmarks
     {
         ulong leftLow = (ulong)left;
         ulong rightLow = (ulong)right;
-        return ((UInt128)(leftLow * (ulong)(right >> 64) + leftLow.MulHigh(rightLow)) << 64) | (UInt128)(leftLow * rightLow);
+        return ((UInt128)(leftLow * (ulong)(right >> 64) + leftLow.MulHighCpu(rightLow)) << 64) | (UInt128)(leftLow * rightLow);
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]

EvenPerfectBitScanner.Benchmarks/MulHighBenchmarks.cs

@@ -3,6 +3,7 @@ using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;
+using PerfectNumbers.Core.Gpu;
 
 namespace EvenPerfectBitScanner.Benchmarks;
 
@@ -36,10 +37,7 @@ public class MulHighBenchmarks
     [Benchmark(Baseline = true)]
     public ulong CurrentImplementation()
     {
-        // TODO: Replace ULongExtensions.MulHigh with the UInt128-based helper on CPU paths; it was
+        return ULongExtensions.MulHighCpu(Input.X, Input.Y);
-        // 11–14× faster in the latest benchmarks while the GPU-specific variant remains available
-        // separately.
-        return ULongExtensions.MulHigh(Input.X, Input.Y);
     }
 
     /// <summary>
@@ -107,7 +105,9 @@ public class MulHighBenchmarks
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static ulong MulHighWithGpuUInt128(ulong x, ulong y)
     {
-        return ULongExtensions.MulHighGpuCompatible(x, y);
+        GpuUInt128 product = new(x);
+        GpuUInt128.Mul64(ref product, 0UL, y);
+        return product.High;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]

EvenPerfectBitScanner.Benchmarks/MulMod64Benchmarks.cs

@@ -240,7 +240,7 @@ public class MulMod64Benchmarks
         ulong left = a % modulus;
         ulong right = b % modulus;
         ulong low = left * right;
-        ulong high = left.MulHigh(right);
+        ulong high = left.MulHighCpu(right);
         UInt128 product = ((UInt128)high << 64) | low;
         return (ulong)(product % modulus);
     }

PerfectNumbers.Core.Tests/ULongExtensionsTests.cs

@@ -131,11 +131,21 @@ public class ULongExtensionsTests
     [InlineData(0UL, 0UL)]
     [InlineData(ulong.MaxValue, 1UL)]
     [InlineData(123456789UL, 987654321UL)]
-    public void MulHigh_matches_high_bits(ulong x, ulong y)
+    public void MulHighCpu_matches_high_bits(ulong x, ulong y)
     {
         ulong expected = (ulong)(((UInt128)x * y) >> 64);
 
-        x.MulHigh(y).Should().Be(expected);
+        x.MulHighCpu(y).Should().Be(expected);
+    }
+
+    [Theory]
+    [Trait("Category", "Fast")]
+    [InlineData(0UL, 0UL)]
+    [InlineData(ulong.MaxValue, 1UL)]
+    [InlineData(123456789UL, 987654321UL)]
+    public void MulHighGpu_matches_cpu_baseline(ulong x, ulong y)
+    {
+        x.MulHighGpu(y).Should().Be(x.MulHighCpu(y));
     }
 
     [Theory]

PerfectNumbers.Core/UInt128Extensions.cs

@@ -760,7 +760,7 @@ public static class UInt128Extensions
     // expression tree around the shift. Mirroring the MulHigh layout lets RyuJIT
     // keep the intermediate sum in registers instead of reloading the partial
     // product from the stack.
-    ulong high = aLow.MulHigh(bLow);
+    ulong high = aLow.MulHighCpu(bLow);
     high += aLow * bHigh;
 
     return ((UInt128)high << 64) | low;

PerfectNumbers.Core/ULongExtensions.Gpu.cs

@@ -11,6 +11,7 @@ namespace PerfectNumbers.Core;
 public static partial class ULongExtensions
 {
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	[Obsolete("Use ULongExtensions.MulHighCpu or ULongExtensions.MulHighGpu.")]
 	public static ulong MulHighGpuCompatible(this ulong x, ulong y)
 	{
 		GpuUInt128 product = new(x);

PerfectNumbers.Core/ULongExtensions.cs

@@ -430,14 +430,19 @@ public static partial class ULongExtensions
 	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	public static UInt128 Mul64(this ulong a, ulong b) => ((UInt128)a.MulHigh(b) << 64) | (UInt128)(a * b);
+	public static UInt128 Mul64(this ulong a, ulong b) => ((UInt128)a.MulHighCpu(b) << 64) | (UInt128)(a * b);
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	public static ulong MulHigh(this ulong x, ulong y)
+	public static ulong MulHighCpu(this ulong x, ulong y)
 	{
-		// TODO: Investigate replacing this manual decomposition with the UInt128-based implementation
+		return (ulong)(((UInt128)x * y) >> 64);
-		// for CPU callers; the latest benchmarks show the intrinsic path is an order of magnitude
+	}
-		// faster, while GPU code can keep using GpuUInt128.MulHigh.
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public static ulong MulHighGpu(this ulong x, ulong y)
+	{
+		// The CPU helpers rely on UInt128 via MulHighCpu; retain this manual decomposition for GPU-style
+		// arithmetic so callers can avoid the intrinsic when staging work for accelerators.
 		ulong xLow = (uint)x;
 		ulong xHigh = x >> 32;
 		ulong yLow = (uint)y;
@@ -554,7 +559,7 @@ public static partial class ULongExtensions
 		ulong m = unchecked(tLow * nPrime);
 		ulong mTimesModulusLow = unchecked(m * modulus);
 
-		ulong result = unchecked(a.MulHigh(b) + m.MulHigh(modulus) + (unchecked(tLow + mTimesModulusLow) < tLow ? 1UL : 0UL));
+		ulong result = unchecked(a.MulHighCpu(b) + m.MulHighCpu(modulus) + (unchecked(tLow + mTimesModulusLow) < tLow ? 1UL : 0UL));
 		if (result >= modulus)
 		{
 			result -= modulus;