Inline GpuUInt128 Mul64 helper

PerfectNumbers.Core/Gpu/GpuUInt128.cs

@@ -456,47 +456,46 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
         return yHigh;
     }
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void Mul64(in ReadOnlyGpuUInt128 other) => Mul64Internal(other.High, other.Low);
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void Mul64(GpuUInt128 other) => Mul64Internal(other.High, other.Low);
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private void Mul64Internal(ulong otherHigh, ulong otherLow)
-    {
-        // Multiply this.Low (assumed 64-bit value) by full 128-bit other
-        ulong operand = Low;
-        Low = operand * otherLow;
-        ulong highProduct = operand * otherHigh;
-        High = highProduct + MulHigh(operand, otherLow);
-    }
-
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     // Kept by-value to coexist with the ref readonly overload below while still signaling read-only intent.
     public void MulMod(ReadOnlyGpuUInt128 value, in ReadOnlyGpuUInt128 modulus)
     {
         GpuUInt128 multiplicand = this;
         GpuUInt128 multiplier = value.ToMutable();
-
-        High = 0UL;
-        Low = 0UL;
+        GpuUInt128 result = new();
 
         while (!multiplier.IsZero)
         {
             if ((multiplier.Low & 1UL) != 0UL)
             {
-                AddMod(multiplicand, modulus);
+                result.Add(multiplicand);
+                if (result.CompareTo(modulus) >= 0)
+                {
+                    result.Sub(modulus);
+                }
             }
 
-            multiplicand.ShiftLeft(1);
+            // The allocating shift path remains faster than the in-place variants in the GpuUInt128MulMod benchmarks.
+            multiplicand = multiplicand << 1;
             if (multiplicand.CompareTo(modulus) >= 0)
             {
                 multiplicand.Sub(modulus);
             }
 
-            multiplier.ShiftRight(1);
+            if (multiplier.High == 0UL)
+            {
+                multiplier.Low >>= 1;
+            }
+            else
+            {
+                ulong newLow = (multiplier.Low >> 1) | (multiplier.High << 63);
+                multiplier.High >>= 1;
+                multiplier.Low = newLow;
+            }
         }
+
+        High = result.High;
+        Low = result.Low;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -743,6 +742,15 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
         Low = lowPart;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static void Mul64(ref GpuUInt128 value, ulong otherHigh, ulong otherLow)
+    {
+        ulong operand = value.Low;
+        value.Low = operand * otherLow;
+        ulong highProduct = operand * otherHigh;
+        value.High = highProduct + MulHigh(operand, otherLow);
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static GpuUInt128 DivideExact(in ReadOnlyGpuUInt128 dividend, in ReadOnlyGpuUInt128 divisor)
     {
@@ -868,54 +876,6 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
         // (e.g., Montgomery n', R2) and provide device-friendly accessors.
     }
 
-    /// <summary>
-    /// Modular multiplication using <see cref="BigInteger"/> reduction. This
-    /// method is intended for validation only and should not be used inside
-    /// GPU kernels.
-    /// </summary>
-    internal void MulModBigInteger(in ReadOnlyGpuUInt128 other, in ReadOnlyGpuUInt128 modulus)
-    {
-        var left = (BigInteger)(UInt128)this;
-        var right = (BigInteger)(UInt128)other;
-        var mod = (BigInteger)(UInt128)modulus;
-        var reduced = (UInt128)((left * right) % mod);
-        High = (ulong)(reduced >> 64);
-        Low = (ulong)reduced;
-    }
-
-    /// <summary>
-    /// Experimental limb-based reduction. The current implementation performs
-    /// repeated subtractions and becomes extremely slow for large remainders.
-    /// Kept for future optimization work.
-    /// </summary>
-    internal void MulModByLimb(in ReadOnlyGpuUInt128 other, in ReadOnlyGpuUInt128 modulus)
-    {
-        // TODO: Relocate this limb-based reducer to the benchmark project once the production
-        // pipeline switches to the faster allocating legacy path demonstrated in the benchmarks.
-        MultiplyFull(this, other, out var p3, out var p2, out var p1, out var p0);
-
-        High = p3;
-        Low = p2;
-        while (CompareTo(modulus) >= 0)
-        {
-            Sub(modulus);
-        }
-
-        ulong limb = p1;
-        for (int i = 0; i < 2; i++)
-        {
-            ShiftLeft(64);
-            Low = limb;
-            while (CompareTo(modulus) >= 0)
-            {
-                Sub(modulus);
-            }
-
-            limb = p0;
-        }
-
-    }
-
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void MulMod(ulong value, in ReadOnlyGpuUInt128 modulus)
     {

PerfectNumbers.Core/Gpu/Kernels/IncrementalKernels.cs

@@ -71,7 +71,7 @@ internal static class IncrementalKernels
         // TODO: Is this expected that the value of kStart is modified?
         GpuUInt128 k = kStart + (GpuUInt128)idx;
         GpuUInt128 q = twoP;
-        q.Mul64(k);
+        GpuUInt128.Mul64(ref q, k.High, k.Low);
         q.Add(GpuUInt128.One);
         ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
 
@@ -174,7 +174,7 @@ internal static class IncrementalKernels
 
         GpuUInt128 k = kStart + (GpuUInt128)idx;
         GpuUInt128 q = twoP;
-        q.Mul64(k);
+        GpuUInt128.Mul64(ref q, k.High, k.Low);
         q.Add(GpuUInt128.One);
         ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
 

PerfectNumbers.Core/Gpu/Kernels/Pow2ModKernels.cs

@@ -64,7 +64,7 @@ internal static class Pow2ModKernels
         // TODO: kStart is modified after this. Is this expected?
         kStart.Add(idx);
         GpuUInt128 q = twoP;
-        q.Mul64(kStart);
+        GpuUInt128.Mul64(ref q, kStart.High, kStart.Low);
         q.Add(GpuUInt128.One);
         ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
         if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
@@ -158,7 +158,7 @@ internal static class Pow2ModKernels
 
         GpuUInt128 k = kStart + (GpuUInt128)idx;
         GpuUInt128 q = twoP;
-        q.Mul64(k);
+        GpuUInt128.Mul64(ref q, k.High, k.Low);
         q.Add(GpuUInt128.One);
         ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
         // Small-cycles in-kernel early rejection from device table