Initial PollardRho implementation for GPU. Added pool for accelerator streams shared across the threads. GPU processing performance and stabilization improvements. GpuUInt128.BinaryGcd switched to the version which outperformed other in benchmarks.

PerfectNumbers.Core/Gpu/Kernels/Pow2MontgomeryKernels.cs

@@ -1,3 +1,4 @@
+using System.Runtime.CompilerServices;
 using ILGPU;
 using ILGPU.Runtime;
 
@@ -5,21 +6,75 @@ namespace PerfectNumbers.Core.Gpu.Kernels;
 
 internal static class Pow2MontgomeryKernels
 {
-    public static void Pow2MontgomeryKernelKeepMontgomery(
-        Index1D index,
-        ArrayView1D<ulong, Stride1D.Dense> exponents,
-        MontgomeryDivisorData divisor,
-        ArrayView1D<ulong, Stride1D.Dense> results)
-    {
-        results[index] = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(divisor, exponents[index]);
-    }
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static GpuUInt128 AdvancePolynomialGpu(GpuUInt128 x, ulong c, ulong modulus)
+	{
+		x.Pow2();
+		x.AddMod(c, modulus);
+		return x;
+	}
 
-    public static void Pow2MontgomeryKernelConvertToStandard(
-        Index1D index,
-        ArrayView1D<ulong, Stride1D.Dense> exponents,
-        MontgomeryDivisorData divisor,
-        ArrayView1D<ulong, Stride1D.Dense> results)
-    {
-        results[index] = ULongExtensions.Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponents[index]);
-    }
+	public static void Pow2MontgomeryKernelKeepMontgomery(
+		Index1D index,
+		ArrayView1D<ulong, Stride1D.Dense> exponents,
+		MontgomeryDivisorData divisor,
+		ArrayView1D<ulong, Stride1D.Dense> results)
+	{
+		results[0] = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(divisor, exponents[0]);
+	}
+
+	public static void Pow2MontgomeryKernelConvertToStandard(
+		Index1D index,
+		ArrayView1D<ulong, Stride1D.Dense> exponents,
+		MontgomeryDivisorData divisor,
+		ArrayView1D<ulong, Stride1D.Dense> results)
+	{
+		results[0] = ULongExtensions.Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponents[0]);
+	}
+
+
+	public static void TryPollardRhoKernel(ulong n, int limit, ArrayView1D<ulong, Stride1D.Dense> randomState, ArrayView1D<byte, Stride1D.Dense> factored, ArrayView1D<ulong, Stride1D.Dense> factor)
+	{
+		factored[0] = 0;
+		if ((n & 1UL) == 0UL)
+		{
+			factor[0] = 2UL;
+			factored[0] = 1;
+			return;
+		}
+
+		int attempt = 0;
+		GpuUInt128 nGpuUInt128 = (GpuUInt128)n;
+		DeterministicRandomGpu random = new(randomState[0]);
+		while (attempt < limit)
+		{
+			ulong c = (random.NextUInt64() % (n - 1UL)) + 1UL;
+			GpuUInt128 x = (random.NextUInt64() % (n - 2UL)) + 2UL;
+			GpuUInt128 y = x;
+			GpuUInt128 d = GpuUInt128.One;
+
+			while (d.CompareTo(GpuUInt128.One) == 0)
+			{
+				x = AdvancePolynomialGpu(x, c, modulus: n);
+				y = AdvancePolynomialGpu(y, c, n);
+				y = AdvancePolynomialGpu(y, c, n);
+				GpuUInt128 diff = x.CompareTo(y) > 0 ? x - y : y - x;
+				d = GpuUInt128.BinaryGcd(diff, nGpuUInt128);
+			}
+
+			if (d != n)
+			{
+				if (d.High == 0)
+				{
+					factor[0] = d.Low;
+					factored[0] = 1;
+					return;
+				}
+			}
+
+			attempt++;
+		}
+
+		randomState[0] = random.State;
+	}
 }