Kernels replaced with pre-compiled actions for better performance

EvenPerfectBitScanner.Benchmarks/PrimeTesterBenchmarks.cs

@@ -28,8 +28,8 @@ public class PrimeTesterBenchmarks
 
 		PrimeOrderCalculatorAccelerator.WarmUp();
 		// HeuristicGroupABPrimeTesterAccelerator.WarmUp();
-        _ = _heuristicTester.IsPrimeCpu(_candidates[0]);
+        _ = HeuristicPrimeTester.IsPrimeCpu(_candidates[0]);
-        _ = _heuristicTester.IsPrimeGpu(_candidates[0]);
+        _ = HeuristicPrimeTester.IsPrimeGpu(_candidates[0]);
         _ = Prime.Numbers.IsPrime(_candidates[0]);
     }
 
@@ -42,7 +42,7 @@ public class PrimeTesterBenchmarks
 
         for (int i = 0; i < values.Length; i++)
         {
-            if (tester.IsPrimeCpu(values[i]))
+            if (HeuristicPrimeTester.IsPrimeCpu(values[i]))
             {
                 primeCount++;
             }
@@ -60,7 +60,7 @@ public class PrimeTesterBenchmarks
 
         for (int i = 0; i < values.Length; i++)
         {
-            if (tester.IsPrimeGpu(values[i]))
+            if (HeuristicPrimeTester.IsPrimeGpu(values[i]))
             {
                 primeCount++;
             }

EvenPerfectBitScanner.ResultsParser/Program.cs

@@ -19,7 +19,7 @@ internal static class Program
 				"/help"
 		};
 
-	private const string DefaultHeader = "p,searchedMersenne,detailedCheck,passedAllTests";
+private const string DefaultHeader = "p,divisor,searchedMersenne,detailedCheck,passedAllTests";
 
 	private static int Main(string[] args)
 	{

EvenPerfectBitScanner/CalculationResultHandler.cs

@@ -7,7 +7,7 @@ namespace EvenPerfectBitScanner;
 
 internal static class CalculationResultHandler
 {
-        private const string ResultsHeader = "p,searchedMersenne,detailedCheck,passedAllTests";
+        private const string ResultsHeader = "p,divisor,searchedMersenne,detailedCheck,passedAllTests";
         private const string PrimeFoundSuffix = " (FOUND VALID CANDIDATES)";
         internal const int DefaultWriteBatchSize = 100;
 
@@ -93,19 +93,19 @@ internal static class CalculationResultHandler
         }
 
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        internal static void HandleResult(ulong currentP, bool searchedMersenne, bool detailedCheck, bool passedAllTests, bool lastWasComposite)
+        internal static void HandleResult(ulong currentP, ulong divisor, bool searchedMersenne, bool detailedCheck, bool passedAllTests, bool lastWasComposite)
         {
                 // Program flow ensures Initialize(...) and InitializeOutputBuffer() ran before this call. Do not add initialization guards here.
 
                 Span<byte> stackBuffer = stackalloc byte[128];
                 byte[]? rentedBuffer = null;
                 Span<byte> utf8Span = stackBuffer;
-                int byteCount = TryFormatResultLine(utf8Span, currentP, searchedMersenne, detailedCheck, passedAllTests);
+                int byteCount = TryFormatResultLine(utf8Span, currentP, divisor, searchedMersenne, detailedCheck, passedAllTests);
                 if (byteCount < 0)
                 {
                         rentedBuffer = ThreadStaticPools.BytePool.Rent(256);
                         utf8Span = rentedBuffer;
-                        byteCount = TryFormatResultLine(utf8Span, currentP, searchedMersenne, detailedCheck, passedAllTests);
+                        byteCount = TryFormatResultLine(utf8Span, currentP, divisor, searchedMersenne, detailedCheck, passedAllTests);
                         if (byteCount < 0)
                         {
                                 ThreadStaticPools.BytePool.Return(rentedBuffer);
@@ -229,7 +229,7 @@ internal static class CalculationResultHandler
         }
 
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        private static int TryFormatResultLine(Span<byte> destination, ulong currentP, bool searchedMersenne, bool detailedCheck, bool passedAllTests)
+        private static int TryFormatResultLine(Span<byte> destination, ulong currentP, ulong divisor, bool searchedMersenne, bool detailedCheck, bool passedAllTests)
         {
                 int offset = 0;
 
@@ -246,6 +246,19 @@ internal static class CalculationResultHandler
 
                 destination[offset++] = (byte)',';
 
+                if (!Utf8Formatter.TryFormat(divisor, destination[offset..], out written))
+                {
+                        return -1;
+                }
+
+                offset += written;
+                if (offset >= destination.Length)
+                {
+                        return -1;
+                }
+
+                destination[offset++] = (byte)',';
+
                 if (!Utf8Formatter.TryFormat(searchedMersenne, destination[offset..], out written))
                 {
                         return -1;

EvenPerfectBitScanner/IO/CalculationResultsFile.cs

@@ -100,6 +100,7 @@ internal static class CalculationResultsFile
                 int first = 0;
                 int second = 0;
                 int third = 0;
+                int fourth = 0;
                 ulong parsedP = 0UL;
                 ReadOnlySpan<char> detailedSpan = default;
                 ReadOnlySpan<char> passedAllTestsSpan = default;
@@ -139,8 +140,15 @@ internal static class CalculationResultsFile
                                 continue;
                         }
 
-                        detailedSpan = span[..third];
+                        span = span[(third + 1)..];
-                        passedAllTestsSpan = span[(third + 1)..];
+                        fourth = span.IndexOf(',');
+                        if (fourth < 0)
+                        {
+                                continue;
+                        }
+
+                        detailedSpan = span[..fourth];
+                        passedAllTestsSpan = span[(fourth + 1)..];
 
                         if (Utf8CliParser.TryParseBoolean(detailedSpan, out detailed) && Utf8CliParser.TryParseBoolean(passedAllTestsSpan, out passedAllTests))
                         {

EvenPerfectBitScanner/Program.cs

@@ -422,7 +422,7 @@ internal static class Program
 						_byDivisorStartPrime,
 						static () => _lastCompositeP = true,
 						static () => _lastCompositeP = false,
-						static (candidate, searchedMersenne, detailedCheck, passedAllTests) => CalculationResultHandler.HandleResult(candidate, searchedMersenne, detailedCheck, passedAllTests, _lastCompositeP),
+						static (candidate, searchedMersenne, detailedCheck, passedAllTests, divisor) => CalculationResultHandler.HandleResult(candidate, divisor, searchedMersenne, detailedCheck, passedAllTests, _lastCompositeP),
 						threadCount,
 						byDivisorPrimeRange);
 						
@@ -483,7 +483,7 @@ internal static class Program
 							{
 								p = buffer[j];
 								passedAllTests = IsEvenPerfectCandidate(p, divisorCyclesSearchLimit, out searchedMersenne, out detailedCheck);
-								CalculationResultHandler.HandleResult(p, searchedMersenne, detailedCheck, passedAllTests, _lastCompositeP);
+								CalculationResultHandler.HandleResult(p, 0UL, searchedMersenne, detailedCheck, passedAllTests, _lastCompositeP);
 							}
 
 							continue;
@@ -506,7 +506,7 @@ internal static class Program
 							}
 
 							passedAllTests = IsEvenPerfectCandidate(p, divisorCyclesSearchLimit, out searchedMersenne, out detailedCheck);
-							CalculationResultHandler.HandleResult(p, searchedMersenne, detailedCheck, passedAllTests, _lastCompositeP);
+							CalculationResultHandler.HandleResult(p, 0UL, searchedMersenne, detailedCheck, passedAllTests, _lastCompositeP);
 
 							if (p == maxP)
 							{
@@ -649,7 +649,7 @@ internal static class Program
 		if (_cliArguments.UseByDivisor)
 		{
 			// Windowed pow2mod kernel handles by-divisor scans.
-			return _byDivisorTester!.IsPrime(p, out detailedCheck);
+			return _byDivisorTester!.IsPrime(p, out detailedCheck, out _);
 		}
 
 		detailedCheck = MersenneTesters.Value!.IsMersennePrime(p);

PerfectNumbers.Core.Tests/MersenneNumberDivisorByDivisorTesterTests.cs

@@ -11,7 +11,7 @@ public class MersenneNumberDivisorByDivisorTesterTests
     {
         var candidates = new List<ulong> { 5UL, 7UL, 11UL, 13UL };
         var tester = new FakeTester();
-        var results = new List<(ulong Prime, bool Searched, bool Detailed, bool Passed)>();
+        var results = new List<(ulong Prime, bool Searched, bool Detailed, bool Passed, ulong Divisor)>();
         int compositeMarks = 0;
         int clearedMarks = 0;
 
@@ -22,7 +22,7 @@ public class MersenneNumberDivisorByDivisorTesterTests
             startPrime: 0UL,
             markComposite: () => compositeMarks++,
             clearComposite: () => clearedMarks++,
-            printResult: (prime, searched, detailed, passed) => results.Add((prime, searched, detailed, passed)),
+            printResult: (prime, searched, detailed, passed, divisor) => results.Add((prime, searched, detailed, passed, divisor)),
             threadCount: 1,
             primesPerTask: 2);
 
@@ -32,10 +32,10 @@ public class MersenneNumberDivisorByDivisorTesterTests
         results.Should().Equal(
             new[]
             {
-                (5UL, true, true, true),
+                (5UL, true, true, true, 0UL),
-                (7UL, true, true, false),
+                (7UL, true, true, false, 7UL),
-                (11UL, true, true, false),
+                (11UL, true, true, false, 11UL),
-                (13UL, true, true, true),
+                (13UL, true, true, true, 0UL),
             });
     }
 
@@ -57,10 +57,23 @@ public class MersenneNumberDivisorByDivisorTesterTests
             return DivisorLimit;
         }
 
-        public bool IsPrime(ulong prime, out bool divisorsExhausted)
+        public bool IsPrime(ulong prime, out bool divisorsExhausted, out ulong divisor)
         {
             divisorsExhausted = true;
-            return prime % 7UL != 0UL && prime % 11UL != 0UL;
+            if (prime % 7UL == 0UL)
+            {
+                divisor = 7UL;
+                return false;
+            }
+
+            if (prime % 11UL == 0UL)
+            {
+                divisor = 11UL;
+                return false;
+            }
+
+            divisor = 0UL;
+            return true;
         }
 
         public IMersenneNumberDivisorByDivisorTester.IDivisorScanSession CreateDivisorSession()

PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs

@@ -13,14 +13,17 @@ public class MersenneNumberDivisorCpuTesterTests
                 var tester = new MersenneNumberDivisorByDivisorCpuTester();
                 tester.ConfigureFromMaxPrime(11UL);
 
-                tester.IsPrime(5UL, out bool divisorsExhausted).Should().BeTrue();
+                tester.IsPrime(5UL, out bool divisorsExhausted, out ulong divisor).Should().BeTrue();
                 divisorsExhausted.Should().BeTrue();
+                divisor.Should().Be(0UL);
 
-                tester.IsPrime(7UL, out divisorsExhausted).Should().BeTrue();
+                tester.IsPrime(7UL, out divisorsExhausted, out divisor).Should().BeTrue();
                 divisorsExhausted.Should().BeTrue();
+                divisor.Should().Be(0UL);
 
-                tester.IsPrime(11UL, out divisorsExhausted).Should().BeFalse();
+                tester.IsPrime(11UL, out divisorsExhausted, out divisor).Should().BeFalse();
                 divisorsExhausted.Should().BeTrue();
+                divisor.Should().BeGreaterThan(0UL);
         }
 
         [Fact]

PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs

@@ -73,14 +73,17 @@ public class MersenneNumberDivisorGpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorGpuTester();
         tester.ConfigureFromMaxPrime(43UL);
 
-        tester.IsPrime(31UL, out bool exhausted).Should().BeTrue();
+        tester.IsPrime(31UL, out bool exhausted, out ulong divisor).Should().BeTrue();
         exhausted.Should().BeTrue();
+        divisor.Should().Be(0UL);
 
-        tester.IsPrime(37UL, out exhausted).Should().BeFalse();
+        tester.IsPrime(37UL, out exhausted, out divisor).Should().BeFalse();
         exhausted.Should().BeTrue();
+        divisor.Should().BeGreaterThan(0UL);
 
-        tester.IsPrime(43UL, out exhausted).Should().BeFalse();
+        tester.IsPrime(43UL, out exhausted, out divisor).Should().BeFalse();
         exhausted.Should().BeTrue();
+        divisor.Should().BeGreaterThan(0UL);
     }
 
     [Fact]
@@ -105,12 +108,15 @@ public class MersenneNumberDivisorGpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorGpuTester();
         tester.ConfigureFromMaxPrime(41UL);
 
-        tester.IsPrime(31UL, out _).Should().BeTrue();
+        tester.IsPrime(31UL, out _, out ulong divisor).Should().BeTrue();
-        tester.IsPrime(37UL, out bool exhausted).Should().BeFalse();
+        divisor.Should().Be(0UL);
+        tester.IsPrime(37UL, out bool exhausted, out divisor).Should().BeFalse();
         exhausted.Should().BeTrue();
+        divisor.Should().BeGreaterThan(0UL);
 
-        tester.IsPrime(41UL, out bool divisorsExhausted).Should().BeFalse();
+        tester.IsPrime(41UL, out bool divisorsExhausted, out divisor).Should().BeFalse();
         divisorsExhausted.Should().BeTrue();
+        divisor.Should().BeGreaterThan(0UL);
     }
 
 
@@ -124,8 +130,16 @@ public class MersenneNumberDivisorGpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorGpuTester();
         tester.ConfigureFromMaxPrime(exponent);
 
-        tester.IsPrime(exponent, out bool exhausted).Should().Be(expectedPrime);
+        tester.IsPrime(exponent, out bool exhausted, out ulong divisor).Should().Be(expectedPrime);
         exhausted.Should().BeTrue();
+        if (expectedPrime)
+        {
+            divisor.Should().Be(0UL);
+        }
+        else
+        {
+            divisor.Should().BeGreaterThan(0UL);
+        }
     }
     [Fact]
     [Trait("Category", "Fast")]
@@ -138,8 +152,9 @@ public class MersenneNumberDivisorGpuTesterTests
 
         tester.ConfigureFromMaxPrime(43UL);
 
-        tester.IsPrime(41UL, out bool divisorsExhausted).Should().BeFalse();
+        tester.IsPrime(41UL, out bool divisorsExhausted, out ulong divisor).Should().BeFalse();
         divisorsExhausted.Should().BeTrue();
+        divisor.Should().BeGreaterThan(0UL);
     }
 
     [Fact]
@@ -309,8 +324,9 @@ public class MersenneNumberDivisorGpuTesterTests
                 .GetField("_divisorLimit", BindingFlags.NonPublic | BindingFlags.Instance)!
                 .SetValue(tester, 200UL);
 
-            tester.IsPrime(19UL, out bool divisorsExhausted).Should().BeTrue();
+            tester.IsPrime(19UL, out bool divisorsExhausted, out ulong divisor).Should().BeTrue();
             divisorsExhausted.Should().BeTrue();
+            divisor.Should().Be(0UL);
         }
         finally
         {

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -42,7 +42,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public ulong GetAllowedMaxDivisor(ulong prime) => ComputeAllowedMaxDivisor(prime, _divisorLimit);
 
-	public bool IsPrime(ulong prime, out bool divisorsExhausted)
+	public bool IsPrime(ulong prime, out bool divisorsExhausted, out ulong divisor)
 	{
 		ulong allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
 
@@ -60,7 +60,8 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 		bool composite = CheckDivisors(
 			prime,
 			allowedMax,
-			out processedAll);
+			out processedAll,
+			out divisor);
 
 		if (composite)
 		{
@@ -69,6 +70,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 		}
 
 		divisorsExhausted = processedAll || composite;
+		divisor = 0UL;
 		return true;
 	}
 
@@ -96,8 +98,10 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 	private bool CheckDivisors(
 		ulong prime,
 		ulong allowedMax,
-		out bool processedAll)
+		out bool processedAll,
+		out ulong foundDivisor)
 	{
+		foundDivisor = 0UL;
 		// The EvenPerfectBitScanner feeds primes >= 138,000,000 here, so allowedMax >= 3 in production runs.
 		// Keeping the guard commented out documents the reasoning for benchmarks and tests.
 		// if (allowedMax < 3UL)
@@ -123,6 +127,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 		if (divisor.CompareTo(limit) > 0)
 		{
 			processedAll = true;
+			foundDivisor = 0UL;
 			return false;
 		}
 
@@ -182,7 +187,8 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 				remainder3,
 				remainder7,
 				remainder11,
-				out processedAll);
+				out processedAll,
+				out foundDivisor);
 		}
 
 		ulong divisorHigh = divisor.High;
@@ -240,6 +246,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 				{
 					// A cycle equal to the tested exponent (which is prime in this path) guarantees that the candidate divides
 					// the corresponding Mersenne number because the order of 2 modulo the divisor is exactly p.
+					foundDivisor = candidate;
 					processedAll = true;
 					PrimeOrderCalculatorAccelerator.Return(gpu);
 					return true;
@@ -261,6 +268,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
 		PrimeOrderCalculatorAccelerator.Return(gpu);
 		processedAll = true;
+		foundDivisor = 0UL;
 		return false;
 	}
 
@@ -280,9 +288,11 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 		byte remainder3,
 		byte remainder7,
 		byte remainder11,
-		out bool processedAll)
+		out bool processedAll,
+		out ulong foundDivisor)
 	{
 		processedAll = false;
+		foundDivisor = 0UL;
 
 		bool canAdvance = step <= limit;
 		var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
@@ -314,6 +324,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
 					if (divisorCycle == prime)
 					{
+						foundDivisor = divisor;
 						processedAll = true;
 						PrimeOrderCalculatorAccelerator.Return(gpu);
 						return true;
@@ -327,12 +338,14 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 			}
 
 			processedAll = true;
+			foundDivisor = 0UL;
 			return false;
 		}
 
 		if (divisor > limit)
 		{
 			processedAll = true;
+			foundDivisor = 0UL;
 			return false;
 		}
 
@@ -365,6 +378,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
 				if (divisorCycle == prime)
 				{
+					foundDivisor = divisor;
 					processedAll = true;
 					PrimeOrderCalculatorAccelerator.Return(gpu);
 					return true;
@@ -380,6 +394,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 			if (remainingIterations == 0UL)
 			{
 				processedAll = true;
+				foundDivisor = 0UL;
 				return false;
 			}
 

PerfectNumbers.Core/Gpu/Accelerators/PrimeOrderCalculatorAccelerator.cs

@@ -115,20 +115,18 @@ public sealed class PrimeOrderCalculatorAccelerator
 
 	public Dictionary<ulong, int> Pow2ModEntriesToTestOnHost = [];
 
-	public readonly Kernel CheckFactorsKernel;
+	public readonly Action<AcceleratorStream, int, ulong, ArrayView1D<KeyValuePair<ulong, int>, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> CheckFactorsKernelLauncher;
-	public readonly Kernel ConvertToStandardKernel;
 
 	public readonly Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> ConvertToStandardKernelLauncher;
 
-	public readonly Kernel HeuristicCombinedTrialDivisionKernel;
 	public readonly Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews> HeuristicCombinedTrialDivisionKernelLauncher;
-	public readonly Kernel KeepMontgomeryKernel;
+	public readonly Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> KeepMontgomeryKernelLauncher;
-	public readonly Kernel PollardRhoKernel;
+	public readonly Action<AcceleratorStream, ulong, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<byte, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> PollardRhoKernelLauncher;
-	public readonly Kernel Pow2ModWideKernel;
+	public readonly Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>> Pow2ModWideKernelLauncher;
-	public readonly Kernel SharesFactorKernel;
+	public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<byte>> SharesFactorKernelLauncher;
-	public readonly Kernel SmallPrimeFactorKernel;
+	public readonly Action<AcceleratorStream, Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> SmallPrimeFactorKernelLauncher;
-	public readonly Kernel SmallPrimeSieveKernel;
+	public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> SmallPrimeSieveKernelLauncher;
-	public readonly Kernel SpecialMaxKernel;
+	public readonly Action<AcceleratorStream, Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> SpecialMaxKernelLauncher;
 
 	public void EnsureCapacity(int factorsCount, int primeTesterCapacity)
 	{
@@ -262,31 +260,25 @@ public sealed class PrimeOrderCalculatorAccelerator
 				SmallPrimeFactorSquares = tables.Squares.View;
 			}
 
-			CheckFactorsKernel = KernelUtil.GetKernel(accelerator.LoadStreamKernel<int, ulong, ArrayView1D<KeyValuePair<ulong, int>, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(PrimeOrderGpuHeuristics.CheckFactorsKernel));
+			CheckFactorsKernelLauncher = KernelUtil.GetKernel(accelerator.LoadStreamKernel<int, ulong, ArrayView1D<KeyValuePair<ulong, int>, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(PrimeOrderGpuHeuristics.CheckFactorsKernel)).CreateLauncherDelegate<Action<AcceleratorStream, int, ulong, ArrayView1D<KeyValuePair<ulong, int>, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
 
-			Kernel convertToStandardKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelConvertToStandard));
+			ConvertToStandardKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelConvertToStandard)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
 
-			ConvertToStandardKernel = convertToStandardKernel;
+			HeuristicCombinedTrialDivisionKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>(PrimeTesterKernels.HeuristicTrialCombinedDivisionKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>>();
-			ConvertToStandardKernelLauncher = convertToStandardKernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
 
-			var heuristicCombinedTrialDivisionKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>(PrimeTesterKernels.HeuristicTrialCombinedDivisionKernel));
+			KeepMontgomeryKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelKeepMontgomery)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
 
-			HeuristicCombinedTrialDivisionKernel = heuristicCombinedTrialDivisionKernel;
+			PollardRhoKernelLauncher = KernelUtil.GetKernel(accelerator.LoadStreamKernel<ulong, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<byte, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.TryPollardRhoKernel)).CreateLauncherDelegate<Action<AcceleratorStream, ulong, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<byte, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
-			HeuristicCombinedTrialDivisionKernelLauncher = heuristicCombinedTrialDivisionKernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>>();
 
-			KeepMontgomeryKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelKeepMontgomery));
+			Pow2ModWideKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>(PrimeOrderGpuHeuristics.Pow2ModKernelWide)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>>();
 
-			PollardRhoKernel = KernelUtil.GetKernel(accelerator.LoadStreamKernel<ulong, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<byte, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.TryPollardRhoKernel));
+			SharesFactorKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SharesFactorKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<byte>>>();
 
-			Pow2ModWideKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>(PrimeOrderGpuHeuristics.Pow2ModKernelWide));
+			SmallPrimeFactorKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(SmallPrimeFactorKernels.SmallPrimeFactorKernelScan)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
 
-			SharesFactorKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SharesFactorKernel));
+			SmallPrimeSieveKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>>();
 
-			SmallPrimeFactorKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(SmallPrimeFactorKernels.SmallPrimeFactorKernelScan));
+			SpecialMaxKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(PrimeOrderGpuHeuristics.EvaluateSpecialMaxCandidatesKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
-
-			SmallPrimeSieveKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel));
-
-			SpecialMaxKernel = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(PrimeOrderGpuHeuristics.EvaluateSpecialMaxCandidatesKernel));
 		}
 	}
 

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -70,7 +70,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
 	private static readonly Accelerator[] _accelerators = AcceleratorPool.Shared.Accelerators;
 
-	public bool IsPrime(ulong prime, out bool divisorsExhausted)
+	public bool IsPrime(ulong prime, out bool divisorsExhausted, out ulong divisor)
 	{
 		ulong allowedMax;
 		int batchCapacity;
@@ -147,10 +147,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 		if (composite)
 		{
 			divisorsExhausted = true;
+			divisor = lastProcessed;
 			return false;
 		}
 
 		divisorsExhausted = coveredRange;
+		divisor = 0UL;
 		return true;
 	}
 

PerfectNumbers.Core/Gpu/Pow2MontgomeryGpuCalculator.cs

@@ -18,16 +18,13 @@ public static class Pow2MontgomeryGpuCalculator
 		Accelerator? accelerator = gpu.Accelerator;
 		MemoryBuffer1D<ulong, Stride1D.Dense> exponentBuffer = gpu.Input;
 		MemoryBuffer1D<ulong, Stride1D.Dense> resultBuffer = gpu.OutputUlong;
-		var kernel = gpu.KeepMontgomeryKernel;
 
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
-
 		exponentBuffer.View.CopyFromCPU(stream, ref exponent, 1);
 		// We don't need to worry about any left-overs here.
 		// resultBuffer.MemSetToZero(stream);
 
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
+		var kernelLauncher = gpu.KeepMontgomeryKernelLauncher;
-
 		kernelLauncher(stream, 1, exponentBuffer.View, divisor, resultBuffer.View);
 
 		resultBuffer.View.CopyToCPU(stream, ref result, 1);

PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs

@@ -604,7 +604,7 @@ internal static partial class PrimeOrderGpuHeuristics
 		}
 
 		exponentBuffer.View.CopyFromCPU(stream, exponentSpan);
-		var kernelLauncher = gpu.Pow2ModWideKernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>>();
+		var kernelLauncher = gpu.Pow2ModWideKernelLauncher;
 
 		kernelLauncher(stream, length, exponentBuffer.View, modulus, remainderBuffer.View);
 		remainderBuffer.View.CopyToCPU(stream, ref MemoryMarshal.GetReference(resultSpan), length);

PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs

@@ -3,7 +3,6 @@ using ILGPU.Runtime;
 using System.Runtime.CompilerServices;
 using PerfectNumbers.Core.Gpu;
 using PerfectNumbers.Core.Gpu.Accelerators;
-using ILGPU;
 
 namespace PerfectNumbers.Core;
 
@@ -236,13 +235,12 @@ public sealed class HeuristicCombinedPrimeTester
 	private static bool HeuristicTrialDivisionGpuDetectsDivisor(PrimeOrderCalculatorAccelerator gpu, ulong n, ulong maxDivisorSquare, byte nMod10)
 	{
 		var acceleratorIndex = gpu.AcceleratorIndex;
-		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
-		var kernel = gpu.HeuristicCombinedTrialDivisionKernel;
 		var flagView1D = gpu.OutputInt!.View;
-
 		bool compositeDetected;
-		// int compositeFlag = 0;
 		Span<int> compositeFlag = stackalloc int[1];
+		// int compositeFlag = 0;
+
+		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		flagView1D.MemSetToZero(stream);
 
 		var kernelLauncher = gpu.HeuristicCombinedTrialDivisionKernelLauncher;
@@ -266,14 +264,10 @@ public sealed class HeuristicCombinedPrimeTester
 
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	private static bool EvaluateWithOpenNumericFallback(ulong n)
+	private static bool EvaluateWithOpenNumericFallback(ulong n) => Prime.Numbers.IsPrime(n);
-	{
+
-		return Prime.Numbers.IsPrime(n);
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	}
+	internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n) => n;
-	internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n)
-	{
-		return n;
-	}
 
 	private static ReadOnlySpan<ulong> GetCombinedDivisors(byte nMod10) => nMod10 switch
 	{
@@ -470,9 +464,7 @@ public sealed class HeuristicCombinedPrimeTester
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
-	{
+		=> new(maxDivisorSquare, nMod10, groupBBuffer);
-		return new HeuristicDivisorEnumerator(maxDivisorSquare, nMod10, groupBBuffer);
-	}
 
 	internal struct HeuristicGroupBSequenceState
 	{
@@ -480,9 +472,7 @@ public sealed class HeuristicCombinedPrimeTester
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	internal static MersenneHeuristicDivisorEnumerator CreateMersenneDivisorEnumerator(ulong exponent, ulong maxDivisor)
-	{
+		=> new(exponent, maxDivisor);
-		return new MersenneHeuristicDivisorEnumerator(exponent, maxDivisor);
-	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	internal static HeuristicDivisorPreparation PrepareHeuristicDivisor(in HeuristicDivisorCandidate candidate)
@@ -490,7 +480,7 @@ public sealed class HeuristicCombinedPrimeTester
 		ulong divisor = candidate.Value;
 		MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
 		bool hasCycleHint = TryGetCycleLengthHint(divisor, out ulong cycleLength);
-		return new HeuristicDivisorPreparation(candidate, divisorData, cycleLength, hasCycleHint);
+		return new(candidate, divisorData, cycleLength, hasCycleHint);
 	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -588,7 +578,7 @@ public sealed class HeuristicCombinedPrimeTester
 				ulong value = entry;
 				byte ending = (byte)(value % 10UL);
 				ushort residue = (ushort)(value % Wheel210);
-				candidate = new HeuristicDivisorCandidate(value, group, ending, 0, residue);
+				candidate = new(value, group, ending, 0, residue);
 				return true;
 			}
 
@@ -691,7 +681,7 @@ public sealed class HeuristicCombinedPrimeTester
 			}
 
 			ushort residue = (ushort)(value % Wheel210);
-			return new HeuristicDivisorCandidate(value, group, ending, 0, residue);
+			return new(value, group, ending, 0, residue);
 		}
 	}
 }

PerfectNumbers.Core/HeuristicPrimeTester.cs

@@ -3,7 +3,6 @@ using System.Runtime.CompilerServices;
 using ILGPU.Runtime;
 using PerfectNumbers.Core.Gpu;
 using PerfectNumbers.Core.Gpu.Accelerators;
-using ILGPU;
 
 namespace PerfectNumbers.Core;
 
@@ -68,7 +67,8 @@ public sealed class HeuristicPrimeTester
 
 	public static HeuristicPrimeTester Exclusive => _tester ??= new();
 
-	public bool IsPrimeCpu(ulong n)
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public static bool IsPrimeCpu(ulong n)
 	{
 		byte nMod10 = (byte)n.Mod10();
 		ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
@@ -82,19 +82,18 @@ public sealed class HeuristicPrimeTester
 		return HeuristicTrialDivisionCpu(n, maxDivisorSquare, nMod10, includeGroupB);
 	}
 
-	public bool IsPrimeGpu(ulong n)
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public static bool IsPrimeGpu(ulong n)
 	{
 		byte nMod10 = (byte)n.Mod10();
 		ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
 		return IsPrimeGpu(n, maxDivisorSquare, nMod10);
 	}
 
-	public bool IsPrimeGpu(ulong n, ulong maxDivisorSquare, byte nMod10)
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	{
+	public static bool IsPrimeGpu(ulong n, ulong maxDivisorSquare, byte nMod10) => HeuristicIsPrimeGpuCore(n, maxDivisorSquare, nMod10);
-		return HeuristicIsPrimeGpuCore(n, maxDivisorSquare, nMod10);
-	}
 
-	private bool HeuristicIsPrimeGpuCore(ulong n, ulong maxDivisorSquare, byte nMod10)
+	private static bool HeuristicIsPrimeGpuCore(ulong n, ulong maxDivisorSquare, byte nMod10)
 	{
 		// TODO: Is this condition ever met on the execution path in EvenPerfectBitScanner?
 		if (maxDivisorSquare < 9UL)
@@ -133,7 +132,7 @@ public sealed class HeuristicPrimeTester
 						break;
 					}
 
-					ulong divisor = (ulong)groupADivisors[groupAIndex];
+					ulong divisor = groupADivisors[groupAIndex];
 					if (n % divisor == 0UL)
 					{
 						return false;
@@ -186,7 +185,7 @@ public sealed class HeuristicPrimeTester
 						break;
 					}
 
-					ulong divisor = (ulong)groupADivisors[groupAIndex];
+					ulong divisor = groupADivisors[groupAIndex];
 					if (n % divisor == 0UL)
 					{
 						return false;
@@ -240,13 +239,12 @@ public sealed class HeuristicPrimeTester
 	}
 
 
-	private bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong maxDivisorSquare, byte nMod10)
+	private static bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong maxDivisorSquare, byte nMod10)
 	{
 		// GpuPrimeWorkLimiter.Acquire();
 		var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
 		int acceleratorIndex = gpu.AcceleratorIndex;
 		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
-		var kernel = gpu.HeuristicCombinedTrialDivisionKernel;
 		var flagView1D = gpu.OutputInt!.View;
 
 		bool compositeDetected;
@@ -261,7 +259,7 @@ public sealed class HeuristicPrimeTester
         // HeuristicGpuDivisorTableKind tableKind,
         // HeuristicGpuDivisorTables tables)
 
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicGpuDivisorTableKind, HeuristicCombinedGpuViews>>();
+		var kernelLauncher = gpu.HeuristicCombinedTrialDivisionKernelLauncher;
 		kernelLauncher(
 				stream,
 				1,
@@ -269,7 +267,6 @@ public sealed class HeuristicPrimeTester
 				flagView1D,
 				n,
 				maxDivisorSquare,
-				HeuristicGpuDivisorTableKind.GroupA,
 				gpu.DivisorTables);
 
 		flagView1D.CopyToCPU(stream, ref compositeFlag, 1);
@@ -321,17 +318,11 @@ public sealed class HeuristicPrimeTester
 		return compositeDetected;
 	}
 
-
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static bool EvaluateWithOpenNumericFallback(ulong n) => Prime.Numbers.IsPrime(n);
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	private static bool EvaluateWithOpenNumericFallback(ulong n)
+	internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n) => n;
-	{
-		return Prime.Numbers.IsPrime(n);
-	}
-	internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n)
-	{
-		return n;
-	}
 
 	private static ReadOnlySpan<byte> GetGroupBEndingOrder(byte nMod10) => nMod10 switch
 	{
@@ -339,7 +330,7 @@ public sealed class HeuristicPrimeTester
 		3 => GroupBEndingOrderMod3,
 		7 => GroupBEndingOrderMod7,
 		9 => GroupBEndingOrderMod9,
-		_ => ReadOnlySpan<byte>.Empty,
+		_ => [],
 	};
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -415,19 +406,19 @@ public sealed class HeuristicPrimeTester
 	private static ReadOnlySpan<uint> GetGroupBDivisors(byte ending) => ending switch
 	{
 		1 => DivisorGenerator.SmallPrimesLastOneWithoutLastThree,
-		3 => ReadOnlySpan<uint>.Empty,
+		3 => [],
 		7 => DivisorGenerator.SmallPrimesLastSevenWithoutLastThree,
 		9 => DivisorGenerator.SmallPrimesLastNineWithoutLastThree,
-		_ => ReadOnlySpan<uint>.Empty,
+		_ => [],
 	};
 
 	private static ReadOnlySpan<ulong> GetGroupBDivisorSquares(byte ending) => ending switch
 	{
 		1 => DivisorGenerator.SmallPrimesPow2LastOneWithoutLastThree,
-		3 => ReadOnlySpan<ulong>.Empty,
+		3 => [],
 		7 => DivisorGenerator.SmallPrimesPow2LastSevenWithoutLastThree,
 		9 => DivisorGenerator.SmallPrimesPow2LastNineWithoutLastThree,
-		_ => ReadOnlySpan<ulong>.Empty,
+		_ => [],
 	};
 
 	private static int InitializeGroupBStates(byte nMod10, Span<HeuristicGroupBSequenceState> buffer)
@@ -444,16 +435,11 @@ public sealed class HeuristicPrimeTester
 	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
+	internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer) => new(maxDivisorSquare, nMod10, groupBBuffer);
-	{
-		return new HeuristicDivisorEnumerator(maxDivisorSquare, nMod10, groupBBuffer);
-	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	internal static MersenneHeuristicDivisorEnumerator CreateMersenneDivisorEnumerator(ulong exponent, ulong maxDivisor)
-	{
+		=> new(exponent, maxDivisor);
-		return new MersenneHeuristicDivisorEnumerator(exponent, maxDivisor);
-	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	internal static HeuristicDivisorPreparation PrepareHeuristicDivisor(in HeuristicDivisorCandidate candidate)
@@ -611,25 +597,18 @@ public sealed class HeuristicPrimeTester
 
 
 
-	internal struct HeuristicGroupBSequenceState
+	internal struct HeuristicGroupBSequenceState(byte ending, byte priorityIndex)
 	{
-		public byte Ending;
+		public byte Ending = ending;
-		public byte PriorityIndex;
+		public byte PriorityIndex = priorityIndex;
-		public int Index;
+		public int Index = 0;
-
-		public HeuristicGroupBSequenceState(byte ending, byte priorityIndex)
-		{
-			Ending = ending;
-			PriorityIndex = priorityIndex;
-			Index = 0;
-		}
 
 		public bool TryPeek(ulong maxDivisorSquare, out ulong divisor)
 		{
 			ReadOnlySpan<uint> divisors = GetGroupBDivisors(Ending);
 			ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(Ending);
 			int index = Index;
-			if ((uint)index >= (uint)divisors.Length)
+			if (index >= divisors.Length)
 			{
 				divisor = 0UL;
 				return false;
@@ -642,7 +621,7 @@ public sealed class HeuristicPrimeTester
 				return false;
 			}
 
-			divisor = (ulong)divisors[index];
+			divisor = divisors[index];
 			return true;
 		}
 
@@ -731,11 +710,11 @@ public sealed class HeuristicPrimeTester
 			residueStepper.Advance();
 		}
 
-		public ulong ProcessedCount => processedCount;
+		public readonly ulong ProcessedCount => processedCount;
 
-		public ulong LastDivisor => lastDivisor;
+		public readonly ulong LastDivisor => lastDivisor;
 
-		public bool Exhausted => !active;
+		public readonly bool Exhausted => !active;
 
 		private static HeuristicDivisorCandidate CreateCandidate(ulong value)
 		{

PerfectNumbers.Core/IMersenneNumberDivisorByDivisorTester.cs

@@ -10,7 +10,7 @@ public interface IMersenneNumberDivisorByDivisorTester
 
     ulong GetAllowedMaxDivisor(ulong prime);
 
-    bool IsPrime(ulong prime, out bool divisorsExhausted);
+    bool IsPrime(ulong prime, out bool divisorsExhausted, out ulong divisor);
 
     IDivisorScanSession CreateDivisorSession();
 

PerfectNumbers.Core/MersenneNumberDivisorByDivisorTester.cs

@@ -14,7 +14,7 @@ public static class MersenneNumberDivisorByDivisorTester
 			ulong startPrime,
 			Action markComposite,
 			Action clearComposite,
-			Action<ulong, bool, bool, bool> printResult,
+			Action<ulong, bool, bool, bool, ulong> printResult,
 			int threadCount,
 			int primesPerTask)
 	{
@@ -242,18 +242,18 @@ public static class MersenneNumberDivisorByDivisorTester
 		void ProcessPrime(ulong prime)
 		{
 			Console.WriteLine($"Processing {prime}");
-			bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted);
+			bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted, out ulong divisor);
 
 			if (!isPrime)
 			{
 				markComposite();
-				printResult(prime, true, true, false);
+				printResult(prime, true, true, false, divisor);
 				Console.WriteLine($"Finished processing {prime}");
 				return;
 			}
 
 			clearComposite();
-			printResult(prime, true, divisorsExhausted, true);
+			printResult(prime, true, divisorsExhausted, true, divisor);
 			Console.WriteLine($"Finished processing {prime}");
 		}
 

PerfectNumbers.Core/PerfectNumberConstants.cs

@@ -8,6 +8,7 @@ public static class PerfectNumberConstants
 	public const int DefaultSmallPrimeFactorSlotCount = 64;
 	public const int DefaultSpecialMaxFactorCapacity = 1024;
     public const ulong ExtraDivisorCycleSearchLimit = 64UL;
+	public const int GpuFrequency = 768 - 1;
     public const int MaxQForDivisorCycles = 4_000_000;
     public static readonly uint PrimesLimit = 1_000_000; //(ulong)Array.MaxLength;// 1_000_000;
     public const int MaxOddPowersCount = 128;

PerfectNumbers.Core/PrimeOrderCalculator.Cpu.cs

@@ -1177,7 +1177,7 @@ internal static partial class PrimeOrderCalculator
 					// bool isPrime = HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite);
 					bool runOnGpu = RunOnGpu();
 
-					bool isPrime = runOnGpu ? PrimeTester.IsPrime(composite) : HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite);
+					bool isPrime = !runOnGpu ? PrimeTester.IsPrime(composite) : HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite);
 					// bool isPrime = PrimeTester.IsPrime(composite);
 					// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(composite);
 
@@ -1375,19 +1375,19 @@ internal static partial class PrimeOrderCalculator
 
 	private static bool RunOnGpu()
 	{
-		const int GpuFrequency = 1024 - 1;
+		// return true;
-
+		int cpuCount = Atomic.Add(ref _cpuCount, 1);
-		int cpuCount = Atomic.Add(target: ref _cpuCount, 1);
+		// return (cpuCount % GpuFrequency) == 0;
-		if (cpuCount == GpuFrequency)
+		if (cpuCount == PerfectNumberConstants.GpuFrequency)
 		{
-			Atomic.Add(ref _cpuCount, -GpuFrequency);
+			Atomic.Add(ref _cpuCount, -PerfectNumberConstants.GpuFrequency);
 		}
-		else if (cpuCount > GpuFrequency)
+		else if (cpuCount > PerfectNumberConstants.GpuFrequency)
 		{
-			cpuCount -= GpuFrequency;
+			cpuCount -= PerfectNumberConstants.GpuFrequency;
 		}
 
-		return cpuCount != GpuFrequency;
+		return cpuCount == PerfectNumberConstants.GpuFrequency;
 	}
 
 	private static void PopulateSmallPrimeFactorsCpu(

PerfectNumbers.Core/PrimeOrderCalculator.Gpu.cs

@@ -36,15 +36,13 @@ internal static partial class PrimeOrderCalculator
 
 		ulong order = phi;
 		var acceleratorIndex = gpu.AcceleratorIndex;
-		var kernel = gpu.CheckFactorsKernel;
 		gpu.EnsureCapacity(entryCount, 1);
 
 		// GpuPrimeWorkLimiter.Acquire();
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		gpu.Pow2ModEntriesToTestOnDevice.View.CopyFromCPU(stream, entries);
 
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, int, ulong, ArrayView1D<KeyValuePair<ulong, int>, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
+		var kernelLauncher = gpu.CheckFactorsKernelLauncher;		
-		
 		kernelLauncher(stream, entryCount, phi, gpu.Pow2ModEntriesToTestOnDevice.View, divisorData, gpu.OutputUlong.View);
 
 		gpu.OutputUlong.View.CopyToCPU(stream, ref order, 1);
@@ -67,19 +65,16 @@ internal static partial class PrimeOrderCalculator
 		int acceleratorIndex = gpu.AcceleratorIndex;
 		var accelerator = gpu.Accelerator;
 
-		// GpuPrimeWorkLimiter.Acquire();
+		var kernelLauncher = gpu.SmallPrimeFactorKernelLauncher;
-		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
-
-		var kernel = gpu.SmallPrimeFactorKernel;
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
-
 		ArrayView1D<int, Stride1D.Dense> smallPrimeFactorCountSlotView = gpu.SmallPrimeFactorCountSlot.View;
 		ArrayView1D<ulong, Stride1D.Dense> smallPrimeFactorRemainingSlotView = gpu.Input.View;
 		ArrayView1D<ulong, Stride1D.Dense> smallPrimeFactorPrimeSlotsView = gpu.OutputUlong.View;
 		ArrayView1D<int, Stride1D.Dense> smallPrimeFactorExponentSlotsView = gpu.OutputInt.View;
-		ArrayView1D<uint, Stride1D.Dense> smallPrimeFactorsPrimesView = gpu.SmallPrimeFactorPrimes;
 		ArrayView1D<ulong, Stride1D.Dense> smallPrimeFactorsSquaresView = gpu.SmallPrimeFactorSquares;
+		ArrayView1D<uint, Stride1D.Dense> smallPrimeFactorsPrimesView = gpu.SmallPrimeFactorPrimes;
 
+		// GpuPrimeWorkLimiter.Acquire();
+		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		kernelLauncher(
 				stream,
 				1,
@@ -136,17 +131,14 @@ internal static partial class PrimeOrderCalculator
 
 		int acceleratorIndex = gpu.AcceleratorIndex;
 		// GpuPrimeWorkLimiter.Acquire();
-		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
-
 		ArrayView1D<ulong, Stride1D.Dense> specialMaxFactorsView = gpu.Input.View;
-		specialMaxFactorsView.SubView(0, factorCount).CopyFromCPU(stream, factors);
 
-		var kernel = gpu.SpecialMaxKernel;
+		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
+		specialMaxFactorsView.SubView(0, factorCount).CopyFromCPU(stream, factors);
 
 		ArrayView1D<ulong, Stride1D.Dense> specialMaxResultView = gpu.SpecialMaxResult.View;
 
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();	
+		var kernelLauncher = gpu.SpecialMaxKernelLauncher;
-
 		kernelLauncher(
 				stream,
 				1,
@@ -178,7 +170,7 @@ internal static partial class PrimeOrderCalculator
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		gpu.Input.View.CopyFromCPU(stream, randomStateSpan);
 
-		var kernelLauncher = gpu.PollardRhoKernel.CreateLauncherDelegate<Action<AcceleratorStream, ulong, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<byte, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
+		var kernelLauncher = gpu.PollardRhoKernelLauncher;
 
 		kernelLauncher(stream, n, 1, gpu.Input.View, gpu.OutputByte.View, gpu.OutputUlong.View);
 

PerfectNumbers.Core/PrimeTester.cs

@@ -90,19 +90,17 @@ public sealed class PrimeTester
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public static bool IsPrimeGpu(ulong n)
 	{
-		byte flag = 0;
 
 		var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
 		int acceleratorIndex = gpu.AcceleratorIndex;
 		var inputView = gpu.Input.View;
 		var outputView = gpu.OutputByte.View;
-		var kernel = gpu.SmallPrimeSieveKernel!;
 
 		// GpuPrimeWorkLimiter.Acquire();
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		inputView.CopyFromCPU(stream, ref n, 1);
 
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>>();
+		var kernelLauncher = gpu.SmallPrimeSieveKernelLauncher;
 
 		kernelLauncher(
 						stream,
@@ -118,6 +116,7 @@ public sealed class PrimeTester
 						gpu.DevicePrimesPow2LastNine,
 						outputView);
 
+		byte flag = 0;
 		outputView.CopyToCPU(stream, ref flag, 1);
 		stream.Synchronize();
 
@@ -136,13 +135,12 @@ public sealed class PrimeTester
 		var inputView = input.View;
 		var output = gpu.OutputByte;
 		var outputView = output.View;
-		Kernel kernel = gpu.SmallPrimeSieveKernel!;
 
 		int acceleratorIndex = gpu.AcceleratorIndex;
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		inputView.CopyFromCPU(stream, ref n, 1);
 
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>>();
+		var kernelLauncher = gpu.SmallPrimeSieveKernelLauncher;
 		
 		kernelLauncher(
 						stream,
@@ -196,7 +194,6 @@ public sealed class PrimeTester
 		// GpuPrimeWorkLimiter.Acquire();
 		var gpu = PrimeOrderCalculatorAccelerator.Rent(GpuBatchSize);
 		int acceleratorIndex = gpu.AcceleratorIndex;
-		var kernel = gpu.SmallPrimeSieveKernel!;
 		int totalLength = values.Length;
 		int batchSize = GpuBatchSize;
 
@@ -207,7 +204,7 @@ public sealed class PrimeTester
 
 		int pos = 0;
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>>();
+		var kernelLauncher = gpu.SmallPrimeSieveKernelLauncher;
 
 		while (pos < totalLength)
 		{
@@ -265,7 +262,7 @@ public sealed class PrimeTester
 		// ResidueComputationBenchmarks so divisor-cycle metadata can short-circuit the test
 		// instead of recomputing binary GCD for every candidate.
 		ulong m = (ulong)BitOperations.Log2(n);
-		return BinaryGcd(n, m) != 1UL;
+		return n.BinaryGcd(m) != 1UL;
 	}
 
 	internal static void SharesFactorWithMaxExponentBatch(ReadOnlySpan<ulong> values, Span<byte> results)
@@ -280,15 +277,14 @@ public sealed class PrimeTester
 
 		var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
 		int acceleratorIndex = gpu.AcceleratorIndex;
-		var kernel = gpu.SharesFactorKernel;
 		gpu.EnsureCapacity(0, length);
 		MemoryBuffer1D<ulong, Stride1D.Dense>? inputBuffer = gpu.Input;
-		MemoryBuffer1D<byte, Stride1D.Dense>? resultBuffer = gpu.OutputByte;
 
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		inputBuffer.View.CopyFromCPU(stream, values);
-		var kernelLauncher = kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<byte>>>();
 
+		MemoryBuffer1D<byte, Stride1D.Dense>? resultBuffer = gpu.OutputByte;
+		var kernelLauncher = gpu.SharesFactorKernelLauncher;
 		kernelLauncher(stream, length, inputBuffer.View, resultBuffer.View);
 
 		resultBuffer.View.CopyToCPU(stream, in results);
@@ -298,39 +294,4 @@ public sealed class PrimeTester
 		PrimeOrderCalculatorAccelerator.Return(gpu);
 	}
 
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	private static ulong BinaryGcd(ulong u, ulong v)
-	{
-		// TODO: Swap this handwritten binary GCD for the optimized helper measured in
-		// GpuUInt128BinaryGcdBenchmarks so CPU callers share the faster subtract-less
-		// ladder once the common implementation is promoted into PerfectNumbers.Core.
-		// You have an example in the benchmarks and you already implemented it in
-		// GpuUInt128, iirc.
-		if (u == 0UL)
-		{
-			return v;
-		}
-
-		if (v == 0UL)
-		{
-			return u;
-		}
-
-		int shift = BitOperations.TrailingZeroCount(u | v);
-		u >>= BitOperations.TrailingZeroCount(u);
-
-		do
-		{
-			v >>= BitOperations.TrailingZeroCount(v);
-			if (u > v)
-			{
-				(u, v) = (v, u);
-			}
-
-			v -= u;
-		}
-		while (v != 0UL);
-
-		return u << shift;
-	}
 }