GPU calculations disabled again

Remove small prime stepper remainder cache

AGENTS.md

@@ -106,11 +106,16 @@ There is only one agents file - this one. Don't search for another one.
 
 Always use indentation with four space characters in source code files, even if a file currently uses tabs or appears to rely on eight-space indentation. Increase indentation level by exactly one indentation unit (four spaces) per nested block. When parameters or long expressions wrap, indent the continuation with two indentation units for clarity.
 Explicitly prefer reusing existing variables once their previous values are no longer required instead of declaring new locals of the same type. Call out the variable reuse in comments when its meaning changes so the intent stays clear and register pressure remains minimal.
+Do not introduce try/finally blocks solely to release pooled resources. Restructure the code so that every return path releases the resources without relying on finally unless the control flow would become unclear or unmaintainable.
 
 Keep the divisor cycle cache limited to a single block in memory (only the on-disk snapshot). When a lookup misses, compute the required cycle on the configured device and discard the transient result instead of scheduling background generation or caching additional blocks.
 
 All code, comments, commit messages, branch names and PR descriptions must be written in American English.
 
+- When modifying existing files, preserve all relevant TODO notes and explanatory comments unless they are no longer valid.
+- Prefer defining data holders as structs or classes with public fields over auto-properties when performance on the hot path is a concern.
+- Do not add or keep methods that simply wrap another method call without adding any logic; inline those calls or extend the wrapper with meaningful work.
+
 ## Performance implementation checklist
 
 - Prefer dedicated kernels over flag-controlled or parameterized kernels. Avoid conditional branches in kernels and tight loops by creating separate kernels when necessary.

EvenPerfectBitScanner.Benchmarks/GpuPow2ModBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128AddBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/GpuUInt128Montgomery64Benchmarks.cs

@@ -1,5 +1,3 @@
-using System;
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128Mul64Benchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/GpuUInt128MulModBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/GpuUInt128MulModByLimbBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128NativeModuloBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128ScalarMulModBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128SubModScalarBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/HeuristicMultiplyShiftBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;

EvenPerfectBitScanner.Benchmarks/MersenneDivisorCycleLengthGpuBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/Mod11ULongBenchmarks.cs

@@ -1,7 +1,6 @@
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
-using PerfectNumbers.Core;
 
 namespace EvenPerfectBitScanner.Benchmarks;
 

EvenPerfectBitScanner.Benchmarks/Mul64Benchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;

EvenPerfectBitScanner.Benchmarks/MulHighBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;

EvenPerfectBitScanner.Benchmarks/MulMod64Benchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModBenchmarks.cs

@@ -1,9 +1,7 @@
-using System;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using System.Numerics;
 using PerfectNumbers.Core;
-using PerfectNumbers.Core.Gpu;
 
 namespace EvenPerfectBitScanner.Benchmarks;
 

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModCycleComputationBenchmarks.cs

@@ -1,6 +1,4 @@
-using System;
 using System.Buffers.Binary;
-using System.Threading;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModUInt128Benchmarks.cs

@@ -1,6 +1,4 @@
-using System;
 using System.Buffers.Binary;
-using System.Numerics;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;

EvenPerfectBitScanner.Benchmarks/Pow2OddPowerTableBenchmarks.cs

@@ -1,8 +1,4 @@
-using System;
-using System.Collections.Generic;
-using System.Linq;
 using System.Runtime.CompilerServices;
-using System.Threading.Tasks;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/Program.cs

@@ -1,5 +1,3 @@
-using BenchmarkDotNet.Configs;
-using BenchmarkDotNet.Running;
 using PerfectNumbers.Core.Gpu;
 
 namespace EvenPerfectBitScanner.Benchmarks;

EvenPerfectBitScanner/Program.cs

@@ -1,5 +1,4 @@
-using System.Buffers;
-using System.Collections.Generic;
+using System.Diagnostics;
 using System.Globalization;
 using System.Numerics;
 using System.Runtime.CompilerServices;
@@ -45,6 +44,11 @@ internal static class Program
     private static readonly Optimized PrimeIterator = new();
     private static ulong _byDivisorStartPrime;
 
+    private static bool _testMode;
+    private static int _testTargetPrimeCount;
+    private static int _testProcessedPrimeCount;
+    private const string TestTimeFileName = "even_perfect_test_time.txt";
+
     [ThreadStatic]
     private static bool _lastCompositeP;
 
@@ -81,6 +85,8 @@ internal static class Program
         int scanBatchSize = 2_097_152, sliceSize = 32;
         ulong residueKMax = 5_000_000UL;
         string filterFile = string.Empty;
+        UInt128 maxPrimeLimit = UInt128.MaxValue;
+        bool maxPrimeConfigured = false;
         string cyclesPath = DefaultCyclesPath;
         int cyclesBatchSize = 512;
         bool continueCyclesGeneration = false;
@@ -93,6 +99,10 @@ internal static class Program
         ulong remainder = 0UL;
         bool startPrimeProvided = false;
 
+        _testMode = false;
+        _testTargetPrimeCount = 0;
+        _testProcessedPrimeCount = 0;
+
         // NTT backend selection (GPU): reference vs staged
         for (; argIndex < args.Length; argIndex++)
         {
@@ -109,6 +119,20 @@ internal static class Program
                 currentP = ulong.Parse(arg.AsSpan(arg.IndexOf('=') + 1));
                 startPrimeProvided = true;
             }
+            else if (arg.StartsWith("--max-prime=", StringComparison.OrdinalIgnoreCase))
+            {
+                ReadOnlySpan<char> value = arg.AsSpan(arg.IndexOf('=') + 1);
+                if (UInt128.TryParse(value, NumberStyles.None, CultureInfo.InvariantCulture, out UInt128 parsedMaxPrime))
+                {
+                    maxPrimeLimit = parsedMaxPrime;
+                    maxPrimeConfigured = true;
+                }
+                else
+                {
+                    Console.WriteLine("Invalid value for --max-prime.");
+                    return;
+                }
+            }
             else if (arg.Equals("--increment=bit", StringComparison.OrdinalIgnoreCase))
             {
                 useBitTransform = true;
@@ -185,6 +209,10 @@ internal static class Program
             {
                 useModuloWorkaround = true;
             }
+            else if (arg.Equals("--test", StringComparison.OrdinalIgnoreCase))
+            {
+                _testMode = true;
+            }
             else if (arg.Equals("--use-order", StringComparison.OrdinalIgnoreCase))
             {
                 useOrder = true;
@@ -377,6 +405,19 @@ internal static class Program
             }
         }
 
+        int testPrimeCandidateLimit = 0;
+
+        if (_testMode)
+        {
+            currentP = 31UL;
+            remainder = currentP % 6UL;
+            filterFile = string.Empty;
+            maxPrimeLimit = UInt128.MaxValue;
+            maxPrimeConfigured = false;
+            startPrimeProvided = true;
+            testPrimeCandidateLimit = Math.Max(1, threadCount) * 3;
+        }
+
         if (useByDivisor)
         {
             _byDivisorStartPrime = startPrimeProvided ? currentP : 0UL;
@@ -386,7 +427,7 @@ internal static class Program
             _byDivisorStartPrime = 0UL;
         }
 
-        if (useByDivisor && string.IsNullOrEmpty(filterFile))
+        if (useByDivisor && !_testMode && string.IsNullOrEmpty(filterFile))
         {
             Console.WriteLine("--mersenne=bydivisor requires --filter-p=<path>.");
             return;
@@ -604,50 +645,101 @@ internal static class Program
             File.WriteAllText(ResultsFileName, $"p,searchedMersenne,detailedCheck,passedAllTests{Environment.NewLine}");
         }
 
-        bool useFilter = !string.IsNullOrEmpty(filterFile);
+        bool useFilter = !_testMode && !string.IsNullOrEmpty(filterFile);
         HashSet<ulong> filter = [];
         List<ulong> byDivisorCandidates = [];
         ulong maxP = 0UL;
         ulong[] localFilter = Array.Empty<ulong>();
         int filterCount = 0;
-        if (useFilter)
+
+        if (_useByDivisorMode)
         {
-            Console.WriteLine("Loading filter...");
-            if (_useByDivisorMode)
+            if (_testMode)
             {
-                byDivisorCandidates = LoadByDivisorCandidates(filterFile);
+                byDivisorCandidates = BuildTestPrimeCandidates(testPrimeCandidateLimit);
             }
             else
             {
-                // TODO: Rent this filter buffer from ArrayPool<ulong> and reuse it across reload batches so
-                // we do not allocate fresh arrays while replaying large result filters.
-                localFilter = new ulong[1024];
-                filterCount = 0;
-                LoadResultsFile(filterFile, (p, detailedCheck, passedAllTests) =>
+                Console.WriteLine("Loading filter...");
+                int skippedByLimit = 0;
+                byDivisorCandidates = LoadByDivisorCandidates(filterFile, maxPrimeLimit, maxPrimeConfigured, out skippedByLimit);
+                if (maxPrimeConfigured)
                 {
-                    if (passedAllTests)
+                    if (skippedByLimit > 0)
                     {
-                        localFilter[filterCount++] = p;
-                        if (p > maxP)
-                        {
-                            maxP = p;
-                        }
-
-                        if (filterCount == 1024)
-                        {
-                            filter.AddRange(localFilter[..filterCount]);
-                            filterCount = 0;
-                            Console.WriteLine($"Added {p}");
-                        }
+                        Console.WriteLine($"Skipped {skippedByLimit} by-divisor candidate(s) above --max-prime limit.");
                     }
-                });
 
-                if (filterCount > 0)
-                {
-                    filter.AddRange(localFilter[..filterCount]);
+                    if (byDivisorCandidates.Count == 0)
+                    {
+                        Console.WriteLine("No by-divisor candidates fall within the --max-prime limit.");
+                        return;
+                    }
                 }
             }
         }
+        else if (useFilter)
+        {
+            Console.WriteLine("Loading filter...");
+            // TODO: Rent this filter buffer from ArrayPool<ulong> and reuse it across reload batches so
+            // we do not allocate fresh arrays while replaying large result filters.
+            localFilter = new ulong[1024];
+            filterCount = 0;
+            bool addedWithinLimit = false;
+            int skippedByLimit = 0;
+            LoadResultsFile(filterFile, (p, detailedCheck, passedAllTests) =>
+            {
+                if (!passedAllTests)
+                {
+                    return;
+                }
+
+                if (maxPrimeConfigured && (UInt128)p > maxPrimeLimit)
+                {
+                    skippedByLimit++;
+                    return;
+                }
+
+                localFilter[filterCount++] = p;
+                addedWithinLimit = true;
+                if (p > maxP)
+                {
+                    maxP = p;
+                }
+
+                if (filterCount == 1024)
+                {
+                    filter.AddRange(localFilter[..filterCount]);
+                    filterCount = 0;
+                    Console.WriteLine($"Added {p}");
+                }
+            });
+
+            if (filterCount > 0)
+            {
+                filter.AddRange(localFilter[..filterCount]);
+            }
+
+            if (maxPrimeConfigured)
+            {
+                if (!addedWithinLimit)
+                {
+                    Console.WriteLine("No filter candidates fall within the --max-prime limit.");
+                    return;
+                }
+
+                if (skippedByLimit > 0)
+                {
+                    Console.WriteLine($"Skipped {skippedByLimit} filter candidate(s) above --max-prime limit.");
+                }
+            }
+        }
+
+
+        if (_testMode)
+        {
+            _testTargetPrimeCount = testPrimeCandidateLimit;
+        }
 
         if (_primeCount >= 2)
         {
@@ -661,6 +753,12 @@ internal static class Program
         // Configure batch size for GPU primality sieve
         PrimeTester.GpuBatchSize = gpuPrimeBatch;
 
+        Stopwatch? stopwatch = null;
+        if (_testMode)
+        {
+            stopwatch = Stopwatch.StartNew();
+        }
+
         Console.WriteLine("Starting scan...");
 
         if (_useByDivisorMode)
@@ -668,6 +766,12 @@ internal static class Program
             RunByDivisorMode(byDivisorCandidates, threadCount);
             FlushBuffer();
             StringBuilderPool.Return(_outputBuilder!);
+            if (stopwatch is not null)
+            {
+                stopwatch.Stop();
+                ReportTestTime(stopwatch.Elapsed);
+            }
+
             return;
         }
 
@@ -682,7 +786,14 @@ internal static class Program
             }
         }
 
+        if (_testMode)
+        {
+            testPrimeCandidateLimit = Math.Max(1, threadCount) * 3;
+            _testTargetPrimeCount = testPrimeCandidateLimit;
+        }
+
         _state = ((long)currentP << 3) | (long)remainder;
+
         Task[] tasks = new Task[threadCount];
 
         int taskIndex = 0;
@@ -752,13 +863,71 @@ internal static class Program
         }
 
         Task.WaitAll(tasks);
+
+        TimeSpan testElapsed = default;
+        bool reportTestTime = false;
+        if (stopwatch is not null)
+        {
+            stopwatch.Stop();
+            testElapsed = stopwatch.Elapsed;
+            reportTestTime = true;
+        }
+
         FlushBuffer();
         StringBuilderPool.Return(_outputBuilder!);
+
+        if (reportTestTime)
+        {
+            ReportTestTime(testElapsed);
+        }
     }
 
-    private static List<ulong> LoadByDivisorCandidates(string candidateFile)
+    private static List<ulong> BuildTestPrimeCandidates(int targetCount)
+    {
+        if (targetCount <= 0)
+        {
+            return [];
+        }
+
+        List<ulong> candidates = new(targetCount);
+        ulong previous = 29UL;
+        int remaining = targetCount;
+        ulong nextPrime = 0UL;
+
+        while (remaining > 0)
+        {
+            try
+            {
+                nextPrime = PrimeIterator.Next(in previous);
+            }
+            catch (InvalidOperationException)
+            {
+                break;
+            }
+
+            if (nextPrime < 31UL)
+            {
+                previous = nextPrime;
+                continue;
+            }
+
+            candidates.Add(nextPrime);
+            remaining--;
+            previous = nextPrime;
+        }
+
+        if (remaining > 0)
+        {
+            Console.WriteLine("Unable to populate the requested number of test primes before reaching the 64-bit limit.");
+        }
+
+        return candidates;
+    }
+
+    private static List<ulong> LoadByDivisorCandidates(string candidateFile, UInt128 maxPrimeLimit, bool maxPrimeConfigured, out int skippedByLimit)
     {
         List<ulong> candidates = [];
+        skippedByLimit = 0;
         using FileStream readStream = new(candidateFile, FileMode.Open, FileAccess.Read, FileShare.ReadWrite);
         using StreamReader reader = new(readStream);
         string? line;
@@ -798,7 +967,14 @@ internal static class Program
                 // arrive so by-divisor candidate loading avoids per-value string allocations.
                 if (ulong.TryParse(span[start..index], NumberStyles.None, CultureInfo.InvariantCulture, out ulong parsed))
                 {
-                    candidates.Add(parsed);
+                    if (!maxPrimeConfigured || (UInt128)parsed <= maxPrimeLimit)
+                    {
+                        candidates.Add(parsed);
+                    }
+                    else
+                    {
+                        skippedByLimit++;
+                    }
                 }
             }
         }
@@ -896,6 +1072,7 @@ internal static class Program
         Console.WriteLine();
         Console.WriteLine("Options:");
         Console.WriteLine("  --prime=<value>        starting exponent (p)");
+        Console.WriteLine("  --max-prime=<value>    inclusive upper bound for primes from filter files");
         Console.WriteLine("  --increment=bit|add    exponent increment method");
         Console.WriteLine("  --threads=<value>      number of worker threads");
         Console.WriteLine("  --block-size=<value>   values processed per thread batch");
@@ -989,6 +1166,21 @@ internal static class Program
         }
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static void OnPrimeCandidateConfirmed()
+    {
+        if (!_testMode)
+        {
+            return;
+        }
+
+        int processed = Interlocked.Increment(ref _testProcessedPrimeCount);
+        if (processed == _testTargetPrimeCount)
+        {
+            Volatile.Write(ref _limitReached, true);
+        }
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static bool TryAcquireConsoleSlot(bool primeCandidate, out bool primeFlag)
     {
@@ -1125,6 +1317,75 @@ internal static class Program
         }
     }
 
+    private static void ReportTestTime(TimeSpan elapsed)
+    {
+        double elapsedSeconds = elapsed.TotalSeconds;
+        double elapsedMilliseconds = elapsed.TotalMilliseconds;
+        Console.WriteLine($"Test elapsed time: {elapsedSeconds:F3} s");
+
+        string filePath = GetTestTimeFilePath();
+        bool hasPrevious = TryReadTestTime(filePath, out double previousMilliseconds);
+        string elapsedText = elapsedMilliseconds.ToString("F3", CultureInfo.InvariantCulture);
+
+        if (!hasPrevious)
+        {
+            WriteTestTime(filePath, elapsedMilliseconds);
+            Console.WriteLine($"FIRST TIME: {elapsedText} ms");
+            return;
+        }
+
+        string previousText = previousMilliseconds.ToString("F3", CultureInfo.InvariantCulture);
+        if (elapsedMilliseconds < previousMilliseconds)
+        {
+            WriteTestTime(filePath, elapsedMilliseconds);
+            Console.WriteLine($"BETTER TIME: {elapsedText} ms (previous {previousText} ms)");
+        }
+        else
+        {
+            Console.WriteLine($"WORSE TIME: {elapsedText} ms (best {previousText} ms)");
+        }
+    }
+
+    private static string GetTestTimeFilePath()
+    {
+        if (string.IsNullOrEmpty(_resultsDir))
+        {
+            return TestTimeFileName;
+        }
+
+        return Path.Combine(_resultsDir!, TestTimeFileName);
+    }
+
+    private static bool TryReadTestTime(string filePath, out double milliseconds)
+    {
+        if (!File.Exists(filePath))
+        {
+            milliseconds = 0.0;
+            return false;
+        }
+
+        string content = File.ReadAllText(filePath).Trim();
+        if (content.Length == 0)
+        {
+            milliseconds = 0.0;
+            return false;
+        }
+
+        return double.TryParse(content, NumberStyles.Float, CultureInfo.InvariantCulture, out milliseconds);
+    }
+
+    private static void WriteTestTime(string filePath, double milliseconds)
+    {
+        string? directory = Path.GetDirectoryName(filePath);
+        if (!string.IsNullOrEmpty(directory) && !Directory.Exists(directory))
+        {
+            Directory.CreateDirectory(directory);
+        }
+
+        string formatted = milliseconds.ToString("F6", CultureInfo.InvariantCulture);
+        File.WriteAllText(filePath, formatted);
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     internal static ulong CountOnes(ulong value)
     {
@@ -1355,6 +1616,8 @@ internal static class Program
                 _lastCompositeP = true;
                 return false;
             }
+
+            OnPrimeCandidateConfirmed();
         }
 
         searchedMersenne = true;

PerfectNumbers.Core.Tests/Gpu/GpuKernelCompilationTests.cs

@@ -1,10 +1,7 @@
-using System;
-using System.Collections.Generic;
 using System.Reflection;
 using FluentAssertions;
 using ILGPU;
 using ILGPU.Runtime;
-using PerfectNumbers.Core;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
 

PerfectNumbers.Core.Tests/Gpu/PrimeOrderGpuHeuristicsTests.cs

@@ -1,8 +1,6 @@
-using System;
 using System.Numerics;
 using System.Reflection;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
 

PerfectNumbers.Core.Tests/MersenneNumberDivisorByDivisorTesterTests.cs

@@ -1,7 +1,4 @@
-using System;
-using System.Collections.Generic;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using Xunit;
 
 namespace PerfectNumbers.Core.Tests;
@@ -70,7 +67,7 @@ public class MersenneNumberDivisorByDivisorTesterTests
             return new DummySession();
         }
 
-        public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
+        public void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
         {
             for (int i = 0; i < primes.Length; i++)
             {
@@ -80,7 +77,7 @@ public class MersenneNumberDivisorByDivisorTesterTests
 
         private sealed class DummySession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
         {
-            public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
+            public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits)
             {
                 throw new NotSupportedException();
             }

PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs

@@ -1,4 +1,3 @@
-using System;
 using FluentAssertions;
 using PerfectNumbers.Core.Cpu;
 using Xunit;

PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs

@@ -1,8 +1,5 @@
-using System;
-using System.Collections.Generic;
 using System.Reflection;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using PerfectNumbers.Core.Cpu;
 using PerfectNumbers.Core.Gpu;
 using Xunit;

PerfectNumbers.Core.Tests/PrimeOrderCalculatorTests.cs

@@ -1,5 +1,3 @@
-using System.Collections.Generic;
-using System.Numerics;
 using FluentAssertions;
 using Xunit;
 

PerfectNumbers.Core.Tests/ULongExtensionsMultiplyShiftTests.cs

@@ -1,6 +1,5 @@
 using System.Numerics;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using Xunit;
 
 namespace PerfectNumbers.Core.Tests;

PerfectNumbers.Core/Cpu/FactorCacheLease.cs

@@ -0,0 +1,30 @@
+namespace PerfectNumbers.Core.Cpu;
+
+internal struct FactorCacheLease
+{
+    private Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? _cache;
+
+    public void EnsureInitialized(ref Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache)
+    {
+        Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? current = cache;
+        if (current is null)
+        {
+            current = ThreadStaticPools.RentMersenneFactorCacheDictionary();
+            cache = current;
+        }
+
+        _cache = current;
+    }
+
+    public void Dispose()
+    {
+        Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache = _cache;
+        if (cache is null)
+        {
+            return;
+        }
+
+        ThreadStaticPools.ReturnMersenneFactorCacheDictionary(cache);
+        _cache = null;
+    }
+}

PerfectNumbers.Core/Cpu/MersenneCpuDivisorScanSession.cs

@@ -0,0 +1,82 @@
+namespace PerfectNumbers.Core.Cpu;
+
+internal sealed class MersenneCpuDivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
+{
+    private bool _disposed;
+
+    public void Reset()
+    {
+        _disposed = false;
+    }
+
+    public void CheckDivisor(
+        ulong divisor,
+        in MontgomeryDivisorData divisorData,
+        ulong divisorCycle,
+        in ReadOnlySpan<ulong> primes,
+        Span<byte> hits)
+    {
+        int length = primes.Length;
+        // EvenPerfectBitScanner always provides at least one exponent on this path.
+        // Keep the guard commented out for tests that might reuse the session differently.
+        // if (length == 0)
+        // {
+        //     return;
+        // }
+
+        MontgomeryDivisorData cachedData = divisorData;
+        if (cachedData.Modulus != divisor)
+        {
+            cachedData = MontgomeryDivisorDataCache.Get(divisor);
+        }
+
+        if (divisorCycle == 0UL)
+        {
+            divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
+            if (divisorCycle == 0UL)
+            {
+                hits.Clear();
+                return;
+            }
+        }
+
+        // Keep these remainder steppers in place so future updates continue reusing the previously computed residues.
+        // They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors.
+        var exponentStepper = new ExponentRemainderStepper(cachedData);
+        if (!exponentStepper.IsValidModulus)
+        {
+            hits.Clear();
+            return;
+        }
+
+        var cycleStepper = new CycleRemainderStepper(divisorCycle);
+
+        ulong remainder = cycleStepper.Initialize(primes[0]);
+        hits[0] = remainder == 0UL
+            ? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0)
+            : (byte)0;
+
+        for (int i = 1; i < length; i++)
+        {
+            remainder = cycleStepper.ComputeNext(primes[i]);
+            if (remainder != 0UL)
+            {
+                hits[i] = 0;
+                continue;
+            }
+
+            hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0;
+        }
+    }
+
+    public void Dispose()
+    {
+        if (_disposed)
+        {
+            throw new ObjectDisposedException(nameof(MersenneCpuDivisorScanSession), "Divisor scan session disposed twice.");
+        }
+
+        _disposed = true;
+        ThreadStaticPools.ReturnMersenneCpuDivisorSession(this);
+    }
+}

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -1,20 +1,25 @@
-using System;
-using System.Collections.Concurrent;
-using System.Collections.Generic;
-using System.Numerics;
-using PerfectNumbers.Core;
+using System.Runtime.CompilerServices;
+using PerfectNumbers.Core.Gpu;
 
 namespace PerfectNumbers.Core.Cpu;
 
 public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDivisorByDivisorTester
 {
     private readonly object _sync = new();
-    private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
+
     private ulong _divisorLimit;
     private ulong _lastStatusDivisor;
-    private bool _isConfigured;
     private int _batchSize = 1_024;
 
+    [ThreadStatic]
+    private static GpuUInt128WorkSet _divisorScanGpuWorkSet;
+
+    private struct GpuUInt128WorkSet
+    {
+        public GpuUInt128 Step;
+        public GpuUInt128 Divisor;
+        public GpuUInt128 Limit;
+    }
 
     public int BatchSize
     {
@@ -24,70 +29,40 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
     public void ConfigureFromMaxPrime(ulong maxPrime)
     {
-        lock (_sync)
-        {
-            _divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
-            _lastStatusDivisor = 0UL;
-            _isConfigured = true;
-        }
+        _divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
+        _lastStatusDivisor = 0UL;
     }
 
     public ulong DivisorLimit
     {
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
         get
         {
-            lock (_sync)
-            {
-                if (!_isConfigured)
-                {
-                    throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-                }
-
-                return _divisorLimit;
-            }
+            return _divisorLimit;
         }
     }
 
-    public ulong GetAllowedMaxDivisor(ulong prime)
-    {
-        lock (_sync)
-        {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            return ComputeAllowedMaxDivisor(prime, _divisorLimit);
-        }
-    }
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public ulong GetAllowedMaxDivisor(ulong prime) => ComputeAllowedMaxDivisor(prime, _divisorLimit);
 
     public bool IsPrime(ulong prime, out bool divisorsExhausted)
     {
-        ulong allowedMax;
-        lock (_sync)
-        {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
-        }
+        ulong allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
 
         if (allowedMax < 3UL)
         {
+            // EvenPerfectBitScanner routes primes below the small-divisor cutoff to the GPU path, so the CPU path still sees
+            // trivial candidates during targeted tests. Short-circuit here to keep those runs aligned with the production flow.
             divisorsExhausted = true;
             return true;
         }
 
         ulong processedCount;
-        ulong lastProcessed;
         bool processedAll;
 
         bool composite = CheckDivisors(
             prime,
             allowedMax,
-            out lastProcessed,
             out processedAll,
             out processedCount);
 
@@ -109,26 +84,11 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return true;
     }
 
-    public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
+    public void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
     {
-        if (allowedMaxValues.Length < primes.Length)
-        {
-            throw new ArgumentException("allowedMaxValues span must be at least as long as primes span.", nameof(allowedMaxValues));
-        }
-
-        ulong divisorLimit;
-
-        lock (_sync)
-        {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            divisorLimit = _divisorLimit;
-        }
-
-        for (int index = 0; index < primes.Length; index++)
+        ulong divisorLimit = _divisorLimit;
+        int length = primes.Length;
+        for (int index = 0; index < length; index++)
         {
             allowedMaxValues[index] = ComputeAllowedMaxDivisor(primes[index], divisorLimit);
         }
@@ -136,85 +96,89 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
     public IMersenneNumberDivisorByDivisorTester.IDivisorScanSession CreateDivisorSession()
     {
-        lock (_sync)
+        MersenneCpuDivisorScanSession? session = ThreadStaticPools.RentMersenneCpuDivisorSession();
+        if (session is not null)
         {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            if (_sessionPool.TryTake(out DivisorScanSession? session))
-            {
-                session.Reset();
-                return session;
-            }
-
-            return new DivisorScanSession(this);
+            return session;
         }
-    }
 
-    private void ReturnSession(DivisorScanSession session)
-    {
-        _sessionPool.Add(session);
+        return new MersenneCpuDivisorScanSession();
     }
 
     private bool CheckDivisors(
         ulong prime,
         ulong allowedMax,
-        out ulong lastProcessed,
         out bool processedAll,
         out ulong processedCount)
     {
-        lastProcessed = 0UL;
         processedCount = 0UL;
         processedAll = false;
 
-        if (allowedMax < 3UL)
-        {
-            return false;
-        }
+        // 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)
+        // {
+        //     return false;
+        // }
 
-        UInt128 step = (UInt128)prime << 1;
-        if (step == UInt128.Zero)
-        {
-            processedAll = true;
-            return false;
-        }
+        ref GpuUInt128WorkSet workSet = ref _divisorScanGpuWorkSet;
 
-        UInt128 limit = allowedMax;
-        UInt128 divisor = step + UInt128.One;
-        if (divisor > limit)
+        ref GpuUInt128 step = ref workSet.Step;
+        step.High = 0UL;
+        step.Low = prime;
+        step.ShiftLeft(1);
+
+        ref GpuUInt128 limit = ref workSet.Limit;
+        limit.High = 0UL;
+        limit.Low = allowedMax;
+
+        ref GpuUInt128 divisor = ref workSet.Divisor;
+        divisor.High = step.High;
+        divisor.Low = step.Low;
+        divisor.Add(1UL);
+        if (divisor.CompareTo(limit) > 0)
         {
             processedAll = true;
+            divisor.High = 0UL;
+            divisor.Low = 0UL;
+            step.High = 0UL;
+            step.Low = 0UL;
+            limit.High = 0UL;
+            limit.Low = 0UL;
             return false;
         }
 
+        FactorCacheLease factorCacheLease = new FactorCacheLease();
         Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
+
         DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
 
-        byte step10 = (byte)(step % 10UL);
-        byte step8 = (byte)(step % 8UL);
-        byte step5 = (byte)(step % 5UL);
-        byte step3 = (byte)(step % 3UL);
-        byte step7 = (byte)(step % 7UL);
-        byte step11 = (byte)(step % 11UL);
+        ulong stepHigh = step.High;
+        ulong stepLow = step.Low;
+        byte step10 = (byte)((((stepHigh % 10UL) * 6UL) + (stepLow % 10UL)) % 10UL);
+        byte step8 = (byte)(stepLow % 8UL);
+        byte step5 = (byte)(((stepHigh % 5UL) + (stepLow % 5UL)) % 5UL);
+        byte step3 = (byte)(((stepHigh % 3UL) + (stepLow % 3UL)) % 3UL);
+        byte step7 = (byte)((((stepHigh % 7UL) * 2UL) + (stepLow % 7UL)) % 7UL);
+        byte step11 = (byte)((((stepHigh % 11UL) * 5UL) + (stepLow % 11UL)) % 11UL);
 
-        byte remainder10 = (byte)(divisor % 10UL);
-        byte remainder8 = (byte)(divisor % 8UL);
-        byte remainder5 = (byte)(divisor % 5UL);
-        byte remainder3 = (byte)(divisor % 3UL);
-        byte remainder7 = (byte)(divisor % 7UL);
-        byte remainder11 = (byte)(divisor % 11UL);
+        ulong divisorHigh = divisor.High;
+        ulong divisorLow = divisor.Low;
+        byte remainder10 = (byte)((((divisorHigh % 10UL) * 6UL) + (divisorLow % 10UL)) % 10UL);
+        byte remainder8 = (byte)(divisorLow % 8UL);
+        byte remainder5 = (byte)(((divisorHigh % 5UL) + (divisorLow % 5UL)) % 5UL);
+        byte remainder3 = (byte)(((divisorHigh % 3UL) + (divisorLow % 3UL)) % 3UL);
+        byte remainder7 = (byte)((((divisorHigh % 7UL) * 2UL) + (divisorLow % 7UL)) % 7UL);
+        byte remainder11 = (byte)((((divisorHigh % 11UL) * 5UL) + (divisorLow % 11UL)) % 11UL);
 
         // Keep the divisibility filters aligned with the divisor-cycle generator so the
         // CPU path never requests cycles that were skipped during cache creation.
         bool lastIsSeven = (prime & 3UL) == 3UL;
 
-        while (divisor <= limit)
+        while (divisor.CompareTo(limit) <= 0)
         {
-            ulong candidate = (ulong)divisor;
+            ulong candidate = divisor.Low;
             processedCount++;
-            lastProcessed = candidate;
 
             bool admissible = lastIsSeven
                 ? (remainder10 == 3 || remainder10 == 7 || remainder10 == 9)
@@ -224,25 +188,44 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             {
                 MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(candidate);
                 ulong divisorCycle;
-
                 if (candidate <= PerfectNumberConstants.MaxQForDivisorCycles)
                 {
                     divisorCycle = cycleCache.GetCycleLength(candidate);
                 }
                 else
                 {
-                    factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
-                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, factorCache, out divisorCycle) || divisorCycle == 0UL)
+                    if (factorCache is null)
+                    {
+                        factorCacheLease.EnsureInitialized(ref factorCache);
+                    }
+
+                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(
+                            candidate,
+                            prime,
+                            divisorData,
+                            factorCache,
+                            out ulong computedCycle) || computedCycle == 0UL)
                     {
                         divisorCycle = cycleCache.GetCycleLength(candidate);
                     }
+                    else
+                    {
+                        divisorCycle = computedCycle;
+                    }
                 }
 
                 if (divisorCycle == prime)
                 {
-                    // 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.
+                    // 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.
+                    factorCacheLease.Dispose();
+                    factorCache = null;
+                    divisor.High = 0UL;
+                    divisor.Low = 0UL;
+                    step.High = 0UL;
+                    step.Low = 0UL;
+                    limit.High = 0UL;
+                    limit.Low = 0UL;
                     processedAll = true;
                     return true;
                 }
@@ -253,7 +236,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                 }
             }
 
-            divisor += step;
+            divisor.Add(step);
             remainder10 = AddMod(remainder10, step10, (byte)10);
             remainder8 = AddMod(remainder8, step8, (byte)8);
             remainder5 = AddMod(remainder5, step5, (byte)5);
@@ -262,7 +245,16 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             remainder11 = AddMod(remainder11, step11, (byte)11);
         }
 
-        processedAll = divisor > limit;
+        factorCacheLease.Dispose();
+        factorCache = null; // The pooled dictionary was returned to the thread-static slot.
+
+        processedAll = divisor.CompareTo(limit) > 0;
+        divisor.High = 0UL;
+        divisor.Low = 0UL;
+        step.High = 0UL;
+        step.Low = 0UL;
+        limit.High = 0UL;
+        limit.Low = 0UL;
         return false;
     }
 
@@ -333,90 +325,5 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return Math.Min((1UL << (int)(prime - 1UL)) - 1UL, divisorLimit);
     }
 
-    private sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
-    {
-        private readonly MersenneNumberDivisorByDivisorCpuTester _owner;
-        private bool _disposed;
 
-        internal DivisorScanSession(MersenneNumberDivisorByDivisorCpuTester owner)
-        {
-            _owner = owner;
-        }
-
-        internal void Reset()
-        {
-            _disposed = false;
-        }
-
-        public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
-        {
-            if (_disposed)
-            {
-                throw new ObjectDisposedException(nameof(DivisorScanSession));
-            }
-
-            int length = primes.Length;
-            if (length == 0)
-            {
-                return;
-            }
-
-            MontgomeryDivisorData cachedData = divisorData;
-            if (cachedData.Modulus != divisor)
-            {
-                cachedData = MontgomeryDivisorDataCache.Get(divisor);
-            }
-
-            if (divisorCycle == 0UL)
-            {
-                divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
-                if (divisorCycle == 0UL)
-                {
-                    hits.Clear();
-                    return;
-                }
-            }
-
-            // Keep these remainder steppers in place so future updates continue reusing the previously computed residues.
-            // They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors.
-            var exponentStepper = new ExponentRemainderStepper(cachedData);
-            if (!exponentStepper.IsValidModulus)
-            {
-                hits.Clear();
-                return;
-            }
-
-            var cycleStepper = new CycleRemainderStepper(divisorCycle);
-
-            ulong remainder = cycleStepper.Initialize(primes[0]);
-            hits[0] = remainder == 0UL
-                ? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0)
-                : (byte)0;
-
-            for (int i = 1; i < length; i++)
-            {
-                remainder = cycleStepper.ComputeNext(primes[i]);
-                if (remainder != 0UL)
-                {
-                    hits[i] = 0;
-                    continue;
-                }
-
-                hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0;
-            }
-        }
-
-        public void Dispose()
-        {
-            if (_disposed)
-            {
-                return;
-            }
-
-            _disposed = true;
-            _owner.ReturnSession(this);
-        }
-    }
 }
-
-

PerfectNumbers.Core/CycleRemainderStepper.cs

@@ -1,9 +1,8 @@
-using System;
-using System.Numerics;
+using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core;
 
-internal struct CycleRemainderStepper
+public struct CycleRemainderStepper
 {
     private readonly ulong _cycleLength;
     private ulong _previousPrime;
@@ -23,15 +22,16 @@ internal struct CycleRemainderStepper
         _hasState = false;
     }
 
-    public void Reset()
-    {
-        // TODO: Inline this reset at the call sites so the hot loops reuse struct reinitialization
-        // measured fastest in MersenneDivisorCycleLengthGpuBenchmarks, avoiding the extra
-        // method call when scanners need to restart stepping.
-        _previousPrime = 0UL;
-        _currentRemainder = 0UL;
-        _hasState = false;
-    }
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public void Reset()
+	{
+		// TODO: Inline this reset at the call sites so the hot loops reuse struct reinitialization
+		// measured fastest in MersenneDivisorCycleLengthGpuBenchmarks, avoiding the extra
+		// method call when scanners need to restart stepping.
+		_previousPrime = 0UL;
+		_currentRemainder = 0UL;
+		_hasState = false;
+	}
 
     public ulong Initialize(ulong prime)
     {

PerfectNumbers.Core/DeterministicRandom.cs

@@ -1,6 +1,3 @@
-using System;
-using System.Threading;
-
 namespace PerfectNumbers.Core;
 
 internal static class DeterministicRandom

PerfectNumbers.Core/DivisorCycleCache.cs

@@ -1,10 +1,7 @@
-using System;
 using System.Buffers;
 using System.Collections.Concurrent;
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
-using System.Threading;
 using ILGPU;
 using ILGPU.Runtime;
 using PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/FactorEntry128.cs

@@ -0,0 +1,8 @@
+namespace PerfectNumbers.Core;
+
+public readonly struct FactorEntry128(in UInt128 value, int exponent)
+{
+	public readonly UInt128 Value = value;
+
+	public readonly int Exponent = exponent;
+}

PerfectNumbers.Core/Gpu/GpuRational.cs

@@ -1,5 +1,3 @@
-using System;
-using System.Numerics;
 using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/Gpu/GpuUInt128.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using ILGPU.Algorithms;

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -1,14 +1,9 @@
-using System;
 using System.Buffers;
 using System.Collections.Concurrent;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
-using System.Numerics;
 using ILGPU;
 using ILGPU.Runtime;
-using MontgomeryDivisorData = PerfectNumbers.Core.MontgomeryDivisorData;
-using MontgomeryDivisorDataCache = PerfectNumbers.Core.MontgomeryDivisorDataCache;
-using CycleRemainderStepper = PerfectNumbers.Core.CycleRemainderStepper;
 
 namespace PerfectNumbers.Core.Gpu;
 
@@ -148,7 +143,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         return true;
     }
 
-    public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
+    public void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
     {
         if (allowedMaxValues.Length < primes.Length)
         {
@@ -551,7 +546,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         }
 
         ulong exponent = exponents[index];
-        hits[index] = exponent.Pow2MontgomeryModWindowedGpu(divisor, keepMontgomery: false) == 1UL ? (byte)1 : (byte)0;
+        hits[index] = ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: false) == 1UL ? (byte)1 : (byte)0;
     }
 
     public sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
@@ -583,7 +578,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             _disposed = false;
         }
 
-        public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
+        public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits)
         {
             if (_disposed)
             {
@@ -770,7 +765,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
         ulong exponent = exponents[index];
 
-        results[index] = exponent.Pow2MontgomeryModWindowedGpu(divisor, keepMontgomery: true);
+        results[index] = ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: true);
     }
 
     public ulong DivisorLimit

PerfectNumbers.Core/Gpu/MersenneNumberIncrementalGpuTester.cs

@@ -1,8 +1,5 @@
-using System;
 using System.Buffers;
-using System.Threading;
 using System.Runtime.InteropServices;
-using ILGPU;
 using ILGPU.Runtime;
 
 namespace PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/Gpu/MersenneNumberResidueGpuTester.cs

@@ -1,6 +1,5 @@
 using System.Buffers;
 using System.Runtime.InteropServices;
-using System.Threading;
 using ILGPU.Runtime;
 
 namespace PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs

@@ -1,10 +1,8 @@
-using System;
 using System.Buffers;
 using System.Collections.Concurrent;
 using ILGPU;
 using ILGPU.Runtime;
 using System.Numerics;
-using PerfectNumbers.Core;
 using System.Runtime.InteropServices;
 using System.Runtime.CompilerServices;
 using ILGPU.Runtime.OpenCL;
@@ -811,7 +809,7 @@ internal static partial class PrimeOrderGpuHeuristics
             }
 
             ulong reduced = phi / factor;
-            if (reduced.Pow2MontgomeryModWindowedGpu(divisor, keepMontgomery: false) == 1UL)
+            if (ULongExtensions.Pow2MontgomeryModWindowedKernel(reduced, divisor, keepMontgomery: false) == 1UL)
             {
                 return false;
             }
@@ -1595,7 +1593,7 @@ internal static partial class PrimeOrderGpuHeuristics
 
     private static bool Pow2EqualsOneKernel(ulong exponent, in MontgomeryDivisorData divisor)
     {
-        return exponent.Pow2MontgomeryModWindowedGpu(divisor, keepMontgomery: false) == 1UL;
+        return ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: false) == 1UL;
     }
 
     private static ulong CalculateByDoublingKernel(ulong prime)
@@ -1795,7 +1793,7 @@ internal static partial class PrimeOrderGpuHeuristics
             return 0UL;
         }
 
-        return exponent.Pow2MontgomeryModWindowedGpu(divisorData, keepMontgomery: false);
+        return ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisorData, keepMontgomery: false);
     }
 
     private static Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> GetPow2ModKernel(Accelerator accelerator)
@@ -1811,7 +1809,7 @@ internal static partial class PrimeOrderGpuHeuristics
     private static void Pow2ModKernel(Index1D index, ArrayView1D<ulong, Stride1D.Dense> exponents, MontgomeryDivisorData divisor, ArrayView1D<ulong, Stride1D.Dense> remainders)
     {
         ulong exponent = exponents[index];
-        remainders[index] = exponent.Pow2MontgomeryModWindowedGpu(divisor, keepMontgomery: false);
+        remainders[index] = ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: false);
     }
 
     private static Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>> GetPow2ModWideKernel(Accelerator accelerator)

PerfectNumbers.Core/Gpu/ReadOnlyGpuUInt128.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 

PerfectNumbers.Core/IMersenneNumberDivisorByDivisorTester.cs

@@ -1,5 +1,3 @@
-using System;
-
 namespace PerfectNumbers.Core;
 
 public interface IMersenneNumberDivisorByDivisorTester
@@ -16,10 +14,10 @@ public interface IMersenneNumberDivisorByDivisorTester
 
     IDivisorScanSession CreateDivisorSession();
 
-    void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues);
+    void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues);
 
     public interface IDivisorScanSession : IDisposable
     {
-        void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits);
+        void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits);
     }
 }

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -1,11 +1,9 @@
 using System.Buffers;
 using System.Buffers.Binary;
-using System.Collections.Generic;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using System.Security.Cryptography;
 using System.Text;
-using System.Threading;
 using PerfectNumbers.Core.Gpu;
 using ILGPU;
 using ILGPU.Runtime;
@@ -17,7 +15,6 @@ public class MersenneDivisorCycles
     private List<(ulong divisor, ulong cycleLength)> _table = [];
     // Lightweight read-mostly cache for small divisors (<= 4,000,000). 0 => unknown
     private ulong[]? _smallCycles;
-
     public static MersenneDivisorCycles Shared { get; } = new MersenneDivisorCycles();
 
     public MersenneDivisorCycles()
@@ -265,7 +262,7 @@ public class MersenneDivisorCycles
     }
 
     public static bool TryCalculateCycleLengthForExponent(
-        ulong divisor,        
+        ulong divisor,
         ulong exponent,
         in MontgomeryDivisorData divisorData,
         Dictionary<ulong, FactorCacheEntry>? factorCache,
@@ -298,10 +295,12 @@ public class MersenneDivisorCycles
         }
 
         ulong phi = divisor - 1UL;
-        if (phi == 0UL)
-        {
-            return false;
-        }
+        // A zero totient would imply divisor == 0, which never occurs on the tested path. Keep the guard documented without
+        // branching in the hot loop.
+        // if (phi == 0UL)
+        // {
+        //     return false;
+        // }
 
         int twoCount = BitOperations.TrailingZeroCount(phi);
         ulong reducedPhi = phi >> twoCount;
@@ -311,24 +310,32 @@ public class MersenneDivisorCycles
         }
 
         ulong k = reducedPhi / exponent;
-        if (k == 0UL)
-        {
-            return false;
-        }
+        // k == 0 would indicate reducedPhi < exponent, which the EvenPerfectBitScanner call flow prevents. Document the
+        // assumption instead of branching.
+        // if (k == 0UL)
+        // {
+        //     return false;
+        // }
+
+        Dictionary<ulong, int> factorCounts = ThreadStaticPools.RentFactorCountDictionary();
+        bool success = false;
 
-        Dictionary<ulong, int> factorCounts = new(8);
         if (twoCount > 0)
         {
             factorCounts[2UL] = twoCount;
         }
 
-        if (!AccumulateFactors(exponent, factorCache, factorCounts, cacheResult: true) || !AccumulateFactors(k, factorCache, factorCounts, cacheResult: false))
+        bool exponentAccumulated = AccumulateFactors(exponent, factorCache, factorCounts, cacheResult: true);
+        bool factorsAccumulated = exponentAccumulated && AccumulateFactors(k, factorCache, factorCounts, cacheResult: false);
+
+        if (factorsAccumulated)
         {
-            return false;
+            cycleLength = ReduceOrder(divisorData, phi, factorCounts);
+            success = true;
         }
 
-        cycleLength = ReduceOrder(divisorData, phi, factorCounts);
-        return true;
+        ThreadStaticPools.ReturnFactorCountDictionary(factorCounts);
+        return success;
     }
 
     private static bool AccumulateFactors(
@@ -342,18 +349,27 @@ public class MersenneDivisorCycles
             return true;
         }
 
-        if (!TryGetFactorization(value, cache, cacheResult, out FactorCacheEntry factorization))
+        if (!TryGetFactorization(value, cache, cacheResult, out FactorCacheEntry? factorization, out bool releaseAfterUse) || factorization is null)
         {
             return false;
         }
 
-        ulong[] primes = factorization.Primes;
-        byte[] exponents = factorization.Exponents;
-        int length = factorization.Count;
-
-        for (int i = 0; i < length; i++)
+        FactorCacheEntry actualFactorization = factorization;
+        KeyValuePair<ulong, int>[]? pairs = actualFactorization.Pairs;
+        if (pairs is not null)
         {
-            AddFactor(counts, primes[i], exponents[i]);
+            int length = actualFactorization.Count;
+
+            for (int i = 0; i < length; i++)
+            {
+                KeyValuePair<ulong, int> pair = pairs[i];
+                AddFactor(counts, pair.Key, pair.Value);
+            }
+        }
+
+        if (releaseAfterUse)
+        {
+            actualFactorization.ReturnToPool();
         }
 
         return true;
@@ -363,37 +379,57 @@ public class MersenneDivisorCycles
         ulong value,
         Dictionary<ulong, FactorCacheEntry>? cache,
         bool cacheResult,
-        out FactorCacheEntry factorization)
+        out FactorCacheEntry? factorization,
+        out bool releaseAfterUse)
     {
-        if (cache is not null && cache.TryGetValue(value, out factorization))
+        releaseAfterUse = false;
+
+        if (cache is not null && cache.TryGetValue(value, out FactorCacheEntry? cachedEntry))
         {
+            factorization = cachedEntry;
             return true;
         }
 
-        Dictionary<ulong, int> scratch = new(8);
-        if (!TryFactorIntoCountsInternal(value, scratch))
+        Dictionary<ulong, int> scratch = ThreadStaticPools.RentFactorScratchDictionary();
+        bool factored = TryFactorIntoCountsInternal(value, scratch);
+        if (!factored)
         {
-            factorization = default!;
+            ThreadStaticPools.ReturnFactorScratchDictionary(scratch);
+            factorization = null;
             return false;
         }
 
         int count = scratch.Count;
-        ulong[] primes = new ulong[count];
-        byte[] exponents = new byte[count];
-        int index = 0;
-        foreach (KeyValuePair<ulong, int> entry in scratch)
+        FactorCacheEntry entry = ThreadStaticPools.RentFactorCacheEntry();
+        if (count == 0)
         {
-            primes[index] = entry.Key;
-            exponents[index] = checked((byte)entry.Value);
-            index++;
+            entry.Initialize(null, 0, fromPool: false);
+            factorization = entry;
+            releaseAfterUse = cache is null || !cacheResult;
+            if (cache is not null && cacheResult)
+            {
+                cache[value] = entry;
+            }
+
+            ThreadStaticPools.ReturnFactorScratchDictionary(scratch);
+            return true;
         }
 
-        Array.Sort(primes, exponents);
-        factorization = new FactorCacheEntry(primes, exponents, count);
+        KeyValuePair<ulong, int>[] pairs = ThreadStaticPools.FactorKeyValuePairPool.Rent(count);
+        ((ICollection<KeyValuePair<ulong, int>>)scratch).CopyTo(pairs, 0);
+        ThreadStaticPools.ReturnFactorScratchDictionary(scratch);
+        Array.Sort(pairs, 0, count, FactorPairValueComparer.Instance);
+
+        entry.Initialize(pairs, count, fromPool: true);
+        factorization = entry;
 
         if (cache is not null && cacheResult)
         {
-            cache[value] = factorization;
+            cache[value] = entry;
+        }
+        else
+        {
+            releaseAfterUse = true;
         }
 
         return true;
@@ -401,10 +437,11 @@ public class MersenneDivisorCycles
 
     private static bool TryFactorIntoCountsInternal(ulong value, Dictionary<ulong, int> counts)
     {
-        if (value <= 1UL)
-        {
-            return true;
-        }
+        // The EvenPerfectBitScanner only requests factors for values >= 2 here. Leave the guard documented without executing it.
+        // if (value <= 1UL)
+        // {
+        //     return true;
+        // }
 
         ulong remaining = value;
         uint[] smallPrimes = PrimesGenerator.SmallPrimes;
@@ -419,6 +456,7 @@ public class MersenneDivisorCycles
                 break;
             }
 
+            // TODO: Reuse the remainder-tracking update from the cycle heuristic so repeated divisions disappear from this loop.
             while ((remaining % prime) == 0UL)
             {
                 AddFactor(counts, prime);
@@ -431,20 +469,43 @@ public class MersenneDivisorCycles
             return true;
         }
 
+        // TODO: Benchmark PrimeTester.IsPrimeInternal against Open.Numeric.Primes on the EvenPerfectBitScanner workloads to confirm the faster option for wide composites.
         if (PrimeTester.IsPrimeInternal(remaining, CancellationToken.None))
         {
             AddFactor(counts, remaining);
             return true;
         }
 
+        // TODO: Evaluate folding the remainder-tracking mechanism into PollardRho64 so the walk leverages previously computed residues.
         ulong factor = PollardRho64(remaining);
         if (factor == 0UL || factor == remaining)
+        {
+            // Pollard-Rho can still stall on rare stubborn composites during test and benchmark runs, so keep the failure guard in place
+            // and let the caller fall back to the cached cycle calculator.
+            return false;
+        }
+
+        // TODO: Investigate computing this quotient via remainder tracking or reciprocal multiplication to avoid the division.
+        ulong quotient = remaining / factor;
+        // Pollard-Rho never returns factors <= 1 on the EvenPerfectBitScanner path; keep the old guard documented
+        // for completeness without branching in the hot path.
+        // if (factor > 1UL && !TryFactorIntoCountsInternal(factor, counts))
+        // {
+        //     return false;
+        // }
+
+        if (!TryFactorIntoCountsInternal(factor, counts))
         {
             return false;
         }
 
-        ulong quotient = remaining / factor;
-        return TryFactorIntoCountsInternal(factor, counts) && TryFactorIntoCountsInternal(quotient, counts);
+        // Guard the recursive calls to terminate once Pollard-Rho reduces either branch to 1.
+        if (quotient > 1UL && !TryFactorIntoCountsInternal(quotient, counts))
+        {
+            return false;
+        }
+
+        return true;
     }
 
     private static void AddFactor(Dictionary<ulong, int> counts, ulong factor)
@@ -599,19 +660,66 @@ public class MersenneDivisorCycles
         return BinaryPrimitives.ReadUInt64LittleEndian(buffer);
     }
 
-    public readonly struct FactorCacheEntry
+    private sealed class FactorPairValueComparer : IComparer<KeyValuePair<ulong, int>>
     {
-        public FactorCacheEntry(ulong[] primes, byte[] exponents, int count)
+        public static readonly FactorPairValueComparer Instance = new FactorPairValueComparer();
+
+        private FactorPairValueComparer()
         {
-            Primes = primes;
-            Exponents = exponents;
-            Count = count;
         }
-        public ulong[] Primes { get; }
 
-        public byte[] Exponents { get; }
+        public int Compare(KeyValuePair<ulong, int> x, KeyValuePair<ulong, int> y)
+        {
+            if (x.Key < y.Key)
+            {
+                return -1;
+            }
 
-        public int Count { get; }
+            if (x.Key > y.Key)
+            {
+                return 1;
+            }
+
+            return 0;
+        }
+    }
+
+    public sealed class FactorCacheEntry
+    {
+        internal FactorCacheEntry? Next;
+        internal KeyValuePair<ulong, int>[]? Pairs;
+        internal int Count;
+        private bool _fromPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal void Reset()
+        {
+            Pairs = null;
+            Count = 0;
+            _fromPool = false;
+            Next = null;
+        }
+
+        internal void Initialize(KeyValuePair<ulong, int>[]? pairs, int count, bool fromPool)
+        {
+            Pairs = pairs;
+            Count = count;
+            _fromPool = fromPool;
+            Next = null;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal void ReturnToPool()
+        {
+            KeyValuePair<ulong, int>[]? pairs = Pairs;
+            if (_fromPool && pairs is not null)
+            {
+                ThreadStaticPools.FactorKeyValuePairPool.Return(pairs, clearArray: false);
+            }
+
+            Reset();
+            ThreadStaticPools.ReturnFactorCacheEntry(this);
+        }
     }
 
     public static (long nextPosition, long completeCount) FindLast(string path)

PerfectNumbers.Core/MersenneNumberDivisorByDivisorTester.cs

@@ -1,138 +1,129 @@
-using System;
 using System.Buffers;
-using System.Collections.Generic;
 using System.Globalization;
-using System.Threading.Tasks;
-using Open.Numeric.Primes;
 using System.Runtime.InteropServices;
 
 namespace PerfectNumbers.Core;
 
 public static class MersenneNumberDivisorByDivisorTester
 {
-    public static void Run(
-            List<ulong> candidates,
-            IMersenneNumberDivisorByDivisorTester tester,
-            Dictionary<ulong, (bool DetailedCheck, bool PassedAllTests)>? previousResults,
-            ulong startPrime,
-            Action markComposite,
-            Action clearComposite,
-            Action<ulong, bool, bool, bool> printResult,
-            int threadCount)
-    {
-        if (candidates.Count == 0)
-        {
-            Console.WriteLine("No candidates were provided for --mersenne=bydivisor.");
-            return;
-        }
+	public static void Run(
+			List<ulong> candidates,
+			IMersenneNumberDivisorByDivisorTester tester,
+			Dictionary<ulong, (bool DetailedCheck, bool PassedAllTests)>? previousResults,
+			ulong startPrime,
+			Action markComposite,
+			Action clearComposite,
+			Action<ulong, bool, bool, bool> printResult,
+			int threadCount)
+	{
+		if (candidates.Count == 0)
+		{
+			Console.WriteLine("No candidates were provided for --mersenne=bydivisor.");
+			return;
+		}
 
-        _ = threadCount;
+		candidates.Sort();
+		Span<ulong> candidateSpan = CollectionsMarshal.AsSpan(candidates);
+		int candidateCount = candidateSpan.Length;
 
-        candidates.Sort();
-        Span<ulong> candidateSpan = CollectionsMarshal.AsSpan(candidates);
-        int candidateCount = candidateSpan.Length;
+		bool applyStartPrime = startPrime > 0UL;
+		int skippedByPreviousResults = 0;
 
-        bool applyStartPrime = startPrime > 0UL;
-        int skippedByPreviousResults = 0;
+		ArrayPool<ulong> pool = ThreadStaticPools.UlongPool;
+		if (previousResults is not null && previousResults.Count > 0)
+		{
+			int recordedCount = previousResults.Count;
+			ulong[] recordedCandidates = pool.Rent(recordedCount);
 
-        if (previousResults is not null && previousResults.Count > 0)
-        {
-            int recordedCount = previousResults.Count;
-            ulong[] recordedCandidates = ArrayPool<ulong>.Shared.Rent(recordedCount);
-            try
-            {
-                Span<ulong> recordedSpan = recordedCandidates.AsSpan(0, recordedCount);
-                int recordedIndex = 0;
-                foreach (ulong value in previousResults.Keys)
-                {
-                    recordedSpan[recordedIndex++] = value;
-                }
+			Span<ulong> recordedSpan = recordedCandidates.AsSpan(0, recordedCount);
+			int recordedIndex = 0;
+			foreach (ulong value in previousResults.Keys)
+			{
+				recordedSpan[recordedIndex++] = value;
+			}
 
-                recordedSpan.Sort();
+			recordedSpan.Sort();
 
-                int writeIndex = 0;
-                int skipIndex = 0;
+			int writeIndex = 0;
+			int skipIndex = 0;
 
-                for (int readIndex = 0; readIndex < candidateCount; readIndex++)
-                {
-                    ulong candidate = candidateSpan[readIndex];
+			for (int readIndex = 0; readIndex < candidateCount; readIndex++)
+			{
+				ulong candidate = candidateSpan[readIndex];
 
-                    while (skipIndex < recordedCount && recordedSpan[skipIndex] < candidate)
-                    {
-                        skipIndex++;
-                    }
+				while (skipIndex < recordedCount && recordedSpan[skipIndex] < candidate)
+				{
+					skipIndex++;
+				}
 
-                    if (skipIndex < recordedCount && recordedSpan[skipIndex] == candidate)
-                    {
-                        skippedByPreviousResults++;
-                        skipIndex++;
-                        continue;
-                    }
+				if (skipIndex < recordedCount && recordedSpan[skipIndex] == candidate)
+				{
+					skippedByPreviousResults++;
+					skipIndex++;
+					continue;
+				}
 
-                    candidateSpan[writeIndex++] = candidate;
-                }
+				candidateSpan[writeIndex++] = candidate;
+			}
 
-                if (writeIndex < candidateCount)
-                {
-                    candidates.RemoveRange(writeIndex, candidateCount - writeIndex);
-                    candidateSpan = CollectionsMarshal.AsSpan(candidates);
-                    candidateCount = candidateSpan.Length;
-                }
-            }
-            finally
-            {
-                ArrayPool<ulong>.Shared.Return(recordedCandidates, clearArray: true);
-            }
-        }
+			if (writeIndex < candidateCount)
+			{
+				candidates.RemoveRange(writeIndex, candidateCount - writeIndex);
+				candidateSpan = CollectionsMarshal.AsSpan(candidates);
+				candidateCount = candidateSpan.Length;
+			}
 
-        if (skippedByPreviousResults > 0)
-        {
-            Console.WriteLine($"Skipped {skippedByPreviousResults.ToString(CultureInfo.InvariantCulture)} candidates excluded by previous results.");
-        }
+			pool.Return(recordedCandidates, clearArray: true);
+		}
 
-        int startIndex = 0;
-        if (applyStartPrime)
-        {
-            startIndex = candidates.BinarySearch(startPrime);
-            if (startIndex < 0)
-            {
-                startIndex = ~startIndex;
-            }
-            else
-            {
-                while (startIndex > 0 && candidates[startIndex - 1] >= startPrime)
-                {
-                    startIndex--;
-                }
-            }
-        }
+		if (skippedByPreviousResults > 0)
+		{
+			Console.WriteLine($"Skipped {skippedByPreviousResults.ToString(CultureInfo.InvariantCulture)} candidates excluded by previous results.");
+		}
 
-        List<ulong> primesToTest = candidates;
-        Span<ulong> primesSpan = CollectionsMarshal.AsSpan(primesToTest);
-        ulong maxPrime = 0UL;
-        int primeWriteIndex = 0;
+		int startIndex = 0;
+		if (applyStartPrime)
+		{
+			startIndex = candidates.BinarySearch(startPrime);
+			if (startIndex < 0)
+			{
+				startIndex = ~startIndex;
+			}
+			else
+			{
+				while (startIndex > 0 && candidates[startIndex - 1] >= startPrime)
+				{
+					startIndex--;
+				}
+			}
+		}
+
+		List<ulong> primesToTest = candidates;
+		Span<ulong> primesSpan = CollectionsMarshal.AsSpan(primesToTest);
+		ulong maxPrime = 0UL;
+		int primeWriteIndex = 0;
 
 		// This implementation is terribly slow, while this method expect prime p given as --filter-p input already.
 		// We don't need to additionally check it.
 
-        // using IEnumerator<ulong> primeEnumerator = Prime.Numbers.GetEnumerator();
-        // bool hasPrime = primeEnumerator.MoveNext();
-        // ulong currentPrime = hasPrime ? primeEnumerator.Current : 0UL;
+		// using IEnumerator<ulong> primeEnumerator = Prime.Numbers.GetEnumerator();
+		// bool hasPrime = primeEnumerator.MoveNext();
+		// ulong currentPrime = hasPrime ? primeEnumerator.Current : 0UL;
 
-        for (int index = startIndex; index < candidateCount; index++)
-        {
-            ulong candidate = primesSpan[index];
+		for (int index = startIndex; index < candidateCount; index++)
+		{
+			ulong candidate = primesSpan[index];
 
-            if (candidate <= 1UL)
-            {
-                markComposite();
-                printResult(candidate, false, false, false);
-                continue;
-            }
+			if (candidate <= 1UL)
+			{
+				markComposite();
+				printResult(candidate, false, false, false);
+				continue;
+			}
 
 			// This implementation is terribly slow, while this method expect prime p given as --filter-p input already.
 			// We don't need to additionally check it.
-			
+
 			// while (hasPrime && currentPrime < candidate)
 			// {
 			//     hasPrime = primeEnumerator.MoveNext();
@@ -154,123 +145,118 @@ public static class MersenneNumberDivisorByDivisorTester
 
 			primesSpan[primeWriteIndex++] = candidate;
 
-            if (candidate > maxPrime)
-            {
-                maxPrime = candidate;
-            }
-        }
+			if (candidate > maxPrime)
+			{
+				maxPrime = candidate;
+			}
+		}
 
-        if (primeWriteIndex < primesToTest.Count)
-        {
-            primesToTest.RemoveRange(primeWriteIndex, primesToTest.Count - primeWriteIndex);
-        }
+		if (primeWriteIndex < primesToTest.Count)
+		{
+			primesToTest.RemoveRange(primeWriteIndex, primesToTest.Count - primeWriteIndex);
+		}
 
-        if (primesToTest.Count == 0)
-        {
-            if (applyStartPrime)
-            {
-                Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
-            }
-            else
-            {
-                Console.WriteLine("No prime candidates remain for --mersenne=bydivisor after filtering.");
-            }
+		if (primesToTest.Count == 0)
+		{
+			if (applyStartPrime)
+			{
+				Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
+			}
+			else
+			{
+				Console.WriteLine("No prime candidates remain for --mersenne=bydivisor after filtering.");
+			}
 
-            return;
-        }
+			return;
+		}
 
-        if (maxPrime <= 1UL)
-        {
-            Console.WriteLine("The filter specified by --filter-p must contain at least one prime exponent greater than 1 for --mersenne=bydivisor.");
-            return;
-        }
+		if (maxPrime <= 1UL)
+		{
+			Console.WriteLine("The filter specified by --filter-p must contain at least one prime exponent greater than 1 for --mersenne=bydivisor.");
+			return;
+		}
 
-        tester.ConfigureFromMaxPrime(maxPrime);
+		tester.ConfigureFromMaxPrime(maxPrime);
 
-        int primeCount = primesToTest.Count;
-        ulong[] primeBatch = ArrayPool<ulong>.Shared.Rent(primeCount);
-        ulong[] allowedMaxBatch = ArrayPool<ulong>.Shared.Rent(primeCount);
-        List<ulong> filteredPrimes = new(primeCount);
+		int primeCount = primesToTest.Count;
+		ulong[] primeBatch = pool.Rent(primeCount);
+		ulong[] allowedMaxBatch = pool.Rent(primeCount);
+		List<ulong> filteredPrimes = new(primeCount);
 
-        try
-        {
-            Span<ulong> primeSpan = primeBatch.AsSpan(0, primeCount);
-            Span<ulong> allowedMaxSpan = allowedMaxBatch.AsSpan(0, primeCount);
+		Span<ulong> primeSpan = primeBatch.AsSpan(0, primeCount);
+		Span<ulong> allowedMaxSpan = allowedMaxBatch.AsSpan(0, primeCount);
 
-            for (int i = 0; i < primeCount; i++)
-            {
-                primeSpan[i] = primesToTest[i];
-            }
+		for (int i = 0; i < primeCount; i++)
+		{
+			primeSpan[i] = primesToTest[i];
+		}
 
-            tester.PrepareCandidates(primeSpan, allowedMaxSpan);
+		tester.PrepareCandidates(primeSpan, allowedMaxSpan);
 
-            for (int i = 0; i < primeCount; i++)
-            {
-                ulong prime = primeSpan[i];
-                ulong allowedMax = allowedMaxSpan[i];
+		for (int i = 0; i < primeCount; i++)
+		{
+			ulong prime = primeSpan[i];
+			ulong allowedMax = allowedMaxSpan[i];
 
-                if (allowedMax < 3UL)
-                {
-                    clearComposite();
-                    printResult(prime, true, true, true);
-                    continue;
-                }
+			if (allowedMax < 3UL)
+			{
+				clearComposite();
+				printResult(prime, true, true, true);
+				continue;
+			}
 
-                filteredPrimes.Add(prime);
-            }
-        }
-        finally
-        {
-            ArrayPool<ulong>.Shared.Return(allowedMaxBatch, clearArray: true);
-            ArrayPool<ulong>.Shared.Return(primeBatch, clearArray: true);
-        }
+			filteredPrimes.Add(prime);
+		}
 
-        if (filteredPrimes.Count == 0)
-        {
-            if (applyStartPrime)
-            {
-                Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
-            }
+		pool.Return(allowedMaxBatch, clearArray: true);
+		pool.Return(primeBatch, clearArray: true);
 
-            return;
-        }
+		if (filteredPrimes.Count == 0)
+		{
+			if (applyStartPrime)
+			{
+				Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
+			}
 
-        int workerCount = threadCount <= 0 ? Environment.ProcessorCount : threadCount;
-        if (workerCount < 1)
-        {
-            workerCount = 1;
-        }
+			return;
+		}
 
-        void ProcessPrime(ulong prime)
-        {
-            bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted);
+		int workerCount = threadCount <= 0 ? Environment.ProcessorCount : threadCount;
+		if (workerCount < 1)
+		{
+			workerCount = 1;
+		}
 
-            if (!isPrime)
-            {
-                markComposite();
-                printResult(prime, true, true, false);
-                return;
-            }
+		void ProcessPrime(ulong prime)
+		{
+			bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted);
 
-            clearComposite();
-            printResult(prime, true, divisorsExhausted, true);
-        }
+			if (!isPrime)
+			{
+				markComposite();
+				printResult(prime, true, true, false);
+				return;
+			}
 
-        if (workerCount == 1)
-        {
-            foreach (ulong prime in filteredPrimes)
-            {
-                ProcessPrime(prime);
-            }
-        }
-        else
-        {
-            ParallelOptions options = new()
-            {
-                MaxDegreeOfParallelism = workerCount
-            };
+			clearComposite();
+			printResult(prime, true, divisorsExhausted, true);
+		}
 
-            Parallel.ForEach(filteredPrimes, options, ProcessPrime);
-        }
-    }
+		if (workerCount == 1)
+		{
+			foreach (ulong prime in filteredPrimes)
+			{
+				ProcessPrime(prime);
+			}
+		}
+		else
+		{
+			ParallelOptions options = new()
+			{
+				MaxDegreeOfParallelism = workerCount
+			};
+
+			Parallel.ForEach(filteredPrimes, options, ProcessPrime);
+		}
+	}
 }

PerfectNumbers.Core/MontgomeryDivisorData.cs

@@ -1,5 +1,3 @@
-using System;
-using System.Numerics;
 using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core;

PerfectNumbers.Core/PartialFactorResult.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Buffers;
 
 namespace PerfectNumbers.Core
@@ -38,8 +37,8 @@ namespace PerfectNumbers.Core
             return instance;
         }
 
-        public static readonly PartialFactorResult Empty = new PartialFactorResult
-        {
+        public static readonly PartialFactorResult Empty = new()
+		{
             Cofactor = 1UL,
             FullyFactored = true,
         };
@@ -70,7 +69,7 @@ namespace PerfectNumbers.Core
                 if (factors is not null)
                 {
                     Factors = null;
-                    ArrayPool<FactorEntry>.Shared.Return(factors, clearArray: false);
+                    ThreadStaticPools.FactorEntryPool.Return(factors, clearArray: false);
                 }
 
                 _next = s_poolHead;

PerfectNumbers.Core/PrimeOrderCalculator.Gpu.cs

@@ -0,0 +1,45 @@
+using PerfectNumbers.Core.Gpu;
+
+namespace PerfectNumbers.Core;
+
+internal static partial class PrimeOrderCalculator
+{
+        private static bool IsGpuPow2Allowed => s_pow2ModeInitialized && s_allowGpuPow2;
+
+        private const int GpuSmallPrimeFactorSlots = 64;
+
+        private static bool TryPopulateSmallPrimeFactorsGpu(ulong value, uint limit, Dictionary<ulong, int> counts, out ulong remaining)
+        {
+                ulong[] primeBufferArray = ThreadStaticPools.UlongPool.Rent(GpuSmallPrimeFactorSlots);
+                int[] exponentBufferArray = ThreadStaticPools.IntPool.Rent(GpuSmallPrimeFactorSlots);
+                Span<ulong> primeBuffer = primeBufferArray.AsSpan(0, GpuSmallPrimeFactorSlots);
+                Span<int> exponentBuffer = exponentBufferArray.AsSpan(0, GpuSmallPrimeFactorSlots);
+                primeBuffer.Clear();
+                exponentBuffer.Clear();
+
+                if (!PrimeOrderGpuHeuristics.TryPartialFactor(value, limit, primeBuffer, exponentBuffer, out int factorCount, out ulong gpuRemaining, out _))
+                {
+                        remaining = value;
+                        ThreadStaticPools.UlongPool.Return(primeBufferArray);
+                        ThreadStaticPools.IntPool.Return(exponentBufferArray);
+                        return false;
+                }
+
+                remaining = gpuRemaining;
+                for (int i = 0; i < factorCount; i++)
+                {
+                        ulong primeValue = primeBuffer[i];
+                        int exponent = exponentBuffer[i];
+                        if (primeValue == 0UL || exponent == 0)
+                        {
+                                continue;
+                        }
+
+                        counts[primeValue] = exponent;
+                }
+
+                ThreadStaticPools.UlongPool.Return(primeBufferArray);
+                ThreadStaticPools.IntPool.Return(exponentBufferArray);
+                return true;
+        }
+}

PerfectNumbers.Core/PrimeOrderCalculator.Shared.cs

@@ -1,55 +1,88 @@
 using System.Buffers;
-using System.Collections.Generic;
 using System.Diagnostics;
 using System.Numerics;
-using System.Threading;
 using PerfectNumbers.Core.Gpu;
 
 namespace PerfectNumbers.Core;
 
 internal static partial class PrimeOrderCalculator
 {
-    public static UInt128 Calculate(
-        UInt128 prime,
-        UInt128? previousOrder,
-        PrimeOrderSearchConfig config,
-        PrimeOrderHeuristicDevice device)
-    {
-        var scope = UsePow2Mode(device);
-        MontgomeryDivisorData divisorData;
-        UInt128 result;
-        if (prime <= ulong.MaxValue)
-        {
-            ulong? previous = null;
-            if (previousOrder.HasValue)
-            {
-                UInt128 previousValue = previousOrder.Value;
-                if (previousValue <= ulong.MaxValue)
-                {
-                    previous = (ulong)previousValue;
-                }
-                else
-                {
-                    previous = ulong.MaxValue;
-                }
-            }
+        [ThreadStatic]
+        private static bool s_pow2ModeInitialized;
 
-            ulong prime64 = (ulong)prime;
-            divisorData = MontgomeryDivisorData.FromModulus(prime64);
-            ulong order64 = Calculate(prime64, previous, divisorData, config, device);
-            result = order64 == 0UL ? UInt128.Zero : (UInt128)order64;
-        }
-        else
+        [ThreadStatic]
+        private static bool s_allowGpuPow2;
+
+        [ThreadStatic]
+        private static PrimeOrderHeuristicDevice s_deviceMode;
+
+        [ThreadStatic]
+        private static bool s_debugLoggingEnabled;
+
+        private static bool IsGpuHeuristicDevice => s_pow2ModeInitialized && s_deviceMode == PrimeOrderHeuristicDevice.Gpu;
+
+        private readonly struct Pow2ModeScope
         {
-            divisorData = default;
-            result = CalculateWideInternal(prime, previousOrder, divisorData, config);
+                private readonly bool _previousInitialized;
+                private readonly bool _previousAllow;
+                private readonly PrimeOrderHeuristicDevice _previousDevice;
+
+                public Pow2ModeScope(PrimeOrderHeuristicDevice device)
+                {
+                        _previousInitialized = s_pow2ModeInitialized;
+                        _previousAllow = s_allowGpuPow2;
+                        _previousDevice = s_deviceMode;
+                        s_pow2ModeInitialized = true;
+                        s_allowGpuPow2 = device == PrimeOrderHeuristicDevice.Gpu;
+                        s_deviceMode = device;
+                }
+
+                public void Dispose()
+                {
+                        s_allowGpuPow2 = _previousAllow;
+                        s_pow2ModeInitialized = _previousInitialized;
+                        s_deviceMode = _previousDevice;
+                }
         }
 
-        scope.Dispose();
-        return result;
-    }
+        private readonly struct DebugLoggingScope
+        {
+                private readonly bool _previous;
 
-    private static UInt128 CalculateWideInternal(UInt128 prime, UInt128? previousOrder, in MontgomeryDivisorData divisorData, PrimeOrderSearchConfig config)
+                public DebugLoggingScope(bool enabled)
+                {
+                        _previous = s_debugLoggingEnabled;
+                        s_debugLoggingEnabled = enabled;
+                }
+
+                public void Dispose()
+                {
+                        s_debugLoggingEnabled = _previous;
+                }
+        }
+
+        private static Pow2ModeScope UsePow2Mode(PrimeOrderHeuristicDevice device) => new(device);
+
+        private static DebugLoggingScope UseDebugLogging(bool enabled) => new(enabled);
+
+        [Conditional("DEBUG")]
+        private static void DebugLog(string message)
+        {
+                if (s_debugLoggingEnabled)
+                {
+                        Console.WriteLine(message);
+                }
+        }
+
+        [Conditional("DEBUG")]
+        private static void DebugLog(Func<string> messageFactory)
+        {
+                if (s_debugLoggingEnabled)
+                {
+                        Console.WriteLine(messageFactory());
+                }
+        }
+    private static UInt128 CalculateWideInternal(in UInt128 prime, in UInt128? previousOrder, in MontgomeryDivisorData divisorData, in PrimeOrderSearchConfig config)
     {
         if (prime <= UInt128.One)
         {
@@ -79,12 +112,12 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static UInt128 RunHeuristicPipelineWide(
-        UInt128 prime,
-        UInt128? previousOrder,
+        in UInt128 prime,
+        in UInt128? previousOrder,
         in MontgomeryDivisorData divisorData,
-        PrimeOrderSearchConfig config,
-        UInt128 phi,
-        PartialFactorResult128 phiFactors)
+        in PrimeOrderSearchConfig config,
+        in UInt128 phi,
+        in PartialFactorResult128 phiFactors)
     {
         if (phiFactors.FullyFactored && TrySpecialMaxWide(phi, prime, divisorData, phiFactors))
         {
@@ -112,12 +145,12 @@ internal static partial class PrimeOrderCalculator
         return candidateOrder;
     }
 
-    private static UInt128 FinishStrictlyWide(UInt128 prime, in MontgomeryDivisorData divisorData)
+    private static UInt128 FinishStrictlyWide(in UInt128 prime, in MontgomeryDivisorData divisorData)
     {
         return CalculateByFactorizationWide(prime, divisorData);
     }
 
-    private static bool TrySpecialMaxWide(UInt128 phi, UInt128 prime, in MontgomeryDivisorData divisorData, PartialFactorResult128 factors)
+    private static bool TrySpecialMaxWide(in UInt128 phi, in UInt128 prime, in MontgomeryDivisorData divisorData, in PartialFactorResult128 factors)
     {
         ReadOnlySpan<FactorEntry128> factorSpan = factors.Factors;
         int length = factors.Count;
@@ -134,7 +167,7 @@ internal static partial class PrimeOrderCalculator
         return true;
     }
 
-    private static UInt128 InitializeStartingOrderWide(UInt128 prime, UInt128 phi, in MontgomeryDivisorData divisorData)
+    private static UInt128 InitializeStartingOrderWide(in UInt128 prime, in UInt128 phi, in MontgomeryDivisorData divisorData)
     {
         UInt128 order = phi;
         UInt128 mod8 = prime & (UInt128)7UL;
@@ -150,19 +183,20 @@ internal static partial class PrimeOrderCalculator
         return order;
     }
 
-    private static UInt128 ExponentLoweringWide(UInt128 order, UInt128 prime, in MontgomeryDivisorData divisorData, PartialFactorResult128 factors)
+    private static UInt128 ExponentLoweringWide(UInt128 order, in UInt128 prime, in MontgomeryDivisorData divisorData, in PartialFactorResult128 factors)
     {
-        FactorEntry128[]? tempArray = null;
+		ArrayPool<FactorEntry128> pool = ThreadStaticPools.FactorEntry128Pool;
+		ReadOnlySpan<FactorEntry128> factorSpan = factors.Factors;
+		int length = factors.Count;
+		// TODO: This should never trigger from production code - check
+		// if (length == 0)
+		// {
+		//     return order;
+		// }
+		FactorEntry128[]? tempArray = pool.Rent(length + 1);
         try
         {
-            ReadOnlySpan<FactorEntry128> factorSpan = factors.Factors;
-            int length = factors.Count;
-            if (length == 0)
-            {
-                return order;
-            }
 
-            tempArray = ArrayPool<FactorEntry128>.Shared.Rent(length + 1);
             Span<FactorEntry128> buffer = tempArray.AsSpan(0, length);
             factorSpan.CopyTo(buffer);
 
@@ -198,14 +232,11 @@ internal static partial class PrimeOrderCalculator
         }
         finally
         {
-            if (tempArray is not null)
-            {
-                ArrayPool<FactorEntry128>.Shared.Return(tempArray, clearArray: false);
-            }
+			pool.Return(tempArray, clearArray: false);
         }
     }
 
-    private static bool TryConfirmOrderWide(UInt128 prime, UInt128 order, in MontgomeryDivisorData divisorData, PrimeOrderSearchConfig config)
+    private static bool TryConfirmOrderWide(in UInt128 prime, in UInt128 order, in MontgomeryDivisorData divisorData, in PrimeOrderSearchConfig config)
     {
         if (order == UInt128.Zero)
         {
@@ -263,11 +294,11 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static bool TryHeuristicFinishWide(
-        UInt128 prime,
-        UInt128 order,
-        UInt128? previousOrder,
+        in UInt128 prime,
+        in UInt128 order,
+        in UInt128? previousOrder,
         in MontgomeryDivisorData divisorData,
-        PrimeOrderSearchConfig config,
+        in PrimeOrderSearchConfig config,
         out UInt128 result)
     {
         result = UInt128.Zero;
@@ -339,7 +370,7 @@ internal static partial class PrimeOrderCalculator
         return false;
     }
 
-    private static void SortCandidatesWide(UInt128 prime, UInt128? previousOrder, List<UInt128> candidates)
+    private static void SortCandidatesWide(UInt128 prime, in UInt128? previousOrder, List<UInt128> candidates)
     {
         UInt128 previous = previousOrder ?? UInt128.Zero;
         int previousGroup = previousOrder.HasValue ? GetGroupWide(previousOrder.Value, prime) : 1;
@@ -367,9 +398,9 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static CandidateKey128 BuildKeyWide(
-        UInt128 value,
-        UInt128 prime,
-        UInt128 previous,
+        in UInt128 value,
+        in UInt128 prime,
+        in UInt128 previous,
         int previousGroup,
         bool hasPrevious)
     {
@@ -391,7 +422,7 @@ internal static partial class PrimeOrderCalculator
         return new CandidateKey128(primary, false, distance, false, value);
     }
 
-    private static int CompareComponents(bool descendingX, UInt128 valueX, bool descendingY, UInt128 valueY)
+    private static int CompareComponents(bool descendingX, in UInt128 valueX, bool descendingY, in UInt128 valueY)
     {
         if (descendingX == descendingY)
         {
@@ -416,7 +447,7 @@ internal static partial class PrimeOrderCalculator
         return valueX > valueY ? 1 : -1;
     }
 
-    private static int GetGroupWide(UInt128 value, UInt128 prime)
+    private static int GetGroupWide(in UInt128 value, in UInt128 prime)
     {
         UInt128 threshold1 = prime >> 3;
         if (value <= threshold1)
@@ -439,7 +470,7 @@ internal static partial class PrimeOrderCalculator
         return 0;
     }
 
-    private static void BuildCandidatesWide(UInt128 order, FactorEntry128[] factors, int count, List<UInt128> candidates, int limit)
+    private static void BuildCandidatesWide(in UInt128 order, FactorEntry128[] factors, int count, List<UInt128> candidates, int limit)
     {
         if (count == 0)
         {
@@ -452,10 +483,10 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static void BuildCandidatesRecursiveWide(
-        UInt128 order,
-        ReadOnlySpan<FactorEntry128> factors,
+        in UInt128 order,
+        in ReadOnlySpan<FactorEntry128> factors,
         int index,
-        UInt128 divisorProduct,
+        in UInt128 divisorProduct,
         List<UInt128> candidates,
         int limit)
     {
@@ -511,7 +542,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static bool TryConfirmCandidateWide(UInt128 prime, UInt128 candidate, PrimeOrderSearchConfig config, ref int powUsed, int powBudget, in MontgomeryDivisorData divisorData)
+    private static bool TryConfirmCandidateWide(in UInt128 prime, in UInt128 candidate, in PrimeOrderSearchConfig config, ref int powUsed, int powBudget, in MontgomeryDivisorData divisorData)
     {
         PartialFactorResult128 factorization = PartialFactorWide(candidate, config);
         if (factorization.Factors is null)
@@ -564,7 +595,7 @@ internal static partial class PrimeOrderCalculator
         return true;
     }
 
-    private static PartialFactorResult128 PartialFactorWide(UInt128 value, PrimeOrderSearchConfig config)
+    private static PartialFactorResult128 PartialFactorWide(in UInt128 value, in PrimeOrderSearchConfig config)
     {
         if (value <= UInt128.One)
         {
@@ -605,12 +636,12 @@ internal static partial class PrimeOrderCalculator
 
         if (config.PollardRhoMilliseconds > 0 && pending.Count > 0)
         {
-            Stopwatch stopwatch = Stopwatch.StartNew();
-            long budgetTicks = TimeSpan.FromMilliseconds(config.PollardRhoMilliseconds).Ticks;
+            long deadlineTimestamp = CreateDeadlineTimestamp(config.PollardRhoMilliseconds);
             Stack<UInt128> stack = new();
             stack.Push(remaining);
             pending.Clear();
 
+            long timestamp = 0L; // reused for deadline checks.
             while (stack.Count > 0)
             {
                 UInt128 composite = stack.Pop();
@@ -625,13 +656,14 @@ internal static partial class PrimeOrderCalculator
                     continue;
                 }
 
-                if (stopwatch.ElapsedTicks > budgetTicks)
+                timestamp = Stopwatch.GetTimestamp();
+                if (timestamp > deadlineTimestamp)
                 {
                     pending.Add(composite);
                     continue;
                 }
 
-                if (!TryPollardRhoWide(composite, stopwatch, budgetTicks, out UInt128 factor))
+                if (!TryPollardRhoWide(composite, deadlineTimestamp, out UInt128 factor))
                 {
                     pending.Add(composite);
                     continue;
@@ -664,7 +696,8 @@ internal static partial class PrimeOrderCalculator
             return new PartialFactorResult128(null, value, false, 0);
         }
 
-        FactorEntry128[]? rented = counts.Count > 0 ? ArrayPool<FactorEntry128>.Shared.Rent(counts.Count) : null;
+		ArrayPool<FactorEntry128>? pool = null;
+		FactorEntry128[]? rented = counts.Count > 0 ?  (pool = ThreadStaticPools.FactorEntry128Pool).Rent(counts.Count) : null;
         int index = 0;
         if (rented is not null)
         {
@@ -676,20 +709,20 @@ internal static partial class PrimeOrderCalculator
         }
 
         FactorEntry128[]? resultArray = null;
-        if (rented is not null)
+        if (pool is not null)
         {
             Span<FactorEntry128> span = rented.AsSpan(0, index);
             span.Sort(static (a, b) => a.Value.CompareTo(b.Value));
             resultArray = new FactorEntry128[index];
             span.CopyTo(resultArray);
-            ArrayPool<FactorEntry128>.Shared.Return(rented, clearArray: false);
+            pool.Return(rented!, clearArray: false);
         }
 
         bool fullyFactored = cofactor == UInt128.One;
         return new PartialFactorResult128(resultArray, cofactor, fullyFactored, index);
     }
 
-    private static UInt128 PopulateSmallPrimeFactorsCpuWide(UInt128 value, uint limit, Dictionary<UInt128, int> counts)
+    private static UInt128 PopulateSmallPrimeFactorsCpuWide(in UInt128 value, uint limit, Dictionary<UInt128, int> counts)
     {
         UInt128 remaining = value;
         uint[] primes = PrimesGenerator.SmallPrimes;
@@ -729,7 +762,7 @@ internal static partial class PrimeOrderCalculator
 
         return remaining;
     }
-    private static bool TryPollardRhoWide(UInt128 n, Stopwatch stopwatch, long budgetTicks, out UInt128 factor)
+    private static bool TryPollardRhoWide(in UInt128 n, long deadlineTimestamp, out UInt128 factor)
     {
         factor = UInt128.Zero;
         if ((n & UInt128.One) == UInt128.Zero)
@@ -741,10 +774,12 @@ internal static partial class PrimeOrderCalculator
         UInt128 c = UInt128.One;
         UInt128 x = (UInt128)2UL;
         UInt128 y = x;
+        long timestamp = 0L; // reused for deadline checks.
 
         while (true)
         {
-            if (stopwatch.ElapsedTicks > budgetTicks)
+            timestamp = Stopwatch.GetTimestamp();
+            if (timestamp > deadlineTimestamp)
             {
                 return false;
             }
@@ -771,7 +806,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static UInt128 AdvancePolynomialWide(UInt128 x, UInt128 c, UInt128 modulus)
+    private static UInt128 AdvancePolynomialWide(in UInt128 x, in UInt128 c, in UInt128 modulus)
     {
         BigInteger value = (BigInteger)x;
         value = (value * value + (BigInteger)c) % (BigInteger)modulus;
@@ -809,7 +844,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static int TrailingZeroCountWide(UInt128 value)
+    private static int TrailingZeroCountWide(in UInt128 value)
     {
         if (value == UInt128.Zero)
         {
@@ -865,7 +900,7 @@ internal static partial class PrimeOrderCalculator
         return order;
     }
 
-    private static void FactorCompletelyWide(UInt128 value, Dictionary<UInt128, int> counts)
+    private static void FactorCompletelyWide(in UInt128 value, Dictionary<UInt128, int> counts)
     {
         if (value <= UInt128.One)
         {
@@ -883,7 +918,7 @@ internal static partial class PrimeOrderCalculator
         FactorCompletelyWide(value / factor, counts);
     }
 
-    private static UInt128 PollardRhoWide(UInt128 n)
+    private static UInt128 PollardRhoWide(in UInt128 n)
     {
         if ((n & UInt128.One) == UInt128.Zero)
         {
@@ -916,7 +951,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static bool IsPrimeWide(UInt128 value)
+    private static bool IsPrimeWide(in UInt128 value)
     {
         if (value <= ulong.MaxValue)
         {
@@ -996,7 +1031,7 @@ internal static partial class PrimeOrderCalculator
         return true;
     }
 
-    private static UInt128 Pow2ModWide(UInt128 exponent, in UInt128 modulus, in MontgomeryDivisorData divisorData)
+    private static UInt128 Pow2ModWide(in UInt128 exponent, in UInt128 modulus, in MontgomeryDivisorData divisorData)
     {
         if (modulus == UInt128.One)
         {
@@ -1026,7 +1061,7 @@ internal static partial class PrimeOrderCalculator
         return exponent.Pow2MontgomeryModWindowed(modulus);
     }
 
-    private static void AddFactor(Dictionary<UInt128, int> counts, UInt128 prime, int exponent)
+    private static void AddFactor(Dictionary<UInt128, int> counts, in UInt128 prime, int exponent)
     {
         if (counts.TryGetValue(prime, out int existing))
         {
@@ -1038,60 +1073,30 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private readonly struct CandidateKey128
-    {
-        public CandidateKey128(int primary, bool secondaryDescending, UInt128 secondary, bool tertiaryDescending, UInt128 tertiary)
-        {
-            Primary = primary;
-            SecondaryDescending = secondaryDescending;
-            Secondary = secondary;
-            TertiaryDescending = tertiaryDescending;
-            Tertiary = tertiary;
-        }
+    private readonly struct CandidateKey128(int primary, bool secondaryDescending, in UInt128 secondary, bool tertiaryDescending, in UInt128 tertiary)
+	{
+		public int Primary { get; } = primary;
 
-        public int Primary { get; }
+		public bool SecondaryDescending { get; } = secondaryDescending;
 
-        public bool SecondaryDescending { get; }
+		public UInt128 Secondary { get; } = secondary;
 
-        public UInt128 Secondary { get; }
+		public bool TertiaryDescending { get; } = tertiaryDescending;
 
-        public bool TertiaryDescending { get; }
+		public UInt128 Tertiary { get; } = tertiary;
+	}
 
-        public UInt128 Tertiary { get; }
-    }
+    private readonly struct PartialFactorResult128(FactorEntry128[]? factors, UInt128 cofactor, bool fullyFactored, int count)
+	{
+		public FactorEntry128[]? Factors { get; } = factors;
 
-    private readonly struct FactorEntry128
-    {
-        public FactorEntry128(UInt128 value, int exponent)
-        {
-            Value = value;
-            Exponent = exponent;
-        }
+		public UInt128 Cofactor { get; } = cofactor;
 
-        public UInt128 Value { get; }
+		public bool FullyFactored { get; } = fullyFactored;
 
-        public int Exponent { get; }
-    }
+		public int Count { get; } = count;
 
-    private readonly struct PartialFactorResult128
-    {
-        public PartialFactorResult128(FactorEntry128[]? factors, UInt128 cofactor, bool fullyFactored, int count)
-        {
-            Factors = factors;
-            Cofactor = cofactor;
-            FullyFactored = fullyFactored;
-            Count = count;
-        }
-
-        public FactorEntry128[]? Factors { get; }
-
-        public UInt128 Cofactor { get; }
-
-        public bool FullyFactored { get; }
-
-        public int Count { get; }
-
-        public static PartialFactorResult128 Empty => new(null, UInt128.One, true, 0);
+		public static PartialFactorResult128 Empty => new(null, UInt128.One, true, 0);
 
         public PartialFactorResult128 WithAdditionalPrime(UInt128 prime)
         {

PerfectNumbers.Core/ThreadStaticPools.cs

@@ -0,0 +1,320 @@
+using System.Buffers;
+using System.Runtime.CompilerServices;
+using PerfectNumbers.Core.Cpu;
+
+namespace PerfectNumbers.Core
+{
+    public readonly struct ThreadStaticPools
+    {
+        [ThreadStatic]
+        private static ArrayPool<FactorEntry>? _factorEntryPool;
+
+        public static ArrayPool<FactorEntry> FactorEntryPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _factorEntryPool ??= ArrayPool<FactorEntry>.Create();
+            }
+        }
+
+        [ThreadStatic]
+        private static ArrayPool<FactorEntry128>? _factorEntry128Pool;
+
+        public static ArrayPool<FactorEntry128> FactorEntry128Pool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _factorEntry128Pool ??= ArrayPool<FactorEntry128>.Create();
+            }
+        }
+
+
+        [ThreadStatic]
+        private static ArrayPool<KeyValuePair<ulong, int>>? _factorKeyValuePairPool;
+
+        public static ArrayPool<KeyValuePair<ulong, int>> FactorKeyValuePairPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _factorKeyValuePairPool ??= ArrayPool<KeyValuePair<ulong, int>>.Create();
+            }
+        }
+        [ThreadStatic]
+        private static MersenneCpuDivisorScanSession? _mersenneCpuDivisorSession;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal static MersenneCpuDivisorScanSession? RentMersenneCpuDivisorSession()
+        {
+            MersenneCpuDivisorScanSession? session = _mersenneCpuDivisorSession;
+            if (session is null)
+            {
+                return null;
+            }
+
+            _mersenneCpuDivisorSession = null;
+            session.Reset();
+            return session;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal static void ReturnMersenneCpuDivisorSession(MersenneCpuDivisorScanSession session)
+        {
+            _mersenneCpuDivisorSession = session;
+        }
+
+        [ThreadStatic]
+        private static ArrayPool<ulong>? _ulongPool;
+
+        public static ArrayPool<ulong> UlongPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _ulongPool ??= ArrayPool<ulong>.Create();
+            }
+        }
+
+        [ThreadStatic]
+        private static ArrayPool<int>? _intPool;
+
+        public static ArrayPool<int> IntPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _intPool ??= ArrayPool<int>.Create();
+            }
+        }
+
+
+        [ThreadStatic]
+        private static List<List<ulong>>? _ulongListPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static List<ulong> RentUlongList(int capacityHint)
+        {
+            List<List<ulong>>? pool = _ulongListPool;
+            if (pool is not null && pool.Count > 0)
+            {
+                int lastIndex = pool.Count - 1;
+                List<ulong> list = pool[lastIndex];
+                pool.RemoveAt(lastIndex);
+                if (list.Count > 0)
+                {
+                    list.Clear();
+                }
+
+                if (list.Capacity < capacityHint)
+                {
+                    list.Capacity = capacityHint;
+                }
+
+                return list;
+            }
+
+            return new List<ulong>(capacityHint);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnUlongList(List<ulong> list)
+        {
+            List<List<ulong>>? pool = _ulongListPool;
+            if (pool is null)
+            {
+                pool = new List<List<ulong>>(4);
+                _ulongListPool = pool;
+            }
+
+            pool.Add(list);
+        }
+
+        [ThreadStatic]
+        private static List<Stack<ulong>>? _ulongStackPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Stack<ulong> RentUlongStack(int capacityHint)
+        {
+            List<Stack<ulong>>? pool = _ulongStackPool;
+            if (pool is not null && pool.Count > 0)
+            {
+                int lastIndex = pool.Count - 1;
+                Stack<ulong> stack = pool[lastIndex];
+                pool.RemoveAt(lastIndex);
+                if (stack.Count > 0)
+                {
+                    stack.Clear();
+                }
+
+                if (stack.Count < capacityHint)
+                {
+                    stack.EnsureCapacity(capacityHint);
+                }
+
+                return stack;
+            }
+
+            return new Stack<ulong>(capacityHint);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnUlongStack(Stack<ulong> stack)
+        {
+            List<Stack<ulong>>? pool = _ulongStackPool;
+            if (pool is null)
+            {
+                pool = new List<Stack<ulong>>(4);
+                _ulongStackPool = pool;
+            }
+
+            pool.Add(stack);
+        }
+
+        [ThreadStatic]
+        private static List<Dictionary<ulong, int>>? _ulongIntDictionaryPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, int> RentUlongIntDictionary(int capacityHint)
+        {
+            List<Dictionary<ulong, int>>? pool = _ulongIntDictionaryPool;
+            if (pool is not null && pool.Count > 0)
+            {
+                int lastIndex = pool.Count - 1;
+                Dictionary<ulong, int> dictionary = pool[lastIndex];
+                pool.RemoveAt(lastIndex);
+                if (dictionary.Count > 0)
+                {
+                    dictionary.Clear();
+                }
+
+                if (dictionary.Count < capacityHint)
+                {
+                    dictionary.EnsureCapacity(capacityHint);
+                }
+
+                return dictionary;
+            }
+
+            return new Dictionary<ulong, int>(capacityHint);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnUlongIntDictionary(Dictionary<ulong, int> dictionary)
+        {
+            List<Dictionary<ulong, int>>? pool = _ulongIntDictionaryPool;
+            if (pool is null)
+            {
+                pool = new List<Dictionary<ulong, int>>(4);
+                _ulongIntDictionaryPool = pool;
+            }
+
+            pool.Add(dictionary);
+        }
+
+        [ThreadStatic]
+        private static Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? _mersenneFactorCacheDictionary;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry> RentMersenneFactorCacheDictionary()
+        {
+            Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache = _mersenneFactorCacheDictionary;
+            if (cache is null)
+            {
+                return new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
+            }
+
+            _mersenneFactorCacheDictionary = null;
+            cache.Clear();
+            return cache;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnMersenneFactorCacheDictionary(Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry> cache)
+        {
+            for (Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>.Enumerator enumerator = cache.GetEnumerator(); enumerator.MoveNext();)
+            {
+                enumerator.Current.Value.ReturnToPool();
+            }
+
+            cache.Clear();
+            _mersenneFactorCacheDictionary = cache;
+        }
+
+        [ThreadStatic]
+        private static MersenneDivisorCycles.FactorCacheEntry? _factorCacheEntryPoolHead;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static MersenneDivisorCycles.FactorCacheEntry RentFactorCacheEntry()
+        {
+            MersenneDivisorCycles.FactorCacheEntry? entry = _factorCacheEntryPoolHead;
+            if (entry is null)
+            {
+                entry = new MersenneDivisorCycles.FactorCacheEntry();
+            }
+            else
+            {
+                _factorCacheEntryPoolHead = entry.Next;
+            }
+
+            entry.Reset();
+            return entry;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnFactorCacheEntry(MersenneDivisorCycles.FactorCacheEntry entry)
+        {
+            entry.Next = _factorCacheEntryPoolHead;
+            _factorCacheEntryPoolHead = entry;
+        }
+
+        [ThreadStatic]
+        private static Dictionary<ulong, int>? _factorCountDictionary;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, int> RentFactorCountDictionary()
+        {
+            Dictionary<ulong, int>? dictionary = _factorCountDictionary;
+            if (dictionary is null)
+            {
+                return new Dictionary<ulong, int>(8);
+            }
+
+            _factorCountDictionary = null;
+            dictionary.Clear();
+            return dictionary;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnFactorCountDictionary(Dictionary<ulong, int> dictionary)
+        {
+            dictionary.Clear();
+            _factorCountDictionary = dictionary;
+        }
+
+        [ThreadStatic]
+        private static Dictionary<ulong, int>? _factorScratchDictionary;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, int> RentFactorScratchDictionary()
+        {
+            Dictionary<ulong, int>? dictionary = _factorScratchDictionary;
+            if (dictionary is null)
+            {
+                return new Dictionary<ulong, int>(8);
+            }
+
+            _factorScratchDictionary = null;
+            dictionary.Clear();
+            return dictionary;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnFactorScratchDictionary(Dictionary<ulong, int> dictionary)
+        {
+            dictionary.Clear();
+            _factorScratchDictionary = dictionary;
+        }
+    }
+}

PerfectNumbers.Core/UInt128Extensions.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using PerfectNumbers.Core.Gpu;