Merge pull request #128 from mlemanczyk/codex/modify-evenperfectbitscanner-execution-path

Remove CPU fallbacks when GPU pow2 fails

EvenPerfectBitScanner/Program.cs

@@ -515,7 +515,9 @@ internal static class Program
         {
             _byDivisorTester = mersenneOnGpu
                     ? new MersenneNumberDivisorByDivisorGpuTester()
-                    : new MersenneNumberDivisorByDivisorCpuTester();
+                    : new MersenneNumberDivisorByDivisorCpuTester(
+                        useGpuPow2Mod: !GpuContextPool.ForceCpu,
+                        useGpuCycleComputation: orderOnGpu);
             _byDivisorTester.BatchSize = scanBatchSize;
         }
 

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -3,6 +3,7 @@ using System.Collections.Concurrent;
 using System.Collections.Generic;
 using System.Numerics;
 using PerfectNumbers.Core;
+using PerfectNumbers.Core.Gpu;
 
 namespace PerfectNumbers.Core.Cpu;
 
@@ -10,13 +11,18 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 {
     private readonly object _sync = new();
     private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
+    private readonly bool _useGpuPow2Mod;
+    private readonly bool _useGpuCycleComputation;
     private ulong _divisorLimit;
     private ulong _lastStatusDivisor;
     private bool _isConfigured;
     private int _batchSize = 1_024;
-    private const int PollardBrentMaxRestarts = 4;
-    private const int PollardBrentIterationBudget = 262_144;
 
+    public MersenneNumberDivisorByDivisorCpuTester(bool useGpuPow2Mod = false, bool useGpuCycleComputation = false)
+    {
+        _useGpuPow2Mod = useGpuPow2Mod;
+        _useGpuCycleComputation = useGpuCycleComputation;
+    }
 
     public int BatchSize
     {
@@ -176,31 +182,6 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             return false;
         }
 
-        ulong pollardIterationCount = 0UL;
-        if (prime > 3UL)
-        {
-            var pollardBrent = new MersennePollardBrent(prime, _batchSize);
-            if (pollardBrent.IsSupported)
-            {
-                bool pollardFound = pollardBrent.TryFindFactor(
-                    allowedMax,
-                    PollardBrentMaxRestarts,
-                    PollardBrentIterationBudget,
-                    out ulong pollardFactor,
-                    out pollardIterationCount);
-
-                if (pollardFound)
-                {
-                    processedCount = pollardIterationCount;
-                    lastProcessed = pollardFactor;
-                    processedAll = true;
-                    return true;
-                }
-            }
-        }
-
-        processedCount = pollardIterationCount;
-
         UInt128 step = (UInt128)prime << 1;
         if (step == UInt128.Zero)
         {
@@ -217,6 +198,8 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         }
 
         Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
+        Dictionary<ulong, ulong>? cycleRemainderCache = null;
+        CycleHint cycleHint = default;
         DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
 
         byte step10 = (byte)(step % 10UL);
@@ -250,35 +233,14 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             if (admissible && (remainder8 == 1 || remainder8 == 7) && remainder3 != 0 && remainder5 != 0 && remainder7 != 0 && remainder11 != 0)
             {
                 MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(candidate);
-                ulong divisorCycle;
+                if (TryResolveDivisorCycle(candidate, prime, divisorData, cycleCache, ref factorCache, ref cycleHint, out ulong divisorCycle) && divisorCycle != 0UL)
-
-                if (candidate <= PerfectNumberConstants.MaxQForDivisorCycles)
                 {
-                    divisorCycle = cycleCache.GetCycleLength(candidate);
+                    if (CheckDivisor(prime, candidate, divisorCycle, divisorData, ref cycleRemainderCache, ref cycleHint) != 0)
-                }
-                else
-                {
-                    factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
-                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, factorCache, out divisorCycle) || divisorCycle == 0UL)
                     {
-                        divisorCycle = cycleCache.GetCycleLength(candidate);
+                        processedAll = true;
+                        return true;
                     }
                 }
-
-				if (divisorCycle != 0 && divisorCycle == prime)
-				{
-					processedAll = true;
-					return true;
-				}
-				else if (divisorCycle == 0)
-				{
-					Console.WriteLine($"Divisor cycle wasn't calculated for ${prime}");
-				}				
-				// if (divisorCycle != 0UL && CheckDivisor(prime, divisorCycle, divisorData) != 0)
-				// {
-				// 	processedAll = true;
-				// 	return true;
-				// }
             }
 
             divisor += step;
@@ -294,12 +256,152 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return false;
     }
 
-    private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
+    private byte CheckDivisor(
+        ulong prime,
+        ulong divisor,
+        ulong divisorCycle,
+        in MontgomeryDivisorData divisorData,
+        ref Dictionary<ulong, ulong>? cycleRemainders,
+        ref CycleHint cycleHint)
     {
-        ulong residue = prime.Pow2MontgomeryModWithCycle(divisorCycle, divisorData);
+        if (divisorCycle == 0UL)
+        {
+            throw new InvalidOperationException($"Cycle length resolution returned zero for divisor {divisor}.");
+        }
+
+        Dictionary<ulong, ulong>? remainderCache = cycleRemainders;
+        if (_useGpuPow2Mod && remainderCache is null)
+        {
+            remainderCache = new Dictionary<ulong, ulong>(8);
+            cycleRemainders = remainderCache;
+        }
+
+        ulong reducedExponent;
+        if (remainderCache is not null && remainderCache.TryGetValue(divisorCycle, out ulong cachedRemainder))
+        {
+            reducedExponent = cachedRemainder;
+        }
+        else if (cycleHint.HasCycle && cycleHint.LastCycleLength == divisorCycle)
+        {
+            reducedExponent = cycleHint.LastReducedExponent;
+        }
+        else
+        {
+            reducedExponent = prime % divisorCycle;
+            if (remainderCache is not null)
+            {
+                remainderCache[divisorCycle] = reducedExponent;
+            }
+        }
+
+        cycleHint.LastCycleLength = divisorCycle;
+        cycleHint.LastReducedExponent = reducedExponent;
+        cycleHint.HasCycle = true;
+
+        if (_useGpuPow2Mod && remainderCache is not null)
+        {
+            GpuPow2ModStatus status = PrimeOrderGpuHeuristics.TryPow2Mod(reducedExponent, divisor, out ulong remainder, divisorData);
+            if (status == GpuPow2ModStatus.Success)
+            {
+                return remainder == 1UL ? (byte)1 : (byte)0;
+            }
+
+            PrimeOrderGpuHeuristics.ReportPow2Failure(
+                "by-divisor residue scan",
+                divisor,
+                status);
+        }
+
+        ulong residue = reducedExponent.Pow2MontgomeryModFromCycleRemainder(divisorData);
         return residue == 1UL ? (byte)1 : (byte)0;
     }
 
+    private bool TryResolveDivisorCycle(
+        ulong divisor,
+        ulong prime,
+        in MontgomeryDivisorData divisorData,
+        DivisorCycleCache cycleCache,
+        ref Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache,
+        ref CycleHint cycleHint,
+        out ulong cycleLength)
+    {
+        if (divisor <= PerfectNumberConstants.MaxQForDivisorCycles)
+        {
+            cycleLength = cycleCache.GetCycleLength(divisor);
+            if (cycleLength == 0UL)
+            {
+                throw new InvalidOperationException($"Missing cached cycle length for divisor {divisor}.");
+            }
+
+            cycleHint.LastCycleLength = cycleLength;
+            cycleHint.HasCycle = true;
+            return true;
+        }
+
+        if (_useGpuCycleComputation && TryCalculateCycleLengthGpu(divisor, prime, divisorData, ref cycleHint, out cycleLength))
+        {
+            return cycleLength != 0UL;
+        }
+
+        factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
+        if (MersenneDivisorCycles.TryCalculateCycleLengthForExponent(
+                divisor,
+                prime,
+                divisorData,
+                factorCache,
+                out cycleLength,
+                allowGpuPow2: _useGpuPow2Mod) && cycleLength != 0UL)
+        {
+            cycleHint.LastCycleLength = cycleLength;
+            cycleHint.HasCycle = true;
+            return true;
+        }
+
+        cycleLength = cycleCache.GetCycleLength(divisor);
+        if (cycleLength == 0UL)
+        {
+            return false;
+        }
+
+        cycleHint.LastCycleLength = cycleLength;
+        cycleHint.HasCycle = true;
+        return true;
+    }
+
+    private bool TryCalculateCycleLengthGpu(
+        ulong divisor,
+        ulong prime,
+        in MontgomeryDivisorData divisorData,
+        ref CycleHint cycleHint,
+        out ulong cycleLength)
+    {
+        PrimeOrderCalculator.PrimeOrderSearchConfig config = PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault;
+        ulong? previousOrder = cycleHint.HasCycle ? cycleHint.LastCycleLength : null;
+
+        try
+        {
+            if (!PrimeOrderGpuHeuristics.TryCalculateOrder(divisor, previousOrder, config, divisorData, out PrimeOrderCalculator.PrimeOrderResult result))
+            {
+                throw new InvalidOperationException("GPU requested fallback.");
+            }
+
+            cycleLength = result.Order;
+            if (cycleLength == 0UL)
+            {
+                return false;
+            }
+
+            cycleHint.LastCycleLength = cycleLength;
+            cycleHint.HasCycle = true;
+            return true;
+        }
+        catch (InvalidOperationException ex)
+        {
+            Console.Error.WriteLine($"GPU cycle length computation failed for divisor {divisor}: {ex.Message}");
+            throw;
+        }
+    }
+
     private static byte AddMod(byte value, byte delta, byte modulus)
     {
         int sum = value + delta;
@@ -346,6 +448,13 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return (1UL << (int)(maxPrime - 1UL)) - 1UL;
     }
 
+    private struct CycleHint
+    {
+        public ulong LastCycleLength;
+        public ulong LastReducedExponent;
+        public bool HasCycle;
+    }
+
     private static ulong ComputeAllowedMaxDivisor(ulong prime, ulong divisorLimit)
     {
         if (prime <= 1UL)

PerfectNumbers.Core/Cpu/MersennePollardBrent.cs

@@ -1,926 +0,0 @@
-using System;
-using System.Buffers;
-using System.Numerics;
-using System.Security.Cryptography;
-using PerfectNumbers.Core;
-using UInt128 = System.UInt128;
-
-namespace PerfectNumbers.Core.Cpu;
-
-internal sealed class MersennePollardBrent
-{
-    private enum ArithmeticMode
-    {
-        Unsupported,
-        UInt64,
-        UInt128,
-        BigInteger,
-    }
-
-    private readonly ArithmeticMode _mode;
-    private readonly int _bitLength;
-    private readonly int _byteLength;
-    private readonly int _bitRemainder;
-    private readonly byte _maskByte;
-    private readonly BigInteger _modulus;
-    private readonly BigInteger _mask;
-    private readonly ulong _modulus64;
-    private readonly ulong _mask64;
-    private readonly UInt128 _modulus128;
-    private readonly UInt128 _mask128;
-    private readonly int _batchSize;
-    private readonly bool _isSupported;
-
-    public MersennePollardBrent(ulong exponent, int batchSize)
-    {
-        if (exponent < 3UL || exponent > int.MaxValue)
-        {
-            _mode = ArithmeticMode.Unsupported;
-            _isSupported = false;
-            _bitLength = 0;
-            _byteLength = 0;
-            _bitRemainder = 0;
-            _maskByte = 0;
-            _modulus = BigInteger.Zero;
-            _mask = BigInteger.Zero;
-            _modulus64 = 0UL;
-            _mask64 = 0UL;
-            _modulus128 = UInt128.Zero;
-            _mask128 = UInt128.Zero;
-            _batchSize = 0;
-            return;
-        }
-
-        _isSupported = true;
-        _bitLength = (int)exponent;
-        _byteLength = (_bitLength + 7) / 8;
-        _bitRemainder = _bitLength & 7;
-        _maskByte = _bitRemainder == 0 ? (byte)0xFF : (byte)((1 << _bitRemainder) - 1);
-        _batchSize = Math.Clamp(batchSize, 8, 1024);
-
-        if (_bitLength <= 64)
-        {
-            _mode = ArithmeticMode.UInt64;
-            if (_bitLength == 64)
-            {
-                _modulus64 = ulong.MaxValue;
-                _mask64 = ulong.MaxValue;
-            }
-            else
-            {
-                _modulus64 = (1UL << _bitLength) - 1UL;
-                _mask64 = _modulus64;
-            }
-
-            _modulus128 = UInt128.Zero;
-            _mask128 = UInt128.Zero;
-            _modulus = BigInteger.Zero;
-            _mask = BigInteger.Zero;
-            return;
-        }
-
-        if (_bitLength <= 128)
-        {
-            _mode = ArithmeticMode.UInt128;
-            if (_bitLength == 128)
-            {
-                _modulus128 = UInt128.MaxValue;
-                _mask128 = UInt128.MaxValue;
-            }
-            else
-            {
-                _modulus128 = (UInt128.One << _bitLength) - UInt128.One;
-                _mask128 = _modulus128;
-            }
-
-            _modulus64 = 0UL;
-            _mask64 = 0UL;
-            _modulus = BigInteger.Zero;
-            _mask = BigInteger.Zero;
-            return;
-        }
-
-        _mode = ArithmeticMode.BigInteger;
-        _modulus = (BigInteger.One << _bitLength) - BigInteger.One;
-        _mask = _modulus;
-        _modulus64 = 0UL;
-        _mask64 = 0UL;
-        _modulus128 = UInt128.Zero;
-        _mask128 = UInt128.Zero;
-    }
-
-    public bool IsSupported => _isSupported;
-
-    public bool TryFindFactor(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        if (!_isSupported)
-        {
-            return false;
-        }
-
-        if (allowedMax <= 1UL)
-        {
-            return false;
-        }
-
-        return _mode switch
-        {
-            ArithmeticMode.UInt64 => TryFindFactorUInt64(allowedMax, maxRestarts, maxIterationsPerRestart, out factor, out iterationCount),
-            ArithmeticMode.UInt128 => TryFindFactorUInt128(allowedMax, maxRestarts, maxIterationsPerRestart, out factor, out iterationCount),
-            ArithmeticMode.BigInteger => TryFindFactorBigInteger(allowedMax, maxRestarts, maxIterationsPerRestart, out factor, out iterationCount),
-            _ => false,
-        };
-    }
-
-    private bool TryFindFactorUInt64(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        int restarts = Math.Max(1, maxRestarts);
-        int iterationBudget = Math.Max(_batchSize, maxIterationsPerRestart);
-
-        for (int restart = 0; restart < restarts; restart++)
-        {
-            ulong x = NextRandomSeed64();
-            ulong y = x;
-            ulong c = NextRandomConstant64();
-            ulong q = 1UL;
-            ulong g = 1UL;
-            ulong ys = 0UL;
-            int r = 1;
-            ulong localIterations = 0UL;
-
-            while (g == 1UL && localIterations < (ulong)iterationBudget)
-            {
-                x = y;
-                for (int i = 0; i < r && localIterations < (ulong)iterationBudget; i++)
-                {
-                    y = Iterate64(y, c, ref localIterations);
-                }
-
-                if (localIterations >= (ulong)iterationBudget)
-                {
-                    break;
-                }
-
-                int k = 0;
-                while (k < r && g == 1UL && localIterations < (ulong)iterationBudget)
-                {
-                    ys = y;
-                    int t = Math.Min(_batchSize, r - k);
-                    for (int i = 0; i < t; i++)
-                    {
-                        y = Iterate64(y, c, ref localIterations);
-                        ulong diff = AbsSub64(y, x);
-                        if (diff == 0UL)
-                        {
-                            continue;
-                        }
-
-                        q = MulMod64(q, diff);
-                    }
-
-                    g = BinaryGcd64(q, _modulus64);
-                    k += t;
-                }
-
-                r <<= 1;
-            }
-
-            if (g == _modulus64)
-            {
-                do
-                {
-                    ys = Iterate64(ys, c, ref localIterations);
-                    ulong diff = AbsSub64(ys, x);
-                    if (diff == 0UL)
-                    {
-                        continue;
-                    }
-
-                    g = BinaryGcd64(diff, _modulus64);
-                }
-                while (g == 1UL);
-            }
-
-            iterationCount += localIterations;
-
-            if (g == 1UL || g == _modulus64)
-            {
-                continue;
-            }
-
-            if (g > 1UL && g <= allowedMax)
-            {
-                factor = g;
-                return true;
-            }
-        }
-
-        return false;
-    }
-
-    private bool TryFindFactorUInt128(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        int restarts = Math.Max(1, maxRestarts);
-        int iterationBudget = Math.Max(_batchSize, maxIterationsPerRestart);
-        UInt128 allowedMaxWide = (UInt128)allowedMax;
-
-        for (int restart = 0; restart < restarts; restart++)
-        {
-            UInt128 x = NextRandomSeed128();
-            UInt128 y = x;
-            UInt128 c = NextRandomConstant128();
-            UInt128 q = UInt128.One;
-            UInt128 g = UInt128.One;
-            UInt128 ys = UInt128.Zero;
-            int r = 1;
-            ulong localIterations = 0UL;
-
-            while (g == UInt128.One && localIterations < (ulong)iterationBudget)
-            {
-                x = y;
-                for (int i = 0; i < r && localIterations < (ulong)iterationBudget; i++)
-                {
-                    y = Iterate128(y, c, ref localIterations);
-                }
-
-                if (localIterations >= (ulong)iterationBudget)
-                {
-                    break;
-                }
-
-                int k = 0;
-                while (k < r && g == UInt128.One && localIterations < (ulong)iterationBudget)
-                {
-                    ys = y;
-                    int t = Math.Min(_batchSize, r - k);
-                    for (int i = 0; i < t; i++)
-                    {
-                        y = Iterate128(y, c, ref localIterations);
-                        UInt128 diff = AbsSub128(y, x);
-                        if (diff == UInt128.Zero)
-                        {
-                            continue;
-                        }
-
-                        q = MulMod128(q, diff);
-                    }
-
-                    g = q.BinaryGcd(_modulus128);
-                    k += t;
-                }
-
-                r <<= 1;
-            }
-
-            if (g == _modulus128)
-            {
-                do
-                {
-                    ys = Iterate128(ys, c, ref localIterations);
-                    UInt128 diff = AbsSub128(ys, x);
-                    if (diff == UInt128.Zero)
-                    {
-                        continue;
-                    }
-
-                    g = diff.BinaryGcd(_modulus128);
-                }
-                while (g == UInt128.One);
-            }
-
-            iterationCount += localIterations;
-
-            if (g == UInt128.One || g == _modulus128)
-            {
-                continue;
-            }
-
-            if (g > UInt128.One && g <= allowedMaxWide)
-            {
-                factor = (ulong)g;
-                return true;
-            }
-        }
-
-        return false;
-    }
-
-    private bool TryFindFactorBigInteger(
-        ulong allowedMax,
-        int maxRestarts,
-        int maxIterationsPerRestart,
-        out ulong factor,
-        out ulong iterationCount)
-    {
-        factor = 0UL;
-        iterationCount = 0UL;
-
-        int restarts = Math.Max(1, maxRestarts);
-        int iterationBudget = Math.Max(_batchSize, maxIterationsPerRestart);
-
-        for (int restart = 0; restart < restarts; restart++)
-        {
-            BigInteger x = NextRandomSeedBigInteger();
-            BigInteger y = x;
-            BigInteger c = NextRandomConstantBigInteger();
-            BigInteger q = BigInteger.One;
-            BigInteger g = BigInteger.One;
-            BigInteger ys = BigInteger.Zero;
-            int r = 1;
-            ulong localIterations = 0UL;
-
-            while (g.IsOne && localIterations < (ulong)iterationBudget)
-            {
-                x = y;
-                for (int i = 0; i < r && localIterations < (ulong)iterationBudget; i++)
-                {
-                    y = IterateBigInteger(y, c, ref localIterations);
-                }
-
-                if (localIterations >= (ulong)iterationBudget)
-                {
-                    break;
-                }
-
-                int k = 0;
-                while (k < r && g.IsOne && localIterations < (ulong)iterationBudget)
-                {
-                    ys = y;
-                    int t = Math.Min(_batchSize, r - k);
-                    for (int i = 0; i < t; i++)
-                    {
-                        y = IterateBigInteger(y, c, ref localIterations);
-                        BigInteger diff = AbsSubBigInteger(y, x);
-                        if (diff.IsZero)
-                        {
-                            continue;
-                        }
-
-                        q = MulModBigInteger(q, diff);
-                    }
-
-                    g = BigInteger.GreatestCommonDivisor(q, _modulus);
-                    k += t;
-                }
-
-                r <<= 1;
-            }
-
-            if (g == _modulus)
-            {
-                do
-                {
-                    ys = IterateBigInteger(ys, c, ref localIterations);
-                    BigInteger diff = AbsSubBigInteger(ys, x);
-                    if (diff.IsZero)
-                    {
-                        continue;
-                    }
-
-                    g = BigInteger.GreatestCommonDivisor(diff, _modulus);
-                }
-                while (g.IsOne);
-            }
-
-            iterationCount += localIterations;
-
-            if (g.IsOne || g == _modulus)
-            {
-                continue;
-            }
-
-            if (g <= ulong.MaxValue)
-            {
-                ulong candidate = (ulong)g;
-                if (candidate > 1UL && candidate <= allowedMax)
-                {
-                    factor = candidate;
-                    return true;
-                }
-            }
-        }
-
-        return false;
-    }
-
-    private ulong Iterate64(ulong value, ulong c, ref ulong iterationCounter)
-    {
-        iterationCounter++;
-        value = SquareMod64(value);
-        value = AddMod64(value, c);
-        return value;
-    }
-
-    private UInt128 Iterate128(UInt128 value, UInt128 c, ref ulong iterationCounter)
-    {
-        iterationCounter++;
-        value = SquareMod128(value);
-        value = AddMod128(value, c);
-        return value;
-    }
-
-    private BigInteger IterateBigInteger(BigInteger value, BigInteger c, ref ulong iterationCounter)
-    {
-        iterationCounter++;
-        value = SquareModBigInteger(value);
-        value = AddModBigInteger(value, c);
-        return value;
-    }
-
-    private ulong AddMod64(ulong a, ulong b)
-    {
-        UInt128 sum = (UInt128)a + b;
-        return Reduce64(sum);
-    }
-
-    private UInt128 AddMod128(UInt128 a, UInt128 b)
-    {
-        UInt128 sum = a + b;
-        bool carryOut = sum < a;
-        if (!carryOut && sum < _modulus128)
-        {
-            return sum;
-        }
-
-        ulong p3 = 0UL;
-        ulong p2 = carryOut ? 1UL : 0UL;
-        ulong p1 = (ulong)(sum >> 64);
-        ulong p0 = (ulong)sum;
-        return ReduceProductBitwise(p3, p2, p1, p0, _modulus128);
-    }
-
-    private BigInteger AddModBigInteger(BigInteger a, BigInteger b)
-    {
-        return ReduceBigInteger(a + b);
-    }
-
-    private ulong SquareMod64(ulong value)
-    {
-        UInt128 square = (UInt128)value * value;
-        return Reduce64(square);
-    }
-
-    private UInt128 SquareMod128(UInt128 value)
-    {
-        return MulMod128(value, value);
-    }
-
-    private BigInteger SquareModBigInteger(BigInteger value)
-    {
-        return ReduceBigInteger(value * value);
-    }
-
-    private ulong MulMod64(ulong a, ulong b)
-    {
-        UInt128 product = (UInt128)a * b;
-        return Reduce64(product);
-    }
-
-    private UInt128 MulMod128(UInt128 a, UInt128 b)
-    {
-        MultiplyFull(a, b, out ulong p3, out ulong p2, out ulong p1, out ulong p0);
-        return ReduceProductBitwise(p3, p2, p1, p0, _modulus128);
-    }
-
-    private BigInteger MulModBigInteger(BigInteger a, BigInteger b)
-    {
-        if (b == _modulus)
-        {
-            return a;
-        }
-
-        if (a == _modulus)
-        {
-            a = BigInteger.Zero;
-        }
-
-        return ReduceBigInteger(a * b);
-    }
-
-    private ulong Reduce64(UInt128 value)
-    {
-        if (_bitLength == 64)
-        {
-            UInt128 combined = (UInt128)(ulong)value + (value >> 64);
-            UInt128 modulus = _modulus64;
-            if (combined >= modulus)
-            {
-                combined -= modulus;
-                if (combined >= modulus)
-                {
-                    combined -= modulus;
-                }
-            }
-
-            return (ulong)combined;
-        }
-
-        UInt128 mask = _mask64;
-        UInt128 modulusValue = _modulus64;
-        UInt128 working = value;
-        while (true)
-        {
-            UInt128 high = working >> _bitLength;
-            if (high == UInt128.Zero)
-            {
-                break;
-            }
-
-            working = (working & mask) + high;
-        }
-
-        if (working >= modulusValue)
-        {
-            working -= modulusValue;
-            if (working >= modulusValue)
-            {
-                working %= modulusValue;
-                if (working >= modulusValue)
-                {
-                    working -= modulusValue;
-                }
-            }
-        }
-
-        return (ulong)working;
-    }
-
-    private BigInteger ReduceBigInteger(BigInteger value)
-    {
-        if (value.Sign < 0)
-        {
-            value %= _modulus;
-            if (value.Sign < 0)
-            {
-                value += _modulus;
-            }
-
-            return value;
-        }
-
-        while (true)
-        {
-            BigInteger high = value >> _bitLength;
-            if (high.IsZero)
-            {
-                break;
-            }
-
-            value &= _mask;
-            value += high;
-        }
-
-        if (value >= _modulus)
-        {
-            value -= _modulus;
-            if (value >= _modulus)
-            {
-                value %= _modulus;
-                if (value.Sign < 0)
-                {
-                    value += _modulus;
-                }
-            }
-        }
-
-        return value;
-    }
-
-    private ulong NextRandomSeed64()
-    {
-        ulong value;
-        do
-        {
-            value = NextRandomBelowModulus64();
-        }
-        while (value <= 1UL);
-
-        return value;
-    }
-
-    private UInt128 NextRandomSeed128()
-    {
-        UInt128 value;
-        do
-        {
-            value = NextRandomBelowModulus128();
-        }
-        while (value <= UInt128.One);
-
-        return value;
-    }
-
-    private BigInteger NextRandomSeedBigInteger()
-    {
-        BigInteger value;
-        do
-        {
-            value = NextRandomBelowModulusBigInteger();
-        }
-        while (value <= BigInteger.One);
-
-        return value;
-    }
-
-    private ulong NextRandomConstant64()
-    {
-        ulong value;
-        do
-        {
-            value = NextRandomBelowModulus64();
-        }
-        while (value == 0UL);
-
-        return value;
-    }
-
-    private UInt128 NextRandomConstant128()
-    {
-        UInt128 value;
-        do
-        {
-            value = NextRandomBelowModulus128();
-        }
-        while (value == UInt128.Zero);
-
-        return value;
-    }
-
-    private BigInteger NextRandomConstantBigInteger()
-    {
-        BigInteger value;
-        do
-        {
-            value = NextRandomBelowModulusBigInteger();
-        }
-        while (value.IsZero);
-
-        return value;
-    }
-
-    private ulong NextRandomBelowModulus64()
-    {
-        if (_byteLength == 0)
-        {
-            return 0UL;
-        }
-
-        Span<byte> buffer = stackalloc byte[_byteLength];
-        ulong candidate;
-        do
-        {
-            RandomNumberGenerator.Fill(buffer);
-            if (_bitRemainder != 0)
-            {
-                buffer[_byteLength - 1] &= _maskByte;
-            }
-
-            candidate = (ulong)ReadUInt128LittleEndian(buffer);
-        }
-        while (candidate >= _modulus64);
-
-        return candidate;
-    }
-
-    private UInt128 NextRandomBelowModulus128()
-    {
-        if (_byteLength == 0)
-        {
-            return UInt128.Zero;
-        }
-
-        Span<byte> buffer = stackalloc byte[_byteLength];
-        UInt128 candidate;
-        do
-        {
-            RandomNumberGenerator.Fill(buffer);
-            if (_bitRemainder != 0)
-            {
-                buffer[_byteLength - 1] &= _maskByte;
-            }
-
-            candidate = ReadUInt128LittleEndian(buffer);
-        }
-        while (candidate >= _modulus128);
-
-        return candidate;
-    }
-
-    private BigInteger NextRandomBelowModulusBigInteger()
-    {
-        if (_byteLength == 0)
-        {
-            return BigInteger.Zero;
-        }
-
-        byte[] buffer = ArrayPool<byte>.Shared.Rent(_byteLength);
-        try
-        {
-            BigInteger value;
-            do
-            {
-                RandomNumberGenerator.Fill(buffer.AsSpan(0, _byteLength));
-                if (_bitRemainder != 0)
-                {
-                    buffer[_byteLength - 1] &= _maskByte;
-                }
-
-                value = new BigInteger(buffer, isUnsigned: true, isBigEndian: false);
-            }
-            while (value >= _modulus);
-
-            return value;
-        }
-        finally
-        {
-            ArrayPool<byte>.Shared.Return(buffer, clearArray: true);
-        }
-    }
-
-    private static ulong AbsSub64(ulong a, ulong b)
-    {
-        return a >= b ? a - b : b - a;
-    }
-
-    private static UInt128 AbsSub128(UInt128 a, UInt128 b)
-    {
-        return a >= b ? a - b : b - a;
-    }
-
-    private static BigInteger AbsSubBigInteger(BigInteger a, BigInteger b)
-    {
-        BigInteger diff = a - b;
-        return diff.Sign < 0 ? -diff : diff;
-    }
-
-    private static ulong BinaryGcd64(ulong u, ulong v)
-    {
-        if (u == 0UL)
-        {
-            return v;
-        }
-
-        if (v == 0UL)
-        {
-            return u;
-        }
-
-        int shift = BitOperations.TrailingZeroCount(u | v);
-        u >>= BitOperations.TrailingZeroCount(u);
-        do
-        {
-            v >>= BitOperations.TrailingZeroCount(v);
-            if (u > v)
-            {
-                (u, v) = (v, u);
-            }
-
-            v -= u;
-        }
-        while (v != 0UL);
-
-        return u << shift;
-    }
-
-    private static void MultiplyFull(UInt128 left, UInt128 right, out ulong p3, out ulong p2, out ulong p1, out ulong p0)
-    {
-        ulong leftLow = (ulong)left;
-        ulong leftHigh = (ulong)(left >> 64);
-        ulong rightLow = (ulong)right;
-        ulong rightHigh = (ulong)(right >> 64);
-
-        (ulong High, ulong Low) partial0 = Multiply64(leftLow, rightLow);
-        (ulong High, ulong Low) partial1 = Multiply64(leftLow, rightHigh);
-        (ulong High, ulong Low) partial2 = Multiply64(leftHigh, rightLow);
-        (ulong High, ulong Low) partial3 = Multiply64(leftHigh, rightHigh);
-
-        p0 = partial0.Low;
-        ulong carry = partial0.High;
-        ulong sum = carry + partial1.Low;
-        ulong carryMid = sum < partial1.Low ? 1UL : 0UL;
-        sum += partial2.Low;
-        if (sum < partial2.Low)
-        {
-            carryMid++;
-        }
-
-        p1 = sum;
-        sum = partial1.High + partial2.High;
-        ulong carryHigh = sum < partial2.High ? 1UL : 0UL;
-        sum += partial3.Low;
-        if (sum < partial3.Low)
-        {
-            carryHigh++;
-        }
-
-        sum += carryMid;
-        if (sum < carryMid)
-        {
-            carryHigh++;
-        }
-
-        p2 = sum;
-        p3 = partial3.High + carryHigh;
-    }
-
-    private static (ulong High, ulong Low) Multiply64(ulong left, ulong right)
-    {
-        ulong a0 = (uint)left;
-        ulong a1 = left >> 32;
-        ulong b0 = (uint)right;
-        ulong b1 = right >> 32;
-
-        ulong lo = a0 * b0;
-        ulong mid1 = a1 * b0;
-        b0 = a0 * b1;
-        b1 *= a1;
-
-        a0 = (lo >> 32) + (uint)mid1 + (uint)b0;
-        a1 = (lo & 0xFFFFFFFFUL) | (a0 << 32);
-        b1 += (mid1 >> 32) + (b0 >> 32) + (a0 >> 32);
-
-        return (b1, a1);
-    }
-
-    private static UInt128 ReduceProductBitwise(ulong p3, ulong p2, ulong p1, ulong p0, UInt128 modulus)
-    {
-        UInt128 remainder = UInt128.Zero;
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p3 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p2 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p1 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        for (int bit = 63; bit >= 0; bit--)
-        {
-            remainder <<= 1;
-            remainder |= (UInt128)((p0 >> bit) & 1UL);
-            if (remainder >= modulus)
-            {
-                remainder -= modulus;
-            }
-        }
-
-        return remainder;
-    }
-
-    private static UInt128 ReadUInt128LittleEndian(ReadOnlySpan<byte> buffer)
-    {
-        UInt128 value = UInt128.Zero;
-        for (int i = buffer.Length - 1; i >= 0; i--)
-        {
-            value <<= 8;
-            value |= buffer[i];
-        }
-
-        return value;
-    }
-}

PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs

@@ -4,10 +4,12 @@ using System.Collections.Concurrent;
 using ILGPU;
 using ILGPU.Runtime;
 using System.Numerics;
+using System.Globalization;
 using PerfectNumbers.Core;
 using System.Runtime.InteropServices;
 using System.Runtime.CompilerServices;
 using ILGPU.Runtime.OpenCL;
+
 namespace PerfectNumbers.Core.Gpu;
 
 internal enum GpuPow2ModStatus
@@ -27,6 +29,25 @@ internal static partial class PrimeOrderGpuHeuristics
     private static readonly ConcurrentDictionary<Accelerator, OrderKernelLauncher> OrderKernelCache = new();
     private static readonly ConcurrentDictionary<Accelerator, SmallPrimeDeviceCache> SmallPrimeDeviceCaches = new();
 
+    private static void ReportPow2FailureCore(string context, string modulusDescription, GpuPow2ModStatus status)
+    {
+        string message = $"GPU pow2mod failed with status {status} for divisor {modulusDescription} during {context}.";
+        Console.Error.WriteLine(message);
+        throw new InvalidOperationException(message);
+    }
+
+    internal static void ReportPow2Failure(string context, ulong modulus, GpuPow2ModStatus status)
+    {
+        string modulusDescription = modulus.ToString(CultureInfo.InvariantCulture);
+        ReportPow2FailureCore(context, modulusDescription, status);
+    }
+
+    internal static void ReportPow2Failure(string context, UInt128 modulus, GpuPow2ModStatus status)
+    {
+        string modulusDescription = modulus.ToString(CultureInfo.InvariantCulture);
+        ReportPow2FailureCore(context, modulusDescription, status);
+    }
+
     public readonly struct OrderKernelConfig(ulong previousOrder, byte hasPreviousOrder, uint smallFactorLimit, int maxPowChecks, int mode)
     {
         public readonly ulong PreviousOrder = previousOrder;

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -269,7 +269,8 @@ public class MersenneDivisorCycles
         ulong exponent,
         in MontgomeryDivisorData divisorData,
         Dictionary<ulong, FactorCacheEntry>? factorCache,
-        out ulong cycleLength)
+        out ulong cycleLength,
+        bool allowGpuPow2 = false)
     {
         cycleLength = 0UL;
 
@@ -290,7 +291,8 @@ public class MersenneDivisorCycles
             previousOrder: null,
             divisorData,
             PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
-            PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu);
+            PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu,
+            allowGpuPow2);
         if (orderResult.Order != 0UL)
         {
             cycleLength = orderResult.Order;
@@ -327,7 +329,7 @@ public class MersenneDivisorCycles
             return false;
         }
 
-        cycleLength = ReduceOrder(divisorData, phi, factorCounts);
+        cycleLength = ReduceOrder(divisorData, phi, factorCounts, allowGpuPow2);
         return true;
     }
 
@@ -471,7 +473,7 @@ public class MersenneDivisorCycles
         }
     }
 
-    private static ulong ReduceOrder(in MontgomeryDivisorData divisorData, ulong initialOrder, Dictionary<ulong, int> factorCounts)
+    private static ulong ReduceOrder(in MontgomeryDivisorData divisorData, ulong initialOrder, Dictionary<ulong, int> factorCounts, bool allowGpuPow2)
     {
         if (factorCounts.Count == 0)
         {
@@ -505,7 +507,7 @@ public class MersenneDivisorCycles
                     }
 
                     ulong candidate = order / prime;
-                    if (candidate.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL)
+                    if (Pow2EqualsOne(candidate, divisorData, allowGpuPow2))
                     {
                         order = candidate;
                         continue;
@@ -523,6 +525,26 @@ public class MersenneDivisorCycles
         }
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static bool Pow2EqualsOne(ulong exponent, in MontgomeryDivisorData divisorData, bool allowGpuPow2)
+    {
+        if (allowGpuPow2)
+        {
+            GpuPow2ModStatus status = PrimeOrderGpuHeuristics.TryPow2Mod(exponent, divisorData.Modulus, out ulong remainder, divisorData);
+            if (status == GpuPow2ModStatus.Success)
+            {
+                return remainder == 1UL;
+            }
+
+            PrimeOrderGpuHeuristics.ReportPow2Failure(
+                "divisor cycle reduction",
+                divisorData.Modulus,
+                status);
+        }
+
+        return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL;
+    }
+
     private static ulong PollardRho64(ulong n)
     {
         if ((n & 1UL) == 0UL)
@@ -924,7 +946,7 @@ public class MersenneDivisorCycles
         return CalculateCycleLengthFallback(divisor);
     }
 
-    internal static bool TryCalculateCycleLengthHeuristic(ulong divisor, in MontgomeryDivisorData divisorData, out ulong cycleLength)
+    internal static bool TryCalculateCycleLengthHeuristic(ulong divisor, in MontgomeryDivisorData divisorData, out ulong cycleLength, bool allowGpuPow2 = false)
     {
         if ((divisor & (divisor - 1UL)) == 0UL)
         {
@@ -945,7 +967,8 @@ public class MersenneDivisorCycles
                     previousOrder: null,
                     divisorData,
                     PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
-                    PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu);
+                    PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu,
+                    allowGpuPow2);
             if (orderResult.Order != 0UL)
             {
                 cycleLength = orderResult.Order;

PerfectNumbers.Core/PrimeOrderCalculator.Wide.cs

@@ -31,7 +31,8 @@ internal static partial class PrimeOrderCalculator
         PrimeOrderSearchConfig config,
         PrimeOrderHeuristicDevice device)
     {
-        using var scope = UsePow2Mode(device);
+        bool enableGpuPow2 = device == PrimeOrderHeuristicDevice.Gpu;
+        using var scope = UsePow2Mode(device, enableGpuPow2);
         MontgomeryDivisorData divisorData;
         if (prime <= ulong.MaxValue)
         {
@@ -51,7 +52,7 @@ internal static partial class PrimeOrderCalculator
 
             ulong prime64 = (ulong)prime;
             divisorData = MontgomeryDivisorData.FromModulus(prime64);
-            PrimeOrderResult result = Calculate(prime64, previous, divisorData, config, device);
+            PrimeOrderResult result = Calculate(prime64, previous, divisorData, config, device, enableGpuPow2);
             return new PrimeOrderResultWide(result.Status, result.Order);
         }
         else
@@ -1030,6 +1031,11 @@ internal static partial class PrimeOrderCalculator
             {
                 return wideRemainder;
             }
+
+            PrimeOrderGpuHeuristics.ReportPow2Failure(
+                "wide prime order pow2 check",
+                modulus,
+                wideStatus);
         }
 
         return exponent.Pow2MontgomeryModWindowed(modulus);

PerfectNumbers.Core/PrimeOrderCalculator.cs

@@ -90,13 +90,13 @@ internal static partial class PrimeOrderCalculator
         private readonly bool _previousAllow;
         private readonly PrimeOrderHeuristicDevice _previousDevice;
 
-        public Pow2ModeScope(PrimeOrderHeuristicDevice device)
+        public Pow2ModeScope(PrimeOrderHeuristicDevice device, bool allowGpuPow2)
         {
             _previousInitialized = s_pow2ModeInitialized;
             _previousAllow = s_allowGpuPow2;
             _previousDevice = s_deviceMode;
             s_pow2ModeInitialized = true;
-            s_allowGpuPow2 = device == PrimeOrderHeuristicDevice.Gpu;
+            s_allowGpuPow2 = allowGpuPow2;
             s_deviceMode = device;
         }
 
@@ -124,7 +124,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static Pow2ModeScope UsePow2Mode(PrimeOrderHeuristicDevice device) => new(device);
+    private static Pow2ModeScope UsePow2Mode(PrimeOrderHeuristicDevice device, bool allowGpuPow2) => new(device, allowGpuPow2);
 
     private static DebugLoggingScope UseDebugLogging(bool enabled) => new(enabled);
 
@@ -154,9 +154,11 @@ internal static partial class PrimeOrderCalculator
         ulong? previousOrder,
         in MontgomeryDivisorData divisorData,
         PrimeOrderSearchConfig config,
-        PrimeOrderHeuristicDevice device)
+        PrimeOrderHeuristicDevice device,
+        bool allowGpuPow2 = false)
     {
-        using var scope = UsePow2Mode(device);
+        bool enableGpuPow2 = allowGpuPow2 || device == PrimeOrderHeuristicDevice.Gpu;
+        using var scope = UsePow2Mode(device, enableGpuPow2);
         return CalculateInternal(prime, previousOrder, divisorData, config);
     }
 
@@ -443,7 +445,6 @@ internal static partial class PrimeOrderCalculator
         int powBudget = config.MaxPowChecks <= 0 ? candidates.Count : config.MaxPowChecks;
         int powUsed = 0;
         int candidateCount = candidates.Count;
-        bool allowGpuBatch = true;
         Span<ulong> candidateSpan = CollectionsMarshal.AsSpan(candidates);
 
         DebugLog(() => $"Checking candidates ({candidateCount} candidates, {powBudget} pow budget)");
@@ -467,9 +468,11 @@ internal static partial class PrimeOrderCalculator
             bool gpuSuccess = false;
             bool gpuStackRemainders = false;
             GpuPow2ModStatus status = GpuPow2ModStatus.Unavailable;
+            bool attemptedGpu = false;
 
-            if (allowGpuBatch && IsGpuPow2Allowed)
+            if (IsGpuPow2Allowed)
             {
+                attemptedGpu = true;
                 if (batchSize <= StackGpuBatchSize)
                 {
                     Span<ulong> localRemainders = stackGpuRemainders.Slice(0, batchSize);
@@ -496,11 +499,14 @@ internal static partial class PrimeOrderCalculator
                         gpuPool = null;
                     }
                 }
+            }
 
-                if (!gpuSuccess && (status == GpuPow2ModStatus.Overflow || status == GpuPow2ModStatus.Unavailable))
+            if (attemptedGpu && !gpuSuccess)
-                {
+            {
-                    allowGpuBatch = false;
+                PrimeOrderGpuHeuristics.ReportPow2Failure(
-                }
+                    "prime order candidate scan",
+                    prime,
+                    status);
             }
 
             for (int i = 0; i < batchSize && powUsed < powBudget; i++)
@@ -780,6 +786,11 @@ internal static partial class PrimeOrderCalculator
             {
                 return remainder == 1UL;
             }
+
+            PrimeOrderGpuHeuristics.ReportPow2Failure(
+                "prime order pow2 check",
+                prime,
+                status);
         }
 
         return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL;