Split CPU and GPU exponent steppers

PerfectNumbers.Core/Cpu/MersenneCpuDivisorScanSession.cs

@@ -42,7 +42,7 @@ internal sealed class MersenneCpuDivisorScanSession : IMersenneNumberDivisorByDi
 
         // 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);
+        var exponentStepper = new ExponentRemainderStepperCpu(cachedData);
 
         var cycleStepper = new CycleRemainderStepper(divisorCycle);
 

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -196,7 +196,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                 // }
                 // else
                 {
-                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(
+                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
                             candidate,
                             prime,
                             divisorData,

PerfectNumbers.Core/ExponentRemainderStepperCpu.cs

@@ -1,10 +1,10 @@
 namespace PerfectNumbers.Core;
 
 /// <summary>
-/// Tracks successive Montgomery residues for a single divisor while scanning exponent candidates.
+/// Tracks successive Montgomery residues for a single divisor while scanning exponent candidates on the CPU path.
 /// Callers are responsible for seeding the stepper once per divisor and then advancing exponents in ascending order.
 /// </summary>
-internal struct ExponentRemainderStepper
+internal struct ExponentRemainderStepperCpu
 {
     private readonly MontgomeryDivisorData _divisor;
     private readonly ulong _modulus;
@@ -13,7 +13,7 @@ internal struct ExponentRemainderStepper
     private ulong _previousExponent;
     private ulong _currentMontgomery;
 
-    public ExponentRemainderStepper(in MontgomeryDivisorData divisor)
+    public ExponentRemainderStepperCpu(in MontgomeryDivisorData divisor)
     {
         _divisor = divisor;
         _modulus = divisor.Modulus;
@@ -81,28 +81,6 @@ internal struct ExponentRemainderStepper
         return ReduceCurrent();
     }
 
-    /// <summary>
-    /// Initializes the stepper for GPU calculations using the first exponent in a strictly ascending sequence.
-    /// </summary>
-    /// <param name="exponent">First exponent evaluated on the GPU path. The same divisor metadata must be reused for future calls.</param>
-    /// <returns>The canonical residue produced by <c>2^exponent mod divisor</c>.</returns>
-    public ulong InitializeGpu(ulong exponent)
-    {
-        InitializeGpuState(exponent);
-        return ReduceCurrent();
-    }
-
-    /// <summary>
-    /// Initializes the GPU stepping state and reports whether the seed exponent produces unity.
-    /// </summary>
-    /// <param name="exponent">First exponent evaluated on the GPU path. Must match the divisor supplied during construction.</param>
-    /// <returns><see langword="true"/> when the seed exponent produces a Montgomery residue equal to one.</returns>
-    public bool InitializeGpuIsUnity(ulong exponent)
-    {
-        InitializeGpuState(exponent);
-        return _currentMontgomery == _montgomeryOne;
-    }
-
     /// <summary>
     /// Advances the CPU stepping state to the next exponent and reports whether it evaluates to unity.
     /// Callers must seed the stepper through <see cref="InitializeCpu(ulong)"/> or <see cref="InitializeCpuIsUnity(ulong)"/> and then
@@ -121,30 +99,6 @@ internal struct ExponentRemainderStepper
         return _currentMontgomery == _montgomeryOne;
     }
 
-    /// <summary>
-    /// Advances the GPU stepping state to the next exponent in a strictly ascending sequence that reuses the same divisor.
-    /// Callers must invoke <see cref="InitializeGpu(ulong)"/> beforehand.
-    /// </summary>
-    /// <param name="exponent">Next exponent in the ascending sequence.</param>
-    /// <returns>The canonical residue produced by <c>2^exponent mod divisor</c>.</returns>
-    public ulong ComputeNextGpu(ulong exponent)
-    {
-        AdvanceGpu(exponent);
-        return ReduceCurrent();
-    }
-
-    /// <summary>
-    /// Advances the GPU stepping state to the next exponent and reports whether it evaluates to unity.
-    /// Callers must seed the stepper through <see cref="InitializeGpu(ulong)"/> or <see cref="InitializeGpuIsUnity(ulong)"/>.
-    /// </summary>
-    /// <param name="exponent">Next exponent in the ascending sequence.</param>
-    /// <returns><see langword="true"/> when the canonical residue equals one.</returns>
-    public bool ComputeNextGpuIsUnity(ulong exponent)
-    {
-        AdvanceGpu(exponent);
-        return _currentMontgomery == _montgomeryOne;
-    }
-
     /// <summary>
     /// Seeds the stepper with a precomputed Montgomery residue produced by the caller.
     /// The provided exponent becomes the new baseline and all subsequent calls must continue with greater exponents.
@@ -169,14 +123,6 @@ internal struct ExponentRemainderStepper
     /// <param name="montgomeryDelta">Montgomery residue delta corresponding to the exponent gap.</param>
     /// <param name="isUnity">Outputs whether the resulting residue equals Montgomery one.</param>
     /// <returns><see langword="true"/> when the advance succeeds.</returns>
-    private void AdvanceGpu(ulong exponent)
-    {
-        ulong delta = exponent - _previousExponent;
-        ulong multiplier = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(_divisor, delta);
-        _currentMontgomery = _currentMontgomery.MontgomeryMultiply(multiplier, _modulus, _nPrime);
-        _previousExponent = exponent;
-    }
-
     public bool TryAdvanceWithMontgomeryDelta(ulong exponent, ulong montgomeryDelta, out bool isUnity)
     {
         // TODO: Once the divisor-cycle cache exposes a direct Montgomery delta, multiply it here instead
@@ -194,11 +140,5 @@ internal struct ExponentRemainderStepper
         _previousExponent = exponent;
     }
 
-    private void InitializeGpuState(ulong exponent)
-    {
-        _currentMontgomery = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(_divisor, exponent);
-        _previousExponent = exponent;
-    }
-
     private ulong ReduceCurrent() => _currentMontgomery.MontgomeryMultiply(1UL, _modulus, _nPrime);
 }

PerfectNumbers.Core/Gpu/ExponentRemainderStepperGpu.cs

@@ -0,0 +1,156 @@
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core.Gpu;
+
+/// <summary>
+/// Tracks successive residues for a single divisor while kernels advance exponent candidates on the GPU path.
+/// Callers must seed the stepper once per divisor and then supply exponents in strictly ascending order.
+/// </summary>
+internal struct ExponentRemainderStepperGpu
+{
+    private readonly MontgomeryDivisorData _divisor;
+    private readonly ulong _modulus;
+    private readonly ulong _nPrime;
+    private readonly ulong _montgomeryOne;
+    private ulong _previousExponent;
+    private ulong _currentMontgomery;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public ExponentRemainderStepperGpu(in MontgomeryDivisorData divisor)
+    {
+        _divisor = divisor;
+        _modulus = divisor.Modulus;
+        _nPrime = divisor.NPrime;
+        _montgomeryOne = divisor.MontgomeryOne;
+        _previousExponent = 0UL;
+        _currentMontgomery = divisor.MontgomeryOne;
+    }
+
+    public ulong PreviousExponent
+    {
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        get => _previousExponent;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public bool MatchesDivisor(in MontgomeryDivisorData divisor)
+    {
+        return _modulus == divisor.Modulus && _nPrime == divisor.NPrime && _montgomeryOne == divisor.MontgomeryOne;
+    }
+
+    /// <summary>
+    /// Clears the cached Montgomery residue so the stepper can be reused for another divisor.
+    /// Callers must reinitialize the stepper before consuming any residues after a reset.
+    /// </summary>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public void Reset()
+    {
+        _previousExponent = 0UL;
+        _currentMontgomery = _montgomeryOne;
+    }
+
+    /// <summary>
+    /// Initializes the stepper for GPU calculations using the first exponent in a strictly ascending sequence.
+    /// The returned value is the canonical residue corresponding to the provided exponent.
+    /// </summary>
+    /// <param name="exponent">First exponent evaluated for the current divisor. The caller must reuse the same divisor metadata.</param>
+    /// <returns>The canonical residue produced by <c>2^exponent mod divisor</c>.</returns>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public ulong InitializeGpu(ulong exponent)
+    {
+        InitializeGpuState(exponent);
+        return ReduceCurrent();
+    }
+
+    /// <summary>
+    /// Initializes the GPU stepping state and reports whether the seed exponent already yields unity.
+    /// </summary>
+    /// <param name="exponent">First exponent evaluated for the current divisor. Must match the divisor passed to the constructor.</param>
+    /// <returns><see langword="true"/> when the seed exponent produces a Montgomery residue equal to one.</returns>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public bool InitializeGpuIsUnity(ulong exponent)
+    {
+        InitializeGpuState(exponent);
+        return _currentMontgomery == _montgomeryOne;
+    }
+
+    /// <summary>
+    /// Advances the GPU stepping state to the next exponent in a strictly ascending sequence that shares the same divisor.
+    /// Callers must invoke <see cref="InitializeGpu(ulong)"/> beforehand.
+    /// </summary>
+    /// <param name="exponent">Next exponent in the ascending sequence. Callers must never move backwards or reuse an older exponent.</param>
+    /// <returns>The canonical residue produced by <c>2^exponent mod divisor</c>.</returns>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public ulong ComputeNextGpu(ulong exponent)
+    {
+        AdvanceGpu(exponent);
+        return ReduceCurrent();
+    }
+
+    /// <summary>
+    /// Advances the GPU stepping state to the next exponent and reports whether it evaluates to unity.
+    /// Callers must seed the stepper through <see cref="InitializeGpu(ulong)"/> or <see cref="InitializeGpuIsUnity(ulong)"/> and then
+    /// pass exponents in strictly ascending order.
+    /// </summary>
+    /// <param name="exponent">Next exponent in the ascending sequence.</param>
+    /// <returns><see langword="true"/> when the canonical residue equals one.</returns>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public bool ComputeNextGpuIsUnity(ulong exponent)
+    {
+        AdvanceGpu(exponent);
+        return _currentMontgomery == _montgomeryOne;
+    }
+
+    /// <summary>
+    /// Seeds the stepper with a precomputed Montgomery residue produced by the caller.
+    /// The provided exponent becomes the new baseline and all subsequent calls must continue with greater exponents.
+    /// </summary>
+    /// <param name="exponent">Exponent associated with <paramref name="montgomeryResult"/>.</param>
+    /// <param name="montgomeryResult">Residue in Montgomery form produced externally for the configured divisor.</param>
+    /// <param name="isUnity">Outputs whether the supplied residue equals Montgomery one.</param>
+    /// <returns><see langword="true"/> when the residue is accepted and cached.</returns>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public bool TryInitializeFromMontgomeryResult(ulong exponent, ulong montgomeryResult, out bool isUnity)
+    {
+        _currentMontgomery = montgomeryResult;
+        _previousExponent = exponent;
+        isUnity = _currentMontgomery == _montgomeryOne;
+        return true;
+    }
+
+    /// <summary>
+    /// Advances the stepper using a caller-supplied Montgomery delta that represents the gap to the next exponent.
+    /// Callers must seed the stepper first, reuse the same divisor metadata, and continue feeding exponents in ascending order so the delta remains valid.
+    /// </summary>
+    /// <param name="exponent">Next exponent in the ascending sequence.</param>
+    /// <param name="montgomeryDelta">Montgomery residue delta corresponding to the exponent gap.</param>
+    /// <param name="isUnity">Outputs whether the resulting residue equals Montgomery one.</param>
+    /// <returns><see langword="true"/> when the advance succeeds.</returns>
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public bool TryAdvanceWithMontgomeryDelta(ulong exponent, ulong montgomeryDelta, out bool isUnity)
+    {
+        _currentMontgomery = _currentMontgomery.MontgomeryMultiply(montgomeryDelta, _modulus, _nPrime);
+        _previousExponent = exponent;
+        isUnity = _currentMontgomery == _montgomeryOne;
+        return true;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private void InitializeGpuState(ulong exponent)
+    {
+        _currentMontgomery = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(_divisor, exponent);
+        _previousExponent = exponent;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private void AdvanceGpu(ulong exponent)
+    {
+        ulong delta = exponent - _previousExponent;
+        ulong multiplier = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(_divisor, delta);
+        _currentMontgomery = _currentMontgomery.MontgomeryMultiply(multiplier, _modulus, _nPrime);
+        _previousExponent = exponent;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private ulong ReduceCurrent() => _currentMontgomery.MontgomeryMultiply(1UL, _modulus, _nPrime);
+}

PerfectNumbers.Core/Gpu/Kernels/DivisorByDivisorKernels.cs

@@ -41,37 +41,34 @@ internal static class DivisorByDivisorKernels
 
         while (index >= 0)
         {
-            result = ULongExtensions.MulMod64Gpu(result, result, modulus);
+            ulong currentBit = (exponent >> index) & 1UL;
+            ulong squared = MultiplyMod(result, result, modulus);
+            bool processWindow = currentBit != 0UL;
 
-            if (((exponent >> index) & 1UL) == 0UL)
+            result = processWindow ? result : squared;
+            index -= (int)(currentBit ^ 1UL);
+
+            int windowStartCandidate = index - windowSize + 1;
+            int negativeMask = windowStartCandidate >> 31;
+            windowStartCandidate &= ~negativeMask;
+
+            int windowStart = processWindow ? GetNextSetBitIndex(exponent, windowStartCandidate) : windowStartCandidate;
+            int windowLength = processWindow ? index - windowStart + 1 : 0;
+
+            for (int square = 0; square < windowLength; square++)
+            {
+                result = MultiplyMod(result, result, modulus);
+            }
+
+            if (!processWindow)
             {
-                index--;
                 continue;
             }
 
-            int windowStart = index - windowSize + 1;
-            if (windowStart < 0)
-            {
-                windowStart = 0;
-            }
-
-            while (((exponent >> windowStart) & 1UL) == 0UL)
-            {
-                windowStart++;
-            }
-
-            int windowLength = index - windowStart + 1;
-
-            for (int square = 1; square < windowLength; square++)
-            {
-                result = ULongExtensions.MulMod64Gpu(result, result, modulus);
-            }
-
             ulong mask = (1UL << windowLength) - 1UL;
             ulong windowValue = (exponent >> windowStart) & mask;
             ulong multiplier = ComputeWindowedOddPower(windowValue, modulus);
-            result = ULongExtensions.MulMod64Gpu(result, multiplier, modulus);
+            result = MultiplyMod(result, multiplier, modulus);
-
             index = windowStart - 1;
         }
 
@@ -82,25 +79,29 @@ internal static class DivisorByDivisorKernels
     private static ulong ComputeWindowedOddPower(ulong windowValue, ulong modulus)
     {
         ulong baseValue = 2UL % modulus;
+        if (windowValue == 1UL)
+        {
+            return baseValue;
+        }
+
         ulong result = baseValue;
         ulong remaining = (windowValue - 1UL) >> 1;
-        ulong squareBase = ULongExtensions.MulMod64Gpu(baseValue, baseValue, modulus);
+        ulong squareBase = MultiplyMod(baseValue, baseValue, modulus);
 
         while (remaining != 0UL)
         {
             if ((remaining & 1UL) != 0UL)
             {
-                result = ULongExtensions.MulMod64Gpu(result, squareBase, modulus);
+                result = MultiplyMod(result, squareBase, modulus);
             }
 
             remaining >>= 1;
-
             if (remaining == 0UL)
             {
                 break;
             }
 
-            squareBase = ULongExtensions.MulMod64Gpu(squareBase, squareBase, modulus);
+            squareBase = MultiplyMod(squareBase, squareBase, modulus);
         }
 
         return result;
@@ -124,6 +125,65 @@ internal static class DivisorByDivisorKernels
         window = bitLength <= 6 ? clamped : window;
         return window;
     }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static int GetNextSetBitIndex(ulong exponent, int startIndex)
+    {
+        ulong guard = (ulong)(((long)startIndex - 64) >> 63);
+        int shift = startIndex & 63;
+        ulong mask = (~0UL << shift) & guard;
+        ulong masked = exponent & mask;
+        return XMath.TrailingZeroCount(masked);
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static ulong MultiplyMod(ulong left, ulong right, ulong modulus)
+    {
+        if (left == 0UL || right == 0UL)
+        {
+            return 0UL;
+        }
+
+        ulong threshold = ulong.MaxValue / left;
+        if (right <= threshold)
+        {
+            ulong product = left * right;
+            return product % modulus;
+        }
+
+        return MultiplyModWide(left, right, modulus);
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static ulong MultiplyModWide(ulong left, ulong right, ulong modulus)
+    {
+        ulong result = 0UL;
+        ulong addend = left;
+        ulong remaining = right;
+
+        while (remaining != 0UL)
+        {
+            if ((remaining & 1UL) != 0UL)
+            {
+                result += addend;
+                if (result >= modulus)
+                {
+                    result -= modulus;
+                }
+            }
+
+            addend <<= 1;
+            if (addend >= modulus)
+            {
+                addend -= modulus;
+            }
+
+            remaining >>= 1;
+        }
+
+        return result;
+    }
+
     public static void EvaluateDivisorWithStepperKernel(
         Index1D _,
         MontgomeryDivisorData divisor,
@@ -140,7 +200,7 @@ internal static class DivisorByDivisorKernels
         //     return;
         // }
 
-        var exponentStepper = new ExponentRemainderStepper(divisor);
+        var exponentStepper = new ExponentRemainderStepperGpu(divisor);
         ulong firstPrime = exponents[0];
         bool firstUnity = exponentStepper.InitializeGpuIsUnity(firstPrime);
         // EvenPerfectBitScanner only schedules divisors with non-zero cycle lengths (equal to the tested prime),

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -307,7 +307,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static ulong ResolveDivisorCycle(ulong divisor, ulong prime, in MontgomeryDivisorData divisorData)
     {
-        if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(divisor, prime, divisorData, out ulong computedCycle, out bool primeOrderFailed) || computedCycle == 0UL)
+        if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentGpu(divisor, prime, divisorData, out ulong computedCycle, out bool primeOrderFailed) || computedCycle == 0UL)
         {
             return MersenneDivisorCycles.CalculateCycleLength(divisor, divisorData, skipPrimeOrderHeuristic: primeOrderFailed);
         }
@@ -318,7 +318,8 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static bool CandidatePassesHeuristics(ulong candidate, bool lastIsSeven)
     {
-        // Mirror the CPU heuristics so the GPU path rejects obvious composites before computing cycles.
+        // Mirror the CPU-side divisor screen so the GPU path rejects multiples of 3, 5, 7, and 11
+        // before resolving cycles, keeping cache lookups aligned with the persisted snapshot.
         ulong remainder10 = candidate % 10UL;
         bool accept10 = lastIsSeven
             ? (remainder10 == 3UL || remainder10 == 7UL || remainder10 == 9UL)
@@ -469,7 +470,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
             if (cycle == 0UL)
             {
-                if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(divisor, firstPrime, cachedData, out ulong computedCycle, out bool primeOrderFailed) || computedCycle == 0UL)
+                if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentGpu(divisor, firstPrime, cachedData, out ulong computedCycle, out bool primeOrderFailed) || computedCycle == 0UL)
                 {
                     cycle = MersenneDivisorCycles.CalculateCycleLength(divisor, cachedData, skipPrimeOrderHeuristic: primeOrderFailed);
                 }

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -81,7 +81,7 @@ public class MersenneDivisorCycles
             return heuristicCycle == exponent;
         }
 
-        if (TryCalculateCycleLengthForExponent(divisor, exponent, divisorData, out ulong cycleLength, out bool _) && cycleLength != 0UL)
+        if (TryCalculateCycleLengthForExponentCpu(divisor, exponent, divisorData, out ulong cycleLength, out bool _) && cycleLength != 0UL)
         {
             return cycleLength == exponent;
         }
@@ -245,7 +245,88 @@ public class MersenneDivisorCycles
         return order;
     }
 
-    public static bool TryCalculateCycleLengthForExponent(
+    public static bool TryCalculateCycleLengthForExponentCpu(
+        ulong divisor,
+        ulong exponent,
+        in MontgomeryDivisorData divisorData,
+        out ulong cycleLength,
+        out bool primeOrderFailed)
+    {
+        cycleLength = 0UL;
+        primeOrderFailed = false;
+
+        if ((divisor & (divisor - 1UL)) == 0UL)
+        {
+            cycleLength = 1UL;
+            return true;
+        }
+
+        if (divisor <= 3UL || exponent <= 1UL)
+        {
+            cycleLength = CalculateCycleLength(divisor, divisorData);
+            return true;
+        }
+
+        ulong computedOrder = PrimeOrderCalculator.Calculate(
+            divisor,
+            previousOrder: null,
+            divisorData,
+            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+            PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu);
+        if (computedOrder != 0UL)
+        {
+            cycleLength = computedOrder;
+            return true;
+        }
+
+        primeOrderFailed = true;
+
+        ulong phi = divisor - 1UL;
+        // 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;
+        if (reducedPhi == 0UL || (reducedPhi % exponent) != 0UL)
+        {
+            return false;
+        }
+
+        ulong k = reducedPhi / exponent;
+        // 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;
+
+        if (twoCount > 0)
+        {
+            factorCounts[2UL] = twoCount;
+        }
+
+        bool exponentAccumulated = AccumulateFactors(exponent, factorCounts);
+        bool factorsAccumulated = exponentAccumulated && AccumulateFactors(k, factorCounts);
+
+        if (factorsAccumulated)
+        {
+            cycleLength = ReduceOrder(divisorData, phi, factorCounts);
+            success = true;
+            primeOrderFailed = false;
+        }
+
+        factorCounts.Clear();
+        ThreadStaticPools.ReturnFactorCountDictionary(factorCounts);
+        return success;
+    }
+    public static bool TryCalculateCycleLengthForExponentGpu(
         ulong divisor,
         ulong exponent,
         in MontgomeryDivisorData divisorData,
@@ -482,7 +563,7 @@ public class MersenneDivisorCycles
         ulong[]? heapCandidateArray = null;
         bool[]? heapEvaluationArray = null;
 
-        ExponentRemainderStepper stepper = ThreadStaticPools.RentExponentStepper(divisorData);
+        ExponentRemainderStepperCpu stepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
 
         ulong order = initialOrder;
         for (int i = 0; i < count; i++)
@@ -513,7 +594,7 @@ public class MersenneDivisorCycles
             ProcessReduceOrderPrime(heapCandidateArray.AsSpan(0, multiplicity), heapEvaluationArray.AsSpan(0, multiplicity), ref order, prime, multiplicity, ref stepper);
         }
 
-        ThreadStaticPools.ReturnExponentStepper(stepper);
+        ThreadStaticPools.ReturnExponentStepperCpu(stepper);
         ThreadStaticPools.UlongPool.Return(primes);
 
         if (heapCandidateArray is not null)
@@ -525,7 +606,7 @@ public class MersenneDivisorCycles
         return order;
     }
 
-    private static void ProcessReduceOrderPrime(Span<ulong> candidateBuffer, Span<bool> evaluationBuffer, ref ulong order, ulong prime, int multiplicity, ref ExponentRemainderStepper stepper)
+    private static void ProcessReduceOrderPrime(Span<ulong> candidateBuffer, Span<bool> evaluationBuffer, ref ulong order, ulong prime, int multiplicity, ref ExponentRemainderStepperCpu stepper)
     {
         ulong working = order;
         int actual = 0;

PerfectNumbers.Core/PrimeOrderCalculator.Cpu.cs

@@ -163,12 +163,12 @@ internal static partial class PrimeOrderCalculator
 		Span<ulong> candidates = buffer[..actual];
 		candidates.Sort();
 
-		ExponentRemainderStepper stepper = ThreadStaticPools.RentExponentStepper(divisorData);
+		ExponentRemainderStepperCpu stepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
 		int candidateCount = candidates.Length;
 
 		if (stepper.InitializeCpuIsUnity(candidates[0]))
 		{
-			ThreadStaticPools.ReturnExponentStepper(stepper);
+			ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 			return false;
 		}
 
@@ -176,12 +176,12 @@ internal static partial class PrimeOrderCalculator
 		{
 			if (stepper.ComputeNextIsUnity(candidates[i]))
 			{
-				ThreadStaticPools.ReturnExponentStepper(stepper);
+				ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 				return false;
 			}
 		}
 
-		ThreadStaticPools.ReturnExponentStepper(stepper);
+		ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 		return true;
 	}
 
@@ -219,7 +219,7 @@ internal static partial class PrimeOrderCalculator
 
 		buffer[..length].Sort(static (a, b) => a.Value.CompareTo(b.Value));
 
-		ExponentRemainderStepper stepper = ThreadStaticPools.RentExponentStepper(divisorData);
+		ExponentRemainderStepperCpu stepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
 
 		const int StackExponentCapacity = 16;
 		const int ExponentHardLimit = 256;
@@ -256,7 +256,7 @@ internal static partial class PrimeOrderCalculator
 			ProcessExponentLoweringPrime(heapCandidateArray.AsSpan(0, exponent), heapEvaluationArray.AsSpan(0, exponent), ref order, primeFactor, exponent, ref stepper);
 		}
 
-		ThreadStaticPools.ReturnExponentStepper(stepper);
+		ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 
 		if (heapCandidateArray is not null)
 		{
@@ -268,7 +268,7 @@ internal static partial class PrimeOrderCalculator
 		return order;
 	}
 
-	private static void ProcessExponentLoweringPrime(Span<ulong> candidateBuffer, Span<bool> evaluationBuffer, ref ulong order, ulong primeFactor, int exponent, ref ExponentRemainderStepper stepper)
+	private static void ProcessExponentLoweringPrime(Span<ulong> candidateBuffer, Span<bool> evaluationBuffer, ref ulong order, ulong primeFactor, int exponent, ref ExponentRemainderStepperCpu stepper)
 	{
 		ulong working = order;
 		int actual = 0;
@@ -388,7 +388,7 @@ internal static partial class PrimeOrderCalculator
 		Span<ulong> stackBuffer = stackalloc ulong[StackExponentCapacity];
 
 		ulong[]? heapCandidateArray = null;
-		ExponentRemainderStepper stepper = ThreadStaticPools.RentExponentStepper(divisorData);
+		ExponentRemainderStepperCpu stepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
 		bool violates = false;
 
 		for (int i = 0; i < length; i++)
@@ -425,7 +425,7 @@ internal static partial class PrimeOrderCalculator
 			}
 		}
 
-		ThreadStaticPools.ReturnExponentStepper(stepper);
+		ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 
 		if (heapCandidateArray is not null)
 		{
@@ -435,7 +435,7 @@ internal static partial class PrimeOrderCalculator
 		return !violates;
 	}
 
-	private static bool ValidateOrderForFactor(Span<ulong> buffer, ulong primeFactor, int exponent, ulong order, ref ExponentRemainderStepper stepper)
+	private static bool ValidateOrderForFactor(Span<ulong> buffer, ulong primeFactor, int exponent, ulong order, ref ExponentRemainderStepperCpu stepper)
 	{
 		ulong working = order;
 		int actual = 0;
@@ -547,7 +547,7 @@ internal static partial class PrimeOrderCalculator
 			int candidateCount = candidates.Count;
 			bool allowGpuBatch = true;
 			Span<ulong> candidateSpan = CollectionsMarshal.AsSpan(candidates);
-			ExponentRemainderStepper powStepper = ThreadStaticPools.RentExponentStepper(divisorData);
+			ExponentRemainderStepperCpu powStepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
 			bool powStepperInitialized = false;
 
 			// DebugLog(() => $"Checking candidates ({candidateCount} candidates, {powBudget} pow budget)");
@@ -626,7 +626,7 @@ internal static partial class PrimeOrderCalculator
 
 						candidates.Clear();
 						ThreadStaticPools.ReturnUlongList(candidates);
-						ThreadStaticPools.ReturnExponentStepper(powStepper);
+						ThreadStaticPools.ReturnExponentStepperCpu(powStepper);
 						result = candidate;
 						return true;
 					}
@@ -666,7 +666,7 @@ internal static partial class PrimeOrderCalculator
 
 					candidates.Clear();
 					ThreadStaticPools.ReturnUlongList(candidates);
-					ThreadStaticPools.ReturnExponentStepper(powStepper);
+					ThreadStaticPools.ReturnExponentStepperCpu(powStepper);
 					result = candidate;
 					return true;
 				}
@@ -681,7 +681,7 @@ internal static partial class PrimeOrderCalculator
 
 			candidates.Clear();
 			ThreadStaticPools.ReturnUlongList(candidates);
-			ThreadStaticPools.ReturnExponentStepper(powStepper);
+			ThreadStaticPools.ReturnExponentStepperCpu(powStepper);
 			// DebugLog("No candidate confirmed");
 			return false;
 		}
@@ -892,7 +892,7 @@ internal static partial class PrimeOrderCalculator
 
 			Span<ulong> stackBuffer = stackalloc ulong[StackExponentCapacity];
 			ulong[]? heapCandidateArray = null;
-			ExponentRemainderStepper stepper = ThreadStaticPools.RentExponentStepper(divisorData);
+			ExponentRemainderStepperCpu stepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
 			bool violates = false;
 
 			for (int i = 0; i < length; i++)
@@ -929,7 +929,7 @@ internal static partial class PrimeOrderCalculator
 				}
 			}
 
-			ThreadStaticPools.ReturnExponentStepper(stepper);
+			ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 
 			if (heapCandidateArray is not null)
 			{
@@ -944,7 +944,7 @@ internal static partial class PrimeOrderCalculator
 		}
 	}
 
-	private static bool CheckCandidateViolation(Span<ulong> buffer, ulong primeFactor, int exponent, ulong candidate, ulong prime, ref int powUsed, int powBudget, ref ExponentRemainderStepper stepper)
+	private static bool CheckCandidateViolation(Span<ulong> buffer, ulong primeFactor, int exponent, ulong candidate, ulong prime, ref int powUsed, int powBudget, ref ExponentRemainderStepperCpu stepper)
 	{
 		ulong working = candidate;
 		int actual = 0;

PerfectNumbers.Core/ThreadStaticPools.cs

@@ -329,31 +329,31 @@ namespace PerfectNumbers.Core
         }
 
         [ThreadStatic]
-        private static ExponentRemainderStepper _exponentRemainderStepper;
+        private static ExponentRemainderStepperCpu _exponentRemainderStepperCpu;
 
         [ThreadStatic]
-        private static bool _hasExponentRemainderStepper;
+        private static bool _hasExponentRemainderStepperCpu;
 
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        internal static ExponentRemainderStepper RentExponentStepper(in MontgomeryDivisorData divisorData)
+        internal static ExponentRemainderStepperCpu RentExponentStepperCpu(in MontgomeryDivisorData divisorData)
         {
-            if (_hasExponentRemainderStepper && _exponentRemainderStepper.MatchesDivisor(divisorData))
+            if (_hasExponentRemainderStepperCpu && _exponentRemainderStepperCpu.MatchesDivisor(divisorData))
             {
-                ExponentRemainderStepper stepper = _exponentRemainderStepper;
+                ExponentRemainderStepperCpu stepper = _exponentRemainderStepperCpu;
-                _hasExponentRemainderStepper = false;
+                _hasExponentRemainderStepperCpu = false;
                 stepper.Reset();
                 return stepper;
             }
 
-            return new ExponentRemainderStepper(divisorData);
+            return new ExponentRemainderStepperCpu(divisorData);
         }
 
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        internal static void ReturnExponentStepper(ExponentRemainderStepper stepper)
+        internal static void ReturnExponentStepperCpu(ExponentRemainderStepperCpu stepper)
         {
             stepper.Reset();
-            _exponentRemainderStepper = stepper;
+            _exponentRemainderStepperCpu = stepper;
-            _hasExponentRemainderStepper = true;
+            _hasExponentRemainderStepperCpu = true;
         }
     }
 }