Streamline by-divisor cycle equality checks

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -1,6 +1,5 @@
 using System;
 using System.Collections.Concurrent;
-using System.Collections.Generic;
 using System.Numerics;
 using PerfectNumbers.Core;
 
@@ -174,70 +173,40 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             return false;
         }
 
-        Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
+        UInt128 step = (UInt128)prime << 1;
-        ulong divisor = 3UL;
+        if (step == UInt128.Zero)
-        while (divisor <= allowedMax)
         {
+            processedAll = true;
+            return false;
+        }
+
+        UInt128 limit = allowedMax;
+        UInt128 divisor = step + UInt128.One;
+        if (divisor > limit)
+        {
+            processedAll = true;
+            return false;
+        }
+
+        while (divisor <= limit)
+        {
+            ulong candidate = (ulong)divisor;
             processedCount++;
-            lastProcessed = divisor;
+            lastProcessed = candidate;
 
-            MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(divisor);
+            if (MersenneDivisorCycles.CycleEqualsExponentForMersenneCandidate(candidate, prime))
-            // TODO: Hoist MontgomeryDivisorData acquisition into the divisor-cycle cache so we reuse the
-            // staged ProcessEightBitWindows-ready metadata instead of reloading the slower Montgomery
-            // structs for every divisor.
-            ulong divisorCycle;
-            if (divisor <= PerfectNumberConstants.MaxQForDivisorCycles)
-            {
-                divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
-            }
-            else
-            {
-                factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
-                if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(divisor, prime, factorCache, out divisorCycle) || divisorCycle == 0UL)
-                {
-                    divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
-                }
-            }
-            if (divisorCycle != 0UL)
-            {
-                byte hit = CheckDivisor(prime, divisorCycle, divisorData);
-                if (hit != 0)
-                {
-                    processedAll = true;
-                    return true;
-                }
-            }
-
-            if (divisor >= allowedMax - 1UL)
             {
                 processedAll = true;
-                break;
+                return true;
             }
 
-            if (divisor > ulong.MaxValue - 2UL)
+            divisor += step;
-            {
-                break;
-            }
-
-            divisor += 2UL;
-            // TODO: Replace this linear increment with the batched divisor-cycle walker validated in the
-            // CPU by-divisor benchmarks so we advance directly to the next cached divisor candidate
-            // instead of testing every odd integer.
         }
 
-        if (!processedAll)
+        processedAll = divisor > limit;
-        {
-            processedAll = divisor > allowedMax;
-        }
         return false;
     }
 
-    private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
-    {
-        ulong residue = prime.Pow2MontgomeryModWithCycle(divisorCycle, divisorData);
-        return residue == 1UL ? (byte)1 : (byte)0;
-    }
-
     private void UpdateStatusUnsafe(ulong lastProcessed, ulong processedCount)
     {
         if (processedCount == 0UL)
@@ -316,44 +285,14 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                 return;
             }
 
-            if (divisorCycle == 0UL)
+            for (int i = 0; i < length; i++)
             {
-                divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
+                ulong prime = primes[i];
-                if (divisorCycle == 0UL)
+                bool divides = MersenneDivisorCycles.CycleEqualsExponentForMersenneCandidate(divisor, prime);
-                {
+                hits[i] = divides ? (byte)1 : (byte)0;
-                    hits.Clear();
-                    return;
-                }
-            }
-
-            MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(divisor);
-
-            var exponentStepper = new ExponentRemainderStepper(divisorData);
-            if (!exponentStepper.IsValidModulus)
-            {
-                hits.Clear();
-                return;
-            }
-
-            var stepper = new CycleRemainderStepper(divisorCycle);
-
-            ulong remainder = stepper.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 = stepper.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)

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -1,7 +1,6 @@
 using System;
 using System.Buffers;
 using System.Collections.Concurrent;
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
 using System.Numerics;
@@ -197,27 +196,19 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         ArrayView1D<ulong, Stride1D.Dense> exponentView;
         ArrayView1D<byte, Stride1D.Dense> hitsView;
 
-        DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
+        int chunkCapacity = Math.Min(batchCapacity, (int)accelerator.MaxNumThreadsPerGroup);
-        int cycleBatchCapacity = Math.Min(batchCapacity, cycleCache.PreferredBatchSize);
+        if (chunkCapacity <= 0)
-        int maxKernelGroupSize = (int)accelerator.MaxNumThreadsPerGroup;
-        if (cycleBatchCapacity > maxKernelGroupSize)
         {
-            cycleBatchCapacity = maxKernelGroupSize;
+            chunkCapacity = batchCapacity;
         }
 
-        if (cycleBatchCapacity <= 0)
+        ulong[] candidateDivisors = ArrayPool<ulong>.Shared.Rent(chunkCapacity);
-        {
+        ulong[] filteredDivisors = ArrayPool<ulong>.Shared.Rent(chunkCapacity);
-            cycleBatchCapacity = batchCapacity;
+        ulong[] divisorGaps = ArrayPool<ulong>.Shared.Rent(chunkCapacity);
-        }
+        byte[] remainder10Buffer = ArrayPool<byte>.Shared.Rent(chunkCapacity);
-
+        byte[] remainder8Buffer = ArrayPool<byte>.Shared.Rent(chunkCapacity);
-        ulong[] candidateDivisors = ArrayPool<ulong>.Shared.Rent(cycleBatchCapacity);
+        byte[] remainder5Buffer = ArrayPool<byte>.Shared.Rent(chunkCapacity);
-        ulong[] filteredDivisors = ArrayPool<ulong>.Shared.Rent(cycleBatchCapacity);
+        byte[] remainder3Buffer = ArrayPool<byte>.Shared.Rent(chunkCapacity);
-        ulong[] filteredCycles = ArrayPool<ulong>.Shared.Rent(cycleBatchCapacity);
-        ulong[] divisorGaps = ArrayPool<ulong>.Shared.Rent(cycleBatchCapacity);
-        byte[] remainder10Buffer = ArrayPool<byte>.Shared.Rent(cycleBatchCapacity);
-        byte[] remainder8Buffer = ArrayPool<byte>.Shared.Rent(cycleBatchCapacity);
-        byte[] remainder5Buffer = ArrayPool<byte>.Shared.Rent(cycleBatchCapacity);
-        byte[] remainder3Buffer = ArrayPool<byte>.Shared.Rent(cycleBatchCapacity);
 
         UInt128 twoP128 = (UInt128)prime << 1;
         if (twoP128 == UInt128.Zero)
@@ -260,7 +251,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         {
             while (currentK <= maxK)
             {
-                int chunkCount = Math.Min(cycleBatchCapacity, batchCapacity);
+                int chunkCount = Math.Min(chunkCapacity, batchCapacity);
                 ulong remainingK = maxK - currentK + 1UL;
                 if ((ulong)chunkCount > remainingK)
                 {
@@ -318,7 +309,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
                 int filteredCount = 0;
                 Span<ulong> filteredDivisorsSpan = filteredDivisors.AsSpan(0, chunkCount);
-                Span<ulong> filteredCyclesSpan = filteredCycles.AsSpan(0, chunkCount);
 
                 for (int i = 0; i < chunkCount; i++)
                 {
@@ -360,42 +350,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
                     continue;
                 }
 
-                cycleCache.GetCycleLengths(filteredDivisorsSpan[..filteredCount], filteredCyclesSpan[..filteredCount]);
-
                 int batchSize = 0;
                 for (int i = 0; i < filteredCount; i++)
                 {
                     ulong divisorValue = filteredDivisorsSpan[i];
-                    ulong cycleLength = filteredCyclesSpan[i];
-
-                    bool includeDivisor = true;
-                    ulong exponent = prime;
-
-                    if (cycleLength > 0UL)
-                    {
-                        ulong remainder = prime;
-                        if (remainder >= cycleLength)
-                        {
-                            remainder %= cycleLength;
-                        }
-
-                        if (remainder != 0UL)
-                        {
-                            includeDivisor = false;
-                        }
-                        else
-                        {
-                            exponent = 0UL;
-                        }
-                    }
-
-                    if (!includeDivisor)
-                    {
-                        continue;
-                    }
-
                     divisors[batchSize] = divisorValue;
-                    exponents[batchSize] = exponent;
+                    exponents[batchSize] = prime;
                     batchSize++;
                 }
 
@@ -450,7 +410,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         {
             ArrayPool<ulong>.Shared.Return(candidateDivisors, clearArray: false);
             ArrayPool<ulong>.Shared.Return(filteredDivisors, clearArray: false);
-            ArrayPool<ulong>.Shared.Return(filteredCycles, clearArray: false);
             ArrayPool<ulong>.Shared.Return(divisorGaps, clearArray: false);
             ArrayPool<byte>.Shared.Return(remainder10Buffer, clearArray: false);
             ArrayPool<byte>.Shared.Return(remainder8Buffer, clearArray: false);
@@ -559,8 +518,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         private MemoryBuffer1D<ulong, Stride1D.Dense> _exponentsBuffer;
         private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer;
         private ulong[] _hostBuffer;
-        private int[]? _positionBuffer;
-        private Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? _factorCache;
         private int _capacity;
         private bool _disposed;
 
@@ -574,13 +531,11 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             _exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
             _resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
             _hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
-            _positionBuffer = null;
         }
 
         internal void Reset()
         {
             _disposed = false;
-            _factorCache?.Clear();
         }
 
         public void CheckDivisor(ulong divisor, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
@@ -590,153 +545,41 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
                 throw new ObjectDisposedException(nameof(DivisorScanSession));
             }
 
-            int primesLength = primes.Length;
+            int length = primes.Length;
-            if (primesLength == 0)
+            if (length == 0)
             {
                 return;
             }
 
             MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(divisor);
-            var exponentStepper = new ExponentRemainderStepper(divisorData);
+            if (divisorData.Modulus <= 1UL || (divisorData.Modulus & 1UL) == 0UL)
-            if (!exponentStepper.IsValidModulus)
             {
                 hits.Clear();
                 return;
             }
 
-            if (divisorCycle == 0UL)
-            {
-                Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry> cache = _factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(16);
-                if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(divisor, primes[0], cache, out divisorCycle) || divisorCycle == 0UL)
-                {
-                    divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
-                    if (divisorCycle == 0UL)
-                    {
-                        hits.Clear();
-                        return;
-                    }
-                }
-            }
-
-            var cycleStepper = new CycleRemainderStepper(divisorCycle);
-            ulong initialCycleRemainder = cycleStepper.Initialize(primes[0]);
-            ProcessWithCycle(ref exponentStepper, ref cycleStepper, initialCycleRemainder, divisorCycle, divisorData, primes, hits);
-        }
-
-
-        private void ProcessWithCycle(
-        ref ExponentRemainderStepper exponentStepper,
-        ref CycleRemainderStepper cycleStepper,
-        ulong initialCycleRemainder,
-        ulong divisorCycle,
-        in MontgomeryDivisorData divisorData,
-        ReadOnlySpan<ulong> primes,
-        Span<byte> hits)
-        {
-            Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> kernel = _kernel;
             ArrayView1D<ulong, Stride1D.Dense> exponentsView = _exponentsBuffer.View;
             ArrayView1D<ulong, Stride1D.Dense> resultsView = _resultsBuffer.View;
-            int capacity = _capacity;
+            Span<ulong> hostSpan = _hostBuffer.AsSpan(0, _capacity);
-            Span<ulong> hostSpan = _hostBuffer.AsSpan(0, capacity);
-            int[]? positionBuffer = _positionBuffer;
-            if (positionBuffer is null)
-            {
-                // Session construction already enforces the batch capacity, so we only
-                // need to rent the position buffer on the first cycle-enabled invocation.
-                positionBuffer = ArrayPool<int>.Shared.Rent(capacity);
-                _positionBuffer = positionBuffer;
-            }
 
-            Span<int> positionSpan = positionBuffer.AsSpan(0, capacity);
-
-            int gpuBatchSize = _owner._gpuBatchSize;
-            int primesLength = primes.Length;
             int offset = 0;
-            bool cycleRemainderPending = true;
+            while (offset < length)
-
-            while (offset < primesLength)
             {
-                int batchSize = Math.Min(gpuBatchSize, primesLength - offset);
+                int batchSize = Math.Min(_capacity, length - offset);
-                ReadOnlySpan<ulong> primesSlice = primes.Slice(offset, batchSize);
+                ReadOnlySpan<ulong> batch = primes.Slice(offset, batchSize);
-                Span<byte> hitsSlice = hits.Slice(offset, batchSize);
+                batch.CopyTo(hostSpan);
 
-                int computeCount = 0;
+                ArrayView1D<ulong, Stride1D.Dense> exponentSlice = exponentsView.SubView(0, batchSize);
-                bool hasState = exponentStepper.HasState;
+                exponentSlice.CopyFromCPU(ref MemoryMarshal.GetReference(hostSpan), batchSize);
-                ulong previousExponent = exponentStepper.PreviousExponent;
-                bool useInitialRemainder = cycleRemainderPending;
 
+                ArrayView1D<ulong, Stride1D.Dense> resultSlice = resultsView.SubView(0, batchSize);
+                _kernel(batchSize, divisorData, exponentSlice, resultSlice);
+                resultSlice.CopyToCPU(ref MemoryMarshal.GetReference(hostSpan), batchSize);
+
+                Span<byte> hitSlice = hits.Slice(offset, batchSize);
                 for (int i = 0; i < batchSize; i++)
                 {
-                    hitsSlice[i] = 0;
+                    hitSlice[i] = hostSpan[i] == 1UL ? (byte)1 : (byte)0;
-                    ulong primeValue = primesSlice[i];
-
-                    ulong remainder = useInitialRemainder
-                        ? initialCycleRemainder
-                        : cycleStepper.ComputeNext(primeValue);
-                    useInitialRemainder = false;
-
-                    if (remainder != 0UL)
-                    {
-                        continue;
-                    }
-
-                    ulong workValue;
-                    if (!hasState)
-                    {
-                        workValue = primeValue;
-                        hasState = true;
-                    }
-                    else
-                    {
-                        workValue = primeValue - previousExponent;
-                    }
-
-                    previousExponent = primeValue;
-
-                    if (workValue >= divisorCycle)
-                    {
-                        // TODO: Replace this `%` with the divisor-cycle remainder helper so we reuse cached
-                        // modulo results instead of recomputing them in the GPU staging loop.
-                        workValue %= divisorCycle;
-                    }
-
-                    hostSpan[computeCount] = workValue;
-                    positionSpan[computeCount] = i;
-                    computeCount++;
-                }
-
-                cycleRemainderPending = useInitialRemainder;
-
-                if (computeCount > 0)
-                {
-                    Span<ulong> exponentSlice = hostSpan[..computeCount];
-                    ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentsView.SubView(0, computeCount);
-                    exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
-
-                    ArrayView1D<ulong, Stride1D.Dense> resultView = resultsView.SubView(0, computeCount);
-                    kernel(computeCount, divisorData, exponentView, resultView);
-                    resultView.CopyToCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
-
-                    bool requiresInitialization = !exponentStepper.HasState;
-                    for (int i = 0; i < computeCount; i++)
-                    {
-                        int position = positionSpan[i];
-                        ulong primeValue = primesSlice[position];
-                        ulong montgomeryResult = exponentSlice[i];
-                        bool isUnity;
-
-                        if (requiresInitialization)
-                        {
-                            exponentStepper.TryInitializeFromMontgomeryResult(primeValue, montgomeryResult, out isUnity);
-                            requiresInitialization = false;
-                        }
-                        else
-                        {
-                            exponentStepper.TryAdvanceWithMontgomeryDelta(primeValue, montgomeryResult, out isUnity);
-                        }
-
-                        hitsSlice[position] = isUnity ? (byte)1 : (byte)0;
-                    }
                 }
 
                 offset += batchSize;
@@ -751,11 +594,9 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             }
 
             _disposed = true;
-            _factorCache?.Clear();
             _owner._sessionPool.Add(this);
         }
     }
-
     private static void ComputeRemainderDeltasKernel(Index1D index, ArrayView<ulong> gaps, ArrayView<byte> deltas, byte modulus)
     {
         deltas[index] = (byte)(gaps[index] % modulus);

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -54,6 +54,100 @@ public class MersenneDivisorCycles
                 return snapshot;
         }
 
+    public static bool CycleEqualsExponent(ulong divisor, ulong exponent)
+    {
+        Dictionary<ulong, FactorCacheEntry>? cache = null;
+        return CycleEqualsExponent(divisor, exponent, ref cache);
+    }
+
+    public static bool CycleEqualsExponent(ulong divisor, ulong exponent, ref Dictionary<ulong, FactorCacheEntry>? factorCache)
+    {
+        if (CycleEqualsExponentForMersenneCandidate(divisor, exponent))
+        {
+            return true;
+        }
+
+        if (exponent <= 1UL || divisor <= 1UL || (divisor & 1UL) == 0UL)
+        {
+            return false;
+        }
+
+        if (divisor <= PerfectNumberConstants.MaxQForDivisorCycles)
+        {
+            var small = Shared._smallCycles;
+            if (small is not null)
+            {
+                ulong cached = small[(int)divisor];
+                if (cached != 0UL)
+                {
+                    return cached == exponent;
+                }
+            }
+        }
+
+        if (TryCalculateCycleLengthHeuristic(divisor, out ulong heuristicCycle) && heuristicCycle != 0UL)
+        {
+            return heuristicCycle == exponent;
+        }
+
+        Dictionary<ulong, FactorCacheEntry>? cache = factorCache;
+        if (cache is null)
+        {
+            cache = new Dictionary<ulong, FactorCacheEntry>(8);
+            factorCache = cache;
+        }
+
+        if (TryCalculateCycleLengthForExponent(divisor, exponent, cache, out ulong cycleLength) && cycleLength != 0UL)
+        {
+            return cycleLength == exponent;
+        }
+
+        MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(divisor);
+        return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL;
+    }
+
+    public static bool CycleEqualsExponentForMersenneCandidate(ulong divisor, ulong exponent)
+    {
+        if (!IsValidMersenneDivisorCandidate(divisor, exponent))
+        {
+            return false;
+        }
+
+        if (divisor <= PerfectNumberConstants.MaxQForDivisorCycles)
+        {
+            MersenneDivisorCycles shared = Shared;
+            ulong[]? small = shared._smallCycles;
+            if (small is not null)
+            {
+                ulong cached = small[(int)divisor];
+                if (cached != 0UL)
+                {
+                    return cached == exponent;
+                }
+            }
+        }
+
+        MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(divisor);
+        return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL;
+    }
+
+    private static bool IsValidMersenneDivisorCandidate(ulong divisor, ulong exponent)
+    {
+        if (exponent <= 1UL || divisor <= 1UL || (divisor & 1UL) == 0UL)
+        {
+            return false;
+        }
+
+        UInt128 step = (UInt128)exponent << 1;
+        if (step == UInt128.Zero)
+        {
+            return false;
+        }
+
+        UInt128 adjusted = (UInt128)divisor - UInt128.One;
+        return adjusted % step == UInt128.Zero;
+    }
+
 	public static IEnumerable<(ulong divisor, ulong cycleLength)> EnumerateStream(Stream compressor)
 	{
 		// Binary pairs: (ulong divisor, ulong cycle)