Batch CPU divisor scanning across reusable buffers

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -1,6 +1,6 @@
 using System;
+using System.Buffers;
 using System.Collections.Concurrent;
-using System.Collections.Generic;
 using System.Numerics;
 using PerfectNumbers.Core;
 
@@ -200,12 +200,25 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             return false;
         }
 
-        Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
+        int batchCapacity = Math.Max(1, _batchSize);
         DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
+        int preferredCycleBatch = cycleCache.PreferredBatchSize;
+        if (preferredCycleBatch > 0 && preferredCycleBatch < batchCapacity)
+        {
+            batchCapacity = preferredCycleBatch;
+        }
 
-        ulong cachedModulus = 0UL;
+        ulong[] candidateBuffer = ArrayPool<ulong>.Shared.Rent(batchCapacity);
-        MontgomeryDivisorData cachedDivisorData = default;
+        ulong[] cycleBuffer = ArrayPool<ulong>.Shared.Rent(batchCapacity);
-        bool hasCachedDivisorData = false;
+        MontgomeryDivisorData[] divisorDataBuffer = ArrayPool<MontgomeryDivisorData>.Shared.Rent(batchCapacity);
+        byte[] remainderBuffer = ArrayPool<byte>.Shared.Rent(batchCapacity * 6);
+
+        Span<byte> remainder10Span = remainderBuffer.AsSpan(0, batchCapacity);
+        Span<byte> remainder8Span = remainderBuffer.AsSpan(batchCapacity, batchCapacity);
+        Span<byte> remainder5Span = remainderBuffer.AsSpan(batchCapacity * 2, batchCapacity);
+        Span<byte> remainder3Span = remainderBuffer.AsSpan(batchCapacity * 3, batchCapacity);
+        Span<byte> remainder7Span = remainderBuffer.AsSpan(batchCapacity * 4, batchCapacity);
+        Span<byte> remainder11Span = remainderBuffer.AsSpan(batchCapacity * 5, batchCapacity);
 
         byte step10 = (byte)(step % 10UL);
         byte step8 = (byte)(step % 8UL);
@@ -221,83 +234,151 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         byte remainder7 = (byte)(divisor % 7UL);
         byte remainder11 = (byte)(divisor % 11UL);
 
-        // Keep the divisibility filters aligned with the divisor-cycle generator so the
-        // CPU path never requests cycles that were skipped during cache creation.
         bool lastIsSeven = (prime & 3UL) == 3UL;
 
-        while (divisor <= limit)
+        try
         {
-            if (enforceLimit && (iterationCounter == 0UL || (iterationCounter & 63UL) == 0UL) && limitGuard.HasExpired())
+            while (divisor <= limit)
             {
-                processedAll = false;
+                Span<ulong> candidateSpan = candidateBuffer.AsSpan(0, batchCapacity);
-                return false;
+                int chunkCount = 0;
-            }
+                UInt128 localDivisor = divisor;
 
-            iterationCounter++;
+                byte localRemainder10 = remainder10;
-            ulong candidate = (ulong)divisor;
+                byte localRemainder8 = remainder8;
-            processedCount++;
+                byte localRemainder5 = remainder5;
-            lastProcessed = candidate;
+                byte localRemainder3 = remainder3;
+                byte localRemainder7 = remainder7;
+                byte localRemainder11 = remainder11;
 
-            bool admissible = lastIsSeven
+                while (chunkCount < batchCapacity && localDivisor <= limit)
-                ? (remainder10 == 3 || remainder10 == 7 || remainder10 == 9)
-                : (remainder10 == 1 || remainder10 == 3 || remainder10 == 9);
-
-            if (admissible && (remainder8 == 1 || remainder8 == 7) && remainder3 != 0 && remainder5 != 0 && remainder7 != 0 && remainder11 != 0)
-            {
-                if (!hasCachedDivisorData || cachedModulus != candidate)
                 {
-                    cachedDivisorData = MontgomeryDivisorData.FromModulus(candidate);
+                    if (enforceLimit && (iterationCounter == 0UL || (iterationCounter & 63UL) == 0UL) && limitGuard.HasExpired())
-                    cachedModulus = candidate;
-                    hasCachedDivisorData = true;
-                }
-
-                MontgomeryDivisorData divisorData = cachedDivisorData;
-                ulong divisorCycle;
-
-                if (candidate <= PerfectNumberConstants.MaxQForDivisorCycles)
-                {
-                    divisorCycle = cycleCache.GetCycleLength(candidate);
-                }
-                else
-                {
-                    factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
-                    // EvenPerfectBitScanner reaches this path only for divisors above the precomputed cycle snapshot.
-                    // Those candidates follow q = 2 * prime * k + 1 with prime >= 5, so the downstream order calculator
-                    // can rely on an odd divisor and a prime exponent when deriving the cycle length.
-                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, factorCache, out divisorCycle) || divisorCycle == 0UL)
                     {
-                        divisorCycle = cycleCache.GetCycleLength(candidate);
+                        processedAll = false;
+                        return false;
+                    }
+
+                    ulong candidate = (ulong)localDivisor;
+                    candidateSpan[chunkCount] = candidate;
+                    remainder10Span[chunkCount] = localRemainder10;
+                    remainder8Span[chunkCount] = localRemainder8;
+                    remainder5Span[chunkCount] = localRemainder5;
+                    remainder3Span[chunkCount] = localRemainder3;
+                    remainder7Span[chunkCount] = localRemainder7;
+                    remainder11Span[chunkCount] = localRemainder11;
+
+                    processedCount++;
+                    lastProcessed = candidate;
+                    iterationCounter++;
+                    chunkCount++;
+
+                    localDivisor += step;
+                    localRemainder10 = AddMod(localRemainder10, step10, (byte)10);
+                    localRemainder8 = AddMod(localRemainder8, step8, (byte)8);
+                    localRemainder5 = AddMod(localRemainder5, step5, (byte)5);
+                    localRemainder3 = AddMod(localRemainder3, step3, (byte)3);
+                    localRemainder7 = AddMod(localRemainder7, step7, (byte)7);
+                    localRemainder11 = AddMod(localRemainder11, step11, (byte)11);
+                }
+
+                if (chunkCount == 0)
+                {
+                    break;
+                }
+
+                divisor = localDivisor;
+                remainder10 = localRemainder10;
+                remainder8 = localRemainder8;
+                remainder5 = localRemainder5;
+                remainder3 = localRemainder3;
+                remainder7 = localRemainder7;
+                remainder11 = localRemainder11;
+
+                // Reuse the candidate buffer in-place so the filtered results stay contiguous without additional arrays.
+                Span<ulong> chunkCandidates = candidateSpan[..chunkCount];
+                int filteredCount = 0;
+
+                for (int i = 0; i < chunkCount; i++)
+                {
+                    bool admissible = lastIsSeven
+                        ? (remainder10Span[i] == 3 || remainder10Span[i] == 7 || remainder10Span[i] == 9)
+                        : (remainder10Span[i] == 1 || remainder10Span[i] == 3 || remainder10Span[i] == 9);
+
+                    if (!admissible)
+                    {
+                        continue;
+                    }
+
+                    if ((remainder8Span[i] != 1 && remainder8Span[i] != 7)
+                        || remainder3Span[i] == 0
+                        || remainder5Span[i] == 0
+                        || remainder7Span[i] == 0
+                        || remainder11Span[i] == 0)
+                    {
+                        continue;
+                    }
+
+                    // Store the accepted candidate at the next free slot so the front of the span becomes the filtered set.
+                    chunkCandidates[filteredCount++] = chunkCandidates[i];
+                }
+
+                if (filteredCount == 0)
+                {
+                    continue;
+                }
+
+                Span<ulong> filteredSpan = chunkCandidates[..filteredCount];
+                Span<ulong> cycleSpan = cycleBuffer.AsSpan(0, filteredCount);
+                cycleCache.GetCycleLengths(filteredSpan, cycleSpan);
+
+                int admissibleCount = 0;
+                Span<MontgomeryDivisorData> divisorDataSpan = divisorDataBuffer.AsSpan(0, filteredCount);
+
+                for (int i = 0; i < filteredCount; i++)
+                {
+                    if (cycleSpan[i] != prime)
+                    {
+                        continue;
+                    }
+
+                    ulong candidate = filteredSpan[i];
+                    // Reuse the filtered span's leading segment to accumulate the admissible divisors for Montgomery checks.
+                    filteredSpan[admissibleCount] = candidate;
+                    divisorDataSpan[admissibleCount] = MontgomeryDivisorData.FromModulus(candidate);
+                    admissibleCount++;
+                }
+
+                if (admissibleCount == 0)
+                {
+                    continue;
+                }
+
+                Span<ulong> admissibleSpan = filteredSpan[..admissibleCount];
+                Span<MontgomeryDivisorData> admissibleDataSpan = divisorDataSpan[..admissibleCount];
+
+                for (int i = 0; i < admissibleCount; i++)
+                {
+                    if (CheckDivisor(prime, prime, in admissibleDataSpan[i]) != 0)
+                    {
+                        lastProcessed = admissibleSpan[i];
+                        processedAll = true;
+                        return true;
                     }
                 }
-
-                if (divisorCycle == prime)
-                {
-                    // A cycle equal to the tested exponent (which is prime in this path)
-                    // guarantees that the candidate divides the corresponding Mersenne
-                    // number because the order of 2 modulo the divisor is exactly p.
-                    processedAll = true;
-                    return true;
-                }
-
-                if (divisorCycle == 0UL)
-                {
-                    Console.WriteLine($"Divisor cycle was not calculated for {prime}");
-                }
             }
-
+        }
-            divisor += step;
+        finally
-            remainder10 = AddMod(remainder10, step10, (byte)10);
+        {
-            remainder8 = AddMod(remainder8, step8, (byte)8);
+            ArrayPool<ulong>.Shared.Return(candidateBuffer, clearArray: false);
-            remainder5 = AddMod(remainder5, step5, (byte)5);
+            ArrayPool<ulong>.Shared.Return(cycleBuffer, clearArray: false);
-            remainder3 = AddMod(remainder3, step3, (byte)3);
+            ArrayPool<MontgomeryDivisorData>.Shared.Return(divisorDataBuffer, clearArray: false);
-            remainder7 = AddMod(remainder7, step7, (byte)7);
+            ArrayPool<byte>.Shared.Return(remainderBuffer, clearArray: false);
-            remainder11 = AddMod(remainder11, step11, (byte)11);
         }
 
         processedAll = divisor > limit;
         return false;
     }
-
     private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
     {
         ulong residue = prime.Pow2MontgomeryModWithCycleCpu(divisorCycle, divisorData);
@@ -372,6 +453,10 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         private bool _hasCachedDivisorData;
         private ulong _cachedDivisor;
         private MontgomeryDivisorData _cachedDivisorData;
+        private ulong[]? _primeDeltas;
+        private ulong[]? _cycleRemainders;
+        private ulong[]? _montgomeryDeltas;
+        private int _bufferCapacity;
 
         internal DivisorScanSession(MersenneNumberDivisorByDivisorCpuTester owner)
         {
@@ -412,6 +497,13 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                 cachedData = _cachedDivisorData;
             }
 
+            ulong modulus = cachedData.Modulus;
+            if (modulus <= 1UL || (modulus & 1UL) == 0UL)
+            {
+                hits.Clear();
+                return;
+            }
+
             if (divisorCycle == 0UL)
             {
                 divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
@@ -422,35 +514,167 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                 }
             }
 
-            // Keep these remainder steppers in place so future updates continue reusing the previously computed residues.
+            EnsureCapacity(length);
-            // They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors.
-            var exponentStepper = new ExponentRemainderStepper(cachedData);
-            if (!exponentStepper.IsValidModulus)
-            {
-                hits.Clear();
-                return;
-            }
 
-            var cycleStepper = new CycleRemainderStepper(divisorCycle);
+            Span<ulong> deltaSpan = _primeDeltas!.AsSpan(0, length);
+            ComputePrimeDeltas(primes, deltaSpan);
 
-            ulong remainder = cycleStepper.Initialize(primes[0]);
+            Span<ulong> remainderSpan = _cycleRemainders!.AsSpan(0, length);
-            hits[0] = remainder == 0UL
+            ComputeCycleRemainders(divisorCycle, primes, deltaSpan, remainderSpan);
-                ? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0)
+
-                : (byte)0;
+            Span<ulong> montgomerySpan = _montgomeryDeltas!.AsSpan(0, length);
+            ComputeMontgomeryDeltas(cachedData, primes, deltaSpan, montgomerySpan);
+
+            ulong nPrime = cachedData.NPrime;
+            ulong montgomeryOne = cachedData.MontgomeryOne;
+            ulong currentMontgomery = montgomerySpan[0];
+
+            hits[0] = remainderSpan[0] == 0UL && currentMontgomery == montgomeryOne ? (byte)1 : (byte)0;
 
             for (int i = 1; i < length; i++)
             {
-                remainder = cycleStepper.ComputeNext(primes[i]);
+                currentMontgomery = currentMontgomery.MontgomeryMultiply(montgomerySpan[i], modulus, nPrime);
-                if (remainder != 0UL)
+                hits[i] = remainderSpan[i] == 0UL && currentMontgomery == montgomeryOne ? (byte)1 : (byte)0;
+            }
+        }
+
+        private void EnsureCapacity(int requiredLength)
+        {
+            if (requiredLength <= 0)
+            {
+                return;
+            }
+
+            if (requiredLength <= _bufferCapacity && _primeDeltas is not null && _cycleRemainders is not null && _montgomeryDeltas is not null)
+            {
+                return;
+            }
+
+            int newCapacity = _bufferCapacity;
+            if (newCapacity == 0)
+            {
+                newCapacity = 1;
+            }
+
+            while (newCapacity < requiredLength)
+            {
+                newCapacity <<= 1;
+            }
+
+            ReturnBuffers();
+
+            _primeDeltas = ArrayPool<ulong>.Shared.Rent(newCapacity);
+            _cycleRemainders = ArrayPool<ulong>.Shared.Rent(newCapacity);
+            _montgomeryDeltas = ArrayPool<ulong>.Shared.Rent(newCapacity);
+            _bufferCapacity = newCapacity;
+        }
+
+        private void ReturnBuffers()
+        {
+            if (_primeDeltas is not null)
+            {
+                ArrayPool<ulong>.Shared.Return(_primeDeltas, clearArray: false);
+                _primeDeltas = null;
+            }
+
+            if (_cycleRemainders is not null)
+            {
+                ArrayPool<ulong>.Shared.Return(_cycleRemainders, clearArray: false);
+                _cycleRemainders = null;
+            }
+
+            if (_montgomeryDeltas is not null)
+            {
+                ArrayPool<ulong>.Shared.Return(_montgomeryDeltas, clearArray: false);
+                _montgomeryDeltas = null;
+            }
+
+            _bufferCapacity = 0;
+        }
+
+        private static void ComputePrimeDeltas(ReadOnlySpan<ulong> primes, Span<ulong> deltas)
+        {
+            if (primes.Length == 0)
+            {
+                return;
+            }
+
+            ulong previous = primes[0];
+            deltas[0] = previous;
+
+            for (int i = 1; i < primes.Length; i++)
+            {
+                ulong current = primes[i];
+                if (current <= previous)
                 {
-                    hits[i] = 0;
+                    throw new ArgumentOutOfRangeException(nameof(primes), "Primes must be strictly increasing.");
-                    continue;
                 }
 
-                hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0;
+                deltas[i] = current - previous;
+                previous = current;
             }
         }
 
+        private static void ComputeCycleRemainders(ulong cycleLength, ReadOnlySpan<ulong> primes, ReadOnlySpan<ulong> deltas, Span<ulong> remainders)
+        {
+            if (cycleLength == 0UL || primes.Length == 0)
+            {
+                remainders.Clear();
+                return;
+            }
+
+            ulong remainder = primes[0] % cycleLength;
+            remainders[0] = remainder;
+
+            for (int i = 1; i < primes.Length; i++)
+            {
+                remainder = AddMod(remainder, deltas[i], cycleLength);
+                remainders[i] = remainder;
+            }
+        }
+
+        private static void ComputeMontgomeryDeltas(in MontgomeryDivisorData divisorData, ReadOnlySpan<ulong> primes, ReadOnlySpan<ulong> deltas, Span<ulong> montgomeryValues)
+        {
+            if (primes.Length == 0)
+            {
+                montgomeryValues.Clear();
+                return;
+            }
+
+            montgomeryValues[0] = primes[0].Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: true);
+
+            for (int i = 1; i < primes.Length; i++)
+            {
+                montgomeryValues[i] = deltas[i].Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: true);
+            }
+        }
+
+        private static ulong AddMod(ulong value, ulong delta, ulong modulus)
+        {
+            if (modulus == 0UL)
+            {
+                return 0UL;
+            }
+
+            if (ulong.MaxValue - value < delta)
+            {
+                UInt128 extended = (UInt128)value + delta;
+                return (ulong)(extended % modulus);
+            }
+
+            ulong sum = value + delta;
+            if (sum >= modulus)
+            {
+                sum -= modulus;
+                if (sum >= modulus)
+                {
+                    sum %= modulus;
+                }
+            }
+
+            return sum;
+        }
+
         public void Dispose()
         {
             if (_disposed)