using System.Collections.Concurrent; using System.Runtime.CompilerServices; namespace PerfectNumbers.Core.Cpu; public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDivisorByDivisorTester { private readonly object _sync = new(); private readonly ConcurrentBag _sessionPool = []; private ulong _divisorLimit; private ulong _lastStatusDivisor; private int _batchSize = 1_024; public int BatchSize { get => _batchSize; set => _batchSize = Math.Max(1, value); } public void ConfigureFromMaxPrime(ulong maxPrime) { _divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime); _lastStatusDivisor = 0UL; } public ulong DivisorLimit { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { return _divisorLimit; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public ulong GetAllowedMaxDivisor(ulong prime) => ComputeAllowedMaxDivisor(prime, _divisorLimit); public bool IsPrime(ulong prime, out bool divisorsExhausted) { ulong allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit); if (allowedMax < 3UL) { divisorsExhausted = true; return true; } ulong processedCount; bool processedAll; bool composite = CheckDivisors( prime, allowedMax, out processedAll, out processedCount); if (processedCount > 0UL) { lock (_sync) { UpdateStatusUnsafe(processedCount); } } if (composite) { divisorsExhausted = true; return false; } divisorsExhausted = processedAll || composite; return true; } public void PrepareCandidates(in ReadOnlySpan primes, Span allowedMaxValues) { ulong divisorLimit = _divisorLimit; int length = primes.Length; for (int index = 0; index < length; index++) { allowedMaxValues[index] = ComputeAllowedMaxDivisor(primes[index], divisorLimit); } } public IMersenneNumberDivisorByDivisorTester.IDivisorScanSession CreateDivisorSession() { if (_sessionPool.TryTake(out DivisorScanSession? session)) { session.Reset(); return session; } return new DivisorScanSession(this); } private void ReturnSession(DivisorScanSession session) { _sessionPool.Add(session); } private bool CheckDivisors( ulong prime, ulong allowedMax, out bool processedAll, out ulong processedCount) { processedCount = 0UL; processedAll = false; if (allowedMax < 3UL) { return false; } UInt128 step = (UInt128)prime << 1; if (step == UInt128.Zero) { processedAll = true; return false; } UInt128 limit = allowedMax; UInt128 divisor = step + UInt128.One; if (divisor > limit) { processedAll = true; return false; } Dictionary? factorCache = null; DivisorCycleCache cycleCache = DivisorCycleCache.Shared; byte step10 = (byte)(step % 10UL); byte step8 = (byte)(step % 8UL); byte step5 = (byte)(step % 5UL); byte step3 = (byte)(step % 3UL); byte step7 = (byte)(step % 7UL); byte step11 = (byte)(step % 11UL); byte remainder10 = (byte)(divisor % 10UL); byte remainder8 = (byte)(divisor % 8UL); byte remainder5 = (byte)(divisor % 5UL); byte remainder3 = (byte)(divisor % 3UL); byte remainder7 = (byte)(divisor % 7UL); byte remainder11 = (byte)(divisor % 11UL); // 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) { ulong candidate = (ulong)divisor; processedCount++; bool admissible = lastIsSeven ? (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) { MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(candidate); ulong divisorCycle; if (candidate <= PerfectNumberConstants.MaxQForDivisorCycles) { divisorCycle = cycleCache.GetCycleLength(candidate); } else { factorCache ??= new Dictionary(8); if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, factorCache, out divisorCycle) || divisorCycle == 0UL) { divisorCycle = cycleCache.GetCycleLength(candidate); } } 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; remainder10 = AddMod(remainder10, step10, (byte)10); remainder8 = AddMod(remainder8, step8, (byte)8); remainder5 = AddMod(remainder5, step5, (byte)5); remainder3 = AddMod(remainder3, step3, (byte)3); remainder7 = AddMod(remainder7, step7, (byte)7); 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); return residue == 1UL ? (byte)1 : (byte)0; } private static byte AddMod(byte value, byte delta, byte modulus) { int sum = value + delta; if (sum >= modulus) { sum -= modulus; } return (byte)sum; } private void UpdateStatusUnsafe(ulong processedCount) { if (processedCount == 0UL) { return; } ulong interval = PerfectNumberConstants.ConsoleInterval; if (interval == 0UL) { _lastStatusDivisor = 0UL; return; } ulong total = _lastStatusDivisor + processedCount; // TODO: Replace this modulo with the ring-buffer style counter (subtract loop) used in the fast CLI // status benchmarks so we avoid `%` in this hot loop while still wrapping progress correctly. _lastStatusDivisor = total % interval; } private static ulong ComputeDivisorLimitFromMaxPrime(ulong maxPrime) { if (maxPrime <= 1UL) { return 0UL; } if (maxPrime - 1UL >= 64UL) { return ulong.MaxValue; } return (1UL << (int)(maxPrime - 1UL)) - 1UL; } private static ulong ComputeAllowedMaxDivisor(ulong prime, ulong divisorLimit) { if (prime <= 1UL) { return 0UL; } if (prime - 1UL >= 64UL) { return divisorLimit; } return Math.Min((1UL << (int)(prime - 1UL)) - 1UL, divisorLimit); } private sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession { private readonly MersenneNumberDivisorByDivisorCpuTester _owner; private bool _disposed; internal DivisorScanSession(MersenneNumberDivisorByDivisorCpuTester owner) { _owner = owner; } internal void Reset() { _disposed = false; } public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan primes, Span hits) { int length = primes.Length; if (length == 0) { return; } MontgomeryDivisorData cachedData = divisorData; if (cachedData.Modulus != divisor) { cachedData = MontgomeryDivisorDataCache.Get(divisor); } if (divisorCycle == 0UL) { divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor); if (divisorCycle == 0UL) { hits.Clear(); return; } } // Keep these remainder steppers in place so future updates continue reusing the previously computed residues. // They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors. var exponentStepper = new ExponentRemainderStepper(cachedData); if (!exponentStepper.IsValidModulus) { hits.Clear(); return; } var cycleStepper = new CycleRemainderStepper(divisorCycle); ulong remainder = cycleStepper.Initialize(primes[0]); hits[0] = remainder == 0UL ? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0) : (byte)0; for (int i = 1; i < length; i++) { remainder = cycleStepper.ComputeNext(primes[i]); if (remainder != 0UL) { hits[i] = 0; continue; } hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0; } } public void Dispose() { if (_disposed) { return; } _disposed = true; _owner.ReturnSession(this); } } }