750 lines
24 KiB
C#
750 lines
24 KiB
C#
using System;
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using System.Buffers;
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using System.Collections.Concurrent;
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using System.Numerics;
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using PerfectNumbers.Core;
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using PerfectNumbers.Core.Gpu;
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namespace PerfectNumbers.Core.Cpu;
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public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDivisorByDivisorTester
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{
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private readonly object _sync = new();
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private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
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private ulong _divisorLimit;
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private ulong _lastStatusDivisor;
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private bool _isConfigured;
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private int _batchSize = 1_024;
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private ulong _configuredMaxPrime;
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private ByDivisorDeltasDevice _deltasDevice = ByDivisorDeltasDevice.Cpu;
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public int BatchSize
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{
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get => _batchSize;
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set
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{
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int sanitized = Math.Max(1, value);
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_batchSize = sanitized;
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}
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}
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public ByDivisorDeltasDevice DeltasDevice
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{
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get => _deltasDevice;
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set
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{
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lock (_sync)
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{
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_deltasDevice = value;
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}
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}
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}
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public void ConfigureFromMaxPrime(ulong maxPrime)
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{
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lock (_sync)
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{
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_configuredMaxPrime = maxPrime;
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_divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
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_lastStatusDivisor = 0UL;
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_isConfigured = true;
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}
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}
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public ulong DivisorLimit
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{
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get
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{
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lock (_sync)
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{
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if (!_isConfigured)
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{
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throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
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}
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return _divisorLimit;
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}
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}
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}
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public ulong GetAllowedMaxDivisor(ulong prime)
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{
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lock (_sync)
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{
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if (!_isConfigured)
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{
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throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
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}
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return ComputeAllowedMaxDivisor(prime, _divisorLimit);
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}
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}
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public bool IsPrime(ulong prime, out bool divisorsExhausted, TimeSpan? timeLimit = null)
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{
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ulong allowedMax;
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lock (_sync)
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{
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if (!_isConfigured)
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{
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throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
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}
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allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
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}
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if (allowedMax < 3UL)
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{
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divisorsExhausted = true;
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return true;
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}
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ulong processedCount;
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ulong lastProcessed;
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bool processedAll;
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bool composite = CheckDivisors(
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prime,
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allowedMax,
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out lastProcessed,
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out processedAll,
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out processedCount,
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timeLimit);
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if (processedCount > 0UL)
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{
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lock (_sync)
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{
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UpdateStatusUnsafe(processedCount);
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}
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}
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if (composite)
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{
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divisorsExhausted = true;
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return false;
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}
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divisorsExhausted = processedAll || composite;
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return true;
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}
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public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
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{
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if (allowedMaxValues.Length < primes.Length)
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{
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throw new ArgumentException("allowedMaxValues span must be at least as long as primes span.", nameof(allowedMaxValues));
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}
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ulong divisorLimit;
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lock (_sync)
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{
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if (!_isConfigured)
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{
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throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
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}
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divisorLimit = _divisorLimit;
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}
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for (int index = 0; index < primes.Length; index++)
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{
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allowedMaxValues[index] = ComputeAllowedMaxDivisor(primes[index], divisorLimit);
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}
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}
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public IMersenneNumberDivisorByDivisorTester.IDivisorScanSession CreateDivisorSession()
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{
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lock (_sync)
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{
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if (!_isConfigured)
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{
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throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
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}
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if (_sessionPool.TryTake(out DivisorScanSession? session))
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{
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session.Reset();
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return session;
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}
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return new DivisorScanSession(this);
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}
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}
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private void ReturnSession(DivisorScanSession session)
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{
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_sessionPool.Add(session);
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}
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private bool CheckDivisors(
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ulong prime,
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ulong allowedMax,
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out ulong lastProcessed,
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out bool processedAll,
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out ulong processedCount,
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TimeSpan? timeLimit)
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{
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lastProcessed = 0UL;
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processedCount = 0UL;
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processedAll = false;
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PrimeTestTimeLimit limitGuard;
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if (!PrimeTestTimeLimit.TryCreate(timeLimit, out limitGuard))
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{
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return false;
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}
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bool enforceLimit = limitGuard.IsActive;
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ulong iterationCounter = 0UL;
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if (allowedMax < 3UL)
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{
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return false;
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}
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UInt128 step = (UInt128)prime << 1;
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if (step == UInt128.Zero)
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{
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processedAll = true;
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return false;
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}
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UInt128 limit = allowedMax;
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UInt128 divisor = step + UInt128.One;
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if (divisor > limit)
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{
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processedAll = true;
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return false;
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}
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int batchCapacity = Math.Max(1, _batchSize);
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DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
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int preferredCycleBatch = cycleCache.PreferredBatchSize;
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if (preferredCycleBatch > 0 && preferredCycleBatch < batchCapacity)
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{
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batchCapacity = preferredCycleBatch;
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}
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ulong[] candidateBuffer = ArrayPool<ulong>.Shared.Rent(batchCapacity);
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ulong[] cycleBuffer = ArrayPool<ulong>.Shared.Rent(batchCapacity);
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MontgomeryDivisorData[] divisorDataBuffer = ArrayPool<MontgomeryDivisorData>.Shared.Rent(batchCapacity);
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byte[] remainderBuffer = ArrayPool<byte>.Shared.Rent(batchCapacity * 6);
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Span<byte> remainder10Span = remainderBuffer.AsSpan(0, batchCapacity);
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Span<byte> remainder8Span = remainderBuffer.AsSpan(batchCapacity, batchCapacity);
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Span<byte> remainder5Span = remainderBuffer.AsSpan(batchCapacity * 2, batchCapacity);
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Span<byte> remainder3Span = remainderBuffer.AsSpan(batchCapacity * 3, batchCapacity);
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Span<byte> remainder7Span = remainderBuffer.AsSpan(batchCapacity * 4, batchCapacity);
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Span<byte> remainder11Span = remainderBuffer.AsSpan(batchCapacity * 5, batchCapacity);
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byte step10 = (byte)(step % 10UL);
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byte step8 = (byte)(step % 8UL);
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byte step5 = (byte)(step % 5UL);
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byte step3 = (byte)(step % 3UL);
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byte step7 = (byte)(step % 7UL);
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byte step11 = (byte)(step % 11UL);
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byte remainder10 = (byte)(divisor % 10UL);
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byte remainder8 = (byte)(divisor % 8UL);
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byte remainder5 = (byte)(divisor % 5UL);
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byte remainder3 = (byte)(divisor % 3UL);
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byte remainder7 = (byte)(divisor % 7UL);
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byte remainder11 = (byte)(divisor % 11UL);
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bool lastIsSeven = (prime & 3UL) == 3UL;
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try
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{
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while (divisor <= limit)
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{
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Span<ulong> candidateSpan = candidateBuffer.AsSpan(0, batchCapacity);
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int chunkCount = 0;
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UInt128 localDivisor = divisor;
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byte localRemainder10 = remainder10;
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byte localRemainder8 = remainder8;
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byte localRemainder5 = remainder5;
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byte localRemainder3 = remainder3;
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byte localRemainder7 = remainder7;
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byte localRemainder11 = remainder11;
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while (chunkCount < batchCapacity && localDivisor <= limit)
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{
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if (enforceLimit && (iterationCounter == 0UL || (iterationCounter & 63UL) == 0UL) && limitGuard.HasExpired())
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{
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processedAll = false;
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return false;
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}
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ulong candidate = (ulong)localDivisor;
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candidateSpan[chunkCount] = candidate;
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remainder10Span[chunkCount] = localRemainder10;
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remainder8Span[chunkCount] = localRemainder8;
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remainder5Span[chunkCount] = localRemainder5;
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remainder3Span[chunkCount] = localRemainder3;
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remainder7Span[chunkCount] = localRemainder7;
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remainder11Span[chunkCount] = localRemainder11;
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processedCount++;
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lastProcessed = candidate;
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iterationCounter++;
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chunkCount++;
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localDivisor += step;
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localRemainder10 = AddMod(localRemainder10, step10, (byte)10);
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localRemainder8 = AddMod(localRemainder8, step8, (byte)8);
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localRemainder5 = AddMod(localRemainder5, step5, (byte)5);
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localRemainder3 = AddMod(localRemainder3, step3, (byte)3);
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localRemainder7 = AddMod(localRemainder7, step7, (byte)7);
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localRemainder11 = AddMod(localRemainder11, step11, (byte)11);
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}
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if (chunkCount == 0)
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{
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break;
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}
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divisor = localDivisor;
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remainder10 = localRemainder10;
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remainder8 = localRemainder8;
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remainder5 = localRemainder5;
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remainder3 = localRemainder3;
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remainder7 = localRemainder7;
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remainder11 = localRemainder11;
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// Reuse the candidate buffer in-place so the filtered results stay contiguous without additional arrays.
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Span<ulong> chunkCandidates = candidateSpan[..chunkCount];
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int filteredCount = 0;
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for (int i = 0; i < chunkCount; i++)
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{
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bool admissible = lastIsSeven
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? (remainder10Span[i] == 3 || remainder10Span[i] == 7 || remainder10Span[i] == 9)
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: (remainder10Span[i] == 1 || remainder10Span[i] == 3 || remainder10Span[i] == 9);
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if (!admissible)
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{
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continue;
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}
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if ((remainder8Span[i] != 1 && remainder8Span[i] != 7)
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|| remainder3Span[i] == 0
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|| remainder5Span[i] == 0
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|| remainder7Span[i] == 0
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|| remainder11Span[i] == 0)
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{
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continue;
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}
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// Store the accepted candidate at the next free slot so the front of the span becomes the filtered set.
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chunkCandidates[filteredCount++] = chunkCandidates[i];
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}
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if (filteredCount == 0)
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{
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continue;
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}
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Span<ulong> filteredSpan = chunkCandidates[..filteredCount];
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Span<ulong> cycleSpan = cycleBuffer.AsSpan(0, filteredCount);
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cycleCache.GetCycleLengths(filteredSpan, cycleSpan);
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int admissibleCount = 0;
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Span<MontgomeryDivisorData> divisorDataSpan = divisorDataBuffer.AsSpan(0, filteredCount);
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for (int i = 0; i < filteredCount; i++)
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{
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if (cycleSpan[i] != prime)
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{
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continue;
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}
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ulong candidate = filteredSpan[i];
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// Reuse the filtered span's leading segment to accumulate the admissible divisors for Montgomery checks.
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filteredSpan[admissibleCount] = candidate;
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divisorDataSpan[admissibleCount] = MontgomeryDivisorData.FromModulus(candidate);
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admissibleCount++;
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}
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if (admissibleCount == 0)
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{
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continue;
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}
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Span<ulong> admissibleSpan = filteredSpan[..admissibleCount];
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Span<MontgomeryDivisorData> admissibleDataSpan = divisorDataSpan[..admissibleCount];
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for (int i = 0; i < admissibleCount; i++)
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{
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if (CheckDivisor(prime, prime, in admissibleDataSpan[i]) != 0)
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{
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lastProcessed = admissibleSpan[i];
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processedAll = true;
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return true;
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}
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}
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}
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}
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finally
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{
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ArrayPool<ulong>.Shared.Return(candidateBuffer, clearArray: false);
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ArrayPool<ulong>.Shared.Return(cycleBuffer, clearArray: false);
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ArrayPool<MontgomeryDivisorData>.Shared.Return(divisorDataBuffer, clearArray: false);
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ArrayPool<byte>.Shared.Return(remainderBuffer, clearArray: false);
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}
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processedAll = divisor > limit;
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return false;
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}
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private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
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{
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ulong residue = prime.Pow2MontgomeryModWithCycleCpu(divisorCycle, divisorData);
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return residue == 1UL ? (byte)1 : (byte)0;
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}
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private static byte AddMod(byte value, byte delta, byte modulus)
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{
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int sum = value + delta;
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if (sum >= modulus)
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{
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sum -= modulus;
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}
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return (byte)sum;
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}
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private void UpdateStatusUnsafe(ulong processedCount)
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{
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if (processedCount == 0UL)
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{
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return;
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}
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ulong interval = PerfectNumberConstants.ConsoleInterval;
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if (interval == 0UL)
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{
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_lastStatusDivisor = 0UL;
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return;
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}
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ulong total = _lastStatusDivisor + processedCount;
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// TODO: Replace this modulo with the ring-buffer style counter (subtract loop) used in the fast CLI
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// status benchmarks so we avoid `%` in this hot loop while still wrapping progress correctly.
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_lastStatusDivisor = total % interval;
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}
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private static ulong ComputeDivisorLimitFromMaxPrime(ulong maxPrime)
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{
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if (maxPrime <= 1UL)
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{
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return 0UL;
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}
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if (maxPrime - 1UL >= 64UL)
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{
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return ulong.MaxValue;
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}
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return (1UL << (int)(maxPrime - 1UL)) - 1UL;
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}
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private static ulong ComputeAllowedMaxDivisor(ulong prime, ulong divisorLimit)
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{
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if (prime <= 1UL)
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{
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return 0UL;
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}
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if (prime - 1UL >= 64UL)
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{
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return divisorLimit;
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}
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return Math.Min((1UL << (int)(prime - 1UL)) - 1UL, divisorLimit);
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}
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private sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
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{
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private readonly MersenneNumberDivisorByDivisorCpuTester _owner;
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private bool _disposed;
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private bool _hasCachedDivisorData;
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private ulong _cachedDivisor;
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private MontgomeryDivisorData _cachedDivisorData;
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private ulong[]? _primeDeltas;
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private ulong[]? _cycleRemainders;
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private ulong[]? _montgomeryDeltas;
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private int _bufferCapacity;
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private MersenneNumberDivisorResidueGpuEvaluator? _gpuResidueEvaluator;
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internal DivisorScanSession(MersenneNumberDivisorByDivisorCpuTester owner)
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{
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_owner = owner;
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}
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internal void Reset()
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{
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_disposed = false;
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_hasCachedDivisorData = false;
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_cachedDivisor = 0UL;
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_cachedDivisorData = default;
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}
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public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
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{
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if (_disposed)
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{
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throw new ObjectDisposedException(nameof(DivisorScanSession));
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}
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int length = primes.Length;
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if (length == 0)
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{
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return;
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}
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MontgomeryDivisorData cachedData = divisorData;
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if (cachedData.Modulus != divisor)
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{
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if (!_hasCachedDivisorData || _cachedDivisor != divisor)
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{
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_cachedDivisorData = MontgomeryDivisorData.FromModulus(divisor);
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_cachedDivisor = divisor;
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_hasCachedDivisorData = true;
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}
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cachedData = _cachedDivisorData;
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}
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ulong modulus = cachedData.Modulus;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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hits.Clear();
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return;
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}
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if (divisorCycle == 0UL)
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{
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divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
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if (divisorCycle == 0UL)
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{
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hits.Clear();
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return;
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}
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}
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EnsureCapacity(length);
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Span<ulong> deltaSpan = _primeDeltas!.AsSpan(0, length);
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ComputePrimeDeltas(primes, deltaSpan);
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Span<ulong> remainderSpan = _cycleRemainders!.AsSpan(0, length);
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ComputeCycleRemainders(divisorCycle, primes, deltaSpan, remainderSpan);
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ulong montgomeryOne = cachedData.MontgomeryOne;
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if (_owner._deltasDevice == ByDivisorDeltasDevice.Gpu)
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{
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EnsureGpuEvaluator();
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Span<ulong> residueSpan = _montgomeryDeltas!.AsSpan(0, length);
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// Reuse the Montgomery delta buffer to hold the final residues returned by the GPU evaluator.
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_gpuResidueEvaluator!.ComputeResidues(primes, cachedData, residueSpan);
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for (int i = 0; i < length; i++)
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{
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hits[i] = remainderSpan[i] == 0UL && residueSpan[i] == montgomeryOne ? (byte)1 : (byte)0;
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}
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return;
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}
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Span<ulong> montgomerySpan = _montgomeryDeltas!.AsSpan(0, length);
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ComputeMontgomeryDeltas(cachedData, primes, deltaSpan, montgomerySpan);
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ulong nPrime = cachedData.NPrime;
|
|
ulong currentMontgomery = montgomerySpan[0];
|
|
|
|
hits[0] = remainderSpan[0] == 0UL && currentMontgomery == montgomeryOne ? (byte)1 : (byte)0;
|
|
|
|
for (int i = 1; i < length; i++)
|
|
{
|
|
currentMontgomery = currentMontgomery.MontgomeryMultiply(montgomerySpan[i], modulus, nPrime);
|
|
hits[i] = remainderSpan[i] == 0UL && currentMontgomery == montgomeryOne ? (byte)1 : (byte)0;
|
|
}
|
|
}
|
|
|
|
private void EnsureGpuEvaluator()
|
|
{
|
|
if (_gpuResidueEvaluator is null)
|
|
{
|
|
_gpuResidueEvaluator = new MersenneNumberDivisorResidueGpuEvaluator(_owner._batchSize);
|
|
}
|
|
}
|
|
|
|
private void ReleaseGpuEvaluator()
|
|
{
|
|
if (_gpuResidueEvaluator is null)
|
|
{
|
|
return;
|
|
}
|
|
|
|
_gpuResidueEvaluator.Dispose();
|
|
_gpuResidueEvaluator = null;
|
|
}
|
|
|
|
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)
|
|
{
|
|
throw new ArgumentOutOfRangeException(nameof(primes), "Primes must be strictly increasing.");
|
|
}
|
|
|
|
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)
|
|
{
|
|
return;
|
|
}
|
|
|
|
_disposed = true;
|
|
ReleaseGpuEvaluator();
|
|
_owner.ReturnSession(this);
|
|
}
|
|
}
|
|
}
|
|
|
|
|