563 lines
22 KiB
C#
563 lines
22 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.Runtime.CompilerServices;
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using PerfectNumbers.Core;
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using PerfectNumbers.Core.Gpu;
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using MontgomeryDivisorData = PerfectNumbers.Core.Gpu.MersenneNumberDivisorByDivisorGpuTester.MontgomeryDivisorData;
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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 bool _useDivisorCycles;
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private int _batchSize = 1_024;
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public bool UseDivisorCycles
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{
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get => _useDivisorCycles;
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set => _useDivisorCycles = value;
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}
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public int BatchSize
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{
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get => _batchSize;
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set => _batchSize = Math.Max(1, value);
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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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_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)
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{
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ulong allowedMax;
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bool useCycles;
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int batchCapacity;
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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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useCycles = _useDivisorCycles;
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batchCapacity = _batchSize;
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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[] divisors = ArrayPool<ulong>.Shared.Rent(batchCapacity);
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byte[] hits = ArrayPool<byte>.Shared.Rent(batchCapacity);
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MontgomeryDivisorData[] divisorData = ArrayPool<MontgomeryDivisorData>.Shared.Rent(batchCapacity);
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ulong processedCount = 0UL;
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ulong lastProcessed = 0UL;
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bool composite = false;
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bool processedAll = false;
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try
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{
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composite = CheckDivisors(
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prime,
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allowedMax,
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useCycles,
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divisors,
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hits,
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divisorData,
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out lastProcessed,
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out processedAll,
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out processedCount);
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}
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finally
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{
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ArrayPool<ulong>.Shared.Return(divisors, clearArray: false);
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ArrayPool<byte>.Shared.Return(hits, clearArray: false);
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ArrayPool<MontgomeryDivisorData>.Shared.Return(divisorData, clearArray: false);
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}
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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(lastProcessed, 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 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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bool useCycles,
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ulong[] divisors,
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byte[] hits,
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MontgomeryDivisorData[] divisorData,
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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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{
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lastProcessed = 0UL;
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processedCount = 0UL;
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processedAll = false;
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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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int batchCapacity = _batchSize;
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ulong divisor = 3UL;
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bool composite = false;
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while (divisor <= allowedMax)
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{
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int batchSize = 0;
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bool reachedEndInBatch = false;
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while (batchSize < batchCapacity && divisor <= allowedMax)
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{
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ulong currentDivisor = divisor;
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ulong nextDivisor = currentDivisor + 2UL;
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divisors[batchSize++] = currentDivisor;
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processedCount++;
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lastProcessed = currentDivisor;
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if (nextDivisor <= currentDivisor)
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{
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reachedEndInBatch = true;
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break;
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}
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if (nextDivisor > allowedMax)
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{
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divisor = nextDivisor;
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reachedEndInBatch = true;
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break;
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}
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divisor = nextDivisor;
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}
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if (batchSize == 0)
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{
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if (reachedEndInBatch)
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{
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processedAll = true;
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}
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break;
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}
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Span<MontgomeryDivisorData> divisorDataSpan = divisorData.AsSpan(0, batchSize);
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Span<ulong> divisorSpan = divisors.AsSpan(0, batchSize);
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Span<byte> hitsSpan = hits.AsSpan(0, batchSize);
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for (int i = 0; i < batchSize; i++)
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{
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divisorDataSpan[i] = CreateMontgomeryDivisorData(divisorSpan[i]);
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}
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for (int i = 0; i < batchSize; i++)
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{
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hitsSpan[i] = CheckDivisor(prime, useCycles, divisorSpan[i], divisorDataSpan[i]);
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if (hitsSpan[i] != 0)
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{
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composite = true;
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lastProcessed = divisorSpan[i];
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break;
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}
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}
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if (!composite)
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{
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lastProcessed = divisorSpan[batchSize - 1];
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}
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if (composite)
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{
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break;
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}
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if (reachedEndInBatch)
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{
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processedAll = true;
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break;
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}
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}
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processedAll = processedAll || divisor > allowedMax;
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return composite;
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}
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private static byte CheckDivisor(ulong prime, bool useCycles, ulong divisor, in MontgomeryDivisorData divisorData)
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{
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ulong modulus = divisorData.Modulus;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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return 0;
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}
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ulong exponent = prime;
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if (useCycles)
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{
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ulong cycle = MersenneDivisorCycles.CalculateCycleLength(divisor);
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if (cycle == 0UL)
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{
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return 0;
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}
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ulong remainder = prime % cycle;
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if (remainder != 0UL)
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{
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return 0;
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}
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exponent = remainder;
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}
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return exponent.Pow2MontgomeryMod(divisorData) == 1UL ? (byte)1 : (byte)0;
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}
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private void UpdateStatusUnsafe(ulong lastProcessed, 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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_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 static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
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{
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL);
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}
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return new MontgomeryDivisorData(
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modulus,
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ComputeMontgomeryNPrime(modulus),
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ComputeMontgomeryResidue(1UL, modulus),
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ComputeMontgomeryResidue(2UL, modulus));
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);
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private static ulong ComputeMontgomeryNPrime(ulong modulus)
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{
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ulong inv = modulus;
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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return unchecked(0UL - inv);
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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 ulong[] _primeBuffer;
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private int[] _positionBuffer;
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private ulong[] _exponentBuffer;
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private int _capacity;
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private bool _disposed;
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internal DivisorScanSession(MersenneNumberDivisorByDivisorCpuTester owner)
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{
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_owner = owner;
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_capacity = Math.Max(1, owner._batchSize);
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_primeBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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_exponentBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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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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}
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public void CheckDivisor(ulong divisor, 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 primesLength = primes.Length;
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if (primesLength == 0)
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{
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return;
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}
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MersenneNumberDivisorByDivisorCpuTester owner = _owner;
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int batchSize = owner._batchSize;
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EnsureCapacity(batchSize);
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ulong modulus = divisor;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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return;
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}
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bool cycleEnabled = owner._useDivisorCycles && divisorCycle != 0UL;
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ulong cycle = divisorCycle;
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MontgomeryDivisorData divisorData = CreateMontgomeryDivisorData(divisor);
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int offset = 0;
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Span<ulong> primeSpan = _primeBuffer.AsSpan();
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Span<int> positionSpan = _positionBuffer.AsSpan();
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Span<ulong> exponentSpan = _exponentBuffer.AsSpan();
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ulong previousResidue = 0UL;
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ulong previousPrime = 0UL;
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bool hasPreviousResidue = false;
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while (offset < primesLength)
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{
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int sliceLength = Math.Min(batchSize, primesLength - offset);
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ReadOnlySpan<ulong> primesSlice = primes.Slice(offset, sliceLength);
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Span<byte> hitsSlice = hits.Slice(offset, sliceLength);
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hitsSlice.Clear();
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int computeCount = 0;
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if (cycleEnabled)
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{
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for (int i = 0; i < sliceLength; i++)
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{
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ulong prime = primesSlice[i];
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if (prime % cycle != 0UL)
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{
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continue;
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}
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primeSpan[computeCount] = prime;
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positionSpan[computeCount] = i;
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computeCount++;
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}
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}
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else
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{
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for (int i = 0; i < sliceLength; i++)
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{
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primeSpan[computeCount] = primesSlice[i];
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positionSpan[computeCount] = i;
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computeCount++;
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}
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}
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if (computeCount > 0)
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{
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Span<ulong> exponentSlice = exponentSpan[..computeCount];
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ulong currentPrime = hasPreviousResidue ? previousPrime : 0UL;
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bool hasDeltaSource = hasPreviousResidue;
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for (int i = 0; i < computeCount; i++)
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{
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ulong prime = primeSpan[i];
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ulong exponentValue;
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if (hasDeltaSource)
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{
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exponentValue = prime - currentPrime;
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}
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else
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{
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exponentValue = prime;
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hasDeltaSource = true;
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}
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if (cycleEnabled)
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{
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exponentValue %= cycle;
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}
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exponentSlice[i] = exponentValue;
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currentPrime = prime;
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}
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for (int i = 0; i < computeCount; i++)
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{
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exponentSlice[i] = exponentSlice[i].Pow2MontgomeryMod(divisorData);
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}
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for (int i = 0; i < computeCount; i++)
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{
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int position = positionSpan[i];
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ulong stepResidue = exponentSlice[i];
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ulong prime = primeSpan[i];
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ulong residue = hasPreviousResidue ? MultiplyMod(previousResidue, stepResidue, modulus) : stepResidue;
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hitsSlice[position] = residue == 1UL ? (byte)1 : (byte)0;
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previousResidue = residue;
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previousPrime = prime;
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hasPreviousResidue = true;
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}
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}
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offset += sliceLength;
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}
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}
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public void Dispose()
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{
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if (_disposed)
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{
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return;
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}
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_disposed = true;
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_owner.ReturnSession(this);
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}
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private void EnsureCapacity(int requiredCapacity)
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{
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if (requiredCapacity <= _capacity)
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{
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return;
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}
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ArrayPool<ulong>.Shared.Return(_primeBuffer, clearArray: false);
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ArrayPool<int>.Shared.Return(_positionBuffer, clearArray: false);
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ArrayPool<ulong>.Shared.Return(_exponentBuffer, clearArray: false);
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_capacity = requiredCapacity;
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_primeBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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_exponentBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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}
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private static ulong MultiplyMod(ulong left, ulong right, ulong modulus)
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{
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if (modulus == 0UL)
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{
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return 0UL;
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}
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UInt128 product = (UInt128)left * right;
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return (ulong)(product % modulus);
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}
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}
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}
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