468 lines
14 KiB
C#
468 lines
14 KiB
C#
using System;
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using System.Collections.Concurrent;
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using System.Collections.Generic;
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using System.Numerics;
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using PerfectNumbers.Core;
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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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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, 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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Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
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DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
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ulong cachedModulus = 0UL;
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MontgomeryDivisorData cachedDivisorData = default;
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bool hasCachedDivisorData = false;
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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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// Keep the divisibility filters aligned with the divisor-cycle generator so the
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// CPU path never requests cycles that were skipped during cache creation.
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bool lastIsSeven = (prime & 3UL) == 3UL;
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while (divisor <= 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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iterationCounter++;
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ulong candidate = (ulong)divisor;
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processedCount++;
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lastProcessed = candidate;
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bool admissible = lastIsSeven
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? (remainder10 == 3 || remainder10 == 7 || remainder10 == 9)
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: (remainder10 == 1 || remainder10 == 3 || remainder10 == 9);
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if (admissible && (remainder8 == 1 || remainder8 == 7) && remainder3 != 0 && remainder5 != 0 && remainder7 != 0 && remainder11 != 0)
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{
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if (!hasCachedDivisorData || cachedModulus != candidate)
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{
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cachedDivisorData = MontgomeryDivisorData.FromModulus(candidate);
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cachedModulus = candidate;
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hasCachedDivisorData = true;
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}
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MontgomeryDivisorData divisorData = cachedDivisorData;
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ulong divisorCycle;
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if (candidate <= PerfectNumberConstants.MaxQForDivisorCycles)
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{
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divisorCycle = cycleCache.GetCycleLength(candidate);
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}
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else
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{
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factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
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// EvenPerfectBitScanner reaches this path only for divisors above the precomputed cycle snapshot.
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// Those candidates follow q = 2 * prime * k + 1 with prime >= 5, so the downstream order calculator
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// can rely on an odd divisor and a prime exponent when deriving the cycle length.
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if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, factorCache, out divisorCycle) || divisorCycle == 0UL)
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{
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divisorCycle = cycleCache.GetCycleLength(candidate);
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}
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}
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if (divisorCycle == prime)
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{
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// A cycle equal to the tested exponent (which is prime in this path)
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// guarantees that the candidate divides the corresponding Mersenne
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// number because the order of 2 modulo the divisor is exactly p.
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processedAll = true;
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return true;
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}
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if (divisorCycle == 0UL)
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{
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Console.WriteLine($"Divisor cycle was not calculated for {prime}");
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}
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}
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divisor += step;
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remainder10 = AddMod(remainder10, step10, (byte)10);
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remainder8 = AddMod(remainder8, step8, (byte)8);
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remainder5 = AddMod(remainder5, step5, (byte)5);
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remainder3 = AddMod(remainder3, step3, (byte)3);
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remainder7 = AddMod(remainder7, step7, (byte)7);
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remainder11 = AddMod(remainder11, step11, (byte)11);
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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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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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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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// Keep these remainder steppers in place so future updates continue reusing the previously computed residues.
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// They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors.
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var exponentStepper = new ExponentRemainderStepper(cachedData);
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if (!exponentStepper.IsValidModulus)
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{
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hits.Clear();
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return;
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}
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var cycleStepper = new CycleRemainderStepper(divisorCycle);
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ulong remainder = cycleStepper.Initialize(primes[0]);
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hits[0] = remainder == 0UL
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? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0)
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: (byte)0;
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for (int i = 1; i < length; i++)
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{
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remainder = cycleStepper.ComputeNext(primes[i]);
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if (remainder != 0UL)
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{
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hits[i] = 0;
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continue;
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}
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hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0;
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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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}
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}
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