405 lines
12 KiB
C#
405 lines
12 KiB
C#
using System;
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using System.Runtime.CompilerServices;
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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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[ThreadStatic]
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private static DivisorScanSession? _threadLocalSession; // The nested session type stays private, so pool it here.
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private ulong _divisorLimit;
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private ulong _lastStatusDivisor;
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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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_divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
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_lastStatusDivisor = 0UL;
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}
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public ulong DivisorLimit
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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get
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{
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return _divisorLimit;
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public ulong GetAllowedMaxDivisor(ulong prime) => ComputeAllowedMaxDivisor(prime, _divisorLimit);
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public bool IsPrime(ulong prime, out bool divisorsExhausted)
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{
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ulong allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
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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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bool processedAll;
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bool composite = CheckDivisors(
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prime,
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allowedMax,
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out processedAll,
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out processedCount);
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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(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
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{
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ulong divisorLimit = _divisorLimit;
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int length = primes.Length;
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for (int index = 0; index < 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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DivisorScanSession? session = _threadLocalSession;
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if (session is not null)
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{
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_threadLocalSession = null;
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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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private void ReturnSession(DivisorScanSession session)
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{
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_threadLocalSession = session;
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}
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private struct FactorCacheLease
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{
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private Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? _cache;
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public void EnsureInitialized(ref Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache)
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{
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Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? current = cache;
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if (current is null)
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{
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current = ThreadStaticPools.RentMersenneFactorCacheDictionary();
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cache = current;
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}
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_cache = current;
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}
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public void Dispose()
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{
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Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache = _cache;
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if (cache is null)
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{
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return;
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}
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ThreadStaticPools.ReturnMersenneFactorCacheDictionary(cache);
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_cache = null;
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}
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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 bool processedAll,
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out ulong processedCount)
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{
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processedCount = 0UL;
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processedAll = false;
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// The EvenPerfectBitScanner feeds primes >= 138,000,000 here, so allowedMax >= 3 in production runs.
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// Keeping the guard commented out documents the reasoning for benchmarks and tests.
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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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// The EvenPerfectBitScanner advances primes far below the overflow boundary, so a zero step here would indicate
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// a corrupted input. Keeping the guard commented out documents the intent without putting a branch on the hot path.
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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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FactorCacheLease factorCacheLease = new FactorCacheLease();
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Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
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bool foundDivisor = false;
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bool requireLargeCycleCache = allowedMax > PerfectNumberConstants.MaxQForDivisorCycles;
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if (requireLargeCycleCache)
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{
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factorCacheLease.EnsureInitialized(ref factorCache);
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}
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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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// DivisorCycleCache cycleCache = DivisorCycleCache.Shared; // Preserve the reference for easy restoration if the fallback cache is re-enabled.
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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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ulong candidate = (ulong)divisor;
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processedCount++;
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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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MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(candidate);
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Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cacheForCycle = null;
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if (requireLargeCycleCache && candidate > PerfectNumberConstants.MaxQForDivisorCycles)
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{
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cacheForCycle = factorCache;
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}
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if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, cacheForCycle, cacheForCycle is not null, out ulong divisorCycle))
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{
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divisorCycle = 0UL;
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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) guarantees that the candidate divides
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// the corresponding Mersenne number because the order of 2 modulo the divisor is exactly p.
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foundDivisor = true;
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break;
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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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factorCacheLease.Dispose();
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factorCache = null; // The pooled dictionary was returned to the thread-static slot.
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if (foundDivisor)
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{
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processedAll = true;
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return true;
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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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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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}
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public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits)
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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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cachedData = MontgomeryDivisorDataCache.Get(divisor);
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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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