683 lines
26 KiB
C#
683 lines
26 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 System.Runtime.InteropServices;
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using System.Numerics;
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using ILGPU;
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using ILGPU.Runtime;
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using MontgomeryDivisorData = PerfectNumbers.Core.MontgomeryDivisorData;
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using MontgomeryDivisorDataCache = PerfectNumbers.Core.MontgomeryDivisorDataCache;
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using CycleRemainderStepper = PerfectNumbers.Core.CycleRemainderStepper;
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namespace PerfectNumbers.Core.Gpu;
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public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDivisorByDivisorTester
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{
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private int _gpuBatchSize = GpuConstants.ScanBatchSize;
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private readonly object _sync = new();
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private ulong _divisorLimit;
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private bool _isConfigured;
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private bool _useDivisorCycles;
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>>> _kernelCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>> _kernelExponentCache = new();
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private readonly ConcurrentDictionary<Accelerator, ConcurrentBag<BatchResources>> _resourcePools = new(AcceleratorReferenceComparer.Instance);
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private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
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private Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>> GetKernel(Accelerator accelerator) =>
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_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>>(CheckKernel));
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private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> GetKernelByPrimeExponent(Accelerator accelerator) =>
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_kernelExponentCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>>(ComputeMontgomeryExponentKernel));
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public int GpuBatchSize
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{
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get => _gpuBatchSize;
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set => _gpuBatchSize = Math.Max(1, value);
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}
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int IMersenneNumberDivisorByDivisorTester.BatchSize
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{
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get => GpuBatchSize;
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set => GpuBatchSize = value;
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}
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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 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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_isConfigured = true;
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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 = _gpuBatchSize;
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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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bool composite;
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bool coveredRange;
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ulong processedCount;
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ulong lastProcessed;
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var gpuLease = GpuContextPool.RentPreferred(preferCpu: false);
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var accelerator = gpuLease.Accelerator;
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var kernel = GetKernel(accelerator);
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BatchResources resources = RentBatchResources(accelerator, batchCapacity);
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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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accelerator,
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kernel,
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resources.DivisorsBuffer,
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resources.ExponentBuffer,
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resources.HitsBuffer,
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resources.Divisors,
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resources.Exponents,
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resources.Hits,
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resources.DivisorData,
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out lastProcessed,
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out coveredRange,
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out processedCount
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);
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}
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finally
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{
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ReturnBatchResources(accelerator, resources);
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gpuLease.Dispose();
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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 = coveredRange;
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return true;
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}
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private static bool CheckDivisors(
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ulong prime,
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ulong allowedMax,
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bool useCycles,
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Accelerator accelerator,
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Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>> kernel,
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MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> divisorsBuffer,
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MemoryBuffer1D<ulong, Stride1D.Dense> exponentBuffer,
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MemoryBuffer1D<byte, Stride1D.Dense> hitsBuffer,
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in ulong[] divisors,
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ulong[] exponents,
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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 coveredRange,
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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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if (allowedMax < 3UL)
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{
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coveredRange = true;
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return false;
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}
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int batchCapacity = (int)divisorsBuffer.Length;
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bool composite = false;
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bool processedAll = false;
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ulong currentDivisor = 3UL, next, nextDivisor;
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int batchSize, i;
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bool reachedEndInBatch;
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Span<MontgomeryDivisorData> divisorDataSpan;
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Span<ulong> divisorSpan;
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Span<ulong> exponentSpan;
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Span<byte> hitsSpan;
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ArrayView1D<MontgomeryDivisorData, Stride1D.Dense> divisorView;
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ArrayView1D<ulong, Stride1D.Dense> exponentView;
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ArrayView1D<byte, Stride1D.Dense> hitsView;
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DivisorCycleCache divisorCyclesCache = DivisorCycleCache.Shared;
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DivisorCycleCache.CycleBlock? cycleLease = useCycles ? divisorCyclesCache.Acquire(currentDivisor) : null;
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ulong cycleLeaseEnd = cycleLease?.End ?? 0UL;
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while (currentDivisor <= allowedMax)
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{
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batchSize = 0;
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reachedEndInBatch = false;
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while (batchSize < batchCapacity && currentDivisor <= allowedMax)
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{
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nextDivisor = currentDivisor + 2UL;
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processedCount++;
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bool includeDivisor = true;
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ulong exponent = prime;
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if (useCycles)
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{
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if (currentDivisor > cycleLeaseEnd)
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{
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cycleLease?.Dispose();
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cycleLease = divisorCyclesCache.Acquire(currentDivisor);
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cycleLeaseEnd = cycleLease.End;
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}
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ulong cycleLength = cycleLease!.GetCycle(currentDivisor);
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if (cycleLength > 0UL)
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{
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ulong remainder = prime % cycleLength;
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if (remainder != 0UL)
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{
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includeDivisor = false;
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}
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else
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{
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exponent = remainder;
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}
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}
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}
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if (includeDivisor)
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{
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divisors[batchSize] = currentDivisor;
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exponents[batchSize] = exponent;
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batchSize++;
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}
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lastProcessed = currentDivisor;
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next = nextDivisor;
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if (next <= 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 (next > allowedMax)
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{
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currentDivisor = next;
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reachedEndInBatch = true;
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break;
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}
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currentDivisor = next;
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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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break;
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}
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continue;
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}
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divisorDataSpan = divisorData.AsSpan(0, batchSize);
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divisorView = divisorsBuffer.View.SubView(0, batchSize);
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exponentView = exponentBuffer.View.SubView(0, batchSize);
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hitsView = hitsBuffer.View.SubView(0, batchSize);
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divisorSpan = divisors.AsSpan(0, batchSize);
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exponentSpan = exponents.AsSpan(0, batchSize);
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hitsSpan = hits.AsSpan(0, batchSize);
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for (i = 0; i < batchSize; i++)
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{
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divisorDataSpan[i] = MontgomeryDivisorDataCache.Get(divisorSpan[i]);
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}
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divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(divisorDataSpan), batchSize);
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exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSpan), batchSize);
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kernel(batchSize, divisorView, exponentView, hitsView);
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accelerator.Synchronize();
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hitsView.CopyToCPU(ref MemoryMarshal.GetReference(hitsSpan), batchSize);
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for (i = 0; i < batchSize; i++)
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{
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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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cycleLease?.Dispose();
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coveredRange = composite || processedAll || currentDivisor > allowedMax;
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return composite;
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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 void CheckKernel(Index1D index, ArrayView<MontgomeryDivisorData> divisors, ArrayView<ulong> exponents, ArrayView<byte> hits)
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{
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MontgomeryDivisorData divisor = divisors[index];
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ulong modulus = divisor.Modulus;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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hits[index] = 0;
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return;
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}
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ulong exponent = exponents[index];
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hits[index] = exponent.Pow2MontgomeryMod(divisor) == 1UL ? (byte)1 : (byte)0;
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}
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public sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
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{
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private readonly MersenneNumberDivisorByDivisorGpuTester _owner;
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private readonly GpuContextPool.GpuContextLease _lease;
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private readonly Accelerator _accelerator;
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private readonly Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> _kernel;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _exponentsBuffer;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _resultsBuffer;
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private ulong[] _hostBuffer;
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private int[] _positionBuffer;
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private byte[] _modeBuffer;
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private int _capacity;
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private bool _disposed;
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internal DivisorScanSession(MersenneNumberDivisorByDivisorGpuTester owner)
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{
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_owner = owner;
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_lease = GpuContextPool.RentPreferred(preferCpu: false);
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_accelerator = _lease.Accelerator;
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_kernel = owner.GetKernelByPrimeExponent(_accelerator);
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_capacity = Math.Max(1, owner._gpuBatchSize);
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_exponentsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_resultsBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_hostBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(_capacity);
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_modeBuffer = ArrayPool<byte>.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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MersenneNumberDivisorByDivisorGpuTester owner = _owner;
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int gpuBatchSize = owner._gpuBatchSize;
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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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EnsureCapacity(gpuBatchSize);
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MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(divisor);
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var exponentStepper = new ExponentRemainderStepper(divisorData);
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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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bool useDivisorCycles = owner._useDivisorCycles;
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if (useDivisorCycles && divisorCycle == 0UL)
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{
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throw new InvalidOperationException($"Missing divisor cycle for divisor {divisor}.");
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}
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CycleRemainderStepper cycleStepper = useDivisorCycles ? new CycleRemainderStepper(divisorCycle) : default;
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Accelerator accelerator = _accelerator;
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Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<ulong>> kernel = _kernel;
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ArrayView1D<ulong, Stride1D.Dense> exponentsView = _exponentsBuffer.View;
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ArrayView1D<ulong, Stride1D.Dense> resultsView = _resultsBuffer.View;
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Span<ulong> hostSpan = _hostBuffer.AsSpan(0, _capacity);
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Span<int> positionSpan = _positionBuffer.AsSpan(0, _capacity);
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Span<byte> modeSpan = _modeBuffer.AsSpan(0, _capacity);
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int offset = 0;
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while (offset < primesLength)
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{
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int batchSize = Math.Min(gpuBatchSize, primesLength - offset);
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ReadOnlySpan<ulong> primesSlice = primes.Slice(offset, batchSize);
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Span<byte> hitsSlice = hits.Slice(offset, batchSize);
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hitsSlice.Clear();
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int computeCount = 0;
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bool localHasState = exponentStepper.HasState;
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ulong localPreviousExponent = exponentStepper.PreviousExponent;
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for (int i = 0; i < batchSize; i++)
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{
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ulong primeValue = primesSlice[i];
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if (useDivisorCycles)
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{
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ulong remainder = cycleStepper.ComputeNext(primeValue);
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if (remainder != 0UL)
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{
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continue;
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}
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}
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ulong workValue;
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byte mode;
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if (!localHasState || primeValue <= localPreviousExponent)
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{
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mode = 0;
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workValue = primeValue;
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localHasState = true;
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}
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else
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{
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mode = 1;
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workValue = primeValue - localPreviousExponent;
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}
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localPreviousExponent = primeValue;
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if (useDivisorCycles)
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{
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workValue %= divisorCycle;
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}
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positionSpan[computeCount] = i;
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hostSpan[computeCount] = workValue;
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modeSpan[computeCount] = mode;
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computeCount++;
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}
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if (computeCount > 0)
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{
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Span<ulong> exponentSlice = hostSpan[..computeCount];
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ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentsView.SubView(0, computeCount);
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exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
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ArrayView1D<ulong, Stride1D.Dense> resultView = resultsView.SubView(0, computeCount);
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kernel(computeCount, divisorData, exponentView, resultView);
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accelerator.Synchronize();
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resultView.CopyToCPU(ref MemoryMarshal.GetReference(exponentSlice), computeCount);
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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 primeValue = primesSlice[position];
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ulong montgomeryResult = exponentSlice[i];
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bool isUnity;
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if (modeSpan[i] == 0)
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{
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exponentStepper.TryInitializeFromMontgomeryResult(primeValue, montgomeryResult, out isUnity);
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}
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else
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{
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exponentStepper.TryAdvanceWithMontgomeryDelta(primeValue, montgomeryResult, out isUnity);
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}
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hitsSlice[position] = isUnity ? (byte)1 : (byte)0;
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}
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}
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offset += batchSize;
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}
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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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_exponentsBuffer.Dispose();
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_resultsBuffer.Dispose();
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ArrayPool<ulong>.Shared.Return(_hostBuffer, clearArray: false);
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ArrayPool<int>.Shared.Return(_positionBuffer, clearArray: false);
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ArrayPool<byte>.Shared.Return(_modeBuffer, clearArray: false);
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int newCapacity = _capacity;
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if (newCapacity < 1)
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{
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newCapacity = 1;
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}
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while (newCapacity < requiredCapacity)
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{
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newCapacity <<= 1;
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}
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_exponentsBuffer = _accelerator.Allocate1D<ulong>(newCapacity);
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_resultsBuffer = _accelerator.Allocate1D<ulong>(newCapacity);
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_hostBuffer = ArrayPool<ulong>.Shared.Rent(newCapacity);
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_positionBuffer = ArrayPool<int>.Shared.Rent(newCapacity);
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_modeBuffer = ArrayPool<byte>.Shared.Rent(newCapacity);
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_capacity = newCapacity;
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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._sessionPool.Add(this);
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}
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}
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private static void ComputeMontgomeryExponentKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> exponents, ArrayView<ulong> results)
|
|
{
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|
ulong modulus = divisor.Modulus;
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
|
{
|
|
results[index] = 0UL;
|
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return;
|
|
}
|
|
|
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ulong exponent = exponents[index];
|
|
|
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results[index] = exponent.Pow2MontgomeryModMontgomery(divisor);
|
|
}
|
|
|
|
public ulong DivisorLimit
|
|
{
|
|
get
|
|
{
|
|
lock (_sync)
|
|
{
|
|
if (!_isConfigured)
|
|
{
|
|
throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
|
|
}
|
|
|
|
return _divisorLimit;
|
|
}
|
|
}
|
|
}
|
|
|
|
private BatchResources RentBatchResources(Accelerator accelerator, int capacity)
|
|
{
|
|
var bag = _resourcePools.GetOrAdd(accelerator, static _ => []);
|
|
if (bag.TryTake(out BatchResources? resources))
|
|
{
|
|
return resources;
|
|
}
|
|
|
|
return new BatchResources(accelerator, capacity);
|
|
}
|
|
|
|
private void ReturnBatchResources(Accelerator accelerator, BatchResources resources) => _resourcePools.GetOrAdd(accelerator, static _ => []).Add(resources);
|
|
|
|
private sealed class BatchResources : IDisposable
|
|
{
|
|
internal BatchResources(Accelerator accelerator, int capacity)
|
|
{
|
|
DivisorsBuffer = accelerator.Allocate1D<MontgomeryDivisorData>(capacity);
|
|
ExponentBuffer = accelerator.Allocate1D<ulong>(capacity);
|
|
HitsBuffer = accelerator.Allocate1D<byte>(capacity);
|
|
Divisors = ArrayPool<ulong>.Shared.Rent(capacity);
|
|
Exponents = ArrayPool<ulong>.Shared.Rent(capacity);
|
|
Hits = ArrayPool<byte>.Shared.Rent(capacity);
|
|
DivisorData = ArrayPool<MontgomeryDivisorData>.Shared.Rent(capacity);
|
|
Capacity = capacity;
|
|
}
|
|
|
|
internal readonly MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> DivisorsBuffer;
|
|
|
|
internal readonly MemoryBuffer1D<ulong, Stride1D.Dense> ExponentBuffer;
|
|
|
|
internal readonly MemoryBuffer1D<byte, Stride1D.Dense> HitsBuffer;
|
|
|
|
internal readonly ulong[] Divisors;
|
|
|
|
internal readonly ulong[] Exponents;
|
|
|
|
internal readonly byte[] Hits;
|
|
|
|
internal readonly MontgomeryDivisorData[] DivisorData;
|
|
|
|
internal readonly int Capacity;
|
|
|
|
public void Dispose()
|
|
{
|
|
DivisorsBuffer.Dispose();
|
|
ExponentBuffer.Dispose();
|
|
HitsBuffer.Dispose();
|
|
ArrayPool<ulong>.Shared.Return(Divisors, clearArray: false);
|
|
ArrayPool<ulong>.Shared.Return(Exponents, clearArray: false);
|
|
ArrayPool<byte>.Shared.Return(Hits, clearArray: false);
|
|
ArrayPool<MontgomeryDivisorData>.Shared.Return(DivisorData, clearArray: false);
|
|
}
|
|
}
|
|
|
|
private sealed class AcceleratorReferenceComparer : IEqualityComparer<Accelerator>
|
|
{
|
|
public static AcceleratorReferenceComparer Instance { get; } = new();
|
|
|
|
public bool Equals(Accelerator? x, Accelerator? y) => ReferenceEquals(x, y);
|
|
|
|
public int GetHashCode(Accelerator obj) => RuntimeHelpers.GetHashCode(obj);
|
|
}
|
|
|
|
public ulong GetAllowedMaxDivisor(ulong prime)
|
|
{
|
|
lock (_sync)
|
|
{
|
|
if (!_isConfigured)
|
|
{
|
|
throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
|
|
}
|
|
|
|
return ComputeAllowedMaxDivisor(prime, _divisorLimit);
|
|
}
|
|
}
|
|
|
|
public DivisorScanSession CreateDivisorSession()
|
|
{
|
|
lock (_sync)
|
|
{
|
|
if (!_isConfigured)
|
|
{
|
|
throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
|
|
}
|
|
|
|
if (_sessionPool.TryTake(out DivisorScanSession? session))
|
|
{
|
|
session.Reset();
|
|
return session;
|
|
}
|
|
|
|
return new DivisorScanSession(this);
|
|
}
|
|
}
|
|
|
|
IMersenneNumberDivisorByDivisorTester.IDivisorScanSession IMersenneNumberDivisorByDivisorTester.CreateDivisorSession() => CreateDivisorSession();
|
|
}
|
|
|