656 lines
17 KiB
C#
656 lines
17 KiB
C#
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 ILGPU;
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using ILGPU.Runtime;
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namespace PerfectNumbers.Core.Gpu;
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public sealed class MersenneNumberDivisorByDivisorGpuTester
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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 ulong _lastStatusDivisor;
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private bool _useDivisorCycles;
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public readonly struct MontgomeryDivisorData(ulong modulus, ulong nPrime, ulong montgomeryOne, ulong montgomeryTwo)
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{
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public readonly ulong Modulus = modulus;
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public readonly ulong NPrime = nPrime;
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public readonly ulong MontgomeryOne = montgomeryOne;
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public readonly ulong MontgomeryTwo = montgomeryTwo;
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}
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>> _kernelCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>>> _kernelByPrimeCache = new();
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private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
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private Action<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>> GetKernel(Accelerator accelerator) =>
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_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>>(CheckKernel));
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private Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>> GetKernelByPrime(Accelerator accelerator) =>
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_kernelByPrimeCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>>(CheckKernelByPrime));
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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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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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_lastStatusDivisor = 0UL;
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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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var divisorsBuffer = accelerator.Allocate1D<MontgomeryDivisorData>(batchCapacity);
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var hitsBuffer = accelerator.Allocate1D<byte>(batchCapacity);
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ulong[] divisors = ArrayPool<ulong>.Shared.Rent(batchCapacity);
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byte[] hits = ArrayPool<byte>.Shared.Rent(batchCapacity);
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MontgomeryDivisorData[] divisorData = ArrayPool<MontgomeryDivisorData>.Shared.Rent(batchCapacity);
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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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divisorsBuffer,
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hitsBuffer,
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divisors,
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hits,
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divisorData,
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out lastProcessed,
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out 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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ArrayPool<byte>.Shared.Return(hits, clearArray: true);
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ArrayPool<ulong>.Shared.Return(divisors, clearArray: true);
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ArrayPool<MontgomeryDivisorData>.Shared.Return(divisorData, clearArray: true);
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hitsBuffer.Dispose();
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divisorsBuffer.Dispose();
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gpuLease.Dispose();
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}
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if (processedCount > 0UL)
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{
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lock (_sync)
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{
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UpdateStatusUnsafe(lastProcessed, processedCount);
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}
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}
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if (composite)
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{
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divisorsExhausted = true;
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return false;
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}
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divisorsExhausted = coveredRange;
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return true;
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}
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private bool CheckDivisors(
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ulong prime,
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ulong allowedMax,
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bool useCycles,
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Accelerator accelerator,
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Action<Index1D, ulong, ArrayView<MontgomeryDivisorData>, ArrayView<byte>> kernel,
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MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> divisorsBuffer,
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MemoryBuffer1D<byte, Stride1D.Dense> hitsBuffer,
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ulong[] divisors,
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byte[] hits,
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MontgomeryDivisorData[] divisorData,
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out ulong lastProcessed,
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out bool 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 cycle, divisor = 3UL, next;
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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<byte> hitsSpan;
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MersenneDivisorCycles divisorCycles = MersenneDivisorCycles.Shared;
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ArrayView1D<MontgomeryDivisorData, Stride1D.Dense> divisorView;
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ArrayView1D<byte, Stride1D.Dense> hitsView;
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while (divisor <= allowedMax)
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{
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batchSize = 0;
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reachedEndInBatch = false;
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while (batchSize < batchCapacity && divisor <= allowedMax)
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{
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ulong currentDivisor = divisor;
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ulong nextDivisor = currentDivisor + 2UL;
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processedCount++;
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if (useCycles)
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{
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cycle = divisorCycles!.GetCycle(currentDivisor);
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if (cycle == 0UL || prime % cycle != 0UL)
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{
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lastProcessed = currentDivisor;
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if (nextDivisor <= currentDivisor)
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{
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reachedEndInBatch = true;
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break;
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}
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if (nextDivisor > allowedMax)
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{
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divisor = nextDivisor;
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reachedEndInBatch = true;
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break;
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}
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divisor = nextDivisor;
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continue;
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}
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}
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divisors[batchSize++] = currentDivisor;
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lastProcessed = currentDivisor;
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next = nextDivisor;
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// This will be only true when we exceed ulong.MaxValue
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if (next <= divisor)
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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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divisor = next;
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reachedEndInBatch = true;
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break;
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}
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divisor = 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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}
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break;
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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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hitsView = hitsBuffer.View.SubView(0, batchSize);
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divisorSpan = divisors.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] = CreateMontgomeryDivisorData(divisorSpan[i]);
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}
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divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(divisorDataSpan), batchSize);
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kernel(batchSize, prime, divisorView, 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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coveredRange = composite || processedAll || divisor > 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 void UpdateStatusUnsafe(ulong lastProcessed, ulong processedCount)
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{
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if (processedCount == 0UL)
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{
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return;
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}
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ulong interval = (ulong)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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ulong messages = total / interval;
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_lastStatusDivisor = total % interval;
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for (ulong i = 0; i < messages; i++)
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{
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Console.WriteLine($"...processed by-divisor candidate = {lastProcessed}");
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}
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}
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private static void CheckKernel(Index1D index, ulong prime, ArrayView<MontgomeryDivisorData> divisors, 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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hits[index] = Pow2Mod(prime, divisor) == 1UL ? (byte)1 : (byte)0;
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}
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public sealed class DivisorScanSession : IDisposable
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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<byte>> _kernel;
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private readonly MemoryBuffer1D<ulong, Stride1D.Dense> _primesBuffer;
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private readonly MemoryBuffer1D<byte, Stride1D.Dense> _hitsBuffer;
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private readonly ulong[] _primesHost;
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private readonly byte[] _hitsHost;
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private readonly int[] _indexHost;
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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.GetKernelByPrime(_accelerator);
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_primesBuffer = _accelerator.Allocate1D<ulong>(owner._gpuBatchSize);
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_hitsBuffer = _accelerator.Allocate1D<byte>(owner._gpuBatchSize);
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_primesHost = ArrayPool<ulong>.Shared.Rent(owner._gpuBatchSize);
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_hitsHost = ArrayPool<byte>.Shared.Rent(owner._gpuBatchSize);
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_indexHost = ArrayPool<int>.Shared.Rent(owner._gpuBatchSize);
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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, 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 offset = 0;
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MersenneNumberDivisorByDivisorGpuTester owner = _owner;
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int gpuBatchSize = owner._gpuBatchSize;
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bool useCycles = owner._useDivisorCycles;
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byte[] hitsHost = _hitsHost;
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int[] indexHost = _indexHost;
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ulong[] primesHost = _primesHost;
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Accelerator accelerator = _accelerator;
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MemoryBuffer1D<byte, Stride1D.Dense> hitsBuffer = _hitsBuffer;
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MemoryBuffer1D<ulong, Stride1D.Dense> primesBuffer = _primesBuffer;
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ArrayView1D<ulong, Stride1D.Dense> primesBufferView = primesBuffer.View;
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ArrayView1D<byte, Stride1D.Dense> hitsBufferView = hitsBuffer.View;
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Action<Index1D, MontgomeryDivisorData, ArrayView<ulong>, ArrayView<byte>> kernel = _kernel;
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ArrayView1D<ulong, Stride1D.Dense> primesView;
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ArrayView1D<byte, Stride1D.Dense> hitsView;
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MersenneDivisorCycles? divisorCycles = MersenneDivisorCycles.Shared;
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ulong cycle = useCycles ? divisorCycles!.GetCycle(divisor) : 0UL, primeValue;
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MontgomeryDivisorData divisorData = CreateMontgomeryDivisorData(divisor);
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Span<ulong> primeSpan = [];
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ReadOnlySpan<ulong> primesSlice;
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Span<int> indexSpan = [];
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Span<byte> hitSpan = [];
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Span<byte> hitsSlice;
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int batchSize, currentSpanSize = -1, gpuCount, i, primesLength = primes.Length;
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while (offset < primesLength)
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{
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batchSize = Math.Min(gpuBatchSize, primesLength - offset);
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primesSlice = primes.Slice(offset, batchSize);
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hitsSlice = hits.Slice(offset, batchSize);
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if (useCycles)
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{
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if (batchSize != currentSpanSize)
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{
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primeSpan = primesHost.AsSpan(0, batchSize);
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indexSpan = indexHost.AsSpan(0, batchSize);
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hitSpan = hitsHost.AsSpan(0, batchSize);
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currentSpanSize = batchSize;
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}
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gpuCount = 0;
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for (i = 0; i < batchSize; i++)
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{
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primeValue = primesSlice[i];
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if (cycle == 0UL || primeValue % cycle != 0UL)
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{
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hitsSlice[i] = 0;
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continue;
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}
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indexSpan[gpuCount] = i;
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primeSpan[gpuCount] = primeValue;
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gpuCount++;
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}
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if (gpuCount > 0)
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{
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primesView = primesBufferView.SubView(0, gpuCount);
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hitsView = hitsBufferView.SubView(0, gpuCount);
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primesView.CopyFromCPU(ref MemoryMarshal.GetReference(primeSpan), gpuCount);
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kernel(gpuCount, divisorData, primesView, hitsView);
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accelerator.Synchronize();
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hitsView.CopyToCPU(ref MemoryMarshal.GetReference(hitSpan), gpuCount);
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for (i = 0; i < gpuCount; i++)
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{
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hitsSlice[indexSpan[i]] = hitSpan[i];
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}
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}
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}
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else
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{
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primesView = primesBufferView.SubView(0, batchSize);
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hitsView = hitsBufferView.SubView(0, batchSize);
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primesView.CopyFromCPU(ref MemoryMarshal.GetReference(primesSlice), batchSize);
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kernel(batchSize, divisorData, primesView, hitsView);
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accelerator.Synchronize();
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hitsView.CopyToCPU(ref MemoryMarshal.GetReference(hitsSlice), batchSize);
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}
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offset += batchSize;
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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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internal void ReturnSession(DivisorScanSession session)
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{
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_sessionPool.Add(session);
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}
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private static ulong Pow2Mod(ulong exponent, in MontgomeryDivisorData divisor)
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{
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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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return 0UL;
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}
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ulong result = divisor.MontgomeryOne;
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ulong baseVal = divisor.MontgomeryTwo;
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ulong nPrime = divisor.NPrime;
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while (exponent > 0UL)
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{
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if ((exponent & 1UL) != 0UL)
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{
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result = MontgomeryMultiply(result, baseVal, modulus, nPrime);
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}
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exponent >>= 1;
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if (exponent == 0UL)
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{
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break;
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}
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baseVal = MontgomeryMultiply(baseVal, baseVal, modulus, nPrime);
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}
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return MontgomeryMultiply(result, 1UL, modulus, nPrime);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong MontgomeryMultiply(ulong a, ulong b, ulong modulus, ulong nPrime)
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{
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ulong tLow = unchecked(a * b);
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ulong m = unchecked(tLow * nPrime);
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// We're reusing tLow variable as the result to perform just a little bit better
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tLow = unchecked(MultiplyHigh(a, b) + MultiplyHigh(m, modulus) + (unchecked(tLow + m * modulus) < tLow ? 1UL : 0UL));
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if (tLow >= modulus)
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{
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tLow -= modulus;
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}
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return tLow;
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}
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|
|
|
private static void CheckKernelByPrime(Index1D index, MontgomeryDivisorData divisor, ArrayView<ulong> primes, ArrayView<byte> hits)
|
|
{
|
|
ulong modulus = divisor.Modulus;
|
|
if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
|
{
|
|
hits[index] = 0;
|
|
return;
|
|
}
|
|
|
|
hits[index] = Pow2Mod(primes[index], divisor) == 1UL ? (byte)1 : (byte)0;
|
|
}
|
|
|
|
private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
|
|
{
|
|
if (modulus <= 1UL || (modulus & 1UL) == 0UL)
|
|
{
|
|
return new(modulus, 0UL, 0UL, 0UL);
|
|
}
|
|
|
|
return new(
|
|
modulus,
|
|
ComputeMontgomeryNPrime(modulus),
|
|
ComputeMontgomeryResidue(1UL, modulus),
|
|
ComputeMontgomeryResidue(2UL, modulus)
|
|
);
|
|
}
|
|
|
|
private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);
|
|
|
|
private static ulong ComputeMontgomeryNPrime(ulong modulus)
|
|
{
|
|
ulong inv = modulus;
|
|
inv *= unchecked(2UL - modulus * inv);
|
|
inv *= unchecked(2UL - modulus * inv);
|
|
inv *= unchecked(2UL - modulus * inv);
|
|
inv *= unchecked(2UL - modulus * inv);
|
|
inv *= unchecked(2UL - modulus * inv);
|
|
inv *= unchecked(2UL - modulus * inv);
|
|
return unchecked(0UL - inv);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private static ulong MultiplyHigh(ulong x, ulong y)
|
|
{
|
|
ulong xLow = (uint)x;
|
|
ulong xHigh = x >> 32;
|
|
ulong yLow = (uint)y;
|
|
ulong yHigh = y >> 32;
|
|
|
|
ulong mid = xHigh * yLow + ((xLow * yLow) >> 32);
|
|
return xHigh * yHigh + (mid >> 32) + (((mid & 0xFFFFFFFFUL) + xLow * yHigh) >> 32);
|
|
}
|
|
|
|
public ulong DivisorLimit
|
|
{
|
|
get
|
|
{
|
|
lock (_sync)
|
|
{
|
|
if (!_isConfigured)
|
|
{
|
|
throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
|
|
}
|
|
|
|
return _divisorLimit;
|
|
}
|
|
}
|
|
}
|
|
|
|
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);
|
|
}
|
|
}
|
|
}
|
|
|