308 lines
12 KiB
C#
308 lines
12 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.Collections.Generic;
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using System.Runtime.InteropServices;
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using ILGPU;
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using ILGPU.Algorithms;
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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 readonly List<ulong> _divisors = new();
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private readonly List<ulong> _remainders = new();
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private readonly List<ulong> _lastPrimes = new();
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private readonly object _sync = new();
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private ulong _divisorLimit;
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>> _updateKernelCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ulong, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>> _initialKernelCache = new();
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private Action<Index1D, ulong, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> GetUpdateKernel(Accelerator accelerator) =>
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_updateKernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(UpdateKernel));
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private Action<Index1D, ulong, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> GetInitialKernel(Accelerator accelerator) =>
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_initialKernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(InitialKernel));
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public bool IsPrime(ulong prime, ulong divisorLimit, out bool divisorsExhausted)
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{
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lock (_sync)
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{
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_divisorLimit = divisorLimit;
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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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bool composite = UpdateExistingDivisors(prime, allowedMax);
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if (!composite)
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{
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composite = ExtendDivisors(prime, allowedMax);
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}
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divisorsExhausted = true;
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return !composite;
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}
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}
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private bool UpdateExistingDivisors(ulong prime, ulong allowedMax)
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{
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int count = _divisors.Count;
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if (count == 0)
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{
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return false;
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}
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var gpuLease = GpuContextPool.RentPreferred(preferCpu: false);
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var accelerator = gpuLease.Accelerator;
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var kernel = GetUpdateKernel(accelerator);
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var divisorsBuffer = accelerator.Allocate1D<ulong>(count);
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var remaindersBuffer = accelerator.Allocate1D<ulong>(count);
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var lastPrimesBuffer = accelerator.Allocate1D<ulong>(count);
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var hitsBuffer = accelerator.Allocate1D<byte>(count);
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Span<ulong> divisorsSpan = CollectionsMarshal.AsSpan(_divisors);
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Span<ulong> remaindersSpan = CollectionsMarshal.AsSpan(_remainders);
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Span<ulong> lastPrimesSpan = CollectionsMarshal.AsSpan(_lastPrimes);
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divisorsBuffer.View.CopyFromCPU(ref MemoryMarshal.GetReference(divisorsSpan), count);
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remaindersBuffer.View.CopyFromCPU(ref MemoryMarshal.GetReference(remaindersSpan), count);
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lastPrimesBuffer.View.CopyFromCPU(ref MemoryMarshal.GetReference(lastPrimesSpan), count);
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hitsBuffer.MemSetToZero();
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kernel(count, prime, divisorsBuffer.View, remaindersBuffer.View, lastPrimesBuffer.View, hitsBuffer.View);
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accelerator.Synchronize();
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remaindersBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(remaindersSpan), count);
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lastPrimesBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(lastPrimesSpan), count);
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byte[] hits = ArrayPool<byte>.Shared.Rent(count);
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Span<byte> hitsSpan = hits.AsSpan(0, count);
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hitsBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(hitsSpan), count);
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bool composite = false;
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for (int i = 0; i < count; i++)
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{
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if (divisorsSpan[i] > allowedMax)
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{
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break;
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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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break;
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}
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}
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ArrayPool<byte>.Shared.Return(hits, clearArray: true);
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hitsBuffer.Dispose();
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lastPrimesBuffer.Dispose();
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remaindersBuffer.Dispose();
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divisorsBuffer.Dispose();
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gpuLease.Dispose();
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return composite;
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}
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private bool ExtendDivisors(ulong prime, ulong allowedMax)
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{
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ulong currentMax = _divisors.Count == 0 ? 1UL : _divisors[^1];
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ulong start = currentMax < 3UL ? 3UL : currentMax + 2UL;
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if (start > allowedMax)
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{
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return false;
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}
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List<ulong> newDivisors = new();
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for (ulong divisor = start; divisor <= allowedMax; divisor += 2UL)
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{
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newDivisors.Add(divisor);
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}
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int count = newDivisors.Count;
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if (count == 0)
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{
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return false;
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}
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var gpuLease = GpuContextPool.RentPreferred(preferCpu: false);
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var accelerator = gpuLease.Accelerator;
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var kernel = GetInitialKernel(accelerator);
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var divisorsBuffer = accelerator.Allocate1D<ulong>(count);
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var remaindersBuffer = accelerator.Allocate1D<ulong>(count);
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var hitsBuffer = accelerator.Allocate1D<byte>(count);
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Span<ulong> newDivisorsSpan = CollectionsMarshal.AsSpan(newDivisors);
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divisorsBuffer.View.CopyFromCPU(ref MemoryMarshal.GetReference(newDivisorsSpan), count);
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hitsBuffer.MemSetToZero();
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kernel(count, prime, divisorsBuffer.View, remaindersBuffer.View, hitsBuffer.View);
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accelerator.Synchronize();
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ulong[] newRemainders = ArrayPool<ulong>.Shared.Rent(count);
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byte[] hits = ArrayPool<byte>.Shared.Rent(count);
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Span<ulong> newRemaindersSpan = newRemainders.AsSpan(0, count);
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Span<byte> hitsSpan = hits.AsSpan(0, count);
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remaindersBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(newRemaindersSpan), count);
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hitsBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(hitsSpan), count);
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bool composite = false;
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for (int i = 0; i < count; i++)
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{
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ulong divisor = newDivisorsSpan[i];
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ulong remainder = newRemaindersSpan[i];
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_divisors.Add(divisor);
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_remainders.Add(remainder);
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_lastPrimes.Add(prime);
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if (!composite && hitsSpan[i] != 0)
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{
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composite = true;
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}
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}
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ArrayPool<ulong>.Shared.Return(newRemainders, clearArray: true);
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ArrayPool<byte>.Shared.Return(hits, clearArray: true);
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hitsBuffer.Dispose();
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remaindersBuffer.Dispose();
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divisorsBuffer.Dispose();
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gpuLease.Dispose();
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return composite;
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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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ulong maxByPrime = (1UL << (int)(prime - 1UL)) - 1UL;
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return Math.Min(maxByPrime, divisorLimit);
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}
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private static void UpdateKernel(Index1D index, ulong prime, ArrayView<ulong> divisors, ArrayView<ulong> remainders, ArrayView<ulong> lastPrimes, ArrayView<byte> hits)
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{
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ulong divisor = divisors[index];
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if (divisor <= 1UL || (divisor & 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 lastPrime = lastPrimes[index];
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ulong remainder = remainders[index] % divisor;
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ulong step = prime >= lastPrime ? prime - lastPrime : 0UL;
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if (step == 0UL)
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{
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hits[index] = remainder == 0UL ? (byte)1 : (byte)0;
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return;
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}
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ulong pow = Pow2Mod(step, divisor);
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ulong temp = remainder + 1UL;
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if (temp >= divisor)
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{
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temp -= divisor;
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}
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ulong product = MulMod(temp, pow, divisor);
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ulong newRemainder = product == 0UL ? divisor - 1UL : product - 1UL;
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bool isZero = newRemainder == 0UL;
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remainders[index] = newRemainder;
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lastPrimes[index] = prime;
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hits[index] = isZero ? (byte)1 : (byte)0;
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}
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private static void InitialKernel(Index1D index, ulong prime, ArrayView<ulong> divisors, ArrayView<ulong> remainders, ArrayView<byte> hits)
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{
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ulong divisor = divisors[index];
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if (divisor <= 1UL || (divisor & 1UL) == 0UL)
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{
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remainders[index] = 0UL;
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hits[index] = 0;
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return;
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}
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ulong pow = Pow2Mod(prime, divisor);
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ulong remainder = pow == 0UL ? divisor - 1UL : (pow == 1UL ? 0UL : pow - 1UL);
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remainders[index] = remainder;
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hits[index] = remainder == 0UL ? (byte)1 : (byte)0;
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}
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private static ulong Pow2Mod(ulong exponent, ulong modulus)
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{
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if (modulus <= 1UL)
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{
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return 0UL;
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}
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ulong result = 1UL % modulus;
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ulong baseVal = 2UL % modulus;
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ulong exp = exponent;
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while (exp > 0UL)
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{
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if ((exp & 1UL) != 0UL)
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{
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result = MulMod(result, baseVal, modulus);
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}
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exp >>= 1;
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if (exp == 0UL)
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{
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break;
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}
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baseVal = MulMod(baseVal, baseVal, modulus);
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}
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return result;
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}
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private static ulong MulMod(ulong a, ulong b, ulong modulus)
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{
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if (modulus == 0UL)
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{
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return 0UL;
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}
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ulong result = 0UL;
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ulong x = a % modulus;
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ulong y = b;
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while (y > 0UL)
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{
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if ((y & 1UL) != 0UL)
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{
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result += x;
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if (result >= modulus)
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{
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result -= modulus;
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}
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}
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x <<= 1;
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if (x >= modulus)
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{
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x -= modulus;
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}
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y >>= 1;
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}
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return result;
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}
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}
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