Add GPU options for by-divisor Montgomery data
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Marek Lemańczyk committed
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using System;
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using System.Buffers;
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using System.Runtime.InteropServices;
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using PerfectNumbers.Core;
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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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internal sealed class MersenneNumberDivisorMontgomeryGpuBuilder : IDisposable
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{
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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, ArrayView<ulong>, ArrayView<MontgomeryDivisorData>> _kernel;
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private MemoryBuffer1D<ulong, Stride1D.Dense> _modulusBuffer;
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private MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> _resultBuffer;
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private ulong[] _hostModulusBuffer;
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private MontgomeryDivisorData[] _hostResultBuffer;
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private int _capacity;
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private bool _disposed;
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internal MersenneNumberDivisorMontgomeryGpuBuilder(int batchSize)
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{
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_lease = GpuContextPool.RentPreferred(preferCpu: false);
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_accelerator = _lease.Accelerator;
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_kernel = _accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<MontgomeryDivisorData>>(BuildKernel);
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_capacity = Math.Max(1, batchSize);
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_modulusBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_resultBuffer = _accelerator.Allocate1D<MontgomeryDivisorData>(_capacity);
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_hostModulusBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_hostResultBuffer = ArrayPool<MontgomeryDivisorData>.Shared.Rent(_capacity);
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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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_modulusBuffer.Dispose();
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_resultBuffer.Dispose();
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ArrayPool<ulong>.Shared.Return(_hostModulusBuffer, clearArray: false);
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ArrayPool<MontgomeryDivisorData>.Shared.Return(_hostResultBuffer, clearArray: false);
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_lease.Dispose();
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}
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internal void Build(ReadOnlySpan<ulong> moduli, Span<MontgomeryDivisorData> destination)
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{
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if (_disposed)
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{
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throw new ObjectDisposedException(nameof(MersenneNumberDivisorMontgomeryGpuBuilder));
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}
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int length = moduli.Length;
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if (length == 0)
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{
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return;
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}
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EnsureCapacity(length);
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Span<ulong> hostModulusSpan = _hostModulusBuffer.AsSpan(0, length);
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moduli.CopyTo(hostModulusSpan);
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ArrayView1D<ulong, Stride1D.Dense> modulusView = _modulusBuffer.View.SubView(0, length);
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modulusView.CopyFromCPU(ref MemoryMarshal.GetReference(hostModulusSpan), length);
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ArrayView1D<MontgomeryDivisorData, Stride1D.Dense> resultView = _resultBuffer.View.SubView(0, length);
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_kernel(length, modulusView, resultView);
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Span<MontgomeryDivisorData> hostResultSpan = _hostResultBuffer.AsSpan(0, length);
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resultView.CopyToCPU(ref MemoryMarshal.GetReference(hostResultSpan), length);
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hostResultSpan.CopyTo(destination);
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}
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private void EnsureCapacity(int required)
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{
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if (required <= _capacity)
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{
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return;
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}
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int newCapacity = _capacity == 0 ? 1 : _capacity;
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while (newCapacity < required)
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{
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newCapacity <<= 1;
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}
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_modulusBuffer.Dispose();
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_resultBuffer.Dispose();
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ArrayPool<ulong>.Shared.Return(_hostModulusBuffer, clearArray: false);
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ArrayPool<MontgomeryDivisorData>.Shared.Return(_hostResultBuffer, clearArray: false);
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_capacity = newCapacity;
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_modulusBuffer = _accelerator.Allocate1D<ulong>(_capacity);
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_resultBuffer = _accelerator.Allocate1D<MontgomeryDivisorData>(_capacity);
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_hostModulusBuffer = ArrayPool<ulong>.Shared.Rent(_capacity);
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_hostResultBuffer = ArrayPool<MontgomeryDivisorData>.Shared.Rent(_capacity);
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}
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private static void BuildKernel(Index1D index, ArrayView<ulong> moduli, ArrayView<MontgomeryDivisorData> destination)
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{
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int idx = index;
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if (idx >= moduli.Length)
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{
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return;
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}
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ulong modulus = moduli[idx];
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if (modulus <= 1UL || (modulus & 1UL) == 0UL)
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{
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destination[idx] = default;
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return;
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}
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ulong nPrime = ComputeMontgomeryNPrime(modulus);
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ulong montgomeryOne = ComputeMontgomeryResidue64(modulus);
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ulong montgomeryTwo = montgomeryOne.MulMod64GpuCompatible(2UL, modulus);
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ulong montgomeryTwoSquared = MontgomeryMultiplyGpu(montgomeryTwo, montgomeryTwo, modulus, nPrime);
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destination[idx] = new MontgomeryDivisorData(
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modulus,
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nPrime,
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montgomeryOne,
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montgomeryTwo,
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montgomeryTwoSquared);
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}
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private static ulong ComputeMontgomeryResidue64(ulong modulus)
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{
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ulong remainder = ulong.MaxValue % modulus;
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remainder++;
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if (remainder >= modulus)
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{
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remainder -= modulus;
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}
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return remainder;
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}
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private static ulong MontgomeryMultiplyGpu(ulong a, ulong b, ulong modulus, ulong nPrime)
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{
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GpuUInt128 product = new(a);
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product.Mul64(new GpuUInt128(b));
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ulong tLow = product.Low;
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ulong tHigh = product.High;
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ulong m = unchecked(tLow * nPrime);
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GpuUInt128 mProduct = new(m);
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mProduct.Mul64(new GpuUInt128(modulus));
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ulong mLow = mProduct.Low;
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ulong mHigh = mProduct.High;
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ulong carry = unchecked((tLow + mLow) < tLow ? 1UL : 0UL);
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ulong result = tHigh + mHigh + carry;
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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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return result;
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}
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private static ulong ComputeMontgomeryNPrime(ulong modulus)
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{
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ulong inv = modulus;
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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inv *= unchecked(2UL - modulus * inv);
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return unchecked(0UL - inv);
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}
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}
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@@ -0,0 +1,135 @@
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using System;
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using System.Buffers;
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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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internal sealed class MersenneNumberDivisorRemainderGpuStepper : IDisposable
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{
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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, int, ArrayView<byte>, ArrayView<byte>, ArrayView<byte>, ArrayView<byte>> _kernel;
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private MemoryBuffer1D<byte, Stride1D.Dense> _remainderBuffer;
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private MemoryBuffer1D<byte, Stride1D.Dense> _stepBuffer;
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private MemoryBuffer1D<byte, Stride1D.Dense> _modulusBuffer;
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private MemoryBuffer1D<byte, Stride1D.Dense> _resultBuffer;
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private byte[] _hostRemainders;
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private byte[] _hostSteps;
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private byte[] _hostModuli;
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private readonly int _length;
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private int _capacity;
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private bool _disposed;
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internal MersenneNumberDivisorRemainderGpuStepper(ReadOnlySpan<byte> steps, ReadOnlySpan<byte> moduli)
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{
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if (steps.Length != moduli.Length)
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{
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throw new ArgumentException("Steps and moduli must have the same length.");
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}
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_lease = GpuContextPool.RentPreferred(preferCpu: false);
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_accelerator = _lease.Accelerator;
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_kernel = _accelerator.LoadAutoGroupedStreamKernel<Index1D, int, ArrayView<byte>, ArrayView<byte>, ArrayView<byte>, ArrayView<byte>>(AdvanceRemaindersKernel);
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_length = steps.Length;
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_capacity = Math.Max(1, _length);
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_remainderBuffer = _accelerator.Allocate1D<byte>(_capacity);
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_stepBuffer = _accelerator.Allocate1D<byte>(_capacity);
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_modulusBuffer = _accelerator.Allocate1D<byte>(_capacity);
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_resultBuffer = _accelerator.Allocate1D<byte>(_capacity);
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_hostRemainders = ArrayPool<byte>.Shared.Rent(_capacity);
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_hostSteps = ArrayPool<byte>.Shared.Rent(_capacity);
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_hostModuli = ArrayPool<byte>.Shared.Rent(_capacity);
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steps.CopyTo(_hostSteps.AsSpan(0, _length));
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moduli.CopyTo(_hostModuli.AsSpan(0, _length));
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ArrayView1D<byte, Stride1D.Dense> stepView = _stepBuffer.View.SubView(0, _length);
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stepView.CopyFromCPU(ref MemoryMarshal.GetReference(_hostSteps.AsSpan(0, _length)), _length);
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ArrayView1D<byte, Stride1D.Dense> modulusView = _modulusBuffer.View.SubView(0, _length);
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modulusView.CopyFromCPU(ref MemoryMarshal.GetReference(_hostModuli.AsSpan(0, _length)), _length);
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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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_remainderBuffer.Dispose();
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_stepBuffer.Dispose();
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_modulusBuffer.Dispose();
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_resultBuffer.Dispose();
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ArrayPool<byte>.Shared.Return(_hostRemainders, clearArray: false);
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ArrayPool<byte>.Shared.Return(_hostSteps, clearArray: false);
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ArrayPool<byte>.Shared.Return(_hostModuli, clearArray: false);
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_lease.Dispose();
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}
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internal void Advance(int advanceCount, Span<byte> remainders)
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{
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if (_disposed)
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{
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throw new ObjectDisposedException(nameof(MersenneNumberDivisorRemainderGpuStepper));
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}
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if (advanceCount <= 0 || remainders.Length == 0)
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{
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return;
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}
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if (remainders.Length != _length)
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{
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throw new ArgumentException("Remainder buffer length must match the configured length.");
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}
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Span<byte> hostRemainderSpan = _hostRemainders.AsSpan(0, _length);
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remainders.CopyTo(hostRemainderSpan);
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ArrayView1D<byte, Stride1D.Dense> remainderView = _remainderBuffer.View.SubView(0, _length);
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remainderView.CopyFromCPU(ref MemoryMarshal.GetReference(hostRemainderSpan), _length);
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ArrayView1D<byte, Stride1D.Dense> stepView = _stepBuffer.View.SubView(0, _length);
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ArrayView1D<byte, Stride1D.Dense> modulusView = _modulusBuffer.View.SubView(0, _length);
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ArrayView1D<byte, Stride1D.Dense> resultView = _resultBuffer.View.SubView(0, _length);
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_kernel(_length, advanceCount, remainderView, stepView, modulusView, resultView);
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resultView.CopyToCPU(ref MemoryMarshal.GetReference(hostRemainderSpan), _length);
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hostRemainderSpan.CopyTo(remainders);
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}
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private static void AdvanceRemaindersKernel(Index1D index, int advanceCount, ArrayView<byte> remainders, ArrayView<byte> steps, ArrayView<byte> moduli, ArrayView<byte> results)
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{
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int idx = index;
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if (idx >= remainders.Length)
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{
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return;
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}
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int modulus = moduli[idx];
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if (modulus == 0)
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{
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results[idx] = remainders[idx];
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return;
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}
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int remainder = remainders[idx] % modulus;
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int step = steps[idx] % modulus;
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long delta = (long)step * advanceCount;
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int adjusted = (int)((remainder + delta) % modulus);
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if (adjusted < 0)
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{
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adjusted += modulus;
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}
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results[idx] = (byte)adjusted;
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}
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}
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