Replace GPU by-divisor kernel with standard modular exponentiation
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Marek Lemańczyk committed
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commit
035956cdb6
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-27
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@@ -1,3 +1,4 @@
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using System.Runtime.CompilerServices;
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using ILGPU;
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using ILGPU.Algorithms;
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using ILGPU.Runtime;
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@@ -8,21 +9,19 @@ namespace PerfectNumbers.Core.Gpu;
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internal static class DivisorByDivisorKernels
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{
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private const int WindowSizeMax = 8;
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public static void CheckKernel(
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Index1D index,
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ArrayView<MontgomeryDivisorData> divisors,
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ArrayView<ulong> divisors,
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ArrayView<ulong> exponents,
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ArrayView<byte> hits,
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ArrayView<int> firstHit)
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{
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int globalIndex = index;
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MontgomeryDivisorData divisor = divisors[globalIndex];
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ulong modulus = divisor.Modulus;
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// The GPU by-divisor pipeline only materializes odd moduli greater than one (q = 2kp + 1),
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// so the defensive guard for invalid values stays disabled here to keep the kernel branch-free.
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ulong modulus = divisors[globalIndex];
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ulong exponent = exponents[globalIndex];
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ulong montgomeryResult = ULongExtensions.Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponent);
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byte hit = montgomeryResult == 1UL ? (byte)1 : (byte)0;
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ulong result = Pow2ModWindowedKernel(exponent, modulus);
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byte hit = result == 1UL ? (byte)1 : (byte)0;
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hits[globalIndex] = hit;
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if (hit != 0)
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@@ -31,6 +30,100 @@ internal static class DivisorByDivisorKernels
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong Pow2ModWindowedKernel(ulong exponent, ulong modulus)
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{
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int bitLength = GetBitLength(exponent);
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int windowSize = GetWindowSize(bitLength);
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ulong result = 1UL;
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int index = bitLength - 1;
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while (index >= 0)
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{
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result = ULongExtensions.MulMod64Gpu(result, result, modulus);
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if (((exponent >> index) & 1UL) == 0UL)
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{
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index--;
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continue;
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}
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int windowStart = index - windowSize + 1;
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if (windowStart < 0)
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{
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windowStart = 0;
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}
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while (((exponent >> windowStart) & 1UL) == 0UL)
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{
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windowStart++;
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}
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int windowLength = index - windowStart + 1;
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for (int square = 1; square < windowLength; square++)
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{
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result = ULongExtensions.MulMod64Gpu(result, result, modulus);
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}
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ulong mask = (1UL << windowLength) - 1UL;
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ulong windowValue = (exponent >> windowStart) & mask;
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ulong multiplier = ComputeWindowedOddPower(windowValue, modulus);
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result = ULongExtensions.MulMod64Gpu(result, multiplier, modulus);
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index = windowStart - 1;
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}
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong ComputeWindowedOddPower(ulong windowValue, ulong modulus)
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{
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ulong baseValue = 2UL % modulus;
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ulong result = baseValue;
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ulong remaining = (windowValue - 1UL) >> 1;
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ulong squareBase = ULongExtensions.MulMod64Gpu(baseValue, baseValue, modulus);
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while (remaining != 0UL)
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{
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if ((remaining & 1UL) != 0UL)
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{
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result = ULongExtensions.MulMod64Gpu(result, squareBase, modulus);
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}
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remaining >>= 1;
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if (remaining == 0UL)
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{
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break;
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}
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squareBase = ULongExtensions.MulMod64Gpu(squareBase, squareBase, modulus);
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}
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetBitLength(ulong value)
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{
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return 64 - XMath.LeadingZeroCount(value);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetWindowSize(int bitLength)
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{
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int window = WindowSizeMax;
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window = bitLength <= 671 ? 7 : window;
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window = bitLength <= 239 ? 6 : window;
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window = bitLength <= 79 ? 5 : window;
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window = bitLength <= 23 ? 4 : window;
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int clamped = bitLength >= 1 ? bitLength : 1;
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window = bitLength <= 6 ? clamped : window;
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return window;
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}
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public static void EvaluateDivisorWithStepperKernel(
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Index1D _,
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MontgomeryDivisorData divisor,
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@@ -23,14 +23,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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private ulong _divisorLimit;
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// private bool _isConfigured;
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>> _kernelCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>> _kernelCache = new();
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private readonly ConcurrentDictionary<Accelerator, Action<Index1D, MontgomeryDivisorData, ulong, ulong, ArrayView<ulong>, ArrayView<byte>>> _stepperKernelCache = new(AcceleratorReferenceComparer.Instance);
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private readonly ConcurrentDictionary<Accelerator, ConcurrentBag<BatchResources>> _resourcePools = new(AcceleratorReferenceComparer.Instance);
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private readonly ConcurrentBag<GpuContextPool.GpuContextLease> _acceleratorPool = new();
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private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
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private Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> GetKernel(Accelerator accelerator) =>
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_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>(DivisorByDivisorKernels.CheckKernel));
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private Action<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> GetKernel(Accelerator accelerator) =>
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_kernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>>(DivisorByDivisorKernels.CheckKernel));
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private Action<Index1D, MontgomeryDivisorData, ulong, ulong, ArrayView<ulong>, ArrayView<byte>> GetStepperKernel(Accelerator accelerator) =>
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_stepperKernelCache.GetOrAdd(accelerator, acc => acc.LoadAutoGroupedStreamKernel<Index1D, MontgomeryDivisorData, ulong, ulong, ArrayView<ulong>, ArrayView<byte>>(DivisorByDivisorKernels.EvaluateDivisorWithStepperKernel));
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@@ -112,7 +112,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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resources.HitIndexBuffer,
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resources.Divisors,
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resources.Exponents,
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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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@@ -163,14 +162,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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private static bool CheckDivisors(
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ulong prime,
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ulong allowedMax,
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Action<Index1D, ArrayView<MontgomeryDivisorData>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> kernel,
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MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> divisorsBuffer,
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Action<Index1D, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>, ArrayView<int>> kernel,
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MemoryBuffer1D<ulong, 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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MemoryBuffer1D<int, Stride1D.Dense> hitIndexBuffer,
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in ulong[] divisors,
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ulong[] exponents,
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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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@@ -205,7 +203,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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ArrayPool<ulong> ulongPool = ThreadStaticPools.UlongPool;
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ulong[] filteredDivisors = ulongPool.Rent(chunkCapacity);
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Span<ulong> filteredStorage = filteredDivisors.AsSpan();
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Span<MontgomeryDivisorData> divisorDataStorage = divisorData.AsSpan();
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Span<ulong> divisorStorage = divisors.AsSpan();
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Span<ulong> exponentStorage = exponents.AsSpan();
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@@ -254,7 +251,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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Span<ulong> filteredDivisorsSpan = filteredStorage[..filteredCount];
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Span<MontgomeryDivisorData> divisorDataSpan = divisorDataStorage;
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Span<ulong> divisorSpan = divisorStorage;
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Span<ulong> exponentSpan = exponentStorage;
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@@ -271,7 +267,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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divisorSpan[admissibleCount] = divisorValue;
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exponentSpan[admissibleCount] = prime;
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divisorDataSpan[admissibleCount] = divisorDataValue;
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admissibleCount++;
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}
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@@ -281,14 +276,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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}
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Span<ulong> activeDivisors = divisorSpan[..admissibleCount];
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Span<MontgomeryDivisorData> activeDivisorData = divisorDataSpan[..admissibleCount];
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Span<ulong> activeExponents = exponentSpan[..admissibleCount];
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ArrayView1D<MontgomeryDivisorData, Stride1D.Dense> divisorView = divisorsBuffer.View.SubView(0, admissibleCount);
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ArrayView1D<ulong, Stride1D.Dense> divisorView = divisorsBuffer.View.SubView(0, admissibleCount);
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ArrayView1D<ulong, Stride1D.Dense> exponentView = exponentBuffer.View.SubView(0, admissibleCount);
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ArrayView1D<byte, Stride1D.Dense> hitsView = hitsBuffer.View.SubView(0, admissibleCount);
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ArrayView1D<int, Stride1D.Dense> hitIndexView = hitIndexBuffer.View.SubView(0, 1);
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divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(activeDivisorData), admissibleCount);
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divisorView.CopyFromCPU(ref MemoryMarshal.GetReference(activeDivisors), admissibleCount);
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exponentView.CopyFromCPU(ref MemoryMarshal.GetReference(activeExponents), admissibleCount);
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int sentinel = int.MaxValue;
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hitIndexView.SubView(0, 1).CopyFromCPU(ref sentinel, 1);
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@@ -586,18 +580,17 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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{
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int actualCapacity = Math.Max(1, capacity);
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DivisorsBuffer = accelerator.Allocate1D<MontgomeryDivisorData>(actualCapacity);
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DivisorsBuffer = accelerator.Allocate1D<ulong>(actualCapacity);
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ExponentBuffer = accelerator.Allocate1D<ulong>(actualCapacity);
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HitsBuffer = accelerator.Allocate1D<byte>(actualCapacity);
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HitIndexBuffer = accelerator.Allocate1D<int>(1);
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ArrayPool<ulong> ulongPool = ThreadStaticPools.UlongPool;
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Divisors = ulongPool.Rent(actualCapacity);
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Exponents = ulongPool.Rent(actualCapacity);
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DivisorData = ThreadStaticPools.MontgomeryDivisorDataPool.Rent(actualCapacity);
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Capacity = actualCapacity;
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}
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internal readonly MemoryBuffer1D<MontgomeryDivisorData, Stride1D.Dense> DivisorsBuffer;
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internal readonly MemoryBuffer1D<ulong, Stride1D.Dense> DivisorsBuffer;
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internal readonly MemoryBuffer1D<ulong, Stride1D.Dense> ExponentBuffer;
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@@ -609,8 +602,6 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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internal readonly ulong[] Exponents;
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internal readonly MontgomeryDivisorData[] DivisorData;
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internal readonly int Capacity;
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public void Dispose()
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@@ -620,10 +611,8 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
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HitsBuffer.Dispose();
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HitIndexBuffer.Dispose();
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ArrayPool<ulong> ulongPool = ThreadStaticPools.UlongPool;
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ArrayPool<MontgomeryDivisorData> divisorPool = ThreadStaticPools.MontgomeryDivisorDataPool;
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ulongPool.Return(Divisors, clearArray: false);
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ulongPool.Return(Exponents, clearArray: false);
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divisorPool.Return(DivisorData, clearArray: false);
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}
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}
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