408 lines
19 KiB
C#
408 lines
19 KiB
C#
using System.Collections.Concurrent;
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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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using PerfectNumbers.Core.Gpu;
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namespace PerfectNumbers.Core;
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public static partial class ULongExtensions
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{
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong MulHighGpuCompatible(this ulong x, ulong y)
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{
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GpuUInt128 product = new(x);
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GpuUInt128.Mul64(ref product, 0UL, y);
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return product.High;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong MulMod64Gpu(this ulong a, ulong b, ulong modulus)
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{
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// TODO: Remove this GPU-compatible shim from production once callers migrate to MulMod64,
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// which the benchmarks show is roughly 6-7× faster on dense 64-bit inputs.
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GpuUInt128 state = new(a % modulus);
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return state.MulMod(b, modulus);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong MulMod64GpuDeferred(this ulong a, ulong b, ulong modulus)
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{
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// TODO: Move this deferred helper to the benchmark suite; the baseline MulMod64 avoids the
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// 5-40× slowdown seen across real-world operand distributions.
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GpuUInt128 state = new(a);
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return state.MulModWithNativeModulo(b, modulus);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Pow2ModWindowedGpu(this ulong exponent, ulong modulus)
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{
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// EvenPerfectBitScanner never routes moduli ≤ 1 through this path; keep the guard commented out so the hot loop stays branch-free.
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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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// EvenPerfectBitScanner always works with positive exponents here; leave the defensive check commented for future reference.
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// if (exponent == 0UL)
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// {
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// return 1UL % modulus;
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// }
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int bitLength = GetPortableBitLengthGpu(exponent);
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int windowSize = GetWindowSizeGpu(bitLength);
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int oddPowerCount = 1 << (windowSize - 1);
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// oddPowerCount is always ≥ 1 for the production workloads handled by EvenPerfectBitScanner.
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// if (oddPowerCount <= 0)
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// {
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// return 1UL;
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// }
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ulong[] oddPowersArray = ThreadStaticPools.UlongPool.Rent(oddPowerCount);
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Span<ulong> oddPowers = oddPowersArray.AsSpan(0, oddPowerCount);
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InitializeStandardOddPowers(modulus, oddPowers);
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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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ulong currentBit = (exponent >> index) & 1UL;
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ulong squared = result.MulMod64Gpu(result, modulus);
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result = currentBit == 0UL ? squared : result;
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index = currentBit == 0UL ? index - 1 : index;
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if (currentBit == 0UL)
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{
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continue;
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}
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int windowStart = index - windowSize + 1;
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// EvenPerfectBitScanner guarantees windowStart stays non-negative for production exponents, so keep the guard commented out to avoid extra branching.
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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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windowStart = GetNextSetBitIndexGpu(exponent, windowStart);
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int windowLength = index - windowStart + 1;
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for (int square = 0; square < windowLength; square++)
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{
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result = result.MulMod64Gpu(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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int tableIndex = (int)((windowValue - 1UL) >> 1);
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ulong multiplier = oddPowers[tableIndex];
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result = result.MulMod64Gpu(multiplier, modulus);
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index = windowStart - 1;
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}
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ThreadStaticPools.UlongPool.Return(oddPowersArray);
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return result;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static ulong Pow2MontgomeryModWindowedGpuKeepMontgomery(in MontgomeryDivisorData divisor, ulong exponent)
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{
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return Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static ulong Pow2MontgomeryModWindowedGpuConvertToStandard(in MontgomeryDivisorData divisor, ulong exponent)
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{
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ulong modulus = divisor.Modulus;
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ulong nPrime = divisor.NPrime;
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ulong montgomeryResult = Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
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return MontgomeryMultiply(montgomeryResult, 1UL, modulus, nPrime);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong Pow2MontgomeryModWindowedGpuMontgomeryResult(in MontgomeryDivisorData divisor, ulong exponent)
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{
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ulong modulus = divisor.Modulus;
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// Reuse the optimized MontgomeryMultiply extension highlighted in MontgomeryMultiplyBenchmarks so the GPU path matches the fastest CPU reduction.
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// We shouldn't hit it in production code. If we do, we're doing something wrong.
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// if (exponent == 0UL)
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// {
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// return divisor.MontgomeryOne;
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// }
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// We barely ever hit it in production code. It's e.g. 772 calls out of billions
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// if (exponent <= Pow2WindowFallbackThreshold)
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// {
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// return Pow2MontgomeryModSingleBit(exponent, divisor);
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// }
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int bitLength = GetPortableBitLengthGpu(exponent);
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int windowSize = GetWindowSizeGpu(bitLength);
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ulong result = divisor.MontgomeryOne;
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ulong nPrime = divisor.NPrime;
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int index = bitLength - 1;
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while (index >= 0)
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{
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ulong currentBit = (exponent >> index) & 1UL;
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ulong squared = MontgomeryMultiply(result, result, modulus, nPrime);
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bool processWindow = currentBit != 0UL;
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result = processWindow ? result : squared;
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index -= (int)(currentBit ^ 1UL);
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int windowStartCandidate = index - windowSize + 1;
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// if (windowStartCandidate < 0)
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// {
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// windowStartCandidate = 0;
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// }
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// Clamp the negative offset without branching so the GPU loop stays divergence-free.
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// This still handles windows that would otherwise extend past the most significant bit.
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int negativeMask = windowStartCandidate >> 31;
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windowStartCandidate &= ~negativeMask;
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int windowStart = processWindow ? GetNextSetBitIndexGpu(exponent, windowStartCandidate) : windowStartCandidate;
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int windowLength = processWindow ? index - windowStart + 1 : 0;
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for (int square = 0; square < windowLength; square++)
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{
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result = MontgomeryMultiply(result, result, modulus, nPrime);
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}
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result = processWindow
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? MontgomeryMultiply(
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result,
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ComputeMontgomeryOddPowerGpu(
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(exponent >> windowStart) & ((1UL << windowLength) - 1UL),
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divisor,
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modulus,
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nPrime),
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modulus,
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nPrime)
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: result;
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index = processWindow ? windowStart - 1 : index;
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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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public static ulong Pow2MontgomeryModWindowedGpu(this ulong exponent, in MontgomeryDivisorData divisor, bool keepMontgomery)
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{
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// We shouldn't hit it in production code. If we do, we're doing something wrong.
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// ulong modulus = divisor.Modulus;
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// if (exponent == 0UL)
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// {
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// return divisor.MontgomeryOne;
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// }
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// We barely ever hit it in production code. It's e.g. 772 calls out of billions
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// if (exponent <= Pow2WindowFallbackThreshold)
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// {
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// return Pow2MontgomeryModSingleBit(exponent, divisor);
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// }
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return keepMontgomery
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? Pow2MontgomeryGpuExecutor.ExecuteKeep(exponent, divisor)
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: Pow2MontgomeryGpuExecutor.ExecuteConvert(exponent, divisor);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void InitializeStandardOddPowers(ulong modulus, Span<ulong> oddPowers)
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{
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// oddPowers spans at least one entry for production workloads; keep the guard commented out to avoid redundant checks in the hot loop.
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// if (oddPowers.IsEmpty)
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// {
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// return;
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// }
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// EvenPerfectBitScanner feeds odd prime moduli (≥ 3) here, so the base value stays within range without a modulo reduction.
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ulong baseValue = 2UL;
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oddPowers[0] = baseValue;
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if (oddPowers.Length == 1)
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{
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return;
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}
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ulong square = baseValue.MulMod64Gpu(baseValue, modulus);
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for (int i = 1; i < oddPowers.Length; i++)
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{
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ulong previous = oddPowers[i - 1];
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oddPowers[i] = previous.MulMod64Gpu(square, modulus);
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static ulong ComputeMontgomeryOddPowerGpu(ulong exponent, in MontgomeryDivisorData divisor, ulong modulus, ulong nPrime)
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{
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ulong baseValue = divisor.MontgomeryTwo;
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ulong power = divisor.MontgomeryOne;
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ulong remaining = exponent;
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while (remaining != 0UL)
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{
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ulong bit = remaining & 1UL;
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ulong multiplied = MontgomeryMultiply(power, baseValue, modulus, nPrime);
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ulong mask = (ulong)-(long)bit;
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power = (power & ~mask) | (multiplied & mask);
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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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baseValue = MontgomeryMultiply(baseValue, baseValue, modulus, nPrime);
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}
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return power;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetPortableBitLengthGpu(ulong value)
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{
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// Keep this commented out. It will never happen in production code.
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// if (value == 0UL)
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// {
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// return 0;
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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 GetWindowSizeGpu(int n)
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{
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int w = Pow2WindowSize;
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w = (n <= 671) ? 7 : w;
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w = (n <= 239) ? 6 : w;
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w = (n <= 79) ? 5 : w;
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w = (n <= 23) ? 4 : w;
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int m = (n >= 1) ? n : 1;
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w = (n <= 6) ? m : w;
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return w;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static int GetNextSetBitIndexGpu(ulong exponent, int startIndex)
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{
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ulong guard = (ulong)(((long)startIndex - 64) >> 63);
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int shift = startIndex & 63;
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ulong mask = (~0UL << shift) & guard;
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ulong masked = exponent & mask;
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return XMath.TrailingZeroCount(masked);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Pow2MontgomeryModWithCycleGpu(this ulong exponent, ulong cycleLength, in MontgomeryDivisorData divisor)
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{
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ulong rotationCount = exponent % cycleLength;
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return Pow2MontgomeryGpuExecutor.ExecuteConvert(rotationCount, divisor);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static ulong Pow2MontgomeryModFromCycleRemainderGpu(this ulong reducedExponent, in MontgomeryDivisorData divisor)
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{
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return Pow2MontgomeryGpuExecutor.ExecuteConvert(reducedExponent, divisor);
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}
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private static class Pow2MontgomeryGpuExecutor
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{
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private static readonly ConcurrentDictionary<Accelerator, Pow2MontgomeryKernelGroup> KernelCache = new();
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public static ulong ExecuteKeep(ulong exponent, in MontgomeryDivisorData divisor)
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{
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return Execute(exponent, divisor, useKeepKernel: true);
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}
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public static ulong ExecuteConvert(ulong exponent, in MontgomeryDivisorData divisor)
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{
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return Execute(exponent, divisor, useKeepKernel: false);
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}
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private static ulong Execute(ulong exponent, in MontgomeryDivisorData divisor, bool useKeepKernel)
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{
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ulong result = 0UL;
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GpuKernelLease lease = GpuKernelPool.GetKernel(useGpuOrder: true);
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var execution = lease.EnterExecutionScope();
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Accelerator accelerator = lease.Accelerator;
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// Keep this commented out. It should never happen in production code.
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// if (accelerator.AcceleratorType == AcceleratorType.CPU)
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// {
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// return 0UL;
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// }
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var kernelGroup = KernelCache.GetOrAdd(accelerator, static accel => Pow2MontgomeryKernelGroup.Create(accel));
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var exponentBuffer = accelerator.Allocate1D<ulong>(1);
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var resultBuffer = accelerator.Allocate1D<ulong>(1);
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exponentBuffer.View.CopyFromCPU(ref exponent, 1);
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// We don't need to worry about any left-overs here.
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// resultBuffer.MemSetToZero();
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var kernel = useKeepKernel ? kernelGroup.KeepMontgomery : kernelGroup.ConvertToStandard;
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AcceleratorStream stream = lease.Stream;
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kernel(stream, 1, exponentBuffer.View, divisor, resultBuffer.View);
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stream.Synchronize();
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resultBuffer.View.CopyToCPU(ref result, 1);
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resultBuffer.Dispose();
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exponentBuffer.Dispose();
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execution.Dispose();
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lease.Dispose();
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// Keep this commented. We don't want to catch any exceptions. All should crash the scanner.
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// catch (AcceleratorException)
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// {
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// return 0UL;
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// }
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// catch (NotSupportedException)
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// {
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// return 0UL;
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// }
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// Intentionally avoid exception handling here; any accelerator failure should crash the scanner.
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return result;
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}
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private sealed class Pow2MontgomeryKernelGroup
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{
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internal Pow2MontgomeryKernelGroup(
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Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> keepMontgomery,
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Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> convertToStandard)
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{
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KeepMontgomery = keepMontgomery;
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ConvertToStandard = convertToStandard;
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}
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internal Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> KeepMontgomery { get; }
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internal Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> ConvertToStandard { get; }
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internal static Pow2MontgomeryKernelGroup Create(Accelerator accelerator)
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{
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var keepKernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelKeepMontgomery);
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var keepLauncher = KernelUtil.GetKernel(keepKernel);
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var keepDelegate = keepLauncher.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
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var convertKernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelConvertToStandard);
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var convertLauncher = KernelUtil.GetKernel(convertKernel);
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var convertDelegate = convertLauncher.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>>();
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return new Pow2MontgomeryKernelGroup(keepDelegate, convertDelegate);
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}
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}
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}
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}
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