Restore GPU-backed UInt128 pow2 Montgomery helper
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Marek Lemańczyk committed
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@@ -1,9 +1,12 @@
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using System;
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using System.Buffers;
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using System.Collections.Concurrent;
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using ILGPU;
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using ILGPU.Runtime;
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using System.Numerics;
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using PerfectNumbers.Core;
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using System.Runtime.InteropServices;
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using System.Runtime.CompilerServices;
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namespace PerfectNumbers.Core.Gpu;
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internal enum GpuPow2ModStatus
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@@ -16,10 +19,24 @@ internal enum GpuPow2ModStatus
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internal static class PrimeOrderGpuHeuristics
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{
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private static readonly ConcurrentDictionary<ulong, byte> OverflowedPrimes = new();
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private static readonly ConcurrentDictionary<UInt128, byte> OverflowedPrimesWide = new();
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private static readonly ConcurrentDictionary<Accelerator, Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>>> Pow2ModKernelCache = new();
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private static readonly ConcurrentDictionary<Accelerator, Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>> Pow2ModKernelWideCache = new();
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private const int WideStackThreshold = 8;
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private static PrimeOrderGpuCapability s_capability = PrimeOrderGpuCapability.Default;
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private const int Pow2WindowSizeBits = 8;
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private const int Pow2WindowOddPowerCount = 1 << (Pow2WindowSizeBits - 1);
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private const ulong Pow2WindowFallbackThreshold = 32UL;
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[InlineArray(Pow2WindowOddPowerCount)]
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private struct Pow2OddPowerTable
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{
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private GpuUInt128 _element0;
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}
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internal static ConcurrentDictionary<ulong, byte> OverflowRegistry => OverflowedPrimes;
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internal static ConcurrentDictionary<UInt128, byte> OverflowRegistryWide => OverflowedPrimesWide;
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internal static void OverrideCapabilitiesForTesting(PrimeOrderGpuCapability capability)
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{
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@@ -89,6 +106,59 @@ internal static class PrimeOrderGpuHeuristics
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return computed ? GpuPow2ModStatus.Success : GpuPow2ModStatus.Unavailable;
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}
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public static GpuPow2ModStatus TryPow2Mod(UInt128 exponent, UInt128 prime, out UInt128 remainder)
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{
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Span<UInt128> exponents = stackalloc UInt128[1];
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Span<UInt128> remainders = stackalloc UInt128[1];
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exponents[0] = exponent;
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GpuPow2ModStatus status = TryPow2ModBatch(exponents, prime, remainders);
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remainder = remainders[0];
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return status;
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}
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public static GpuPow2ModStatus TryPow2ModBatch(ReadOnlySpan<UInt128> exponents, UInt128 prime, Span<UInt128> remainders)
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{
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if (exponents.Length == 0)
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{
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return GpuPow2ModStatus.Success;
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}
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if (remainders.Length < exponents.Length)
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{
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throw new ArgumentException("Remainder span is shorter than the exponent span.", nameof(remainders));
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}
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Span<UInt128> target = remainders.Slice(0, exponents.Length);
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target.Clear();
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ConcurrentDictionary<UInt128, byte> overflowRegistryWide = OverflowedPrimesWide;
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if (overflowRegistryWide.ContainsKey(prime))
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{
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return GpuPow2ModStatus.Overflow;
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}
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PrimeOrderGpuCapability capability = s_capability;
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if (prime.GetBitLength() > capability.ModulusBits)
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{
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overflowRegistryWide[prime] = 0;
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return GpuPow2ModStatus.Overflow;
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}
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for (int i = 0; i < exponents.Length; i++)
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{
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if (exponents[i].GetBitLength() > capability.ExponentBits)
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{
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return GpuPow2ModStatus.Overflow;
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}
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}
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bool computed = TryComputeOnGpuWide(exponents, prime, target);
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return computed ? GpuPow2ModStatus.Success : GpuPow2ModStatus.Unavailable;
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}
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private static bool TryComputeOnGpu(ReadOnlySpan<ulong> exponents, ulong prime, Span<ulong> results)
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{
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try
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@@ -128,12 +198,94 @@ internal static class PrimeOrderGpuHeuristics
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private static void ComputePow2ModCpu(ReadOnlySpan<ulong> exponents, ulong prime, Span<ulong> results)
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{
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for (int i = 0; i < exponents.Length; i++)
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int length = exponents.Length;
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for (int i = 0; i < length; i++)
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{
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results[i] = Pow2ModCpu(exponents[i], prime);
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}
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}
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private static bool TryComputeOnGpuWide(ReadOnlySpan<UInt128> exponents, UInt128 prime, Span<UInt128> results)
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{
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int length = exponents.Length;
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if (length == 0)
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{
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return true;
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}
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GpuUInt128[]? rentedExponents = null;
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GpuUInt128[]? rentedResults = null;
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var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
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try
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{
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using var execution = lease.EnterExecutionScope();
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Accelerator accelerator = lease.Accelerator;
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AcceleratorStream stream = lease.Stream;
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var kernel = GetPow2ModWideKernel(accelerator);
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using var exponentBuffer = accelerator.Allocate1D<GpuUInt128>(length);
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using var remainderBuffer = accelerator.Allocate1D<GpuUInt128>(length);
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Span<GpuUInt128> exponentSpan = length <= WideStackThreshold
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? stackalloc GpuUInt128[length]
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: new Span<GpuUInt128>(rentedExponents = ArrayPool<GpuUInt128>.Shared.Rent(length), 0, length);
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for (int i = 0; i < length; i++)
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{
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exponentSpan[i] = (GpuUInt128)exponents[i];
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}
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exponentBuffer.View.CopyFromCPU(ref MemoryMarshal.GetReference(exponentSpan), length);
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remainderBuffer.MemSetToZero();
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GpuUInt128 modulus = (GpuUInt128)prime;
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kernel(stream, length, exponentBuffer.View, modulus, remainderBuffer.View);
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stream.Synchronize();
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Span<GpuUInt128> resultSpan = length <= WideStackThreshold
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? stackalloc GpuUInt128[length]
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: new Span<GpuUInt128>(rentedResults = ArrayPool<GpuUInt128>.Shared.Rent(length), 0, length);
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remainderBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(resultSpan), length);
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for (int i = 0; i < length; i++)
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{
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results[i] = (UInt128)resultSpan[i];
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}
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return true;
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}
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catch (Exception ex) when (ex is AcceleratorException or InternalCompilerException or NotSupportedException or InvalidOperationException or AggregateException)
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{
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ComputePow2ModCpuWide(exponents, prime, results);
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return true;
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}
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finally
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{
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if (rentedExponents is not null)
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{
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ArrayPool<GpuUInt128>.Shared.Return(rentedExponents, clearArray: false);
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}
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if (rentedResults is not null)
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{
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ArrayPool<GpuUInt128>.Shared.Return(rentedResults, clearArray: false);
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}
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lease.Dispose();
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}
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}
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private static void ComputePow2ModCpuWide(ReadOnlySpan<UInt128> exponents, UInt128 prime, Span<UInt128> results)
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{
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int length = exponents.Length;
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for (int i = 0; i < length; i++)
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{
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results[i] = exponents[i].Pow2MontgomeryModWindowed(prime);
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}
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}
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private static ulong Pow2ModCpu(ulong exponent, ulong modulus)
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{
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if (modulus <= 1UL)
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@@ -161,8 +313,191 @@ internal static class PrimeOrderGpuHeuristics
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remainders[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false);
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}
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private static Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>> GetPow2ModWideKernel(Accelerator accelerator)
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{
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return Pow2ModKernelWideCache.GetOrAdd(accelerator, static accel =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>(Pow2ModKernelWide);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>>>();
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});
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}
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private static void Pow2ModKernelWide(Index1D index, ArrayView1D<GpuUInt128, Stride1D.Dense> exponents, GpuUInt128 modulus, ArrayView1D<GpuUInt128, Stride1D.Dense> remainders)
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{
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GpuUInt128 exponent = exponents[index];
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remainders[index] = Pow2ModKernelCore(exponent, modulus);
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}
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private static GpuUInt128 Pow2ModKernelCore(GpuUInt128 exponent, GpuUInt128 modulus)
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{
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if (modulus == GpuUInt128.One)
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{
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return GpuUInt128.Zero;
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}
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if (exponent.IsZero)
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{
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return GpuUInt128.One;
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}
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GpuUInt128 baseValue = new GpuUInt128(2UL);
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if (baseValue.CompareTo(modulus) >= 0)
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{
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baseValue.Sub(modulus);
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}
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if (ShouldUseSingleBit(exponent))
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{
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return Pow2MontgomeryModSingleBit(exponent, modulus, baseValue);
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}
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int bitLength = exponent.GetBitLength();
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int windowSize = GetWindowSize(bitLength);
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int oddPowerCount = 1 << (windowSize - 1);
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Pow2OddPowerTable oddPowers = default;
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InitializeOddPowers(ref oddPowers, baseValue, modulus, oddPowerCount);
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GpuUInt128 result = GpuUInt128.One;
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int index = bitLength - 1;
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while (index >= 0)
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{
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if (!IsBitSet(exponent, index))
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{
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result.MulMod(result, modulus);
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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 (!IsBitSet(exponent, windowStart))
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{
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windowStart++;
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}
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int windowBitCount = index - windowStart + 1;
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for (int square = 0; square < windowBitCount; square++)
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{
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result.MulMod(result, modulus);
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}
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ulong windowValue = ExtractWindowValue(exponent, windowStart, windowBitCount);
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int tableIndex = (int)((windowValue - 1UL) >> 1);
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GpuUInt128 factor = oddPowers[tableIndex];
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result.MulMod(factor, 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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private static bool ShouldUseSingleBit(in GpuUInt128 exponent) => exponent.High == 0UL && exponent.Low <= Pow2WindowFallbackThreshold;
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private static int GetWindowSize(int bitLength)
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{
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if (bitLength <= Pow2WindowSizeBits)
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{
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return Math.Max(bitLength, 1);
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}
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if (bitLength <= 23)
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{
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return 4;
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}
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if (bitLength <= 79)
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{
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return 5;
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}
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if (bitLength <= 239)
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{
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return 6;
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}
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if (bitLength <= 671)
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{
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return 7;
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}
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return Pow2WindowSizeBits;
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}
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private static void InitializeOddPowers(ref Pow2OddPowerTable oddPowers, GpuUInt128 baseValue, GpuUInt128 modulus, int oddPowerCount)
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{
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oddPowers[0] = baseValue;
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if (oddPowerCount == 1)
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{
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return;
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}
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// Reusing baseValue to hold base^2 for the shared odd-power ladder that follows.
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baseValue.MulMod(baseValue, modulus);
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for (int i = 1; i < oddPowerCount; i++)
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{
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oddPowers[i] = oddPowers[i - 1];
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oddPowers[i].MulMod(baseValue, modulus);
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}
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}
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private static GpuUInt128 Pow2MontgomeryModSingleBit(GpuUInt128 exponent, GpuUInt128 modulus, GpuUInt128 baseValue)
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{
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GpuUInt128 result = GpuUInt128.One;
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while (!exponent.IsZero)
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{
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if ((exponent.Low & 1UL) != 0UL)
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{
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result.MulMod(baseValue, modulus);
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}
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exponent.ShiftRight(1);
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if (exponent.IsZero)
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{
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break;
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}
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// Reusing baseValue to store the squared base for the next iteration.
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baseValue.MulMod(baseValue, modulus);
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}
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return result;
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}
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private static bool IsBitSet(in GpuUInt128 value, int bitIndex)
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{
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if (bitIndex >= 64)
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{
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return ((value.High >> (bitIndex - 64)) & 1UL) != 0UL;
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}
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return ((value.Low >> bitIndex) & 1UL) != 0UL;
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}
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private static ulong ExtractWindowValue(in GpuUInt128 exponent, int windowStart, int windowBitCount)
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{
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if (windowStart != 0)
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{
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GpuUInt128 shifted = exponent;
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shifted.ShiftRight(windowStart);
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ulong mask = (1UL << windowBitCount) - 1UL;
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return shifted.Low & mask;
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}
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ulong directMask = (1UL << windowBitCount) - 1UL;
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return exponent.Low & directMask;
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}
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internal readonly record struct PrimeOrderGpuCapability(int ModulusBits, int ExponentBits)
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{
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public static PrimeOrderGpuCapability Default => new(128, 64);
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public static PrimeOrderGpuCapability Default => new(128, 128);
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}
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}
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