730 lines
26 KiB
C#
730 lines
26 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.Runtime;
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using static PerfectNumbers.Core.Gpu.GpuContextPool;
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namespace PerfectNumbers.Core.Gpu;
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public sealed class GpuKernelLease
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{
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private static readonly ConcurrentQueue<GpuKernelLease> Pool = new();
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private IDisposable? _limiter;
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private GpuContextLease? _gpu;
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private KernelContainer? _kernels;
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private AcceleratorStream? _stream;
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private object? _executionLock;
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private bool _disposed;
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private GpuKernelLease()
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{
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}
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internal static GpuKernelLease Rent(IDisposable limiter, GpuContextLease gpu, KernelContainer kernels)
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{
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if (!Pool.TryDequeue(out var lease))
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{
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lease = new GpuKernelLease();
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}
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lease._limiter = limiter;
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lease._gpu = gpu;
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lease._kernels = kernels;
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lease._stream = null;
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lease._executionLock = gpu.ExecutionLock;
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lease._disposed = false;
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return lease;
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}
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public Accelerator Accelerator => _gpu?.Accelerator ?? throw new NullReferenceException("GPU context is already released");
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public AcceleratorStream Stream
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{
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get
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{
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if (_stream is { } stream)
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{
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return stream;
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}
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// It feels that we can combine these into 1 return statement, but that increases the max stack frame size to 3 from 2
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stream = Accelerator.CreateStream();
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_stream = stream;
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return stream;
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}
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}
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public ExecutionScope EnterExecutionScope() => new ExecutionScope(_executionLock);
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public Action<AcceleratorStream, Index1D, ulong, ulong, ArrayView<GpuUInt128>, ArrayView<ulong>> OrderKernel
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{
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get
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{
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var accel = Accelerator; // avoid capturing 'this' in lambda
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lock (_gpu!.Value.KernelInitLock)
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{
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return KernelContainer.InitOnce(ref _kernels!.Order, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, ulong, ArrayView<GpuUInt128>, ArrayView<ulong>>(OrderKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, ulong, ArrayView<GpuUInt128>, ArrayView<ulong>>>();
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});
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}
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}
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}
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> Pow2ModKernel
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{
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get
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{
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var accel = Accelerator;
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lock (_gpu!.Value.KernelInitLock)
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{
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return KernelContainer.InitOnce(ref _kernels!.Pow2Mod, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(Pow2ModKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
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});
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}
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}
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}
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ulong, ulong, ulong, ulong, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>> IncrementalKernel
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{
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get
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{
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var accel = Accelerator;
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lock (_gpu!.Value.KernelInitLock)
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{
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return KernelContainer.InitOnce(ref _kernels!.Incremental, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ulong, ulong, ulong, ulong, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>>(IncrementalKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ulong, ulong, ulong, ulong, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>>>();
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});
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}
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}
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}
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>> IncrementalOrderKernel
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{
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get
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{
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var accel = Accelerator;
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lock (_gpu!.Value.KernelInitLock)
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{
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return KernelContainer.InitOnce(ref _kernels!.IncrementalOrder, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>(IncrementalOrderKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>>();
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});
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}
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}
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}
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>> Pow2ModOrderKernel
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{
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get
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{
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var accel = Accelerator;
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lock (_gpu!.Value.KernelInitLock)
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{
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return KernelContainer.InitOnce(ref _kernels!.Pow2ModOrder, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>(Pow2ModOrderKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>>();
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});
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}
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}
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}
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public Action<AcceleratorStream, Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> SmallPrimeFactorKernel
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{
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get
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{
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var accel = Accelerator;
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lock (_gpu!.Value.KernelInitLock)
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{
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return KernelContainer.InitOnce(ref _kernels!.SmallPrimeFactor, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(SmallPrimeFactorKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
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});
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}
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}
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}
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private static void SmallPrimeFactorKernelScan(
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Index1D index,
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ulong value,
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uint limit,
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ArrayView1D<uint, Stride1D.Dense> primes,
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ArrayView1D<ulong, Stride1D.Dense> squares,
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int primeCount,
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ArrayView1D<ulong, Stride1D.Dense> primeSlots,
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ArrayView1D<int, Stride1D.Dense> exponentSlots,
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ArrayView1D<int, Stride1D.Dense> countSlot,
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ArrayView1D<ulong, Stride1D.Dense> remainingSlot)
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{
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if (index != 0)
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{
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return;
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}
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uint effectiveLimit = limit == 0 ? uint.MaxValue : limit;
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ulong remaining = value;
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int count = 0;
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int capacity = (int)primeSlots.Length;
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for (int i = 0; i < primeCount && remaining > 1UL && count < capacity; i++)
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{
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uint primeCandidate = primes[i];
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if (primeCandidate == 0U || primeCandidate > effectiveLimit)
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{
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break;
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}
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ulong primeSquare = squares[i];
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if (primeSquare != 0UL && primeSquare > remaining)
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{
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break;
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}
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ulong primeValue = primeCandidate;
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if ((remaining % primeValue) != 0UL)
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{
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continue;
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}
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int exponent = 0;
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do
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{
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remaining /= primeValue;
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exponent++;
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}
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while ((remaining % primeValue) == 0UL);
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primeSlots[count] = primeValue;
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exponentSlots[count] = exponent;
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count++;
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}
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countSlot[0] = count;
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remainingSlot[0] = remaining;
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}
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// TODO: Plumb the small-cycles device buffer into all kernels that can benefit
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// (some already accept it). Consider a compact type (byte/ushort) for memory footprint.
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private static void IncrementalKernelScan(Index1D index, ulong exponent, GpuUInt128 twoP, GpuUInt128 kStart, byte lastIsSeven, ulong divMul,
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ulong q0m10, ulong q0m8, ulong q0m3, ulong q0m5, ArrayView<ulong> orders,
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ArrayView1D<ulong, Stride1D.Dense> smallCycles)
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{
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ulong idx = (ulong)index.X;
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// TODO: Replace these `%` computations with the precomputed Mod3/Mod5 tables so GPU kernels reuse cached residues
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// instead of performing modulo operations that the benchmarks showed slower on wide sweeps.
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ulong idxMod3 = idx % 3UL;
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ulong idxMod5 = idx % 5UL;
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// residue automaton
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ulong step10 = (exponent.Mod10() << 1).Mod10();
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ulong r10 = q0m10 + (step10 * idx).Mod10();
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r10 -= (r10 >= 10UL) ? 10UL : 0UL;
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bool shouldCheck = r10 != 5UL; // skip q ≡ 5 (mod 10); other residues handled by r8/r3/r5
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if (shouldCheck)
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{
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ulong step8 = ((exponent & 7UL) << 1) & 7UL;
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ulong r8 = (q0m8 + ((step8 * idx) & 7UL)) & 7UL;
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if (r8 != 1UL && r8 != 7UL)
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{
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shouldCheck = false;
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}
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else
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{
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// TODO: Swap these `%` filters to the shared Mod helpers so the residue automaton matches the benchmarked
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// bitmask-based implementation for GPU workloads.
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ulong step3 = ((exponent % 3UL) << 1) % 3UL;
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ulong r3 = q0m3 + (step3 * idxMod3); r3 -= (r3 >= 3UL) ? 3UL : 0UL;
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if (r3 == 0UL)
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{
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shouldCheck = false;
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}
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else
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{
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ulong step5Loc = ((exponent % 5UL) << 1) % 5UL;
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ulong r5 = q0m5 + (step5Loc * idxMod5); if (r5 >= 5UL) r5 -= 5UL;
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if (r5 == 0UL)
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{
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shouldCheck = false;
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}
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}
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}
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}
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if (!shouldCheck)
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{
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orders[index] = 0UL;
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return;
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}
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// TODO: Is this expected that the value of kStart is modified?
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GpuUInt128 k = kStart + (GpuUInt128)idx;
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GpuUInt128 q = twoP;
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q.Mul64(k);
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q.Add(GpuUInt128.One);
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ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
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// Small-cycles in-kernel early rejection from device table
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if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
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{
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ulong cycle = smallCycles[(int)q.Low];
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if (cycle != 0UL && cycle <= exponent && (exponent % cycle) != 0UL)
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{
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orders[index] = 0UL;
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return;
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}
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}
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// TODO: q will be lowered by GpuUInt128.One here. Is this expected? Maybe that's why we have issues with the incremental kernel? Review other places where we use GpuUInt128 operators.
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GpuUInt128 phi = q - GpuUInt128.One;
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// TODO: Do we have the check here because we don't support high values or this is expected result?
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if (phi.High != 0UL)
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{
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orders[index] = 0UL;
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return;
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}
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ulong phi64 = phi.Low;
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// TODO: Replace these Pow2Mod calls with the ProcessEightBitWindows helper when the shared windowed
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// scalar implementation lands; benchmarks showed the windowed kernel trimming per-divisor runtime by ~2.4×.
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if (GpuUInt128.Pow2Mod(phi64, in readOnlyQ) != GpuUInt128.One)
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{
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orders[index] = 0UL;
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return;
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}
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GpuUInt128 halfPow = GpuUInt128.Pow2Mod(phi64 >> 1, in readOnlyQ) - GpuUInt128.One;
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if (GpuUInt128.BinaryGcd(halfPow, q) != GpuUInt128.One)
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{
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orders[index] = 0UL;
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return;
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}
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ulong div = FastDiv64Gpu(phi64, exponent, divMul);
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GpuUInt128 divPow = GpuUInt128.Pow2Mod(div, in readOnlyQ) - GpuUInt128.One;
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if (GpuUInt128.BinaryGcd(divPow, q) != GpuUInt128.One)
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{
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orders[index] = 0UL;
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return;
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}
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orders[index] = 1UL;
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}
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private static void OrderKernelScan(Index1D index, ulong exponent, ulong divMul, ArrayView<GpuUInt128> qs, ArrayView<ulong> orders)
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{
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GpuUInt128 q = qs[index];
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ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
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GpuUInt128 phi = q - GpuUInt128.One;
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if (phi.High != 0UL)
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{
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orders[index] = 0UL;
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return;
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}
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ulong phi64 = phi.Low;
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// TODO: Once the ProcessEightBitWindows helper is available, switch this order kernel to that faster
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// Pow2Mod variant so cycle checks inherit the same gains observed in GpuPow2ModBenchmarks.
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GpuUInt128 pow = GpuUInt128.Pow2Mod(phi64, in readOnlyQ);
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if (pow != GpuUInt128.One)
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{
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orders[index] = 0UL;
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return;
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}
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GpuUInt128 halfPow = GpuUInt128.Pow2Mod(phi64 >> 1, in readOnlyQ) - GpuUInt128.One;
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if (GpuUInt128.BinaryGcd(halfPow, q) != GpuUInt128.One)
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{
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orders[index] = 0UL;
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return;
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}
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ulong div = FastDiv64Gpu(phi64, exponent, divMul);
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GpuUInt128 divPow = GpuUInt128.Pow2Mod(div, in readOnlyQ) - GpuUInt128.One;
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if (GpuUInt128.BinaryGcd(divPow, q) != GpuUInt128.One)
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{
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orders[index] = 0UL;
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return;
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}
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orders[index] = exponent;
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}
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private void Dispose(bool disposing)
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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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if (disposing)
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{
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_stream?.Dispose();
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_stream = null;
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_gpu?.Dispose();
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_gpu = null;
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_executionLock = null;
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_limiter?.Dispose();
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_limiter = null;
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}
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_kernels = null;
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_disposed = true;
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Pool.Enqueue(this);
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}
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private static void Pow2ModKernelScan(Index1D index, ulong exponent, GpuUInt128 twoP, GpuUInt128 kStart, byte lastIsSeven, ulong _,
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ResidueAutomatonArgs ra, ArrayView<ulong> orders,
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ArrayView1D<ulong, Stride1D.Dense> smallCycles,
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ArrayView1D<uint, Stride1D.Dense> smallPrimesLastOne,
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ArrayView1D<uint, Stride1D.Dense> smallPrimesLastSeven,
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ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastOne,
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ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastSeven)
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{
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ulong idx = (ulong)index.X;
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ulong idxMod3 = idx % 3UL;
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ulong idxMod5 = idx % 5UL;
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ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
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bool shouldCheck = r10 != 5UL;
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if (shouldCheck)
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{
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ulong r8 = (ra.Q0M8 + ((ra.Step8 * idx) & 7UL)) & 7UL;
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if (r8 != 1UL && r8 != 7UL)
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{
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shouldCheck = false;
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}
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else
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{
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ulong r3 = ra.Q0M3 + (ra.Step3 * idxMod3);
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if (r3 >= 6UL) r3 -= 6UL;
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if (r3 >= 3UL) r3 -= 3UL;
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if (r3 == 0UL)
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{
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shouldCheck = false;
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}
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else
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{
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ulong r5 = ra.Q0M5 + (ra.Step5 * idxMod5);
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if (r5 >= 15UL) r5 -= 15UL;
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if (r5 >= 10UL) r5 -= 10UL;
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if (r5 >= 5UL) r5 -= 5UL;
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if (r5 == 0UL)
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{
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shouldCheck = false;
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}
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}
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}
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}
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if (!shouldCheck)
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{
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orders[index] = 0UL;
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return;
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}
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// TODO: kStart is modified after this. Is this expected?
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kStart.Add(idx);
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GpuUInt128 q = twoP;
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q.Mul64(kStart);
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q.Add(GpuUInt128.One);
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ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
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if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
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{
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ulong cycle = smallCycles[(int)q.Low];
|
||
// cycle should always be initialized if we're within array limit in production code
|
||
if (cycle != 0UL && cycle <= exponent && (exponent % cycle) != 0UL)
|
||
{
|
||
orders[index] = 0UL;
|
||
return;
|
||
}
|
||
}
|
||
// TODO: Swap Pow2Minus1Mod for the eight-bit window helper once the scalar version switches;
|
||
// benchmarks show the windowed variant cuts large-divisor scans from ~51 µs to ~21 µs.
|
||
if (GpuUInt128.Pow2Minus1Mod(exponent, in readOnlyQ) != GpuUInt128.Zero)
|
||
{
|
||
orders[index] = 0UL;
|
||
return;
|
||
}
|
||
|
||
ArrayView1D<uint, Stride1D.Dense> primes = lastIsSeven != 0 ? smallPrimesLastSeven : smallPrimesLastOne;
|
||
ArrayView1D<ulong, Stride1D.Dense> primesPow2 = lastIsSeven != 0 ? smallPrimesPow2LastSeven : smallPrimesPow2LastOne;
|
||
int primesLen = (int)primes.Length;
|
||
for (int i = 0; i < primesLen; i++)
|
||
{
|
||
ulong square = primesPow2[i];
|
||
if (new GpuUInt128(0UL, square) > q)
|
||
{
|
||
break;
|
||
}
|
||
ulong prime = primes[i];
|
||
if (Mod128By64(q, prime) == 0UL)
|
||
{
|
||
orders[index] = 0UL;
|
||
return;
|
||
}
|
||
}
|
||
|
||
orders[index] = exponent;
|
||
}
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static ulong FastDiv64Gpu(ulong value, ulong divisor, ulong mul)
|
||
{
|
||
ulong quotient = GpuUInt128.MulHigh(value, mul);
|
||
GpuUInt128 remainder = new(0UL, value);
|
||
GpuUInt128 product = new(GpuUInt128.MulHigh(quotient, divisor), quotient * divisor);
|
||
remainder.Sub(product);
|
||
|
||
if (remainder.High != 0UL || remainder.Low >= divisor)
|
||
{
|
||
quotient++;
|
||
}
|
||
|
||
return quotient;
|
||
}
|
||
|
||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||
private static ulong Mod128By64(GpuUInt128 value, ulong modulus)
|
||
{
|
||
ulong rem = 0UL;
|
||
ulong part = value.High;
|
||
for (int i = 0; i < 64; i++)
|
||
{
|
||
rem = (rem << 1) | (part >> 63);
|
||
if (rem >= modulus)
|
||
{
|
||
rem -= modulus;
|
||
}
|
||
part <<= 1;
|
||
}
|
||
|
||
part = value.Low;
|
||
for (int i = 0; i < 64; i++)
|
||
{
|
||
rem = (rem << 1) | (part >> 63);
|
||
if (rem >= modulus)
|
||
{
|
||
rem -= modulus;
|
||
}
|
||
part <<= 1;
|
||
}
|
||
|
||
return rem;
|
||
}
|
||
|
||
// Device-friendly small cycle length for 2 mod divisor
|
||
private static ulong CalculateCycleLengthSmall(ulong divisor)
|
||
{
|
||
if ((divisor & (divisor - 1UL)) == 0UL)
|
||
return 1UL;
|
||
|
||
ulong order = 1UL, pow = 2UL;
|
||
while (pow != 1UL)
|
||
{
|
||
pow <<= 1;
|
||
if (pow > divisor)
|
||
pow -= divisor;
|
||
|
||
order++;
|
||
}
|
||
|
||
return order;
|
||
}
|
||
|
||
private static void IncrementalOrderKernelScan(Index1D index, ulong exponent, GpuUInt128 twoP, GpuUInt128 kStart, byte lastIsSeven, ulong divMul,
|
||
ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<ulong, Stride1D.Dense> smallCycles)
|
||
{
|
||
ulong idx = (ulong)index.X;
|
||
ulong idxMod3 = idx % 3UL;
|
||
ulong idxMod5 = idx % 5UL;
|
||
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
|
||
bool shouldCheck = r10 != 5UL;
|
||
if (shouldCheck)
|
||
{
|
||
ulong r8 = (ra.Q0M8 + ((ra.Step8 * idx) & 7UL)) & 7UL;
|
||
if (r8 != 1UL && r8 != 7UL)
|
||
{
|
||
shouldCheck = false;
|
||
}
|
||
else
|
||
{
|
||
ulong r3 = ra.Q0M3 + (ra.Step3 * idxMod3);
|
||
if (r3 >= 6UL) r3 -= 6UL;
|
||
if (r3 >= 3UL) r3 -= 3UL;
|
||
if (r3 == 0UL)
|
||
{
|
||
shouldCheck = false;
|
||
}
|
||
else
|
||
{
|
||
ulong r5 = ra.Q0M5 + (ra.Step5 * idxMod5);
|
||
if (r5 >= 15UL) r5 -= 15UL;
|
||
if (r5 >= 10UL) r5 -= 10UL;
|
||
if (r5 >= 5UL) r5 -= 5UL;
|
||
if (r5 == 0UL)
|
||
{
|
||
shouldCheck = false;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
if (!shouldCheck)
|
||
{
|
||
return;
|
||
}
|
||
|
||
GpuUInt128 k = kStart + (GpuUInt128)idx;
|
||
GpuUInt128 q = twoP;
|
||
q.Mul64(k);
|
||
q.Add(GpuUInt128.One);
|
||
ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
|
||
|
||
// Small-cycles in-kernel early rejection from device table
|
||
if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
|
||
{
|
||
ulong cycle = smallCycles[(int)q.Low];
|
||
if (cycle != 0UL && cycle <= exponent && (exponent % cycle) != 0UL)
|
||
{
|
||
return;
|
||
}
|
||
}
|
||
GpuUInt128 phi = q - GpuUInt128.One;
|
||
if (phi.High != 0UL)
|
||
{
|
||
return;
|
||
}
|
||
|
||
ulong phi64 = phi.Low;
|
||
// TODO: Upgrade this pow2mod order kernel to the ProcessEightBitWindows helper once available so GPU residue
|
||
// scans avoid the single-bit ladder that benchmarks found to be 2.3× slower on large exponents.
|
||
if (GpuUInt128.Pow2Mod(phi64, in readOnlyQ) != GpuUInt128.One)
|
||
{
|
||
return;
|
||
}
|
||
|
||
GpuUInt128 halfPow = GpuUInt128.Pow2Mod(phi64 >> 1, in readOnlyQ) - GpuUInt128.One;
|
||
if (GpuUInt128.BinaryGcd(halfPow, q) != GpuUInt128.One)
|
||
{
|
||
return;
|
||
}
|
||
|
||
ulong div = FastDiv64Gpu(phi64, exponent, divMul);
|
||
GpuUInt128 divPow = GpuUInt128.Pow2Mod(div, in readOnlyQ) - GpuUInt128.One;
|
||
if (GpuUInt128.BinaryGcd(divPow, q) != GpuUInt128.One)
|
||
{
|
||
return;
|
||
}
|
||
|
||
Atomic.Or(ref found[0], 1);
|
||
}
|
||
|
||
private static void Pow2ModOrderKernelScan(Index1D index, ulong exponent, GpuUInt128 twoP, GpuUInt128 kStart, byte lastIsSeven, ulong _,
|
||
ResidueAutomatonArgs ra, ArrayView<int> found, ArrayView1D<ulong, Stride1D.Dense> smallCycles)
|
||
{
|
||
ulong idx = (ulong)index.X;
|
||
ulong idxMod3 = idx % 3UL;
|
||
ulong idxMod5 = idx % 5UL;
|
||
ulong r10 = ra.Q0M10 + (ra.Step10 * idx).Mod10(); r10 -= (r10 >= 10UL) ? 10UL : 0UL;
|
||
bool shouldCheck = r10 != 5UL;
|
||
if (shouldCheck)
|
||
{
|
||
ulong r8 = (ra.Q0M8 + ((ra.Step8 * idx) & 7UL)) & 7UL;
|
||
if (r8 != 1UL && r8 != 7UL)
|
||
{
|
||
shouldCheck = false;
|
||
}
|
||
else
|
||
{
|
||
ulong r3 = ra.Q0M3 + (ra.Step3 * idxMod3);
|
||
if (r3 >= 6UL) r3 -= 6UL;
|
||
if (r3 >= 3UL) r3 -= 3UL;
|
||
if (r3 == 0UL)
|
||
{
|
||
shouldCheck = false;
|
||
}
|
||
else
|
||
{
|
||
ulong r5 = ra.Q0M5 + (ra.Step5 * idxMod5);
|
||
if (r5 >= 15UL) r5 -= 15UL;
|
||
if (r5 >= 10UL) r5 -= 10UL;
|
||
if (r5 >= 5UL) r5 -= 5UL;
|
||
if (r5 == 0UL)
|
||
{
|
||
shouldCheck = false;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
if (!shouldCheck)
|
||
{
|
||
return;
|
||
}
|
||
|
||
GpuUInt128 k = kStart + (GpuUInt128)idx;
|
||
GpuUInt128 q = twoP;
|
||
q.Mul64(k);
|
||
q.Add(GpuUInt128.One);
|
||
ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
|
||
// Small-cycles in-kernel early rejection from device table
|
||
if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
|
||
{
|
||
ulong cycle = smallCycles[(int)q.Low];
|
||
if (cycle != 0UL && cycle <= exponent && (exponent % cycle) != 0UL)
|
||
{
|
||
return;
|
||
}
|
||
}
|
||
// TODO: Replace this Pow2Mod check with the ProcessEightBitWindows helper once Pow2Minus1Mod adopts it;
|
||
// residue order scans will then benefit from the same 2× speedup the benchmarked windowed kernel delivered.
|
||
if (GpuUInt128.Pow2Mod(exponent, in readOnlyQ) != GpuUInt128.One)
|
||
{
|
||
return;
|
||
}
|
||
|
||
Atomic.Or(ref found[0], 1);
|
||
}
|
||
|
||
public void Dispose()
|
||
{
|
||
Dispose(disposing: false);
|
||
}
|
||
|
||
public readonly struct ExecutionScope
|
||
{
|
||
private readonly object? _lock;
|
||
|
||
public ExecutionScope(object? sync)
|
||
{
|
||
_lock = sync;
|
||
if (_lock is not null)
|
||
{
|
||
Monitor.Enter(_lock);
|
||
}
|
||
}
|
||
|
||
public void Dispose()
|
||
{
|
||
if (_lock is not null)
|
||
{
|
||
Monitor.Exit(_lock);
|
||
}
|
||
}
|
||
}
|
||
}
|