865 lines
34 KiB
C#
865 lines
34 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 readonly struct ResidueAutomatonArgs
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{
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public readonly ulong Q0M10;
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public readonly ulong Step10;
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public readonly ulong Q0M8;
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public readonly ulong Step8;
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public readonly ulong Q0M3;
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public readonly ulong Step3;
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public readonly ulong Q0M5;
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public readonly ulong Step5;
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public ResidueAutomatonArgs(ulong q0m10, ulong step10, ulong q0m8, ulong step8, ulong q0m3, ulong step3, ulong q0m5, ulong step5)
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{
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Q0M10 = q0m10; Step10 = step10; Q0M8 = q0m8; Step8 = step8; Q0M3 = q0m3; Step3 = step3; Q0M5 = q0m5; Step5 = step5;
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}
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}
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public sealed class KernelContainer
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{
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// Serializes first-time initialization of kernels/buffers per accelerator.
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public Action<AcceleratorStream, Index1D, ulong, ulong, ArrayView<GpuUInt128>, ArrayView<ulong>>? Order;
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong,
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ulong, ulong, ulong, ulong, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>>? Incremental;
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong,
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ResidueAutomatonArgs, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>,
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ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>,
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ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>? Pow2Mod;
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong,
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ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>? IncrementalOrder;
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public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong,
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ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>? Pow2ModOrder;
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public Action<AcceleratorStream, Index1D, ArrayView1D<MontgomeryDivisorData, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int>? MontgomeryOddPowers;
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// Optional device buffer with small divisor cycles (<= 4M). Index = divisor, value = cycle length.
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public MemoryBuffer1D<ulong, Stride1D.Dense>? SmallCycles;
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public MemoryBuffer1D<uint, Stride1D.Dense>? SmallPrimesLastOne;
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public MemoryBuffer1D<ulong, Stride1D.Dense>? SmallPrimesPow2LastOne;
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public MemoryBuffer1D<uint, Stride1D.Dense>? SmallPrimesLastSeven;
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public MemoryBuffer1D<ulong, Stride1D.Dense>? SmallPrimesPow2LastSeven;
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public static T InitOnce<T>(ref T? slot, Func<T> factory) where T : class
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{
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var current = Volatile.Read(ref slot);
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if (current is not null)
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{
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return current;
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}
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current = Volatile.Read(ref slot);
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if (current is null)
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{
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current = factory();
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Volatile.Write(ref slot, current);
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}
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return current;
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}
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}
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public readonly struct ResiduePrimeViews(
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ArrayView1D<uint, Stride1D.Dense> lastOne,
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ArrayView1D<uint, Stride1D.Dense> lastSeven,
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ArrayView1D<ulong, Stride1D.Dense> lastOnePow2,
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ArrayView1D<ulong, Stride1D.Dense> lastSevenPow2)
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{
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public readonly ArrayView1D<uint, Stride1D.Dense> LastOne = lastOne;
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public readonly ArrayView1D<uint, Stride1D.Dense> LastSeven = lastSeven;
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public readonly ArrayView1D<ulong, Stride1D.Dense> LastOnePow2 = lastOnePow2;
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public readonly ArrayView1D<ulong, Stride1D.Dense> LastSevenPow2 = lastSevenPow2;
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}
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public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, KernelContainer kernels)
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{
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private bool disposedValue;
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private IDisposable? _limiter = limiter;
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private GpuContextLease? _gpu = gpu;
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private KernelContainer _kernels = kernels;
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private AcceleratorStream? _stream;
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private object? _executionLock = gpu.ExecutionLock;
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public readonly 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 readonly ExecutionScope EnterExecutionScope() => new ExecutionScope(_executionLock);
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public readonly 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 readonly 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 readonly 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 readonly 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 readonly 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 readonly Action<AcceleratorStream, Index1D, ArrayView1D<MontgomeryDivisorData, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int> MontgomeryOddPowerKernel
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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.MontgomeryOddPowers, () =>
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{
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var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<MontgomeryDivisorData, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int>(MontgomeryOddPowerKernelScan);
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var kernel = KernelUtil.GetKernel(loaded);
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return kernel.CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<MontgomeryDivisorData, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int>>();
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});
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}
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}
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}
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private static void MontgomeryOddPowerKernelScan(
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Index1D index,
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ArrayView1D<MontgomeryDivisorData, Stride1D.Dense> divisors,
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ArrayView1D<int, Stride1D.Dense> counts,
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ArrayView1D<ulong, Stride1D.Dense> results,
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int stride)
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{
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int tableIndex = index.X;
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int baseOffset = tableIndex * stride;
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MontgomeryDivisorData divisor = divisors[tableIndex];
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int oddPowerCount = counts[tableIndex];
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if (oddPowerCount <= 0)
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{
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return;
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}
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ulong montgomeryTwo = divisor.MontgomeryTwo;
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results[baseOffset] = montgomeryTwo;
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if (oddPowerCount == 1)
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{
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return;
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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 square = divisor.MontgomeryTwoSquared;
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ulong current = montgomeryTwo;
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for (int i = 1; i < oddPowerCount; i++)
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{
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current = ULongExtensions.MontgomeryMultiply(current, square, modulus, nPrime);
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results[baseOffset + i] = current;
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}
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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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|
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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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|
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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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|
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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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|
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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;
|
||
}
|
||
|
||
orders[index] = exponent;
|
||
}
|
||
|
||
private void Dispose(bool disposing)
|
||
{
|
||
if (!disposedValue)
|
||
{
|
||
if (disposing)
|
||
{
|
||
_stream?.Dispose();
|
||
_stream = null;
|
||
|
||
if (_gpu.HasValue)
|
||
{
|
||
_gpu.Value.ReturnToPool();
|
||
}
|
||
_gpu = null;
|
||
|
||
_executionLock = null;
|
||
|
||
_limiter?.Dispose();
|
||
_limiter = null;
|
||
}
|
||
|
||
// free unmanaged resources (unmanaged objects) and override finalizer
|
||
// set large fields to null
|
||
disposedValue = true;
|
||
}
|
||
}
|
||
|
||
private static void Pow2ModKernelScan(Index1D index, ulong exponent, GpuUInt128 twoP, GpuUInt128 kStart, byte lastIsSeven, ulong _,
|
||
ResidueAutomatonArgs ra, ArrayView<ulong> orders,
|
||
ArrayView1D<ulong, Stride1D.Dense> smallCycles,
|
||
ArrayView1D<uint, Stride1D.Dense> smallPrimesLastOne,
|
||
ArrayView1D<uint, Stride1D.Dense> smallPrimesLastSeven,
|
||
ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastOne,
|
||
ArrayView1D<ulong, Stride1D.Dense> smallPrimesPow2LastSeven)
|
||
{
|
||
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)
|
||
{
|
||
orders[index] = 0UL;
|
||
return;
|
||
}
|
||
|
||
// TODO: kStart is modified after this. Is this expected?
|
||
kStart.Add(idx);
|
||
GpuUInt128 q = twoP;
|
||
q.Mul64(kStart);
|
||
q.Add(GpuUInt128.One);
|
||
ReadOnlyGpuUInt128 readOnlyQ = q.AsReadOnly();
|
||
if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
|
||
{
|
||
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()
|
||
{
|
||
// Do not change this code. Put cleanup code in 'Dispose(bool disposing)' method
|
||
Dispose(disposing: true);
|
||
// Enabled this when the struct is converted to a class
|
||
// GC.SuppressFinalize(this);
|
||
}
|
||
|
||
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);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
public class GpuKernelPool
|
||
{
|
||
private static readonly ConcurrentDictionary<Accelerator, KernelContainer> KernelCache = new(); // TODO: Replace this concurrent map with a simple accelerator-indexed lookup once kernel launchers are prewarmed during startup so we can drop the thread-safe wrapper entirely.
|
||
|
||
public static bool CpuCycleUsesGpu { get; set; }
|
||
|
||
private static KernelContainer GetKernels(Accelerator accelerator)
|
||
{
|
||
return KernelCache.GetOrAdd(accelerator, _ => new KernelContainer());
|
||
}
|
||
|
||
// Ensures the small cycles table is uploaded to the device for the given accelerator.
|
||
// Returns the ArrayView to pass into kernels (when kernels are extended to accept it).
|
||
public static ArrayView1D<ulong, Stride1D.Dense> EnsureSmallCyclesOnDevice(Accelerator accelerator)
|
||
{
|
||
var kernels = GetKernels(accelerator);
|
||
if (kernels.SmallCycles is { } buffer)
|
||
{
|
||
return buffer.View;
|
||
}
|
||
|
||
// Ensure single upload per accelerator even if multiple threads race here.
|
||
lock (kernels) // TODO: Remove this lock by pre-uploading the immutable small-cycle snapshot during initialization; once no mutation happens at runtime, the pool must expose a simple reference without synchronization.
|
||
{
|
||
if (kernels.SmallCycles is { } existing)
|
||
{
|
||
return existing.View;
|
||
}
|
||
|
||
var host = MersenneDivisorCycles.Shared.ExportSmallCyclesSnapshot(); // TODO: Preload this device buffer during startup and keep it immutable so we can delete the lock above in favor of the preloaded snapshot.
|
||
var device = accelerator.Allocate1D<ulong>(host.Length);
|
||
device.View.CopyFromCPU(host);
|
||
kernels.SmallCycles = device;
|
||
return device.View;
|
||
}
|
||
}
|
||
|
||
public static ResiduePrimeViews EnsureSmallPrimesOnDevice(Accelerator accelerator)
|
||
{
|
||
var kernels = GetKernels(accelerator);
|
||
if (kernels.SmallPrimesLastOne is { } lastOne &&
|
||
kernels.SmallPrimesLastSeven is { } lastSeven &&
|
||
kernels.SmallPrimesPow2LastOne is { } lastOnePow2 &&
|
||
kernels.SmallPrimesPow2LastSeven is { } lastSevenPow2)
|
||
{
|
||
return new ResiduePrimeViews(lastOne.View, lastSeven.View, lastOnePow2.View, lastSevenPow2.View);
|
||
}
|
||
|
||
lock (kernels) // TODO: Inline these small-prime uploads into startup initialization alongside the small-cycle snapshot so we can drop runtime locking and keep the GPU pool free of synchronization.
|
||
{
|
||
if (kernels.SmallPrimesLastOne is { } existingLastOne &&
|
||
kernels.SmallPrimesLastSeven is { } existingLastSeven &&
|
||
kernels.SmallPrimesPow2LastOne is { } existingLastOnePow2 &&
|
||
kernels.SmallPrimesPow2LastSeven is { } existingLastSevenPow2)
|
||
{
|
||
return new ResiduePrimeViews(existingLastOne.View, existingLastSeven.View, existingLastOnePow2.View, existingLastSevenPow2.View);
|
||
}
|
||
|
||
var hostLastOne = PrimesGenerator.SmallPrimesLastOne;
|
||
var hostLastSeven = PrimesGenerator.SmallPrimesLastSeven;
|
||
var hostLastOnePow2 = PrimesGenerator.SmallPrimesPow2LastOne;
|
||
var hostLastSevenPow2 = PrimesGenerator.SmallPrimesPow2LastSeven;
|
||
|
||
var deviceLastOne = accelerator.Allocate1D<uint>(hostLastOne.Length);
|
||
deviceLastOne.View.CopyFromCPU(hostLastOne);
|
||
var deviceLastSeven = accelerator.Allocate1D<uint>(hostLastSeven.Length);
|
||
deviceLastSeven.View.CopyFromCPU(hostLastSeven);
|
||
var deviceLastOnePow2 = accelerator.Allocate1D<ulong>(hostLastOnePow2.Length);
|
||
deviceLastOnePow2.View.CopyFromCPU(hostLastOnePow2);
|
||
var deviceLastSevenPow2 = accelerator.Allocate1D<ulong>(hostLastSevenPow2.Length);
|
||
deviceLastSevenPow2.View.CopyFromCPU(hostLastSevenPow2);
|
||
|
||
kernels.SmallPrimesLastOne = deviceLastOne;
|
||
kernels.SmallPrimesLastSeven = deviceLastSeven;
|
||
kernels.SmallPrimesPow2LastOne = deviceLastOnePow2;
|
||
kernels.SmallPrimesPow2LastSeven = deviceLastSevenPow2;
|
||
|
||
return new ResiduePrimeViews(deviceLastOne.View, deviceLastSeven.View, deviceLastOnePow2.View, deviceLastSevenPow2.View);
|
||
}
|
||
}
|
||
|
||
public static GpuKernelLease GetKernel(bool useGpuOrder)
|
||
{
|
||
var limiter = GpuPrimeWorkLimiter.Acquire();
|
||
var gpu = RentPreferred(preferCpu: !useGpuOrder);
|
||
var accelerator = gpu.Accelerator;
|
||
var kernels = GetKernels(accelerator);
|
||
return new(limiter, gpu, kernels);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Runs a GPU action with an acquired accelerator and stream.
|
||
/// </summary>
|
||
/// <param name="action">Action to run with (Accelerator, Stream).</param>
|
||
public static void Run(Action<Accelerator, AcceleratorStream> action)
|
||
{
|
||
var lease = GetKernel(useGpuOrder: true);
|
||
var execution = lease.EnterExecutionScope();
|
||
var accelerator = lease.Accelerator;
|
||
var stream = accelerator.CreateStream();
|
||
action(accelerator, stream);
|
||
stream.Dispose();
|
||
execution.Dispose();
|
||
lease.Dispose();
|
||
|
||
}
|
||
}
|