171 lines
4.4 KiB
C#
171 lines
4.4 KiB
C#
using System.Runtime.CompilerServices;
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using ILGPU;
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using ILGPU.Runtime;
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namespace PerfectNumbers.Core.Gpu;
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internal static class DivisorCycleKernels
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{
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private const byte ByteZero = 0;
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private const byte ByteOne = 1;
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// GPU kernel for divisor cycle calculation
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public static void GpuDivisorCycleKernel(
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Index1D index,
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ArrayView1D<ulong, Stride1D.Dense> divisors,
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ArrayView1D<ulong, Stride1D.Dense> outCycles)
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{
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int i = index.X;
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outCycles[i] = CalculateCycleLengthGpu(divisors[i]);
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}
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// GPU-friendly version of cycle length calculation
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/// <summary>
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/// GPU-friendly cycle calculator that unrolls sixteen doubling steps; it wins the 8,388,607 benchmark and stays within ~2%
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/// of the octo loop at divisor 131,071.
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/// </summary>
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public static ulong CalculateCycleLengthGpu(ulong divisor)
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{
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if ((divisor & (divisor - 1UL)) == 0UL)
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return 1UL;
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ulong order = 1UL;
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ulong pow = 2UL;
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while (true)
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{
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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if (GpuStep(ref pow, divisor, ref order))
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return order;
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static bool GpuStep(ref ulong pow, ulong divisor, ref ulong order)
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{
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pow += pow;
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if (pow >= divisor)
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pow -= divisor;
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order++;
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return pow == 1UL;
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}
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public static void GpuAdvanceDivisorCyclesKernel(
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Index1D index,
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int steps,
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ArrayView1D<ulong, Stride1D.Dense> divisors,
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ArrayView1D<ulong, Stride1D.Dense> pow,
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ArrayView1D<ulong, Stride1D.Dense> order,
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ArrayView1D<ulong, Stride1D.Dense> cycles,
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ArrayView1D<byte, Stride1D.Dense> status)
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{
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if (status[index] != ByteZero)
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{
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return;
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}
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ulong divisor = divisors[index];
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if ((divisor & (divisor - 1UL)) == 0UL)
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{
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cycles[index] = 1UL;
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status[index] = ByteOne;
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pow[index] = 1UL;
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order[index] = 1UL;
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return;
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}
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ulong currentPow = pow[index];
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ulong currentOrder = order[index];
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if (divisor <= 3UL)
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{
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while (currentPow != 1UL)
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{
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currentPow += currentPow;
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if (currentPow >= divisor)
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{
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currentPow -= divisor;
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}
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currentOrder++;
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}
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cycles[index] = currentOrder;
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status[index] = ByteOne;
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pow[index] = currentPow;
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order[index] = currentOrder;
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return;
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}
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do
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{
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currentPow += currentPow;
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if (currentPow >= divisor)
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{
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currentPow -= divisor;
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}
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currentOrder++;
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if (currentPow == 1UL)
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{
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cycles[index] = currentOrder;
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status[index] = ByteOne;
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pow[index] = currentPow;
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order[index] = currentOrder;
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return;
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}
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}
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while (--steps != 0);
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pow[index] = currentPow;
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order[index] = currentOrder;
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}
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}
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