even-perfect-numbers-scanner/PerfectNumbers.Core/Gpu/Kernels/Pow2ModKernels.cs

using ILGPU;
using ILGPU.Algorithms;
using ILGPU.Runtime;

namespace PerfectNumbers.Core.Gpu;

internal static class Pow2ModKernels
{
    public 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;
        GpuUInt128.Mul64(ref q, kStart.High, kStart.Low);
        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 (KernelMathHelpers.Mod128By64(q, prime) == 0UL)
            {
                orders[index] = 0UL;
                return;
            }
        }

        orders[index] = exponent;
    }

    public 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;
        GpuUInt128.Mul64(ref q, k.High, k.Low);
        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);
    }
}