Document GPU kernel audit progress
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Marek Lemańczyk committed
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using ILGPU;
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using ILGPU.Algorithms;
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using ILGPU.Runtime;
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namespace PerfectNumbers.Core.Gpu;
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internal static class Pow2ModKernels
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{
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public static void Pow2ModKernelScan(
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Index1D index,
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ulong exponent,
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GpuUInt128 twoP,
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GpuUInt128 kStart,
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byte lastIsSeven,
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ulong _,
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ResidueAutomatonArgs ra,
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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];
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// cycle should always be initialized if we're within array limit in production code
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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: Swap Pow2Minus1Mod for the eight-bit window helper once the scalar version switches;
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// benchmarks show the windowed variant cuts large-divisor scans from ~51 µs to ~21 µs.
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if (GpuUInt128.Pow2Minus1Mod(exponent, in readOnlyQ) != GpuUInt128.Zero)
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{
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orders[index] = 0UL;
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return;
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}
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ArrayView1D<uint, Stride1D.Dense> primes = lastIsSeven != 0 ? smallPrimesLastSeven : smallPrimesLastOne;
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ArrayView1D<ulong, Stride1D.Dense> primesPow2 = lastIsSeven != 0 ? smallPrimesPow2LastSeven : smallPrimesPow2LastOne;
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int primesLen = (int)primes.Length;
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for (int i = 0; i < primesLen; i++)
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{
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ulong square = primesPow2[i];
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if (new GpuUInt128(0UL, square) > q)
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{
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break;
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}
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ulong prime = primes[i];
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if (KernelMathHelpers.Mod128By64(q, prime) == 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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orders[index] = exponent;
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}
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public static void Pow2ModOrderKernelScan(
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Index1D index,
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ulong exponent,
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GpuUInt128 twoP,
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GpuUInt128 kStart,
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byte lastIsSeven,
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ulong _,
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ResidueAutomatonArgs ra,
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ArrayView<int> found,
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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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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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return;
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}
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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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return;
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}
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}
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// TODO: Replace this Pow2Mod check with the ProcessEightBitWindows helper once Pow2Minus1Mod adopts it;
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// residue order scans will then benefit from the same 2× speedup the benchmarked windowed kernel delivered.
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if (GpuUInt128.Pow2Mod(exponent, in readOnlyQ) != GpuUInt128.One)
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{
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return;
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}
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Atomic.Or(ref found[0], 1);
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}
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}
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