using ILGPU; using ILGPU.Runtime; using PerfectNumbers.Core; namespace PerfectNumbers.Core.Gpu; internal static class DivisorByDivisorKernels { public static void CheckKernel(Index1D index, ArrayView divisors, ArrayView exponents, ArrayView hits) { MontgomeryDivisorData divisor = divisors[index]; ulong modulus = divisor.Modulus; // The GPU by-divisor pipeline only materializes odd moduli greater than one (q = 2kp + 1), // so the defensive guard for invalid values stays disabled here to keep the kernel branch-free. ulong exponent = exponents[index]; ulong montgomeryResult = ULongExtensions.Pow2MontgomeryModWindowedGpuConvertToStandard(divisor, exponent); hits[index] = montgomeryResult == 1UL ? (byte)1 : (byte)0; } public static void GenerateCandidatesAndGapsKernel( Index1D index, ArrayView candidates, ArrayView gaps, GpuUInt128 startValue, GpuUInt128 stride) { int globalIndex = index; int candidateLength = (int)candidates.Length; if (globalIndex >= candidateLength) { return; } ulong offset = (ulong)globalIndex; GpuUInt128 candidateValue; if (offset == 0UL) { candidateValue = startValue; } else { candidateValue = stride; candidateValue.Mul(offset); candidateValue.Add(startValue); } candidates[globalIndex] = candidateValue.Low; int gapLength = (int)gaps.Length; if (globalIndex >= gapLength) { return; } if (offset == 0UL) { gaps[globalIndex] = 0UL; return; } GpuUInt128 previousValue = startValue; ulong previousOffset = offset - 1UL; if (previousOffset != 0UL) { GpuUInt128 scaledStride = stride; scaledStride.Mul(previousOffset); previousValue.Add(scaledStride); } GpuUInt128 gapValue = candidateValue; gapValue.Sub(previousValue); gaps[globalIndex] = gapValue.Low; } public static void ComputeRemainderDeltasKernel(Index1D index, ArrayView gaps, ArrayView deltas, byte modulus) { deltas[index] = (byte)(gaps[index] % modulus); } public static void AccumulateRemaindersKernel( Index1D index, ArrayView deltas, ArrayView remainders, byte baseRemainder, byte modulus) { int globalIndex = index; int length = (int)remainders.Length; if (globalIndex >= length) { return; } int localIndex = Group.IdxX; int groupSize = Group.Dimension.X; var shared = SharedMemory.GetDynamic(); shared[localIndex] = deltas[globalIndex]; Group.Barrier(); int offset = 1; int mod = modulus; while (offset < groupSize) { bool apply = localIndex >= offset; int addend = apply ? shared[localIndex - offset] : 0; Group.Barrier(); int current = shared[localIndex]; int sum = apply ? current + addend : current; int wrap = sum >= mod ? 1 : 0; sum -= wrap * mod; shared[localIndex] = apply ? sum : current; Group.Barrier(); offset <<= 1; } int remainder = baseRemainder + shared[localIndex]; int remainderWrap = remainder >= mod ? 1 : 0; remainder -= remainderWrap * mod; remainders[globalIndex] = (byte)remainder; } public static void EvaluateCandidateMaskKernel( Index1D index, ArrayView remainder10, ArrayView remainder8, ArrayView remainder5, ArrayView remainder3, byte lastIsSevenFlag, ArrayView mask) { int globalIndex = index; int length = (int)mask.Length; if (globalIndex >= length) { return; } byte value10 = remainder10[globalIndex]; bool lastIsSeven = lastIsSevenFlag != 0; bool acceptSeven = value10 == 3 || value10 == 7 || value10 == 9; bool acceptNonSeven = value10 == 1 || value10 == 3 || value10 == 7 || value10 == 9; bool accept10 = lastIsSeven ? acceptSeven : acceptNonSeven; byte value8 = remainder8[globalIndex]; bool accept8 = value8 == 1 || value8 == 7; bool accept5 = remainder5[globalIndex] != 0; bool accept3 = remainder3[globalIndex] != 0; byte accepted = (byte)((accept10 && accept8 && accept3 && accept5) ? 1 : 0); mask[globalIndex] = accepted; } public static void ComputeMontgomeryExponentKernel(Index1D index, MontgomeryDivisorData divisor, ArrayView exponents, ArrayView results) { ulong modulus = divisor.Modulus; // Each divisor flowing through this kernel follows q = 2kp + 1 with k >= 1, so modulus is always odd and exceeds one. ulong exponent = exponents[index]; ulong montgomeryResult = ULongExtensions.Pow2MontgomeryModWindowedGpuKeepMontgomery(divisor, exponent); results[index] = montgomeryResult; } }