2.1 KiB
2.1 KiB
GPU Modular Arithmetic in the --mersenne=bydivisor Path
The GPU implementation now routes single-use exponent checks through standard modular arithmetic while keeping Montgomery reduction only where repeated multiplications reuse the same modulus.
Kernels using standard modular arithmetic
CheckKernelinMersenneNumberDivisorByDivisorGpuTesterevaluates each divisor candidate withPow2ModBinaryGpuand compares the result directly against 1. 【F:PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs†L561-L645】【F:PerfectNumbers.Core/ULongExtensions.cs†L314-L339】ComputeExponentKernelin the same tester precomputes batched residues with the plain helper so CPU lookups receive standard-domain results. 【F:PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs†L780-L791】【F:PerfectNumbers.Core/ULongExtensions.cs†L314-L339】ComputeResiduesKernelinsideMersenneNumberDivisorResidueGpuEvaluatornow mirrors that logic when building residue tables for mixed CPU/GPU scans. 【F:PerfectNumbers.Core/Gpu/MersenneNumberDivisorResidueGpuEvaluator.cs†L102-L114】【F:PerfectNumbers.Core/ULongExtensions.cs†L314-L339】- The order-search helpers in
PrimeOrderGpuHeuristics(TrySpecialMaxKernel,ExponentLoweringKernel,Pow2EqualsOneKernel, and the narrowPow2ModKernel) also rely onPow2ModBinaryGpufor their equality checks and residue generation. 【F:PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs†L798-L866】【F:PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs†L1812-L1823】
Kernels still using Montgomery arithmetic
MontgomeryOddPowerKernelScaninGpuKernelPoolcontinues to build windowed odd-power tables withMontgomeryMultiply, which amortizes the Montgomery setup over many multiplications per modulus. 【F:PerfectNumbers.Core/Gpu/GpuKernelPool.cs†L200-L237】【F:PerfectNumbers.Core/ULongExtensions.cs†L532-L559】
Shared helper
Pow2ModBinaryGpuinULongExtensionsimplements the GPU-friendly binary exponentiation loop that powers the standard modular path across these kernels. 【F:PerfectNumbers.Core/ULongExtensions.cs†L314-L339】