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small prime FFT based on ulong #2107
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This PR aims to have an ulong-based version of small prime FFT. This is a draft, comments and suggestions highly welcome (on any aspect: for example I have no idea if
n_fft
is relevant naming).For the moment, the features implemented are:
Performance: observed on a few different machines, AMD zen 4 and various Intel. This slightly outperforms NTL's versions of the forward and inverse FFTs (acceleration of 0% to 30% depending on lengths). This is between 2 and 4 times slower, often around 3, than the vectorized floating point-based small-prime FFT in
fft_small
(or than the similar AVX-based version in NTL). This version uses no simd: enabling/disabling automatic vectorization does not change performance, and a straightforward "manual" vectorization should not bring much. The reason being that every few operations there is a full 64 bit multiplication (umul_ppmm
) happening. (Still, I made some experiments that suggest avx could help, maybe substantially on AMD processors which have a very fast vpmullq, but I leave this aside for later.)Planned:
Planned, but likely not within this PR: