mpn_ctx_init, mpn_ctx_clear

The eight primes are $p_0 = p$ (or, if $p$ is not prime, the first prime in the sequence below) and then the next primes of the sequence obtained by repeatedly subtracting $2^{v + 1}$ from the previous value, where $2^v \| p - 1$; when that would lose a bit, the bit size is kept and the two-adic valuation is decreased by one. Each prime must pass fft_small_mulmod_satisfies_bounds and have $2^4 \mid p - 1$, or sd_fft_ctx_init_prime throws. Other starting values are meant only for testing: the packing profiles, the two-prime pipeline and the shortcut for moduli that are context primes all assume 50-bit primes.

Initialisation computes the twiddle factors for transforms of length up to $2^{12}$, the cofactors $P/p_i$ for the Chinese remainder theorem, and the tables $2^j \bmod p_i$ for $j < 256$. Longer twiddle tables are added on first use.

@misc{flint-doc-fft-small-mpn-ctx-init,
  author       = {{The FLINT team}},
  title        = {{mpn\_ctx\_init, mpn\_ctx\_clear (fft\_small.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fft_small/mpn_ctx_init.html},
  note         = {Generated 2026-11-02}
}