`mpn_ctx_struct, mpn_ctx_t`

Synopsis#include <flint/fft_small.h>

mpn_ctx_struct

mpn_ctx_t

A multiplication context. It holds the transform contexts of MPN_CTX_NCRTS = 8 primes, the Chinese remaindering data for the first $k$ of them for every $k \le 8$ , tables of powers of two modulo each prime for converting integers, the table of packing profiles, the constants of the two-prime pipeline, and a scratch buffer that grows on demand and is kept between calls.

The primes are generated from the initial prime given to mpn_ctx_init. FLINT always uses $p_0 = 63 \cdot 2^{44} + 1$ , which yields

$i$	$p_i$	form
0	1108307720798209	$63 \cdot 2^{44} + 1$
1	659706976665601	$75 \cdot 2^{43} + 1$
2	1086317488242689	$247 \cdot 2^{42} + 1$
3	910395627798529	$207 \cdot 2^{42} + 1$
4	699289395265537	$159 \cdot 2^{42} + 1$
5	1022545813831681	$465 \cdot 2^{41} + 1$
6	1013749720809473	$461 \cdot 2^{41} + 1$
7	868614185943041	$395 \cdot 2^{41} + 1$

All have 50 bits. A transform of length $2^d$ modulo the first $k$ primes needs $2^d \mid p_i - 1$ for each of them, so $d \le 41$ in general and $d \le 43$ for the two-prime pipeline: far beyond any realistic size. The fields are described with the low-level functions in Chinese remaindering and integer conversion.

Guides#

Cite this page

The FLINT team, “mpn_ctx_struct, mpn_ctx_t (fft_small.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fft_small/mpn_ctx_struct.html (generated 2026-11-02).

@misc{flint-doc-fft-small-mpn-ctx-struct,
  author       = {{The FLINT team}},
  title        = {{mpn\_ctx\_struct, mpn\_ctx\_t (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_struct.html},
  note         = {Generated 2026-11-02}
}

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