`flint_mpn_bdiv_qr, flint_mpn_bdiv_q`

Synopsis#include <flint/mpn_extras.h>

void flint_mpn_bdiv_qr(mp_ptr q, mp_ptr r, mp_srcptr a, mp_size_t an, mp_srcptr b, mp_size_t bn, mp_size_t n)source

void flint_mpn_bdiv_q(mp_ptr q, mp_srcptr a, mp_size_t an, mp_srcptr b, mp_size_t bn, mp_size_t n)source

Hensel division: for odd $(b, \mathit{bn})$ , sets $(q, n)$ to the 2-adic quotient with $qb \equiv a \pmod{B^n}$ . If $r$ is not NULL (it is NULL for bdiv_q), the remainder $(a - qb)/B^n \bmod B^{\mathit{bn}}$ is written to $(r, \mathit{bn})$ , so that $a \equiv qb + B^n r \pmod{B^{n + \mathit{bn}}}$ ; the division is exact with an $n$ -limb quotient if and only if $r = 0$ and $a$ has no nonzero limbs at positions $\ge n + \mathit{bn}$ . $q$ may alias $a$ . Unlike GMP's mpn_bdiv_qr, the number $n$ of quotient limbs is a parameter independent of $\mathit{an}$ and $\mathit{bn}$ .

Cite this page

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

@misc{flint-doc-mpn-extras-flint-mpn-bdiv-qr,
  author       = {{The FLINT team}},
  title        = {{flint\_mpn\_bdiv\_qr, flint\_mpn\_bdiv\_q (mpn\_extras.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/mpn_extras/flint_mpn_bdiv_qr.html},
  note         = {Generated 2026-11-02}
}

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