`_mp_real_submul_bounded`

Synopsis#include <flint/mp_real.h>

void _mp_real_submul_bounded(mp_real_t res, const mp_real_t a, const mp_real_t b, const mp_real_t c, slong E, slong n)source

Set res to $a - bc$ , given that $|a - bc| < B^E$ . Only the window of the product that reaches the result is computed, and the result is wrong if the bound does not hold.

This is the residual of a Newton or Taylor step, whose bound comes from the radius of the previous approximation. The sign of $a - bc$ is read off the top limb of the product window, so the bound must be rigorous.

Guides#

Computing with mp_real balls

Cite this page

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

@misc{flint-doc-mp-real-mp-real-submul-bounded,
  author       = {{The FLINT team}},
  title        = {{\_mp\_real\_submul\_bounded (mp\_real.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/mp_real/_mp_real_submul_bounded.html},
  note         = {Generated 2026-11-02}
}

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