arb_atan, arb_atan_arf
Synopsis
#include <flint/arb.h>arb_atan computes the arctangent of the midpoint with arb_atan_arf and adds the propagated error, bounded by r / (1 + (|m| - r)^2) for r < |m| and by \min(\pi, r) in general; inaccurate input is evaluated at the endpoints. arb_atan_arf uses tables and a Taylor series below 3400 bits and a Newton iteration on arb_sin_cos above; the bit-burst algorithm arb_atan_arf_bb is the fallback when the tables are not precise enough.
Guides#
Cite this page
The FLINT team, “arb_atan, arb_atan_arf (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_atan.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-atan,
author = {{The FLINT team}},
title = {{arb\_atan, arb\_atan\_arf (arb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb/arb_atan.html},
note = {Generated 2026-10-20}
}