arb_atan_arf_bb
Synopsis
#include <flint/arb.h>The argument-halving formula \operatorname{atan}(x) = 2 \operatorname{atan}(x / (1 + \sqrt{1 + x^2})) is applied up to 8 times, and then \operatorname{atan}(x) = \operatorname{atan}(p/q) + \operatorname{atan}(w) with w = (qx - p)/(px + q), p = \lfloor qx \rfloor, is applied repeatedly with growing q = 2^k, the arctangents of the rational numbers p/q being computed by binary splitting.
Cite this page
The FLINT team, “arb_atan_arf_bb (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_atan_arf_bb.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-atan-arf-bb,
author = {{The FLINT team}},
title = {{arb\_atan\_arf\_bb (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_arf_bb.html},
note = {Generated 2026-10-20}
}