arb_atan_newton, arb_atan_arf_newton
Synopsis
#include <flint/arb.h>Compute \operatorname{atan} x from a lower-precision value t by \operatorname{atan} x = t + \operatorname{atan}((x \cos t - \sin t)/(\cos t + x \sin t)), with the correction evaluated by a short Taylor series, so that the precision multiplies by 5 to 11 per step. Arguments with |x| > 16 use \operatorname{atan} x = \pm\pi/2 - \operatorname{atan}(1/x). Used for arb_atan_arf from 3400 bits.
Cite this page
The FLINT team, “arb_atan_newton, arb_atan_arf_newton (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_atan_newton.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-atan-newton,
author = {{The FLINT team}},
title = {{arb\_atan\_newton, arb\_atan\_arf\_newton (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_newton.html},
note = {Generated 2026-10-20}
}