d1b_sin, d2b_sin, d3b_sin, d4b_sin, d1b_cos, d2b_cos, d3b_cos, d4b_cos, d1b_sin_cos, d2b_sin_cos, d3b_sin_cos, d4b_sin_cos
Synopsis
#include <flint/dfloat.h>void d1b_sin(d1b_t res, d1b_srcptr x)void d2b_sin(d2b_t res, d2b_srcptr x)void d3b_sin(d3b_t res, d3b_srcptr x)void d4b_sin(d4b_t res, d4b_srcptr x)void d1b_cos(d1b_t res, d1b_srcptr x)void d2b_cos(d2b_t res, d2b_srcptr x)void d3b_cos(d3b_t res, d3b_srcptr x)void d4b_cos(d4b_t res, d4b_srcptr x)void d1b_sin_cos(d1b_t sn, d1b_t cs, d1b_srcptr x)void d2b_sin_cos(d2b_t sn, d2b_t cs, d2b_srcptr x)void d3b_sin_cos(d3b_t sn, d3b_t cs, d3b_srcptr x)void d4b_sin_cos(d4b_t sn, d4b_t cs, d4b_srcptr x)The sine and cosine of a ball. The radius is \varepsilon(|m| + a) + r with a = \min(|m|, 1) for the sine and a = 1 for the cosine, for the midpoint m and the input radius r (both functions are 1-Lipschitz); a radius of 1 or more is replaced by the enclosure [0 \pm 1]. Infinite radii, nonfinite midpoints and midpoints beyond the kernel range go through arb_t. \sin([0 \pm 0]) = [0 \pm 0] and \cos([0 \pm 0]) = [1 \pm 0].
Cite this page
The FLINT team, “d1b_sin, d2b_sin, d3b_sin, d4b_sin, d1b_cos, d2b_cos, d3b_cos, d4b_cos, d1b_sin_cos, d2b_sin_cos, d3b_sin_cos, d4b_sin_cos (dfloat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/dfloat/d1b_sin.html (generated 2026-10-20).
@misc{flint-doc-dfloat-d1b-sin,
author = {{The FLINT team}},
title = {{d1b\_sin, d2b\_sin, d3b\_sin, d4b\_sin, d1b\_cos, d2b\_cos, d3b\_cos, d4b\_cos, d1b\_sin\_cos, d2b\_sin\_cos, d3b\_sin\_cos, d4b\_sin\_cos (dfloat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/dfloat/d1b_sin.html},
note = {Generated 2026-10-20}
}