FLINT3.7.0-dev
/

arb_sin_cos_wide, _arb_sin_cos_wide

Synopsis#include <flint/arb.h>
void arb_sin_cos_wide(arb_t s, arb_t c, const arb_t x, slong prec)source
void _arb_sin_cos_wide(arb_t s, arb_t c, const arf_t x, const mag_t r, slong prec)source

Compute enclosures of the ranges of \sin and \cos on a wide ball x = [m \pm r], with both endpoints optimal to within about 2^{-30}.

The sine and cosine are evaluated in double arithmetic at the endpoints, and the extrema \pm 1 are included when a peak lies between them; the result is converted back to a ball. The accumulated error of the simple floating-point algorithm is below 2^{-30}, the dominant part coming from a single approximate reduction by \pi/2, which is safe in double arithmetic up to about 2^{20}; larger arguments are first reduced in arb_t arithmetic.

Cite this page

The FLINT team, “arb_sin_cos_wide, _arb_sin_cos_wide (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_sin_cos_wide.html (generated 2026-10-20).