FLINT3.7.0-dev
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arb_sin, arb_cos, arb_sin_cos

Synopsis#include <flint/arb.h>
void arb_sin(arb_t s, const arb_t x, slong prec)source
void arb_cos(arb_t c, const arb_t x, slong prec)source
void arb_sin_cos(arb_t s, arb_t c, const arb_t x, slong prec)source

Set s to sin⁡x\sin x and c to cos⁡x\cos x. Computing both together costs little more than one.

The propagated error for a radius rr is at most min⁡(2,r)\min(2, r). Balls with a radius larger than about 2−242^{-24} are handled by arb_sin_cos_wide, which computes a near-optimal enclosure of the range. If the midpoint exceeds 2max⁡(65536,4 prec)2^{\max(65536, 4\,\mathit{prec})}, the result is [0±1][0 \pm 1]: reducing such an argument modulo π\pi would take time exponential in the size of the input.

Guides#

Cite this page

The FLINT team, “arb_sin, arb_cos, arb_sin_cos (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_sin.html (generated 2026-11-02).