_arb_sin_cos_taylor_naive, _arb_sin_cos_taylor_rs
Synopsis
#include <flint/arb.h>void _arb_sin_cos_taylor_naive(nn_ptr ysin, nn_ptr ycos, ulong * error, nn_srcptr x, slong xn, ulong N)sourcevoid _arb_sin_cos_taylor_rs(nn_ptr ysin, nn_ptr ycos, ulong * error, nn_srcptr x, slong xn, ulong N, int sinonly, int alternating)sourceSet ysin and ycos to approximations of \sum_{k=0}^{N-1} (-1)^k x^{2k+1}/(2k+1)! and \sum_{k=0}^{N-1} (-1)^k x^{2k}/(2k)!, with xn fractional limbs, and write an error bound in ulps to error. Require N \le 143, 0 \le x \le 1/16 and \mathit{xn} > 0.
In the rs version, sinonly = 1 computes only the sine, and alternating = 0 computes the series without signs (the hyperbolic sine, intended for use with sinonly, as in the exponential at high precision, where \cosh is then obtained from \sqrt{1 + \sinh^2}).
Cite this page
The FLINT team, “_arb_sin_cos_taylor_naive, _arb_sin_cos_taylor_rs (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/_arb_sin_cos_taylor_naive.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-sin-cos-taylor-naive,
author = {{The FLINT team}},
title = {{\_arb\_sin\_cos\_taylor\_naive, \_arb\_sin\_cos\_taylor\_rs (arb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb/_arb_sin_cos_taylor_naive.html},
note = {Generated 2026-10-20}
}