_mp_real_series_rs, _mp_real_series_rs_sin_cos
#include <flint/mp_real.h>void _mp_real_series_rs(nn_ptr res, nn_srcptr x, slong n, flint_bitcnt_t r, int func)sourcevoid _mp_real_series_rs_sin_cos(nn_ptr ysin, nn_ptr yg, nn_srcptr x, slong n, flint_bitcnt_t r, int hyperbolic)sourceTapered rectangular splitting for a fraction 0 \le x < 2^{-r}, r \ge 8, of n limbs. The first function computes \exp(\pm x) (n + 1 limbs, within 5 ulps) or \sin x, \sinh x, \operatorname{atan} x, \operatorname{atanh} x, 1 - \cos x, \cosh x - 1 (n limbs, within 2 ulps) as selected by func. The second computes the sine and 1 - \cos (or \sinh and \cosh - 1 when hyperbolic is set) sharing the powers; either output may be NULL. Outputs may alias x.
With v = x (exp) or v = x^2, the series \sum_{k<N} a_k v^k is split into blocks of m \approx \sqrt{N/1.5} terms, the powers v, \ldots, v^m computed once and every term a single mpn_addmul_1 or mpn_submul_1 by a one-limb coefficient. Block b enters the sum multiplied by v^{mb} < 2^{-smb} (s = r resp. 2r), so it runs in a window shortened by smb bits. See Series and rectangular splitting.
Guides#
The FLINT team, “_mp_real_series_rs, _mp_real_series_rs_sin_cos (mp_real.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/mp_real/_mp_real_series_rs.html (generated 2026-10-20).
@misc{flint-doc-mp-real-mp-real-series-rs,
author = {{The FLINT team}},
title = {{\_mp\_real\_series\_rs, \_mp\_real\_series\_rs\_sin\_cos (mp\_real.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/mp_real/_mp_real_series_rs.html},
note = {Generated 2026-10-20}
}