`_mp_real_series_tapered`

Synopsis#include <flint/mp_real.h>

void _mp_real_series_tapered(nn_ptr res, nn_srcptr x, slong n, flint_bitcnt_t r, int func)source

Set $(\mathit{res}, n)$ to $\tan x$ , $\operatorname{atan} x$ , $\operatorname{atanh} x$ , $\sin x$ or $1 - \cos x$ (selected by func) for $0 \le x < 2^{-r}$ , within 6 ulps, by Horner's rule in $x^2$ over tapered widths with static coefficient tables. The supported ranges are $n \le 80$ , $r \ge 32$ for the tangent, $n \le 13$ , $r \ge 10$ for atan and atanh, and $n \le 16$ , $r \ge 18$ for the sine and cosine.

Guides#

Fixed-point kernels

Cite this page

The FLINT team, “_mp_real_series_tapered (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_tapered.html (generated 2026-11-02).

@misc{flint-doc-mp-real-mp-real-series-tapered,
  author       = {{The FLINT team}},
  title        = {{\_mp\_real\_series\_tapered (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_tapered.html},
  note         = {Generated 2026-11-02}
}

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