`_arb_atan_taylor_naive, _arb_atan_taylor_rs`

Synopsis#include <flint/arb.h>

void _arb_atan_taylor_naive(nn_ptr y, ulong * error, nn_srcptr x, slong xn, ulong N, int alternating)source

void _arb_atan_taylor_rs(nn_ptr y, ulong * error, nn_srcptr x, slong xn, ulong N, int alternating)source

Set $y \approx \sum_{k=0}^{N-1} (\pm 1)^k x^{2k+1}/(2k+1)$ , alternating (the arctangent series) if alternating is 1 and not (the atanh series, used for logarithms) if it is 0, and write an error bound in ulps to error. Require $N \le 255$ , $0 \le x \le 1/16$ and $\mathit{xn} > 0$ .

Cite this page

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

@misc{flint-doc-arb-arb-atan-taylor-naive,
  author       = {{The FLINT team}},
  title        = {{\_arb\_atan\_taylor\_naive, \_arb\_atan\_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_atan_taylor_naive.html},
  note         = {Generated 2026-11-02}
}

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