`arb_exp_arf`

Synopsis#include <flint/arb.h>

void arb_exp_arf(arb_t z, const arf_t x, slong prec, int minus_one, slong maglim)source

Sets z to $e^x$ , or $e^x - 1$ if minus_one is set, for an exact x, choosing among all algorithms; inputs with $|x| \ge 2^{\mathit{maglim}}$ give the crude overflow results of arb_exp.

Tiny $x$ uses $1 + x$ with error $x^2$ . Below 2240 bits the argument is reduced modulo $\log 2$ and by one or two table lookups in arb_exp_tab1, respectively arb_exp_tab21 and arb_exp_tab22, and a Taylor series is evaluated with _arb_exp_taylor_rs. From 2240 bits to 4 million bits, arb_exp_arf_log_reduction is used, and above that arb_exp_arf_generic.

Cite this page

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

@misc{flint-doc-arb-arb-exp-arf,
  author       = {{The FLINT team}},
  title        = {{arb\_exp\_arf (arb.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arb/arb_exp_arf.html},
  note         = {Generated 2026-11-02}
}

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