FLINT3.7.0-dev
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arb_exp

Synopsis#include <flint/arb.h>
void arb_exp(arb_t z, const arb_t x, slong prec)source

Sets z to exe^x.

For x=[m±r]x = [m \pm r], the midpoint is eme^m computed with arb_exp_arf and the propagated error is bounded by em(er−1)e^m (e^r - 1), evaluated with mag_expm1; wide balls are evaluated at the endpoints. If the input is inexact, eme^m is computed only to about the accuracy of the input plus 30 bits. If ∣m∣>2max⁡(128,2 prec)|m| > 2^{\max(128, 2\,\mathit{prec})}, the result is [0±∞][0 \pm \infty] for positive mm and a tiny ball near 0 for negative mm, so that the cost stays polynomial in prec.

Guides#

Cite this page

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