FLINT3.7.0-dev
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arb_log, arb_log_arf, arb_log_ui, arb_log_fmpz

Synopsis#include <flint/arb.h>
void arb_log(arb_t z, const arb_t x, slong prec)source
void arb_log_arf(arb_t z, const arf_t x, slong prec)source
void arb_log_ui(arb_t z, ulong x, slong prec)source
void arb_log_fmpz(arb_t z, const fmpz_t x, slong prec)source

Set z to \log x. If x contains nonpositive numbers, the result is indeterminate.

arb_log computes the logarithm of the midpoint with arb_log_arf and bounds the propagated error for x = [m \pm r], r < m, by \log(1 + r/(m - r)). Up to about 2800 bits, arb_log_arf reduces the argument with precomputed tables and sums an arctangent series by rectangular splitting; above, it uses a Newton-type iteration on arb_exp, and logarithms of smooth integers use precomputed logarithms of primes.

Guides#

Cite this page

The FLINT team, “arb_log, arb_log_arf, arb_log_ui, arb_log_fmpz (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_log.html (generated 2026-10-20).