bernoulli_bound_2exp_si
Synopsis
#include <flint/bernoulli.h>Returns an integer b with |B_n| \le 2^b, using a table for n < 512 and otherwise the inequality |B_n| < 4\, n!/(2\pi)^n < 4 (n+1)^{n+1} e^{-n}/(2\pi)^n evaluated in integer arithmetic with a table of logarithms. Returns WORD_MIN if B_n = 0. The bound exceeds the true exponent by at most one percent. Throws if n > 2^{\mathtt{FLINT\_BITS} - 6} or the computation would overflow; the function is meant for n small enough that B_n could be computed exactly.
Cite this page
The FLINT team, “bernoulli_bound_2exp_si (bernoulli.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/bernoulli/bernoulli_bound_2exp_si.html (generated 2026-10-20).
@misc{flint-doc-bernoulli-bernoulli-bound-2exp-si,
author = {{The FLINT team}},
title = {{bernoulli\_bound\_2exp\_si (bernoulli.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/bernoulli/bernoulli_bound_2exp_si.html},
note = {Generated 2026-10-20}
}