_acb_dirichlet_l_fmpq_use_afe, _acb_dirichlet_l_jet_use_afe
#include <flint/acb_dirichlet.h>Return whether the approximate functional equation is estimated to be faster than the generic algorithms for , respectively for its expansion to length len, where is the conductor of ( for the Riemann zeta function). These are the heuristics used by acb_dirichlet_l, acb_dirichlet_l_fmpq, acb_dirichlet_l_jet, acb_dirichlet_zeta and acb_dirichlet_zeta_jet (and therefore by acb_dirichlet_stieltjes and arb_const_glaisher, which call acb_dirichlet_zeta_jet). The cutoffs come from timings (wall time) with 1 and 8 threads. They decrease with (for , values at half-integers, and for , jets, always use the approximate functional equation), and with the number of threads (flint_get_num_threads), since the terms of the approximate functional equation are computed in parallel with nearly perfect speedup while Euler–Maclaurin summation and the Hurwitz zeta functions gain less from threads. For they are about bits for , bits for other values, bits for jets at and bits for other jets of length 2 (somewhat higher for longer jets), the latter capped at bits because of the memory of Euler–Maclaurin summation (4 GB at bits). The choice of algorithm, and hence the radius of the output, can therefore depend on the number of threads.
The FLINT team, “_acb_dirichlet_l_fmpq_use_afe, _acb_dirichlet_l_jet_use_afe (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/_acb_dirichlet_l_fmpq_use_afe.html (generated 2026-11-02).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-l-fmpq-use-afe,
author = {{The FLINT team}},
title = {{\_acb\_dirichlet\_l\_fmpq\_use\_afe, \_acb\_dirichlet\_l\_jet\_use\_afe (acb\_dirichlet.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_dirichlet/_acb_dirichlet_l_fmpq_use_afe.html},
note = {Generated 2026-11-02}
}