arb_sin_cos_arf_atan_reduction
Synopsis
#include <flint/arb.h>Computes \sin x and \cos x by reduction with the arguments of small Gaussian primes [HJ2024]: x - \sum c_i \theta_i is made small with \theta_i = \arg(a_i + b_i i), and the result is multiplied by the Gaussian integer \prod (a_i + b_i i)^{c_i} normalised to modulus 1. Used for arb_sin_cos from 2600 bits to 4 million bits.
References#
- [HJ2024] J. van der Hoeven and F. Johansson, "Fast multiple precision exp(x) with precomputations", 2024 IEEE 31st Symposium on Computer Arithmetic (ARITH) (2024), https://hal.science/hal-04454093
Cite this page
The FLINT team, “arb_sin_cos_arf_atan_reduction (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_sin_cos_arf_atan_reduction.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-sin-cos-arf-atan-reduction,
author = {{The FLINT team}},
title = {{arb\_sin\_cos\_arf\_atan\_reduction (arb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb/arb_sin_cos_arf_atan_reduction.html},
note = {Generated 2026-10-20}
}