_arb_atan_sum_bs_simple, _arb_atan_sum_bs_powtab
Synopsis
#include <flint/arb.h>void _arb_atan_sum_bs_simple(fmpz_t T, fmpz_t Q, flint_bitcnt_t * Qexp, const fmpz_t x, flint_bitcnt_t r, slong N)sourcevoid _arb_atan_sum_bs_powtab(fmpz_t T, fmpz_t Q, flint_bitcnt_t * Qexp, const fmpz_t x, flint_bitcnt_t r, slong N)sourceCompute T, Q and Q_{\exp} with T/(Q \cdot 2^{Q_{\exp}}) = \sum_{k=1}^{N} (-1)^k (x/2^r)^{2k}/(2k+1) by binary splitting; the sum must be multiplied by x/2^r and the linear term added to give the arctangent.
Cite this page
The FLINT team, “_arb_atan_sum_bs_simple, _arb_atan_sum_bs_powtab (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/_arb_atan_sum_bs_simple.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-atan-sum-bs-simple,
author = {{The FLINT team}},
title = {{\_arb\_atan\_sum\_bs\_simple, \_arb\_atan\_sum\_bs\_powtab (arb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb/_arb_atan_sum_bs_simple.html},
note = {Generated 2026-10-20}
}