FLINT3.7.0-dev
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arb_atan_arf_bb

Synopsis#include <flint/arb.h>
void arb_atan_arf_bb(arb_t z, const arf_t x, slong prec)source

Computes atan⁡x\operatorname{atan} x by the bit-burst algorithm.

The argument-halving formula atan⁡(x)=2atan⁡(x/(1+1+x2))\operatorname{atan}(x) = 2 \operatorname{atan}(x / (1 + \sqrt{1 + x^2})) is applied up to 8 times, and then atan⁡(x)=atan⁡(p/q)+atan⁡(w)\operatorname{atan}(x) = \operatorname{atan}(p/q) + \operatorname{atan}(w) with w=(qx−p)/(px+q)w = (qx - p)/(px + q), p=⌊qx⌋p = \lfloor qx \rfloor, is applied repeatedly with growing q=2kq = 2^k, the arctangents of the rational numbers p/qp/q being computed by binary splitting.

Cite this page

The FLINT team, “arb_atan_arf_bb (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_atan_arf_bb.html (generated 2026-11-02).