FLINT3.7.0-dev
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DFLOAT_TRIG_EPS_1, DFLOAT_TRIG_EPS_2, DFLOAT_TRIG_EPS_3, DFLOAT_TRIG_EPS_4, DFLOAT_TRIG_EPS

Synopsis#include <flint/dfloat.h>
DFLOAT_TRIG_EPS_1source
DFLOAT_TRIG_EPS_2source
DFLOAT_TRIG_EPS_3source
DFLOAT_TRIG_EPS_4source
DFLOAT_TRIG_EPS(n)source

Error bounds of the sine and cosine kernels, about 2−50.42^{-50.4}, 2−98.52^{-98.5}, 2−148.52^{-148.5} and 2−200.12^{-200.1}: for ∣x∣≤220π/2−1|x| \le 2^{20} \pi/2 - 1, dN_sin has an absolute error of at most ε(∣x∣+min⁡(∣x∣,1))\varepsilon (|x| + \min(|x|, 1)) and dN_cos of at most ε(∣x∣+1)\varepsilon (|x| + 1), with ε\varepsilon = DFLOAT_TRIG_EPS_N. The bounds are absolute and scaled by ∣x∣|x|: the relative accuracy near the zeros of the functions is not preserved, since the argument is reduced with π/2\pi/2 to about 53N+4853N + 48 bits and the reduced argument keeps the absolute accuracy uN∣x∣u^N |x| of the input. For ∣x∣≤1|x| \le 1 the sine bound 2ε∣x∣2\varepsilon|x| is relative.

Cite this page

The FLINT team, “DFLOAT_TRIG_EPS_1, DFLOAT_TRIG_EPS_2, DFLOAT_TRIG_EPS_3, DFLOAT_TRIG_EPS_4, DFLOAT_TRIG_EPS (dfloat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/dfloat/DFLOAT_TRIG_EPS_1.html (generated 2026-11-02).