DFLOAT_TRIG_EPS_1, DFLOAT_TRIG_EPS_2, DFLOAT_TRIG_EPS_3, DFLOAT_TRIG_EPS_4, DFLOAT_TRIG_EPS
#include <flint/dfloat.h>DFLOAT_TRIG_EPS_1sourceDFLOAT_TRIG_EPS_2sourceDFLOAT_TRIG_EPS_3sourceDFLOAT_TRIG_EPS_4sourceDFLOAT_TRIG_EPS(n)sourceError bounds of the sine and cosine kernels, about 2^{-50.4}, 2^{-98.5}, 2^{-148.5} and 2^{-200.1}: for |x| \le 2^{20} \pi/2 - 1, dN_sin has an absolute error of at most \varepsilon (|x| + \min(|x|, 1)) and dN_cos of at most \varepsilon (|x| + 1), with \varepsilon = DFLOAT_TRIG_EPS_N. The bounds are absolute and scaled by |x|: the relative accuracy near the zeros of the functions is not preserved, since the argument is reduced with \pi/2 to about 53N + 48 bits and the reduced argument keeps the absolute accuracy u^N |x| of the input. For |x| \le 1 the sine bound 2\varepsilon|x| is relative.
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 2026-10-20).
@misc{flint-doc-dfloat-DFLOAT-TRIG-EPS-1,
author = {{The FLINT team}},
title = {{DFLOAT\_TRIG\_EPS\_1, DFLOAT\_TRIG\_EPS\_2, DFLOAT\_TRIG\_EPS\_3, DFLOAT\_TRIG\_EPS\_4, DFLOAT\_TRIG\_EPS (dfloat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/dfloat/DFLOAT_TRIG_EPS_1.html},
note = {Generated 2026-10-20}
}