DFLOAT_LOG_EPS_1, DFLOAT_LOG_EPS_2, DFLOAT_LOG_EPS_3, DFLOAT_LOG_EPS_4, DFLOAT_LOG_EPS, DFLOAT_ATAN_EPS_1, DFLOAT_ATAN_EPS_2, DFLOAT_ATAN_EPS_3, DFLOAT_ATAN_EPS_4, DFLOAT_ATAN_EPS
#include <flint/dfloat.h>DFLOAT_LOG_EPS_1sourceDFLOAT_LOG_EPS_2sourceDFLOAT_LOG_EPS_3sourceDFLOAT_LOG_EPS_4sourceDFLOAT_LOG_EPS(n)sourceDFLOAT_ATAN_EPS_1sourceDFLOAT_ATAN_EPS_2sourceDFLOAT_ATAN_EPS_3sourceDFLOAT_ATAN_EPS_4sourceDFLOAT_ATAN_EPS(n)sourceRelative error bounds of the logarithm and arctangent kernels: |\mathtt{dN\_log}(x) - \log x| \le \varepsilon |\log x| for 2^{-1022} \le x < 2^{1022}, with \varepsilon about 2^{-49.3}, 2^{-99.3}, 2^{-150.2} and 2^{-200.8}, and |\mathtt{dN\_atan}(x) - \operatorname{atan} x| \le \varepsilon |\operatorname{atan} x| for all finite x, with \varepsilon about 2^{-49.8}, 2^{-99.6}, 2^{-150.5} and 2^{-201.3}. Both bounds are relative everywhere, including near x = 1 for the logarithm and near 0 for the arctangent.
The FLINT team, “DFLOAT_LOG_EPS_1, DFLOAT_LOG_EPS_2, DFLOAT_LOG_EPS_3, DFLOAT_LOG_EPS_4, DFLOAT_LOG_EPS, DFLOAT_ATAN_EPS_1, DFLOAT_ATAN_EPS_2, DFLOAT_ATAN_EPS_3, DFLOAT_ATAN_EPS_4, DFLOAT_ATAN_EPS (dfloat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/dfloat/DFLOAT_LOG_EPS_1.html (generated 2026-10-20).
@misc{flint-doc-dfloat-DFLOAT-LOG-EPS-1,
author = {{The FLINT team}},
title = {{DFLOAT\_LOG\_EPS\_1, DFLOAT\_LOG\_EPS\_2, DFLOAT\_LOG\_EPS\_3, DFLOAT\_LOG\_EPS\_4, DFLOAT\_LOG\_EPS, DFLOAT\_ATAN\_EPS\_1, DFLOAT\_ATAN\_EPS\_2, DFLOAT\_ATAN\_EPS\_3, DFLOAT\_ATAN\_EPS\_4, DFLOAT\_ATAN\_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_LOG_EPS_1.html},
note = {Generated 2026-10-20}
}