DFLOAT_EXPM1_EPS_1, DFLOAT_EXPM1_EPS_2, DFLOAT_EXPM1_EPS_3, DFLOAT_EXPM1_EPS_4, DFLOAT_EXPM1_EPS, DFLOAT_LOG1P_EPS_1, DFLOAT_LOG1P_EPS_2, DFLOAT_LOG1P_EPS_3, DFLOAT_LOG1P_EPS_4, DFLOAT_LOG1P_EPS
Synopsis
#include <flint/dfloat.h>DFLOAT_EXPM1_EPS_1sourceDFLOAT_EXPM1_EPS_2sourceDFLOAT_EXPM1_EPS_3sourceDFLOAT_EXPM1_EPS_4sourceDFLOAT_EXPM1_EPS(n)sourceDFLOAT_LOG1P_EPS_1sourceDFLOAT_LOG1P_EPS_2sourceDFLOAT_LOG1P_EPS_3sourceDFLOAT_LOG1P_EPS_4sourceDFLOAT_LOG1P_EPS(n)sourceRelative error bounds of dN_expm1, valid for -746 \le x \le 709.9 (about 2^{-48.9}, 2^{-98.3}, 2^{-149.2}, 2^{-199.8}), and of dN_log1p, valid for 1 + x \in [2^{-1022}, 2^{1022}) (about 2^{-49.3}, 2^{-99.1}, 2^{-149.9}, 2^{-200.5}). They are relative everywhere, in particular near 0, where both functions are x(1 + O(x)).
Cite this page
The FLINT team, “DFLOAT_EXPM1_EPS_1, DFLOAT_EXPM1_EPS_2, DFLOAT_EXPM1_EPS_3, DFLOAT_EXPM1_EPS_4, DFLOAT_EXPM1_EPS, DFLOAT_LOG1P_EPS_1, DFLOAT_LOG1P_EPS_2, DFLOAT_LOG1P_EPS_3, DFLOAT_LOG1P_EPS_4, DFLOAT_LOG1P_EPS (dfloat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/dfloat/DFLOAT_EXPM1_EPS_1.html (generated 2026-10-20).
@misc{flint-doc-dfloat-DFLOAT-EXPM1-EPS-1,
author = {{The FLINT team}},
title = {{DFLOAT\_EXPM1\_EPS\_1, DFLOAT\_EXPM1\_EPS\_2, DFLOAT\_EXPM1\_EPS\_3, DFLOAT\_EXPM1\_EPS\_4, DFLOAT\_EXPM1\_EPS, DFLOAT\_LOG1P\_EPS\_1, DFLOAT\_LOG1P\_EPS\_2, DFLOAT\_LOG1P\_EPS\_3, DFLOAT\_LOG1P\_EPS\_4, DFLOAT\_LOG1P\_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_EXPM1_EPS_1.html},
note = {Generated 2026-10-20}
}