FLINT3.7.0-dev
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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_1source
DFLOAT_EXPM1_EPS_2source
DFLOAT_EXPM1_EPS_3source
DFLOAT_EXPM1_EPS_4source
DFLOAT_EXPM1_EPS(n)source
DFLOAT_LOG1P_EPS_1source
DFLOAT_LOG1P_EPS_2source
DFLOAT_LOG1P_EPS_3source
DFLOAT_LOG1P_EPS_4source
DFLOAT_LOG1P_EPS(n)source

Relative error bounds of dN_expm1, valid for −746≤x≤709.9-746 \le x \le 709.9 (about 2−48.92^{-48.9}, 2−98.32^{-98.3}, 2−149.22^{-149.2}, 2−199.82^{-199.8}), and of dN_log1p, valid for 1+x∈[2−1022,21022)1 + x \in [2^{-1022}, 2^{1022}) (about 2−49.32^{-49.3}, 2−99.12^{-99.1}, 2−149.92^{-149.9}, 2−200.52^{-200.5}). They are relative everywhere, in particular near 0, where both functions are x(1+O(x))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 2026-11-02).