Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq - Archive ouverte HAL Access content directly
Journal Articles Journal of Automated Reasoning Year : 2016

Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq

(1) , (2, 3)
1
2
3

Abstract

The verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq's logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples.
Fichier principal
Vignette du fichier
article.pdf (277.01 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01086460 , version 1 (24-11-2014)
hal-01086460 , version 2 (14-09-2015)

Identifiers

Cite

Érik Martin-Dorel, Guillaume Melquiond. Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq. Journal of Automated Reasoning, 2016, 57 (3), pp.187-217. ⟨10.1007/s10817-015-9350-4⟩. ⟨hal-01086460v2⟩
304 View
673 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More