Proving Tight Bounds on Univariate Expressions in Coq - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2014

Proving Tight Bounds on Univariate Expressions in Coq

Résumé

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 traditional tools. In fact, the inherent difficulty of computing such bounds often mandate 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 kernel 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 (237.78 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

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

Identifiants

  • HAL Id : hal-01086460 , version 1

Citer

Érik Martin-Dorel, Guillaume Melquiond. Proving Tight Bounds on Univariate Expressions in Coq. 2014. ⟨hal-01086460v1⟩
362 Consultations
711 Téléchargements

Partager

Gmail Facebook X LinkedIn More