Certifying the floating-point implementation of an elementary function using Gappa - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Transactions on Computers Year : 2011

Certifying the floating-point implementation of an elementary function using Gappa

Abstract

High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well bounded. This certification may require a time-consuming proof for each line of code, and it is usually broken by the smallest change to the code, e.g. for maintenance or optimization purpose. Certifying floating-point programs by hand is therefore very tedious and error-prone. The Gappa proof assistant is designed to make this task both easier and more secure, thanks to the following novel features. It automates the evaluation and propagation of rounding errors using interval arithmetic. Its input format is very close to the actual code to validate. It can be used incrementally to prove complex mathematical properties pertaining to the code. It generates a formal proof of the results, which can be checked independently by a lower-level proof assistant like Coq. Yet it does not require any specific knowledge about automatic theorem proving, and thus is accessible to a wide community. This article demonstrates the practical use of this tool for a widely used class of floating-point programs: implementations of elementary functions in a mathematical library.
Fichier principal
Vignette du fichier
10-tc.pdf (297.02 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

ensl-00200830 , version 1 (21-12-2007)
ensl-00200830 , version 2 (08-11-2010)

Identifiers

Cite

Florent de Dinechin, Christoph Lauter, Guillaume Melquiond. Certifying the floating-point implementation of an elementary function using Gappa. IEEE Transactions on Computers, 2011, 60 (2), pp.242-253. ⟨10.1109/TC.2010.128⟩. ⟨ensl-00200830v2⟩
753 View
884 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More