Provably Faithful Evaluation of Polynomials

Sylvie Boldo (1) , César Muñoz (2)

1 PROVAL - Proof of Programs
2 NIA - National Institute of Aerospace [Hampton]

We provide sufficient conditions that formally guarantee that the floating-point computation of a polynomial evaluation is faithful. To this end, we develop a formalization of floating-point numbers and rounding modes in the Program Verification System (PVS). Our work is based on a well-known formalization of floating-point arithmetic in the proof assistant Coq, where polynomial evaluation has been already studied. However, thanks to the powerful proof automation provided by PVS, the sufficient conditions proposed in our work are more general than the original ones.

Domaines: Logique en informatique [cs.LO]; Analyse numérique [cs.NA]

Sylvie Boldo, César Muñoz. Provably Faithful Evaluation of Polynomials. 21st Annual ACM Symposium on Applied Computing, Apr 2006, Dijon, France. ⟨inria-00000892⟩