Provably faithful evaluation of polynomials

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 floatingpoint 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. Categories and Subject Descriptors B.2.3 [Hardware]: Arithmetic and Logic Structures—Reliability, Testing, and Fault-Tolerance; F.4 [Theory of Computation]: Mathematical Logic and Formal Languages Keywords Floating-point, polynomial evaluation, formal verification

• Type: Conference
• Year: 2006
• Where: SAC
• Authors: Sylvie Boldo, César Muñoz
• Keywords: Applied Computing, Polynomial Evaluation, Proof Assistant Coq, SAC 2006, Sufficient Conditions