Automating the Verification of Floating-Point Programs

Clément Fumex (1, 2, 3) , Claude Marché (1, 2) , Yannick Moy (3)

1 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
2 LRI - Laboratoire de Recherche en Informatique
3 AdaCore (FRANCE)

In the context of deductive program verification, handling floating-point computations is challenging. The level of proof success and proof automation highly depends on the way the floating-point operations are interpreted in the logic supported by back-end provers. We address this challenge by combining multiple techniques to separately prove different parts of the desired properties. We use abstract interpretation to compute numerical bounds of expressions, and we use multiple automated provers, relying on different strategies for representing floating-point computations. One of these strategies is based on the native support for floating-point arithmetic recently added in the SMT-LIB standard. Our approach is implemented in the Why3 environment and its front-end SPARK 2014 for the development of safety-critical Ada programs. It is validated experimentally on several examples originating from industrial use of SPARK 2014.

Mots clés: Deductive program verification; Floating-point arithmetic; Satisfiability Modulo Theory; Why3 program verifier; Verification environment SPARK 2014

Domaines: Logique en informatique [cs.LO]; Arithmétique des ordinateurs

Clément Fumex, Claude Marché, Yannick Moy. Automating the Verification of Floating-Point Programs. 9th Working Conference on Verified Software: Theories, Tools and Experiments, Jul 2017, Heidelberg, Germany. ⟨hal-01534533⟩