Formal Methods for Computer Arithmetic

Overview

We are interested in the use of formal methods for verifying algorithms that handle numerical values, be they floating-point numbers as described by the IEEE-754 standard, arbitrary-precision integer as in GMP, or intervals. These algorithms range from basic blocks of mathematical libraries to whole programs for numerical analysis. They are usually simple when it comes to control flow and data structures, but their correctness might depend on some intricate mathematical reasoning in number theorem, real analysis, and so on. This makes their verification out of range of purely automatic approaches.

We cover a wide range of aspects of the field: formalization of arithmetic and analysis, design of dedicated decision procedures, specification and verification of libraries and programs.

Members

Permanent

PhD Students

Selected publications

• G. Melquiond, R. Rieu-Helft. WhyMP, a formally verified arbitrary-precision integer library. ISSAC, 2020. HAL
• A. Mahboubi, G. Melquiond, T. Sibut-Pinote. Formally verified approximations of definite integrals. JAR, 2019. HAL
• S. Boldo, F. Faissole, A. Chapoutot. Round-off error and exceptional behavior analysis of explicit Runge-Kutta methods. IEEE TC, 2019. HAL
• S. Boldo, G. Melquiond. Computer arithmetic and formal proofs: Verifying floating-point algorithms with the Coq System. ISTE-Elsevier, 2018.
• J-M. Muller et al. Handbook of floating-point arithmetic. Birkhaüser, 2010, 2018.
• S. Conchon, M. Iguernelala, K. Ji, G. Melquiond, C. Fumex. A three-tier strategy for reasoning about floating-point numbers in SMT. CAV, 2017. HAL
• C. Fumex, C. Marché, Y. Moy. Automating the verification of floating-point programs. VSTTE, 2017. HAL
• S. Boldo, J-H. Jourdan, G. Melquiond, X. Leroy. Verified compilation of floating-point computations. JAR, 2015. HAL

Selected software

Projects