How to Get an Efficient yet Verified Arbitrary-Precision Integer Library

Raphaël Rieu-Helft (1, 2, 3) , Claude Marché (2, 3) , Guillaume Melquiond (2, 3)

1 ENS-PSL - École normale supérieure - Paris
2 LRI - Laboratoire de Recherche en Informatique
3 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations

The GNU Multi-Precision library is a widely used, safety-critical, library for arbitrary-precision arithmetic. Its source code is written in C and assembly, and includes intricate state-of-the-art algorithms for the sake of high performance. Formally verifying the functional behavior of such highly optimized code, not designed with verification in mind, is challenging. We present a fully verified library designed using the Why3 program verifier. The use of a dedicated memory model makes it possible to have the Why3 code be very similar to the original GMP code. This library is extracted to C and is compatible and performance-competitive with GMP.

Mots clés: arbitrary-precision arithmetic; deductive program verification; C language; Why3 program verifier

Domaines: Arithmétique des ordinateurs; Langage de programmation [cs.PL]; Performance et fiabilité [cs.PF]

Raphaël Rieu-Helft, Claude Marché, Guillaume Melquiond. How to Get an Efficient yet Verified Arbitrary-Precision Integer Library. 9th Working Conference on Verified Software: Theories, Tools, and Experiments, Jul 2017, Heidelberg, Germany. pp.84-101, ⟨10.1007/978-3-319-72308-2_6⟩. ⟨hal-01519732v2⟩