WhyMP, a Formally Verified Arbitrary-Precision Integer Library

Guillaume Melquiond (1) , Raphaël Rieu-Helft (2, 1)

1 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
2 TIS - TrustInSoft

Arbitrary-precision integer libraries such as GMP are a critical building block of computer algebra systems. GMP provides state-of-the-art algorithms that are intricate enough to justify formal verification. In this paper, we present a C library that has been formally verified using the Why3 verification platform in about four person-years. This verification deals not only with safety, but with full functional correctness. It has been performed using a mixture of mechanically checked handwritten proofs and automated theorem proving. We have implemented and verified a nontrivial subset of GMP's algorithms, including their optimizations and intricacies. Our library provides the same interface as GMP and is almost as efficient for smaller inputs. We detail our verification methodology and the algorithms we have implemented, and include some benchmarks to compare our library with GMP.

Keywords: Integer arithmetic; Deductive program verification; Mathematical library

Domains: Computer Arithmetic; Logic in Computer Science [cs.LO]

Guillaume Melquiond, Raphaël Rieu-Helft. WhyMP, a Formally Verified Arbitrary-Precision Integer Library. ISSAC 2020 - 45th International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. pp.352-359, ⟨10.1145/3373207.3404029⟩. ⟨hal-02566654v2⟩