Formal Verification of a State-of-the-Art Integer Square Root

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

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

We present the automatic formal verification of a state-of-the-art algorithm from the GMP library that computes the square root of a 64-bit integer. Although it uses only integer operations, the best way to understand the program is to view it as a fixed-point arithmetic algorithm that implements Newton's method. The C code is short but intricate, involving magic constants and intentional arithmetic overflows. We have verified the algorithm using the Why3 tool and automated solvers such as Gappa.

Mots clés: Formal verification; Fixed-point arithmetic

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

Guillaume Melquiond, Raphaël Rieu-Helft. Formal Verification of a State-of-the-Art Integer Square Root. ARITH-26 2019 - 26th IEEE 26th Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.183-186, ⟨10.1109/ARITH.2019.00041⟩. ⟨hal-02092970⟩