Section: New Results
Floating-Point and Numerical Programs
The PhD thesis of T. Nguyen was defended in June [12] . It includes an improved version of the former approach [102] that we proposed for proving floating-point programs while taking into account architecture- and compiler-dependent features, such as the use of the x87 stack in Intel micro-processors. The underlying tool analyzes the assembly code generated by the compiler. It also includes a preliminary and independent approach for proving floating-point programs involving bit-level operations.
C. Lelay, under the supervision of S. Boldo and G. Melquiond, has worked on easing proofs of differentiability and integrability in Coq. The use case was the existence of a solution to the wave equation thanks to D'Alembert's formula; the goal was to automate the process as much as possible [30] . While a major improvement with respect to Coq standard library, this first approach was not user-friendly enough for parametric intervals. So a different approach based on the pervasive use of total functions has been experimented with [22] .
S. Boldo, F. Clément, J.-C. Filliâtre, M. Mayero, G. Melquiond and P. Weis finished the formal proof of a numerical analysis program: the second order centered finite difference scheme for the one-dimensional acoustic wave [14] .
S. Boldo has developed a formal proof of an algorithm for computing the area of a triangle, an improvement of its error bound and new investigations in case of underflow [60] .
S. Boldo, J.-H. Jourdan, X. Leroy, and G. Melquiond have extended CompCert to get the first formally verified compiler that provably preserves the semantics of floating-point programs [63] .
G. Melquiond has kept improving the floating-point and interval theories used to perform proofs by computations in Coq [16] .