Taking architecture and compiler into account in formal proofs of numerical programs. (Preuves formelles de programmes numériques en prenant en compte l'architecture et le compilateur)

On some recently developed architectures, a numerical program may give different answersdepending on the execution hardware and the compilation. These discrepancies of the resultscome from the fact that each floating-point computation is calculated with different precisions.The goal of this thesis is to formally prove properties about numerical programs while takingthe architecture and the compiler into account. In order to do that, we propose two differentapproaches. The first approach is to prove properties of floating-point programs that are true formultiple architectures and compilers. This approach states the rounding error of each floating-point computation whatever the environment and the compiler choices. It is implemented inthe Frama-C platform for static analysis of C code. The second approach is to prove behavioralproperties of numerical programs by analyzing their compiled assembly code. We focus on theissues and traps that may arise on floating-point computations. Direct analysis of the assemblycode allows us to take into account architectureor compiler-dependent features such as thepossible use of extended precision registers. It is implemented above the Why platform fordeductive verification.