Static Analysis of the Accuracy in Control Systems: Principles and Experiments

Finite precision computations can severely affect the accuracy of computed solutions. We present a complete survey of a static analysis based on abstract interpretation, and a prototype implementing this analysis for C codes, for studying the propagation of rounding errors occurring at every intermediary step in floating-point computations. In the first part of this paper we briefly present all the domains and techniques used in the implemented analyzer, called FLUCTUAT. We describe in the second part, the experiments made on real industrial codes, at Institut de Radioprotection et de Sûreté Nucléaire and at Hispano-Suiza, respectively coming from the nuclear industry and from aeronautics industry. This paper aims at filling in the gaps between some theoretical aspects of the static analysis of floating-point computations that have been described in [13, 14, 21], and the necessary choices of algorithms and implementation, in accordance with practical motivations drawn from real industrial cases.