Refining Abstract Interpretation-based Approximations with Constraint Solvers

Programs with floating-point computations are tricky to develop because floating-point arithmetic differs from real arithmetic and has many counterintuitive properties. A classical approach to verify such programs consists in estimating the precision of floating-point computations with respect to the same sequence of operations in an idealized semantics of real numbers. Tools like Fluctuat—based on abstract interpretation—have been designed to address this problem. However, such tools compute an over-approximation of the domains of the variables, both in the semantics of the floating-point numbers and in the semantics of the real numbers. This over-approximation can be very coarse on some programs. In this paper, we show that constraint solvers over floating-point numbers and real numbers can significantly refine the approximations computed by Fluctuat. We managed to reduce drastically the domains of variables of C programs that are difficult to handle for abstract interpretation techniques implemented in Fluctuat.