Refining Abstract Interpretation-based Approximations with a Floating-point Constraint Solver

Floating-point arithmetic differs from real arithmetic, which makes programming with floating-point numbers tricky. Estimating the precision of a floating-point computation in a program, i.e., estimating the difference with the result of the same sequence of operations in an idealized real number semantics, is then necessary. Tools like Fluctuat, based on abstract interpretation, have been designed to address this problem. However, these tools compute an over-approximation of the domains of the floating-point variables that may be very coarse on some tricky programs. In this paper, we use a constraint solver over floatingpoint numbers to refine the over-approximation computed by Fluctuat and reduce the domains of floating-point variables. Our approach could be successfully applied to C programs that are difficult for abstract interpretation techniques as implemented in Fluctuat.