Floating-Point Format Inference in Mixed-Precision

In this article, we address the problem of determining the minimal precision on the inputs and on the intermediary results of a program containing floating-point computations in order to ensure a desired accuracy on the outputs. The first originality of our approach is to combine a forward and a backward static analysis, done by abstract interpretation. The backward analysis computes the minimal precision needed for the inputs and intermediary values in order to have a desired accuracy on the results, specified by the user. The second originality is to express our analysis as a set of constraints made of first order predicates and affine integer relations only, even if the analyzed programs contain non-linear computations. These constraints can be easily checked by an SMT Solver. In practice, the information collected by our analysis may help to optimize the formats used to represent the values stored in the floating-point variables of programs or to select the appropriate precision for sensors. A prototype implementing our analysis has been realized and experimental results are presented.