Floating-point Semantics of Analyzed Programs

Abstract

This chapter focuses on floating-point semantics. It first outlines these semantics. The chapter then revisits previous results and adapts them to account for floating-point computations, assuming a bound on the rounding error is provided. A last part focuses on the approaches to bound these imprecisions, over-approximating the floating-point errors. Here, provided bounds on each variable, computing the floating-point error can be performed with classical interval-based analysis. Kleene-based iterations with interval abstract domain provide the appropriate framework to compute such bounds. This is even simpler in this setting because of the focus on bounding the floating-point error on a single call of the dynamic system transition function, that is, a single loop body execution without internal loops.