## Section: New Results

### A Non-local Method for Robustness Analysis of Floating Point Programs

Participants : Dale Miller, Ivan Gazeau.

Programs that must deal with floating point programs and their associate errors can have erratic behavior. In particular, a program that yields outputs that depend continuously on their inputs (in an idealized arithmetic setting) can behave non-continuously when using floating point arithmetic. There are few tools for reasoning about program correctness in a setting that allows for such discontinuous operators.

In [23] , Gazeau, Miller, and Palamidessi provide an approach to reason about some programs that are not continuous. In that paper, they introduce the notion of “robustness”, which intuitively means that if the input to the program changes less than a fixed small amount then the output changes only slightly. This notion is useful in the analysis of rounding error for floating point programs because it helps to establish bounds on output errors introduced by both measurement errors and by floating point computation. Compositional methods often do not work since key constructs—like the conditional and the while-loop—are not robust. The authors proposed a method for proving the robustness of a while-loop. This method is non-local in the sense that instead of breaking the analysis down to single lines of code, it checks certain global properties of its structure. This paper shows that both the CORDIC computation of the cosine and Dijkstra's shortest path algorithm are robust.