A non-local method for robustness analysis of floating point programs

TL;DR

This paper introduces a non-local method for analyzing the robustness of floating point programs, especially handling complex constructs like loops, and demonstrates its effectiveness on standard algorithms.

Contribution

It presents a novel non-local approach for proving robustness of while-loops in floating point programs, addressing limitations of compositional methods.

Findings

Method successfully applied to CORDIC cosine computation

Method successfully applied to Dijkstra's shortest path algorithm

Provides global structural properties for robustness analysis

Abstract

Robustness is a standard correctness property 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. We propose 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. We show the applicability of our method on two standard algorithms: the CORDIC computation of the cosine and Dijkstra's shortest path algorithm.