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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 789213, 12 pages
http://dx.doi.org/10.1155/2014/789213
Research Article

Robustness Analysis of Floating-Point Programs by Self-Composition

National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha 410073, China

Received 14 February 2014; Accepted 7 April 2014; Published 20 May 2014

Academic Editor: Xiaoyu Song

Copyright © 2014 Liqian Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Robustness is a key property for critical systems that run in uncertain environments, to ensure that small input perturbations can cause only small output changes. Current critical systems often involve lots of floating-point computations which are inexact. Robustness analysis of floating-point programs needs to consider both the uncertain inputs and the inexact computation. In this paper, we propose to leverage the idea of self-composition to transform the robustness analysis problem into a reachability problem, which enables the use of standard reachability analysis techniques such as software model checking and symbolic execution for robustness analysis. To handle floating-point arithmetic, we employ an abstraction that encompasses the effect of rounding and that can encompass all rounding modes. It converts floating-point expressions into linear expressions with interval coefficients in exact real arithmetic. On this basis, we employ interval linear programming to compute the maximum output change or maximum allowed input perturbation for the abstracted programs. Preliminary experimental results of our prototype implementation are encouraging.