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

Ivan Gazeau 1, 2, * Dale Miller 1, 3 Catuscia Palamidessi 1, 2
* Corresponding author
2 COMETE - Concurrency, Mobility and Transactions
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
3 PARSIFAL - Proof search and reasoning with logic specifications
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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.
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Ivan Gazeau, Dale Miller, Catuscia Palamidessi. A non-local method for robustness analysis of floating point programs. QAPL - Tenth Workshop on Quantitative Aspects of Programming Languages, Mar 2012, Tallinn, Estonia. pp.63-76, ⟨10.4204/EPTCS.85.5⟩. ⟨hal-00665995v3⟩

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