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Pré-Publication, Document De Travail Année : 2010

Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

Résumé

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. It is hence adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems.
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Dates et versions

hal-00469007 , version 1 (01-04-2010)
hal-00469007 , version 2 (01-04-2010)
hal-00469007 , version 3 (14-06-2010)
hal-00469007 , version 4 (18-06-2010)

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Alexandre Chapoutot. Interval Slopes as Numerical Abstract Domain for Floating-Point Variables. 2010. ⟨hal-00469007v2⟩
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