Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

Alexandre Chapoutot (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

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 partially 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. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems.

Mots clés: Abstract interpretation; Interval domain

Domaines: Langage de programmation [cs.PL]

Alexandre Chapoutot. Interval Slopes as Numerical Abstract Domain for Floating-Point Variables. SAS 2010 - 17th Static Analysis Symposium, Sep 2010, Perpignan, France. pp.184-200, ⟨10.1007/978-3-642-15769-1_12⟩. ⟨hal-00469007v4⟩