Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

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

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems

Since its inception as a student project in 2001, initially just for the handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library has been continuously improved and extended by joining scrupulous research on the theoretical foundations of (possibly non-convex) numerical abstractions to a total adherence to the best available practices in software development. Even though it is still not fully mature and functionally complete, the Parma Polyhedra Library already offers a combination of functionality, reliability, usability and performance that is not matched by similar, freely available libraries. In this paper, we present the main features of the current version of the library, emphasizing those that distinguish it from other similar libraries and those that are important for applications in the field of analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table

Improving static analyses of C programs with conditional predicates

Extended version of the FMICS 2014 paperInternational audienceStatic code analysis is increasingly used to guarantee the absence of undesirable behaviors in industrial programs. Designing sound analyses is a continuing trade-off between precision and complexity. Notably, dataflow analyses often perform overly wide approximations when two control-flow paths meet, by merging states from each path.This paper presents a generic abstract interpretation based framework to enhance the precision of such analyses on join points. It relies on predicated domains, that preserve and reuse information valid only inside some branches of the code. Our predicates are derived from conditional statements, and postpone the loss of information.The work has been integrated into Frama-C, a C source code analysis platform. Experiments on real generated code show that our approach scales, and improves significantly the precision of the existing analyses of Frama-C

Improving static analyses of C programs with conditional predicates

Best paper awardInternational audienceStatic code analysis is increasingly used to guarantee the absence of undesirable behaviors in industrial programs. Designing sound analyses is a continuing trade-off between precision and complexity. Notably, dataflow analyses often perform overly wide approximations when two control-flow paths meet, by merging states from each path. This paper presents a generic abstract interpretation based framework to enhance the precision of such analyses on join points. It relies on predicated domains, that preserve and reuse information valid only inside some branches of the code. Our predicates are derived from conditionals statements, and postpone the loss of information. The work has been integrated into Frama-C, a C source code analysis platform. Experiments on real code show that our approach scales, and improves significantly the precision of the existing analyses of Frama-C