The octagon abstract domain

The Octagon Abstract Domain

This article presents the octagon abstract domain, a relational numerical abstract domain for static analysis by abstract interpretation. It allows representing conjunctions of constraints of the form ±X ± Y ≤ c where X and Y range among program variables and c is a constant in Z, Q, or R automatically inferred. Abstract elements are represented using modified Difference Bound Matrices and we u...

The Octagon Abstract Domain Library

A Fast Implementation of the Octagon Abstract Domain on Graphics Hardware

We propose an efficient implementation of the Octagon Abstract Domain (OAD) on Graphics Processing Unit (GPU) by exploiting stream processing to speed-up OAD computations. OAD is a relational numerical abstract domain which approximates invariants as conjunctions of constraints of the form ±x±y <= c, where x and y are program variables and c is a constant which can be an integer, rational or re...

Meshing the hyperbolic octagon

This short report describes a preliminary study of a method computing meshes of the standard hyperbolic octagon that respects its symmetries. A prototype software was written, using the 2D meshing package of the CGAL library [1, 10] and a software computing hyperbolic triangulations, currently under development [4]. Key-words: Hyperbolic geometry, Poincaré disk, Schwarz triangle, mesh ∗ This wo...

The Octahedron Abstract Domain

An interesting area in static analysis is the study of numerical properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numerical...