Fully Bounded Polyhedral Analysis of Integers with Wrapping

  • Authors:

  • Stefan Bygde;BjöRn Lisper;Niklas Holsti

  • Affiliations:

  • School of Innovation, Design and Technology, Mälardalen University, Västerås, Sweden;School of Innovation, Design and Technology, Mälardalen University, Västerås, Sweden;Tidorum Ltd, Helsinki, Finland

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2012

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Abstract

Analysis of convex polyhedra using abstract interpretation is a common and powerful program analysis technique to discover linear relationships among variables in a program. However, the classical way of performing polyhedral analysis does not model the fact that values typically are stored as fixed-size binary strings and usually have a wrap-around semantics in the case of overflows. In embedded systems where 16-bit or even 8-bit processors are used, wrapping behaviour may even be used intentionally. Thus, to accurately and correctly analyse such systems, the wrapping has to be modelled. We present an approach to polyhedral analysis which derives polyhedra that are bounded in all dimensions and thus provides polyhedra that contain a finite number of integer points. Our approach uses a previously suggested wrapping technique for polyhedra but combines it in a novel way with limited widening, a suitable placement of widening points and restrictions on unbounded variables. We show how our method has the potential to significantly increase the precision compared to the previously suggested wrapping method.