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Improved Precision in Polyhedral Analysis with Wrapping

Fulltext:


Authors:

Stefan Bygde, Björn Lisper, Niklas Holsti

Research group:


Publication Type:

Report


Abstract

Abstract interpretation using convex polyhedra 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 xed-size binary strings and usually have wrap-around semantics in the case of over ows. In resource-constrained embedded systems, where 8- or 16-bit processors are used, wrapping behaviour may even be used intentionally to save instructions and execution time. Thus, to analyse such systems accurately and correctly, the wrapping has to be modelled. We present an approach to polyhedral analysis which derives polyhedra that are bounded in all dimensions. Our approach is based on a previously suggested wrapping technique by Simon and King, combined with limited widening, a suitable placement of widening points and size-induced restrictions on unbounded variables. With this method, we can derive fully bounded polyhedra in every step of the analysis. We have implemented our method and Simon and King's method compared them. Our experiments show that for a suite of benchmark programs it gives at least as precise result as Simon and King's method. In some cases we obtain a significantly improved result.

Bibtex

@techreport{Bygde2628,
author = {Stefan Bygde and Bj{\"o}rn Lisper and Niklas Holsti},
title = {Improved Precision in Polyhedral Analysis with Wrapping},
month = {June},
year = {2012},
url = {http://www.es.mdh.se/publications/2628-}
}