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Improved Precision in Polyhedral Analysis with Wrapping
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.mdu.se/publications/2628-}
}