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A Practical Tool for Analyzing the Distribution of Numerical Values

Roberto Bagnara
Enea Zaffanella
Dipartimento di Matematica
Università di Parma
Via D'Azeglio, 85/A
I-43100 Parma
Italy

Katy Dobson
Patricia M. Hill
Matthew Mundell
School of Computing
The University of Leeds
Leeds LS2 9JT
England

Abstract:

The abstract domain of grids (or lattices) is a domain that is able to represent sets of equally spaced points and hyperplanes over an n-dimensional vector space. Such a domain is useful for the static analysis of the patterns of distribution of the values that program variables can take. This paper explores how this domain may be used in program analysis, describing grid operations such as affine image, affine preimage and widenings needed by such an application. The paper also shows how any grid may be approximated by a less precise non-relational grid and describes how such an approximation can be computed. Illustrative examples show how the domain may be used in the analysis of programs containing simple assignment statements, while loops and recursive procedures.

Available: Gzipped postscript. BibTeX entry.
[Page last updated on 2006.04.24.]