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Grids: A Domain 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:

This paper explores the abstract domain of grids, 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 program variables can take. We present the domain, its representation and the basic operations on grids necessary to define the abstract semantics. We show how the definition of the domain and its operations exploit well-known techniques from linear algebra as well as a dual representation that allows, among other things, for a concise and efficient implementation.

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[Page last updated on 2006.04.24.]