@Techreport{BagnaraDHMZ05TR, Author = "R. Bagnara and K. Dobson and P. M. Hill and M. Mundell and E. Zaffanella", Title = "A Linear Domain for Analyzing the Distribution of Numerical Values", Number = "2005.06", Type = "Report", Institution = "School of Computing, University of Leeds, UK", Year = 2005, Note = "Available at \url{http://www.comp.leeds.ac.uk/research/pubs/reports.shtml}", Abstract = "This paper explores the abstract domain of \emph{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. Besides the bare abstract domain, we present a complete set of operations on grids that includes all that is necessary to define the abstract semantics and the widening operators required to compute it in a finite number of steps. 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.", }