Grids: A Domain for Analyzing the Distribution of Numerical Values

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.