Polyhedral Abstract Interpretation

The polyhedral model is a collection of techniques developed around a common intermediate representation of programs : integer polyhedra. Such a mathematical representation of programs inherits nice structural properties. For instance, when loop transformations are represented as affine functions, compositions of transformations are also affine functions due to their closure properties. The polyhedral representation was linked to loop programs by an analysis proposed by Feautrier [1]. This analysis provides exact dependence analysis information where statement instances (i.e., statements executed at different loop iterations) and array elements are distinguished. The exact dependence information obtained through this analysis and the use of linear programming techniques to explore the space of legal schedules [2] is what constitutes the basis of the polyhedral model for loop transformations. j