Projet CHLOEOne major point in loop restructuring for data locality optimization is the choice and the evaluation of a data locality criteria. We show in this paper how to compute approximations of window sets defined by Gannon, Jalby and Gallivan (the window associated with an iteration i describes the "active" portion of array : elements which have already been referenced before iteration i and which will be referenced after iteration i. Such a notion is extremely useful for data localization since it identifies the portions of arrays which are worth keeping in local memory because they are going to be referenced later. The computation of these window approximations can be performed symbolically at compile time and generates simple geometrical shape that simplifies the management of the data transfers. This allow to derive a global strategy of data management for local memories. . . Moreover, the effects of loop transformations fit naturally in the geometrical framework we use for the calculations. The determination of window approximations is studied both from a theoretical and a computational point of view and examples of applications are given
