Minimal Data Dependence Abstractions for Loop Transformations

Data Dependence Abstractions for Loop Transformations Yi-Qing Yang Corinne Ancourt Francois Irigoin Ecole des Mines de Paris/CRI 77305 Fontainebleau Cedex France tractions of program dependences have already been proposed, such as the Dependence Distance, the Dependence Direction Vector, the Dependence Level or the Dependence Cone. These di erent abstractions have di erent precision. The minimal abstraction associated to a transformation is the abstraction that contains the minimal amount of information necessary to decide when such a transformation is legal. The minimal abstractionsfor loop reorderingand unimodulartransformationsare presented. As an example, the dependence cone, that approximates dependences by a convex cone of the dependence distance vectors, is the minimal abstraction for unimodular transformations. It also contains enough information for legally applying all loop reordering transformations and nding the same set of valid mono- and multi-dimensional linear scheduli...

• Type: Conference
• Year: 1994
• Where: LCPC
• Authors: Yi-Qing Yang, Corinne Ancourt, François Irigoin
• Keywords: Data Dependence Abstractions, Dependence Cone, Dependence Distance, LCPC 1994, System Software