On Tiling as a Loop Transformation

Jingling Xue Department of Mathematics, Statistics and Computing Science University of New England, Armidale 2351, Australia ABSTRACT This paper is a follow-up to Irigoin and Triolet's earlier work and our recent work on tiling. In this paper, tiling is discussed in terms of its e ects on the dependences between tiles, the dependenceswithin a tile and the required dependence test for legality. A necessary and su cient condition is given for enforcing the data dependences of the program,while Irigoin and Triolet's atomic tile constraint is only su cient. A condition is identi ed under which both Irigoin and Triolet's and our constraints are equivalent. The results of this paper are discussed in terms of their impact on dependence abstractions suitable for legality test and on tiling to optimise a certain given goal.