Traditional dependence analysis techniques usually attempt to recognize the existence of dependencies between iterations of a loop and, in some cases, characterize these dependencies by finding direction vectors or distance vectors. In this paper, a more general form of data dependence called hyperplane dependence is introduced. It is a dependence whose source and destination are subspaces of the iteration space. This dependence form can be useful mainly for expressing dependencies across loop-nests, and consequently better understand the interaction between the loops. In order to be able to express across loop dependencies and analyze all loops in the code simultaneously, a global iteration space for all loops in the code is formed. Hyperplane dependence analysis is used in this paper to improve automatic generation of communication statements across loops and index alignment for n-dimensional grid target machines.
['A. Zaafrani', 'Mabo Robert Ito']
Expressing cross-loop dependencies through hyperplane data dependence analysis