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Abstract

Relations and digraphs (directed graphs) are ubiquitous in the the- ory of loop transformations. To study something as basic as the execution ordering of the iterations of a loop nest, we need to know about several ways of partially ordering integer vectors. The most important concept in loop transformations, namely that of depen- dence, can be viewed as a relation between the members of a certain set. This set could be the set of iterations of a loop nest, or the set of statements in the body of the nest, or the set of instances of the statements. We can even go to a lower level and talk about dependence between ‘loads’ and ‘stores,’ or to a higher level and discuss dependence between large parts of a program.

Keywords

Equivalence Relation Partial Order Maximal Element Direction Vector Minimal Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Utpal Banerjee
    • 1
  1. 1.Intel CorporationUSA

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