Abstract

This paper surveys scheduling techniques for loop nests with uniform dependences. First we introduce the hyperplane method and related variants. Then we extend it by using a different affine scheduling for each statement within the nest. In both cases we present a new, constructive and efficient method to determine optimal solutions, i.e. schedules whose total execution time is minimum. 1 Introduction Loop nests lie in the heart of supercompilers-parallelizers for supercomputers. On one hand their importance in terms of applications is evident: in many scientific programs, the time spent in the execution of a small number of loops represents a large fraction of the total execution time, while the potential parallelism of these loops is very important. On the other hand, the regular and repetitive structure of loop nests greatly facilitates the use of dependence analysis techniques and of scheduling and allocation strategies. The general problem of finding the optimal scheduling for a ...

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