# A geometric approach for partitioning n-dimensional non-rectangular iteration spaces

LANGUAGES AND COMPILERS FOR HIGH PERFORMANCE COMPUTING（2008）

摘要

Parallel loops account for the greatest percentage of program parallelism. The degree to which parallelism can be exploited and the amount of overhead involved during parallel execution of a nested loop directly depend on partitioning, i.e., the way the different iterations of a parallel loop are distributed across different processors. Thus, partitioning of parallel loops is of key importance for high performance and efficient use of multiprocessor systems. Although a significant amount of work has been done in partitioning and scheduling of rectangular iteration spaces, the problem of partitioning of non-rectangular iteration spaces – e.g. triangular, trapezoidal iteration spaces – has not been given enough attention so far. In this paper, we present a geometric approach for partitioning N-dimensional non-rectangular iteration spaces for optimizing performance on parallel processor systems. Speedup measurements for kernels (loop nests) of linear algebra packages are presented.

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关键词

different iteration,parallel loop,trapezoidal iteration space,parallel execution,rectangular iteration space,nested loop,loop nest,geometric approach,n-dimensional non-rectangular iteration space,parallel processor system,partitioning n-dimensional non-rectangular iteration,non-rectangular iteration space,linear algebra,nested loops

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