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

LANGUAGES AND COMPILERS FOR HIGH PERFORMANCE COMPUTING(2008)

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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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