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In our description of "much better" and "best" algorithm, we assumed that one broadcasts each J block to each processor
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There are some different ways of setting this up which can be more efficient on some architectures
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Especially on classic architectures of times gone by where there different costs for different communication paths
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The data parallel part of foils in fact describes the natural pipeline algorithm which rotates J blocks through processors one step at a time
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This has the feature (different from previous explanation) that each processor is handling a different set of j's at a given stage in computation.
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