Polyhedral Data-Flow Analysis for Data Storage and Transfer Exploration
This chapter describes a theoretical polyhedral basis for data-flow analysis of multi-dimensional signal processing algorithms, especially in the context of DTSE. As mentioned in chapter 1, a data-flow analysis operating with groups of scalars is necessary in order to handle realistic RMSP applications. Formally, these groups are represented by images of polyhedra and are noted as basic sets further on. They can be used to identify useful signal partitions for almost all other DTSE steps but the actual decision on which partitions to withhold depends on the step and on the actual application at hand. The results also have to be carefully evaluated because in some cases the partitioning can lead to an explosion into small basic sets which are too fine grain for an acceptable solution complexity of our steps.
Section 6.1 introduces the basic definitions and concepts of this chapter. Section 6.2 describes an analytical decomposition of indexed signals in basic sets. Section 6.3 presents the construction of data-flow graphs at the level of basic sets of signals. The material in this chapter is based on , chapters 2 and 3 (see also ).
KeywordsNest Loop Affine Mapping Index Space Loop Boundary Array Reference
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