Graduate Thesis Or Dissertation
 

Scheduling system of affine recurrence equations by means of piecewise affine timing functions

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/mw22v9223

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  • Many systematic methods exist for mapping algorithms to processor arrays. The algorithm is usually specified as a set of recurrence equations, and the processor arrays are synthesized by finding timing and allocation functions which transform index points in the recurrences into points in a space-time domain. The problem of scheduling (i.e. finding the timing function) of recurrence equations has been studied by a number of researchers. Of particular interest here are Systems of Affine Recurrence Equations (SAREs). The existing methods are limited to affine (or linear) schedules over the entire domain of computation. For some algorithms, there are points in the computation domain where the dependencies point in opposite directions, and an affine schedule does not exist, although a valid Piecewise Affine Schedule (PAS) can exist. The objective of this thesis is to examine these schedules and obtain a systematic method for deriving such schedules for SAREs. PAS can be found by first partitioning the computation domain and then obtaining a new SARE by renaming the variables. By partitioning the computation domain, we can obtain additional parallelism from the dependency graph, and find faster schedules over subspaces of the domain. In this paper, we describe a procedure for partitioning the domain and to generate a new SARE by renaming the variables. Some heuristics are introduced for partitioning the domain based on the properties of dependence vectors. After the partitioning and renaming, an existing method (due to Mauras et al.) is applied to find the schedules. Examples of Toeplitz System and Algebraic Path Problem are used to illustrate the results.
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