Automatic Partitioning of Parallel Loops and Data Arrays for Distributed Shared-memory Multiprocessors
Name
MIT-LCS-TM-538.pdf
Size
8.44 MB
Format
Adobe PDF
Checksum (MD5)
dfe11f33d4cef1d95fd4698982842094
Author(s)
Agarwal, Anant
Kranz, David A.
Natarajan, Venkat
Date Issued
September 1995
Series/Report no.
MIT-LCS-TM-538
Abstract
This paper presents a theoretical framework for automatically partitioning parallel loops to minimize cache coherency traffic on shared-memory multiprocessors. While several previous papers have looked at hyperplane partitioning of iteration spaces to reduce communication traffic, the problem of deriving the optimal tiling parameters for minimal communication in loops with general affine index expressions had remained open. Our paper solves this open problem by presenting a method for deriving an optimal hyperparallelepiped tiling of iteration spaces for minimal communication in multiprocessors with caches. We show that the same theoretical framework can also be used to determine optimal tiling parameters for both data and loop partitioning in distributed memory multicomputers. Our framework uses matrices to represent iteration and data space mappings and the notion of uniformly intersecting references to capture temporal locality in array references. We introduce the notion of data footprints to estimate the communication traffic between processors and use linear algebraic methods and lattice theory to compute precisely the size of data footprints. We have implemented this framework in a compiler for Alewife, a distributed shared-memory multiprocessor.
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