Hexagonal systolic arrays for matrix multiplication

Authors:
M. P. Bekakos;I. Ž. Milovanović;E. I. Milovanović;T. I. Tokić;M. K. Stojčev
Affiliations:
Laboratory of Digital Systems, School of Engineering, Democritus University of Thrace,Greece;-;-;-;Faculty of Electronic Engineering, University of Nis, Beogradska 14, P. O.Box 73, 18000 Nis, Serbia
Venue:
Highly parallel computaions
Year:
2001

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Abstract

We consider the problem of matrix multiplication on hexagonal systolic arrays (SA). We begin with the description of the procedure for systolic array designing which is based on data dependency and space-time mapping of the nested loop algorithms. Then we introduce some performance measures which are used throughout the chapter for comparison of various SAs. We proceed with modification of the standard design procedure which enables synthesis of systolic arrays with the optimal number of processing elements (PE) for a given problem size and minimal execution time for a given number of PEs. Then we analyse and compare different hexagonal arrays. Further, we show how execution time of matrix multiplication algorithm can be reduced if the number of PEs is increased with respect to the optimal one. Finally, we address the problem of fault-tolerant matrix multiplication on hexagonal arrays.