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Building Systolic Messy Arrays for Infinite Iterative Algorithms
Makio ISHIHARA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E90A
No.8
pp.17191723 Publication Date: 2007/08/01 Online ISSN: 17451337
DOI: 10.1093/ietfec/e90a.8.1719 Print ISSN: 09168508 Type of Manuscript: LETTER Category: General Fundamentals and Boundaries Keyword: infinite iterative algorithms, systolic messy arrays, systolic arrays,
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Summary:
The sizedependent array problem is a problem with systolic arrays such that the size of systolic arrays limits the size of calculations, which in a doloop structure controls how many times it is repeated and how deep the nesting loops are. A systolic array cannot deal with larger calculations. For the sizedependent array problem, a spiral systolic array has been studied so far. It has nonadjacent connections between PEs, such as loop paths for sending data back so that data flows over the array independently of its own size. This paper takes an approach to the problem without nonadjacent connections. This paper discusses systolic messy arrays for infinite iterative algorithms so that they are independent from the size of calculations. First a systolic messy array called twosquare shape is introduced then the properties of twosquare shape are summarized: memory function, cyclic addition, and cyclic multiplication. Finally a way of building systolic messy arrays that calculate infinite iterative algorithms is illustrated with concrete examples such as an arithmetic progression, a geometric progression, N factorial, and Fibonacci numbers.

