Perfect Latin squares and parallel array access

A new nonlinear skewing scheme is proposed for parallel array access. We introduce a new Latin square(perfect Latin square) which has several properties useful for parallel array access. A sufficient condition for the existence of perfect Latin squares and a simple construction method for perfect Latin squares are presented. The resulting skewing scheme provides conflict free access to various subsets of an <italic>N</italic> x <italic>N</italic> array using <italic>N</italic> memory modules. When the number of memory modules is an even power of two, address generation is performed in constant time using a simple circuit. This scheme is the first memory scheme that achieves constant time access to rows, columns, diagonals, and <italic>N</italic><supscrpt>1/2</supscrpt> x <italic>N</italic><supscrpt>1/2</supscrpt> subarrays of an <italic>N</italic> x <italic>N</italic> array using the minimum number of memory modules.

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