Latin squares for parallel array access

Abstract

A parallel memory system for efficient parallel array access using perfect latin squares as skewing functions is discussed. Simple construction methods for building perfect latin squares are presented. The resulting skewing scheme provides conflict free access to several important subsets of an array. The address generation can be performed in constant time with simple circuitry. The skewing scheme can provide constant time access to rows, columns, diagonals, and N/sup 1/2/*N/sup 1/2/ subarrays of an N*N array with maximum memory utilization. Self-routing Benes networks can be used to realize the permutations needed between the processing elements and the memory modules. Two skewing schemes that provide conflict free access to three-dimensional arrays are also discussed. Combined with self-routing Benes networks, these schemes provide efficient access to frequently used subsets of three-dimensional arrays. >