The odd-even expansion storage scheme and its implementation issues

Abstract

The authors present a parallel storage scheme to distribute the elements of an N*N matrix over N memory banks, where N is any (odd or even) power of two, such that any rows, columns, forward and backward diagonals, and square or rectangular blocks can be accessed simultaneously without memory conflict. They present a simple scheme for address generation, which requires only logic operations and can be completed in constant time. They present two network implementation methods for data alignments for this storage scheme. Different from previously proposed routing algorithms, the algorithms for hypercube routing in this paper are free from network conflict. They do not require buffering and time length of a 'step' is shorter, therefore they are more efficient in terms of both hardware cost and speed. The authors also present a simple MIN implementation scheme for the realization of the data alignments. Schemes for processing smaller matrices efficiently on larger scale systems are also developed. >