Odd Memory Systems: A New Approach

Abstract

To reject the use of a prime (or odd) number N of memory banks in a vector processor, it is generally advanced that address computation for such a memory system would require systematic Euclidean division by the number N. We first show that the Chinese Remainder Theorem allows one to define a very simple mapping of data onto the memory banks for which address computation does not require any Euclidean division. Massively parallel SIMD computers may have thousands of processors. When the memory on such a machine is globally shared, routing vectors from memory to the processors is a major difficulty; the control for the interconnection network cannot be generally computed at execution time. When the number of memory banks and processors is a product of prime numbers, the family of permutations needed for routing vectors from memory to the processors through the interconnection network has very specific properties. The Chinese Remainder Network presented in the paper is able to execute all these permutations in a single path and may be easily controlled.