Odd Memory Systems May Be Quite Interesting

Abstract

Using a prime number of N of memory banks on a vector processor allows a conflict-free access for any slice of N consecutive elements of a vector stored with a stride not multiple of N. To reject the use of a prime (or odd) number N of memory banks, 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 well known Chinese Remainder Theorem allows 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 several 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 for memory to the processors through the interconnection network have 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 self-routed.