Efficient implementation of Chinese remainder theorem in minimally redundant residue number system

Abstract

The Chinese remainder theorem is widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic that is used in the residue number system. The proposed method does not use large modulo addition operations as compared to a straightforward implementation of the Chinese remainder theorem algorithm. The rank of a number is equal to the sum of an inexact rank and a two-valued correction factor that only takes on values of 0 or 1. We propose a minimally redundant residue number system that provides a low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed regarding a conventional non-redundant residue number system. Owing to the extension of the residue code, the complexity of the rank calculation goes down from $O(k^{2})$ to $O(k)$ by adding the extra residue modulo 2 (where $k$ equals the number of non-redundant residues).