Comparison of modular numbers based on the chinese remainder theorem with fractional values

Abstract

New algorithms for determining the sign of a modular number and comparing numbers in a residue number system (RNS) have been developed using the Chinese remainder theorem with fractional values. These algorithms are based on calculations of approximate values of fractional values determined by moduli of the system. Instrumental implementations of the new algorithms are proposed and examples of their applications are given. Modeling these developments on Xilinx Kintex 7 FPGA showed that the proposed methods of decrease computational complexity of determining signs and comparing numbers in the RNS compared to that in well-known architectures based on the Chinese remainder theorem with generalized positional notation