Improvement of the Approximate Method for the Comparison Operation in the RNS

Abstract

The operation of number comparison is widely used in the implementation of most modern algorithms. The implementation of the algorithm for number comparison in the Residue Number System (RNS) consists of two stages. The first stage is calculating the positional characteristic of the modular number. The second stage is comparing positional characteristics of modular numbers in the positional number system. The article studies various comparison algorithms with software implementation in the Python programming language. The research consists in testing algorithms with different bit width and length of the RNS module vector. Also in this work, the improvement of the approximate method on the reduction of requirements for accuracy is carried out. The use of this method is based on low precision requirements for the comparison operation. It was found that in a certain range accuracy is not critical, which makes it possible to apply this method in a fairly wide range of problems.