ON ОNE APPROACH TO CREATING AN EFFICIENT ALGORITHM FOR PERFORMING A COMPLEX OPERATION IN THE SYSTEM OF RESIDUE CLASSES

Abstract

Data processing in the non-positional number system of residual classes allows to significantly increase the speed of computational operations. The purpose of the work is to study a new approach to creating an effective algorithm for performing a complex operation of comparing numbers and comparing numbers using this approach. Comparison of the current state of the controlled object of the system with the state of the object specified by the functioning algorithm is the subject of solving any control problem. System analysis, number theory and the Chinese residue theorem are tools of the research methodology. The approach is based on representing each number as the sum of the incomplete fraction and the remainder for a given modulus. The comparison itself is an iterative process of comparing the values ​of the components of the specified sums at each iteration, the results of which are used to select actions for the next iteration. This approach should be considered as one of the directions of research into ways to increase the efficiency of calculations.