UDC 621.3.037.372.7:004.021
ACCELERATE ARITHMETIC OPERATIONS IN RESIDUE NUMBER SYSTEM USING SCALING
M. D. Novichkov, post-graduate student, National Research University «Moscow Power Engineering Institute», Moscow, Russia; orcid.org/0000-0002-6591-3666, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
D. A. Orlov, Ph.D (Tech.), associate professor, National Research University «Moscow Power Engineering Institute», Moscow, Russia; orcid.org/0009-0008-4395-9760, е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The problem of reducing the time spent to obtain a result in high-precision calculations by using methods and algorithms that perform arithmetic operations on the numbers represented in residue number system (RNS) is considered. The aim of the work is to reduce execution time of non-modular operations in RNS. Within the framework of this work, the task was to develop a modification of the method for performing the arithmetic operation of division in RNS, using such a positional characteristic of numbers in RNS as a relative value. An analysis of block diagram features for hardware implementation of the considered method for dividing numbers in RNS was carried out. This analysis allowed to identify the ways to improve the process of forming a quotient represented as a sum of numbers each being equal to two by exponentiation with variable exponent. To solve this problem, an approach is proposed which allows speeding up calculations using the analyzed method to a required extent by introducing redundancy in terms of equipment volume. Comparison of the time spent on the calculation by SRT method, traditionally used in most processors for dividing numbers, and a new accelerated method developed by the author and working in RNS is made. The comparison was carried out using simulation modeling. Execution time of division operation was measured in discrete model time, the unit of measurement being clock signal. An example is given showing that in the worst case for SRT and the proposed method, the latter will have an advantage.
Key words: : division methods, multimodule number systems, system of residual classes, analysis of algorithms, scalable acceleration approach.