Investigating the rank of the number in a residue number system
https://doi.org/10.37493/2307-910X.2023.2.4
Abstract
The rank of a number in a residue number system indicates the count of transitions through a range when a number is converted to a positional number system and allows for more efficient non-modular operations and detection of values out of range. The main approach to calculate the rank is the use of the Chinese Remainder Theorem. In this article the approach which allows to compute the rank using a set of special numbers for which ranks are computed in advance is proposed. The simulation of the considered methods is done in the Python programming language. The results are analyzed and recommendations for further use of the proposed method are given.
Supporting agencies: The research was supported by Russian Federation President Grant SP3186.2022.5.
About the Authors
V. A. Kuchukov
North-Caucasus Federal University
Russian Federation
Russian Federation
Kuchukov Viktor A. - Associate Researcher, Department of Number-Theoretical Systems,
Regional Scientific and Educational Mathematical Centre “North Caucasus Centre for
Mathematical Research”,
355000, Stavropol
M. G. Babenko
North-Caucasus Federal University
Russian Federation
Russian Federation
Babenko Mikhail G. - the head of the department of computational mathematics and
cybernetics, Faculty of mathematics and computer science named after Professor N.I. Chervyakov,
355000, Stavropol
N. N. Kucherov
North-Caucasus Federal University
Russian Federation
Russian Federation
Kucherov Nikolay N. - Senior Researcher, Educational and Scientific Center "Computational
Mathematics and Parallel Programming on Supercomputers", Faculty of mathematics and computer science named after Professor N. I. Chervyakov,
355000, Stavropol
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Review
For citations:
Kuchukov V.A., Babenko M.G., Kucherov N.N. Investigating the rank of the number in a residue number system. Modern Science and Innovations. 2023;(2):41-49. https://doi.org/10.37493/2307-910X.2023.2.4
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