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Title: | A division algorithm in a redundant residue number system using fractions |
Authors: | Chervyakov, N. I. Червяков, Н. И. Lyakhov, P. A. Ляхов, П. А. Babenko, M. G. Бабенко, М. Г. Lavrinenko, I. N. Лавриненко, И. Н. Deryabin, M. A. Дерябин, М. А. Lavrinenko, A. V. Лавриненко, А. В. Nazarov, A. S. Назаров, А. С. Valueva, M. V. Валуева, М. В. |
Keywords: | Algorithm;Fraction;Modular division;Redundant residue number system;Residue number system (RNS) |
Issue Date: | 2020 |
Publisher: | MDPI AG |
Citation: | Chervyakov, N., Lyakhov, P., Babenko, M., Lavrinenko, I., Deryabin, M., Lavrinenko, A., Nazarov, A., Valueva, M., Voznesensky, A., Kaplun, D. A division algorithm in a redundant residue number system using fractions // Applied Sciences (Switzerland). - 2020. - Volume 10. - Issue 2. - Номер статьи 695 |
Series/Report no.: | Applied Sciences (Switzerland) |
Abstract: | The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach |
URI: | http://hdl.handle.net/20.500.12258/11909 |
Appears in Collections: | Статьи, проиндексированные в SCOPUS, WOS |
Files in This Item:
File | Description | Size | Format | |
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scopusresults 1228 .pdf Restricted Access | 1.15 MB | Adobe PDF | View/Open | |
WoS 827 .pdf Restricted Access | 193.47 kB | Adobe PDF | View/Open |
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