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.
Highlights
The new algorithm described in this paper speeds up the modular division procedure in the residue number system (RNS)
The new in algorithm described in well-known this paper speeds up This the modular division procedure in the representation comparison with the analogs
Fact can be explained by the rather representation in comparison with the well-known analogs
Summary
Nikolay Chervyakov 1 , Pavel Lyakhov 1,2, * , Mikhail Babenko 1 , Irina Lavrinenko 3 , Maxim Deryabin 1 , Anton Lavrinenko 3 , Anton Nazarov 1 , Maria Valueva 1 , Alexander Voznesensky 2 and Dmitry Kaplun 2. Received: 3 December 2019; Accepted: 15 January 2020; Published: 19 January 2020
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