Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System

The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional nu...

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Автори:	Kuchukov, V. A., Кучуков, В. А., Babenko, M. G., Бабенко, М. Г., Kucherov, N. N., Кучеров, Н. Н.
Формат:	Статья
Мова:	English
Опубліковано:	2023
Предмети:	Residue number system (RNS) Reference points Mixed-radix conversion Chinese remainder theorem
Онлайн доступ:	https://dspace.ncfu.ru/handle/20.500.12258/22276
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id	ir-20.500.12258-22276
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spelling	ir-20.500.12258-222762023-01-27T10:14:06Z Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System Kuchukov, V. A. Кучуков, В. А. Babenko, M. G. Бабенко, М. Г. Kucherov, N. N. Кучеров, Н. Н. Residue number system (RNS) Reference points Mixed-radix conversion Chinese remainder theorem The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional number system. The methods of reverse conversion for general form moduli based on the Chinese remainder theorem and the mixed-radix conversion are considered, as well as the optimized methods for special form moduli. In this paper, a method is proposed that develops the authors’ ideas based on the modified mixed-radix conversion and reference points. The modified method based on the mixed-radix conversion in this case makes it possible to replace the operation of finding the residue of division by a large modulo with the sequential calculation of the residue. The method of reference points allows to reduce the size of the stored information compared to the use of ROM to store all the residues of RNS. The application of this approach makes it possible to find a balance between the speed of the calculation and the hardware used, by varying the number of moduli of one method and the other. 2023-01-27T10:12:45Z 2023-01-27T10:12:45Z 2022 Статья Kuchukov, V., Telpukhov, D., Babenko, M., Mkrtchan, I., Stempkovsky, A., Kucherov, N., Ermakova, T., Grigoryan, M. Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System // Applied Sciences (Switzerland). - 2022. - 12 (23), статья № 12355. - DOI: 10.3390/app122312355 http://hdl.handle.net/20.500.12258/22276 en Applied Sciences (Switzerland) application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Residue number system (RNS) Reference points Mixed-radix conversion Chinese remainder theorem
spellingShingle	Residue number system (RNS) Reference points Mixed-radix conversion Chinese remainder theorem Kuchukov, V. A. Кучуков, В. А. Babenko, M. G. Бабенко, М. Г. Kucherov, N. N. Кучеров, Н. Н. Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
description	The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional number system. The methods of reverse conversion for general form moduli based on the Chinese remainder theorem and the mixed-radix conversion are considered, as well as the optimized methods for special form moduli. In this paper, a method is proposed that develops the authors’ ideas based on the modified mixed-radix conversion and reference points. The modified method based on the mixed-radix conversion in this case makes it possible to replace the operation of finding the residue of division by a large modulo with the sequential calculation of the residue. The method of reference points allows to reduce the size of the stored information compared to the use of ROM to store all the residues of RNS. The application of this approach makes it possible to find a balance between the speed of the calculation and the hardware used, by varying the number of moduli of one method and the other.
format	Статья
author	Kuchukov, V. A. Кучуков, В. А. Babenko, M. G. Бабенко, М. Г. Kucherov, N. N. Кучеров, Н. Н.
author_facet	Kuchukov, V. A. Кучуков, В. А. Babenko, M. G. Бабенко, М. Г. Kucherov, N. N. Кучеров, Н. Н.
author_sort	Kuchukov, V. A.
title	Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
title_short	Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
title_full	Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
title_fullStr	Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
title_full_unstemmed	Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System
title_sort	performance analysis of hardware implementations of reverse conversion from the residue number system
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/22276
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Performance Analysis of Hardware Implementations of Reverse Conversion from the Residue Number System

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