Classification of moduli sets for residue number system with special diagonal functions

The paper presents algorithms for the generation of Residue Number System (RNS) triples with SQ=2k-1 and quadruples with SQ=2k for some k. Triples and quadruples allow us to design efficient hardware implementations of non-modular operations in RNS such as division, sign detection, comparison of num...

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Главные авторы:	Chervyakov, N. I., Червяков, Н. И., Lyakhov, P. A., Ляхов, П. А., Semyonova, N. F., Семенова, Н. Ф., Nazarov, A. S., Назаров, А. С., Valueva, M. V., Валуева, М. В.
פורמט:	Статья
שפה:	English
יצא לאור:	Institute of Electrical and Electronics Engineers Inc. 2020
נושאים:	Average bit-width Diagonal Function (DF) FPGA Hardware implementation Non-modular operations Quadruples Residue number system (RNS) RNS balance Computer hardware
גישה מקוונת:	https://dspace.ncfu.ru/handle/20.500.12258/14198
תגים:	הוספת תג אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!

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record_format	dspace
spelling	ir-20.500.12258-141982020-09-28T14:41:34Z Classification of moduli sets for residue number system with special diagonal functions Chervyakov, N. I. Червяков, Н. И. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф. Nazarov, A. S. Назаров, А. С. Valueva, M. V. Валуева, М. В. Average bit-width Diagonal Function (DF) FPGA Hardware implementation Non-modular operations Quadruples Residue number system (RNS) RNS balance Computer hardware The paper presents algorithms for the generation of Residue Number System (RNS) triples with SQ=2k-1 and quadruples with SQ=2k for some k. Triples and quadruples allow us to design efficient hardware implementations of non-modular operations in RNS such as division, sign detection, comparison of numbers, reverse conversion with using of a diagonal function from requiring division with the remainder by the diagonal module SQ. Division with a remainder in the general case is the most complex arithmetic operation in computer technology. However, the consideration of special cases can significantly simplify this operation and increase the efficiency of hardware implementation. We show that there are 5573 good RNS triples (2301 even and 2372 odd) with elements less than 10 000, as the values of SQ vary from 25-1 to 227-1. In contrast, RNS quadruples with SQ=2k seem to be quite rare. Restricting our search to sums of the elements in a quadruple less than 4000 we find that exactly 31 such quadruples exist. Their values of SQ vary between 220 and 230 with always even exponent. We suggest the measure of RNS balance and find perfectly balanced RNS among triples according to this measure. We demonstrate the advantages of more balanced quadruples by means of hardware implementation 2020-09-28T14:40:05Z 2020-09-28T14:40:05Z 2020 Статья Boyvalenkov, P., Chervyakov, N.I., Lyakhov, P., Semyonova, N., Nazarov, A., Valueva, M., Boyvalenkov, G., Bogaevskiy, D., Kaplun, D. Classification of moduli sets for residue number system with special diagonal functions // IEEE Access. - 2020. - Volume 8. - Номер статьи 9177128. - Pages 156104-156116 http://hdl.handle.net/20.500.12258/14198 en IEEE Access application/pdf application/pdf Institute of Electrical and Electronics Engineers Inc.
institution	СКФУ
collection	Репозиторий
language	English
topic	Average bit-width Diagonal Function (DF) FPGA Hardware implementation Non-modular operations Quadruples Residue number system (RNS) RNS balance Computer hardware
spellingShingle	Average bit-width Diagonal Function (DF) FPGA Hardware implementation Non-modular operations Quadruples Residue number system (RNS) RNS balance Computer hardware Chervyakov, N. I. Червяков, Н. И. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф. Nazarov, A. S. Назаров, А. С. Valueva, M. V. Валуева, М. В. Classification of moduli sets for residue number system with special diagonal functions
description	The paper presents algorithms for the generation of Residue Number System (RNS) triples with SQ=2k-1 and quadruples with SQ=2k for some k. Triples and quadruples allow us to design efficient hardware implementations of non-modular operations in RNS such as division, sign detection, comparison of numbers, reverse conversion with using of a diagonal function from requiring division with the remainder by the diagonal module SQ. Division with a remainder in the general case is the most complex arithmetic operation in computer technology. However, the consideration of special cases can significantly simplify this operation and increase the efficiency of hardware implementation. We show that there are 5573 good RNS triples (2301 even and 2372 odd) with elements less than 10 000, as the values of SQ vary from 25-1 to 227-1. In contrast, RNS quadruples with SQ=2k seem to be quite rare. Restricting our search to sums of the elements in a quadruple less than 4000 we find that exactly 31 such quadruples exist. Their values of SQ vary between 220 and 230 with always even exponent. We suggest the measure of RNS balance and find perfectly balanced RNS among triples according to this measure. We demonstrate the advantages of more balanced quadruples by means of hardware implementation
format	Статья
author	Chervyakov, N. I. Червяков, Н. И. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф. Nazarov, A. S. Назаров, А. С. Valueva, M. V. Валуева, М. В.
author_facet	Chervyakov, N. I. Червяков, Н. И. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф. Nazarov, A. S. Назаров, А. С. Valueva, M. V. Валуева, М. В.
author_sort	Chervyakov, N. I.
title	Classification of moduli sets for residue number system with special diagonal functions
title_short	Classification of moduli sets for residue number system with special diagonal functions
title_full	Classification of moduli sets for residue number system with special diagonal functions
title_fullStr	Classification of moduli sets for residue number system with special diagonal functions
title_full_unstemmed	Classification of moduli sets for residue number system with special diagonal functions
title_sort	classification of moduli sets for residue number system with special diagonal functions
publisher	Institute of Electrical and Electronics Engineers Inc.
publishDate	2020
url	https://dspace.ncfu.ru/handle/20.500.12258/14198
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Classification of moduli sets for residue number system with special diagonal functions

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