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https://dspace.ncfu.ru/handle/20.500.12258/5079
Название: | A high-speed division algorithm for modular numbers based on the chinese remainder theorem with fractions and its hardware implementation |
Авторы: | Chervyakov, N. I. Червяков, Н. И. Lyakhov, P. A. Ляхов, П. А. Babenko, M. G. Бабенко, М. Г. Nazarov, A. S. Назаров, А. С. Deryabin, M. A. Дерябин, М. А. Lavrinenko, I. N. Лавриненко, И. Н. Lavrinenko, A. V. Лавриненко, А. В. |
Ключевые слова: | Division algorithm;Modular arithmetic;Residue number system (RNS) |
Дата публикации: | 2019 |
Издатель: | MDPI AG |
Библиографическое описание: | Chervyakov, N., Lyakhov, P.E., Babenko, M., Nazarov, A., Deryabin, M., Lavrinenko, I., Lavrinenko, A. A high-speed division algorithm for modular numbers based on the chinese remainder theorem with fractions and its hardware implementation // Electronics (Switzerland). - 2019. - Volume 8. - Issue 3. - Номер статьи 261 |
Источник: | Electronics (Switzerland) |
Краткий осмотр (реферат): | In this paper, a new simplified iterative division algorithm for modular numbers that is optimized on the basis of the Chinese remainder theorem (CRT) with fractions is developed. It requires less computational resources than the CRT with integers and mixed radix number systems (MRNS). The main idea of the algorithm is (a) to transform the residual representation of the dividend and divisor into a weighted fixed-point code and (b) to find the higher power of 2 in the divisor written in a residue number system (RNS). This information is acquired using the CRT with fractions: higher power is defined by the number of zeros standing before the first significant digit. All intermediate calculations of the algorithm involve the operations of right shift and subtraction, which explains its good performance. Due to the abovementioned techniques, the algorithm has higher speed and consumes less computational resources, thereby being more appropriate for the multidigit division of modular numbers than the algorithms described earlier. The new algorithm suggested in this paper has O (log 2 Q) iterations, where Q is the quotient. For multidigit numbers, its modular division complexity is Q(N), where N denotes the number of bits in a certain fraction required to restore the number by remainders. Since the number N is written in a weighed system, the subtraction-based comparison runs very fast. Hence, this algorithm might be the best currently available |
URI (Унифицированный идентификатор ресурса): | https://www.scopus.com/record/display.uri?eid=2-s2.0-85063445845&origin=resultslist&sort=plf-f&src=s&st1=%09A+high-speed+division+algorithm+for+modular+numbers+based+on+the+chinese+remainder+theorem+with+fractions+and+its+hardware+implementation&st2=&sid=892029d19f7c728d4bff772c02120f7f&sot=b&sdt=b&sl=153&s=TITLE-ABS-KEY%28%09A+high-speed+division+algorithm+for+modular+numbers+based+on+the+chinese+remainder+theorem+with+fractions+and+its+hardware+implementation%29&relpos=0&citeCnt=0&searchTerm= http://hdl.handle.net/20.500.12258/5079 |
Располагается в коллекциях: | Статьи, проиндексированные в SCOPUS, WOS |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
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scopusresults 880 .pdf Доступ ограничен | 909.26 kB | Adobe PDF | Просмотреть/Открыть | |
WoS 585 .pdf Доступ ограничен | 75.77 kB | Adobe PDF | Просмотреть/Открыть |
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