Analysis of algorithms performing basic arithmetic operations in the quadratic RNS
In this paper we explore the question of representing complex numbers in a residue number system and build algorithms for the operations of addition and multiplication. The idea of the construction of such systems is in determining how the set of complex numbers the ring of integers. The main attent...
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| Language: | Russian |
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North-Caucasus Federal University
2022-09-01
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| Series: | Наука. Инновации. Технологии |
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| Online Access: | https://scienceit.elpub.ru/jour/article/view/261 |
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| _version_ | 1839591813952831488 |
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| author | Lyudmila Borisovna Kopytkova |
| author_facet | Lyudmila Borisovna Kopytkova |
| author_sort | Lyudmila Borisovna Kopytkova |
| collection | DOAJ |
| description | In this paper we explore the question of representing complex numbers in a residue number system and build algorithms for the operations of addition and multiplication. The idea of the construction of such systems is in determining how the set of complex numbers the ring of integers. The main attention is paid to quadratic residue number system. The idea of building such a system is to provide a complex number z as a pair of integers (X' Y for the selected modules. The rules of arithmetic operations on complex numbers presented residue pairs at selected bases, do not differ from the rules of arithmetic operations in the RNS for real integers. The operations of addition and multiplication two complex numbers in quadratic RNS is modular, parallel channels and contains only two arithmetic operations that can reduce the volume of calculation. |
| format | Article |
| id | doaj-art-cd88629c246e4a7d89d19e66c8fcc17f |
| institution | Matheson Library |
| issn | 2308-4758 |
| language | Russian |
| publishDate | 2022-09-01 |
| publisher | North-Caucasus Federal University |
| record_format | Article |
| series | Наука. Инновации. Технологии |
| spelling | doaj-art-cd88629c246e4a7d89d19e66c8fcc17f2025-08-03T12:59:59ZrusNorth-Caucasus Federal UniversityНаука. Инновации. Технологии2308-47582022-09-01021728260Analysis of algorithms performing basic arithmetic operations in the quadratic RNSLyudmila Borisovna Kopytkova0North-Caucasus Federal UniversityIn this paper we explore the question of representing complex numbers in a residue number system and build algorithms for the operations of addition and multiplication. The idea of the construction of such systems is in determining how the set of complex numbers the ring of integers. The main attention is paid to quadratic residue number system. The idea of building such a system is to provide a complex number z as a pair of integers (X' Y for the selected modules. The rules of arithmetic operations on complex numbers presented residue pairs at selected bases, do not differ from the rules of arithmetic operations in the RNS for real integers. The operations of addition and multiplication two complex numbers in quadratic RNS is modular, parallel channels and contains only two arithmetic operations that can reduce the volume of calculation.https://scienceit.elpub.ru/jour/article/view/261система остаточных классовкомплексная система остаточных классовквадратичная система остаточных классовмодулярная арифметикапараллельные вычисленияоперация нахождения остаткаresidue number systemcomplex-number rns (crns)quadratic rns (qrns)modular arithmeticparallel computationthe operation of finding the residues |
| spellingShingle | Lyudmila Borisovna Kopytkova Analysis of algorithms performing basic arithmetic operations in the quadratic RNS Наука. Инновации. Технологии система остаточных классов комплексная система остаточных классов квадратичная система остаточных классов модулярная арифметика параллельные вычисления операция нахождения остатка residue number system complex-number rns (crns) quadratic rns (qrns) modular arithmetic parallel computation the operation of finding the residues |
| title | Analysis of algorithms performing basic arithmetic operations in the quadratic RNS |
| title_full | Analysis of algorithms performing basic arithmetic operations in the quadratic RNS |
| title_fullStr | Analysis of algorithms performing basic arithmetic operations in the quadratic RNS |
| title_full_unstemmed | Analysis of algorithms performing basic arithmetic operations in the quadratic RNS |
| title_short | Analysis of algorithms performing basic arithmetic operations in the quadratic RNS |
| title_sort | analysis of algorithms performing basic arithmetic operations in the quadratic rns |
| topic | система остаточных классов комплексная система остаточных классов квадратичная система остаточных классов модулярная арифметика параллельные вычисления операция нахождения остатка residue number system complex-number rns (crns) quadratic rns (qrns) modular arithmetic parallel computation the operation of finding the residues |
| url | https://scienceit.elpub.ru/jour/article/view/261 |
| work_keys_str_mv | AT lyudmilaborisovnakopytkova analysisofalgorithmsperformingbasicarithmeticoperationsinthequadraticrns |