Improved Modular Division Implementation with the Akushsky Core Function
The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-01-01
|
| Series: | Computation |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-3197/10/1/9 |
| _version_ | 1797494971220099072 |
|---|---|
| author | Mikhail Babenko Andrei Tchernykh Viktor Kuchukov |
| author_facet | Mikhail Babenko Andrei Tchernykh Viktor Kuchukov |
| author_sort | Mikhail Babenko |
| collection | DOAJ |
| description | The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method. |
| first_indexed | 2024-03-10T01:41:49Z |
| format | Article |
| id | doaj.art-df85d0f1b8c046afa15419f81534995c |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T01:41:49Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-df85d0f1b8c046afa15419f81534995c2023-11-23T13:23:19ZengMDPI AGComputation2079-31972022-01-01101910.3390/computation10010009Improved Modular Division Implementation with the Akushsky Core FunctionMikhail Babenko0Andrei Tchernykh1Viktor Kuchukov2North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, RussiaInstitute for System Programming of the Russian Academy of Sciences, 109004 Moscow, RussiaNorth-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017 Stavropol, RussiaThe residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.https://www.mdpi.com/2079-3197/10/1/9Akushsky core functionresidue number systemRNSmodular division |
| spellingShingle | Mikhail Babenko Andrei Tchernykh Viktor Kuchukov Improved Modular Division Implementation with the Akushsky Core Function Computation Akushsky core function residue number system RNS modular division |
| title | Improved Modular Division Implementation with the Akushsky Core Function |
| title_full | Improved Modular Division Implementation with the Akushsky Core Function |
| title_fullStr | Improved Modular Division Implementation with the Akushsky Core Function |
| title_full_unstemmed | Improved Modular Division Implementation with the Akushsky Core Function |
| title_short | Improved Modular Division Implementation with the Akushsky Core Function |
| title_sort | improved modular division implementation with the akushsky core function |
| topic | Akushsky core function residue number system RNS modular division |
| url | https://www.mdpi.com/2079-3197/10/1/9 |
| work_keys_str_mv | AT mikhailbabenko improvedmodulardivisionimplementationwiththeakushskycorefunction AT andreitchernykh improvedmodulardivisionimplementationwiththeakushskycorefunction AT viktorkuchukov improvedmodulardivisionimplementationwiththeakushskycorefunction |