ВЫЧИСЛИТЕЛЬНЫЕ СИСТЕМЫ И СЕТИ
В.М. Хачумов "Вычисление математических функций на основе разряднопараллельных схем"
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ И АНАЛИЗ ДАННЫХ
ИНТЕЛЛЕКТУАЛЬНЫЕ СИСТЕМЫ
ПРИКЛАДНЫЕ АСПЕКТЫ ИНФОРМАТИКИ
В.М. Хачумов "Вычисление математических функций на основе разряднопараллельных схем"

Аннотация.

Показана возможность разрядного представления математических функций для их быстрого вычисления на основе различных подходов. Для быстрого вычисления функций предложены разрядно-параллельные схемы, ориентированные на применение многовходовых сумматоров, приведена архитектура специализированного геометрического процессорного элемента. Даны оценки вычислительной сложности. Рассмотренная разрядная технология может быть применена в бортовых вычислителях, использующих технику FPGA для обработки сигналов и выработки управлений.

Ключевые слова:

математические функции, разрядные схемы, параллельные вычисления, алгоритмы CORDIC, многовходовый сумматор, специализированный процессорный элемент.

Стр. 26-44.

V.M. Khachumov

"The calculation of mathematical functions based on bit-parallel schemes"

Тhe possibility of bit representations of mathematical functions for fast calculations on the basis of different approaches is shown. For a fast calculation functions offered bit- parallel computing scheme, focused on the use of multi-input adders, shows the architecture of the specialized geometric processing element. Estimates of the computational complexity. Considered bit technology can be applied in the onboard computer, using FPGA technology for signal processing and control production.

Keywords:

mathematical functions, bit scheme, parallel computing, the CORDIC algorithms, multi-input adder, a specialized processing element.

Полная версия статьи в формате pdf. 

REFERENCES

1. Volder J.E. The Cordic trigonometric computing technique. – IRE Transactions on Electronic Computers, Vol. 8, pp. 330-334, 1959.
2. Baykov V.D., Smolov V.B. Spetsializirovannye protsessory. Iteratsionnye algoritmy i struktury. – M.: Radio i svyaz, 1985. – 288 s.
3. Baykov V.D., Vashkevich S.N. Reshenie traektornykh zadach v mikroprotsessornykh sistemakh ChPU. – L.: Mashinostroenie, 1986. – 106 s.
4. Trig functions – how do TI products calculate them? –http://education.ti.com/product/tech/30xa/faqs/faq83086.html
5. Yuen A.K. Intel's Floating-Point Processors. – Electro/88 Conference Record, 1998, pp. 48
6. Rui Xu, Zhanpeng Jiang, Hai Huang, Changchun Dong. An Optimization of CORDIC Algorithm and FPGA Implementation. – International Journal of Hybrid Information Technology Vol.8, No.6 (2015), pp.217-228. – URL:
http://www.sersc.org/journals/IJHIT/vol8_no6_2015/21.pdf
7. Shrugal Varde, Dr. Nisha Sarwade, Richa Upadhyay. Hardware Implementation Of Hyperbolic Tan Using Cordic On FPGA International Journal of Engineering Research and Applications (IJERA), Vol.3, Issue 2, March-April 2013, pp.696-699. –
URL: http://www.ijera.com/papers/Vol3_issue2/DK32696699.pdf
8. Gadekar S.R. CORDIC Algorithm for WLAN. – Int. Journal of Engineering Research and Applications, Vol. 5, Issue 8, (Part2) August 2015, pp.01-04. URL: http://www.ijera.com/papers/Vol5_issue8/Part%20-%202/A58020104.pdf
9. Godbole B.B., Nikam R.H. FPGA implementation of CORDIC algorithm used in DDS based modulators. – International Journal of Advanced Research in Computer and Communication Engineering, Vol.4, Issue 1, January 2015, pp.94-97. –
URL: http://www.ijarcce.com/upload/2015/january/IJARCCE2D.pdf
10. Tokarev V.A., Khludenev A.V. CORDIC-algoritm. – Otsenka effektivnosti algoritmov tsifrovoy obrabotki signalov pri konveyernoy realizatsii. – Ogarev on-line. Elektronnoe periodicheskoe izdanie dlya studentov i aspirantov,
Opublikovano 16.10.2015, s.1-4. – URL: http://journal.mrsu.ru/tag/cordic-algoritm/, http://journal.mrsu.ru/wpcontent/
uploads/2015/10/statya-tokarev-orenburg-.pdf
11. Nikhil Dhume, Ramakrishnan Srinivasakannan. Parameterizable CORDIC-Based Floating-Point Library Operations (XAPP552 (v1.0) June 1, 2012). – URL: http://www.xilinx.com/support/documentation/application_notes/xapp552-cordicfloating-point-operations.pdf
12. CORDIC v6.0. LogiCORE IP Product Guide-Vivado Design Suite, PG105 November 18, 2015. URL: http://www.xilinx.com/support/documentation/ip_documentation/cordic/v6_0/pg105-cordic.pdf
13. Zotov V. Razrabotka bazovykh komponentov tsifrovykh ustroystv, realizuemykh na baze PLIS FPGA firmy Xilinx®, s pomoshchyu generatora parametrizirovannykh moduley CORE Generator. − Komponenty i tekhnologii, №2, 2008, s. 49-56.
14. CORDIC IP Core User’s Guide. © 2012 Lattice Semiconductor Corp. – IPUG81_1.3, August 2012.
15. «MULTIKOR» – otechestvennye mikroskhemy OAO NPTs «ELVIS». – URL: http://multicore.ru/
16. Artamonov Ye.I., Kokaev O.G., Ismailov Sh-M.A., Khachumov V.M. Parallelnyy algoritm Voldera dlya operatsii povorota i ego primenenie v mashinnoy grafike. – Upravlyayushchie sistemy i mashiny, 1990, №1, s.106-109.
17. Khachumov V.M. Razryadno-parallelnoe predstavlenie algoritmov Voldera. – Informatika i vychislitelnaya tekhnika. Teoriya i prilozheniya. Chast II. – Makhachkala: Dag.otd. Mezhdunarodnoy akad. informat.,1995, s.19-28.
18. Khachumov V.M. Disparalleling problems in Volder algorithms. – Materialy Mezhdunarodnoy konferentsii "Interaktivnye sistemy: Problemy cheloveko- kompyuternogo vzaimodeystviya", Ulyanovsk (27-31 avgusta 1995 g.). – Ulyanovsk: UGTU,1995, s.56-57.
19. Khachumov V.M. Bit-parallel algorithms and devices. – Conference Proceedings of the 11-th International Conference on Computer Graphics & Vision GRAPHICON’2001 (September 10-15, 2001, Nizny Novgorod), 2001, pp224-226.
20. Khachumov V.M. Razryadno-parallelnye struktury dlya obrabotki i analiza izobrazheniy. – Materialy 6-oy Mezhdunarodnoy konferentsii «Raspoznavanie obrazov i analiz izobrazheniy: novye informatsionnye tekhnologii» ROAI-6-2002 (21-26 oktyabrya 2002). – Velikiy Novgorod: Izd-vo Nov. GU, Tom 2, 2002, s.597-601.
21. Khachumov V.M. Bit-Parallel Structures for Image Processing and Analysis. – Pattern Recognition and Image Analysis, Vol. 13, No 2, 2003, pp. 214-216.
22. Khachumov V.M. Bit-Parallel Structures for Image Processing and Analysis. – Pattern Recognition and Image Analysis, Vol. 13, No 4, 2003, pp. 633-639.
23. Zakharov A.V., Khachumov V.M. Razryadno-parallelnye vychisleniya v sistemakh realnogo vremeni. – Matematika, informatika: teoriya i praktika. Sb. trudov, posvyashchennyy 10-letiyu Universiteta g. Pereslavlya, pod red. Aylamazyana A.K., izdatelstvo «Universitet goroda Pereslavlya», 2003, s. 97-104.
24. Zakharov A.V., Khachumov V.M. Algoritmy CORDIC. Sovremennoe sostoyanie i perspektivy // Programmnye sistemy: teoriya i prilozheniya. – M.: Fizmatlit, may 2004, s.353-372.
25. Khachumov V.M. Razryadno-parallelnye vychislitelnye skhemy. – Trudy Vserossiyskoy nauchno konferentsii «Metody i sredstva obrabotki informatsii» (Moskva, 5-7 oktyabrya 2005 g.). – M.: MGU, 2005, s.288-294.
26. Khachumov V.M. Razryadno-parallelnye algoritmy otsenki mestopolozheniya i orientatsii kosmicheskogo apparata. – Aviakosmicheskoe priborostroenie, №6, 2010, s.18-24.
27. Pukhov G.Ye., Yevdokimov V.F., Sinkov M.V. Razryadno-analogovye vychislitelnye sistemy. – M.: Sov. Radio, 1978. – 256 s.

 

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