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Pipelined division of signed numbers with the use of residue arithmetic for small number range with the programmable gate array

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Identyfikatory
Warianty tytułu
Konferencja
Computer Applications in Electrical Engineering 2013 (15-16.04.2013; Poznań, Polska)
Języki publikacji
EN
Abstrakty
EN
In this work an architecture of the pipelined signed residue divider for the small number range is presented. Its operation is based on reciprocal calculation and multiplication by the dividend. The divisor in the signed binary form is used to compute the approximated reciprocal in the residue form by the table look-up. In order to limit the look-up table address an algoritm based on segmentation of the divisor into two segments is used. The approximate reciprocal transformed to residue representation with the proper sign is stored in look-up tables. During operation it is multiplied by the dividend in the residue form and subsequently scaled. The pipelined realization of the divider in the FPGA environment is also shown.
Słowa kluczowe
Rocznik
Tom
Strony
117--126
Opis fizyczny
Bibliogr. 14 poz., rys.
Twórcy
autor
  • Gdańsk University of Technology
autor
  • Gdańsk University of Technology
autor
  • Gdańsk University of Technology
Bibliografia
  • [1] Szabo N.S., Tanaka R.I.: Residue Arithmetic and its Applications to Computer Technology, McGraw-Hill, New York, 1967.
  • [2] Soderstrand M. et al., Residue Number System Arithmetic, Modern Applications in Digital Signal Processing, IEEE Press, NY, 1986.
  • [3] Omondi A., Premkumar B., Residue Number Systems: Theory and Implementation, London, Imperial College Press, 2007.
  • [4] Jenkins W.K., Krogmeier J.V.: The design of dual-mode complex signal processors based on quadratic modular number codes, IEEE Trans. on Circuits and Systems, Volume 34, Number 4, pp. 354-364, 1987.
  • [5] Keir, Y.A, Cheney P.W., Tanenbaum M.: Division and overflow detection in residue number systems, IRE Trans. Electron. Comput., Volume EC-11, pp. 501-507, 1962.
  • [6] Kinoshita E., Kosako H., Koyima Y.: General division in symmetric residue number systems, IEEE Trans, on Computers, Volume C-22, pp. 134-142, 1973.
  • [7] Banerji D.K., Cheung T.Y., Ganesan V.: A high speed division method in residue arithmetic, Proc. of 5th IEEE Symp. on Comput. Arithm., pp. 331-342, 1981.
  • [8] Lin, M. L., Leiss, E., Mclnnis B.: Division and sign detection algorithms for residue number systems, Comput. Math. Appl. Volume 10, Number4/5, pp. 331-342, 1984.
  • [9] Chren W.A., Jr.: A new residue number system division algorithm, Comput. Math. Appl., vol. 19, Number 7, pp. 13-29, 1990.
  • [10] Lu M, Chiang Jen-Shiun: A novel division algorithm for the residue number system, IEEE Trans, on Comput., Volume C-41, pp. 1026-1032, 1992.
  • [11] Hiasat A.A., Zohdy, H.A.A.: Semi-custom VLSI design and implementation of a new efficient RNS division algorithm, Computer Journal, Volume 42, Number3, pp. 232-240, 1999.
  • [12] Talameh S., Siy P.: Arithmetic division in RNS using Galois field GF(p), Comput. Math. Appl., Volume 39, pp. 227-238, 2000.
  • [13] Hitz, M.A., Kaltofen, E.: Integer division in residue number system, IEEE Trans, on Computers, Volume C-44, pp. 983-989, 1995.
  • [14] Czyzak, M.: Noniterative small range residue division, RADIOELEKTRONIKA 2002, May 14-16, Bratislava, pp. 111-114, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-efa79ce9-ffe5-4f3f-bf4b-b180c04dd5fe
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