Comparison of modular numbers based on the chinese remainder theorem with fractional values

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• 作者：N. I. Chervyakov ; A. S. Molahosseini…
• 关键词：residue number system ; Chinese remainder theorem ; modular arithmetic ; positional characteristic ; fractional values ; approximate method ; generalized positional notation
• 刊名：Automatic Control and Computer Sciences
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：49
• 期：6
• 页码：354-365
• 全文大小：467 KB
• 参考文献：1.Chervyakov, N.I., Sakhnyuk, P.A., Shaposhnikov, A.V., and Makokha, A.N., Neirokomp’yutery v ostatochnykh klassakh. Uchebnoe posobie dlya vuzov (Neurocomputers in Residual Classes. Textbook for High Schools), Moscow: Radiotekhnika, 2003.
  2.Chervyakov, N.I., Sakhnyuk, P.A., Shaposhnikov, A.V., and Ryadnov, S.A., Modulyarnye parallel’nye vychislitel’nye struktury neiroprotsessornykh system (Modular Parallel Computing Structures of Neuroprocessor Systems), Moscow: Fizmatlit, 2003.
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  6.Chervyakov, N.I., Lyakhov, P.A., and Babenko, M.G., Digital filtering of images in a residue number system using finite-field wavelets, Autom. Control Comput. Sci., 2014, vol. 48, no. 3, pp. 180–189.CrossRef
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  12.Chervyakov, N.I., Babenko, M.G., Lyakhov, P.A., and Lavrinenko, I.N., An approximate method for comparing modular numbers and its application to the division of numbers in residue number systems, Cybern. Syst. Anal., 2014, vol. 50, no. 6, pp. 977–984.CrossRef
  13.Molahosseini, A.S., Sorouri, S., and Zarandi, A.A.E., Research challenges in next-generation residue number system architectures, Proc. IEEE 7th International Conference on Computer Science & Education (ICCSE), 2012, pp. 1658–1661.
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  15.Hung, C.Y. and Parhami, B., An approximate sign detection method for residue numbers and its application to RNS division, Comput. Math. Appl., 1994, vol. 27, no. 4, pp. 23–25.MATH MathSciNet CrossRef
  16.Chervyakov, N.I., Methods and principles of modular neural computers, in “50 let modulyarnoi arifmetike”. Sbornik nauchnykh trudov (50 Years of Modular Arithmetic. Collection of Scientific Papers), Moscow: OAO Angstrem, MIET, 2005.
  
• 作者单位：N. I. Chervyakov (1)
  A. S. Molahosseini (2)
  P. A. Lyakhov (1)
  M. G. Babenko (1)
  I. N. Lavrinenko (1)
  A. V. Lavrinenko (1)
  
  1. North Caucasus Federal University, Stavropol, 355009, Russia
  2. Department of Computer Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran
  
• 刊物类别：Computer Science
• 刊物主题：Control Structures and Microprogramming
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1558-108X

文摘

New algorithms for determining the sign of a modular number and comparing numbers in a residue number system (RNS) have been developed using the Chinese remainder theorem with fractional values. These algorithms are based on calculations of approximate values of fractional values determined by moduli of the system. Instrumental implementations of the new algorithms are proposed and examples of their applications are given. Modeling these developments on Xilinx Kintex 7 FPGA showed that the proposed methods of decrease computational complexity of determining signs and comparing numbers in the RNS compared to that in well-known architectures based on the Chinese remainder theorem with generalized positional notation. Keywords residue number system Chinese remainder theorem modular arithmetic positional characteristic fractional values approximate method generalized positional notation