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Tabular minimal redundant modular structures for fast and high-precision computations using general-purpose computers

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EN
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The present paper is a continuation of research in parallel information processing based on the tabular modular computing structures. We deal with the methodology of using a minimal redundant modular number system for high-speed and high-precision computation by means of modern universal multicore processors. Advantages of formal computing mode on the base of modular arithmetic are demonstrated by the example of implementation of digital signal processing procedures. The additive and additive multiplicative formal computing schemes with the obtained estimations of the cardinality of working ranges for the realization of calculations are presented in the article.
Twórcy
  • Jan Długosz University, Institute of Technics and Safety Systems, 42-200 Czestochowa, Al. Armii Krajowej 13/15, Poland
Bibliografia
  • [1] S.W. Smith, Digital Signal Processing: A Practical Guide for Engineers and Scientists. 1st Edition. Newnes, Burlington, MA, 2002.
  • [2] R.G. Lyons, D.L. Fugal, The Essential Guide to Digital Signal Processing. Prentice Hall Press, NJ, 2014.
  • [3] L. Deligiannidis, H. Arabnia, Emerging Trends in Image Processing. Prentice Hall Press, NJ, 2014.
  • [4] R. Szeliski, Computer Vision: Algorithms and Applications. Springer-Verlag, NJ, 2010, DOI 10.1007/978-1-84882-935-0.
  • [5] C.W. Ueberhuber, Numerical Computation 1: Methods, Software, and Analysis. Springer-Verlag, Berlin, 2013, DOI 10.1007/978-3-642-59118-1.
  • [6] C.W. Ueberhuber, Numerical Computation 2: Methods, Software, and Analysis. Springer-Verlag, Berlin, 2013.
  • [7] A.A. Kolyada, I.T. Pak, Modular Structures of Pipeline Digital Information Processing. University Press, Minsk, 1992 (in Russian).
  • [8] A.F. Chernyavsky, V.V. Danilevich, A.A. Kolyada, M.Y. Selyaninov, High-speed Methods and Systems of Digital Information Processing. Belarusian State University Press, Minsk, 1996 (in Russian).
  • [9] P.V. Ananda Mohan, Residue Number Systems: Algorithms and Architectures. Kluwer Academic Publishers, 2002.
  • [10] A. Omondi, B. Premkumar, Residue Number Systems: Theory and Implementation. Imperial College Press, London, 2007.
  • [11] M. Selyaninov, Modular technique of parallel information processing. Scientific Issues of Jan Długosz University of Czestochowa, Mathematics XIII (2008), 43–52.
  • [12] M. Selyaninov, Construction of modular number system with arbitrary finite ranges. Scientific Issues of Jan Długosz University of Czestochowa, Mathematics XIV (2009), 105–115.
  • [13] M. Selianinau, High-speed modular structures for parallel computing in the space of orthogonal projections. Scientific Issues, Jan Długosz University of Czestochowa, Ser. Technical and IT Education, V (2010), 87–96.
  • [14] M. Selianinau, Modular principles of high-speed adaptive filtration of discrete signals. Scientific Issues, Jan Długosz University of Czestochowa, Ser. Technical and IT Education, VI (2011), 75–84.
  • [15] M. Selyaninov, Application of modular computing technique for high-speed implementation of cyclic convolution. Scientific Issues of Jan Długosz University of Czestochowa, Mathematics XIX (2014), 217–226.
  • [16] M. Selyaninov, Modular number systems in a complex plane. Scientific Issues of Jan Długosz University of Czestochowa, Mathematics XV (2010), 131–138.
  • [17] M. Selyaninov, Arithmetic of quadratic minimal redundant modular number systems. Scientific Issues of Jan Długosz University of Czestochowa, Mathematics XVI (2011), 129–134.
  • [18] M. Selyaninov, Modular technique of high-speed parallel computing on the sets of polynomials. Scientific Issues of Jan Długosz University of Czestochowa, Mathematics XVII (2012), 69–76.
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Bibliografia
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