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Theoretical and methodological bases of modular technology of parallel tabular computations using universal processors

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EN
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In this paper, we deal with the methodology for application of the theory and methods of the tabular technology of modular information processing on the basis of modern computing machinery. The use of the minimal redundant modular number system and the interval-modular form of representation of an integer number determined by its modular code creates the computer-arithmetical basis of a methodology under consideration. The main advantage of the offered methodology consists inincrease of the computation speed and accuracy at the organization of high-precision arithmetic processing of multidigit data by means of universal processors on the basis of minimal redundant modular encoding method.
Twórcy
  • Jan Długosz University, Institute of Technics and Safety Systems, 42-200 Czestochowa, Al. Armii Krajowej 13/15, Poland
Bibliografia
  • [1] U. Kulisch, Computer Arithmetic and Validity: Theory, Implementation, and Applications. De Gruyter Studies in Mathematics 33, Berlin, 2013.
  • [2] G.B. Arfken, H.J.Weber, F.E. Harris, Mathematical Methods for Physicists. A Comprehensive Guide. 7th edition. Academic Press, Boston, 2012.
  • [3] C.W. Ueberhuber, Numerical Computation 1: Methods, Software, and Analysis. Springer-Verlag, Berlin, 2013, DOI 10.1007/978-3-642-59118-1.
  • [4] C.W. Ueberhuber, Numerical Computation 2: Methods, Software, and Analysis. Springer-Verlag, Berlin, 2013.
  • [5] A.R. Krommer, C.W. Ueberhuber, Numerical Integration: on Advanced Computer Systems (Lecture Notes in Computer Science). Springer-Verlag, Berlin, 2008.
  • [6] S. Mittal, A Survey of Techniques for Architecting and Managing Asymmetric Multicore Processors. ACM Computing Surveys, 48:3 (2016), 45:1–45:38, DOI 10.1145/2856125.
  • [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] I.M. Vinogradov, Fundamentals of Number Theory. Nauka, Moscow, 1981 (in Russian).
  • [12] M.F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra. Addison- Wesley Publishing Co., Reading, Massachusetts, 1969.
  • [13] D.S. Dummit, R.M. Foote, Abstract algebra. 3rd edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004.
  • [14] A.A. Kolyada, M.Y. Selyaninov, On the formation of the integral characteristics of the codes of residue number systems with the symmetrical range. Cybernetics 4 (1986), 20–24 (in Russian).
  • [15] M. Selyaninov, Modular technique of parallel information processing. Scientific Issues of Jan Długosz University of Częstochowa, Mathematics XIII (2008), 43–52.
  • [16] M. Selyaninov, Construction of modular number system with arbitrary finite ranges. Scientific Issues of Jan Długosz University of Częstochowa, Mathematics XIV (2009), 105–115.
  • [17] M. Selianinau, High- speed modular structures for parallel computing in the space of orthogonal projections. Scientific Issues, Jan Długosz University of Częstochowa, Ser. Technical and IT Education, V (2010), 87–96.
  • [18] M. Selyaninov, Modular number systems in a complex plane. Scientific Issues of Jan Długosz University of Częstochowa, Mathematics XV (2010), 131–138.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9f16fd63-6407-45cb-80ff-9c4aa82aa275
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