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Symbolic Calculation Behind Floating-Point Arithmetic: Didactic Examples and Experiment Using CAS

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Computational Science – ICCS 2023 (ICCS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 10477))

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Abstract

Floating-point arithmetic (FP) is taught at universities in the framework of different academic courses, for example: Numerical Analysis, Computer Architecture or Operational Systems. In this paper we present some simple “pathological” and “non-pathological” examples for comparison with symbolic calculations which lie behind calculations in FP with double precision. The CAS programs: Mathematica and wxMaxima are used for calculation. We explain, by making calculations directly from the definition of double precision, why in the presented examples such final results were obtained. We present a didactic experiment for students of the Informatics Faculty of Warsaw University of Life Sciences within the course of Numerical Methods.

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References

  1. The GNU MPFR (multiple-precision floating-point computations) Library. https://www.mpfr.org

  2. IEEE 754 Floating Point Standard. https://en.wikipedia.org/wiki/IEEE_754

  3. Arnold, J.: An Introduction to Floating-Point Arithmetic and Computation, CERN OpenLab, 9 May 2017. https://indico.cern.ch/event/626147/attachments/1456066/2247140/FloatingPoint.Handout.pdf

  4. Goldberg, D.: What every computer scientist should know about floating point arithmetic. ACM Comput. Surv. 23, 5–48 (1991)

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  5. Muller, J.-M., et al.: Handbook of Floating-Point Arithmetic. Birkhäuser, Boston (2010)

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Warsaw University of Life Sciences (SGGW), ul. Nowoursynowska 159, 02-776, Warsaw, Poland

    Włodzimierz Wojas & Jan Krupa

Authors
  1. Włodzimierz Wojas
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  2. Jan Krupa
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Corresponding author

Correspondence to Włodzimierz Wojas .

Editor information

Editors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Jiří Mikyška

  2. University of Amsterdam, Amsterdam, The Netherlands

    Clélia de Mulatier

  3. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  4. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  5. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  6. University of Amsterdam, Amsterdam, The Netherlands

    Peter M.A. Sloot

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Wojas, W., Krupa, J. (2023). Symbolic Calculation Behind Floating-Point Arithmetic: Didactic Examples and Experiment Using CAS. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 10477. Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_56

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  • DOI: https://doi.org/10.1007/978-3-031-36030-5_56

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-36029-9

  • Online ISBN: 978-3-031-36030-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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