Programming and Computer Software

, Volume 27, Issue 2, pp 101–110 | Cite as

Evaluating Elementary Functions with Guaranteed Precision

  • M. Yu. Loenko


Because of changes in the computer markets, the problem of efficient evaluation of elementary functions (which seemed to be already solved) becomes important again. In this paper, after a brief review of current approaches to this problem, algorithms for finding guaranteed bounds for values of elementary functions are suggested. The evaluation time is reduced through increasing the amount of memory used.


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  1. 1.
    Alefeld, G. and Herzberger, J., Introduction to Interval Computations, New York: Academic, 1983. Translated under the title Vvedenie v interval'nye vychisleniya, Moscow: Mir, 1987.Google Scholar
  2. 2.
    Dobronets, B.S. and Shaidurov, V.V., Dvustoronnie chislennye metody (Duplex Numerical Methods), Novosibirsk: Nauka, 1990.Google Scholar
  3. 3.
    Kalmykov, S.A., Shokin, Yu.I., and Yuldashev, Z.Kh., Metody interval'nogo analiza (Methods for Interval Analysis), Novosibirsk: Nauka, 1986.Google Scholar
  4. 4.
    Korn, G. and Korn, T., Mathematical Handbook for Scientists and Engineers, New York: McGraw-Hill, 1971. Translated under the title Spravochnik po matematike, Moscow: Nauka, 1974.Google Scholar
  5. 5.
    Remez, U.Ya., Osnovy chislennykh metodov chebyshevskogo priblizheniya (Fundamentals of Numerical Methods for Chebyshev Approximation), Kiev: Naukova Dumka, 1969.Google Scholar
  6. 6.
    Shokin, Yu.I., Interval'nyi analiz (Interval Analysis), Novosibirsk: Nauka, 1981.Google Scholar
  7. 7.
    Benhamou, F.,Interval Constraint Logic Programming, in Constraint Programming: Basics and Trends, Podelski, A., Ed., LNCS, 1995, vol. 910, pp. 1–21.Google Scholar
  8. 8.
    elefunt.bib, BibTeX Bibliography, Scholar
  9. 9.
    Glibc, Library for Use with GNU/HURD and GNU/LINUX, http://www.gnu/org/gnulist/production/glibc.html.Google Scholar
  10. 10.
    Goto, E. and Wong, W.F., Fast Evaluation of the Elementary Function in Double Precision, Proc. 27th Hawaii Int. Conf. on System Sci., 1994, vol. 1, pp. 349–358.Google Scholar
  11. 11.
    Hansen, E., Global Optimization Using Interval Analysis, New York: Marcel Dekker, 1992.Google Scholar
  12. 12.
    IEEE Standard for Binary Floating-Point Arithmetic, Techn. Report ANSI/IEEE Std 754-1985, New York: IEEE, 1985.Google Scholar
  13. 13.
    Mathematical Library fdlibm v. 5.1, Scholar
  14. 14.
    Muller, J.-M. and Tisserand, A., Towards Exact Rounding of the Elementary Functions, Proc. SCAN-95 Symp., Wuppertal, 1995.Google Scholar
  15. 15.
    Numerical Computation Guide, Mountain View, 1995.Google Scholar
  16. 16.
    Older, W. and Vellino, A., Constraint Arithmetic on Real Intervals, in Constraint Logic Programming: Selected Research, Benhamou, F. and Colmerauer, A., Eds., MIT Press, 1993, pp. 175–195.Google Scholar
  17. 17.
    XSC Software, Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • M. Yu. Loenko
    • 1
  1. 1.Ershov Institute of Information Systems, Siberian DivisionRussian Academy of SciencesNovosibirskRussia

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