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Algorithm for Calculating Correctly Rounded Exponential Function in Double Precision Using Double-Extended Arithmetic

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Abstract

Functions that calculate correctly rounded exponents provide the best approximation and ensure cross-platform portability. This paper presents an algorithm for calculating the correctly rounded value of the exponential function when its argument and value are double-precision numbers and the calculations use extended double-precision arithmetic. The formal description of the algorithm is provided. The proposed algorithm is implemented as a C function. The results of its testing, including the measurement of its time characteristics and comparison with other algorithms, are presented.

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REFERENCES

  1. IEEE Std. 754-2008, IEEE Standard for Floating-Point Arithmetic, 2018.

  2. Lefèvre, V. and Muller, J.-M., Worst cases for correct rounding of the elementary functions in double precision, Proc. 15th IEEE Symp. Computer Arithmetic, 2001, p. 111–118.

  3. Lefèvre, V., Hardest-to-round cases: Part 2, 2013. http://tamadiwiki.enslyon.fr/tamadiwiki/images/c/c1/Lefevre2013.pdf.

  4. Godunov, A., Algorithms for calculating correctly rounded exponential function in double-precision arithmetic, IEEE Trans. Comput., 2020, vol. 69, no. 5, pp. 1–12. https://doi.org/10.1109/TC.2020.2972901

    Article  MathSciNet  MATH  Google Scholar 

  5. Daramy-Loirat, C., Defour, D., de Dinechin, F., Gallet, M., Gast, N., Lauter, C.Q., and Muller, J.-M., CR-LIBM: A library of correctly rounded elementary functions in double-precision, LIP, Research report, 2006. https://hal-enslyon.archives-ouvertes.fr/ensl-01529804.

  6. Chevillard, S., Joldeş, M., and Lauter, C., Sollya: An environment for the development of numerical codes, Math. Software, 2010, pp. 28–31.

    MATH  Google Scholar 

  7. Muller, J.-M., Elementary Functions: Algorithms and Implementation, Birkhauser, 2005.

    Google Scholar 

  8. Lauter, C., A correctly rounded implementation of the exponential function on the Intel Itanium architecture, INRIA, Research report, 2003. https://hal.inria.fr/inria-00071560/document.

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Funding

This work was carried out in the framework of the state task “Investigation and implementation of a software platform for advanced multicore processors” (FNEF-2022-002).

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Authors and Affiliations

  1. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Nakhimovskii pr. 36/1, 117218, Moscow, Russia

    A. N. Godunov

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  1. A. N. Godunov
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Correspondence to A. N. Godunov.

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Translated by Yu. Kornienko

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Godunov, A.N. Algorithm for Calculating Correctly Rounded Exponential Function in Double Precision Using Double-Extended Arithmetic. Program Comput Soft 48, 369–375 (2022). https://doi.org/10.1134/S0361768822060032

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  • DOI: https://doi.org/10.1134/S0361768822060032

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