DOI: 10.17587/prin.14.531-549

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

A. N. Godunov, PhD, Head of Department, nkag@niisi.ras.ru, Federal State Institution Scientific Research Institute for System Analysis of the Russian Academy of Sciences (SRISA), Moscow, 117218, Russian Federation

Corresponding author: Aleksandr N. Godunov, PhD, Head of Department, Federal State Institution "Scientific Research Institute for System Analysis of the Russian Academy of Sciences" (SRISA), Moscow, 117218, Russian Federation, E-mail: nkag@niisi.ras.ru

The article presents an effective algorithm for calculating the correctly rounded exponent for any of the rounding modes specified by the IEEE 754 standard. The argument and the function value are double-precision numbers, but the algorithm itself uses extended double-precision arithmetic for calculations. At the argument reduction stage, we approximate the argument with numbers whose exponent value has a short mantissa, which makes calculations faster. The article gives a formal description of the algorithm and a proof of its correctness. The function has the shortest maximum execution time among the considered functions calculating correctly rounded exponent. The execution time slightly depends on the value of the argument, which may be important for critical applications.

Keywords: algorithm, exponent, correct rounding, double-precision

pp. 531–549

For citation:
Godunov A. N. Calculating Correctly Rounded Exponential Function in Double-Precision Using Extended Double-Precision Arithmetic, Programmnaya Ingeneria, 2023, vol. 14, no. 11, pp. 531—549. DOI: 10.17587/prin.14.531-549.

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