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Zbl 0892.65007
Xu, Guoliang; Li, Jiakai
Evaluation of elementary functions for variable precision. (English. Chinese original)
[J] Chin. J. Numer. Math. Appl. 17, No.1, 13-24 (1995); translation from J. Numer. Methods Comput. Appl. 15, No.3, 161-171 (1994). ISSN 0899-4358

Summary: Based on Padé approximants of the exponential function, an efficient algorithm for the calculation of exponential and trigonometric functions with variable precision is presented. The computational complexity of the algorithm is analysed in detail. Several methods for minimizing $W(k,j)$ -- the total amount of required operations in the algorithm -- are proposed. Furthermore, the asymptotic estimation of $W(k,j)$ is also given. In comparison with the Smith algorithm, the results of numerical experiments show that our algorithm is more efficient.

MSC 2000:: *65D20 Computation of special functions
65Y20 Complexity and performance of numerical algorithms
33B10 Elementary functions

Keywords: Padé approximants; exponential function; algorithm; trigonometric functions; variable precision; computational complexity; Smith algorithm; numerical experiments

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