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Evaluation of elementary functions for variable precision. (English) Zbl 0892.65007
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:
65D20Computation of special functions, construction of tables
65Y20Complexity and performance of numerical algorithms
33B10Exponential and trigonometric functions