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Zbl 0993.65030
Loenko, M.Yu.
Evaluating elementary functions with guaranteed precision. (English. Russian original)
[J] Program. Comput. Softw. 27, No.2, 101-110 (2001); translation from Programmirovanie 2001, No.2, 68-80 (2001). ISSN 0361-7688; ISSN 1608-3261/e

The numerical algorithms to evaluate trigonometrical, exponential and logarithmic functions are adapted to the double precision calculation in IEEE-754 standard. The operation time for above evaluations makes about 50\% of that for the standard methods, but the number of precalculated constants is considerably increased (up to about 10000 constants for each function). Each algorithm starts from the evaluation in the so called ``good'' interval by means of the Taylor expansion with Peano remainder. For instance the $sin$ is first evaluated at the rational points $\frac{n}{512}\in[0,\frac{\pi}{2}]$ and next the calculation is extended outside the ``good'' interval with estimation of error.
[Jacek Gilewicz (Marseille)]

MSC 2000:: *65D20 Computation of special functions
68N20 Compilers and generators
26A09 Elementary functions of one real variable
33B10 Elementary functions

Keywords: evaluation of functions; elementary functions; guaranteed precision; trigonometrical, exponential and logarithmic functions; double precision calculation; algorithm

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