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Zbl 0657.65032
Smith, David M.
Efficient multiple-precision evaluation of elementary functions. (English)
[J] Math. Comput. 52, No.185, 131-134 (1989). ISSN 0025-5718; ISSN 1088-6842/e

The author proposes an efficient multiple-precision evaluation method of elementary functions. His idea is to rearrange the Taylor expansion of exp x into j concurrent sums with optimal value of j. Logarithm is computed using Newton iteration and the exponential function, and trigonometric functions are computed using recursively the formulas for triple arguments. All his methods require $O(t\sp{1/3}M(t))$ time, where m(t) denots the time required to multiply two t-digits numbers. This improves the best methods currently in use run in $O(t\sp{1/2}M(t))$ time.
[S.Hitotumatu]

MSC 2000:: *65D20 Computation of special functions
26A09 Elementary functions of one real variable
33B10 Elementary functions
68Q25 Analysis of algorithms and problem complexity

Keywords: multiple-precision; elementary functions; Taylor expansion; Logarithm; Newton iteration; exponential function; trigonometric functions

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