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Efficient multiple-precision evaluation of elementary functions. (English) Zbl 0657.65032
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 $O\left({t}^{1/3}M\left(t\right)\right)$ time, where m(t) denots the time required to multiply two t-digits numbers. This improves the best methods currently in use run in $O\left({t}^{1/2}M\left(t\right)\right)$ time.
Reviewer: S.Hitotumatu
##### MSC:
 65D20 Computation of special functions, construction of tables 26A09 Elementary functions of one real variable 33B10 Exponential and trigonometric functions 68Q25 Analysis of algorithms and problem complexity