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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(t 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 1/2 M(t)) time.
Reviewer: S.Hitotumatu
MSC:
65D20Computation of special functions, construction of tables
26A09Elementary functions of one real variable
33B10Exponential and trigonometric functions
68Q25Analysis of algorithms and problem complexity
Software:
Algorithm 524