# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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 $W\left(k,j\right)$ – the total amount of required operations in the algorithm – are proposed. Furthermore, the asymptotic estimation of $W\left(k,j\right)$ is also given. In comparison with the Smith algorithm, the results of numerical experiments show that our algorithm is more efficient.
##### MSC:
 65D20 Computation of special functions, construction of tables 65Y20 Complexity and performance of numerical algorithms 33B10 Exponential and trigonometric functions