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Zbl 0607.65004
Hull, T.E.; Abrham, A.
Variable precision exponential function. (English)
[J] ACM Trans. Math. Softw. 12, 79-91 (1986). ISSN 0098-3500

The exponential function presented here returns a result which differs from $e\sp x$ by less than one unit in the last place, for any representable value of x which is not too close to values for which $e\sp x$ would overflow or underflow. (For values of x which are not within this range, an error condition is raised.) It is a "variable precision" function in that it returs a p-digit approximation for a p-digit argument, for any $p>0$ (p-digit means p-decimal-digit). The program and analysis are valid for all $p>0$, but current implementations place a restriction on p. The program is presented in a Pascal-like programming language called Numerical Turing which has special facilities for scientific computing, including precision control, directed roundings, and built-in functions for getting and setting exponents.

MSC 2000:: *65D20 Computation of special functions
33B10 Elementary functions

Keywords: correctness proof; error analysis; numerical algorithms; exponential function; variable precision; Pascal-like programming language; Numerical Turing; precision control; directed roundings

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