Abstract
The exponential function presented here returns a result which differs from e 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 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 returns 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.
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