Istituto di Informatica e Telematica     
Favati P., Lotti G., Menchi O., Romani F. Separable Asymptotic Cost of Evaluating Elementary Functions. Technical report, 1996.
The asymptotic computational cost of evaluating a real function $f(x)$ in a point $x$, in the bit model of computation, is analyzed, with $x$ varying in an interval containing also critical points for the function $f$. We find an upper bound to the cost as a function of two variables: the number $d$ of correct digits in the result and the point $x$. More precisely we study a class of algorithms for which it is possible to give upper bounds on the cost as functions of 'separated variables' $d$ and $x$, that is as products of two functions, each of one variable. We find conditions under which elementary functions can be computed through algorithms belonging to this class.
Subject G.1.0 General
65Y20 Complexity and performance of numerical algorithms

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