The computational cost, in the bit model of computation, of the evaluation of a real function f(x) in a point x is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on x also when x approaches a critical point for the function f. We investigate yhe hypotheses under which it is possible to give upper bounds on the cost as functions of "separated variables" d and x, that is as products of the two functions, each of one variable. We examine in particular the case of elementary functions.
Separable Asymptotic Cost of Evaluating Elementary Functions
MENCHI, ORNELLA;ROMANI, FRANCESCO
2000-01-01
Abstract
The computational cost, in the bit model of computation, of the evaluation of a real function f(x) in a point x is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on x also when x approaches a critical point for the function f. We investigate yhe hypotheses under which it is possible to give upper bounds on the cost as functions of "separated variables" d and x, that is as products of the two functions, each of one variable. We examine in particular the case of elementary functions.File in questo prodotto:
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