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

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.
Favati, P; Lotti, G; Menchi, Ornella; Romani, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/190721
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