Worst Cases of a Periodic Function for Large Arguments (original) (raw)

Résumé

One considers the problem of finding hard to round cases of a periodic function for large floating-point inputs, more precisely when the function cannot be efficiently approximated by a polynomial. This is one of the last few issues that prevents from guaranteeing an efficient computation of correctly rounded transcendentals for the whole IEEE-754 double precision format. The first non-naive algorithm for that problem is presented, with an heuristic complexity of O(20.676p)O(2^{0.676 p})O(20.676p) for a precision of ppp bits. The efficiency of the algorithm is shown on the largest IEEE-754 double precision binade for the sine function, and some corresponding bad cases are given. We can hope that all the worst cases of the trigonometric functions in their whole domain will be found within a few years, a task that was considered out of reach until now.

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Soumis le : lundi 29 janvier 2007-14:56:55

Dernière modification le : mercredi 18 mars 2026-11:52:02

Archivage à long terme le : mardi 21 septembre 2010-12:28:06

Dates et versions

inria-00126474 , version 1 (25-01-2007)

inria-00126474 , version 2 (29-01-2007)

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Guillaume Hanrot, Vincent Lefèvre, Damien Stehlé, Paul Zimmermann. Worst Cases of a Periodic Function for Large Arguments. 18th IEEE Symposium in Computer Arithmetic, Jun 2007, Montpellier, France. pp.133-140, ⟨10.1109/ARITH.2007.37⟩. ⟨inria-00126474v2⟩

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