Worst cases of a periodic function for large arguments

Guillaume Hanrot, Vincent Lefèvre, Damien Stehlé, Paul Zimmermann

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

8 Citations (Scopus)


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 a heuristic complexity of O(2°.⁶⁷⁶p) for a precision of p 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.
Original languageEnglish
Title of host publicationProceedings
Subtitle of host publication18th IEEE Symposium on Computer Arithmetic : ARITH 18, Montpellier, France, June 25-27, 2007
EditorsPeter Kornerup, Jean-Michel Muller
Place of PublicationLos Alamitos, Calif.
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages8
ISBN (Print)0769528546
Publication statusPublished - 2007
EventSymposium on Computer Arithmetic (18th : 2007) - Montpellier, France
Duration: 25 Jun 200727 Jun 2007


ConferenceSymposium on Computer Arithmetic (18th : 2007)
CityMontpellier, France


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