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SUMMARY:Nicolas Brisebarre (ENS Lyon\, France)
DTSTART:20210119T150000Z
DTEND:20210119T160000Z
DTSTAMP:20260423T024744Z
UID:CRM-CAMP/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/26/
 ">Correct rounding for transcendental functions</a>\nby Nicolas Brisebarre
  (ENS Lyon\, France) as part of CRM CAMP (Computer-Assisted Mathematical P
 roofs) in Nonlinear Analysis\n\n\nAbstract\nOn a computer\, real numbers a
 re usually represented by a finite set of numbers called floating-point nu
 mbers. When one performs an operation on these numbers\, such as an evalua
 tion by a function\, one returns a floating-point number\, hopefully close
  to the mathematical result of the operation. Ideally\, the returned resul
 t should be the exact rounding of this mathematical value. If we’re only
  allowed a unique and fast evaluation (a constraint often met in practice)
 \, one knows how to guarantee such a quality of results for arithmetical o
 perations like +\,−\,x\,/ and square root but\, as of today\, it is stil
 l an issue when it comes to evaluate an elementary function such as cos\, 
 exp\, cube root for instance. This problem\, called Table Maker’s Dilemm
 a\, is actually a diophantine approximation problem. It was tackled\, over
  the last fifteen years\, by V. Lefèvre\, J.M. Muller\, D. Stehlé\, A. T
 isserand and P. Zimmermann (LIP\, ÉNS Lyon and LORIA\, Nancy)\, using too
 ls from algorithmic number theory. Their work made it possible to partiall
 y solve this question but it remains an open problem. In this talk\, I wil
 l present a joint work with Guillaume Hanrot (ÉNS Lyon\, LIP\, AriC) that
  improve on a part of the existing results.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/26/
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