Towards exact rounding of the elementary functions

[David G. Hough at validgh]

I'd like to draw your attention to the web page

http://www.ens-lyon.fr/LIP/lip/publis/research_reports.us.html

where you can find reports like

Towards exact rounding of the elementary functions
Jean-Michel Muller ,  Arnaud Tisserand

Always getting exactly rounded results when implementing the  elementary functions in floating-point arithmetic has been an  open problem for many years. After a brief recall of previous  results in that domain, we show that that problem can be  solved,
and we discuss the time required
to always provide  exactly rounded results.


and other pertinent reports by Muller and his colleagues.
I am indebted to Stuart McDonald for pointing it out to me.