progress in Table Maker's Dilemma worst cases

[David G Hough at validgh]

Reported by J.-M. Muller:

> Dear colleagues,
> 
> Please feel free to publicize this announce, that deals with our work on
> the Table Maker's Dilemma.
> 
> This is to inform you that we have updated our public web page that
> gives the worst cases for the Table Maker's Dilemma in double precision
> arithmetic. The URL is
> 
> http://www.ens-lyon.fr/~jmmuller/TMD.html
> 
> and there is some explanation at the URL
> 
> http://www.ens-lyon.fr/~jmmuller/Intro-to-TMD.htm
> 
> Here is the list of the functions and domains for which you will find
> worst cases in our public web page:
> 
> - exponential  (base e) function, for input numbers between -16 and +32
> - natural (base e) logarithm, for input numbers between 1 and e^16 =
> 8.8861105... 10^6
> - sine of  numbers between 1/32 and 2
> - cosine of numbers between 1/32 and 12867/8192 = 1.5706787...
> (slightly less than pi/2)
> - arc sine of numbers between sin(1/32) = 0.0312449... and 1
> - arc cosine of numbers between cos(12867/8192) = 1.176 .10^(-4) and
> cos(1/32) = .99951...
> - 2^x, for input numbers between 1/2 and 1
> 
> Regards,
> 
> Jean-Michel Muller
> 
> PS. Our methods will be described in Vincent Lefevre's PhD manuscript.
> The defense is scheduled for january 10.
> --
> Jean-Michel Muller, CNRS-LIP, projet CNRS/INRIA/ENSL ARENAIRE
> Ecole Normale Sup. de Lyon, 46 Allee d'Italie, 69364 Lyon Cedex 07
> FRANCE
> Tel. (+33) 4 72728229 Secr. (+33) 4 72728037  Fax. (+33) 4 72728080
> Email: Jean-Michel.Mulleraens-lyon.fr, j.mulleracomputer.org
> http://www.ens-lyon.fr/~jmmuller