Bug in libm or libstdc++.

[Joern Rennecke]

> I may be mathematically inclined but I have none of the
> numerical-computation background necessary to know how to implement these
> things in an optimized way. Best I could probably do is a slowly converging
> Taylor series for these things. You ened a volunteer with a bit more
> knowledge in techniques of rapid numerical computation of trig functions.


When you want to use a Polynom approximation, you should rather use a
Tschebyscheff polynom.  Look it up in a mathematical enceclopedia.
If you just want to get something working, you can skip the proofs and go
straight for the recipes ;-)

I happen to have written sqrt functions when I worked on an XFmode /
TFmode fp-bit.c .  ( The project got stuck for lack of priority. )
I'll send it to you in private email.