Computing exponentials and Trig functions

[Jim White]

> Still not as satisfying as doing it oneself.

Building one's own wheel from first principles can
certainly be educational, so I can relate to that. 

It can also be time-consuming, I should add!
 
The good folk at MPFR describe their algorithms - you
will have discovered this if you have visited their
home page.  Their trig functions are the fastest
"off-the-shelf" ones available, as you'll see from
their timings data.

The next fastest (for std trig functions) is CLN, and 
their approach is certainly worth studying.  The
primary source document there is a 1997/98 paper by
Bruno Haible and Thomas Papanikolau (Springer, LNCS
1423).  

http://www.springerlink.com/content/rw37g65qmb44vfl5/


There are also some useful tips, as I recall, in a
general overview of Elementary Function Algorithms
that I originally found at yacas.sourceforge.net, and
I think is till there.


Cheers

Jim White
MSI, ANU