Re: Math Functions

From: Eric Ford (eford_at_[hidden])
Date: 2001-09-05 16:59:17

> PS Do you know a source of high precision values of the incomplete
beta
> (at least 64 bit double) to check accuracy of an improved algorithm
by
> Doman.

The continued fraction expansion that I used provides arbitrary
accuracy (you would need to change a the constant on line 151 of
beta.h that is ineligantly in the code), but that's for the
unregularized incomplete beta function.  

I implemented the regularized incomplete beta function in terms of the
standard exp and log as well as my gamma function (which in tern uses
log, exp, sin, Pi, and sqrt(2*Pi) ).  Pi and sqrt(2*pi) can be easily
improved to whatever you need.  I'd guess log, exp, and sin are
currently the limiting factor in accuracey for my regularized
incomplete beta function.  There are probably more accurate versions
readily avaliable somewhere.  Even as it is, the discussion at
http://winnie.fit.edu/~gabdo/gamma.txt suggests the mean fractional
error is about 10^-13 and the worst case 10^-14.  

In any case, I agree with Kevin that initially it's more important to
setup a good interface, even if the algorithms can't deliver arbitrary
accuracey at first.  A good interface will practically invite people
to contribute algorithms to fill them in.

E