Implementation of the Incomplete Beta function

Dieter Kaiser wrote:
>
> The implementation is not as complete as for other functions, but it might be
> good to have an example for the package bigfloat. I will add further
> functionality to beta_incomplete.
>   
Yes, I think an example of how to use the bigfloat package is a good
idea.  Thanks for doing this.

An alternative way would be to put an (in-package "BIGFLOAT") before the
implementation so you don't have to type the package qualifier
everywhere.  Just remember to put a (in-package "MAXIMA") afterwords!
> A Maxima rational as the first argument:
>
> (%i4) beta_incomplete(1/2,2.8,0.73);
> Maxima encountered a Lisp error:
>
> Error in MACSYMA-TOP-LEVEL [or a callee]: No matching method for the
> generic-function #<compiled-closure BIGFLOAT::TWO-ARG-*>,
> when called with arguments (NIL 1.6764907877644366).
>   
This is tricky.  It fails because the beta_incomplete calls ($gamma a),
a = 1/2.  It return sqrt(%pi) and wants bigfloat:to to convert it.  I
think that's outside the scope of bigfloat.  The code needs to convert
that to either a float or a bfloat.
>
> The symbol %i as argument:
>
> (%i10) beta_incomplete(0.5,%i,1.5);
> BIGFLOAT:  Unable to convert %i to a CL or BIGFLOAT number
>  -- an error.  To debug this try debugmode(true);
>   
This is a bug in bigfloat:to.  It needs to recognize $%i.  I'll fix
this.  But I don't think bigfloat:to can handle %pi, %e or %gamma.  The
caller needs to convert those to a float or bfloat before calling
bigfloat routines.
> Remark: It is necessary to support rationals also in expressions like
> 1/2+0.5*%i.
>   
Yes, this should work.  I'll fix it.
> I would be posssible to do some workarounds in the code of beta_incomplete. But
> I think it is better to have the package bigfloat as complete as possible.
>   
I agree.  The intent is that if you have some code that works for
double-floats, then you should be able to use that code unchanged
(almost) in the bigfloat package.   If the code uses declarations or
double-float constants, you'll have to change  that, of course.

Ray