Long-float variant giving more precision to numerical computations.

R Fateman wrote:
> 
> There are software versions of quad  (that is, 4 doubles) that are 
> implemented in pretty much standard CL -- in CMU-CL, this is done by 
> doubling the (already built-in) double-double.  In other lisps (I tried 
> Allegro), it can be done by mimicking the quad arithmetic available for 
> C,  or just calling the C library.

The implementation is at http://common-lisp.net/project/oct.
> 
> Deciding how to integrate this into Maxima has been a puzzle. Ray Toy 
> and I were messing with this recently, but I think we both got tired of 
> it. One point is that we have versions of sin/cos/ etc  for quad. As 

I haven't forgotten about it but I've been distracted a bit. :-(
> 
> Integrating all this with the fortran code would not be automatic, for 
> sure.  But  I think Ray has made progress on that, too.
> After all, once you have done fortran --> lisp, why not do  double 
> -->quad  too.

I did a very simple proof of concept.  I took some of the BLAS routines 
that were converted to Lisp via f2cl.  Then I ran a really hacky program 
to read in the Lisp code and convert all references of double-float to 
qd-real.  A quick test showed that I did get quad-double results. 
Unfortunately, I also got distracted so I never went any farther.  I 
would like to at least try a Gaussian elimination or eigenvalue routine 
to see if that will work.

With some more work. I think it would be possible to provide a bfloat 
implementation of the LAPACK routines that maxima already has.  I think 
all that's need would be some CLOS wrappers to call bfloat routines as 
needed.  That would be pretty cool.

Ray