Lapack results with extended precision calculations.

On Thu, Nov 17, 2011 at 1:49 AM, Michel Talon <talon at lpthe.jussieu.fr>wrote:

> Douglas Crosher wrote:
> > With patches to the Fortran libraries it is possible to build Maxima
> using
> extended precision float types (of the CL implementation)
> > for the 'flonum type, and below are some timing and accuracy results for
> a
> Lapack test across a range of CL implementations and
> > choices for the Maxima 'flonum type.  The Scieneer CL 80 long-floats
> give a
> little extra precision without a significant performance
> > loss.  The CMU CL 128 bit double-double floats roughly double the
> precision
> but slows the test by roughly 50 times.  CLISP has
> > arbitrary precision long-floats and an example result at 1024 bits is
> given
> but slows the test over 500 times - some people have
> > requested this precision and this is one option. CLISP is a lot faster at
> lower precisions and to be fair a result is also given for
> > 128 bit long-floats and it is only about three times slower than CMU CL's
> double-double float test but more accurate.  So with this
> > approach there are a range of precisions and performances available if
> you
> are prepared to change the CL implementations to suit.
> >
>
>
> This is very interesting, i think it solves the problem i mentioned
> (diagonalizing matrices of order 1000x1000 which are very far from random,
> so
> that the eigenvalues are very sensitive to calculational errors) using
> clisp and a lot of time (which is no problem). Getting many digits correct
> on the eigenvalues is not important, but having at least 2 or 3 digits
> correct
> at the end of the computation is not obvious at all.
>
>
This is really interesting.  It would be interesting to see how lapack
would work with bigfloats, especially compared to clisp's builtin
long-floats.  I suspect it would be quite a bit slower, but could be used
by other lisps.

Ray