Lapack results with extended precision calculations.

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.



-- 
Michel Talon