Long-float variant giving more precision to numerical computations.

Adding extra precision algorithms (good for 80 bits) when the hardware 
only does 64 bits might slow down the programs for those less-precise 
systems.  (For example, 80-bit sin/cos/log/exp/bessel/...).  So maybe 
the libraries should be kept separate.

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.

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 
well as some more substantial programs like root-finding, various 
quadrature programs, and FFT.
The code is open, and some papers describing it are online as well.
I think http://www.cs.berkeley.edu/~fateman/generic     see files quad*

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.

RJF


Douglas Crosher wrote:
> A variant of Maxima 5.14.0cvs is available that replaces the use of the Common Lisp
> 'double-float type with the 'long-float type for Maxima floating point numbers.
> This change gives more precision and range to some numerical calculations which
> do not currently support the Maxima bfloat type, such as the Fortran based code.
>
> The changes have been tested on the Scieneer CL and CLISP.  The Scieneer CL x86
> and AMD64 ports support extended precision 80-bit floating point numbers for the
> 'long-float type, and CLISP supports a much more precise 'long-float type.  The
> change should be neutral on CL implementations for with the 'long-float type is
> equivalent for the 'double-float type.  I understand that CMUCL now has a
> double-double-float type and with some more work it may be possible to support this
> too.
>
> I needed more accuracy from numerical calculations and this was the quickest path
> and it extends the number of computations that Maxima can perform to high precision.
> However there are still a good number numerical approximations in Maxima that
> have not been improved and still give only 'double-float level accuracy.
>
> It is not clear to me that this is a change that should be integrated into the
> main source now, but the modified source code can be downloaded from:
> http://www.scieneer.com/s/product.html?code=58636
>
> Regards
> Douglas Crosher
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