Long-float variant giving more precision to numerical computations.

Douglas Crosher wrote:
> Hello,
> 
> Reworking the changes to use the maxima 'flonum type appears to work on GCL, CMUCL,
> and CLISP.  The following changes are proposed as a first step:
> 
> 1. Replace all float constants with the general form, e.g. 1d0 -> 1e0, and increase
> the precision to at least quad float precision.  The *read-default-float-format*
> can then be modified to change all constants to an alternative format.
> 
> 2. Replace all references to the double-float type with the 'flonum type, allowing
> the format used for a 'flonum to be changed easily.

I would accept changes to use flonum as the floating-point type.

> 
> The handling of the Fortran code needs more thought, so would not be changed yet.
> Extending f2cl to allow translating the Fortran double precision type to a long-float
> or other type may be cleaner.

I modifying f2cl would be better.  I think it's a bad idea to 
hand-modify the generated code.  f2cl already supports a :float-format 
option, but I'm not sure that will work if it's changed from 
'double-float to, say, 'flonum.

> 
> An attempt has been made to use the CMUCL double-double-float type, and it does build
> but there are a few problems in CMUCL that need work, such as (rationalize 0.25w0)
> failing, and the lack of constants such as double-double-float-epsilon.  If anyone

Oops.  Rationalize is an oversight.  I'll fix that.  If you find other 
issues, please let me know.

The problem with double-double-float-epsilon is that it's kind of fuzzy. 
  Look at what happens with (+ 1w0 1w-100).  You get 1.<lots of 
zeroes>1w0.  This is an artifact of double-double representation.  A 
reasonable approximation would be (scale-float 1w0 -106), since there 
are 106 bits of accuracy in a double-double.

Ray