Re: +-Inf and NaN

The unums (posit..) number formats are described in the wikipedia
article "unum (number format).  John Gustafson has been working on
this since before the IEEE committee on floating point convened. He
was a contributor to that standard.

While it is interesting, there are some significant downsides which are
discussed in several of the references to the Wikipedia entry, typically
by W. Kahan. for instance
 https://people.eecs.berkeley.edu/~wkahan/UnumSORN.pdf
or see, for a more detailed analysis
https://people.eecs.berkeley.edu/~demmel/ma221_Fall20/Dinechin_etal_2019.pdf

For the particular situation of computer algebra systems, it may be more
useful to support arbitrary (i.e. growing) precision arithmetic, interval
arithmetic  (for which there is a new IEEE standard), and (for compatibility
with the huge and growing software collection) IEEE 754 floats.
If there is some interest in the Maxima community for working on "new"
arithmetic, I suggest that finishing the implementation of intervals would
be of some benefit, rather than posits (which sometimes are intervals).

Integrating mpfr (external fast bigfloat library) would be nice but runs
into
the political problem, in the Maxima community, that different Lisps need
different interface code, so requires considerable effort.

What makes CAS different?
1. symbols for Infinity etc are available.
2. bigfloats are already part of the system.
3. exact rational numbers of arbitrary precision are available.
4. people may not agree on the model of extended real numbers,
either affine or projective.
5. (generally) there are considerable resources of memory and CPU.

There is a software implementation of unums in Lisp  (SBCL) here.
https://github.com/amb007/cl-unum   so it is possible to experiment with
interfacing it to Maxima.
RJF


On Sat, Feb 24, 2024 at 7:08 PM James Cloos <[email protected]> wrote:

> >>>>> "RT" == Raymond Toy <[email protected]> writes:
>
> RT> Is there any existing lisp that doesn't support IEEE single and double
> RT> precision floats?
>
> I don't know of any cl implementations, but not all interesting hardware
> has hw fp.  And while packages like maxima may not get run on such
> systems, lisp in general still makes sense.
>
> And as fpga and the like grow larger, lisps -- including common -- would
> make great programming environments for them.
>
> In either case, if the fp has to be done in software, I strongly suspect
> posit or gmp-style will be better than 754.
>
> -JimC
> --
> James Cloos <[email protected]>
>             OpenPGP: https://jhcloos.com/0x997A9F17ED7DAEA6.asc
>
>
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