On Numbers

[Bengt Richter]

On Sat, 14 Jan 2006 18:18:12 -0500, Mike Meyer <mwm at mired.org> wrote:

>In the discussion of equality, the issue that decimal('3.0') == 3.0 is
>False came up as a reason for changing the behavior of ==. The problem
>with this is that the proposed change doesn't really fix anything, it
>just gives different wrong behavior. The correct fix would seem to be
>fixing python's handling of numbers.
>
>It's not clear from the PEP why test for equality always fails. While
>the PEP says that interactions with floats are disallowed as "to
>tricky", comparisons seem to be an exception. In particular, equality
>comparisons seem to always return false, whereas checking for
>magnitude seems to work.
>
>What appears to be missing in Python is a coherent model for all
>numberic types. Other languages have this, so there's no obvious
>reason that Python can't. Or maybe Python does, and I've overlooked
>it. In that case, pointers to documentation would be appreciated.
>If it doesn't exist, then I think this is something that should be
>addressed for Py3K.
>
>I'd like to work on that. The idea would be that all the numeric types
>are representations of reals with different properties that make them
>appropriate for different uses. The goal would be a model for a
>numeric type that captures those properties in a way that allows them
>to be combined to give sane behavior without being "to tricky".
>
>To get started on that, I want to consider how other languages with
>rich numeric type systems model them. I'm going to look at a couple of
>languages in the LISP family. I'd like to solicit the community for
>the names of languages (and pointers to references, if possible!) with
>a coherent view of a rich set of numeric types.
>
I suppose you have already found scheme's rsr5 spec, e.g.,
    http://www.schemers.org/Documents/Standards/R5RS/

while thinking about numbers, the issue of equivalence that got us here
is also explored in scheme
    http://www.schemers.org/Documents/Standards/R5RS/HTML/r5rs-Z-H-9.html#%_sec_6.1
and the section that follows in  on numbers
    http://www.schemers.org/Documents/Standards/R5RS/HTML/r5rs-Z-H-9.html#%_sec_6.2

for common lisP
    http://www.lispworks.com/documentation/HyperSpec/Front/index.htm
you can also chase lots of interesting links (some dead though) from
    http://www.cetus-links.org/oo_clos.html
cltl2 is at
    http://www.cs.cmu.edu/Groups/AI/html/cltl/cltl2.html

Now try to get some work done ;-)

BTW, IIRC Ada's numbers include some interesting provisions for representing numbers
in fixed point with specified fractional accuracy
I google and found
    http://www.adaic.org/standards/95lrm/html/RM-0-1.html
browsing a bit, scalar types are at
    http://www.adaic.org/standards/95lrm/html/RM-3-5.html
integers include unsigned by way of genera modular definition
    http://www.adaic.org/standards/95lrm/html/RM-3-5-4.html
and here is the fixed point
    http://www.adaic.org/standards/95lrm/html/RM-3-5-9.html
Whoo, I haven't been into that stuff almost since Ada was "green" ;-)
Makes me wonder if generators could usefully have rendezvous('?, es?) ;-)

Regards,
Bengt Richter