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Newsgroups: comp.lang.python
Date: Tue, 31 May 2011 20:30:30 -0700 (PDT)
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Subject: Re: float("nan") in set or as key
From: Carl Banks <pavlovevidence@gmail.com>
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Xref: x330-a1.tempe.blueboxinc.net comp.lang.python:6780

On Tuesday, May 31, 2011 8:05:43 PM UTC-7, Chris Angelico wrote:
> On Wed, Jun 1, 2011 at 12:59 PM, Carl Banks=20
>  wrote:
> > On Sunday, May 29, 2011 7:53:59 PM UTC-7, Chris Angelico wrote:
> >> Okay, here's a question. The Python 'float' value - is it meant to be
> >> "a Python representation of an IEEE double-precision floating point
> >> value", or "a Python representation of a real number"?
> >
> > The former. =A0Unlike the case with integers, there is no way that I kn=
ow of to represent an abstract real number on a digital computer.
>=20
> This seems peculiar. Normally Python seeks to define its data types in
> the abstract and then leave the concrete up to the various
> implementations - note, for instance, how Python 3 has dispensed with
> 'int' vs 'long' and just made a single 'int' type that can hold any
> integer. Does this mean that an implementation of Python on hardware
> that has some other type of floating point must simulate IEEE
> double-precision in all its nuances?

I think you misunderstood what I was saying.

It's not *possible* to represent a real number abstractly in any digital co=
mputer.  Python couldn't have an "abstract real number" type even it wanted=
 to.

(Math aside: Real numbers are not countable, meaning they cannot be put int=
o one-to-one correspondence with integers.  A digital computer can only rep=
resent countable things exactly, for obvious reasons; therefore, to model n=
on-countable things like real numbers, one must use a countable approximati=
on like floating-point.)

You might be able to get away with saying float() merely represents an "abs=
tract floating-point number with provisions for nan and inf", but pretty mu=
ch everyone uses IEEE format, so what's the point?  And no it doesn't mean =
Python has to support every nuance (and it doesn't).


Carl Banks