[Python-Dev] Fraction arithmetic (Was: Decimal ... float comparisons in py3k)

[Guido van Rossum]

On Sat, Mar 20, 2010 at 4:58 AM, Mark Dickinson <dickinsm at gmail.com> wrote:
> On Sat, Mar 20, 2010 at 11:41 AM, Paul Moore <p.f.moore at gmail.com> wrote:
>> On 20 March 2010 04:20, Nick Coghlan <ncoghlan at gmail.com> wrote:
>>> In the case of floats and Decimals, there's no ambiguity here that
>>> creates any temptation to guess - to determine a true/false result for a
>>> comparison, floats can be converted explicitly to Decimals without any
>>> loss of accuracy. For Fractions, the precedent has already been set by
>>> allowing implicit (potentially lossy) conversion to binary floats - a
>>> lossy conversion to Decimal wouldn't be any worse.
>>
>> Hmm, given that a float can be converted losslessly to a fraction, why
>> was the decision taken to convert the fraction to a float rather than
>> the other way round?
>
> I'm not sure of the actual reason for this decision, but one argument
> I've seen used for other languages is that it's desirable for the
> inexactness of the float type to be contagious:  rationals are
> perceived as exact, while floats are perceived as approximations.

You hit the nail on the head.

> Note that this only applies to arithmetic operations:  for
> comparisons, an exact conversion *is* performed.  This is much like
> what currently happens with ints and floats in the core:  a mixed-type
> arithmetic operation between an int and a float first converts the int
> to a float (possibly changing the value in the process).  A mixed-type
> comparison makes an exact comparison without doing such a conversion.
> For example (in any non-ancient version of Python):
>
>>>> n = 2**53 + 1
>>>> x = 2.**53
>>>> n > x   # compares exact values;  no conversion performed
> True
>>>> n - x    # converts n to a float before subtracting
> 0.0
>
>> I don't see a PEP for the fractions module, and my google-fu has
>> failed to find anything. Was there a discussion on this?
>
> There's PEP 3141 (http://www.python.org/dev/peps/pep-3141/), which was
> the motivation for adding the fractions module in the first place, and
> there's the issue tracker item for the fractions module
> (http://bugs.python.org/issue1682).

-- 
--Guido van Rossum (python.org/~guido)