[Python-Dev] Re: PEP239 (Rational Numbers) Reference Implementation and new issues

[François Pinard]

[Eric S. Raymond]

>> 1) Should future division return rationals rather than floats.

> +1 for returning rationals.  It's the right thing -- and if it fails, 
> it will fail noisily, right?

While I agree with the theoretical arguments, I have the practical fear that
rationals could grow very big, rather quickly, in the course of a long
computation involving them in various ways.  By big, I mean the numerator
and denominator of the fraction taken in isolation, not the number itself.
Consider inversions of an integer matrices, approximations with truncated
series, or worse things like, maybe, discrete Fourier transforms.

Bigger rationals are, slower they become, and more memory they take.  The
danger is that programmers may get surprised or hurt by Python performance
degradation, raising frequent and recurrent questions here and elsewhere.

On the other hand, I would love if Python was not loosing precision on
non-truncating integer division, so let me try a bit to destroy my own
fears.  On average, most programs will not use matrices of rational numbers,
nor play with series.  Moreover, most programs do not use so many different
numeric variables anyway, nor perform long computations involving them.
Many programs do not go beyond adding or subtracting one, once in a while!

So, I would guess that _on the average_, using rational numbers might be
acceptable and go almost unnoticed by most people.  So it might be more
worth accepting as a community to warn programmers who are more prone to
numerical algorithms of the intrinsic dangers of integer division in Python.

But those feelings are no proof of anything.  How do we get the confirmation
that using rationals in Python would be easy going and innocuous in
practice, beforehand?  It would surely be nice relying in such a feature!

-- 
François Pinard   http://www.iro.umontreal.ca/~pinard