[Python-Dev] Floor division

[Nick Maclaren]

"Tim Peters" <tim.peters at gmail.com> wrote:
>
> OTOH, I am a fan of analyzing FP operations as if the inputs were in
> fact exactly what they claim to be, which 754 went a long way toward
> popularizing.  That largely replaced mountains of idiosyncratic
> "probabilistic arguments" (and where it seemed no two debaters ever
> agreed on the "proper" approach)  with a common approach that
> sometimes allows surprisingly sharp analysis.  Since I spent a good
> part of my early career as a professional apologist for Seymour Cray's
> "creative" floating point, I'm probably much more grateful to leave
> sloppy arithmetic behind than most.

Well, I spent some of it working with code (and writing code) that
was expected to work, unchanged, on an ICL 1900, CDC 6600/7600,
IBM 370 and others.  I have seen the harm caused by the 'exact
arithmetic' mindset and so don't like it, but I agree about your
objections to the "probabilistic arguments" (which were and are
mostly twaddle).  But that is seriously off-topic.

> [remquo]  It's really off-topic for Python-Dev, so
> I didn't/don't want to belabor it.

Agreed, except in one respect.  I stand by my opinion that the C99
specification has no known PRACTICAL use (your example is correct,
but I know of no such use in a real application), and so PLEASE
don't copy it as a model for Python divmod/remainder.

> No, /Python's/ definition of mod is inexact for that example.  fmod
> (which is not Python's definition) is always exact:  fmod(-1, 1e100) =
> -1, and -1 is trivially exactly congruent to -1 modulo anything
> (including modulo 1e100).  The result of fmod(x, y) has the same sign
> as x; Python's x.__mod__(y) has the same sign as y; and that makes all
> the difference in the world as to whether the exact result is always
> exactly representable as a float.

Oops.  You're right, of course.


Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email:  nmm1 at cam.ac.uk
Tel.:  +44 1223 334761    Fax:  +44 1223 334679