[Python-Dev] RE: [Python-checkins] python/dist/src/Objects
Mon, 15 Apr 2002 19:22:37 -0400
> I presume that you also object against allowing certain "int-
> requiring" operations (like use as sequence index) on floats when
> the fraction is zero.
Not if you *know* the fractional part is 0. If you don't know that for
sure, then you're saying sequence indices are fuzzy, subject to change
across platforms and releases. I'm acutely aware of this because I spent 10
years using Cray machines where int(6./3.) == 1. That doesn't happen in a
754 world, and 754 also supplies an "exact" flag so you can know for sure
that 24./6. is exact and 24./5. is not. The same kind of thing can still
happen, though, if "3." is really the result of an fp computation that just
happens to round to something a little bigger than 3.0 on the nose; this in
turn could be due to a 1-bit difference in the platform exp() implementation
for a given input. Over the years, I've tracked down dozens and dozens of
x-platform program failures to such tiny platform differences (and, perhaps
paradoxically, I spent more time per year doing that at Dragon than at
> Unified numbers are rapidly becoming less attractive this way...
To the extent that they expose platform accidents, they've always been
suspect. A fancy hand calculator gets away with it because it's a single
platform where all the numerics are under the control of the system (HW and
SW) designers, and they can do whatever it takes to avoid visible surprises.
They don't care much about speed, either. A pure-SW equivalent would need
to stay away from HW fp, or use it in limited known-safe ways.
> To me, unified numbers means that there's only one numeric type, and
> it always has the same properties. That means that all numbers must
> have an imag field, which is zero when it's not a complex number.
> But it seems you want some other indicator that says it's never been
> part of a calculation involving complex numbers...
If you're to avoid platform accidents, it doesn't matter whether it's ever
been complex, what matters is that when you're "downcasting" you *know*
whether that's safe, or whether you're just guessing. CL refuses to guess;
Scheme tries to make safe guesses possible, but half-heartedly.
[on an "exact?" bit]
> Unified numbers are becoming even less attractive...
It's taken from Scheme: exactness is Scheme's way of trying to allow for
guaranteed-safe downcasting (or "down towering") when possible. In
practice, though, the Scheme standard says so little about how inexactness
propagates that you can't count on it across Scheme implementations.
> Too much to read. :-(
Approximate computer arithmetic is a bitch. If you want a system that's
easy to define and to use, stay away from HW fp and it's almost easy. Else
rounding errors are inescapable, and so have to be dealt with.
> But if the end result is that users will write trunc() or round()
> calls whenever they have a float value that they believe is an int and
> that they want to use in an int context -- but then when it's not even
> close to an int, they won't notice.
I was wondering when someone would get to that <wink>. Implicit in that
complaint is that, if we left magical float->int up to "the system", then
the system could benevolently decide when a given float was or wasn't "close
enough" to an exact int to make no difference. Been there, done that, too.
IMO it just increases the complication, and the difficulty of writing
correct portable code: it's another layer of hidden magic to trip over.
For example, if you decide that 1.9 is "close enough" to 2 that it should be
treated as 2 on the nose, but that anything in (1.1, 1.9) is "too far away",
then you've effectively just moved the boundaries where the tiniest possible
1-bit rounding accidents lead to radically different behavior. Systems that
do stuff like that (APL is an example) then grow global "fuzz" settings so
that users can override the system, when, through painful experience, they
learn the system *can't* guess reliably.
Some hand calculators deal with this by computing to several extra decimal
digits internally, and then saying "it's close enough to an int" if and only
if the extra-precision hidden result rounds to an exact normal-precision
int. That's effective, but perhaps would break down if hand calculators
normally did millions (billions, ...) of computations before needing to
Forget complex. How is sequence.__getitem__(x) to be defined for a float x
(this is the under-the-covers "float"; whether that's a user-visible type
distinction isn't material to the question here)? Scheme says that in
(list-ref sequence x), x must be an "exact integer", where "integer"
includes things like a complex with a 0 imaginary part, but "exact" says
you've got to *know* it's a 0 imaginary part, not just an approximation to a
0 imaginary part. That would be sane, except that most Scheme
implementations call *all* internal floats "inexact", so in practice it ends
up meaning "an internal integer", and all the words allowing for other
possiblities just confuse the issue. Common Lisp says "screw that -- if you
think this is usable as an int, you convert it to an int yourself: your
choice, your responsibility, and here are 4 convenient functions for
choosing the rounding you want". Either is preferable to "don't worry,
trust me" <wink>.