[Pharo-project] Fwd: [ANN] Number comparison, hash, NaN, Point, and other partially ordered sets
nicolas cellier
ncellier at ifrance.com
Mon Jan 5 13:38:35 EST 2009
Stéphane Ducasse <stephane.ducasse at ...> writes:
>
> Nicolas
>
> could you summarize your solution?
>
> Stef
>
> On Jan 5, 2009, at 12:55 AM, nicolas cellier wrote:
>
Here is the summary:
1) equality relation is not transitive due to inexact asFloat conversion
example:
(1/2) = 0.5. "This is exact"
(1/2) + (1/(2 raisedTo: 100)) = 0.5. "This is an inexact conversion"
(1/2) + (1/(2 raisedTo: 100)) ~= (1/2). "If equal where transitive, they
should be equal"
Solution: base comparison on inexact->exact conversions rather than the
contrary...
inexact->exact is called #asTrueFraction (#asExactFraction in GNU
Smalltalk).
This solution is known from the wise lispers for so long...
http://www.lispworks.com/documentation/lcl50/aug/aug-170.html
This is http://bugs.squeak.org/view.php?id=3374
2) Some numbers are equal, but have different hash codes
Since some Float can equal some Integer or Fraction, it is necessary to
change at least 2 out of 3 hash implementations.
Solution I retained:
- preserve Integer hash
- change Float hash if they have a fractionPart = 0.0 (they are equal to
anInteger)
- change Fraction hash if they could be equal to a Float (I only test
that denominator is a power of two, which is a necessary but not a
sufficient condition).
This is http://bugs.squeak.org/view.php?id=6601, and
http://bugs.squeak.org/view.php?id=3360, solution has been posted at #3374.
Note: this results in loosing a little speed for small Float hash, and
lot more for large Float hash.
But make it right > make it fast...
3) Comparing Float nan to a Float or an Integer does not follow IEEE 754
conventions
comparison should always return false since nan cannot be ordered.
Magnitude assume subInstances form a totally ordered set.
Thus Number is not a well behaved Magnitude.
Consequently, Number must define not only < but also <= >= and >
Note that only < and <= would be strictly necessary.
The other two could be defined like this:
> b
^b < self
>= b
^b <= self
I choose to change >= implementation in Magnitude, and reimplement
everything in Number subclasses
(though > and >= would not be strictly necessary).
This is http://bugs.squeak.org/view.php?id=6719
But the VM also makes same assumption as Magnitude and must be changed
too - this is http://bugs.squeak.org/view.php?id=7260
4) Comparing a Number and a Point is weird (different result with an
Integer and a Float)
Float did coerce to a Point, then compare.
Integer did use a false total order assumption through super Magnitude.
Two main solutions:
- either coerce Number to a Point (might be implicitely used this way in
the image... hard to tell).
- or raise an Exception
Solution: I choosed to raise an Exception.
This is http://bugs.squeak.org/view.php?id=7259
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