[Pharo-project] Fwd: [ANN] Number comparison, hash, NaN, Point, and other partially ordered sets

Alexandre Bergel alexandre at bergel.eu
Tue Jan 6 09:13:33 EST 2009


Thanks Nicolas,

You made really good points!

Alexandre


On 5 Jan 2009, at 15:38, nicolas cellier wrote:

> 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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Alexandre Bergel  http://www.bergel.eu
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