[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

(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 
inexact->exact is called #asTrueFraction (#asExactFraction in GNU 

This solution is known from the wise lispers for so long... 
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 
- 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 
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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