[Pharo-dev] float & fraction equality bug

Raffaello Giulietti raffaello.giulietti at lifeware.ch
Thu Nov 9 14:10:33 EST 2017


On 2017-11-09 19:04, Nicolas Cellier wrote:
> 
> 
> 2017-11-09 18:02 GMT+01:00 Raffaello Giulietti 
> <raffaello.giulietti at lifeware.ch <mailto:raffaello.giulietti at lifeware.ch>>:
> 
> 
> 
> 
>         Anyway relying upon Float equality should allways be subject to
>         extreme caution and examination
> 
>         For example, what do you expect with plain old arithmetic in mind:
> 
>               a := 0.1.
>               b := 0.3 - 0.2.
>               a = b
> 
>         This will lead to (a - b) reciprocal = 3.602879701896397e16
>         If it is in a Graphics context, I'm not sure that it's the
>         expected scale...
> 
> 
> 
>     a = b evaluates to false in this example, so no wonder (a - b)
>     evaluates to a big number.
> 
> 
> Writing a = b with floating point is rarely a good idea, so asking about 
> the context which could justify such approach makes sense IMO.
> 

Simple contexts, like the one which is the subject of this trail, are 
the one we should strive at because they are the ones most likely used 
in day-to-day working. Having useful properties and regularity for 
simple cases might perhaps cover 99% of the everyday usages (just a 
dishonestly biased estimate ;-) )

Complex contexts, with heavy arithmetic, are best dealt by numericists 
when Floats are involved, or with unlimited precision numbers like 
Fractions by other programmers.





>     But the example is not plain old arithmetic.
> 
>     Here, 0.1, 0.2, 0.3 are just a shorthands to say "the Floats closest
>     to 0.1, 0.2, 0.3" (if implemented correctly, like in Pharo as it
>     seems). Every user of Floats should be fully aware of the implicit
>     loss of precision that using Floats entails.
> 
> 
> Yes, it makes perfect sense!
> But precisely because you are aware that 0.1e0 is "the Float closest to 
> 0.1" and not exactly 1/10, you should then not be surprised that they 
> are not equal.
> 

Indeed, I'm not surprised. But then
     0.1 - (1/10)
shall not evaluate to 0. If it evaluates to 0, then the numbers shall 
compare as being equal.

The surprise lies in the inconsistency between the comparison and the 
subtraction, not in the isolated operations.



> 
> I agree that following assertion hold:
>      self assert: a ~= b & a isFloat & b isFloat & a isFinite & b 
> isFinite ==> (a - b) isZero not
> 

The arrow ==> is bidirectional even for finite Floats:

self assert: (a - b) isZero not & a isFloat & b isFloat & a isFinite & b 
isFinite ==> a ~= b




> But (1/10) is not a Float and there is no Float that can represent it 
> exactly, so you can simply not apply the rules of FloatingPoint on it.
> 
> When you write (1/10) - 0.1, you implicitely perform (1/10) asFloat - 0.1.
> It is the rounding operation asFloat that made the operation inexact, so 
> it's no more surprising than other floating point common sense

See above my observation about what I consider surprising.




> 
> 
>     In the case of mixed-mode Float/Fraction operations, I personally
>     prefer reducing the Fraction to a Float because other commercial
>     Smalltalk implementations do so, so there would be less pain porting
>     code to Pharo, perhaps attracting more Smalltalkers to Pharo.
> 
> Mixed arithmetic is problematic, and from my experience mostly happens 
> in graphics in Smalltalk.
> 
> If ever I would change something according to this principle (but I'm 
> not convinced it's necessary, it might lead to other strange side effects),
> maybe it would be how mixed arithmetic is performed...
> Something like exact difference like Martin suggested, then converting 
> to nearest Float because result is inexact:
>      ((1/10) - 0.1 asFraction) asFloat
> 
> This way, you would have a less surprising result in most cases.
> But i could craft a fraction such that the difference underflows, and 
> the assertion a ~= b ==> (a - b) isZero not would still not hold.
> Is it really worth it?
> Will it be adopted in other dialects?
> 
> 

As an alternative, the Float>>asFraction method could return the 
Fraction with the smallest denominator that would convert to the 
receiver by the Fraction>>asFloat method.

So, 0.1 asFraction would return 1/10 rather than the beefy Fraction it 
currently returns. To return the beast, one would have to intentionally 
invoke asExactFraction or something similar.

This might cause less surprising behavior. But I have to think more.





>     But the main point here, I repeat myself, is to be consistent and to
>     have as much regularity as intrinsically possible.
> 
> 
> 
> I think we have as much as possible already.
> Non equality resolve more surprising behavior than it creates.
> It makes the implementation more mathematically consistent (understand 
> preserving more properties).
> Tell me how you are going to sort these 3 numbers:
> 
> {1.0 . 1<<60+1/(1<<60).  1<<61+1/(1<<61)} sort.
> 
> tell me the expectation of:
> 
> {1.0 . 1<<60+1/(1<<60). 1<<61+1/(1<<61)} asSet size.
> 

A clearly stated rule, consistently applied and known to everybody, helps.

In presence of heterogeneous numbers, the rule should state the common 
denominator, so to say. Hence, the numbers involved in mixed-mode 
arithmetic are either all converted to one representation or all to the 
other: whether they are compared or added, subtracted or divided, etc. 
One rule for mixed-mode conversions, not two.




> tell me why = is not a relation of equivalence anymore (not associative)
> 
> 

Ensuring that equality is an equivalence is always a problem when the 
entities involved are of different nature, like here. This is not a new 
problem and not inherent in numbers. (Logicians and set theorists would 
have much to tell.) Even comparing Points and ColoredPoints is 
problematic, so I have no final answer.

In Smalltalk, furthermore, implementing equality makes it necessary to 
(publicly) expose much more internal details about an object than in 
other environments.








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