On 2017-11-09 19:04, Nicolas Cellier wrote:
2017-11-09 18:02 GMT+01:00 Raffaello Giulietti
<[email protected] <mailto:[email protected]>>:
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.
