> On Nov 1, 2017, at 12:51 PM, Greg Titus via swift-dev <swift-dev@swift.org>
> wrote:
>
>> On Nov 1, 2017, at 9:16 AM, Ben Cohen via swift-dev <swift-dev@swift.org>
>> wrote:
>>> On Oct 31, 2017, at 10:11 PM, Chris Lattner via swift-dev
>>> <swift-dev@swift.org> wrote:
>>> On Oct 31, 2017, at 9:07 AM, Stephen Canon via swift-dev
>>> <swift-dev@swift.org> wrote:
>>>> [Replying to the thread as a whole]
>>>>
>>>> There have been a bunch of suggestions for variants of `==` that either
>>>> trap on NaN or return `Bool?`. I think that these suggestions result from
>>>> people getting tunnel-vision on the idea of “make FloatingPoint equality
>>>> satisfy desired axioms of Equatable / Comparable”. This is misguided. Our
>>>> goal is (should be) to make a language usable by developers; satisfying
>>>> axioms is only useful in as much as they serve that goal.
>>>>
>>>> Trapping or returning `Bool?` does not make it easier to write correct
>>>> concrete code, and it does not enable writing generic algorithms that
>>>> operate on Comparable or Equatable. Those are the problems to be solved.
>>>
>>> +100. Swift isn’t the first language to face the problems of floating
>>> point, nor is it the first to try to shoehorn it into a framework like
>>> Equatable.
>>
>> Java and C# do not have this problem with their generic algorithms (albeit
>> possibly because of limitations in their languages that Swift doesn’t have).
>> Swift is setting itself up as a major language with confusing and
>> unjustifiable behavior by comparison. That some other languages are also bad
>> at this doesn’t seem relevant.
>
> The common (and correct!) wisdom in _any_ programming language that uses IEEE
> floating point is that checking equality of two floating point values is
> almost always a terrible idea. Usually what you want in any real world code
> is to check for a difference less than some epsilon value, which depends upon
> context. There are just too many issues with values that aren’t exactly
> representable, rounding errors during computations, et cetera, for perfectly
> normal floats even if you completely left aside equality rules for NaN.
The common wisdom is fundamentally bogus. One should *often* use a tolerance
for floating-point comparison, but there’s a whole host of situations in which
exact equality is perfectly appropriate. Of particular note for us, those
situations include most generic contexts based on Equatable or Comparable.
s.contains(2)
should not return `true` if `s` contains something two-ish. It should return
`true` if and only if `s` contains the actual value `2`.
One might want to have an additional method on sets of FloatingPoint-conforming
types that uses a tolerance, but contains should do precisely what it says on
the tin.
> I completely understand the desire in this thread to make floating point
> really satisfy the axioms of Equatable, but the fact is, even if you did,
> using a generic algorithm that depends upon equatability with floating point
> types is almost always just a programming error waiting to happen. It’s
> implicit in the representation and use of floating point values themselves,
> no matter what particular implementation you decide on for == or &==.
>
> If you really want to make the language better for developers, provide and
> emphasize fixed point or infinite precision or rational types for doing
> various things instead, and encourage them to shun floats as much as
> possible. If you really need to change anything about the standard library of
> Swift, my preferred solution would be to continue to provide ==(lhs : Float,
> rhs: Float) and != but NOT declare conformance to Equatable at all so that
> generic algorithms involving floats would fail to compile.
Fixed point representations have their place[1], but rationals are strictly
worse than floating-point representations in every way except for their ability
to exactly represent 1/3 in toy problems and efficiency of division until you
saturate the size of the denominator. I am not exaggerating. They waste space,
they have a highly non-uniform distribution of representable values, they have
many redundant representations, and denominators grow exponentially in almost
every non-toy problem.
Floating-point is the worst approximation to the real numbers except for all
the others.
– Steve
[1] Unfortunately they are generally unusable for libraries due to complete
lack of scale invariance. This can be worked around, but doing so requires more
hand-holding than floating-point.
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