[swift-dev] Rationalizing FloatingPoint conformance to Equatable

Xiaodi Wu xiaodi.wu at gmail.com
Tue Oct 24 20:48:18 CDT 2017

On Tue, Oct 24, 2017 at 1:55 PM, Ben Cohen <ben_cohen at apple.com> wrote:

> On Oct 19, 2017, at 4:29 PM, Xiaodi Wu via swift-dev <swift-dev at swift.org>
> wrote:
> Differing behavior in generic and concrete contexts is simply too subtle
> to be understandable to the reader.
> Hardly more subtle then the current “Equatable works like this, with these
> strong guarantees. Oh, except for some cases it doesn’t, in which case
> ¯\_(ツ)_/¯”

I'm not saying that the status quo is a superior alternative.

However, one option is to _weaken_ the guarantees of Equatable such that it
guarantees only partial equivalence for `==`. From the perspective of
documented semantics, it's not subtle at all but a giant hammer of a
change. However, from an actual what-does-the-implementation-do standpoint,
it would be acknowledging what is already true. Only code that is already
broken when used with floating-point values would become formally
"incorrect" in the sense of relying on semantics that are then no longer

Such a solution would avoid, as you might say, perpetuating the ¯\_(ツ)_/¯
approach to floating point.

I realize that Comparable admits an exception for FP. This is, IMO, a
> serious mistake and needs to be reversed. Equatable has no such exception
> and rightly so.
> The clearest demonstrations of how flawed this approach is can be found in
> the Standard Library. You can throw a brick at it and hit an example of
> something that’s broken by the presence of .nan: random sort orders, ==
> implementations that differ based on the identify of the buffer,

In my view, if a sort algorithm cannot accommodate NaN, it's entirely
acceptable to trap on NaN--and that is a trivial change. After all, NaN is
unordered with respect to everything and one cannot sort the unsortable.
And, as shown, the `Array.==` implementation is trivially fixable. The
entire standard library can be made NaN-safe in like manner.

> arbitrary duplication in Set/Dictionary etc.

(I disagree that it's arbitrary. If NaN != NaN, then every NaN is properly

> The important point to take from this is not “how do we fix the Standard
> Library?” but rather “these errors are easy to make” by anyone writing
> generic code using standard protocols. If the Standard Library can’t get
> these right, how can we expect others to? There are potentially far worse
> bugs that could result. A differently-written sorting algorithm could
> corrupt elements (because it relied on substitutability). Other sorting or
> searching algorithms could easily go into an infinite loop. These problems
> exist because the code relies on the documented behavior of the protocol,
> because if you can’t, then what is the point in documenting that behavior?

It's not that the standard library *can't* get these right, but that it
currently *doesn't*, because it documents one set of semantics but
implements another, then relies on documented semantics that it knows it
does not implement. We both agree that this needs to be fixed.

The question here is whether it is to be fixed by sticking to the
documented semantic guarantees of `==` and bringing all implementations
into proper conformance, or alternatively sticking to the implemented
behavior of `==` and aligning the documented semantic guarantees to that.

> I don’t support solutions such as adding a property indicating
> “containsExceptionalValues” (whatever that means), and expecting every
> author of a generic algorithm that uses Equatable to remember to call it,
> and craft custom paranoid behavior (if there is any reasonable behavior)
> based on it. With recursive conformance landed on master, we finally have a
> generics system where writing algorithms against Collection can be
> considered approachable by ordinary users. You no longer have to know
> things like how Collection.SubSequence needs to be constrained to also be a
> Collection – it just is. We would be negating this good work to now
> introduce a whole new set of gotchas that we expect people to know (without
> the type system even helping them in this case) about how some types,
> including standard library types, flout the documented rules for Equatable
> and Comparable, and that you need to use one of a handful of properties to
> hack in special cases to handle it.

The gotchas aren't new; they arise when using floating point values,
originate with the IEEE definition of floating point equivalence, and exist
in some form in every language that has implemented collections of floating
point values. Crucially, they exist today in Swift; only, we haven't
documented it.

And as a user of algorithms, what should you do? If a generic algorithm
> doesn’t document how it handles these special cases, should you assume it
> doesn’t? Check the code? Experiment to find out?
> This problem also spreads, virus-like, once we have conditional
> conformance that makes containers equatable when their elements are.
> [Double] would need to propagate it’s elements’ “exceptionality", to
> avoid problems with [Double]. Double? will have to do the same.

This isn't a _problem_. In fact, I consider this to be a key _feature_.
Naturally, every protocol conformance (conditional or not) must implement
all protocol requirements, so if we add additional requirements they must
be implemented. What I'm saying here is that *it may be desirable* to have
some protocol-based API to distinguish partial from full equivalence
relations. If you accept that premise, then it is the logical consequence
that if you conditionally conform `Array` to `Equatable`, you will have to
implement any new APIs, and in so doing, document how equivalence of arrays
of floating point values relates to floating point equivalence. For me,
this is a _good thing_: it documents _in code_ something that today is
muddled through.

The explanation that a method on `Float` is a "floating-point context" but
> a method on `[Float]` is *not a "floating point context"* is, IMO,
> indefensible.
> Nevertheless, I will attempt to defend it :)
> I find it odd that violating the documented requirements of a protocol is
> considered defensible, but expecting types comply with those requirements
> is indefensible. A principled stance would be to say that Float shouldn’t
> conform to Equatable (because… it doesn’t!) and requiring all calls to
> supply a predicate (and maybe amending types like Dictionary to allow you
> to supply one). That won’t fly though – users would complain – so instead
> we are in this murky ground.

I don't think we should defend violating the documented requirements of a
protocol. Either (a) Float should not conform to Equatable (agree, this is
a non-starter); (b) how Float conforms to Equatable should be brought into
conformance with documented semantics (your stance); or (c) what semantics
are documented should be brought into alignment with how conformance is
actually implemented (my stance). Naturally, in the last case, additional
APIs should be added as needed to make such reduced semantic guarantees
useful for generic algorithms.

Later in the thread, you mention a possible fix for sort:
> `sort()` is problematic, but not if a custom predicate is supplied.
> So, we are potentially trading off one subtlety (that < behaves
> differently in generic and non-generic contexts) for another (that you need
> to know that you need to pass in a special predicate for sorting, or you
> get nonsense results). Knowing when an algorithm requires you to supply a
> predicate (like sort) vs when handling for the special case is built in
> (like equatable) seems far worse complication to me than knowing one rule:
> that generically when constrained to Comparable, Float adheres to the
> requirements of Comparable. Always. That is a consistent rule that you need
> to learn once and that doesn’t vary depending on which algorithm you’re
> using.

I would argue that Float should _always_ adhere to the requirements of
Comparable, in all contexts. The question is, rather: what can be the
requirements of Comparable such that Float can always adhere to them?

Another alternative proposed in previous threads is to give Comparable an
> additional operator (<=> or .compare(to:) that will always enforce a total
> ordering, and sort can use that. This is, afaict, C#’s solution –
> double.NaN < 1.0, 1.0 < double.NaN and double.NaN == double.NaN all return
> false, but Comparer<double>.Default.compare returns -1, 1 and 0
> respectively.

This is, essentially, the endpoint of what I'm proposing.

Equatable would vend (modulo bikeshedding):
`==`, a partial equivalence relation
`~`, a full equivalence relation
`containsExceptionalValues` (yes, this is a deliberately terrible name,
because it's meant to go through bikeshedding), a Boolean value to indicate
whether `==` is the same as `~`

Comparable would vend (modulo bikeshedding):
`<`, `>`, <=`, `>=`, defined as now
`<=>`, as in C# `compare` (or maybe, to emphasize the point, `<~>`)
`containsExceptionalValues`, inherited from `Equatable`, to document the
relationship between `<` (etc.) and the spaceship operator

> This is essentially a backdoor to having one comparison concretely, and
> another generically, except whether you get that different behavior is left
> to the whim of the algorithm’s implementor, depending on whether they used
> < or <=>. And what should sets use? Should a hashed set use == and allow
> multiple nan, but an ordered set use <=> and exclude them?

This should absolutely be in the control of the implementor and not the
type system. It's superior to have the question of whether
`MyCollection.==` uses floating-point equivalence or not be a decision
that's made in the implementation of `==` and then explicitly recorded in
code (`containsExceptionalValues`); it *shouldn't* be a subtlety of whether
it's `MyCollection<T> where T : Equatable` that conditionally conforms to
`Equatable` or instead `MyCollection<T> where T : FloatingPoint`.

- `index(of:)` works perfectly sensibly without such a relation; if no NaN
> is equal to any other NaN, `index(of: .nan)` is appropriately `nil`.
> It works sensibly when you are calling it from a concrete context, and you
> know that you have is a collection of floating point elements.
> But it does not work sensibly if you are using index(of:) as a building
> block in a wider generic algorithm on Collection, which relies on the rules
> set out by Equatable. I find myself using index(of:) within generic
> algorithms frequently, and I really don’t know how I should reason about
> its use if it’s accepted that the rules of Equatable just don’t hold in the
> all cases. When operating generically more than one level deep like this,
> you really need to be able to rely on those rules.

But, since `index(of:)` is a generic extension method itself, having
different behaviors for `==` in the generic vs. concrete context would mean
that the behavior of this method *would no longer make sense if you are
using `index(of:)` from a concrete context* where you know you have a
collection of floating-point elements. And while one may write generic
algorithms frequently, I'll bet that the average user of Swift calls
`index(of:)` in concrete contexts far more frequently than in generic ones.

To follow your line of argument, you'd also want `index(of:)` to have
different behaviors in the generic vs. concrete context, just like `==`
does. Carrying this out consistently would ultimately require having an
alternative implementation on every collection type of every generic
algorithm such as `index(of:)`, using the constraint `Element :

This leads to the other argument against having algorithms generic over
> Equatable behave differently to ones on Float/Double (or FloatingPoint):
> that when you take your FP algorithm, and then loosen the constraints, it
> changes behavior in a way that may no longer be correct.
> But we aready have the opposite case, where algorithms are written
> generically and then don’t work correctly for floats. I would argue that is
> far more harmful and subtle an issue. I honestly don’t think the situation
> where someone writes an algorithm first against floats, then generalizes
> it, is a very common path to creating a generic algorithm.  The inverse –
> where someone writes an algorithm using Equatable, and then people use it
> with floats – is certainly common, hence this discussion.
> There really is no way to square this circle. Every option is going to
> have downsides. We have to balance correctness, least surprise/most
> expected behavior for most people, and consistency. For me, making generic
> use of Equatable and Comparable stick to the documented conformance
> generically, while keeping FP-specific uses the way they are, is the least
> bad option.
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