[swift-dev] Rationalizing FloatingPoint conformance to Equatable

[Xiaodi Wu]

On Sat, Oct 21, 2017 at 7:52 PM, Jonathan Hull <jhull at gbis.com> wrote:

>
> On Oct 21, 2017, at 3:02 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Fri, Oct 20, 2017 at 2:42 PM, Stephen Canon <scanon at apple.com> wrote:
>
>> On Oct 20, 2017, at 8:21 AM, David Zarzycki via swift-dev <
>> swift-dev at swift.org> wrote:
>>
>>
>> On Oct 20, 2017, at 07:51, Xiaodi Wu via swift-dev <swift-dev at swift.org>
>> wrote:
>>
>> On Fri, Oct 20, 2017 at 1:22 AM, Jonathan Hull <jhull at gbis.com> wrote:
>>
>>> +1 for trapping unless using &==.  In the case of ‘Float?’ we could also
>>> map to nil.
>>>
>>> This is probably a more appropriate discussion for evolution though...
>>>
>>>
>>> On Oct 19, 2017, at 9:48 PM, Brent Royal-Gordon via swift-dev <
>>> swift-dev at swift.org> wrote:
>>>
>>> On Oct 19, 2017, at 4:29 PM, Xiaodi Wu via swift-dev <
>>> swift-dev at swift.org> wrote:
>>>
>>> D) Must floating-point IEEE-compliant equivalence be spelled `==`?
>>>
>>> In my view, this is something open for debate. I see no reason why it
>>> cannot be migrated to `&==` if it were felt that `==` *must* be a full
>>> equivalence relation. I believe this is controversial, however.
>>>
>>>
>>> I actually got partway through writing up a pitch on this yesterday, but
>>> my opinion is that NaNs are so exceptional, and so prone to misuse, that we
>>> ought to treat them like integer arithmetic overflows: trap when they're
>>> detected, unless you use an `&` variant operator which indicates you know
>>> what you're doing.
>>>
>>> I strongly suspect that, in practice, most float-manipulating code is
>>> not prepared to handle NaN and will not do anything sensible in its
>>> presence. For example, Apple platforms use floating-point types for
>>> geometry, color components, GPS locations, etc. Very little of this code
>>> will do anything sensible in the presence of a NaN. Arguably, it'd be
>>> better to exclude them through the type system, but I don't think that's a
>>> realistic possibility—we would need to have done that in a more
>>> source-break-friendly era. But that doesn't have to mean we're completely
>>> stuck.
>>>
>>>
>> Built-in floating point operators, as well as libc/libm math functions,
>> are designed to propagate NaN correctly. This is not meant to be a thread
>> about NaN, and we need to be cautious to define the scope of the problem to
>> be solved from the outset. The tendency of having ever-expanding discussion
>> where issues such as method names turn into discussions about the entire
>> standard library go nowhere.
>>
>> The question here is about `==` specifically and how to accommodate
>> partial equivalence relations. For sanity, we start with the premise that
>> NaN will forever be as it is.
>>
>>
>> I support Jonathan’s argument. If Swift wants to trap on NaN to improve
>> self-consistency and simplicity, then the tradeoff might be worth it. The
>> alternative, teaching the Equality protocol about NaNs, feels like “the
>> tail wagging the dog".
>>
>> In short: what IEEE requires of floating-point hardware is separable from
>> IEEE’s opinions about language/library design.
>>
>>
>> Just to be precise: IEEE 754 places no requirements on hardware. The
>> entirety of IEEE 754 is about what *languages* should provide. It just
>> happens to be advantageous to implement many of the requirements directly
>> in hardware.
>>
>> [The rest of this is a response to the thread as a whole, not to Dave]
>>
>> I have no philosophical objection to trapping on NaN. IEEE 754 says that
>> the default behavior should be to not trap, but other non-default forms of
>> exception handling* are explicitly allowed by IEEE 754.
>>
>> From a practical standpoint, it’s is counter to everything about the way
>> much floating-point hardware is designed, and that should give us some
>> pause. On x86 it’s possible to unmask the “invalid floating point
>> exception”, which results in any operation that generates a NaN faulting.
>> However, it will *not* cause a fault if an operand is already a quiet NaN,
>> so Swift would need to either test every operand that’s read from memory at
>> the time that it’s moved into register, or test every result.
>>
>> On some non-x86 architectures (including in particular most ARM
>> implementations) there is no hardware support for unmasking exceptions, so
>> there’s no way to automatically trap on invalid operations, you would have
>> to explicitly check for NaN on every operation. This is much, much more
>> expensive than checking for overflow on integer arithmetic (where for
>> addition / subtraction, it’s just an easily-predicted conditional branch).
>> Including these checks would introduce significant code bloat and slow down
>> naive arithmetic by roughly an order of magnitude on current hardware,
>> which is probably a non-starter.
>>
>> Trapping only for == is much, much more palatable, but as Xiaodi said,
>> doesn’t actually get you the semantics that you want for ==.
>>
>> &== is ugly but workable. You will have inevitable bugs from people who
>> naively adapt code from literally any other language that assumes IEEE 754
>> semantics for ==, however.
>>
>> – Steve
>>
>> [*] note that “exception handling” in an IEEE 754 context does not mean
>> what you think it does if you’re coming from a generic CS
>> not-floating-point background.
>>
>
> The performance aspect of this issue are daunting, and I'm glad you
> brought it up. On a cursory reading, having every NaN value compare equal
> to every other NaN value is likely to be several times, if not orders of
> magnitude, slower than the hardware IEEE implementation. This would be an
> extraordinary cost and makes me wonder if this is at all a good idea.
>
>
> One counter argument is that &== will retain full speed where important
> (e.g. in a tight loop).
>
> Off the top of my head, a naive implementation of == for Float (where Nan
> == Nan) would be:
>
> func == (a: Float, b: Float)->Bool {
> return (a &== b) || !(a &== a) || !(b &== b)
> }
>

That's not correct :P (Consider what happens when `a = 42` and `b = .nan`.)


> The good news is that ‘a' and ‘b' only need to be loaded into registers
> once.  Also, it could short circuit if 'a &== b' is true (if that is
> faster).  We could probably do better with a little cleverness.
>

Steve can describe the exact number of additional machine instructions on
each architecture, but from my cursory reading the performance cost is not
good and there's little cleverness to be had.

My overarching point is that, if most generic algorithms don't break
without a full equivalence relation and others can be trivially rewritten
to accommodate floating point behavior, then incurring a non-trivial cost
by default is not a good idea.

> It would serve us well to re-evaluate what generic algorithms absolutely
> require a full equivalence relation. Let's take a look at `Array`, for
> example.
>
> - `index(of:)` works perfectly sensibly without such a relation; if no NaN
> is equal to any other NaN, `index(of: .nan)` is appropriately `nil`.
> - `min()` and `max()` are something else entirely, as we're talking here
> only of equivalence and not of total order, which is another issue
> altogether.
> - `sort()` is problematic, but not if a custom predicate is supplied.
> - `split()` only runs into problems if specifically trying to split a
> sequence on `.nan`, but again this would be unsurprising if no NaN is equal
> to any other NaN.
> - `==` is broken but can be fixed as shown in PR #12503.
>
>
> My main worry would be generic algorithms on something one level of
> generalization away.  For example, how should a Set handle double insertion
> of a struct which has a Float in it.  It is very likely that the creator of
> that struct just && together == of the elements, so the set will end up
> with two identical entries (neither of which would register as being a
> member when the set is asked).
>

Consider a comparison of two instances of Complex<Float>: it should
absolutely return `false` when evaluating `Complex(1.0, .nan) ==
Complex(1.0, .nan)`. Likewise, if (actually, let's put it another way: as
long as) NaN != NaN, then an instance of Set<Float> should not deduplicate
NaN, and NaN should never be a member of that Set, and neither should an
instance of Set<Complex<Float>>. That's _correct_ in my view.

The wonkiness with `Array.==` is one of the few places where the behavior
of the generic algorithm is inexplicable on the basis of what's publicly
explained to the user. By contrast, `index(of:)`, `split`, etc. all behave
predictably given the fact that NaN != NaN.

I am currently leaning towards NaN == NaN behavior, with a warning
> explaining &== when used with Float == Float (and a way to silence it).
> That way, you at least have progressive disclosure.
>
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