> On Jul 22, 2016, at 9:20 PM, Xiaodi Wu <xiaodi...@gmail.com> wrote: > > On Fri, Jul 22, 2016 at 9:19 PM, Matthew Johnson <matt...@anandabits.com > <mailto:matt...@anandabits.com>> wrote: > >> On Jul 22, 2016, at 9:12 PM, Xiaodi Wu <xiaodi...@gmail.com >> <mailto:xiaodi...@gmail.com>> wrote: >> >> On Fri, Jul 22, 2016 at 9:09 PM, Jaden Geller <jaden.gel...@gmail.com >> <mailto:jaden.gel...@gmail.com>> wrote: >>> 1. NaN != NaN and +0 == -0 [what the traditional comparison operators are >>> constrained to do] >>> 2. NaN == NaN, +0 == -0, and the same number encoded different ways compare >>> equal >>> 3. NaN == NaN, +0 != -0, and the same number encoded different ways compare >>> not equal >> >> >> Though it seems super confusing that a language have THREE ways to compare >> values, that does almost seem necessary here. Do we actually need an >> operator that performs #3? I understand that that is equality under total >> ordering, but couldn't users just write `(a <=> b) == .same` if they want >> that? >> >> For floating point types, I think `===` shouldn't be #3. From a practical >> standpoint, no one ever wants that definition unless they are ordering >> things. Whereas you'd want #2 for things like `.index(of:)` and #1 for the >> traditional comparison operators. > > However, we have to introduce a new notion of identity for floating point > types if `===` isn’t #3. Floating points are tricky enough already. Is that > really a good thing? > > Further, it encodes three separate meanings of equality in the protocols. We > should avoid that if we can. > > It feels like maybe the right solution is floating point specific algorithm > overloads. It doesn’t seem like too big a surprise that this is the case > when you really dig into the details. > > > I see what you're getting at here. But I like your other alternative better, > which is to define identity in a generically useful way for floating point > types, and preserve IEEE semantics in its own method for floating point types.
That wasn’t actually my idea - it was yours! :) > >>> On Jul 22, 2016, at 7:04 PM, Xiaodi Wu <xiaodi...@gmail.com >>> <mailto:xiaodi...@gmail.com>> wrote: >>> >>> On Fri, Jul 22, 2016 at 8:57 PM, Matthew Johnson <matt...@anandabits.com >>> <mailto:matt...@anandabits.com>> wrote: >>> >>>> On Jul 22, 2016, at 8:54 PM, Xiaodi Wu via swift-evolution >>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org>> wrote: >>>> >>>> On Fri, Jul 22, 2016 at 8:52 PM, Jaden Geller via swift-evolution >>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org>> wrote: >>>> "The totalOrder predicate will order these cases, and it also >>>> distinguishes between different representations of NaNs and between the >>>> same decimal floating point number encoded in different ways." >>>> - >>>> [Wikipedia](https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate >>>> >>>> <https://en.wikipedia.org/wiki/IEEE_floating_point#Total-ordering_predicate>) >>>> >>>> Sounds like `===` should not return `true` for zeros of different signs, >>>> then. >>>> >>>> Fair enough; the result of that will be, as Pyry noted above, that: >>>> >>>> ``` >>>> [-0.0, 1.0, .nan, 0.0].firstIndex(of: 0.0) //=> 3, not 0 >>>> ``` >>> >>> Maybe we need floating point specific implementations of some algorithms to >>> resolve this problem? >>> >>> It doesn’t seem like there is a way to provide the semantics required by >>> generic algorithms and still provide the expected behavior for floating >>> point values. >>> >>> Well, what I'm trying to say is that generic algorithms such as >>> `index(of:)` require only an equivalence relation. For floating point >>> types, there are three ways to slice it: >>> >>> 1. NaN != NaN and +0 == -0 [what the traditional comparison operators are >>> constrained to do] >>> 2. NaN == NaN, +0 == -0, and the same number encoded different ways compare >>> equal >>> 3. NaN == NaN, +0 != -0, and the same number encoded different ways compare >>> not equal >>> >>> Both #2 and #3 can fall out of valid equivalence relations; if `===` >>> behaved like #2 for FloatingPoint types, then generic algorithms work just >>> fine. If we insist on using a total ordering defined by `<=>` all the time, >>> then we've got problems. >>> >>> >>> >>>> >>>>> On Jul 22, 2016, at 6:48 PM, Dave Abrahams via swift-evolution >>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org>> wrote: >>>>> >>>>> >>>>> on Fri Jul 22 2016, Jaden Geller <swift-evolution@swift.org >>>>> <mailto:swift-evolution@swift.org>> wrote: >>>>> >>>>>>> For floating point, I'd hope that `a === b` if `(a <=> b) == .same` >>>>>>> *but not iff*. This is to satisfy IEEE 754: "Comparisons shall >>>>>>> ignore the sign of zero (so +0 = −0)". >>>>>> >>>>>> I don't see why both `(+0) === (-0)` and `(+0) <=> (-0)` can't return >>>>>> `true` and `.same`, respectively. This doesn't break the total >>>>>> ordering of values. `===` doesn't do raw memory comparison. They're >>>>>> "identical", so it ought to return `true`. >>>>> >>>>> It ought to do whatever IEEE-754 specifies that its total ordering test >>>>> does. That is, IEEE-754 gets to decide whether the difference between >>>>> +0 and -0 is “essential” to IEEE-754 floating point types, or not. >>>>> >>>>>> >>>>>>> On Jul 22, 2016, at 6:37 PM, Xiaodi Wu via swift-evolution >>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org>> wrote: >>>>>>> >>>>>>> On Fri, Jul 22, 2016 at 8:20 PM, Dave Abrahams via swift-evolution >>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org>>> >>>>>>> wrote: >>>>>>> >>>>>>> on Fri Jul 22 2016, Daniel Duan <daniel-AT-duan.org >>>>>>> <http://daniel-at-duan.org/>> wrote: >>>>>>> >>>>>>>>> On Jul 22, 2016, at 3:00 PM, Dave Abrahams via swift-evolution >>>>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org>>> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> on Fri Jul 22 2016, Daniel Duan >>>>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org>> >>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>> <mailto:swift-evolution@swift.org>>>> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>> >>>>>>>>>>> On Jul 22, 2016, at 11:05 AM, Dave Abrahams via swift-evolution >>>>>>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>> <mailto:swift-evolution@swift.org>> >>>>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>> <mailto:swift-evolution@swift.org>>>> >>>>>>>>>>> wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> on Thu Jul 21 2016, Duan >>>>>>>>>> >>>>>>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>> <mailto:swift-evolution@swift.org>> >>>>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>> <mailto:swift-evolution@swift.org>>> >>>>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>> <mailto:swift-evolution@swift.org>> >>>>>>>>>>> <mailto:swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>> <mailto:swift-evolution@swift.org>>>>> >>>>>>>>>>> wrote: >>>>>>>>>>> >>>>>>>>>>>> Great proposal. I want to second that areSame may mislead user to >>>>>>>>>>>> think this is about identity. >>>>>>>>>>>> >>>>>>>>>>>> I like areEquivalent() but there may be better names. >>>>>>>>>>> >>>>>>>>>>> It really *is* about identity as I posted in a previous message. >>>>>>>>>>> But >>>>>>>>>>> that doesn't change the fact that areEquivalent might be a better >>>>>>>>>>> name. >>>>>>>>>>> It's one of the things we considered; it just seemed long for no >>>>>>>>>>> real >>>>>>>>>>> benefit. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> If the addresses of the arguments aren’t being used, then we don’t >>>>>>>>>> consider >>>>>>>>>> them part of their *identity*. I can follow this logic. My fear is >>>>>>>>>> most users >>>>>>>>>> won’t make this leap on their own and get the same initial >>>>>>>>>> impression as I did. >>>>>>>>>> It's entirely possible this fear is unfounded. Some educated >>>>>>>>>> bikesheding >>>>>>>>>> wouldn't hurt here IMO :) >>>>>>>>> >>>>>>>>> Well, it's still a very real question whether we ought to have the >>>>>>>>> additional API surface implied by areSame, or wether we should >>>>>>>>> collapse >>>>>>>>> it with ===. >>>>>>>>> >>>>>>>> >>>>>>>> To spell this out (because I had to think about it for a second): === >>>>>>>> will be derived from >>>>>>>> <=>, >>>>>>>> but also becomes default implementation for ==, which remains open for >>>>>>>> customization. >>>>>>> >>>>>>> I was imagining roughly this (untested): >>>>>>> >>>>>>> /// Two references are identical if they refer to the same >>>>>>> /// instance. >>>>>>> /// >>>>>>> /// - Note: Classes with a more-refined notion of “identical” >>>>>>> /// should conform to `Identifiable` and implement `===`. >>>>>>> func ===(lhs: AnyObject, rhs: AnyObject) -> Bool { >>>>>>> ObjectIdentifier(lhs) == ObjectIdentifier(rhs) >>>>>>> } >>>>>>> >>>>>>> /// Supports testing that two values of `Self` are identical >>>>>>> /// >>>>>>> /// If `a` and `b` are of type `Self`, `a === b` means that >>>>>>> /// `a` and `b` are interchangeable in most code. A conforming >>>>>>> /// type can document that specific observable characteristics >>>>>>> /// (such as the `capacity` of an `Array`) are inessential and >>>>>>> /// thus not to be considered as part of the interchangeability >>>>>>> /// guarantee. >>>>>>> /// >>>>>>> /// - Requires: `===` induces an equivalence relation over >>>>>>> /// instances. >>>>>>> /// - Note: conforming types will gain an `==` operator that >>>>>>> /// forwards to `===`. >>>>>>> /// - Note: Types that require domain-specific `==` >>>>>>> /// implementations with different semantics (e.g. floating >>>>>>> /// point) should define a more-specific overload of `==`, >>>>>>> /// which will be used in contexts where the static type is >>>>>>> /// known to the compiler. >>>>>>> /// - Note: Generic code should usually use `==` to compare >>>>>>> /// conforming instances; that will always dispatch to `===` >>>>>>> /// and will be unaffected by more specific overloads of >>>>>>> /// `==`. >>>>>>> protocol Identifiable { // née Equatable name is negotiable >>>>>>> func ===(_: Self, _: aSelf) -> Bool >>>>>>> } >>>>>>> >>>>>>> /// Default definition of `==` for Identifiable types. >>>>>>> func ==<T: Identifiable>(lhs: T, rhs: T) -> Bool { >>>>>>> return lhs === rhs >>>>>>> } >>>>>>> >>>>>>> /// Conforming types have a default total ordering. >>>>>>> /// >>>>>>> /// If `a` and `b` are of type `Self`, `a <=> b` means that >>>>>>> /// `a` and `b` are interchangeable in most code. A conforming >>>>>>> /// type can document that specific observable characteristics >>>>>>> /// (such as the `capacity` of an `Array`) are inessential and >>>>>>> /// thus not to be considered as part of the interchangeability >>>>>>> /// guarantee. >>>>>>> /// >>>>>>> /// - Requires: `<=>` induces a total ordering over >>>>>>> /// instances. >>>>>>> /// - Requires: the semantics of `<=>` are consistent with >>>>>>> /// those of `===`. That is, `(a <=> b) == .equivalent` >>>>>>> /// iff `a === b`. >>>>>>> >>>>>>> For floating point, I'd hope that `a === b` if `(a <=> b) == .same` >>>>>>> *but not iff*. This is to satisfy IEEE 754: "Comparisons shall ignore >>>>>>> the sign of zero (so +0 = −0)". >>>>>>> >>>>>>> /// - Note: conforming types will gain `<`, `<=`, `>`, and `>=` >>>>>>> /// operators defined in terms of `<=>`. >>>>>>> /// - Note: Types that require domain-specific `<`, etc. >>>>>>> /// implementations with different semantics (e.g. floating >>>>>>> /// point) should define more-specific overloads of those >>>>>>> /// operators, which will be used in contexts where the >>>>>>> /// static type is known to the compiler. >>>>>>> /// - Note: Generic code can freely use `<=>` or the traditional >>>>>>> /// comparison operators to compare conforming instances; >>>>>>> /// the result will always be supplied by `<=>` >>>>>>> /// and will be unaffected by more specific overloads of >>>>>>> /// the other operators. >>>>>>> protocol Comparable : Identifiable { >>>>>>> func <=> (lhs: Self, rhs: Self) -> Ordering >>>>>>> } >>>>>>> >>>>>>> /// Default implementations of `<`, `<=`, `>`, and `>=`. >>>>>>> extension Comparable { >>>>>>> static func <(lhs: Self, rhs: Self) -> Bool { >>>>>>> return (lhs <=> rhs) == .ascending >>>>>>> } >>>>>>> static func <=(lhs: Self, rhs: Self) -> Bool { >>>>>>> return (rhs <=> lhs) != .ascending >>>>>>> } >>>>>>> static func >(lhs: Self, rhs: Self) -> Bool { >>>>>>> return (lhs <=> rhs) == .descending >>>>>>> } >>>>>>> static func >=(lhs: Self, rhs: Self) -> Bool { >>>>>>> return (rhs <=> lhs) != .descending >>>>>>> } >>>>>>> } >>>>>>> >>>>>>>> I like this idea. If we keep === as a separate thing, now users have 3 >>>>>>>> “opportunities” to define >>>>>>>> equality. The must be few, if any, use cases for this. >>>>>>>> >>>>>>>> Would love to see if anyone on the list can give us an example. >>>>>>>> Otherwise we should make >>>>>>>> areSame === again™! >>>>>>>> >>>>>>>>>> >>>>>>>>>>>> Daniel Duan >>>>>>>>>>>> Sent from my iPhone >>>>>>>>>>>> >>>>>>>>>>>>> On Jul 21, 2016, at 6:32 PM, Robert Widmann via swift-evolution >>>>>>>>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>>>> <mailto:swift-evolution@swift.org>>> >>>>>>>>>>>>> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>>> On Jul 21, 2016, at 6:19 PM, Xiaodi Wu >>>>>>>>>>>>>> <xiaodi...@gmail.com <mailto:xiaodi...@gmail.com> >>>>>>>>>>>>>> <mailto:xiaodi...@gmail.com <mailto:xiaodi...@gmail.com>>> >>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> This is nice. Is `areSame()` being proposed because static `==` >>>>>>>>>>>>>> is >>>>>>>>>>>>>> the status quo and you're trying to make the point that `==` in >>>>>>>>>>>>>> the >>>>>>>>>>>>>> future need not guarantee the same semantics? >>>>>>>>>>>>> >>>>>>>>>>>>> Yep! Equivalence and equality are strictly very different things. >>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Nit: I think the more common term in stdlib would be >>>>>>>>>>>>>> `areEquivalent()`. Do you think `same` in that context >>>>>>>>>>>>>> (independent >>>>>>>>>>>>>> of the word "ordering") might erroneously suggest identity? >>>>>>>>>>>>> >>>>>>>>>>>>> There is room for improvement here. Keep ‘em coming. >>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>>> On Thu, Jul 21, 2016 at 8:11 PM, Robert Widmann via >>>>>>>>>>>>>>> swift-evolution >>>>>>>>>>>>>>> <swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>>>>>> <mailto:swift-evolution@swift.org>>> >>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>> Hello Swift Community, >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Harlan Haskins, Jaden Geller, and I have been working on a >>>>>>>>>>>>>>> proposal to clean up the semantics of ordering relations in the >>>>>>>>>>>>>>> standard library. We have a draft that you can get as a gist. >>>>>>>>>>>>>>> Any feedback you might have about this proposal helps - though >>>>>>>>>>>>>>> please keeps your comments on Swift-Evolution and not on the >>>>>>>>>>>>>>> gist. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Cheers, >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> ~Robert Widmann >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> _______________________________________________ >>>>>>>>>>>>>>> swift-evolution mailing list >>>>>>>>>>>>>>> swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>>>>>> <mailto:swift-evolution@swift.org>> >>>>>>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> _______________________________________________ >>>>>>>>>>>>> swift-evolution mailing list >>>>>>>>>>>>> swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>>>> <mailto:swift-evolution@swift.org>> >>>>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>> >>>>>>>>>>>> _______________________________________________ >>>>>>>>>>>> swift-evolution mailing list >>>>>>>>>>>> swift-evolution@swift.org <mailto:swift-evolution@swift.org> >>>>>>>>>>>> <mailto:swift-evolution@swift.org >>>>>>>>>>>> <mailto:swift-evolution@swift.org>> >>>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>>>>>> 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