> 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? > On Jul 22, 2016, at 7:04 PM, Xiaodi Wu <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 >>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution> >>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>>>> <https://lists.swift.org/mailman/listinfo/swift-evolution>> >>>>>>>>>> >>>>>>>>> >>>>>>>>> -- >>>>>>>>> Dave >>>>>>>>> >>>>>>>>> _______________________________________________ >>>>>>>>> swift-evolution mailing list >>>>>>>>> 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>>>> >>>>>>>>> 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>> >>>>>>>>> <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>>> >>>>>>>>> <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>> >>>>>>>>> <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>> >>>>>>>> <mailto: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>> >>>>>>>> <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>>> >>>>>>>> >>>>>>> >>>>>>> -- >>>>>>> Dave >>>>>>> >>>>>>> _______________________________________________ >>>>>>> swift-evolution mailing list >>>>>>> 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>>> >>>>>>> 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>> >>>>>>> <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>>> >>>>> >>>>> -- >>>>> Dave >>>>> _______________________________________________ >>>>> 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> >>>> 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