As I am thinking about it more, this means that for == and <
NaN == NaN
-0 == +0
+Inf < NaN
Since this would break from IEEE, I think we should also consider taking the
opportunity to make == and < work with a default tolerance. That is, 'a == b'
would check that (a - b) < epsilon for some reasonable choice of epsilon that
works for common usage. I know this would make the hash function harder to
write, but I think it is worthwhile.
Then, as I mentioned before, people who need strict IEEE conformance would
explicitly declare that need by using 'compare(with: other, using: .IEEE)' or
whatever we want to call that metric. We can even provide metrics for
different IEEE levels, if desired.
We could also provide a function ‘tolerance(_:Self) -> Comparable.Metric’ on
FloatingPoint which returns a comparison metric that defines equality as (a -
b) < tolerance, for those who want to specify a specific tolerance for their
use-case/algorithm...
Thanks,
Jon
> On Apr 23, 2017, at 7:18 AM, Jonathan Hull via swift-evolution
> <swift-evolution@swift.org> wrote:
>
> There is one more option which hasn’t really been considered:
>
> • == and != are tied to the Equatable protocol, which is essentially the ==
> operation.
> • <, <=, >, >= are tied to the Comparable protocol (which is kept the same
> except for minor changes/additions listed below)
> • Hashable still requires Equatable
> • There is a new ComparisonMetric concept which lets an algorithm specify
> exactly how the comparison is done (see below)
>
>
> Tl;dr: There are different definitions of ‘comparison’ which make sense in
> different domains… so let’s make it explicit so it doesn’t surprise anyone.
>
> The question then becomes, which metric should be the default (i.e. the one
> defined by ‘<‘ and ‘==‘), and the answer is: the one which lets us use
> floats/doubles in dictionaries and sets. People and algorithms which need
> full IEEE correctness can use a different metric which specifically
> guarantees it. They can even build their own metric if needed.
>
>
> ====The Design====
> // (Note: I wrote this code in mail, so it may not compile)
>
>
> //This defines the result of a comparison. It would ideally be nested in the
> protocol below if that becomes possible.
> enum ComparisonResult : Int {
> case ascending = -1
> case equal = 0
> case descending = 1
> }
>
> protocol Comparable {
> typealias Metric = (Self, Self) -> ComparisonResult //Give ourselves
> an easy way to refer to this function type
>
> var defaultMetric: Metric
> static func <(lhs: Self, rhs: Self) -> Bool
> }
>
> extension Comparable {
> //Not shown: We would define <=, etc… plus ≤,≥,and ≠ (because, hey, it
> is my proposal)
>
> func compare(with other: Self, using metric: Metric) ->
> ComparisonResult {
> return metric(self, other)
> }
>
> func compare(with other: Self) -> ComparisonResult {
> return self.defaultMetric(self, other)
> }
>
> static func <=> (lhs: Self, rhs: Self) -> Int {
> return self.defaultMetric(lhs, rhs).rawValue
> }
>
> var defaultMetric: Metric {
> return { lhs, rhs in
> if lhs == rhs {
> return .equal
> } else if lhs < rhs {
> return .ascending
> }
> return .descending
> }
> }
> }
>
> ============
>
> Then for Double, we would make a second metric for IEEE compliant (or
> multiple for different levels)
>
> extension Double : Comparable {
>
> static func < (lhs: Self, rhs: Self) -> Bool {
> //define using best for dictionaries / sets / layman
> understanding
> }
>
> static func == (lhs: Self, rhs: Self) -> Bool {
> //define using best for dictionaries / sets / layman
> understanding
> }
>
> static var IEEEcompare:Comparable.Metric {
> //return function here that does full IEEE comparison
> }
>
> }
>
> Then we can call ‘myDouble.compare(with: otherDouble, using: .IEEEcompare)’
> when needed.
>
>
> Thanks,
> Jon
>
>
>
>> On Apr 22, 2017, at 9:58 PM, Chris Lattner via swift-evolution
>> <swift-evolution@swift.org> wrote:
>>
>> On Apr 22, 2017, at 6:06 PM, Xiaodi Wu <xiaodi...@gmail.com> wrote:
>>> but my quick reaction to `&==` is that it would make me quite nervous to
>>> have `==` not bound to 754-equals as it is in essentially every other
>>> language. In particular, I worry about the risk of people porting numerical
>>> code that depends on isnan(x) <—> !(x < y) in non-obvious ways that they
>>> are unlikely to test. I’ll try to follow up with more detailed thoughts
>>> tomorrow.
>>>
>>> Indeed, it makes me a little nervous too. That said, `==` being either
>>> bound or not bound to 754 depending on the context is what makes me even
>>> more nervous.
>>>
>>> I was once adamantly against a new spelling for `==`, but on
>>> reconsideration it's clear to me that few if any numerical recipes can be
>>> ported verbatim from C-like languages and we should probably not encourage
>>> people to do so. Already, `+` needs to be rewritten as `&+`, `<<` probably
>>> should be rewritten as `&<<` (I still haven't had enough time to think
>>> about this), and the bitwise operators have differing precedences that
>>> require careful proofreading.
>>
>>
>> I haven’t been following this proposal or discussion closely, but it seems
>> to me that there are a few workable approaches with different tradeoffs:
>>
>> 1. The strictly correct but user hostile approach:
>>
>> * == and != are tied to the Equatable protocol, which is essentially the ==
>> operation.
>> * <, <=, >, >= are tied to the Comparable protocol, which is essentially the
>> <=> operation.
>> * Hashable doesn’t require equatable, it requires a related
>> StrictlyEquatable protocol.
>> * StrictlyEquatable refines Equatable (with no other requirements, it is
>> just a marker protocol), in which case FP types can’t conform to it, and
>> thus can’t participate as dictionary keys
>>
>> => This approach sucks because you can’t have Set<Float>, or
>> Dictionary<Float, String>.
>>
>> 2. The strictly correct but somewhat user hostile approach:
>>
>> * == and != are tied to the Equatable protocol, which is essentially the ==
>> operation.
>> * <, <=, >, >= are tied to the Comparable protocol, which is essentially the
>> <=> operation.
>> * Hashable doesn’t require equatable, it requires a related
>> StrictlyEquatable protocol.
>> * StrictlyEquatable doesn’t refine Equatable: it has a different
>> requirement, and FP types can therefore implement both Equatable and
>> StrictlyEquatable.
>>
>> => This approach is suboptimal because implementing your own type requires
>> you to implement the <=> operation, as well as the StrictlyEquatable
>> protocol, both.
>>
>> 3. The user friendly but incorrect model:
>>
>> * == and != are tied to the Equatable protocol, which is essentially the ==
>> operation.
>> * <, <=, >, >= are tied to the Comparable protocol, which is essentially the
>> <=> operation.
>> * Hashable is defined in terms of Equatable.
>>
>> => This is easy (types just have to define <=>), but fails for FP types.
>>
>>
>> I don’t think that this proposal is acceptable as written. I think it is
>> really bad that abstracting a concrete algorithm would change its behavior
>> so substantially. I don’t care about SNaNs, but I do care about the
>> difference between +0/-1 and secondarily that of NaN handling. It seems
>> really bad that generalizing something like:
>>
>> func doThing(a : Double, b : Double) -> Bool {
>> ….
>> return a != b
>> }
>>
>> to:
>>
>> func doThing<T : FloatingPoint> (a : T, b : T) -> Bool {
>> ….
>> return a != b
>> }
>>
>> would change behavior (e.g. when a is -0.0 and b is +0.0). Likewise, "T :
>> Equatable".
>>
>> -Chris
>>
>>
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>
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