[swift-evolution] Add a `clamp` function to Algorithm.swift

[Jaden Geller]

> On Mar 10, 2017, at 8:04 PM, Robert Bennett via swift-evolution <swift-evolution at swift.org> wrote:
> 
> I really like this proposal, and think that it does have a place in Swift 4. Two quick notes in light of the discussion: first, I think it should be called clamped, not clamp; second, I think it should only take ClosedRange. More on those later, but first I'll respond to the six questions raised by Xiaodi.
> 
>> 1. Is it truly a frequent operation?
> I think so. I've certainly wished for it on an occasion or two. I settle for min(upper, max(lower, value)).
> 
>> 2. Is the helper more readable? Is the composed equivalent obvious at a glance?
> Definitely (or I imagine it will be once we get the details figured out). There are two equivalent forms of the min-max version, the other being max(lower, min(upper, value)), not to mention the commutativity of the arguments themselves. I am under the impression that Swift is not a big fan of having multiple equivalent ways to do the same thing — that was part of the reason ++ was nixed. value.clamp(to: closedRange) is clear and is not interchangeable with any one thing in the language.
> 
>> 3. Does the helper have the flexibility to cover all common cases?
> I see three cases: value < lower, lower <= value <= upper, and upper < value. All are covered.
> 
>> 4. Is there a correctness trap with the composed equivalent? Is there a correctness trap with the helper?
> I don't think so, if we limit to ClosedRange.
> 
>> 5. Is there a performance trap with the composed equivalent? Or with the helper?
> I don't know, is there a significant cost associated to constructing a ClosedRange solely for the purpose of using its bounds? I would imagine not, but someone who knows more about Swift can answer.
> 
>> 6. Does the helper actually encourage misuse?
> I don't see how, if we limit its argument to ClosedRange.
> 
> 
> Going back to my earlier points — I think that to keep things in line with Swift's naming conventions, this function should be called clamped, as it returns a modified version of the calling object. Alternatively, we could follow the standard set by other numeric types and provide the non-mutating clamped and the mutating clamp, like multiplied/multiply for Double.
> 
> Finally, I don't think it makes mathematical sense to clamp to a non-closed range. Refer back to the original definition proposed, `min(upperBound, max(lowerBound, value))`. ClosedRange was proposed as a convenience for providing those bounds. This makes sense because a ClosedRange contains its bounds. Since (mathematical) non-closed ranges don't contain their bounds, it doesn't make sense to use a non-closed range to provide those bounds.

I think open ranges should be supported, but not for all `Comparable` types. It would however be reasonable to support it for types with discrete ordered values, all `Integer` types for example. I think we might be able to provide it for `T: Strideable where T.Stride: Integer` even. We definitely cannot provide it for all types though; it’s nonsensical to clamp a real value to a closed range.

> 
> Also, the above notwithstanding, I have a hard time figuring out when you would actually want to constrain a number to be strictly less than an upper bound, violating Question 1 above. If this behavior were really desired, better to be explicit and subtract the appropriate delta — 1 for Int, Double.epsilon (or whatever it's called) for Double. I definitely foresee a correctness trap with the non-closed Range.
> 
> Another reason not to allow half-open ranges is because of their asymmetry. Half open ranges are only open at their upper end, so you would have the ability to open-clamp from above but not from below. Seems arbitrary (see Question 3).

We already have this asymmetry. Adding a clamp function doesn’t worsen it. Besides, we have half-open [above] ranges because they are useful for indices:

`arr[idx.clamped(to: arr.startIndex..<arr.endIndex)`

We can even write this!

`arr[idx.clamped(to: arr.indices)]`

This seems like a useful enough feature to consider it IMO.

> 
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