# [swift-evolution] protocol-oriented integers (take 2)

David Sweeris davesweeris at mac.com
Sun Jan 15 20:19:07 CST 2017

```> On Jan 15, 2017, at 19:24, Dave Abrahams <dabrahams at apple.com> wrote:
>
>
>> on Sun Jan 15 2017, Xiaodi Wu <xiaodi.wu-AT-gmail.com> wrote:
>>
>>> On Sun, Jan 15, 2017 at 6:42 PM, David Sweeris <davesweeris at mac.com> wrote:
>>>
>>>
>>>
>>>
>>>
>>> On Jan 15, 2017, at 18:02, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>>>
>>> "Mathematically correct" integers behave just like Int in that there is
>>> not a multiplicative inverse. What we're trying to do here is to determine
>>> how much of what we know about mathematics is usefully modeled in the
>>> standard library. The answer is not zero, because there is more than just
>>> counting that people do with integers.
>>>
>>>
>>> It's an interesting problem... When I was in school, "integer" division
>>> "returned" a "quotient and remainder", a "fraction" (which, occasionally,
>>> could be simplified to just an integer), or a "real". We never talked about
>>> division in the context of "(Int, Int) -> Int", though. OTOH, I never took
>>> any math classes past Differential Equations or Linear Algebra, either...
>>> I'm *aware* of areas of math where you formally restrict yourself to the
>>> kind of "(Int, Int) -> Int" operations we're doing here, but I don't
>>> really know much about it. Is division even well-defined in that context?
>>>
>>> - Dave Sweeris
>>>
>>
>> I'm no mathematician, and I'm not sure how to tackle the question of
>> "well-defined." Hopefully someone who is more knowledgable can chime in
>> here.
>>
>> But I'll have a go at replying to your point as it relates to the practical
>> issue here. Two Int values can be "divided" to produce another Int, and
>> that gives a predictable and well-understood result. It's an operation
>> that's always going to be there--first, because it'd be insane to remove it
>> since much working code relies on it, and second, because we're only
>> re-designing integer protocols and not the concrete types. However, it _is_
>> true that such an operation has very different semantics from division as
>> you learned it in math.
>>
>> This is why I'm advocating for perhaps another look at the top of this
>> integer protocol hierarchy. At the moment, `Arithmetic` offers reasonable
>> semantic guarantees for a lot of things, but `/` has different semantics
>> for integer types and floating point types
>
> Well, that really depends on how closely you look.  From one
> point-of-view, floating point division and integer division *both*
> produce approximate results.

Yeah, but integer division tends to be so "approximate" that the answer can easily be useless without also calculating x%y. Floating point division will generally give you at least a few correct digits, won't it?

- Dave Sweeris
```