> On Jan 15, 2017, at 19:24, Dave Abrahams <[email protected]> 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 <[email protected]> wrote: >>> >>> >>> >>> >>> >>> On Jan 15, 2017, at 18:02, Xiaodi Wu <[email protected]> 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 _______________________________________________ swift-evolution mailing list [email protected] https://lists.swift.org/mailman/listinfo/swift-evolution
