[swift-evolution] [Review] SE-0104: Protocol-oriented integers

[Károly Lőrentey]

The operation I want is the inverse of doubleWidthMultiply, where you have a (high, low) word pair and you want to divide it by a single word, getting a quotient and remainder. This is an important building block for implementing arbitrary precision division. Intel’s DIV can do this in a single instruction, while doing it in code requires a lot of work:

https://github.com/lorentey/BigInt/blob/swift3/Sources/BigDigit.swift#L119-L176

> On 2016-06-24, at 20:52, Haravikk <swift-evolution at haravikk.me> wrote:
> 
> 
>> On 24 Jun 2016, at 18:17, Károly Lőrentey via swift-evolution <swift-evolution at swift.org> wrote:
>> I’m especially stoked about `FixedWidthInteger.doubleWidthMultiply`, which will likely lead to a measurable speedup. Why is there no `doubleWidthQuotientAndRemainder` or `doubleWidthDivide`, though?
> 
> Double-width isn't needed for these as it's impossible for an integer to become larger when dividing (the smallest value you can divide by and get a result is 2, which will halve the value), and the remainder can't be larger than the original value.
> 
> 
> Anyway, I'm hugely in favour of this proposal, it's desperately needed!