Add `div'`, `mod'`, `quot'`, and `rem'`.

[ekmett]

We can't really implement Integral, because of toInteger, but the other methods in there are sane. We could have our own copies.

[echatav]

I needed these and used the NumB and IntegralB class from Boolean.

[ekmett]

Not really comfortable incurring the dep here, but it is good to know there was a way to work around it.

[echatav]

That's fine. Would you still want these functions in the library outside of a typeclass? I think they are

  quot (I l u) (I l' u') =
    if l' <= 0 && 0 <= u' then throw DivideByZero else I
      (minimum [a `Prelude.quot` b | a <- [l,u], b <- [l',u']])
      (maximum [a `Prelude.quot` b | a <- [l,u], b <- [l',u']])
  rem (I l u) (I l' u') =
    if l' <= 0 && 0 <= u' then throw DivideByZero else I
      (minimum [0, signum l * (abs u' - 1), signum l * (abs l' - 1)])
      (maximum [0, signum u * (abs u' - 1), signum u * (abs l' - 1)])
  div (I l u) (I l' u') =
    if l' <= 0 && 0 <= u' then throw DivideByZero else I
      (min (l `Prelude.div` max 1 l') (u `Prelude.div` min (-1) u'))
      (max (u `Prelude.div` max 1 l') (l `Prelude.div` min (-1) u'))
  mod _ (I l' u') =
    if l' <= 0 && 0 <= u' then throw DivideByZero else
      I (min (l'+1) 0) (max 0 (u'-1))

[ekmett]

That seems reasonable.

On Wed, Aug 17, 2016 at 4:44 PM, Eitan Chatav notifications@github.com wrote:

That's fine. Would you still want these functions in the library outside of a typeclass? I think they are

quot (I l u) (I l' u') = if l' <= 0 && 0 <= u' then throw DivideByZero else I (minimum [a Prelude.quot b | a <- [l,u], b <- [l',u']]) (maximum [a Prelude.quot b | a <- [l,u], b <- [l',u']]) rem (I l u) (I l' u') = if l' <= 0 && 0 <= u' then throw DivideByZero else I (minimum [0, signum l * (abs u' - 1), signum l * (abs l' - 1)]) (maximum [0, signum u * (abs u' - 1), signum u * (abs l' - 1)]) div (I l u) (I l' u') = if l' <= 0 && 0 <= u' then throw DivideByZero else I (min (l Prelude.div max 1 l') (u Prelude.div min (-1) u')) (max (u Prelude.div max 1 l') (l Prelude.div min (-1) u')) mod _ (INT (Interval.I l' u')) = if l' <= 0 && 0 <= u' then throw DivideByZero else I (min (l'+1) 0) (max 0 (u'-1))

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