{-# OPTIONS -fno-implicit-prelude #-} {- | Generally before using 'quot' and 'rem', think twice. In most cases 'divMod' and friends are the right choice, because they fulfill more of the wanted properties. On some systems 'quot' and 'rem' are more efficient and if you only use positive numbers, you may be happy with them. But we cannot warrant the efficiency advantage. See also: Daan Leijen: Division and Modulus for Computer Scientists <http://www.cs.uu.nl/%7Edaan/download/papers/divmodnote-letter.pdf>, <http://www.haskell.org/pipermail/haskell-cafe/2007-August/030394.html> -} module Algebra.RealIntegral ( C(quot, rem, quotRem), ) where import qualified Algebra.IntegralDomain as Integral import qualified Algebra.Real as Real import qualified Algebra.Ring as Ring import qualified Algebra.Additive as Additive import Algebra.Real (signum, ) import Algebra.IntegralDomain (divMod, ) import Algebra.Ring (one, ) -- fromInteger import Algebra.Additive (zero, (+), (-), ) import PreludeBase import Prelude (Int, Integer, ) infixl 7 `quot`, `rem` {- | Remember that 'divMod' does not specify exactly what @a `quot` b@ should be, mainly because there is no sensible way to define it in general. For an instance of @Algebra.RealIntegral.C a@, it is expected that @a `quot` b@ will round towards 0 and @a `Prelude.div` b@ will round towards minus infinity. Minimal definition: nothing required -} class (Real.C a, Integral.C a) => C a where quot, rem :: a -> a -> a quotRem :: a -> a -> (a,a) quot a b = fst (quotRem a b) rem a b = snd (quotRem a b) quotRem a b = let (d,m) = divMod a b in if (signum d < zero) then (d+one,m-b) else (d,m) instance C Integer instance C Int