«K12/K13» Q_.hs «PDF», «POD»

module Q_ (Q_(..)) where

import Base
import Z (Z)
import qualified Z (zero, one)
import GHC.Real

data Q_ = Frac Z Z
one = Frac Z.one Z.one

instance Show Q_ where
  show a = "Q[" ++ (show . toRational $ a) ++ "]"

instance Eq Q_ where
  (Frac a b) == (Frac c d) | all (== Z.zero) [a,c] = True
  (Frac a b) == (Frac c d) | otherwise             = (a*d) == (c*b)

instance Num Q_ where
  (Frac a b) + (Frac c d) = Frac (a*d + c*b) (b*d)
  (Frac a b) - (Frac c d) = Frac (a*d - c*b) (b*d)
  (Frac a b) * (Frac c d) = Frac (a*c) (b*d)

  abs    (Frac a b) = Frac (abs a) (abs b)
  negate (Frac a b) = Frac (-a) (b)
  signum (Frac a b) = Frac (signum $ a*b) Z.one

  fromInteger n = Frac (fromInteger n) Z.one

instance Real Q_ where
  toRational (Frac a b) = (toInteger a) % (toInteger b)

instance Fractional Q_ where
  (Frac a b) / (Frac c d) = Frac (a*d) (b*c)
  fromRational (a :% b)   = Frac (fromInteger a) (fromInteger b)

instance Ord Q_ where
  (Frac a b) <= (Frac c d) = s (a*d <= c*b) where
    s k | b*d >= Z.zero = k
    s k | otherwise     = not k