module Rational
  (Rat, normRat, negRat, addRat, mulRat, divRat, eqRat, showRat, 
   youDirtyRat )
where

type Rat = (Int,Int)

normRat :: Rat -> Rat 
normRat (x,0) = error ( "Invalid rational number (in normRat) " 
                         ++ showRat (x,0) ++ "\n" ) 
normRat (0,y) = (0,1) 
normRat (x,y) = (a `div` d, b `div` d) 
                where a = (signum' y) * x 
                      b = abs y 
                      d = gcd' a b 

signum' :: (Num a, Ord a) => a -> Int
signum' n | n == 0 =  0 
          | n > 0  =  1 
          | n < 0  = -1

gcd' :: Int -> Int -> Int 
gcd' x y = gcd'' (abs x) (abs y) 
         where gcd'' x 0 = x 
               gcd'' x y = gcd'' y (x `rem` y)

negRat :: Rat -> Rat 
negRat (a,b) = normRat (-a,b) 

addRat, subRat, mulRat, divRat :: Rat -> Rat -> Rat 
addRat (a,b) (c,d) = normRat (a*d + c*b, b*d) 
subRat (a,b) (c,d) = normRat (a*d - c*b, b*d) 
mulRat (a,b) (c,d) = normRat (a*c, b*d)
divRat (a,b) (c,d) = normRat (a*d, b*c) 

eqRat :: Rat -> Rat -> Bool 
eqRat (a,0) (c,d) = errRat (a,0)
eqRat (a,b) (c,0) = errRat (c,0) 
eqRat (a,b) (c,d) = (a*d == b*c)        

errRat (x,y) = error ("Invalid rational number" 
                      ++ showRat (x,y))

showRat :: Rat -> String
showRat (a,b) = show a ++ "/" ++ show b

youDirtyRat :: String
youDirtyRat = "You dirty rat!\n" ++ youDirtyRat