import Data.Ratio ((%))
import GHC.Real

-- 10 decimal places
newtype Fixed = Fixed Integer deriving (Eq, Ord, Enum)

instance Show Fixed where
  show (Fixed a) = show whole ++ "." ++ trailing where
    (whole, part) = a `divMod` (10 ^ 10)
    digits = show part
    trailing = replicate (10 - (length digits)) '0'  ++ digits

instance Num Fixed where
  fromInteger n = Fixed (n * 10 ^ 10)
  Fixed a + Fixed b = Fixed (a + b)
  Fixed a - Fixed b = Fixed (a - b)
  Fixed a * Fixed b = Fixed ((a * b) `div` 10 ^ 10)
  abs (Fixed a) = Fixed (abs a)
  signum (Fixed a) = fromInteger (signum a)

instance Real Fixed where
  toRational (Fixed a) = a % (10 ^ 10)

instance Integral Fixed where
  toInteger (Fixed a) = a `div` 10 ^ 10
  Fixed a `quotRem` Fixed b = (fromInteger q, Fixed r) where
    (q, r) = a `quotRem` b

instance Fractional Fixed where
  fromRational (e :% d) = fromInteger e / fromInteger d
  Fixed a / Fixed b = Fixed (a * 10 ^ 10 `div` b)