class  (RealFrac a, Floating a) => RealFloat a  where
    floatRadix       :: a -> Integer
    floatDigits      :: a -> Int
    floatRange       :: a -> (Int,Int)
    decodeFloat      :: a -> (Integer,Int)
    encodeFloat      :: Integer -> Int -> a
    exponent         :: a -> Int
    significand      :: a -> a
    scaleFloat       :: Int -> a -> a
    isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
                     :: a -> Bool
    atan2            :: a -> a -> a

        -- Minimal complete definition:
        --      All except exponent, significand, 
        --                 scaleFloat, atan2
    exponent x       =  if m == 0 then 0 else n + floatDigits x
                        where (m,n) = decodeFloat x

    significand x    =  encodeFloat m (- floatDigits x)
                        where (m,_) = decodeFloat x

    scaleFloat k x   =  encodeFloat m (n+k)
                        where (m,n) = decodeFloat x

    atan2 y x
      | x>0           =  atan (y/x)
      | x==0 && y>0   =  pi/2
      | x<0  && y>0   =  pi + atan (y/x) 
      |(x<=0 && y<0)  ||
       (x<0 && isNegativeZero y) ||
       (isNegativeZero x && isNegativeZero y)
                      = -atan2 (-y) x
      | y==0 && (x<0 || isNegativeZero x)
                      =  pi    -- must be after the previous test on zero y
      | x==0 && y==0  =  y     -- must be after the other double zero tests
      | otherwise     =  x + y -- x or y is a NaN, return a NaN (via +)

instance RealFloat Float where
  
...

instance RealFloat Double where
  
...