import Prelude
import Data.Typeable
+#ifdef __GLASGOW_HASKELL__
+import Data.Data (Data)
+#endif
#ifdef __HUGS__
import Hugs.Prelude(Num(fromInt), Fractional(fromDouble))
data (RealFloat a) => Complex a
= !a :+ !a -- ^ forms a complex number from its real and imaginary
-- rectangular components.
+# if __GLASGOW_HASKELL__
+ deriving (Eq, Show, Read, Data)
+# else
deriving (Eq, Show, Read)
+# endif
-- -----------------------------------------------------------------------------
-- Functions over Complex
{-# SPECIALISE magnitude :: Complex Double -> Double #-}
magnitude :: (RealFloat a) => Complex a -> a
magnitude (x:+y) = scaleFloat k
- (sqrt ((scaleFloat mk x)^(2::Int) + (scaleFloat mk y)^(2::Int)))
+ (sqrt (sqr (scaleFloat mk x) + sqr (scaleFloat mk y)))
where k = max (exponent x) (exponent y)
mk = - k
+ sqr z = z * z
-- | The phase of a complex number, in the range @(-'pi', 'pi']@.
-- If the magnitude is zero, then so is the phase.