-- Stability : provisional
-- Portability : portable
--
--- $Id: Complex.hs,v 1.1 2001/06/28 14:15:02 simonmar Exp $
+-- $Id: Complex.hs,v 1.2 2001/12/21 15:07:21 simonmar Exp $
--
-- Complex numbers.
--
realPart (x :+ _) = x
imagPart (_ :+ y) = y
+{-# SPECIALISE conjugate :: Complex Double -> Complex Double #-}
conjugate :: (RealFloat a) => Complex a -> Complex a
conjugate (x:+y) = x :+ (-y)
+{-# SPECIALISE mkPolar :: Double -> Double -> Complex Double #-}
mkPolar :: (RealFloat a) => a -> a -> Complex a
mkPolar r theta = r * cos theta :+ r * sin theta
+{-# SPECIALISE cis :: Double -> Complex Double #-}
cis :: (RealFloat a) => a -> Complex a
cis theta = cos theta :+ sin theta
+{-# SPECIALISE polar :: Complex Double -> (Double,Double) #-}
polar :: (RealFloat a) => Complex a -> (a,a)
polar z = (magnitude z, phase z)
+{-# 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)))
where k = max (exponent x) (exponent y)
mk = - k
+{-# SPECIALISE phase :: Complex Double -> Double #-}
phase :: (RealFloat a) => Complex a -> a
phase (0 :+ 0) = 0 -- SLPJ July 97 from John Peterson
phase (x:+y) = atan2 y x