+% -----------------------------------------------------------------------------
+% $Id: Complex.lhs,v 1.7 2001/09/19 14:06:03 simonmar Exp $
%
-% (c) The AQUA Project, Glasgow University, 1994-1999
+% (c) The University of Glasgow, 1994-2000
%
\section[Complex]{Module @Complex@}
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