-----------------------------------------------------------------------------
---
+-- |
-- Module : Data.Complex
-- Copyright : (c) The University of Glasgow 2001
--- License : BSD-style (see the file libraries/core/LICENSE)
+-- License : BSD-style (see the file libraries/base/LICENSE)
--
-- Maintainer : libraries@haskell.org
-- Stability : provisional
-- Portability : portable
--
--- $Id: Complex.hs,v 1.1 2001/06/28 14:15:02 simonmar Exp $
---
-- Complex numbers.
--
-----------------------------------------------------------------------------
import Prelude
-import Data.Dynamic
+#ifndef __NHC__
+import Data.Typeable
+#endif
+
+#ifdef __HUGS__
+import Hugs.Prelude(Num(fromInt), Fractional(fromDouble))
+#endif
infix 6 :+
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
-- -----------------------------------------------------------------------------
-- Instances of Complex
-#include "Dynamic.h"
+#ifndef __NHC__
+#include "Typeable.h"
INSTANCE_TYPEABLE1(Complex,complexTc,"Complex")
+#endif
instance (RealFloat a) => Num (Complex a) where
{-# SPECIALISE instance Num (Complex Float) #-}
signum 0 = 0
signum z@(x:+y) = x/r :+ y/r where r = magnitude z
fromInteger n = fromInteger n :+ 0
+#ifdef __HUGS__
+ fromInt n = fromInt n :+ 0
+#endif
instance (RealFloat a) => Fractional (Complex a) where
{-# SPECIALISE instance Fractional (Complex Float) #-}
d = x'*x'' + y'*y''
fromRational a = fromRational a :+ 0
+#ifdef __HUGS__
+ fromDouble a = fromDouble a :+ 0
+#endif
instance (RealFloat a) => Floating (Complex a) where
{-# SPECIALISE instance Floating (Complex Float) #-}