X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=Data%2FComplex.hs;h=749ba91982b9d44a13340138010ca1fab5923639;hb=d71aee821935e29a3569bc4b401f695536209c85;hp=c9f83341595db00c6f5fe02f0d85184443c0bc51;hpb=d12c4f3de454ea031f2258627d388d3d994a3cfd;p=haskell-directory.git

diff --git a/Data/Complex.hs b/Data/Complex.hs
index c9f8334..749ba91 100644
--- a/Data/Complex.hs
+++ b/Data/Complex.hs
@@ -13,17 +13,21 @@
 -----------------------------------------------------------------------------
 
 module Data.Complex
-	( Complex((:+))
-	
+	(
+	-- * Rectangular form
+	  Complex((:+))
+
 	, realPart	-- :: (RealFloat a) => Complex a -> a
 	, imagPart      -- :: (RealFloat a) => Complex a -> a
-	, conjugate     -- :: (RealFloat a) => Complex a -> Complex a
+	-- * Polar form
 	, mkPolar       -- :: (RealFloat a) => a -> a -> Complex a
 	, cis           -- :: (RealFloat a) => a -> Complex a
 	, polar         -- :: (RealFloat a) => Complex a -> (a,a)
 	, magnitude     -- :: (RealFloat a) => Complex a -> a
 	, phase         -- :: (RealFloat a) => Complex a -> a
-	
+	-- * Conjugate
+	, conjugate     -- :: (RealFloat a) => Complex a -> Complex a
+
 	-- Complex instances:
 	--
 	--  (RealFloat a) => Eq         (Complex a)
@@ -39,8 +43,10 @@ module Data.Complex
 
 import Prelude
 
-#ifndef __NHC__
-import Data.Dynamic
+import Data.Typeable
+
+#ifdef __HUGS__
+import Hugs.Prelude(Num(fromInt), Fractional(fromDouble))
 #endif
 
 infix  6  :+
@@ -48,32 +54,52 @@ infix  6  :+
 -- -----------------------------------------------------------------------------
 -- The Complex type
 
-data  (RealFloat a)     => Complex a = !a :+ !a  deriving (Eq, Read, Show)
-
+-- | Complex numbers are an algebraic type.
+--
+-- For a complex number @z@, @'abs' z@ is a number with the magnitude of @z@,
+-- but oriented in the positive real direction, whereas @'signum' z@
+-- has the phase of @z@, but unit magnitude.
+data (RealFloat a) => Complex a
+  = !a :+ !a	-- ^ forms a complex number from its real and imaginary
+		-- rectangular components.
+  deriving (Eq, Read, Show)
 
 -- -----------------------------------------------------------------------------
 -- Functions over Complex
 
-realPart, imagPart :: (RealFloat a) => Complex a -> a
+-- | Extracts the real part of a complex number.
+realPart :: (RealFloat a) => Complex a -> a
 realPart (x :+ _) =  x
+
+-- | Extracts the imaginary part of a complex number.
+imagPart :: (RealFloat a) => Complex a -> a
 imagPart (_ :+ y) =  y
 
+-- | The conjugate of a complex number.
 {-# SPECIALISE conjugate :: Complex Double -> Complex Double #-}
 conjugate	 :: (RealFloat a) => Complex a -> Complex a
 conjugate (x:+y) =  x :+ (-y)
 
+-- | Form a complex number from polar components of magnitude and phase.
 {-# SPECIALISE mkPolar :: Double -> Double -> Complex Double #-}
 mkPolar		 :: (RealFloat a) => a -> a -> Complex a
 mkPolar r theta	 =  r * cos theta :+ r * sin theta
 
+-- | @'cis' t@ is a complex value with magnitude @1@
+-- and phase @t@ (modulo @2*'pi'@).
 {-# SPECIALISE cis :: Double -> Complex Double #-}
 cis		 :: (RealFloat a) => a -> Complex a
 cis theta	 =  cos theta :+ sin theta
 
+-- | The function 'polar' takes a complex number and
+-- returns a (magnitude, phase) pair in canonical form:
+-- the magnitude is nonnegative, and the phase in the range @(-'pi', 'pi']@;
+-- if the magnitude is zero, then so is the phase.
 {-# SPECIALISE polar :: Complex Double -> (Double,Double) #-}
 polar		 :: (RealFloat a) => Complex a -> (a,a)
 polar z		 =  (magnitude z, phase z)
 
+-- | The nonnegative magnitude of a complex number.
 {-# SPECIALISE magnitude :: Complex Double -> Double #-}
 magnitude :: (RealFloat a) => Complex a -> a
 magnitude (x:+y) =  scaleFloat k
@@ -81,6 +107,8 @@ magnitude (x:+y) =  scaleFloat k
 		    where k  = max (exponent x) (exponent y)
 		          mk = - k
 
+-- | The phase of a complex number, in the range @(-'pi', 'pi']@.
+-- If the magnitude is zero, then so is the phase.
 {-# SPECIALISE phase :: Complex Double -> Double #-}
 phase :: (RealFloat a) => Complex a -> a
 phase (0 :+ 0)   = 0		-- SLPJ July 97 from John Peterson
@@ -90,10 +118,8 @@ phase (x:+y)	 = atan2 y x
 -- -----------------------------------------------------------------------------
 -- Instances of Complex
 
-#ifndef __NHC__
-#include "Dynamic.h"
+#include "Typeable.h"
 INSTANCE_TYPEABLE1(Complex,complexTc,"Complex")
-#endif
 
 instance  (RealFloat a) => Num (Complex a)  where
     {-# SPECIALISE instance Num (Complex Float) #-}
@@ -106,6 +132,9 @@ instance  (RealFloat a) => Num (Complex a)  where
     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) #-}
@@ -117,6 +146,9 @@ instance  (RealFloat a) => Fractional (Complex a)  where
 				 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) #-}