[project @ 1999-09-30 12:35:04 by sof]

[ghc-hetmet.git] / ghc / lib / std / Complex.lhs

diff --git a/ghc/lib/std/Complex.lhs b/ghc/lib/std/Complex.lhs
index 573beb7..eca2738 100644 (file)
--- a/ghc/lib/std/Complex.lhs
+++ b/ghc/lib/std/Complex.lhs
@@ -1,16 +1,34 @@
 %
-% (c) The AQUA Project, Glasgow University, 1994-1997
+% (c) The AQUA Project, Glasgow University, 1994-1999
 %
 
 \section[Complex]{Module @Complex@}
 
 \begin{code}
-module Complex (
-       Complex((:+)), 
-
-       realPart, imagPart, conjugate, mkPolar,
-       cis, polar, magnitude, phase
-    )  where
+module Complex
+       ( Complex((:+))
+       
+       , realPart      -- :: (RealFloat a) => Complex a -> a
+       , imagPart      -- :: (RealFloat a) => Complex a -> a
+       , conjugate     -- :: (RealFloat a) => Complex a -> Complex a
+       , 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
+       
+       -- Complex instances:
+       --
+       --  (RealFloat a) => Eq         (Complex a)
+       --  (RealFloat a) => Read       (Complex a)
+       --  (RealFloat a) => Show       (Complex a)
+       --  (RealFloat a) => Num        (Complex a)
+       --  (RealFloat a) => Fractional (Complex a)
+       --  (RealFloat a) => Floating   (Complex a)
+       -- 
+        -- Implementation checked wrt. Haskell 98 lib report, 1/99.
+
+        )  where
 
 import Prelude
 
@@ -24,7 +42,7 @@ infix  6  :+
 %*********************************************************
 
 \begin{code}
-data  (RealFloat a)     => Complex a = !a :+ !a  deriving (Eq,Read,Show)
+data  (RealFloat a)     => Complex a = !a :+ !a  deriving (Eq, Read, Show)
 \end{code}
 
 
@@ -36,8 +54,8 @@ data  (RealFloat a)     => Complex a = !a :+ !a  deriving (Eq,Read,Show)
 
 \begin{code}
 realPart, imagPart :: (RealFloat a) => Complex a -> a
-realPart (x:+y)         =  x
-imagPart (x:+y)         =  y
+realPart (x :+ _) =  x
+imagPart (_ :+ y) =  y
 
 conjugate       :: (RealFloat a) => Complex a -> Complex a
 conjugate (x:+y) =  x :+ (-y)
@@ -51,14 +69,15 @@ cis theta    =  cos theta :+ sin theta
 polar           :: (RealFloat a) => Complex a -> (a,a)
 polar z                 =  (magnitude z, phase z)
 
-magnitude, phase :: (RealFloat a) => Complex a -> a
+magnitude :: (RealFloat a) => Complex a -> a
 magnitude (x:+y) =  scaleFloat k
-                    (sqrt ((scaleFloat mk x)^2 + (scaleFloat mk y)^2))
+                    (sqrt ((scaleFloat mk x)^(2::Int) + (scaleFloat mk y)^(2::Int)))
                    where k  = max (exponent x) (exponent y)
                          mk = - k
 
+phase :: (RealFloat a) => Complex a -> a
 phase (0 :+ 0)   = 0           -- SLPJ July 97 from John Peterson
-phase (x:+y)    =  atan2 y x
+phase (x:+y)    = atan2 y x
 \end{code}
 
 
@@ -70,6 +89,8 @@ phase (x:+y)   =  atan2 y x
 
 \begin{code}
 instance  (RealFloat a) => Num (Complex a)  where
+    {-# SPECIALISE instance Num (Complex Float) #-}
+    {-# SPECIALISE instance Num (Complex Double) #-}
     (x:+y) + (x':+y')  =  (x+x') :+ (y+y')
     (x:+y) - (x':+y')  =  (x-x') :+ (y-y')
     (x:+y) * (x':+y')  =  (x*x'-y*y') :+ (x*y'+y*x')
@@ -80,6 +101,8 @@ instance  (RealFloat a) => Num (Complex a)  where
     fromInteger n      =  fromInteger n :+ 0
 
 instance  (RealFloat a) => Fractional (Complex a)  where
+    {-# SPECIALISE instance Fractional (Complex Float) #-}
+    {-# SPECIALISE instance Fractional (Complex Double) #-}
     (x:+y) / (x':+y')  =  (x*x''+y*y'') / d :+ (y*x''-x*y'') / d
                           where x'' = scaleFloat k x'
                                 y'' = scaleFloat k y'
@@ -89,6 +112,8 @@ instance  (RealFloat a) => Fractional (Complex a)  where
     fromRational a     =  fromRational a :+ 0
 
 instance  (RealFloat a) => Floating (Complex a)        where
+    {-# SPECIALISE instance Floating (Complex Float) #-}
+    {-# SPECIALISE instance Floating (Complex Double) #-}
     pi             =  pi :+ 0
     exp (x:+y)     =  expx * cos y :+ expx * sin y
                       where expx = exp x
@@ -118,7 +143,7 @@ instance  (RealFloat a) => Floating (Complex a)     where
 
     asin z@(x:+y)  =  y':+(-x')
                       where  (x':+y') = log (((-y):+x) + sqrt (1 - z*z))
-    acos z@(x:+y)  =  y'':+(-x'')
+    acos z         =  y'':+(-x'')
                       where (x'':+y'') = log (z + ((-y'):+x'))
                             (x':+y')   = sqrt (1 - z*z)
     atan z@(x:+y)  =  y':+(-x')