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authorDon Stewart <dons@galois.com>2008-03-10 00:54:55 +0000
committerDon Stewart <dons@galois.com>2008-03-10 00:54:55 +0000
commit0363aee684bd67ad60e990369dddc2055bf292fb (patch)
treec0a42dfc46ddd5614f84b49eaf90036f4ca171fc /libraries/base/Data/Complex.hs
parent450f869b1e73e96bb0c75a40e6921f17a908471b (diff)
downloadhaskell-0363aee684bd67ad60e990369dddc2055bf292fb.tar.gz
untabify
Diffstat (limited to 'libraries/base/Data/Complex.hs')
-rw-r--r--libraries/base/Data/Complex.hs114
1 files changed, 57 insertions, 57 deletions
diff --git a/libraries/base/Data/Complex.hs b/libraries/base/Data/Complex.hs
index 3b37f6c91f..7d29e778e2 100644
--- a/libraries/base/Data/Complex.hs
+++ b/libraries/base/Data/Complex.hs
@@ -13,30 +13,30 @@
-----------------------------------------------------------------------------
module Data.Complex
- (
- -- * Rectangular form
- Complex((:+))
-
- , realPart -- :: (RealFloat a) => Complex a -> a
- , imagPart -- :: (RealFloat a) => Complex a -> 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)
- -- (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)
- --
+ (
+ -- * Rectangular form
+ Complex((:+))
+
+ , realPart -- :: (RealFloat a) => Complex a -> a
+ , imagPart -- :: (RealFloat a) => Complex a -> 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)
+ -- (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
@@ -63,12 +63,12 @@ infix 6 :+
-- 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.
+ = !a :+ !a -- ^ forms a complex number from its real and imaginary
+ -- rectangular components.
# if __GLASGOW_HASKELL__
- deriving (Eq, Show, Read, Data)
+ deriving (Eq, Show, Read, Data)
# else
- deriving (Eq, Show, Read)
+ deriving (Eq, Show, Read)
# endif
-- -----------------------------------------------------------------------------
@@ -84,42 +84,42 @@ imagPart (_ :+ y) = y
-- | The conjugate of a complex number.
{-# SPECIALISE conjugate :: Complex Double -> Complex Double #-}
-conjugate :: (RealFloat a) => Complex a -> Complex a
+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
+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
+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)
+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
- (sqrt ((scaleFloat mk x)^(2::Int) + (scaleFloat mk y)^(2::Int)))
- where k = max (exponent x) (exponent y)
- mk = - k
+ (sqrt ((scaleFloat mk x)^(2::Int) + (scaleFloat mk y)^(2::Int)))
+ 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
-phase (x:+y) = atan2 y x
+phase (0 :+ 0) = 0 -- SLPJ July 97 from John Peterson
+phase (x:+y) = atan2 y x
-- -----------------------------------------------------------------------------
@@ -131,33 +131,33 @@ INSTANCE_TYPEABLE1(Complex,complexTc,"Complex")
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')
- negate (x:+y) = negate x :+ negate y
- abs z = magnitude z :+ 0
- signum (0:+0) = 0
- signum z@(x:+y) = x/r :+ y/r where r = magnitude z
- fromInteger n = fromInteger n :+ 0
+ (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')
+ negate (x:+y) = negate x :+ negate y
+ abs z = magnitude z :+ 0
+ signum (0:+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
+ fromInt n = fromInt n :+ 0
#endif
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'
- k = - max (exponent x') (exponent y')
- d = x'*x'' + y'*y''
+ (x:+y) / (x':+y') = (x*x''+y*y'') / d :+ (y*x''-x*y'') / d
+ where x'' = scaleFloat k x'
+ y'' = scaleFloat k y'
+ k = - max (exponent x') (exponent y')
+ d = x'*x'' + y'*y''
- fromRational a = fromRational a :+ 0
+ fromRational a = fromRational a :+ 0
#ifdef __HUGS__
- fromDouble a = fromDouble a :+ 0
+ fromDouble a = fromDouble a :+ 0
#endif
-instance (RealFloat a) => Floating (Complex a) where
+instance (RealFloat a) => Floating (Complex a) where
{-# SPECIALISE instance Floating (Complex Float) #-}
{-# SPECIALISE instance Floating (Complex Double) #-}
pi = pi :+ 0