{-# GHC_PRAGMA INTERFACE VERSION 6 #-}
interface PreludeComplex where
import PreludeBuiltin(Double(..), Tuple2)
import PreludeCore(Eq(..), Floating(..), Fractional(..), Num(..), RealFloat(..), Text(..))
cis :: RealFloat a => a -> Complex a
	{-# GHC_PRAGMA _A_ 2 _U_ 12 _N_ _N_ _N_ _SPECIALISE_ [ Double ] 1 { _A_ 1 _U_ 2 _N_ _N_ _N_ _N_ } #-}
conjugate :: RealFloat a => Complex a -> Complex a
	{-# GHC_PRAGMA _A_ 2 _U_ 11 _N_ _S_ "LU(LL)" {_A_ 3 _U_ 122 _N_ _N_ _N_ _N_} _N_ _SPECIALISE_ [ Double ] 1 { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 21 _N_ _N_ _N_ _N_} _N_ _N_ } #-}
imagPart :: Complex a -> a
	{-# GHC_PRAGMA _A_ 1 _U_ 1 _N_ _S_ "U(AS)" {_A_ 1 _U_ 1 _N_ _N_ _F_ _IF_ARGS_ 1 1 X 1 _/\_ u0 -> \ (u1 :: u0) -> u1 _N_} _F_ _IF_ARGS_ 1 1 C 2 _/\_ u0 -> \ (u1 :: Complex u0) -> case u1 of { _ALG_ (:+) (u2 :: u0) (u3 :: u0) -> u3; _NO_DEFLT_ } _N_ #-}
magnitude :: RealFloat a => Complex a -> a
	{-# GHC_PRAGMA _A_ 1 _U_ 12 _N_ _S_ "U(ALAAAAALAS)" {_A_ 3 _U_ 2221 _N_ _N_ _N_ _N_} _N_ _SPECIALISE_ [ Double ] 1 { _A_ 1 _U_ 1 _N_ _S_ "U(U(P)U(P))" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ } #-}
mkPolar :: RealFloat a => a -> a -> Complex a
	{-# GHC_PRAGMA _A_ 3 _U_ 122 _N_ _N_ _N_ _SPECIALISE_ [ Double ] 1 { _A_ 2 _U_ 22 _N_ _N_ _N_ _N_ } #-}
phase :: RealFloat a => Complex a -> a
	{-# GHC_PRAGMA _A_ 1 _U_ 12 _N_ _S_ "U(U(U(AU(U(ALAASAAA)AAAA)A)AAAAAA)U(U(SLAA)LAAAAAAAAAALAAAAAA)AAAAAAAA)" {_A_ 5 _U_ 222221 _N_ _N_ _N_ _N_} _N_ _SPECIALISE_ [ Double ] 1 { _A_ 1 _U_ 1 _N_ _S_ "U(U(P)U(P))" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ } #-}
polar :: RealFloat a => Complex a -> (a, a)
	{-# GHC_PRAGMA _A_ 1 _U_ 22 _N_ _N_ _N_ _SPECIALISE_ [ Double ] 1 { _A_ 1 _U_ 2 _N_ _N_ _N_ _N_ } #-}
realPart :: Complex a -> a
	{-# GHC_PRAGMA _A_ 1 _U_ 1 _N_ _S_ "U(SA)" {_A_ 1 _U_ 1 _N_ _N_ _F_ _IF_ARGS_ 1 1 X 1 _/\_ u0 -> \ (u1 :: u0) -> u1 _N_} _F_ _IF_ARGS_ 1 1 C 2 _/\_ u0 -> \ (u1 :: Complex u0) -> case u1 of { _ALG_ (:+) (u2 :: u0) (u3 :: u0) -> u2; _NO_DEFLT_ } _N_ #-}
instance Eq a => Eq (Complex a)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 1 _U_ 2 _N_ _N_ _N_ _N_ #-}
instance Eq (Complex Double)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 0 _N_ _N_ _N_ _F_ _IF_ARGS_ 0 0 X 3 _!_ _TUP_2 [(Complex Double -> Complex Double -> Bool), (Complex Double -> Complex Double -> Bool)] [_CONSTM_ Eq (==) (Complex Double), _CONSTM_ Eq (/=) (Complex Double)] _N_
	 (==) = { _A_ 2 _U_ 11 _N_ _S_ "U(U(P)L)U(U(P)L)" {_A_ 4 _U_ 2121 _N_ _N_ _F_ _IF_ARGS_ 0 4 XCXC 7 \ (u0 :: Double#) (u1 :: Double) (u2 :: Double#) (u3 :: Double) -> case _#_ eqDouble# [] [u0, u2] of { _ALG_ True  -> case u1 of { _ALG_ D# (u4 :: Double#) -> case u3 of { _ALG_ D# (u5 :: Double#) -> _#_ eqDouble# [] [u4, u5]; _NO_DEFLT_ }; _NO_DEFLT_ }; False  -> _!_ False [] []; _NO_DEFLT_ } _N_} _F_ _ALWAYS_ \ (u0 :: Complex Double) (u1 :: Complex Double) -> case u0 of { _ALG_ (:+) (u2 :: Double) (u3 :: Double) -> case u2 of { _ALG_ D# (u4 :: Double#) -> case u1 of { _ALG_ (:+) (u5 :: Double) (u6 :: Double) -> case u5 of { _ALG_ D# (u7 :: Double#) -> case _#_ eqDouble# [] [u4, u7] of { _ALG_ True  -> case u3 of { _ALG_ D# (u8 :: Double#) -> case u6 of { _ALG_ D# (u9 :: Double#) -> _#_ eqDouble# [] [u8, u9]; _NO_DEFLT_ }; _NO_DEFLT_ }; False  -> _!_ False [] []; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ } _N_ },
	 (/=) = { _A_ 2 _U_ 11 _N_ _S_ "U(U(P)L)U(U(P)L)" {_A_ 4 _U_ 2121 _N_ _N_ _F_ _IF_ARGS_ 0 4 XCXC 7 \ (u0 :: Double#) (u1 :: Double) (u2 :: Double#) (u3 :: Double) -> case _#_ neDouble# [] [u0, u2] of { _ALG_ True  -> _!_ True [] []; False  -> case u1 of { _ALG_ D# (u4 :: Double#) -> case u3 of { _ALG_ D# (u5 :: Double#) -> _#_ neDouble# [] [u4, u5]; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ } _N_} _F_ _ALWAYS_ \ (u0 :: Complex Double) (u1 :: Complex Double) -> case u0 of { _ALG_ (:+) (u2 :: Double) (u3 :: Double) -> case u2 of { _ALG_ D# (u4 :: Double#) -> case u1 of { _ALG_ (:+) (u5 :: Double) (u6 :: Double) -> case u5 of { _ALG_ D# (u7 :: Double#) -> case _#_ neDouble# [] [u4, u7] of { _ALG_ True  -> _!_ True [] []; False  -> case u3 of { _ALG_ D# (u8 :: Double#) -> case u6 of { _ALG_ D# (u9 :: Double#) -> _#_ neDouble# [] [u8, u9]; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ }; _NO_DEFLT_ } _N_ } #-}
instance RealFloat a => Floating (Complex a)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 2 _U_ 22 _N_ _N_ _N_ _N_ #-}
instance Floating (Complex Double)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 0 _N_ _N_ _N_ _F_ _IF_ARGS_ 0 0 X 20 _!_ _TUP_19 [{{Fractional (Complex Double)}}, (Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double -> Complex Double), (Complex Double -> Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double)] [_DFUN_ Fractional (Complex Double), _CONSTM_ Floating pi (Complex Double), _CONSTM_ Floating exp (Complex Double), _CONSTM_ Floating log (Complex Double), _CONSTM_ Floating sqrt (Complex Double), _CONSTM_ Floating (**) (Complex Double), _CONSTM_ Floating logBase (Complex Double), _CONSTM_ Floating sin (Complex Double), _CONSTM_ Floating cos (Complex Double), _CONSTM_ Floating tan (Complex Double), _CONSTM_ Floating asin (Complex Double), _CONSTM_ Floating acos (Complex Double), _CONSTM_ Floating atan (Complex Double), _CONSTM_ Floating sinh (Complex Double), _CONSTM_ Floating cosh (Complex Double), _CONSTM_ Floating tanh (Complex Double), _CONSTM_ Floating asinh (Complex Double), _CONSTM_ Floating acosh (Complex Double), _CONSTM_ Floating atanh (Complex Double)] _N_
	 pi = { _A_ 0 _N_ _N_ _N_ _F_ _IF_ARGS_ 0 0 X 3 _!_ (:+) [Double] [_CONSTM_ Floating pi (Double), _SPEC_ _ORIG_ PreludeCore __i0 [ (Double) ]] _N_ },
	 exp = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 12 _N_ _N_ _N_ _N_} _N_ _N_ },
	 log = { _A_ 1 _U_ 2 _N_ _N_ _N_ _N_ },
	 sqrt = { _A_ 1 _U_ 1 _N_ _S_ "U(U(P)L)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 (**) = { _A_ 2 _U_ 21 _N_ _S_ "LU(LL)" {_A_ 3 _U_ 222 _N_ _N_ _N_ _N_} _N_ _N_ },
	 logBase = { _A_ 2 _U_ 22 _N_ _N_ _N_ _N_ },
	 sin = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 cos = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 tan = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 asin = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 acos = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 atan = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 sinh = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 cosh = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 tanh = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 asinh = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ },
	 acosh = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ },
	 atanh = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ } #-}
instance RealFloat a => Fractional (Complex a)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 2 _U_ 22 _N_ _N_ _N_ _N_ #-}
instance Fractional (Complex Double)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 0 _N_ _N_ _N_ _F_ _IF_ARGS_ 0 0 X 5 _!_ _TUP_4 [{{Num (Complex Double)}}, (Complex Double -> Complex Double -> Complex Double), (Complex Double -> Complex Double), (Ratio Integer -> Complex Double)] [_DFUN_ Num (Complex Double), _CONSTM_ Fractional (/) (Complex Double), _CONSTM_ Fractional recip (Complex Double), _CONSTM_ Fractional fromRational (Complex Double)] _N_
	 (/) = { _A_ 2 _U_ 11 _N_ _S_ "U(LL)U(LL)" {_A_ 4 _U_ 2222 _N_ _N_ _N_ _N_} _N_ _N_ },
	 recip = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _F_ _IF_ARGS_ 0 1 X 3 \ (u0 :: Complex Double) -> _APP_  _CONSTM_ Fractional (/) (Complex Double) [ _SPEC_ _ORIG_ PreludeCore __i1 [ (Complex Double) ], u0 ] _N_ },
	 fromRational = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ } #-}
instance RealFloat a => Num (Complex a)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 3 _U_ 222 _N_ _N_ _N_ _N_ #-}
instance Num (Complex Double)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 0 _N_ _N_ _N_ _F_ _IF_ARGS_ 0 0 X 11 _!_ _TUP_10 [{{Eq (Complex Double)}}, {{Text (Complex Double)}}, (Complex Double -> Complex Double -> Complex Double), (Complex Double -> Complex Double -> Complex Double), (Complex Double -> Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Complex Double -> Complex Double), (Integer -> Complex Double), (Int -> Complex Double)] [_DFUN_ Eq (Complex Double), _DFUN_ Text (Complex Double), _CONSTM_ Num (+) (Complex Double), _CONSTM_ Num (-) (Complex Double), _CONSTM_ Num (*) (Complex Double), _CONSTM_ Num negate (Complex Double), _CONSTM_ Num abs (Complex Double), _CONSTM_ Num signum (Complex Double), _CONSTM_ Num fromInteger (Complex Double), _CONSTM_ Num fromInt (Complex Double)] _N_
	 (+) = { _A_ 2 _U_ 11 _N_ _S_ "U(LL)U(LL)" {_A_ 4 _U_ 1111 _N_ _N_ _N_ _N_} _N_ _N_ },
	 (-) = { _A_ 2 _U_ 11 _N_ _S_ "U(LL)U(LL)" {_A_ 4 _U_ 1111 _N_ _N_ _N_ _N_} _N_ _N_ },
	 (*) = { _A_ 2 _U_ 11 _N_ _S_ "U(LL)U(LL)" {_A_ 4 _U_ 2222 _N_ _N_ _N_ _N_} _N_ _N_ },
	 negate = { _A_ 1 _U_ 1 _N_ _S_ "U(LL)" {_A_ 2 _U_ 11 _N_ _N_ _N_ _N_} _N_ _N_ },
	 abs = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ },
	 signum = { _A_ 1 _U_ 1 _N_ _S_ "U(U(P)L)" {_A_ 2 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 fromInteger = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ },
	 fromInt = { _A_ 1 _U_ 1 _N_ _N_ _N_ _N_ } #-}
instance Text a => Text (Complex a)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 1 _U_ 2 _N_ _N_ _N_ _N_ #-}
instance Text (Complex Double)
	{-# GHC_PRAGMA _M_ PreludeComplex {-dfun-} _A_ 0 _N_ _N_ _N_ _F_ _IF_ARGS_ 0 0 X 5 _!_ _TUP_4 [(Int -> [Char] -> [(Complex Double, [Char])]), (Int -> Complex Double -> [Char] -> [Char]), ([Char] -> [([Complex Double], [Char])]), ([Complex Double] -> [Char] -> [Char])] [_CONSTM_ Text readsPrec (Complex Double), _CONSTM_ Text showsPrec (Complex Double), _CONSTM_ Text readList (Complex Double), _CONSTM_ Text showList (Complex Double)] _N_
	 readsPrec = { _A_ 1 _U_ 12 _N_ _S_ "U(P)" {_A_ 1 _U_ 22 _N_ _N_ _N_ _N_} _N_ _N_ },
	 showsPrec = { _A_ 2 _U_ 112 _N_ _S_ "LU(LL)" {_A_ 3 _U_ 1222 _N_ _N_ _N_ _N_} _N_ _N_ },
	 readList = { _A_ 0 _U_ 2 _N_ _N_ _N_ _N_ },
	 showList = { _A_ 1 _U_ 12 _N_ _N_ _N_ _N_ } #-}