module Data.AEq (
AEq(..),
) where
import Foreign.C.Types
import Data.Int
import Data.Word
import Data.Complex
import Numeric.IEEE
infix 4 ===, ~==
class Eq a => AEq a where
(===) :: a -> a -> Bool
(===) = (==)
(~==) :: a -> a -> Bool
(~==) = (==)
identicalRealFloat :: (RealFloat a) => a -> a -> Bool
identicalRealFloat x y =
(x == y) || (isNaN x && isNaN y)
approxEqRealFloat :: (RealFloat a) => a -> a -> Bool
approxEqRealFloat x y =
(x == y) || (abs (x y) < epsilon) || (eqRel delta x y) || (isNaN x && isNaN y)
identicalComplexFloat :: (RealFloat a) => Complex a -> Complex a -> Bool
identicalComplexFloat (x1 :+ y1) (x2 :+ y2) =
(identicalRealFloat x1 x2) && (identicalRealFloat y1 y2)
approxEqComplexFloat :: (RealFloat a) => Complex a -> Complex a -> Bool
approxEqComplexFloat z1@(x1 :+ y1) z2@(x2 :+ y2) = let
(r1,c1) = polar z1
(r2,c2) = polar z2
c = min c1 c2
c' = max c1 c2 in
((approxEqRealFloat x1 x2 && approxEqRealFloat y1 y2)
|| ((approxEqRealFloat r1 r2)
&& ((approxEqRealFloat c1 c2) || (approxEqRealFloat (c + 2 * pi) c'))))
instance AEq Float where
(===) = identicalRealFloat
(~==) = approxEqRealFloat
instance AEq Double where
(===) = identicalRealFloat
(~==) = approxEqRealFloat
instance (RealFloat a) => AEq (Complex a) where
(===) = identicalComplexFloat
(~==) = approxEqComplexFloat
instance AEq Bool where
(===) = (==)
(~==) = (==)
instance AEq Char where
(===) = (==)
(~==) = (==)
instance AEq Int where
(===) = (==)
(~==) = (==)
instance AEq Int8 where
(===) = (==)
(~==) = (==)
instance AEq Int16 where
(===) = (==)
(~==) = (==)
instance AEq Int32 where
(===) = (==)
(~==) = (==)
instance AEq Int64 where
(===) = (==)
(~==) = (==)
instance AEq Integer where
(===) = (==)
(~==) = (==)
instance AEq Ordering where
(===) = (==)
(~==) = (==)
instance AEq Word where
(===) = (==)
(~==) = (==)
instance AEq Word8 where
(===) = (==)
(~==) = (==)
instance AEq Word16 where
(===) = (==)
(~==) = (==)
instance AEq Word32 where
(===) = (==)
(~==) = (==)
instance AEq Word64 where
(===) = (==)
(~==) = (==)
instance AEq () where
(===) = (==)
(~==) = (==)
instance AEq CChar where
(===) = (==)
(~==) = (==)
instance AEq CSChar where
(===) = (==)
(~==) = (==)
instance AEq CUChar where
(===) = (==)
(~==) = (==)
instance AEq CShort where
(===) = (==)
(~==) = (==)
instance AEq CUShort where
(===) = (==)
(~==) = (==)
instance AEq CInt where
(===) = (==)
(~==) = (==)
instance AEq CUInt where
(===) = (==)
(~==) = (==)
instance AEq CLong where
(===) = (==)
(~==) = (==)
instance AEq CULong where
(===) = (==)
(~==) = (==)
instance AEq CPtrdiff where
(===) = (==)
(~==) = (==)
instance AEq CSize where
(===) = (==)
(~==) = (==)
instance AEq CWchar where
(===) = (==)
(~==) = (==)
instance AEq CSigAtomic where
(===) = (==)
(~==) = (==)
instance AEq CLLong where
(===) = (==)
(~==) = (==)
instance AEq CULLong where
(===) = (==)
(~==) = (==)
instance AEq CIntPtr where
(===) = (==)
(~==) = (==)
instance AEq CUIntPtr where
(===) = (==)
(~==) = (==)
instance AEq CIntMax where
(===) = (==)
(~==) = (==)
instance AEq CUIntMax where
(===) = (==)
(~==) = (==)
instance AEq CClock where
(===) = (==)
(~==) = (==)
instance AEq CTime where
(===) = (==)
(~==) = (==)
instance AEq CFloat where
(===) = identicalRealFloat
(~==) = approxEqRealFloat
instance AEq CDouble where
(===) = identicalRealFloat
(~==) = approxEqRealFloat
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ <= 610
instance AEq CLDouble where
(===) = identicalRealFloat
(~==) = approxEqRealFloat
#endif
instance (AEq a, AEq b) => AEq (a,b) where
(===) (a1,b1) (a2,b2) = ((===) a1 a2) && ((===) b1 b2)
(~==) (a1,b1) (a2,b2) = ((~==) a1 a2) && ((~==) b1 b2)
instance (AEq a, AEq b, AEq c) => AEq (a,b,c) where
(===) (a1,b1,c1) (a2,b2,c2) = ((===) a1 a2) && ((===) b1 b2) && ((===) c1 c2)
(~==) (a1,b1,c1) (a2,b2,c2) = ((~==) a1 a2) && ((~==) b1 b2) && ((~==) c1 c2)
instance (AEq a, AEq b, AEq c, AEq d) => AEq (a,b,c,d) where
(===) (a1,b1,c1,d1) (a2,b2,c2,d2) = ((===) a1 a2) && ((===) b1 b2) && ((===) c1 c2) && ((===) d1 d2)
(~==) (a1,b1,c1,d1) (a2,b2,c2,d2) = ((~==) a1 a2) && ((~==) b1 b2) && ((~==) c1 c2) && ((~==) d1 d2)
instance (AEq a, AEq b, AEq c, AEq d, AEq e) => AEq (a,b,c,d,e) where
(===) (a1,b1,c1,d1,e1) (a2,b2,c2,d2,e2) = ((===) a1 a2) && ((===) b1 b2) && ((===) c1 c2) && ((===) d1 d2) && ((===) e1 e2)
(~==) (a1,b1,c1,d1,e1) (a2,b2,c2,d2,e2) = ((~==) a1 a2) && ((~==) b1 b2) && ((~==) c1 c2) && ((~==) d1 d2) && ((~==) e1 e2)
compareListsWith :: (a -> a -> Bool) -> [a] -> [a] -> Bool
compareListsWith _ [] [] = True
compareListsWith f (x:xs) (y:ys) = (f x y) && (compareListsWith f xs ys)
compareListsWith _ _ _ = False
instance (AEq a) => AEq [a] where
(===) = compareListsWith (===)
(~==) = compareListsWith (~==)
instance (AEq a) => AEq (Maybe a) where
(===) Nothing Nothing = True
(===) (Just x) (Just y) = (===) x y
(===) _ _ = False
(~==) Nothing Nothing = True
(~==) (Just x) (Just y) = (~==) x y
(~==) _ _ = False
instance (AEq a, AEq b) => AEq (Either a b) where
(===) (Left a1) (Left a2) = (===) a1 a2
(===) (Right b1) (Right b2) = (===) b1 b2
(===) _ _ = False
(~==) (Left a1) (Left a2) = (~==) a1 a2
(~==) (Right b1) (Right b2) = (~==) b1 b2
(~==) _ _ = False