Copyright	Copyright (c) 2010 Patrick Perry <patperry@gmail.com>
License	BSD3
Maintainer	Patrick Perry <patperry@gmail.com>
Stability	experimental
Safe Haskell	None
Language	Haskell98

Data.AEq

Description

A type class for approximate and exact equalilty comparisons and instances for common data types.

Synopsis

class Eq a => AEq a where

Documentation

class Eq a => AEq a where #

Types with approximate and exact equality comparisons.

Methods

(===) :: a -> a -> Bool infix 4 #

An exact equality comparison.

For real IEEE types, two values are equivalent in the following cases:

both values are +0;
both values are -0;
both values are nonzero and equal to each other (according to ==);
both values are NaN with the same payload and sign.

For complex IEEE types, two values are equivalent if their real and imaginary parts are equivalent.

(~==) :: a -> a -> Bool infix 4 #

An approximate equality comparison operator.

For real IEEE types, two values are approximately equal in the following cases:

at least half of their significand bits agree;
both values are less than epsilon;
both values are NaN.

For complex IEEE types, two values are approximately equal in the followiing cases:

their magnitudes are approximately equal and the angle between them is less than 32*epsilon;
both magnitudes are less than epsilon;
both have a NaN real or imaginary part.

Admitedly, the 32 is a bit of a hack. Future versions of the library may switch to a more principled test of the angle.

Instances

AEq Bool #
Instance details Defined in Data.AEq Methods (===) :: Bool -> Bool -> Bool # (~==) :: Bool -> Bool -> Bool #
AEq Char #
Instance details Defined in Data.AEq Methods (===) :: Char -> Char -> Bool # (~==) :: Char -> Char -> Bool #
AEq Double #
Instance details Defined in Data.AEq Methods (===) :: Double -> Double -> Bool # (~==) :: Double -> Double -> Bool #
AEq Float #
Instance details Defined in Data.AEq Methods (===) :: Float -> Float -> Bool # (~==) :: Float -> Float -> Bool #
AEq Int #
Instance details Defined in Data.AEq Methods (===) :: Int -> Int -> Bool # (~==) :: Int -> Int -> Bool #
AEq Int8 #
Instance details Defined in Data.AEq Methods (===) :: Int8 -> Int8 -> Bool # (~==) :: Int8 -> Int8 -> Bool #
AEq Int16 #
Instance details Defined in Data.AEq Methods (===) :: Int16 -> Int16 -> Bool # (~==) :: Int16 -> Int16 -> Bool #
AEq Int32 #
Instance details Defined in Data.AEq Methods (===) :: Int32 -> Int32 -> Bool # (~==) :: Int32 -> Int32 -> Bool #
AEq Int64 #
Instance details Defined in Data.AEq Methods (===) :: Int64 -> Int64 -> Bool # (~==) :: Int64 -> Int64 -> Bool #
AEq Integer #
Instance details Defined in Data.AEq Methods (===) :: Integer -> Integer -> Bool # (~==) :: Integer -> Integer -> Bool #
AEq Ordering #
Instance details Defined in Data.AEq Methods (===) :: Ordering -> Ordering -> Bool # (~==) :: Ordering -> Ordering -> Bool #
AEq Word #
Instance details Defined in Data.AEq Methods (===) :: Word -> Word -> Bool # (~==) :: Word -> Word -> Bool #
AEq Word8 #
Instance details Defined in Data.AEq Methods (===) :: Word8 -> Word8 -> Bool # (~==) :: Word8 -> Word8 -> Bool #
AEq Word16 #
Instance details Defined in Data.AEq Methods (===) :: Word16 -> Word16 -> Bool # (~==) :: Word16 -> Word16 -> Bool #
AEq Word32 #
Instance details Defined in Data.AEq Methods (===) :: Word32 -> Word32 -> Bool # (~==) :: Word32 -> Word32 -> Bool #
AEq Word64 #
Instance details Defined in Data.AEq Methods (===) :: Word64 -> Word64 -> Bool # (~==) :: Word64 -> Word64 -> Bool #
AEq () #
Instance details Defined in Data.AEq Methods (===) :: () -> () -> Bool # (~==) :: () -> () -> Bool #
AEq CChar #
Instance details Defined in Data.AEq Methods (===) :: CChar -> CChar -> Bool # (~==) :: CChar -> CChar -> Bool #
AEq CSChar #
Instance details Defined in Data.AEq Methods (===) :: CSChar -> CSChar -> Bool # (~==) :: CSChar -> CSChar -> Bool #
AEq CUChar #
Instance details Defined in Data.AEq Methods (===) :: CUChar -> CUChar -> Bool # (~==) :: CUChar -> CUChar -> Bool #
AEq CShort #
Instance details Defined in Data.AEq Methods (===) :: CShort -> CShort -> Bool # (~==) :: CShort -> CShort -> Bool #
AEq CUShort #
Instance details Defined in Data.AEq Methods (===) :: CUShort -> CUShort -> Bool # (~==) :: CUShort -> CUShort -> Bool #
AEq CInt #
Instance details Defined in Data.AEq Methods (===) :: CInt -> CInt -> Bool # (~==) :: CInt -> CInt -> Bool #
AEq CUInt #
Instance details Defined in Data.AEq Methods (===) :: CUInt -> CUInt -> Bool # (~==) :: CUInt -> CUInt -> Bool #
AEq CLong #
Instance details Defined in Data.AEq Methods (===) :: CLong -> CLong -> Bool # (~==) :: CLong -> CLong -> Bool #
AEq CULong #
Instance details Defined in Data.AEq Methods (===) :: CULong -> CULong -> Bool # (~==) :: CULong -> CULong -> Bool #
AEq CLLong #
Instance details Defined in Data.AEq Methods (===) :: CLLong -> CLLong -> Bool # (~==) :: CLLong -> CLLong -> Bool #
AEq CULLong #
Instance details Defined in Data.AEq Methods (===) :: CULLong -> CULLong -> Bool # (~==) :: CULLong -> CULLong -> Bool #
AEq CFloat #
Instance details Defined in Data.AEq Methods (===) :: CFloat -> CFloat -> Bool # (~==) :: CFloat -> CFloat -> Bool #
AEq CDouble #
Instance details Defined in Data.AEq Methods (===) :: CDouble -> CDouble -> Bool # (~==) :: CDouble -> CDouble -> Bool #
AEq CPtrdiff #
Instance details Defined in Data.AEq Methods (===) :: CPtrdiff -> CPtrdiff -> Bool # (~==) :: CPtrdiff -> CPtrdiff -> Bool #
AEq CSize #
Instance details Defined in Data.AEq Methods (===) :: CSize -> CSize -> Bool # (~==) :: CSize -> CSize -> Bool #
AEq CWchar #
Instance details Defined in Data.AEq Methods (===) :: CWchar -> CWchar -> Bool # (~==) :: CWchar -> CWchar -> Bool #
AEq CSigAtomic #
Instance details Defined in Data.AEq Methods (===) :: CSigAtomic -> CSigAtomic -> Bool # (~==) :: CSigAtomic -> CSigAtomic -> Bool #
AEq CClock #
Instance details Defined in Data.AEq Methods (===) :: CClock -> CClock -> Bool # (~==) :: CClock -> CClock -> Bool #
AEq CTime #
Instance details Defined in Data.AEq Methods (===) :: CTime -> CTime -> Bool # (~==) :: CTime -> CTime -> Bool #
AEq CIntPtr #
Instance details Defined in Data.AEq Methods (===) :: CIntPtr -> CIntPtr -> Bool # (~==) :: CIntPtr -> CIntPtr -> Bool #
AEq CUIntPtr #
Instance details Defined in Data.AEq Methods (===) :: CUIntPtr -> CUIntPtr -> Bool # (~==) :: CUIntPtr -> CUIntPtr -> Bool #
AEq CIntMax #
Instance details Defined in Data.AEq Methods (===) :: CIntMax -> CIntMax -> Bool # (~==) :: CIntMax -> CIntMax -> Bool #
AEq CUIntMax #
Instance details Defined in Data.AEq Methods (===) :: CUIntMax -> CUIntMax -> Bool # (~==) :: CUIntMax -> CUIntMax -> Bool #
AEq WordPtr #
Instance details Defined in Data.AEq Methods (===) :: WordPtr -> WordPtr -> Bool # (~==) :: WordPtr -> WordPtr -> Bool #
AEq IntPtr #
Instance details Defined in Data.AEq Methods (===) :: IntPtr -> IntPtr -> Bool # (~==) :: IntPtr -> IntPtr -> Bool #
AEq a => AEq [a] #
Instance details Defined in Data.AEq Methods (===) :: [a] -> [a] -> Bool # (~==) :: [a] -> [a] -> Bool #
AEq a => AEq (Maybe a) #
Instance details Defined in Data.AEq Methods (===) :: Maybe a -> Maybe a -> Bool # (~==) :: Maybe a -> Maybe a -> Bool #
AEq (StablePtr a) #
Instance details Defined in Data.AEq Methods (===) :: StablePtr a -> StablePtr a -> Bool # (~==) :: StablePtr a -> StablePtr a -> Bool #
AEq (Ptr a) #
Instance details Defined in Data.AEq Methods (===) :: Ptr a -> Ptr a -> Bool # (~==) :: Ptr a -> Ptr a -> Bool #
AEq (FunPtr a) #
Instance details Defined in Data.AEq Methods (===) :: FunPtr a -> FunPtr a -> Bool # (~==) :: FunPtr a -> FunPtr a -> Bool #
AEq (Complex Double) #
Instance details Defined in Data.AEq Methods (===) :: Complex Double -> Complex Double -> Bool # (~==) :: Complex Double -> Complex Double -> Bool #
AEq (Complex Float) #
Instance details Defined in Data.AEq Methods (===) :: Complex Float -> Complex Float -> Bool # (~==) :: Complex Float -> Complex Float -> Bool #
AEq (Complex CFloat) #
Instance details Defined in Data.AEq Methods (===) :: Complex CFloat -> Complex CFloat -> Bool # (~==) :: Complex CFloat -> Complex CFloat -> Bool #
AEq (Complex CDouble) #
Instance details Defined in Data.AEq Methods (===) :: Complex CDouble -> Complex CDouble -> Bool # (~==) :: Complex CDouble -> Complex CDouble -> Bool #
AEq (ForeignPtr a) #
Instance details Defined in Data.AEq Methods (===) :: ForeignPtr a -> ForeignPtr a -> Bool # (~==) :: ForeignPtr a -> ForeignPtr a -> Bool #
(AEq a, AEq b) => AEq (Either a b) #
Instance details Defined in Data.AEq Methods (===) :: Either a b -> Either a b -> Bool # (~==) :: Either a b -> Either a b -> Bool #
(AEq a, AEq b) => AEq (a, b) #
Instance details Defined in Data.AEq Methods (===) :: (a, b) -> (a, b) -> Bool # (~==) :: (a, b) -> (a, b) -> Bool #
(AEq a, AEq b, AEq c) => AEq (a, b, c) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c) -> (a, b, c) -> Bool # (~==) :: (a, b, c) -> (a, b, c) -> Bool #
(AEq a, AEq b, AEq c, AEq d) => AEq (a, b, c, d) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d) -> (a, b, c, d) -> Bool # (~==) :: (a, b, c, d) -> (a, b, c, d) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e) => AEq (a, b, c, d, e) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (~==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f) => AEq (a, b, c, d, e, f) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (~==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g) => AEq (a, b, c, d, e, f, g) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (~==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h) => AEq (a, b, c, d, e, f, g, h) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (~==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i) => AEq (a, b, c, d, e, f, g, h, i) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i, AEq j) => AEq (a, b, c, d, e, f, g, h, i, j) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i, AEq j, AEq k) => AEq (a, b, c, d, e, f, g, h, i, j, k) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i, AEq j, AEq k, AEq l) => AEq (a, b, c, d, e, f, g, h, i, j, k, l) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i, AEq j, AEq k, AEq l, AEq m) => AEq (a, b, c, d, e, f, g, h, i, j, k, l, m) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i, AEq j, AEq k, AEq l, AEq m, AEq n) => AEq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #
(AEq a, AEq b, AEq c, AEq d, AEq e, AEq f, AEq g, AEq h, AEq i, AEq j, AEq k, AEq l, AEq m, AEq n, AEq o) => AEq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #
Instance details Defined in Data.AEq Methods (===) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # (~==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #