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 Source #

Types with approximate and exact equality comparisons.

Methods

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

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 Source #

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